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Analysis of flow in a 3D chamber and a 2D spray nozzle to approximate the exiting jet free surface

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Title:
Analysis of flow in a 3D chamber and a 2D spray nozzle to approximate the exiting jet free surface
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Book
Language:
English
Creator:
Hong, Chin Tung
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University of South Florida
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Tampa, Fla.
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Subjects

Subjects / Keywords:
liquid-gas interface
atomizer
cone angle
mixing length
spraying cooling
Dissertations, Academic -- Mechanical Engineering -- Masters -- USF
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government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

Notes

Summary:
ABSTRACT: The purpose of this investigation is to analyze the flow pattern of cooling fluids in the 3D "twister-effect" mixing chamber and to approximate the free surface behaviors exiting the 2D spray nozzle. The cone angle and free surface height located at the end of the free surface are two significant factors to determine the spraying area on a heated plane. This process is a reasonable representation of many industrial cooling application. The whole system consists of 4 inlet tubes connected to the top of the mixing chamber, and the spray nozzle is located under the chamber. Four different refrigerants, like FC-72, FC-77, FC-87 and methanol were used for the turbulent flow simulations. According to different fluid properties, the cone angle, free surface, pressure drop and Reynolds number can be investigated at different flow rates.First, at a certain volumetric flow rates, the velocities in x, y, z directions were found on the positive x-axis (0 degree), y-axis (90 degrees), negative x-axis (180 degrees) and y-axis (270 degrees) at 8.0 x 10⁻⁴ m below the top of chamber. After the transformations, the interpolated and averaged radial, circumferential and axial velocities were used in the 2D nozzle simulations. Finally, the cone angle, the radial locations of the free surface and the pressure drop were obtained in each scenario. As the results, higher volumetric flow rate produced higher free surface height and cone angle. Also, FC-87 created the highest free surface height and cone angle among all four working fluids in both volumetric flow rates. It means that FC-87 can produce the largest spraying area on the heated surface. Fluctuation, spinning and eddy circulation can be found in the velocity plot because of the turbulent flow syndromes.When comparing two different nozzle designs, it was found that the nozzle without mixing chamber gave a larger cone angle and free surface height. Alternatively, the design in this investigation produced a relatively narrow jet concentrated to the stagnation zone.
Thesis:
Thesis (M.S.M.E.)--University of South Florida, 2004.
Bibliography:
Includes bibliographical references.
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Mode of access: World Wide Web.
Statement of Responsibility:
by Chin Tung Hong.
General Note:
Title from PDF of title page.
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Document formatted into pages; contains 184 pages.

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University of South Florida Library
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University of South Florida
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oclc - 57723580
notis - AJU6742
usfldc doi - E14-SFE0000560
usfldc handle - e14.560
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1 Analysis of Flow in a 3D Chamber and a 2D Spray Nozzle to Approximate the Exiting Jet Free Surface by Chin Tung Hong A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering Department of Mechanical Engineering College of Engineering University of South Florida Major Professor: Muhammad M. Rahman, Ph.D. Thomas Eason, Ph.D. Autar K. Kaw, Ph.D. Date of Approval: November 8th, 2004 Keywords: spray cooling, cone angle, mixi ng length, liquid-gas interface, atomizer Copyright 2004, Chin Tung Hong

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2 TABLE OF CONTENTS LIST OF TABLES iii LIST OF FIGURES iv LIST OF SYMBOLS xi ABSTRACT xiv CHAPTER 1 INTRODUCTION 1 CHAPTER 2 MATHEMATICAL MODEL 9 CHAPTER 3 NUMERICAL COMPUTATION 14 CHAPTER 4 SIMULATION PROCEDURES 19 4.1 Inlet Velocity 19 4.2 Transformation of Velocity from Cartesian to Cylindrical System 20 4.3 Cone Angle and Free Surface Height 22 4.4 Pressure Drop 23 4.5 Cavitation 26 CHAPTER 5 RESULTS AND DISCUSSION 27 5.1 3D Mixing Chamber 27 5.1.1 Refrigerant FC-72 27 5.1.2 Refrigerant FC-77 36 5.1.3 Refrigerant FC-87 44 5.1.4 Methanol 53 5.2 2D Nozzles 66 5.2.1 Refrigerant FC-72 66 5.2.2 Refrigerant FC-77 72 5.2.3 Refrigerant FC-87 77 5.2.4 Methanol 82 5.2.5 Cone Angle and Free Surface Height 87 5.2.6 Pressure Drop 91 5.2.7 Cavitation 92 i

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ii CHAPTER 6 COMPARISON OF NOZZLE DESIGNS 93 CHAPTER 7 CONCLUSIONS AND RECOMMENDATIONS 97 REFERENCES 99 APPENDICES 101 Appendix I: Fluid Properties 102 Appendix II: FIJOUR File for the 3D mixing Chamber (Coordinates) 103 Appendix III: FIPREP File for the 3D Mixing Chamber (Sample: FC-72) 107 Appendix IV: FIJOUR File for the Small Nozzle with Free Surface (4.416 x 10-7 and 5.678 x 10-7 m3/s) 111 Appendix V: FIPREP File for the Small Nozzle with Free Surface (4.416 x 10-7 m3/s, FC-72) 121 Appendix VI: FIPREP File for the Small Nozzle with Free Surface (5.678 x 10-7 m3/s, FC-72) 127 Appendix VII: FIPREP File for the Small Nozzle with Free Surface (4.416 x 10-7 m3/s, FC-77) 133 Appendix VIII: FIPREP File for the Small Nozzle with Free Surface (5.678 x 10-7 m3/s, FC-77) 139 Appendix IX: FIPREP File for the Small Nozzle with Free Surface (4.416 x 10-7 m3/s, FC-77) 145 Appendix IX: FIPREP File for the Small Nozzle with Free Surface (4.416 x 10-7 m3/s, FC-77) 151 Appendix IX: FIPREP File for the Small Nozzle with Free Surface (4.416 x 10-7 m3/s, FC-77) 157 Appendix IX: FIPREP File for the Small Nozzle with Free Surface (4.416 x 10-7 m3/s, FC-77) 163

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iii LIST OF TABLES Table 1: Inlet velocity for different volumetric flow rates. 9 Table 2: The boundary conditions app lied to the 3D chamber model. 12 Table 3: The initial conditions and boundary cond itions applied to the 2D spray nozzle model. 13 Table 4: Physical properties of working fluids in this analysis. 13 Table 5: Results of velocity transformation in four different axes. 22 Table 6: Cone angle and free surface height for each working fluid at various flow rates. 87 Table 7: Cone angle, free surface height, and Reynolds number at the nozzle outlet for each working fluid (Q = 4.416 x 10-7 m3/s). 88 Table 8: Cone angle, free surface height, and Reynolds number at the nozzle outlet for each working fluid (Q = 5.678 x 10-7 m3/s). 88 Table 9: Comparison of the working fluids pressure drop calculated using Bernoulli’s equation and FIDAP simulation (Q= 4.416 x 10-7m3/s). 91 Table 10: 91 Comparison of the working fluids pressure drop calculated using Bernoulli’s equation and FIDAP simulation (Q= 5.678 x 10-7m3/s). 92 Table 11: Cavitation number of various refri gerants at different Reynolds numbers. Table 12: Cone angle and free surface height for each working fluid at various flow rates of the nozzle with outer slot radius 4.43 x 10-4 m. 96

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iv LIST OF FIGURES Figure 1: 10 Schematic of the inlet tubes, mixing chamber, and the nozzle geometries. Figure 2: Three-dimensional meshed structure of the mixing chamber. 15 Figure 3: Mesh viewed at the top of inlet tubes and cylindrical chamber. 15 Figure 4: Velocity plot of the chamber in a vertical cross-sectional view. 16 Figure 5: 16 Pressure contour plot of the chamber in a vertical cross-sectional view. Figure 6: 2D Axi-symmetrical nozzle mesh with integrated free surface. 17 18 Figure 7: Velocity profiles in z-direction on x-axis in the 3D chamber for various grid sizes. Figure 8: 20 Schematic of velocity transformation from cartesian system to cylindrical system and average. Figure 9: 21 Velocity transformation from cartesian system to cylindrical system using vector addition. Figure 10: 23 Schematic of the entire geometry to compute the pressure drop using Bernoulli's equation. Figure 11: 28 Velocity in x-direction on the x-axis at various levels below the top of mixing chamber (FC-72, 4.416 x 10-7 m3/s). Figure 12: 28 Velocity in x-direction on the x-axis at various levels below the top of mixing chamber (FC-72, 5.678 x 10-7 m3/s). Figure 13: 29 Velocity in y-direction on the x-axis at various levels below the top of mixing chamber (FC-72, 4.416 x 10-7 m3/s). Figure 14: 30 Velocity in y-direction on the x-axis at various levels below the top of mixing chamber (FC-72, 5.678 x 10-7 m3/s). Figure 15: Velocity in z-direction on the x-axis at various levels below the top of mixing chamber (FC-72, 4.416 x 10-7 m3/s). 31

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v Figure 16: 31 Velocity in z-direction on the x-axis at various levels below the top of mixing chamber (FC-72, 5.678 x 10-7 m3/s). Figure 17: 32 Velocity in x-direction on the y-axis at various levels below the top of mixing chamber (FC-72, 4.416 x 10-7 m3/s). Figure 18: 33 Velocity in x-direction on the y-axis at various levels below the top of mixing chamber (FC-72, 5.678 x 10-7 m3/s). Figure 19: 34 Velocity in y-direction on the y-axis at various levels below the top of mixing chamber (FC-72, 4.416 x 10-7 m3/s). Figure 20: 34 Velocity in y-direction on the y-axis at various levels below the top of mixing chamber (FC-72, 5.678 x 10-7 m3/s). Figure 21: 35 Velocity in z-direction on the y-axis at various levels below the top of mixing chamber (FC-72, 4.416 x 10-7 m3/s). Figure 22: 35 Velocity in z-direction on the y-axis at various levels below the top of mixing chamber (FC-72, 5.678 x 10-7 m3/s). Figure 23: 36 Velocity in x-direction on the x-axis at various levels below the top of mixing chamber (FC-77, 4.416 x 10-7 m3/s). Figure 24: 37 Velocity in x-direction on the x-axis at various levels below the top of mixing chamber (FC-77, 5.678 x 10-7 m3/s). Figure 25: 38 Velocity in y-direction on the x-axis at various levels below the top of mixing chamber (FC-77, 4.416 x 10-7 m3/s). Figure 26: 38 Velocity in y-direction on the x-axis at various levels below the top of mixing chamber (FC-77, 5.678 x 10-7 m3/s). Figure 27: 39 Velocity in z-direction on the x-axis at various levels below the top of mixing chamber (FC-77, 4.416 x 10-7 m3/s). Figure 28: 40 Velocity in z-direction on the x-axis at various levels below the top of mixing chamber (FC-77, 5.678 x 10-7 m3/s). Figure 29: 41 Velocity in x-direction on the y-axis at various levels below the top of mixing chamber (FC-77, 4.416 x 10-7 m3/s). Figure 30: 41 Velocity in x-direction on the y-axis at various levels below the top of mixing chamber (FC-77, 5.678 x 10-7 m3/s). Figure 31: 42 Velocity in y-direction on the y-axis at various levels below the top of mixing chamber (FC-77, 4.416 x 10-7 m3/s).

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vi Figure 32: Velocity in y-direction on the y-axis at various levels below the top of mixing chamber (FC-77, 5.678 x 10-7 m3/s). 42 Figure 33: 43 Velocity in z-direction on the y-axis at various levels below the top of mixing chamber (FC-77, 4.416 x 10-7 m3/s). Figure 34: 44 Velocity in z-direction on the y-axis at various levels below the top of mixing chamber (FC-77, 5.678 x 10-7 m3/s). Figure 35: 45 Velocity in x-direction on the x-axis at various levels below the top of mixing chamber (FC-87, 4.416 x 10-7 m3/s). Figure 36: 45 Velocity in x-direction on the x-axis at various levels below the top of mixing chamber (FC-87, 5.678 x 10-7 m3/s). Figure 37: 46 Velocity in y-direction on the x-axis at various levels below the top of mixing chamber (FC-87, 4.416 x 10-7 m3/s). Figure 38: 47 Velocity in y-direction on the x-axis at various levels below the top of mixing chamber (FC-87, 5.678 x 10-7 m3/s). Figure 39: 48 Velocity in z-direction on the x-axis at various levels below the top of mixing chamber (FC-87, 4.416 x 10-7 m3/s). Figure 40: 48 Velocity in z-direction on the x-axis at various levels below the top of mixing chamber (FC-87, 5.678 x 10-7 m3/s). Figure 41: 49 Velocity in x-direction on the y-axis at various levels below the top of mixing chamber (FC-87, 4.416 x 10-7 m3/s). Figure 42: 50 Velocity in x-direction on the y-axis at various levels below the top of mixing chamber (FC-87, 5.678 x 10-7 m3/s). Figure 43: 51 Velocity in y-direction on the y-axis at various levels below the top of mixing chamber (FC-87, 4.416 x 10-7 m3/s). Figure 44: 51 Velocity in y-direction on the y-axis at various levels below the top of mixing chamber (FC-87, 5.678 x 10-7 m3/s). Figure 45: 52 Velocity in z-direction on the y-axis at various levels below the top of mixing chamber (FC-87, 4.416 x 10-7 m3/s). Figure 46: 52 Velocity in z-direction on the y-axis at various levels below the top of mixing chamber (FC-87, 5.678 x 10-7 m3/s). Figure 47: 53 Velocity in x-direction on the x-axis at various levels below the top of mixing chamber (Methanol, 4.416 x 10-7 m3/s).

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vii Figure 48: 54 Velocity in x-direction on the x-axis at various levels below the top of mixing chamber (Methanol, 5.678 x 10-7 m3/s). 55 Figure 49: Velocity in y-direction on the xaxis at various levels below the top of mixing chamber (Methanol, 4.416 x 10-7 m3/s). Figure 50: 55 Velocity in y-direction on the x-axis at various levels below the top of mixing chamber (Methanol, 5.678 x 10-7 m3/s). Figure 51: 56 Velocity in z-direction on the x-axis at various levels below the top of mixing chamber (Methanol, 4.416 x 10-7 m3/s). Figure 52: 56 Velocity in z-direction on the x-axis at various levels below the top of mixing chamber (Methanol, 5.678 x 10-7 m3/s). Figure 53: 57 Velocity in x-direction on the y-axis at various levels below the top of mixing chamber (Methanol, 4.416 x 10-7 m3/s). Figure 54: 58 Velocity in x-direction on the y-axis at various levels below the top of mixing chamber (Methanol, 5.678 x 10-7 m3/s). Figure 55: 59 Velocity in y-direction on the y-axis at various levels below the top of mixing chamber (Methanol, 4.416 x 10-7 m3/s). Figure 56: 59 Velocity in y-direction on the y-axis at various levels below the top of mixing chamber (Methanol, 5.678 x 10-7 m3/s). Figure 57: 60 Velocity in z-direction on the y-axis at various levels below the top of mixing chamber (Methanol, 4.416 x 10-7 m3/s). Figure 58: 60 Velocity in z-direction on the y-axis at various levels below the top of mixing chamber (Methanol, 5.678 x 10-7 m3/s). Figure 59: 62 Cross-sectional velocity plot at 8.0 x 10-4 m below the top of chamber to show the circulation of FC-72 (Q = 4.416 x 10-7 m3/s) in clockwise direction. Figure 60: 62 Cross-sectional velocity plot at 8.0 x 10-4 m below the top of chamber to show the circulation of FC-72 (Q = 5.678 x 10-7 m3/s) in clockwise direction. Figure 61: 63 Cross-sectional velocity plot at 8.0 x 10-4 m below the top of chamber to show the circulation of FC-77 (Q = 4.416 x 10-7 m3/s) in clockwise direction. Figure 62: Cross-sectional velocity plot at 8.0 x 10-4 m below the top of chamber to show the circulation of FC-77 (Q = 5.678 x 10-7 m3/s) in clockwise direction. 63

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viii Figure 63: Cross-sectional velocity plot at 8.0 x 10-4 m below the top of chamber to show the circulation of FC-87 (Q = 4.416 x 10-7 m3/s) in clockwise direction. 64 Figure 64: 64 Cross-sectional velocity plot at 8.0 x 10-4 m below the top of chamber to show the circulation of FC-87 (Q = 5.678 x 10-7 m3/s) in clockwise direction. 65 Figure 65: Cross-sectional velocity plot at 8.0 x 10-4 m below the top of chamber to show the circulation of Methanol (Q = 4.416 x 10-7 m3/s) in clockwise direction. Figure 66: 65 Cross-sectional velocity plot at 8.0 x 10-4 m below the top of chamber to show the circulation of Methanol (Q = 5.678 x 10-7 m3/s) in clockwise direction. Figure 67: Velocity vector plot for FC-72 (Q = 4.416 x 10-7 m3/s).Units are cm/s. 66 Figure 68: 67 Pressure contour plot for FC-72 (Q = 4.416 x 10-7 m3/s). Units are gm/cm s2 (x101 Pa). Figure 69: Streamline contour plot for FC-72 (Q = 4.416 x 10-7 m3/s). 68 Figure 70: Velocity vector plot for FC-72 (Q = 5.678 x 10-7 m3/s).Units are cm/s. 69 Figure 71: 70 Pressure contour plot for FC-72 (Q = 5.678 x 10-7 m3/s). Units are gm/cm s2 (x101 Pa). Figure 72: Streamline contour plot for FC-72 (Q = 5.678 x 10-7 m3/s). 70 Figure 73: Free surface profile for FC-72 at various flow rates. 71 Figure 74: Magnified free surface profile for FC-72 at various flow rates. 71 Figure 75: Velocity vector plot for FC-77 (Q = 4.416 x 10-7 m3/s).Units are cm/s. 72 Figure 76: 73 Pressure contour plot for FC-77 (Q = 4.416 x 10-7 m3/s). Units are gm/cm s2 (x101 Pa). Figure 77: Streamline contour plot for FC-77 (Q = 4.416 x 10-7 m3/s). 73 Figure 78: Velocity vector plot for FC-77 (Q = 5.678 x 10-7 m3/s).Units are cm/s. 74 Figure 79: Pressure contour plot for FC-77 (Q = 5.678 x 10-7 m3/s). Units are gm/cm s2 (x101 Pa). 75

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ix Figure 80: Streamline contour plot for FC-77 (Q = 5.678 x 10-7 m3/s). 75 Figure 81: Free surface profile for FC-77 at various flow rates. 76 Figure 82: Magnified free surface profile for FC-77 at various flow rates. 76 Figure 83: Velocity vector plot for FC-87 (Q = 4.416 x 10-7 m3/s).Units are cm/s. 77 Figure 84: 78 Pressure contour plot for FC-87 (Q = 4.416 x 10-7 m3/s). Units are gm/cm s2 (x101 Pa). Figure 85: Streamline contour plot for FC-87 (Q = 4.416 x 10-7 m3/s). 78 Figure 86: Velocity vector plot for FC-87 (Q = 5.678 x 10-7 m3/s).Units are cm/s. 79 Figure 87: 80 Pressure contour plot for FC-87 (Q = 5.678 x 10-7 m3/s). Units are gm/cm s2 (x101 Pa). Figure 88: Streamline contour plot for FC-87 (Q = 5.678 x 10-7 m3/s). 80 Figure 89: Free surface profile for FC-87 at various flow rates. 81 Figure 90: Magnified free surface profile for FC-87 at various flow rates. 81 Figure 91: Velocity vector plot for Methanol (Q = 4.416 x 10-7 m3/s).Units are cm/s. 82 Figure 92: 83 Pressure contour plot for Methanol (Q = 4.416 x 10-7 m3/s). Units are gm/cm s2 (x101 Pa). Figure 93: Streamline contour plot for Methanol (Q = 4.416 x 10-7 m3/s). 83 Figure 94: Velocity vector plot for Methanol (Q = 5.678 x 10-7 m3/s).Units are cm/s. 84 Figure 95: 85 Pressure contour plot for Methanol (Q = 5.678 x 10-7 m3/s). Units are gm/cm s2 (x101 Pa). Figure 96: Streamline contour plot for Methanol (Q = 5.678 x 10-7 m3/s). 85 Figure 97: Free surface profile for Methanol at various flow rates. 86 Figure 98: Magnified free surface profile for Methanol at various flow rates. 86 Figure 99: Free surface profile for various fluids (Q=4.416 x 10-7 m3/s). 88

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x Figure 100: 89 Magnified free surface profile for various fluids (Q=4.416 x 10-7 m3/s). Figure 101: Free surface profile for various fluids (Q=5.678 x 10-7 m3/s). 89 Figure 102: Magnified free surface profile for various fluids (Q=5.678 x 10-7 m3/s). 90 Figure 103: 93 Schematic of the nozzle geometry with outer slot radius 4.43 x 10-4 m. Figure 104: 94 Magnified free surface profiles comparison for FC-72 with two different nozzle designs (Q=4.416 x 10-7 m3/s). Figure 105: 94 Magnified free surface profiles comparison for FC-87 with two different nozzle designs (Q=4.416 x 10-7 m3/s). Figure 106: 95 Magnified free surface profiles comparison for Methanol with two different nozzle designs (Q=4.416 x 10-7 m3/s). Figure 107: 95 Magnified free surface profiles comparison for FC-72 with two different nozzle designs (Q=5.678 x 10-7 m3/s). 96 Figure 108: Magnified free surface profiles comparison for Methanol with two different nozzle designs (Q=5.678 x 10-7 m3/s).

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xi LIST OF SYMBOLS Arabic Symbols A Total Area [m2] B Damping Constant [non-dim] Ca Cavitation number [non-dim] D Diameter [m] f Frictional factor [non-dim] g Gravitational constant [m/s2] hf Head (or frictional) loss [m] hm Minor loss [m] K Loss coefficient [non-dim] l Mixing length [m] L Length [m] Lf Free surface height [m] P Pressure [N/m2] Q Volumetric flow rate [m3/s] r radius [m] Re Reynold's number [non-dim]

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xii v Velocity [m/s] v Average velocity [m/s] V Velocity [m/s] y Distance from the node [m] Greek Symbols Angular position [rad] Angle in the second quadrant [rad] Angle in the third quadrant [rad] Angle in the fourth quadrant [rad] Density [kg/m3] Dynamic viscosity [kg/(ms)] Kinematic viscosity [m2/s] Von Karman Constant [non-dim]

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xiii Subscripts be Beveled outlet gc Gradual contraction n Normal direction r Radial direction t Turbulent x X-direction y Y-direction z Axial or z-direction min Minimum sat Saturated theta Circumferential

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xiv ANALYSIS OF FLOW IN A 3D CHAMBER AND A 2D SPRAY NOZZLE TO APPROXIMATE THE EXITING JET FREE SURFACE Chin Tung Hong ABSTRACT The purpose of this investigation is to analyze the flow pattern of cooling fluids in the 3D “twister-effect” mixing chamber and to approximate the free surface behaviors exiting the 2D spray nozzle. The cone angle and free surface height located at the end of the free surface are two significant factors to determine the spraying area on a heated plane. This pro cess is a reasonable representation of many industrial cooling application. The whole sy stem consists of 4 inlet tubes connected to the top of the mixing chamber, and the spray nozzle is located under the chamber. Four different refrigerants, like FC-72, FC77, FC-87 and methanol were used for the turbulent flow simulations. According to di fferent fluid properties, the cone angle, free surface, pressure drop and Reynolds num ber can be investigated at different flow rates. First, at a certain volumet ric flow rates, the velocities in x, y, z directions were found on the positive x-axis (0 degree), y-axis (90 degrees), negative x-axis (180 degrees) and y-axis (270 degrees) at 8.0 x 10-4 m below the top of chamber. After the transformations, th e interpolated and averaged radial, circumferential and axial velocities were us ed in the 2D nozzle simulations. Finally, the cone angle, the radial locations of the free surface and the pressure drop were obtained in each scenario. As the resu lts, higher volumetric flow rate produced

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xv higher free surface height and cone angle. Also, FC-87 created the highest free surface height and cone angle among all four working fluids in both volumetric flow rates. It means that FC-87 can produce the largest spraying area on the heated surface. Fluctuation, spinning and eddy circul ation can be found in the velocity plot because of the turbulent flow syndromes. When comparing two different nozzle designs, it was found that the nozzle without mixing chamber gave a larger cone angle and free surface height. Alternatively, the design in this investigation produced a relatively narrow jet concentrated to the stagnation zone.

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xvi CHAPTER 1 INTRODUCTION Jet impingement or spray cooling is commonly used throughout the industry for heat transfer applications, and also commonly studied by researchers because of the high heat transfer rates that are achievable. It is used in a variety of applications from the metal sheet industry to cooling of laser and electronic equipment. Also it is frequently used in plastic film manufact uring, surface drying processes for paper, cooling of fission and fusion components, and combustion walls and turbine blades cooling. Micro spray cooling is also a new technology that may improve the cooling efficiency of communications platforms in stalled on the unmanned aircraft and the performance of the electronic drives for el ectric cars and train motors. Spray cooling allows transistors to be driven harder and produce more power. Spray cooling also enables chips to survive in harsh environm ents that would otherwise cause them to fail. Spray nozzle plays a very important role in the cooling of electronics. Cooling electronic circuit integration is a vital part in maintaining the efficiency and reliability of the circuitry. Undesirably hi gh temperatures can severely strain the operational safety and effectiveness of the electronics. Micro spray cooling concentrates the spray to the hottest areas on a chip. Targeting the hottest areas on the chip not only improves the heat removal capability but also minimizes the amount 1

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2 of liquid required, making it more efficient fr om a system standpoint. To prevent the cooling substance from affecting the elect ronics, the manufacturers coated the top surface of silicon die with Parylene-C, a truly conformal polymer coating with excellent dielectric properties. The polymer covers the sidewalls, trenches, and other exposed surfaces on the chip. At present, most of the electronic co mponents are cooled by the heat sinks attached to them and by blowing air with fans. Unfortunately, this technique does not allow removing very high power without the heat sinks size becoming bulky or the fan becoming too large. Conventionall y, heat sinks and heat pipes touched down on the chip were mechanically held to the chip surface. The heat, produced uniformly over the postage stamp size surface area, diffused across the interface. The interface produced significant temperature difference between the chip and the heat sink. An even bigger limitation of direct air-cooling appears when dealing with high heat fluxes, which are common since th e chip’s size is becoming smaller by the day. Because reliability and speed of any chip depend on the working temperature, which is normally up to 120 degrees Celsius, new techniques are needed to improve the heat removed per unit surface area and volume. However, before determining the heat transfer properties of the system, it is important to determine the geometry of the jet spray exiting the chamber and nozzle. Prediction of nozzle performance for desi gn and analysis is critical in helping designers to meet effective and inexpensiv e performance. A set of design rules is based on the experimentation with variable parameters of height, nozzle diameter, and nozzle spacing in the submillmeter range. It can be used to develop an efficient

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3 and economical heat exchanger that will meet present and future integrated circuit microchip cooling requirements. The researchers mainly considered its ability to transfer heat from the chip surface to a transport medium, usually air, and also the medium’s heat capacity. A high-speed cool gas directly impinges on the hot surface through MEMS nozzle or slot array, and pene trates deep into the boundary layer to form a sharp temperature gradient. For inst ance, the cone angle of a particular spray would be an important number to determine. A larger cone angle means that the spray would be covering a greater surface area, and thus cooling a larger portion of the electronics. Another important factor is how wide the spray becomes after it exits the nozzle, or the radial height of th e free surface. In addition, a greater radial height produces more film surface area for the cooling purpose. A larger radial height and cone angle of the free surface is beneficial, because this would indicate that a greater fraction of the electronics w ould be cooled. This is significant for efficiency, and consequently, the cost of the design. The researchers recognized that a future microchip with multiple functionalities would have some areas of hi gh heat, low heat and no heat. Targeted spray cooling is essential to avoid pooling. Using the re-engineered inkjet heads, the researchers are able to target coolant spray to precise areas of the chip. The mechanism sprays a measured amount of dielectric liquid coolant onto the chip according to its heat level. The device controls the distribution, flow rate and velocity of the liquid in much the same wa y inkjet printers control the placement of ink on a printed page. The liquid vapori zes on impact, cooling the chip, and the

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4 vapor is then passed through a heat exchange r and pumped back into a reservoir that feeds the spray device. One well-known method is phase-change cooling. Such phase change, utilizing latent heat of vaporization of the liquid, removes significant heat flux. However, as the pooled liquid changes phase, vapor bubbles form that adhere to the wall of the chip. Also, the bubbles form rea lly quickly in the dielectric fluids. At a certain point on a tiny chip, a bubble will form on the hottest spots. If a bubble sits on top, it becomes an insulator. At that point, heat transfer through the bubbles is greatly limited, and the chip wall temperat ure quickly exceeds specifications. Laser diodes, that are used greatly in nowaday s communication applications, are very high heat density sources, and it requires this type of cooling to maintain high working efficiency. It has been recognized that the nozzle design may affect the change in geometry of the exiting spray. Jeng et al. (1998) performed experiments on 15 different nozzle geometries with four diffe rent flow rates and used the ArbitraryLangrangian-Eulerian (ALE) method to calcu late the position of the free surface. The finite element predictions were in good agreement with their experiments. They concluded that the geometry of the nozzle had a significant effect on the parameters of the exiting free surface that they were investigating. Dumouchel et al. (1993) proposed that th e nozzle geometry plays a major role in the nozzle performance. They also applie d numerical analysis to the velocity field throughout a swirl spray nozzle, and more sp ecifically, at the nozzle orifice. What they found was that the conical liquid sh eet produced at the nozzle’s orifice was

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5 mainly dependent on the shape of the nozzle. Also an agreement with this statement is Sakman et al. (2000). They studied the length-to-diameter ratio of the swirl chamber and orifice, stating that an incr ease in the length-to-diameter ratio for both the swirl chamber and orifice resulted in a d ecrease in the cone angle. However, an increase in the length-to-diameter ratio for the swirl chamber produced an increase in film thickness; an increase in the length-to-d iameter ratio for the orifice resulted in a decrease in the film thickness. Miller and Ellis (2000) investigated spra y nozzles for agricultural uses, mainly focusing on spray characteristics and dropl et size. They concluded that the interaction between the physical properties of the spray liquid and the characteristics of the spray formed was a function of the nozzle design. While some of the changes in spray formation could be related to the dynamic surface tension of the spray liquid, there was evidence to show that th ere were other physical parameters that influenced spray formation. Som and Bi swas (1986) agreed, stating that the pertinent governing parameters regarding the spray dispersion included the liquid velocity, liquid viscosity, liquid surface tension, the density of the ambient atmosphere, as well as the geometrical dimensions of the nozzle. Some other investigations were performed that observed the effect some parameters had on the free surface position and the cone angle of the fluid exiting the nozzle. Datta and Som (2000) studied ways to provide theoretical predictions of the cone angle produced by swirl spray pressure nozzles using numerical computations of the flow. They realized that an incr ease in the fluid flow rate created a sharp increase in the cone angle of the fluid exiting the swirl nozzle. Rothe and Block

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6 (1977) examined the effect that the pressure of the ambient environment to which the fluid is being sprayed had on the shape of the liquid sheet. Their work, which agrees with many other studies, found that an increase in ambient pressure and nozzle pressure drop created an increase in contr action of the liquid sheet emanating from the nozzle. However, an increase in nozzl e diameter aided in decreasing the amount of contraction. Gavaises and Arcoumanis (2001) state that an accurate estimation of the nozzle flow exit conditions are significant in the calculation of sprays ejected from the nozzle. Therefore, it is important to know the conditions at the location where the fluid exits the nozzle in order to truthfully predict the position of the free surface, as well as other interesting variables. After the free surface of the fluid has been modeled correctly, the heat transfer potentia l can then be evaluated. Ciofalo et al. (1999) performed experiments with full cone swirl atomizers onto a heated wall. They confirmed that the heat transfer coefficient and maximum heat flux was dependent of the mass flux of the spray, as well as the droplet velocity. Fabbri et al. (2003) concluded that the lo cal heat transfer decreases sharply as one moves radially outward from the sta gnation region to the periphery. Also, the major conclusions are that the jet impingement flow can be divided in four regions. Region 1 is the stagnation zone where it was found that the thickness of the hydrodynamic and thermal boundary layers is constant. In the second region, both boundary layers are developing and none have reached the free surface. Region 3 is characterized by the face that the hydrodyna mic boundary layer has reached the free surface, whereas the thermal boundary layer is still thinner than the film thickness.

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7 Finally in region 4, both boundary layers ha ve reached the free surface of the liquid film. Recently, attention has been focused on ci rcular arrays of free surface micro jets. The jet Reynolds number is the mostly concerned parameter. Micro impinging jets can be highly efficient, f ound by Wu et al. (1999), when compared to existing macro impinging-jet microelectronics packages. As the transistor density and/or the number of transistors on a standard -sized chip increases in IC’s, the power dissipation also increases. It is therefore necessary to investigate better thermal cooling methods for future chip cooling. A more efficient micro heat exchanger should be invented, as micro jets can be placed much closer to the hot surface than conventional macro jets. The goal of thei r work was then to study micro impinging jet cooling, focusing on experimentation with variable parameters of height, nozzle diameter, and nozzle spacing in the sub-millim eter range. It is found that a micro impinging jet can provide effective cooli ng. Higher driving pressure gives better cooling, but lower efficiency. This tr adeoff should be considered when using MEMS impinging-jet heat exchangers. Objectives The objectives of this investigation are shown as the following: 1. To approximate the flow pattern of some refrigerants, such as FC-72, FC-77, FC87, and Methanol in this specially desi gned “twister-effect” mixing chamber and spray nozzle.

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8 2. To understand the relationship among cone angle, free surface height, pressure drop, Reynolds number created in this nozzle with mixing chamber, and the fluid properties. 3. To compare the results of the nozzle de sign in this investigation and one from another.

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9 CHAPTER 2 MATHEMATICAL MODEL All the results in this analysis are based on the design shown as below in Figure 1. The radius of the inlets is 1 x 10-4 m, and the total length of each inlet tube is 1.5 x 10-3 m. Then, the radius and height of the chamber are 7.43 x 10-4 m and 1.0 x 10-3 m respectively. Viewing the inclined tubes from the top, the entrance and the exit of each tube is 60 degrees apart away fr om the center. In addition, the radius of the nozzle orifice is 1.25 x 10-4 m. In this analysis, the fluid flow rates entering the chamber are 4.416 x 10-7 m3/s or 5.678 x 10-7 m3/s, provided by the experimental data. The inlet velocity for each flow rate is presented in Table 1. The entire fluid simulation is under gravitational acceleration (9.81 m/s2). Adiabatic, incompressible, steady state, and turbulent flow were assumed in this investigation. Volumetric Flow Rate, Q (m3/s) Inlet Velocity (m/s) 4.416 x 10-7 3.51 5.678 x 10-7 4.52 Table 1: Inlet velocit y for different volumetric flow rates.

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10 Figure 1: Schematic of the inlet tubes, mi xing chamber, and the nozzle geometries. RADIUS 0.0743 CM RADIUS 0.0125 CM RADIUS 0.01 CM ( X7 ) 0.045 CM 60 0.05 CM 0.1 CM 0.1 CM 0.122 CM 0.0125 CM 0.107 CM 3D Section 2D Section

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11 Turbulent flow consists of random ve locity fluctuations, so there is no exact solution to approximate the turbulen t boundary layer. The only way to find the turbulent velocity profile is by statistical methods (time-averaged value) or momentum integral equation. Theoretically, the velocity and pressure drop of fluid can be found using the differential equa tions below with the boundary conditions provided. Conservation of mass is for an in finitesimal control volume. It is often called the equation of continuity (1) becau se it requires no assumption except that the density and velocity are continuum functions. 0 ) ( ) ( 1 ) ( 1 z rv z v r rv r r Momentum equation can also be used to find the force acting on a control volume. The differential momentum equa tion (2,3,4) for a Newtonian fluid with constant density and viscosity (or Navier-Stokes equations) are 2 2 2 21 1 r v z v r v r r r r p z v v r v r v vr r r t r z r r 2 2 21 r v z v r v r r r z v v r v v r v vt z r r 2 21 1 z v r v r r r z p g z v v r v vz z t z z z r Also, the mixing length model was used for simulation of turbulence in this problem. The mixing length turbulence model is a zero-equation model that uses the following relationship to determine the turbulent viscosity. ( 1 ) (2) (3) (4)

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12 r v v lr r t 2 B y y ln nexp 1 where is the Von Karman constant ( = 0.4), yn is the normal distance from the node to the wall yn + is a scale used to non-dimensionalize the problem, and B is the damping constant. The Van Driest damping f actor is located within the brackets [ ]. *v y yn n where v* is the friction velocity. By applying the boundary conditions gi ven in Tables 2 and 3 and the assumption to the above mathematical models, the equation of continuity and Navier-Stokes equations can be simplified. Also, the fluid properties in Table 4 can also be used for the same purpose. Location Boundary Conditions Inlets Velocity at the inlet depends on the volumetric flow rate. Inlet walls Velocity is set to be zero. (Vx = Vy = Vz = 0) Top of the chamber Velocity is set to be zero. (Vx = Vy = Vz = 0) Chamber wall Velocity is set to be zero. (Vx = Vy = Vz = 0) Chamber outlet All the velocities on each of the four axes resulted from the 3D simulation will be linearly interpolated and averaged, and they will then be used as the initial conditions and boundary conditions at the inlet of 2D nozzle. (5) (6) (7) Table 2: The boundar y conditions a pp lied to the 3D chamber model.

