<%BANNER%>

Transverse jet penetration in supersonic flows with variable boundary layer thickness

University of Florida Institutional Repository
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PAGE 1

TRANSVERSE JET PENETRATION IN SUPERSONIC FLOWS WITH VARIABLE BOUNDARY LAYER THICKNESS By RON PORTZ A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2005

PAGE 2

ACKNOWLEDGMENTS This work was performed with support from NASA grant NCC3-994 with Claudia Meyer as the Program Manager. Dr. Corin Segal, of the Department of Mechanical and Aerospace Engineering provided direction for this research and contributed valuable guidance in the preparation of this thesis. Utmost thanks are due my wife Pamela and our children Elijah and Sammy, who have borne with the vicissitudes of life with a graduate student. I am grateful for my parents confidence and support of me and my family from birth. I would also like to thank my mother-in-law and father-in-law, who in addition to letting me marry their daughter have been of emotional and material support. ii

PAGE 3

TABLE OF CONTENTS page ACKNOWLEDGMENTS..................................................................................................ii LIST OF TABLES.............................................................................................................iv LIST OF FIGURES.............................................................................................................v ABSTRACT.......................................................................................................................vi CHAPTER 1 INTRODUCTION........................................................................................................1 2 NEAR FIELD AND FAR FIELD MIXING OF TRANSVERSE JETS......................5 3 EXPERIMENTS...........................................................................................................9 Experimental Facility....................................................................................................9 Boundary Layer Thickness...........................................................................................9 4 RESULTS AND ANALYSIS.....................................................................................13 Penetration Visualization............................................................................................13 Effect of Dynamic Pressure Ratio and Downstream Distance...................................17 Effect of BL Thickness...............................................................................................18 Effect of Molecular Weight Ratio..............................................................................19 5 A PROPOSED, IMPROVED PENETRATION FORMULA....................................21 Comparison To Previous Studies................................................................................21 General Penetration Formula......................................................................................23 6 CONCLUSIONS........................................................................................................29 LIST OF REFERENCES...................................................................................................30 BIOGRAPHICAL SKETCH.............................................................................................33 iii

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LIST OF TABLES Table page 5-1 Penetration Formula Parameters Resulting From Various Studies..........................23 5-2 Penetration Equation Parameters as Functions of Air Mach number......................24 iv

PAGE 5

LIST OF FIGURES Figure page 1-1 Model of Transverse, Underexpanded Injection into a Supersonic Airstream..........2 1-2 Interaction Between the Boundary Layer and Jet in Supersonic Flow......................3 3-1 Schematic of the test section with dimensions normalized by duct height, L=25 mm............................................................................................................................10 3-2 Boundary layer measurement at the collar outlet.....................................................11 3-3 The BL at measured locations bounding the injector port and assuming linear growth.......................................................................................................................12 4-1 Schlieren Images of Underexpanded, Circular, Sonic Gas Injection.......................14 4-2 Curve Fit for Ar, He and H 2 injection into Mach 1.6 air at Varied BL thickness....17 4-3 Penetration Varies Greatly With Increasing Dynamic Pressure Ratio M a =2, /D=2, M j /M a =0.070...............................................................................................18 4-4 Penetration Variation with BL Thickness................................................................18 4-5 Variation in Penetration Due to Variation in Injectant Molecular Weight M a =1.6, q j /q a =2, /D=1............................................................................................19 5-1 Penetration Correlations for Various Studies Exhibit Scatter; q j /q a =1.5.................22 5-2 Penetration Equation Parameters versus Air Mach number.....................................24 5-3 Comparison of the Present Study with Previous Research......................................25 5-4 Predicted and Measured Penetration of Sonic Hydrogen Transversely Injected into Mach 2.5 Air.....................................................................................................26 5-5 Dynamic Pressure Ratio Across a Normal Shock versus Mach number.................27 v

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Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science TRANSVERSE JET PENETRATION IN SUPERSONIC FLOWS WITH VARIABLE BOUNDARY LAYER THICKNESS By Ron Portz December 2005 Chair: Corin Segal Major Department: Mechanical and Aerospace Engineering Penetration of gases injected transversely into a supersonic air stream was measured over varied conditions of fuel molecular weight, relative air boundary layer thickness and Mach number to verify and complement previous studies. Air Mach numbers of 1.6 and 2.5 were tested and compared to published data from Mach 1.5 to 4. Boundary layer thickness was measured and jets of 1 mm, 1.5 mm, and 3.2 mm diam. were injected in a test section with a square section 25 mm wide, followed by a 450 mm long constant area duct. Hydrogen, helium and argon were injected to observe the effects of density and viscosity on penetration. Schlieren imaging was used to visualize and measure penetration. This study compared penetration to existing models using dynamic pressure ratio, air Mach number and boundary layer thickness as independent variables. Significant penetration dependence on air Mach number was identified. Penetration was found to increase strongly with boundary layer thickness at low Mach numbers but as Mach number increases, boundary layer thickness has less effect. A new vi

PAGE 7

formula is proposed to predict penetration based on a set of independent variables. This formula is compared to new test data and previous results and achieves good correlation for all studies. vii

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CHAPTER 1 INTRODUCTION When a gas is injected transversely into a supersonic air stream, significant shock and viscous interactions occur. The results of these interactions are not always intuitive as has been shown for external flows, 1,2 and are strongly affected by the ratio of injectant to air dynamic pressures, 22jjjaaUqqU a (1) where jet properties are taken at the jet exit and air properties are for the freestream before encountering jet-induced shocks. The dynamic pressure ratio is used in lieu of the momentum flux ratio in most of the literature on this subject and the terms are sometimes considered interchangeable. The momentum flux ratio is only truly equal to the dynamic pressure ratio if the areas through which the respective fluids pass are equal, which is virtually never the case. Regardless, the dynamic pressure ratio has come to be an accepted datum for the empirical correlation of transverse jet penetration. In most circumstances the injected plume acts almost as a solid object resulting in the generation of a bow shock, turbulent shear layer and a system of vortices spilling off the semi-cylindrical obstruction, as shown in Figure 1-1. The injectant is turned nearly parallel to the air within a short distance and the vortices rotation axes align nearly with the air stream. Mixing of the injectant with the air is facilitated by the streamwise vortices spilling off of the turned injectant plume. Near-field mixing is dominated by 1

PAGE 9

2 bulk mass transfer and the far field mixing by the development of compressible shear layers. Velocity Profile Concentration Profiles Spilled Vortex, same on both sides Bow Shock Outer limit of turbulent shear layer/penetration Potential Core Figure 1-1. Model of Transverse, Underexpanded Injection into a Supersonic Airstream. Two general cases of interaction between the jet and the boundary layer (BL) have been recognized and are illustrated in Figure 1-2, which is adapted from Schetz and Billig. 3 The determining factor in the shape of the barrel shock around the jet is the degree of BL separation ahead of the jet, which is in turn determined by jet strength compared to freestream properties. When the separation region thickness is much smaller than the height of the Mach disc at the end of the barrel shock, the gas penetrates through the BL and a strong, nearly normal, bow shock forms in the air stream. The barrel shock is bent backward by high pressure air downstream of the bow shock as shown in Figure 1-2A. When the BL separation region is at least of the same order as the first Mach disc height, the jet penetrates straight as shown in Figure 1-2B and as described by Kaufman, 2 Rogers 4 and Schetz and Billig. 3 The Mach disc is nearly parallel to the wall. Kaufman 2 and Schetz and Billig 3 further discuss the criteria that lead to BL separation.

PAGE 10

3 A B Maair Strong Bow Shock Weak Bow Shock Maair Figure 1-2. Interaction Between the Boundary Layer and Jet in Supersonic Flow. A) Attached and B) Separated Boundary Layer Flows (Adapted from Schetz and Billig 3 ) In the case of vehicles with a body-integrated scramjet design, a long inlet ramp with a continuous, strong, adverse pressure gradient is likely to result in a thick BL in the combustor, conducive to flow separation. High stagnation temperature, intrinsic to hypersonic flight, does not facilitate bleeding the BL so this condition becomes of substantial interest. In a supersonic combustor fuel must penetrate and mix in the cooler high speed core flow beyond the BL to maximize cycle efficiency. Various methods have been suggested such as pylons and ramp injectors to deliver the majority of fuel into the free stream, away from the wall and BL. 5-7 Simple transverse injection is desirable for the sake of simplicity, but it introduces some known disadvantages. The strong shocks that typically accompany transverse injection result in irreversible loss of total pressure in the air. Flameholding is not provided by simple transverse injection and must be provided by combustor features that establish recirculation zones which add to total pressure losses. Empirically derived models of penetration in supersonic air flows with transverse fuel injection describe the dimensions of the fuel plume penetration and spreading for an injected gas using a definition for the plume boundary based variously on injectant

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4 concentration of 1%, injectant mole fraction of 0.005, intensity of an image, or other criteria, depending on the particular study. 8-10 Different researchers have studied various ranges of experimental conditions and incorporated different sets of independent variables including the dynamic pressure ratio, downstream distance, boundary layer thickness and jet Mach number in the curve fits used to predict penetration. Both jet penetration and boundary layer thickness are usually non-dimensionalized by jet diameter. The variation in definitions and test conditions has resulted in some disagreement in the curve fits produced in previous studies, as will be shown below. It should be noted that although greater penetration generally results in better mixing, deep penetration is not sufficient to ensure enhanced combustion. For transverse injection tests relying on auto-ignition due to temperature increase across the bow shock it has been observed that cooler air passing through oblique shocks curving off of the bow shock inhibit combustion in zones where the equivalence ratio is otherwise within flammability limits. 11 Results reported in reference 11 indicate that burning was restricted to a small recirculation kernel in the stagnation zone upstream of the fuel jet and in a thin sheet immediately aft of the bow shock where temperatures were high. The majority of the fuel did not react with the air despite good fuel penetration and mixing. Good fuel and air mixing is only one of the factors resulting in efficient combustion.

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CHAPTER 2 NEAR FIELD AND FAR FIELD MIXING OF TRANSVERSE JETS For combustion to occur fuel and air must mix and diffuse at a molecular level. The transport of one molecular species into another is described by Ficks Law 12 ()AABAAdYmYmmDdx AB (2) where A m is the bulk mass flow rate of species A into species B is the bulk mass flow rate of species B into species A Bm Y A is the mass fraction of species A is the density of species A D AB is the binary diffusion coefficient for species A diffusing into species B defined as 1/233223BABARTTDPM (3) where R B is the gas constant for species B, T is the temperature, M A is the molecular mass of species A, is the molecular collision diameter, or weighted average of the diameters of molecules A and B P is the pressure. 5

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6 The first term in (2), is the bulk flow of species A into B and does not result directly in molecular mixing. The second term, (ABAYmm ) ABADdYdx shows that the diffusive mass flow rate of species A into B increases with increasing density, binary diffusion coefficient and species gradient. Inspection of (3) reveals that the diffusion coefficient increases with temperature to the 32 power, with pressure to the -1 power, molecular weight of species A to the 12 power and molecular diameter to the -2 power. For perfect gases the overall mass flow rate due to diffusion changes with the square root of temperature, and is neutral for pressure changes. The overall rate of diffusion is maximized for small, light molecules at high temperature. Intuitively, this is due to increasing average molecular speed while decreasing the rate of collision between the diffusing gas molecules. Frequent collisions impede the average motion of molecules in the direction of decreasing concentration. This contributes to the preference of hydrogen to fuel supersonic combustion; in addition to the rapidity of reaction associated with hydrogen once it has mixed with oxidizer, it will diffuse and mix more quickly in air than any other fuel due to its small molecule size. Once a design flight condition is chosen which fixes engine inlet temperature and pressure and a fuel is selected there are limited options for the combustor designer to affect diffusion. For this reason it turns out that controlling bulk flow processes dominates the eventual mixing efficiency of fuel injected into a supersonic air stream. When a gas is injected transversely into an air stream non-linear penetration is apparent in the near field. Large momentum flux transfer between the air and the jet dominates the penetration and mixing process. Bulk mass transfer is brought about by significant jet penetration. In some studies 4, 9 greater lateral spreading than axial penetration was

