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A New Mechanistic Understanding and Modeling of Pool Boiling Crticial Heat Flux on Horizontal Surface

Permanent Link: http://ufdc.ufl.edu/UFE0043584/00001

Material Information

Title: A New Mechanistic Understanding and Modeling of Pool Boiling Crticial Heat Flux on Horizontal Surface
Physical Description: 1 online resource (113 p.)
Language: english
Creator: Guan, Cheng Kang
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2011

Subjects

Subjects / Keywords: boiling -- capillary -- chf -- critical -- flux -- force -- heat -- hydrodynamic -- model -- pool -- wettability
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: This work proposes a new mechanistic model for predicting the critical heat flux (CHF) in horizontal pool boiling systems. It is postulated that when the vapor momentum flux is sufficient to lift the liquid macrolayer from the heating surface, wetting is no longer feasible, and a transition from nucleate to film boiling occurs. The model considers liquid/vapor interfaces in the horizontal configuration during the transition from nucleate to film boiling. An experimental investigation of CHF with pentane, hexane, methanol, FC-72, FC-87, and R113 in saturated horizontal pool boiling with reduced pressure from 0.01 to 0.24 (100 kPa to 450 kPa) provides evidence that the new model captures the variation of CHF with pressure reasonably well compared with previous well-known models. The new model predicts CHF with pentane, hexane, and methanol well and slightly overpredicts the change in CHF with increasing pressure. The predictive capability of the new CHF model is better with fluids which produce larger departing bubbles, because the local dryout phenomenon affects CHF more significant with smaller departing bubbles. The new model is also compared with existing data from the literature with a reduced pressure range from 2x10^-5 to 2x10^-1. The mean deviation between the predicted and measured CHF in hydrocarbon fluids is typically within 20% over the parameter space covered. The predicted CHF follows the trends of the measured CHF for water on different heating surfaces. The roughness effect on CHF in pool boiling is investigated on a 25.4 mm diameter flat brass heater from random RMS roughness from 150 nm, 650 nm, 2.3 µm, and up to 5.5 µm with pentane, hexane, and FC-72. The results show that CHF increases with increasing roughness, and the roughness effect on CHF decreases with increasing pressure. The capillary forces might play an important role in CHF with roughness as well as structured surfaces and nanofluids. There are two major areas to focus on for future studies. The first is that the local dryout effect should be incorporated in the new model. The second is determining capillary forces and adding the capillary forces into the momentum balance of the lift-off model.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Cheng Kang Guan.
Thesis: Thesis (Ph.D.)--University of Florida, 2011.
Local: Adviser: Klausner, James F.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2011
System ID: UFE0043584:00001

Permanent Link: http://ufdc.ufl.edu/UFE0043584/00001

Material Information

Title: A New Mechanistic Understanding and Modeling of Pool Boiling Crticial Heat Flux on Horizontal Surface
Physical Description: 1 online resource (113 p.)
Language: english
Creator: Guan, Cheng Kang
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2011

Subjects

Subjects / Keywords: boiling -- capillary -- chf -- critical -- flux -- force -- heat -- hydrodynamic -- model -- pool -- wettability
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: This work proposes a new mechanistic model for predicting the critical heat flux (CHF) in horizontal pool boiling systems. It is postulated that when the vapor momentum flux is sufficient to lift the liquid macrolayer from the heating surface, wetting is no longer feasible, and a transition from nucleate to film boiling occurs. The model considers liquid/vapor interfaces in the horizontal configuration during the transition from nucleate to film boiling. An experimental investigation of CHF with pentane, hexane, methanol, FC-72, FC-87, and R113 in saturated horizontal pool boiling with reduced pressure from 0.01 to 0.24 (100 kPa to 450 kPa) provides evidence that the new model captures the variation of CHF with pressure reasonably well compared with previous well-known models. The new model predicts CHF with pentane, hexane, and methanol well and slightly overpredicts the change in CHF with increasing pressure. The predictive capability of the new CHF model is better with fluids which produce larger departing bubbles, because the local dryout phenomenon affects CHF more significant with smaller departing bubbles. The new model is also compared with existing data from the literature with a reduced pressure range from 2x10^-5 to 2x10^-1. The mean deviation between the predicted and measured CHF in hydrocarbon fluids is typically within 20% over the parameter space covered. The predicted CHF follows the trends of the measured CHF for water on different heating surfaces. The roughness effect on CHF in pool boiling is investigated on a 25.4 mm diameter flat brass heater from random RMS roughness from 150 nm, 650 nm, 2.3 µm, and up to 5.5 µm with pentane, hexane, and FC-72. The results show that CHF increases with increasing roughness, and the roughness effect on CHF decreases with increasing pressure. The capillary forces might play an important role in CHF with roughness as well as structured surfaces and nanofluids. There are two major areas to focus on for future studies. The first is that the local dryout effect should be incorporated in the new model. The second is determining capillary forces and adding the capillary forces into the momentum balance of the lift-off model.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Cheng Kang Guan.
Thesis: Thesis (Ph.D.)--University of Florida, 2011.
Local: Adviser: Klausner, James F.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2011
System ID: UFE0043584:00001


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1 A NEW MECHANISTIC UNDERSTANDING AND MODEL ING OF POOL BOILING CRTICIAL HEAT FLUX ON HORIZONTAL SURFACE By CHENG KANG GUAN 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 2011

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2 2011 Cheng Kang Guan

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3 To my f amily

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4 ACKNOWLEDGMENTS I would like to acknowledge my advisor, Dr. James F. Klausner, for his expertise, understanding, and patience. He is always available to students for discuss ing all matters both academic and personal. He also patiently provided vision, encouragement and advic e to guide me through my doctorial program and complete my disser tation. I gratefully thank the members of my committee, Dr. Renwei Mei, Dr. David Hahn, Dr. Jason Butler, and Dr. Duwayne S chubring, for their academic advice and instruction. I also appreciate the time and effort they have given me I also wish to thank National Science Foundation and ExxonMobile Research Company for the financial support of my work. I would like to thank Brad ley Bon who is not only a good friend but a wonderful labmate for always willing to help and give me suggestions. I also thank Ri cher Parker, Prasanna V enu vanalingam, Benjamin Griffin, and Like Li for helping me and making the lab friendly Special thanks should be given to my parents my brother and Fanny Liu for their love and full support for my study in the U S.

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5 TABLE OF CONTE NTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF ABBREV IATIONS ................................ ................................ ........................... 11 NOMENCLATURE ................................ ................................ ................................ ........ 11 ABSTRACT ................................ ................................ ................................ ................... 14 CHAPTER 1 INTRODUCTION AND LITERATURE REVIEW ................................ ..................... 16 1.1 Hydrodynamic Models ................................ ................................ ................ 18 1.2 Bubble Packing Models ................................ ................................ .............. 25 1.3 Surface Effects ................................ ................................ ........................... 27 2 THEORETICAL CHF MODEL FOR SATURATED POOL BOILING ....................... 35 2.1 Observation of Physical Phenomena ................................ .......................... 35 2.2 Theoretical Lift off CHF Model ................................ ................................ .... 37 3 SATURATED POOL BOILING FACILITY ................................ ............................... 44 3.1 Facility Overview ................................ ................................ ........................ 44 3.2 Saturated Pool Boiling Chamber ................................ ................................ 45 3.3 The Surface Test Section ................................ ................................ ........... 46 3.4 Surface Finish ................................ ................................ ............................ 46 3.5 Measur ement and Calibration ................................ ................................ .... 47 3.6 Procedure for the Saturated Pool Boiling Experiment ................................ 49 4 COMPARISON BETWEEN THE EXPERIMENTAL RESULT AND THE CHF MODELS ................................ ................................ ................................ ................. 55 5 RESULTS AND DISCUSSION WITH DIFFERENT ROUGHNESS ON CHF .......... 82 6 FUTURE STUDIES ................................ ................................ ................................ 94 APPENDIX A RAYLEIGH TAYLOR INSTABILITY ................................ ................................ ..... 95 B ORDINAEY DIFFERENTIAL EQUATION FOR THE BUBBLE GROWTH ............ 102 C THERMAL PROPERTY OF FLUID ................................ ................................ ....... 105

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6 LIST OF REFERENCES ................................ ................................ ............................. 106 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 113

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7 LIST OF TABLES Table page 1 1 Summary of CHF models for a flat horizontal surface ................................ ........ 34 4 1 Measured CHF for pentane, hexane, and methanol FC 87, FC 72, and R113 for pool boiling at different pressures ................................ ................................ .. 78 4 2 Comparison between Taylor wavelength and mushroom bubble major chord length in transition. ................................ ................................ ............................. 79 4 3 The images of transition between nucleate and film boiling with different test fluids at various pressures. ................................ ................................ ................. 80 4 4 Mean deviation between experimental and predicted CHF ................................ 81 5 1 CHF data on a 25.4 mm diameter brass disk with various roughness and pentane at three different pressures for saturated pool boiling. .......................... 92 5 2 CHF data on a 25.4 mm diameter brass disk with various roughness and hexane at three different pressures for saturated pool boiling. ........................... 92 5 3 CHF data on a 25.4 mm diameter brass disk with various roughness and FC 72 at three different pressures for saturated pool boiling. ................................ ... 93

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8 LIST OF FIGURES Figure page 1 1 Three different pool boiling heat transfer regimes. ................................ ............. 31 1 2 Pool boiling curve with increasing controlled heat flux. ................................ ....... 31 1 3 The mushroom bubble behavior right after CHF in water pool boiling on 10 mm copper disc. The time interval between each frame: 8.8 ms [11]. ................ 32 1 4 Idealized representation of liquid macrolayer and mushroom bubble. ................ 32 1 5 Boiling behavior near CHF on a flat nichrome surface in water at different pressure used with permission from Sakashitia, 2009, page 748, Figure 6 [13]. ................................ ................................ ................................ .................... 32 1 6 Liquid film under the mushroom bubble on a copper ribbon (40 mm length, 0.5 mm wide, and 0.2 mm height) in pentane at 92% of CHF [23]. .................... 33 1 7 Procedure for determining asymptotic thickness ................................ ................ 33 2 1 Time series images depicting transition from nucleate to film boiling for pentane on a 150 nm RMS roughness brass surface ................................ ......... 42 2 2 Control volume around differential slice of liquid macrolayer. ............................. 43 3 1 Sketch of the saturated pool boiling facility. ................................ ........................ 51 3 2 Sketch of the saturated pool boiling chamber. ................................ .................... 51 3 3 Cross section area of the surface test section. ................................ ................... 52 3 4 Roughness image and profile from the profilometer. ................................ .......... 52 3 5 Temperature calibration curve fit. ................................ ................................ ....... 53 3 6 Pressure calibration linear fit. ................................ ................................ ............. 53 3 7 Heat flux and temperature versus time in transition boiling. ............................... 54 4 1 Boiling curves for pentane on brass heater surface with 650nm RMS roughness. ................................ ................................ ................................ .......... 66 4 2 Boiling curves for hexane on brass heater surface with 650nm RMS roughness. ................................ ................................ ................................ .......... 66 4 3 Boiling curves for FC 72 on brass heater surface with 650nm RMS roughness. ................................ ................................ ................................ .......... 67

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9 4 4 Boiling curves for FC 87 on brass heater surface with 650nm RMS roughness. ................................ ................................ ................................ .......... 67 4 5 Boiling curves for R113 on brass heater surface with 650nm RMS roughness. ................................ ................................ ................................ .......... 68 4 6 Boiling curves for methanol on brass heater surface with 650nm RMS roughness. ................................ ................................ ................................ .......... 68 4 7 Heat Transfer coefficient for pentane on brass heater surf ace with 650nm RMS roughness with different pressure. ................................ ............................. 69 4 8 Heat Transfer coefficient for hexane on brass heater surface with 65 0nm RMS roughness with different pressure. ................................ ............................. 6 9 4 9 Heat Transfer coefficient for FC 72 on brass heater surface with 650nm RMS roughness with different pressure. ................................ ................................ ...... 70 4 10 Heat Transfer coefficient for FC 87 on brass heater surface with 650nm RMS roughness with different pressure. ................................ ................................ ...... 70 4 11 Heat Transfer coefficient for R113 on brass heater surface with 650nm RMS roughness with different pressure. ................................ ................................ ...... 71 4 12 Heat Transfer coefficient for methanol on brass heater surface with 650nm RMS roughness with different pressure. ................................ ............................. 71 4 13 Comparison of CHF models with pentane data ................................ ................. 72 4 14 Change in CHF with reduced pressure for pentane. ................................ ........... 72 4 15 Comparison of CHF models with hexane data. ................................ .................. 73 4 16 Comparison of CHF models with methanol data. ................................ ............... 73 4 17 Comparison of CHF models with FC 72 data. ................................ .................... 74 4 18 Comparison of CHF models with FC 87 data. ................................ .................... 74 4 19 Comparison of CHF models with R113 data. ................................ ...................... 75 4 20 Comparison of predicted CHF using lift off model with pentane data. ................ 75 4 21 Comparison of predicted CHF using lift off model with hexane data. ................. 76 4 22 Compa rison of predicted CHF using lift off model with methanol, R133, and benzene. ................................ ................................ ................................ ............. 76

