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PAGE 1 1 PHYSICAL AND COMPUTATIONAL FLUID DYNAMICS MODELING OF UNIT OPERATIONS UNDER TRANSIENT HYDRAULIC LOADINGS By GIUSEPPINA GAROFALO A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2012 PAGE 2 2 2012 Giuseppina Garofalo PAGE 3 3 T o my family PAGE 4 4 ACKNOWLEDGMENTS I would like to thank my advisor, Dr. John Sansalone for his encouragement and guidance. He always believed in my potential and supported me. I also extend my sincere gratitude to the members of my committee: Dr. James Heaney, Dr. Ben Koopman and Dr. Jennifer Curtis for t heir valuable input, advice and accessibility. I am forever in debt to them for their guidance. I thank my dear colleagues and friends who have helped me in the lab and in the field: Dr. Jong Yeop Kim, Dr. Srikanth Pathapati, Dr. Gaoxiang Ying, Dr. Josh Di ckenson Dr. Ruben Kerte sz Dr. Tingting Wu, Dr. Hwan chul Cho Saurabh Raje, Greg Brenner, Earendil Wilson, Sandeep Gulati Hao Zhang, Julie Midgette. I thank the many friends I have made during these years and those in Italy for being there for me thr oughout this experience, no matter the distance, the differences in culture and background. I thank my family for believing in me and supporting me in any moments with unlimited strength, patience and love. They have been my greatest source of energy to ov erpass the many obstacles present along the way. PAGE 5 5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ ............... 4 LIST OF TABLES ................................ ................................ ................................ ........................... 9 LIST OF FIGURES ................................ ................................ ................................ ....................... 11 LIST OF ABBREVIATIONS ................................ ................................ ................................ ........ 17 ABSTRACT ................................ ................................ ................................ ................................ ... 21 CHAPTER 1 GLOBAL BACKGROUND ................................ ................................ ................................ ... 23 2 TRANSIENT ELUTION OF PARTICULATE MATTER FROM HYDRODYNAMIC UNIT OPERATIONS AS A FUNCTION OF COMPUTATIONAL PARAMETERS AND HYDROGRAPH UNSTEADINESS ................................ ................................ ............ 28 Summary ................................ ................................ ................................ ................................ 28 Introduction ................................ ................................ ................................ ............................. 28 Material and Methods ................................ ................................ ................................ ............. 32 Full Scale Physical Model Setup ................................ ................................ ..................... 33 CFD Modeling ................................ ................................ ................................ ................. 35 Results and Discussion ................................ ................................ ................................ ........... 42 Impact of Time Step (TS) and Mesh Size (MS) ................................ .............................. 42 Event Based Separated PSDs and DN for PSDs ................................ ............................. 45 Effect of Hydrograph Unsteadiness ................................ ................................ ................. 46 Conclusion ................................ ................................ ................................ .............................. 47 3 STORMWATER CLARIFIER HYDRAULIC RESPONSE AS A FUNCTION OF FLOW, UNSTEADINESS AND BAFFLING ................................ ................................ ....... 56 Summary ................................ ................................ ................................ ................................ 56 Introduction ................................ ................................ ................................ ............................. 56 Material and Methods ................................ ................................ ................................ ............. 59 RTD Curves a nd Assessment of Hydraulic Indices ................................ ........................ 60 CFD Modeling ................................ ................................ ................................ ................. 61 Results and Discussion ................................ ................................ ................................ ........... 65 Steady Flow Hydraulic Indices as F unction of Flow Tortuosity (equivalent L/W) ........ 65 Unsteady Flow Hydraulic Ind ic es as Function of Flow Tortuosity (Equivalent L/W) ... 68 4 CAN A STEPWISE STEADY FLOW CFD MODEL PREDICT PM SEPARATION FROM STORMWATER UNIT OPERATIONS AS A FUNCTION OF HYDROGRAPH UNSTEADINESS AND PM GRANULOMETRY? ................................ 78 PAGE 6 6 Summary ................................ ................................ ................................ ................................ 78 Introduction ................................ ................................ ................................ ............................. 79 Methodology ................................ ................................ ................................ ........................... 83 Physical Model Setup ................................ ................................ ................................ ...... 83 CFD Modeling of Fluid and PM Phases ................................ ................................ .......... 87 CFD m odeling under u nsteady c onditions ................................ ............................... 90 Stepwise s teady CFD m odeling ................................ ................................ ............... 91 Results and Discussion ................................ ................................ ................................ ........... 94 Comparison of the Stepwise Steady and Fully Unsteady CFD Results .......................... 94 Automatic Sampling, PM Granulometry and CFD Results ................................ ............ 97 Conclusion ................................ ................................ ................................ .............................. 99 5 A STEPWISE CFD STEADY FLOW MODEL FOR EVALUATING LONG TERM UO SEPARATION PERFORMANCE ................................ ................................ ................ 111 Summary ................................ ................................ ................................ ............................... 111 Introduction ................................ ................................ ................................ ........................... 111 Methodology ................................ ................................ ................................ ......................... 115 Hydrology Analysis ................................ ................................ ................................ ....... 115 Physical Ful l Scale Model for PM Separation ................................ .............................. 116 Physical F ull S cale M odel for PM W ashout ................................ ................................ 118 CFD Modeling ................................ ................................ ................................ ............... 119 CFD model for PM s eparation ................................ ................................ ............... 120 CFD model of PM washout ................................ ................................ .................... 121 Validation analysis for fully unsteady CFD model ................................ ................ 123 Stepwise steady CFD model ................................ ................................ .................. 124 Evalua tion of PM Elution D ue to Washout in the Continuous Simulation Model ....... 126 Time Domain Continuous Simulation Model and its Assumption s .............................. 127 Results and Discussion ................................ ................................ ................................ ......... 128 CFD Model for PM Separation and Washout ................................ ............................... 128 PM Washout as F unction of Flow Rate and Pluviated PM Depth ................................ 129 Stepwise CFD Steady Flow Model and Time Domain Continuous Si mulation ........... 131 Conclusion ................................ ................................ ................................ ............................ 134 6 GLOBAL CONCLUSION ................................ ................................ ................................ ... 147 APPENDIX A PARTICULATE MATTER FROM HYDRODYNAMIC UNIT OPERATIONS AS A FUNCTION OF COMPUTATIONAL PARAMETERS AND HYDROGRAPH ................................ ................................ ................................ ............... 151 Detailed Sampling Methodology and Protocol ................................ ................................ ..... 151 Effluent Sampling ................................ ................................ ................................ .......... 151 Mass Recovery and Sample Protocol ................................ ................................ ............ 151 Laboratory Analysis ................................ ................................ ................................ ...... 152 PAGE 7 7 Verification of Mass Balance ................................ ................................ ........................ 153 Verification of PSD Balance ................................ ................................ ......................... 153 Resu lts under Steady C ondition ................................ ................................ ............................ 154 Morsi and Alexander K V alues (Morsi and Alexander, 1972): ................................ ......... 154 Effect of T emperature ................................ ................................ ................................ ........... 155 B SUPPLEME HYDRAULIC RESPONSE AS A FUNCTION OF FLOW, UNSTEADINESS AND ................................ ................................ ................................ ......................... 165 Full s cale Physical Model Setup ................................ ................................ .......................... 165 Generation of Hydrographs U sed for the Validation of the Full Scale Physical Model of Clarifier under Transient Conditions ................................ ................................ ................ 167 Hyetographs ................................ ................................ ................................ ................... 167 Particle Size Distribution ................................ ................................ ................................ ...... 167 PSD Selection ................................ ................................ ................................ ................ 167 PSD Significance ................................ ................................ ................................ ........... 168 Transformation of Rainfall Hyetographs to Runoff Hydrographs ................................ ....... 168 Definition of N ................................ ................................ ................................ ...................... 169 Geometry and Mesh Generation of Full Scale Rectangular Clarifier ................................ .. 170 Turbulent Dispersion Model ................................ ................................ ................................ 170 CFD Modeling and Population Balance ................................ ................................ ............... 171 Validation Analysis of Steady RTDs and PM Separation Efficiency on Full Scale Physical Model of Rectangular Clarifier ................................ ................................ ........... 172 C FLOW CFD MODEL PREDICT PM SEPARATION FROM STORMWATER UNIT OPERATIONS AS A FUNCTION OF HYDROGRAPH UNSTEADINESS AND PM ................................ ................................ ................................ ......... 191 Stepwise Steady Flow Model ................................ ................................ ............................... 191 UDF for Fully Unsteady and Stepwise Steady Flow CFD Models ................................ ...... 193 D FLOW MODEL FOR EVALUATING LONG TERM UO SEPARATION ................................ ................................ ................................ ............... 211 Disaggregation Rainfall Method ................................ ................................ ........................... 211 Full Scale Physical Model Setup of the Rectangular Clarifier ................................ ............. 211 Generation of Hydrographs U sed for the Validation of the Full Scale Physical Model of Clarifier under Transient Conditions ................................ ................................ ................ 212 Hyetographs ................................ ................................ ................................ ................... 212 Transformation of Rainfall Hyetographs to Runoff Hydrographs ................................ 213 Particle Size Distribution ................................ ................................ ................................ ...... 214 PSD Selection ................................ ................................ ................................ ................ 214 PSD Significance ................................ ................................ ................................ ........... 214 Geometry and Mesh Generation of Full Scale Models ................................ ........................ 214 PAGE 8 8 CFD Modeling and Population Balance ................................ ................................ ............... 215 Liquid Phase Governing Equations ................................ ................................ ............... 215 Particulate Phase Governing Equations (the DPM) ................................ ...................... 216 Numerical Solution ................................ ................................ ................................ ........ 218 Stepwise Steady Flow Model ................................ ................................ ............................... 218 LIST OF REFERENCES ................................ ................................ ................................ ............. 243 BIOGRAPHICAL SKETCH ................................ ................................ ................................ ....... 250 PAGE 9 9 LIST OF TABLES Table page 2 1 Physical model (baffled HS) hydraulic and PM loading and PM separated ...................... 49 4 1 Physical model (baffled HS and rectangular clarifier) hydraulic and PM loading and PM separated ................................ ................................ ................................ .................... 110 5 1 Physical and CFD model hydraulic loadings and washout PM results for the clarifier subject to the hydrographs and the hetero disperse gradation ................................ ......... 144 5 2 Measured and modeled washout PM are reported for two units, SH S (D = 1.7 m) and SHS (D = 1.0 m) along with the char acteristics of the washout runs .............................. 145 5 3 Unsteady and steady CFD PM washout res ults for rectangul ar clarifier and SHS (D = 1.7m) ................................ ................................ ................................ ................................ 146 A 1 Experimental matrix and summary of treatment run results for the baffled H S unit loaded by a hetero disperse (NJDEP) gradation under 100 mg/L ................................ ... 164 A 2 Morsi and Alexander constants for the equation fit of the drag coefficient for a sphere ................................ ................................ ................................ ............................... 164 B 1 Summary of measured and modeled treatment performance results for full scale rectangular clarifier (RC) and rectangular clarifier with 11 baffle clarifier (B11) .......... 186 B 2 Summary of RTD test for pilot scale rectangular cross section linear clarifier configuration loaded with sodium chloride injected as a pulse at t = 0. .......................... 186 B 3 Number of baffles and corresponding value of tortuosity, Le/L for the clarifier with transverse baffles and opening of 0.60 m and 0.20 m, with longitudinal baffles ............ 187 B 4 Parameter values of the curves used to fit the volumetric effici ency versus tortuosi ty for the clarifier configuration with longitudina l baffles and opening of 0.20 m ............. 187 B 5 Parameter values of the curves used to fit the volumetric efficiency versus tortuosity, for the clarifier config uration with transverse baffles ................................ ...................... 188 B 6 Parameter values of the curves used to fit the Morrill index, MI data versus tortuosity, for the clarifier configuration with longitudina l baffles and opening of 0.20 m ................................ ................................ ................................ .............................. 188 B 7 Parameter values of the curves used to fit the Morrill index, MI data versus tortuosity, for the clarifier config uration with transverse baffles ................................ .... 189 B 8 Parameter values of the curves used to fi t the N data versus tortuosity for the clarifier configuration with longitudinal baffles and opening of 0.20 m ................................ ....... 189 PAGE 10 10 B 9 Parameter values of the curves used to fi t the N data versus tortuosity for the clarifier configuration with transverse baffles ................................ ................................ ............... 189 B 10 Parameter values of the curves used to fit the MI data for degrees of unsteadiness for the clarifier configuration with transvers e baffles and opening of 0 .20 m ...................... 190 B 11 Parameter values of the curves used to fit the N data for degrees of unsteadiness for the clarifier configuration wit h transverse baffles and opening of 0.20 m ...................... 190 C 1 Compu tational time expressed in hour for the CFD stepwise steady flow and the fu lly unsteady models. ................................ ................................ ................................ ..... 210 C 2 Example of the output from UDF developed for recording particle residence time, injection time and diameter ................................ ................................ .............................. 210 D 1 Summary of measured and modeled treatment performance results for full scale rectangular clarifier loaded by heter o disperse silt particle size gradation ...................... 241 D 2 Morsi and Alexander constants for the equation fit of the drag coefficient for a sph ere ................................ ................................ ................................ ............................... 241 D 3 Under relaxation factors utilized in the CFD simulations ................................ ............... 242 PAGE 11 11 LIST OF FIGURES Figure page 2 1 Schematic representation of the full scale physical model facility setup with baffl ed hydrodynamic separator (BHS) ................................ ................................ ......................... 50 2 2 T hree hydrographs loading physical model (baffled HS shown in inset) and influent and effluent measured and modeled particle size distributions (PSDs) for each loading ................................ ................................ ................................ ................................ 51 2 3 The effect of time step (TS) on modeled in tra event effluent PM as a function of hydrograph unsteadiness ( ) ................................ ................................ .............................. 52 2 4 The CFD model error (e n ) and computational time simulating eluted PM as function of TS and MS for hydrograph unsteadiness ................................ ................................ ....... 53 2 5 The e ffect of mesh size (MS) on CFD modeled intra event effluent PM as a function of hydrograph unsteadiness ( ) ................................ ................................ .......................... 54 2 6 Separated event based PSDs from CFD model as compared to physical mo del data. Separated event based PSDs for Q p and Q median are also reported ................................ ..... 55 3 1 T he conceptual process flo w diagram for the stepwise CFD steady flow methodology ... 71 3 2 Physical model and CFD model results for PM and PSDs for the validation analysis for f ull scale physical model of the rectangular clarifier ................................ ................... 72 3 3 Comparison between rectangular and trapezoidal cross section clarifier configurations. ................................ ................................ ................................ ................... 73 3 4 Volumetric efficiency as function of clarifier flow path tortuosity, Le/L for the clarifier configurations with transverse and longitudinal internal baffling ....................... 74 3 5 N as function of clarifier flow path tortuosity, Le/L for the clarifier co nfigurations with transverse and longitudinal inte rnal baffling ................................ ............................. 75 3 6 Pe as function of N tanks in series for the configurations w ith respectively transverse baffles and opening of 0.20 m and longitudinal baffles ................................ ..................... 76 3 7 Modeled cumulative RTD function, F as function of time for highly unsteady, unsteady and quasi steady hydrographs respectively for rectangular clarifier .................. 77 4 1 Influ ent h ydraulic loadings and PSDs ................................ ................................ .............. 101 4 2 Effluent PM response of a baffled HS to the fine r hetero disperse PSD transported by the hydrogr aphs of varying unsteadiness ................................ ................................ ..... 102 PAGE 12 12 4 3 Effluent PM response of a BHS to the coarser hetero disperse PSD transported by the hydrographs of varying unsteadiness ................................ ................................ ...... 103 4 4 Effluent PM response of a rectangular clarifier to each hydrograph (volume = 122 m 3 ) loading of varying unsteadiness ................................ ................................ ............. 104 4 5 Each plot displays the influent PM mass recovery provided by auto sampling of the BHS as a function of hydrograph unsteadiness ( ) and PSD ................................ .......... 105 4 6 Each plot displays the effluent PM mass recovery comparing auto and manual sampling methods for the BHS as a function of hyd rograph unsteadiness ( and PSD ................................ ................................ ................................ ................................ .. 106 4 7 Each plot displays the effluent PM response of the BHS to a coarser PSD as a function of h ydrograph unsteadiness ( ................................ ................................ ......... 107 4 8 Each plot displays the effluent PM response of the BHS to a finer PSD as a function of hydrograph unsteadiness ( ................................ ................................ ........................ 108 4 9 Each plot displays the effluent PM response of the BHS to a source area PSD as a function of hyd rograph unsteadiness ( ................................ ................................ ......... 109 5 1 Th e subject Gainesville, Fl (GNV) watershed for physical, the contin uous simulation (SWMM) modelin g and time of concentration as function of rainfall intensity ............. 138 5 2 Influe nt hydraulic loadings and PSDs. I nfluent particle size distribution (PSD) is reported in A), the scaled hydrographs obtained from design hy etographs in B) ........... 139 5 3 ntra event effluent PM w ashout generated by physically validated CFD model. Plot A) and B) generated from a triangular hyetograph loading the subject watershed ......... 140 5 4 CFD model of event based washout of PM at 50% and 100% of sediment capacity in sump area and no PM depth in the volute area ................................ ................................ 141 5 5 CFD model of PM washout mass as a function of flow rate, Q for the rec tangular clarifier and SHS unit ................................ ................................ ................................ ....... 142 5 6 Effluent PM results generated through the conti nuous simulation model for 2007 ........ 143 A 1 Validation of measured vs. model ed PM separation for HS subject to hetero disperse PSD loading at a gravimetric PM concentration of 100 mg/L at steady flow rates ......... 156 A 2 Effluent PSDs for differing hydrographs. Effluent PSDs for highly unsteady hydrograph, unsteady hydrograph quasi unsteady hydrograph ................................ ...... 157 A 3 Effect of time step (TS) on modeled effluent PM at DN = 16 and MS = 3.1*10 6 for three hydrologic unsteadiness ................................ ................................ .......................... 158 PAGE 13 13 A 4 Normalized root mean squared error (e n ) of CFD model effluent PM as function of time step for three levels of hydrologic event unsteadiness investigated ........................ 159 A 5 Effect of mesh size on modeled effluent PM at DN = 16 and TS = 10 sec for three hydrograph s investigated respectively, highly unsteady, unsteady and quasi s teady. .... 160 A 6 Captured CFD model particle size distribution (PSD) at TS = 10 sec, MS = 3.1*10 6 DN = 16, 32, 64 generated by baffl ed HS loaded by an influent hetero disperse PSD ... 161 A 7 Effect of temperature on PM removal percentage of HS unit subject to the hetero disperse PM gradation of this study at the peak flow rate of 18 L/s ................................ 162 A 8 CFD model snapshots. Pathlines are colored by ve locity magnitude (m/s) .................... 163 B 1 Triangular hyetograph. Td is the recession time, ta is the time to peak, and r is the storm advancem ent coefficient ................................ ................................ ........................ 173 B 2 Frequency distribution of rainfall precipitation for Gainesville, Florida. The frequency distribution is obt ained from a series of 1999 2008 hourly precipitation data ................................ ................................ ................................ ................................ ... 173 B 3 Historical event collected on 8 July 2008 ................................ ................................ ........ 174 B 4 Influent PSD for fine PM {SM I, <75 m}. SM is sandy silt in the Unified Soil Classificat ion System (USCS). SM is SCS 75 ................................ ................................ 174 B 5 Hydraulic loadings utilized for full scale physical model. The rainfall runoff modeling is performed in Storm Water Management M odel (SWMM) for the catchment ................................ ................................ ................................ ......................... 175 B 6 Relationship between N tanks in series and the difference between median and peak residence time ................................ ................................ ................................ .................. 176 B 7 Isometric view of full scale physical model and mesh of the rectangular cross section clarifier with eleven baffles ................................ ................................ ............................. 177 B 8 Isometric view of full scale physical model and mesh of the rectangular cross section clarifier ................................ ................................ ................................ ............................. 178 B 9 Grid convergence for full scale rectangular clarifier. The mesh utilized comprimes 3.1*10 6 tetrahedral cells ................................ ................................ ................................ ... 179 B 10 Physical and CFD Modeled RTDs for flow rates, representing 100%, 50%, 10% and 5% of Q d on no baffle rectangular clarifier ................................ ................................ ..... 180 B 11 Physical model and CFD model results for the triangular hydrograph used for the validation analysis for full scale physical model of a rectangular clarifie r ..................... 181 PAGE 14 14 B 12 Velocity magnitude (m/s) contours at a horizontal plane at mid depth for the configuration with transverse baffles and opening of 0.60 m ................................ .......... 182 B 13 Velocity magnitude (m/s) contours at a horizontal plane at mid depth for the configuration with transvers e baffles and opening of 0.20 m ................................ .......... 183 B 14 Velocity magnitude (m/s) contours at a horizontal plane at mid depth for the configuration with longitudinal baffles ................................ ................................ ............ 184 B 15 Morrill index as function of clarifier flow path tortuosity, Le/L for the clarifier configuration s with transverse and longitudinal internal baffling ................................ ... 185 C 1 Schematic representation of the full scale physical model facility setup with rectangular clarifier ................................ ................................ ................................ .......... 196 C 2 Schematic representation of the full scale physical model facility setup with baffled HS ................................ ................................ ................................ ................................ .... 197 C 3 Triangular hyetograph. T d is the recession time, t a is the time to peak, and r is the storm advancement coefficient (Chow et al., 1988) ................................ ........................ 197 C 4 Frequency distribution of rainfall precipitation for Gainesville, Florida. The frequency distribution is obtained from a series of 199 9 2008 hourly precipitation data ................................ ................................ ................................ ................................ ... 198 C 5 Historical event collected on 8 July 2008 ................................ ................................ ........ 198 C 6 Hydraulic loadings utilized for full scale physical model of rectangular clarifier: triangular hyetograph, Historic al 8 July 2008 hydrologic eve nt ................................ ...... 199 C 7 Unit hydrograph (UH) theory (Chow et al., 1988) ................................ .......................... 200 C 8 Stepwise steady flow model analogy with UH ................................ ................................ 201 C 9 Stepwise steady flow model. Particle residence time distribution, U p as function of flow rate ................................ ................................ ................................ ........................... 202 C 10 Stepwise steady flow model methodology ................................ ................................ ...... 203 C 11 Up as function of time for the finer PSD for two steady flow rates. The U p distributions are fit by a gamma distribution with parameters, and .......................... 204 C 12 Shape and scale gamma paremeters ( and ) as function of Q. The gamma parameters are used to fit the Up,Q with a gamma distribution function ........................ 205 C 13 Effluent PM response of a rectangular clarifi er to the highly unsteady ( =1.54) and unsteady ( =0.33) hydrographs ................................ ................................ ....................... 206 PAGE 15 15 C 14 Effluent PM for the fully unsteady CFD model and the stepwise steady model from Pathapati and Sansalone (2011) ................................ ................................ ....................... 207 C 15 Effluent PM response of a rectangular clarifier to the highly unsteady ( =1.54) and unsteady ( =0.33) hydrographs generated through the stepwise steady model .............. 208 C 16 Influent coarser and finer PSDs as compared to measured effluent PSDs generated through auto sampling for the three hydrographs shown in Figure 1B ........................... 209 D 1 Precipitation data disaggregation (Orsmbee, 1988)) ................................ ....................... 221 D 2 Rainfall intensity frequency distribution for the period 1998 2011 an d for 2007 and t ime domain distribution of rainfall and runoff for June 2007 ................................ ........ 222 D 3 Total rainfall depth as function of month for th e year 2007 ................................ ............ 223 D 4 Cumulative and incremental r unoff frequency distribution for 2007 for a watershed of 1.6 ha, with 1% slope, 75% of imperviousnes s and sand soil characteristics ............. 223 D 5 Schematic representation of the full scale physical model facility setup wit h rectangular clarifier ................................ ................................ ................................ .......... 224 D 6 Frequency distribution of rainfall precipitation for Gainesville, Florida. The frequency distribution is obtained from a series of 1999 2008 hourly precipit ation data ................................ ................................ ................................ ................................ ... 225 D 7 Influent PSD for fine PM {SM I, <75 m}. SM is sandy silt in the Unified Soil Classificat ion System (USCS). SM is SCS 75 ................................ ................................ 225 D 8 Hydraulic loadings utilized for full scale physical model. The rainfall runoff modeling is performed in Storm Water Management Model (SWMM) for the catchment ................................ ................................ ................................ ......................... 226 D 9 Isometric view of full scale physical model and mesh of the rectangular cross section clarifier. The number of computational cells is 3.5*10 6 D is diameter .......................... 227 D 10 Grid convergence for full scale recta ngular clarifier. The mesh utilized comprimes 3.5*10 6 tetrahedral cells ................................ ................................ ................................ ... 228 D 11 View of the full scale physical model of screened H S (SHS) unit. D represents the diameter ................................ ................................ ................................ ............................ 228 D 12 Scour hole generated after a transient physical model te st on the rectangular clarifier .. 229 D 13 Schematic of scour CFD model by integrating across surfaces (not to scale) ................. 229 D 14 Particle residence time distributions, Up for RC and SHS as function of steady flow rate. The flow rates vary from 1 to 50 L/s (ma ximum hydraulic capacity of RC) .......... 230 PAGE 16 16 D 15 Unit hydrograph (UH) theory (Chow et al., 1988) ................................ .......................... 231 D 16 Stepwise steady flow model analogy with UH ................................ ................................ 232 D 17 Stepwise steady flow model. Particle residence time distribution, Up as function of flow rate ................................ ................................ ................................ ........................... 233 D 18 Stepwis e steady flow model methodology ................................ ................................ ...... 234 D 19 Effluent PM generated from the stepwise steady model as func tion of the number of flow rates ................................ ................................ ................................ .......................... 235 D 20 Physical and CFD model results for PM and PSDs for the triangular hydrograph and for 8th July 2008 storm for full sca le physical m odel of a rectangular clarifier ............. 236 D 21 CFD model of washout PM concentration as a function of flow rate, Q for the r ecta ngular clarifier and SHS unit ................................ ................................ .................... 237 D 22 CFD model of PM washout mass and concentration for the SHS unit for PM depths in volute section ranging from 10 to 100 mm with 100% of PM capacity in sump area. ................................ ................................ ................................ ................................ .. 238 D 23 Effluent PM mass and PM mass depth as function of month for the screened HS unit in the representative year 2007 for 100% of sediment capacity of sump area ................ 239 D 24 Normalized mean fluid velocity distributions inside the inner and outer volute area of SHS, and RC. Bin sizes are consistent for SHS and RC ................................ .................. 