PAGE 14

7 noticed for transverse fuel injection indicating that the shear forces due to the vortices spilling off of the side of the fuel jet were a more effective transport mechanism than the transverse injection momentum. In the far field, more than ten jet diameters downstream of the injection location, penetration increases by essentially tangential shear layer growth where the penetration distance assumes a nearly linear relationship with downstream distance. In this regime the jet centerline is essentially parallel to the air and the slope of the penetration curve is directly related to the shear layer growth. 13 For practical supersonic combustors and the test equipment employed in this study the Reynolds number exceeds 10 6 At Reynolds numbers above 10 4 the shear layer is turbulent with macroscopic vortex structures moving at a convective velocity, U c defined as. 13 211212CUaUaUaa (4) where U i and a i are respectively the velocity and speed of sound of each of the fluids. The convective Mach numbers, M ci for two fluids are defined as 111CCUUMa and 222CCUUMa (5) Shear layer growth is a function of the ratio of fluid velocities, the ratio of fluid densities and M c 13 The shear layer growth rate decreases with increased compressibility and increases with increased density ratio between the two fluids. For a detailed discussion of mixing in shear layers, see reference 13. Enhanced mixing schemes have been described elsewhere 14, 15 which convert some of the tangential momentum of the air into transverse momentum along with generation of vortical structures. An example is the swept ramp injector in which air passes over an

PAGE 15

8 upward incline adjacent to either a flat or a downward inclined surface. 16-18 Spillage from the ramp creates a vortex that enhances bulk fuel flow into air while causing oblique shocks and relatively small losses unlike simple transverse injection which produces normal shocks and strong vortices that result in significant stagnation pressure loss. Angled injection from a wall has been studied with the intent to retain the simplicity of transverse injection while minimizing the stagnation pressure loss. 7, 18 Studies with gaseous hydrogen as the injected fuel have observed that significant additional thrust results from injection of fuel with a tangential velocity component. 18 Tangentially injected fuel will contribute some small thrust and the specific impulse of hydrogen may be high if it is used to cool hot engine parts before injection. However, the thrust addition is minor, because of the small fuel mass involved, for example ~3% H 2 by mass at stoichiometric mixture ratio. Both near and far-field mixing mechanisms are present in both transverse and angled jet injection. Deep penetration facilitates mixing and with appropriate flame-holding devices promotes efficient supersonic combustion chambers. The results of experimental penetration analysis and its correlation to the jet flow thermodynamic properties of gaseous jets are described below.

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CHAPTER 3 EXPERIMENTS Experimental Facility Figure 3-1 is a schematic representation of the continuous-flow, direct-connect, supersonic-combustion wind tunnel used in these experiments. This tunnel can deliver .454 kg/s of air continuously at combustor Mach numbers from 1.3 to 3.6, with stagnation temperature up to 1,200K and stagnation pressure from 207 to 827 kPa. Higher flow rates and pressures up to 1,520 kPa are subject to limited duration. These conditions correspond to flight enthalpy of up to Mach 4.75. This facility has been previously described in detail by Owens. 5 For the purpose of measuring jet penetration this study used unheated air, consistent with previous studies. 4, 9, 10, 18 The entrance to the test section was an L = 25.4 mm wide square section. The cross-section was constant along its length of 18L. Hydrogen, helium or argon were injected transversely, at a location where the BL thickness was known, through 1 mm, 1.5 mm, and 3.2 mm orifices to vary the ratio of BL thickness, to jet diameter, D. Boundary Layer Thickness BL thickness was measured using a probe with a square-cut tip of 0.25 mm outside diameter, and 0.13 mm bore diameter. The probe was inserted through any of three holes in the side-wall of the test section normally used for optical access (see Figure 3-1) and was traversed in 0.2mm increments while measuring the stagnation pressure. Measurements were taken around the isolator outlet circumference for unheated air at 414 9

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10 Nozzle Isolator Test Section 127 mm 76 mm 25 mm W i ndows 146 mm L = 25 mm Fuel In j ecto r Air from stagnation chamber 0.26L 0.145L 114 mm Boundary layer growth at Mach 1.56 and 414 kPa a ir 0.15 38 mm 0.13 Figure 3-1. Schematic of the test section with dimensions normalized by duct height, L=25 mm. The measured BL at selected locations is also shown. kPa stagnation pressure and nozzle exit Mach number of 1.6. The results of this measurement are shown in Figure 3-2. Lack of physical access to the East side of the test apparatus restricted BL measurements to three sides. Symmetery of the apparatus ensures that use of the West-to-East BL measurement accurately represents the East-to-West BL. The BL measurement was repeated in the West-to-East direction at both Mach 1.6 and Mach 2.5. Fuel is injected from the East wall. The BL was measured at several stations downstream of the nozzle exit, as indicated in Figure 3-2. Measurements showed a relatively small inviscid core flow at the point of injection since the measured BL occupies over 50% of the cross section area. At Mach 1.6 BL growth in the 18L long constant-area test section resulted in choking unless a substantial bleed from the last third of the test section was established. At each station, the BL thickness is taken as the point

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11 Figure 3-2. Boundary layer measurement at the collar outlet. The collar exit is 76 mm, or 3L upstream of the fuel injector. Measurements are taken from the outside edge toward the center of the flow, along the section centerline. The cardinal directions are used as references. 0.00.20.40.60.81.01.20.00.10.20.30.4Probe Position (y/L)Relative Pitot Pressure (p/p-max) North to South South to North West to East of 99% velocity, or where the measured pitot pressure was 98% of the maximum value. The BL thickness at the point of gas injection was approximated by linear interpolation between the two stations measured on either side of the port as shown in Figure 3-3. For 552 kPa stagnation pressure and Mach 1.6 flow, the BL thickness at the injector port was 3.7 mm. For Mach 2.5 flow the BL thickness was 2.5 mm. It is known from measurements taken here and elsewhere 19 that rectangular, 2-D nozzles yield boundary layers that are not uniform around the passage circumference. Along the contoured nozzle walls, the boundary layer is uniform in thickness and thinner than on the flat walls of the 2-D nozzle. The flat walls have a non-uniform BL as shown in Figure 3-1, with greater thickness at the center than at the edges, where BL thickness is

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12 similar to the contoured walls. At the station 1.75L forward of the point of gas injection, the BL thickness was 3.3 mm on the contoured walls, while the maximum BL thickness on the flat walls was 6.6 mm. This is due to the stronger favorable pressure gradient along the contoured walls. 05101504080120160Length From Isolator Outlet (mm) (mm) Section Centerline Injector Station Figure 3-3. The BL at measured locations bounding the injector port and assuming linear growth.

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CHAPTER 4 RESULTS AND ANALYSIS Penetration Visualization Flow and fluid mixing are visualized by use of a lens-based Schlieren system. Optical assessment of jet penetration has been demonstrated to give accurate and consistent depth compared to chemical sampling methods. 13, 20 Images were collected with an SVHS video camera. To capture average penetration rather than instantaneous variations each camera exposure was of the order of 20 ms which is long compared to transient flow excursions. Schlieren systems make flow phenomena and optical irregularities visible by passing collimated light through transparent media. Changes in the refractive index between fluids or between regions where the thermodynamic properties of a fluid change, such as a shock wave, result in light refracting out of collimation. The collimated light is focused onto a sharp edge, which cuts off the refracted light and creates a shadow which shows where the change in species or properties occurs. For an in-depth and wide-ranging discussion of schlieren techniques, see reference 21. Measuring penetration by visual examination is influenced by the indices of refraction of the air and fuel. The boundary between fluids becomes more distinct as the indices of refraction are more different. The helium/air interface for example is unambiguous with airs index of refraction being 1.000293 and heliums being 1.000036 at 586.3 nm. Argon visualization requires greater sensitivity since its index of refraction, at 1.000281, is very close to airs. Adjustment of the amount of schlieren cutoff to 13

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14 increase sensitivity was successful in establishing the gas jet boundary with certainty in a minority of cases where argon was injected. Hydrogens index of refraction is 1.000140, which gives results intermediate between argon and helium. Figure 4-1A shows that A Boundary Layer Thickness, approximately 3.7mm Air Flow Direction B C Figure 4-1. Schlieren Images of Underexpanded, Circular, Sonic Gas Injection. A) 3.2 mm He jet at P 0 = 621 kPa. Air velocity increases from 0 to Mach 1.56 at P 0a =414 kPa, /D=1.16. B) 1.5 mm H 2 jet, q j /q a =0.50 (left) and q j /q a =1.5 (right) at Ma a =1.56, P 0a =552 kPa, /D=2.42. Approximate BL and air velocity profiles superimposed. C) 1 mm H 2 jet, q j /q a =1.0 (left) and q j /q a =2.5 (right) at Ma a =2.48, P 0a =552 kPa, /D=2.54. determining the injection centerline from the recorded image requires use of the leeward jet exit point as a datum, because the windward exit point is deformed by air stagnation pressure.

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15 The schlieren images in Figure 4-1A make visible the vortex that spills off of the injectant. Figure 4-1A shows helium injected into quiescent air through a 3.2 mm orifice. As air flow increases, a shadow is increasingly visible downstream of and below the jet. This shadow extends far downstream parallel to the flow marking the lower extent of the mixing vortices. When near-field penetration is weaker, as shown in Figure 4-1B, where the jet diameter is 1.5 mm, the jet is turned close to the wall and exits the BL at a shallow angle. The great majority of mixing must occur within the BL. Rogers 4 shows that gas concentrations and spreading are greatest in the BL especially in the near field when the BL is thick. Deeper near-field penetration results in better defined mixing vortices, which are known to enhance spreading and mixing. 22 Argon, hydrogen and helium gas were transversely injected into the supersonic flow through circular orifices of 1.0 mm, 1.5 mm, and 3.2 mm diameter. Inspection of the schlieren images shows that the windward side of the gas plume is deflected at an angle downstream from the normal direction by subsonic air close to the wall, but that the lee side of the jet is not deflected. The supersonic free stream is presented with an oblique obstacle, resulting in a weaker oblique shock wave displaced from the wall, as shown in Figure 4-1B. Gases injected into a Mach 1.6 air stream do not penetrate far beyond the boundary layer if the jet diameter is less than half the BL thickness and q j /q a is no more than 1.5, as shown in Figure 4-1B. For Mach 1.6 air, the classic picture of the bow shock is not accurate when the BL is significantly thicker than the injector diameter. At the point in the BL where oncoming air is supersonic the injected plume has already turned, presenting the air with an oblique obstacle that does not span the test section, resulting in

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16 a weak shock structure that is only minimally visible. The outer edge of the plume is identified on the Schlieren image by a band where light has been refracted away leaving an outline of the plume edge as shown in figures 4-1A, B and C. For Mach 2.5 flow, shown in Figure 4-1C, a distinct bow shock is visible and the interaction of the bow shock with the boundary layer is visible. This is consistent with higher Mach number in the BL and the reduced measured BL thickness. The depth of argon, helium and hydrogen penetration is presented in Figure 4-2 as a function of a correlation of independent variables considered to have an effect on gas penetration for measurements taken at Mach 1.6. The relative importance of each variable is modified by exponents that were determined empirically to minimize the summation of the squared relative data scatter about the mean power-law curve. Penetration was expressed as P/D, the depth of penetration divided by the jet exit diameter. The independent variables most commonly represented in literature are the dynamic pressure ratio between the jet at its exit and the air freestream and the downstream distance ratio at which penetration was measured, x/D. Additional variables that may affect penetration are the BL thickness ratio, /D, the ratio of jet to air Reynolds numbers and the ratio of jet to air molecular weight. The resulting penetration formula, based on the data gathered in the present study, is 0.568.276.2210.00840.025/1.362(/)(1.5)()(Re/Re)(/)jajajaxPDqqDD MM (6)

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17 y = 1.3623x0.2089110110100100010000(qj/qa)2.72(x/D-1.5)1.32(/D)1.06(Mj/Ma)-0.11(Rej/Rea)-0.04Penetration (P/D) Ar P/D (/D=2.42) Ar P/D (/D=3.72) He P/D (/D=2.42) He P/D (/D=3.72) H P/D (/D=2.42) H P/D (/D=3.72) 2 2 Figure 4-2. Curve Fit for Ar, He and H 2 injection into Mach 1.6 air at Varied BL thickness. Effect of Dynamic Pressure Ratio and Downstream Distance The ratio of jet to air dynamic pressure has the strongest effect on penetration of the variables examined. Figure 4-3 shows how varying q j /q a from 1 to 4 over x/D from 0 to 30 with the other variables held constant results in significant changes to the curve predicted by eqn. 6. Here M a =2.0, /D=2 and M j /M a =0.070. The effect of x/D is also apparent in Figure 4-3. Near-field penetration increases quickly with increasing x/D, but far-field penetration increases relatively slowly and beyond ~10D almost linearly with increasing x/D.