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10 4 23 Comparison of predicted CHF using lift off model with elevated pressure water data. ................................ ................................ ................................ .......... 77 5 1 CHF data in saturated pool boiling with various RMS roughness at different pressur e for pentane. ................................ ................................ ......................... 88 5 2 CHF data in saturated pool boiling with various RMS roughness at different pressure for hexane. ................................ ................................ ........................... 88 5 3 CHF data in saturated pool boiling with various RMS roughness at different pressure for FC 72. ................................ ................................ ............................ 89 5 4 Sketch of the hoodoo structure surface: a) top view and b) side view ................ 89 5 5 re entreating Liquid flow due to the capillary force ................................ ............. 90 5 6 Plot of CHF enhancement versus A. ................................ ................................ .. 90 5 7 The predicted CHF enhancement from Equation (5 3) vs. gi ven wicking velocity with hexane, and FC 72 at 1atm. ................................ ........................... 91 A 1 Wavy interface between two fluids of different densities moving with different velocities with finite thickness. ................................ ................................ .......... 101 B 1 Bubble growth for pentane nucleate pool boiling. ................................ ............. 104

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11 LIST OF ABBREVIATION S CHF c ritical h eat f lux DNB departure from nucleate boiling HVAC heating, ventilating and air conditioning NOMENCLATURE Latin letters A area (m 2 ) A v cross sectional area of vapor stem on the heating surface (m 2 ) A w area of the heating surface (m 2 ) c wave speed (m/s) D diameter of bubble (m) F force (kgm/s 2 ) f frequency (1/s) G 0 v 1 H fg 1 ) g gravity (m/s 2 ) H height (m) H fg latent heat (kJ/kg) k wave numbers m mass (kg) n growth rate of the disturbance (m/s) P pressure P r reduced pressure q heat (W) heat flux (W/m 2 ) r radius (m)

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12 s the transient height of a bubble (m) T temperature (C) t time (s) u x direction velocity (m/s) v y direction velocity (m/s) Greek letters potential function thermal diffusivity (m 2 /s) contact angle (degree) radius of curvature (m) macrolayer thickness (m) secondary ripple (m) volumetric ratio of the accompanying liquid to the moving bubble interface boundary function ( m ) curvature ( 1/m ) wavelength ( m ) d most dangerous Taylor wavelength ( m ) dynamic viscosity (kg/ms) density (kg/m 3 ) surface tension (N/m) d the time period of the mushroom bubble departure (s) kinematic viscosity (m 2 /s) stream function surface inclination angle (degree) Subscripts

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13 asy asymptotic condition CHF critical heat flux condition C cirtical condition d departure H Helmholtz l liquid meas measured o normal condition pred predicted s solid sat saturation condition T Rayleigh Taylor wavelength superheat temperature (T w T sat ) v vapor w wall (heating surface)

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14 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillm ent of the Requirements for the Degree of Doctor of Philosophy A NEW MECHANISTIC UNDERSTANDING AND MODELING OF POOL BOILING CRTICIAL HEAT FLUX ON HORIZONTAL SURFACE By Cheng Kang Guan D ecember 2011 Chair: James F. Klausner Major: Mechanical Engineering This work proposes a new mechan istic model for predicting the c ritical heat flux (CHF) in horizontal pool boiling systems. It is postulated that when the vapor momentum flux is sufficient to lift the liquid macrolayer from the heating surface, wetting is no longer feasible, and a transition from nucleate to film boiling occurs. The model considers liquid/vapor interfaces in the horizontal configuration during the transition from nucleate to film boiling. An experimental investigation of CHF with pentane, h exane, methanol, FC 72, FC 87, and R113 in saturated horizontal pool boiling with reduced pressure from 0.01 to 0.24 ( 100 kPa to 450 kPa ) provides evidence that the new model captures the variation of CHF with pressure reasonably well compared with previou s well known models. The new model predicts CHF with pentane, hexane, and methanol well and slightly over predicts the change in CHF with increasing pressure. The predictive capability of the new CHF model is better with fluids which produce larger depart ing bubble s, because the local dryout phenomenon affects CHF more significant with smaller departing bubbles. The new model is also compared with existing data from the

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15 literature with a reduced pressure range from to The mean deviation between the predicted and measured CHF in hydrocarbon fluids is typically within 20% over the parameter space covered. The predicted CHF follows the trends of the measured CHF for water on different heating surfa ces. The roughness effect on CHF in pool boiling is investigated on a 25.4 mm diameter flat brass heater from random RMS roughness from 150 nm, 650 nm, 2.3 m, and up to 5.5 m with pentane, hexane, and FC 72. The results show that CHF increases with incr easing roughness, and the roughness effect on CHF decreases with increasing pressure. The capillary forces might play an important role in CHF with roughness as well as structured surfaces and nanofluids. There are two major areas to focus on for future s tudies The first is that the local dryout effect should be incorporated in the new model. The second is determining capillary forces and adding the capillary forces into the momentum balance of the lift off model

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16 CHAPTER 1 INTRODUCTION AND LITERATURE REVIE W Critical heat flux (CHF), also called departure from nucleate boiling (DNB), in pool boiling has been extensively investigated for decades due to its destructive consequences when exceeded Figure 1 1 illustrates three different heat transfer regimes in pool boiling (a) natural convection regime in which the amount of heat provided to the heating surface is insufficient to trigger the nucleation sites on the surface, (b) nucleate boiling regime in which the heat flux is sufficiently high to generate bubbles on the heating surface, (c) film boiling regime in wh ich the momentum of the vapor patches formed by coalesced vapor bubbles is sufficient to lift liquid layer away from the surface. Hence, a vapor layer is formed on the top of the surface. Figure 1 2 shows a boiling curve with increasing heat flux. The boiling curve illustrates the change in wall superheat for changes in applied heat flux. In the natural convection regime, superheat temperature increa ses with increasing heat flux until the heat flux reaches incipience, which is defined as the moment when the first nucleation site is activated on the heating surface. Some of the bubbles from the first nucleation site depart from the surface, and some o f the bubbles float around on the heating surface and activate other nucleation sites. As soon as the nucleation sites are activated, heat immediately is taken away from the bubbles through latent heat; consequently, superheat temperature drops at incipien ce (point a) as shown in Figure 1 2 In the nucleate boiling regime, the surface temperature increases slightly with massively increasing heat flux before the heat flux reaches CHF. CHF demarcates a transition between the nucleate boiling and the film boiling regimes. When CHF is reached, a vapor film that has poor thermal conductivity, blankets the heating surface.

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17 The temperature of the heating s urface increases rapidly since the working liquid cannot rewet the heating surface to move the high heat flux away. As a result, there is a superheat temperature jump from point b to point c after CHF in the boiling curve as shown in Figure 1 2 This phenomenon is also referred to as a boiling crisis or burnout. Nucleate boiling heat transfer is widely used in industry, for example, nuclear reactors, electronics cooling, chemical distillation, steam generators, and heating, ventilating and air conditioning (HVAC). For industrial applications, it is desirable to operate with high heat fluxes and low wall superheat. However, CHF is an operational limi t that must not be exceeded due to safety concerns. There are typically different types of nucleate heat transfer. Nucleate boiling can be characterized as homogenous or heterogeneous nucleate boiling. In homogeneous nucleate boiling, the working fluid c hanges phases spontaneously due to the high energy of the molecules of the working fluid. In heterogeneous nucleate boiling, a superheated surface needs to be introduced. Thus nucleation sites appear on the surface due to the gas traps or the existing va por in cavities. The focus of this work is to understand the CHF event from the boiling surface; therefore, only heterogeneous nucleate boiling will be considered. A majority of the present models can be mainly classified into two groups: hydrodynamic mod els and bubble packing models. Many of these models for predicting CHF in saturated nucleate pool boiling assume an ideally smooth surface. However, most industrial surfaces are not ideally smooth and possess varying magnitudes of surface roughness. Sur face roughness affects wettability, and wettability has an effect

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18 on CHF. Therefore, this work not only proposed a new CHF model but determined the roughness effect on CHF. 1.1 Hydrodynamic Models In 1948, Addoms [1] investigated CHF with metal wires, aluminum nickel platinum and chromel for water at atmospheric pressure. Addoms reported visual observations for the nucleate boiling and the film boiling regimes. From his experimental results, he suggests a linear relationship between ( 1 1 ) In 1951, Kutateladze [2] proposed a hydrodynamic model for predicting CHF in pool boiling based on the Kelvin Helmholtz instability which is the interface instability governed by hydrodynamics. In this model, the vapor moves upward through vapor columns, and the liquid surrounding the vapor columns flows downward. CHF occurs when the drag created by vapor columns is large enough to prevent th e liquid from flowing downward. The model given below has a constant term which needs to be determined by experimental data. The constant, c, varies between 1.2 and 1.9 depending on pressure, working fluids, and the heating surfaces. ( 1 2 ) In 1959, Zuber [3] suggested that the spacing between the nucleation sites is somewhere between the critical to the most dangerous Rayleigh Taylor wavelength (see the appendix A [2] ( 1 3 )

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19 s are similar when and This condition is satisfied as long as the pressure is smaller than the critical pressure. Therefore, E quation ( 1 1 ) with constant, 0.131, is named the Kutateladze / Zuber model and is widely used. Kirichenko and Chernyakov [4] developed an expression for the constant term that accounts for contact angle by calculating the bubble departure diameter with a force balance between the buoyancy force and surface tension force. The use of the surface tension force in the force balance was proposed by Fritz [5] The model is listed in Ta ble 1 1 In 1963 Semeria [6] m easured the primary and coalesced bubble diameters in pool boiling on a cylinder with water at high pressure, 5 MPa and 14 MPa, using high speed cinematography. In 1965, Gaertner [7] studied the active sites in nucleate pool boiling with water on a horizontal 50.8 mm diameter copper disk; visual observations were also reported for high heat flux. However, Gaertner and Semeria did not present visual studies of CHF. Kirby and Westwater [8] observed a thin liquid film on the surface near CHF. The first CHF photographic study was conducted in 1968 by Katto and Yokoya [9] Their photographic study is for saturated pool boiling of water on a horizontal 10 mm diameter copper disk from shown in Figure 1 3 They proposed a mechanism for CHF based on the existence of a liquid film beneath the massive bubbles (mushroom bubbles) on the top of the heating surface Yu and Mesler [10] called this liquid layer the macrolayer. The macrolayer can only rewet the surface when the mushroom bubbles depart. Hence, the amount of heat which can be transferred depends on the departure frequency of the mushroom bubbles and the macrolayer thickness When the liquid macrolayer dries out before the

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20 mushroom bubbles depart, CHF occurs. Katto and Yokoya [9] used an idealized configuration where the liquid macrolayer i s assumed to be of uniform thickness shown in Figure 1 4 Their p roposed model is ( 1 4 ) In their 1976 work, Katto and Yokoya [11] applied a momentum balance between the buoyancy of the bubbles and the inertia force of the fluid to obtain the frequency of the departing bubbles. In 1983, Haramura and Katto [12] found a new expression for the vapor area ratio, of the heating surface which is pressure dependent. The vapor area ratio is the cross sectional area of the vapor jets to the heating surface area. Their CHF model shown in Table 1 1 is based on the mechanism of Equation ( 1 4 ) Sakashita and Ono [13] assumed that the mushroom bubbles are spheri cal and grow uniformly. They applied a force balance between the buoyancy and the drag force acting on the coalesced bubbles to determine the frequency in Equation ( 1 4 ) An empirical constant is required for the departure frequency expression. The CHF model proposed by Sakashita and Ono is listed in Table 1 1 Kandlikar [14] developed a CHF model by considering a momentum b alance between the surface tension force, the gravity force, and the fluid inertia on a single isolated bubble parallel to the heating surface. Kandlikar hypothesized that CHF is triggered when the bubble interface expands rapidly due to the larger inert ial force. Table 1 1 The model includes the contact angle and the surface inclination angle. No explanation is given as to why the moving interface of an isolated bubble would trigger CHF. Lienhard et al. [15] in 1973 used a 6.35 mm diameter copper surface to boil acetone, benzene, isopropanol, methanol and

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21 distilled water to investigate CHF at sub atmospheric pressure with different measured CHF varied from 59 % Lienhard and Dhir [16] in 1973 improved the Kutateladze/Zuber model for flat surfaces by using the most dangerous Rayleigh Taylor wavelength. The constant term becomes 0.149. Lienhard et al. [15] show ed that the model with c=1.49 agrees better with flat surfaces. Mokrushin [17] in 1988 calculated the macrolyer thickness by model. However, superheat temperature is In 1987, Ramilison and Lienhard [18] heated a 63.5 mm diameter and 15.24 mm thickness copper plate and reached CHF with pool boiling of pentane, Freon 133, [19] In 1988 Samokhin and Yagov [20] compared CHF on a 64 mm diameter, 30 mm thick copper disk at low and high reduced pressures with hexane, F 133, and water. model with constant c=0.14. The empirical formula is suggested as within 13 % error. Bailey [21] tested CHF on a 100 mm 2 nickel coated copper disk in pool boiling with pentane, methanol, and water under the pressure from 100 to 600 kPa. Again, the measured CHF data show that al. [21] s uggested that the constant term should be 0.17 based on their experimental data. Sakashita and Ono [13] collected CHF data at high pressure up to 7 MPa, on a 27.5 mm long, 4 mm wide, and 20 m thick nichrome heater with water. A visualization of the boiling behavior at different

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22 pressure for their work is shown in Figure 1 5 None of the available CHF models are adequate for predicting CHF at high pressure with water without modifying the frequency of the mushroom bubble departure suggested by Sakashita and Ono [13] Nishio et al. [22; 23] observed that the liquid film and the wavy interface of filmwise bubbles (mushroom bubbles) exist on top of the heater surface. They attribute this to the interface instability, Figure 1 6 The subfilm seen in Figure 1 6 is defined as the liquid film including the un departed bubbles. This observation suggests that mushroom bubble departure is controlled by Rayleigh Taylor instability. Galloway and Mudawar [24; 25] studie d vertical flow boiling CHF using high speed cinematography They observed that periodic wetting fronts are the cause of sustain able nucleate boiling. When the evaporating vapor momentum flux is larger than the normal stresses acting on the liquid wetting front s on the heating surface, the liquid layer lifts off, and the heating surface becomes covered with a vapor film. This mechanism describes the process of the transition from the nucleate boiling to the film boiling regime. The CHF mech anism is identified as a high vapor momentum flux lifting the liquid wetting front away from the heating surface. The pressure difference acting on the wetting front is evaluated using a two fluid model coupled with a Kelvin Helmholtz instability analys is. Sturgis and Mudawar [26] extended the analysis to horizontal flo w boiling. The macrolayer was previously defined as the thin liquid layer between the heating surface and the massive vapor bubble, called the mushroom bubble Previous researchers have postulated the thickness of the macrolayer.