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13 Location Initial Conditions and Boundary Conditions Nozzle inlet Velocity at the inlet depends on the results at the 3D chamber outlet. Nozzle wall Velocity is set to be zero. (Vr = Vtheta = Vz = 0) Axis of symmetry Radial velocity is set to be zero. (Vr = 0) Refrigerants Type of Chemicals Density [kg/m3] Viscosity [kg/m-s] Surface Tension [N/m] FC-72 Fluorocarbon 1680 6.4 x 10-4 0.01 FC-77 Fluorocarbon 1780 1.424 x 10-3 0.015 FC-87 Fluorocarbon 1630 4.53 x 10-4 0.0095 Methanol Hydrocarbon 785.5 5.5 x 10-4 0.0222 Depending on the density, viscosity and su rface tension of the refrigerants, the cone angle, free surface height, and even cooling efficiency may varied. Table 4 basically shows the physical properties of the refrigerants used in the finite-element approximation. Because of the huge amount of numerical computations required in the analysis, a finite-element software has been used for the simulation. The details are presented in the next chapter. Table 3: The initial conditions and boundar y conditions a pp lied to the 2D s p ra y nozzle model. Table 4: Physical properties of working fluid refrigerants in this analysis.

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14 CHAPTER 3 NUMERICAL COMPUTATION Since the entire simulation requires tremendous amount of quadrilateral elements, it is divided into a 3D mixi ng chamber portion and 2D axi-symmetrical nozzle portion. They were both constructed and solved by a finite-element software named FIDAP. During the production of this 3D mesh, boundary edges were applied to guarantee the fine quality of mesh on each boundary surface. Pave and map meshing method were used to construct th e 3D chamber as shown in Figure 2 and Figure 3. To achieve the higher accuracy in the 3D simulation, the number of element was increased as much as the se rver can possibly handle. Segregated method and steady state turbulent assumptions have been chosen to solve this 3D chamber problem for the limited memory storage provided and short simulation period. Eventually, some results were obtai ned as shown in Figur es 4 and 5. Next, the 2D nozzle was made by map meshing me thod because of its simple geometric structure. Newton-Raphson was found to be the best method solving a 2D mixing length turbulent free surface problem. In this case, the problem was set to be transient as the change in free surface can be examined in each time step. Moreover, to ensure the accuracy of computation at the dynamic regions, the 2D mesh, shown in Figure 6, has been integrated by increasing the amount of element in where the free surface started and ended. The grid size of the 2D mesh is 30 x 142.

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15 Figure 2: Three-dimensional meshed structure of the mixing chamber. Figure 3: Mesh viewed at the top of inlet tubes and cylindrical chamber.

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16 Figure 4: Velocity plot of the chamb er in a vertical cross-sectional view. Figure 5: Pressure contour plot of the ch amber in a vertical cross-sectional view.

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17 In order to obtain an accurate and consta nt solution, the number of element in the mesh has to be enough. To perform so me computations for several numbers of mesh element is necessary. As shown in Figure 7, the 3D chamber mesh containing 37280 elements was adequate for a steady re sult, and it was found that the numerical computation became grid independent when the element number went above 37280. However, to achieve higher accuracy, the number of element in the 3D mesh was increased to 65724 for all final computati on. According to Figure 7, nearby the center of the chamber, the z-velocity per centage difference between the meshes with 50570 and 65724 elements is 0.974 %. Figure 6: 2D Axi-symmetrical nozzle mes h with integrated free surface.

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18 The quantitative difference in grid independence can be calculated using the following equation: e N D C V (8) where N is the number of elements along an axis, and C, D, and e were constants to be evaluated. V is the velocity at a given radi al coordinate along the outlet of the nozzle. Equation (8) has three unknowns at three sets of velocities taken at three different grid sizes. The result is a set of non-linear equations with three variables. An initial value of e is assumed. After performing a number of iterations, a correct value for e is determined. By definition, the value of e mu st be greater than one. After solving e and substituting back into Equation (8), the values of C and D were found. To obtain a percent error for the various computations, the following equation was used. 100 C C V -70 -60 -50 -40 -30 -20 -10 0 10 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 17904 Elements 37280 Elements 50570 Elements 65724 Elements x-axis coordinate [ 10-2m ] Figure 7: Velocity profiles in z-direction on xaxis in the 3D chamber for various grid sizes. Velocity in z-direction [10-2 m/s] ( 9 )

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19 CHAPTER 4 SIMULATION PROCEDURES Before start working on this analysis, so me preparations are needed to provide enough information for the finite-element si mulation. Also, manipulation of result data is very important. As seen below, the simulation procedures are described in detailed. 4.1 Inlet Velocity To calculate the inlet velocity Vinlet, the cross-sectional area of all inlets is needed. ) 3 (inclined central inletA A V Q where Qis the fluid volumetric flow rate. There are four refrigerants (FC-72, FC-77, FC-87, and Methanol) at two different flow rates (4.416 x 10-7 m3/s and 5.678 x 10-7 m3/s) in this work. After providing the fluid properties and inlet ve locity (see Appendix III), the 3D chamber simulation was run until it reached steady stat e. Based on the Cartesian coordinate system, the fluid sectional velocity was then obtained in four axial directions (+x, +y, -x, and –y) only at 0.02 cm above the cham ber exit and was then transferred to the 2D simulation (see Appendices IV to XII). ( 10 )

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20 4.2 Transformation of Velocity from Cartesian to Cylindrical System Because the 3D free surface simulation is nearly impossible to work, it can only be achieved by using a 2D axi-symmetri cal nozzle mesh. All sectional velocity data (Vx, Vy, and Vz) from the 3D chamber outlet has to be changed to the velocity under Cylindrical coordinate system (Vr, Vtheta, and Vz). By using the vector transformation from the Cartesian system to Cylindrical system, the radial and circumferential velocity can be figured out as the following. 1st quadrant 2nd quadrant 3rd quadrant 4th quadrant B(+ve y-axis) A(+ve x-axis) C(-ve x-axis) D(-ve y-axis) Fi g ure 8: Schematic of velocit y transformation from cartesian s y stem to c y lindrical s y stem and average.

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21 In the first quadrant: sin cos, y x r y r x rv v v v v cos sin, y x y xv v v v v In the second quadrant: cos sin, y x r y r x rv v v v v sin cos, y x y xv v v v v where 2 In the third quadrant: sin cos, y x r y r x rv v v v v cos sin, y x y xv v v v v where Figure 9: Velocity transformation from cartes ian system to cylindrical system using vector addition. (11) (12) (13) (14) (15) (16)

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22 In the fourth quadrant: cos sin, y x r y r x rv v v v v sin cos, y x y xv v v v v where 2 Vr Vtheta Vz Line A (+ve x-axis) Vx Vy Vz Line B (+ve y-axis) Vy minus Vx Vz Line C (-ve x-axis) minus Vx minus Vy Vz Line D (-ve y-axis) minus Vy Vx Vz Each of the four axes was broken up into thirty divisions as in Figure 8. By linear interpolation, the velocities in x, y, z-directions resulted from the 3D simulation were remodified using Equations (11) to (18) and Table 5 and became the radial, circumferential, and axial veloc ities at each node on the axis. Then, on the axes, the velocities of nodes located at the same distance from the origin are added and averaged. These averaged results (Vr-avg, Vtheta-avg, and Vz-avg) were applied into the 2D axi-symmetrical nozzle transient simulation to approximate the free surface height and cone angle. 4.3 Cone Angle and Free Surface Height The cone angle basically is the angle of elevation or the slope at the end of the free surface. Based on the mesh, it can be found by the coordinates of last two nodes on the free surface. Then, free surface height is the highest radial displacement of the jet out of the nozzle orifice. Table 5: Results of velocit y transformation in four different axes. (17) (18)

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23 4.4 Pressure Drop The pressure drop between the inlets above the mixing chamber and the outlet of the nozzle is also important in this je t impingement analysis. The finite-element software provided the pressure difference after the simulation. Nevertheless, the pressure difference can be calculated by us ing Bernoulli’s Equations (22), (24), (27), and (29). It was assumed that it was constant flow rate in the whole fluid simulation. The nozzle was made of new stainless st eel material that has 0.002 mm as the roughness height. Because of the high inlet velocity, the flow was considered as turbulent for the Bernoulli’s equation. Figure 10: Schematic of the entire geometry to compute the pressure drop by Bernoulli’s equation. Location A (1.5 x 10-3 m) inlet Location 1 (1.0 x 10-3 m) Location 2 (0 m) reference point Location 3 (-1.0 x 10-3 m) Location 4 (-1.7 x 10-3 m) outlet

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24 Length of the center pipe, Lcenter pipe = 0.001 m Length of the inclined pipe, Linclined pipe = 0.0011 m Loss Coefficient at the entrance, Kentrance (for sharp-edge inlet) = 0.5 Loss Coefficient at the exit, Kexit (for all shape of exit) = 1.0 Loss Coefficient for gradual contraction of the nozzle, Kgc = 0.07 Loss Coefficient for beveled entrance, Kbe = 0.15 Radius of center hole, rcenter = 0.0001 m Radius of inclined hole, rinclined = 0.0001 m Cross-sectional area of the center pipe, A1 = 3.14 x 10-8 m2 Cross-sectional area of the inclined pipe, A2 (or A3, A4) = 3.14 x 10-8 m2 Roughness Height for Steel as nozzle material = 2 x 10-6 m Useful Formulas D V D VD Re g V D L f hf22 K g V hm22 Re 64f (if the flow is laminar) f can be found in the Moody’s Chart according to the Reynolds Number, Re (if the flow is turbulent). Bernoulli’s Equation used in the Inlet Section (Location A to 1) f A A Ah z g V g P z g V g P 1 2 1 1 22 2 AV V 1 g V D L f hf22 where V = V1, L= Lvertical-tubes ( 19 ) (20) (21) (22) (23)

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25 Bernoulli’s Equation used in the Inlet Section (Location 1 to 2) m fh h z g V g P z g V g P 2 2 2 2 1 2 1 12 2 2 1V V g V D L f hf22 where V = V1, L= Lcenter-tube or Linclined-tube ) ( 22 exit entrance mK K g V h where V = V1 Bernoulli’s Equation used in the Inlet Section (Location 2 to 3) fh z g V g P z g V g P 3 2 3 3 2 2 2 22 2 3 2V V g V D L f hf22 where V = V2, L = height of the chamber (=1.07x10 -3 m) Bernoulli’s Equation used in the Inlet Section (Location 3 to 4) m fh h z g V g P z g V g P 4 2 4 4 3 2 3 32 2 3 3A Q V, where A3 is the cross-sectional area of the nozzle at Location 3 (= 1.734 x 10-6m2) 4 4A Q V, where A4 is the cross-sectional area of the nozzle at Location 4 (= 4.909 x 10-8m2) 2 1f f fh h h g V D L f hf22 1 where 24 3V V V 24 3D D D (24) (25) (26) (27) (28) (29) (30) (31)

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26 L = Lnozzle-inclined section = 0.00107 m g V D L f hf22 2 where V = V4 and L = Lnozzleoutletsection = 0.00015 m ) ( 22exit be gc mK K K g V h where V = V4 4.5 Cavitation Cavitation occurs if the liquid pressure falls below the saturation pressure for that particular fluid. The fluid eva porates at the boundary surface ,and the tiny bubbles becomes a thin gas layer. It may eventually erode and destroy the system, or prevent the heat conduction process acr oss the boundary surface. The cavitation number is found by Equation (34). Once it goes negative, cavitation takes place. 2 min5 0 V p p Casat (32) (33) (34)

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27 CHAPTER 5 RESULTS AND DISCUSSION After the description of simulation procedures, in this chapter, the results and discussion are presented in section 5.5 for the 3D mixing chamber and section 5.6 for the 2D nozzle. 5.1 3D Mixing Chamber In this section, the velocity distributi on can be seen inside the 3D chamber. For each particular fluid, the flow pattern in the chamber at each level under a certain flow rate are presented in Figures 11 to 58. All the plots are based on the results on the x, y, z-axis at various levels belo w the top of the mixing chamber. Also, obviously there is a change between the velo city ranges created by two different flow rates. 5.1.1 Refrigerant FC-72 In Figures 11 and 12, they reveal the pl ots of velocity in x-direction on the xaxis at various levels below the top of chamber at 4.416 x 10-7 m3/s and 5.678 x 10-7 m3/s. All the velocity profiles become stabili zed at the lower level of chamber. The maximum velocity shown in Figures 11 and 12 are 0.69 m/s and 0.88 m/s respectively at -1.0 x 10-4 m.

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28 -60 -40 -20 0 20 40 60 80 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m -60 -40 -20 0 20 40 60 80 100 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m x-axis coordinate [ 10-2m ] Figure 11: Velocity in x-direction on the x-axis at various levels below the top of mixing chamber (FC-72, 4.416 x 10-7 m3/s). Velocity in x-direction [10-2 m/s] x-axis coordinate [ 10-2m ] Figure 12: Velocity in x-direction on the x-axis at various levels below the top of mixing chamber (FC-72, 5.678 x 10-7 m3/s). Velocity in x-direction [10-2 m/s]

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29 In Figures 13 and 14, they show veloc ity in y-direction on the x-axis at various levels below the top of chamber at 4.416 x 10-7 m3/s and 5.678 x 10-7 m3/s. All the velocity profiles become stabilized at the lower level of chamber. The maximum velocity shown in Figures 13 a nd 14 are 0.95 m/s and 1.2 m/s respectively at -1.0 x 10-4 m. -120 -100 -80 -60 -40 -20 0 20 40 60 80 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m Figure 13: Velocity in y-direction on the x-axis at various levels below the top of mixing chamber (FC-72, 4.416 x 10-7 m3/s). x-axis coordinate [ 10-2m ] Velocity in y-direction [10-2 m/s]

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30 Then, in Figures 15 and 16, they reveal the plots of velocity in z-direction on the x-axis at various levels belo w the top of chamber at 4.416 x 10-7 m3/s and 5.678 x 10-7 m3/s. All the velocity profiles become stab ilized at the lower level of chamber. The maximum velocity shown in Figur es 15 and 16 are 2.64 m/s and 3.40 m/s respectively at -1.0 x 10-4 m. -150 -100 -50 0 50 100 150 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m Figure 14: Velocity in y-direction on the x-axis at various levels below the top of mixing chamber (FC-72, 5.678 x 10-7 m3/s). x-axis coordinate [ 10-2m ] Velocity in y-direction [10-2 m/s]

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31 -300 -250 -200 -150 -100 -50 0 50 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m -400 -350 -300 -250 -200 -150 -100 -50 0 50 100 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m x-axis coordinate [ 10-2m ] Figure 15: Velocity in z-direction on the x-axis at various levels below the top of mixing chamber (FC-72, 4.416 x 10-7 m3/s). Velocity in z-direction [10-2 m/s] x-axis coordinate [ 10-2m ] Figure 16: Velocity in z-direction on the x-axis at various levels below the top of mixing chamber (FC-72, 5.678 x 10-7 m3/s). Velocity in z-direction [10-2 m/s]

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32 Next, in Figure 17 and Figure 18, the plots of velocity in x-direction on the yaxis at various levels below the top of chamber at 4.416 x 10-7 m3/s and 5.678 x 10-7 m3/s are displayed. All the velocity profile s become stabilized at the lower level of chamber. The maximum velocity shown in Figures 17 and 18 are 0.77 m/s and 1.00 m/s respectively at -3.0 x 10-4 m. -60 -40 -20 0 20 40 60 80 100 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m Figure 17: Velocity in x-direction on the y-axis at various levels below the top of mixing chamber (FC-72, 4.416 x 10-7 m3/s). y -axis coordinate [ 10-2m ] Velocity in x-direction [10-2 m/s]

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33 In Figures 19 and 20, the velocity in y-direction on the y-axis at various levels below the top of chamber at th e volumetric flow rate 4.416 x 10-7 m3/s and 5.678 x 10-7 m3/s are plotted. All the velocity profile s become stabilized at the lower level of chamber. The maximum velocity shown in Figures 19 and 20 are 0.45 m/s and 0.59 m/s respectively at -1.0 x 10-4 m. Then Figures 21 and 22 show the plots of velocity in z-direction on the y-axis at various levels below the top of cham ber at the volumetric flow rate 4.416 x 10-7 m3/s and 5.678 x 10-7 m3/s. All the velocity profiles become stabilized at the lower level of chamber. The maximum velocity shown in Figures 21 and 22 are both 2.63 m/s at -1.0 x 10-4 m. -80 -60 -40 -20 0 20 40 60 80 100 120 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m y -axis coordinate [ 10-2m ] Figure 18: Velocity in x-direction on the y-axis at various levels below the top of mixing chamber (FC-72, 5.678 x 10-7 m3/s). Velocity in x-direction [10-2 m/s]

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34 -50 -40 -30 -20 -10 0 10 20 30 40 50 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m -60 -40 -20 0 20 40 60 80 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m y -axis coordinate [ 10-2m ] Velocity in y-direction [10-2 m/s] Figure 19: Velocity in y-direction on the y-axis at various levels below the top of mixing chamber (FC-72, 4.416 x 10-7 m3/s). y -axis coordinate [ 10-2m ] Velocity in y-direction [10-2 m/s] Figure 20: Velocity in y-direction on the y-axis at various levels below the top of mixing chamber (FC-72, 5.678 x 10-7 m3/s).

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35 -300 -250 -200 -150 -100 -50 0 50 100 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m -300 -250 -200 -150 -100 -50 0 50 100 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m y -axis coordinate [ 10-2m ] Velocity in z-direction [10-2 m/s] Figure 21: Velocity in z-direction on the y-axis at various levels below the top of mixing chamber (FC-72, 4.416 x 10-7 m3/s). y -axis coordinate [ 10-2m ] Figure 22: Velocity in z-direction on the y-axis at various levels below the top of mixing chamber (FC-72, 5.678 x 10-7 m3/s). Velocity in z-direction [10-2 m/s]

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36 5.1.2 Refrigerant FC-77 In Figures 23 and 24, the plots of velo city in x-direction on the x-axis at various levels below the top of chamber at 4.416 x 10-7 m3/s and 5.678 x 10-7 m3/s are shown. All the velocity profiles become stabilized at the lower level of chamber. The maximum velocity shown in Figur es 23 and 24 are 0.71 m/s and 0.90 m/s respectively at -1.0 x 10-4 m. -60 -40 -20 0 20 40 60 80 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m Figure 23: Velocity in x-direction on the x-axi s at various levels below the top of mixin g chamber (FC-77, 4.416 x 10-7 m3/s). x-axis coordinate [ 10-2m ] Velocity in x-direction [10-2 m/s]

PAGE 53

37 Then, in Figures 25 and 26, they reveal the plots of velocity in y-direction on the x-axis at various levels belo w the top of chamber at 4.416 x 10-7 m3/s and 5.678 x 10-7 m3/s. All the velocity profiles become stab ilized at the lower level of chamber. The maximum velocity shown in Figur es 25 and 26 are 0.94 m/s and 1.22 m/s respectively at -1.0 x 10-4 m. -60 -40 -20 0 20 40 60 80 100 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m Figure 24: Velocity in x-direction on the x-axis at various levels below the top of mixing chamber (FC-77, 5.678 x 10-7 m3/s). x-axis coordinate [ 10-2m ] Velocity in x-direction [10-2 m/s]

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38 -120 -100 -80 -60 -40 -20 0 20 40 60 80 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m -150 -100 -50 0 50 100 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m x-axis coordinate [ 10-2m ] Figure 25: Velocity in y-direction on the x-axis at various levels below the top of mixing chamber (FC-77, 4.416 x 10-7 m3/s). Velocity in y-direction [10-2 m/s] x-axis coordinate [ 10-2m ] Figure 26: Velocity in y-direction on the x-axis at various levels below the top of mixing chamber (FC-77, 5.678 x 10-7 m3/s). Velocity in y-direction [10-2 m/s]

PAGE 55

39 Next, in Figure 27 and Figure 28, the plot s of velocity in z-direction on the xaxis at various levels below the top of chamber at 4.416 x 10-7 m3/s and 5.678 x 10-7 m3/s are shown. All the velocity profiles become stabilized at the lower level of chamber. The maximum velocity shown in Figures 27 and 28 are 2.66 m/s and 3.42 m/s respectively at -1.0 x 10-4 m. -300 -250 -200 -150 -100 -50 0 50 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m Figure 27: Velocity in z-direction on the x-axis at various levels below the top of mixing chamber (FC-77, 4.416 x 10-7 m3/s). x-axis coordinate [ 10-2m ] Velocity in z-direction [10-2 m/s]

PAGE 56

40 Figure 29 and Figure 30 are the plots of velocity in x-direction on the y-axis at various levels below the top of chambe r at the volumetric flow rate 4.416 x 10-7 m3/s and 5.678 x 10-7 m3/s. All the velocity profiles become stabilized at the lower level of chamber. The maximum velocity s hown in Figures 29 and 30 are 0.74 m/s and 0.96 m/s respectively at -3.0 x 10-4 m. In Figure 31 and Figure 32, they show the velocity in y-direction on the y-axis at various levels below the top of cham ber at the volumetric flow rate 4.416 x 10-7 m3/s and 5.678 x 10-7 m3/s. All the velocity profiles become stabilized at the lower level of chamber. The maximum velocity shown in Figures 31 and 32 are both 0.45 m/s and 0.58 m/s respectively at -1.0 x 10-4 m. -400 -350 -300 -250 -200 -150 -100 -50 0 50 100 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m x-axis coordinate [ 10-2m ] Figure 28: Velocity in z-direction on the x-axis at various levels below the top of mixing chamber (FC-77, 5.678 x 10-7 m3/s). Velocity in z-direction [10-2 m/s]

PAGE 57

41 -60 -40 -20 0 20 40 60 80 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m -80 -60 -40 -20 0 20 40 60 80 100 120 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m y -axis coordinate [ 10-2m ] Velocity in x-direction [10-2 m/s] Figure 29: Velocity in x-direction on the y-axis at various levels below the top of mixing chamber (FC-77, 4.416 x 10-7 m3/s). y -axis coordinate [ 10-2m ] Velocity in x-direction [10-2 m/s] Figure 30: Velocity in x-direction on the y-axis at various levels below the top of mixing chamber (FC-77, 5.678 x 10-7 m3/s).

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42 -40 -30 -20 -10 0 10 20 30 40 50 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m -60 -40 -20 0 20 40 60 80 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m y -axis coordinate [ 10-2m ] Velocity in y-direction [10-2 m/s] Figure 31: Velocity in y-direction on the y-axis at various levels below the top of mixing chamber (FC-77, 4.416 x 10-7 m3/s). y -axis coordinate [ 10-2m ] Figure 32: Velocity in y-direction on the y-axis at various levels below the top of mixing chamber (FC-77, 5.678 x 10-7 m3/s). Velocity in y-direction [10-2 m/s]

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43 Figure 33 and Figure 34 are the plots of velocity in z-direction on the y-axis at various levels below the top of cham ber at the volumetric flow rate 4.416 x 10-7 m3/s and 5.678 x 10-7 m3/s. All the velocity profiles become stabilized at the lower level of chamber. The maximum velocity shown in Figures 33 and 34 are both 2.04 m/s and 2.63 m/s respectively at -1.0 x 10-4 m. -250 -200 -150 -100 -50 0 50 100 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m y-axis coordinate [10-2 m] Velocity in z-direction [10-2 m/s] Figure 33: Velocity in z-direction on the y-axis at various levels below the top of mixing chamber (FC-77, 4.416 x 10-7 m3/s).

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44 5.1.3 Refrigerant FC-87 In Figures 35 and 36, they reveal the pl ots of velocity in x-direction on the xaxis at various levels below the top of chamber at 4.416 x 10-7 m3/s and 5.678 x 10-7 m3/s. All the velocity profiles become stabili zed at the lower level of chamber. The maximum velocity shown in Figures 35 and 36 are 0.68 m/s and 0.88 m/s respectively at -1.0 x 10-4 m. -300 -250 -200 -150 -100 -50 0 50 100 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m y -axis coordinate [ 10-2m ] Figure 34: Velocity in z-direction on the y-axis at various levels below the top of mixing chamber (FC-77, 5.678 x 10-7 m3/s). Velocity in z-direction [10-2 m/s]

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45 -40 -20 0 20 40 60 80 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m -60 -40 -20 0 20 40 60 80 100 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m x-axis coordinate [ 10-2m ] Velocity in x-direction [10-2 m/s] Figure 35: Velocity in x-direction on the x-axis at various levels below the top of mixing chamber (FC-87, 4.416 x 10-7 m3/s). x-axis coordinate [ 10-2m ] Figure 36: Velocity in x-direction on the x-axis at various levels below the top of mixing chamber (FC-87, 5.678 x 10-7 m3/s). Velocity in x-direction [10-2 m/s]

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46 Then Figure 37 and Figure 38 show the plot s of velocity in y-direction on the x-axis at various levels below the top of chamber at the volumetric flow rate 4.416 x 10-7 m3/s and 5.678 x 10-7 m3/s. All the velocity profiles become stabilized at the lower level of chamber. The maximum ve locity shown in Figures 37 and 38 are both 0.95 m/s and 1.22 m/s respectively at -1.0 x 10-4 m. -120 -100 -80 -60 -40 -20 0 20 40 60 80 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m x-axis coordinate [ 10-2m ] Velocity in y-direction [10-2 m/s] Figure 37: Velocity in y-direction on the x-axis at various levels below the top of mixing chamber (FC-87, 4.416 x 10-7 m3/s).

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47 In Figures 39 and 40, they reveal the pl ots of velocity in z-direction on the xaxis at various levels below the top of chamber at the volumetric flow rate 4.416 x 10-7 m3/s and 5.678 x 10-7 m3/s. All the velocity profiles become stabilized at the lower level of chamber. The maximum ve locity shown in Figures 39 and 40 are 2.64 m/s and 3.40 m/s respectively at -1.0 x 10-4 m. -150 -100 -50 0 50 100 150 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m x-axis coordinate [ 10-2m ] Figure 38: Velocity in y-direction on the x-axis at various levels below the top of mixing chamber (FC-87, 5.678 x 10-7 m3/s). Velocity in y-direction [10-2 m/s]

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48 -300 -250 -200 -150 -100 -50 0 50 100 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m -400 -350 -300 -250 -200 -150 -100 -50 0 50 100 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m x-axis coordinate [ 10-2m ] Velocity in z-direction [10-2 m/s] Figure 39: Velocity in z-direction on the x-axis at various levels below the top of mixing chamber (FC-87, 4.416 x 10-7 m3/s). x-axis coordinate [ 10-2m ] Velocity in z-direction [10-2 m/s] Figure 40: Velocity in z-direction on the x-axis at various levels below the top of mixing chamber (FC-87, 5.678 x 10-7 m3/s).

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49 Next, Figure 41 and Figure 42 reveal the pl ots of velocity in x-direction on the y-axis at various levels below the top of chamber at the volumetric flow rate 4.416 x 10-7 m3/s and 5.678 x 10-7 m3/s. All the velocity profiles become stabilized at the lower level of chamber. The maximum ve locity shown in Figures 41 and 42 are 0.78 m/s and 1.01 m/s respectively at -3.0 x 10-4 m. -80 -60 -40 -20 0 20 40 60 80 100 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m y -axis coordinate [ 10-2m ] Velocity in x-direction [10-2 m/s] Figure 41: Velocity in x-direction on the y-axis at various levels below the top of mixing chamber (FC-87, 4.416 x 10-7 m3/s).

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50 In Figures 43 and 44, the plots of velo city in y-direction on the y-axis at various levels below the top of chambe r at the volumetric flow rate 4.416 x 10-7 m3/s and 5.678 x 10-7 m3/s are displayed. All the veloc ity profiles become stabilized at the lower level of chamber. The maximu m velocity shown in Figures 43 and 44 are 0.46 m/s and 0.59 m/s respectively at -1.0 x 10-4 m. In Figure 45 and Figure 46, they show th e plots of velocity in z-direction on the y-axis at various levels below the top of chamber at the volumetric flow rate 4.416 x 10-7 m3/s and 5.678 x 10-7 m3/s. All the velocity profiles become stabilized at the lower level of chamber. The ma ximum velocity shown in Figures 45 and 46 are both 2.04 m/s and 3.37 m/s respectively at -1.0 x 10-4 m. -100 -80 -60 -40 -20 0 20 40 60 80 100 120 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m y -axis coordinate [ 10-2m ] Figure 42: Velocity in x-direction on the y-axis at various levels below the top of mixing chamber (FC-87, 5.678 x 10-7 m3/s). Velocity in x-direction [10-2 m/s]

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51 -40 -30 -20 -10 0 10 20 30 40 50 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m -60 -40 -20 0 20 40 60 80 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m y -axis coordinate [ 10-2m ] Velocity in y-direction [10-2 m/s] Figure 43: Velocity in y-direction on the y-axis at various levels below the top of mixing chamber (FC-87, 4.416 x 10-7 m3/s). y -axis coordinate [ 10-2m ] Velocity in y-direction [10-2 m/s] Figure 44: Velocity in y-direction on the y-axis at various levels below the top of mixing chamber (FC-87, 5.678 x 10-7 m3/s).

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52 -250 -200 -150 -100 -50 0 50 100 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m -400 -350 -300 -250 -200 -150 -100 -50 0 50 100 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m y-axis coordinate [10-2 m] Velocity in z-direction [10-2 m/s] Figure 45: Velocity in z-direction on the y-axis at various levels below the top of mixing chamber (FC-87, 4.416 x 10-7 m3/s). y -axis coordinate [ 10-2m ] Figure 46: Velocity in z-direction on the y-axis at various levels below the top of mixing chamber (FC-87, 5.678 x 10-7 m3/s). Velocity in z-direction [10-2 m/s]

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53 5.1.4 Methanol In this scenario, Figures 47 and 48 are th e plots of velocity in x-direction on the x-axis at various levels belo w the top of chamber at 4.416 x 10-7 m3/s and 5.678 x 10-7 m3/s. All the velocity profiles become stab ilized at the lower level of chamber. The maximum velocity shown in Figur es 47 and 48 are 0.70 m/s and 0.90 m/s respectively at -1.0 x 10-4 m. -60 -40 -20 0 20 40 60 80 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m x-axis coordinate [10-2 m] Velocity in x-direction [10-2 m/s] Figure 47: Velocity in x-direction on the x-axis at various levels below the top of mixing chamber (Methanol, 4.416 x 10-7 m3/s).

PAGE 70

54 In Figures 49 and 50, they reveal the pl ots of velocity in y-direction on the xaxis at various levels below the top of chamber at the volumetric flow rate 4.416 x 10-7 m3/s and 5.678 x 10-7 m3/s. All the velocity profiles become stabilized at the lower level of chamber. The maximum ve locity shown in Figures 49 and 50 are 0.94 m/s and 1.22 m/s respectively at -1.0 x 10-4 m. Then, Figure 51 and Figure 52 show the plot s of velocity in z-direction on the x-axis at various levels below the top of chamber at the volumetric flow rate 4.416 x 10-7 m3/s and 5.678 x 10-7 m3/s. All the velocity profiles become stabilized at the lower level of chamber. The maximum ve locity shown in Figures 51 and 52 are both 2.65 m/s and 3.41 m/s respectively at -1.0 x 10-4 m. -60 -40 -20 0 20 40 60 80 100 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m x-axis coordinate [ 10-2m ] Figure 48: Velocity in x-direction on the x-axis at various levels below the top of mixing chamber (Methanol, 5.678 x 10-7 m3/s). Velocity in x-direction [10-2 m/s]

PAGE 71

55 -120 -100 -80 -60 -40 -20 0 20 40 60 80 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m -150 -100 -50 0 50 100 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m x-axis coordinate [ 10-2m ] Velocity in y-direction [10-2 m/s] Figure 49: Velocity in y-direction on the x-axis at various levels below the top of mixing chamber (Methanol, 4.416 x 10-7 m3/s). x-axis coordinate [ 10-2m ] Velocity in y-direction [10-2 m/s] Figure 50: Velocity in y-direction on the x-axis at various levels below the top of mixing chamber (Methanol, 5.678 x 10-7 m3/s).

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56 -300 -250 -200 -150 -100 -50 0 50 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m -400 -350 -300 -250 -200 -150 -100 -50 0 50 100 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m x-axis coordinate [ 10-2m ] Velocity in z-direction [10-2 m/s] Figure 51: Velocity in z-direction on the x-axis at various levels below the top of mixing chamber (Methanol, 4.416 x 10-7 m3/s). x-axis coordinate [ 10-2m ] Figure 52: Velocity in z-direction on the x-axis at various levels below the top of mixing chamber (Methanol, 5.678 x 10-7 m3/s). Velocity in z-direction [10-2 m/s]

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57 In Figures 53 and 54, they display the pl ots of velocity in x-direction on the yaxis at various levels below the top of chamber at 4.416 x 10-7 m3/s and 5.678 x 10-7 m3/s. All the velocity profiles become stabili zed at the lower level of chamber. The maximum velocity shown in Figures 53 and 54 are 0.74 m/s and 0.97 m/s respectively at -3.0 x 10-4 m. -60 -40 -20 0 20 40 60 80 100 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m y-axis coordinate [10-2 m] Velocity in x-direction [10-2 m/s] Figure 53: Velocity in x-direction on the y-axis at various levels below the top of mixing chamber (Methanol, 4.416 x 10-7 m3/s).

PAGE 74

58 Both Figures 55 and 56 reveal the plots of velocity in y-direction on the y-axis at various levels below the top of cham ber at the volumetric flow rate 4.416 x 10-7 m3/s and 5.678 x 10-7 m3/s. All the velocity profiles become stabilized at the lower level of chamber. The maximum velocity shown in Figures 55 and 56 are 0.45 m/s and 0.56 m/s respectively at -1.0 x 10-4 m. Now, in Figures 57 and 58, th e plots of velocity in z-direction on the y-axis at various levels below the top of chambe r at the volumetric flow rate 4.416 x 10-7 m3/s and 5.678 x 10-7 m3/s are shown. All the velocity profiles become stabilized at the lower level of chamber. The maximum ve locity shown in Figures 57 and 58 are 2.04 m/s and 2.63 m/s respectively at -1.0 x 10-4 m. -80 -60 -40 -20 0 20 40 60 80 100 120 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m y-axis coordinate [10-2 m] Figure 54: Velocity in x-direction on the y-axis at various levels below the top of mixing chamber (Methanol, 5.678 x 10-7 m3/s) Velocity in x-direction [10-2 m/s]

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59 -40 -30 -20 -10 0 10 20 30 40 50 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m -60 -40 -20 0 20 40 60 80 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m y-axis coordinate [10-2 m] Velocity in y-direction [10-2 m/s] Figure 55: Velocity in y-direction on the y-axis at various levels below the top of mixing chamber (Methanol, 4.416 x 10-7 m3/s). y-axis coordinate [10-2 m] Velocity in y-direction [10-2 m/s] Figure 56: Velocity in y-direction on the y-axis at various levels below the top of mixing chamber (Methanol, 5.678 x 10-7 m3/s).