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18 0246810010203 0 Downstream Distance (x/D)Jet Penetration (P/D) q / q = 1 q / q = 2 q / q = 3 q / q = 4j a j a j a j a Figure 4-3. Penetration Varies Greatly With Increasing Dynamic Pressure Ratio. M a =2, /D=2, M j /M a =0.070. Effect of BL Thickness The thickness of the BL will effect jet penetration as shown in Figure 4-4. Increasing /D results in increased penetration into Mach 1.6 air. The degree by which penetration is increased decreases with increased air Mach number. When the supersonic Mach number is high much of the BL flow is also supersonic. The bow shock within the BL is strong with downstream conditions similar to conditions downstream of the free stream bow shock. 02468100102030Downstream Distance (x/D)Jet Penetration (P/D) /D = .5 /D = 1 /D = 2 /D = 3 Figure 4-4. Penetration Variation with BL Thickness. M a =1.6, q j /q a =2, M j /M a =0.070.

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19 Effect of Molecular Weight Ratio The effect of variation in molecular weight is illustrated in Figure 4-5. This figure shows that variation of injecant molecular weight has very little effect on penetration. As a result the exponent applied to the molecular weight is small and hydrogen penetrates nearly as far as argon which has a molecular mass 20 times greater. This is similar to the result of Torrences study. 23 Torrence found that at x/D=30 argon penetrated slightly deeper than hydrogen or helium, in agreement with the present study, but also found a minimium at intermediate molecular weights, which the resolution of the present study did not reveal. Torrence also found that the most significant affect of molecular mass was to decrease lateral spreading with increasing molecular mass while the depth of maximum penetrant concentration was essentially unaffected. 02468100102030Downstream Distance (x/D)Jet Penetration (P/D ) M j/ M a = 0.070 M j/ M a = 0.56 M j / M a= 0.1 4 M j / M a= 1.4 Figure 4-5. Variation in Penetration Due to Variation in Injectant Molecular Weight. M a =1.6, q j /q a =2, /D=1.

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20 The Reynolds number ratio has an exponent very close to zero indicating negligible effect. It was therefore considered reasonable to drop any Re dependence and eqn. 6 becomes, 0.568.276.2210.025/1.362(/)(1.5)()(/)jajaxPDqqDD MM (7) Povinelli and Povinelli 24 included a function of the ratio of air to jet Mach number in the correlation function which was not considered in the present study since only sonic injection was considered here. In their study as well as in a study by Billig, et al., 25 the effect of supersonic fuel injection was considered weak.

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CHAPTER 5 A PROPOSED, IMPROVED PENETRATION FORMULA Comparison To Previous Studies Figure 5-1 shows plots resulting from empirical formulae for predicting the outer limit of jet penetration that resulted from this and several previous studies of transverse injection. Each of these tests was conducted at different conditions which has affected the results. Schetz and Billig 3 analytically predicted transverse penetration at the centerline of an injected flow using the momentum transfer for a non-deforming plug. Their results are also plotted in Figure 5-1. In the analytical model of Schetz and Billig the injected plug of fluid carries transverse momentum into the air stream which initially has zero transverse momentum. This fluid particle is accelerated by transfer of momentum from the air stream to the particle while the air stream reacts by receiving and dissipating transverse momentum from the jet and converting some of its linear momentum to transverse momentum primarily in the form of the spilled vortices. Equation (7) determined in this study agrees well with the results of Leuchter 8 and Hersch, et al. 20 at q j /q a =1.5 however there are differences between these results and the other studies. The curve of Schetz and Billig 3 identifies the injected jet centerline whereas all others identify the outer limit of gas penetration. This curve is complemented with another curve marking jet diameter from the analytical centerline, which is maintained constant at all x/D for simplicity as in the study by Billig et al. 25 The curve of Schetz and Billig 3 plus jet diameter approaches the present study in the far field, beyond x/D=20. 21

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22 02468100102030Downstream Distance (x/D)Jet Penetration (P/D) Schetz & Billig(centerline) Schetz & Billig(center + D/2) Leuchter McClinton(/D = 2.42) Rogers Hersch, et al. Present Study ( /D = 2.42 ) 2 0 4 9 8 3 3 Figure 5-1. Penetration Correlations for Various Studies Exhibit Scatter; q j /q a =1.5. One factor that will influence the penetration measurement is the definition of the outer limit of penetration, which varies between studies. Near the penetration limit the concentration gradient is shallow as shown by Rogers 4 so any variation in definition can affect the measured penetration. This effect is assumed to be small for comparing the results of different studies and for generating an engineering estimate of penetration. The test conditions employed by each researcher affect the derived correlation. For example the correlation of Leuchter 8 is very similar to the formula derived in this study. Leuchters test condition of Mach 1.5 corresponds closely with the Mach 1.6 flows that dominate the data gathered for this study. Studies performed at Mach 2 freestream conditions resulted in slightly deeper prediction of penetration and studies at higher air Mach numbers indicated further penetration increases. This dependence is stronger than the ratio of jet to freestream Mach number effect found by Povinelli and Povinelli 24 and by Billig, et al. 25 because their work varied the injector rather than the freestream Mach number to specifically investigate that particular effect while leaving any shock

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23 interactions in the air stream essentially unaffected. It may be concluded that there is a relationship of penetration with air Mach number that has previously not been accounted for. General Penetration Formula A generic form for the penetration equation used in any of the studies cited above is /()()BGEFjjaaqxPDACqDDMM (8) Table 5-1. Penetration Formula Parameters Resulting From Various Studies A B C E F G Mach No. Schetz and Billig 3 1 0.435 0 0.435 0 0 N/A Leuchter 8 1.45 0.5 0.5 0.35 0 0 1.5 Hersch. et al. 20 1.92 0.35 0.5 0.277 0 0 2 Rogers 4 3.87 0.3 0 0.143 0 0 4 McClinton 9 4.2 0.3 0 0.143 0.057 0 4 Present study 1.36 0.568 -1.5 0.276 0.221 -0.0251 1.56 The values for each of the terms, A, B, C, E, F and G were placed in Table 5-1, along with the air Mach number of the tests used to derive the formula. Since a trend in experimental data was noticed as the air Mach number changed, the values of the exponents in equation (8) were plotted versus air Mach number and curves were fit to these values as shown in Figure 5-2. Linear curves were used in all cases except for term E which was better fit with a power law curve due to a rapid change at lower Mach numbers and more gradual change at higher Mach numbers. A refinement of the

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24 y = 1.0491x 0.1924y = -0.0803x + 0.6145y = 0.454x-0.8228y = -0.0666x + 0.32520.010.111012345Mach NumberFormula A B E F Figure 5-2. Penetration Equation Parameters versus Air Mach number. constants derived from Figure 5-2 was needed when fitting test data to the formula most likely due to the relatively small sample size used to derive the correlations in Figure 5-2. Insufficient data were available to establish a Mach number relation for G so the constant derived in the present study is used as shown in Table 5-1. The functional forms of A, B, C, E and F are shown in Table 5-2. Table 5-2. Penetration Equation Parameters as Functions of Air Mach number. Coefficients for Equation (8) Function of Air Mach Number, M a A = 1.0491 M a 0.1924 B = -0.0803 M a + 0.6145 C = -2.34/M a E = 0.395 M a -0.8228 F = -0.0666 M a + 0.3252 G = -0.02507 The resulting equation is /PD (.0803.615).395.823.0666.325.0251(1.05.192)(/)(2.34/)()(/)aaaMMMajaajaxMqqMDD MM (9) Figure 5-3 shows good correlation of this formula with all the test results compiled by the other researchers cited here. The inputs to the formula, including Mach number, BL thickness and dynamic pressure ratio are taken directly from test data compiled in the

PAGE 32

25 previous studies and are shown in Figure 5-3. Independent verification with test data obtained in the present study at M a = 2.5, which was not used to create the formula, is presented in Figure 5-4. Generally good agreement is evident in particular in the midfield. Close to the injection location where the slopes are large or in the far field beyond 30 jet diameters the differences between prediction and test data are much less than one jet diameter. qj/qa = 2.0, Ma = 1.5, /D = 2.402468100102030Downstream Distance (x/D)Penetration (P/D) Leuchter Present Study qj/qa = 6.3, Ma = 2.0, /D = 0.7602468100102030Downstream Distance (x/D)Penetration (P/D) Hersch, et al. Present Study qj/qa = 1.0, Ma = 4.0, /D = 2.702468100102030Downstream Distance (x/D)Penetration (P/D) McClinton Rogers Present Study Figure 5-3. Comparison of the Present Study with Previous Research. A) vs Leuchter 8 for H 2 ; M a =1.5. B) vs Hersch 20 et al. for He; M a =2 C)vs Rogers 4 and McClinton 9 for H 2 ; M a =4 Examination of equation (9) shows that penetration increases with increased dynamic pressure ratio, downstream distance and BL thickness to jet diameter ratio as expected; the penetration also increases with increased air Mach number which is not intuitively expected.

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26 012345670102030x/DPenetration (P/D) q /q =1, curve fit q /q = 1, data q /q = 1.5, curve fit q /q = 1.5, data q /q = 2, curve fit q /q = 2, dataj aj aj aj aj aj a Figure 5-4. Predicted and Measured Penetration of Sonic Hydrogen Transversely Injected into Mach 2.5 Air The increased penetration due to increased Mach number can be attributed to the stronger bow shock structure associated with higher Mach flows. As shown in Figure 5-6 the dynamic pressure on the downstream side of the shock is an increasingly small percentage of the upstream dynamic pressure as Mach number increases, so the dynamic pressure ratio actually seen by the injected gas is much lower than the freestream value. For example, a Mach 4 air stream with static conditions of 300 K and 101 kPa will have a dynamic pressure of 1131 kPa. After passing through a normal shock, the static conditions will be 1214 K and 1869 kPa with a dynamic pressure of only 247 kPa, a 78% reduction in dynamic pressure. Application of the 1-D, inviscid compressible flow equations for a normal shock is not sufficient to correct the dynamic pressure ratio effect since the bow shock is only normal over a portion of the plume. An empirical method lends itself to more practical implementation. It was shown in figure 5-1 that for injection into Mach 4 air the near-field penetration was much deeper than for injection at lower Mach numbers, but the far-field

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27 penetration did not increase as rapidly. The increased near-field penetration is explained above and the decreased rate of far-field penetration is logically due to the greater free stream momentum, which at this point is only minimally altered by compressibility. 00.20.40.60.811.20246810Mach Numberqy/qx Figure 5-5. Dynamic Pressure Ratio Across a Normal Shock versus Mach number. Despite increased penetration from the wall when the Mach number is low supersonic and the BL is thick, the penetration out of the BL and into the free stream is decreased by a thick BL. The strong, nearly normal bow shock is absent at low supersonic Mach number and thick BL. The supersonic freestream interacts with the deflected plume by forming a weaker oblique shock. With the weakened virtual obstruction of the injectant jet in the freestream, the vortex generation essential to effective bulk mixing processes is weakened. The resulting flow approaches the case of tangential, rather than transverse injection. When the supersonic Mach number is high, much of the BL flow is also supersonic, so a strong bow shock extends deep into the BL with consequent low dynamic pressure downstream of the bow shock leading to increased penetration. The drop in dynamic pressure across the shock wave is more effective at increasing

PAGE 35

28 penetration than velocity reduction in the BL. This explains the decreased effect of BL thickness on improving penetration as Mach number increases.