240 PAGE 17 17 LIST OF ABBREVIATION S BHS Baffled Hydrodynamic Separator C eff Effluent Concentration [mg L 1] C D i Drag coefficient C i I nfluent concentration (mg L 1) C 1 C 2 Empirical constants in the standard k model CFD Computational fluid dynamics DN Discretization number d p P article diameter ( m) DPM Discrete particle model d 50 Particle diameter at which 50% of particle gradation mass is finer ( m) e n Normalized root mean squared error FD i Buoyancy/gravitational force per unit particle mass g i S um of body sources in the ith direction (m s 2 ) HS Hydrodynamic separator k T urbulent kinetic ene rgy per unit mass (m 2 s 2 ) K 1 K 2 K 3 E mpirical constants as function of particle Re i L Clarifier length (m) L e Clarifier flow path tortuosity (m) M PM mass associated to particle size range MB Mass balance M eff Effluent total mass (Kg) M inf Influent total mass (Kg) MI Morrill Index MS Mesh size PAGE 18 18 M sep Separated total mass (Kg) N T otal number of particle injected N S Navier Sto kes p n Mass per particle (Kg) PM Particulate matter (Kg) PBM Population balance model PSD Particle size distribution Q N ormalized flow rate respect to the median flow rate Q p Peak flow rate (L/s) Q 50 Median flow rate (L s 1 ) Q Flow rate (L s 1 ) p j Reynolds averaged pressure (Kg m 2 ) RANS Reynolds Averaged Navier Stokes RC Rectangular clarifier Re Reynold number Re i Reynold number for a particle RTD Residence Time Distribution S Mean strain rate (m s 1 ) SC Sump capacity SHS Screened Hydrodynamic Separator SIMPLE Semi Implicit Method for Pressure Linked Equations SSC Suspended sediment concentration (mg L 1 ) SWMM Storm Water Management Model t 50 Time at which 50% of tracer has exited the clarifier t N ormalized elapsed time respect to the duration of the storm PAGE 19 19 t d Duration of the event (min) t i Time instant (min) t p Time of peak flow rate (min) t r Total running time (min) TS Time step (sec) u i Reynolds averaged velocity in the ith direction (m s 1 ) u j Reynolds averaged velocity in the jth direction (m s 1 ) u i j Reynold Stresses (m 2 s 2 ) U p Particle Residence Time Distribution UDF User defined function UO Unit Operation UOP Unit O peration and P rocess V Event Total Volume (L) VE Volumetric Efficiency (%) v i F luid velocity (m s 1 ) v pi Particle velocity (m s 1 ) VF Volume fraction x m M odeled variable x m,max M aximum value of modeled variable x i ith direction vector (m) x j jth direction vector (m) x o M easured variable x o,max M aximum value of measured variable Gamma dis t r i bution scale factor for U p Gamma distribution scale factor for PSD PAGE 20 20 Gamma distribution shape factor for PSD PM Mass PM separation (%) t Temporal d iscretization (min) Turbulent energy dissipation viscosity (m 2 s 2 ) Unsteadiness parameter Dynamic viscosity (Kg m 1 s 1 ) 50 Median value Fluid viscosity (m 2 s 1 ) Eddy viscosity m 2 s 1 Particle size range m Fluid density (Kg m 3 ) p Particle density (Kg m 3 ) b Bulk density (Kg m 3 ) Gamma distribution shape fac tor for U p Prand t l number (ratio eddy diffusion of k to the momentum eddy viscosity ) Prand t l number (ratio eddy diffusion of to the momentum eddy viscosity ) Injection time (min) 50 Theoretical residence time at median flow rate, Q 50 (min) PAGE 21 21 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy PHYSICAL AND C OMPUTATIONAL F LUID D YNAMICS MODELING OF UNIT OPERATION S UNDER TRANSIENT HYDRAULIC LOADINGS By Giuseppina Garofalo August 2012 Chair: John J. Sansalone Major: Environmental Engineering Sciences U nit operations (UOs) are used t o manage the fate of urban rainfall runoff particulate matter (PM) and compounds in runoff that partition to and from PM. For UOs subject to runoff loadings, computational fluid dynamics (CFD) is emerging as a de sign and analysis tool, albeit utilization has been primarily for time independent flows In contrast to the common use of steady CFD models there are few transient validated models of UOs This dissertation aims to investigate the transient hydraulic and PM response of common runoff UOs Utilizing a baffled hydrodynamic separator ( BHS) the potential of CFD model to predict PM elution as a function of hydrograph unsteadiness is investigated. T he role of mesh size (MS), time step (TS) and discretization number (DN) of particle size distribution (PSD) to simulate PM elution is examined. T he impact of baffle configuration, flow rate, and hydrograph unsteadiness on hydraulic response of a rectangular clarifier (RC) is quantified through Morrill index (MI), v olumetric efficiency (VE) and N tanks in series (N) metrics. A stepwise steady flow CFD model is proposed and tested for transient events to predict PM separation with reduced computational overhead. The stepwise steady approach models response of a BHS a nd a RC to a hydrograph. The stepwise steady CFD flow model i s extended to evaluate PM fate (separation and washout) in a RC and a screened HS (SHS) on annual basis. PAGE 22 22 R esults for BHS demonstrate MS TS and DN significantly impact prediction of PM elution, P SDs and computational effort as influenced by the unsteadiness level. F or a RC with no baffles, VE and N increase while MI decreases with flow rate. For a RC with baffles MI and N are functions of unsteadiness level and number of baffles The stepwise stea dy CFD model produce s effluent PM results in good agreement with measured physical model data at a significantly reduced time compared to unsteady CFD models. T he coupling of a stepwise steady CFD approach and time domain continuous simulation represents a valuable tool to estimate PM fate on annual basis. Results provide a macroscopic evaluation for finding the optimal control strategy and defining maintenance requirements to improve UO treatment. PAGE 23 23 CHAPTER 1 GLOBAL BACKGROUND Urban rainfall runoff particulate matter (PM) is a reactive substrate that is size hetero disperse. PM functions as a vehicle for chemical and microbial transport, and a discrete phase to and from which chemicals partition (Sansalone, 2002; USEPA, 2000; Stumm and Morgan 1996; Sansalone et al. 1998; Sansalone et al., 1998; Sansalone and Buchberger, 1997). Stormwater PM represents a cause of impairment for surface waters (Heaney and Huber, 1984) and in 1972 the Clean Water Act (revised in 1987) to mitigate PM stormwater discharge s into receiving waters introduced the use of unit operations (UOs) (USEPA, 2000). CFD model based on numerically solving the fundamental equations of fluid flow, the Navier Stokes (N S) equations is emergin g as a design and analysis tool f or modeling hydraulic and PM response of UOs. In CFD a hydrodynamic model solves and simulates the flow field, while a discrete phase model (DPM) coupled with granulometric data, such as PSD and specific gravity ( s), predicts three dimensional particle traje ctories and velocities ( Pathapati and Sansalone, 2009a,b). Recent CFD research is very active on the development of dependable particle flow models which provide helpful insights into PM process phenomena and accelerate the achievement of ameliorative proc ess solutions (Curtis and Wachem, 2004) Steady CFD models were utilized to reproduce PM settling and resuspension processes in sedimentation storage tanks (Andersson et al., 2003; Dufresne, 2008). Pathapati and Sansalone conducted a steady CFD model ana lysis of PM separation process of a passive radial cartridge filter system and a hydrodynamic separator (Pathapati and Sansalone, 2009a,b). Dickenson and Sansalone (2009) demonstrated the influence of PSD discretization (as DN) in steady CFD model in predi cting PM separation and provided DN guidance based on PM dispersivity. Steady PAGE 24 24 flow studies have also used a DPM to examine PM settling and scour processes in tanks and basins (Dusfrene et al., 2009; Wals et al., 2010; Samaras et al., 2010). Although steady PM performance evaluations of UOs represents a basic tier of testing certification (TARP, 2001), final regulatory certification requires monitoring of unsteady runoff events and PM delivery to assess actual UO behavior under in situ conditions. In contras t to wastewater and drinking water systems that are loaded by steady to quasi steady flows, stormwater UOs are, in fact, subjected to a very wide range of flows or highly unsteady episodic flows. Validated unsteady CFD models are also necessary for design and analysis (Cristina and Sansalone, 2003) given the current cost of an in situ unit operation certification program is between 200 and 300 hundred thousand dollars Few validated or three dimensional (3D) models of UOs subject to unsteady hydrologic load s are present in literature (Pathapati and Sansalone, 2009) due to added computational efforts to resolve variably unsteady hydrodynamics and the complexity of coupling a CFD model with a monitored physical model for validation (Valloulls and List, 1984a b ; Wang et al., 2008). These studies did not investigate PM elution as a function of differing levels of unsteadiness. Furthermore, the influent particle size distributions ( PSDs ) were either uniform, divided into a DN of six to eight, or simply simulated a s a continuous function. Effluent PM reported in these studies was not a function of time but lumped as PM removal efficiency, sludge thickness, sludge or effluent PSD. Finally, these studies generated simulation results primarily without physical model va lidation. A major issue in highly polluted urban environments is that UOs, such as clarification type basins, are constrained by infrastructures and land uses. To improve hydraulic and PM response, clarifiers are retrofit with baffles. The role of interna l baffling on improving hydraulic PAGE 25 25 behavior of clarifiers was examined in previous literature by examining hydraulic indices, such as Morrill Index residence time distribution (RTDs), volumetric efficiency and N tanks indices with steady CFD models. Studies have examined the hydraulic efficiency of baffled systems, typically at constant flow (Wilson and Venayagamoorthy, 2010; Kim and Bae, 2007; Amini et al., 2011; Kawamura, 2000). For example, Wilson and Venayagamoorthy (2010) analyzed a baffled tank with up to 11 transverse baffles at the design flow; concluding that the maximum hydraulic efficiency was reached at six baffles. However, for stormwater clarifiers the hydraulic efficiency as a function of flow rate, unsteadiness ( and number of baffles (as an equivalent L/W for baffling) has not been examined. Although unsteady CFD modeling represents a tool to accurately predict hydraulic and PM response in UOs, it also requires an added computational overhead with respect to steady modeling. Pathapati and S ansalone (2011) in an attempt of balancing modeled error and computational time, introduced a stepwise steady flow CFD model to reproduce unsteady PM separation for stormwater UOs. The method is based on PM separation efficiency results generated from stea dy CFD modeling. The steady CFD results at each discretized flow level are flow weighted across the unsteady runoff events (Pathapati and Sansalone, 2011). According to this method, the UO instantaneously responses to each discretized flow level delivered into the system. The study concluded the stepwise steady model does not accurately reproduce PM separation for HS and clarifier units. Previous literature has evaluated PM separation efficiency of UOs by using unsteady CFD models solely on event basis. While i n the design and analysis, the performance of UOs is frequently assessed for either a single represen tative storm or a design storm, an annual basis evaluation can provide the UO`s overall response to the wide spectrum of long term rainfall PAGE 26 26 runoff e vents. In addition to the PM elution from UOs, a long term analysis can also include an estimation of the PM washout. Recent studies demonstrated that PM washout strongly impacts the overall response of UO, depending on the type of UO and maintenance frequ ency. While coupling fully unsteady CFD model with a long term continuous simulation can be a reasonable concept, the computational overhead can be unreasonable. For this reason, transient CFD modeling has never been implemented into a continuous model fra mework. The second chapter`s objective is to perform a parameterization study for unsteady CFD modeling. The assumption is that numerical parameters, such as MS TS and discretization of influent PM granulometry strongly affect the accuracy and running tim e of CFD unsteady solution. CFD model is applied to a baffled HS, which represents a common unit operation used in urban drainage system to separate PM constituents from stormwater flows through gravitational settling (Type I settling). The system is loade d with coarse hetero disperse PM gradation at constant concentration. The analysis intends to model not only lumped descriptors such as overall PM separation efficiency but also specific parameters, which provide a unique signature of the system behavior, such as spatially distribution of PM mass and PSD as function of flow rate. The third chapter`s objective is to examine the role of baffle configurations, flow rate and hydrograph unsteadiness on the hydraulic behavior of a clarifier subject to stormwater flows. A validated CFD model of a RC with different baffling configurations is utilized to investigate the hydraulic behavior of the unit using RTD, MI, VE, Peclet number (Pe) and N tanks in series parameters (Hazen, 1904, Morrill, 1932; Metcalf and Eddy, 2003). The number of baffles is indexed by flow tortuosity (Le/L) as a surrogate for flow path L/W ratio. Results are generated using a CFD model validated with full scale physical models. PAGE 27 27 The fourth chapter introduces a new stepwise steady model for pre dicting PM separation by a clarifier and a HS. This model takes into account that UO response to a hydraulic and PM loading is not instantaneous but varies according to the hydrodynamic characteristics of the system (for example, residence time). Idealizin g clarifier and HS as linear systems, the overall response of the UO subject to an unsteady event is obtained by convoluting particle residence time distributions across the series of flow rates in which the hydrograph is discretized. The CFD model is util ized to produce the particle residence time distributions for a series of steady flow rates and for specific PM gradations. The CFD model is validated with full scale physical model data. In addition, this chapter examines the efficiency of PM recovery pro duced through auto sampling at the influent and effluent sections of the HS and illustrates the effect of influent auto sampling in predicting the effluent time dependent PM on CFD stepwise steady model. The fifth chapter`s aim is to extend the stepwise steady flow CFD model to evaluate long term response of two common UOs a RC and a BHS for PM separation and washout at a reasonable computational overhead. The time domain continuous simulation model is performed for a representative year of rainfall runo ff, by using a validated CFD model for PM separation and washout and transient hydraulic loadings. PAGE 28 28 CHAPTER 2 TRANSIENT ELUTION OF PARTICULATE MATTER FROM HYDRODYNAMIC UNIT OPERATIONS AS A FUNCTION OF COMPUTATIONAL PARAMETERS AND HYDROGRAPH UNSTEADINESS Summary While computational fluid dynamics (CFD) is utilized to simulate particulate matter (PM) separation and particle size distributions (PSDs) from unit operations, the role of computational paramet ers and hydrograph unsteadiness to simulate intra event elution of PM mass has not been examined. An Euler Lagrangian CFD model is utilized to simulate PM separation by a common hydrodynamic unit operation subject to unsteady flow events and a hetero dispe rse PM gradation. Utilizing a baffled hydrodynamic separator (HS) this study illustrates CFD model potential to predict eluted PM subject as a function of hydrograph unsteadiness. The study hypothesizes that accurate simulation of unit behavior as a funct ion of unsteadiness is dependent on mesh size (MS), time step (TS) and PSD discretization number (DN). CFD and full scale physical model results are compared. Results demonstrate that MS, TS and DN significantly influence prediction of transient PM mass, P SD and computational effort. Results demonstrate that each parameter generates model error for transient PM elution that is significantly influenced by the level of unsteadiness. In contrast, TS, MS and DN selection each have a statistically significantly smaller i nfluence on event based PM mass. Introduction Urban rainfall runoff PM is a reactive substrate that is size hetero disperse. PM functions as a vehicle for chemical and microbial transport, and a discrete phase to and from which chemicals partiti on. Runoff PM is also i mpairment for receiving waters (Weiss et al., 2007) Reprinted from Chemical Engineering Journal, 175, Garofalo, G., Sansalone, J., Transient elution of particulate matter from hydrodynamic unit operation as a function of computational parameters and runoff hydrograph unsteadiness 150 159, 2011, with permission from Elsevier PAGE 29 29 Whether runoff unit operations are clarification type basins (residence time of hours) or hydrodynamic units of short residence time (minutes), PM mass separation is predominately discrete Type I sedimentation (Wilson et al. 2009; MetCalf & Eddy, 2003). For unit operations subject to runoff loadings CFD is emerging as a design and analysis tool, albeit utilization has been primarily for time independent (steady) flows (Dickenson a nd Sansalone, 2009; Dufresne et al., 2009) CFD solves the Navier Stokes (N S) equations for the continuous fluid phase and can allow coupling of PM transport through a discrete phase model (DPM) (He et al., 2006; Wang et al., 2008; Wachem et al., 2003; Al Sammaerraee et al., 2009) CFD is a fundamental approach to model PM fate in unit operations as compared to lumped ideal overflow methods for steady flows (Pathapati and Sansalone, 2009a b) Using a steady CFD model the role of discretization (as a DN) h as demonstrated that the DN strongly influences model error for PM separation by runoff unit operations, and provides DN guidance based on PM hetero dispersivity (Dickenson and Sansalone, 2009). Steady flow studies have also used a DPM to examine PM settli ng and scour processes in tanks and basins (Dufresne et al., 2009; Wols et al., 2010; Samaras et al., 2010) While steady flow evaluations of unit operations are a basic tier of testing certification (TARP, 2001) actual unit operation behavior and final regulatory certification requires monitoring of unsteady runoff events and PM delivery. In addition to regulatory requirements, validated CFD models of unsteady phenomena are needed for design and analysis (Cristina and Sansalone, 2003) given the current cost of an in situ unit operation certification program is between 200 to 300 hundred thousand dollars. In contrast to the common use of steady CFD models there are few validated or three dimensional (3D) models of unit operations such as an HS subject t o unsteady hydrologic loads PAGE 30 30 and Type I settling (Dickenson and Sansalone, 2009). Whether for a clarifier or HS this is in part due to added computational efforts to resolve variably unsteady hydrodynamics and the complexity of coupling a CFD model with a m onitored physical model for validation. There have been many 2D modeling studies of wastewater clarifiers. Valloulls and List (Valloulls and List, 1984a b) developed a 2D model of effluent PM from a rectangular wastewater basin subject to Type II settling under steady and periodic sinusoidal flows. The simulated input and output demonstrated that effluent PM was influenced by mass concentration, PSDs, floc density and collision efficiency. Jin et al. (Jin et al., 2000) developed a 1D model for Type I settli ng in rectangular tanks to evaluate separate efficiency, captured and effluent PSDs. The model evaluated an unsteady process as a series of steady flow and concentration steps. The DN of the influent PSD was eight. Huang et al. (Huang and Jin, 2011) prop osed an unsteady 2D model for circular Type I settling tanks based on the model of Jin et al. (Jin et al., 2000) While the model was not validated a sensitivity analysis was performed. The DN of the influent PSD was six. Zhou and McCorquodale (Zhou and McCorquodale, 1992) utilized a 2D model to simulate flow and PM fate in rectangular wastewater tanks. The model was solved for transient flows until a steady state solution was reached. The transient model was used to examine temporal density variations an d avoid d ivergence. Kleine and Reddy (Kleine and Reddy, 2005) proposed a 2D unsteady finite element method to simulate steady hydrodynamics from an initially unsteady condition. Velocity and pressure fields as well as wastewater sludge distribution were m odeled. In contrast to 2D simulations, Wang et al. (Wang et al., 2008) built a 3D model for a secondary wastewater clarifier to simulate 3D velocity and PM concentration distributions as well as dynamic sludge settling. He et al. (He et al., 2008) utilize d a 3D model of a prismatic horizontal flow clarifier. The DPM was generated by injecting a fixed amount of PM at the clarifier inlet. PAGE 31 31 The PSD was mono disperse; a single 50 m particle size. Clarifier designs were compared based on inlet configurations. Whether as 2D or 3D analysis of wastewater clarifiers these studies did not investigate PM elution as a function of differing levels of unsteadiness. The studies that examined transience did so as a transition to steady conditions or as a fixed periodic v ariation in influent flow rate. Furthermore, the influent PSDs were either uniform, divided into a DN of six to eight, or simply simulated as a continuous function. Effluent PM reported in these studies was not a function of time but lumped as PM removal efficiency, sludge thickness, sludge or effluent PSD. Finally, these studies generated simulation results primarily without physical model validation. In comparison to wastewater clarifiers which are loaded by quasi steady flows with cohesive and largely organic PM subject to Type II settling, runoff unit operations are loaded by unsteady flows with PM that is more hetero disperse and inorganic. Pathapati and Sansalone (Pathapati and Sansalone, 2009c) demonstrated that event based steady flow indices for a CFD model of unsteady runoff events can generate significant error as compared to physical model data. In a follow up study Pathapati and Sansalone (Pathapati and Sansalone, 2011) illustrated that a stepwise steady CFD model of effluent PM and PSDs for unsteady runoff did not reproduce physical model results for a HS and primary clarifier but in contrast did replicate the response of a volumetric filter. The study demonstrated that unsteady CFD model s provide an accurate representation of PM fate for each unit operation. However these study or other studies of urban runoff unit operations have not examined the role of MS, TS, DN or unsteadiness. Towards the eventuality that validated CFD models will be relied upon to reproduce unit operation behavior, a defensible unsteady CFD model requires investigation of the spatial discretization (MS) of the computational domain, TS resolution of the hydrodynamics, and a DN PAGE 32 32 for the PM granulometry. It is hypoth esized that these parameters impact the accuracy of the unsteady CFD solution. Elucidation of computational effort as a function of unsteadiness is needed if CFD is eventually coupled with continuous simulation models such as the Stormwater Management Mod el (SWMM) to extend CFD beyond an intra event time scale to simulate longer term unit operation behavior and unit maintenance (Huber et al., 2005; Heaney and Small, 2003). This study hypothesizes that CFD model accuracy for simulating elution of hetero dis perse PM under transient hydraulic loadings is dependent on time resolution of the flow field, spatial discretization of the computational domain, and the PSD size discretization. These computational parameters have impacts on computational effort, hypoth esizing that increasing model accuracy as a function of unsteadiness comes at the expense of computational effort. This study utilizes a baffled HS as a circular sedimentation tank. The HS is a unit operation for separation of non aqueous phase constituen ts such as PM in runoff with over 30,000 HS units operating in North America. Objectives of this study are to develop an unsteady CFD model to predict the effluent PM variation of a HS as a function of MS, TS and DN model parameters for increasing unstead y loadings. Objectives also include prediction of time dependent PM measured as suspended sediment concentration (SSC) and PSDs. The computational expense of model parameterization (MS, TS, DN) is also examined as a function of hydrologic unsteadiness. M aterial and Methods This study utilizes a common 1.83 m (~ 6 ft) diameter baffled HS that provides gravitational settling (Type I) and retention of separated PM mass for small commercial, retail or otherwise developed land parcels. Separate or combined se wers concrete appurtenances are precast with this nominal diameter and most HS units are manufactured to insert into precast appurtenances or tanks. A horizontal baffle separates oil, grease and floatables from PM that PAGE 33 33 settles in the HS. Without regular maintenance, buildup of coarser PM and anaerobic conditions occur in the HS. Full Scale Physical Model Setup A schematic process flow diagram of the physical model is illustrated in Figure 2 1. The inset of Figure 2 2A illustrates the HS. Influent runof f to the HS is directed by a 200 mm high inflow weir through an orifice plate into the clarification chamber as conveyed through a drop tee inlet pipe. PM is separated in the clarification chamber. Runoff in the clarification chamber is conveyed through the outlet riser to the downstream side of an effluent channel before discharge through an outlet pipe. The HS volume is 4.62 m 3. The lower section of the clarification chamber is approximately 1.82 m tall and the unit diameter is 1.8 m. The flow rate th rough the clarification chamber is driven by the available head generated by the weir and orifice plate. Physical model runs are performed on a commercial HS for unsteady hydraulic loads at 20 ring unsteadiness are utilized as shown in Figure 2 2A. Hydrograph formulations are based on the use of a step function to model the SCS dimensionless unit hydrograph (Malcom, 1989) The hydrographs are scaled based on the HS maximum hydraulic capacity (18 L/s), maintaining constant volume (V = 22,840 L) and a constant time of peak flow, t p of 15 minutes (Sansalone and Teng, 2005). In Figure 2 2B the event based measured PSD is presented The physical model of the HS is utilized to validate the CFD model b ased on effluent PM as illustrated in the Appendix in Figure A 1. Selected illustrations of CFD model flow pathlines and temporal variation of PSDs throughout each event is reported in Figure A 2 and A 3. There is a range of hydrographs generated from smal l urban watersheds (scaled at 0.1 to 0.2 impervious hectares for this HS) depending on rainfall depth duration frequency, abstraction functions, geometrics and flow routing. Hydrographs with PAGE 34 34 differing unsteadiness are contained within this range (Fluent, 2006) In addition to differing unsteadiness the peak flow of 18 L/s is the maximum hydraulic capacity of the full scale physical model with other peak flows selected to represent 50% and 25% of this hydraulic capacity (2,500 < Re < 50,000). An unsteadin ess parameter, is defined for each hydrograph and the values of summarized in Table 2 1 In this Q med represents the median flow rate The values of for highly unsteady, unsteady and quasi steady hydrographs are 1.15, 0.24 and 0.09, respectively. The quasi steady of 0.09 is comparable to 0.085 for the sinusoidal wastewater loading of Valloulls and List (Vallouls and List, 1984) and a wastewater clar ifier with a peaking factor of 4 has a of less than 0.09. The for the unsteady and highly unsteady hydrographs are significantly higher. Based on monitoring data of Pathapati and Sansalone (Pathapati and Sansalone, 2009) the of actual hydrographs f rom a similar size paved watershed are typically 1 or greater; considered highly unsteady. Physical model runs are conducted at constant influent PM concentration (C i ) and constant hetero disperse PSD with a d 50 of 67 m as shown in Figure 2 2B. PSDs are modeled as cumulative gamma distribution in which (shape factor) and (scale factor) represent the PSD uniformity and the PSD relative coarseness, respectively (Dickenson and Sansalone, 2009). For the physical model the unsteady influent flow rate is d elivered by a pumping station and measured by two calibrated magnetic flow meters and a volumetric meter for low flows. Flow measurements are recorded by a data logger every second. PM is injected into the inlet drop box mixing with the influent flow. Repr esentative effluent samples are taken manually at the effluent section of the HS unit as discrete samples in 1L wide mouth bottles. Samples are collected in ( 2 1 ) PAGE 35 35 duplicate for the entire run duration at variable sampling frequencies according to the flow rate g radients and event duration to provide representative sampling of effluent variability for PM concentration and PSD. The minimum sampling interval is 1 minute. After a treatment run, supernatant samples and captured PM are collected. Samples are analyzed f or PM (gravimetrically as SSC) and PSDs. Separated PM mass is recovered, dried, weighted and analyzed by laser diffraction to obtain PSDs. A PM mass balance evaluation is conducted for each physical model run, summarized as: In the mass balance expression M inf is influent mass load and C eff is effluent concentration which varies with tim e, t i M sep is separated PM recovered. The PM separation (%) is also determined. PM separation and mass balance (MB) are reported in Table 2 1. Measured results including effluent PSDs and PM obtained from physical modeling are utilized to validate the CFD model. Physical model runs at steady flow rates are also performed as described in the Supporting Information. CFD Modeling A 3D unsteady CFD model is built for the full scale HS physical model using FLUENT v 13 .0. The code is finite volume based, written in C programming language and solves Navier Stokes (N S) equations across a com putational domain. CFD methodology comprises three general steps: (1) geometry and mesh generation (pre processing), (2) creating boundary and ( 2 2 ) ( 2 3 ) PAGE 36 36 initial conditions and (3) defining and solving the physical model (processing) and post processing model data. Due to the complex HS geometry, the mesh is completely comprised of tetrahedral elements, a non uniform meshing scheme where nodes do not reside on a grid. The mesh is checked to ensure equi angle skewness and local variations in cell size are minimized. In this study, the liquid particle phase flow in the HS is simulated by combining the Eulerian fluid dynamics model with a discrete particle model (DPM). The model is based on Euler Lagrangian approach in which the fluid phase is treated as a continuum i n an Eulerian frame of reference and solved by integrating the time dependent N S equations. The particulate phase behavior in the system is predicted by the DPM as a discrete phase in a Lagrangian frame of reference. At each simulation time interval the f low field is solved first. Liquid Phase Governing Equation The governing equations for the continuous phase are a variant of the N S equations, the Reynolds Averaged N S (RANS) equations for a turbulent flow regime. The RANS conservation equations are ob tained from the N S equations by mean value and fluctuating component. The mean velocity is defined as a time average for a period t which is larger than the time scale of the f luctuations. Time dependent RANS equations for continuity and momentum conservation are summarized. In these equations is fluid density, xi is the ith direction vector, uj is the Reynolds averaged velocity in the ith direction; pj is the Reynolds averaged pressure; and gi is the sum of ( 2 4 ) ( 2 5 ) PAGE 37 37 body forces in the ith direction. Decomposition of the momentum equation with Reynolds decomposition generates a term o riginating from the nonlinear convection component in the original equation; these Reynolds stresses are represented by Reynolds stresses contain information about the flow turbulence structure. Since Reynolds stresses are unknown, closure approximations can be made to obtain approximate solution of the equations (Pope, 2000). In this study the realizable k model (Shi et al., 1995) is used to resolve the closure problem. This model is suitable for boundary free shear flow (baffled HS) applications and consists of turbulent kinetic energy and turbulence energy dissipation rate equations, respectively reported below (Shi et al., 1995) k = 1.2, C 1 = 1.44, C 2 is the turbulent energy T fluid viscosity; and u ji u j i are previously defined. Particulate Phase Governing Equations (DPM) After solving the flow field, the DPM is applied. The DPM simulates 3D particle trajectories through the domain to model PM separation and elution in a Lagrangian frame of reference where particles are individually tracked through the flow field. This analysis assumes PM motion is influenced by the fluid phase, but the fluid phase is not affected by PM motion ( 2 6 ) ( 2 7 ) ( 2 8 ) PAGE 38 38 (one way coupling) and particle particle interactions are negligible. These assumptions are applicable, since the particulate phase is dilute (volume fraction (VF) around 0.01%) (Brennen, 2005) The DPM integrates the gov erning equation of PM motion and tracks each particle through the flow field by balancing gravitational body force, drag force, inertial force, and buoyancy forces on the PM phase. The motion of a single particle without collisions is modeled by the Newton `s law. Particle trajectories are calculated by integrating the force balance equation in the ith direction. The first term on the right hand side of the equation is the drag force per unit particle mass. The second term is the buoyancy/gravitational force per unit particle mass. In these equations, p is particle density, vi is fluid velocity, vpi is particle ve locity, dp is particle diameter, Rei is the particle Reynolds number, FDi is the buoyancy/ gravitational force per unit mass of particle and CDi is the particle drag coefficient (Morsi and Alexander, 1972). The last three variables are defined as follows. K 1 K 2 K 3 are empirical constants as a function of particle Re i and tabulated in Table A 2. ( 2 9 ) ( 2 10 ) ( 2 11 ) ( 2 12 ) PAGE 39 39 Particle injections are uniformly released from the HS inlet surface and each par ticle is tracked within the domain at each time step. To model the temporal PM fate, a computational subroutine as a user defined function (UDF) is written in C to record PM injection properties, residence time and size of each particle eluted from the sys tem throughout the entire simulation. A trap condition is defined for the HS lower boundary so that PM settling to this boundary is not reflected and the particle trajectory is terminated This assumption is physically reasonable given the volumetric isol ation of settled PM in the HS sump, and is verified by comparing modeled results for trapping or reflecting boundary conditions. The difference in eluted PM is approximately 1%, and for PSDs approximately 0.4%. The PM trapping assumption reduces the DPM co mputational effort since the particle numbers are reduced during the simulation. The PSD is discretized into size classes with an equal gravimetric basis. Studies have demonstrated that PM tracking lengths (TL) of 8 m and DN from 8 to 16 are generally a ble to reproduce accurate results for hetero disperse PM in this HS subject to steady flows (Dickenson and Sansalone, 2009). The DN baseline of this study is 8 and higher DN (16, 32 and 64) values are utilized to explore the impact of DN. A population bal ance model (PBM) is utilized to model PM separation. Assuming no flocculation in the dispersed PM phase, the PBM equation (Jakobsen, 2008) can be written. In this equation and represent particle size range and injection time ranging from 0 to the runoff event duration, td, respectively. The term () inf indicates influent PM, () eff effluent PM and () sep separated PM. p represents the mass per particle and is obtained as follow s: ( 2 13 ) PAGE 40 40 M is PM mass associated with the particle size range as function of injection time N i s the total number of particles injected at the inlet section, td is the event duration. A constant temperature of 20 C is utilized in this study. Full scale physical model water temperature varied by 2 C. It is hypothesized that the temperature do es not significantly impact the PM separation in a Type I settling unit subject to a hetero disperse PSD loading. This assumption is shown to be reasonable based on the study conducted by Ying and Sansalone (Ying and Sansalone, 2011) in which they examine the influence of temperature on Type I settling in a screened HS unit by using a CFD model validated with physical model data. For a hetero disperse PSD their study illustrated a relatively small influence of temperature (< 5% based on PM mass) or salinity as compared to particle density or PSD in a screened HS unit. The role of temperature on PM separation efficiency of the baffled HS in this study is provided in the Appendix Numerical solution The numerical solver is pressure based for incompressible flows that are governed by motion based on pressure gradients. The spatial discretization schemes are second order for pressure, the second order upwind scheme for momentum and the Pressure Implicit Splitting of Operators (SIMPLE) algorithm for pressure ve locity coupling. Temporal discretization of the governing equations is performed by a second order implicit scheme Table A 3 summarizes the under relaxation factors utilized. The under relaxation factors summarized in Table A 3 are based on a parametric e valuation of these factors from 0.1 to 1 at different TS. It is observed that as the TS increases the impact of the under relaxation factor on the results increased. These factors are selected to ensure simulation stability and minimize model error ( 2 14 ) PAGE 41 41 while b alancing computational time. Convergence criteria are set so that scaled residuals for all governing equations are below 0.001 (Ranade, 2002) All simulations are run in parallel on a Dell Precision 690 with two quad core Intel Xeon 2.33GHz processors and 16 GB of RAM. A TS analysis quantifies modeling error and computational effort as a function of TS and unsteadiness. TS values of 10, 30, 60, 300 and 900 seconds are investigated noting that a TS below 10 seconds are computationally expensive while 10 sec onds provides temporal grid independence; and is therefore the baseline TS. A TL of 8 m is utilized for PM. The HS geometry is spatially discretized into four mesh sizes (MS) of 0.2, 1, 3.1 and 5 million tetrahedral computational cells. A MS less than 0. 