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60 -250 -200 -150 -100 -50 0 50 100 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m -300 -250 -200 -150 -100 -50 0 50 100 -0.10-0.08-0.06-0.04-0.020.000.020.040.060.080.10 z = -1.0E-04 m z = -3.0E-04 m z = -5.0E-04 m z = -8.0E-04 m y-axis coordinate [10-2 m] Velocity in z-direction [10-2 m/s] Figure 57: Velocity in z-direction on the y-axis at various levels below the top of mixing chamber (Methanol, 4.416 x 10-7 m3/s). y-axis coordinate [10-2 m] Figure 58: Velocity in z-direction on the y-axis at various levels below the top of mixing chamber (Methanol, 5.678 x 10-7 m3/s). Velocity in z-direction [10-2 m/s]

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61 Based on the results of the 3D simulati on, the flow patterns for each working fluid at different flow rates were nearly iden tical. First, the velocity of fluid flowing inside the inlet tubes was much faster than its velocity in the chamber. Besides, the pressure decreased gradually from the inle ts to the chamber bottom. Obviously, the velocities in x, y, and z directions increased when the volumetric flow rate increased. Next, the velocity profiles in each directi on became stabilized as the fluid eventually approached the bottom of chamber. Also, there was a flow spinning in a clockwise motion shown in Figure 59 to Figure 66. After that, the velocities in x, y, z-dir ections were obtained, and they were all transformed into radial, circumferential, and axial velocities. Since the transformed velocities in each direction were not the sa me, they were then averaged and became the average velocities in cylindrical system for the axi-symmetrical nozzle simulations.

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62 Figure 59: Cross-sectional Velocity Plot at 8.0 x 10-4m below the Top of Chamber to show the circulation of FC-72 (Q = 4.416 x 10-7 m3/s) in clockwise direction. Figure 60: Cross-sectional velocity plot at 8.0 x 10-4m below the top of chamber to show the circulation of FC-72 (Q = 5.678 x 10-7 m3/s) in clockwise direction.

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63 Figure 61: Cross-sectional velocity plot at 8.0 x 10-4m below the top of chamber to show the circulation of FC-77 (Q = 4.416 x 10-7 m3/s) in clockwise direction. Figure 62: Cross-sectional velocity plot at 8.0 x 10-4 m below the top of chamber to show the circulation of FC-77 (Q = 5.678 x 10-7 m3/s) in clockwise direction.

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64 Figure 63: Cross-sectional velocity plot at 8.0 x 10-4m below the top of chamber to show the circulation of FC-87 (Q = 4.416 x 10-7 m3/s) in clockwise direction. Figure 64: Cross-sectional velocity plot at 8.0 x 10-4m below the top of chamber to show the circulation of FC-87 (Q = 5.678 x 10-7 m3/s) in clockwise direction.

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65 Figure 65: Cross-sectional velocity plot at 8.0 x 10-4 m below the top of chamber to show the circulation of Methanol (Q = 4.416 x 10-7 m3/s) in clockwise direction. Figure 66: Cross-sectional velocity plot at 8.0 x 10-4m below the top of chamber to show the circulation of Methanol (Q = 5.678 x 10-7 m3/s) in clockwise direction.

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66 5.2 2D Nozzles After the 3D mixing chamber simulati on, all the velocity data for each working fluid and flow rate were transformed to radial, circumferential, and axial velocities. Using Figure 8, all these ve locities were interpolated linearly and averaged. All the averaged results from four axes were then applied to the 2D axisymmetrical nozzle simulation. Finally the cone angle and free surface were obtained with the converged transient soluti ons. The results of both inlet flow rates (4.416 x 10-7 and 5.678 x 10-7 m3/s) are illustrated in this section. 5.2.1 Refrigerant FC-72 Figure 67 shows the velocity vector pl ot for FC-72 as the working fluid flowing at 4.416 x 10-7 m3/s. The maximum velocity was found to be around 8.93 m/s, located near the outlet section of the nozzle. The free surface began at an initial height of 1.250 x 10-4 m, but decreased to a final height of 1.227 x 10-4 m. Figure 67: Velocity vector plot for FC-72 (Q = 4.416 x 10-7 m3/s). Units are cm/s.

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67 Figure 68 and 69 show the pressure and st reamline contour plots, respectively. The maximum pressure within th e nozzle was found to be 7.17 x 104 Pa, while the minimum pressure was -2.18 x 104 Pa. The inlet-to-outlet pressure drop was calculated to be about 7.20 x 104 Pa. The streamline contour plot shows that most of the fluid entering the outer slot flows along the nozzle wall toward the outlet, while some of that fluid initially flowed toward the center of the nozzle. The fluid entering closed to the center of nozzle flows sligh tly outward in the radial direction as it moved toward the outlet. Figure 68: Pressure contour plot for FC-72 (Q = 4.416 x 10-7 m3/s). Units are gm/cm s2 (x101 Pa).

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68 Figure 69: Streamline contour plot for FC-72 (Q = 4.416 x 10-7 m3/s). The next flow rate that was used with FC-72 as the fluid was 5.678 x 10-7 m3/s. The velocity vector plot for this scenario is shown in Figure 70. The maximum velocity within the nozzle was found to be about 11.56 m/s. The free surface of the liquid exiting the nozzle began at a height of 1.250 x 10-4 m, and steadily declined to a final height of 1.230 x 10-4 m. In Figure 70, it is observed that as the fluid enters the throat of the nozzle, the velocity of the fluid near the wall and the outer portion of the free surface have lowe r velocities than elsewhere in the flow. This phenomenon is due to the boundary c ondition of zero velocity at the nozzle walls.

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69 Figure 70: Velocity vector plot for FC-72 (Q = 5.678 x 10-7 m3/s). Units are cm/s. Figures 71 and 72 show the pressure c ontour plot and the streamline contour plot for this case. The maximum pressure was found to be 1.18 x 105 Pa, whereas the minimum pressure was found to be -3.77 x 104 Pa. The pressure drop from the inlet to the outlet of the nozzle was cal culated to be approximately 1.18 x 105 Pa. Similar to the other cases, the streamline c ontour plot shows that most of the fluid that enters through the outer slot follows th e nozzle wall to the outlet, while some of the fluid move toward the center of the nozzle as it flows to the outlet. The fluid that enters at the axis of symmetry has almost a purely axial flow.

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70 Figure 71: Pressure contour plot for FC-72 (Q = 5.678 x 10-7 m3/s). Units are gm/cm s2 (x101 Pa). Figure 72: Streamline contour plot for FC-72 (Q = 5.678 x 10-7 m3/s). Figure 73 and Figure 74 depict the prof ile of the free surface obtained when the working fluid was FC-72. It was noted that the inlet flow rate had little effect on the height of the free surface; however, 5.678 x 10-7 m3/s produced a slightly greater height.

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71 1.00E-04 1.10E-04 1.20E-04 1.30E-04 1.40E-04 1.50E-04 1.20E-031.40E-031.60E-031.80E-03 4.416E-07 m3/s 5.678E-07 m3/s Figure 73: Free surface profile for FC-72 at various flow rates. 1.219E-04 1.224E-04 1.229E-04 1.234E-04 1.239E-04 1.244E-04 1.249E-04 1.254E-04 1.20E-031.40E-031.60E-031.80E-03 4.416E-07 m3/s 5.678E-07 m3/s Figure 74: Magnified free surface profile for FC-72 at various flow rates. Axial Coordinate [m]Radial Coordinate [ m ] Axial Coordinate [m] Radial Coordinate [ m ]

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72 5.2.2 Refrigerant FC-77 Figure 75 reveals the velocity vector plot for the case where 4.416 x 10-7 m3/s is used as the inlet flow rate with FC -77 as the working fluid. The maximum velocity was found to be around 8.78 m/s, and was also located in the throat of the nozzle. The free surface began at a height of 1.250 x 10-4 m, decreased to a height 1.214 x 10-4 m, then increased back to a height of 1.219 x 10-4 m. This flow was determined to be turbulent, and the mixing length turbulence model was employed for this case. Figure 75: Velocity vector plot for FC-77 (Q = 4.416 x 10-7 m3/s). Units are cm/s. Figure 76 shows the pressure contour pl ot for this case; the maximum and minimum pressures plotted were determined to be 7.73 x 104 Pa and -1.88 x 104 Pa, respectively. The inlet-to-outlet pressure drop was calculated to be 7.73 x 104 Pa. The streamline contour plot is depicted in Figure 77. The fluid entering near the axis of symmetry moves slightly outward in the radial direction before heading toward

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73 the outlet because the circumferential velocity increases from the center to the wall at the nozzle inlet section. Figure 76: Pressure contour plot for FC-77 (Q = 4.416 x 10-7 m3/s). Units are gm/cm s2 (x101 Pa). Figure 77: Streamline contour plot for FC-77 (Q = 4.416 x 10-7 m3/s). The velocity vector plot for FC-77 traveling at 5.678 x 10-7 m3/s is shown in Figure 78. This was also found to be turbulent, and again, the mixing length

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74 turbulence model was used. The maximum velocity, like the other trials, was found to be in the throat of the nozzle, and equi valent to about 11.26 m/s. Also similar to the previous trial, the free surface height started at 1.250 x 10-4 m, declined to 1.217 x 10-4 m, and then rose to 1.219 x 10-4 m. It was observed from this data, that the inlet flow rate had very little effect on th e free surface height; however, out of all of the variations, the inlet flow rate affected the free surface height and the cone angle the most. Figure 78: Velocity vector plot for FC-77 (Q = 5.678 x 10-7 m3/s). Units are cm/s. Figure 79 and Figure 80 show the pressu re and streamline contour plots for this situation. The maximum pressu re was determined to be 1.27 x 105 Pa, whereas the minimum pressure was determined to be -3.44 x 104 Pa. The two extremes were located at the inlet and outlet of the nozzl e, respectively. The pressure drop from inlet to outlet was calculated to be 1.27 x 105 Pa. Similar to the cases above, the streamline plot shows that the fluid moves s lightly outward in the radial direction at

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75 the inlet section. Also, the fluid ente ring through the central inlet area flows along the line of symmetry. Figure 79: Pressure contour plot for FC-77 (Q = 5.678 x 10-7 m3/s). Units are gm/cm s2 (x101 Pa). Figure 80: Streamline contour plot for FC-77 (Q = 5.678 x 10-7 m3/s). Figure 81 and Figure 82 depict the prof ile of the free surface obtained when the working fluid was FC-77. It was noted that the inlet flow rate had little effect on

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76 the height of the free surface; however, 5.678 x 10-7 m3/s produced a slightly greater height. 1.00E-04 1.10E-04 1.20E-04 1.30E-04 1.40E-04 1.50E-04 1.20E-031.40E-031.60E-031.80E-03 4.416E-07 m3/s 5.678E-07 m3/s Figure 81: Free surface profile for FC-77 at various flow rates. 1.210E-04 1.215E-04 1.220E-04 1.225E-04 1.230E-04 1.235E-04 1.240E-04 1.245E-04 1.250E-04 1.20E-031.40E-031.60E-031.80E-03 4.416E-07 m3/s 5.678E-07 m3/s Figure 82: Magnified free surface profile for FC-77 at various flow rates. Axial Coordinate [m] Radial Coordinate [ m ] Axial Coordinate [m] Radial Coordinate [ m ]

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77 5.2.3 Refrigerant FC-87 Figure 83 shows the velocity vector pl ot for FC-87 as the working fluid flowing at 4.416 x 10-7 m3/s. The maximum velocity was found to be around 8.91 m/s, located near the outlet section of the nozzle. The free surface began at an initial height of 1.250 x 10-4 m, but decreased to a final height of 1.230 x 10-4 m. Figure 83: Velocity vector plot for FC-87 (Q = 4.416 x 10-7 m3/s). Units are cm/s. Figures 84 and 85 show the pressure and streamline contour plots, respectively. The maximum pressure w ithin the nozzle was found to be 6.87 x 104 Pa, while the minimum pressure was -2.23 x 104 Pa. The inlet-to-outlet pressure drop was calculated to be about 6.92 x 104 Pa. The streamline contour plot shows that the fluid entering closed to the center of nozzle flows slightly outward in the radial direction as it moved toward the outlet.

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78 Figure 84: Pressure contour plot for FC-87 (Q = 4.416 x 10-7 m3/s). Units are gm/cm s2 (x101 Pa). Figure 85: Streamline contour plot for FC-87 (Q = 4.416 x 10-7 m3/s). The next flow rate that was used with FC-87 as the fluid was 5.678 x 10-7 m3/s. The velocity vector plot for this scenario is shown in Figure 86. The maximum velocity within the nozzle was found to be about 11.49 m/s. The free surface of the liquid exiting the nozzle began at a height of 1.250 x 10-4 m, steadily

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79 declined to a lowest height of 1.224 x 10-4 m, and rose back up to 1.232 x 10-4 m. In Figure 86, it is again observed that as the fluid enters the throat of the nozzle, the velocity of the fluid near the wall and th e outer portion of the free surface have lower velocities than elsewhere in the flow. This phenomenon is due to the boundary condition of zero velocity at the nozzle walls. Figure 86: Velocity vector plot for FC-87 (Q = 5.678 x 10-7 m3/s). Units are cm/s. Figure 87 and Figure 88 show the pressu re contour plot and the streamline contour plot for this case. The maxi mum pressure was found to be 1.13 x 105 Pa, whereas the minimum pressure was found to be -3.80 x 104 Pa. The pressure drop from the inlet to the outlet of the nozzle was calculated to be approximately 1.14 x 105 Pa. Similar to the other cases, the str eamline contour plot shows the fluid that enters at the axis of symmetry has almost a purely axial flow.

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80 Figure 87: Pressure contour plot for FC-87 (Q = 5.678 x 10-7 m3/s). Units are gm/cm s2 (x101 Pa). Figure 88: Streamline contour plot for FC-87 (Q = 5.678 x 10-7 m3/s). Figures 89 and 90 depict the profile of the free surface obtained when the working fluid was FC-87. It was noted that the inlet flow rate had little effect on the height of the free surface; however, 5.678 x 10-7 m3/s produced a slightly greater height.

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81 1.00E-04 1.10E-04 1.20E-04 1.30E-04 1.40E-04 1.50E-04 1.20E-031.40E-031.60E-031.80E-03 4.416E-07 m3/s 5.678E-07 m3/s Figure 89: Free surface profile for FC-87 at various flow rates. 1.220E-04 1.225E-04 1.230E-04 1.235E-04 1.240E-04 1.245E-04 1.250E-04 1.255E-04 1.20E-031.40E-031.60E-031.80E-03 4.416E-07 m3/s 5.678E-07 m3/s Figure 90: Magnified free surface profile for FC-87 at various flow rates. Axial Coordinate [m] Radial Coordinate [ m ] Axial Coordinate [m ] Radial Coordinate [ m ]

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82 5.2.4 Methanol Figure 91 shows the velocity vector plot for Methanol as the working fluid flowing at 4.416 x 10-7 m3/s. The maximum velocity was found to be around 8.78 m/s, located near the outlet section of the nozzle. The free surface began at an initial height of 1.250 x 10-4 m, but decreased to a final height of 1.220 x 10-4 m. Figure 91: Velocity vector plot for Methanol (Q = 4.416 x 10-7 m3/s). Units are cm/s. Figures 92 and 93 show the pressure and streamline contour plots, respectively. The maximum pressure w ithin the nozzle was found to be 3.41 x 104 Pa, while the minimum pressure was -8.71 x 103 Pa. The inlet-to-outlet pressure drop was calculated to be about 3.41 x 104 Pa. The streamline contour plot also shows the fluid entering closed to the cente r of nozzle flows sli ghtly outward in the radial direction as it moved toward the outlet.

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83 Figure 92: Pressure contour plot for Methanol (Q = 4.416 x 10-7 m3/s). Units are gm/cm s2 (x101 Pa). Figure 93: Streamline contour plot for Methanol (Q = 4.416 x 10-7 m3/s). The next flow rate that was used w ith Methanol as the fluid was 5.678 x 10-7 m3/s. The velocity vector plot for this scenario is shown in Figure 94. The maximum velocity within the nozzle was found to be about 11.26 m/s. The free surface of the liquid exiting the nozzle began at a height of 1.250 x 10-4 m, and steadily declined to a final height of 1.223 x 10-4 m. In Figure 94, it is observed that

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84 as the fluid enters the throat of the nozzle, the velocity of the fluid near the wall and the outer portion of the free surface have lowe r velocities than elsewhere in the flow. Again, this phenomenon is due to the bounda ry condition of zero velocity at the nozzle walls. Figure 94: Velocity vector plot for Methanol (Q = 5.678 x 10-7 m3/s). Units are cm/s. Figures 95 and 96 show the pressure c ontour plot and the streamline contour plot for this case. The maximum pressure was found to be 5.61 x 104 Pa, whereas the minimum pressure was found to be -1.55 x 104 Pa. The pressure drop from the inlet to the outlet of the nozzle was cal culated to be approximately 5.62 x 104 Pa. Similar to the other cases, the streamline c ontour plot shows that most of the fluid that enters through the outer slot follows th e nozzle wall to the outlet, while some of the fluid move toward the center of the nozzle as it flows to the outlet. The fluid that enters at the axis of symmetry has almost a purely axial flow.

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85 Figure 95: Pressure contour plot for Methanol (Q = 5.678 x 10-7 m3/s). Units are gm/cm s2 (x101 Pa). Figure 96: Streamline contour plot for Methanol (Q = 5.678 x 10-7 m3/s). Figures 97 and 98 depict the profile of the free surface obtained when the working fluid was Methanol. It was noted th at the inlet flow rate had little effect on the height of the free surface; however, 5.678 x 10-7 m3/s produced a slightly greater height.

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86 1.00E-04 1.10E-04 1.20E-04 1.30E-04 1.40E-04 1.50E-04 1.20E-031.40E-031.60E-031.80E-03 4.416E-07 m3/s 5.678E-07 m3/s Figure 97: Free surface profile for Methanol at various flow rates. 1.210E-04 1.215E-04 1.220E-04 1.225E-04 1.230E-04 1.235E-04 1.240E-04 1.245E-04 1.250E-04 1.255E-04 1.20E-031.40E-031.60E-031.80E-03 4.416E-07 m3/s 5.678E-07 m3/s Figure 98: Magnified free surface profile for Methanol at various flow rates. Axial Coordinate [m] Radial Coordinate [m] Axial Coordinate [m] Radial Coordinate [ m ]

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87 5.2.5 Cone Angle and Free Surface Height For each refrigerant or working fluid in th is analysis, as shown in Tables 6 to 8, Reynolds number has a little effect to the cone angle and free surface height. From Figures 99 to 102, FC-87 is the work ing fluid produced the highest free surface height (1.232 x 10-4m), while FC-77 produced the largest cone angle (5.75 degrees) among all fluids in this investigation. The free surfaces of all fluids have the same characteristics. At the nozzle outlet, the radial displacement of free surface decreased dramatically, and then became st eady. After that, it rose back up and created an elevation at the end. Cone Angle [degrees] Free Surface Height [10-4 m] Refrigerants 4.416 x 10-7 m3/s 5.678 x 10-7 m3/s 4.416 x 10-7 m3/s 5.678 x 10-7 m3/s FC-72 1.91 2.88 1.227 1.230 FC-77 2.87 5.75 1.219 1.219 FC-87 2.87 2.87 1.230 1.232 Methanol 1.91 1.91 1.220 1.223 Table 6: Cone angle and free surface height fo r each working fluid at various flow rates.

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88 4.416 x 10-7 m3/s Refrigerants Reynolds Number [non-dim] Cone Angle [degrees] Free Surface Height [10-4m] FC-72 5904 1.91 1.227 FC-77 2811 2.87 1.219 FC-87 8093 2.87 1.23 Methanol 3212 1.91 1.22 5.678 x 10-7 m3/s Refrigerants Reynolds Number [non-dim] Cone Angle [degrees] Free Surface Height [10-4m] FC-72 7591 2.88 1.23 FC-77 3615 5.75 1.219 FC-87 10405 2.87 1.232 Methanol 4130 1.91 1.223 Table 7: Cone angle, free surface height, and Reynolds number at the nozzle outlet for each working fluid (Q = 4.416 x 10-7 m3/s). Table 8: Cone an g le, free surface hei g ht, and Re y nolds number at the nozzle outlet for each working fluid (Q = 5.678 x 10-7 m3/s).

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89 1.000E-04 1.100E-04 1.200E-04 1.300E-04 1.400E-04 1.500E-04 1.20E-031.40E-031.60E-031.80E-03 FC-72 FC-77 FC-87 Methanol 1.210E-04 1.215E-04 1.220E-04 1.225E-04 1.230E-04 1.235E-04 1.240E-04 1.245E-04 1.250E-04 1.255E-04 1.20E-031.40E-031.60E-031.80E-03 FC-72 FC-77 FC-87 Methanol Axial Coordinate [m] Radial Coordinate [ m ] Figure 100: Magnified free surface profile for various fluids (Q=4.416 x 10-7 m3/s). Figure 99: Free surface profile for various fluids (Q=4.416 x 10-7 m3/s). Axial Coordinate [m] Radial Coordinate [ m ]

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90 1.000E-04 1.100E-04 1.200E-04 1.300E-04 1.400E-04 1.500E-04 1.20E-031.40E-031.60E-031.80E-03 FC-72 FC-77 FC-87 Methanol 1.215E-04 1.220E-04 1.225E-04 1.230E-04 1.235E-04 1.240E-04 1.245E-04 1.250E-04 1.255E-04 1.20E-031.40E-031.60E-031.80E-03 FC-72 FC-77 FC-87 Methanol Figure 101: Free surface profile for various fluids (Q=5.678 x 10-7 m3/s). Axial Coordinate [m] Radial Coordinate [ m ] Figure 102: Magnified free surface profile for various fluids (Q=5.678 x 10-7 m3/s). Axial Coordinate [m] Radial Coordinate [ m ]

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91 5.2.6 Pressure Drop From Tables 9 to 10, it can be seen th at FC-77 has the largest pressure drop either calculated using Bernoulli’s equation or obtaining results from FIDAP. Also, the pressure drop of Methanol is the lowest among all working fluids. The percentage difference between the calculated pressure drops and those from the simulations are around 45 to 50 %. Refrigerants Calculated Pressure Drop [N/m2] FIDAP Pressure Drop [N/m2] Percentage Difference [%] FC-72 1.60 x 105 1.09 x 105 46.79 FC-77 1.73 x 105 1.20 x 105 44.17 FC-87 1.55 x 105 1.04 x 105 49.04 Methanol 7.63 x 104 5.26 x 104 45.06 Refrigerants Calculated Pressure Drop [N/m2] FIDAP Pressure Drop [N/m2] Percentage Difference [%] FC-72 2.64 x 105 1.78 x 105 48.31 FC-77 2.85 x 105 1.96 x 105 45.41 FC-87 2.56 x 105 1.71 x 105 49.71 Methanol 1.25 x 105 8.60 x 104 45.35 Table 9: Comparison of the working fluids pressure drop calculated using Bernoulli’s equation and FIDAP simulation (Q= 4.416 x 10-7 m3/s). Table 10: Comparison of the workin g fluids pressure drop calculated usin g Bernoulli’s equation and FIDAP simulation (Q= 5.678 x 10-7 m3/s).

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92 5.2.7 Cavitation Cavitation happens when the liquid pressure falls below the saturation pressure for that particular fluid. The fluid evaporates at the boundary surface, and the tiny bubbles becomes a thin gas layer. It may eventually erode and destroy the system, or prevent the heat conduction pr ocess across the boundary surface. Table 11 is the quantitative explanation to show whether the refrigerant creates cavitation at flow rate either 4.416 x 10-7 or 5.678 x 10-7 m3/s in the nozzle. FC-72 and methanol produced cavitation when the flow rate was 4.416 x 10-7 m3/s. Next, there was a cavitation for FC-87 in both flow ra tes. On the other hand, FC-77 never produced cavitation in both flow rate trials. Saturation Pressure Reynolds Number Minimum Pressure Pressure Difference Cavitation Number Psat Re Pmin Pmin Psat Ca Refrigerants [Pa] [non-dim] [Pa] [Pa] [non-dim] 5904 21800 -9100 -0.1339 FC-72 30900 7591 37700 6800 0.0606 2811 18800 13180 0.1830 FC-77 5620 3615 34400 28780 0.2420 8093 22300 -58800 -0.8915 FC-87 81100 10405 38000 -43100 -0.3957 3212 8710 -1290 -0.0406 Methanol 10000 4130 15500 5500 0.1048 Table 11: Cavitation number of various refri g erants at different Re y nolds numbers.

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93 CHAPTER 6 COMPARISON OF NOZZLE DESIGNS In this analysis of spray cooling, a comparison of the cone angle and free surface height has also been completed between our nozzle design and the design in Figure 103. The nozzle below with the out er slot radius, R2 that is 4.43 x 10-4 m. This outer slot radius is closed to the radial location of inlets (4.50 x 10-4 m) at the top of 3D mixing chamber. Both of the flow rates (4.416 x 10-7 and 5.678 x 10-7 m3/s) are used at this section. From the results in Table 11, the nozzle in Figure 103 produces a larger cone angle and higher free surface than my design. R1 R2 R3 0.000743 m 0.00107 m 0.00015 m L 0.000125 m R(r) N ozzle Swirl Chamber Center Inlet Jet Outer Inlet Swirl Jets Swirl Jet Insert Disc Flow Inlet Flow Exit Orifice Spray Free Surface Envelope Lf Z r Figure 103: Schematic of the nozzle geometry with outer slot radius 4.43 x 10-4 m.

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94 1.21E-04 1.22E-04 1.23E-04 1.24E-04 1.25E-04 1.26E-04 1.27E-04 1.28E-04 1.20E-031.40E-031.60E-031.80E-03 r=4.43E-04m (w/o chamber) r=4.50E-04m (w/chamber) 1.21E-04 1.22E-04 1.23E-04 1.24E-04 1.25E-04 1.26E-04 1.27E-04 1.28E-04 1.20E-031.40E-031.60E-031.80E-03 r=4.43E-04m (w/o chamber) r =4.50E-04m (w/chamber) Axial Coordinate [m] Figure 104: Magnified free surface profiles comparison for FC-72 with two different nozzle designs (Q=4.416 x 10-7 m3/s). Radial Coordinate [ m ] Figure 105: Magnified free surface profiles comparison for FC-87 with two different nozzle designs (Q=4.416 x 10-7 m3/s). Axial Coordinate [m] Radial Coordinate [ m ]

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95 1.21E-04 1.22E-04 1.23E-04 1.24E-04 1.25E-04 1.26E-04 1.27E-04 1.20E-031.40E-031.60E-031.80E-03 r=4.43E-04m (w/o chamber) r=4.50E-04m (w/chamber) 1.21E-04 1.22E-04 1.23E-04 1.24E-04 1.25E-04 1.26E-04 1.27E-04 1.28E-04 1.20E-031.40E-031.60E-031.80E-03 r=4.43E-04m (w/o chamber) r=4.50E-04m (w/chamber) Axial Coordinate [m] Radial Coordinate [ m ] Figure 106: Magnified free surface profile s comparison for Methanol with two different nozzle designs (Q=4.416 x 10-7 m3/s). Axial Coordinate [m] Figure 107: Magnified free surface profiles comparison for FC-72 with two different nozzle designs (Q=5.678 x 10-7 m3/s). Radial Coordinate [ m ]

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96 1.21E-04 1.22E-04 1.23E-04 1.24E-04 1.25E-04 1.26E-04 1.27E-04 1.20E-031.40E-031.60E-031.80E-03 r=4.43E-04m (w/o chamber) r=4.50E-04m (w/chamber) Outer Slot Location R2 Cone Angle [degrees] Free Surface Height [10-4 m] [m] Refrigerants 4.416 x 10-7 m3/s 5.678 x 10-7 m3/s 4.416 x 10-7 m3/s 5.678 x 10-7 m3/s FC-72 4.194 4.194 1.268 1.272 FC-87 4.194 -1.274 -4.43 x 10-4 Methanol 3.814 4.764 1.261 1.265 Figure 108: Magnified free surface profile s comparison for Methanol with two different nozzle designs (Q=5.678 x 10-7 m3/s). Axial Coordinate [m] Radial Coordinate [ m ] Table 12: Cone angle and free surf ace height for each working fl uid at various flow rates by the nozzle with outer slot radius 4.43 x 10-4 m.

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97 CHAPTER 7 CONCLUSIONS AND RECOMMENDATIONS Based on the 3D and 2D simulations, the conclusion can be drawn as the following: 1. During the increase of volumetric flow rate, the velocities in radial, circumferential, and axial directions inside the entire system are increased. 2. The fluid pressure decreases gradually from the inlets to the nozzle outlet. 3. The fluid flowing profiles get stabilized as the fluid approaches to the bottom of chamber. 4. Disorder, efficient mixing, and vorticity can be obviously seen in the chamber and nozzle, as the flow is turbulent. 5. According to the velocity plot inside the chamber, clockwise spinning and eddy circulation of fluid can be found in the mixing chamber. 6. Cone angle and free surface height increase when the volumetric flow rates of FC-72, FC-77, FC-87, and Methanol increase. 7. Among all working fluid in this analysis, FC-87 produces the highest free surface height in both flow rates, while FC-77 has the lowest. 8. Calculated pressure drop is reasonably higher than the pressure drop found by computer simulation because Bernoulli’s equation, which is for ideal flow, ignores the effect created by shear and viscosity of the fluid.

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98 9. In the comparison with our nozzle design, the nozzle without mixing chamber produces larger cone angle and free surface height. 10. The results may be improved by increasing the amount of element in the mesh. 11. The mesh quality should be examined and improved. 12. More data may be obtained at the outlet of mixing chamber for the computation of averaged radial, circumferential, and axial velocities. 13. More volumetric flow rate may be applied to the simulation.

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99 REFERENCES Burmeister, L.C., Convective Heat Transfer Wiley, New York, 1993. Ciofalo, M., DiPiazza, I., Brucato, V., “I nvestigation of Cooling of Hot Walls by Liquid Water Sprays,” International Journal of Heat and Mass Transfer Vol. 42, No. 7, 1999, pp. 1157-1175. Datta, A., and Som, S.K., “Numerical Predic tion of Air Core Diameter Coefficient of Discharge and Spray Cone Angle of a Swirl Spray Pressure Nozzle,” International Journal of Heat and Fluid Flow Vol. 21, No. 4, 2000, pp. 412-419. Dumouchel, C., Blook, M. I. G., Dimbro wski, N., Ingham, D. B., and Ledoux, M., “Viscous Flow in a Swirl Atomizer,” Chemical Engineering Science Vol. 48, No. 1, 1993, pp. 81-87. Gavaises, M., Arcoumanis, C., “Modeling of Sprays from High-Pressure Swirl Atomizers,” International Journal of Engine Research Vol. 2, No. 2, 2001, pp. 95-117. Guarino, J.R., Manno, V.P., “Characteri zation of Laminar Jet Impingement Cooling in Portable Computer Applications,” IEEE Transactions on Components and Packaging Technologies Vol. 25, No. 3, September 2002. Fabbri, M., Jiang, S., and Dhir, V.K., “E xperimental Investigation of Single Phase Micro Jets Impingement Cooling for Electronic Applications,” 2003 ASME Summer Conference Paper pp. 1,4, and 7. Jeng, S. M., Jog, M. A., and Benjamin M. A., “Computation and Experimental Study of Liquid Sheet Emanating from Simplex Fuel Nozzle,” AIAA Journal Vol. 36, No. 2, 1998, pp. 201-207. Miller, P.C.H., and Ellis, M.C., “Eff ects of Formulation of Spray Nozzle Performance for Applications from Ground-Based Boom Sprayers,” Crop Protection Vol. 19, No. 8-10, 2000, pp. 609-615. Rothe, P.H., and Block, J.A., “Aer odynamic Behavior of Liquid Sprays,” International Journal of Multiphase Flow Vol. 3, No. 3, 1977, pp. 263-272.

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100 Sakman, A. T., Jog, M. A., Jeng, S. M., and Benjamin, M. A., “Parametric Study of Simplex Fuel Nozzle Internal Flow and Performance,” AIAA Journal Vol. 38, No. 7, 2000, pp. 1214-1218. Som, S.K., and Biswas, G., “Dispers ion of Spray from Swirl Nozzles,” Chemical Engineering and Processing Vol. 20, No. 4, 1986, pp. 191-200. Wang, E.N., Zhang, L., Jiang, L., Koo, J.M., Goodson, K.E., and Kenny, T.W.,” Micromachined Jet Arrays for Liquid Impingement Cooling of VLSI Chips ,” Mechanical Engineering, Stanford University, 2002. White, Frank M. Fluid Mechanics: Fourth Edition Boston, McGraw-Hill, 1999. Wu, S., Mai, J., Tai, Y.C., and Ho, C.M.,” Micro Heat Exchanger by Using MEMS Impinging Jets ,” Electrical Engineering, California Institute of Technology, 1999.