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CHAPTER 6 CONCLUSIONS This study has evaluated the penetration of gas jets into supersonic flows with thick boundary layers over various Mach numbers. Comparison with previous studies shows the following: Transverse jet penetration is dependent on q j /q a x/D, /D and air Mach number. Among the parameters under the designers control q j /q a has the strongest effect. The Mach number will modify the impact of the other variables and can have a dramatic effect on penetration which was not previously recognized. Generally, increased air Mach number results in increased penetration due to greater dynamic pressure reduction downstream of stronger shock waves. The effect of the boundary layer thickness on increasing near-field jet penetration is significant at low supersonic Mach numbers but decreases with increased Mach number. Deeper near-field penetration results in stronger vortex formation, which is known to enhance mixing and spreading. The effect of molecular weight ratio on penetration is small and not monotonic. The effect of Reynolds number is negligible. 29

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LIST OF REFERENCES 1. Glass, C. E., A Parametric Study of Jet Interactions with Rarefied Flow, 21st International Symposium on Rarefied Gas Dynamics, edited by R. Brun, R. Campargue, R. Gatingnol, and J. C. Lengrand, Cepadues Editions, Toulouse France, 1998, Vol. 1, pp 615-622. 2. Kaufman, Louis G. II, Hypersonic Flows Past Transverse Jets, Journal of Propulsion and Power, Vol. 4, No. 9, September 1967, pp 1230-1235. 3. Schetz, J., Billig, F., Penetration of Gaseous Jets Injected into a Supersonic Stream, Journal of Spacecraft and Rockets, Vol. 3, No. 11, November 1966, pp 1658-1665. 4. Rogers, R. C., A Study of the Mixing of Hydrogen Injected Normal to a Supersonic Airstream, NASA TN D-6114, 1971. 5. Owens, M., Tehranian, S., Segal, C. and Vinogradov, V., Flame-Holding configurations for Kerosene Combustion in a Mach 1.8 Airflow, Journal of Propulsion and Power, Vol. 14, No. 4, July-August 1998, pp 456-461. 6. Gallimore, S., Jabobsen, L., OBrien, W. and Schetz, J., Operational Sensitivities of an Integrated Scramjet Ignition/Fuel Injection System, Journal of Propulsion and Power, Vol. 19, March-April 2003, pp183-189. 7. Parent, B. and Sislian, J., Effect of Geometrical Parameters on the Mixing Performance of Cantilevered Ramp Injectors, AIAA Journal, Vol. 41, No. 3, pp 448-456. 8. F. H. Falempin, Scramjet Development in France, Scramjet Propulsion, E. T. Curran and S. N. B. Murthy Editors, Progress in Astronautics and Aeronautics, AIAA, Washington D. C., 2000, vol. 189, pp 47-117. 9. McClinton, C. R., Effect of Ratio of Wall Boundary-Layer Thickness to Jet Diameter on Mixing of a Normal Hydrogen Jet in a Supersonic Stream, NASA TM X-3030, June 1974, pp 1-42. 10. Gruber, M. R., Nejad, A. S., Chen, T. H. and Dutton, J. C., Transverse Injection From Circular and Elliptic Nozzles into a Supersonic Crossflow, Journal of Propulsion and Power, Vol. 16, No. 3, May-June 2000, pp 449-457. 30

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31 11. Ben-Yakar, A. and Hanson, R., Experimental Investigation of Flame-Holding Capability of Hydrogen Transverse Jet in Supersonic Cross-flow, 27th Symposium (International) on Combustion/The Combustion Institute, 1998, pp 2173-2180. 12. Turns, S. R., An Introduction to Combustion: Concepts and Applications, Second Edition, McGraw-Hill, Boston, 2000, pp 84-88. 13. Dimotakis, P. E., Turbulent Free Shear Layer Mixing and Combustion, High Speed Flight Propulsion Systems, in Progress in Astronautics and Aeronautics, AIAA, Washington D. C., 1991, Vol. 137, pp 265-340. 14. Billig, F. S., Research on Supersonic Combustion, Journal of Propulsion and Power, Vol. 9, No. 4, July-August 1993, pp 499-520. 15. Seiner, J. Dash, S. and Kenzakowski, D., Historical Survey on enhanced Mixing in Scramjet Engines, Journal of Propulsion and Power, Vol. 17, No. 6, November-December 2001, pp 1273-1286. 16. Northam, G. B., Greenberg, I., Byington, C. S. and Caprotti, D. P., Evaluation of Parallel Injector Configurations for Mach 2 Combustion, Journal of Propulsion and Power, Vol. 8, No. 2, March-april 1992, pp 491-499. 17. Owens, M. G., Segal, C. and Auslander, A. H., Effects of Mixing Schemes on Kerosene Combustion in a Supersonic Airstream, Journal of Propulsion and Power, Vol. 13, No. 4, July-August 1997, pp 525-531. 18. McClinton, C. R., The Effect of Injection angle on the Interaction Between Sonic Secondary Jets and a Supersonic Free Stream, NASA TN D-6669, February 1972. 19. Gaffney, R. L. Jr. and Korte, J., Analysis and Design of Rectangular Cross-Section Nozzles For Scramjet Engine Testing, AIAA Aerospace Science Meeting and Exhibit, 5-8 January 2004, AIAA 2004-1137, pp 1-16. 20. Hersch, M., Povinelli, L. and Povinelli, F., A Schlieren Technique for Measuring Jet Penetration into a Supersonic Stream, Journal of Spacecraft and Rockets, Vol. 7, No. 6, June 1970, pp 755-756. 21. Settles, G. S., Schlieren and Shadowgraph Techniques, Visualizing Phenomena in Transparent Media, Springer-Verlag, Berlin, 2001. 22. Swithenbank, J., Eames, I., Chin, S., Ewan, B., Yang, Z., Cao, J. and Zhao, X., Turbulence Mixing in Supersonic Combustion Systems, AIAA Paper 89-0260, January 1989. 23. Torrence, M. G., Effect of Injectant Molecular Weight on Mixing of a Normal Jet in a Mach 4 Airstream, NASA TN D-6061, January 1971, pp 1-104.

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32 24. Povinelli, F. P. and Povinelli, L. A., Correlation of Secondary Sonic and Supersonic Gaseous Jet Penetration into Supersonic Crossflows, NASA TN D-6370, June 1971, pp 1-20. 25. Billig, F. S., Orth, R. C. and Lasky, M., A Unified Analysis of Gaseous Jet Penetration, AIAA Journal, Vol. 9, No. 6, June 1971, pp 1048-1058.

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BIOGRAPHICAL SKETCH Ron Portz was born in Rockledge, Florida, on May 31, 1965. He is a 1983 honor graduate of Cocoa High School, where he excelled in academic and artistic competition. He was both a National Merit Scholarship Finalist and a Scholastic Art Awards Gold Key recipient. Mr. Portz served two years as a missionary for the Church of Jesus Christ of Latter Day Saints from 1986 to 1988 whereupon he resumed his academic career, graduating from the University of Florida in 1991 with a Bachelor of Science degree in Mechanical Engineering. Mr. Portz has been happily married to the former Pamela Pierson since May 12, 1990. The couple currently have two adopted sons, Elijah and Samuel. Following college graduation Mr. Portz worked for Rockwell International and The Boeing Corporation as a Test Engineer and a Depot Engineer for the Space Shuttle Main Propulsion System, Attitude Control System and Environmental Control/Life-Support System at NASAs Shuttle Logistics Depot in Cape Canaveral, Florida. In 1998, Mr. Portz began work for Orbital Sciences Corporation in Chandler, Arizona. His work responsibilities included the design, assembly, test and post-flight analysis of cold-gas, solid and liquid propellant propulsion systems. He is the recipient of multiple awards and recognitions for the quality of his work. In 2003, Mr. Portz returned to the University of Florida to pursue a graduate degree in mechanical engineering. The University of Florida had been selected to lead the 33

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34 Institute for Future Space Transport, which was described as paving the way for design of second and third generation reusable launch vehicles to replace the Space Shuttle. As space transportation has occupied the majority of his professional life and its future is precarious, he determined to participate in this program in the hope of applying his practical experience to provide needed direction to the industry. He is grateful for the opportunity to return to school and improve the depth of his academic knowledge.


Permanent Link: http://ufdc.ufl.edu/UFE0010827/00001

Material Information

Title: Transverse jet penetration in supersonic flows with variable boundary layer thickness
Physical Description: Mixed Material
Language: English
Creator: Portz, Ron ( Dissertant )
Segal, Corin ( Thesis advisor )
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2005
Copyright Date: 2005

Subjects

Subjects / Keywords: Mechanical and Aerospace Engineering thesis, M.S
Dissertations, Academic -- UF -- Mechanical and Aerospace Engineering

Notes

Abstract: Penetration of gases injected transversely into a supersonic air stream was measured over varied conditions of fuel molecular weight, relative air boundary layer thickness and Mach number to verify and complement previous studies. Air Mach numbers of 1.6 and 2.5 were tested and compared to published data from Mach 1.5 to 4. Boundary layer thickness was measured and jets of 1 mm, 1.5 mm, and 3.2 mm diam. were injected in a test section with a square section 25 mm wide, followed by a 450 mm long constant area duct. Hydrogen, helium and argon were injected to observe the effects of density and viscosity on penetration. Schlieren imaging was used to visualize and measure penetration. This study compared penetration to existing models using dynamic pressure ratio, air Mach number and boundary layer thickness as independent variables. Significant penetration dependence on air Mach number was identified. Penetration was found to increase strongly with boundary layer thickness at low Mach numbers but as Mach number increases, boundary layer thickness has less effect. A new formula is proposed to predict penetration based on a set of independent variables. This formula is compared to new test data and previous results and achieves good correlation for all studies.
Abstract: air, breathing, propulsion, scramjet
General Note: Title from title page of source document.
General Note: Document formatted into pages; contains 41 pages.
General Note: Includes vita.
Thesis: Thesis (M.S.)--University of Florida, 2005.
Bibliography: Includes bibliographical references.
General Note: Text (Electronic thesis) in PDF format.