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23 Gaertner and Westwater [27] measured the a verage bubble departure diameter, on a 5 cm flat horizontal copper disc with water at ambient pre ssure in saturated pool boiling, and assumed the following relationship between the bubble departure diameter and the macrolayer thickness, The best empirical fit for the macrolayer thickness based on the data from Gaertner and Westwater is proposed by Bhat et al. [28] ( 1 5 ) Later, Iida and Kobayasi [29] also measured the macrolayer thickness with a horizontal copper disc of 2.9 cm diameter with water at atmosphere pressure and Bhat et al. [28] found the best fit as ( 1 6 ) Serizawa [30] suggested that the macr olayer has a primar y effect on CHF In 1983, Bhat et al. [28] predicted the ma cr olayer thickness by using bubble coalescence and heat transfer effects a nd compared the prediction with data of Gaertner and Westwater [27] and Iida and Kobayasi [29] In the same year, Haramura and Katto [12] postulated a hydrodynamic model for predicting CHF with the assumption of that the macrolayer thickness is a quarter of the critical wavele ngth of the Kevin Helmholtz instability which is written as, ( 1 7 ) Haramura and Katto [12] suggested that the vapor area ratio is ( 1 8 ) Substituting Equation ( 1 8 ) into Equation ( 1 7 ) gives

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24 ( 1 9 ) In 1992, after measuring the macrolayer thickness using electrical impendence probes method on a 9 m roughness copper suface with ethanol, methanol, methyl ethyl ketone, isopropanol, acetone, and water, Rajvanshi et al. [31] suggest ed that the macrolayer thickness is a half of the critical wavelength of Keven Helmholtz instability, which is given by, ( 1 10 ) The deviation between the predicted and measured macrolayer is within 20 %. Kumada and Sakashita [32] in 1992 proposed a semi empirical correlation for the macrolayer thickness based on forces acting on bubbles which coalesce and form the macrolayer thickness. The correlation is written, ( 1 11 ) where : blowing velocity of vapor (m/s) Sakashita et al. [33] applied the approach from Kumada and Sakashita [ 34] and introduced the growth of the mushroom bubbles which are independent of the superheat temperature from [35] to obtain the following correlation for macrolayer thickness, ( 1 12 ) The Equation ( 1 12 ) represents the data well as long as the blowing velocity of vapor in the range of

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25 1.2 Bubble Packing Models Rohsenow and Griffith [36] in 1956, developed a bubble packing model for CHF in pool boiling. The nucleation site density on the surface increases with increasing heat flu x. They postulated that once the spacing of the nucleation sites is smaller than the size of the bubbles on the surface, all the bubbles coalesce and form a vapor film to cover the heating surface. Based on the data from Addoms [1] and the departure bubble frequency from Jakob [37] Rohsenow and Griffith [36] correlated the CHF model to be, ( 1 13 ) Chang and Snyder [38] introduced a CHF model by employing the motion of departing bubble s They used the bubble departure model proposed by Jakob and Fritz [37] in order to predict CHF. The model includes the contact angle te rm as shown below, ( 1 14 ) Moreover, after comparing the predicted and measured CHF with the range of contact angle from 46 to 60 degrees, Chan g and Snyder suggested that the constant term in Equation ( 1 2 ) should be in the range from 0.17 to 0.23. Ha and No [39] proposed a dry out theory for predicting CHF based on two major assumptions. First, the nucleation sites on the heating surface scatter randomly according to a Poisson distribution. This assumption was first proposed by Gaerner and Westwater [27; 40] Later, Kenning and Del Valle [41] and Wang and Dhir [42] also suggested that the potential active nucleation sites follow the Poisson distribution. Second, the influence of the overlap between bubbles on heat transfer is negligible.

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26 Based on their assumption the heat flux can be obtained if the average density of the nucleation sites and heat transfer by a single bubble site are specified. ( 1 15 ) where : heat transfer by a single bubble site : average density of the nucleation sites The second assumption is doubtful because Kenning and Del Valle [41] concluded the effect of o verlap bubbles on heat transfer is not large as long as the bubbles still can retain individual identities on the surface. However, the bubbles coalesce before departing from the surface near the CHF condition. As a result, the individual bubble does not e xist on the surface near the CHF condition. To improve Equation ( 1 15 ) Chung and Ho [43] introduced a parameter, called nucleate boiling fraction. ( 1 16 ) Wehre : number of isolated bubbles based on the dry spot area : expected number of isolated bubbles on the surface area ( = ) A: surface area The number of isolated bubbles, is counted from the dry spot area, Chung and Ho [44] and the expected numbers of isolated bubbles is calculated based on Wang and Dhir [42] assumption that all the bubbles are isolated. The predicted CHF is obtained by multiplying Equation ( 1 15 ) and ( 1 16 ) ( 1 17 ) Chung and Ho correlated the nucleate boiling fraction with the measured experimental data on a 40 5 mm sapphire plate with R 133 [44]

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27 1.3 Surface Effects The effects of the heating surface in pool boiling on CHF have been studied since [45] Houchi n and Lienhard [46] Guglielmini and Nannei [47] have shown that CHF increases with increasing heater thickness. Increasing heater thickness beyond a critical value is observed to have minimal effect on improving CHF. This critical value, generally referred to as the asymptotic heater thickness, corre sponds to the heater thickness at which 90% of the asymptotic CHF ( Figure 1 7 ) is suggested with increasing CHF. Asymptotic CHF is reached when further increasing the heater thickness has no effect on CHF. Previous researchers have suggested different parameters to correlate the asymptotic heater thickness. The CHF results of Carvalho and Bergles [48] illustrate that the asymptotic thickness is normally less than 1 mm. In the present investigation, the thickness of the heating surface is kept at 25 mm in order to avoid any heater thickness effects on CHF. The size of the heater has been studied by Lie nhard [15] Kutatelad ze [2] and Rainey [49] When the characteristic length of the heater is smaller than twice of the Taylor wavelength, Bobrovich et al. [50] suggested that s maller heater sizes result in higher CHF. The characteristic length of the heating surface tested in this work is at least larger than twice of the Taylor wavelength corresponding to the work ing fluids, pentane, hexane, methanol, FC 72 FC 87, and R113 A lso CHF depends on the orientation [49; 51; 52; 53; 5 4] and the shapes of the surface, for example, ribbon [55; 56; 57] wire [58] tube [6; 59; 60] and flat [13; 15; 18; 21; 61; 62] This work is confined to a horizontal flat surface. Berenson [63] prepared a 50.8 mm diameter copper surface with different roughness, material, and cleanliness to compare with pentane pool boiling CHF. The

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28 results show that CHF is independent of surface co nditions. The repeatability of CHF is approximately within 10 percent. Lienhard et al. [15] tested CHF on different sizes of horizontal square surface from 8.9 mm to 21.6 mm width with isopropanol, methanol and ethanol. The result shows the smaller surfaces have higher CHF wh en the width is less than twice the most dangerous Taylor wavelength, ( 1 18 ) Gogonin and Kutatzladze [64] suggested that CHF is independent of the heater size as long as the heater size is twice as large as the capillary length. ( 1 19 ) Auracher and Marquardt [65] used the same sized heater with different materials including aluminum, Nichrome, Teflon, tantalum, platinum, and steel to investigate CHF in pool boiling with water. They proposed an experimental correlation written below between CHF and the contact angle in the pool boiling with water on different heating surface at atmospheric pressure. ( 1 20 ) where Jung and Kwak [66] suggested that CHF changes from 240 kW/m2 to 172 kW/m2 by decreasing roughnes s from 307 nm RMS to 150nm RMS on a 23 mm 23 mm square silicon chip with FC 72. Jones et al. [67] investigated CHF with FC 77 and various RMS roughness of the heating surface finished with electrical discharge machining from 0.03 m, 1.08 m, 2.22 m, 5.89 m, to 5.89 The CHF, 188 kW/m 2

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29 does not change with the RMS roughness over 1 m. Nev ertheless, CHF is 137 kW/m 2 with the RMS roughness 0.03 m. Wu et al. [68] tested CHF for water and FC 72 on a 10 mm width square flat copper surface coated with SiO 2 and TiO 2 The water contact angles on these three surfaces change from 62 57 to 9 respectively, and the FC 72 contact angles are too small to measure with all surfaces (highly wetting). CHF with water increases 50% with decreasing contact angles. Even though the contact angle is negligible in FC 72, CHF still increases 38% between the copper surface and the TiO 2 coated surface. The roughness is similar betwee n the two coated surfaces. However, CHF is at least 15% different between the two coated surfaces with both water and FC 72. The experimental results show that surface roughness has influence on CHF in saturated pool boiling. This work establishes a new CHF model, called the lift off CHF model, to predict CHF based on the existence of the liquid macrolayer. The reason it is called the lift off CHF model is that CHF occurs when the liquid macrolayer lifts from the heating surfa ce and will not be able to further wet the surface. Based on experimental observations, a physical mechanism is postulated for CHF, and a new mechanistic model for saturated pool boiling CHF on horizontal surfaces is developed using Rayleigh Taylor insta bility, Kevin Helmholtz instability and the macrolayer theory presented in Chapter 2 Chapter 3 provides details on the experimental boiling facility and the preparation of the heater sections. The measurement and calibration of the thermocouples and th e pressure transducers are discussed. Finally, the pool boiling experimental procedures are discussed at the end of Chapter 3

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30 The comparison between the experimental CHF data and the CHF models with pentane, hexane, methanol, FC 72, FC 87, R113, and water is discussed in Chapter 4 The heat transfer coefficients at CHF for different testing fluid are also compared in this chapter. The CHF lift off model agrees well with the pentane, hexane, and methanol FC 72, and FC 87 experimentally measured CHF. The local dryout phenomenon appears with FC 72 and R113 in pool boiling. The lift off model follows the correct trend for changes in pressure with pentane, hexane, methanol, and water. The wettability might play a major role with water because it is moderatel y wetting compared with pentane, hexane, methanol, FC 72, FC 87, and R1 1 3. The focus of Chapter 5 is the roughness effect on CHF in saturated pool boiling on a flat surface. The range of root mean square (RMS) roughness on the heating surface is tested f rom 150 nm to 5.5 m. The results show that CHF increases 10 20 % with increasing roughness. The capillary forces might play an important role in increasing CHF with increasing roughness. In Chapter 6, f uture work will study local dryout phenomenon in pool boiling, and determine the capillary forces acting on the liquid macrolayer. The lift off model will be improved by adding those two effects.

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31 Figure 1 1 Three different pool boiling heat transfer regimes Figure 1 2 Pool boiling curve with increasing controlled heat flux. (a) (b) (c) Natural convection Nucleate Boiling Film Boiling

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32 Figure 1 3 The mushroom bubble behavior right after CHF in water pool boiling on 10 mm copper disc. The time interval between each frame: 8.8 ms used with permission from Katto, 1976, page 49, Figure 2 [11] Figure 1 4 Idealized representation of liquid macrolayer and mushroom bubble. Figure 1 5 Boiling behavior near CHF on a flat nichrome surface in water at different pressure used with permission from Sakashitia, 2009, page 748, Figure 6 [13]

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33 Figure 1 6 Liquid film under the mushroom bubble on a copper ribbon (40 mm length, 0.5 mm wide, and 0.2 mm height) in pentane at 92% of CHF used with permission from Nishio, 1998, page 9, Figure 15. [23] Figure 1 7 Procedure for determining asymptotic thickness

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34 Table 1 1 Summary of CHF models for a flat horizontal surface Critical Heat Flux Models Kutateladze [2] Where Zuber [3] Kirichenko and Chernyakov [4] Where is the contact angle in degree Lienhard and Dhir [16] Haramura and Katto [12] Where Kandlikar [14] Where is the contact angle ; is the surface inclination angle Bailey et al. [21] Sakashita and Ono [13] cr olayer thickness (1995)) Current Lift off Model

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35 CHAPTER 2 T HEORETICAL CHF MODEL FOR SATURATED POOL BOILING 2.1 Observation of Physical Phenomena In the present study, high speed video is used to capture the transition from nucleate boiling to film boiling (i.e. CHF). The observed transition time from nucleate boiling to film boiling varied from 2 5 seconds. Based on visual observation, the transition time was determined to be pressure dependent. Shorter times were observed with higher pressure and conversely longer times were observed for lower pressure. Figure 2 1 shows a typical time sequence of the transition from nucleate to film boiling for the pool boiling of pentane on a brass horizontal flat circular heating surface with a diameter of 25.4 mm. It should be noted that the black bar visible in the images is an unheated section of a bulk coil heater. It is positioned approximately 2 cm behind the boiling surface. Its proximity to the heating surface has no influence on the near surface flow field, as confirmed by visual observation. For Figure 2 1 the applied heat flux is 316 kW/m2 and the measured wall superheat is Tsat= 20 C at 150 kPa. The first image shows fully developed nucleate boiling in the vigorous nucleate boiling regime, which precedes CHF. It can be seen that three to four similar sized mushroom bubbles are growing and departing from the surface. These large mushroom bubbles were observed to hover above the surface for longer periods of time, as compared with isolated bubbles observed during nucleate boiling. This can be attributed to their low departure frequency which is further dictated by the rate of vaporization from the macr olayer. Even though the liquid macrolayer is not visible in the image, due to the large vapor production, its existence has been confirmed and its thickness has been measured by Rajvanshi et al. [31] using an impedance probe.