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101 APPENDICES

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102 Appendix I – Fluid Properties FC-77 Density: 1780 kg/m3 Viscosity: 0.001424 kg/m s Surface Tension: 0.015 N/m FC-72 Density: 1680 kg/m3 Viscosity: 0.00064 kg/m s Surface Tension: 0.010 N/m FC-87 Density: 1630 kg/m3 Viscosity: 0.000453 kg/m s Surface Tension: 0.0095 N/m Methanol Density: 785.5 kg/m3 Viscosity: 0.00055 kg/m s Surface Tension: 0.0222 N/m

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103 Appendix II: FIJOUR File for the 3D Mixing Chamber UTILITY( SELE = 0.01 ) UTILITY( TOLE = 1e-06 ) // POINT( ADD, COOR, X = 0, Y = 0, Z = 0.15 ) POINT( ADD, COOR, X = 0, Y = 0, Z = 0.1 ) POINT( ADD, COOR, X = 0, Y = 0, Z = 0 ) POINT( ADD, COOR, X = 0, Y = 0, Z = -0.1 ) // // Surface on each Level // POINT( ADD, COOR, X = 0.08, Y = 0.08, Z = 0.15 ) POINT( ADD, COOR, X = 0.08, Y = -0.08, Z = 0.15 ) POINT( ADD, COOR, X = -0.08, Y = 0.08, Z = 0.15 ) POINT( ADD, COOR, X = -0.08, Y = -0.08, Z = 0.15 ) // POINT( ADD, COOR, X = 0.08, Y = 0.08, Z = 0 ) POINT( ADD, COOR, X = 0.08, Y = -0.08, Z = 0 ) POINT( ADD, COOR, X = -0.08, Y = 0.08, Z = 0 ) POINT( ADD, COOR, X = -0.08, Y = -0.08, Z = 0 ) // POINT( ADD, COOR, X = 0.08, Y = 0.08, Z = 0.1 ) POINT( ADD, COOR, X = 0.08, Y = -0.08, Z = 0.1 ) POINT( ADD, COOR, X = -0.08, Y = 0.08, Z = 0.1 ) POINT( ADD, COOR, X = -0.08, Y = -0.08, Z = 0.1 ) // POINT( ADD, COOR, X = 0.08, Y = 0.08, Z = -0.1 ) POINT( ADD, COOR, X = 0.08, Y = -0.08, Z = -0.1 ) POINT( ADD, COOR, X = -0.08, Y = 0.08, Z = -0.1 ) POINT( ADD, COOR, X = -0.08, Y = -0.08, Z = -0.1 ) // // (Level 0) // // Outer Edge (Level 0) // POINT( ADD, COOR, X = -0.0743, Y = 0, Z = 0 ) POINT( ADD, COOR, X = 0.0743, Y = 0, Z = 0 ) POINT( ADD, COOR, X = 0, Y = 0.0743, Z = 0 ) POINT( ADD, COOR, X = 0, Y = -0.0743, Z = 0 ) // // Center Inlet r = 0.01 cm // POINT( ADD, COOR, X = -0.01, Y = 0, Z = 0 ) POINT( ADD, COOR, X = 0, Y = 0.01, Z = 0 ) POINT( ADD, COOR, X = 0.01, Y = 0, Z = 0 ) POINT( ADD, COOR, X = 0, Y = -0.01, Z = 0 )

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104 Appendix II (Continued) // Inclined Inlet A0 POINT( ADD, COOR, X = 0.045, Y = 0, Z = 0 ) // POINT( ADD, COOR, X = 0.035, Y = 0, Z = 0 ) POINT( ADD, COOR, X = 0.045, Y = 0.01, Z = 0 ) POINT( ADD, COOR, X = 0.055, Y = 0, Z = 0 ) POINT( ADD, COOR, X = 0.045, Y = -0.01, Z = 0 ) // // Inclined Inlet B0 // POINT( ADD, COOR, X = -0.0225, Y = 0.03897, Z = 0 ) // POINT( ADD, COOR, X = -0.0325, Y = 0.03897, Z = 0 ) POINT( ADD, COOR, X = -0.0225, Y = 0.04897, Z = 0 ) POINT( ADD, COOR, X = -0.0125, Y = 0.03897, Z = 0 ) POINT( ADD, COOR, X = -0.0225, Y = 0.02897, Z = 0 ) // // Inclined Inlet C0 // POINT( ADD, COOR, X = -0.0225, Y = -0.03897, Z = 0 ) // POINT( ADD, COOR, X = -0.0325, Y = -0.03897, Z = 0 ) POINT( ADD, COOR, X = -0.0225, Y = -0.02897, Z = 0 ) POINT( ADD, COOR, X = -0.0125, Y = -0.03897, Z = 0 ) POINT( ADD, COOR, X = -0.0225, Y = -0.04897, Z = 0 ) // // Inlet Top (Level 0.15) // // Inlet A1 -0.045 0 0.15 POINT( ADD, COOR, X = -0.045, Y = 0, Z = 0.15 ) // POINT( ADD, COOR, X = -0.055, Y = 0, Z = 0.15 ) POINT( ADD, COOR, X = -0.045, Y = 0.01, Z = 0.15 ) POINT( ADD, COOR, X = -0.035, Y = 0, Z = 0.15 ) POINT( ADD, COOR, X = -0.045, Y = -0.01, Z = 0.15 ) // // Inlet B1 0.0225 0.03897 0.15 // POINT( ADD, COOR, X = 0.0225, Y = 0.03897, Z = 0.15 ) // POINT( ADD, COOR, X = 0.0125, Y = 0.03897, Z = 0.15 ) POINT( ADD, COOR, X = 0.0225, Y = 0.04897, Z = 0.15 ) POINT( ADD, COOR, X = 0.0325, Y = 0.03897, Z = 0.15 ) POINT( ADD, COOR, X = 0.0225, Y = 0.02897, Z = 0.15 ) // // Inlet C1 0.0225 -0.03897 0.15 // POINT( ADD, COOR, X = 0.0225, Y = -0.03897, Z = 0.15 ) // POINT( ADD, COOR, X = 0.0125, Y = -0.03897, Z = 0.15 ) POINT( ADD, COOR, X = 0.0225, Y = -0.02897, Z = 0.15 ) POINT( ADD, COOR, X = 0.0325, Y = -0.03897, Z = 0.15 ) POINT( ADD, COOR, X = 0.0225, Y = -0.04897, Z = 0.15 )

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105 Appendix II (Continued) // Center Inlet POINT( ADD, COOR, X = -0.01, Y = 0, Z = 0.15 ) POINT( ADD, COOR, X = 0, Y = 0.01, Z = 0.15 ) POINT( ADD, COOR, X = 0.01, Y = 0, Z = 0.15 ) POINT( ADD, COOR, X = 0, Y = -0.01, Z = 0.15 ) // // // Inlet (Level 0.1) // // Inlet A1 -0.045 0 0.1 POINT( ADD, COOR, X = -0.045, Y = 0, Z = 0.1 ) // POINT( ADD, COOR, X = -0.055, Y = 0, Z = 0.1 ) POINT( ADD, COOR, X = -0.045, Y = 0.01, Z = 0.1 ) POINT( ADD, COOR, X = -0.035, Y = 0, Z = 0.1 ) POINT( ADD, COOR, X = -0.045, Y = -0.01, Z = 0.1 ) // // Inlet B1 0.0225 0.03897 0.1 // POINT( ADD, COOR, X = 0.0225, Y = 0.03897, Z = 0.1 ) // POINT( ADD, COOR, X = 0.0125, Y = 0.03897, Z = 0.1 ) POINT( ADD, COOR, X = 0.0225, Y = 0.04897, Z = 0.1 ) POINT( ADD, COOR, X = 0.0325, Y = 0.03897, Z = 0.1 ) POINT( ADD, COOR, X = 0.0225, Y = 0.02897, Z = 0.1 ) // // Inlet C1 0.0225 -0.03897 0.1 // POINT( ADD, COOR, X = 0.0225, Y = -0.03897, Z = 0.1 ) // POINT( ADD, COOR, X = 0.0125, Y = -0.03897, Z = 0.1 ) POINT( ADD, COOR, X = 0.0225, Y = -0.02897, Z = 0.1 ) POINT( ADD, COOR, X = 0.0325, Y = -0.03897, Z = 0.1 ) POINT( ADD, COOR, X = 0.0225, Y = -0.04897, Z = 0.1 ) // // Center Inlet // POINT( ADD, COOR, X = -0.01, Y = 0, Z = 0.1 ) POINT( ADD, COOR, X = 0, Y = 0.01, Z = 0.1 ) POINT( ADD, COOR, X = 0.01, Y = 0, Z = 0.1 ) POINT( ADD, COOR, X = 0, Y = -0.01, Z = 0.1 ) // // (Level -0.1) // // Outer Edge (Level -0.1) // POINT( ADD, COOR, X = -0.0743, Y = 0, Z = -0.1 ) POINT( ADD, COOR, X = 0.0743, Y = 0, Z = -0.1 ) POINT( ADD, COOR, X = 0, Y = 0.0743, Z = -0.1 ) POINT( ADD, COOR, X = 0, Y = -0.0743, Z = -0.1 )

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106 Appendix II (Continued) // Center Inlet r = 0.01 cm // POINT( ADD, COOR, X = -0.01, Y = 0, Z = -0.1 ) POINT( ADD, COOR, X = 0, Y = 0.01, Z = -0.1 ) POINT( ADD, COOR, X = 0.01, Y = 0, Z = -0.1 ) POINT( ADD, COOR, X = 0, Y = -0.01, Z = -0.1 ) // // Inclined Inlet A2 // POINT( ADD, COOR, X = 0.045, Y = 0, Z = -0.1 ) // POINT( ADD, COOR, X = 0.035, Y = 0, Z = -0.1 ) POINT( ADD, COOR, X = 0.045, Y = 0.01, Z = -0.1 ) POINT( ADD, COOR, X = 0.055, Y = 0, Z = -0.1 ) POINT( ADD, COOR, X = 0.045, Y = -0.01, Z = -0.1 ) // // Inclined Inlet B2 // POINT( ADD, COOR, X = -0.0225, Y = 0.03897, Z = -0.1 ) // POINT( ADD, COOR, X = -0.0325, Y = 0.03897, Z = -0.1 ) POINT( ADD, COOR, X = -0.0225, Y = 0.04897, Z = -0.1 ) POINT( ADD, COOR, X = -0.0125, Y = 0.03897, Z = -0.1 ) POINT( ADD, COOR, X = -0.0225, Y = 0.02897, Z = -0.1 ) // // Inclined Inlet C2 // POINT( ADD, COOR, X = -0.0225, Y = -0.03897, Z = -0.1 ) // POINT( ADD, COOR, X = -0.0325, Y = -0.03897, Z = -0.1 ) POINT( ADD, COOR, X = -0.0225, Y = -0.02897, Z = -0.1 ) POINT( ADD, COOR, X = -0.0125, Y = -0.03897, Z = -0.1 ) POINT( ADD, COOR, X = -0.0225, Y = -0.04897, Z = -0.1 )

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107 Appendix III: FIPREP File for the 3D Mixing Chamber (Sample:FC-72) FIPREP( ) // // DENSITY OF FC-72 DENSITY( ADD, SET = "fc-72", CONS = 1.68 ) // VISCOSITY OF FC-72 VISCOSITY( ADD, SET = "fc-72", CONS = 0.0064, MIXL ) // SURFACE TENSION OF FC-72 SURFACETENSION( ADD, SET = "fc-72", CONS = 10 ) // //GRAVITY BODYFORCE( ADD, CONS, FX = 0, FY = 0, FZ = -981 ) // DATAPRINT( ADD, CONT ) EXECUTION( ADD, NEWJ ) PRESSURE( ADD, MIXE = 1e-08, DISC ) PRINTOUT( ADD, NONE ) PROBLEM( ADD, 3-D, INCO, STEA, TURB, NONL, NEWT, MOME, ISOT, FIXE, SING ) SOLUTION( ADD, SEGR = 2000, KINE = 25, VELC = 0.001, CGS = 2000, CR = 2000, NCGC = 1e-06, SCGC = 1e-06, SCHA = 0 ) RENUMBER( ADD, PROF ) EDDYVISCOSITY( ADD, SPEZ ) OPTIONS( ADD, UPWI ) UPWINDING( ADD, STRE ) RELAXATION( HYBR ) 0.3, 0.3, 0.3, 0.5, 0, 0, 0, 0 // ENTITY( ADD, NAME = "fluid-01", FLUI, PROP = "fc-72" ) ENTITY( ADD, NAME = "fluid-02", FLUI, PROP = "fc-72" ) ENTITY( ADD, NAME = "fluid-03", FLUI, PROP = "fc-72" ) ENTITY( ADD, NAME = "fluid-04", FLUI, PROP = "fc-72" ) // ENTITY( ADD, NAME = "wall-c-01", WALL ) ENTITY( ADD, NAME = "wall-c-02", WALL ) ENTITY( ADD, NAME = "wall-c-03", WALL ) ENTITY( ADD, NAME = "wall-c-04", WALL ) ENTITY( ADD, NAME = "wall-c-05", WALL ) ENTITY( ADD, NAME = "wall-c-06", WALL ) ENTITY( ADD, NAME = "wall-c-07", WALL ) ENTITY( ADD, NAME = "wall-c-08", WALL ) // ENTITY( ADD, NAME = "wall-01-01", WALL ) ENTITY( ADD, NAME = "wall-01-02", WALL ) ENTITY( ADD, NAME = "wall-01-03", WALL ) ENTITY( ADD, NAME = "wall-01-04", WALL ) ENTITY( ADD, NAME = "wall-01-05", WALL ) ENTITY( ADD, NAME = "wall-01-06", WALL ) ENTITY( ADD, NAME = "wall-01-07", WALL ) ENTITY( ADD, NAME = "wall-01-08", WALL ) //

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108 Appendix III (Continued) ENTITY( ADD, NAME = "wall-02-01", WALL ) ENTITY( ADD, NAME = "wall-02-02", WALL ) ENTITY( ADD, NAME = "wall-02-03", WALL ) ENTITY( ADD, NAME = "wall-02-04", WALL ) ENTITY( ADD, NAME = "wall-02-05", WALL ) ENTITY( ADD, NAME = "wall-02-06", WALL ) ENTITY( ADD, NAME = "wall-02-07", WALL ) ENTITY( ADD, NAME = "wall-02-08", WALL ) // ENTITY( ADD, NAME = "wall-03-01", WALL ) ENTITY( ADD, NAME = "wall-03-02", WALL ) ENTITY( ADD, NAME = "wall-03-03", WALL ) ENTITY( ADD, NAME = "wall-03-04", WALL ) ENTITY( ADD, NAME = "wall-03-05", WALL ) ENTITY( ADD, NAME = "wall-03-06", WALL ) ENTITY( ADD, NAME = "wall-03-07", WALL ) ENTITY( ADD, NAME = "wall-03-08", WALL ) // ENTITY( ADD, NAME = "inlet-c", PLOT ) ENTITY( ADD, NAME = "inlet-01", PLOT ) ENTITY( ADD, NAME = "inlet-02", PLOT ) ENTITY( ADD, NAME = "inlet-03", PLOT ) // ENTITY( ADD, NAME = "inlet-top-c", PLOT, ATTA = "fluid-02", NATT = "fluid-01" ) ENTITY( ADD, NAME = "inlet-top-01", PLOT, ATTA = "fluid-02", NATT = "fluid-01" ) ENTITY( ADD, NAME = "inlet-top-02", PLOT, ATTA = "fluid-02", NATT = "fluid-01" ) ENTITY( ADD, NAME = "inlet-top-03", PLOT, ATTA = "fluid-02", NATT = "fluid-01" ) // ENTITY( ADD, NAME = "top-c", PLOT, ATTA = "fluid-03", NATT = "fluid04" ) ENTITY( ADD, NAME = "top-01", PLOT, ATTA = "fluid-03", NATT = "fluid-04" ) ENTITY( ADD, NAME = "top-02", PLOT, ATTA = "fluid-03", NATT = "fluid-04" ) ENTITY( ADD, NAME = "top-03", PLOT, ATTA = "fluid-03", NATT = "fluid-04" ) // ENTITY( ADD, NAME = "outlet-c", PLOT, ATTA = "fluid-03", NATT = "fluid-04" ) ENTITY( ADD, NAME = "outlet-01", PLOT, ATTA = "fluid-03", NATT = "fluid-04" ) ENTITY( ADD, NAME = "outlet-02", PLOT, ATTA = "fluid-03", NATT = "fluid-04" ) ENTITY( ADD, NAME = "outlet-03", PLOT, ATTA = "fluid-03", NATT = "fluid-04" ) ENTITY( ADD, NAME = "chamber-outlet", PLOT, ATTA = "fluid-04", NATT = "fluid-03" ) // ENTITY( ADD, NAME = "chamber-wall", WALL )

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109 Appendix III (Continued) ENTITY( ADD, NAME = "chamber-top", PLOT, ATTA = "fluid-04", NATT = "fluid-03" ) ENTITY( ADD, NAME = "sc-01", PLOT, ATTA = "fluid-03", NATT = "fluid04" ) ENTITY( ADD, NAME = "sc-02", PLOT, ATTA = "fluid-03", NATT = "fluid04" ) ENTITY( ADD, NAME = "sc-03", PLOT, ATTA = "fluid-03", NATT = "fluid04" ) ENTITY( ADD, NAME = "sc-04", PLOT, ATTA = "fluid-03", NATT = "fluid04" ) // ENTITY( ADD, NAME = "s01-01", PLOT, ATTA = "fluid-03", NATT = "fluid-04" ) ENTITY( ADD, NAME = "s01-02", PLOT, ATTA = "fluid-03", NATT = "fluid-04" ) ENTITY( ADD, NAME = "s01-03", PLOT, ATTA = "fluid-03", NATT = "fluid-04" ) ENTITY( ADD, NAME = "s01-04", PLOT, ATTA = "fluid-03", NATT = "fluid-04" ) // ENTITY( ADD, NAME = "s02-01", PLOT, ATTA = "fluid-03", NATT = "fluid-04" ) ENTITY( ADD, NAME = "s02-02", PLOT, ATTA = "fluid-03", NATT = "fluid-04" ) ENTITY( ADD, NAME = "s02-03", PLOT, ATTA = "fluid-03", NATT = "fluid-04" ) ENTITY( ADD, NAME = "s02-04", PLOT, ATTA = "fluid-03", NATT = "fluid-04" ) // ENTITY( ADD, NAME = "s03-01", PLOT, ATTA = "fluid-03", NATT = "fluid-04" ) ENTITY( ADD, NAME = "s03-02", PLOT, ATTA = "fluid-03", NATT = "fluid-04" ) ENTITY( ADD, NAME = "s03-03", PLOT, ATTA = "fluid-03", NATT = "fluid-04" ) ENTITY( ADD, NAME = "s03-04", PLOT, ATTA = "fluid-03", NATT = "fluid-04" ) // //INLET VELOCITY IS –351, WHEN Q = 4.416 X 10-7 m3/s BCNODE( ADD, UZ, ENTI = "inlet-c", CONS = -351 ) BCNODE( ADD, UZ, ENTI = "inlet-01", CONS = -351 ) BCNODE( ADD, UZ, ENTI = "inlet-02", CONS = -351 ) BCNODE( ADD, UZ, ENTI = "inlet-03", CONS = -351 ) // //**INLET VELOCITY IS –452, WHEN Q = 5.678 X 10-7 m3/s** // BCNODE( ADD, VELO, ENTI = "wall-c-01", ZERO, X, Y, Z ) BCNODE( ADD, VELO, ENTI = "wall-c-02", ZERO, X, Y, Z ) BCNODE( ADD, VELO, ENTI = "wall-c-03", ZERO, X, Y, Z ) BCNODE( ADD, VELO, ENTI = "wall-c-04", ZERO, X, Y, Z ) BCNODE( ADD, VELO, ENTI = "wall-c-05", ZERO, X, Y, Z ) BCNODE( ADD, VELO, ENTI = "wall-c-06", ZERO, X, Y, Z ) BCNODE( ADD, VELO, ENTI = "wall-c-07", ZERO, X, Y, Z ) BCNODE( ADD, VELO, ENTI = "wall-c-08", ZERO, X, Y, Z )

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110 Appendix III (Continued) BCNODE( ADD, VELO, ENTI = "wall-01-01", ZERO, X, Y, Z ) BCNODE( ADD, VELO, ENTI = "wall-01-02", ZERO, X, Y, Z ) BCNODE( ADD, VELO, ENTI = "wall-01-03", ZERO, X, Y, Z ) BCNODE( ADD, VELO, ENTI = "wall-01-04", ZERO, X, Y, Z ) BCNODE( ADD, VELO, ENTI = "wall-01-05", ZERO, X, Y, Z ) BCNODE( ADD, VELO, ENTI = "wall-01-06", ZERO, X, Y, Z ) BCNODE( ADD, VELO, ENTI = "wall-01-07", ZERO, X, Y, Z ) BCNODE( ADD, VELO, ENTI = "wall-01-08", ZERO, X, Y, Z ) // BCNODE( ADD, VELO, ENTI = "wall-02-01", ZERO, X, Y, Z ) BCNODE( ADD, VELO, ENTI = "wall-02-02", ZERO, X, Y, Z ) BCNODE( ADD, VELO, ENTI = "wall-02-03", ZERO, X, Y, Z ) BCNODE( ADD, VELO, ENTI = "wall-02-04", ZERO, X, Y, Z ) BCNODE( ADD, VELO, ENTI = "wall-02-05", ZERO, X, Y, Z ) BCNODE( ADD, VELO, ENTI = "wall-02-06", ZERO, X, Y, Z ) BCNODE( ADD, VELO, ENTI = "wall-02-07", ZERO, X, Y, Z ) BCNODE( ADD, VELO, ENTI = "wall-02-08", ZERO, X, Y, Z ) // BCNODE( ADD, VELO, ENTI = "wall-03-01", ZERO, X, Y, Z ) BCNODE( ADD, VELO, ENTI = "wall-03-02", ZERO, X, Y, Z ) BCNODE( ADD, VELO, ENTI = "wall-03-03", ZERO, X, Y, Z ) BCNODE( ADD, VELO, ENTI = "wall-03-04", ZERO, X, Y, Z ) BCNODE( ADD, VELO, ENTI = "wall-03-05", ZERO, X, Y, Z ) BCNODE( ADD, VELO, ENTI = "wall-03-06", ZERO, X, Y, Z ) BCNODE( ADD, VELO, ENTI = "wall-03-07", ZERO, X, Y, Z ) BCNODE( ADD, VELO, ENTI = "wall-03-08", ZERO, X, Y, Z ) // BCNODE( ADD, VELO, ENTI = "chamber-wall", ZERO, X, Y, Z ) BCNODE( ADD, VELO, ENTI = "chamber-top", ZERO, X, Y, Z ) // END( )

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111 Appendix IV: FIJOUR File for the Small Nozzle with Free Surface (4.416 x 10-7 and 5.678 x 10-7 m3/s) FI-GEN( ELEM = 1, POIN = 1, CURV = 1, SURF = 1, NODE = 0, MEDG = 1, MLOO = 1, MFAC = 1, BEDG = 1, SPAV = 1, MSHE = 1, MSOL = 1, COOR = 1, TOLE = 1e-07 ) WINDOW(CHANGE= 1, MATRIX ) 1.000000 0.000000 0.000000 0.000000 0.000000 1.000000 0.000000 0.000000 0.000000 0.000000 1.000000 0.000000 0.000000 0.000000 0.000000 1.000000 -10.00000 10.00000 -7.50000 7.50000 -7.50000 7.50000 WINDOW( CHAN = 1, MATR ) 1, 0, 0, 0 0, 1, 0, 0 0, 0, 1, 0 0, 0, 0, 1 -10, 10, -7.5, 7.5, -7.5, 7.5 UTILITY( SELE = 0.01 ) POINT( ADD, COOR, X = 0, Y = 0, Z = 0 ) POINT( ADD, COOR, X = 0.107, Y = 0, Z = 0 ) POINT( ADD, COOR, X = 0.122, Y = 0, Z = 0 ) POINT( ADD, COOR, X = 0.17, Y = 0, Z = 0 ) POINT( ADD, COOR, X = 0.17, Y = 0.0125, Z = 0 ) POINT( ADD, COOR, X = 0.122, Y = 0.0125, Z = 0 ) POINT( ADD, COOR, X = 0.107, Y = 0.0125, Z = 0 ) POINT( ADD, COOR, X = 0, Y = 0.0743, Z = 0 ) POINT( ADD, COOR, X = -0.02, Y = 0.0743, Z = 0 ) POINT( ADD, COOR, X = -0.02, Y = 0, Z = 0 ) WINDOW( CHAN = 1, MATR ) 1, 0, 0, 0 0, 1, 0, 0 0, 0, 1, 0 0, 0, 0, 1 -0.02475, 0.17475, -0.03766, 0.11196, -0.1995, 0.1995 45, 45, 45, 45 POINT( ADD, COOR, X = 0.17, Y = 0.0743, Z = 0 ) POINT( SELE, LOCA, WIND = 1 ) 0.0239163, 0.253114 / ID = 10 / ID = 10 0.0269058, 0.743398 / ID = 9 / ID = 9 CURVE( ADD, ORDE = 1 ) POINT( SELE, LOCA, WIND = 1 ) 0.0254111, 0.747384 / ID = 9 / ID = 9 0.124066, 0.75137 / ID = 8 / ID = 8 CURVE( ADD, ORDE = 1 ) POINT( SELE, LOCA, WIND = 1 )

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112 Appendix IV (Continued) 0.125561, 0.745391 / ID = 8 / ID = 8 0.662182, 0.334828 / ID = 7 / ID = 7 CURVE( ADD, ORDE = 1 ) POINT( SELE, LOCA, WIND = 1 ) 0.659193, 0.332835 / ID = 7 / ID = 7 0.736921, 0.336821 / ID = 6 / ID = 6 CURVE( ADD, ORDE = 1 ) POINT( SELE, LOCA, WIND = 1 ) 0.736921, 0.328849 / ID = 6 / ID = 6 0.982063, 0.334828 / ID = 5 / ID = 5 CURVE( ADD, ORDE = 1 ) POINT( SELE, LOCA, WIND = 1 ) 0.979073, 0.332835 / ID = 5 / ID = 5 0.974589, 0.249128 / ID = 4 / ID = 4 CURVE( ADD, ORDE = 1 ) POINT( SELE, LOCA, WIND = 1 ) 0.977578, 0.247135 / ID = 4 / ID = 4 0.738416, 0.251121 / ID = 3 / ID = 3 CURVE( ADD, ORDE = 1 ) POINT( SELE, LOCA, WIND = 1 ) 0.733931, 0.245142 / ID = 3 / ID = 3 0.659193, 0.245142 / ID = 2 / ID = 2 CURVE( ADD, ORDE = 1 ) POINT( SELE, LOCA, WIND = 1 ) 0.659193, 0.249128 / ID = 2 / ID = 2 0.124066, 0.249128 / ID = 1 / ID = 1

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113 Appendix IV (Continued) CURVE( ADD, ORDE = 1 ) POINT( SELE, LOCA, WIND = 1 ) 0.12855, 0.249128 / ID = 1 / ID = 1 0.0269058, 0.249128 / ID = 10 / ID = 10 CURVE( ADD, ORDE = 1 ) POINT( SELE, LOCA, WIND = 1 ) 0.125561, 0.251121 / ID = 1 / ID = 1 0.127055, 0.745391 / ID = 8 / ID = 8 CURVE( ADD, ORDE = 1 ) POINT( SELE, LOCA, WIND = 1 ) 0.660688, 0.247135 / ID = 2 / ID = 2 0.656203, 0.334828 / ID = 7 / ID = 7 CURVE( ADD, ORDE = 1 ) POINT( SELE, LOCA, WIND = 1 ) 0.735426, 0.255107 / ID = 3 / ID = 3 0.735426, 0.334828 / ID = 6 / ID = 6 CURVE( ADD, ORDE = 1 ) POINT( SELE, LOCA, WIND = 1 ) 0.0254111, 0.75137 / ID = 9 / ID = 9 0.977578, 0.753363 / ID = 11 / ID = 11 0.0269058, 0.251121 / ID = 10 / ID = 10 0.980568, 0.245142 / ID = 4 / ID = 4 SURFACE( ADD, POIN, ROWW = 2, NOAD ) CURVE( SELE, LOCA, WIND = 1 ) 0.0224215, 0.460389 / ID = 1 / ID = 1 MEDGE( ADD, SUCC, INTE = 30, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, LOCA, WIND = 1 ) 0.124066, 0.442451

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114 Appendix IV (Continued) / ID = 11 / ID = 11 MEDGE( ADD, SUCC, INTE = 30, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, LOCA, WIND = 1 ) 0.659193, 0.292975 / ID = 12 / ID = 12 MEDGE( ADD, LSTF, INTE = 30, RATI = 0.05, 2RAT = 0, PCEN = 0 ) WINDOW( CHAN = 1, MATR ) 1, 0, 0, 0 0, 1, 0, 0 0, 0, 1, 0 0, 0, 0, 1 0.09453, 0.1172, -0.00068, 0.01661, -0.1995, 0.1995 45, 45, 45, 45 WINDOW( CHAN = 1, MATR ) 1, 0, 0, 0 0, 1, 0, 0 0, 0, 1, 0 0, 0, 0, 1 0.10514, 0.10863, 0.01093, 0.01359, -0.1995, 0.1995 45, 45, 45, 45 WINDOW( CHAN = 1, MATR ) 1, 0, 0, 0 0, 1, 0, 0 0, 0, 1, 0 0, 0, 0, 1 -0.02475, 0.17475, -0.03766, 0.11196, -0.1995, 0.1995 45, 45, 45, 45 CURVE( SELE, LOCA, WIND = 1 ) 0.733931, 0.294968 / ID = 13 / ID = 13 MEDGE( ADD, LSTF, INTE = 30, RATI = 0.05, 2RAT = 0, PCEN = 0 ) CURVE( SELE, LOCA, WIND = 1 ) 0.971599, 0.288989 / ID = 6 / ID = 6 MEDGE( ADD, LSTF, INTE = 30, RATI = 0.05, 2RAT = 0, PCEN = 0 ) WINDOW( CHAN = 1, MATR ) 1, 0, 0, 0 0, 1, 0, 0 0, 0, 1, 0 0, 0, 0, 1 0.15686, 0.18161, -0.00307, 0.01572, -0.1995, 0.1995 45, 45, 45, 45 WINDOW( CHAN = 1, MATR ) 1, 0, 0, 0 0, 1, 0, 0 0, 0, 1, 0 0, 0, 0, 1 -0.02475, 0.17475, -0.03766, 0.11196, -0.1995, 0.1995 45, 45, 45, 45 WINDOW( CHAN = 1, MATR )

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115 Appendix IV (Continued) 1, 0, 0, 0 0, 1, 0, 0 0, 0, 1, 0 0, 0, 0, 1 0.1002, 0.1336, -0.00546, 0.01959, -0.1995, 0.1995 45, 45, 45, 45 WINDOW( CHAN = 1, MATR ) 1, 0, 0, 0 0, 1, 0, 0 0, 0, 1, 0 0, 0, 0, 1 -0.02475, 0.17475, -0.03766, 0.11196, -0.1995, 0.1995 45, 45, 45, 45 MEDGE( SELE, LOCA, WIND = 1 ) 0.977578, 0.292975 / ID = 5 / ID = 5 MEDGE( DELE ) CURVE( SELE, LOCA, WIND = 1 ) 0.974589, 0.296961 / ID = 6 / ID = 6 MEDGE( ADD, FRST, INTE = 30, RATI = 0.05, 2RAT = 0, PCEN = 0 ) WINDOW( CHAN = 1, MATR ) 1, 0, 0, 0 0, 1, 0, 0 0, 0, 1, 0 0, 0, 0, 1 0.16223, 0.17624, 0.00588, 0.01661, -0.1995, 0.1995 45, 45, 45, 45 WINDOW( CHAN = 1, MATR ) 1, 0, 0, 0 0, 1, 0, 0 0, 0, 1, 0 0, 0, 0, 1 -0.02475, 0.17475, -0.03766, 0.11196, -0.1995, 0.1995 45, 45, 45, 45 CURVE( SELE, LOCA, WIND = 1 ) 0.0612855, 0.75137 / ID = 2 / ID = 2 MEDGE( ADD, FRST, INTE = 20, RATI = 0.05, 2RAT = 0, PCEN = 0 ) MEDGE( SELE, LOCA, WIND = 1 ) 0.0792227, 0.753363 / ID = 6 / ID = 6 MEDGE( DELE ) CURVE( SELE, LOCA, WIND = 1 ) 0.0687593, 0.749377 / ID = 2 / ID = 2 MEDGE( ADD, SUCC, INTE = 20, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, LOCA, WIND = 1 ) 0.064275, 0.251121

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116 Appendix IV (Continued) / ID = 10 / ID = 10 MEDGE( ADD, SUCC, INTE = 20, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, LOCA, WIND = 1 ) 0.367713, 0.558047 / ID = 3 / ID = 3 MEDGE( ADD, SUCC, INTE = 107, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, LOCA, WIND = 1 ) 0.358744, 0.247135 / ID = 9 / ID = 9 MEDGE( ADD, SUCC, INTE = 107, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, LOCA, WIND = 1 ) 0.693572, 0.336821 / ID = 4 / ID = 4 MEDGE( ADD, SUCC, INTE = 15, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, LOCA, WIND = 1 ) 0.695067, 0.253114 / ID = 8 / ID = 8 MEDGE( ADD, SUCC, INTE = 15, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, LOCA, WIND = 1 ) 0.786248, 0.340807 / ID = 5 / ID = 5 MEDGE( ADD, FRST, INTE = 48, RATI = 0.05, 2RAT = 0.05, PCEN = 0 ) CURVE( SELE, LOCA, WIND = 1 ) 0.823617, 0.247135 / ID = 7 / ID = 7 MEDGE( ADD, FRST, INTE = 48, RATI = 0.05, 2RAT = 0.05, PCEN = 0 ) WINDOW( CHAN = 1, MATR ) 1, 0, 0, 0 0, 1, 0, 0 0, 0, 1, 0 0, 0, 0, 1 0.10736, 0.13926, -0.00456, 0.01959, -0.1995, 0.1995 45, 45, 45, 45 WINDOW( CHAN = 1, MATR ) 1, 0, 0, 0 0, 1, 0, 0 0, 0, 1, 0 0, 0, 0, 1 -0.02475, 0.17475, -0.03766, 0.11196, -0.1995, 0.1995 45, 45, 45, 45 WINDOW( CHAN = 1, MATR ) 1, 0, 0, 0 0, 1, 0, 0 0, 0, 1, 0 0, 0, 0, 1 0.15298, 0.18131, -0.00307, 0.0184, -0.1995, 0.1995 45, 45, 45, 45

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117 Appendix IV (Continued) WINDOW( CHAN = 1, MATR ) 1, 0, 0, 0 0, 1, 0, 0 0, 0, 1, 0 0, 0, 0, 1 -0.02475, 0.17475, -0.03766, 0.11196, -0.1995, 0.1995 45, 45, 45, 45 MEDGE( SELE, LOCA, WIND = 1 ) 0.0254111, 0.422521 / ID = 1 / ID = 1 ELEMENT( SETD, EDGE, NODE = 2 ) MEDGE( MESH, MAP, ENTI = "inlet" ) MEDGE( SELE, LOCA, WIND = 1 ) 0.0627803, 0.749377 / ID = 6 / ID = 6 MEDGE( MESH, MAP, ENTI = "wall" ) MEDGE( SELE, LOCA, WIND = 1 ) 0.245142, 0.657698 / ID = 8 / ID = 8 MEDGE( MESH, MAP, ENTI = "wall" ) MEDGE( SELE, LOCA, WIND = 1 ) 0.699552, 0.336821 / ID = 10 / ID = 10 MEDGE( MESH, MAP, ENTI = "wall" ) MEDGE( SELE, LOCA, WIND = 1 ) 0.853513, 0.334828 / ID = 12 / ID = 12 MEDGE( MESH, MAP, ENTI = "free" ) MEDGE( SELE, LOCA, WIND = 1 ) 0.974589, 0.290982 / ID = 5 / ID = 5 MEDGE( MESH, MAP, ENTI = "outlet" ) MEDGE( SELE, LOCA, WIND = 1 ) 0.0792227, 0.251121 / ID = 7 / ID = 7 MEDGE( MESH, MAP, ENTI = "axi-sym" ) MEDGE( SELE, LOCA, WIND = 1 ) 0.230194, 0.253114 / ID = 9 / ID = 9 MEDGE( MESH, MAP, ENTI = "axi-sym" ) MEDGE( SELE, LOCA, WIND = 1 ) 0.696562, 0.255107 / ID = 11 / ID = 11 MEDGE( MESH, MAP, ENTI = "axi-sym" ) MEDGE( SELE, LOCA, WIND = 1 )

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118 Appendix IV (Continued) 0.822123, 0.253114 / ID = 13 / ID = 13 MEDGE( MESH, MAP, ENTI = "axi-sym" ) CURVE( SELE, LOCA, WIND = 1 ) 0.0269058, 0.49427 / ID = 1 / ID = 1 0.0747384, 0.749377 / ID = 2 / ID = 2 0.122571, 0.629796 / ID = 11 / ID = 11 0.0657698, 0.255107 / ID = 10 / ID = 10 MLOOP( ADD, MAP, VISI, NOSH, EDG1 = 1, EDG2 = 1, EDG3 = 1, EDG4 = 1 ) CURVE( SELE, LOCA, WIND = 1 ) 0.127055, 0.47434 / ID = 11 / ID = 11 0.276532, 0.633782 / ID = 3 / ID = 3 0.659193, 0.300947 / ID = 12 / ID = 12 0.523169, 0.243149 / ID = 9 / ID = 9 MLOOP( ADD, MAP, VISI, NOSH, EDG1 = 1, EDG2 = 1, EDG3 = 1, EDG4 = 1 ) CURVE( SELE, LOCA, WIND = 1 ) 0.659193, 0.30294 / ID = 12 / ID = 12 0.698057, 0.340807 / ID = 4 / ID = 4 0.735426, 0.300947 / ID = 13 / ID = 13 0.696562, 0.2571 / ID = 8 / ID = 8 MLOOP( ADD, MAP, VISI, NOSH, EDG1 = 1, EDG2 = 1, EDG3 = 1, EDG4 = 1 ) CURVE( SELE, LOCA, WIND = 1 ) 0.735426, 0.286996 / ID = 13 / ID = 13 0.799701, 0.332835

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119 Appendix IV (Continued) / ID = 5 / ID = 5 0.977578, 0.30294 / ID = 6 / ID = 6 0.889387, 0.2571 / ID = 7 / ID = 7 MLOOP( ADD, MAP, VISI, NOSH, EDG1 = 1, EDG2 = 1, EDG3 = 1, EDG4 = 1 ) SURFACE( SELE, LOCA, WIND = 1 ) 0.500747, 0.619831 / ID = 1 / ID = 1 UTILITY( HIGH = 9 ) MLOOP( SELE, LOCA, WIND = 1 ) 0.124066, 0.562033 / ID = 1 / ID = 1 UTILITY( HIGH = 3 ) MFACE( ADD ) SURFACE( SELE, LOCA, WIND = 1 ) 0.499253, 0.62581 / ID = 1 / ID = 1 UTILITY( HIGH = 9 ) MLOOP( SELE, LOCA, WIND = 1 ) 0.659193, 0.296961 / ID = 2 / ID = 2 UTILITY( HIGH = 3 ) MFACE( ADD ) SURFACE( SELE, LOCA, WIND = 1 ) 0.499253, 0.615845 / ID = 1 / ID = 1 UTILITY( HIGH = 9 ) MLOOP( SELE, LOCA, WIND = 1 ) 0.698057, 0.330842 / ID = 3 / ID = 3 UTILITY( HIGH = 3 ) MFACE( ADD ) SURFACE( SELE, LOCA, WIND = 1 ) 0.497758, 0.585949 / ID = 1 / ID = 1 UTILITY( HIGH = 9 ) MLOOP( SELE, LOCA, WIND = 1 ) 0.846039, 0.334828 / ID = 4 / ID = 4 UTILITY( HIGH = 3 ) MFACE( ADD )