2 million cells does not satisfy convergence criteria. Validation analysis A normalized root mean squared error, en is used to evaluate CFD model results with respect to the full scale physical model. In this equation xo is measured, and xm the modeled variable. The validation study consists of comparing the full scale HS physical model results and the results obtained from the full scale CFD model. Validation is based on full scale physical model results (1) temporal intra event eluted PM results, (2) event based PM mass separation, (3) event based PSDs, and (4) PM mass separation at steady flow rates. In the validation process CFD model results for PM mass and PSD are compared to physical model results measured for each level of hydrograph unsteadiness. ( 2 15 ) PAGE 42 42 Results and Discussion CFD model results are valida ted with respect to physical model results for each 2 1B. Figure 2 2B illustrates the CFD model replication of eluted PSDs. Effluent PSDs are represented as cumulative gamma functions and par ameters are shown in Figure 2 2B. The HS unit provides a transformation between influent and effluent PSDs with the quasi steady hydrograph of the lowest Qp, gener ating the finest effluent PSD For higher Qp the physical model and gamma parameter results t rend in the direction of influent PSD parameters; increasing larger particles are eluted. The CFD model is also validated for steady flows with results in Figure A 1. Additionally, selected instantaneous solutions of the CFD mo del are illustrated in Figure A 2. Impact of Time Step (TS) and Mesh Size (MS) For the TS analysis, physical and CFD model (DN = 8 and MS = 3.1 x 10 6 ) results are summarized as temporal effluent PM mass in Figure 2 3 as a function of hydrograph unsteadiness. For clarity only the modeled effluent PM mass values for TS of 1 0, 300 and 900 sec are reported TS results indicate that the CFD model accurately simulates the temporal distribution of the physical model effluent PM for a TS range of 10 to 300 sec at each level of unsteadines s. CFD model error varies from approximately 4 to 9%. In comparison the CFD model at TS of 900 sec is less accurate at each level of unsteadiness, varying from 8 to 37% with larger error at higher unsteadiness. At higher hydrograph unsteadiness typical of small watershed with a lag time similar to the TS of 900 sec (15 min) the CFD model results in an underestimation during the hydrograph rising limb and an overestimated near the peak. With higher unsteadiness the TS of 900 sec does not account for this uns cell properties across the TS leads to less accurate results. Results in Figure 2 3 illustrate the largest change in en occurs around the hydrograph peak. PAGE 43 43 TS results are summarized in the three left hand plots of Figure 2 4 (A, C, E). Figure 2 4A illustrates an exponential decrease in CFD model error (DN = 8, MS = 3.1 x 106) that asymptotically approaches 5% at 1 minute TS based on PM mass. While Figure 2 4A illustrates an exponential decrease in model error for decreasing TS there is an increase in computational time as illustrated in Figure 2 4C. The increase of computational time is not only influenced by the duration of the event but also by the number of particles tracked (TL = 8 m ) throughout the entire event. Figure 2 4 E compares the PM mass separation (%) between the physical and CFD models. The CFD range bars define the range of event based modeled results obtained across the TS series. The maximum error in PM mass separation between measured and modeled data for va rying TS values is approximately 5% for this relatively coarse hetero disperse PSD loading the HS. Previous research has shown for steady flows that as this PSD becomes finer the model error for PM mass separation can increase significantly (Dickenson and Sansalone, 2009) While TS analysis demonstrates that the temporal distribution of effluent PM is significantly influenced by the TS selection, TS influence is muted for event based PM for this hetero disperse PSD modeled with a DN of 8. For MS analysis physical model and CFD model (DN = 8 and TS = 10 sec) results as temporal eluted PM mass are compared in Figure 2 5 A, B, C. Parallel to the accumulation of CFD error illustrated in Figure 2 3 for TS the accumulation of CFD model error is shown at the t op of each plot in Figure 2 5 As with TS results the highest variation in CFD model error associated with MS corresponds to the rapidly varying flows around the hydrograph peak. The CFD model accurately simulates temporal PM elution for a MS of 3.1 milli on cells while errors are consistently larger than 10% for each coarser MS. Since the turbulent fluid flows and PM PAGE 44 44 loadings with a coarser mesh cross fewer computational cells at a given TS a mesh of fewer cells produces less accurate results. MS results are summarized in the three right hand plots of Figure 2 4 (B, D, F). Analogous to the TS analysis, the model error generated based on MS is illustrated in Figure 2 4B. Model error for effluent PM mass in Figure 2 4B also illustrates an exponential decre ase approaching 2% with increasing MS. In contrast to the computation time increase with smaller TS, there is an exponential and larger increase in computational time with an increase number of computation cells as shown in Figure 2 4D. For 1 minute of r eal time operation of the full scale HS there is a corresponding 10 15 minute computational time for the full scale HS CFD model. The computational time considerations presented as a function of TS are further accentuated as a function of MS. This is large ly due to the DPM process which becomes more computational expensive as the unsteady event duration increases; more particles enter and are tracked at each computational cell in the domain. For a MS of 5 x 10 6 the computational time for a runoff event of 1 25 minutes reaches 120 hours. The MS selection has a significant impact on the computing time due to the tracking of particles in each cell of a highly discretized domain which increases the computational time Parallel to TS results, results in Figure 2 4F compare the PM mass separation (%) between the physical and CFD models for varying MS. Range bars for CFD results define the CFD model results across the range of MS. Similar to TS results, model results of temporal effluent PM mass is significantly i nfluenced by the MS selection. In contrast to temporal results there is a much more muted influence of MS on the event based PM separation for this coarse hetero disperse PSD modeled with a DN of 8. The maximum error in PM mass separation between physical model and event based CFD model results for MS values is approximately 3%. PAGE 45 45 Event Based Separated PSDs and DN for PSDs The event based separated PSDs as a function of unsteadiness are reported in Figure 2 6. The CFD model (MS = 3.1 x 10 6 TS = 10 sec, DN = 8) PSDs are compared to the PSDs separated by the physical model. The CFD model error varies from 2.4 to 6% as a function of unsteadiness. Physically, results illustrate that the finer gradation of PM is eluted by higher flows and the coarse PM dominat es the separated PSD on a gravimetric basis. As a function of TS a parallel set of CFD model results at a higher DN (MS = 3.1*10 6 TS = 10 s, DN = 16) are summarized in Figures A 4 and 5. Results indicate that the CFD model error with respect to the temp oral distribution of effluent PM mass is further decreased as compared to a DN of 8 for each TS but at the cost of increased computational time. This reduction in model error is particularly apparent for the highly unsteady hydrograph. However, while the m odeling error does decrease with a DN of 16 the computational time almost doubles. For this coarse hetero disperse PSD and a baffled HS a DN of 16 may not provide a significant benefit as compared to a DN of 8 based on PM mass given the additional computa tional time. Additionally, as a function of MS a parallel set of CFD model results at a higher DN (MS = 3.1*10 6 TS = 10 s, DN = 16) are summarized in Figure A 4 and 5. Parallel to the TS results at a DN of 16 the CFD model error with respect to the tempo ral distribution of effluent PM mass is further decreased, again at a cost of increasing computational time. Figure A 4 illustrates the model error decreases slightly for each MS, in particular for the highly unsteady hydrograph as compared to a DN of 8 re sults in Figure 2 4. As is the case for TS results at a DN of 16 the resulting decrease in CFD model error is accompanied by increased computational time. While temporal effluent PSD and PM mass are a function of TS and MS, separated PSD are separately mod eled to examine the role of MS on separated PSD results. Results in Table A 4 through A 6 indicate no significant difference (p = 0.05) for the MS range tested with the PAGE 46 46 requirement that the MS selected satisfy convergence criteria. While these results ind icate that CFD model results for the separated PSD are independent of MS, this result is a function of the relatively coarse hetero disperse PSD and as with TS will vary with PSD granulometry. The role of DN on captured PSD is also explored. Figure A 7 depicts the captured CFD model PSDs. CFD model errors range from 2.4 to 5.7%. The captured PSDs obtained for varying DNs are not statistically significantly different (p = 0.05); noting that captured PSDs are coarser and less hetero disperse than the ef fluent. Effect of Hydrograph Unsteadiness Figure 2 3 and 2 5 reports the CFD model results in comparison to physical model results for effluent PM mass as a function of hydrograph unsteadiness. For example, results at TS of 900 sec illustrate increasing e rror with increasing unsteadiness. Results in Figure 2 3 indicate that as unsteadiness decreases the model error decreases. As hydrograph unsteadiness increases coarser TS and MS values do not capture the variability of computational cell properties in th e computational domain as compared to greater discretization in time and spatial grid resolution. Figure 2 4 and F igure A 4 include a range of HS residence times. For each hydrograph the normalized axis TS/ 50 is generated, where 50 is the theoretical r esidence time for the HS median flow rate, Q 50 With Q 50 hydrograph Q p and 50 of the HS the error for a given TS can be determined. To illustrate TS results normalized to hydrograph duration the normalized axis TS/td is generated. Previous studies mod el the PM response of a screened HS subject to unsteady loadings in which one minute TS are utilized to reproduce actual runoff event effluent PM. In these events the hydrograph td varies from 15 to 408 minutes and hydrograph Q p varies from 0.6 L/s to 17. 5 L/s for a small impervious urban watershed (Pathapati and Sansalone, 2009c) Results in Figure 2 4A are supported by physical and CFD model results from a PAGE 47 47 separate study for a screened HS. In that study the CFD model TS is 60 sec and MS is 3.86 x 10 6 From that study model results for a 14 March 2004 event (Qp = 6.4 L/s, td = 400 minutes, V = 24,076 L) produced an error for effluent PM mass of 4.7% while for a 21 August 2005 event (Q p = 17.3 L/s, td = 106 minutes, V = 50,002 L) produced an error of 6.6 % (Pathapati and Sansalone, 2009c). The small watershed hydrologic loading parameters, CFD model parameters for the in situ screened HS and error results are similar to those of this study. Results in Figure 2 4E F are compared to steady flow CFD model pre dictions of effluent PM mass using the median and peak flow rates. The median and peak steady flow rates underestimate (up to 13.5%) and overestimate (up to 6%), respectively the physical model event based effluent PM. Results indicate that steady flow s tatistics typically cannot represent unsteady PM mass separation behavior, especially for highly unsteady hydrographs. These results are supported by previous studies indicating a singular steady flow statistic (Pathapati and Sansalone, 2009c) or steady fl ow rate steps do not reproduce unsteady phenomena controlling PM mass separation in a baffled or screened HS or clarifier unless loadings approach a quasi steady condition. Event based separated PSD results for each hydrograph are compared to CFD model re sults using steady peak or median hydrograph flows as shown in Figure 2 6. While steady flow results diverge from physical model PSDs, only for the highly unsteady hydrograph, typical of small watersheds, do steady flow indices not accurately reproduce sep arated PSDs (p = 0.05). Conclusion This study develops a validated CFD model to predict PM separation and eluted PM of a hydrodynamic separator (HS), a treatment unit utilized worldwide for treatment of wet and dry weather flows, subject to a hetero disper se PSD gradation and unsteady hydrologic loadings. An accurate parameterization of mesh size (MS), time step (TS) and PSD discretization number PAGE 48 48 (DN) is performed. Results (PM and PSD) demonstrate that the full scale CFD model is able to accurately predict the response of a full scale physical model across the range of quasi steady to highly unsteady flow loadings. However, time dependent profiles of PM indices are strongly influenced by model parameterization. Results demonstrate that TS and MS have a sig nificant impact on time dependent eluted PM mass and SSC. The influence of TS and MS also varies for increasing unsteadiness. Hydrologic events with higher degree of unsteadiness require a finer spatial discretization (higher MS) of the computational domai n and finer time resolution (smaller TS). Results also demonstrated that increasing the model accuracy through higher MS, higher DN or smaller TS requires increasing computational effort. The matrix of results are applicable to different geometries due to the scaling procedure applied to TS and MS. Results also indicate that a DN of 8 to 16 for this coarser hetero disperse PSD will reproduce effluent PM load. This study serves as a benchmark for future CFD applications to facilitate modeling of unit operati ons and processes (UOPs) under highly unsteady hydrologic loading typical of small watersheds. Finally this investigation provides a quantitative assessment of modeling accuracy for different TS and MS subject to hydrograph unsteadiness with results that a re validated from a monitored physical model. This set of results represents a detailed and useful guideline for modelers in selecting or evaluating computational parameters as a function of loading unsteadiness in order to balance model accuracy, computin g time and computational resources. PAGE 49 49 T able 2 1. Physical model (baffled HS) hydraulic and PM loading and PM separated. Q p V, t p C i t d MB PM, and are peak flow, volume, time to peak, influent PM, hydrograph duration, mass balance, separated PM, gamma shape and scale factors, and unsteadiness, respectively Q p Q p V t p C i t d MB PM Mass Influent PSD Hydrograph (L/s) (%) (L) (min) [mg/L] (min) (%) (%) Description 18 100 22.75 15 200 74 93.9 64.03 0.58 271 1.15 Highly unsteady 9 50 23.37 15 200 87 97.9 63.51 0.58 271 0.24 Unsteady 4.5 25 22.85 15 300 125 98 71.82 0.58 271 0.09 Quasi steady PAGE 50 50 Figure 2 1 Schematic representation of the full scale physical model facility setup with baffled hydrodynamic separator (BHS) Baffled HS cm pipe cm pipe Flow meter Flow meter Municipal water line 45,425 L Storage tank 45,425 L Storage tank Pump skid Drop Box: Influent PM Injection Effluent Sampling Inflow Outflow Flow Control Valve Flow Valve PAGE 51 51 Figure 2 2 Influent hydraulic loadings and PSD. A) illustrates t hree hydrographs loading physical model (baffled HS shown in inset) and B) i nfluent and effluent measured and modeled particle size distributions (PSDs) fo r each loading A B Outflow 1.83 m 1.73 m Inflow Baffled HS PAGE 52 52 Figure 2 3 The effect of time step (TS) on modeled intra event effluent PM as a function of hydrograph unsteadiness ( ). The model error (e n ) is calculated with respect to physical model data. A, B and C report respectively the effluent PM variation throughout the highly unsteady ( =1.15), unsteady ( =0.24) and quasi steady ( =0.09) A B C PAGE 53 53 Figure 2 4. CFD model error (e n ), computational time simulating eluted PM as function of TS and MS for hydrograph unsteadiness and measured and modeled event based overall removal efficiency, as well as the modeled overa ll efficiency at Q peak and Q median A B C D E F PAGE 54 54 Figure 2 5 The e ffect of mesh size (MS) on CFD modeled intra event effluent PM as a function of hydrograph unsteadiness ( ). The model error (e n ) is calculated with r espect to physical model data. A), B) and C) report respectively the effluent PM variation throughout the highly unsteady ( =1.15), unsteady ( =0.24) and quasi steady ( =0.09) A B C PAGE 55 55 Figure 2 6 Separated event based PSDs from CFD model as compared to physical model data. Separated event based PSDs for Q p and Q median are also reported. e n represents the normalized root mean squared error between captured event based measured and modeled PSDs A B C PAGE 56 56 CHAPTER 3 STORMWATER CLARIFIER HYDRAULIC RESPONSE AS A FUNCTION OF FLOW, UNSTEADINESS AND BAFFLING Summary A primary function of clarifiers (basins) loaded by stormwater is separation of particulate matter (PM). Clarifier geometry and response are often indexed by surface area (SA) or length to width (L/W) ratio. In the built environs, clarifier geometry is con strained by infrastructure and alternative opportunity land uses that impact SA and L/W. As a result, retrofitting clarifiers with internal bafflers is often considered in order to improve hydraulic and PM response. While most studies and practices evalu ate hydraulic response based on steady flow, stormwater unit operations (UO), including clarifiers, are also subject to highly unsteady flows. This study quantifies the impact of baffle configuration, (direction and flow tortuosity (Le/L) as an analog to L /W), flow rate and hydrograph unsteadiness ( ) on hydraulic response using the Morrill index (MI), volumetric efficiency (VE) and N tanks in series (N) metrics. Data are generated with both physical models and unsteady computational fluid dynamics (CFD) m odels of clarifiers with rectangular (with and without baffles) and trapezoidal cross sections. For un baffled configurations, VE and N increase while MI decreases with flow rate. For baffled configurations, there is an asymptotic relationship between N a nd the Peclet number (Pe). MI and N are functions of and Le/L as may be seen in the hydrograph results. A higher baffle number (higher Le/L) generates greater PM separation. Introduction Urban stormwater PM is a cause of impairment and deterioration for surface waters (Heaney and Huber, 1984) PM is also a mobile substrate for partitioning of chemicals such as metals and nutrients (Sansalone, 2002; USEPA, 2000) Separation of PM from stormwater is commonly facilitated with clarifier systems such as reten tion basins based on gravitational PAGE 57 57 settling. In many urban settings, clarifier dimensions such as SA, L/W and volume are limited. As a result, internal retrofitting with bafflers is often considered to improve hydraulic behavior and, commensurately, PM s eparation. While clarifiers are frequently idealized as approximating plug flow with increasing L/W, the actual hydraulic behavior deviates from plug flow, not only because of external constraints on L/W but also as a result of dispersion, channeling, rec ycling of fluid or creation of stagnant zones (Levenspiel, 1999 ) Hydraulic behavior can be quantified with MI, residence time distribution (RTDs), VE and N tanks in series indices. MI is a mixing index, accounting for the random spread of fluid due to sta gnation zones, turbulent diffusion and recirculation (Morrill, 1932) RTD is the time a fluid element resides in a clarifier, expressed as a probability distribution function (Morrill, 1932) VE is the inverse of MI. N tanks in series can be determined fr om an RTD (Hazen, 1904) The N tanks model idealizes a clarifier as a series of completely mixed tanks with higher N values indicating an increasing similarity to ideal plug flow behavior (Metcalf and Eddy, 2003) While physical modeling may facilitate the determination of these indices, they are often prohibitively expensive. CFD modeling provides an approach to more economically simulate the hydraulic (continuous phase) and the coupled PM behavior (discrete phase) (Pathapati and Sansalone, 2011; Dickenso n and Sansalone, 2009) CFD also provides a tool to examine these hydraulic indices for UOs subject to design and load variations. Studies have examined the hydraulic efficiency of baffled systems, typic ally at constant flow (Wilson and Venayagamoorthy, 2 010; Kim and Bae 2007; Amini et al., 2011; Kawamura, 2000) For example, Wilson and Venayagamoorthy (20 10 ) analyzed a baffled tank with up to 11 transverse baffles; concluding that that maximum hydraulic efficiency was reached at six baffles. Kim and Bae (2007) studied the hydraulic efficiency of a pilot scale baffled contactor as a PAGE 58 58 function of the number of transverse baffles and demonstrated that the rate of plug flow increased as the number of baffles (up to 25) increased. Amini et al. (2011) used a val idated scaled down physical model of a chlorine contact tank (CCT) to conclude, using the MI, that the recommended number of channels within the tank was 6 to 9. Kawamura (2000) recommended that, for the design of CCTs, a tank should be divided into 2 to 4 longitudinal baffles, with a L/W ranging from 5:1 to 15:1. Not all studies agree on the relationship between flow rate and N. For example, Lopez et al. (2008) analyzed a lab scale clarifier as a function of flow rate steps and type of feed under three f low regimes and concluded that as flow rate increases, N decreases. Conversely, Metcalf & Eddy (2003) and Abu Reesh (2003) argued that N should be proportional to Pe, and since for increasing flow rate there is increasing advection, Pe also increases. The refore they concluded that N also increases. In contrast to wastewater and drinking water systems that are loaded by steady to quasi steady flows, stormwater UOs are subjected to a very wide range of flows or highly unsteady episodic flows. For stormwater clarifiers, a determination of N or MI as a function of flow rate, or Le/L (as an equivalent L/W for baffling) has not been examined. The objective of this study is to elucidate the role of baffle configurations, flow rate and hydrograph unsteadiness o n the hydraulic behavior of a clarifier subject to stormwater flows. Hydraulic behavior is indexed using RTD, MI, VE, Pe and N. The baffle configuration parameters are direction (transverse or longitudinal) and the number of baffles. The number of baffl es is indexed by flow tortuosity (Le/L) as a surrogate for flow path length to width ratio. Results are generated using a CFD model validated with a full scale physical model. PAGE 59 59 Material and Methods The physical modeling and tracer study was conducted on a full scale primary rectangular clarification basin typically used for PM separation from runoff collected in a small urban catchment. Depending on land use and infrastructure constraints, this precast concrete clarifier would be constructed at grade or b elow grade. In Figure 3 1, the conceptual process flow diagram for the methodology and the scaling between the actual physical model and the catchment characteristics is shown. Physical loadings and scaling are representative of predominately impervious, developed urban parcels facilitating motor vehicle movement or parking. The particle size distribution (PSD) and PM loadings represent the fine PM fraction (< 75 m) of urban runoff PM while the rainfall depth and duration generates a hydrograph with a pe ak flow and volume that is representative of a one hour event with a two year recurrence time event for the North Florida catchment. The clarifier design flow, Q d was ~50 L/s as an open channel system. With programmable variable frequency drives for the pumping system, hydrographs with differing peak flows (up to 50 L/s) and levels were generated with schedules as shown in Figure 3 1. As a control, a constant con centration of 200 mg/L was also studied. Monitoring of PM and PSDs was conducted. Tracer tests were conducted to determine RTDs for steady flows (2, 5, 10, 25, 50, 75 and 100% of Q d ). Full scale physical models of an un baffled rectangular, an 11 baffle rectangular clarifier of the same surface area, and an un baffled trapezoidal clarifier were fabricated. In addition to steady flows, validation of the CFD model was conducted with an unsteady event. A description of the physical modeling is provided in t he Appendix. Figure 3 2 summarizes the validation results of the 8 July 2008 storm for PM and PSDs. Supporting figures ( B 5) are provided in the Appendix PAGE 60 60 RTD C urves and A ssessment of H ydraulic I ndices RTD functions, E(t) and cumulative function, F(t) we re derived from tracer tests and calculated (Morrill, 1932) The definitions are as follows: MI is defined as (Morrill, 1932; Metcalf and Eddy, 2003) : In this expression t 10 and t 90 indicate the period of time necessary for 10 and 90% of the mass of tracer that was injected at the inlet to reach the clarifier outlet. For ideal plug flow, MI = 1 and increases for a completely mixed clarifier. Metcalf & Eddy (2003) indicate 22 as an ap proximate upper bound. The inverse of MI is the hydraulic VE (Morrill, 1932; Metcalf and Eddy, 2003) The N tanks in series model introduced by Hazen (Hazen, 1904) concept ualizes a non ideal clarifier as consisting of a cascade of N equal sized completely mixed tanks arranged in completely mixed tank to that of a plug flow clari fier. N is defined for horizontal flow settling basins (Letterman, 1999; Fair et al., 1966) ( 3 1 ) ( 3 2 ) ( 3 3 ) ( 3 4 ) ( 3 5 ) PAGE 61 61 In this expression t 50 is the time at which 50% of tracer has exited the clarifier and t p is the time at which the peak tracer concentration is observed. In literature there are other definitions of N which are related to equation 3 5 as shown in the Appendix CFD M odeling The 3D geometry and mesh of the full scale physical mo dels were generated in a GAMBIT (Fluent, 2010) e nvironment as shown in Figure B 6, B 7, B 8, with details of the mesh generation shown Figure B 9 and described in the Appendix The CFD models were built for a trapezoidal cross section clarifier, a rectangular clarifier with a varying number of transverse baffles, and separately with longitudinal baffles. The number of transverse baffles varied from 3 to 36 and from 2 to 9 for the longitudinal baffles. The CFD models were built using the finite volum e based code Fluent (Fluent, 2010) The CFD developed in this study treated the fluid phase as a continuum in an Eulerian frame of reference while coupled discrete phase model (DPM) used a Lagrangian frame of reference for describing behavior of the PM in the system. The turbulence model of this study is based on a variant of the Navier Stokes (N S) equations, the Reynolds Averaged Navier Stokes (RANS) equations (Pope, 2000) : The turbulence model used was the realizable k model (Shih et al., 1995) This model is suitable for boundary free shear flow (baffled clarifier) applications and consists of turbulent kinetic energy and energy dissipation rate equations recorded below (Shih et al., 1995) ( 3 6 ) ( 3 7 ) ( 3 8 ) PAGE 62 62 In t k = 1.2, C 1 = 1.44, C 2 T fluid viscosity; and u ji u j i were previously defined. The numerical solver used was pressure based, meaning that it was and suited for incompressible flows where motion is mainly governed by pressure gradients. The SIMPLE (Semi Implicit Method for Pressure Linked Equations) pressure velocity coupling scheme was used. Convergence criteria were set so that scaled residuals for all governing equations were below 0.001 (Ranade, 2002) Regarding boundary conditions, the inlet velocity was specified and the free surface was approximated as a shear free wall with ve locity components normal to the surface. From the balance of tangential stresses at the interface assuming air dynamic viscosity is much less than water viscosity, shear stresses becomes negligible at the free surface. boundary. To model the RTDs, one hundred neutrally buoyant particles (1 m) were uniformly released across the inlet as an instantaneous pulse at (t = 0) and tracked through the flow using stochast ic particle tracking. Since the dispersed phase was sufficiently dilute (volume fraction (VF) was less than 10%) the DPM was used to predict PM transport and fate within the system (2005) The DPM integrated the equations of motion of the discrete phase and tracked individual particles through the flow field by balancing the forces acting on the particles. Particle trajectory was calculated by integrating the force balance equation, written below in the ith direction. ( 3 9 ) ( 3 10 ) PAGE 63 63 The first term on the right hand side of eq. 3 11 is the drag force per unit particle mass, in which FD i is defined in eq. 3 12. The second term is buoyancy/gravitational force per unit particle mass. Re i is Reynolds number for a spherical particle, and CD i is drag coefficient. From Eq 3 11 to Eq. 3 14, is the fluid density, p is particle density, v i is fluid velocity, v pi is particle velocity, d p is particle diameter, is the dynamic viscosity, and K 1 ,K 2 ,K 3 are empirical constants as function of Re i The dispersion of particles due to turbulence in the fluid phase is predicted using a stochastic tracking model, integrating the trajectory equation for individual particl es (Eq. 3 11), using the instantaneous fluid velocity, along the particle path during the integration (Thomson, 1987; Hutchinson et al., 1971) The random effects of turbulence on the particle dispersion were considered by computing the trajectory for a sufficient number of representative particles. A user defined function (UDF) was written to record the time at which each particle passed through the outlet surface. The CFD model was loaded with a constant flow rate at the inlet and, after solving the flow field, the DPM equations were integrated numerically. For transient RTD, the CFD model was loaded with the hydrographs of different (Equation 3 15) ( 3 11 ) (3 12 ) ( 3 13 ) ( 3 14 ) PAGE 64 64 and Q p as shown in Figure 3 1. The UDF recorded the residence times of the particl es passing the outlet section during each time step. The dimensionless unit hydrograph was modeled as a step function (Sansalone and Teng, 2005) The physical model hydrographs are scaled by the HS design hydraulic capacity (50 L/s), maintaining constant v olume (V= 125,200 L) and a constant time to peak flow, t p of 30 min. The time to peak flow is established from the SWMM (Storm Water Management Model) (Huber and Dickinson, 1988) in which the size of a catchment is matched to deliver peak runoff flow rate equal to the design flow rate of the unit operation. A parameter, is determined to quantify the unsteadiness of each hydrograph (Garofalo and Sansalone, 2011) : In this equation, Q median represents the median flow rate The values of for highly unsteady, unsteady and quasi steady were 1.54, 0.33 and 0.01, respectively. The physical model of the rectangular and trapezoidal cross section clarifiers without baffle s and the rectangular clarifier with transverse baffles were used to validate effluent PM and PSD response generated by the CFD method detailed by Garofalo and Sansalone (Garofalo and Sansalone, 2011) The physical models were loaded by two hydrographs, a triangular hyetograph generating 0.5 inches of runoff and a simulation of a historical event of 8 July 2008 in Gainesville, Florida from the small catchment. The two hydrographs are described in the Appendix and their characteristics are summarized in Tab le B 2. The validation analysis consisted of comparison between measured and CFD modeled RTD curves. A root mean squared error, RMSE was used to evaluate CFD model error in predicting RTDs with respect to the physical model data. The errors reported in T able B 1 show RMSEs between measured and ( 3 15 ) PAGE 65 65 modeled RTDs within 10%. The validated RTD curves from which the hydraulic indexes are generated are reported in Figure B 10. The error between the measured and modeled event based PSDs was also calculated as a RM SE. The validation of CFD modeled data in terms of measured PM mass removal was based on a relative percentage error, The modeling error was within 10%. The validation analysis is described in detail in the Appendix Results and Discussion Validation results from the physical and CFD model are shown in Figure 3 2 and B 10 for effluent PM and PSDs. Results from both the CFD and the physical model are compared for the full scale rectangular cross section clarifier with and without 11 baffles for the Ju ly 8, 2008 hydrograph (Figure 3 2). Figure 3 2 also illustrates the impact of baffling on PM eluted as a function of time or as an event based PM mass. As in Figure 3 2, Figure B 11 summarizes PM elution results for a validation hydrograph generated from a triangular hyetograph. The CFD model reproduces PM elution from the physical clarifier with and without baffles. PM separation is related to the hydraulic behavior of the clarifier and increases with a higher number of baffles. Figure 3 2 shows the mea sured effluent PM eluted from the system for the July 8th hydrograph for the rectangular clarifier with 0 baffles and 11 baffles. PM removal efficiency for the un baffled clarifier is 56% and with 11 baffles it is 71%, as shown in Table B 2. The percent di fference between the two configurations of 26%, thus demonstrating the beneficial effect of internal baffling on PM separation. Steady F low H ydraulic I ndices as F unction of F low T ortuosity (equivalent L/W) The results in Figure 3 3 compare the hydraulic indices for the un baffled rectangular and trapezoidal clarifiers. Figure 3 3A indicates that VE linearly increases as Q n increases and varies from 5 10% and 12 22% for the rectangular and trapezoidal clarifiers. The results als o indicate that the trapezoidal cross section is hydraulically more efficient than the rectangular cross PAGE 66 66 section. In the rectangular clarifier, the areas proximate to the two lateral walls mostly represent stagnant zones. The trapezoidal cross section conf iguration with lateral inclined walls minimizes the side stagnant areas and, therefore, offers a higher volume utilization than the rectangular configuration. In contrast to the VE results, Figure 3 3B shows that MI decreases with Q n for both clarifier con figurations, but that the rate is significantly greater for the rectangular clarifier. At the design flow rate, Q d there is approximate convergence of the MI values for each configuration. In a pattern similar to VE results, Figure 3 3C shows the value o f N for the N tanks in series model increases linearly with Q n for the rectangular and trapezoidal no baffle configurations. The rectangular clarifier behaved as a mixed reactor with N varying from 1 to 1.7 while N for the trapezoidal clarifier ranged betw een 1.5 and 3. The trapezoidal clarifier deviated from the completely mixed reactor behavior (N = 1), a result also supported by higher VE results of the trapezoidal clarifier. The impact of baffle configuration (e.g. number of baffles and orientation) wa s investigated with the CFD model. While the physical models were constructed with either 0 or 11 baffles for the rectangular clarifier, the simulations were capable of modeling the rectangular clarifier with various numbers and configurations of baffles, thus producing data for clarifier flow path tortuosity, Le/L (Table B 3). In Figure 3 4, simulated VE results are reported as a function of the number of baffles as indexed by tortuosity (as well as equivalent L/W) and fit by two parameter sigmoid curves with parameters summarized in Table B 4. VE results vary up to approximately 50% across the range of steady flows tested and the tortuosity varied up to approximately 70%. For all simulated baffling configurations, the maximum VE achieved was 80%; a sign ificant increase with respect to the un baffled configurations. Figure 3 3, 3 4 illustrates that the increase in VE is a function of increasing tortuosity and increasing Q n The PAGE 67 67 rate of increase in VE, as a function of tortuosity, is greater at high Q n as compared to low Q n for low values of tortuosity. For both baffle directions, at the highest values of tortuosity the VE approaches a common asymptotic value beyond which VE does not significantly change. While wastewater and drinking water unit operation s and processes are subjected to fairly steady flows, stormwater units are subjected to highly variable and transient flows that can vary by orders of magnitude in an event. Therefore, to achieve a target VE in a baffled clarifier subjected to rainfall run off events, the representative Q n range requires determination (for instance, probabilistically) in order to identify a tortuosity range. The velocity magnitude contours generated from the simulation results at the design flow rate of 50 L/s are shown for the rectangular clarifier with 0, 3, 24 baffles in Figures B 12, B 13, B 14. In the clarifier without baffles, the results show a direct flow path (short circuiting) from the inlet to the outlet. With an increasing number of baffles the dead zone areas ( low velocity areas) decreased with respect to the non baffled rectangular configuration, as shown qualitatively in these simulation results. As the number of baffles increased (increasing flow tortuosity) the VE also increased. MI values from the validat ed steady CFD model are reported in Figure B 15. MI curves, modeled as two parameter exponential functions (Table B 5), decrease with increasing flow rates. MI curves reach an asymptote beyond 6 baffles (transverse baffling) at Qd, in agreement with the re sults from Amini et al. (2011) However at lower Qn, the MI approaches an asymptote at 11 to 24 baffles, indicating that the number of baffles beyond which MI is constant varies as a function of Qn. In Figure B 15B the MI curve at Qd approaches a constant v alue beyond 2 4 longitudinal baffles with a L/W of 38, in accordance with the rule of thumb given by Kawamura (Kawamura, 2000) ; however at Qn values lower than Qd, MI reaches an asymptote beyond 5 6 baffles with 100 L/W. PAGE 68 68 Since the work of Hazen (Hazen, 193 2) there has been ongoing interest in conceptualizing the behavior of a clarifier as series of N well mixed tanks such that increasing values of N approach plug flow behavior. In Figure 3 5, the simulation results for N tanks in series are shown as funct ion of flow rate and flow path tortuosity. As the tortuosity increases N also increases. The increase in N is a function of increasing flow rate, with an increase in N that is much greater at higher flow rates for the same tortuosity. For an increasing n umber of baffles in either direction the clarifier approaches plug flow conditions at higher flow rates. The baffling has a higher impact on N at high Q n enhancing plug flow condition (N up to 500). N turns out to be proportional to Q n The Peclet (Pe) n umber is the ratio of the convective to dispersive transport. Convection is quantified as the product of the fluid velocity, u, and the characteristic length, which in this case it is selected as the clarifier flow path, Le. As Qn increases convection incr easingly dominates dispersion and Pe increases. N also increases in proportion to Pe. The fitting curve parameters are reported in Table B 