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36 At time t = 0.0 s, a small vapor patch appears at the right edge of the heater surface and is circled for identification in Figure 2 1 The vapor patch, which propagates from right to left, is also circled at t = 0.2 s. As time progresses, the vapor patch propagates across the surface as a vapor front. The de parting bubbles tend to lean to the left due to the liquid momentum of the moving front. At time t = 2.4 s and t = 2.6 s the disturbance has propagated across the heater as identified by the circles. At t = 2.8 s the entire heater is blanketed with vapor and the transition to film boiling is complete. The slow and periodic production of vapor after t = 2.8 s is characteristic of film boiling. Hence, CHF does not occur instan taneously a cross the entire surface but in fact occurs locally and propagates across the surface. Kutalatedze [2] and Zuber [3] assumed that CHF occurs when the liquid flow to the surface is reduced due to vapor drag produced at the interface of the vapor jets. Bas ed on their assumption, CHF should occur instantaneously. For this reason their proposed CHF mechanisms do not agree with the observ ed chain of events depicted in Figure 2 1 It is observed that liquid macrolayer dry out is initiated locally and propagates across the heating surface. Uniformity of the macrolayer thickness is not guaranteed because dry out occurs locally on the heating surface. Conse quently CHF models based on that of Katto and Yakoya [11] which assumed a existence of a uniform liquid macrolayer thi ckness in Equation ( 1 4 ) Close inspection of Equation ( 1 4 ) shows that CHF depends on the average departure frequency of the mushroom bubbles, which is difficult to measure. Therefore, most CHF models use empirical correlations for departure frequenc y. From visual observations, no isolated bubbles are observed on the surface at high heat flux; therefore, the CHF

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37 models based on the bubble packing theory are unlikely to produce accurate results. Therefore, this work presents a new CHF mechanism to ad dress the observed phenomena. 2.2 Theoretical Lift off CHF Model In developing the present lift off CHF model, the idealized nucleate boiling configuration suggested by Haramura and Katto [12] is applied. Figure 1 4 depict ed a two dimensional liquid/ vapor structure operating near the critical heat flux where a liquid macrolayer resides on the heating surface L arge mushroom bubbles, fed by vapor jets, hover over the liquid ma crolayer. The large mushroom bubbles depart from the liquid macrolayer in a periodic manner. The vapor stems are highly unstable; therefore they are sensitive to small disturbances. Vapor jet coalescence results in the formation of vapor patches, as shown in Figure 2 2 Leftover vapor stems that do not coalesce into the vapor patch do coalesce with nearby vapor stems to form vapor slugs. It is assum ed that the spacing of the vapor slugs is the most dangerous Rayleigh Taylor wavelength suggested by Lienhard and Dhir [16] and Haramura and Katto [12] The vapor patch resides beneath the liquid macrolayer, and nuc leate boiling can only be sustained when the liquid macrolayer re wets the heating surface. It is also assumed that the interface between the vapor patch and the liquid macrolayer is a wavy interface. Since it is a wavy interface, the liquid macrolayer i s not uniform and therefore local dry out phenomenon is more likely to occur. Haramura and Katto [12] proposed that t he li quid macrolayer thickness is one quarter of the critical wavelength for the Kelvin Helmholtz instability. Rajvanshi et al. [31] provide experimental measurements of the liquid macrolayer thickness that are

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38 better correlated with one half the critical wavelength for Kelvin Helmholtz instability. Here the liquid macrolayer thickness suggested by Rajvanshi et al. [31] is adopted as shown in Equa tion ( 1 10 ) A differential slice of the liquid macrolayer is displayed in Figure 2 2 Note that there is a liquid/vapor interface above and below the macrolayer. Vapor is ejected beneath the macrolayer due to evaporation of the superheated liquid. It is assumed that the vapor ejected from the liquid macrolayer i s directed downward toward the solid heating surface, and the velocity field is relatively invariant within the time scale required for CHF to occur. The difference in the pressure stress above and below the liquid/vapor interface (interface 1) drives the interface toward the heating surface, and the vapor momentum flux acts to lift the interface away from the surface. When the two entities balance, the critical vapor velocity required for CHF is identified. Galloway and Mudawar [25] used a similar approach to predict CHF in flow boiling. As such, conservation of momentum applied to a control volume at the bottom of the liquid layer around interface 1 requires, ( 2 1 ) where P is the pressure and is the vapor velocity. Since the liquid vapor interface is infinitesimally thin, the effect of the body force vanishes in the limit. Should the interface move very close to the surface, there will be a lubrication effect and disjoining pressure effects may significantly alter the local pressure field which would require a modification of Equation ( 2 1 ) to account for these effects. Nevertheless, it is satisfactory for identifying the vapor velocity at CHF. On the other hand the Young Laplace condition at the liquid/vapor interfaces dictates that,

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39 ( 2 2 ) where r 1 is the local radius of curvature at interface 1. Combining Equation ( 2 1 ) and ( 2 2 ) gives an expression for the critical heat flux vapor velocity as, ( 2 3 ) As depicted in Figure 2 2 there is a liquid layer that resides over the mushroom bubble, and the liquid macrolayer resides over the vapor patch disturbance. Therefore, i t is reasonable to expect that the vapor structure for both liquid/vapor layers is governed by the Rayleigh Taylor instability. The most dangerous Rayleigh Taylor wavelength (see the appendix A ) for liquid and vapor layers of infinite extent is, ( 2 4 ) It is found that the most dangerous wavelength for liquid and vapor layers of infinite extent given by Equation ( 2 3 ) only differ s from those of finite extent by a few percent as discussed in the appendix A For the purpose of the present study, Equation ( 2 4 ) is thus deemed satisfactory. It is assumed that the shape of liquid/vapor inte rface 1 follows a cosine form as, ( 2 5 ) where is the macrolayer thickness from Equation ( 1 10 ) c is the wavelength of the disturbance interface, and is added to account for secondary ripples that may appear at the interface. Since the liquid/vapor interface is subject to evaporati on, the interface will remain smooth and it is safe to let 0. Note that a two dimensional analysis is

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40 assumed satisfactory since the disturbance wave primarily propagates unidirectionally as observed in Figure 2 1 The radius of curvature of interface 1 is, ( 2 6 ) Only a positive radius of curvature is considered here because interfaces with a negative radius of curvature are consistent with a net pressure stress lifting the liquid macrolayer from the surface. The liquid macrolayer only wets the surface when the interface radius of curvature is positive. Portions of the interfa ce for which the radius of curvature is a minimum are where the vapor velocity is at a maximum (Equation ( 2 3 ) ). Reaching the critical vapor velocity in the minimum r adius of curvature region guarantees that the entire macrolayer can be removed from the surface. The minimum radius of curvature is ( 2 7 ) An energy balance on the liquid macrolayer relates the vapor velocity to the surface heat flux, ( 2 8 ) substituting Equation ( 1 10 ) and ( 2 4 ) into Equation ( 2 7 ) and substituting Equation ( 2 7 ) and ( 2 3 ) into Equation ( 2 8 ) yields the critical heat flux, ( 2 9 ) It is of interest that the proposed liquid macrolayer lift off CHF mechanism results in a CHF ex pression similar in form to that of Zuber and many others. The ratio of the critical heat flux predicted by the lift off model compared with that of Zuber is

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41 The lift off model predicts a larger increase in CHF with Table 1 1 summarizes the ratio of various CHF models to that of Z uber. It will be instructive to compare the CHF predictions from these various models with different surface/fluid combinations in an increasing pressure environment. A further discussion of the comparison between experimental results and the currently a vailable CHF models is presented in Chapter

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42 Figure 2 1 Time series images depicting transition from nucleate to film boiling for pentane on a 150 nm RMS roughness brass surface ( T sat kW /m 2 P=150 kPa)

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43 Figure 2 2 Control volume around differential slice of liquid macrolayer. v Vapor Slug

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44 CHAPTER 3 SATURATED POOL BOILI NG FACILITY 3.1 Facility Overview The saturated pool boiling experimental facility was originally designed by Qi [69] for low pressure (around ambient pressure) and bulk fluid temperatures under 100 C. The modified pool boiling experimental facility shown in Figure 3 1 has more capabilities, such as higher operating pressure and temperature, more stable flow field within the chamber, better control of system pressure, reduced heat loss, and improved accurac y of the pressure and temperature measurements. The maximum working pressure inside the saturated pool boiling chamber is 500 kPa and is limited by the hoop stress on the transparent pyrex containment cylinder shown in Figure 3 2 The maximum operating temperature is 200 C. A refrigerated chiller, model R075S made by Raskris, feeds 15 C water to the copper cooling coil of the saturated pool boiling c hamber through a 6.35 mm diameter PVC hose. The chiller returnline is designed to accomodate superheated vapor and thus a 6.35 mm diameter copper tube is used. The needle valve at the outlet of the cooling coils adjusts the flow to control the rate of c ondensation and thus the pressure inside the chamber. The needle valve is placed at the discharge of the cooling coil so that pressure and flow fluctuation are avoided The analog signals from the pressure transducer and thermocouples are digitized by a multifunction data acquisition (DAQ) board, model NI USB 6218, manufactured by National Instruments. The bulk coil heater and the surface test section heater are controlled by analog autotransformers (from 0 to 220 volts)

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45 3.2 Saturated Pool Boiling Chamber The chamber contains 6 major parts as shown in Figure 3 2 ; stainless steel base and top with 152.4 mm diameter, a 101.6 mm diameter transparent pyrex containment cylinder (101.6 mm diameter, 6.35 mm thickness, and 0.45 m length), a 6.35 mm diameter copper cooling coil a bulk coil heater, and a 25.4 mm diameter surface test section. Each stainless steel plate has a circular groove to fit the pyrex cyl inder. Two viton o rings coated with high temperature vacuum grease are placed in the grooves on the plates. The two plates are bolted with 6 rods to compress the o rings between the pyrex cylinder and each stainless steel plate to prevent leakage. The stainless steel base holds a copper drain tube, a bulk coil heater with 46.5 kW/m 2 of heat flux, a 3.8 mm diameter bulk E type thermocouple which sticks out 25. 4 mm from the base and the 25.4 mm diameter surface test section. The top plate is assembled with a relief valve held at 470 kPag the copper cooling coil outlet and inlet, a vent tube, a fluid inlet tube, a pressure gauge, and an extension tube which co nnects to a pressure transducer. The bulk coil heater has a spiral shape with 2.5 circulars. The spiral shape d heater hover ing 55 mm above the surface creates even heating to avoid an unbalanced convection field which may disturb the boiling experiment in the bulk. For safety the relief valve will be activated when the gauge pressure exceed s 470 kPa inside the chamber. The reason to have the extension copper tube to connect the pressure transducer instead of having the pressure transducer directly assemb le d on the top plates is that the operating temperature of the pressure transducer cannot exceed 85 C. The copper extension tube cools down the saturated vapor of the working fluid which then condenses to liquid at the hook before the vapor reaches the pr essure transducer as shown in Figure 3 2

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46 3.3 The Surface Test Section The horizontal brass cylindrical heater section is shown in Figure 3 3 The diameter of the upper boiling surface is 25.4 mm. Four 6.35 mm diameter, 5 cm long cartridge heaters are inserted through the bottom side of the heater b lock and can produce a maximum of 1578 kW/m 2 heat flux at the boiling surface. The heater block is covered with high temperature fiberglass with a thermal conductivity less than 0.04 Wm 1 K 1 Two sets of three type E thermocouples are embedded vertically into the heater block with an equal separation of 5 mm. The distance between the test surface and the closest thermocouple is 10 mm. A low viscosity epoxy, which binds to brass and endures up to 315 C, is introduced to seal the edge of the test surface for two reasons. First it prevents bubbles from nucleating at the heater edge, and second it prevents the heater edge from being damaged while polishing, transferring, and assembling the heating surface. After the heater section is assembled with a bras s bushing and the base plate, the assembled heater section is covered with another layer of high temperature fiberglass. The flange material used to seal the heater section is polyether ether ketone (PEEK). The thermal conductivity and temperature limit of the PEEK flange are 0.25 W/m K and 343 C, respectively. The brass heater thermal conductivity is 109 W/m K, and the heat fl ux to the boiling surface is approximately one dimensional. Thus, the surface temperature and heat flux can be determined by li nearly extrapolating the measured temperature to the surface. 3.4 Surface Finish The brass surface is polished with 60 grit, 300 grit, 600 grit, and up to 1000 grit sandpapers with a polishing wheel to reach a roughness of the heating surface from 5.5 m, 2.3 m, 650 nm to 150 nm, respectively The root mean square (RMS) roughness

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47 is measured with a n optical profilometer to within 10 nm uncertainty with smooth surfaces (the RMS roughness is less than one micron ) The optical profilometer use s white light inte rferometry to produce high quality three dimensional surface maps of the test samples. Normally, the optical profilometer cannot test the surface roughness which is rougher than 2 m because the light scatters too many times and cannot reflect back to the optical sensors. The image and the profile of the surface roughness, which is 150 nm RMS, are shown in Figure 3 4 A stylus profilometer is used to test the surfaces rougher than one micron The stylus profilometer u s es a spring with a diamond tip touching test samples and moving a cross the samples and tracking the surface profile The limitation of the stylus profi lometer is the size of the ti p so t he measurement range of the stylus profilometer is from 0.1 m to 60 m. The surface is cleaned with ethanol prior to being installed in the saturated pool boiling chamber. The polishing cloth discs and alumina compound powders are used on a polishing wheel after the surface is polished by the 1000 grit sandpaper in order to achieve a RMS roughness less than 150 nm. The compound powders and the clean distilled water have to be mixed completely without grouping particles in advance to avoid unexpected scratches from grouping particles. Clean distilled water is continuously supplied on the polishing cloth discs during the polishing process. The particle sizes of the alumina co mpound powders are gradually decreased from 3 m, 0.9 m, and 0.5 m until the RMS roughness of the heating surface reaches 20 nm. 3.5 Measurement and Calibration The E type thermocouples braided with fiberglass which can operate up to 320 C within 1 C error are used for the heater, and the size of the wire s is 0.0254 mm diameter. The response time of the thermocouples is 0.05 seconds.