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120 Appendix IV (Continued) MFACE( SELE, LOCA, WIND = 1 ) 0.119581, 0.552068 / ID = 1 / ID = 1 ELEMENT( SETD, QUAD, NODE = 4 ) MFACE( MESH, MAP, ENTI = "fluid" ) MFACE( SELE, LOCA, WIND = 1 ) 0.234679, 0.659691 / ID = 2 / ID = 2 MFACE( MESH, MAP, ENTI = "fluid" ) MFACE( SELE, LOCA, WIND = 1 ) 0.693572, 0.332835 / ID = 3 / ID = 3 MFACE( MESH, MAP, ENTI = "fluid" ) MFACE( SELE, LOCA, WIND = 1 ) 0.798206, 0.332835 / ID = 4 / ID = 4 MFACE( MESH, MAP, ENTI = "fluid" ) END( )

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121 Appendix V: FIPREP File for the Small Nozzle with Free Surface (4.416 x 10-7 m3/s, FC-72) FIPREP( ) DENSITY( ADD, SET = "fc-72", CONS = 1.68 ) VISCOSITY( ADD, SET = "fc-72", CONS = 0.0064, MIXL ) SURFACETENSION( ADD, SET = "fc-72", CONS = 10 ) // PRESSURE( ADD, MIXE = 1e-16, DISC ) DATAPRINT( ADD, CONT ) EXECUTION( ADD, NEWJ ) PRINTOUT( ADD, NONE, BOUN ) PROBLEM( ADD, CYLI, INCO, TRAN, TURB, NONL, NEWT, MOME, ISOT, FREE, SING ) SOLUTION( ADD, N.R. = 80, KINE = 25, VELC = 0.0001, RESC = 0.01, SURF = 0.001 ) BODYFORCE( ADD, CONS, FZC = 981, FRC = 0, FTHE = 0 ) TIMEINTEGRATION( ADD, BACK, NSTE = 600, TSTA = 0, DT = 1e-07, VARI, WIND = 0.9, NOFI = 10 ) OPTIONS( ADD, UPWI ) UPWINDING( ADD, STRE ) RELAXATION( ) 0.6, 0.6, 0.6, 0, 0, 0.1 RENUMBER( ADD, PROF ) EDDYVISCOSITY( ADD, SPEZ ) POSTPROCESS( ADD, NBLO = 2, NOPT, NOPA ) 1, 200, 200 201, 600, 5 // ENTITY( ADD, NAME = "fluid", FLUI, PROP = "fc-72" ) ENTITY( ADD, NAME = "inlet", PLOT ) ENTITY( ADD, NAME = "outlet", PLOT ) ENTITY( ADD, NAME = "axi-sym", PLOT ) ENTITY( ADD, NAME = "wall", WALL ) ENTITY( ADD, NAME = "free", SURF, DEPT = 0, SPIN, STRA ) // BCNODE( ADD, URC, NODE = 1, CONS = 0 ) BCNODE( ADD, UTHE, NODE = 1, CONS = 0 ) BCNODE( ADD, UZC, NODE = 1, CONS = 49.68964 ) // BCNODE( ADD, URC, NODE = 3, CONS = 0.94431 ) BCNODE( ADD, UTHE, NODE = 3, CONS = -0.56976 ) BCNODE( ADD, UZC, NODE = 3, CONS = 20.62872 ) // BCNODE( ADD, URC, NODE = 4, CONS = 1.88863 ) BCNODE( ADD, UTHE, NODE = 4, CONS = -1.13952 ) BCNODE( ADD, UZC, NODE = 4, CONS = 41.25745 ) // BCNODE( ADD, URC, NODE = 5, CONS = 3.46882 ) BCNODE( ADD, UTHE, NODE = 5, CONS = -1.73082 ) BCNODE( ADD, UZC, NODE = 5, CONS = 47.44428 ) // BCNODE( ADD, URC, NODE = 6, CONS = 3.52389 ) BCNODE( ADD, UTHE, NODE = 6, CONS = -2.34216 ) BCNODE( ADD, UZC, NODE = 6, CONS = 44.18421 )

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122 Appendix V (Continued) BCNODE( ADD, URC, NODE = 7, CONS = 5.21716 ) BCNODE( ADD, UTHE, NODE = 7, CONS = -2.98653 ) BCNODE( ADD, UZC, NODE = 7, CONS = 39.81574 ) // BCNODE( ADD, URC, NODE = 8, CONS = 5.20597 ) BCNODE( ADD, UTHE, NODE = 8, CONS = -3.65693 ) BCNODE( ADD, UZC, NODE = 8, CONS = 35.60161 ) // BCNODE( ADD, URC, NODE = 9, CONS = 5.58063 ) BCNODE( ADD, UTHE, NODE = 9, CONS = -4.35591 ) BCNODE( ADD, UZC, NODE = 9, CONS = 31.04352 ) // BCNODE( ADD, URC, NODE = 10, CONS = 6.42356 ) BCNODE( ADD, UTHE, NODE = 10, CONS = -5.13488 ) BCNODE( ADD, UZC, NODE = 10, CONS = 26.64832 ) // BCNODE( ADD, URC, NODE = 11, CONS = 5.62397 ) BCNODE( ADD, UTHE, NODE = 11, CONS = -5.95534 ) BCNODE( ADD, UZC, NODE = 11, CONS = 22.2078 ) // BCNODE( ADD, URC, NODE = 12, CONS = 5.72756 ) BCNODE( ADD, UTHE, NODE = 12, CONS = -7.34427 ) BCNODE( ADD, UZC, NODE = 12, CONS = 19.02035 ) // BCNODE( ADD, URC, NODE = 13, CONS = 5.48385 ) BCNODE( ADD, UTHE, NODE = 13, CONS = -8.75015 ) BCNODE( ADD, UZC, NODE = 13, CONS = 16.01264 ) // BCNODE( ADD, URC, NODE = 14, CONS = 5.15911 ) BCNODE( ADD, UTHE, NODE = 14, CONS = -10.19677 ) BCNODE( ADD, UZC, NODE = 14, CONS = 13.38975 ) // BCNODE( ADD, URC, NODE = 15, CONS = 5.05374 ) BCNODE( ADD, UTHE, NODE = 15, CONS = -11.92467 ) BCNODE( ADD, UZC, NODE = 15, CONS = 11.96041 ) // BCNODE( ADD, URC, NODE = 16, CONS = 4.77261 ) BCNODE( ADD, UTHE, NODE = 16, CONS = -13.68611 ) BCNODE( ADD, UZC, NODE = 16, CONS = 10.92775 ) // BCNODE( ADD, URC, NODE = 17, CONS = 4.56535 ) BCNODE( ADD, UTHE, NODE = 17, CONS = -15.56074 ) BCNODE( ADD, UZC, NODE = 17, CONS = 10.11604 ) // BCNODE( ADD, URC, NODE = 18, CONS = 4.4314 ) BCNODE( ADD, UTHE, NODE = 18, CONS = -17.3999 ) BCNODE( ADD, UZC, NODE = 18, CONS = 10.58209 ) // BCNODE( ADD, URC, NODE = 19, CONS = 4.49074 ) BCNODE( ADD, UTHE, NODE = 19, CONS = -19.32783 ) BCNODE( ADD, UZC, NODE = 19, CONS = 11.64568 ) // BCNODE( ADD, URC, NODE = 20, CONS = 4.49002 ) BCNODE( ADD, UTHE, NODE = 20, CONS = -21.33699 )

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123 Appendix V (Continued) BCNODE( ADD, UZC, NODE = 20, CONS = 13.13784 ) // BCNODE( ADD, URC, NODE = 21, CONS = 4.53724 ) BCNODE( ADD, UTHE, NODE = 21, CONS = -23.18616 ) BCNODE( ADD, UZC, NODE = 21, CONS = 14.70284 ) // BCNODE( ADD, URC, NODE = 22, CONS = 4.62719 ) BCNODE( ADD, UTHE, NODE = 22, CONS = -24.89264 ) BCNODE( ADD, UZC, NODE = 22, CONS = 16.33282 ) // BCNODE( ADD, URC, NODE = 23, CONS = 4.78398 ) BCNODE( ADD, UTHE, NODE = 23, CONS = -26.6102 ) BCNODE( ADD, UZC, NODE = 23, CONS = 18.16162 ) // BCNODE( ADD, URC, NODE = 24, CONS = 4.64768 ) BCNODE( ADD, UTHE, NODE = 24, CONS = -28.44521 ) BCNODE( ADD, UZC, NODE = 24, CONS = 20.19784 ) // BCNODE( ADD, URC, NODE = 25, CONS = 4.78788 ) BCNODE( ADD, UTHE, NODE = 25, CONS = -30.42269 ) BCNODE( ADD, UZC, NODE = 25, CONS = 22.20482 ) // BCNODE( ADD, URC, NODE = 26, CONS = 4.43739 ) BCNODE( ADD, UTHE, NODE = 26, CONS = -32.59866 ) BCNODE( ADD, UZC, NODE = 26, CONS = 24.26073 ) // BCNODE( ADD, URC, NODE = 27, CONS = 4.05382 ) BCNODE( ADD, UTHE, NODE = 27, CONS = -35.62384 ) BCNODE( ADD, UZC, NODE = 27, CONS = 27.54981 ) // BCNODE( ADD, URC, NODE = 28, CONS = 3.33494 ) BCNODE( ADD, UTHE, NODE = 28, CONS = -38.73045 ) BCNODE( ADD, UZC, NODE = 28, CONS = 30.87673 ) // BCNODE( ADD, URC, NODE = 29, CONS = 2.84129 ) BCNODE( ADD, UTHE, NODE = 29, CONS = -41.62208 ) BCNODE( ADD, UZC, NODE = 29, CONS = 34.15707 ) // BCNODE( ADD, URC, NODE = 30, CONS = 1.76006 ) BCNODE( ADD, UTHE, NODE = 30, CONS = -41.34139 ) BCNODE( ADD, UZC, NODE = 30, CONS = 34.88655 ) // BCNODE( ADD, URC, NODE = 31, CONS = 0.29811 ) BCNODE( ADD, UTHE, NODE = 31, CONS = -32.28292 ) BCNODE( ADD, UZC, NODE = 31, CONS = 28.37171 ) // BCNODE( ADD, URC, NODE = 2, CONS = 0 ) BCNODE( ADD, UTHE, NODE = 2, CONS = 0 ) BCNODE( ADD, UZC, NODE = 2, CONS = 0 ) // BCNODE( ADD, VELO, ENTI = "wall", ZERO, X, Y, Z ) BCNODE( ADD, URC, ENTI = "axi-sym", ZERO, X, Y, Z ) // BCNODE( SURF, CONS = 0, NODE = 95 )

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124 Appendix V (Continued) BCNODE( SURF, CONS = 0, NODE = 434 ) BCNODE( ADD, COOR, NODE = 95 ) BCNODE( ADD, COOR, NODE = 125 ) // ICNODE( ADD, URC, NODE = 1, CONS = 0 ) ICNODE( ADD, UTHE, NODE = 1, CONS = 0 ) ICNODE( ADD, UZC, NODE = 1, CONS = 49.68964 ) // ICNODE( ADD, URC, NODE = 3, CONS = 0.94431 ) ICNODE( ADD, UTHE, NODE = 3, CONS = -0.56976 ) ICNODE( ADD, UZC, NODE = 3, CONS = 20.62872 ) // ICNODE( ADD, URC, NODE = 4, CONS = 1.88863 ) ICNODE( ADD, UTHE, NODE = 4, CONS = -1.13952 ) ICNODE( ADD, UZC, NODE = 4, CONS = 41.25745 ) // ICNODE( ADD, URC, NODE = 5, CONS = 3.46882 ) ICNODE( ADD, UTHE, NODE = 5, CONS = -1.73082 ) ICNODE( ADD, UZC, NODE = 5, CONS = 47.44428 ) // ICNODE( ADD, URC, NODE = 6, CONS = 3.52389 ) ICNODE( ADD, UTHE, NODE = 6, CONS = -2.34216 ) ICNODE( ADD, UZC, NODE = 6, CONS = 44.18421 ) // ICNODE( ADD, URC, NODE = 7, CONS = 5.21716 ) ICNODE( ADD, UTHE, NODE = 7, CONS = -2.98653 ) ICNODE( ADD, UZC, NODE = 7, CONS = 39.81574 ) // ICNODE( ADD, URC, NODE = 8, CONS = 5.20597 ) ICNODE( ADD, UTHE, NODE = 8, CONS = -3.65693 ) ICNODE( ADD, UZC, NODE = 8, CONS = 35.60161 ) // ICNODE( ADD, URC, NODE = 9, CONS = 5.58063 ) ICNODE( ADD, UTHE, NODE = 9, CONS = -4.35591 ) ICNODE( ADD, UZC, NODE = 9, CONS = 31.04352 ) // ICNODE( ADD, URC, NODE = 10, CONS = 6.42356 ) ICNODE( ADD, UTHE, NODE = 10, CONS = -5.13488 ) ICNODE( ADD, UZC, NODE = 10, CONS = 26.64832 ) // ICNODE( ADD, URC, NODE = 11, CONS = 5.62397 ) ICNODE( ADD, UTHE, NODE = 11, CONS = -5.95534 ) ICNODE( ADD, UZC, NODE = 11, CONS = 22.2078 ) // ICNODE( ADD, URC, NODE = 12, CONS = 5.72756 ) ICNODE( ADD, UTHE, NODE = 12, CONS = -7.34427 ) ICNODE( ADD, UZC, NODE = 12, CONS = 19.02035 ) // ICNODE( ADD, URC, NODE = 13, CONS = 5.48385 ) ICNODE( ADD, UTHE, NODE = 13, CONS = -8.75015 ) ICNODE( ADD, UZC, NODE = 13, CONS = 16.01264 ) // ICNODE( ADD, URC, NODE = 14, CONS = 5.15911 ) ICNODE( ADD, UTHE, NODE = 14, CONS = -10.19677 )

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125 Appendix V (Continued) ICNODE( ADD, UZC, NODE = 14, CONS = 13.38975 ) // ICNODE( ADD, URC, NODE = 15, CONS = 5.05374 ) ICNODE( ADD, UTHE, NODE = 15, CONS = -11.92467 ) ICNODE( ADD, UZC, NODE = 15, CONS = 11.96041 ) // ICNODE( ADD, URC, NODE = 16, CONS = 4.77261 ) ICNODE( ADD, UTHE, NODE = 16, CONS = -13.68611 ) ICNODE( ADD, UZC, NODE = 16, CONS = 10.92775 ) // ICNODE( ADD, URC, NODE = 17, CONS = 4.56535 ) ICNODE( ADD, UTHE, NODE = 17, CONS = -15.56074 ) ICNODE( ADD, UZC, NODE = 17, CONS = 10.11604 ) // ICNODE( ADD, URC, NODE = 18, CONS = 4.4314 ) ICNODE( ADD, UTHE, NODE = 18, CONS = -17.3999 ) ICNODE( ADD, UZC, NODE = 18, CONS = 10.58209 ) // ICNODE( ADD, URC, NODE = 19, CONS = 4.49074 ) ICNODE( ADD, UTHE, NODE = 19, CONS = -19.32783 ) ICNODE( ADD, UZC, NODE = 19, CONS = 11.64568 ) // ICNODE( ADD, URC, NODE = 20, CONS = 4.49002 ) ICNODE( ADD, UTHE, NODE = 20, CONS = -21.33699 ) ICNODE( ADD, UZC, NODE = 20, CONS = 13.13784 ) // ICNODE( ADD, URC, NODE = 21, CONS = 4.53724 ) ICNODE( ADD, UTHE, NODE = 21, CONS = -23.18616 ) ICNODE( ADD, UZC, NODE = 21, CONS = 14.70284 ) // ICNODE( ADD, URC, NODE = 22, CONS = 4.62719 ) ICNODE( ADD, UTHE, NODE = 22, CONS = -24.89264 ) ICNODE( ADD, UZC, NODE = 22, CONS = 16.33282 ) // ICNODE( ADD, URC, NODE = 23, CONS = 4.78398 ) ICNODE( ADD, UTHE, NODE = 23, CONS = -26.6102 ) ICNODE( ADD, UZC, NODE = 23, CONS = 18.16162 ) // ICNODE( ADD, URC, NODE = 24, CONS = 4.64768 ) ICNODE( ADD, UTHE, NODE = 24, CONS = -28.44521 ) ICNODE( ADD, UZC, NODE = 24, CONS = 20.19784 ) // ICNODE( ADD, URC, NODE = 25, CONS = 4.78788 ) ICNODE( ADD, UTHE, NODE = 25, CONS = -30.42269 ) ICNODE( ADD, UZC, NODE = 25, CONS = 22.20482 ) // ICNODE( ADD, URC, NODE = 26, CONS = 4.43739 ) ICNODE( ADD, UTHE, NODE = 26, CONS = -32.59866 ) ICNODE( ADD, UZC, NODE = 26, CONS = 24.26073 ) // ICNODE( ADD, URC, NODE = 27, CONS = 4.05382 ) ICNODE( ADD, UTHE, NODE = 27, CONS = -35.62384 ) ICNODE( ADD, UZC, NODE = 27, CONS = 27.54981 ) //

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126 Appendix V (Continued) ICNODE( ADD, URC, NODE = 28, CONS = 3.33494 ) ICNODE( ADD, UTHE, NODE = 28, CONS = -38.73045 ) ICNODE( ADD, UZC, NODE = 28, CONS = 30.87673 ) // ICNODE( ADD, URC, NODE = 29, CONS = 2.84129 ) ICNODE( ADD, UTHE, NODE = 29, CONS = -41.62208 ) ICNODE( ADD, UZC, NODE = 29, CONS = 34.15707 ) // ICNODE( ADD, URC, NODE = 30, CONS = 1.76006 ) ICNODE( ADD, UTHE, NODE = 30, CONS = -41.34139 ) ICNODE( ADD, UZC, NODE = 30, CONS = 34.88655 ) // ICNODE( ADD, URC, NODE = 31, CONS = 0.29811 ) ICNODE( ADD, UTHE, NODE = 31, CONS = -32.28292 ) ICNODE( ADD, UZC, NODE = 31, CONS = 28.37171 ) // ICNODE( ADD, URC, NODE = 2, CONS = 0 ) ICNODE( ADD, UTHE, NODE = 2, CONS = 0 ) ICNODE( ADD, UZC, NODE = 2, CONS = 0 ) // ICNODE( ADD, VELO, ENTI = "wall", ZERO, X, Y, Z ) ICNODE( ADD, URC, ENTI = "axi-sym", ZERO, X, Y, Z ) END( )

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127 Appendix VI: FIPREP File for the Small Nozzle with Free Surface (5.678 x 10-7 m3/s, FC-72) FIPREP( ) DENSITY( ADD, SET = "fc-72", CONS = 1.68 ) VISCOSITY( ADD, SET = "fc-72", CONS = 0.0064, MIXL ) SURFACETENSION( ADD, SET = "fc-72", CONS = 10 ) // PRESSURE( ADD, MIXE = 1e-16, DISC ) DATAPRINT( ADD, CONT ) EXECUTION( ADD, NEWJ ) PRINTOUT( ADD, NONE, BOUN ) PROBLEM( ADD, CYLI, INCO, TRAN, TURB, NONL, NEWT, MOME, ISOT, FREE, SING ) SOLUTION( ADD, N.R. = 80, KINE = 25, VELC = 0.0001, RESC = 0.01, SURF = 0.001 ) BODYFORCE( ADD, CONS, FZC = 981, FRC = 0, FTHE = 0 ) TIMEINTEGRATION( ADD, BACK, NSTE = 600, TSTA = 0, DT = 1e-07, VARI, WIND = 0.9, NOFI = 10 ) OPTIONS( ADD, UPWI ) UPWINDING( ADD, STRE ) RELAXATION( ) 0.6, 0.6, 0.6, 0, 0, 0.1 RENUMBER( ADD, PROF ) EDDYVISCOSITY( ADD, SPEZ ) POSTPROCESS( ADD, NBLO = 2, NOPT, NOPA ) 1, 200, 200 201, 600, 5 // ENTITY( ADD, NAME = "fluid", FLUI, PROP = "fc-72" ) ENTITY( ADD, NAME = "inlet", PLOT ) ENTITY( ADD, NAME = "outlet", PLOT ) ENTITY( ADD, NAME = "axi-sym", PLOT ) ENTITY( ADD, NAME = "wall", WALL ) ENTITY( ADD, NAME = "free", SURF, DEPT = 0, SPIN, STRA ) // BCNODE( ADD, URC, NODE = 1, CONS = 0 ) BCNODE( ADD, UTHE, NODE = 1, CONS = 0 ) BCNODE( ADD, UZC, NODE = 1, CONS = 62.65485 ) // BCNODE( ADD, URC, NODE = 3, CONS = 1.361 ) BCNODE( ADD, UTHE, NODE = 3, CONS = -0.72779 ) BCNODE( ADD, UZC, NODE = 3, CONS = 22.82843 ) // BCNODE( ADD, URC, NODE = 4, CONS = 2.722 ) BCNODE( ADD, UTHE, NODE = 4, CONS = -1.45557 ) BCNODE( ADD, UZC, NODE = 4, CONS = 45.65685 ) // BCNODE( ADD, URC, NODE = 5, CONS = 4.44517 ) BCNODE( ADD, UTHE, NODE = 5, CONS = -2.21825 ) BCNODE( ADD, UZC, NODE = 5, CONS = 59.08974 ) // BCNODE( ADD, URC, NODE = 6, CONS = 4.62449 ) BCNODE( ADD, UTHE, NODE = 6, CONS = -3.02287 ) BCNODE( ADD, UZC, NODE = 6, CONS = 57.43928 )

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128 Appendix VI (Continued) BCNODE( ADD, URC, NODE = 7, CONS = 6.67544 ) BCNODE( ADD, UTHE, NODE = 7, CONS = -3.81945 ) BCNODE( ADD, UZC, NODE = 7, CONS = 51.78623 ) // BCNODE( ADD, URC, NODE = 8, CONS = 6.99527 ) BCNODE( ADD, UTHE, NODE = 8, CONS = -4.66305 ) BCNODE( ADD, UZC, NODE = 8, CONS = 46.2266 ) // BCNODE( ADD, URC, NODE = 9, CONS = 7.1904 ) BCNODE( ADD, UTHE, NODE = 9, CONS = -5.61362 ) BCNODE( ADD, UZC, NODE = 9, CONS = 40.32383 ) // BCNODE( ADD, URC, NODE = 10, CONS = 8.06577 ) BCNODE( ADD, UTHE, NODE = 10, CONS = -6.5426 ) BCNODE( ADD, UZC, NODE = 10, CONS = 34.59965 ) // BCNODE( ADD, URC, NODE = 11, CONS = 7.52835 ) BCNODE( ADD, UTHE, NODE = 11, CONS = -7.53253 ) BCNODE( ADD, UZC, NODE = 11, CONS = 28.78764 ) // BCNODE( ADD, URC, NODE = 12, CONS = 7.63101 ) BCNODE( ADD, UTHE, NODE = 12, CONS = -8.83656 ) BCNODE( ADD, UZC, NODE = 12, CONS = 23.65376 ) // BCNODE( ADD, URC, NODE = 13, CONS = 7.52023 ) BCNODE( ADD, UTHE, NODE = 13, CONS = -10.33336 ) BCNODE( ADD, UZC, NODE = 13, CONS = 18.84217 ) // BCNODE( ADD, URC, NODE = 14, CONS = 7.26479 ) BCNODE( ADD, UTHE, NODE = 14, CONS = -11.87913 ) BCNODE( ADD, UZC, NODE = 14, CONS = 15.17604 ) // BCNODE( ADD, URC, NODE = 15, CONS = 7.11926 ) BCNODE( ADD, UTHE, NODE = 15, CONS = -13.26154 ) BCNODE( ADD, UZC, NODE = 15, CONS = 12.58037 ) // BCNODE( ADD, URC, NODE = 16, CONS = 6.52001 ) BCNODE( ADD, UTHE, NODE = 16, CONS = -15.41647 ) BCNODE( ADD, UZC, NODE = 16, CONS = 11.94326 ) // BCNODE( ADD, URC, NODE = 17, CONS = 6.0807 ) BCNODE( ADD, UTHE, NODE = 17, CONS = -17.89999 ) BCNODE( ADD, UZC, NODE = 17, CONS = 12.59188 ) // BCNODE( ADD, URC, NODE = 18, CONS = 5.50781 ) BCNODE( ADD, UTHE, NODE = 18, CONS = -20.50235 ) BCNODE( ADD, UZC, NODE = 18, CONS = 13.68295 ) // BCNODE( ADD, URC, NODE = 19, CONS = 5.17638 ) BCNODE( ADD, UTHE, NODE = 19, CONS = -23.14653 ) BCNODE( ADD, UZC, NODE = 19, CONS = 15.31945 ) // BCNODE( ADD, URC, NODE = 20, CONS = 4.96087 ) BCNODE( ADD, UTHE, NODE = 20, CONS = -25.72643 )

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129 Appendix VI (Continued) BCNODE( ADD, UZC, NODE = 20, CONS = 17.075 ) // BCNODE( ADD, URC, NODE = 21, CONS = 4.85869 ) BCNODE( ADD, UTHE, NODE = 21, CONS = -28.26402 ) BCNODE( ADD, UZC, NODE = 21, CONS = 18.98738 ) // BCNODE( ADD, URC, NODE = 22, CONS = 4.85992 ) BCNODE( ADD, UTHE, NODE = 22, CONS = -30.26417 ) BCNODE( ADD, UZC, NODE = 22, CONS = 21.04099 ) // BCNODE( ADD, URC, NODE = 23, CONS = 5.19398 ) BCNODE( ADD, UTHE, NODE = 23, CONS = -32.35916 ) BCNODE( ADD, UZC, NODE = 23, CONS = 23.13346 ) // BCNODE( ADD, URC, NODE = 24, CONS = 4.95843 ) BCNODE( ADD, UTHE, NODE = 24, CONS = -35.25145 ) BCNODE( ADD, UZC, NODE = 24, CONS = 26.28834 ) // BCNODE( ADD, URC, NODE = 25, CONS = 5.2396 ) BCNODE( ADD, UTHE, NODE = 25, CONS = -38.41067 ) BCNODE( ADD, UZC, NODE = 25, CONS = 29.53426 ) // BCNODE( ADD, URC, NODE = 26, CONS = 4.82357 ) BCNODE( ADD, UTHE, NODE = 26, CONS = -41.83582 ) BCNODE( ADD, UZC, NODE = 26, CONS = 32.81552 ) // BCNODE( ADD, URC, NODE = 27, CONS = 4.99691 ) BCNODE( ADD, UTHE, NODE = 27, CONS = -46.05391 ) BCNODE( ADD, UZC, NODE = 27, CONS = 36.47581 ) // BCNODE( ADD, URC, NODE = 28, CONS = 4.89695 ) BCNODE( ADD, UTHE, NODE = 28, CONS = -50.17309 ) BCNODE( ADD, UZC, NODE = 28, CONS = 40.20812 ) // BCNODE( ADD, URC, NODE = 29, CONS = 4.05724 ) BCNODE( ADD, UTHE, NODE = 29, CONS = -54.11514 ) BCNODE( ADD, UZC, NODE = 29, CONS = 43.89333 ) // BCNODE( ADD, URC, NODE = 30, CONS = 2.53412 ) BCNODE( ADD, UTHE, NODE = 30, CONS = -54.78068 ) BCNODE( ADD, UZC, NODE = 30, CONS = 45.37476 ) // BCNODE( ADD, URC, NODE = 31, CONS = -0.4527 ) BCNODE( ADD, UTHE, NODE = 31, CONS = -43.51621 ) BCNODE( ADD, UZC, NODE = 31, CONS = 37.5847 ) // BCNODE( ADD, URC, NODE = 2, CONS = 0 ) BCNODE( ADD, UTHE, NODE = 2, CONS = 0 ) BCNODE( ADD, UZC, NODE = 2, CONS = 0 ) // BCNODE( ADD, VELO, ENTI = "wall", ZERO, X, Y, Z ) BCNODE( ADD, URC, ENTI = "axi-sym", ZERO, X, Y, Z ) // BCNODE( SURF, CONS = 0, NODE = 95 )

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130 Appendix VI (Continued) BCNODE( SURF, CONS = 0, NODE = 434 ) BCNODE( ADD, COOR, NODE = 95 ) BCNODE( ADD, COOR, NODE = 125 ) // ICNODE( ADD, URC, NODE = 1, CONS = 0 ) ICNODE( ADD, UTHE, NODE = 1, CONS = 0 ) ICNODE( ADD, UZC, NODE = 1, CONS = 62.65485 ) // ICNODE( ADD, URC, NODE = 3, CONS = 1.361 ) ICNODE( ADD, UTHE, NODE = 3, CONS = -0.72779 ) ICNODE( ADD, UZC, NODE = 3, CONS = 22.82843 ) // ICNODE( ADD, URC, NODE = 4, CONS = 2.722 ) ICNODE( ADD, UTHE, NODE = 4, CONS = -1.45557 ) ICNODE( ADD, UZC, NODE = 4, CONS = 45.65685 ) // ICNODE( ADD, URC, NODE = 5, CONS = 4.44517 ) ICNODE( ADD, UTHE, NODE = 5, CONS = -2.21825 ) ICNODE( ADD, UZC, NODE = 5, CONS = 59.08974 ) // ICNODE( ADD, URC, NODE = 6, CONS = 4.62449 ) ICNODE( ADD, UTHE, NODE = 6, CONS = -3.02287 ) ICNODE( ADD, UZC, NODE = 6, CONS = 57.43928 ) // ICNODE( ADD, URC, NODE = 7, CONS = 6.67544 ) ICNODE( ADD, UTHE, NODE = 7, CONS = -3.81945 ) ICNODE( ADD, UZC, NODE = 7, CONS = 51.78623 ) // ICNODE( ADD, URC, NODE = 8, CONS = 6.99527 ) ICNODE( ADD, UTHE, NODE = 8, CONS = -4.66305 ) ICNODE( ADD, UZC, NODE = 8, CONS = 46.2266 ) // ICNODE( ADD, URC, NODE = 9, CONS = 7.1904 ) ICNODE( ADD, UTHE, NODE = 9, CONS = -5.61362 ) ICNODE( ADD, UZC, NODE = 9, CONS = 40.32383 ) // ICNODE( ADD, URC, NODE = 10, CONS = 8.06577 ) ICNODE( ADD, UTHE, NODE = 10, CONS = -6.5426 ) ICNODE( ADD, UZC, NODE = 10, CONS = 34.59965 ) // ICNODE( ADD, URC, NODE = 11, CONS = 7.52835 ) ICNODE( ADD, UTHE, NODE = 11, CONS = -7.53253 ) ICNODE( ADD, UZC, NODE = 11, CONS = 28.78764 ) // ICNODE( ADD, URC, NODE = 12, CONS = 7.63101 ) ICNODE( ADD, UTHE, NODE = 12, CONS = -8.83656 ) ICNODE( ADD, UZC, NODE = 12, CONS = 23.65376 ) // ICNODE( ADD, URC, NODE = 13, CONS = 7.52023 ) ICNODE( ADD, UTHE, NODE = 13, CONS = -10.33336 ) ICNODE( ADD, UZC, NODE = 13, CONS = 18.84217 ) // ICNODE( ADD, URC, NODE = 14, CONS = 7.26479 ) ICNODE( ADD, UTHE, NODE = 14, CONS = -11.87913 )

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131 Appendix VI (Continued) ICNODE( ADD, UZC, NODE = 14, CONS = 15.17604 ) ICNODE( ADD, URC, NODE = 15, CONS = 7.11926 ) ICNODE( ADD, UTHE, NODE = 15, CONS = -13.26154 ) ICNODE( ADD, UZC, NODE = 15, CONS = 12.58037 ) // ICNODE( ADD, URC, NODE = 16, CONS = 6.52001 ) ICNODE( ADD, UTHE, NODE = 16, CONS = -15.41647 ) ICNODE( ADD, UZC, NODE = 16, CONS = 11.94326 ) // ICNODE( ADD, URC, NODE = 17, CONS = 6.0807 ) ICNODE( ADD, UTHE, NODE = 17, CONS = -17.89999 ) ICNODE( ADD, UZC, NODE = 17, CONS = 12.59188 ) // ICNODE( ADD, URC, NODE = 18, CONS = 5.50781 ) ICNODE( ADD, UTHE, NODE = 18, CONS = -20.50235 ) ICNODE( ADD, UZC, NODE = 18, CONS = 13.68295 ) // ICNODE( ADD, URC, NODE = 19, CONS = 5.17638 ) ICNODE( ADD, UTHE, NODE = 19, CONS = -23.14653 ) ICNODE( ADD, UZC, NODE = 19, CONS = 15.31945 ) // ICNODE( ADD, URC, NODE = 20, CONS = 4.96087 ) ICNODE( ADD, UTHE, NODE = 20, CONS = -25.72643 ) ICNODE( ADD, UZC, NODE = 20, CONS = 17.075 ) // ICNODE( ADD, URC, NODE = 21, CONS = 4.85869 ) ICNODE( ADD, UTHE, NODE = 21, CONS = -28.26402 ) ICNODE( ADD, UZC, NODE = 21, CONS = 18.98738 ) // ICNODE( ADD, URC, NODE = 22, CONS = 4.85992 ) ICNODE( ADD, UTHE, NODE = 22, CONS = -30.26417 ) ICNODE( ADD, UZC, NODE = 22, CONS = 21.04099 ) // ICNODE( ADD, URC, NODE = 23, CONS = 5.19398 ) ICNODE( ADD, UTHE, NODE = 23, CONS = -32.35916 ) ICNODE( ADD, UZC, NODE = 23, CONS = 23.13346 ) // ICNODE( ADD, URC, NODE = 24, CONS = 4.95843 ) ICNODE( ADD, UTHE, NODE = 24, CONS = -35.25145 ) ICNODE( ADD, UZC, NODE = 24, CONS = 26.28834 ) // ICNODE( ADD, URC, NODE = 25, CONS = 5.2396 ) ICNODE( ADD, UTHE, NODE = 25, CONS = -38.41067 ) ICNODE( ADD, UZC, NODE = 25, CONS = 29.53426 ) // ICNODE( ADD, URC, NODE = 26, CONS = 4.82357 ) ICNODE( ADD, UTHE, NODE = 26, CONS = -41.83582 ) ICNODE( ADD, UZC, NODE = 26, CONS = 32.81552 ) // ICNODE( ADD, URC, NODE = 27, CONS = 4.99691 ) ICNODE( ADD, UTHE, NODE = 27, CONS = -46.05391 ) ICNODE( ADD, UZC, NODE = 27, CONS = 36.47581 ) // ICNODE( ADD, URC, NODE = 28, CONS = 4.89695 )

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132 Appendix VI (Continued) ICNODE( ADD, UTHE, NODE = 28, CONS = -50.17309 ) ICNODE( ADD, UZC, NODE = 28, CONS = 40.20812 ) // ICNODE( ADD, URC, NODE = 29, CONS = 4.05724 ) ICNODE( ADD, UTHE, NODE = 29, CONS = -54.11514 ) ICNODE( ADD, UZC, NODE = 29, CONS = 43.89333 ) // ICNODE( ADD, URC, NODE = 30, CONS = 2.53412 ) ICNODE( ADD, UTHE, NODE = 30, CONS = -54.78068 ) ICNODE( ADD, UZC, NODE = 30, CONS = 45.37476 ) // ICNODE( ADD, URC, NODE = 31, CONS = -0.4527 ) ICNODE( ADD, UTHE, NODE = 31, CONS = -43.51621 ) ICNODE( ADD, UZC, NODE = 31, CONS = 37.5847 ) // ICNODE( ADD, URC, NODE = 2, CONS = 0 ) ICNODE( ADD, UTHE, NODE = 2, CONS = 0 ) ICNODE( ADD, UZC, NODE = 2, CONS = 0 ) // ICNODE( ADD, VELO, ENTI = "wall", ZERO, X, Y, Z ) ICNODE( ADD, URC, ENTI = "axi-sym", ZERO, X, Y, Z ) // END( )