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0010827:00001

Permanent Link: http://ufdc.ufl.edu/UFE0010827/00001

Material Information

Title: Transverse jet penetration in supersonic flows with variable boundary layer thickness
Physical Description: Mixed Material
Language: English
Creator: Portz, Ron ( Dissertant )
Segal, Corin ( Thesis advisor )
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2005
Copyright Date: 2005

Subjects

Subjects / Keywords: Mechanical and Aerospace Engineering thesis, M.S
Dissertations, Academic -- UF -- Mechanical and Aerospace Engineering

Notes

Abstract: Penetration of gases injected transversely into a supersonic air stream was measured over varied conditions of fuel molecular weight, relative air boundary layer thickness and Mach number to verify and complement previous studies. Air Mach numbers of 1.6 and 2.5 were tested and compared to published data from Mach 1.5 to 4. Boundary layer thickness was measured and jets of 1 mm, 1.5 mm, and 3.2 mm diam. were injected in a test section with a square section 25 mm wide, followed by a 450 mm long constant area duct. Hydrogen, helium and argon were injected to observe the effects of density and viscosity on penetration. Schlieren imaging was used to visualize and measure penetration. This study compared penetration to existing models using dynamic pressure ratio, air Mach number and boundary layer thickness as independent variables. Significant penetration dependence on air Mach number was identified. Penetration was found to increase strongly with boundary layer thickness at low Mach numbers but as Mach number increases, boundary layer thickness has less effect. A new formula is proposed to predict penetration based on a set of independent variables. This formula is compared to new test data and previous results and achieves good correlation for all studies.
Abstract: air, breathing, propulsion, scramjet
General Note: Title from title page of source document.
General Note: Document formatted into pages; contains 41 pages.
General Note: Includes vita.
Thesis: Thesis (M.S.)--University of Florida, 2005.
Bibliography: Includes bibliographical references.
General Note: Text (Electronic thesis) in PDF format.

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0010827:00001


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TRANSVERSE JET PENETRATION IN SUPERSONIC FLOWS WITH VARIABLE
BOUNDARY LAYER THICKNESS

















By

RON PORTZ


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA


2005















ACKNOWLEDGMENTS

This work was performed with support from NASA grant NCC3-994 with Claudia

Meyer as the Program Manager.

Dr. Corin Segal, of the Department of Mechanical and Aerospace Engineering

provided direction for this research and contributed valuable guidance in the preparation

of this thesis.

Utmost thanks are due my wife Pamela and our children Elijah and Sammy, who

have borne with the vicissitudes of life with a graduate student. I am grateful for my

parents' confidence and support of me and my family from birth. I would also like to

thank my mother-in-law and father-in-law, who in addition to letting me marry their

daughter have been of emotional and material support.
















TABLE OF CONTENTS

page

A C K N O W L E D G M E N T S .................................................................................................. ii

LIST OF TABLES .............................. .................... ... .... iv

LIST OF FIGURES ................................. ...... ... ................. .v

ABSTRACT ........ .............. ............. ...... .......... .......... vi

CHAPTER

1 IN T R O D U C T IO N ............................................................................. .............. ...

2 NEAR FIELD AND FAR FIELD MIXING OF TRANSVERSE JETS...................5

3 E X P E R IM E N T S ................................................................................ .......... .. .. ...9

E x p erim ental F facility ............ .......................................................... .. ...... ..... ..9
B oundary Layer Thickness ........................................................... .............9

4 RESULTS AND ANALY SIS........................................ .....................................13

Penetration V isualization ................................. ..................... ..................... 13
Effect of Dynamic Pressure Ratio and Downstream Distance .............................. 17
Effect of BL Thickness ................................................... .. .... .. ................. 18
Effect of M olecular W eight Ratio ................................................... .. ... .......... 19

5 A PROPOSED, IMPROVED PENETRATION FORMULA.................................21

C om prison T o Previous Studies..................................................... .....................2 1
G general Penetration Form ula........................................................... ............... 23

6 C O N C L U SIO N S ..................... .... .......................... ........ ........ ...... ........... 29

LIST OF REFEREN CES ............................................................................. 30

B IO G R A PH IC A L SK E TCH ..................................................................... ..................33
















LIST OF TABLES


Table page

5-1 Penetration Formula Parameters Resulting From Various Studies..........................23

5-2 Penetration Equation Parameters as Functions of Air Mach number. ...................24
















LIST OF FIGURES


Figure page

1-1 Model of Transverse, Underexpanded Injection into a Supersonic Airstream. .........2

1-2 Interaction Between the Boundary Layer and Jet in Supersonic Flow ..................3

3-1 Schematic of the test section with dimensions normalized by duct height, L=25
m m ............... ........................... .............................................. .1 0

3-2 Boundary layer measurement at the collar outlet...............................................11

3-3 The BL at measured locations bounding the injector port and assuming linear
g ro w th ........................................................................................... 12

4-1 Schlieren Images of Underexpanded, Circular, Sonic Gas Injection....................14

4-2 Curve Fit for Ar, He and H2 injection into Mach 1.6 air at Varied BL thickness....17

4-3 Penetration Varies Greatly With Increasing Dynamic Pressure Ratio. Ma=2,
6/D =2, 1/J/1 a=0.070 .................................. ..........................................18

4-4 Penetration Variation with BL Thickness. .................................... .................18

4-5 Variation in Penetration Due to Variation in Injectant Molecular Weight.
M = 1.6, q/q,=2, /D = 1 .......................... ........................ ........... .............. 19

5-1 Penetration Correlations for Various Studies Exhibit Scatter; q,/qa=1.5 ...............22

5-2 Penetration Equation Parameters versus Air Mach number................................24

5-3 Comparison of the Present Study with Previous Research ................................25

5-4 Predicted and Measured Penetration of Sonic Hydrogen Transversely Injected
into M ach 2 .5 A ir ................................................... ................ 2 6

5-5 Dynamic Pressure Ratio Across a Normal Shock versus Mach number. ...............27















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

TRANSVERSE JET PENETRATION IN SUPERSONIC FLOWS WITH VARIABLE
BOUNDARY LAYER THICKNESS

By

Ron Portz

December 2005

Chair: Corin Segal
Major Department: Mechanical and Aerospace Engineering

Penetration of gases injected transversely into a supersonic air stream was

measured over varied conditions of fuel molecular weight, relative air boundary layer

thickness and Mach number to verify and complement previous studies. Air Mach

numbers of 1.6 and 2.5 were tested and compared to published data from Mach 1.5 to 4.

Boundary layer thickness was measured and jets of 1 mm, 1.5 mm, and 3.2 mm diam.

were injected in a test section with a square section 25 mm wide, followed by a 450 mm

long constant area duct. Hydrogen, helium and argon were injected to observe the effects

of density and viscosity on penetration. Schlieren imaging was used to visualize and

measure penetration. This study compared penetration to existing models using dynamic

pressure ratio, air Mach number and boundary layer thickness as independent variables.

Significant penetration dependence on air Mach number was identified.

Penetration was found to increase strongly with boundary layer thickness at low Mach

numbers but as Mach number increases, boundary layer thickness has less effect. A new









formula is proposed to predict penetration based on a set of independent variables. This

formula is compared to new test data and previous results and achieves good correlation

for all studies.














CHAPTER 1
INTRODUCTION

When a gas is injected transversely into a supersonic air stream, significant shock

and viscous interactions occur. The results of these interactions are not always intuitive

as has been shown for external flows,1'2 and are strongly affected by the ratio of injectant

to air dynamic pressures,


q- (1)
q, PaU,2

where jet properties are taken at the jet exit and air properties are for the freestream

before encountering jet-induced shocks. The dynamic pressure ratio is used in lieu of the

momentum flux ratio in most of the literature on this subject and the terms are sometimes

considered interchangeable. The momentum flux ratio is only truly equal to the dynamic

pressure ratio if the areas through which the respective fluids pass are equal, which is

virtually never the case. Regardless, the dynamic pressure ratio has come to be an

accepted datum for the empirical correlation of transverse jet penetration.

In most circumstances the injected plume acts almost as a solid object resulting in

the generation of a bow shock, turbulent shear layer and a system of vortices spilling off

the semi-cylindrical obstruction, as shown in Figure 1-1. The injectant is turned nearly

parallel to the air within a short distance and the vortices' rotation axes align nearly with

the air stream. Mixing of the injectant with the air is facilitated by the streamwise

vortices spilling off of the turned injectant plume. Near-field mixing is dominated by









bulk mass transfer and the far field mixing by the development of compressible shear

layers.


Velocity Outer limit of turbulent
Profile Bow Shock shear layer/penetration






Spilled Vorte
same on both
sides
S\ /Concentration
Potential Core Pro


Figure 1-1. Model of Transverse, Underexpanded Injection into a Supersonic Airstream.

Two general cases of interaction between the jet and the boundary layer (BL) have

been recognized and are illustrated in Figure 1-2, which is adapted from Schetz and

Billig.3 The determining factor in the shape of the barrel shock around the jet is the

degree of BL separation ahead of the jet, which is in turn determined by jet strength

compared to freestream properties. When the separation region thickness is much

smaller than the height of the Mach disc at the end of the barrel shock, the gas penetrates

through the BL and a strong, nearly normal, bow shock forms in the air stream. The

barrel shock is bent backward by high pressure air downstream of the bow shock as

shown in Figure 1-2A. When the BL separation region is at least of the same order as the

first Mach disc height, the jet penetrates straight as shown in Figure 1-2B and as

described by Kaufman,2 Rogers4 and Schetz and Billig.3 The Mach disc is nearly parallel

to the wall. Kaufman2 and Schetz and Billig3 further discuss the criteria that lead to BL

separation.











Maair Maair

Strong Bow Weak Bow .-
Shock / Shock






Figure 1-2. Interaction Between the Boundary Layer and Jet in Supersonic Flow. A)
Attached and B) Separated Boundary Layer Flows (Adapted from Schetz and
Billig3)

In the case of vehicles with a body-integrated scramjet design, a long inlet ramp

with a continuous, strong, adverse pressure gradient is likely to result in a thick BL in the

combustor, conducive to flow separation. High stagnation temperature, intrinsic to

hypersonic flight, does not facilitate bleeding the BL so this condition becomes of

substantial interest.

In a supersonic combustor fuel must penetrate and mix in the cooler high speed

core flow beyond the BL to maximize cycle efficiency. Various methods have been

suggested such as pylons and ramp injectors to deliver the majority of fuel into the free

stream, away from the wall and BL.57 Simple transverse injection is desirable for the

sake of simplicity, but it introduces some known disadvantages. The strong shocks that

typically accompany transverse injection result in irreversible loss of total pressure in the

air. Flameholding is not provided by simple transverse injection and must be provided by

combustor features that establish recirculation zones which add to total pressure losses.

Empirically derived models of penetration in supersonic air flows with transverse

fuel injection describe the dimensions of the fuel plume penetration and spreading for an

injected gas using a definition for the plume boundary based variously on injectant









concentration of 1%, injectant mole fraction of 0.005, intensity of an image, or other

criteria, depending on the particular study.8-10 Different researchers have studied various

ranges of experimental conditions and incorporated different sets of independent

variables including the dynamic pressure ratio, downstream distance, boundary layer

thickness and jet Mach number in the curve fits used to predict penetration. Both jet

penetration and boundary layer thickness are usually non-dimensionalized by jet

diameter. The variation in definitions and test conditions has resulted in some

disagreement in the curve fits produced in previous studies, as will be shown below.

It should be noted that although greater penetration generally results in better

mixing, deep penetration is not sufficient to ensure enhanced combustion. For transverse

injection tests relying on auto-ignition due to temperature increase across the bow shock

it has been observed that cooler air passing through oblique shocks curving off of the

bow shock inhibit combustion in zones where the equivalence ratio is otherwise within

flammability limits.1 Results reported in reference 11 indicate that burning was

restricted to a small recirculation kernel in the stagnation zone upstream of the fuel jet

and in a thin sheet immediately aft of the bow shock where temperatures were high. The

majority of the fuel did not react with the air despite good fuel penetration and mixing.

Good fuel and air mixing is only one of the factors resulting in efficient combustion.















CHAPTER 2
NEAR FIELD AND FAR FIELD MIXING OF TRANSVERSE JETS

For combustion to occur fuel and air must mix and diffuse at a molecular level.