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48 The thermocouples are calibrated in a bath with silicon e bath fluid on a hot plate. The icing point a nd the boiling point of the silicon bath fluid are 40 C and 315 C, respectively. The calibration temperature range is from room temperature to 170 C. There are 11 calibration points in the entire range. All the thermocouples agree with each other, as s hown in Figure 3 5 One 2nd order polynomial curve fit is applied to each thermocouple. All R squared values are larger than 0.9999. The standard devi ation between the measured and predicted temperature is 0.02 degrees Celsius. The pressure transducer is calibrated using a compressed gas tank with a digital calibration pressure gauge to within 0.05% accuracy in the temperature range from 18 C to 66 C. The calibration process is done at room temperature, 25 C. The data fit a l inear line with R squared value 0.9999 shown in Figure 3 6 The stand ard deviation is less than 1.4 kPa. The USB multifunction data acquisition (DAQ) board from National Instrument s has 16 bit resolution with the full measured voltage range Therefore, the resolution and the quantization error are ( 3 1 ) For E type thermocouples, when the temperature increases from 0 C to 1 C, the voltage increases 0.06 mV; from 150 C to 151 C, the voltage increases 0.071 mV which is at least 4 to 5 times smaller than the resolution, according to the E type thermocouple database from the Nation Institute of Standards and Technology [10]. As a result, the DAQ board can only detect the change of temperature when the change is more than 4~5 C. In short, the resolution is limited by the 16 bit b oar d with the full

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49 range of the voltage. Nevertheless, the voltage range for E type thermocouples from 0 C to 300 C is from 0 V to 20 mV. Hence, the minimum and maximum operating voltages are set as 1 mV and 30 mV, respectively. The DAQ board will automatically adjust the resolution with a given operating range. After adjusted the resolution is much smaller than the error of E type therm ocouple which is 0.2 C. It is guaranteed that the A/D converter does not limit the ability of the measurement. Digital multimeters made by Keithely are used to measure the analog voltages and currents of the cartridge heaters for calculating the heat f lux from the surface. The uncertainty of the measured analog voltage (AC) is 1% of the reading and that of the measured AC current is 1.25% of the reading. As a result, the uncertainty of the calculated heat flu x is 7 kW/m 2 3.6 Procedure for the Saturated Pool Boiling Experiment Before the saturated pool boiling experiment is conducted, two procedures must be completed to avoid non condensable gas in the chamber and to prevent gas and vapor tra pped on the surface. First, the working fluid goes into the chamber from the fluid inlet through a funnel with the opened vent valve and the closed drain valve until the level of the working fluid reaches 100 mm. With the liquid level, the surface test se ction, the bulk thermocouple, and the bulk coil heater completely immersed in the working fluid, boiling experiments commence In order to reach the saturation temperature for the working fluid at the desired pressure, the bulk heater and the surface test section heater are powered by the autotransformers to heat the working fluid with all the valves closed. During the heating process, the vent valve should be opened periodically until all the non condensable gases are purged. The layer between the non c ondensable gas and the

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50 vapor phase of the working fluid is observable. The layer goes up throughout the purging process until it reaches the top of the plate. Once the working fluid reaches saturation temperature at the desired pressure, the pressure can be controlled by the water flow rate in the cooling coil and the bulk heater via adjusting the autotransformer within 3 kPa uncertainty. Second, the heat flux at the surface is kept at 95 % of the critical heat flux for at least an hour to entrap the t rapped air and gas in the cavities on the surface. After the heater power is off, i t is necessary to wait until the temperature of the surface is cooled down to the saturation temperature allowing the liquid to rewet the surface completely before the expe riment is started. The procedures to conduct the saturated pool boiling experiment are as follows: In the natural convection heat transfer regime, the heat flux to the heating surface is raised in increments of 2 5 kW/m 2 and the system is allowed to reac h steady state before heat transfer measurements are collected In the boiling regime, the heat flux is continually increased in larger increments of 50 100 kW/m 2 before the heat flux reaches 95% of the critical heat flux. The increments of heat flux are then raised in 5 10 kW/m 2 until the heating surface shows a very rapid rise in temperature, which signals the transition from nucleation to film boiling as shown in Figure 3 7 In Figure 3 7 the heat flux drops rapidly after CHF because the vapor film is formed to prevent the heat transferred thr ough latent heat from the surface. The power to the heating section is immediately cut off when the CHF threshold is crossed.

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51 Figure 3 1 Sketch of the saturated pool boiling facility. Figure 3 2 Sketch of the saturated pool boiling chamber.

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52 Figure 3 3 Cross section area of the surface test section. Figure 3 4 Roughness image and profile from the profilometer

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53 Figure 3 5 Temperature calibration curve fit. Figure 3 6 Pressure calibration linear fit.

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54 Figure 3 7 Heat flux and temperature versus time in transition boiling.

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55 CHAPTER 4 COMPARISON BETWEEN T HE EXPERIMENTAL RESU LT AND THE CHF MODEL S Pool boiling heat transfer has been investigated for pentane, hexane, FC 72, FC 87, and R113 on a brass heating surface with RMS roughness of 650 nm for 5 different pressure s, 150, 225, 300, 375, 450 kPa. Because all the fluids are highly wetting the heating surface is considered smooth for boiling applications. Due to rapidly increasing temperature after CHF, the heating surface temperature may exceed 280 C at a pressure higher than 175 kPa with methanol. At this high temperature and pressure, the epoxies at the edge of the heater and around the PEEK flange as shown in Figure 3 3 start degrading. CHF for methanol is higher than that for other fluids. Therefore, the temperature of the surface for methanol increases higher than that for other fluids after CHF and increases more rapidly Besides, CHF increases with increasing pressure. Hence the methanol CHF measurements are made at pressures of 100, 125, 150, and 175 kPa in order to avoid heating surface temperature exceeding 280 C after CHF The saturate d pool boiling experiments for all the fluids at different pressures are repeated at least twice to check for repeatability. The CHF measurements for all the working fluids are reported in and the repeatability is within 5% as shown The saturated pool boiling curves for pentane, hexane, FC 72, FC 87, R113 and methanol at five different pressures are shown in Figures 4 1 to 4 5 respectively. In the boiling curves, the wall superheat temperature varies more than 20% with given heat flux under the same pressure and testing fluid before and at incipience. The reason for the substantial wall superheat temperature fluctuations is due to the edge boiling effect. After incipience, the wall superheat temperature with a given heat flux

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56 varies within 10% for R113 and methanol and varies within 5% for pentane, hexane, FC 72 and FC 87. Hence, edge boiling only affect s the incipient superheat and does not impact CHF. The pool boiling curves displayed in Figure 4 1 to 4 6 clearly illustrate that the rate of heat transfer increases with increasing pressure as reflected by boiling curves shifting to the left, as expected. Decreasing vapor bubble departure diame ter from nucleation sites is also observed with increasing system pressure as suggested by Zeng et al. [70] On average, nucleation sites with smaller departing bubbles can remove heat at a faster rate than those with larger departing bubbles. The methanol boiling curves shown in Figure 4 6 for pressures ranging from 100 to 175 kPa show only a slight improvement in the heat transfer rate with increasing pressure. This is consistent with the observation that methanol vapor bubbles departing the heating surface do not vary appreciably with increasing pressure. The large mushroom bubbles that depart from the liquid macrolayer are measured during the transition from the nucleate to film boiling regime. Fifty major chord length s of the bubbles for each test fluid is measured and listed in Table 4 2 and compared with the Taylor wavelength. It is observed that the major cord length o f the departing mushroom bubbles agrees reasonably well with the Taylor wavelength. The mushroom bubble major chord length is measured using image processing with Matlab. The video recordings are captured during the transition from nucleate to film boili ng at a rate of a thousand frames per second. The number of pixels corresponding to the surface dimension and the mushroom bubble major chord length can be obtained from the

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57 frames with Matlab. Since the length of the surface 25.4 mm, the major chord length can be calculated with the pixel ratio of the chord length to the surface length. Shows the nucleate to film boiling transition images for different test fluids at vario us pressures. It is clear that the size s o f the mushroom bubbles decrease with increasing pressure in pool boiling. The pool boiling curves for R113 ( Fi gure 4 5 ) re veal some unusual behavior as CHF is approached. It is observed that small incremental increases in heat flux result in large increases in wall superheat, which is not characteristic of nucleate boiling. Such behavior is characteristic of the formation o f local dry patches as would be found during transition boiling. The low pressure FC 72 ( Figure 4 3 ) boiling curves display similar behavior. C.M. Rops. et al. [71] observe this transition behavior on smaller surfaces with water. They tested the heating surface from 4.5 mm to 15 mm diameter disk in pool boiling, the transition section is more obvious with smaller surface size. Based on observations, the transition time takes seconds between nucleate boiling to film boiling for all the test fluids except R113. The transition time for R113 takes minutes to complete once CHF is reaches. The measured heat flux just prior to the transition regime for R113 is denoted as heat flux of transition (HFT). As reflected in R113 boiling curves, it appears th at the local dryout can be stable with slight increase in heat flux. Figures 4 7 to 4 12 show the heat transfer coefficient versus heat flux with different pressures for pentane, hexane FC 72, FC 87, R113 and methanol respectively. As expected the heat transfer coefficient in creases with increasing pressure. It is because the size s of the departure bubbles decrease with increasing

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5 8 pressure. The decrease in departure bubble size increases the frequency of the bubble departure. Heat transfer becomes better with higher frequen cy of the bubble departure, i.e. more vapor leaves the surface. Again, it is not obvious enough to recognize the increase of the heat transfer coefficient for methanol as shown in Figure 4 12 because the increment of the pressure is much smaller than other fluids. Therefore, the decrease in bubble departure diameter is not significant with increasing pressure. As the reduced pressure approaches zero, the difference b etween the different CHF models as listed in Table 1 1 is within 10%. However, as the reduced pressure increases, the difference in predictions from different models becomes significant. Thus, it is instructive to evaluate the efficacy of the different models at higher pressure. The experimentally measured CHF data summarized in Table 1 1 for pentane are compared with the predicted CHF models in Figure 4 13 The models of Zuber [3] and Haramura and Katto [12] [14] tends to over predict CHF when compared with exper imental data. The lift off model gives the best CHF prediction for reduced pressures ranging from 0.04 to 0.13 (150 kPa to 450 kPa). It is also observed that the lift off model is best at matching the CHF dependence on pressure. The uncertainties of the thermal properties, densities latent heat, and surface tension, for pentane that are applied in the models are 0.2% [72] 0.2% [73] and 3.2% [74] respectively. The uncertaint y of the model predictions due to the uncertainties of the fluid properties is approximately 0.8 %. Figure 4 13 only shows the uncertainty range for the lift off mod el. Another way to illustrate the dependence of CHF on pressure is to compare the predicted change in CHF with respect to change in pressure (slope of the CHF vs. P r

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59 curve) with that measured. The measured slopes are calculated using first order forward d ifference for the lowest and midrange pressures and using first order backward difference for the highest pressures. First order forward difference ( 4 1 ) Where The uncertainty of the measured CHF is 5 % for pentane. The uncertainty of the predicted change in CHF with respect to change in pressure can be calculated by substitutin g the uncertainty of the measured CHF in to Equation ( 4 1 ) ( 4 2 ) When both uncertaint ies, and are positive, t he maximum uncertainty of the slope can be obtained from Equation ( 4 2 ) Figure 4 14 shows the change in CHF with reduced pressure (slope of CHF vs. P r ) for pentane. Since the range of the uncertainties of the measured CHF is wider than that of the slopes for all the models, it is not instructive to compare the change in CHF with reduce d pressure. Figure 4 15 shows a comparison of the measured CHF for hexane with the four models over the reduced pre ssure range 0.04 to 0.15 (150 kPato 450 kPa). The lift off model gives a reasonably good prediction. Zuber and Haramura and Katto models The uncertainties of the thermal properties, de nsities latent heat, and surface tension, for hexane that are applied in the models are 0.2% [72] 0.3% [73] and 7.7% [74]