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133 Appendix VII: FIPREP File for the Small Nozzle with Free Surface (4.416 x 10-7 m3/s, FC-77) FIPREP( ) DENSITY( ADD, SET = "fc-77", CONS = 1.78 ) VISCOSITY( ADD, SET = "fc-77", CONS = 0.01424, MIXL ) SURFACETENSION( ADD, SET = "fc-77", CONS = 15 ) // PRESSURE( ADD, MIXE = 1e-16, DISC ) DATAPRINT( ADD, CONT ) EXECUTION( ADD, NEWJ ) PRINTOUT( ADD, NONE, BOUN ) PROBLEM( ADD, CYLI, INCO, TRAN, TURB, NONL, NEWT, MOME, ISOT, FREE, SING ) SOLUTION( ADD, N.R. = 80, KINE = 25, VELC = 0.0001, RESC = 0.01, SURF = 0.001 ) BODYFORCE( ADD, CONS, FZC = 981, FRC = 0, FTHE = 0 ) TIMEINTEGRATION( ADD, BACK, NSTE = 600, TSTA = 0, DT = 1e-07, VARI, WIND = 0.9, NOFI = 10 ) OPTIONS( ADD, UPWI ) UPWINDING( ADD, STRE ) RELAXATION( ) 0.6, 0.6, 0.6, 0, 0, 0.1 RENUMBER( ADD, PROF ) EDDYVISCOSITY( ADD, SPEZ ) POSTPROCESS( ADD, NBLO = 2, NOPT, NOPA ) 1, 200, 200 201, 600, 5 // ENTITY( ADD, NAME = "fluid", FLUI, PROP = "fc-77" ) ENTITY( ADD, NAME = "inlet", PLOT ) ENTITY( ADD, NAME = "outlet", PLOT ) ENTITY( ADD, NAME = "axi-sym", PLOT ) ENTITY( ADD, NAME = "wall", WALL ) ENTITY( ADD, NAME = "free", SURF, DEPT = 0, SPIN, STRA ) // BCNODE( ADD, URC, NODE = 1, CONS = 0 ) BCNODE( ADD, UTHE, NODE = 1, CONS = 0 ) BCNODE( ADD, UZC, NODE = 1, CONS = 47.19336 ) // BCNODE( ADD, URC, NODE = 3, CONS = 1.08732 ) BCNODE( ADD, UTHE, NODE = 3, CONS = -0.53563 ) BCNODE( ADD, UZC, NODE = 3, CONS = 17.19441 ) // BCNODE( ADD, URC, NODE = 4, CONS = 2.17465 ) BCNODE( ADD, UTHE, NODE = 4, CONS = -1.07127 ) BCNODE( ADD, UZC, NODE = 4, CONS = 34.38882 ) // BCNODE( ADD, URC, NODE = 5, CONS = 3.52669 ) BCNODE( ADD, UTHE, NODE = 5, CONS = -1.63022 ) BCNODE( ADD, UZC, NODE = 5, CONS = 44.52068 ) // BCNODE( ADD, URC, NODE = 6, CONS = 3.72529 ) BCNODE( ADD, UTHE, NODE = 6, CONS = -2.22102 ) BCNODE( ADD, UZC, NODE = 6, CONS = 43.30954 )

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134 Appendix VII (Continued) BCNODE( ADD, URC, NODE = 7, CONS = 5.31261 ) BCNODE( ADD, UTHE, NODE = 7, CONS = -2.80722 ) BCNODE( ADD, UZC, NODE = 7, CONS = 39.04591 ) // BCNODE( ADD, URC, NODE = 8, CONS = 5.59452 ) BCNODE( ADD, UTHE, NODE = 8, CONS = -3.42835 ) BCNODE( ADD, UZC, NODE = 8, CONS = 34.83996 ) // BCNODE( ADD, URC, NODE = 9, CONS = 5.77731 ) BCNODE( ADD, UTHE, NODE = 9, CONS = -4.13563 ) BCNODE( ADD, UZC, NODE = 9, CONS = 30.35985 ) // BCNODE( ADD, URC, NODE = 10, CONS = 6.4748 ) BCNODE( ADD, UTHE, NODE = 10, CONS = -4.8297 ) BCNODE( ADD, UZC, NODE = 10, CONS = 26.00255 ) // BCNODE( ADD, URC, NODE = 11, CONS = 6.08714 ) BCNODE( ADD, UTHE, NODE = 11, CONS = -5.56654 ) BCNODE( ADD, UZC, NODE = 11, CONS = 21.58722 ) // BCNODE( ADD, URC, NODE = 12, CONS = 6.17664 ) BCNODE( ADD, UTHE, NODE = 12, CONS = -6.55613 ) BCNODE( ADD, UZC, NODE = 12, CONS = 17.6622 ) // BCNODE( ADD, URC, NODE = 13, CONS = 6.1046 ) BCNODE( ADD, UTHE, NODE = 13, CONS = -7.69538 ) BCNODE( ADD, UZC, NODE = 13, CONS = 13.98276 ) // BCNODE( ADD, URC, NODE = 14, CONS = 5.91907 ) BCNODE( ADD, UTHE, NODE = 14, CONS = -8.8751 ) BCNODE( ADD, UZC, NODE = 14, CONS = 11.17852 ) // BCNODE( ADD, URC, NODE = 15, CONS = 5.79201 ) BCNODE( ADD, UTHE, NODE = 15, CONS = -9.95338 ) BCNODE( ADD, UZC, NODE = 15, CONS = 9.18139 ) // BCNODE( ADD, URC, NODE = 16, CONS = 5.29163 ) BCNODE( ADD, UTHE, NODE = 16, CONS = -11.65498 ) BCNODE( ADD, UZC, NODE = 16, CONS = 8.71487 ) // BCNODE( ADD, URC, NODE = 17, CONS = 4.92335 ) BCNODE( ADD, UTHE, NODE = 17, CONS = -13.6164 ) BCNODE( ADD, UZC, NODE = 17, CONS = 9.33896 ) // BCNODE( ADD, URC, NODE = 18, CONS = 4.41826 ) BCNODE( ADD, UTHE, NODE = 18, CONS = -15.63676 ) BCNODE( ADD, UZC, NODE = 18, CONS = 10.32914 ) // BCNODE( ADD, URC, NODE = 19, CONS = 4.08265 ) BCNODE( ADD, UTHE, NODE = 19, CONS = -17.65407 ) BCNODE( ADD, UZC, NODE = 19, CONS = 11.78129 ) // BCNODE( ADD, URC, NODE = 20, CONS = 3.82908 ) BCNODE( ADD, UTHE, NODE = 20, CONS = -19.62029 )

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135 Appendix VII (Continued) BCNODE( ADD, UZC, NODE = 20, CONS = 13.34846 ) // BCNODE( ADD, URC, NODE = 21, CONS = 3.6567 ) BCNODE( ADD, UTHE, NODE = 21, CONS = -21.55171 ) BCNODE( ADD, UZC, NODE = 21, CONS = 15.06358 ) // BCNODE( ADD, URC, NODE = 22, CONS = 3.47798 ) BCNODE( ADD, UTHE, NODE = 22, CONS = -23.06131 ) BCNODE( ADD, UZC, NODE = 22, CONS = 16.85193 ) // BCNODE( ADD, URC, NODE = 23, CONS = 3.56426 ) BCNODE( ADD, UTHE, NODE = 23, CONS = -24.60996 ) BCNODE( ADD, UZC, NODE = 23, CONS = 18.65726 ) // BCNODE( ADD, URC, NODE = 24, CONS = 3.2607 ) BCNODE( ADD, UTHE, NODE = 24, CONS = -26.69053 ) BCNODE( ADD, UZC, NODE = 24, CONS = 21.20417 ) // BCNODE( ADD, URC, NODE = 25, CONS = 3.384 ) BCNODE( ADD, UTHE, NODE = 25, CONS = -28.92644 ) BCNODE( ADD, UZC, NODE = 25, CONS = 23.78581 ) // BCNODE( ADD, URC, NODE = 26, CONS = 2.99219 ) BCNODE( ADD, UTHE, NODE = 26, CONS = -31.26015 ) BCNODE( ADD, UZC, NODE = 26, CONS = 26.35917 ) // BCNODE( ADD, URC, NODE = 27, CONS = 3.19456 ) BCNODE( ADD, UTHE, NODE = 27, CONS = -33.94675 ) BCNODE( ADD, UZC, NODE = 27, CONS = 29.07778 ) // BCNODE( ADD, URC, NODE = 28, CONS = 3.21875 ) BCNODE( ADD, UTHE, NODE = 28, CONS = -36.382 ) BCNODE( ADD, UZC, NODE = 28, CONS = 31.79309 ) // BCNODE( ADD, URC, NODE = 29, CONS = 2.64956 ) BCNODE( ADD, UTHE, NODE = 29, CONS = -38.22577 ) BCNODE( ADD, UZC, NODE = 29, CONS = 33.99281 ) // BCNODE( ADD, URC, NODE = 30, CONS = 1.53897 ) BCNODE( ADD, UTHE, NODE = 30, CONS = -36.02643 ) BCNODE( ADD, UZC, NODE = 30, CONS = 32.62016 ) // BCNODE( ADD, URC, NODE = 31, CONS = -0.45382 ) BCNODE( ADD, UTHE, NODE = 31, CONS = -26.0839 ) BCNODE( ADD, UZC, NODE = 31, CONS = 24.74999 ) // BCNODE( ADD, URC, NODE = 2, CONS = 0 ) BCNODE( ADD, UTHE, NODE = 2, CONS = 0 ) BCNODE( ADD, UZC, NODE = 2, CONS = 0 ) // BCNODE( ADD, VELO, ENTI = "wall", ZERO, X, Y, Z ) BCNODE( ADD, URC, ENTI = "axi-sym", ZERO, X, Y, Z ) // BCNODE( SURF, CONS = 0, NODE = 95 )

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136 Appendix VII (Continued) BCNODE( SURF, CONS = 0, NODE = 434 ) BCNODE( ADD, COOR, NODE = 95 ) BCNODE( ADD, COOR, NODE = 125 ) // ICNODE( ADD, URC, NODE = 1, CONS = 0 ) ICNODE( ADD, UTHE, NODE = 1, CONS = 0 ) ICNODE( ADD, UZC, NODE = 1, CONS = 47.19336 ) // ICNODE( ADD, URC, NODE = 3, CONS = 1.08732 ) ICNODE( ADD, UTHE, NODE = 3, CONS = -0.53563 ) ICNODE( ADD, UZC, NODE = 3, CONS = 17.19441 ) // ICNODE( ADD, URC, NODE = 4, CONS = 2.17465 ) ICNODE( ADD, UTHE, NODE = 4, CONS = -1.07127 ) ICNODE( ADD, UZC, NODE = 4, CONS = 34.38882 ) // ICNODE( ADD, URC, NODE = 5, CONS = 3.52669 ) ICNODE( ADD, UTHE, NODE = 5, CONS = -1.63022 ) ICNODE( ADD, UZC, NODE = 5, CONS = 44.52068 ) // ICNODE( ADD, URC, NODE = 6, CONS = 3.72529 ) ICNODE( ADD, UTHE, NODE = 6, CONS = -2.22102 ) ICNODE( ADD, UZC, NODE = 6, CONS = 43.30954 ) // ICNODE( ADD, URC, NODE = 7, CONS = 5.31261 ) ICNODE( ADD, UTHE, NODE = 7, CONS = -2.80722 ) ICNODE( ADD, UZC, NODE = 7, CONS = 39.04591 ) // ICNODE( ADD, URC, NODE = 8, CONS = 5.59452 ) ICNODE( ADD, UTHE, NODE = 8, CONS = -3.42835 ) ICNODE( ADD, UZC, NODE = 8, CONS = 34.83996 ) // ICNODE( ADD, URC, NODE = 9, CONS = 5.77731 ) ICNODE( ADD, UTHE, NODE = 9, CONS = -4.13563 ) ICNODE( ADD, UZC, NODE = 9, CONS = 30.35985 ) // ICNODE( ADD, URC, NODE = 10, CONS = 6.4748 ) ICNODE( ADD, UTHE, NODE = 10, CONS = -4.8297 ) ICNODE( ADD, UZC, NODE = 10, CONS = 26.00255 ) // ICNODE( ADD, URC, NODE = 11, CONS = 6.08714 ) ICNODE( ADD, UTHE, NODE = 11, CONS = -5.56654 ) ICNODE( ADD, UZC, NODE = 11, CONS = 21.58722 ) // ICNODE( ADD, URC, NODE = 12, CONS = 6.17664 ) ICNODE( ADD, UTHE, NODE = 12, CONS = -6.55613 ) ICNODE( ADD, UZC, NODE = 12, CONS = 17.6622 ) // ICNODE( ADD, URC, NODE = 13, CONS = 6.1046 ) ICNODE( ADD, UTHE, NODE = 13, CONS = -7.69538 ) ICNODE( ADD, UZC, NODE = 13, CONS = 13.98276 ) // ICNODE( ADD, URC, NODE = 14, CONS = 5.91907 ) ICNODE( ADD, UTHE, NODE = 14, CONS = -8.8751 )

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137 Appendix VII (Continued) ICNODE( ADD, UZC, NODE = 14, CONS = 11.17852 ) // ICNODE( ADD, URC, NODE = 15, CONS = 5.79201 ) ICNODE( ADD, UTHE, NODE = 15, CONS = -9.95338 ) ICNODE( ADD, UZC, NODE = 15, CONS = 9.18139 ) // ICNODE( ADD, URC, NODE = 16, CONS = 5.29163 ) ICNODE( ADD, UTHE, NODE = 16, CONS = -11.65498 ) ICNODE( ADD, UZC, NODE = 16, CONS = 8.71487 ) // ICNODE( ADD, URC, NODE = 17, CONS = 4.92335 ) ICNODE( ADD, UTHE, NODE = 17, CONS = -13.6164 ) ICNODE( ADD, UZC, NODE = 17, CONS = 9.33896 ) // ICNODE( ADD, URC, NODE = 18, CONS = 4.41826 ) ICNODE( ADD, UTHE, NODE = 18, CONS = -15.63676 ) ICNODE( ADD, UZC, NODE = 18, CONS = 10.32914 ) // ICNODE( ADD, URC, NODE = 19, CONS = 4.08265 ) ICNODE( ADD, UTHE, NODE = 19, CONS = -17.65407 ) ICNODE( ADD, UZC, NODE = 19, CONS = 11.78129 ) // ICNODE( ADD, URC, NODE = 20, CONS = 3.82908 ) ICNODE( ADD, UTHE, NODE = 20, CONS = -19.62029 ) ICNODE( ADD, UZC, NODE = 20, CONS = 13.34846 ) // ICNODE( ADD, URC, NODE = 21, CONS = 3.6567 ) ICNODE( ADD, UTHE, NODE = 21, CONS = -21.55171 ) ICNODE( ADD, UZC, NODE = 21, CONS = 15.06358 ) // ICNODE( ADD, URC, NODE = 22, CONS = 3.47798 ) ICNODE( ADD, UTHE, NODE = 22, CONS = -23.06131 ) ICNODE( ADD, UZC, NODE = 22, CONS = 16.85193 ) // ICNODE( ADD, URC, NODE = 23, CONS = 3.56426 ) ICNODE( ADD, UTHE, NODE = 23, CONS = -24.60996 ) ICNODE( ADD, UZC, NODE = 23, CONS = 18.65726 ) // ICNODE( ADD, URC, NODE = 24, CONS = 3.2607 ) ICNODE( ADD, UTHE, NODE = 24, CONS = -26.69053 ) ICNODE( ADD, UZC, NODE = 24, CONS = 21.20417 ) // ICNODE( ADD, URC, NODE = 25, CONS = 3.384 ) ICNODE( ADD, UTHE, NODE = 25, CONS = -28.92644 ) ICNODE( ADD, UZC, NODE = 25, CONS = 23.78581 ) // ICNODE( ADD, URC, NODE = 26, CONS = 2.99219 ) ICNODE( ADD, UTHE, NODE = 26, CONS = -31.26015 ) ICNODE( ADD, UZC, NODE = 26, CONS = 26.35917 ) // ICNODE( ADD, URC, NODE = 27, CONS = 3.19456 ) ICNODE( ADD, UTHE, NODE = 27, CONS = -33.94675 ) ICNODE( ADD, UZC, NODE = 27, CONS = 29.07778 ) //

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138 Appendix VII (Continued) ICNODE( ADD, URC, NODE = 28, CONS = 3.21875 ) ICNODE( ADD, UTHE, NODE = 28, CONS = -36.382 ) ICNODE( ADD, UZC, NODE = 28, CONS = 31.79309 ) // ICNODE( ADD, URC, NODE = 29, CONS = 2.64956 ) ICNODE( ADD, UTHE, NODE = 29, CONS = -38.22577 ) ICNODE( ADD, UZC, NODE = 29, CONS = 33.99281 ) // ICNODE( ADD, URC, NODE = 30, CONS = 1.53897 ) ICNODE( ADD, UTHE, NODE = 30, CONS = -36.02643 ) ICNODE( ADD, UZC, NODE = 30, CONS = 32.62016 ) // ICNODE( ADD, URC, NODE = 31, CONS = -0.45382 ) ICNODE( ADD, UTHE, NODE = 31, CONS = -26.0839 ) ICNODE( ADD, UZC, NODE = 31, CONS = 24.74999 ) // ICNODE( ADD, URC, NODE = 2, CONS = 0 ) ICNODE( ADD, UTHE, NODE = 2, CONS = 0 ) ICNODE( ADD, UZC, NODE = 2, CONS = 0 ) // ICNODE( ADD, VELO, ENTI = "wall", ZERO, X, Y, Z ) ICNODE( ADD, URC, ENTI = "axi-sym", ZERO, X, Y, Z ) // END( )

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139 Appendix VIII: FIPREP File for the Small Nozzle with Free Surface (5.678 x 10-7 m3/s, FC-77) FIPREP( ) DENSITY( ADD, SET = "fc-77", CONS = 1.78 ) VISCOSITY( ADD, SET = "fc-77", CONS = 0.01424, MIXL ) SURFACETENSION( ADD, SET = "fc-77", CONS = 15 ) // PRESSURE( ADD, MIXE = 1e-16, DISC ) DATAPRINT( ADD, CONT ) EXECUTION( ADD, NEWJ ) PRINTOUT( ADD, NONE, BOUN ) PROBLEM( ADD, CYLI, INCO, TRAN, TURB, NONL, NEWT, MOME, ISOT, FREE, SING ) SOLUTION( ADD, N.R. = 80, KINE = 25, VELC = 0.0001, RESC = 0.01, SURF = 0.001 ) BODYFORCE( ADD, CONS, FZC = 981, FRC = 0, FTHE = 0 ) TIMEINTEGRATION( ADD, BACK, NSTE = 600, TSTA = 0, DT = 1e-07, VARI, WIND = 0.9, NOFI = 10 ) OPTIONS( ADD, UPWI ) UPWINDING( ADD, STRE ) RELAXATION( ) 0.6, 0.6, 0.6, 0, 0, 0.1 RENUMBER( ADD, PROF ) EDDYVISCOSITY( ADD, SPEZ ) POSTPROCESS( ADD, NBLO = 2, NOPT, NOPA ) 1, 200, 200 201, 600, 5 // ENTITY( ADD, NAME = "fluid", FLUI, PROP = "fc-77" ) ENTITY( ADD, NAME = "inlet", PLOT ) ENTITY( ADD, NAME = "outlet", PLOT ) ENTITY( ADD, NAME = "axi-sym", PLOT ) ENTITY( ADD, NAME = "wall", WALL ) ENTITY( ADD, NAME = "free", SURF, DEPT = 0, SPIN, STRA ) // BCNODE( ADD, URC, NODE = 1, CONS = 0 ) BCNODE( ADD, UTHE, NODE = 1, CONS = 0 ) BCNODE( ADD, UZC, NODE = 1, CONS = 61.46608 ) // BCNODE( ADD, URC, NODE = 3, CONS = 1.38923 ) BCNODE( ADD, UTHE, NODE = 3, CONS = -0.69815 ) BCNODE( ADD, UZC, NODE = 3, CONS = 22.39484 ) // BCNODE( ADD, URC, NODE = 4, CONS = 2.77846 ) BCNODE( ADD, UTHE, NODE = 4, CONS = -1.39631 ) BCNODE( ADD, UZC, NODE = 4, CONS = 44.78969 ) // BCNODE( ADD, URC, NODE = 5, CONS = 4.51594 ) BCNODE( ADD, UTHE, NODE = 5, CONS = -2.12749 ) BCNODE( ADD, UZC, NODE = 5, CONS = 57.97758 ) // BCNODE( ADD, URC, NODE = 6, CONS = 4.74756 ) BCNODE( ADD, UTHE, NODE = 6, CONS = -2.90002 ) BCNODE( ADD, UZC, NODE = 6, CONS = 56.37952 )

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140 Appendix VIII (Continued) BCNODE( ADD, URC, NODE = 7, CONS = 6.79597 ) BCNODE( ADD, UTHE, NODE = 7, CONS = -3.66347 ) BCNODE( ADD, UZC, NODE = 7, CONS = 50.81691 ) // BCNODE( ADD, URC, NODE = 8, CONS = 7.14607 ) BCNODE( ADD, UTHE, NODE = 8, CONS = -4.47245 ) BCNODE( ADD, UZC, NODE = 8, CONS = 45.33659 ) // BCNODE( ADD, URC, NODE = 9, CONS = 7.36961 ) BCNODE( ADD, UTHE, NODE = 9, CONS = -5.39415 ) BCNODE( ADD, UZC, NODE = 9, CONS = 39.50485 ) // BCNODE( ADD, URC, NODE = 10, CONS = 8.26038 ) BCNODE( ADD, UTHE, NODE = 10, CONS = -6.29716 ) BCNODE( ADD, UZC, NODE = 10, CONS = 33.83576 ) // BCNODE( ADD, URC, NODE = 11, CONS = 7.75489 ) BCNODE( ADD, UTHE, NODE = 11, CONS = -7.24336 ) BCNODE( ADD, UZC, NODE = 11, CONS = 28.09456 ) // BCNODE( ADD, URC, NODE = 12, CONS = 7.87079 ) BCNODE( ADD, UTHE, NODE = 12, CONS = -8.52651 ) BCNODE( ADD, UZC, NODE = 12, CONS = 22.98879 ) // BCNODE( ADD, URC, NODE = 13, CONS = 7.77814 ) BCNODE( ADD, UTHE, NODE = 13, CONS = -10.00076 ) BCNODE( ADD, UZC, NODE = 13, CONS = 18.20037 ) // BCNODE( ADD, URC, NODE = 14, CONS = 7.54143 ) BCNODE( ADD, UTHE, NODE = 14, CONS = -11.51883 ) BCNODE( ADD, UZC, NODE = 14, CONS = 14.54412 ) // BCNODE( ADD, URC, NODE = 15, CONS = 7.38675 ) BCNODE( ADD, UTHE, NODE = 15, CONS = -12.90445 ) BCNODE( ADD, UZC, NODE = 15, CONS = 11.93906 ) // BCNODE( ADD, URC, NODE = 16, CONS = 6.7616 ) BCNODE( ADD, UTHE, NODE = 16, CONS = -15.0828 ) BCNODE( ADD, UZC, NODE = 16, CONS = 11.31395 ) // BCNODE( ADD, URC, NODE = 17, CONS = 6.3059 ) BCNODE( ADD, UTHE, NODE = 17, CONS = -17.61089 ) BCNODE( ADD, UZC, NODE = 17, CONS = 12.06558 ) // BCNODE( ADD, URC, NODE = 18, CONS = 5.68535 ) BCNODE( ADD, UTHE, NODE = 18, CONS = -20.20623 ) BCNODE( ADD, UZC, NODE = 18, CONS = 13.29073 ) // BCNODE( ADD, URC, NODE = 19, CONS = 5.27988 ) BCNODE( ADD, UTHE, NODE = 19, CONS = -22.82784 ) BCNODE( ADD, UZC, NODE = 19, CONS = 15.09659 ) // BCNODE( ADD, URC, NODE = 20, CONS = 4.98541 ) BCNODE( ADD, UTHE, NODE = 20, CONS = -25.38318 )

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141 Appendix VIII (Continued) BCNODE( ADD, UZC, NODE = 20, CONS = 17.04449 ) // BCNODE( ADD, URC, NODE = 21, CONS = 4.80042 ) BCNODE( ADD, UTHE, NODE = 21, CONS = -27.89366 ) BCNODE( ADD, UZC, NODE = 21, CONS = 19.17568 ) // BCNODE( ADD, URC, NODE = 22, CONS = 4.63737 ) BCNODE( ADD, UTHE, NODE = 22, CONS = -29.86397 ) BCNODE( ADD, UZC, NODE = 22, CONS = 21.44165 ) // BCNODE( ADD, URC, NODE = 23, CONS = 4.81106 ) BCNODE( ADD, UTHE, NODE = 23, CONS = -31.91627 ) BCNODE( ADD, UZC, NODE = 23, CONS = 23.73389 ) // BCNODE( ADD, URC, NODE = 24, CONS = 4.46516 ) BCNODE( ADD, UTHE, NODE = 24, CONS = -34.67404 ) BCNODE( ADD, UZC, NODE = 24, CONS = 27.02544 ) // BCNODE( ADD, URC, NODE = 25, CONS = 4.6563 ) BCNODE( ADD, UTHE, NODE = 25, CONS = -37.68634 ) BCNODE( ADD, UZC, NODE = 25, CONS = 30.37641 ) // BCNODE( ADD, URC, NODE = 26, CONS = 4.17992 ) BCNODE( ADD, UTHE, NODE = 26, CONS = -40.82009 ) BCNODE( ADD, UZC, NODE = 26, CONS = 33.73497 ) // BCNODE( ADD, URC, NODE = 27, CONS = 4.41656 ) BCNODE( ADD, UTHE, NODE = 27, CONS = -44.58921 ) BCNODE( ADD, UZC, NODE = 27, CONS = 37.34748 ) // BCNODE( ADD, URC, NODE = 28, CONS = 4.42043 ) BCNODE( ADD, UTHE, NODE = 28, CONS = -48.06489 ) BCNODE( ADD, UZC, NODE = 28, CONS = 40.97633 ) // BCNODE( ADD, URC, NODE = 29, CONS = 3.65784 ) BCNODE( ADD, UTHE, NODE = 29, CONS = -50.96504 ) BCNODE( ADD, UZC, NODE = 29, CONS = 44.15613 ) // BCNODE( ADD, URC, NODE = 30, CONS = 2.17363 ) BCNODE( ADD, UTHE, NODE = 30, CONS = -49.1287 ) BCNODE( ADD, UZC, NODE = 30, CONS = 43.39886 ) // BCNODE( ADD, URC, NODE = 31, CONS = -0.54621 ) BCNODE( ADD, UTHE, NODE = 31, CONS = -36.59103 ) BCNODE( ADD, UZC, NODE = 31, CONS = 33.82282 ) // BCNODE( ADD, URC, NODE = 2, CONS = 0 ) BCNODE( ADD, UTHE, NODE = 2, CONS = 0 ) BCNODE( ADD, UZC, NODE = 2, CONS = 0 ) // BCNODE( ADD, VELO, ENTI = "wall", ZERO, X, Y, Z ) BCNODE( ADD, URC, ENTI = "axi-sym", ZERO, X, Y, Z ) // BCNODE( SURF, CONS = 0, NODE = 95 )

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142 Appendix VIII (Continued) BCNODE( SURF, CONS = 0, NODE = 434 ) BCNODE( ADD, COOR, NODE = 95 ) BCNODE( ADD, COOR, NODE = 125 ) // ICNODE( ADD, URC, NODE = 1, CONS = 0 ) ICNODE( ADD, UTHE, NODE = 1, CONS = 0 ) ICNODE( ADD, UZC, NODE = 1, CONS = 61.46608 ) // ICNODE( ADD, URC, NODE = 3, CONS = 1.38923 ) ICNODE( ADD, UTHE, NODE = 3, CONS = -0.69815 ) ICNODE( ADD, UZC, NODE = 3, CONS = 22.39484 ) // ICNODE( ADD, URC, NODE = 4, CONS = 2.77846 ) ICNODE( ADD, UTHE, NODE = 4, CONS = -1.39631 ) ICNODE( ADD, UZC, NODE = 4, CONS = 44.78969 ) // ICNODE( ADD, URC, NODE = 5, CONS = 4.51594 ) ICNODE( ADD, UTHE, NODE = 5, CONS = -2.12749 ) ICNODE( ADD, UZC, NODE = 5, CONS = 57.97758 ) // ICNODE( ADD, URC, NODE = 6, CONS = 4.74756 ) ICNODE( ADD, UTHE, NODE = 6, CONS = -2.90002 ) ICNODE( ADD, UZC, NODE = 6, CONS = 56.37952 ) // ICNODE( ADD, URC, NODE = 7, CONS = 6.79597 ) ICNODE( ADD, UTHE, NODE = 7, CONS = -3.66347 ) ICNODE( ADD, UZC, NODE = 7, CONS = 50.81691 ) // ICNODE( ADD, URC, NODE = 8, CONS = 7.14607 ) ICNODE( ADD, UTHE, NODE = 8, CONS = -4.47245 ) ICNODE( ADD, UZC, NODE = 8, CONS = 45.33659 ) // ICNODE( ADD, URC, NODE = 9, CONS = 7.36961 ) ICNODE( ADD, UTHE, NODE = 9, CONS = -5.39415 ) ICNODE( ADD, UZC, NODE = 9, CONS = 39.50485 ) // ICNODE( ADD, URC, NODE = 10, CONS = 8.26038 ) ICNODE( ADD, UTHE, NODE = 10, CONS = -6.29716 ) ICNODE( ADD, UZC, NODE = 10, CONS = 33.83576 ) // ICNODE( ADD, URC, NODE = 11, CONS = 7.75489 ) ICNODE( ADD, UTHE, NODE = 11, CONS = -7.24336 ) ICNODE( ADD, UZC, NODE = 11, CONS = 28.09456 ) // ICNODE( ADD, URC, NODE = 12, CONS = 7.87079 ) ICNODE( ADD, UTHE, NODE = 12, CONS = -8.52651 ) ICNODE( ADD, UZC, NODE = 12, CONS = 22.98879 ) // ICNODE( ADD, URC, NODE = 13, CONS = 7.77814 ) ICNODE( ADD, UTHE, NODE = 13, CONS = -10.00076 ) ICNODE( ADD, UZC, NODE = 13, CONS = 18.20037 ) // ICNODE( ADD, URC, NODE = 14, CONS = 7.54143 ) ICNODE( ADD, UTHE, NODE = 14, CONS = -11.51883 )

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143 Appendix VIII (Continued) ICNODE( ADD, UZC, NODE = 14, CONS = 14.54412 ) // ICNODE( ADD, URC, NODE = 15, CONS = 7.38675 ) ICNODE( ADD, UTHE, NODE = 15, CONS = -12.90445 ) ICNODE( ADD, UZC, NODE = 15, CONS = 11.93906 ) // ICNODE( ADD, URC, NODE = 16, CONS = 6.7616 ) ICNODE( ADD, UTHE, NODE = 16, CONS = -15.0828 ) ICNODE( ADD, UZC, NODE = 16, CONS = 11.31395 ) // ICNODE( ADD, URC, NODE = 17, CONS = 6.3059 ) ICNODE( ADD, UTHE, NODE = 17, CONS = -17.61089 ) ICNODE( ADD, UZC, NODE = 17, CONS = 12.06558 ) // ICNODE( ADD, URC, NODE = 18, CONS = 5.68535 ) ICNODE( ADD, UTHE, NODE = 18, CONS = -20.20623 ) ICNODE( ADD, UZC, NODE = 18, CONS = 13.29073 ) // ICNODE( ADD, URC, NODE = 19, CONS = 5.27988 ) ICNODE( ADD, UTHE, NODE = 19, CONS = -22.82784 ) ICNODE( ADD, UZC, NODE = 19, CONS = 15.09659 ) // ICNODE( ADD, URC, NODE = 20, CONS = 4.98541 ) ICNODE( ADD, UTHE, NODE = 20, CONS = -25.38318 ) ICNODE( ADD, UZC, NODE = 20, CONS = 17.04449 ) // ICNODE( ADD, URC, NODE = 21, CONS = 4.80042 ) ICNODE( ADD, UTHE, NODE = 21, CONS = -27.89366 ) ICNODE( ADD, UZC, NODE = 21, CONS = 19.17568 ) // ICNODE( ADD, URC, NODE = 22, CONS = 4.63737 ) ICNODE( ADD, UTHE, NODE = 22, CONS = -29.86397 ) ICNODE( ADD, UZC, NODE = 22, CONS = 21.44165 ) // ICNODE( ADD, URC, NODE = 23, CONS = 4.81106 ) ICNODE( ADD, UTHE, NODE = 23, CONS = -31.91627 ) ICNODE( ADD, UZC, NODE = 23, CONS = 23.73389 ) // ICNODE( ADD, URC, NODE = 24, CONS = 4.46516 ) ICNODE( ADD, UTHE, NODE = 24, CONS = -34.67404 ) ICNODE( ADD, UZC, NODE = 24, CONS = 27.02544 ) // ICNODE( ADD, URC, NODE = 25, CONS = 4.6563 ) ICNODE( ADD, UTHE, NODE = 25, CONS = -37.68634 ) ICNODE( ADD, UZC, NODE = 25, CONS = 30.37641 ) // ICNODE( ADD, URC, NODE = 26, CONS = 4.17992 ) ICNODE( ADD, UTHE, NODE = 26, CONS = -40.82009 ) ICNODE( ADD, UZC, NODE = 26, CONS = 33.73497 ) // ICNODE( ADD, URC, NODE = 27, CONS = 4.41656 ) ICNODE( ADD, UTHE, NODE = 27, CONS = -44.58921 ) ICNODE( ADD, UZC, NODE = 27, CONS = 37.34748 ) //

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144 Appendix VIII (Continued) ICNODE( ADD, URC, NODE = 28, CONS = 4.42043 ) ICNODE( ADD, UTHE, NODE = 28, CONS = -48.06489 ) ICNODE( ADD, UZC, NODE = 28, CONS = 40.97633 ) // ICNODE( ADD, URC, NODE = 29, CONS = 3.65784 ) ICNODE( ADD, UTHE, NODE = 29, CONS = -50.96504 ) ICNODE( ADD, UZC, NODE = 29, CONS = 44.15613 ) // ICNODE( ADD, URC, NODE = 30, CONS = 2.17363 ) ICNODE( ADD, UTHE, NODE = 30, CONS = -49.1287 ) ICNODE( ADD, UZC, NODE = 30, CONS = 43.39886 ) // ICNODE( ADD, URC, NODE = 31, CONS = -0.54621 ) ICNODE( ADD, UTHE, NODE = 31, CONS = -36.59103 ) ICNODE( ADD, UZC, NODE = 31, CONS = 33.82282 ) // ICNODE( ADD, URC, NODE = 2, CONS = 0 ) ICNODE( ADD, UTHE, NODE = 2, CONS = 0 ) ICNODE( ADD, UZC, NODE = 2, CONS = 0 ) // ICNODE( ADD, VELO, ENTI = "wall", ZERO, X, Y, Z ) ICNODE( ADD, URC, ENTI = "axi-sym", ZERO, X, Y, Z ) // END( )