The transport of one molecular species into another is described by Fick's Law12


h = Y4 (1A + 2B ) DAB dA (2)
Adx
where
hA is the bulk mass flow rate of species A into species B

iyh is the bulk mass flow rate of species B into species A

YA is the mass fraction of species A

p is the density of species A

DAB, is the binary diffusion coefficient for species A diffusing into species B

defined as



A 3 3 U, P

where

RB is the gas constant for species B, Tis the temperature,

4A is the molecular mass of species A,


a is the molecular collision diameter, or weighted average of the diameters of

molecules A and B

Pis the pressure.









The first term in (2), Y, (th + rh ), is the bulk flow of species A into B and does not

result directly in molecular mixing. The second term, -pDA dYA /dx, shows that the

diffusive mass flow rate of species A into B increases with increasing density, binary

diffusion coefficient and species gradient. Inspection of (3) reveals that the diffusion

coefficient increases with temperature to the 2 power, with pressure to the -1 power,

molecular weight of species A to the 1 power and molecular diameter to the -2 power.

For perfect gases the overall mass flow rate due to diffusion changes with the square root

of temperature, and is neutral for pressure changes. The overall rate of diffusion is

maximized for small, light molecules at high temperature. Intuitively, this is due to

increasing average molecular speed while decreasing the rate of collision between the

diffusing gas molecules. Frequent collisions impede the average motion of molecules in

the direction of decreasing concentration. This contributes to the preference of hydrogen

to fuel supersonic combustion; in addition to the rapidity of reaction associated with

hydrogen once it has mixed with oxidizer, it will diffuse and mix more quickly in air than

any other fuel due to its small molecule size.

Once a design flight condition is chosen which fixes engine inlet temperature and

pressure and a fuel is selected there are limited options for the combustor designer to

affect diffusion. For this reason it turns out that controlling bulk flow processes

dominates the eventual mixing efficiency of fuel injected into a supersonic air stream.

When a gas is injected transversely into an air stream non-linear penetration is apparent

in the near field. Large momentum flux transfer between the air and the jet dominates the

penetration and mixing process. Bulk mass transfer is brought about by significant jet

penetration. In some studies4' 9 greater lateral spreading than axial penetration was









noticed for transverse fuel injection indicating that the shear forces due to the vortices

spilling off of the side of the fuel jet were a more effective transport mechanism than the

transverse injection momentum.

In the far field, more than ten jet diameters downstream of the injection location,

penetration increases by essentially tangential shear layer growth where the penetration

distance assumes a nearly linear relationship with downstream distance. In this regime

the jet centerline is essentially parallel to the air and the slope of the penetration curve is

directly related to the shear layer growth.13 For practical supersonic combustors and the

test equipment employed in this study the Reynolds number exceeds 106. At Reynolds

numbers above 104 the shear layer is turbulent with macroscopic vortex structures

moving at a convective velocity, Uc, defined as.13


Uc U2 + U2 (4)
a1 +a2

where U, and a, are respectively the velocity and speed of sound of each of the fluids.

The convective Mach numbers, Mi for two fluids are defined as

U, U- U U
Mc1 U Uc andMC2 U -U2 (5)
a1 a2

Shear layer growth is a function of the ratio of fluid velocities, the ratio of fluid

densities and MC.13 The shear layer growth rate decreases with increased compressibility

and increases with increased density ratio between the two fluids. For a detailed

discussion of mixing in shear layers, see reference 13.

Enhanced mixing schemes have been described elsewhere14' 15 which convert some of

the tangential momentum of the air into transverse momentum along with generation of

vortical structures. An example is the swept ramp injector in which air passes over an









upward incline adjacent to either a flat or a downward inclined surface.16-18 Spillage

from the ramp creates a vortex that enhances bulk fuel flow into air while causing oblique

shocks and relatively small losses unlike simple transverse injection which produces

normal shocks and strong vortices that result in significant stagnation pressure loss.

Angled injection from a wall has been studied with the intent to retain the simplicity of

transverse injection while minimizing the stagnation pressure loss.7' 18

Studies with gaseous hydrogen as the injected fuel have observed that significant

additional thrust results from injection of fuel with a tangential velocity component.18

Tangentially injected fuel will contribute some small thrust and the specific impulse of

hydrogen may be high if it is used to cool hot engine parts before injection. However, the

thrust addition is minor, because of the small fuel mass involved, for example -3% H2 by

mass at stoichiometric mixture ratio.

Both near and far-field mixing mechanisms are present in both transverse and

angled jet injection. Deep penetration facilitates mixing and with appropriate flame-

holding devices promotes efficient supersonic combustion chambers. The results of

experimental penetration analysis and its correlation to the jet flow thermodynamic

properties of gaseous jets are described below.














CHAPTER 3
EXPERIMENTS

Experimental Facility

Figure 3-1 is a schematic representation of the continuous-flow, direct-connect,

supersonic-combustion wind tunnel used in these experiments. This tunnel can deliver

.454 kg/s of air continuously at combustor Mach numbers from 1.3 to 3.6, with stagnation

temperature up to 1,200K and stagnation pressure from 207 to 827 kPa. Higher flow

rates and pressures up to 1,520 kPa are subject to limited duration. These conditions

correspond to flight enthalpy of up to Mach 4.75. This facility has been previously

described in detail by Owens.5

For the purpose of measuring jet penetration this study used unheated air,

consistent with previous studies.4 9, 10, 18 The entrance to the test section was an L = 25.4

mm wide square section. The cross-section was constant along its length of 18L.

Hydrogen, helium or argon were injected transversely, at a location where the BL

thickness was known, through 1 mm, 1.5 mm, and 3.2 mm orifices to vary the ratio of BL

thickness, 6, to jet diameter, D.

Boundary Layer Thickness

BL thickness was measured using a probe with a square-cut tip of 0.25 mm outside

diameter, and 0.13 mm bore diameter. The probe was inserted through any of three holes

in the side-wall of the test section normally used for optical access (see Figure 3-1) and

was traversed in 0.2mm increments while measuring the stagnation pressure.

Measurements were taken around the isolator outlet circumference for unheated air at 414












0.145L Boundary layer
growth at Mach 1.56
and 414 kPa air
0.13 0.26L 015



Air from stagnation
chamber

3R mm 114 mm
Nnzzl e
N7nlat7nr




146 127 mm Test Sectinn
mm mm 76 Fuel wT= 25 mm
mm 25 mm Wind1nwm
mm Injector

Figure 3-1. Schematic of the test section with dimensions normalized by duct height,
L=25 mm. The measured BL at selected locations is also shown.

kPa stagnation pressure and nozzle exit Mach number of 1.6. The results of this

measurement are shown in Figure 3-2. Lack of physical access to the East side of the test

apparatus restricted BL measurements to three sides. Symmetery of the apparatus

ensures that use of the West-to-East BL measurement accurately represents the East-to-

West BL. The BL measurement was repeated in the West-to-East direction at both Mach

1.6 and Mach 2.5. Fuel is injected from the East wall. The BL was measured at several

stations downstream of the nozzle exit, as indicated in Figure 3-2. Measurements showed

a relatively small inviscid core flow at the point of injection since the measured BL

occupies over 50% of the cross section area. At Mach 1.6 BL growth in the 18L long

constant-area test section resulted in choking unless a substantial bleed from the last third

of the test section was established. At each station, the BL thickness is taken as the point











1.2


1. 0 ,. ***.44tt4***
^ xx




Sx so o North to South
x South to North
'. 0.2
o X








0.0 -



Probe Position (y/L)

Figure 3-2. Boundary layer measurement at the collar outlet. The collar exit is 76 mm,
or 3L upstream of the fuel injector. Measurements are taken from the outside
edge toward the center of the flow, along the section centerline. The cardinal
directions are used as references.

of 99% velocity, or where the measured pitot pressure was 98% of the maximum value.

The BL thickness at the point of gas injection was approximated by linear interpolation

between the two stations measured on either side of the port as shown in Figure 3-3. For

552 kPa stagnation pressure and Mach 1.6 flow, the BL thickness at the injector port was

3.7 mm. For Mach 2.5 flow the BL thickness was 2.5 mm.

It is known from measurements taken here and elsewhere19 that rectangular, 2-D

nozzles yield boundary layers that are not uniform around the passage circumference.

Along the contoured nozzle walls, the boundary layer is uniform in thickness and thinner

than on the flat walls of the 2-D nozzle. The flat walls have a non-uniform BL as shown

in Figure 3-1, with greater thickness at the center than at the edges, where BL thickness is










similar to the contoured walls. At the station 1.75L forward of the point of gas injection,

the BL thickness was 3.3 mm on the contoured walls, while the maximum BL thickness

on the flat walls was 6.6 mm. This is due to the stronger favorable pressure gradient

along the contoured walls.


15 -
15



0
0 40 80 120 160
length From Isolator Outlet (mm)
0 Section Centerline A Injector Station


Figure 3-3. The BL at measured locations bounding the injector port and assuming linear
growth.














CHAPTER 4
RESULTS AND ANALYSIS

Penetration Visualization

Flow and fluid mixing are visualized by use of a lens-based Schlieren system.

Optical assessment of jet penetration has been demonstrated to give accurate and

consistent depth compared to chemical sampling methods. 13,20 Images were collected

with an SVHS video camera. To capture average penetration rather than instantaneous

variations each camera exposure was of the order of 20 ms which is long compared to

transient flow excursions.

Schlieren systems make flow phenomena and optical irregularities visible by

passing collimated light through transparent media. Changes in the refractive index

between fluids or between regions where the thermodynamic properties of a fluid change,

such as a shock wave, result in light refracting out of collimation. The collimated light is

focused onto a sharp edge, which cuts off the refracted light and creates a shadow which

shows where the change in species or properties occurs. For an in-depth and wide-

ranging discussion of schlieren techniques, see reference 21.

Measuring penetration by visual examination is influenced by the indices of

refraction of the air and fuel. The boundary between fluids becomes more distinct as the

indices of refraction are more different. The helium/air interface for example is

unambiguous with air's index of refraction being 1.000293 and helium's being 1.000036

at 586.3 nm. Argon visualization requires greater sensitivity since its index of refraction,

at 1.000281, is very close to air's. Adjustment of the amount of schlieren cutoff to









increase sensitivity was successful in establishing the gas jet boundary with certainty in a

minority of cases where argon was injected. Hydrogen's index of refraction is 1.000140,

which gives results intermediate between argon and helium. Figure 4-1A shows that


Figure 4-1. Schlieren Images of Underexpanded, Circular, Sonic Gas Injection. A) 3.2
mm He jet at Po= 621 kPa. Air velocity increases from 0 to Mach 1.56 at
Poa=414 kPa, 6/D=1.16. B) 1.5 mm H2 jet, q/qa=0.50 (left) and q/qa=1.5
(right) at Maa=1.56, Poa=552 kPa, 6/D=2.42. Approximate BL and air
velocity profiles superimposed. C) 1 mm H2 jet, q/qa=l.O (left) and q/qa=2.5
(right) at Ma,=2.48, Po,=552 kPa, 6/D=2.54.

determining the injection centerline from the recorded image requires use of the leeward

jet exit point as a datum, because the windward exit point is deformed by air stagnation

pressure.









The schlieren images in Figure 4-1A make visible the vortex that spills off of the

injectant. Figure 4-1A shows helium injected into quiescent air through a 3.2 mm orifice.

As air flow increases, a shadow is increasingly visible downstream of and below the jet.

This shadow extends far downstream parallel to the flow marking the lower extent of the

mixing vortices. When near-field penetration is weaker, as shown in Figure 4-1B, where

the jet diameter is 1.5 mm, the jet is turned close to the wall and exits the BL at a shallow

angle. The great majority of mixing must occur within the BL. Rogers4 shows that gas

concentrations and spreading are greatest in the BL especially in the near field when the

BL is thick. Deeper near-field penetration results in better defined mixing vortices,

which are known to enhance spreading and mixing.22

Argon, hydrogen and helium gas were transversely injected into the supersonic

flow through circular orifices of 1.0 mm, 1.5 mm, and 3.2 mm diameter. Inspection of

the schlieren images shows that the windward side of the gas plume is deflected at an

angle downstream from the normal direction by subsonic air close to the wall, but that the

lee side of the jet is not deflected. The supersonic free stream is presented with an

oblique obstacle, resulting in a weaker oblique shock wave displaced from the wall, as

shown in Figure 4-1B.