6. Figures 3 6A and 3 6B summarizes the relationship between the Pe number and N for varying flow rates. Results ar e fit with a hyperbolic function. Unsteady F low H ydraulic I nd ic es as F unction of F low T ortuosity ( E quivalent L/W) In addition to results generated at a series of steady flow rates up to Qd of the clarifier, and separately from the unsteady validation loadings for the physical models, unsteady loading were simulated for the hydrographs shown in Figure 3 1. The unstead iness ( ) of these hydrographs ranged from a of 1.54 for the highly unsteady hydrograph to a of 0.01 for the quasi steady hydrograph. The MI and N tanks in series results for each of these hydrographs are reported in Figure 3 6C and 3 6D. At low value s of tortuosity, the MI is higher (indicating lower efficiency) and varies significantly across the degree of unsteadiness. As the tortuosity increases, the MI PAGE 69 69 decreases (approaching plug flow) and unsteadiness does not significantly impact the MI values. For the given range of unsteadiness and tortuosity, the N values range from 1 to 80. N values are influenced by increasing unsteadiness, but in contrast to MI results, this influence occurs for increasing tortuosity values. The data are fit and the param eters are reported in Tables B 13, B 14. Hydrograph based RTDs are modeled for each hydrograph shown in Figure 3 1 in order to examine the behavior of the rectangular clarifier with transverse baffles as a function of unsteadiness. In Figure 3 7, the cum ulative RTDs are reported as function of tortuosity and unsteadiness. At low tortuosity, (1 and 1.9 corresponding to 0 and 3 baffles) the clarifier behavior approximates more of a plug flow behavior for the highly unsteady hydrograph. At lower levels of u nsteadiness the clarifier behavior increasingly approximates a mixed reactor RTD. The RTD gradients increase as the degree of unsteadiness increases, indicating that convective transport dominates dispersive transport for higher unsteadiness levels and low er tortuosity. These results are similar to the Pe number results in Figure 3 6A and 3 6B. At higher tortuosity (3.6 and 6.4, corresponding to 11 and 24 baffles) the clarifier increasingly approximates plug flow behavior for all levels of unsteadiness. At higher tortuosity the RTD curves are characterized by a similar constant slope and are offset in parallel along the time axis. Therefore, regardless the level of unsteadiness, the hydraulic behavior remains invariant with a higher number of baffles and to rtuosity. In contrast to wastewater and drinking water unit operations and processes, evaluation of the hydraulic response of clarifiers (basins) retrofitted with internal baffles and loaded by unsteady rainfall runoff has not been conducted. Resul ts indicate that the hydraulic response (as N, MI or RTD) of a baffled or un baffled basin is function of flow rate, unsteadiness and PAGE 70 70 tortuosity (as an equivalent L/W ratio). Given that stormwater systems are loaded by a wide range of flows and unsteadine ss, a singular hydraulic response, whether as N, MI, VE or RTD, cannot be expected, although high tortuosity (high number of baffles) does confer a more consistent, albeit dependable, response as a function of unsteadiness. Based on physical and CFD model results, this study indicates that internal baffling does alter unsteady hydraulic response and increase PM separation. For stormwater systems subject to a wide range of uncontrolled loadings, hydrograph unsteadiness is an important parameter. While the full scale physical modeling system of this study was able to meter a constant PM concentration and PSD, the quest for a unique relationship between a particular hydraulic response (for example N) and PM or PSD elution from a rainfall runoff clarifier is further complicated by the separate unsteadiness of PM and PSD inflows. For future study, it is hypothesized that such a relationship is not unique. Such a relationship would be tested as a function of hydrograph unsteadiness, PM and PSD loadings and uns teadiness (the temporal or volumetric transport of each) and the PM accumulation and PSD thereof in the system (maintenance interval). Such relationships could most effectively be examined with a CFD model validated by physical model data. PAGE 71 71 Figure 3 1. This figure illustrates the conceptual process flow diagram for the methodology. Clarifier configurations are either: a. rectangular or trapezoidal cross section with no baffles, b. clarifier of rectangular cross section with transverse baffles that rang e from n = 3 to 35 baffles, c. clarifier of rectangular cross section with longitudinal baffles that range from n = 2 to 8 baffles, P t : rainfall depth, T d : rainfall duration, L c : watershed length, V t : hydrograph volume, Q p : peak flow rate (L/s), Q d : desig n flow rate of 50 L/s, VE: volumetric efficiency, RTD: residence time distribution, N: tanks in series value, MI is Morrill dispersion index, V: clarifier volume, L: clarifier length, Le: clarifier flow path tortuosity and PSD is particle size distribution The watershed area is 0.25 ha, slope of 1%, P t of 50 mm and T d = 60 min. Length of catchment of 200 m. and represent the gamma function parameters L = 7.3 m n Clarifier configuration RTD, N, VE, Output V t = 125,200 L a b c L e Watershed Influent PSD Effluent PSD Inlet Out let 1.8 m V = 24,000 L a PAGE 72 72 Figure 3 2. Physical model and CFD model results for PM and PSDs for the July 8, 2008 hydrograph used for the validation analysis for full scale physical model of the rectangular clarifier with no baffles and 11 transverse baffles. In A) and C) the dash line represents the incremental effluent PM, the solid line the cumulative effl uent PM and the dot points the measured data with the range bars fr om duplicate samples. In B), D) the shaded area indicates the range of variation of effluent PSDs throughout the hydrological events. The dot points are the influent measured PSD (white) an d the minimum and maximum measured PSDs (black). RMSE is the root mean squared error between effluent average measured and modeled PSDs. Q p is the peak influent flow rate and t d is the total duration of the hydrological event, s is the particle density A C B D Rectangular clarifier Rectangular clarifier Rectangular clarifier Rectangular clarifier PAGE 73 73 Figure 3 3. Comparison between rectangular and trapezoidal cross sec tion clarifier configurations. A) illustrates volumetric efficiency, VE as function of Q n normalized flow rate with respect to the hydraulic design flow rate, Q d B) illustrates Morrill index, MI as function of Q n C) illustrates N as function o f Q n The parameter of the fitting curves, a represents respectively in A) and C) the minimum value of VE and N. The parameter of the f itting curves, b represents in B) the maximum value of MI. The parameter c represents the slope of the fitting curves Rectangular clarifier (L/W=4) A B C PAGE 74 74 Figure 3 4. Volumetric efficiency as function of clarifier flow path tortuosity, Le/L for the clarifier configurations with transverse and longitudinal internal baffling. O is the opening between the baffle edges and the clarifier walls. Q n is the normalized flow rate with respect to the hydraulic design flow rate, Q d of 50 L/s for the clarifier .00 6.6 4 262 35 118 Equivalent length to width, L/W Transverse baffles (O = 0.20 m) Longitudinal baffles A B 4 38 103 328 Equivalent length to width, L/W PAGE 75 75 Figure 3 5. N as function of clarifier flow path tortuosity, Le/L for the clarifier co nfigurations with transverse and longitudinal internal baffling. O is the opening between the baffle edges and the clarifier walls. Q n is the normalized flow rate with respect to the hydraulic design flow rate, Q d of 50 L/s 4 262 35 118 Equivalent length to width, L/W .00 Transverse baffles (O = 0.20 m) Longitudinal baffles A B 4 38 103 328 Equivalent length to width, L/W PAGE 76 76 Figure 3 6. Pe as function of N tanks in series for the configurations with respectively tra nsverse baffles and opening of 0. 20 m and longitudinal baffles The Peclet number illustrated in A) and B) is calculated as ratio of convective forces to dispersion coefficient, D. The convective forces are given by the product between the fluid velocity, u and the characteristic length, Le. The data are fitted by a hyperbole function with parameter a, representing the maximum value of Pe and b, the rate of Pe change as function of N tank s in serie s. Morrill index, MI C) and N D) as function of clarifier flow path tortuosity, Le/L for highly unsteady, unsteady and quasi steady hydrographs A Transverse baffles a = 102 b = 18 R 2 =0.97 Longitudinal baffles B a = 121 b = 56 R 2 =0.91 C D 4 35 118 Equivalent length to width, L/W 6.6 PAGE 77 77 Figure 3 7. Modeled cumulative RTD function, F as function of time for h ighly unsteady, unsteady and quasi steady hydrographs respectively for rectangular clarifier with no baffle (Le/L = 1), 3 (Le/L=1.9), 11 (Le/L = 3.6) and 24 baffles (Le/L = 6.4) PAGE 78 78 C HAPTER 4 CAN A STEPWISE STEADY FLOW CFD MODEL PREDICT PM SEPARATIO N FROM STORMWATER UNIT OPERATIONS AS A FUNCTION OF HYDROGRAPH UNSTEADINESS AND PM GRANULOMETRY? Summary Computational fluid dynamics (CFD) is an emerging model used to predict PM separation from runoff unit operations (UOs) loaded by hetero disperse parti culate matter (PM) and unsteady hydraulics. However unsteady CFD modeling requires significantly more computational overhead compared to steady modeling. As a result this study examines a stepwise steady CFD model methodology designed to reproduce UO respo nse to unsteady loadings with lower computational overhead. The method assumes that the UO response for differing flow rates and particle size distributions (PSDs) can be based on particle residence time distribution (U p ) in a UO. Conceptualizing the linearity and superposition of a UO response subject to a hydrograph, each U p is convoluted across a hydrograph that was discretized into a series of steady flow rates. The model is applied to a rectangular clarifier (RC) su bjected to three hydrographs with differing levels of unsteadiness ( ) and PSDs. The role of representative PSD sampling for the model is also shown for a baffled hydrodynamic separator (BHS). The stepwise steady model loaded with accurately monitored PSD s reproduced PM mass when compared to RC physical model data while the BHS was used to elucidate the need for accurate PSDs. Computational times for the RC were reduced by an order of magnitude compared to fully unsteady CFD models. When applied to the me asured PSD data from the BHS generated through automatic sampling, the physical model PM mass balance ranged from 40 to 60% as a function of hydrograph Results from automatic sampling of the BHS translated into CFD modeling errors from 15% to 70%. PAGE 79 79 Intr oduction Urban runoff PM is a mobile, reactive hetero disperse substrate for which chemical species such as metals, organics and nutrients partition during mobilization, transport and treatment. PM is recognized as a significant contributor for the impair ment of receiving waters (USEPA, 2000). One common category of unit operation (UO) to separate PM in runoff is hydrodynamic separators (HS) as preliminary UOs with mean residence times on the order of minutes. A second category of UO is primary clarifier type basins (retention/detention/equalizing basins or tanks with mean residence times that can range from approximately an hour to days). From an urban water treatment perspective, clarifiers (basins) are more traditional, non proprietary, more commonly implemented given their potential to provide coupled hydrologic (volumetric/hydraulic) and PM control. During the last decade regulatory programs have developed to require physical modeling of UOs subject to steady flows and PM loadings for initial certif ication of performance (TARP, 2003). Final certification of a UO in these programs can require augmentation of the testing program with fully unsteady performance testing of UOs subject to unsteady hydrologic loadings (TARP, 2003). While these programs m ay require a series of analyses beyond PM (either as total suspended solids (TSS), suspended sediment concentration (SSC) and/or PSDs), the performance focus is separation of PM. While physical modeling is increasingly required for UO, numerical models of UOs utilizing computational fluid dynamics (CFD) have not developed to the same extent for regulatory programs (Chen, 2003) despite recent research and engineering utilization of numerical models (Al Sammarrace et al., 2009; Tamburini et al., 2011). CFD is an emerging model based on the Navier Stokes (N S) equations utilizing a finite volume method that can simulate the coupled hydrodynamics and particulate matter (PM) phenomena i n UOs (Dickenson and Sansalone, 2009; He et al., 2006; Pathapati and Sansalone, 2009a b). CFD models have been PAGE 80 80 validated with steady flow UO physical models to examine requirements for numerical simulations. For example, Dickenson and Sansalone (2009) inv estigated the PSD discretization requirements of a steady flow CFD model of a baffled HS (BHS) to predict PM fate and minimize CFD model error for size granulometry that ranged from mono to hetero disperse. He et al. (2006) examined the performance of a c ombined sewer overflow (CSO) storage to improve the maximum treatment flow rate by using a validated steady CFD model. Pathapati and Sansalone (2009a b) utilized a validated full scale CFD model to predict PM separation as function of particle size and flo w rate for a radial filter and a screened HS (SHS) under steady conditions. Beyond steady flow modeling and initial certification of UOs, actual rainfall runoff events are unsteady flow phenomena and field deployed physical model testing subject to actua l rainfall runoff events and PM delivery is required for final regulatory certification. Unsteady or transient loading CFD models are more complex than steady flow models because of coupling variable hydrology with PM transport and require increasing comp utational overhead for a given level of model accuracy. Recent studies employing unsteady CFD models have reproduced PM separation by UOs subject to unsteady loadings (Pathapati and Sansalone, 2009c; Garofalo and Sansalone, 2011). Pathapati and Sansalone (2009c) demonstrated CFD unsteady modeling reproduces the PM mass response of a SHS subject to unsteady runoff with model errors of 10% with respect to physical model data. However, in the same study the use of event based steady flow indices to predict P M separation generated significantly higher errors; in some cases over 100% albeit at a much lower level of computational overhead compared to the accurate fully unsteady model. Garofalo and Sansalone (2011) conducted a parameterization study on a CFD mode l of BHS to balance model accuracy, computational overhead based on mesh size (MS), PAGE 81 81 time step (TS) and PSD discretization number (DN). The computational time for solving an unsteady CFD model varied from 10 to 100 hours as a function of TS, MS, DN and the influent hydrograph`s degree of unsteadiness ( commonly ranges from 0.09 to 1.15) (Garofalo and Sansalone, 2011). In an attempt to balance CFD model error and computational overhead, Pathapati and Sansalone (2011) introduced a simple first generation step wise steady flow methodology for a CFD model to reproduce unsteady PM separation for UOs loaded by rainfall runoff. This CFD methodology was based on modeled at PM separation results generated at a series of discrete steady flow levels across the unsteady hydrographs. The CFD results at each discretized flow level were flow weighted across the hydrograph (Pathapati and Sansalone, 2011). The method implicitly assumed an instantaneous PM response to each discretized flow level loading a UO system which leade d to an inaccurate prediction of time dependent effluent PM distributions, especially for UOs with longer residence times. Subject to this methodology and assumptions the study concluded that a stepwise steady model accurately reproduced PM separation by filters but not HS and clarifier units. Granulometric data (for example, PSD or specific gravity) required for physical or CFD modeling of a UO have been collected through manual or automatic sampling with subsequent granulometric analysis. Wastewater tr eatment plants (WWTPs) are characterized by fairly constant flow rates ( ranges from 0.08 to 0.095), largely organic with a range of specific gravity from 1.03 to 1.05 g/cm3, relatively mono disperse, finer PSDs (Dick, 1974; Fisher, 1975; Hettler et al., 2011) and automatic sampling has been commonly used and accepted in conjunction with wastewater treatment analysis (Koopman et al., 1989) including measurement of suspended PM (as TSS, Standard Methods, 2540D (APHA, 1998)). While automatic sampling of urb an runoff UOs has been adopted from WWTP sampling there is increasing acceptance that the PAGE 82 82 convenience of automatic sampling may be outweighed by the potential mis representation of urban runoff separation and washout by UOs due to the pluviometric and gran ulometric differences (Gettel et al., 2011). In contrast to wastewater, urban runoff flows are highly unsteady ( ranges from 0.09 to 1.2), with PM granulometry that is size hetero disperse and largely inorganic with a particle density in the range of 2.1 to 2.6 with PM that is not uniformly distributed across the flow cross section (Kim and Sansalone, 2010). Despite these differences automatic sampling is commonly used for urban runoff UOs and gravimetric analysis of urban runoff PM includes the traditio nal wastewater TSS method and increasingly suspended sediment concentration (SSC) as developed by the United States Geological Survey (ASTM D3977 97 (ASTM, 2000)). A mass balance on PM for a field monitoring campaign of a UO has demonstrated the represent ativeness of manual sampling and SSC (Sansalone et al., 2009). PM misrepresentation with automatic sampling leads to inaccuracy in the PSD, SSC and therefore PM separation (Sansalone et al., 1998). Despite the ongoing debate over the representativeness of automatic or manual sampling for runoff UOs (Gettel and al., 2011), most monitoring of UOs is performed with automatic samplers and TSS. Building from these previous CFD model developments the current study proposes a second generation stepwise steady C FD model to accurately predict PM separation by an HS and clarifier unit. In contrast to the assumption of an instantaneous UO response this model conceptualizes a UO as a linear system with a response that varies according to the hydrodynamic characteris tics of the system (for example, residence time distribution, RTD). Conceptualizing a clarifier and HS as linear systems, the overall response of the UO subject to an unsteady event is obtained by convoluting the RTDs of particle size ranges (based on a D N) comprising a PSD across the series of steady flow rates for which the hydrograph is discretized. PAGE 83 83 The method hypothesizes that the CFD model can be used to produce the particle RTD for a series of steady flow rates across the PSD. The study hypothesizes that the model based on the particle RTD is able to properly predict flow and PM response times of UOs, in contrast to the previous stepwise steady model approach (Pathapati and Sansalone, 2011). In addition, since the PM eluted at a generic time t a is mo deled as a result of the influent mass PM delivered at times equal and less than t a the new approach models the transient behavior of UO as a continuously evolving system, in which the output at each instant is also influenced by the previous conditions i n the UO. As with the first generation stepwise steady CFD model (Pathapati and Sansalone, 2011) and steady flow CFD models (Dickenson and Sansalone, 2009) an accurate of physical model results requires representative PSD data. The objective of this stud y is to demonstrate that PM separation and time dependent PM elution by a clarifier and a BHS loaded with unsteady hydraulic and PM loadings can be reproduced with a stepwise steady flow model for three runoff hydrographs of differing levels of The accu racy of the stepwise steady CFD model will be validated with physical model data as a function of hydrograph and PM granulometry. Finally this study examines the PM mass balance produced through automatic sampling to illustrates the role of influent auto matic sampling for the prediction of effluent time dependent PM with the stepwise steady CFD model. Methodology Physical Model S etup This study utilizes a 1.83 m (nominal 6 feet) diameter BHS and a rectangular clarifier (RC) with a length/width ratio of 4 :1, designed to provide gravitational settling (Type I settling) and retention of separated PM mass for small developed, largely paved parcels of urban land. The PAGE 84 84 two UOs are illustrated in the inset of Figure 4 1. The schematic representation of the full scale physical model and the testing setup are shown in Figure s C 1 and C 2 of the Appendix In the BHS influent flow is conveyed by a 200 mm high inflow weir through the opening of the horizontal baffle to the clarification chamber (where PM separation oc curs) and directed to the effluent pipe through an outlet riser. The RC and BHS are sedimentation type UO. Physical model runs were performed on the full scale BHS and RC loaded by unsteady hydrographs at 20 levels we re used for the BHS and RC as shown in Figure 4 1B and 4 1C. The unsteady inflow is delivered by a pumping station equipped with programmable variable frequency drives and flows were measured by two magnetic flow meters illustrated in Figure s C 1 and C 2 The hydrograph formulations are based on the use of a step function to model a SCS Type II dimensionless unit hydrograph (Malcom, 1989). The physical model hydrographs were scaled based on the maximum hydraulic capacity of 18 L/s for the BHS and 50 L/s for the RC, maintaining constant volume for each (22,840 L and 125,000 L) and a constant time of peak flow, t p of 15 minutes for BHS and 30 minutes for the RC (Sansalone and Teng, 2005). In addition to differing levels the peak flow of 18 and 50 L/s were matched to the maximum hydraulic capacity of the physical models with the other hydrograph peak flows represent 50 and 25% of the hydraulic capacity. is defined for each hydrograph and summarized in Table 4 1 (Garofalo and Sansalone, 2011): where i=1*dt.....td*dt In this expression Q med dt, V, t d represent the median value of Q, the time step, the storm volum e and the storm duration, respectively. (4 1) PAGE 85 85 The values of for the BHS were from 0.09 to 1.15 and 0.015 to 1.54 for the RC. Physical model runs of the BHS were conducted at 200 mg/L of PM and a constant PSDs. In Figure 4 1A the two influent PSDs used are rep orted as compared to a measured source area PSD (Berretta and Sansalone, 2012). The finer PSD is hetero disperse ranging from 0.01 to 100 m with a d 50 of 15 m. The coarser PSD is also hetero disperse with a d 50 of 67 m and a size range from 0.01 to 1000 m. The measured source area PSD with d 50 of 107 m was collected from the outlet section of a 500 m 2 paved surface parking (Berretta and Sansalone, 2012). The influent and effluent PSDs are modeled as cumulative gamma distribution in which (shape fact or) and (scale factor) represent the PSD uniformity and the PSD relative coarseness, reported in Table 4 1. PM is released from a calibrated slurry system which works under transient conditions to the inlet drop box and mixed with the influent flow (Fig ure s C 1 C 2). The three hydrographs shown in Figure 4 1B are used for the full scale physical and CFD modeling of the BHS loaded with finer and coarser PSDs. For the BHS an automatic sampler was used to collect influent samples downstream the inlet drop box. All samples were taken in duplicate, with a volume of 1 L each. In the effluent, automatic and manual sampling is performed. The sampling interval varies according to the influent flow gradients. Less frequent sampling intervals (5 to 10 min) are us ed in the beginning and ending parts of the hydrograph (where the flow rate is fairly constant) with 1 to 3 minutes for the duration of the hydrograph (where flow rate rapidly changes). The sampling intervals were the same for the influent and effluent. To provide mass balance verification, separated PM and supernatant samples were also collected after each run. Sample analyses included PSDs conducted by laser diffraction and PM (as SSC). A PM mass balance (MB) was checked for each physical model run: PAGE 86 86 In the mass balance expression Minf is influent mass load and Ceff is effluent concentration which varied with time, ti. Msep is the separated PM reco vered. The PM separation is determined as: PM separation and the MB are reported in Table 4 1 Measured results including effluent PSDs and PM obtained from physical modeling are utilized to validate the CFD model of the BHS. The three hydrographs reported in Figure 4 1C were utilized for CFD modeling of the RC loaded with finer PSD. The validation of the model is performed by using two hydrographs. The physi cal model of the RC is loaded by two hydrographs. The first hydrograph was generated from a triangular hyetograph with 12.7 mm of runoff volume and duration of 15 minutes. This loading was selected as a common short and intense rainfall event during the we t season in Florida (Figure C 3 C 4). The second hydrograph was generated from an historical event collected on 8 July 2008 in Gainesville, Florida with total rainfall depth of 71 mm. This event was chosen as an intense historical event, with a peak rainf all intensity of about 165 mm/h (Figure C 5). The hyetographs were transformed as event based hydrographs through the Storm Water Management Model (SWMM) (Figure C 6) (Huber and Dickinson, 1988). In the rainfall runoff transformation for the scaled physica l model basin the watershed peak runoff flow rate approximated the design flow rate of the RC. The methodology used to retrieve the physical model data for the validation of the unsteady CFD model is the same as the method described in Garofalo and Sansalo ne (2011) and for brevity not reported herein. The influent PSD used for RC is the finer PSD reported in Figure 4 1A. (4 2 ) (4 3 ) PAGE 87 87 CFD M odeling of Fluid and PM Phases A three dimensional (3D) CFD model was utilized to characterize the continuous phase hydrodynamics and to predict PM phase transport and fate in the HBS and RC loaded by hydrographs (Fluent, 2006). The CFD numerically solves the Navier Stokes (N S) equations across a computational domain by using a finite volume approach. The physical model of BHS and R C is built and meshed in Gambit environment (Fluent, 20 10 ). The mesh was comprised of tetrahedral elements. The size of the mesh was determined by a grid convergence study. The CFD model developed for this study couples the continuous fluid phase with a di screte particulate phase model (DPM) based on Eulerian and Langragian approaches. To solve the continuous fluid phase the Reynolds Averaged Navier Stokes (RANS) formulation was utilized. The RANS conservation equations were obtained from the N S equations, by applying the mean value and fluctuating component. The mean velocity is defined as a time average for a period t which is larger than the time scale of the fluctuations The time averaged fluctuations tends to zero and do not contribute to the bulk mass transport. The time dependent RANS equations for continuity and momentum conservation are summarized (Panton, 2000). In these equations is fluid densit y, xi is the ith direction vector, uj is the Reynolds averaged velocity in the ith direction; pj is the Reynolds averaged pressure; and gi is the sum of body forces in the ith direction. The decomposition of the momentum equation with Reynolds (4 4 ) (4 5 ) PAGE 88 88 decompositio n generates the Reynolds stresses term, from the nonlinear convection component. Since the Reynolds stresses are unknown, the realizable k model (Shih et al., 1995) was used to resolve the closure problem. Studies have shown the r ealizable k provides more accurate results respect to the standard k model where the flow features include strong streamline curvature, vortices and rotation (Rahimi and Parvareh, 2005). The realizable model is suitable for boundary free shear flow (BH S and RC) applications (Kim and Choudhury, 1995). The realizable k model consists of a turbulent kinetic energy equation and a turbulence energy dissipation rate equation, respectively reported below (Shih et al., 1995). k = 1.2, C 2 T viscosity; and u ji and u j i are defined in equations 4 5 a nd 4 6. The inlet is specified as velocity inlet and each free surface is approximated as shear free wall with velocity components normal to the surface. The numerical solver utilized is a pressure based solver, suited for incompressible flows governed by motion based on pressure gradients. The spatial discretization schemes adopted are the second order for the pressure, the second order upwind scheme for the momentum and the Pressure Implicit Splitting of Operators (SIMPLE) algorithm for pressure velocity coupling. The temporal discretization of the governing equations was performed by (4 6 ) (4 7 ) (4 8 ) PAGE 89 89 using the second order implicit scheme. Convergence criteria are set so that the scaled residuals for all governing equations are below 0.001 (Ranade, 2002). The DPM was us ed to simulate three dimensional trajectories of discrete particles through the computational domain and to model particle separation. The CFD model was based on Eulerian Lagrangian approach. While the fluid phase is treated as a continuum in an Eulerian f rame and solved by integrating the time averaged N S equations, the DPM tracks each individual particle through the flow field in a Lagrangian frame of reference. The DPM model assumes PM motion is influenced by the fluid phase, but not vice versa (one way coupled model) and particle particle collisions are negligible. These assumptions were satisfied in this study since the volume fraction (VF) was less than 10%, indicating that the dispersed phase was sufficiently dilute (Brennen, 2005). The DPM tracks i ndividual particles through the flow field by balancing the forces acting on the particles such as gravitational body force, drag force, inertial force, and buoyancy. Each particle trajectory therefore is calculated by integrating the force balance equatio n written below in the ith direction: The first term on the right hand side of equation 4 9 is the drag force per unit particle mass, in which FD i is defined in equation 4 10. The second term is buoyancy/gravitational force per unit particle mass. In this equation Re i is the Reynolds number for a particle, and CD i is the drag coefficient. (4 9 ) (4 10 ) PAGE 90 90 The first term on the right hand side of the equation is the drag force per unit particle mass. In these equations, p is particle density, v i is fluid velocity, v p i is particle ve locity, d p is particle diameter, K 1 ,K 2 ,K 3 are empirical constants as a function of particle Re i To model the influent PSD, the PM gradation was discretized into discrete PM size classes on a symmetric gravimetric basis. Studies have demonstrated that a DN of 8 to 16 is generally able to produce accurate results for size hetero disperse granulometry subject to steady (Dickenson and Sansalone, 2009) or unsteady flows (Garofalo and Sansalone, 2011). The DN baseline of this study was 16 for the finer PSD a nd 8 for the coarser PSD. In transient CFD model, at each time step the fluid phase is solved. PM phase is then tracked throughout the solved flow field by using Equation 4 9. CFD M odeling under u nsteady c onditions For a fully unsteady CFD model, the TS typically ranged from 10 to 60 seconds as a function of for the hydrograph (Garofalo and Sansalone, 2011). PM particles were injected from the inlet surface and tracked through the domain at each TS. A computational subroutine as a user defined function (UDF) was developed to record PM injection properties, residence time and particle size of each particle eluted from the system throughout the entire simulation. Further details about the UDF are reported in Appendix. A population balance model (PBM) was coupled with CFD to model particle separation. Assuming no flocculation in the dispersed PM phase, a PBM (Jakobsen, 2008) is written. (4 11 ) (4 12 ) PAGE 91 91 In this equation and represent particle size range and injection time ranging from 0 to the runoff event duration, t d respectively. The term () inf indicates influent PM, () eff effluent PM and () sep separated PM. p represents the mass per part icle and is obtained as follows: In this expression M is PM mass associated with the particle size range and injected at time N represents the total number of particles injected at the inlet section (Garofalo and Sansalone, 2011). In Garofalo and Sansalone (2011) the CFD fully unsteady model was used to predict effluent PM from BHS subjected to storm even ts with differing level of unsteadiness. The study illustrated modeling error and computing time produced by a transient CFD model as function of computational parameters. Stepwise s teady CFD m odeling The conceptual foundation for stepwise steady flow mode l is analogous to unit hydrograph theory used to predict surface runoff from a watershed (Bedient and Huber, 2002). The stepwise steady model is based on the assumption that the temporal effluent PM distribution from a UO is given by the superposition of PM residence times across the entire hydrograph. For this analog, I is the event based influent PM for a given PSD. The hydrograph is discretized into a series of m steady flow rate, Q m for a fixed time step, t. I m represents the influent PM for a given PSD and a fixed time step, t delivered into the system at Q m U p is function of flow rate, Q m ; therefore, let define U p ,Q m the UO response to I m for the specific flow rate, Q m (Figure s C 7 C 9). U p ,Q m is computed from steady CFD models. The UO is assumed to (4 13 ) (4 14 ) PAGE 92 92 be a linear system. Based on this assumption the event based effluent mass PM, E can be modeled as sum (convolution) of the responses U p ,Q m to inputs I m The effluent mass PM at each time step t, E n is given by the discrete convolution equation: In these expressions, n and m are the number of steps in which the effluent PM distribution a nd the influent hydrograph are respectively discretized. A schematic of this methodology is shown in Figure C 10. In this study the DPM loading of the CFD model was represented by three hetero disperse (finer, coarser and source area) PSDs. These PSDs loa ded the physical models in this study. The coarser and source area PSDs were discretized into 8 size classes (DN = 8) with an equal gravimetric basis and a DN of 16 for the finer PSD. Throughout each stepwise steady flow simulation a computational subroutine as a user defined function (UDF) was run to record residence times of each particle size and generate U p ,Q. UDF is described in the Appendix The temporal step is chosen to be less than the flow response time of the system. Since the mean re sidence time of the BHS and RC is less than 2 min at the respective peak flow rates, a t of 1 min is considered appropriate for both UOs. For each discrete flow rate a steady CFD modeled U p ,Q m is determined. In this study the continuous phase loading of the CFD model was represented by the hydrographs show in Figure 4 1 that were varied based on unsteadiness, and peak flow, Q p and the UO. Each hydrograph was divided into one minute intervals, t and converted in a series of discrete steady flow rates. To associate to each discretized flow rate the corresponding U p the following procedure was used. The modeled CFD Up,Q obtained from the UDF was fit by a gamma distribution (4 15 ) PAGE 93 93 function; therefore, U p ,Q was uniquely described by two gamma distribution parame ters, and as shown in Figure C 11 set of steady flow rates was run to derive the relationship between Q and U p ,Q gamma parameters as shown in Figure C 12. This relationship allowed to obtain U p gamma parameters, and hence U p ,Q for each discretized flow rate. From the findings shown in Figure A 13, a set of 7 flow rates chosen as 100%, 75%, 50%, 25%, 10%, 5%, 2% of the UO`s design flow rate produced accurate results (accuracy error of 6%). A higher number of flow rates did not generate more accurate results. Therefore, in this study a number of seven flow rates was run for each unit to obtain U p as function of flow rate. The coupling of particle residence time, U p ,Q and influent PM, I m at each time interval through applying the convolution equation by Equation 4 15 was conducted in order to obtain time dependent effluent PM. To evaluate the error in predicting the temporal effluent PM variation between the fully unsteady and stepwise steady CFD models, the normalized root mean squared error, en was int roduced and represents the error generated by the stepwise steady model as compared to the fully unsteady CFD model at each time interval. The en is computed as follows. In this equation x unsteady represents the value obtained from the unsteady modeling and x stepwise steady represents the value obtained from the stepwise steady modeling. CFD simulations are solved in parallel on a Dell Precision T7500 Workstation equipped with two quad core Intel Xeon 3.33GHz (a total of eight cores) processors. The workstation has 48 GB of RAM. (4 16 ) PAGE 94 94 Results and Discussion Comparison of the S tepwise S teady and F ully U nsteady CFD R esults In Figure 4 2 the stepwise steady and unsteady CFD model results for the BHS are compared to measured physical model data for the finer PSD and differing levels of With respect to the unsteady CFD model the stepwise steady model accurately reproduces t he temporal effluent PM distribution from the BHS. The modeling errors (e n ) ranged from 9.6 to 7.8%. As the hydrograph decreases to quasi steady condition the performance of the stepwise steady model further improves. Quasi stationary conditions reduce t he complexity of the model and tend towards a steady solution with further improved model accuracy. The computational time required for the unsteady and stepwise steady models are reported in Figure 4 2D. The computing time for the fully unsteady model was represented by the sum of unsteadiness degree and duration of the hydrograph, while the post processing was constant (about 1 hour) regardless the hydrograph`s charact