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60 respectively. The uncertainty of the model predictio ns due to the uncertainties of the fluid properties is approximately 1. 87 %. The variation of the measured methanol CHF with increasing pressure is shown in Figure 4 16 over the reduced pressure range of 0.012 to 0.022 (100 kPa to 175 kPa). The lift off, Zuber, and Haramura and Katto models agree well with the measured CHF, while the Kandlikar model over pr edicts the CHF. The uncertainties of the thermal properties, densities latent heat, and surface tension, for methanol that are applied in the models are 0.1% [72] 0.2% [73] and 10% [74] respectively. The uncertainty of the model predictions due to the uncertainties of the fluid properties is approximately 2.4 %. Figure 4 17 shows the com parison of measured CHF for FC 72 over the reduced pressure range from 0.05 to 0.25 (150 kPa to 450 kPa). Haraumra and Katto and Zuber models under predict CHF. Both of the lift off and Kandlikar model over predict CHF data for FC 72. The uncertainty of FC 72 surface tension is approximately 5 % [75] The other fluid properties for FC 72 are provided by 3M Corp. The saturated tables are generated using a correlation with limited measur ed data points. The latent heat of FC 72 at 1 atm is reported as 88J/g in the 3M product information sheet, but the latent heat is reported as 93.7 J/g in the saturated tables. The percent difference in the latent heat prediction is 6.5%. Since CHF is d irectly proportional to the latent heat, there is at least a 6.5% uncertainty in predicting the CHF due to uncertainty in the latent heat. Figure 4 18 shows a comparison of the measured FC 87 CHF data with the four models over reduced pressure range 0.05 to 0.25 (150 kPa to 450 kPa). The Zuber and Haramura and Katto models under predict th e CHF, and the Kandlikar model over

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61 predicts CHF. The experimental CHF data agree well with the lift off model. The uncertainty of FC 87 surface tension is approximately 2% [75] The reported latent heat of FC 87 has a similar problem to that of FC 72. The latent heat is 103 J/g from the product information sheet and 99.7 J/g from the saturated tables. The percent difference in reported latent heat between these two sources is 3 .3 %. Figure 4 19 shows both the measured CHF data and the measured heat flux (HFT) just prior to the transition regime for R113 with the four models over reduced pressure range 0.04 to 0.14 (150 kPa to 450 kPa) As reflected in the R113 boiling curves, it appears that the local dryout can be stable with slight increase in heat flux. Hence, the transition between the nucleate boiling regime and the film boiling regime for R113 requires higher heat flux. All of the models under predict the CHF for R113. The Kandlikar model gives the best prediction of HFT. The uncertainties of the thermal properties, latent heat and surface tension, for R113 that applied in the models are 0. 1 % [73] and 1 % [76] respectively. The uncertainty of the models due to the uncertainties of the fluid properties is approximately 0.25 %. The lift off model predicts CHF well w ith pentane, hexane, methanol, and FC 87. The FC 72 and R113 CHF predictions show more deviation from the data. A significant uncertainty for predicting CHF for FC 72 is the 6.5 difference in the reported latent heat from different sources. The boiling curves for R113 show there is a transition regime with local dryout before CHF occurs, and this is not accounted for in the lift off model. The measured change in CHF with increasing reduced pressure with FC 72, FC 87, and R113 is lower than that for penta ne, hexane, and methanol. It is believed that local dryout prior to CHF is more pervasive with FC 72, FC 87, and R113 compared

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62 with pentane, hexane, and methanol. It is not clear why this is, although, it is observed that the fluids experiencing local dr y out tend to have smaller departing bubbles and higher nucleation site density in the isolated bubble regime than those that do not experience local dryout. The average bubble departure diameters for the isolated bubble regime are computed using a force balance model proposed by Zeng et al. [70] ( 4 3 ) where d is the departure bubble diameter, Cs is the empirical constant equal to 20/3, K and n are the respective leading coefficient and the exponent constant for the power law fit of the vapor bubble growth, ( 4 4 ) where R (t) describes the vapor bubble growth. The vapor bubble growth is computed using a simplified model described by Chen et al. [77] They developed a first order ordinary differential equation for the bubble growth rate based on a liquid microlayer and a lumped thermal analysis for a solid heater in heterogeneous pool boiling. The detail is shown in Appendix B. The estimated bubble de parture diameters for FC 72, FC 87, and R113 at 150 kPa are 0.67 mm, 0.65 mm, and 0.86 mm, respectively Additionally the estimated bubble departure diameters for pentane, hexane, and methanol at 150 kPa a re 1.9 mm, 1.7 mm, and 3.7 mm, respectively All the estimated bubble departure diameters are for an applied heat flux of 2 The departure diameters for pentane, hexane, and methanol are at least twice larger than those for FC 72, FC 87, and R113.

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63 In general, the Zuber [3] and Katto and Haramura [12] models under predict CHF while the Kandlikar [14] model over predicts CHF. Table 4 4 tabulates the mean deviation for the CHF models in Table 1 1 and the current pentane, hexane, and FC 72 CHF data. The mean deviation is de fined as ( 4 5 ) Berenson [63] and Ramilison and Lienhard [18] investigated CH F for boiling of pentane at atmospheric pressure with different surface features. Bailey et al. [21] tested CHF for boiling of pentane on a nickel coated copper heater over a range of pressure. In Figure 4 20 it is observed that the lift off model agrees reasonably well with the measured CHF over a range of pressure. The biggest disparity is the comparison with atmospheric pressure data with different surface features. The current model does not explicitly account for differences in surface properties. Figure 4 21 compares the CHF pr edicted from the lift off model with the low pressure hexane data of Samokhin and Yagov [20] At low pressure the lift off model and that of Zuber coincide, and both models slightly under predict the Samokhin and Yagov CHF data. The Kandlikar model has good agreement at low pressure. Figure 4 22 compares the predicted CHF using the lift off model with methanol CHF data collected by Lienhard et al. [15] and Bailey et al. [21] R 113 CHF data collected by Sterman and Korychanek [78] Abuaf and Staub [79] and Samokhin and Yagov [20] and benzene CHF data co llected by Sterman and Korychanek [78] At both low and moderate pressure the agreement is generally quite good.

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64 Figure 4 23 compares the predicted CHF based on the lift off model with water data published by Lienhard et al. [15] Yagov [61] Bailey et al. [21] and Sakashita and Ono [13] While the predicted trend with increasing pressure is good, CHF is under predicted. The reason the lift off model under predicts CHF for water is likely because wat er is a moderately wetting fluid, and the liquid macrolayer thickness correlation given by Equation ( 1 10 ) tends to under predict the macrolayer thickness for water. All the test fluids have approximately zero contant angle with the brass surface; however, water has 60 to 70 degree contact angle with the brass surface. The comparisons suggest that there is room and need for improving the liquid macrolayer thickness c orrelation. Table 4 4 also compares the mean deviations for different CHF models with the various experimental data sets considered. For the current model, the mean d eviation is approximately within 20%, with the exception of the Samokhin and Yagov [20] and Abuaf and Staub [79] data. This is a very encouraging result considering that the current lift off model does not account for variations in surface wettability and surface characteristics. Other models that give reasonably good prediction over the whole parameter space incl ude Zuber [3] Haramura and Katto [12] and Kandlikar [14] As mentioned previously, visualization of the liquid macrol a yer dynamics is not possible due to interference fr om the extensive vapor production. However, the piece of quantitative information on the flow structure that can be garnered from the video frames shown in is the major chord length of the mushroom bubbles. Should the Rayleigh Taylor instability govern the structure of the liquid/vapor interface in the upper region depicted

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65 in Figure 2 2 the variation in mushroom bubble chord lengths should be close ly correlated with the Rayleigh Taylor wavelength as shown in Equation ( 1 9 ) Chord lengths have been measured and averaged for fifty different observations of mushroo m bubbles that appear in the transition from nucleate to film boiling M easure ments for pentane, hexane, methanol, FC 72 FC 87, and R113 on brass for system pressures of 150, 300, and 450 kPa have been made The average chord length and standard deviation are summarized in Table 4 2 Also shown is the Rayleigh Taylor wavelength. Both the magnitude and trend of bubble chord length and the Rayleigh Taylor wave length show good agreement. The decrease in chord length with increasing pressure is mainly a result of lower surface tension at higher saturation temperature and pressure. Clearly, these data support the supposition that the interfacial structure in the upper region is governed by the Rayleigh Taylor instability. In view of the analysis in appendix A that shows that the Rayleigh Taylor wavelength is insensitive to the thickness of the liquid and vapor layers, it is reasonable to conclude that the Raylei gh Taylor instability also governs the liquid/vapor interaction between the liquid macrolayer and the vapor disturbance patch in the lower region of Figure 2 2

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66 Figure 4 1 Boiling curves for pentane on brass heater surface with 650nm RMS roughness. Figure 4 2 Boiling curves for hexane on brass heater surface with 650nm RMS roughness.

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67 Figure 4 3 Boiling curves for FC 72 on brass heater surface with 650nm RMS roughness. Figure 4 4 Boiling curves for FC 87 on brass heater surface with 650nm RMS roughness.

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68 Fi gure 4 5 Boiling curves for R113 on brass heater surface with 650nm RMS roughness. Figure 4 6 Boiling curves for methanol on brass heater surface with 650nm RMS roughness. Transition

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69 Figure 4 7 Heat Transfer coefficient for pentane on brass heater surface with 650nm RMS roughness with differ ent pressure. Figure 4 8 Heat Transfer coefficient for hexane on brass heater surface with 650nm RMS roughness with different pressure.

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70 Figure 4 9 Heat Transfer coefficient for FC 72 on brass heater surface with 650nm RMS roughness with different pressure. Figure 4 10 Heat Transfer coefficient for FC 87 on brass heater surface with 650nm RMS roughness with different pressure.

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71 Figure 4 11 Heat Transfer coefficient for R113 on brass heater surface with 650nm RMS roughness with different pressure. Figure 4 12 Heat Transfer coefficient for methanol on brass heater surfa ce with 650nm RMS roughness with different pressure.

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72 Figure 4 13 Comparison of CHF models with pentane data Figure 4 14 Change in CHF with reduced pressure for pentane.

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73 Figure 4 15 Comparison of CHF models with hexane data Figure 4 16 Comparison of CHF models with methanol data

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74 Figure 4 17 Comparison of CHF models with FC 72 data. Figure 4 18 Comparison of CHF models with FC 87 data

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75 Figure 4 19 Comparison of CHF models with R113 data Figure 4 20 Comparison of predicted CHF using lift off model with pentane data.

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76 Figure 4 21 Comparison of predicted CHF using lift off model with hexane data. Figure 4 22 Com parison of predicted CHF using lift off model with methanol, R133, and benzene.

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77 Figure 4 23 Comparison of predicted CHF using lift off model with elevated pressure water data.

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78 Table 4 1 Measured CHF for pentane, hexane, and methanol FC 87, FC 72, and R113 for pool boiling at different pressures Saturated Pool Boiling CHF on 25.4 mm Diameter Brass Surface with 6 50nm RMS Roughness Pressure (kPa) Pentane Hexane Methanol FC 87 FC 72 R113 C 5 H 12 C 6 H 14 CH 3 OH C 5 F 12 C 6 F 14 CCl 2 FCClF 2 P r CHF (KW/m 2 ) P r CHF (KW/m 2 ) P r CHF (KW/m 2 ) P r CHF (KW/m 2 ) P r CHF (KW/m 2 ) P r CHF (KW/m 2 ) 100 0.012 513.6 100 0.012 516.7 125 0.015 583. 6 125 0.015 585.0 125 0.015 584. 4 150 0.045 326.9 0.019 62 1.0 0.01 9 621.0 0.074 231.5 0.080 181. 1 0.044 356.7 150 0.045 326.6 0.019 622.8 0.01 9 622.8 0.074 227.8 0.080 181.2 0.044 361.4 150 0.045 326.1 0.019 631.8 0.01 9 631.8 0.074 226.3 0.080 179.6 0.044 361.1 175 0.022 691.8 175 0.022 706.6 175 0.022 711.5 225 0.067 372.4 0.074 331. 3 0.110 247.3 0.121 202. 8 0.044 359. 3 225 0.067 372. 5 0.074 332.4 0.110 248.3 0.121 200.1 0.066 398. 4 225 0.067 368.4 0.074 331.6 0.110 244. 5 0.121 200.5 0.066 398.1 300 0.089 401.7 0.099 369. 3 0.147 265.7 0.161 209. 8 0.066 399. 3 300 0.089 403. 2 0.099 365 .8 0.147 257.5 0.161 2 10.0 0.088 420.0 300 0.089 406.2 0.099 374. 3 0.147 257.4 0.161 210.0 0.088 420.1 375 0.111 434.1 0.124 40 4.0 0.184 268. 9 0.201 219.4 0.088 421. 5 375 0.111 433. 2 0.124 399.2 0.184 267.5 0.201 213.6 0.111 440. 5 375 0.111 437.2 0.124 396. 7 0.184 269. 4 0.201 216. 5 0.111 437.5 450 0.134 45 8.0 0.148 418.1 0.221 273.5 0.241 222.3 0.111 43 5.0 450 0.134 455. 5 0.148 419. 2 0.221 277.5 0.241 221. 2 0.133 448.4 450 0.134 461.7 0.148 42 2.0 0.221 278. 1 0.241 223. 3 0.133 448. 9

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79 Table 4 2 Comparison between Taylor wavelength and mushroom bubble major chord length in transition Fluid P l v Surface Tension Taylor Wavelength Mushroom Bubble Chord length Standard Deviation (50 data) kPa kg/m 3 kg/m 3 N/m mm mm mm Pentane 150 597.3 4.3 0.013 9.4 10.4 1.8 300 571.1 8.3 0.010 8.7 8.9 1.6 450 552. 3 12.3 0.009 8.1 8.8 1.5 Hexane 150 599.8 4. 7 0.012 9.0 10.0 1.7 300 572 0 9.1 0.009 8.2 7.9 1.3 450 55 2.0 13. 6 0.008 7.7 6.9 1.3 Methanol 100 748. 7 1.2 0.019 10.3 10.2 1.9 175 733. 6 2. 1 0.017 9.9 10.0 1.4 FC 72 150 1552.5 19.5 0.00 7 4.2 4.4 0.7 300 1558.0 38.7 0.00 5 3.6 3.5 0.6 450 1387.9 58.7 0.00 4 3.4 3.1 0.3 FC 87 150 1526.2 18. 5 0.00 8 4.6 4.9 0.8 300 1440.0 36. 3 0.00 6 4.1 4.1 0.8 450 1382.0 53. 5 0.00 5 3.7 3.4 0.5 R113 150 1477.1 10.7 0.013 6.1 7.5 1.6 300 1411.7 20. 8 0.01 1 5.6 6.5 0.9 450 1364.9 30. 8 0.009 5.2 5.8 1.1

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80 Table 4 3 The images of transition between nucleate and film boiling with different test fluids at various pressures.