Gases injected into a Mach 1.6 air stream do not penetrate far beyond the boundary

layer if the jet diameter is less than half the BL thickness and q,/qa is no more than 1.5, as

shown in Figure 4-1B. For Mach 1.6 air, the classic picture of the bow shock is not

accurate when the BL is significantly thicker than the injector diameter. At the point in

the BL where oncoming air is supersonic the injected plume has already turned,

presenting the air with an oblique obstacle that does not span the test section, resulting in









a weak shock structure that is only minimally visible. The outer edge of the plume is

identified on the Schlieren image by a band where light has been refracted away leaving

an outline of the plume edge as shown in figures 4-1A, B and C.

For Mach 2.5 flow, shown in Figure 4-1C, a distinct bow shock is visible and the

interaction of the bow shock with the boundary layer is visible. This is consistent with

higher Mach number in the BL and the reduced measured BL thickness.

The depth of argon, helium and hydrogen penetration is presented in Figure 4-2 as

a function of a correlation of independent variables considered to have an effect on gas

penetration for measurements taken at Mach 1.6. The relative importance of each

variable is modified by exponents that were determined empirically to minimize the

summation of the squared relative data scatter about the mean power-law curve.

Penetration was expressed as P/D, the depth of penetration divided by the jet exit

diameter. The independent variables most commonly represented in literature are the

dynamic pressure ratio between the jet at its exit and the air freestream and the

downstream distance ratio at which penetration was measured, x/D. Additional variables

that may affect penetration are the BL thickness ratio, 6/D, the ratio of jet to air Reynolds

numbers and the ratio of jet to air molecular weight.

The resulting penetration formula, based on the data gathered in the present study,

is



P/D = 1.362(q, / q,)568(D -1.5)276( D221(Re/Rea) 00084( / ) 0025 (6)










10
^-13 =- 3 x Ar P/D (6/D=2.42)
Ar P/D (6/D=3.72)
SA. He P/D (6/D=2.42)
S. A He P/D (6/D=3.72)

= H2P/D/D /D=2.42)
H2P/D (6/D=3.72)
1-
1 10 100 1000 10000
(qj/q)2.72 (x/D-1.5) 1.32(6D)1.06
(dt/LIdta)-" ) (Rej/Re,)-0.04


Figure 4-2. Curve Fit for Ar, He and H2 injection into Mach 1.6 air at Varied BL
thickness.

Effect of Dynamic Pressure Ratio and Downstream Distance

The ratio of jet to air dynamic pressure has the strongest effect on penetration of the

variables examined. Figure 4-3 shows how varying q1/qa from 1 to 4 over x/D from 0 to

30 with the other variables held constant results in significant changes to the curve

predicted by eqn. 6. Here Ma=2.0, 6/D=2 and lj/J/ la=0.070. The effect of x/D is also

apparent in Figure 4-3. Near-field penetration increases quickly with increasing x/D, but

far-field penetration increases relatively slowly and beyond -10D almost linearly with

increasing x/D.






18



$10
8



4
S2
0
0 10 20 3
Downstream Distance (x/D)
q,/qa q/q a 2 -~-q /qa=3 -q, /qa- 4


Figure 4-3. Penetration Varies Greatly With Increasing Dynamic Pressure Ratio. Ma=2,
6/D=2, A/Ja=0.070.

Effect of BL Thickness

The thickness of the BL will effect jet penetration as shown in Figure 4-4.

Increasing /6D results in increased penetration into Mach 1.6 air. The degree by which

penetration is increased decreases with increased air Mach number. When the supersonic

Mach number is high much of the BL flow is also supersonic. The bow shock within the

BL is strong with downstream conditions similar to conditions downstream of the free

stream bow shock.


S10
'8
6
4
2
0
PI


0 10 20 30
Downstream Distance (x/D)
6/D =.5 6/D = 1 6/D = 2 6/D= 3


Figure 4-4. Penetration Variation with BL Thickness. Ma=1.6, qq/qa=2, U1/ J ,=0.070.








Effect of Molecular Weight Ratio

The effect of variation in molecular weight is illustrated in Figure 4-5. This figure

shows that variation of injecant molecular weight has very little effect on penetration. As

a result the exponent applied to the molecular weight is small and hydrogen penetrates

nearly as far as argon which has a molecular mass 20 times greater. This is similar to the

result of Torrence's study.23 Torrence found that at x/D=30 argon penetrated slightly

deeper than hydrogen or helium, in agreement with the present study, but also found a

minimum at intermediate molecular weights, which the resolution of the present study

did not reveal. Torrence also found that the most significant affect of molecular mass

was to decrease lateral spreading with increasing molecular mass while the depth of

maximum penetrant concentration was essentially unaffected.


10
8

S6

4
S2
0


0 10 20 30
Downstream Distance (x/D)
/A/ 0.070 -A- /J = 0.56
/A 0.14 A-- -/A, =1.4


Figure 4-5. Variation in Penetration Due to Variation in Injectant Molecular Weight.
Ma=1.6, q/q,=2, 8/D=1.


I


t~--i---~









The Reynolds number ratio has an exponent very close to zero indicating negligible

effect. It was therefore considered reasonable to drop any Re dependence and eqn. 6

becomes,

P /D =1.362(q, / q)O568(XD 1.5)276/D)221(j/ i/ ) 0025 (7)

Povinelli and Povinelli24 included a function of the ratio of air to jet Mach number in the

correlation function which was not considered in the present study since only sonic

injection was considered here. In their study as well as in a study by Billig, et al.,25 the

effect of supersonic fuel injection was considered weak.














CHAPTER 5
A PROPOSED, IMPROVED PENETRATION FORMULA

Comparison To Previous Studies

Figure 5-1 shows plots resulting from empirical formulae for predicting the outer

limit of jet penetration that resulted from this and several previous studies of transverse

injection. Each of these tests was conducted at different conditions which has affected

the results. Schetz and Billig3 analytically predicted transverse penetration at the

centerline of an injected flow using the momentum transfer for a non-deforming plug.

Their results are also plotted in Figure 5-1. In the analytical model of Schetz and Billig

the injected plug of fluid carries transverse momentum into the air stream which initially

has zero transverse momentum. This fluid particle is accelerated by transfer of

momentum from the air stream to the particle while the air stream reacts by receiving and

dissipating transverse momentum from the jet and converting some of its linear

momentum to transverse momentum primarily in the form of the spilled vortices.

Equation (7) determined in this study agrees well with the results of Leuchter8 and

Hersch, et al.20 at q/qa,=1.5 however there are differences between these results and the

other studies. The curve of Schetz and Billig3 identifies the injected jet centerline

whereas all others identify the outer limit of gas penetration. This curve is complemented

with another curve marking 1/ jet diameter from the analytical centerline, which is

maintained constant at all x/D for simplicity as in the study by Billig et al.25 The curve of

Schetz and Billig3 plus 1/2jet diameter approaches the present study in the far field,

beyond x/D=20.










10

8

6

4

I2

0
cs
a*


- Schetz & Billig3
(centerline)
SSchetz & Billig3
(center + D/2)
S-Leuchter 8

-McClinton9
(6/D = 2.42)
SRogers 4

Hersch, et al20


0 10 20 30- Present Study
Downstream Distance (x/D) (6/D = 2.42)

Figure 5-1. Penetration Correlations for Various Studies Exhibit Scatter; q/qa=1.5.

One factor that will influence the penetration measurement is the definition of the

outer limit of penetration, which varies between studies. Near the penetration limit the

concentration gradient is shallow as shown by Rogers4 so any variation in definition can

affect the measured penetration. This effect is assumed to be small for comparing the

results of different studies and for generating an engineering estimate of penetration.

The test conditions employed by each researcher affect the derived correlation. For

example the correlation of Leuchter8 is very similar to the formula derived in this study.

Leuchter's test condition of Mach 1.5 corresponds closely with the Mach 1.6 flows that

dominate the data gathered for this study. Studies performed at Mach 2 freestream

conditions resulted in slightly deeper prediction of penetration and studies at higher air

Mach numbers indicated further penetration increases. This dependence is stronger than

the ratio of jet to freestream Mach number effect found by Povinelli and Povinelli24 and

by Billig, et al.25 because their work varied the injector rather than the freestream Mach

number to specifically investigate that particular effect while leaving any shock









interactions in the air stream essentially unaffected. It may be concluded that there is a

relationship of penetration with air Mach number that has previously not been accounted

for.

General Penetration Formula

A generic form for the penetration equation used in any of the studies cited above is


P/D =- A ( CE( F (8)


Table 5-1. Penetration Formula Parameters Resulting From Various Studies
A B C E F G Mach No.
Schetz and Billig3 1 0.435 0 0.435 0 0 N/A
Leuchter8 1.45 0.5 0.5 0.35 0 0 1.5
Hersch. et al.20 1.92 0.35 0.5 0.277 0 0 2
Rogers4 3.87 0.3 0 0.143 0 0 4
McClinton9 4.2 0.3 0 0.143 0.057 0 4
Present study 1.36 0.568 -1.5 0.276 0.221 -0.0251 1.56

The values for each of the terms, A, B, C, E, F and G were placed in Table 5-1,

along with the air Mach number of the tests used to derive the formula. Since a trend in

experimental data was noticed as the air Mach number changed, the values of the

exponents in equation (8) were plotted versus air Mach number and curves were fit to

these values as shown in Figure 5-2. Linear curves were used in all cases except for term

"E" which was better fit with a power law curve due to a rapid change at lower Mach

numbers and more gradual change at higher Mach numbers. A refinement of the










10

S11

0.01

0.01


1 2 3 4 5
Malch Number

Figure 5-2. Penetration Equation Parameters versus Air Mach number.

constants derived from Figure 5-2 was needed when fitting test data to the formula most

likely due to the relatively small sample size used to derive the correlations in Figure 5-2.

Insufficient data were available to establish a Mach number relation for G so the constant

derived in the present study is used as shown in Table 5-1. The functional forms of A, B,

C, E and F are shown in Table 5-2.

Table 5-2. Penetration Equation Parameters as Functions of Air Mach number.
Coefficients for Function of Air Mach
Equation (8) Number, Ma
A = 1.0491 Ma 0.1924
B = -0.0803 M, + 0.6145
C = -2.34/Ma
E = 0.395 M, -0.8228
F = -0.0666 M, + 0.3252
G = -0.02507

The resulting equation is

P/D=
(1.05MA -.192)(q, /q)(- 0803M+ 615)(D 2.34/MJ)395M- 823(D- 0666M+ 325( // -0251

(9)

Figure 5-3 shows good correlation of this formula with all the test results compiled

by the other researchers cited here. The inputs to the formula, including Mach number,

BL thickness and dynamic pressure ratio are taken directly from test data compiled in the


y= 1.04 1x- 0.19 4.--

Sv= -0.0833x + 0.6145

y= -0.06 6x + 0.3252 ''-


M










previous studies and are shown in Figure 5-3. Independent verification with test data

obtained in the present study at Ma = 2.5, which was not used to create the formula, is

presented in Figure 5-4. Generally good agreement is evident in particular in the

midfield. Close to the injection location where the slopes are large or in the far field

beyond 30 jet diameters the differences between prediction and test data are much less

than one jet diameter.


qj/qa = 2.0, MN = 1.5, 6/D= 2.4


10 20
Downstream Distance (x/D)
- Leuchter Present Study


10

6
S4
2
0


10 20
Downstream Distance (x/D)
-Hersch, et al Present Stu


a


9/9a


: 1.0, M = 4.0, 6/D


10


4

0
0 10 20 30
Downstream Distance (x/D)
McClinton -x- Rogers Present Study


Figure 5-3. Comparison of the Present Study with Previous Research. A) vs Leuchter8
for H2; M= 1.5. B) vs Hersch20, et al. for He; Ma=2 C)vs Rogers4 and
McClinton9 for H2; Ma=4

Examination of equation (9) shows that penetration increases with increased

dynamic pressure ratio, downstream distance and BL thickness to jet diameter ratio as

expected; the penetration also increases with increased air Mach number which is not

intuitively expected.