eristics. The fully unsteady model computing time ranged from 15.5 to 55 hours for hydrograph loadings (durations, ) from (125 min, ) to (84 min, ) with a mean of 30.3 hours. In contrast, the computational time for the stepwise steady model was no t dependent on the duration and the unsteadiness level of the hydrograph and consisted of two computing components. The first component represents the processing time to run a series of steady simulations. As previously described seven steady flow rates we re run to identify the relationship between Up and Q. For seven steady simulations the CFD model required approximately 9 hours. The second part consisted of the post processing time, the time employed by the user to implement the excel spreadsheet for com puting the convolution integral defined by Equation 4 15. The post processing time was approximately 2 hours. The total PAGE 95 95 approximately 12. Since in this study three hydrogr aphs were analyzed, the computing time per event was 4 hours as compared to the mean average of 30.3 hours for fully unsteady model. Since the processing and post processing times were constant in a stepwise steady flow rate, higher the number of events wa s, lower the computing time per event became. These results showed that the stepwise steady model drastically drops the computing time from an average of around 31 hours to 4 hours per event and this is due to the fact that the stepwise steady model is bas ed on the set of fixed steady flow rates run to generate the unique relationship between Up and Q for the specific UO and remains invariant regardless the hydrographs run. In addition, this stepwise steady flow model produced more accurate results in comp arison to the previous steady flow model for the BHS. In Figure C 14 effluent PM distributions from the BHS subjected to the finer gradation and the highly unsteady hydrograph ( = 1.15) was shown by using new and previous stepwise steady approaches and th e fully unsteady CFD model. The results showed that the previous stepwise steady model overestimated the effluent PM from the BHS, especially in the first part of the hydrograph (Q < Q p ). At the beginning of the storm, the BHS was filled with clear water. Therefore, the PM initially injected at low flow rates is translated to the outlet with a delay, depending on the PM response time of the unit. The previous stepwise steady approach was not able to model this delay occurring at low flow rates, causing not only an earlier delivery of PM at the outlet section but also an overestimation of it. The new stepwise steady model instead was able to predict the PM delay by modeling the actual PM response for low flow rates through the U p ,Q distributions. For the coar ser PSD, Figure 4 3 summarizes the temporal effluent PM mass for differing levels of With respect to the unsteady CFD model the stepwise steady model accurately PAGE 96 96 reproduces the temporal effluent PM distribution from the BHS. The modeling errors (en) ran ged from 9.7 to 5.8%. The total computational time (processing and post processing) time for the stepwise steady model was approximately 11 hours. In contrast for the fully unsteady model the mean total computational time for the fully unsteady CFD model was 28.6 with a range for hydrograph loadings (durations, ) from (125 min, ) to (84 min, ) of 15 to 52 hours. In Table C 1 the computational time for fully unsteady and the stepwise steady model is reported along with event characteristics, including influent PSD and hydrological parameters. While the influences the modeling errors, finer and coarser influent PSDs produce the same order of error and therefore the granulometry did not influence the accuracy of the stepwise steady CFD model. To verify the applicability of the stepwise steady model to UOs different from a BHS, the model was compared to the fully unsteady validated CFD model of the RC as shown in Figure 4 4. Results indicate that the stepwise steady model accurately reproduced the effluent PM eluted from the RC with modeling error that ranged from 8.5 to 5.6% for decreasing levels of The total c omputational time (processing and post processing) for the stepwise steady model was approximately 15 hours. In contrast for the fully unsteady model the mean total computational time for the fully unsteady CFD model was with a range for hydrograph loading s (durations, ) from (282 min, ) to (124 min, ) of 21.5 to 70 hours. Figure C 15 showed the selection of t of 1 min was able to produce the most accurate results. In Figure C 14 effluent PM distributions from the RC subjected to the finer gradati on and the highly unsteady hydrograph ( = 1.54) was shown by using new and previous stepwise steady approaches and the fully unsteady CFD model. The results showed that the previous stepwise steady model overestimated the effluent PM from the RC, especial ly in the first part of the hydrograph (Q < Q p ). PAGE 97 97 These results show that the assumptions on which the stepwise steady model is based; the linearity of the UO system response, the superposition of discrete loadings, and uniqueness of the RTD for each partic le within the PSD, U are valid for BHS and RC. The stepwise steady CFD results also demonstrate the conceptual analog for this second generation model is applicable to volumetric clarifiers or settling tanks and for HS units. Automatic S ampling, PM G ranul ometry and CFD R esults Figure 4 5 summarizes the automatic sampling data collected for the BHS influent for the finer (d 50 = 15 m) and coarser (d 50 = 67 m) PSDs. In Figure 4 5A the influent cumulative PM dry mass from automatic sampling is reported as fu nction of elapsed time. Throughout the entire storm the metered (measured) overall influent PM is 4.5 kg. The results show for the highly unsteady hydrograph ( = 1.15) the automatic sampling was able to recover around 62% of the total influent mass for th e finer PSD, and approximately 50% for coarser PSD. For the source area PSD (d 50 = 130 m) the recovery was approximately 40%. As the level of increased the recovery of influent PM decreased. For the coarser PSD the percentage of influent PM recovered by automatic sampling for the unsteady ( = 0.24) event drops slightly to 58% and for the quasi steady ( = 0.09) to approximately 45%. For the finer PSD (d 50 = 15 m) the percentage of influent PM samples for the unsteady event ( = 0.24) decreases to 65%, for the quasi steady ( = 0.24) to approximately 63%. For the coarser PSD (d 50 = 67 m) the percentage of influent PM samples for the unsteady event ( = 0.24) decreases to 50%, for the quasi steady ( = 0.24) to approximately 48%. For the source area PSD (d 50 = 130 m) the percentage of influent PM samples for the unsteady event ( = 0.24) decreases to 40%, for the quasi steady ( = 0.24) to approximately 47%. For the coarser PSD the PM fraction great er than 75 m represents 50% of PM mass in the gradation. The automatic sampling tube which was placed at the mid depth of PAGE 98 98 the inlet section was not able to collect the coarser particles which settled and became bed load transport in the inlet channel. Th e lower the flow rate the higher the rate of settling of this sediment PM fraction. In fact the turbulent mixing generated by higher flows in the influent channel can resuspend coarser PM, allowing the automatic sampler to collect a component of the PM fra ction greater than 75 m. This explains the low percentage of PM recovery from the influent as the level of decreases. For the finer PSD, the PSD is predominately suspended particles that are mixed more uniformly in the influent especially for high flow rate and these particles have the potential to be collected more accurately by the automatic sampler. In Figure C 16 the influent target PSDs are compared to measured influent PSDs generated through automatic sampling for the three hydrographs shown in Fig ure 4 1B. The influent PSDs is represented as the median PSDs for each hydrograph with range bars representing the variability of PSDs across the entire hydrograph. Figure C 16A shows for the coarser PM gradation that the measured PSDs are coarser as inc reases. Figure C 16B shows that the influent PSDs from the BHS for the finer gradation are not statistically different ( = 0.05) regardless the hydrograph`s level of For the effluent the automatic sampling results are not significantly different from the manual sampling results ( =0.05) since PM larger than 75 m and which is less likely to be sampled representatively by an automatic sampler has been settled by the UO. This mixture of finer suspended PM in the effluent was also distributed more homoge nously in the effluent flow section. Therefore, automatic sampling of the effluent was able to provide representative samples similar to those collected through effluent manual sampling. The stepwise steady CFD model utilized to generate Figure 4 3 result s was applied using the coarser PSD results generated from automatic sampling as shown in Figure 4 5 (as PM). The PAGE 99 99 results illustrated in Figure 4 7 demonstrated that the modeling error significantly increases when an underestimated influent PM generated f rom automatic sampling is utilized in the CFD model. The accuracy errors ranging from 49% ( = 1.15) to 69% ( = 0.09) became larger as the hydrograph`s unsteadiness degree decreased. The stepwise steady CFD model used to generate Figure 4 2 results was ap plied using the fine PSD results produced through automatic sampling as shown in Figure 4 5 (as PM). The results shown in Figure 4 8 demonstrated accuracy errors ranging from 45% ( = 1.15) to 77% ( = 0.09) became larger as the hydrograph`s unsteadiness d egree decreased. This is due to the underestimation of the influent PM produced by the automatic sampling which increases as the degree of unsteadiness decreases. Figure 4 9 reports the unsteady CFD model used to generate Figure 4 3 results for a source ar ea PSD with concentration of 200 mg/L and the stepwise steady CFD model results generated by using the automatic sampling of source area influent PM illustrated in Figure 4 5. The results shown in Figure 4 9 demonstrated accuracy errors ranging from 12% ( = 1.15) to 17% ( = 0.09) became larger as the hydrograph`s unsteadiness degree decreased. For the source area PSD the accuracy errors were lower than those generated for the finer and coarser PSDs. This is because for the source gradation all the particl es not captured by the samplers at the influent section settle nevertheless inside the BHS. These results demonstrated that the inaccuracy of influent PM data produced through automatic sampling leads to an underestimation of time dependent PM eluted from the BHS, and therefore, to an overestimation of unit`s PM separation efficiency. Conclusion The stepwise steady CFD model is validated with measured physical model and it shows good agreement with results generated through unsteady CFD modeling for two Typ e I settling units. The method proposed requires a series of steady state CFD simulations which require less PAGE 100 100 computational time. The convolution equation is applied to this series of steady CFD results for coupling hydrodynamics and PM gradations. The comp uting time per event drops from several hours of unsteady CFD modeling to few hours (approximately 5 hours). The CFD model accuracy relies on the input PM data, which if not properly collected can generate significant modeling errors. This study demonstrat es the automatic sampling produces representative samples of PM eluted from a BHS for both finer and coarser PSDs, but it does not accurately characterize the influent samples for either PSDs. The automatic sampling is not able to collect the coarser fract ion of PSD (>75 m) to which is associated most of the influent PM mass. This study investigates the effect of influent automatic sampling in predicting effluent PM for a BHS and rectangular clarifier by using CFD model, demonstrating the importance of repr esentative and accurate influent PM recovery is crucial not only in monitoring and testing but also for modeling purposes. PAGE 101 101 Figure 4 1 Influent hydraulic loadings and PSDs. In A) i nfluent particle size distributions (PSDs) as compared to a measured source area PSD, in B) three hydrographs loading the physical model of the baffled HS, BHS (v 3 ), and in C) three hydrographs 3 ) A B C Inflow Out flo w 1.83 m 1.73 m Inflow Out flow 7.3 m 1.8 m PAGE 102 102 Figure 4 2. Effluent PM response of a baffled HS (BHS), diameter = 1.83 m, unit volume = 3.4 m 3 to the finer hetero disperse PSD (Figure 4 1A) transported by the hydrographs (Figure 4 1B) (volume = 22 m 3 ) of varying unsteadiness The range bars indicate the variability of the measured data. The en represents the normalized root mean square error between the unsteady and stepwise steady model results e n = 9.6 % e n = 9.1 % e n = 7.8 % A B C PAGE 103 103 Figure 4 3. Effluent PM response of a baffled HS (BHS), diameter = 1.83 m, unit volume = 3.4 m 3 to the coarser hetero disperse PSD (Figure 4 1A) transported by the hydrographs (Figure 4 1B) (volume = 22 m 3 ) of varying unsteadiness The range bars indicate the variability of the measured data. The en represents the normalized root mean square error between the unsteady and stepwise steady model results e n = 9.7 % e n = 6.7 % e n = 5.8 % A B C PAGE 104 104 Figure 4 4. Effluent PM response of a rectangular clarifier, unit volume = 12 m 3 to each hydrograph (volume = 122 m 3 ) loading of varying unsteadiness Each hydrograph transports a constant finer PSD (Figure 4 1A). The en represents the normalized root mean square error between the unsteady and stepwise steady model results e n = 8.5 % e n = 6.5 % e n = 5.6 % A B C PAGE 105 105 Figure 4 5. Each plot displays the influent PM mass recovery provided by auto sampling of the BHS as a function of hydrograph unsteadiness ( ) and PSD. Each PM mass result is normalized to the total influent dry mass (M t ) of 4.50 kg delivered at a constant 200 mg/L for each hydrograph (volume = 22 m3) displayed in Figure 4 1B A B C PAGE 106 106 Figure 4 6. Each plot displays the effluent PM mass recovery comparing auto and manual sampling methods for the BHS as a function of hydrograph unsteadiness ( and PSD. Each PM mass result is normalized to the total in fluent dry mass (Mt) of 4.50 kg delivered at a constant 200 mg/L for each hydrograph (volume = 22 m 3 ) displayed in Figure 4 1B. The measured results from manual and auto sampling are not statistically different ( =0.05) A B C PAGE 107 107 Figure 4 7. Each plot displays the effluent PM response of the BHS to a coarser PSD as a function of hydrograph unsteadiness ( The en represents the normalized root mean square error between the measu red and stepwise steady model results. The stepwise steady CFD model utilized to generate Figure 4 3 results was applied using the coarser influent PSD produced through auto sampling as shown in Figure 4 5 (as PM) in order to demonstrate the error associat ed with using auto sampling e n = 28 % e n = 24 % e n = 34 % A B C PAGE 108 108 Figure 4 8. Each plot displays the effluent PM response of the BHS to a finer PSD as a function of hydrograph unsteadiness ( The en represents the normalized root mean square error between the measured and stepwise steady model results. The stepwise steady CFD model utilized to generate Figure 4 3 results was applied using the finer influent PSD produced through auto sampling as shown in Figure 4 5 (as PM) in order to demonstrate the error associated with using auto sampling e n = 31 % e n = 41 % e n = 32 % A B C PAGE 109 109 Figure 4 9. Each plot displays the effluent PM response of the BHS to a source area PSD as a function of hydrograph unsteadiness ( The en represents the normalized root mean square error between the measured and stepwise steady model results. The unsteady CFD model utilized to generate Figure 4 3 results was applied using the source area influent PSD delivered at a constant concentration of 200 mg/L. The stepwise steady CFD model utilized to generate Figure 4 3 results was applied using the source area influent PSD produced through auto sampling as shown in Figure 4 5 (as PM) in order to demonstrate the error associated with using auto sampling A B C PAGE 110 110 Table 4 1. Physical model (baffled HS and rectangular clarifier) hydraulic and PM loading and PM separated. Q p V, t p PM, td, MB, PM mass, PSD, are peak flow, hydrograph volume, time to peak, influent particle matter, hydrograph duration, mass balance, PM removal efficiency, influent particle size distribution, gamma shape and scale factors, and unsteadiness factor, respectively Q p Q p V t p C t d MB PM mass Influent PSD Hydrograph (%) L/s) (m 3 ) min mg/L min (%) (%) Description Baffled HS (1 turnover v = 3.4 m 3 ) 18 100 22.8 15 200 74 93.9 64.03 0.64 177 1.15 Highly Unsteady 9 50 23.4 15 200 87 97.9 63.53 0.64 177 0.24 Unsteady 4.5 25 22.9 15 200 125 98 .2 71.82 0.64 177 0.09 Quasi steady 18 100 22.8 15 200 74 100.3 33.00 0.79 28 1.15 Highly Unsteady 9 50 22.7 15 200 87 92.8 34.26 0.79 28 0.24 Unsteady 4.5 25 22.8 15 200 125 107.1 57.60 0.79 28 0.09 Quasi steady Rectangular clarifier (1 turnover v = 12 m 3 ) 50 100 124.1 30 200 74 0.79 28 1.54 Highly Unsteady 25 50 125.1 30 200 87 0.79 28 0.33 Unsteady 12.5 25 125.8 30 200 125 0.79 28 0.01 Quasi steady PAGE 111 111 C HAPTER 5 A STEPWISE CFD STEADY FLOW MODEL FOR EVALUATING LONG TERM UO SEPARATION PERFORMANCE Summary Computational fluid dynamics (CFD) is an emerging tool to predict the coupled hydrodynamics and PM fate in unit operations (UOs) subject to transient rainfall runoff events. Frequently, CFD is applied for the rapid analysis of steady flows. Recently an integrated stepwise steady flow CFD model for transient events predicted separation PM with reduced computational overhead as compared to transient CFD modeling. This study ext ends the stepwise steady CFD model to evaluate long term UO performance on annual basis. A validated stepwise steady flow CFD model simulated PM fate (separation and washout) in a rectangular clarifier (RC) and a screened hydrodynamic separator (SHS) for a representative year of rainfall runoff. Throughout the year, prediction of PM washout for transient events was integrated into the time domain continuous simulation model. The CFD model was validated with measured PM separation and washout data from full scale physical models. In comparison to the RC, results show that the SHS is prone to washout and that neglecting PM washout from the SHS overestimates SHS performance. The coupling of a stepwise steady CFD approach and time domain continuous simulation r epresents a valuable tool to estimate the fate of PM on an annual basis. The model can provide a macroscopic evaluation for finding the overall optimal control strategy and for defining maintenance requirements to improve UO treatment. Introduction The relative imperviousness and conveyance of constructed urban surfaces such as pavements facilitates the transformation of rainfall to runoff. These unsteady processes at the urban interface mobilize and transport a hetero disperse gradation of particul ate matter (PM), inorganic and organic compounds generated by urban infrastructure and activities. PM has been PAGE 112 112 identified as a major contributor to the deterioration of surface waters (USEPA, 2000) and a significant vector for many reactive PM bound compo unds, including metals and nutrients (Sansalone and Kim, 2007). To manage the fate of PM and compounds in runoff that partition to and from PM, unit operations (UOs) have been applied to control loads otherwise discharged through runoff to receiving water s (USEPA, 2000) and to address regulations for watersheds such as total maximum daily loads (TMDLs). These UOs range from the common retention/detention clarifier to less common adsorptive filtration and a primary function of these units is PM and PM boun d compound separation (Nix et al., 1988; Sansalone, 1999). Simulation of rainfall to runoff transformations and UO treatment can be based on deterministic equations or derived probability distributions of meteorological event statistics. Deterministic mo dels can be viable for a wide range of hydraulic conditions and basin configurations, but can require more computational effort than statistical methods (Medina et al., 1981; Ferrara and Hildick smith, 1982; Amandens and Bedient, 1980). In a deterministic model introduced by Nix et al. (1988), PM separation of a detention basin was estimated by settling velocity distribution (Nix et al. 1988). In this study a time domain continuous simulation model, Storm Water Management Model (SWMM) (Huber and Dickinson, 1988) was used to generate event based as well as long term transformation of rainfall to runoff for the given watershed and conveyance conditions. The statistica l techniques rely, instead, on a set of statistics of rainfall or runoff and a relatively simple representation of the detention facility (DiToro and Small, 1979; Goforth et al. 1983; Adams and Papa, 2000; Lee et al., 2010). Lee et al. (2010) proposed a fr equency analysis model based on system response time using long term precipitation data to examine the behavior of an infiltration UO. This model is able to analyze PAGE 113 113 the response of UOs to the wide spectrum of long term rainfall runoff phenomena, avoiding t he selection of a single representative storm for water quality control. However, it is not as accurate as a continuous simulation because it ignores the actual timing of the precipitation and storage effects. These models have been a major advancement in the field of urban drainage; however these models were not designed to provide a description of hydrodynamics and particle fate for UOs loaded by different PSDs. In addition, clarification methods in these models are commonly based on concepts of as ideal overflow theory, reasonably steady influent hydraulics as well as sparse PM characteristics such as PSDs. Therefore, the clarification components of these models do not account for the dynamic, unsteady nature of the runoff hydrodynamics flows, constitutiv e properties of PM loads, and the state of the UO system. Computational fluid dynamics (CFD) modeling is an emerging tool capable of predicting the flow field and PM fate within UOs subjected to either steady and unsteady hydraulic and PM loadings (Dicken son and Sansalone, 2009; Pathapati and Sansalone, 2009; He et al., 2008; Wang et al., 2008). Previous studies analyzed the performance of CFD models for UOs subjected to a series of runoff events. Pathapati and Sansalone (2011) demonstrated CFD unsteady mo deling reproduces the response of a HS to unsteady runoff with modeling errors within 10% respect to physical model data, while the use of event based steady flow indices to predict PM separation generated much larger errors. Garofalo and Sansalone (2011) conducted a parameterization study on the CFD model of a baffled hydrodynamic separator (HS) to balance model accuracy and computing time based on mesh size (MS), time step (TS) and PSD discretization number (DN). Despite the precise and accurate represent ation of the physical model behavior, the computational detailed information provided by unsteady CFD modeling, the computational PAGE 114 114 overhead was significant. For a single unsteady rainfall runoff event the computational time required for solving a fully unst eady CFD model varied from 10 to approximately 100 hours (on a Dell Precision 690 with two quad core Intel Xeon 2.33GHz processors and 16 GB of RAM), depending on the TS, MS and DN required for the input hydrograph`s unsteadiness and the disper sivity (Garofalo and Sansalone, 2011). While coupling a fully unsteady CFD model with a long term continuous simulation to evaluate the response of an UO for a time series of rainfall runoff events is a reasonable concept, the computational overhead can b e unreasonable. To reduce computational overhead while ensuring an accurate representation of the physical model response, Pathapati and Sansalone (2011) introduced a stepwise steady flow CFD model to reproduce unsteady PM separation for stormwater UOs. However the model was based on a single storm event. In contrast, this study develops a stepwise steady flow CFD model providing an accurate long term UO response to unsteady loading for PM response with reasonable computational overhead. While the impo rtance of a UO to separate and retain captured PM is recognized, physical modeling and quantification of washout of previously separated PM from a UO has been examined for less than a decade. Recent studies have shown that PM washout can impact the overal l response of a UO, and in part depends on the type of UO and the maintenance frequency (Avila et al., 2011). Pathapati and Sansalone (2012) demonstrated the Eulerian Lagrangian approach in a validated CFD model is able to accurately predict PM washout. Av ila and al. (2011) utilized a validated CFD model to estimate the PM washout for catch basin sumps with an Eulerian Eulerian approach, considering a bed fluidized bed. This study develops and tests a stepwise steady flow CFD model with the goal of simulati ng the long term response of an UO (rectangular clarifier, RC and screened PAGE 115 115 hydrodynamic separator, SHS) to unsteady hydrologic loading for PM separation and also washout at a reasonable computational overhead. For a representative year of rainfall depth o ver a small impervious watershed, the continuous simulation unsteady runoff response results was coupled with CFD to quantify the separate responses of separation and washout for each UO. Methodology Hydrology A nalysis The UOs investigated in this study a re primary applied in relatively small developed urban parcels of land. A largely impervious catchment translates the rainfall to runoff and the runoff is transported by gravity to the RC or SHS in SWMM. The catchment generates flows that are equal to or l ess than the maximum hydraulic capacity of the RC, 50 L/s. A long term precipitation data series is collected for Gainesville, FL (KGNV) for the period 1998 2011 as hourly rainfall data from the National Climatic Data Center (NCDC) with rainfall depth res olution of 2.54 mm (0.01 in.). The hourly rainfall data are downloaded from the NCDC website (http://www.ncdc.noaa.gov). Since the catchment is small with times of concentration time less than 1 h, the hourly rainfall data was disaggregated into 15 minute data. The deterministic disaggregation procedure utilized was proposed by Ormsbee (1989) (Nix et al., 1988) and the procedure is summarized in Figure D 1 of the Appendix D From the resulting 15 minute rainfall data series, total rainfall volume, number of events and rainfall intensity frequency distribution were evaluated for each year from 1998 to 2011 and the overall period. The rainfall intensity frequency distribution is shown in Figure D 2. For the period of 1998 2011 mean annual rainfall depth and m ean number of events per year is respectively 1214 mm and 133. The mean number of events for the wet season is 81 and for dry season 52. A representative year (2007) with hydrological characteristics similar to the annual mean for Gainesville was selected and is shown in Figure D 2. In 2007 the total rainfall depth and the PAGE 116 116 number of events are 1171 mm and 147 respectively. The rainfall intensity frequency distributions shown in Figure D 2A for the period 1998 2011 and for 2007 are not statistically differe nt (p > 0.05). Therefore, the year 2007 is chosen to be representative of the period 1998 2011. Figure D 3 shows monthly rainfall depth for the year 2007. SWMM is used to generate unsteady runoff flow loadings from the rainfall time series data of 2007. A catchment which delivers runoff to the RC and SHS was input into SWMM. The catchment area generated a runoff time series with 99% of flows less than 50 L/s, the design flow rate of the RC. The SWMM model parameters are summarized in Figure 5 1A, and repres ent a catchment from the paved surface parking source area described by Berretta and and Sansalone (2012). The catchment area is 1.6 ha. The catchment time of concentration is based on the kinematic wave approach and is approximately 30 minutes for the m edian intensity of 1 mm/h as shown in Figure s 5 1B and D 1 The minimum inter event time (MIT) utilized the approach of Adams and Papa (2000) and based on the annual average number of events the MIT was 1.36 h as shown in Figure 5 1C. Therefore, since the MIT for a small catchment can approach the time of concentration, a MIT of 1.0 hours was utilized for this catchment. The cumulative runoff and discrete frequency distributions generated at one minute interval are reported in Figure D 4 Physical F ull S c ale M odel for PM S eparation PM separation validation was performed with a full scale physical model of the RC under unsteady hydrograph conditions as shown in Figure D 5. The RC is shown in the inset of Figure 5 2. The RC is 1.87 m high, 1.8 m wide and 7.31 m long with a volumetric capacity of approximately 12,000 L. The design flow rate, Q d of the physical model (50 L/s) corresponds to the hydraulic capacity of physical model. Further information about the geometry of the system and a plan view are repo rted in the Appendix in Figure D 5 PAGE 117 117 PM separation validation was performed with a full scale physical model of the SHs under steady hydrograph conditions (Pathapati and Sansalone, 2012). The SHS unit consists of two concentric cylindrical chambers separa ted by a static screen with 2,400 m apertures. The HS inlet is tangential to the inner sump chamber which has a diameter of 1.7 m. Surrounding the sump chamber is the outer annular volute chamber with a diameter of 1.7 m. The volute chamber functions as a settling tank and flow exits the volute chamber through the effluent section. A sump is located at the bottom of the unit where PM is deposited after separation or subsequently re suspended by incoming flows. The volute area also functions as a PM separ ation and re suspension area. The SHS is shown in the inset of Figure 5 2D. The Appendix provides information about the geometry and the plan view of the physical model. Two hydrographs were delivered to the physical model of the RC. The first hydrograp h was generated from a triangular hyetograph with 12.7 mm (0.5 inch) of rainfall depth and duration of 15 minutes. This loading is selected as a common short and intense rainfall event during the wet season in Florida and is shown in Figure D 6. The second hydrograph was generated from an 8 July 2008 in Gainesville, Florida with total rainfall depth of 71 mm. This event was chosen as a high intensity event with a peak rainfall intensity of about 165 mm/h as shown in Figure D 7. An unsteadiness parameter, is defined for each hydrograph and the values of are summarized in Table 5 1 (Garofalo and Sansalone, 2011). where i=1*dt.....td*dt In this expression Q med rep resents the median value of Q, dt is the time step. The particle size distribution (PSD) used for the physical testing is reported in Figure D 8 and is a fine hetero disperse gradation classified as sandy silt based on the Unified Soil (5 1) PAGE 118 118 Classification Syste m (USCS) with a d 50 of 15 m. More detailed information regarding the generation of the two hydrographs utilized for the validation ar e reporte d in Section 3 of the Appendix D The physical model results are reported in Table D 1. Physical model testing w as conducted at constant influent PM concentration (C i ) of 200 mg/L and constant PSD shown in Figure 5 2A. For each run discrete duplicate samples were taken manually with a frequency that ranged from 2 to 5 minutes. Analysis included PSD by laser diffract ion and PM gravimetric analysis as suspended sediment concentration (SSC). A PM mass balance was conducted for each physical model test. In the mass balance expression M inf is influent mass load and C eff is effluent concentration which varies with time, t i M sep is separated PM recovered. The PM separation (%) is also determined. PM separation and mass balance (MB) are reported in Table D 1. Measured results obtained from physical modeling were utilized to validate the CFD model. Physical F ull S cale Model for PM W ashout PM washout was also exami ned for each UO. Physical model runs for PM washout were performed on the full Figure D 5. The runs are carried out to evaluate washout PM from the RC. The PSD of the pre deposited PM bed in the RC is reported in Figure 5 2A and is a fine hetero disperse gradation classified as an SM with a d50 of 15 m. The dry bulk density of the deposit was 1.04 g/cm 3 The PSD was modeled as cumulative gamma distribution in which (shape factor) and (scale (5 2 ) (5 3 ) PAGE 119 119 factor) represent the PSD uniformity and the PSD relative coarseness. The washout hydrographs are those reported in Figure 5 2B C. The July 8th storm and the triangular hydrograph with peak flow rates of 50 L/s and 28 L/s, respectively were p reviously described. For washout other two hydrographs were considered. These hydrographs are scaled based on the RC maximum hydraulic capacity (50 L/s), maintaining constant shape, volume (V = 15,000 L) and time of peak flow, tp of 15 min of the triangula r hydrographs. The two hydrographs has peak flow rate of 21 L/s and 35 L/s, respectively. For the RC, each washout run was conducted by first pluviating PM across the entire surface area of the RC for two depths of PM deposits: 5 and 15 mm. The RC was then filled with water at a flow rate of around 0.2 L/s to avoid any re suspension of the PM bed. For each washout test, discrete duplicate effluent samples were taken manually within a frequency range of 2 to 5 minutes. Analysis included PSD by laser diffrac tion and PM gravimetric analysis as suspended sediment concentration (SSC). Measured effluent PSDs and PM obtained from physical modeling were utilized to validate the CFD model. The measured data for the SHS was generated from a mono disperse PM gradatio n described in Appendix The methodology is the same of that described for the RC. PM deposition depths investigated were 50% and 100% of sump storage capacity with no PM in the volute chamber, and 50% of sump capacity and 2.5 cm of PM deposit in the volut e chamber. Further details about the physical modeling methodology of the SHS are reported in Pathapati and Sansalone (2012). CFD M odeling A three dimensional (3D) unsteady CFD model was built based on the full scale physical model of the RC and the SHS units using FLUENT version 13.0 (Fluent, 20 10 ). The code is finite volume based, written in C programming language and solves the Navier Stokes (N S) PAGE 120 120 equations within the computational domain boundaries of each unit. The geometry and mesh of the RC physica l model were built in Gambit (Fluent, 2010) and shown in Figure D 9. After a grid convergence study, the final grid was comprised of 3.5 million tetrahedral elements. Further information about the grid convergence is reported in Figure D 10 of the Appendix The validated CFD model for the SHS is described in details in Pathapati and Sansalone (2012). The mesh of SHS consists of 2.1 million cells as shown in Figure D 11. The CFD model is based on Euler Lagrangian approach in which the fluid phase is treated as a continuum in an Eulerian frame of reference and solved by integrating the time dependent N S equations. The particulate phase behavior in the system is predicted by the discrete phase model (DPM) in a Lagrangian frame of reference. To simulate the t ime dependent PM eluted from the units during separation (treatment) and also washout testing a fully unsteady CFD model and physical model validation thereof are summarized for the RC in Section 4 of the Appendix ( B ) This physically validated CFD model is then utilized to generate the stepwise steady flow CFD model. CFD m odel for PM s eparation In a fully unsteady CFD model the TS is typically in the range of 10 seconds to 1 minute depending in the hydrograph unsteadiness, (Garofalo and Sansalone, 20 11). The individual particles across the PSD were injected into the UO inlet (at the computational domain boundary) and tracked within the computational domain at each TS. The number of TS used to integrate the particle motion (Equation D 8 of the Appendi x D ) was based on a tracer study. Buoyant, 1 m particles were injected from the inlet surface and then tracked through the computational domain p This flow rate is adopted to determine the maximum num ber of steps needed to track the particles thought the system. A computational PAGE 121 121 subroutine as a user defined function (UDF) written in C records PM injection properties, tracer elution, residence time and particle size of each particle eluted from the syste m throughout the entire simulation. A population balance model (PBM) was coupled with CFD to model particle separation. Assuming no flocculation in the dispersed PM phase, the PBM equation (Jakobsen, 2008) can be written. In this equation and represent particle size range and injection time ranging from 0 to the runoff event duration, td, respectively. The term () inf indicates influent PM, () eff effluent PM and () sep separated PM. p represents the mass per particle and is obtained as follows: In these expressions, M is PM mass associated with the particle size range as function of injection time N represents the total number of particles injected at the inlet section and t d is the event duration (Garofalo and Sansalone, 2011). CFD model of PM washout The pluviated PM bed consists of sandy silt PM. The re suspended PM is sufficiently dilute to have negligible effect on the turbulence structure in the carrier fluid. Due to the dilute nature of these PM laden flows the use of a Lagrangian Eulerian approa ch is appropriate to describe the re suspension and washout of PM (Elgobashi, 1991). From the physical model testing the formation of a scour hole was observed after each run and corresponded to the area where the incoming flow jet plunged downward through the water column of the RC and impinged on the PM deposit. This observation aided in the CFD methodology for washout. The (5 4 ) (5 5 ) PAGE 122 122 geometry of this area is shown in Figure D 13 and was used in the modeling and mass balance process. In order to support the methodology for washout, from the physical model testing a semi circular scour hole was observed in the inlet section of the clarifier. This suggests the PM mass washout from the system was mainly generated from the scour hole due t o the impinging jet. The scour hole was measured and subsequently, was represented in CFD