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81 Table 4 4 Mean deviation between experimental and predicted CHF Data Set Liquid/ Surface ` Reduced Pressure Range (P r ) Mean Deviation (%) Zuber [3] Lienhard and Dhir [16] Haramura and Katto [12] Kandlikar [14] Bailey et al. [21] Sakashita and Ono [13] Current Current Data Pentane/ Brass 0.04~ 0.13 15.5 3.7 1 7.7 16. 8 9. 9 60.4 2.5 Hexane/ Brass 0.05~ 0.15 12.3 3.4 14.9 20.7 13.6 67 .4 5 .0 Methanol/ Brass 0.012~ 0.022 2.8 14.5 2.8 39.3 30.6 110.6 1.5 FC 72/ Brass 0.08~ 0.24 12.9 1.0 15.5 20.0 13.3 48.1 10.6 FC 87/ Brass 0.05~ 0.025 20.4 9.2 22.7 9.8 3.6 53.6 4.4 R113/ Brass 0.04~ 0.014 34.3 25.0 36.0 9.1 14.5 37.2 21.2 [63] Pentane/ Copper, Inconel and Nickel 0.03 14.8 9.9 16.4 18.9 12.7 70.9 10.8 [78] Benzene 0.002~ 0.03 12.6 11.7 13.8 26.5 20.7 97.4 16.8 [15] Water/ Copper 0.0006~ 0.002 57.0 79.0 54.0 117.8 104.2 228.9 22.8 Methanol/ Copper 0.005~ 0.01 3.1 16.5 2.3 41.7 32.9 129.8 4.1 [79] Freon 113/ Copper 0.003~ 0.03 29.4 21.5 30.9 13.8 16.1 70.4 29.9 [18] Pentane/ Teflon and Copper 0.03 11.3 13.6 11.8 31.3 23.2 88.8 11.1 R 113/ Teflon 0.03 9.3 7.4 10.5 26.8 19.0 105.4 7.4 [20] Hexane/ Copper 0.002~ 0.03 24.1 17.0 25.7 12.9 11.2 65.2 29.5 Water/ Copper 0.00007~ 0.005 47.2 39.8 48.2 31.6 33.4 25.0 59.3 R 113/ Copper 0.005~ 0.03 15.1 12.1 17.0 22.5 17.0 97.4 15.4 Pentane/ Nickel Coated Copper 0.02~ 0.18 31.6 22.0 33.3 7.8 11.7 31.7 21.3 [21] Water/ Nickel Coated Copper 0.0009~ 0.01 17.1 17.7 17.6 30.0 24.9 80.7 20.9 Methanol/ Nickel Coated Copper 0.0025~ 0.03 17.8 6.8 19.6 13.8 6.9 83.5 21.4 Water/ Nichrome 0.004~ 0.3 36.1 28.1 37.9 16.3 20.0 13.4 23.7 [13]

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82 CHAPTER 5 RESULTS AND DISCUSSI ON WITH DIFFERENT RO UGHNESS ON CHF This chapter investigates the effects of surface roughness on CHF with pentane, hexane, and FC 72 at different pressures The current set of experiments utilizes a 25.4 mm diameter flat brass heater. Different RMS roughnesses of 150 nm, 550 nm, 2300 nm and 5500 nm were tested for pool boiling of pentane at 150 kPa, 300 kPa, and 450 kPa as listed in Table 5 1 A slight increase in CHF is observed with increasing RMS roughness for pentane, Figure 5 1 This trend is more distinct for hexane, as illustrated in Figure 5 2 and listed in Table 5 2 The influence of roughness on CHF decreases with increasing pressure. At the low er pressure, 150 kPa, CHF increases from 272.0 kW/m 2 to 343.5 kW/m 2 This is approximately a 20~25% increase in CHF. At 300 kPa, CHF goes from 344.5 kW/m 2 to 405 kW/m 2 which corresponds to a maximum CHF variation of 15~17%. Similarly at 450 kPa, CHF increases from 393 kW/m 2 to 440.1 kW/m 2 a less than 10% variation of CHF. This confirms the reduced effect of roughness with increasing pressure. Table 5 3 shows that the measured CHF increases with increasing roughness for FC 72 The change in CHF is 20% at 150 kPa, and becomes 12% 450 kPa. The change in CHF becomes smaller with increasing pressure as shown in Figure 5 3 Despite varying the RMS roughness by three orders of ma gnitude the change in CHF for pentane, hexane, and FC 72 are all less than 25%. The repeatability of the measured CHF data for pentane, hexane, and FC 72 for this work is within 7%. B ased on the experimental data from this work it can be concluded that surface typically has a secondary effect on CHF.

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83 Similarly, Jones et al. [67] proposed th at CHF increases with increasing R a (average roughness ) from 20 nm to 10 m on a 25 .4x 25.4 mm 2 aluminum block with water and FC 77. Rainey and You [49] measured CHF with FC 72 for two copper surface microgeometri es: plain and microporous coated The result s show that not only is CHF enhance d 30 ~ 40 % but the heat transfer coefficient is improved 3 times on the microporous coated surface. From the ir result s it can be concluded that CHF is enhanced significantly by the microporous structure Recently, Bon and Klausner [80] observed the presence of small vortices on structured surfaces possessing re entr an t i nter connect ed cavit ies called the hoodoo s as shown in Figure 5 4 The hoodoo structure results in the liquid being pulled into the macrolayer during pool boiling due to capillary force s CHF increases up to 50% on the hoodoo surface compared with that on the RMS 20 nm smooth silicon surface with FC 72. The vapor beneath interface 1 as shown in Figure 5 5 is lifting the macrolayer off due to the vaporization, and the re ent ering liquid is pushing the interface 1 toward the surface due to capillary force s In order for the vapor to lift off the macrolayer, the vapor momentum has to overcome not only the p ressure gradient cross the interface but the liquid momentum act ing at interface 1 against the vapor momentum. Therefore, the vapor velocity must increase with increasing capillary force to lift the macrolayer Since the higher heat flux is required to i ncrease the vapor velocity, the required heat flux increases to lift off the macrolayer with capillary force ; hence, higher CHF is observed. To prevent the macrolayer from drying out during nucleate boiling, the liquid flows into the macrolayer due to the capillary force. Since the mushroom bubbles depart at the center region of the macrolayer, it is unlikely the liquid can flow into the macrolayer

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84 from the center. Instead, the macrolayer probably pulls liquid from the side of the macrolayer as shown in Figure 5 5 For simplicity, it is assumed that the capillary momentum is uniformly acting normal to the surface, and the average liquid velocity is Hence, the conservation of momentum in Equation ( 2 1 ) can be rewritten as ( 5 1 ) Where Substituting Equation ( 2 2 ) (Young Laplace condition) into Equation ( 5 1 ) yields the vapor velocity, ( 5 2 ) Substituting Equation ( 5 2 ) ( 2 4 ) ( interface wavelength), ( 1 10 ) (macrolayer thickness), and ( 2 7 ) (radius of curvature) in to ( 2 8 ) (energy balance) yields the fourth order polynomial equation, ( 5 3 ) Where is the predicted CHF with capillary wicking, and is the predicted CHF for smooth surfaces which is obtained from Equation ( 2 9 ) Let the CHF enhancement factor be defined as then Equation ( 5 3 ) can be simplified to be ( 5 4 ) where ( 5 5 )

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85 Substituting Equation ( 2 9 ) into Equation ( 5 5 ) yields the complete expression for A based on the current lift off model. The con stant A is a non dimensional constant and only contains fluid properties except for the wicking velocity, ( 5 6 ) When the average liquid velocity due to wickin g can be measured or predicted, then the amount of CHF enhancement can be calculated using Equation ( 5 3 ) ( 5 7 ) Figure 5 6 shows the relations hip between CHF enhancement and A. Before A reaches two, CHF enhancement can be approximated by a quadratic function. For A greater than two, the relationship between A and CHF enhancement is linear. Moreover, Figure 5 7 shows the predicted CHF enhancement from Equation ( 5 3 ) by giving wicking velocity with hexane and FC 72 at 1 atm. In Figure 5 7 FC 72 requires slower wicking velocity to reach the same CHF enhancement compared with hexane. It is because the density of FC 72 is higher than that of hexane. Therefore, the wicking velocity of FC 72 does not need to be as fast as that of hexane to bring enough liquid to reach the same CHF enhancement. The predicted CHF enhancement is 1.67 when the wicking velocity is 23 mm/s based on Equation ( 5 3 ) Bon. [80] measured the CHF on a smooth silicon surface and a 20 micron hoodoo structured surface with hexane at 1atm. The CHF enhancement is 1.45. He also measured the wicking velocity on the hoodoo surface with hexane using a high speed camera. The wicking velocity is observed to decrease with time However the initial wicking velocity is about 20~40 mm/s with hexane on the hoodoo surface.

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86 With the same CHF enhancement, the wicking velocity corresponding to the predicted CHF enhancement has the same order of magnitude compared with the measured wic king velocity. These results confirm that the modified lift off model can predict CHF enhancement for different structured surfaces. For the fluids which have smaller Rayleigh Taylor wavelengths, local dryout occurs when the vapor velocity is high en ough to lift off the macrolayer in one region, and the macrolayer in rest of region might not be affected. The complete vapor film will be form once the heat flux is high enough to allow local dryout regions to merge. With the fluids which have larger Ray leigh Taylor wavelengths, once local dryout occurs, the phenomenon tends to affect the adjacent regions and spreads throughout the entire surface. In order to understand the local dryout phenomenon, it is necessary to investigate what the maximum perce nt of dryout region on the surface can be present in nucleate boiling regime. C apillary force s increase with increasing surface roughness as well and capillary force s on microporous surface s are stronger than th ose on rough ened surfaces. Therefore, the critical heat flux is enhanced on the microporous surfaces more than on the rough surfaces. This mechanism also explains why nanofluids enhance CHF in pool boiling S. J. Kim et al. [81] observed that the nanoparticles deposit on the surface during nucleate boiling. The RMS roughness measured by SEM changes varied from 0.1 m to 2 m after boiling in the water based nanofluid containing 0.01% of volume of alu mina (Al 2 0 3 ) nanoparticles. The nanoparticle deposition as a result of boiling the nanofluids creates a microporous layer on the surface. The capillary force is stronger on porous structure d surfaces compared with that on smooth surfaces. Therefore, as

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87 e xpected, CHF is enhanced 20 45% depending on the nanoparticle concentration volume [81] You [82] measured that CHF increases 7%, 174% and 211% with alumina nanopart icle concentrations, 0.001 g/liter, 0.01 g/liter, and 0.025 g/lit er in pure water at 20 kPa respectively. H. Kim et al. [83] also investigated that the enhancement of CHF is about 30% on a copper disk heater with water based nanofluid containing 0.01vol.% alumina nanoparticles. The capillary mechanism can also links to wettability in terms of contact angles. Ahn et al. [84] used an anod ic oxidation process to prepare artificial micro and nano structures of the surface. The liquid/solid contact angle changes from 50 to 5 degree s on zirconium alloy pla tes (25 mm x 15 mm) with water. The SEM measurement s shows that the contact angle decreases with increasing the thickness of the micro/nano structures [85] Hence, the contact angle decreases with increasing c apillary force. Therefore, the capillary force plays a dominant role in the pool boiling CHF enhancement mechanism for structured surface s

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88 Figure 5 1 CHF data in saturated pool boiling with various RMS roughness at different pressure for pentane. Figure 5 2 CHF data in saturated pool boiling with various RMS roughness at different pressure for hexane.

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89 Figure 5 3 CHF data in saturated pool boiling with various RMS roughness at diff erent pressure for FC 72. Figure 5 4 Sketch of the hoodoo structure surface: a) top view and b) side view Surface a) b)

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90 Figure 5 5 re entreating Liquid flow due to the capillary force Figure 5 6 Plot of CHF enhancement versus A.

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91 Figure 5 7 The predicted CHF enhancement from Equation ( 5 3 ) vs. given wicking velocity with hexane, and FC 72 at 1atm.