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145 Appendix IX: FIPREP File for the Small Nozzle with Free Surface (4.416 x 10-7 m3/s, FC-87) FIPREP( ) DENSITY( ADD, SET = "fc-87", CONS = 1.63 ) VISCOSITY( ADD, SET = "fc-87", CONS = 0.00453, MIXL ) SURFACETENSION( ADD, SET = "fc-87", CONS = 9.5 ) // PRESSURE( ADD, MIXE = 1e-16, DISC ) DATAPRINT( ADD, CONT ) EXECUTION( ADD, NEWJ ) PRINTOUT( ADD, NONE, BOUN ) PROBLEM( ADD, CYLI, INCO, TRAN, TURB, NONL, NEWT, MOME, ISOT, FREE, SING ) SOLUTION( ADD, N.R. = 80, KINE = 25, VELC = 0.0001, RESC = 0.01, SURF = 0.001 ) BODYFORCE( ADD, CONS, FZC = 981, FRC = 0, FTHE = 0 ) TIMEINTEGRATION( ADD, BACK, NSTE = 600, TSTA = 0, DT = 1e-07, VARI, WIND = 0.9, NOFI = 10 ) OPTIONS( ADD, UPWI ) UPWINDING( ADD, STRE ) RELAXATION( ) 0.6, 0.6, 0.6, 0, 0, 0.1 RENUMBER( ADD, PROF ) EDDYVISCOSITY( ADD, SPEZ ) POSTPROCESS( ADD, NBLO = 2, NOPT, NOPA ) 1, 200, 200 201, 600, 5 // ENTITY( ADD, NAME = "fluid", FLUI, PROP = "fc-87" ) ENTITY( ADD, NAME = "inlet", PLOT ) ENTITY( ADD, NAME = "outlet", PLOT ) ENTITY( ADD, NAME = "axi-sym", PLOT ) ENTITY( ADD, NAME = "wall", WALL ) ENTITY( ADD, NAME = "free", SURF, DEPT = 0, SPIN, STRA ) // BCNODE( ADD, URC, NODE = 1, CONS = 0 ) BCNODE( ADD, UTHE, NODE = 1, CONS = 0 ) BCNODE( ADD, UZC, NODE = 1, CONS = 48.76409 ) // BCNODE( ADD, URC, NODE = 3, CONS = 1.05741 ) BCNODE( ADD, UTHE, NODE = 3, CONS = -0.56415 ) BCNODE( ADD, UZC, NODE = 3, CONS = 17.76712 ) // BCNODE( ADD, URC, NODE = 4, CONS = 2.11483 ) BCNODE( ADD, UTHE, NODE = 4, CONS = -1.12831 ) BCNODE( ADD, UZC, NODE = 4, CONS = 35.53424 ) // BCNODE( ADD, URC, NODE = 5, CONS = 3.45464 ) BCNODE( ADD, UTHE, NODE = 5, CONS = -1.71901 ) BCNODE( ADD, UZC, NODE = 5, CONS = 45.98943 ) // BCNODE( ADD, URC, NODE = 6, CONS = 3.59231 ) BCNODE( ADD, UTHE, NODE = 6, CONS = -2.3428 ) BCNODE( ADD, UZC, NODE = 6, CONS = 44.68405 )

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146 Appendix IX (Continued) BCNODE( ADD, URC, NODE = 7, CONS = 5.18527 ) BCNODE( ADD, UTHE, NODE = 7, CONS = -2.96061 ) BCNODE( ADD, UZC, NODE = 7, CONS = 40.26961 ) // BCNODE( ADD, URC, NODE = 8, CONS = 5.43305 ) BCNODE( ADD, UTHE, NODE = 8, CONS = -3.61412 ) BCNODE( ADD, UZC, NODE = 8, CONS = 35.92418 ) // BCNODE( ADD, URC, NODE = 9, CONS = 5.58447 ) BCNODE( ADD, UTHE, NODE = 9, CONS = -4.35033 ) BCNODE( ADD, UZC, NODE = 9, CONS = 31.31462 ) // BCNODE( ADD, URC, NODE = 10, CONS = 6.26426 ) BCNODE( ADD, UTHE, NODE = 10, CONS = -5.06892 ) BCNODE( ADD, UZC, NODE = 10, CONS = 26.84638 ) // BCNODE( ADD, URC, NODE = 11, CONS = 5.85134 ) BCNODE( ADD, UTHE, NODE = 11, CONS = -5.8287 ) BCNODE( ADD, UZC, NODE = 11, CONS = 22.33005 ) // BCNODE( ADD, URC, NODE = 12, CONS = 5.93474 ) BCNODE( ADD, UTHE, NODE = 12, CONS = -6.83626 ) BCNODE( ADD, UZC, NODE = 12, CONS = 18.32279 ) // BCNODE( ADD, URC, NODE = 13, CONS = 5.85521 ) BCNODE( ADD, UTHE, NODE = 13, CONS = -7.99433 ) BCNODE( ADD, UZC, NODE = 13, CONS = 14.56398 ) // BCNODE( ADD, URC, NODE = 14, CONS = 5.66799 ) BCNODE( ADD, UTHE, NODE = 14, CONS = -9.19129 ) BCNODE( ADD, UZC, NODE = 14, CONS = 11.69289 ) // BCNODE( ADD, URC, NODE = 15, CONS = 5.56124 ) BCNODE( ADD, UTHE, NODE = 15, CONS = -10.26318 ) BCNODE( ADD, UZC, NODE = 15, CONS = 9.65426 ) // BCNODE( ADD, URC, NODE = 16, CONS = 5.1037 ) BCNODE( ADD, UTHE, NODE = 16, CONS = -11.93734 ) BCNODE( ADD, UZC, NODE = 16, CONS = 9.14815 ) // BCNODE( ADD, URC, NODE = 17, CONS = 4.76974 ) BCNODE( ADD, UTHE, NODE = 17, CONS = -13.86929 ) BCNODE( ADD, UZC, NODE = 17, CONS = 9.66416 ) // BCNODE( ADD, URC, NODE = 18, CONS = 4.32997 ) BCNODE( ADD, UTHE, NODE = 18, CONS = -15.89418 ) BCNODE( ADD, UZC, NODE = 18, CONS = 10.52186 ) // BCNODE( ADD, URC, NODE = 19, CONS = 4.07234 ) BCNODE( ADD, UTHE, NODE = 19, CONS = -17.95097 ) BCNODE( ADD, UZC, NODE = 19, CONS = 11.79999 ) // BCNODE( ADD, URC, NODE = 20, CONS = 3.90474 ) BCNODE( ADD, UTHE, NODE = 20, CONS = -19.95912 )

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147 Appendix IX (Continued) BCNODE( ADD, UZC, NODE = 20, CONS = 13.17338 ) // BCNODE( ADD, URC, NODE = 21, CONS = 3.82529 ) BCNODE( ADD, UTHE, NODE = 21, CONS = -21.9358 ) BCNODE( ADD, UZC, NODE = 21, CONS = 14.67173 ) // BCNODE( ADD, URC, NODE = 22, CONS = 3.82126 ) BCNODE( ADD, UTHE, NODE = 22, CONS = -23.49885 ) BCNODE( ADD, UZC, NODE = 22, CONS = 16.29199 ) // BCNODE( ADD, URC, NODE = 23, CONS = 4.07645 ) BCNODE( ADD, UTHE, NODE = 23, CONS = -25.13544 ) BCNODE( ADD, UZC, NODE = 23, CONS = 17.94082 ) // BCNODE( ADD, URC, NODE = 24, CONS = 3.89705 ) BCNODE( ADD, UTHE, NODE = 24, CONS = -27.38302 ) BCNODE( ADD, UZC, NODE = 24, CONS = 20.41095 ) // BCNODE( ADD, URC, NODE = 25, CONS = 4.118 ) BCNODE( ADD, UTHE, NODE = 25, CONS = -29.83608 ) BCNODE( ADD, UZC, NODE = 25, CONS = 22.95457 ) // BCNODE( ADD, URC, NODE = 26, CONS = 3.80065 ) BCNODE( ADD, UTHE, NODE = 26, CONS = -32.49339 ) BCNODE( ADD, UZC, NODE = 26, CONS = 25.52205 ) // BCNODE( ADD, URC, NODE = 27, CONS = 3.94158 ) BCNODE( ADD, UTHE, NODE = 27, CONS = -35.78861 ) BCNODE( ADD, UZC, NODE = 27, CONS = 28.39568 ) // BCNODE( ADD, URC, NODE = 28, CONS = 3.86758 ) BCNODE( ADD, UTHE, NODE = 28, CONS = -39.00389 ) BCNODE( ADD, UZC, NODE = 28, CONS = 31.32629 ) // BCNODE( ADD, URC, NODE = 29, CONS = 3.21539 ) BCNODE( ADD, UTHE, NODE = 29, CONS = -42.10453 ) BCNODE( ADD, UZC, NODE = 29, CONS = 34.23171 ) // BCNODE( ADD, URC, NODE = 30, CONS = 2.01872 ) BCNODE( ADD, UTHE, NODE = 30, CONS = -42.78249 ) BCNODE( ADD, UZC, NODE = 30, CONS = 35.4695 ) // BCNODE( ADD, URC, NODE = 31, CONS = -0.34308 ) BCNODE( ADD, UTHE, NODE = 31, CONS = -34.1668 ) BCNODE( ADD, UZC, NODE = 31, CONS = 29.48666 ) // BCNODE( ADD, URC, NODE = 2, CONS = 0 ) BCNODE( ADD, UTHE, NODE = 2, CONS = 0 ) BCNODE( ADD, UZC, NODE = 2, CONS = 0 ) // BCNODE( ADD, VELO, ENTI = "wall", ZERO, X, Y, Z ) BCNODE( ADD, URC, ENTI = "axi-sym", ZERO, X, Y, Z ) // BCNODE( SURF, CONS = 0, NODE = 95 )

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148 Appendix IX (Continued) BCNODE( SURF, CONS = 0, NODE = 434 ) BCNODE( ADD, COOR, NODE = 95 ) BCNODE( ADD, COOR, NODE = 125 ) // ICNODE( ADD, URC, NODE = 1, CONS = 0 ) ICNODE( ADD, UTHE, NODE = 1, CONS = 0 ) ICNODE( ADD, UZC, NODE = 1, CONS = 48.76409 ) // ICNODE( ADD, URC, NODE = 3, CONS = 1.05741 ) ICNODE( ADD, UTHE, NODE = 3, CONS = -0.56415 ) ICNODE( ADD, UZC, NODE = 3, CONS = 17.76712 ) // ICNODE( ADD, URC, NODE = 4, CONS = 2.11483 ) ICNODE( ADD, UTHE, NODE = 4, CONS = -1.12831 ) ICNODE( ADD, UZC, NODE = 4, CONS = 35.53424 ) // ICNODE( ADD, URC, NODE = 5, CONS = 3.45464 ) ICNODE( ADD, UTHE, NODE = 5, CONS = -1.71901 ) ICNODE( ADD, UZC, NODE = 5, CONS = 45.98943 ) // ICNODE( ADD, URC, NODE = 6, CONS = 3.59231 ) ICNODE( ADD, UTHE, NODE = 6, CONS = -2.3428 ) ICNODE( ADD, UZC, NODE = 6, CONS = 44.68405 ) // ICNODE( ADD, URC, NODE = 7, CONS = 5.18527 ) ICNODE( ADD, UTHE, NODE = 7, CONS = -2.96061 ) ICNODE( ADD, UZC, NODE = 7, CONS = 40.26961 ) // ICNODE( ADD, URC, NODE = 8, CONS = 5.43305 ) ICNODE( ADD, UTHE, NODE = 8, CONS = -3.61412 ) ICNODE( ADD, UZC, NODE = 8, CONS = 35.92418 ) // ICNODE( ADD, URC, NODE = 9, CONS = 5.58447 ) ICNODE( ADD, UTHE, NODE = 9, CONS = -4.35033 ) ICNODE( ADD, UZC, NODE = 9, CONS = 31.31462 ) // ICNODE( ADD, URC, NODE = 10, CONS = 6.26426 ) ICNODE( ADD, UTHE, NODE = 10, CONS = -5.06892 ) ICNODE( ADD, UZC, NODE = 10, CONS = 26.84638 ) // ICNODE( ADD, URC, NODE = 11, CONS = 5.85134 ) ICNODE( ADD, UTHE, NODE = 11, CONS = -5.8287 ) ICNODE( ADD, UZC, NODE = 11, CONS = 22.33005 ) // ICNODE( ADD, URC, NODE = 12, CONS = 5.93474 ) ICNODE( ADD, UTHE, NODE = 12, CONS = -6.83626 ) ICNODE( ADD, UZC, NODE = 12, CONS = 18.32279 ) // ICNODE( ADD, URC, NODE = 13, CONS = 5.85521 ) ICNODE( ADD, UTHE, NODE = 13, CONS = -7.99433 ) ICNODE( ADD, UZC, NODE = 13, CONS = 14.56398 ) // ICNODE( ADD, URC, NODE = 14, CONS = 5.66799 ) ICNODE( ADD, UTHE, NODE = 14, CONS = -9.19129 )

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149 Appendix IX (Continued) ICNODE( ADD, UZC, NODE = 14, CONS = 11.69289 ) // ICNODE( ADD, URC, NODE = 15, CONS = 5.56124 ) ICNODE( ADD, UTHE, NODE = 15, CONS = -10.26318 ) ICNODE( ADD, UZC, NODE = 15, CONS = 9.65426 ) // ICNODE( ADD, URC, NODE = 16, CONS = 5.1037 ) ICNODE( ADD, UTHE, NODE = 16, CONS = -11.93734 ) ICNODE( ADD, UZC, NODE = 16, CONS = 9.14815 ) // ICNODE( ADD, URC, NODE = 17, CONS = 4.76974 ) ICNODE( ADD, UTHE, NODE = 17, CONS = -13.86929 ) ICNODE( ADD, UZC, NODE = 17, CONS = 9.66416 ) // ICNODE( ADD, URC, NODE = 18, CONS = 4.32997 ) ICNODE( ADD, UTHE, NODE = 18, CONS = -15.89418 ) ICNODE( ADD, UZC, NODE = 18, CONS = 10.52186 ) // ICNODE( ADD, URC, NODE = 19, CONS = 4.07234 ) ICNODE( ADD, UTHE, NODE = 19, CONS = -17.95097 ) ICNODE( ADD, UZC, NODE = 19, CONS = 11.79999 ) // ICNODE( ADD, URC, NODE = 20, CONS = 3.90474 ) ICNODE( ADD, UTHE, NODE = 20, CONS = -19.95912 ) ICNODE( ADD, UZC, NODE = 20, CONS = 13.17338 ) // ICNODE( ADD, URC, NODE = 21, CONS = 3.82529 ) ICNODE( ADD, UTHE, NODE = 21, CONS = -21.9358 ) ICNODE( ADD, UZC, NODE = 21, CONS = 14.67173 ) // ICNODE( ADD, URC, NODE = 22, CONS = 3.82126 ) ICNODE( ADD, UTHE, NODE = 22, CONS = -23.49885 ) ICNODE( ADD, UZC, NODE = 22, CONS = 16.29199 ) // ICNODE( ADD, URC, NODE = 23, CONS = 4.07645 ) ICNODE( ADD, UTHE, NODE = 23, CONS = -25.13544 ) ICNODE( ADD, UZC, NODE = 23, CONS = 17.94082 ) // ICNODE( ADD, URC, NODE = 24, CONS = 3.89705 ) ICNODE( ADD, UTHE, NODE = 24, CONS = -27.38302 ) ICNODE( ADD, UZC, NODE = 24, CONS = 20.41095 ) // ICNODE( ADD, URC, NODE = 25, CONS = 4.118 ) ICNODE( ADD, UTHE, NODE = 25, CONS = -29.83608 ) ICNODE( ADD, UZC, NODE = 25, CONS = 22.95457 ) // ICNODE( ADD, URC, NODE = 26, CONS = 3.80065 ) ICNODE( ADD, UTHE, NODE = 26, CONS = -32.49339 ) ICNODE( ADD, UZC, NODE = 26, CONS = 25.52205 ) // ICNODE( ADD, URC, NODE = 27, CONS = 3.94158 ) ICNODE( ADD, UTHE, NODE = 27, CONS = -35.78861 ) ICNODE( ADD, UZC, NODE = 27, CONS = 28.39568 ) //

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150 Appendix IX (Continued) ICNODE( ADD, URC, NODE = 28, CONS = 3.86758 ) ICNODE( ADD, UTHE, NODE = 28, CONS = -39.00389 ) ICNODE( ADD, UZC, NODE = 28, CONS = 31.32629 ) // ICNODE( ADD, URC, NODE = 29, CONS = 3.21539 ) ICNODE( ADD, UTHE, NODE = 29, CONS = -42.10453 ) ICNODE( ADD, UZC, NODE = 29, CONS = 34.23171 ) // ICNODE( ADD, URC, NODE = 30, CONS = 2.01872 ) ICNODE( ADD, UTHE, NODE = 30, CONS = -42.78249 ) ICNODE( ADD, UZC, NODE = 30, CONS = 35.4695 ) // ICNODE( ADD, URC, NODE = 31, CONS = -0.34308 ) ICNODE( ADD, UTHE, NODE = 31, CONS = -34.1668 ) ICNODE( ADD, UZC, NODE = 31, CONS = 29.48666 ) // ICNODE( ADD, URC, NODE = 2, CONS = 0 ) ICNODE( ADD, UTHE, NODE = 2, CONS = 0 ) ICNODE( ADD, UZC, NODE = 2, CONS = 0 ) // ICNODE( ADD, VELO, ENTI = "wall", ZERO, X, Y, Z ) ICNODE( ADD, URC, ENTI = "axi-sym", ZERO, X, Y, Z ) // END( )

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151 Appendix X: FIPREP File for the Small Nozzle with Free Surface (5.678 x 10-7 m3/s, FC-87) FIPREP( ) DENSITY( ADD, SET = "fc-87", CONS = 1.63 ) VISCOSITY( ADD, SET = "fc-87", CONS = 0.00453, MIXL ) SURFACETENSION( ADD, SET = "fc-87", CONS = 9.5 ) // PRESSURE( ADD, MIXE = 1e-16, DISC ) DATAPRINT( ADD, CONT ) EXECUTION( ADD, NEWJ ) PRINTOUT( ADD, NONE, BOUN ) PROBLEM( ADD, CYLI, INCO, TRAN, TURB, NONL, NEWT, MOME, ISOT, FREE, SING ) SOLUTION( ADD, N.R. = 80, KINE = 25, VELC = 0.0001, RESC = 0.01, SURF = 0.001 ) BODYFORCE( ADD, CONS, FZC = 981, FRC = 0, FTHE = 0 ) TIMEINTEGRATION( ADD, BACK, NSTE = 600, TSTA = 0, DT = 1e-07, VARI, WIND = 0.9, NOFI = 10 ) OPTIONS( ADD, UPWI ) UPWINDING( ADD, STRE ) RELAXATION( ) 0.6, 0.6, 0.6, 0, 0, 0.1 RENUMBER( ADD, PROF ) EDDYVISCOSITY( ADD, SPEZ ) POSTPROCESS( ADD, NBLO = 2, NOPT, NOPA ) 1, 200, 200 201, 600, 5 // ENTITY( ADD, NAME = "fluid", FLUI, PROP = "fc-87" ) ENTITY( ADD, NAME = "inlet", PLOT ) ENTITY( ADD, NAME = "outlet", PLOT ) ENTITY( ADD, NAME = "axi-sym", PLOT ) ENTITY( ADD, NAME = "wall", WALL ) ENTITY( ADD, NAME = "free", SURF, DEPT = 0, SPIN, STRA ) // BCNODE( ADD, URC, NODE = 1, CONS = 0 ) BCNODE( ADD, UTHE, NODE = 1, CONS = 0 ) BCNODE( ADD, UZC, NODE = 1, CONS = 58.00512 ) // BCNODE( ADD, URC, NODE = 3, CONS = 1.19229 ) BCNODE( ADD, UTHE, NODE = 3, CONS = -0.74943 ) BCNODE( ADD, UZC, NODE = 3, CONS = 26.8299 ) // BCNODE( ADD, URC, NODE = 4, CONS = 2.38458 ) BCNODE( ADD, UTHE, NODE = 4, CONS = -1.49887 ) BCNODE( ADD, UZC, NODE = 4, CONS = 53.65979 ) // BCNODE( ADD, URC, NODE = 5, CONS = 4.41079 ) BCNODE( ADD, UTHE, NODE = 5, CONS = -2.27705 ) BCNODE( ADD, UZC, NODE = 5, CONS = 61.69395 ) // BCNODE( ADD, URC, NODE = 6, CONS = 4.45431 ) BCNODE( ADD, UTHE, NODE = 6, CONS = -3.08178 ) BCNODE( ADD, UZC, NODE = 6, CONS = 57.43798 )

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152 Appendix X (Continued) BCNODE( ADD, URC, NODE = 7, CONS = 6.62769 ) BCNODE( ADD, UTHE, NODE = 7, CONS = -3.93 ) BCNODE( ADD, UZC, NODE = 7, CONS = 51.76173 ) // BCNODE( ADD, URC, NODE = 8, CONS = 6.58981 ) BCNODE( ADD, UTHE, NODE = 8, CONS = -4.81199 ) BCNODE( ADD, UZC, NODE = 8, CONS = 46.29317 ) // BCNODE( ADD, URC, NODE = 9, CONS = 7.05564 ) BCNODE( ADD, UTHE, NODE = 9, CONS = -5.73013 ) BCNODE( ADD, UZC, NODE = 9, CONS = 40.38772 ) // BCNODE( ADD, URC, NODE = 10, CONS = 8.1226 ) BCNODE( ADD, UTHE, NODE = 10, CONS = -6.7518 ) BCNODE( ADD, UZC, NODE = 10, CONS = 34.70366 ) // BCNODE( ADD, URC, NODE = 11, CONS = 7.07488 ) BCNODE( ADD, UTHE, NODE = 11, CONS = -7.82399 ) BCNODE( ADD, UZC, NODE = 11, CONS = 28.94858 ) // BCNODE( ADD, URC, NODE = 12, CONS = 7.18622 ) BCNODE( ADD, UTHE, NODE = 12, CONS = -9.62553 ) BCNODE( ADD, UZC, NODE = 12, CONS = 24.82288 ) // BCNODE( ADD, URC, NODE = 13, CONS = 6.85361 ) BCNODE( ADD, UTHE, NODE = 13, CONS = -11.44768 ) BCNODE( ADD, UZC, NODE = 13, CONS = 20.94139 ) // BCNODE( ADD, URC, NODE = 14, CONS = 6.42043 ) BCNODE( ADD, UTHE, NODE = 14, CONS = -13.32141 ) BCNODE( ADD, UZC, NODE = 14, CONS = 17.557 ) // BCNODE( ADD, URC, NODE = 15, CONS = 6.27272 ) BCNODE( ADD, UTHE, NODE = 15, CONS = -15.55008 ) BCNODE( ADD, UZC, NODE = 15, CONS = 15.7061 ) // BCNODE( ADD, URC, NODE = 16, CONS = 5.90918 ) BCNODE( ADD, UTHE, NODE = 16, CONS = -17.81734 ) BCNODE( ADD, UZC, NODE = 16, CONS = 14.35825 ) // BCNODE( ADD, URC, NODE = 17, CONS = 5.6408 ) BCNODE( ADD, UTHE, NODE = 17, CONS = -20.22658 ) BCNODE( ADD, UZC, NODE = 17, CONS = 13.28283 ) // BCNODE( ADD, URC, NODE = 18, CONS = 5.48869 ) BCNODE( ADD, UTHE, NODE = 18, CONS = -22.59701 ) BCNODE( ADD, UZC, NODE = 18, CONS = 13.81114 ) // BCNODE( ADD, URC, NODE = 19, CONS = 5.59303 ) BCNODE( ADD, UTHE, NODE = 19, CONS = -25.07952 ) BCNODE( ADD, UZC, NODE = 19, CONS = 15.09109 ) // BCNODE( ADD, URC, NODE = 20, CONS = 5.62481 ) BCNODE( ADD, UTHE, NODE = 20, CONS = -27.65924 )

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153 Appendix X (Continued) BCNODE( ADD, UZC, NODE = 20, CONS = 16.90254 ) // BCNODE( ADD, URC, NODE = 21, CONS = 5.72671 ) BCNODE( ADD, UTHE, NODE = 21, CONS = -30.0348 ) BCNODE( ADD, UZC, NODE = 21, CONS = 18.79615 ) // BCNODE( ADD, URC, NODE = 22, CONS = 5.89116 ) BCNODE( ADD, UTHE, NODE = 22, CONS = -32.22826 ) BCNODE( ADD, UZC, NODE = 22, CONS = 20.76304 ) // BCNODE( ADD, URC, NODE = 23, CONS = 6.1562 ) BCNODE( ADD, UTHE, NODE = 23, CONS = -34.43557 ) BCNODE( ADD, UZC, NODE = 23, CONS = 22.96749 ) // BCNODE( ADD, URC, NODE = 24, CONS = 6.0469 ) BCNODE( ADD, UTHE, NODE = 24, CONS = -36.81884 ) BCNODE( ADD, UZC, NODE = 24, CONS = 25.47115 ) // BCNODE( ADD, URC, NODE = 25, CONS = 6.28969 ) BCNODE( ADD, UTHE, NODE = 25, CONS = -39.41296 ) BCNODE( ADD, UZC, NODE = 25, CONS = 27.95979 ) // BCNODE( ADD, URC, NODE = 26, CONS = 5.92434 ) BCNODE( ADD, UTHE, NODE = 26, CONS = -42.21611 ) BCNODE( ADD, UZC, NODE = 26, CONS = 30.44738 ) // BCNODE( ADD, URC, NODE = 27, CONS = 5.40699 ) BCNODE( ADD, UTHE, NODE = 27, CONS = -46.40055 ) BCNODE( ADD, UZC, NODE = 27, CONS = 34.79335 ) // BCNODE( ADD, URC, NODE = 28, CONS = 4.47442 ) BCNODE( ADD, UTHE, NODE = 28, CONS = -50.70026 ) BCNODE( ADD, UZC, NODE = 28, CONS = 39.12051 ) // BCNODE( ADD, URC, NODE = 29, CONS = 3.79006 ) BCNODE( ADD, UTHE, NODE = 29, CONS = -54.96573 ) BCNODE( ADD, UZC, NODE = 29, CONS = 43.56562 ) // BCNODE( ADD, URC, NODE = 30, CONS = 2.35629 ) BCNODE( ADD, UTHE, NODE = 30, CONS = -56.15047 ) BCNODE( ADD, UZC, NODE = 30, CONS = 45.64182 ) // BCNODE( ADD, URC, NODE = 31, CONS = 0.36862 ) BCNODE( ADD, UTHE, NODE = 31, CONS = -45.56946 ) BCNODE( ADD, UZC, NODE = 31, CONS = 38.39096 ) // BCNODE( ADD, URC, NODE = 2, CONS = 0 ) BCNODE( ADD, UTHE, NODE = 2, CONS = 0 ) BCNODE( ADD, UZC, NODE = 2, CONS = 0 ) // BCNODE( ADD, VELO, ENTI = "wall", ZERO, X, Y, Z ) BCNODE( ADD, URC, ENTI = "axi-sym", ZERO, X, Y, Z ) // BCNODE( SURF, CONS = 0, NODE = 95 )

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154 Appendix X (Continued) BCNODE( SURF, CONS = 0, NODE = 434 ) BCNODE( ADD, COOR, NODE = 95 ) BCNODE( ADD, COOR, NODE = 125 ) // ICNODE( ADD, URC, NODE = 1, CONS = 0 ) ICNODE( ADD, UTHE, NODE = 1, CONS = 0 ) ICNODE( ADD, UZC, NODE = 1, CONS = 58.00512 ) // ICNODE( ADD, URC, NODE = 3, CONS = 1.19229 ) ICNODE( ADD, UTHE, NODE = 3, CONS = -0.74943 ) ICNODE( ADD, UZC, NODE = 3, CONS = 26.8299 ) // ICNODE( ADD, URC, NODE = 4, CONS = 2.38458 ) ICNODE( ADD, UTHE, NODE = 4, CONS = -1.49887 ) ICNODE( ADD, UZC, NODE = 4, CONS = 53.65979 ) // ICNODE( ADD, URC, NODE = 5, CONS = 4.41079 ) ICNODE( ADD, UTHE, NODE = 5, CONS = -2.27705 ) ICNODE( ADD, UZC, NODE = 5, CONS = 61.69395 ) // ICNODE( ADD, URC, NODE = 6, CONS = 4.45431 ) ICNODE( ADD, UTHE, NODE = 6, CONS = -3.08178 ) ICNODE( ADD, UZC, NODE = 6, CONS = 57.43798 ) // ICNODE( ADD, URC, NODE = 7, CONS = 6.62769 ) ICNODE( ADD, UTHE, NODE = 7, CONS = -3.93 ) ICNODE( ADD, UZC, NODE = 7, CONS = 51.76173 ) // ICNODE( ADD, URC, NODE = 8, CONS = 6.58981 ) ICNODE( ADD, UTHE, NODE = 8, CONS = -4.81199 ) ICNODE( ADD, UZC, NODE = 8, CONS = 46.29317 ) // ICNODE( ADD, URC, NODE = 9, CONS = 7.05564 ) ICNODE( ADD, UTHE, NODE = 9, CONS = -5.73013 ) ICNODE( ADD, UZC, NODE = 9, CONS = 40.38772 ) // ICNODE( ADD, URC, NODE = 10, CONS = 8.1226 ) ICNODE( ADD, UTHE, NODE = 10, CONS = -6.7518 ) ICNODE( ADD, UZC, NODE = 10, CONS = 34.70366 ) // ICNODE( ADD, URC, NODE = 11, CONS = 7.07488 ) ICNODE( ADD, UTHE, NODE = 11, CONS = -7.82399 ) ICNODE( ADD, UZC, NODE = 11, CONS = 28.94858 ) // ICNODE( ADD, URC, NODE = 12, CONS = 7.18622 ) ICNODE( ADD, UTHE, NODE = 12, CONS = -9.62553 ) ICNODE( ADD, UZC, NODE = 12, CONS = 24.82288 ) // ICNODE( ADD, URC, NODE = 13, CONS = 6.85361 ) ICNODE( ADD, UTHE, NODE = 13, CONS = -11.44768 ) ICNODE( ADD, UZC, NODE = 13, CONS = 20.94139 ) // ICNODE( ADD, URC, NODE = 14, CONS = 6.42043 ) ICNODE( ADD, UTHE, NODE = 14, CONS = -13.32141 )

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155 Appendix X (Continued) ICNODE( ADD, UZC, NODE = 14, CONS = 17.557 ) // ICNODE( ADD, URC, NODE = 15, CONS = 6.27272 ) ICNODE( ADD, UTHE, NODE = 15, CONS = -15.55008 ) ICNODE( ADD, UZC, NODE = 15, CONS = 15.7061 ) // ICNODE( ADD, URC, NODE = 16, CONS = 5.90918 ) ICNODE( ADD, UTHE, NODE = 16, CONS = -17.81734 ) ICNODE( ADD, UZC, NODE = 16, CONS = 14.35825 ) // ICNODE( ADD, URC, NODE = 17, CONS = 5.6408 ) ICNODE( ADD, UTHE, NODE = 17, CONS = -20.22658 ) ICNODE( ADD, UZC, NODE = 17, CONS = 13.28283 ) // ICNODE( ADD, URC, NODE = 18, CONS = 5.48869 ) ICNODE( ADD, UTHE, NODE = 18, CONS = -22.59701 ) ICNODE( ADD, UZC, NODE = 18, CONS = 13.81114 ) // ICNODE( ADD, URC, NODE = 19, CONS = 5.59303 ) ICNODE( ADD, UTHE, NODE = 19, CONS = -25.07952 ) ICNODE( ADD, UZC, NODE = 19, CONS = 15.09109 ) // ICNODE( ADD, URC, NODE = 20, CONS = 5.62481 ) ICNODE( ADD, UTHE, NODE = 20, CONS = -27.65924 ) ICNODE( ADD, UZC, NODE = 20, CONS = 16.90254 ) // ICNODE( ADD, URC, NODE = 21, CONS = 5.72671 ) ICNODE( ADD, UTHE, NODE = 21, CONS = -30.0348 ) ICNODE( ADD, UZC, NODE = 21, CONS = 18.79615 ) // ICNODE( ADD, URC, NODE = 22, CONS = 5.89116 ) ICNODE( ADD, UTHE, NODE = 22, CONS = -32.22826 ) ICNODE( ADD, UZC, NODE = 22, CONS = 20.76304 ) // ICNODE( ADD, URC, NODE = 23, CONS = 6.1562 ) ICNODE( ADD, UTHE, NODE = 23, CONS = -34.43557 ) ICNODE( ADD, UZC, NODE = 23, CONS = 22.96749 ) // ICNODE( ADD, URC, NODE = 24, CONS = 6.0469 ) ICNODE( ADD, UTHE, NODE = 24, CONS = -36.81884 ) ICNODE( ADD, UZC, NODE = 24, CONS = 25.47115 ) // ICNODE( ADD, URC, NODE = 25, CONS = 6.28969 ) ICNODE( ADD, UTHE, NODE = 25, CONS = -39.41296 ) ICNODE( ADD, UZC, NODE = 25, CONS = 27.95979 ) // ICNODE( ADD, URC, NODE = 26, CONS = 5.92434 ) ICNODE( ADD, UTHE, NODE = 26, CONS = -42.21611 ) ICNODE( ADD, UZC, NODE = 26, CONS = 30.44738 ) // ICNODE( ADD, URC, NODE = 27, CONS = 5.40699 ) ICNODE( ADD, UTHE, NODE = 27, CONS = -46.40055 ) ICNODE( ADD, UZC, NODE = 27, CONS = 34.79335 ) //

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156 Appendix X (Continued) ICNODE( ADD, URC, NODE = 28, CONS = 4.47442 ) ICNODE( ADD, UTHE, NODE = 28, CONS = -50.70026 ) ICNODE( ADD, UZC, NODE = 28, CONS = 39.12051 ) // ICNODE( ADD, URC, NODE = 29, CONS = 3.79006 ) ICNODE( ADD, UTHE, NODE = 29, CONS = -54.96573 ) ICNODE( ADD, UZC, NODE = 29, CONS = 43.56562 ) // ICNODE( ADD, URC, NODE = 30, CONS = 2.35629 ) ICNODE( ADD, UTHE, NODE = 30, CONS = -56.15047 ) ICNODE( ADD, UZC, NODE = 30, CONS = 45.64182 ) // ICNODE( ADD, URC, NODE = 31, CONS = 0.36862 ) ICNODE( ADD, UTHE, NODE = 31, CONS = -45.56946 ) ICNODE( ADD, UZC, NODE = 31, CONS = 38.39096 ) // ICNODE( ADD, URC, NODE = 2, CONS = 0 ) ICNODE( ADD, UTHE, NODE = 2, CONS = 0 ) ICNODE( ADD, UZC, NODE = 2, CONS = 0 ) // ICNODE( ADD, VELO, ENTI = "wall", ZERO, X, Y, Z ) ICNODE( ADD, URC, ENTI = "axi-sym", ZERO, X, Y, Z ) // END( )