by an equivalent rectangular area (60 x 20 cm) shown in Figure D 13. Layers were created in the region of computational domain that consisted of the pluviated PM bed where the scour hole was produced. A series of 60 x 20 cm layers were built in CFD based on visual observations and physical measurements of the scour area. The interval size between these layers was 1.0 mm and smaller intervals did not produce more accu rate results. A horizontal grid of 1,600 nodes with spacing of 0.5 mm was built in each horizontal layer. Further refinement of the horizontal grid did not result in significant change in PM washout ( = 0.05). From each node 16 PSD particle sizes (Garofal o and Sansalone, 2011) are released for a total of 25,600 particles for each horizontal plane. A schematic of the methodology is shown in Figure D 13. The number of steps utilized to integrate the particle motion (Equation D 8 in the Appendix ) was determi ned based on a tracer study. A neutrally buoyant tracer was released from each plane and the number of steps is modified until all the tracer is eluted from the unit. The largest TS number obtained for each layer was selected for the entire simulation. PSD particles were then tracked through the computational domain with the DPM A computational subroutine as a user defined function (UDF) was written in C to record the number of particles eluted and retained in the computational domain of the unit and their residence times shown in Figure D 14. The effluent mass load is calculated. PAGE 123 123 In this expression, p, n, M p,n are the DN (number of PSD size classes), the number of layers in which the pluviated PM bed is discretized, and PM mass between layers associated with PSD size classes, respectively. The clarifier is loaded with the hydrographs and the PSD shown in Figure 5 1 for pre deposited PM depths of 5 and 15 mm. For the SHS unit a similar methodology des cribed in details in Pathapati and Sansalone (2012) is applied. For washout CFD modeling the SHS was loaded with a fine hetero disperse PSD shown in Figure 5 2D and four hydrographs reported in Figures 5 2E and 5 2F. The hydrographs were scaled based on th e SHS design flow rate (31 L/s), maintaining constant the shape of the RC`s hydrographs illustrated in Figures 5 2B and 5 2C. Validation analysis for fully unsteady CFD model Measured PM separation and also washout results were utilized to validate the fu lly unsteady CFD models. The measure of error between measured and modeled results is the relative percent difference (RPD). PMmeasured and PMmodeled are the event based PM mass from the physical and CFD model. The validation was considered satisfactory when RPD is less than 10%. The events used to validate the CFD model for PM separation by the RC are the runoff events show in Figure 5 2C and 5 2 D with Q p of 28 and 50 L/s. The hydrographs reported in Figure 5 2C and 5 2 D are used for the pluviated PM depths of 5 and 15 mm in the CFD washout model. For the SHS the measured data reported by Pathapati and Sansalone (2012) were comp ared to the CFD model results. The CFD validation results are reported in Figure 5 4 in which the washout PM at 50 and ( 5 6 ) ( 5 7 ) PAGE 124 124 100% of sump PM capacity, and for two different PM depths in the volute area (0 and 2.54 cm), are analyzed at 100 % (31.1 L/s) and 125% ( 38.8 L/s) of Q d for the SHS. Subsequently, fully unsteady model results for RC were validated against the stepwise CFD steady model results. Stepwise steady CFD model In this study a stepwise steady flow CFD model was developed with the goal of simulatin g the long term response of the RC and SHS to unsteady hydrologic loading for PM separation and washout at a reasonable computational overhead. The analogous conceptual basis for a stepwise steady flow model is the unit hydrograph (Chow et al. 1988) used to predict runoff from a watershed. The analogy is described in details in SI and shown in Figure D 15 and D 16. The stepwise steady model is based on the assumption that the temporal distribution of effluent PM from a specific UO can be represented as the superposition of the residence time distributions (RTDs) of mass PM for a given PSD, U p For this analog, I is the event based influent PM for a given PSD. The hydrograph is discretized into a series of m steady flow rate, Q m for a fixed time step, t. Im represents the influent PM for a given PSD and a fixed time step, t, delivered into the system at Q m U p is function of flow rate, Q m ; therefore, let define U p ,Q m the UO response to I m for the specific flow rate, Q m (Figure D 15). U p ,Q m is computed from steady CFD models. The UO is assumed to be a linear system. Based on this assumption the event based effluent mass PM, E can be modeled as sum (convolution) of the responses U p ,Q m to inputs I m The effluent mass PM at each time step t, En is given by the discrete convolution equation: ( 5 8 ) PAGE 125 125 In these expressions, n and m are the number of steps in which the effluent PM distr ibution and the influent hydrograph are respectively discretized. A schematic of this methodology is shown in Figure D 17 and D 18. The methodology has the following steps. The CFD model is loaded with the fine hetero disperse PM gradation shown in Figure 5 1A and is run under steady conditions for stepwise steady levels. The influent PSD is discretized into 16 size classes on an equal gravimetric basis. Particles from each PSD size classes are injected at the inlet surface of the UO. Throughout each simula tion a computational subroutine, written as a user defined function (UDF) in C, is run to record residence times of influent PSD and generate U p ,Q. The influent hydrographs are divided into 1 minute intervals, t and converted in a series of discrete s teady flow rates. The temporal step is chosen to be less than the flow response time of the system. Since the mean residence time of the RC is 1.5 min at the peak flow rate of 50 L/s, a t of 1 min is considered appropriate. For each discrete flow rate a s teady CFD modeled U p ,Q m is determined. Finally U p ,Q m is coupled to I m at each time interval by using the convolution equation in order to obtain the temporal effluent PM distribution. A more detailed description of the methodo logy is reported in the Appendix To associate to each discretized flow rate the corresponding U p the following procedure is used. The modeled CFD U p is well fit by a gamma distribution function; therefore, a U p can be uniquely described by two gamma distribution parameters, and set of steady flow rates is run to derive the relationship between flow rate and U p gamma parameters. This relationship allows to obtain U p gamma parameters, and hence U p for each discretized flow rate. From the findings shown in Figure D 19, a set of 7 flow rates chosen as 100%, 75%, 50%, 25%, 10%, 5%, 2% of the UO`s design flow rate produces accurate results. A higher number of flow rates does PAGE 126 126 not produce more accurate results. Therefore, in this study a number of seven flow rates was run for each unit to obtain Up for each discretized flow rate. Previous studies proposed a stepwise steady model based on discretizing the hydrograph into a series of steady flow rates and then, simply integrating the results for each discretized flow level (Patha pati and Sansalone, 2011). This methodology implicitly assumes the flow response of the system is nearly instantaneous (very short residence times) regardless the flow rate. In addition, the difference between PM and flow response times is also assumed neg ligible. The stepwise steady approach used in this study takes into account the actual PM response times of the system as function of flow rate by modeling the PM residence time distributions (U m ,Q m ) shown in Figure D 14. In addition, the PM eluted at a g eneric time t a is given not only by the influent mass PM delivered at t a but also by the influent mass PM previously delivered and still in suspension in the UO. The model, therefore, recognizes the transient behavior of UO as a continuously evolving sys tem, in which the outputs at each instant are influenced by the previous conditions in the UO. For such reasons the stepwise steady model presented in this study is able to reproduce fully unsteady results. Evaluation of PM E lution D ue to W ashout in the C ontinuous S imulation M odel An approach to evaluate PM washout from UOs within a continuous simulation framework is defined. Pathapati and Sansalone (2009) demonstrated that from a comparison of steady flow statistical indices (mean, median, peak) that the peak flow rate (Q p ) provides the most accurate estimation of the total PM mass eluted from a UO subject to unsteady event based hydrograph loadings. For unsteady flow in open channels, Q p has been used to estimate the maximum depth of scour and therefore, the maximum mass eroded from the channel bed for no cohesive PM (Tregnaghi et al., 2010). In this study Q p is utilized to provide a prediction of the effluent PM mass due to washout. This re suspended mass represents potential washout from the UO system. PAGE 127 127 To verify whether Q p reproduces physical model results, the PM washout mass from the hydrographs reported in Figure D 2 for the RC and SHS are compared to the results obtained at flow rates equal to each hydrograph`s Q p For this purpose, a relationship b etween a range of Q p values and PM washout mass is built for several PM depths for the RC and SHS. The errors are measured as RPD. If results based on Q p can reproduce physical model results, then the relationship between PM washout mass and hydrograph Q p can be implemented in the stepwise steady flow CFD model to account for washout phenomena. Time D omain Continuous Simulation M odel and its A ssumptions Outside of CFD, a MatLab code was written to discretize the hydrograph in a series of steady flow rates and to compute the convolution equation (Equation 5 8) described in previous s ection. The code is implemented to run across an annual time series of run off data computed from the time domain continuous simulation and shown in Figure D 4 of the Appendix for the RC. The assumptions for the time domain continuous simulation model were: (1) an event based PM influent concentration of 200 mg/L and the influen t PSD is shown in Figure 5 1A are maintained constant throughout the runoff event, (2) the distribution of settled PM mass is approximately uniform across the bottom of the RC, and (3) the PM remained in suspension after the storm event is predominately se ttled before the beginning of the subsequent event. For the SHS, PM is primarily settled in the sump and as the sump capacity exceeds 50%, there is also a net PM settling in the volute chamber (Kim and Sansalone, 2008). The relationship between the washo ut of PM mass and flow rate is implemented in the stepwise steady flow CFD model to account for PM washout. After generating the runoff distribution for each rainfall event of the rainfall time series, the PM washout as a function of flow rate relationship is applied to determine the mass of PM washout from the UO based on the event`s peak flow rate. As a result PAGE 128 128 of the PM washout the total PM depth in the UO is updated and the next hydrologic event is run. This process is continued for the entire time seri es of interest, in this case for 2007. Results and Discussion CFD M odel for PM S eparation and W ashout A mass balance validation was performed on the physical model for RC and SHS to ensure the validity of the measured mass data. For RC and SHS the RPDs w ere within 10 %. Subsequently, the fully unsteady CFD modeled PM results were compared to physical model data as shown in Figure D 20. The RPDs for each hydrograph loading were computed to estimate the CFD model error in predicting PM elution with respect to the physical model data. The RPDs were less than 10%. The validation results for PM washout from the RC and SHS are reported in Figure 5 3 and 5 4. In the CFD model the pluviated PM bed was discretized into a series of layers with an interval size of 1 mm. The selection of 1 mm interval size was able to reproduce accurate re sults. A smaller interval sizes up to 0.3 mm did not generate more accurate results. The method reduces the computational overhead respect to the approach used from Pathapati and Sansalone (2012) where the interval size was approximately equal to one parti cle diameter. In Figure 5 3 the intra event effluent PM generated by the fully unsteady CFD model for the RC as compared to the measured effluent PM data from the physical model. The washout PM results are reported for the triangular hyetograph loading and the 8 July 2008 loading; each for 5 and 15 mm of PM uniformly pluviated across the bottom of the RC and SHS. The measured and fully unsteady modeled results are also reported for the hydrographs shown in Figure 5 2B with a Q p of 28 L/s and 21 L/s, respec tively. The results show agreement between the fully unsteady CFD model and washout measured data. Also the trend of the time PAGE 129 129 dependent washout measured PM data is accurately modeled by CFD. In Table 5 1 the physical and CFD model results are reported alon g with their RPDs. All RPDs were less than 10%. Results show the mass of PM washout mass increased as Q p and PM bed depth increased. Flow duration aside, results suggest that the hydrograph Q p is a primary parameter which influences the PM re suspension an d washout phenomena. Based on the CFD model, Figure 5 4 summarizes the PM washout for the SHS at 50% and 100% of sump capacity for PM and for 0 and 2.54 cm of PM depths in the volute area. Results are obtained at 100 and 125% of Q d ; for a coarser (d50 = 110 m) and finer PM gradation (d 50 = 67 m). Results show the SHS is more conductive to washout than the RC. Table 5 2 summarizes RPDs for the validation; showing agreement between measured and modeled results. PM W ashout as F unction of F low R ate and P lu viated PM D epth After validating the CFD model, the PM washout mass for both UOs was modeled for different pluviated PM depths and flow rates. Figure 5 5A summarizes PM washout mass as function of flow rate (up to 50 L/s, Q d ) for the RC for PM depths ranging from 5 to 50 mm. As anticipated, the washout mass increases for increasing flow rate and PM depth. The washout from the SHS unit is explored as function of flow rate ranging from 1.5 to 31.1 L/s (Q d ) and PM depths in the SHS sump and volute chambe r. In Figure 5 5B the washout mass from the SHS unit is modeled for 50% of sump capacity of PM and depths ranging from 10 to 100 mm in the volute chamber. As anticipated, the PM mass washout increases as flow rate and sediment depth increase. In Figure 5 5C the PM washout from the SHS sump is shown for PM depths ranging from 25 to 450 mm (no PM pluviated in volute area). At the design flow rate of 31.1 L/s with the sump capacity filled to 50% of capacity the PM washout mass is 4.3 Kg, while at the same flo w rate with a PM depth of 10 mm in the volute area the washout mass is 5 Kg. For lower PM PAGE 130 130 depths the volute area with a lower velocity distribution is more conducive to retain PM as compared to the sump area (Kim and Sansalone, 2008). However when the vol ute PM depth is higher than 50 mm, the PM washout mass from the volute chamber significantly increase. In Figure D 21 the effluent PM concentrations due to the washout are reported for the RC and SHS. The PM bed load PSD used for both units is the fine he tero disperse PSD characterized by = 0.79, = 28 and d50 = 15 m, as shown in Figure 5 2A. The concentration values are based on 6.5 turnovers (1 turnover is equal to the runoff volumetric capacity of each unit) (Cho and Sansalone, 2012). For the RC th e effluent PM ranged from approximately 10 to 70 mg/L at Qd, while for the SHS at 50% of sump capacity and PM in the volute chamber, the effluent PM ranged from 200 to 700 mg/L, an order of magnitude higher. The PM from solely the volute chamber was appro ximately from 30 to 670 mg/L. While at 50% of the sump capacity, effluent PM is approximately 200 mg/L, at 100% of the sump capacity 350 mg/L at Q d From 10 to 100 mm of PM depth in the volute area and 100% of sump capacity the effluent concentration varie s from around 400 to 900 mg/L as show in Figure D 22. Results indicate that t he PM washout from the RC is significantly less than the SHS. The RC provides volumetric isolation of previously separated PM and produced lower washout respect to the SHS as bot h modeled with a fine hetero disperse PSD. By comparison, the SHS does not provide volumetric isolation. Instead, the flow entering into the screen area tangentially generates a vortex throughout the inner screen chamber with the flow momentum transferred directly into the sump region and given conservation of momentum, reflected upward and through the volute chamber towards the SHS outlet (Pathapati and Sansalone, 2012). This high velocity field, established within the inner chamber, re suspends previousl y separated PM in the sump. Therefore, the sump is prone to significant re suspension; while the volute chamber is PAGE 131 131 prone to a lesser degree except at greater PM depths. Results corroborate the need for regular maintenance of the SHS and that the net treat ment functionality of unit operations deteriorates without regular maintenance. To further assess the role of the hydrograph`s peak flow rate as a statistical index to predict PM mass washout, the results from Table 5 1 and 5 2 are compared to those in Fig ure 5 5 for flow rates equal to the hydrograph`s peak flow rate. The errors generated are reported in Table 5 3. The mean RPDs are 10%. The washout mass results obtained from each hydrograph reasonably match those generated from the hydrograph`s peak flow rate. Under steady conditions the flow rate is kept invariant for a number of 6.5 turnovers and the washout mass is associated with the total volume passing through the UO. Once the peak flow rate(s) of an event re suspends mass, this mass is available for washout by the remaining storm hydrograph. Therefore, the washout mass may be less under unsteady conditions respect to that under steady conditions. The RPDs between the fully unsteady and steady washout CFD model results reported in Table 5 3 are negat ive, demonstrating in fact the steady CFD model results slightly overestimate the unsteady CFD model results. Stepwise CFD S teady F low M odel and T ime D omain C ontinuous S imulation The stepwise steady flow model was applied for the entire runoff time serie s generated from SWMM for 2007 and the catchment shown in Figure 5 1A by using the MatLab code Subsequently, the results shown in Figure 5 5 are used to account for washout into the continuous simulation model. Specifically, the washout PM produced by a storm event is predicted by linearly interpolating the results from Figure 5 5 based on the hydrograph`s peak flow rate and the PM depth accumulated within the unit during previous storms. The total effluent mass for a storm event is given by the sum of th e effluent mass predicted by the stepwise steady model and the washout mass from Figure 5 5. Based on the amount of mass settled and PAGE 132 132 washout during a storm event, the PM depth within the unit is then updated and the model set to run the subsequent storm ev ent. The computational time required to run a time domain simulation model is given by the time needed for solving and post processing steady CFD runs and the time for running the MatLab code for a long term series of runoff events. As previously mentione d, 7 steady flow rates run were sufficient to build the stepwise steady model and produce accurate results. The computing time for the steady CFD runs was approximately 7 hours for RC and SHS (on a Dell Precision 690 with two quad core Intel Xeon 2.33GHz processors and 16 GB of RAM), while for post processing was 4 hours. The MatLab code for one year of runoff events (2007) run in 2 hours. Therefore, the total computing time required by the time domain simulation model is 13 hours. The computing time is s ignificantly reduced respect to that required for running a fully unsteady CFD model over a year of rainfall runoff events (for the watershed studied, approximately a number of 133 events). An example of the output of the time domain continuous simulation model is illustrated in Figure 5 2B, where PM mass eluted from the RC loaded with the runoff data series from Figure D 2B is reported for June 2007. Figure 5 6A reports the cumulative effluent PM mass as function of cumulative runoff volume for 2007 for the RC loaded with fine hetero disperse PSD shown in Figure 5 2A and constant influent concentration of 200 mg/L. One set of results is obtained by applying the stepwise steady CFD model without accounting for PM washout. A second set of results is produced by applying the relationships in Figure 5 5A to account for PM washout. The two sets of results are modeled and interpolated by power law model. The PM washo ut from the RC is reasonably flow limited; indicating the washout is limited by the flow and not by the PM mass PAGE 133 133 available in the RC. The effluent PM mass and the PM depth for 2007 are also shown as function of month in Figure 5 6B and 5 6C. For the RC du ring 2007, 522 Kg are separated by the unit (no washout). When accounting the washout phenomena, the results do not change significantly; with a washout of 543 Kg. The RPD between the total effluent PM mass with scour and the total effluent PM mass without scour is 4%. For the RC the final PM depth in the end of 2007 is 25 mm (no washout). When accounting for washout, the results do not vary significantly; with a depth of 27.5 mm. In Figure 5 6D the cumulative effluent PM mass as function of cumulative run off volume during 2007 for the SHS with fine hetero disperse PSD shown in Figure 5 2A and constant influent concentration of 200 mg/L is reported. The time domain simulation model is based on the assumption that PM mass mainly deposits in the sump region f or up to 50% of the sump capacity before there is any significant accumulation in the volute chamber. The cumulative effluent PM results for SHS in Figure 5 6D are modeled and interpolated by power law functions, also suggesting the washout in the SHS is f low limited. As previously observed, the SHS is significantly more prone washout as compared to the RC. These results for one year of separation and washout demonstrate that the long term performance of the SHS was significantly influenced by washout. In Figure 5 6E the effluent mass is reported as function of months. The total annual PM effluent with no washout is 600 Kg, and with washout is 800 Kg. The difference between these two results of annual effluent mass is 33%. More specifically, the difference between the two sets of results as shown in Figure 5 6F is accentuated beginning in June when the wet weather season starts for Gainesville. In Figure D 23 the time domain simulation model results are reported based on the assumption that the sump is at 100% of PM capacity, before PM accumulation occurs in the PAGE 134 134 volute section. In this maintenance condition the effluent PM mass also increases. Figure D 23B shows that under the assumption of no PM washout the sump fills to 100% of capacity from January to t he beginning of July with a PM accumulation of 60 mm in the volute chamber between July and the end of the 2007. By comparison when washout is considered the sump capacity is exceeded by July 29th with a subsequent PM accumulation of 20 mm in the volute se ction. After August the PM accumulated in the volute chamber decreases due to washout and in the end of year approaches to zero. The continuous simulation model for the SHS indicates that a significant difference between the results with and without washo ut occurs after the month of July. The slopes of the curves reported in Figure 5 6E show that the period in which most of the PM elution occurs is between July and October (summer season). The reason is that during the summer season the runoff volume large ly increases, generating larger amount of PM wash off from the watershed and delivered into the system. Consequently, during summer season larger fractions of PM is eluted or re suspended and washout from the system. Conclusion This study developed and test ed a stepwise steady flow CFD model coupled with a time domain continuous simulation model to simulate the long term response of two common UOs (rectangular clarifier, RC and screened hydrodynamic separator, SHS) subject to unsteady hydrologic loading for PM separation and also washout at a reasonable computational overhead. Full scale physical model testing of the two UOs was performed to validate the CFD models of PM separation and washout. These UO physical models were hydraulically loaded with unst eady hydrographs as well as a series of hydrograph peak flow (Q d ) steady loadings. These hydraulic loadings were coupled with a range of particle size distributions (PSD). For the RC, PM separation as well as washout was tested with a finer PSD (d 50 = 15 m, = 0.79, = PAGE 135 135 28) while for the SHS, PM separation was tested with a finer PSD (d 50 = 15 m, = 0.79, = 28) and PM washout was tested with a medium (d 50 = 67 m, = 0.58, = 271) and coarse PSD (d 50 = 110, = 9.81, = 15.8). The fully unsteady CFD model and subsequently the stepwise steady model reproduced the PM separation and washout of the physical model testing for the RC and SHS. The findings from the washout CFD model demonstrate that neglecting PM washout leads to significantly underesti mate PM mass eluted from UOs such as the SHS where the PM storage zones are not volumetrically or hydraulically isolated from flows capable of re suspending and transporting PM from the UO (Figure D 24). The validated fully unsteady CFD model for PM washou t was then used to predict PM washout as function of flow rate (as the Q p of a hydrograph) and separated PM depth in the UO under steady conditions. These results allowed the integration of washout phenomena into the continuous simulation model. Based on t he time series of results generated from rainfall loadings for the representative year of 2007 on a 1.6 ha largely impervious Gainesville, FL catchment, the SHS unit is significantly more prone to PM washout than the RC. In comparison to the RC the washout of previously separated PM mass significantly deteriorates the annual performance of the SHS. The coupling of the stepwise steady CFD model with time domain continuous simulation also quantified the temporal evolution of PM separation, accumulation and w ashout for the RC and SHS. This temporal evolution across the year for any UO under any set of climate and catchment conditions is crucial to for maintenance and management of the UO to achieve targeted or promoted levels of treatment. The primary advanta ge of the continuous simulation model based on the stepwise steady CFD approach is the reduced computational overhead respect to fully unsteady CFD modeling. PAGE 136 136 The computational time is given by the sum of the modeling time to run steady flow CFD simulation and post processing time for the steady CFD results (total of 11 hours) and modeling time for running the MatLab code for a year of storm events (2 hour). The total time required for the time domain continuous simulation model presented in this study is 13 hours for a year of rainfall runoff events (133 events for the given watershed), in contrast to a fully unsteady CFD model which requires at least 20 hours to run only a single storm event. Time domain continuous simulation model base d on the stepwise steady CFD approach is valid for UOs, such as clarifier or HS subject to constant influent PM concentration and PSD. In future study, the continuous simulation model may be developed to consider variable influent PM concentration and PSD throughout the storm events. The coupling of a stepwise steady CFD model and time domain continuous simulation model provides a set of tools to quantify the capability of UOs to separate and retain PM on annual basis. Results are directly applicable to no t only UO separation behavior but also washout mis behavior; providing information needs to effectively maintain and manage UOs. Outcomes of this study indicate that, irrespective of intra SHS water chemistry degradation between events that the SHS should be maintained (cleaned) every half year. Specifically for the Gainesville, FL climate that exhibits two distinct seasons, wet and dry, maintenance of the SHS is required before the start and after the end of the wet season to reduce the impacts of PM wash out from the SHS. By comparison, the RC illustrated only a nominal quantity of PM mass washout through an entire year of loadings, with a maintenance interval that is at least one year and potentially up to two years, irrespective of intra RC water chemis try degradation. Although UOs, whether manufactured or constructed, are subject to testing and certification requirements before installation in situ, their treatment performance will deteriorate PAGE 137 137 without regular operation and maintenance inputs. Indeed, the storage of rainfall runoff and accumulation of PM mass will generate changing of water chemistry that can occur as rapidly as the mean time between events (2.5 days on an annual basis for 2007 in GNV) and an increasing intra event washout response with an increasing interval between UO maintenance. In particular the SHS demonstrated increasing washout during the year where the washout from the RC was only nominal event across the entire year. A stepwise steady CFD model coupled with time domain contin uous simulation is a method to predict the temporal PM elution and PM accumulation for a UO on a long term basis. PAGE 138 138 Figure 5 1. Hydrology analysis. In A) t he subject Gainesville, Fl (GNV) watershed for physical and continuous simulation (SWMM) modeling. In B) t ime of concentration as function of rainfall intensity for the watershed o f 1.6 ha, with 1% slope, 75% of imperviousness and silty sand soil. K sat D i represents the soil saturated hydraulic conductivity, initial soil moisture deficit and soil capilla ry suction head, respectively. In C) t he mean number of rainfall events for the period 1998 2011 as function of MIT. The knee of the curve represents the appropriate minimum inter event time, MIT. In D) Runoff and effluent PM mass eluted from the rectangular clarifier subject to the hydraulic loading generated from the watershed i n the month June 2007. The June 2007 results are illustrative of monthly time domain continuous results generated by the CFD stepwise steady model Watershed properties: Area is 75% paved k sat = 10.9 mm/h mm D i = 0.2 s N (impervious) = 0.017 A B L = 16 0 m Watershed area = 1.6 ha C D June 2007 MIT PAGE 139 139 Figure 5 2. Influent hydraulic loadings and PSDs. I n A) i nfluent particle size distribution (PSD) (plan v iew of clarifier shown in inset A) ). B) reports the scaled hydrographs obtained from design hyetographs described in Appendix In C) a n historical hydrograph collected on 8 July 2008 from Gainesville, Fl. In E ) and F) hydrographs loading the 3 ). In E) hydrographs generated from the scaling of hydrographs in B) respect to the maximum hydraulic capacity of the unit, Q d of 31 .1 L/s. In F) hydrograph generated from the scaling of historical hydrograph collected on 8 July 2008 in Gainesville, Florida in C) respect to the SHS`s Q d A B C D E F 7.3 m 1.8 m Influent PSD = 0.79 = 28 d 50 = 15 m s = 2.63 g/cm 3 b = 1.04 g/cm 3 Influent PSD = 0.79 = 28 d 50 = 15 m s = 2.63 g/cm 3 b = 1.04 g/cm 3 V C 12 m 3 V SHS 4 m 3 1.8 m Out flow D = 1.7m Inflow PAGE 140 140 Figure 5 3. Intra event effluent PM washout generated by physic ally validated CFD model. Plot A ) and B) generated from a triangular hyetograph loading the subject watershed; plots C ) and D) generated from the 8 July 2008 hydrograph. Plot E ) and F) generated from hydrographs of F igure 5 2B with Q p of 22 L/s a nd 35 L/s, respectively. Plots A ) C ) E ) F) generated with uniformly pluviated PM depth o f 5 mm while plot B ) and D) generated with 15 mm of PM across the bottom of the rectangular clarifier. The range bars represent duplica te samples taken at each discrete time across each hydrograph A B C D E F PAGE 141 141 Figure 5 4. CFD model of event based washout of PM at 50% and 100% of sediment capacity in sump area and no PM depth in the volute area, and also for 50% of PM capacity in sump area and 2.54 cm sediment depth in volute area for SHS (D =1.7m). The results are obtained at maximum hydraulic capacity, Q d of 31.1 L/s and for 1.25Q d In addition, CFD modeled overall washout results are reported for SHS unit (D = 1 m) subject to a hetero disperse PSD at flow rate of 10 L/s at 50% and 100% of PM capacity of sump area (no pre deposited PM in the volute area). The range bars indicate the variability of the measured duplicated physical model results SHS (D = 1 .7 m) Influent PSD = 9.81 = 15.8 d 50 = 110 m s = 2.63 g/cm 3 b = 1.04 g/cm 3 SHS (D = 1 m) Influent PSD = 0.58 = 271 d 50 = 67 m PAGE 142 142 Figure 5 5. CFD model of PM washout mass as a function of flow rate, Q for the rectangular clari fier and SHS unit In A) washout PM mass from the rectangular clarifier is shown for different PM dept hs ranging from 5 to 50 mm. In B) washout PM mass from the SHS is reported for 50% of PM capacity in sump area and PM depths in volute section ranging from 10 to 100 mm. In C) washout PM mass from the sump of SHS unit is shown for different PM depths ranging from 25 to 450 mm (no PM in volute region) A Influent PSD = 0.79 = 28 d 50 = 50 mm s = 2.63 g/cm 3 b = 1.04 g/cm 3 B C PAGE 143 143 Figure 5 6. Results from the continuous simulation model for 2007. In A ) and D) illustrate the flow limited washout from the RC and SHS where physical model data are fit by a power law. B ) and E) compare the effluent PM mass from a RC and SHS with and without PM washo ut as a function of month runoff. C ) and F) compare the accumulated uniform PM depth with and without washout for the RC and SHS. Results in F) produced by assuming PM mass accumulates first in the sump area (negligible PM deposition in the volute area) an d subsequently as the PM mass reaches 50% of the sump capacity, PM accumulates in the volute area. Influent PSD = 0.79 ; = 28 s = 2.63 g/cm 3 = 1.035 g/cm 3 C inf = 200 mg/L D C F A B E PAGE 144 144 Table 5 1. Physical and CFD model hydraulic loadings and washout PM results for the clarifier subject to the hydrographs shown in Figure 5 1(B) and (C) and the hetero disperse gradation shown in Figure 5 1(A). Q p Q d td, V, PM depth, RPD are peak flow, design flow rate, hydrograph duration, hydrograph volume, unsteadiness factor, depth of PM mass inside the system and relative percent difference, respect ively Rectangular clarifier, Q d =50 L/s Hydrologic event Washout results Q p t d V PM pluviation depth Effluent mass PM load RPD Measured Modeled (L/s) (min) (m 3) ( ) (mm) (g) (g) (%) 28 44 15 1.87 5 142 133 6.77 28 44 15 1.87 15 305 311 4.18 50 110 89 4.39 5 385 388 1.21 50 110 89 4.39 15 1071 1025 4.50 35 44 15 2.14 5 160 158 1.27 22 44 15 1.61 5 75 82 8.54 PAGE 145 145 Table 5 2. Measured and modeled washout PM are reported for two units, SHS (D = 1.7 m) and SHS (D = 1.0 m) along with the characteristics of the washout runs. RPD is the relative percent difference and Qd represents the design flow rate of the system Screened HS (D = 1.7 m), Q d = 31.1 L/s and (D = 1.0 m), Qd = 10 L/s PM pluviation Effluent mass depth in : PM load Q Unit dia. Volute Sump Measured Modeled RPD (L/s) (m) (mm) (mm) (Kg) (Kg) (%) 31.1 1.7 0 228 2.76 2.86 3.62 31.1 1.7 25.4 228 2.98 3.20 7.42 31.1 1.7 0 456 4.51 4.50 0.22 38.8 1.7 0 228 3.22 3.53 9.64 38.8 1.7 25.4 228 3.16 3.37 6.61 38.8 1.7 0 456 5.48 5.97 8.90 10.0 1.0 0 228 0.05 0.04 10.64 10.0 1.0 0 456 0.08 0.09 11.31 PAGE 146 146 Table 5 3. Unsteady and steady CFD PM washout results for rectangular clarifier and SHS (D = 1.7m). The unsteady results are obtained for the hydrographs shown in Figure 5 2(B) and (C) and Figure 5 2(E) and (F). Steady PM results are obtained from the steady CFD mod el subject to flow rate equal to peak flow rate of each hydrograph shown in Figure 5 2. RPD represents the relative percent difference between the fully unsteady and steady CFD model results Rectangular clarifier, Q d =50 L/s Q PM pluviation Effluent mass PM load RPD depth Steady Unsteady (L/s) (mm) (g) (g) (%) 28 5 147 133 10.38 28 15 342 311 10.12 50 5 410 380 7.78 50 15 1077 1025 5.09 35 5 180 158 13.67 22 5 91 82 11.41 Screened HS (D = 1.7m), Q d = 31.1 L/s Q PM pluviation depth Effluent mass PM load RPD Volute Sump Steady Unsteady L/s (mm) (mm) (Kg) (Kg) (%) 31.1 0 228 4.7 4.20 11.90 31.1 25.4 228 6.9 6.30 9.52 21.0 0 228 3.0 2.74 8.76 17.0 0 228 2.8 2.55 7.84 17.0 25.4 228 4.2 3.90 8.72 13.0 0 228 2.4 2.15 13.02 PAGE 147 147 C HAPTER 6 GLOBAL CONCLUSION This study developed a validated fully unsteady CFD model to predict PM separation and time dependent effluent PM of a BHS, a SHS and a RC, treatment units utilized worldwide for treatment of wet and dry weather flows subjected to fine and coarse hetero disperse PSD gradations. An accurate parameterization of MS, TS and DN was performed on the fully unsteady CFD model for BHS. Results (PM and PSD) demonstrated that the full scale CFD model was able to accurately predict the response of a full scale physical model across the range of quasi steady to highly unsteady flow loadings. Results also showed that TS and MS ha d a significant impact on time dependent profiles of PM indices. The influence of TS and MS also varie d for increasing A DN of 8 16 for this coarser hetero disperse PSD reproduce d effluent PM load. Results also demonstrated that increasing the model accuracy through higher MS, higher DN or smaller TS requires increasing computational effort. The validated CFD model of the RC was utilized to examine the hydraulic response of clarif iers retrofitted with baffles and loaded by unsteady stormwater inflows. Results indicated that the hydraulic response (as N, MI or RTD) of a baffled or un baffled basin was function of flow rate, and Le/L (as an equivalent L/W ratio). Given that storm water systems are loaded by a wide range of flows and a singular hydraulic response (whether as N, MI, VE or RTD) cannot be expected, although high number of baffles did confer a more consistent, reproducible response even subject to unsteadiness. Base d on physical and CFD model results, this study indicated that internal baffling d id alter unsteady hydraulic response and