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92 Table 5 1 CHF data on a 25.4 mm diameter brass disk with various roughness and pentane at three different pressures, 150 kPa, 300 kPa, and 450 kPa for saturated pool boiling. Pentane CHF (kW/m 2 ) Roughness 0.15 m 0.65 m 2 3 m 5 5 m Pressure 150kPa 316.9 326.9 345.5 373.0 319.2 326.6 343.5 372.1 326.2 347.6 300kPa 386.2 401.7 421.8 444.5 408.9 406.2 427.5 403.2 450kPa 475.7 457.9 475.0 478.5 469.3 455.4 469.1 479.6 461.7 466.8 Table 5 2 CHF data on a 25.4 mm diameter brass disk with various roughness and hexane at three different pressures, 150 kPa, 300 kPa, and 450 kPa for saturated pool boiling. H exane CHF (kW/m 2 ) Roughness 0.15 m 0.65 m 2 3 m 5 5 m Pressure 150kPa 272.2 289.5 332.7 343.5 272.0 290.8 331.5 337.4 279.7 285.7 335.6 300kPa 344.5 369.2 399.4 398.9 356.1 365.8 405.0 395.6 374.3 450kPa 393.0 418.3 431.1 440.1 409.7 419.2 433.9 407.1 422.0 430.2

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93 Table 5 3 CHF data on a 25.4 mm diameter brass disk with various roughness and FC 72 at three different pressures, 150 kPa, 300 kPa, and 450 kPa for saturated pool boiling. FC 72 CHF (kW/m 2 ) Roughness 0.65 m 2 3 m 5 5 m Pressure 150kPa 181.1 205.3 216.5 181.2 205.3 217.2 179.6 335.6 300kPa 209.8 233.8 241.4 203.0 234.6 241.2 210.0 450kPa 222.3 241.4 250.0 221.2 241.2 249.5 223.3

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94 CHAPTER 6 FUTURE STUDIES While the lift off model gives a very good prediction for CHF on smooth surfaces, it is apparent that the model includes several idealizations, and does not account for the full complexity of boiling phenomena at high heat flux. As discussed structured s urfaces with good wicking properties can significantly enhance CHF. The local dryout phenomenon affects the heat transfer in boiling in high heat flux. There are two major areas to focus on for future studies The first focus is to establish a more rigo rous treatment of capillary forces in the lift off model. The detailed mechanism for wicking effect on different structured surface in pool boiling should be the next step. Then, the lift off model can be improved with a better prediction of capillary forces The second is how to characterize the dryout phenomena and include the dryout effect in the lift off model U nderstand ing the lin k between local dryout mechanis m and transition boiling is the key.

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95 APPENDIX A RAYLEIGH TAYLOR INSTABILITY The interface between two fluids of different densities tends to be stability when the density of the top fluid is higher than that of the bottom fluid. For instance, water is poured in a cup, the interface between air and water eventually will become stable. On the contrary, the interface becomes unstable when the density of the top fluid is higher than that of the bottom fluid. It is like when the water cup is upside down. The interface between water and air will because unstable. This instability at the interface is called Rayleigh Taylor instability. Rayleigh Taylor instability for fluids with finite thickness is analyzed here [86] F igure A 1 shows the Sketch of the wavy interface between two fluids of different densities moving with different velocities with finite thickness. the flow fields are inviscid and irrotational. Hence, th e Laplace potential equations are where (A 1 ) The boundary conditions are as shown in Figure A 1 It is assumed that the top flow does not have the velocity in y direction at i.e. the interface effect does not affect the flow field when y is larger than (A 2 ) The bottom flow cannot pass through the wall; therefore, the velocity normal to the wall is zero. (A 3 ) The location of the interface

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96 (A 4 ) where is the interface function The interface kinematic boundary condition on It is also called impermeable boundary. The fluids cannot cross the interface, i.e. the normal velocity of the flow is zero at the interface. (A 5 ) After simplifying Equation (A 5 ) (A 6 ) the normal stress at the interface is (A 7 ) where is surface tension and is the curvature of the interface The dynamic boundary condition at the interface is a Bernoulli equation for inviscid flows. (A 8 ) For simplicity, the flow is assumed to be two dimensional, and the interface (x, t) only deviates slightly from y=0 Therefore, the equations for the potential function, pressure, and the interface can be written as (A 9 )

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97 w here and The following equations can be obtained by substituting Equation (A 9 ) into Equation (A 1 ) and (A 7 ) (A 10 ) Since and (A 11 ) the dynamic boundary condition at the interface, Equation (A 8 ) can be rewritten as (A 12 ) The forms of the waves are assumed to be traveling waves as following to satisfy Equation (A 1 ) (A 2 ) and (A 3 ) (A 13 )

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98 where and c is the wave speed Combining Equation (A 12 ) and Equation (A 10 ) gives (A 14 ) Substituting Equation (A 13 ) into Equation (A 6 ) and (A 8 ) the following expressions are obtained, (A 15 ) In order to obtain a non trivial solution for A, B, and D, the determinant in Equation (A 15 ) has to be zero. In the pool boiling, the mean velocities of the liquid and vapor are zeros, i.e. Hence, (A 16 ) The growth rate of the disturbance is (A 17 ) If H l and H v are infinite (A 18 ) The critical wave number is obtain when Equation (A 18 ) is zero, (A 19 ) Then, the critical Rayleigh Taylor wavelength is given

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99 (A 20 ) The highest growth rate occurs when the first derivative of n with respect to k is zero (A 21 ) which leads to the most dangerous wave number, (A 22 ) From Equation (A 22 ) the most dangerous wavelength with infinite thickness is given (A 23 ) Equation is the most dangerous wavelength that Zuber [3] suggested for pool boiling. For finite thickness, Equation (A 23 ) gives (A 24 ) After simplifying Equation (A 24 ) simplifies to (A 25 ) w here, In order to evaluate the most dangerous wave number that satisfies Equation (A 25 ) it is assumed that and with the Rajvanshi et al. [31] assertion that

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100 it follows that For the condition where = Equation (A 25 ) is solved for the most dangerous wave number, (A 26 ) In contrast, when and are of infinite extent, the solution is Equation (A 22 ) The difference between k c and k 0 is less than 10% of k 0 and thus using Equation (A 23 ) to evaluate the most dangerous wavelength is satisfactory. In the case where density ratio, varies from 0.00 1 to 1.0 and and are different by an order of magnitude, the ratio of varies from 1.0 to 1.2, and thus the solution for liquid and vapor layers of infinite extent is still satisfactory with an acceptable range for the prediction of CHF.

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101 Figure A 1 Wavy interface between two fluids of different densities moving with different velocities with finite thickness.

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102 APPENDIX B ORDINAEY DIFFERENTIA L EQUATION FOR THE B UBBLE GROWTH Chen et al. [77] proposed a simplified model for predicting vapor bubble growth in heter ogeneous boiling based on a liquid microlayer and a lumped thermal analysis for a solid heater. The result of this model is a first order ordinary differential equation. The first order ordinary differential equation for the growing bubble is ( B 1 ) w here Q and B are constants ( B 2 ) where is the internal heat generation per unit volume, is wall superheat, is solid heater density, is the specific heat capacity of the solid heater, and ( B 3 ) w here ( B 4 ) ( B 5 ) ( B 6 ) ( B 7 ) where is the initial superheat at incipience, is the liquid to solid thermal conductivity ratio, and is the liquid thermal diffusivity. The constant B is

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103 ( B 8 ) where ( B 9 ) (B 10 ) (B 11 ) is the Fourier number, and is the microlayer wedge angle, is the liquid to solid thermal diffusivity ratio, and H is the thickness of the solid heater. in Equation ( B 1 ) is dimensionless time, and is the dimensionless bubble growth where (B 12 ) A modified Fourier number, is used to replac e (B 13 ) The first order ordinary differential equation for the bubble growth Equation ( B 1 ), can be solved numerically using a Runge Kutta Method. For example, Figure B 1 is the isolated bubble growth on a 25.4 mm diameter circular brass heater with 20 mm thickness for pentane at 1 50 kPa. The applied heat flux is 100 kW/m 2 and the wall superheat is 10 C the bubble growth may be fit to a power laws, with k=0.0097 and n=0.545. (B 14 )

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104 Figure B 1 Bubble growth for pentane nucleate pool boiling. R 2 =0.999 R(t)=0.0097t 0.5454

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105 APPENDIX C THERMAL PROPERTY OF FLUID Liquid Density l Liquid Density v Latent Heat H fg S urface T ension L iquid V iscosity (kg/m 3 ) (kg/m 3 ) kJ/kg N/m Pa.s Penane 150kPa 597.3 4.3 347.7 0.0130 0.00018 [87] 225kPa 582.8 6.3 335.7 0.0115 0.00016 300kPa 571.1 8.3 325.9 0.0100 0.00015 375kPa 561.1 10.3 317.4 0.0096 0.00014 450kPa 552.3 12.4 309.6 0.0088 0.00013 Hexane 150kPa 599.8 4.7 324.8 0.0120 0.00018 [87] 225kPa 584.4 6.9 312.7 0.0106 0.00016 300kPa 572.0 9.1 302.7 0.0095 0.00014 375kPa 561.4 11.3 294.0 0.0086 0.00013 450kPa 552.0 13.6 286.2 0.0078 0.00012 Methanol 100kPa 748.7 1.2 1101.7 0.0189 0.00028 [87; 88] 125kPa 742.9 1.5 1090.3 0.0185 0.00026 150kPa 738.0 1.8 1080.3 0.0180 0.00025 175kPa 733.6 2.1 1071.3 0.0177 0.00024 FC 72 150kPa 1552.6 19.5 90.7 0.0068 0.00039 [89] 225kPa 1498.7 29.1 85.7 0.0058 0.00034 300kPa 1456.5 39.1 81.5 0.0048 0.00032 375kPa 1419.7 48.2 78.2 0.0043 0.00030 450kPa 1386.6 59.2 75.1 0.0037 0.00029 FC 87 150kPa 1526.2 18.5 95.4 0.0078 0.00037 [89] 225kPa 1480.7 27.0 90.8 0.0067 0.00033 300kPa 1440.0 36.3 86.8 0.0058 0.00031 375kPa 1407.2 45.4 83.3 0.0051 0.00029 450kPa 1380.3 54.5 80.7 0.0046 0.00028 R113 150kPa 1477.1 10.7 140.3 0.0133 0.00043 [76; 87] 225kPa 1440.7 15.8 135.4 0.0118 0.00036 300kPa 1411.7 20.7 131.4 0.0107 0.00032 375kPa 1386.9 25.7 128.0 0.0098 0.00030 450kPa 1364.9 30.8 124.9 0.0090 0.00028

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110 [51] M.S. El Genk, and Z. Guo, Transient boiling from i nclined and downward facing surfaces in a saturated pool, International Journal of Refrigeration 16 (6) (1993) 414 422. [52] M.J. Brusstar, and H. Merte, Effects of heater surface orientation on the critical heat flux -II. A model for pool and forced conve ction subcooled boiling, International Journal of Heat and Mass Transfer 40 (17) (1997) 4021 4030. [53] A.H. Howard, and I. Mudawar, Orientation effects on pool boiling critical heat flux (CHF) and modeling of CHF for near vertical surfaces, International Journal of Heat and Mass Transfer 42 (9) (1999) 1665 1688. [54] L. Liao, R. Bao, and Z. Liu, Compositive effects of orientation and contact angle on critical heat flux in pool boiling of water, Heat and Mass Transfer/Waerme und Stoffuebertragung 44 (12) ( 2008) 1447 1453. [55] M. Carne, and D.H. Charlesworth, Thermal conduction effects on the critical heat flux in pool boiling., Chem. Enging. Prog. Symp. Ser. 62 (64) (1966) 24 34. [56] I. Golobic, and A.E. Bergles, Effects of heater side factors on the satu rated pool boiling critical heat flux, Experimental Thermal and Fluid Science 15 (1) (1997) 43 51. [57] K. Ferjancic, and I. Golobic, Surface effects on pool boiling CHF, Experimental Thermal and Fluid Science 25 (7) (2002) 565 571. [58] C.C. Pitts, and G. Leppert, The critical heat flux for electrically heated wires in saturated pool boiling, International Journal of Heat and Mass Transfer 9 (4) (1966) 365 370, IN3 IN4, 371 377. [59] W. Gambill, An experimental investigation of the inherent uncertainty in pool boiling critical heat fluxes to saturated water, AIChE Journal 10 (4) (1964) 502 508. [60] D. Gorenflo, E. Baumhger, T. Windmann, and G. Herres, Nucleate pool boiling, film boiling and single phase free convection at pressures up to the critical state Part I: Integral heat transfer for horizontal copper cylinders, International Journal of Refrigeration 33 (7) (2010) 1229 1250. [61] V.V. Yagov, The mechanism of the pool boiling crisis, Teploenergetika (3) (2003) 2 10. [62] B. Bon, C. K. Guan, and J.F. Klausner, Heterogeneous nucleation on ultra smooth surfaces, Experimental Thermal and Fluid Science In Press, Corrected Proof (2010). [63] P.J. Berenson, Experiments on pool boiling heat transfer, International Journal of Heat and Mass Transfer 5 (1962) 98 5 999.

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113 BIOGRAPHICAL SKETCH Cheng Kang Guan, born in Taipei, Taiwan, in 1979, received his Bachelor of Science in mechanical engineering from I Shou University in Taiwan in 2001. Cheng Kang studied his in power mechanical engineering at National Tsing Hua University from 2002 to 2004. Meanwhile, as a researche r in Advance Thermal Technology Co., Cheng Kang designed flat arrayed heat pipes that are heat dissipating components in electronic devices. After studying the icing issue on the aerofoil on commercial aircrafts in aerospace engineering at the University o f Kansas for one year in 200 6, Cheng Kang decided to pursue his Ph.D degree in mechanical and aerospace engineering at the University of Florida in 2007.