,10



2
S6


qj/q = 6.3, ML = 2.0, 6/D= 0.76


{ _______ _______ _______ _______ _______ _______











7
6 -j /q 1, curve fit
5 qj /q 1, data
o 4 ----q./q= 1.5, curvefit
j a
3 x q /q a- 1.5, data
1 qqJ /q 2, curve fit
1j a
0 q/q- 2, data

0 10 20 30
x/D

Figure 5-4. Predicted and Measured Penetration of Sonic Hydrogen Transversely Injected
into Mach 2.5 Air

The increased penetration due to increased Mach number can be attributed to the

stronger bow shock structure associated with higher Mach flows. As shown in Figure 5-6

the dynamic pressure on the downstream side of the shock is an increasingly small

percentage of the upstream dynamic pressure as Mach number increases, so the dynamic

pressure ratio actually seen by the injected gas is much lower than the freestream value.

For example, a Mach 4 air stream with static conditions of 300 K and 101 kPa will have a

dynamic pressure of 1131 kPa. After passing through a normal shock, the static

conditions will be 1214 K and 1869 kPa with a dynamic pressure of only 247 kPa, a 78%

reduction in dynamic pressure. Application of the 1-D, inviscid compressible flow

equations for a normal shock is not sufficient to correct the dynamic pressure ratio effect

since the bow shock is only normal over a portion of the plume. An empirical method

lends itself to more practical implementation.

It was shown in figure 5-1 that for injection into Mach 4 air the near-field

penetration was much deeper than for injection at lower Mach numbers, but the far-field









penetration did not increase as rapidly. The increased near-field penetration is explained

above and the decreased rate of far-field penetration is logically due to the greater free

stream momentum, which at this point is only minimally altered by compressibility.


1.2

0.8
S0.6
0.4
0.2
0
0 2 4 6 8 10
Mach Number

Figure 5-5. Dynamic Pressure Ratio Across a Normal Shock versus Mach number.

Despite increased penetration from the wall when the Mach number is low

supersonic and the BL is thick, the penetration out of the BL and into the free stream is

decreased by a thick BL. The strong, nearly normal bow shock is absent at low

supersonic Mach number and thick BL. The supersonic freestream interacts with the

deflected plume by forming a weaker oblique shock. With the weakened virtual

obstruction of the injectantjet in the freestream, the vortex generation essential to

effective bulk mixing processes is weakened. The resulting flow approaches the case of

tangential, rather than transverse injection.

When the supersonic Mach number is high, much of the BL flow is also

supersonic, so a strong bow shock extends deep into the BL with consequent low

dynamic pressure downstream of the bow shock leading to increased penetration. The

drop in dynamic pressure across the shock wave is more effective at increasing






28


penetration than velocity reduction in the BL. This explains the decreased effect of BL

thickness on improving penetration as Mach number increases.














CHAPTER 6
CONCLUSIONS

This study has evaluated the penetration of gas jets into supersonic flows with thick

boundary layers over various Mach numbers. Comparison with previous studies shows

the following:

* Transverse jet penetration is dependent on q/qa, x/D, 6/D and air Mach number.
Among the parameters under the designer's control q/qa has the strongest effect.
The Mach number will modify the impact of the other variables and can have a
dramatic effect on penetration which was not previously recognized.

* Generally, increased air Mach number results in increased penetration due to
greater dynamic pressure reduction downstream of stronger shock waves.

* The effect of the boundary layer thickness on increasing near-field jet penetration is
significant at low supersonic Mach numbers but decreases with increased Mach
number.

* Deeper near-field penetration results in stronger vortex formation, which is known
to enhance mixing and spreading.

* The effect of molecular weight ratio on penetration is small and not monotonic.
The effect of Reynolds number is negligible.
















LIST OF REFERENCES


1. Glass, C. E., "A Parametric Study of Jet Interactions with Rarefied Flow," 21st
International Symposium on Rarefied Gas Dynamics, edited by R. Brun, R.
Campargue, R. Gatingnol, and J. C. Lengrand, Cepadues Editions, Toulouse
France, 1998, Vol. 1, pp 615-622.

2. Kaufman, Louis G. II, "Hypersonic Flows Past Transverse Jets," Journal of
Propulsion andPower, Vol. 4, No. 9, September 1967, pp 1230-1235.

3. Schetz, J., Billig, F., "Penetration of Gaseous Jets Injected into a Supersonic
Stream," Journal of Spacecraft and Rockets, Vol. 3, No. 11, November 1966, pp
1658-1665.

4. Rogers, R. C., "A Study of the Mixing of Hydrogen Injected Normal to a
Supersonic Airstream," NASA TN D-6114, 1971.

5. Owens, M., Tehranian, S., Segal, C. and Vinogradov, V., "Flame-Holding
configurations for Kerosene Combustion in a Mach 1.8 Airflow," Journal of
Propulsion andPower, Vol. 14, No. 4, July-August 1998, pp 456-461.

6. Gallimore, S., Jabobsen, L., O'Brien, W. and Schetz, J., "Operational Sensitivities
of an Integrated Scramjet Ignition/Fuel Injection System," Journal of Propulsion
andPower, Vol. 19, March-April 2003, pp183-189.

7. Parent, B. and Sislian, J., "Effect of Geometrical Parameters on the Mixing
Performance of Cantilevered Ramp Injectors," AIAA Journal, Vol. 41, No. 3, pp
448-456.

8. F. H. Falempin, "Scramjet Development in France," Scramjet Propulsion, E. T.
Curran and S. N. B. Murthy Editors, Progress in Astronautics and Aeronautics,
AIAA, Washington D. C., 2000, vol. 189, pp 47-117.

9. McClinton, C. R., "Effect of Ratio of Wall Boundary-Layer Thickness to Jet
Diameter on Mixing of a Normal Hydrogen Jet in a Supersonic Stream," NASA
TM X-3030, June 1974, pp 1-42.

10. Gruber, M. R., Nejad, A. S., Chen, T. H. and Dutton, J. C., "Transverse Injection
From Circular and Elliptic Nozzles into a Supersonic Crossflow," Journal of
Propulsion andPower, Vol. 16, No. 3, May-June 2000, pp 449-457.









11. Ben-Yakar, A. and Hanson, R., "Experimental Investigation of Flame-Holding
Capability of Hydrogen Transverse Jet in Supersonic Cross-flow," 27th Symposium
(International) on Combustion/The Combustion Institute, 1998, pp 2173-2180.

12. Turns, S. R., An Introduction to Combustion: Concepts and Applications, Second
Edition, McGraw-Hill, Boston, 2000, pp 84-88.

13. Dimotakis, P. E., "Turbulent Free Shear Layer Mixing and Combustion," High
Speed Flight Propulsion Systems, in Progress in Astronautics and Aeronautics,
AIAA, Washington D. C., 1991, Vol. 137, pp 265-340.

14. Billig, F. S., "Research on Supersonic Combustion," Journal of Propulsion and
Power, Vol. 9, No. 4, July-August 1993, pp 499-520.

15. Seiner, J. Dash, S. and Kenzakowski, D., "Historical Survey on enhanced Mixing
in Scramjet Engines," Journal of Propulsion and Power, Vol. 17, No. 6,
November-December 2001, pp 1273-1286.

16. Northam, G. B., Greenberg, I., Byington, C. S. and Caprotti, D. P., "Evaluation of
Parallel Injector Configurations for Mach 2 Combustion," Journal of Propulsion
andPower, Vol. 8, No. 2, March-april 1992, pp 491-499.

17. Owens, M. G., Segal, C. and Auslander, A. H., "Effects of Mixing Schemes on
Kerosene Combustion in a Supersonic Airstream," Journal of Propulsion and
Power, Vol. 13, No. 4, July-August 1997, pp 525-531.

18. McClinton, C. R., "The Effect of Injection angle on the Interaction Between Sonic
Secondary Jets and a Supersonic Free Stream," NASA TN D-6669, February 1972.

19. Gaffney, R. L. Jr. and Korte, J., "Analysis and Design of Rectangular Cross-
Section Nozzles For Scramjet Engine Testing," AIAA Aerospace Science Meeting
and Exhibit, 5-8 January 2004, AIAA 2004-1137, pp 1-16.

20. Hersch, M., Povinelli, L. and Povinelli, F., "A Schlieren Technique for Measuring
Jet Penetration into a Supersonic Stream," Journal of Spacecraft and Rockets, Vol.
7, No. 6, June 1970, pp 755-756.

21. Settles, G. S., Schlieren and .,\1h, /,, gii pl, Techniques, Visualizing Phenomena in
Transparent Media, Springer-Verlag, Berlin, 2001.

22. Swithenbank, J., Eames, I., Chin, S., Ewan, B., Yang, Z., Cao, J. and Zhao, X.,
"Turbulence Mixing in Supersonic Combustion Systems," AIAA Paper 89-0260,
January 1989.

23. Torrence, M. G., "Effect of Injectant Molecular Weight on Mixing of a Normal Jet
in a Mach 4 Airstream," NASA TN D-6061, January 1971, pp 1-104.






32


24. Povinelli, F. P. and Povinelli, L. A., "Correlation of Secondary Sonic and
Supersonic Gaseous Jet Penetration into Supersonic Crossflows," NASA TN D-
6370, June 1971, pp 1-20.

25. Billig, F. S., Orth, R. C. and Lasky, M., "A Unified Analysis of Gaseous Jet
Penetration," AIAA Journal, Vol. 9, No. 6, June 1971, pp 1048-1058.















BIOGRAPHICAL SKETCH

Ron Portz was born in Rockledge, Florida, on May 31, 1965. He is a 1983 honor

graduate of Cocoa High School, where he excelled in academic and artistic competition.

He was both a National Merit Scholarship Finalist and a Scholastic Art Awards Gold Key

recipient.

Mr. Portz served two years as a missionary for the Church of Jesus Christ of Latter

Day Saints from 1986 to 1988 whereupon he resumed his academic career, graduating

from the University of Florida in 1991 with a Bachelor of Science degree in Mechanical

Engineering.

Mr. Portz has been happily married to the former Pamela Pierson since May 12,

1990. The couple currently have two adopted sons, Elijah and Samuel.

Following college graduation Mr. Portz worked for Rockwell International and The

Boeing Corporation as a Test Engineer and a Depot Engineer for the Space Shuttle Main

Propulsion System, Attitude Control System and Environmental Control/Life-Support

System at NASA's Shuttle Logistics Depot in Cape Canaveral, Florida. In 1998, Mr.

Portz began work for Orbital Sciences Corporation in Chandler, Arizona. His work

responsibilities included the design, assembly, test and post-flight analysis of cold-gas,

solid and liquid propellant propulsion systems. He is the recipient of multiple awards and

recognition for the quality of his work.

In 2003, Mr. Portz returned to the University of Florida to pursue a graduate degree

in mechanical engineering. The University of Florida had been selected to lead the






34


Institute for Future Space Transport, which was described as paving the way for design of

second and third generation reusable launch vehicles to replace the Space Shuttle. As

space transportation has occupied the majority of his professional life and its future is

precarious, he determined to participate in this program in the hope of applying his

practical experience to provide needed direction to the industry. He is grateful for the

opportunity to return to school and improve the depth of his academic knowledge.