increase d PM separation. For stormwater UOs subject to a wide range of uncontrolled loadings, hydrograph was an important paramete r. While the full scale physical modeling system of this study PAGE 148 148 metered a constant PM concentration and PSD, the quest for a unique relationship between a particular hydraulic response (for example N) and PM or PSD elution from a stormwater clarifier was f urther complicated by the separate unsteadiness of PM and PSD inflows. To reduce the computational overhead of fully unsteady CFD model the stepwise steady CFD model based on the UH analog was introduced and tested. The stepwise steady flow model was val idated with measured physical model and it showed good agreement with results generated by unsteady CFD modeling for two Type I settling units, a RC and a BHS. The primary advantage of the stepwise steady CFD approach was to achieve a satisfactory modeling accuracy at a reduced computational overhead. The computational time required for the time domain continuous simulation model which include d steady CFD modeling, post processing and running the MatLab code for a year of storm events (a number of 133 even ts) was 13 hours in total. In contrast, a fully unsteady CFD model require d 13 hours at minimum to solely run one single hydrological event. This study demonstrated the auto sampling produced representative samples of PM eluted from a BHS for both finer a nd coarser PSDs, but it did not accurately characterize the influent samples for either PSDs. The auto sampling was not able to collect the coarser fraction of PSD (>75 m) to which was associated most of the influent PM mass. This study investigate d the ef fect of influent auto sampling in predicting effluent PM for a BHS and RC by using CFD model, demonstrating the importance of representative and accurate influent PM recovery was crucial not only in monitoring and testing but also for modeling purposes. F inally this study tested the stepwise steady flow CFD model coupled with a time domain continuous simulation model to simulate the long term response of the RC and SHS subject to unsteady hydrologic loading for PM separation and also washout at a reasonabl e computational PAGE 149 149 overhead. The findings from the washout CFD model demonstrate d that neglecting PM washout lead ed to significantly underestimate PM mass eluted from UOs such as the SHS where the PM storage zones were not volumetrically or hydraulically isol ated from flows capable of re suspending and transporting PM from the UO. The validated fully unsteady CFD model for PM washout was then used to predict PM washout as function of flow rate (as the Qp of a hydrograph) and separated PM depth in the UO under steady conditions. These results allowed the integration of washout phenomena into the continuous simulation model. Based on the time series of results generated from rainfall loadings for the representative year of 2007 on a 1.6 ha largely impervious Gain esville, FL catchment, the SHS unit was significantly more prone to PM washout than the RC. In comparison to the RC the washout of previously separated PM mass significantly deteriorates the annual performance of the SHS. The coupling of the stepwise stea dy CFD model with time domain continuous simulation was able to quantify the temporal evolution of PM separation, accumulation and washout for the RC and SHS. This temporal evolution across the year for any UO under any set of climate and catchment conditi ons is crucial for maintenance and management of the UO to achieve targeted or promoted levels of treatment. In conclusion, this investigation provided a quantitative assessment of modeling accuracy for different TS and MS subject to hydrograph unsteadine ss with results that were validated from a monitored physical model. This set of results represent ed a detailed and useful guideline for modelers in selecting or evaluating computational parameters as a function of loading unsteadiness in order to balance model accuracy, computing time and computational resources. Furthermore, the coupling of a stepwise steady CFD model and time domain continuous simulation model represented a valuable set of tools to quantify the capability of UOs to separate PAGE 150 150 and retain PM on annual basis and to provide necessary information to effectively maintain and manage UOs. PAGE 151 151 APPENDIX A TRANSIENT ELUTION OF PARTICULATE MATTER FROM HYDRODYNAMIC UNIT OPERATIONS AS A FUNCTION OF COMPUTATIONAL PARAMETERS AND HYDROGRAPH UNSTEADINESS Detailed Sampling Methodology and Protocol Effluent Sampling The sampling is conducted according the following procedure. During the test running time, representative efflue nt samples are taken manually across the entire cross section of the effluent section of the unit as discrete samples in 1L wide mouthed bottles. Samples are collected in duplicate through the entire duration of the run at variable time sampling frequency according to the flow rate gradients and event duration to provide a reasonable estimate of effluent variability of PM concentration and PSD. The minimum sampling time interval is 1 minute. The sampling protocol used to characterize the supernatant PSD con sists of taking a duplicate sample at the geometric midpoint of the supernatant after overnight settling. In particular, four PSD and SSC duplicate samples are taken at four evenly spaced intervals of height of the stored supernatant volume. Mass Recovery and Sample Protocol After the supernatant sample has been collected the wet slurry from the system is recovered from the bottom of the unit by manually sweeping it through the washout points into buckets and taken to the laboratory where they are allowed to stand for quiescent settling and dried in glass trays at 105 degrees Celsius in an oven. After the slurry completely dries the dry silica is disaggregated and collected in pre weighed glass bottles and the gross weight is recorded to find the overall ef ficiency of the system based on mass and for the mass balance. Laser diffraction analysis for the collected dry sample is then performed to analyze the PSD of the captured particle. PAGE 152 152 Laboratory Analysis The experimental analyses include PSD measurements for influent, effluent and captured PM by laser diffraction analysis, effluent gravimetric analysis based on PM concentration as suspended solid concentration (SSC). SSC analysis is performed to quantify particle concentration for each effluent composite samp le as collected from each run and to calculate the effluent mass load for the operating flow rates. Fully characterizing the entire PSD and utilizing SSC allow a mass balance to be conducted which is not possible when utilizing an index component and metho d of PM, such as total suspended solids, TSS. The protocol specifically followed for this laboratory analysis is the ASTM D 3977 (Jillavenkatesa et al., 2001). To perform the PSD analysis the Malvern Mastersizer 2000, a commercial laser diffraction analyz er is utilized in this experimental analysis. The instrument technology is based on laser diffraction, occurring when a laser beam passing through a dispersion of particles in air or in a liquid is diffracted at the particle surface. The angle of diffracti on is influenced by the size and the shape of the particle. As the particle size decreases, the scattering angle increases (Kim and Sansalone, 2008). in spherical diameter. During a sample measurement, the instrument is programmed to characterize the PSD three times. These three PSD curves are then analyzed for stability to ensure that the measurement settings for the instrument are adequately suited for the sample and to ensure t hat any bubbles that might be present and affect the reliability of the measurement are purged from the system. The three measured and stable PSDs for the individual sample are averaged into a representative curve for that sample. An event mean PSD is ge nerated from averaging the individual Mastersizer measurements (both A and B). Finally, the captured PSD is measured with the laser diffraction analyzer in dry phase. In order to representatively sub sample the dry mass the silica is uniformly mixed to obt ain a sub PAGE 153 153 sample as representative as is physica lly obtainable. Duplicate 20 g samples are taken for the dry phase of the laser diffraction analyzer. The dry dispersion cell is connected to the laser diffraction analyzer and the dry sample is measured by forming a PM aerosol with a high pressure, high velocity air stream. The PSDs measured are observed for stability and averaged. Verification of Mass Balance A mass balance evaluation is conducted to ensure representative and defensible event based treatm ent performance results for the unit. The PM mass balance is calculated from dried captured mass, effluent mass load, and supernatant mass load. The mass balance error (MBE) criteria is 10% MBE and determined by the following equation (ASTM, 200 0 ): where In the mass balance expression M inf is influent mass load and C eff is effluent concentration which varies with time, t i M sep is separated PM recovered. Verification of PSD Balance The gravimetric PSD of the effluent, supernatant and recovered mass is measured and compared with that of the influent to verify the balance of influent and effluent PSDs. This QC measurement is performed by quantifying the deviation between the r epresentative silt influent loading and the summation PSD of the effluent, recovered, and supernatant mass. ( A 1) ( A 2 ) ( A 3 ) PAGE 154 154 In this expression each i is a discrete measurement at a specific particle size of the cumulative PSD. Results un der S teady C ondition Experimental testing runs were performed on a full scale baffled HS unit located at the testing Gainesville, FL. In this section, the monito ring data collected from the experimental tests are reported. In this analysis the particulate matter removal efficiency of the system is analyzed when it is subjected to the influent NJDEP gradation. Testing experiments were carried out at 2, 5, 10, 25, 50, 75, 100, and 125 percent of the design flow rate (0 18 L/s ) and at influent NJCAT sediment concentrations of 100 mg/L. The run operational parameters and the treatment run results for baffled HS are summarized in T able A 1. The treatment efficiencies obtained from the physical model are compared graphically below to the CFD modeled efficiencies under steady conditions To assess the accuracy of the CFD results with the monitoring data, the relative percentage difference (RPD) is computed. In particular, the RPD is calculated on the basis of the baffled HS removal efficiency values calculated experimentally as effluent event mean concentration ( EMC). The RPDs computed are 4.5% for influent PM concentration of 100 mg/L. The values obtained are within the control limit defined for RPD, which is 10%. M orsi and Alexander K V alues (Morsi and Alexander, 1972) In equations 2 10 to 2 12 Re i is the Reynolds number for a particle, and C D i is the drag coefficient. ( A 4 ) PAGE 155 155 ( A 5 ) ( A 6 ) In th ese equation s is fluid density, p is particle density, v i is fluid velocity, v pi is particle velocity d p is particle diameter, is dynamic viscosity, K 1 ,K 2 ,K 3 are empirical constants as a function of particle Re i Morsi and Alexander K values as function of Reynolds number are reported in Table A 2. Effect of T emperature To verify the hypothesis tha t the temperature does not significantly impact the PM remov al efficiency of Type I settling unit, a set of steady state simulations are performed in CFD on a HS system. The unit is loaded with a hetero disperse PM gradation and the effluent PSDs are predicted for a wide range of temperature. The temperature s inves tigated are 1, 5, 10, 15 and 20. The results show ed in Figures A 7 demonstrate that temperature variation does not significantly influence the effluent PSD of PM eluted from a HS unit. PAGE 156 156 Figure A 1 Validation of measured vs. modeled PM separation for the HS subject to the hetero disperse PSD loading at a gravimetric PM concentration of 100 mg/L at steady flow rates PAGE 157 157 Figure A 2 Effluent PSDs measured by laser diffraction analysis for differing hydrographs. Effluent PSDs for highly unsteady hydrograph (A B), unsteady hydrograph (C D), quasi unsteady hydrograph (E F). The PSDs reported are produced in effluent by the baffled HS loaded by a hetero disperse PSD. The measured influent gradation is in each plot shown in gray dots on the left side Q + Q Influent gradation 0 < t/t d <0.2 Q + Q Influent gradation 0 < t/t d <0.4 0.4 < t/t d <1 Q + Q Influent gradation 0 < t/t d <0.2 0.2 < t/t d <1 Influent gradation Influent gradation Influent gradation Q p = 18 L/s t d = 74 min Q p = 18 L/s t d = 74 min Q p = 9 L/s t d = 87 min Q p = 9 L/s t d = 87 min Q p = 4.5 L/s t d = 125 min Q p = 4.5 L/s t d = 125 min A B C D E F PAGE 158 158 Figure A 3 Effect of time step (TS) on modeled effluent PM at DN = 16 and MS = 3.1*10 6 for three hydrologic unsteadiness levels investigated respectively, highly unsteady, unsteady and quasi steady. The CFD model results are compared to t he measured data. The value of e n calculated respect to the measured data is reported for each time step explored A B C PAGE 159 159 Figure A 4 Normalized root mean squared error (e n ) of CFD model effluent PM as function of time step for three levels of hydrologic event unsteadiness investigated The error is calculated based on the measured effluent data. The model parameters are PSD discretization number (DN) of 16 and computational domain mesh size (MS) of 3.1 x 10 6 A B C D PAGE 160 160 Figure A 5 Effect of mesh size (MS) on modeled effluent PM at DN = 16 and TS = 10 sec for three hydrographs investigated respectively, A) highly unsteady, B) unsteady and C) quasi steady. The CFD model results are compared to the measured data. The value of en calculated respect to the measured data is reported for each time step explored A B C PAGE 161 161 Figure A 6 Captured CFD model particle size distribution (PSD) at TS = 10 sec, MS = 3.1*10 6 DN = 16, 32, 64 generated by baffled HS loaded by an influent hetero disperse PSD for three hydrographs investigated, respectively, A) highly unsteady B) unsteady and C) qu asi steady The modeled PSD results are compared to measured data. t r represents the overall computational time employed to run each simulation A B C PAGE 162 162 Figure A 7. Effect of temperature on PM removal percentage of HS unit subject to the hetero disperse PM gradation of this study at the peak flow rate of 18 L/s PAGE 163 163 Figure A 8 CFD model snapshots. Pathlines are colored by velocity magnitude (m/s) PAGE 164 164 Table A 1. Experim ental matrix and summary of treatment run results for the baffled HS unit loaded by a hetero disperse (NJDEP) gradation under 100 mg/L and various operating flow rates Flow rate Influent conc. Influent mass load Effluent conc. a Effluent mass load Total mass captured b MBE Design Actual Target Actual (%) (gpm) [mg/L] [mg/L] (g) [mg/L] (g) (g) (%) 100 294.0 100 97.8 3375 48.0 1655 1802 2.4 125 364.6 100 98.5 3375 46.3 1588 1747 1.2 10 29.3 100 97.8 3375 29.8 1028 2660 9.3 25 73.2 100 96.5 3375 36.0 1242 2225 2.7 75 220.1 100 96.9 3375 44.5 1551 1885 1.8 2 5.4 100 106.0 1042 11.1 109 917 1.5 50 146.8 100 97.8 3375 37.6 1295 2318 7.1 5 16.6 100 86.3 2606 14.8 448 2186 1.1 Note: a Effluent event mean concentration b Total mass captured is the sum of suspended PM in supernatant and settled PM recovered as wet slurry from the unit Table A 2 Morsi and Alexander constants for the equation fit of the drag coefficient for a sphere Reynolds Number K1 K2 K3 <0.1 24.0 0 0 0.1 < Re < 1 22.73 0.0903 3.69 1 < Re < 10 29.16 3.8889 1.222 10 < Re < 100 46.5 116.67 0.6167 100 < Re < 1000 98.33 2778 0.3644 1000 < Re < 5000 148.62 4.75 10 4 0.357 5000 < Re < 10,000 490.54 57.87 10 4 0.46 10,000 < Re < 50,000 1662.5 5.4167 10 6 0.5191 PAGE 165 165 APPENDIX B HYDRAULIC RESPONSE AS A FUNCTION OF FLOW, UNSTEADINESS AND Full scale P hysical M odel S etup The analysis is carried out on full scale physical models of primary clarifiers, which represent the most traditional and common clarification systems used in rainfall runoff PM treatment. The first configuration is a rectangular clarifier, approximately 1.87 m tall, 1.8 m wide and 7.31 m long with hydraulic capacity of approximately 12,000 L. The second configuration has the same geometrical characteristics of the first one, but with eleven baffles placed in the unit to avoid the potential for short circuiting. The baffles have a length of 1.22 m and inter distance of 0.61 m. The distance from the edge of the baffles to the wall, O, is 0.60 m. The influent and effluent pipe diameters are of 0.2 m. Two units are characterized by the same surface area. The design flow rate, Q d of the physi cal model is about 50 L/s, corresponding to the hydraulic capacity of physical model as an open channel system. (NaCl). The flow rates tested are 1, 2.5 5 12.5, 25 37.5 and 50 L/s ( respectively, 2, 5, 10, 25, 50, 75 and 100% of the design flow rate, Q d ). RTD experiments are conducted at constant flow rate by injecting a single pulse of a known volume of tracer into the drop box upstream of the clarifier Prior to tr acer injection, the conductivity of the potable water used for background testing is measured. A calibrated conductivity probe, manufactured by YSI Inc., is placed fully submerged at the outlet section of the clarifier to take real time conductivity measur ements every 5 seconds. The running time of the experiments is based on the time taken by the conductivity to drop back to the background (potable water) conductivity. A calibration curve is developed to establish the relationship between concentrations an d conductivity. The concentrations are thus PAGE 166 166 calculated from conductivity measurements. Each tracer run is validated by a mass balance check with an allowable error of +/ 10 %. The mass recovery percent is reported in Table B 1 for the tracer tests. To vali date the CFD model under transient conditions, effluent PM and PSDs eluted from the full scale rectangular clarifier with no baffles and 11 transverse baffles subjected to two hydrological events are collected. The first hydrograph is generated from a tria ngular hyetograph with 12.7 mm (0.5 inch) of rainfall depth and duration of 15 minutes. This loading is selected as a common short and intense rainfall event during the wet season in Florida (Figure B 1 2). The second hydrograph is generated from a h istorical event collected on 8 July 2008 in Gainesville, Florida with total rainfall depth of 71 mm. This event is chosen since it is an extremely intense historical event, with a peak rainfall inten sity of about 165 mm/h (Figure B 3). The particle size di stribution (PSD) used is reported in Figure B 4 and is a fine hetero disperse gradation classified from Unified Soil Classification System (USCS) as SM I with a d 50 of 18 m. The hyetographs are transformed to event based hydrographs by using Storm Water M anagement Model (SWMM) ( Huber and Dickinson, 1988 ) for each physical and CFD model. The objective of the rainfall runoff simulations is to generate unsteady runoff flow loadings for the scaled physical model and CFD model. In this transformation from rainf all to runoff for the scaled physical basins, the watershed area is matched to deliver peak runoff flow rates equal to the design flow rate of the unit operation. More details information about the two hydrographs utilized for the validation are reported i n Appendix (Figure B 5). The protocol used to retrieve the experimental data for the validation of transient CFD model is the same as that described in Garofalo and Sansalone (Garofalo and Sansalone, 2011) and for brevity not reported here. In PAGE 167 167 Appendix, th e generation of the two hydrographs utilized is explained in detail. The results retrieved from the experiments are reported in Table B 2. Generation of H ydrographs U sed for the V alidation of the F ull S cale P hysical M odel of Clarifier under T ransient C ondi tions Study Hyetographs An essential component of this study is the definition of the hydrological loadings. The three hyetographs selected are: Triangular hyetograph with 12.7 mm (0.5 inches) of rainfall volume and duration of 15 minutes. This loading is selected as a common short and intense rainfall event during the wet season in Florida. A triangular shape is used to define the hyetograph as shown in Figure B 1 (Chow et al., 2008). The maximum rainfall intensity of the triangular hyetograph is approximately 101 mm per hour (4 inches per hour) and the total excess precipitation depth is 12.7 mm (0.5 inches). The hyetograph selected is considered a fairly extreme event, since 80% of s torm events occurring in Gainesville are characterized by a total precipitation depth equal or less than 12.7 mm (0.5 inches). Figure B 2 reported bel ow depicts the frequency distribution of 1999 2008 hourly rainfall data for Gainesville Regional Airport (KGNV). Historical event collected on 8 July 2008 by UF with total rainfall depth of 71 mm. This event is chosen since it is an extremely intense historical event, with a peak rainfall intensity of about 165 mm/h (Figure B 3). This value is higher than peak precipitation intensity of the 24 hour 25 year design storm described in the following paragraph. Particle Size Distribution PSD Selection The influent particulate loading used throughout the entire study for CFD wet pond simulation runs and experimental full scale physical mode l testing consists of a PSD that is in the silt size range. The PSD, ranging from less than 1 m to 75 m is reported in Figure B 4 The PM specific gravity is 2.63 g/cm 3 The m ass based PSD is well described by a gamma distribution function. The probabili ty density function is given by Equation B 1 as a function of particle diameter d, where is a distribution shape factor and a scaling parameter. The cumulative gamma distribution function is expressed in Equation B 2 PAGE 168 168 PSD Significance PM is widely recognized as a primary vehicle for the transport and partitioning of pollutants. Moreover, PM is a pollutant itself that impacts the deterioration of receiving surface water s. The potential for water chemistry impairment strongly depends on PM loading and PSD. Furthermore, many PM bound constituents, such as metals, nutrients and other pollutants, partition to and from PM while transported by PM through rainfall runoff events Therefore, PSD plays an important role in the transport and chemical processes occurring in urban stormwater runoff and an understanding of its behavior is crucial for the analysis and the selection of unit operations. Transformation of R ainfall H yetogra phs to R unoff H ydrographs The hyetographs reported in Figure B 1 and B 3 are transformed to event based hydrographs by using the Storm Water Management Model (SWMM) (Huber and Dickinson, 1988) for each physical and CFD model. The objective of the rainfall runoff simulations is to generate unsteady runoff flow loadings for the scaled physical model and CFD model. SWMM translates rainfall in runoff for th e specific catchment properties. In this transformation the watershed area is matched to delive r peak runoff flow rate equal to the design flow rate of the unit operation. As shown pereviously, July 8 th 2008 historical hyetograph is characterized by the highest rainfall peak intensity (approximately 165 mm /h) in comparison to the other selected hyet ographs. Therefore, the historical hyetograph is utilized as a reference to perform the flow scaling of the physical testing model. Since the maximum (B 1) (B 2) PAGE 169 169 hydrualic load of the physical models is 50 L/s the area of the catchment implemented in SWMM is defined to deliver peak flow rate equal to 50 L/s for the historical storm of 8 July 2008. The modeling parameters adopted are referred to an asphalt pavement of a typical airport runway/taxiway. Green Ampt method is used to model infiltration process. T he rainf all runoff modeling for the three hyetographs are shown in Figure B 5 Definition of N The tanks in series model equation is given by (Levespiel, 2002): Because the total reactor volume is nV i then the residence time in one of the reactor, i is equal to /n, where t is the total volume divided by the flow rate, Q: where =t/ The number of tanks in series can be determined by calculating the dimensionless variance from a tracer study: which can be proved equal to: (B 3) (B 4) (B 5) (B 6) PAGE 170 170 For the tanks in series model it is possible to define simple relations between the parameters of the distribution and the variance (Kandlec and Wallace, 2009). For instance the tanks in series model has a dimensionless variance given by: From this expression we can derive that (Letterman, 1999) In Figure B 6 the relationship between N tanks in series parameter obtained from Equation B 7 8 is shown. The relationship is linear and the coefficients of the regression line suggest that is approximately a bisector. Geometry and M esh G eneration of F ull S cale R ectangular C larifier The mesh is comprised of tetrahedral elements and it is checked carefully to ensure that equiangle skewness and local variations in c ell size are minimized in order to produce a high quality mesh. Several iterations of grid refinement are performed to determine the necessary mesh density that balances the accuracy of the solution with the exponentially increasing demand on computationa l resources. The final mesh used in this study is discretized into approximately 3.5 million cells (Figure B 7 8). Turbulent Dispersion Model The dispersion of particles due to turbulence in the fluid phase is predicted using stochastic tracking model as m entioned (Thomson, 1987; Hutchinson et al., 1971; Jacobsen, 2008). In this model, the turbulent dispersion of particles is predicted by integrating the trajectory equation for individual particles (Eq. B 3 11) using the instantaneous fluid velocity, along the particle path during the integration. The random effects of turbulence on particle dispersion are (B 7) (B 8) PAGE 171 171 considered by computing the trajectory for a sufficient number of representative particles. In this approach, the interaction of a particle with a succession of discrete turbulent eddies is simulated. Each eddy is characterized by Gaussian distributed random velocity fluctuations, and w and a timescale of interaction. The velocity fluctuations are related to the local turbule nt kinetic energy as: where is a normally distributed random number. The characteristic eddy lifetime is expressed in terms of the local values of k and e: where r is the uniformly distributed random number between 0 and 1 and C L is a constant having a value of about 0.15. The particle is assumed to interact with the fluid phase e ddy over this lifetime, after which a new value of the instantaneous velocity is obtained by sampling again. CFD Modeling and P opulation B alance A population balance model (PBM) is coupled with CFD to model PM separation. Assuming no flocculation in the dispersed p article phase, the PBM equation (Jacobsen, 2008) and mass per particle, p n are as follows. M is PM mass associated with the particle size range as function of injection time N is the total number of particles injected at the inlet section, and t d is the event duration. (B 9) (B 10) (B 11) (B 12) PAGE 172 172 Validation A nalysis of S teady RTDs and PM S eparation E fficiency on F ull S cale P hysical M odel of R ectangular C larifier The validation analysis consists of two parts. First part comprises a comparison between measured and CFD modeled RTD curves for the full scale physical model of the no baffle rectangular clarifier. The second part includes t he validation of CFD modeled data in terms of PM removal efficiency for the trapezoidal cross section clarifier and the rectangular clarifier wi th no baffle and with 11 baffles. The CFD model is loaded with two hydrographs summarized in Table B 2. For RTD validation, a root mean squared error, RMSE was used to evaluate CFD model error in predicting RTDs with respect to the full scale physical model data: In this equation x o is the measured and x m the modeled variable. The error reported in Table S1 shows that RMSEs between CFD model RTDs and measured RTDs are within 10%. The comparison between measured and CFD modeled RTDs are graphically reported in Figure B 3 6 The validation of CFD modeled data in terms of PM removal efficiency is performed as follows. The error between the measured and modeled removal efficiency is computed as relative percentage error, given by: Where mod is the modeled PM removal efficiency and meas is the measured PM removal efficiency. The error between the measured and modeled event based PSDs is also calculated as a RMSE. (B 13 ) (B 14) PAGE 173 173 Figure B 1. Triangular hyetograph. Td is the recession time, ta is the time to peak, a nd r is the storm advancement coefficient Figure B 2. Frequency distribution of rainfall precipitation for Gainesville, Florida. The frequency distribution is obtained from a series of 1999 2008 hourly precipitation data for Gainesville Regional Airport (KGNV) PAGE 174 174 Figure B 3. Historical event collected on 8 July 2008 Figure B 4. Influent PSD for fine PM {SM I, <75 m}. SM is sandy silt in the Unified Soil Classification System (USCS). SM is SCS 75. PSD data are fit by gamma function (GF) based on distribution parameters, shape factor and scale factor, g / c m 3 PAGE 175 175 Figure B 5. Hydraulic loadings utilized for full scale physical model. The rainfall runoff modeling is performed in Storm Water Management Model (SWMM) for the catchment. The two hydrologic events investigated are: A) triangular hyetograph and B) historical 8 Jul y 2008 loading hydrologic event Q p = 28.3 L/s T tot = 93 min V = 1,541 L Q p = 50 L/s T tot = 248 min V = 89,000 L A B PAGE 176 176 Figure B 6. Relationship between N tanks in series computed from the inverse of the RTD variance and the ratio between median residence time and the difference between median and peak residence time PAGE 177 177 Figure B 7. Isometric view of full scale physical model and mesh of the rectangular cross section clarifier with eleven baffles Outlet 7.3 m 0.60 m 1.2 m 1.67 m Vertical Wall Free surface PAGE 178 178 Figure B 8. Isometric view of full scale physical model and mesh of the rectangular cross section clarifier Inlet Outlet 7. 3 m 1.67 m 1.4 m PAGE 179 179 Figure S9. Grid convergence Figure B 9. Grid convergence for full scale rectangular clarifier. The mesh utilized comprimes 3.1*10 6 tetrahedral cells Mesh size utilized PAGE 180 180 Figure B 10. Physical and CFD Modeled RTDs for flow rates, representing 100%, 50%, 10% and 5% of Q d on no baffle rectangular clarifier PAGE 181 181 Figure B 11. Physical mode l and CFD model results for the tri angular hydrograph used for the validation analysis for full scale physical model of a rectangular clarifier and a rectangular clarifier with 11 transverse baffles. In A) and C) results for PM and PSDs for the rectangular clarifier. In B) and D) results for PM and PSDs for the rectangular clarifier with 11 baffles. Q p is the peak influent flow rate and td is the total duration of the hydrological event. In C ), and D) the shaded area indicates the range of v ariation of effluent PSDs throughout the hydrological events. RMSE is the root mean squared error between effluent average measured and modeled PSDs, s is the particle density, Q p is the peak influent flow rate and td is the total duration of the hydrolog ical event A B C D PAGE 182 182 Figure B 12. Velocity magnitude (m/s) contours at a horizontal plane at mid depth for the configuration with transverse baffles and opening of 0.60 m Inlet Out let Inlet Out let Inlet Out let PAGE 183 183 Figure B 13. Velocity magnitude (m/s) contours at a horizontal plane at mid depth for the configuration with transverse baffles and opening of 0.20 m Inlet Out let Inlet Out let Inlet Out let PAGE 184 184 Figure B 14. Velocity magnitude (m/s) contours at a horizontal plane at mid depth for the configuration with longitudinal baffles Inlet Out let Inlet Out let Inlet Out let PAGE 185 185 Figure B 15. Morrill index as function of clarifier flow path tortuosity, Le/L for the clarifier configurations with transverse and longitudinal internal baffling. O is the opening between the baf fle edges and the clarifier walls. Q n is the normalized flow rate with respect to the hydraulic design flow rate, Q d of 50 L/s A B Equivalent length to width, L/W 6.6 4 262 35 118 .00 4 38 103 328 Equivalent length to width, L/W Transverse baffles (O = 0.2 m) Longitudinal baffles PAGE 186 186 Table B 1. Summary of measured and modeled treatment performance results for full scale rectangular clarifier (RC) and rectangular clarifier with 11 baffle clarifier (B11) loaded by hetero disperse silt particle size gradation for two different hydrological events. V t is the total influent volume, Q p is the peak influent flow rate, T tot is the duration of the hydrological event, measured is measured PM removal efficiency, modeled i s modeled PM removal efficiency and is absolute percentage error, and represen t the gamma parameters for effluent measured PSDs. The gamma parameters for the influent PSD are respectively 0.8 and 29 Hydrograph Type Q p V t t d measured modeled PSD model (L/s) (L) (min) (%) (%) % Triangular RC 28.4 15.1 44 88.38 88.4 0.07 0.97 20.15 8 July 08 RC 50.8 88.9 110 56.78 51.7 9.03 0.90 18.00 Triangular B11 28.4 15.1 44 98.34 98 0.34 0.87 23.00 8 July 08 B11 50.8 88.9 110 71.32 68 4.65 1.20 16.60 Table B 2. Summary of RTD test for pilot scale rectangular cross section linear clarifier configuration loaded with sodium chloride injected as a pulse at t = 0. Q n is the normalized flow rate, Q respect to the design flow rate, Q d of 50 L/s is residence time and RMSE is root mean squared error Q n Q Mass Recovery RMSE L/s min % % 1.00 50.00 6.2 92.0 0.3 0.75 37.50 8.3 93.5 0.2 0.50 25.00 12.4 95.7 0.4 0.25 12.50 24.9 95.8 0.5 0.10 5.00 62.2 96.9 0.4 0.03 2.50 248.8 95.5 1.7 0.01 1.00 622.0 97.4 2.5 PAGE 187 187 Table B 3. Number of baffles and corresponding value of tortuosity, Le/L for the rectangular clarifier with (1) transverse baffles and opening of 0.60 m, (2) with transverse baffles and opening of 0.20 m, (3) with longitudinal baffles Number of baffle s L e /L (1) L e /L (2) L e /L (3) 0 1.00 1.00 1.00 2 3.16 3 1.66 1.88 4 5.11 5 1.99 8 9.00 11 2.97 3.63 17 3.96 23 4.95 6.48 29 5.93 35 7.08 9.11 Table B 4. Parameter values of the curves used to fit the volumetric efficiency, VE data versus tortuosity, L e /L for each flow rate, Q n for the clarifier configuration with longitudinal baffles and opening of 0.20 m. In the equation, a represents the maximum value o f VE, b the rate of VE variation for unity change of tortuosity Q n Q (L/s) a b x o R 2 1.00 50.0 83.84 1.12 2.72 0.99 0.75 37.5 84.27 1.11 2.84 0.99 0.50 25.0 84.92 1.09 3.06 0.99 0.25 12.5 85.00 1.14 3.43 0.99 0.10 5.0 85.38 1.35 3.80 0.99 0.05 2.5 87.96 1.65 4.25 0.99 0.02 1.0 98.46 2.22 5.33 0.98 PAGE 188 188 Table B 5. Parameter values of the curves used to fit the volumetric efficiency, VE data versus tortuosity, L e /L for each flow rate, Q n for the clarifier configuration with transverse baffles. In the equation, a represents the maximum value of VE, b the rate of VE variation for unity change of tortuosity Q n Q (L/s) a b x o R 2 1.00 50.0 88.20 0.96 2.75 0.99 0.75 37.5 87.70 0.94 2.87 0.99 0.50 25.0 86.52 0.88 3.04 0.99 0.25 12.5 88.20 0.94 3.48 0.99 0.10 5.0 87.24 0.98 3.95 0.99 0.05 2.5 88.50 1.23 4.27 0.99 0.02 1.0 93.37 1.64 4.92 0.99 Table B 6. Parameter values of the curves used to fit the Morrill index, MI data versus tortuosity, Le/L for each flow rate, Q n for the clarifier configuration with longitudinal baffles and opening of 0.20 m. In the equation, a represents the maximum value of MI, b the rate of MI variation for unity change of tortuosity, y o the minimum value of MI Q n Q (L/s) a b y o R 2 1.00 50.0 19.13 1.11 1.26 0.99 0.75 37.5 23.75 1.17 1.26 0.99 0.50 25.0 29.46 1.17 1.26 0.99 0.25 12.5 36.45 1.11 1.28 0.99 0.10 5.0 50.31 1.31 1.46 0.99 0.05 2.5 82.53 1.67 1.68 0.99 0.02 1.0 83.22 1.60 1.70 0.99 PAGE 189 189 Table B 7. Parameter values of the curves used to fit the Morrill index, MI data versus tortuosity, L e /L for each flow rate, Q n for the clarifier configuration with transverse baffles. In the equation, a represents the maximum value of MI, b the rate of MI variation for unity change of tortuosity, y o the minimum value of MI Q n Q (L/s) a b y o R 2 1.00 50.0 17.10 0.98 1.12 0.99 0.75 37.5 20.23 0.99 1.13 0.99 0.50 25.0 25.30 1.00 1.13 0.99 0.25 12.5 30.37 0.91 1.09 0.99 0.10 5.0 30.00 0.75 1.02 0.99 0.05 2.5 36.06 0.81 1.13 0.99 0.02 1.0 41.38 0.88 1.33 0.99 Table B 8. Parameter values of the curves used to fit the N data versus tortuosity, L e /L for each flow rate, Q n for the clarifier configuration with longitudinal baffles and opening of 0.20 m. In the equation, a represents the maximum value of N, b the rate of N var iation for unity change of tortuosity, x o the minimum value of N Q n Q (L/s) a b x o R 2 1.00 50.0 313.50 1.23 7.42 0.99 0.75 37.5 160.90 1.34 6.95 0.99 0.50 25.0 2061.00 2.34 16.07 0.99 0.25 12.5 12680.00 2.40 21.17 0.99 0.10 5.0 120.00 1.61 8.60 0.99 0.05 2.5 95.00 1.49 8.12 0.99 0.02 1.0 43.42 0.82 6.36 0.99 Table B 9. Parameter values of the curves used to fit the N data versus tortuosity, L e /L for each flow rate, Q n for the clarifier configuration with transverse baffles. In the equation, a represents the maximum value of N, b the rate of N variation for unity change of tortuosity, x o the minimum value of N Q n Q (L/s) a b x o R 2 1.00 50.0 646.40 1.12 7.60 0.99 0.75 37.5 398.90 1.14 7.08 0.99 0.50 25.0 216.00 1.03 6.19 0.99 0.25 12.5 60.88 0.57 4.32 0.99 0.10 5.0 28.88 0.54 4.87 0.99 0.05 2.5 20.22 0.53 3.65 0.99 0.02 1.0 13.45 0.51 3.21 0.99 PAGE 190 190 Table B 10. Parameter values of the curves used to fit the MI data for different degrees of unsteadiness, Qn for the clarifier configuration with transverse baffles and opening of 0.20 m. In the equation, a represents the maximum value of MI, b the rate of MI variati on for unity change of tortuosity, yo the minimum value of MI Descriptor a b y o R 2 Quasi steady 0.01 22.67 1.18 1.24 0.99 Unsteady 0.33 11.39 0.92 1.26 0.99 Highly Unsteady 1.54 5.61 0.62 1.27 0.97 Table B 11. Parameter values of the curves used to fit the N data for different degrees of unsteadiness, Qn for the clarifier configuration with transverse baffles and opening of 0.20 