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157 Appendix XI: FIPREP File for the Small Nozzle with Free Surface (4.416 x 10-7 m3/s, Methanol) FIPREP( ) //DENSITY OF METHANOL DENSITY( ADD, SET = "methanol", CONS = 0.7855 ) //VISCOSITY OF METHANOL VISCOSITY( ADD, SET = "methanol", CONS = 0.0055, MIXLENGTH ) //SURFACE TENSION OF METHANOL SURFACETENSION( ADD, SET = "methanol", CONS = 22.2 ) // PRESSURE( ADD, MIXE = 1e-16, DISC ) DATAPRINT( ADD, CONT ) EXECUTION( ADD, NEWJ ) PRINTOUT( ADD, NONE, BOUN ) PROBLEM( ADD, CYLI, INCO, TRAN, TURB, NONL, NEWT, MOME, ISOT, FREE, SING ) SOLUTION( ADD, N.R. = 80, KINE = 25, VELC = 0.0001, RESC = 0.01, SURF = 0.001 ) // //GRAVITY BODYFORCE( ADD, CONS, FZC = 981, FRC = 0, FTHE = 0 ) // TIMEINTEGRATION( ADD, BACK, NSTE = 1000, TSTA = 0, DT = 1e-7, VARI, WIND = 0.9, NOFI = 10 ) OPTIONS( ADD, UPWI ) UPWINDING( ADD, STRE ) RELAXATION( ) 0.6, 0.6, 0.6, 0, 0, 0.1 RENUMBER( ADD, PROF ) EDDYVISCOSITY( ADD, SPEZ ) POSTPROCESS( ADD, NBLO = 2, NOPT, NOPA ) 1 200 200 201 1000 5 // ENTITY( ADD, NAME = "fluid", FLUI, PROP = "methanol" ) ENTITY( ADD, NAME = "inlet", PLOT ) ENTITY( ADD, NAME = "outlet", PLOT ) ENTITY( ADD, NAME = "axi-sym", PLOT ) ENTITY( ADD, NAME = "wall", WALL ) ENTITY( ADD, NAME = "free", SURF, DEPT = 0, SPINES, STRAIGHT ) // //BOUNDARY CONDITIONS AT EACH NODE BCNODE( ADD, URC, NODE = 1, CONS = 0 ) BCNODE( ADD, UTHE, NODE = 1, CONS = 0 ) BCNODE( ADD, UZC, NODE = 1, CONS = 47.49754 ) // BCNODE( ADD, URC, NODE = 3, CONS = 1.07786 ) BCNODE( ADD, UTHE, NODE = 3, CONS = -0.54841 ) BCNODE( ADD, UZC, NODE = 3, CONS = 17.3042 ) // BCNODE( ADD, URC, NODE = 4, CONS = 2.15572 ) BCNODE( ADD, UTHE, NODE = 4, CONS = -1.09681 ) BCNODE( ADD, UZC, NODE = 4, CONS = 34.60839 )

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158 Appendix XI (Continued) BCNODE( ADD, URC, NODE = 5, CONS = 3.50662 ) BCNODE( ADD, UTHE, NODE = 5, CONS = -1.66813 ) BCNODE( ADD, UZC, NODE = 5, CONS = 44.81096 ) // BCNODE( ADD, URC, NODE = 6, CONS = 3.68413 ) BCNODE( ADD, UTHE, NODE = 6, CONS = -2.27468 ) BCNODE( ADD, UZC, NODE = 6, CONS = 43.56053 ) // BCNODE( ADD, URC, NODE = 7, CONS = 5.27484 ) BCNODE( ADD, UTHE, NODE = 7, CONS = -2.87342 ) BCNODE( ADD, UZC, NODE = 7, CONS = 39.28467 ) // BCNODE( ADD, URC, NODE = 8, CONS = 5.54557 ) BCNODE( ADD, UTHE, NODE = 8, CONS = -3.51059 ) BCNODE( ADD, UZC, NODE = 8, CONS = 35.04664 ) // BCNODE( ADD, URC, NODE = 9, CONS = 5.71948 ) BCNODE( ADD, UTHE, NODE = 9, CONS = -4.23339 ) BCNODE( ADD, UZC, NODE = 9, CONS = 30.53951 ) // BCNODE( ADD, URC, NODE = 10, CONS = 6.41072 ) BCNODE( ADD, UTHE, NODE = 10, CONS = -4.93917 ) BCNODE( ADD, UZC, NODE = 10, CONS = 26.16700 ) // BCNODE( ADD, URC, NODE = 11, CONS = 6.01882 ) BCNODE( ADD, UTHE, NODE = 11, CONS = -5.68851 ) BCNODE( ADD, UZC, NODE = 11, CONS = 21.74019 ) // BCNODE( ADD, URC, NODE = 12, CONS = 6.10722 ) BCNODE( ADD, UTHE, NODE = 12, CONS = -6.69096 ) BCNODE( ADD, UZC, NODE = 12, CONS = 17.80720 ) // BCNODE( ADD, URC, NODE = 13, CONS = 6.03523 ) BCNODE( ADD, UTHE, NODE = 13, CONS = -7.84324 ) BCNODE( ADD, UZC, NODE = 13, CONS = 14.12019 ) // BCNODE( ADD, URC, NODE = 14, CONS = 5.85328 ) BCNODE( ADD, UTHE, NODE = 14, CONS = -9.03578 ) BCNODE( ADD, UZC, NODE = 14, CONS = 11.31132 ) // BCNODE( ADD, URC, NODE = 15, CONS = 5.73239 ) BCNODE( ADD, UTHE, NODE = 15, CONS = -10.12003 ) BCNODE( ADD, UZC, NODE = 15, CONS = 9.31211 ) // BCNODE( ADD, URC, NODE = 16, CONS = 5.24099 ) BCNODE( ADD, UTHE, NODE = 16, CONS = -11.81902 ) BCNODE( ADD, UZC, NODE = 16, CONS = 8.84625 ) // BCNODE( ADD, URC, NODE = 17, CONS = 4.88189 ) BCNODE( ADD, UTHE, NODE = 17, CONS = -13.77587 ) BCNODE( ADD, UZC, NODE = 17, CONS = 9.45191 ) // BCNODE( ADD, URC, NODE = 18, CONS = 4.38880 ) BCNODE( ADD, UTHE, NODE = 18, CONS = -15.80336 )

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159 Appendix XI (Continued) BCNODE( ADD, UZC, NODE = 18, CONS = 10.42002 ) BCNODE( ADD, URC, NODE = 19, CONS = 4.06889 ) BCNODE( ADD, UTHE, NODE = 19, CONS = -17.83779 ) BCNODE( ADD, UZC, NODE = 19, CONS = 11.83354 ) // BCNODE( ADD, URC, NODE = 20, CONS = 3.83398 ) BCNODE( ADD, UTHE, NODE = 20, CONS = -19.82056 ) BCNODE( ADD, UZC, NODE = 20, CONS = 13.35872 ) // BCNODE( ADD, URC, NODE = 21, CONS = 3.68295 ) BCNODE( ADD, UTHE, NODE = 21, CONS = -21.76817 ) BCNODE( ADD, UZC, NODE = 21, CONS = 15.02764 ) // BCNODE( ADD, URC, NODE = 22, CONS = 3.54688 ) BCNODE( ADD, UTHE, NODE = 22, CONS = -23.29079 ) BCNODE( ADD, UZC, NODE = 22, CONS = 16.78542 ) // BCNODE( ADD, URC, NODE = 23, CONS = 3.67325 ) BCNODE( ADD, UTHE, NODE = 23, CONS = -24.86242 ) BCNODE( ADD, UZC, NODE = 23, CONS = 18.55709 ) // BCNODE( ADD, URC, NODE = 24, CONS = 3.39594 ) BCNODE( ADD, UTHE, NODE = 24, CONS = -26.98265 ) BCNODE( ADD, UZC, NODE = 24, CONS = 21.10042 ) // BCNODE( ADD, URC, NODE = 25, CONS = 3.53771 ) BCNODE( ADD, UTHE, NODE = 25, CONS = -29.27460 ) BCNODE( ADD, UZC, NODE = 25, CONS = 23.67158 ) // BCNODE( ADD, URC, NODE = 26, CONS = 3.15843 ) BCNODE( ADD, UTHE, NODE = 26, CONS = -31.68486 ) BCNODE( ADD, UZC, NODE = 26, CONS = 26.26948 ) // BCNODE( ADD, URC, NODE = 27, CONS = 3.34382 ) BCNODE( ADD, UTHE, NODE = 27, CONS = -34.50851 ) BCNODE( ADD, UZC, NODE = 27, CONS = 29.02105 ) // BCNODE( ADD, URC, NODE = 28, CONS = 3.34690 ) BCNODE( ADD, UTHE, NODE = 28, CONS = -37.10643 ) BCNODE( ADD, UZC, NODE = 28, CONS = 31.79592 ) // BCNODE( ADD, URC, NODE = 29, CONS = 2.75530 ) BCNODE( ADD, UTHE, NODE = 29, CONS = -39.18089 ) BCNODE( ADD, UZC, NODE = 29, CONS = 34.15012 ) // BCNODE( ADD, URC, NODE = 30, CONS = 1.61627 ) BCNODE( ADD, UTHE, NODE = 30, CONS = -37.35644 ) BCNODE( ADD, UZC, NODE = 30, CONS = 33.21002 ) // BCNODE( ADD, URC, NODE = 31, CONS = -0.44058 ) BCNODE( ADD, UTHE, NODE = 31, CONS = -27.45943 ) BCNODE( ADD, UZC, NODE = 31, CONS = 25.58646 ) // BCNODE( ADD, URC, NODE = 2, CONS = 0 )

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160 Appendix XI (Continued) BCNODE( ADD, UTHE, NODE = 2, CONS = 0 ) BCNODE( ADD, UZC, NODE = 2, CONS = 0 ) BCNODE( ADD, VELO, ENTI = "wall", ZERO, X, Y, Z ) BCNODE( ADD, URC, ENTI = "axi-sym", ZERO, X, Y, Z ) // //FREE SURFACE CONTROL BCNODE( SURFACE, CONS = 0, NODE = 95 ) BCNODE( SURFACE, CONS = 0, NODE = 434 ) BCNODE( ADD, COOR, NODE = 95 ) BCNODE( ADD, COOR, NODE = 125 ) // //INITIAL CONDITION AT EACH NODE ICNODE( ADD, URC, NODE = 1, CONS = 0 ) ICNODE( ADD, UTHE, NODE = 1, CONS = 0 ) ICNODE( ADD, UZC, NODE = 1, CONS = 47.49754 ) // ICNODE( ADD, URC, NODE = 3, CONS = 1.07786 ) ICNODE( ADD, UTHE, NODE = 3, CONS = -0.54841 ) ICNODE( ADD, UZC, NODE = 3, CONS = 17.3042 ) // ICNODE( ADD, URC, NODE = 4, CONS = 2.15572 ) ICNODE( ADD, UTHE, NODE = 4, CONS = -1.09681 ) ICNODE( ADD, UZC, NODE = 4, CONS = 34.60839 ) // ICNODE( ADD, URC, NODE = 5, CONS = 3.50662 ) ICNODE( ADD, UTHE, NODE = 5, CONS = -1.66813 ) ICNODE( ADD, UZC, NODE = 5, CONS = 44.81096 ) // ICNODE( ADD, URC, NODE = 6, CONS = 3.68413 ) ICNODE( ADD, UTHE, NODE = 6, CONS = -2.27468 ) ICNODE( ADD, UZC, NODE = 6, CONS = 43.56053 ) // ICNODE( ADD, URC, NODE = 7, CONS = 5.27484 ) ICNODE( ADD, UTHE, NODE = 7, CONS = -2.87342 ) ICNODE( ADD, UZC, NODE = 7, CONS = 39.28467 ) // ICNODE( ADD, URC, NODE = 8, CONS = 5.54557 ) ICNODE( ADD, UTHE, NODE = 8, CONS = -3.51059 ) ICNODE( ADD, UZC, NODE = 8, CONS = 35.04664 ) // ICNODE( ADD, URC, NODE = 9, CONS = 5.71948 ) ICNODE( ADD, UTHE, NODE = 9, CONS = -4.23339 ) ICNODE( ADD, UZC, NODE = 9, CONS = 30.53951 ) // ICNODE( ADD, URC, NODE = 10, CONS = 6.41072 ) ICNODE( ADD, UTHE, NODE = 10, CONS = -4.93917 ) ICNODE( ADD, UZC, NODE = 10, CONS = 26.16700 ) // ICNODE( ADD, URC, NODE = 11, CONS = 6.01882 ) ICNODE( ADD, UTHE, NODE = 11, CONS = -5.68851 ) ICNODE( ADD, UZC, NODE = 11, CONS = 21.74019 ) // ICNODE( ADD, URC, NODE = 12, CONS = 6.10722 ) ICNODE( ADD, UTHE, NODE = 12, CONS = -6.69096 )

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161 Appendix XI (Continued) ICNODE( ADD, UZC, NODE = 12, CONS = 17.80720 ) ICNODE( ADD, URC, NODE = 13, CONS = 6.03523 ) ICNODE( ADD, UTHE, NODE = 13, CONS = -7.84324 ) ICNODE( ADD, UZC, NODE = 13, CONS = 14.12019 ) // ICNODE( ADD, URC, NODE = 14, CONS = 5.85328 ) ICNODE( ADD, UTHE, NODE = 14, CONS = -9.03578 ) ICNODE( ADD, UZC, NODE = 14, CONS = 11.31132 ) // ICNODE( ADD, URC, NODE = 15, CONS = 5.73239 ) ICNODE( ADD, UTHE, NODE = 15, CONS = -10.12003 ) ICNODE( ADD, UZC, NODE = 15, CONS = 9.31211 ) // ICNODE( ADD, URC, NODE = 16, CONS = 5.24099 ) ICNODE( ADD, UTHE, NODE = 16, CONS = -11.81902 ) ICNODE( ADD, UZC, NODE = 16, CONS = 8.84625 ) // ICNODE( ADD, URC, NODE = 17, CONS = 4.88189 ) ICNODE( ADD, UTHE, NODE = 17, CONS = -13.77587 ) ICNODE( ADD, UZC, NODE = 17, CONS = 9.45191 ) // ICNODE( ADD, URC, NODE = 18, CONS = 4.38880 ) ICNODE( ADD, UTHE, NODE = 18, CONS = -15.80336 ) ICNODE( ADD, UZC, NODE = 18, CONS = 10.42002 ) // ICNODE( ADD, URC, NODE = 19, CONS = 4.06889 ) ICNODE( ADD, UTHE, NODE = 19, CONS = -17.83779 ) ICNODE( ADD, UZC, NODE = 19, CONS = 11.83354 ) // ICNODE( ADD, URC, NODE = 20, CONS = 3.83398 ) ICNODE( ADD, UTHE, NODE = 20, CONS = -19.82056 ) ICNODE( ADD, UZC, NODE = 20, CONS = 13.35872 ) // ICNODE( ADD, URC, NODE = 21, CONS = 3.68295 ) ICNODE( ADD, UTHE, NODE = 21, CONS = -21.76817 ) ICNODE( ADD, UZC, NODE = 21, CONS = 15.02764 ) // ICNODE( ADD, URC, NODE = 22, CONS = 3.54688 ) ICNODE( ADD, UTHE, NODE = 22, CONS = -23.29079 ) ICNODE( ADD, UZC, NODE = 22, CONS = 16.78542 ) // ICNODE( ADD, URC, NODE = 23, CONS = 3.67325 ) ICNODE( ADD, UTHE, NODE = 23, CONS = -24.86242 ) ICNODE( ADD, UZC, NODE = 23, CONS = 18.55709 ) // ICNODE( ADD, URC, NODE = 24, CONS = 3.39594 ) ICNODE( ADD, UTHE, NODE = 24, CONS = -26.98265 ) ICNODE( ADD, UZC, NODE = 24, CONS = 21.10042 ) // ICNODE( ADD, URC, NODE = 25, CONS = 3.53771 ) ICNODE( ADD, UTHE, NODE = 25, CONS = -29.27460 ) ICNODE( ADD, UZC, NODE = 25, CONS = 23.67158 ) // ICNODE( ADD, URC, NODE = 26, CONS = 3.15843 )

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162 Appendix XI (Continued) ICNODE( ADD, UTHE, NODE = 26, CONS = -31.68486 ) ICNODE( ADD, UZC, NODE = 26, CONS = 26.26948 ) ICNODE( ADD, URC, NODE = 27, CONS = 3.34382 ) ICNODE( ADD, UTHE, NODE = 27, CONS = -34.50851 ) ICNODE( ADD, UZC, NODE = 27, CONS = 29.02105 ) ICNODE( ADD, URC, NODE = 28, CONS = 3.34690 ) ICNODE( ADD, UTHE, NODE = 28, CONS = -37.10643 ) ICNODE( ADD, UZC, NODE = 28, CONS = 31.79592 ) // ICNODE( ADD, URC, NODE = 29, CONS = 2.75530 ) ICNODE( ADD, UTHE, NODE = 29, CONS = -39.18089 ) ICNODE( ADD, UZC, NODE = 29, CONS = 34.15012 ) // ICNODE( ADD, URC, NODE = 30, CONS = 1.61627 ) ICNODE( ADD, UTHE, NODE = 30, CONS = -37.35644 ) ICNODE( ADD, UZC, NODE = 30, CONS = 33.21002 ) // ICNODE( ADD, URC, NODE = 31, CONS = -0.44058 ) ICNODE( ADD, UTHE, NODE = 31, CONS = -27.45943 ) ICNODE( ADD, UZC, NODE = 31, CONS = 25.58646 ) // ICNODE( ADD, URC, NODE = 2, CONS = 0 ) ICNODE( ADD, UTHE, NODE = 2, CONS = 0 ) ICNODE( ADD, UZC, NODE = 2, CONS = 0 ) // ICNODE( ADD, VELO, ENTI = "wall", ZERO, X, Y, Z ) ICNODE( ADD, URC, ENTI = "axi-sym", ZERO, X, Y, Z ) // END( )

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163 Appendix XII: FIPREP File for the Small Nozzle with Free Surface (5.678 x 10-7 m3/s, Methanol) FIPREP( ) DENSITY( ADD, SET = "methanol", CONS = 0.7855 ) VISCOSITY( ADD, SET = "methanol", CONS = 0.0055, MIXL ) SURFACETENSION( ADD, SET = "methanol", CONS = 22.2 ) // PRESSURE( ADD, MIXE = 1e-16, DISC ) DATAPRINT( ADD, CONT ) EXECUTION( ADD, NEWJ ) PRINTOUT( ADD, NONE, BOUN ) PROBLEM( ADD, CYLI, INCO, TRAN, TURB, NONL, NEWT, MOME, ISOT, FREE, SING ) SOLUTION( ADD, N.R. = 80, KINE = 25, VELC = 0.0001, RESC = 0.01, SURF = 0.001 ) BODYFORCE( ADD, CONS, FZC = 981, FRC = 0, FTHE = 0 ) TIMEINTEGRATION( ADD, BACK, NSTE = 600, TSTA = 0, DT = 1e-07, VARI, WIND = 0.9, NOFI = 10 ) OPTIONS( ADD, UPWI ) UPWINDING( ADD, STRE ) RELAXATION( ) 0.6, 0.6, 0.6, 0, 0, 0.1 RENUMBER( ADD, PROF ) EDDYVISCOSITY( ADD, SPEZ ) POSTPROCESS( ADD, NBLO = 2, NOPT, NOPA ) 1, 200, 200 201, 600, 5 // ENTITY( ADD, NAME = "fluid", FLUI, PROP = "methanol" ) ENTITY( ADD, NAME = "inlet", PLOT ) ENTITY( ADD, NAME = "outlet", PLOT ) ENTITY( ADD, NAME = "axi-sym", PLOT ) ENTITY( ADD, NAME = "wall", WALL ) ENTITY( ADD, NAME = "free", SURF, DEPT = 0, SPIN, STRA ) // BCNODE( ADD, URC, NODE = 1, CONS = 0 ) BCNODE( ADD, UTHE, NODE = 1, CONS = 0 ) BCNODE( ADD, UZC, NODE = 1, CONS = 61.7765 ) // BCNODE( ADD, URC, NODE = 3, CONS = 1.383 ) BCNODE( ADD, UTHE, NODE = 3, CONS = -0.70458 ) BCNODE( ADD, UZC, NODE = 3, CONS = 22.5079 ) // BCNODE( ADD, URC, NODE = 4, CONS = 2.766 ) BCNODE( ADD, UTHE, NODE = 4, CONS = -1.40916 ) BCNODE( ADD, UZC, NODE = 4, CONS = 45.0158 ) // BCNODE( ADD, URC, NODE = 5, CONS = 4.50136 ) BCNODE( ADD, UTHE, NODE = 5, CONS = -2.14566 ) BCNODE( ADD, UZC, NODE = 5, CONS = 58.27075 ) // BCNODE( ADD, URC, NODE = 6, CONS = 4.72119 ) BCNODE( ADD, UTHE, NODE = 6, CONS = -2.92375 ) BCNODE( ADD, UZC, NODE = 6, CONS = 56.64958 )

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164 Appendix XII (Continued) BCNODE( ADD, URC, NODE = 7, CONS = 6.77091 ) BCNODE( ADD, UTHE, NODE = 7, CONS = -3.6949 ) BCNODE( ADD, UZC, NODE = 7, CONS = 51.06079 ) // BCNODE( ADD, URC, NODE = 8, CONS = 7.11479 ) BCNODE( ADD, UTHE, NODE = 8, CONS = -4.51112 ) BCNODE( ADD, UZC, NODE = 8, CONS = 45.55059 ) // BCNODE( ADD, URC, NODE = 9, CONS = 7.33269 ) BCNODE( ADD, UTHE, NODE = 9, CONS = -5.43592 ) BCNODE( ADD, UZC, NODE = 9, CONS = 39.69268 ) // BCNODE( ADD, URC, NODE = 10, CONS = 8.2219 ) BCNODE( ADD, UTHE, NODE = 10, CONS = -6.34077 ) BCNODE( ADD, UZC, NODE = 10, CONS = 34.00125 ) // BCNODE( ADD, URC, NODE = 11, CONS = 7.70924 ) BCNODE( ADD, UTHE, NODE = 11, CONS = -7.29851 ) BCNODE( ADD, UZC, NODE = 11, CONS = 28.23605 ) // BCNODE( ADD, URC, NODE = 12, CONS = 7.82384 ) BCNODE( ADD, UTHE, NODE = 12, CONS = -8.57813 ) BCNODE( ADD, UZC, NODE = 12, CONS = 23.11373 ) // BCNODE( ADD, URC, NODE = 13, CONS = 7.72966 ) BCNODE( ADD, UTHE, NODE = 13, CONS = -10.05122 ) BCNODE( ADD, UZC, NODE = 13, CONS = 18.30851 ) // BCNODE( ADD, URC, NODE = 14, CONS = 7.49335 ) BCNODE( ADD, UTHE, NODE = 14, CONS = -11.57644 ) BCNODE( ADD, UZC, NODE = 14, CONS = 14.63418 ) // BCNODE( ADD, URC, NODE = 15, CONS = 7.34386 ) BCNODE( ADD, UTHE, NODE = 15, CONS = -12.96026 ) BCNODE( ADD, UZC, NODE = 15, CONS = 12.01776 ) // BCNODE( ADD, URC, NODE = 16, CONS = 6.72864 ) BCNODE( ADD, UTHE, NODE = 16, CONS = -15.13882 ) BCNODE( ADD, UZC, NODE = 16, CONS = 11.37676 ) // BCNODE( ADD, URC, NODE = 17, CONS = 6.28118 ) BCNODE( ADD, UTHE, NODE = 17, CONS = -17.65215 ) BCNODE( ADD, UZC, NODE = 17, CONS = 12.10976 ) // BCNODE( ADD, URC, NODE = 18, CONS = 5.6745 ) BCNODE( ADD, UTHE, NODE = 18, CONS = -20.26343 ) BCNODE( ADD, UZC, NODE = 18, CONS = 13.29978 ) // BCNODE( ADD, URC, NODE = 19, CONS = 5.29119 ) BCNODE( ADD, UTHE, NODE = 19, CONS = -22.89354 ) BCNODE( ADD, UZC, NODE = 19, CONS = 15.07154 ) // BCNODE( ADD, URC, NODE = 20, CONS = 5.01902 ) BCNODE( ADD, UTHE, NODE = 20, CONS = -25.45875 )

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165 Appendix XII (Continued) BCNODE( ADD, UZC, NODE = 20, CONS = 16.98224 ) // BCNODE( ADD, URC, NODE = 21, CONS = 4.8565 ) BCNODE( ADD, UTHE, NODE = 21, CONS = -27.98061 ) BCNODE( ADD, UZC, NODE = 21, CONS = 19.07252 ) // BCNODE( ADD, URC, NODE = 22, CONS = 4.72659 ) BCNODE( ADD, UTHE, NODE = 22, CONS = -29.96394 ) BCNODE( ADD, UZC, NODE = 22, CONS = 21.31204 ) // BCNODE( ADD, URC, NODE = 23, CONS = 4.93384 ) BCNODE( ADD, UTHE, NODE = 23, CONS = -32.01968 ) BCNODE( ADD, UZC, NODE = 23, CONS = 23.58516 ) // BCNODE( ADD, URC, NODE = 24, CONS = 4.61029 ) BCNODE( ADD, UTHE, NODE = 24, CONS = -34.81914 ) BCNODE( ADD, UZC, NODE = 24, CONS = 26.86834 ) // BCNODE( ADD, URC, NODE = 25, CONS = 4.81962 ) BCNODE( ADD, UTHE, NODE = 25, CONS = -37.85144 ) BCNODE( ADD, UZC, NODE = 25, CONS = 30.22411 ) // BCNODE( ADD, URC, NODE = 26, CONS = 4.35261 ) BCNODE( ADD, UTHE, NODE = 26, CONS = -41.07731 ) BCNODE( ADD, UZC, NODE = 26, CONS = 33.58767 ) // BCNODE( ADD, URC, NODE = 27, CONS = 4.5757 ) BCNODE( ADD, UTHE, NODE = 27, CONS = -44.94583 ) BCNODE( ADD, UZC, NODE = 27, CONS = 37.24106 ) // BCNODE( ADD, URC, NODE = 28, CONS = 4.55803 ) BCNODE( ADD, UTHE, NODE = 28, CONS = -48.58367 ) BCNODE( ADD, UZC, NODE = 28, CONS = 40.92054 ) // BCNODE( ADD, URC, NODE = 29, CONS = 3.77308 ) BCNODE( ADD, UTHE, NODE = 29, CONS = -51.73271 ) BCNODE( ADD, UZC, NODE = 29, CONS = 44.24629 ) // BCNODE( ADD, URC, NODE = 30, CONS = 2.26124 ) BCNODE( ADD, UTHE, NODE = 30, CONS = -50.40475 ) BCNODE( ADD, UZC, NODE = 30, CONS = 43.97659 ) // BCNODE( ADD, URC, NODE = 31, CONS = -0.52661 ) BCNODE( ADD, UTHE, NODE = 31, CONS = -38.03983 ) BCNODE( ADD, UZC, NODE = 31, CONS = 34.72785 ) // BCNODE( ADD, URC, NODE = 2, CONS = 0 ) BCNODE( ADD, UTHE, NODE = 2, CONS = 0 ) BCNODE( ADD, UZC, NODE = 2, CONS = 0 ) // BCNODE( ADD, VELO, ENTI = "wall", ZERO, X, Y, Z ) BCNODE( ADD, URC, ENTI = "axi-sym", ZERO, X, Y, Z ) // BCNODE( SURF, CONS = 0, NODE = 95 )

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166 Appendix XII (Continued) BCNODE( SURF, CONS = 0, NODE = 434 ) BCNODE( ADD, COOR, NODE = 95 ) BCNODE( ADD, COOR, NODE = 125 ) // ICNODE( ADD, URC, NODE = 1, CONS = 0 ) ICNODE( ADD, UTHE, NODE = 1, CONS = 0 ) ICNODE( ADD, UZC, NODE = 1, CONS = 61.7765 ) // ICNODE( ADD, URC, NODE = 3, CONS = 1.383 ) ICNODE( ADD, UTHE, NODE = 3, CONS = -0.70458 ) ICNODE( ADD, UZC, NODE = 3, CONS = 22.5079 ) // ICNODE( ADD, URC, NODE = 4, CONS = 2.766 ) ICNODE( ADD, UTHE, NODE = 4, CONS = -1.40916 ) ICNODE( ADD, UZC, NODE = 4, CONS = 45.0158 ) // ICNODE( ADD, URC, NODE = 5, CONS = 4.50136 ) ICNODE( ADD, UTHE, NODE = 5, CONS = -2.14566 ) ICNODE( ADD, UZC, NODE = 5, CONS = 58.27075 ) // ICNODE( ADD, URC, NODE = 6, CONS = 4.72119 ) ICNODE( ADD, UTHE, NODE = 6, CONS = -2.92375 ) ICNODE( ADD, UZC, NODE = 6, CONS = 56.64958 ) // ICNODE( ADD, URC, NODE = 7, CONS = 6.77091 ) ICNODE( ADD, UTHE, NODE = 7, CONS = -3.6949 ) ICNODE( ADD, UZC, NODE = 7, CONS = 51.06079 ) // ICNODE( ADD, URC, NODE = 8, CONS = 7.11479 ) ICNODE( ADD, UTHE, NODE = 8, CONS = -4.51112 ) ICNODE( ADD, UZC, NODE = 8, CONS = 45.55059 ) // ICNODE( ADD, URC, NODE = 9, CONS = 7.33269 ) ICNODE( ADD, UTHE, NODE = 9, CONS = -5.43592 ) ICNODE( ADD, UZC, NODE = 9, CONS = 39.69268 ) // ICNODE( ADD, URC, NODE = 10, CONS = 8.2219 ) ICNODE( ADD, UTHE, NODE = 10, CONS = -6.34077 ) ICNODE( ADD, UZC, NODE = 10, CONS = 34.00125 ) // ICNODE( ADD, URC, NODE = 11, CONS = 7.70924 ) ICNODE( ADD, UTHE, NODE = 11, CONS = -7.29851 ) ICNODE( ADD, UZC, NODE = 11, CONS = 28.23605 ) // ICNODE( ADD, URC, NODE = 12, CONS = 7.82384 ) ICNODE( ADD, UTHE, NODE = 12, CONS = -8.57813 ) ICNODE( ADD, UZC, NODE = 12, CONS = 23.11373 ) // ICNODE( ADD, URC, NODE = 13, CONS = 7.72966 ) ICNODE( ADD, UTHE, NODE = 13, CONS = -10.05122 ) ICNODE( ADD, UZC, NODE = 13, CONS = 18.30851 ) // ICNODE( ADD, URC, NODE = 14, CONS = 7.49335 ) ICNODE( ADD, UTHE, NODE = 14, CONS = -11.57644 )

PAGE 183

167 Appendix XII (Continued) ICNODE( ADD, UZC, NODE = 14, CONS = 14.63418 ) // ICNODE( ADD, URC, NODE = 15, CONS = 7.34386 ) ICNODE( ADD, UTHE, NODE = 15, CONS = -12.96026 ) ICNODE( ADD, UZC, NODE = 15, CONS = 12.01776 ) // ICNODE( ADD, URC, NODE = 16, CONS = 6.72864 ) ICNODE( ADD, UTHE, NODE = 16, CONS = -15.13882 ) ICNODE( ADD, UZC, NODE = 16, CONS = 11.37676 ) // ICNODE( ADD, URC, NODE = 17, CONS = 6.28118 ) ICNODE( ADD, UTHE, NODE = 17, CONS = -17.65215 ) ICNODE( ADD, UZC, NODE = 17, CONS = 12.10976 ) // ICNODE( ADD, URC, NODE = 18, CONS = 5.6745 ) ICNODE( ADD, UTHE, NODE = 18, CONS = -20.26343 ) ICNODE( ADD, UZC, NODE = 18, CONS = 13.29978 ) // ICNODE( ADD, URC, NODE = 19, CONS = 5.29119 ) ICNODE( ADD, UTHE, NODE = 19, CONS = -22.89354 ) ICNODE( ADD, UZC, NODE = 19, CONS = 15.07154 ) // ICNODE( ADD, URC, NODE = 20, CONS = 5.01902 ) ICNODE( ADD, UTHE, NODE = 20, CONS = -25.45875 ) ICNODE( ADD, UZC, NODE = 20, CONS = 16.98224 ) // ICNODE( ADD, URC, NODE = 21, CONS = 4.8565 ) ICNODE( ADD, UTHE, NODE = 21, CONS = -27.98061 ) ICNODE( ADD, UZC, NODE = 21, CONS = 19.07252 ) // ICNODE( ADD, URC, NODE = 22, CONS = 4.72659 ) ICNODE( ADD, UTHE, NODE = 22, CONS = -29.96394 ) ICNODE( ADD, UZC, NODE = 22, CONS = 21.31204 ) // ICNODE( ADD, URC, NODE = 23, CONS = 4.93384 ) ICNODE( ADD, UTHE, NODE = 23, CONS = -32.01968 ) ICNODE( ADD, UZC, NODE = 23, CONS = 23.58516 ) // ICNODE( ADD, URC, NODE = 24, CONS = 4.61029 ) ICNODE( ADD, UTHE, NODE = 24, CONS = -34.81914 ) ICNODE( ADD, UZC, NODE = 24, CONS = 26.86834 ) // ICNODE( ADD, URC, NODE = 25, CONS = 4.81962 ) ICNODE( ADD, UTHE, NODE = 25, CONS = -37.85144 ) ICNODE( ADD, UZC, NODE = 25, CONS = 30.22411 ) // ICNODE( ADD, URC, NODE = 26, CONS = 4.35261 ) ICNODE( ADD, UTHE, NODE = 26, CONS = -41.07731 ) ICNODE( ADD, UZC, NODE = 26, CONS = 33.58767 ) // ICNODE( ADD, URC, NODE = 27, CONS = 4.5757 ) ICNODE( ADD, UTHE, NODE = 27, CONS = -44.94583 ) ICNODE( ADD, UZC, NODE = 27, CONS = 37.24106 ) //

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168 Appendix XII (Continued) ICNODE( ADD, URC, NODE = 28, CONS = 4.55803 ) ICNODE( ADD, UTHE, NODE = 28, CONS = -48.58367 ) ICNODE( ADD, UZC, NODE = 28, CONS = 40.92054 ) // ICNODE( ADD, URC, NODE = 29, CONS = 3.77308 ) ICNODE( ADD, UTHE, NODE = 29, CONS = -51.73271 ) ICNODE( ADD, UZC, NODE = 29, CONS = 44.24629 ) // ICNODE( ADD, URC, NODE = 30, CONS = 2.26124 ) ICNODE( ADD, UTHE, NODE = 30, CONS = -50.40475 ) ICNODE( ADD, UZC, NODE = 30, CONS = 43.97659 ) // ICNODE( ADD, URC, NODE = 31, CONS = -0.52661 ) ICNODE( ADD, UTHE, NODE = 31, CONS = -38.03983 ) ICNODE( ADD, UZC, NODE = 31, CONS = 34.72785 ) // ICNODE( ADD, URC, NODE = 2, CONS = 0 ) ICNODE( ADD, UTHE, NODE = 2, CONS = 0 ) ICNODE( ADD, UZC, NODE = 2, CONS = 0 ) // ICNODE( ADD, VELO, ENTI = "wall", ZERO, X, Y, Z ) ICNODE( ADD, URC, ENTI = "axi-sym", ZERO, X, Y, Z ) // END( )


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TJ145 (ONLINE)
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Hong, Chin Tung.
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Analysis of flow in a 3D chamber and a 2D spray nozzle to approximate the exiting jet free surface
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by Chin Tung Hong.
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[Tampa, Fla.] :
University of South Florida,
2004.
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Thesis (M.S.M.E.)--University of South Florida, 2004.
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ABSTRACT: The purpose of this investigation is to analyze the flow pattern of cooling fluids in the 3D "twister-effect" mixing chamber and to approximate the free surface behaviors exiting the 2D spray nozzle. The cone angle and free surface height located at the end of the free surface are two significant factors to determine the spraying area on a heated plane. This process is a reasonable representation of many industrial cooling application. The whole system consists of 4 inlet tubes connected to the top of the mixing chamber, and the spray nozzle is located under the chamber. Four different refrigerants, like FC-72, FC-77, FC-87 and methanol were used for the turbulent flow simulations. According to different fluid properties, the cone angle, free surface, pressure drop and Reynolds number can be investigated at different flow rates.First, at a certain volumetric flow rates, the velocities in x, y, z directions were found on the positive x-axis (0 degree), y-axis (90 degrees), negative x-axis (180 degrees) and y-axis (270 degrees) at 8.0 x 10 m below the top of chamber. After the transformations, the interpolated and averaged radial, circumferential and axial velocities were used in the 2D nozzle simulations. Finally, the cone angle, the radial locations of the free surface and the pressure drop were obtained in each scenario. As the results, higher volumetric flow rate produced higher free surface height and cone angle. Also, FC-87 created the highest free surface height and cone angle among all four working fluids in both volumetric flow rates. It means that FC-87 can produce the largest spraying area on the heated surface. Fluctuation, spinning and eddy circulation can be found in the velocity plot because of the turbulent flow syndromes.When comparing two different nozzle designs, it was found that the nozzle without mixing chamber gave a larger cone angle and free surface height. Alternatively, the design in this investigation produced a relatively narrow jet concentrated to the stagnation zone.
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Adviser: Rahman, Muhammad M.
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liquid-gas interface.
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cone angle.
mixing length.
spraying cooling.
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