m. In the equation, a represents the maximum value of N, b the rate of N variation for unity change of tortuosity, xo the minimum value of N Descriptor a b x o R 2 Quasi steady 0.01 77.21 1.26 5.60 0.99 Unsteady 0.33 83.30 1.20 5.46 0.99 Highly Unsteady 1.54 84.10 0.89 4.27 0.99 PAGE 191 191 APPENDIX C SUPPLEMENTAL INFORMATION A STEPWISE STEADY FLOW CFD MODEL PREDICT PM SEPARATION FROM STORMWATER UNIT OPERATIONS AS A FUNCTION OF HYDROGRAPH UNSTEADINESS AND PM GRANULOMETRY? Stepwise S teady F low M odel The conceptual foundation for stepwise steady flow model is analogous to the u nit hydrograph theory used to predict surface watershed runof f (Chow et al., 1988). The unit hydrograph represents the unit response function of a linear hydrologic system. The assumptions of the unit hydrograph theory are the system (watershed) is linear and the unit hydrograph response function, U is time invariant and unique for a given watershed (Chow et al., 1988). Define P n m the effluent flow rate as shown in Figure C 7 The discrete convolution equation allows the computa tion of direct runoff Q m given excess rainfall P n : Based on the assumption that a unit operation can b e idealized as a hydrological watershed in this study, the concept of UH is applied to unit operations, subjected to unst eady hydraulic and PM loadings as shown in Figure C 8 The main assumptions of the stepwise steady flow model are: UO is a linear system U p is unique f or a given UO flow rate and PSD Let I be the event based influent PM for a given PSD. I m represents the influent PM for a given PSD and a fixed time step, t, delivered into the system at Q m U p is function of flow rate, Q m ; therefore, let define U p ,Q m the UO response to I m for the specific flow rate, Q m ( Figure C 9 10 ) U p ,Q m is computed from steady CFD models. The UO is assumed to be a linear system. (C 1 ) PAGE 192 192 Based on this assumption the event based effluent mass PM E can be modeled as sum (convolution) of th e responses U p ,Q m to inputs I m The effluent mass PM at each time step t, E n is given by the discrete convolution equation: In these expressions, n and m are the number of steps in which the effluent PM distribution and the influent hydrograph are respectively discretized. The stepwise steady CFD model approach consists of the following steps. Steady CFD model is run for seven steady flow rates (100 %, 75%, 50%, 25%, 10%, 5%, 2% of the design flow rate) for each unit. The CFD model is loaded a constant PM loading. For coarser gradations PSD is discretized into 8 size classes with an equal gravimetric basis and for finer gradation into 16 size classes (Garofalo and Sansalone, 2011). Throughout each steady simulation a computational subroutine as a user defined function (UDF) is run to record residence times of each particle size and generate U p ,Q m The particle residence time distribution, U p for ea ch Q is fit by a gamma distribution as shown in Figure S11 The and gamma factors are determined by minimizing the error between the CFD modeled particle size distributions and gamma fitting curves. The gamma factors are considered satisfactory when producing a R 2 greater than 0.95. A relationship between gamma factors and steady flow rates is determined as shown in Figure C 12 The hydrograph is divided into a series of discrete steady flow rates based on a fixed time interval, t (for example, 1 m in). Based on the relationship derived between particle residence time distribution and flow rate, a CFD modeled U p ,Q m is associated to each discrete flow rate in the hydrograph. Each flow rate generates a unique U p for the specific PM gradation. For examp le, (C 2) PAGE 193 193 Q 1 and Q 2 produce respectively U p,1 and U p,2 If Q 1 is lower than Q 2, U p,1 is longer than U P,2 and has a peak lower than U P,1. The influent PM and the particle residence time distributions are coupled by using the discrete convolution equation to prod uce the effluent PM, by using Equation C 2. Figure C 10 illustrates the convolution formula concept. The effluent PM is given by the sum of the products between I m and U p,Q for each discretization time step. The mathematical operation of the discrete convo lution integral is here derived: UDF for F ully U nsteady and S tepwise S teady F low CFD M odels The user defined function (UDF) built in this study is a function that can be loaded with the FLUENT solver to enhance and customize the standard features of the code and it is written in C programming language. The UDF developed consists of a series of commands which allows to record the particles eluted from the computational domain and their residence times during steady and unsteady CFD simulations. The UDF code is as follows. #include "udf.h" #define REMOVE_ PARTICLES FALSE DEFINE_DPM_OUTPUT(discrete_phase_sample,header,fp,p,t,plane) { char name[100]; real flow_time = solver_par.flow_time; if(header) par_fprintf_head(fp," \ Particle Size Range N ame \ \ "Injection Time [s] \ \ "#Residence Time [s] \ \ Diamete r [m] \ \ n"); PAGE 194 194 if(NULLP(p)) return; sprintf(name,"%s:%d",p >injection >name,p >part_id); #if PARALLEL par_fprintf(fp,"%d %d %s %e %e %f \ n",p >injection >try_id,p >part_id, name, p >time_of_birth, P_TIME(p),P_INIT_DIAM(p)); #else par_fprintf(fp,"%s %e %e %f \ n",name, p >time_of_birth, P_TIME(p), P_INIT_DIAM(p)); #endif #if REMOVE_PARCELS p >stream_index= 1; #endif } The output is reported in a notepad file as follows in Table C 2. This UDF is used for the fully unsteady and the stepwise flow CFD models. For the fully unsteady model, injection time is used in the following equation to evaluate the mass per particle, p : In this expression M i s PM mass associated with the particle size range and injected at time N represents the total number of particles injected at the inlet section (Garofalo and Sansalone, 2011). The residence time output is used to evaluate the number of par ticles which injected at time for the particles size range are eluted from the system at each time step. The total effluent mass is determined as follows: In this equation and represent particle size range and injection time ranging from 0 to the runoff event duration, t d respectively. The term () eff represents PM recorded in effluent. The (C 3) (C 4) PAGE 195 195 particle size fractions are not including on the calculations, simply because the particle size ranges are equally weighted due to the symmetric, gravimetric PSD discretization on an arithmetic scale. For the stepwise steady model the same UDF is used to evaluate the particle residen ce time distribution, U p After each steady simulation, U p is determined by computing the number of particles escaped from the computational domain as function of time (from UDF`s residence time output) over the total number of particles injected. PAGE 196 196 Figure C 1. Schematic representation of the full scale physical model facility setup with rectangular clarifier cm pipe cm pipe Flow meter Flow meter Supplied Water 45,425 L S torage tank 45,425 L S torage tank Pump skid Drop box ( PM influent sampling point) PM delivery system T ank Drop box (manual and automatic e ffluent sampling point for eluted PM) PAGE 197 197 Figure C 2. Schematic representation of the full scale physical model facility setup with baffled HS Figure C 3. Triangular hyetograph. T d is the recession time, ta is the time to peak, and r is the storm advancement coefficient (Chow et al., 1988) T d t a Baffled tank cm pipe cm pipe Flow meter Flow meter Supplied Water 45,425 L S torage tank 45,425 L S torage tank Pump skid Drop box ( PM influent sampling point) Manual Effluent sampling point for eluted PM PM delivery system Automatic Effluent sampling point for eluted PM PAGE 198 1 98 Figure C 4. Frequency distribution of rainfall precipitation for Gainesville, Florida. The frequency distribution is obtained from a series of 1999 2008 hourly precipitation data for Gainesville regional airport (KGNV) Figure C 5. Historical event collected on 8 July 2008 PAGE 199 199 Figure C 6. Hydraulic loadings utilized for full scale physical model of rectangular clarifier: triangular hyetograph, Historical 8 July 2008 hydrologic event. The rainfall runoff modeling is performed in Storm Water Management Model (SWMM) for the catchment Q p = 28.3 L/s T tot = 93 min V = 1,541 L Q p = 50 L/s T tot = 248 min V = 89,000 L A B PAGE 200 200 Figure C 7 Unit hydrograph (UH) theory (Chow et al., 1988) Input P m P 1 P 2 P 3 n m+1 n m+1 Output Q n U n m+1 U n m+1 U 1 U 2 U 3 P 1 U 1 P 1 U 2 P 2 U 2 P 2 U 1 P 2 U 3 PAGE 201 201 Figure C 8. Stepwise steady flow model analogy with UH PAGE 202 202 Figure C 9. Stepwise steady flow model. Particle residence time distribution, U p as function of flow rate PAGE 203 203 Figure C 10. Stepwise steady flow model methodology PAGE 204 204 Figure C 11. Up as function of time for the finer PSD for two steady flow rates. The U p distributions are fit by a gamma distribution with parameters, and BHS Finer PSD = 0.79 = 28 Q = 18 L/s = 0.8 = 2.70 BHS Finer PSD = 0.79 = 28 Q = 1.8 L/s = 1.2 = 33.73 PAGE 205 205 Figure C 12. Shape and scale gamma paremeters ( and ) as function of Q. The gamma parameters are used to fit the Up,Q with a gamma distribution function BHS Finer PSD = 0.79 = 28 R 2 = 0.99 BHS Finer PSD = 0.79 = 28 R 2 = 0.98 PAGE 206 206 Figure C 13. Effluent PM response of a rectangular clarifier to the highly unsteady ( =1.54) and unsteady ( =0.33) hydrographs generated through the stepwise steady model as function of number of steady flow rates used t o determine the relationship between gamma parameters and Q. NRMSE is the normalized root mean squared error respect to the unsteady modeling data PAGE 207 207 Figure C 14. Effluent PM for the fully unsteady CFD model and the stepwise steady model from Pathapati and Sansalone (2011). The models are applied to a RC and a BHS subjected to a highly unsteady hydraulic load. The stepwise steady model overestimates PM eluted from both systems, especially during the first part of the hydrographs (Q PAGE 208 208 Figure C 15. Effluent PM response of a rectangular clarifier to the highly unsteady ( =1.54) and unsteady ( =0.33) hydrographs generated through the stepwise steady model as func tion of hydrograph time discretization, t. NRMSE is the normalized root mean squared error respect to the unsteady modeling data PAGE 209 209 Figure C 16. Influent coarser and finer PSDs as compared to measured effluent PSDs generated through auto sampling for the three hydrographs shown in Figure 1B. The effluent PSDs represent the median PSDs for each hydrograph. The range bars represent the v ariability of PSDs across the entire hydrograph Coarser PSD (d 50 = 67 m) Finer PSD (d 50 = 15 m) (B) ( A ) PAGE 210 210 Table C 1. Computational time expressed in hour (hr) for the CFD stepwise steady flow and the fully unsteady models. Qp, td, are peak flow, hydrograph duration, unsteadiness factor, shap e and scale parameters of the gamma distribution, respectively Unit Q p t d Stepwise Unsteady (L/s) (min) ( ) ( ) ( ) (hr) (hr) RC 50 124 1.54 0.79 28 4.8 21.5 RC 25 136 0.33 0.79 28 4.8 35.5 RC 12.5 282 0.015 0.79 28 4.8 69.5 BHS 18 84 1.15 0.79 28 3.9 15.5 BHS 9 87 0.24 0.79 28 3.9 20.5 BHS 4.5 125 0.09 0.79 28 3.9 55 BHS 18 84 1.15 0.79 28 3.7 15.1 BHS 9 87 0.24 0.79 28 3.7 19.2 BHS 4.5 125 0.09 0.79 28 3.7 52.3 Table C 2. Example of the output from UDF developed for recording particle residence time, injection time and diameter Particle size class name Injection Time (s) Residence Time (s) Diameter (m) njcat dn8 d6 1.4um:0 2.900000e+002 1.623725e+003 0.000001 njcat dn8 d6 1.4um:0 1.310000e+003 3.092848e+003 0.000001 njcat dn8 d6 1.4um:0 3.590000e+003 5.194801e+003 0.000001 PAGE 211 211 APPENDIX D SUPPLEMENTAL INFORMATION MODEL FOR EVALUATING LONG TERM UO Disaggregation R ainfall M ethod The hourly rainfall data for the period of 1998 2011 downloaded from the National Climatic Data Center (NCDC) are disaggregated in 15 min by using Ormsbee`s continuous deterministic disaggregation proc edure. The basic assumptions of Ormsbee`s method is the distribution of precipitation within a time step is proportional to the distribution of precipitation over three time step sequence with adjacent before and after time steps (Ormsbee, 1989; Lee et al. 2010). Figure D 1 shows a schematic of the precipitation data disaggregation method. Using this deterministic linear assumption, precipitation data can be disaggregated into smaller time steps of, e. g., 1, 2, 3, 5, 10, 15, 20 or 30 min. A unique disaggr egated time series data set will be obtained from an input precipitation data set on basis of the applied temporal and volumetric resolutions for output data. This disaggregation feature is particularly important for small catchments with short system resp onse times (Lee et al., 2010). Full S cale P hysical M odel S etup of the R ectangular C larifier The analysis is carried out on full scale physical model of a rectangular clarifier, which represents the most traditional and common clarification systems used in rainfall runoff PM treatment. The rectangular clarifier is 1.87 m tall, 1.8 m wide and 7.31 m long with hydraulic capacity of approximately 12,000 L. The influent and effluent pipe diameters are of 0.2 m. The design flow rate, Q d of the physical model is a bout 50 L/s, corresponding to the hydraulic capacity of physical model as an open channel system (Figure D 5). To validate the CFD model under transient conditions, effluent PM and PSDs eluted from the full scale rectangular clarifier subjected to two hydrological events are collected. The first hydrograph is generated from a triangular hyetograph with 12.7 mm (0.5 inch) of rainfall depth PAGE 212 212 and duration of 15 minutes. This loading is selected as a common short and intense rainfall event during the wet season in Florida (Figure D 7). The second hydrograph is generated from a h istorical event collected on 8 July 2008 in Gainesville, Florida with total rainfall depth of 71 mm. This event is chosen since it is an extremely intense historical event, with a peak rainfall intensity of about 165 mm/h (Figure D 7). The particle size distribution (PSD) used is reported in Figure D 8 and is a fine hetero disperse gradation classified from Unified Soil Classification System (USCS) as SM I with a d 50 of 18 m. The hyetographs are transformed to event based hydrographs by using Storm Water Management Model (SWMM) (Huber and Dickinson 1988) for each physical and CFD model. The objective of the rainfall runoff simulation is to generate unsteady runoff flow loadings for the scaled physical model and CFD model. In this transformation from rainfall to runoff for the scaled physical basin, the watershed area is matched to deliver peak runoff flow rates equal to the design flow rate of the unit operation. More details information about the two hydrographs utilized for the validation are reported in Section 3 of the Appendix (Figure D 11). In Supplemental information section, the generation of the two hydrographs utilized is explained in detail. The results retrieved from the experiments are reported in Table D 1. Generation of H ydrographs U sed for the V alidation of the F ull S cale P hysical M od el of C larifier under T ransient C onditions Study Hyetographs An essential component of this study is the definition of the hydrological loadings. The three hyetographs selected are: Triangular hyetograph with 12.7 mm (0.5 inches) of rainfall volume and du ration of 15 minutes. This loading is selected as a common short and intense rainfall event during the wet season in Florida. A triangular shape is used to define the hyetograph as shown in Figure D 7 (Chow et al., 1988). The maximum rainfall intensity of the triangular hyetograph is approximately 101 mm per hour (4 inches per hour) and the total excess precipitation depth is 12.7 mm (0.5 inches). The hyetograph selected is considered a fairly PAGE 213 213 extrem e event, since 80% of storm events occurring in Gainesville are characterized by a total precipitation depth equal or less than 12.7 mm (0.5 inches). Figure D 6 reported below depicts the frequency distribution of 1999 2008 hourly rainfall data for Gainesville Regional Airport (KGNV). Historical event collected on 8 July 2008 by UF with total rainfall depth of 71 mm. This event is chosen since it is an extremely intense historical event, with a peak rainfall intensity of about 165 mm/h (Figure D 7). This value is higher than peak precipitation intensity of the 24 hour 25 year design storm described in the following paragraph. Transformation of R ainfall H yetographs to R unoff H ydrographs The hyetographs reported in Figure D 7 are transformed to event based hydrographs by using the SWMM (Huber and Dickinso n, 1988) for each physical and CFD model. The objective of the rainfall runoff simulations is to generate unsteady runoff flow loadings for the scaled physical and CFD model. SWMM translates rainfall in runoff for the specific catchment properties. In th is transformation the watershed area is matched to deliver peak runoff flow rate equal to the design flow rate of the unit operation. As shown pereviously, July 8 th 2008 historical hyetograph is characterized by the highest rainfall peak intensity (approxi mately 165 mm/h) in comparison to the other selected hyetographs. Therefore, the historical hyetograph is utilized as a reference to perform the flow scaling of the physical testing model. Since the maximum hydrualic load of the physical models is 50 L/s the area of the catchment implemented in SWMM is defined to deliver peak flow rate equal to 50 L/s for the historical storm of 8 July 2008. The modeling parameters adopted are referred to an asphalt pavement of a typical airport runway/taxiway. Green Ampt method is used to model infiltration process. T he rainfall runoff modeling for the three hyetographs are shown in Figure D 7. PAGE 214 214 Particle Size Distribution PSD Selection The influent particulate loading used for CFD and full scale physical model consists of a PSD that is in the silt size range. The PSD, ranging from less than 1 m to 75 m is reported in Figure S8. The PM specific gravity i s 2.63 g/cm 3 The mass based PSD is well described by a gamma distribution function. The probability density function is given by Equation D 1 as a function of particle diameter d, where is a distribution shape factor and a scaling parameter. The cumul ative gamma distribution function is expressed in Equation D 2. PSD Significance PM is widely recognized as a primary vehicle for the transport and partitioning of pollutants. Moreover, PM is a pollutant itself that impacts the deterioration of receiving surface waters. The potential for water chemistry impairment strongly depends on PM loading and PSD. Furthermor e, many PM bound constituents, such as metals, nutrients and other pollutants, partition to and from PM while transported by PM through rainfall runoff events. Therefore, PSD plays an important role in the transport and chemical processes occurring in urba n stormwater runoff and an understanding of its behavior is crucial for the analysis and the selection of unit operations. Geometry and M esh G eneration of F ull S cale M odels The mesh is comprised of tetrahedral elements and it is checked carefully to ensure that equiangle skewness and local variations in cell size are minimized in order to produce a high (D 1) (D 2) PAGE 215 215 quality mesh. Several iterations of grid refinement are performed to det ermine the necessary mesh density that balances the accuracy of the solution with the exponentially increasing demand on computational resources. The final mesh used in this study is discretized into approximately 3.5 million cells (Figure s D 9 and D 10). The mesh generated for the screened hydrodynamic separator (SHS) is described in Pathapati and Sansalone (2012) (Figure D 11). CFD Modeling and P opulation B alance Liquid P hase G overning E quations The governing equations for the continuous phase are a vari ant of the N S equations, the Reynolds Averaged N S (RANS) equations for a turbulent flow regime. The RANS conservation equations are obtained from the N flow properties into their time mean valu e and fluctuating component. The mean velocity is defined as a time average for a period t which is larger than the time scale of the fluctuations. The RANS equations for continuity and momentum conservation are summarized. In these equations is fluid density, x i is the i th direction vector, u j is the Reynolds averaged velocity in the i th direction; p j is the Reynolds averaged pressure; and g i is the sum of body forces in the i th direction. Decomposition of the momentum equation with Reynolds decomposition generates a term o riginating from the nonlinear convection component in the original equation; these Reynolds stresses are represented by Reynolds stresses contain information about the flow turbulence structure. Since Reynolds stresses are unknown, closure (D 3) (D 4) PAGE 216 216 approximations can be made to obtain approximate solution of the equations (Panton, 2005). In this study the realizable k model (Shih and al., 1995) is used to resolve the closure problem. This model is suitable for boundary free shear flow app lications and consists of turbulent kinetic energy and turbulence energy dissipation rate equations, respectively reported below (Shih and al., 1995). k = 1.2, C 1 = 1.44, C 2 = 1.9, k is the T fluid viscosity; and u ji u j i are previously defined. The free surface of the rectangular clarifier is modeled as a fix ed shear free wall defined by zero normal velocity and zero gradients of all variables. The boundary conditions for the screened HS are described in Pathapati and Sansalone (2012). Particulate P hase G overning E quations (the DPM) The DPM simulates 3D parti cle trajectories through the flow domain to model PM separation and elution in a Lagrangian frame of reference where particles are individually tracked through the flow field. This analysis assumes PM motion is influenced by the fluid phase, but the fluid phase is not affected by PM motion (one way coupling) and particle particle interactions are negligible, since the particulate phase is dilute (volume fraction (VF) around 0.01%) (Brennen, 2005). The DPM integrates the governing equation of PM motion and t racks (D 5) (D 6) (D 7) PAGE 217 217 each particle through the flow field by balancing gravitational body force, drag force, inertial force, and buoyancy forces on the PM phase. The motion of a single particle without collisions is modeled by the Newton`s law. Particle trajectories are calculated by integrating the force balance equation in the i th direction. The first term on the right hand side of the equation is the drag force per unit particle mass. The second term is the buoyancy/gravitational force per unit particle mass. In these equations, p is particle density, v i is fluid velocity, v pi is particle v elocity, d p is particle diameter, R ei is the particle Reynolds number, F Di is the buoyancy/ gravitational force per unit mass of particle and C Di is the particle drag coefficient (Morsi and Alexander, 1972) The last three variables are defined as follows. K 1 K 2 K 3 are empirical constants as a function of particle Re i reported in Table D 2. The PSD is discretized into PM size clas ses with a symmetric gravimetric basis. Studies have demonstrated that a discretization number (DN) of 16 is generally able to reproduce accurate results for fine hetero disperse PM gradations subject to steady flows (Dickenson and Sansalone, 2009). Part icles are defined as silica particles with specific gravity of 2.65 g/cm 3 (D 8) (D 9) (D 10) (D 12) PAGE 218 218 Numerical S olution The numerical solver is pressure based for incompressible flows that are governed by motion based on pressure gradients. The spatial discretization schemes are s econd order for pressure, the second order upwind scheme for momentum and the Pressure Implicit Splitting of Operators (SIMPLE) algorithm for pressure velocity coupling. Temporal discretization of the governing equations is performed by a second order impl icit scheme. Under relaxation parameters used in the CFD simulations are reported in Tables D 3. Convergence criteria are set so that scaled residuals for all governing equations are below 0.001 (Ranade, 2002). All simulations are run in parallel on a Dell Precision 690 with two quad core Intel Xeon 2.33GHz processors and 16 GB of RAM. A population balance model (PBM) is coupled with CFD to model PM separation. Assuming no flocculation in the dispersed particle phase, the PBM equation (Jacobsen, 2008) and mass per particle, p n are as follows. M is PM mass associated with the particle size range, as function of injection time, N is the total number of particles injected at the inlet section, and t d is the event duration. Stepwise S teady F low M odel The conceptual founda tion for stepwise steady flow model is analogous to the unit hydrograph theory used to predict surface watershed runoff (Chow et al., 1988). The unit hydrograph represents the unit response function of a linear hydrologic system. The assumptions (D 14) (D 13) PAGE 219 219 of the un it hydrograph theory are the system (watershed) is linear and the unit hydrograph response function, U is time invariant and unique for a given watershed (Chow et al., 1988). Define P n m the effluent flow rate (Figure D 15). The discrete convolution equation allows the computation of direct runoff Q m given excess rainfall P n : Based on the assumption that a unit operation can be idealized as a hydrological watershed, in this study, the concept of UH is applied to unit op erations, subjected to unsteady hydraulic and PM loadings (Figure D 16). The main assumptions of the stepwise steady flow model are: UO is a linear system U p is unique for a given UO, flow rate and PSD Let I be the event based influent PM for a given PSD. I m represents the influent PM for a given PSD and a fixed time step, t, delivered into the system at Q m U p is function of flow rate, Q m ; therefore, let define U p ,Q m the UO response to I m for the specific flow rate, Q m (Figure D 15). U p ,Q m is computed from steady CFD models. The UO is assumed to be a linear system. Based on this assumption the event based effluent mass PM E can be modeled as sum (convolution) of the responses U p ,Q m to inputs I m The effluent mass PM at each time step t, E n is given by the discrete convolution equation: In these expressions, n and m are the number of steps in which the effluent PM distribution and the influent hydrograph are respectively discretized. The stepwise steady CFD model approach consists of the following steps. Steady CFD model is run for seven steady flow rates (100%, 75% 50%, 25%, 10%, 5%, 2% of the design flow rate) for each unit. The CFD model is loaded a constant PM loading. (D 15) (A5 15) (D 15) PAGE 220 220 For coarser gradations PSD is discretized into 8 size classes with an equal gravimetric basis and for finer gradation into 16 size classes (Garof alo and Sansalone, 2011). Throughout each steady simulation a computational subroutine as a user defined function (UDF) is run to record residence times of each particle size and generate U p ,Q m The particle residence time distribution, U p for each Q is fit by a gamma distribution. The and gamma factors are determined by minimizing the error between the CFD modeled particle size distributions and gamma fitting curves. The gamma factors are considered satisfactory when producing a R 2 grea ter than 0.95. A relationship between gamma factors and steady flow rates is determined. The hydrograph is divided into a series of discrete steady flow rates based on a fixed time interval, t (for example, 1 min). Based on the relationship derived betw een particle residence time distribution and flow rate, a CFD modeled U p ,Q m is associated to each discrete flow rate in the hydrograph. Each flow rate generates a unique U p for the specific PM gradation. For example, Q 1 and Q 2 produce respectively U p,1 and U p,2 If Q 1 is lower than Q 2, U p,1 is longer than U P,2 and has a peak lower than U P,1. The influent PM is discretized into a series of pulse inputs, I m with t equal to 1 min. The influent PM and the particle residence time distributions are coupled by using the discrete convolution equation to produce the effluent PM, by using Equation D 15. Figure D 18 illustrates the convolution formula concept. The effluent PM is given by the sum of the products between I m and U p,Q for each discretization time ste p. The mathematical operation of the discrete convolution integral is here derived: PAGE 221 221 Figure D 1. Precipitation data disaggregation (Orsmbee, 1988)) Rainfall Time (A) Input data Rainfall (B) Disaggregat ed data PAGE 222 222 Figure D 2. Hydrology analysis. R ainfall intensity frequency distribution for the period 1998 2011 and for 2007 is illustrated in A) I r represents the rainfall intensity, i r50 represents the median rainfall intensity. The number of events is calculated based on a minimum inter event time, MIT of 1 h. Time domain distribution of rainfall and runof f for June 2007 is reported in B) A B June 2007 PAGE 223 223 Figure D 3. Total rainfall depth as function of month for the year 2007 Figure D 4. Runoff frequency distribution for 2007 for a watershed of 1.6 ha, with 1% slope, 75% of imperviousness and sand soil characteristics. The cumulative frequency distribution in A) is based 15 minute runoff data. In (B) the incremental runoff frequency distribution is also based on 30 minute runoff data Watershed area = 1.6 ha A B 2007 PAGE 224 224 Figure D 5. Schematic representation of the full scale physical model facility setup with rectangular clarifier cm pipe cm pipe Flow meter Flow meter Supplied Water 45,425 L S torage tank 45,425 L S torage tank Pump skid Drop box ( PM influent sampling point) PM delivery system Drop box (manual eff luent sampling point for eluted PM) Clarif ier PAGE 225 225 Figure D 6. Frequency distribution of rainfall precipitation for Gainesville, Florida. The frequency distribution is obtained from a series of 1999 2008 hourly precipitation data for Gainesville Regional Airport (KGNV) Figure D 7. Influent PSD for fine PM {SM I, <75 m}. SM is sandy silt in the Unified Soil Classification System (USCS). SM is SCS 75. PSD data are fit by gamma function (GF) based on distribution parameters, shape factor, and scale factor, g / c m 3 PAGE 226 226 Figure D 8. Hydraulic loadings utilized for full scale physical model. The rainfall runoff modeling is performed in Storm Water Management Model (SWMM) for the catchment. The two hydrologic events investigated are: triangular hyetograph (A), historical 8 July 2008 loading hydrologic event (B). Td is the recession time, ta is the time to peak, and r is the storm advancement coeffici ent (Chow et al., 2008) Q p = 28.3 L/s T tot = 93 min V = 1,541 L Q p = 50 L/s T tot = 248 min V = 89,000 L T d = 0.15 h t a = 0.25 h r = t a /T d = 0.5 A B PAGE 227 227 Figure D 9. Isometric view of full scale physical model and mesh of the rectangular cross section clarifier. The number of computational cells is 3.5*10 6 D is diameter 7. 3 m 1.67 m 1.4 m 1.8 m Influent and effluent pipe D = 0.2 m Inlet Outlet PAGE 228 228 Figure S9. Grid convergence Figure D 10. Grid convergence for full scale rectangular clarifier. The mesh utilized comprimes 3.5*10 6 tetrahedral cells Figure D 11. View of the full scale physical model of screened HS (SHS) unit. D represents the diameter Mesh size utilized 1.8 m Outflow (Effluent pipe D = 0.25 m) Inflow (Influent pipe D = 0.25 m equivalent) D = 1.7 m Sump (D = 0.65 m) 2400 m screen 0.46 m 0.62 m PAGE 229 229 Figure D 12. Scour hole generated after a transient physical model test on the rectangular clarifier. While a scour hole is produced by the impinging jet (A), indicating a fraction of PM mass is resuspended in the inlet section of the system, in the rest of the tank (B) no a visually appreciable scour occurs Figure D 13. Schematic of scour CFD model by integrating across surfaces (not to scale). Based on Figure D 12 is assumed washout PM mass is generated from the scour hole located in the inlet section of the rectangular clarifier. Therefore, in CFD a squared grid (60 by 20 cm) is built where the scour hole may occur. From the nodes of this grid are injected the DPM particles. The grid is generated on different planes, n with heights equal to the pre deposited PM depth divided by n. W is the width of the layer, L is the length of the layer, D is the pre deposited PM depth (A) ( B ) W = 60 cm W = 60 cm D D n layers Inlet Outlet Scour hole L = 20 cm L = 20 cm PAGE 230 230 Figure D 14. Particle residence time distributions, Up for RC and SHS as function of steady flow rate. The flow rates vary from 1 to 50 L/s (maximum hydraulic capacity of RC). Both units are loaded with the fine hetero disperse gradation shown in Fig ure 5 2A Elapsed time, t (sec) Influent PSD = 0.79 = 28 Influent PSD = 0.79 = 28 SHS RC U p U p SHS PAGE 231 231 Figure D 15. Unit hydrograph (UH) theory (Chow et al., 1988) Input P m P 1 P 2 P 3 n m+1 n m+1 Output Q n U n m+1 U n m+1 U 1 U 2 U 3 P 1 U 1 P 1 U 2 P 2 U 2 P 2 U 1 P 2 U 3 PAGE 232 232 Figure D 16. Stepwise steady flow model analogy with UH PAGE 233 233 Figure D 17. Stepwise steady flow model. Particle residence time distribution, Up as function of flow rate PAGE 234 234 Figure D 18. Stepwise steady flow model methodology PAGE 235 235 Figure D 19. Effluent PM generated from the stepwise steady model as function of the number of flow rates used to generate the relationship between gamma parameters describing particle residence time distribution, Up and flow rate. The results show a set o f minimum 3 flow rates chosen as 5%, 25% and 100% of RC`s design flow rate, Qd generates a accurate results (6%). A higher number of flow rates does not produce more accurate results. In this study a number of 7 flow rates were used since CFD model results were already available. NRMSE is normalized root mean squared error PAGE 236 236 Figure D 20. Physical model and CFD model results for PM and PSDs for the triangular hydrograph and for 8th July 2008 storm used for the validation analysis for full scale physical model of a rectangular clarifier. These results are showed in A) and B) Q p is the peak influent flow rate and td is the total duration of the hydrological event. In B) and D) the shaded area indicates the range of variation of effluent PSDs throughout the hydrological events. RPD is the relative percentage difference between the measured and modeled data. RMSE is the root mean squared error between effluent average measured and modeled PSDs, s is the particle density, Q p is the peak influent flow rate and td is the total duration of the hydrological event A C B D RPD = 0.07% RPD = 9.30 % Rectangular Clarifier Rectangular Clarifier Rectangular Clarifier Rectangular Clarifier PAGE 237 237 Figure D 21. CFD model of washout PM concentration as a function of flow rate, Q for the rectangular clarifier and SHS unit. In (A) washout PM concentration from the rectangular clarifier is shown for different PM depths ranging from 5 to 50 mm. In (B) washout PM mass from the SHS is reported for 50% of PM capacity in sump area and PM depths in volute section ranging from 10 to 100 mm. In (C) washout PM concentration from the sump of SHS unit is shown for different PM dept hs ranging from 25 to 450 mm (no PM in volute region) A B C PAGE 238 238 Figure D 22. CFD model of PM washout mass and concentration as a function of flow rate, for the SHS unit for PM depths in volute section ranging from 10 to 100 mm with 100% of PM capacity in sump area. In (A) the PM washout mass is reported, in (B) PM washout concentration A B PAGE 239 239 Figure D 23. Effluent PM mass and PM mass depth as function of month for the screened HS unit in the representative year 2007 for 100% of sediment capacity of sump area. The results in (A) are generated by using the stepwise steady flow model with and without considering washout phenomena for the hetero disperse PM gradation shown in Figure 1A ( and respectively 0.79 and 28). In (B) the results are produced by assuming PM mass accumulates first in the sump area (negligible PM deposition in the volute area) and subsequently as the PM mass reaches 100% of the sump capacity, it starts to build up in the volute area. C inf is the influent concentration A Influent PSD = 0.79 ; = 28 s = 2.63 g/cm 3 = 1.035 g/cm 3 B C inf = 200 mg/L Representative year: 2007 SHS SHS PAGE 240 240 Figure D 24. Normalized mean fluid velocity distributions inside the inner and outer volute area of SHS, and RC. Bin sizes are consistent for SHS and RC RC SHS Inner area SHS Outer volute area PAGE 241 241 Table D 1. Summary of measured and modeled treatment performance results for full scale rectangular clarifier loaded by hetero disperse silt particle size gradation for two different hydrological events. Vt i s the total influent volume, Q p is the peak influent flow rate, T tot is the duration of the hydrological event, measured is measured PM removal efficiency, modele d is modeled PM removal efficiency and RPD is absolute percentage error, and represent the gamma parameters for effluent measured PSDs. The gamma parameters for the influent PSD are respectively 0.8 and 29 Hydrograph Type Q p V t t d measured modeled RPD PSD model (L/s) (L) (min) (%) (%) % Tr iangular RC 28.4 15.1 44 88.38 88.4 0.07 0.97 20.15 8 July 08 RC 50.8 88.9 110 56.78 51.7 9.03 0.90 18.00 Table D 2. Morsi and Alexander constants for the equation fit of the drag coefficient for a sphere Reynolds Number K1 K2 K3 <0.1 24.0 0 0 0.1 < Re < 1 22.73 0.0903 3.69 1 < Re < 10 29.16 3.8889 1.222 10 < Re < 100 46.5 116.67 0.6167 100 < Re < 1000 98.33 2778 0.3644 1000 < Re < 5000 148.62 4.75 10 4 0.357 5000 < Re < 10,000 490.54 57.87 10 4 0.46 10,000 < Re < 50,000 1662.5 5.4167 10 6 0.5191 PAGE 242 242 Table D 3. 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Modeling of Rectangular Settling Tanks. Journal of Hydraulic Engin e ering 118, 1391 1405. PAGE 250 250 B IOGRAPHICAL SKETCH Giuseppina Garofalo received her b achelor `s and m aster `s degrees in c ivil e ngineering at University of Calabri a, Italy. She came to the United States in August 2007 to pursue her Ph.D in e nvironmental e ngineering s ciences. In May 2012 she received her M.E. in e nvironmental e ngineering s ciences from University of Florida. Her doctoral research focuses on physical and CFD modeling of unit operations for rainfall runoff. She worked under the guidance of Dr. Sansalone in the Department of Environmental Engineering Sciences. 