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Mukka, Santosh Kumar.
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Computation of fluid circulation in a cryogenic storage tank and heat transfer analysis during jet impingement
h [electronic resource] /
by Santosh Kumar Mukka.
260
[Tampa, Fla.] :
b University of South Florida,
2005.
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Thesis (M.S.M.E.)University of South Florida, 2005.
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Includes bibliographical references.
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Text (Electronic thesis) in PDF format.
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ABSTRACT: The study presents a systematic single and twophase analysis of fluid flow and heat transfer in a liquid hydrogen storage vessel for both earth and space applications.The study considered a cylindrical tank with elliptical top and bottom. The tank wall ismade of aluminum and a multilayered blanket of cryogenic insulation (MLI) has been attached on the top of the aluminum. The tank is connected to a cryocooler to dissipate the heat leak through the insulation and tank wall into the fluid within the tank. The cryocooler has not been modeled; only the flow in and out of the tank to the cryocooler system has been included. The primary emphasis of this research has been the fluid circulation within the tank for different fluid distribution scenario and for different level of gravity to simulate all potential earth and space based applications. The equations solved in the liquid region included the conservation of mass, conservation of energy, and conservation of momentum.For the solid region only the heat conduction equation was solved. The steadystate velocity, temperature and pressure distributions were calculated for different inlet positions, inlet opening sizes, inlet velocities and for different gravity values. The above simulations were carried out for constant heat flux and constant wall temperature cases. It was observed from singlephase analysis that a good flow circulation can be obtained when the cold entering fluid was made to flow in radial direction and the inlet opening was placed close to the tank wall. For a twophase analysis the mass and energy balance at the evaporating interface was taken into account by incorporating the change in specific volume and latent heat of evaporation. A good flow circulation in the liquid region was observed when the cold entering fluid was made to flow at an angle to the axis of the tank or aligned to the bottom surface of the tank.The fluid velocity in the vapor region was found to be higher compared to the liquid region.The focus of the study for the later part of the present investigation was the conjugate heat transfer during a confined liquid jet impingement on a uniform and discrete heating source. Equations governing the conservation of mass, momentum, and energy were solved in the fluid region. In the solid region, the heat conduction equation was solved. The solidfluid interface temperature shows a strong dependence on several geometric, fluid flow, and heat transfer parameters. For uniform and discrete heat sources the Nusselt number increased with Reynolds number. For a given flow rate, a higher heat transfer coefficient was obtained with smaller slot width and lower impingement height.The average Nusselt number and average heat transfer coefficient are greater for a lower thermal conductivity substrate.
590
Adviser: Dr. Rahman M.M.
653
Zero boiloff.
Cryocooler.
Multilayer insulation.
Ammonia.
Uniform and discrete heating.
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Dissertations, Academic
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x Mechanical Engineering
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TJ145 (Online)
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Computation Of Fluid Ci rculation In A Cryogenic Stor age Tank And Heat Transfer Analysis During Jet Impingement by Santosh Kumar Mukka 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 Mustafizur Rahman, Ph.D. Autar K. Kaw, Ph.D. Venkat R. Bhethanabotla, Ph.D. Date of Approval: March 7, 2005 Keywords: zero boiloff, cryocooler, multilayer insulation, ammonia, uniform and discrete heating Copyright 2005 Santosh Kumar Mukka
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i TABLE OF CONTENTS LIST OF TABLES iii LIST OF FIGURES iv LIST OF SYMBOLS xii ABSTRACT xvi CHAPTER ONE: INTRODUCTION AND LITERATU RE REVIEW 1 1.1 Introduction 1 1.2 Literature review (ZBO storage of cryogens) 3 1.3 Literature review (Jet impingement) 6 1.4 Objective 12 CHAPTER TWO: COMPUTATION OF FLUID (LIQUID HYDROGEN) CIRCULATION IN A HYDROGEN STORAGE TANK 14 2.1 Mathematical model 14 2.2 Numerical simulation 17 2.3 Results and discussion 18 CHAPTER THREE: COMPUTATION OF FLUI D (LIQUID AND VAPOR HYDROGEN) IN A HYDROGEN STORAGE TANK 35 3.1 Mathematical model 35 3.2 Numerical simulation 39 3.3 Results and discussion 40 CHAPTER FOUR: COMPUTATION OF HEAT TRANSFER DURING CONFIN ED LIQUID JET IMPINGEME NT WITH UNIFORM HEAT SOURCE 57 4.1 Mathematical model 57 4.2 Numerical simulation 58 4.3 Results and discussion 60
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ii CHAPTER FIVE: ANALYSIS OF FLUID FLOW DURING CONFINED LIQUID JET IMPINGEMENT FO R DIFFERENT NUMBER OF DISCRETE HEAT SOURCES 82 5.1 Mathematical model 82 5.2 Numerical simulation 84 5.3 Results and discussion 88 CHAPTER SIX: HEAT TRANSFER CO MPUTATION DURING CONFINED LIQUID JET IMPINGEME NT WITH DISRETE HEAT SOURCES 106 6.1 Mathematical model 106 6.2 Numerical simulation 108 6.3 Results and discussion 109 CHAPTER SEVEN: CONCLUSIONS 137 7.1 Cryogenic storage 137 7.2 Jet impingement 138 7.3 Recommendations for future research 142 REFERENCES 143 APPENDICES 147 Appendix A: Computation of fluid (liquid hydrogen) circulation in a hydrogen storage tank 148 Appendix B: Computation of fluid (l iquid and vapor hydrogen) circulation in a hydrogen storage tank 160 Appendix C: Computation of heat tr ansfer during confined liquid jet impingement with uniform heat source 172 Appendix D: Analysis of fl uid flow during confined liquid jet impingement for different number of discrete heat sources 182 Appendix E: Heat transfer computation during confine liquid jet impingement with discrete heat sources 189
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iii LIST OF TABLES Table 2.1 Average outlet temperature of the fluid and maximum fluid temperature obtained for different positions of the inlet pipe for liquid hydrogen 33 Table 3.1 Average outlet temperature of the fluid and maximum fluid temperature obtained for different positions of the inlet pipe for liquidvapor hydrogen 56 Table 4.1 Average heat transfer coefficient and average Nusselt number for an uniformly heated plate 81 Table 5.1 Average heat transfer coefficient and Nusselt number for a varying number of heat sources 105 Table 6.1 Average heat transfer coefficient and Nusselt number for a discretely heated plate 135
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iv LIST OF FIGURES Figure 2.1 Schematic diagram of the liquid hydrogen cylindrical tank 15 Figure 2.2 Graph showing the temperature at a particular section in the insulation with elliptical top and bottom 15 Figure 2.3 Streamline contour for the tank with the inlet at the bottom 18 Figure 2.4 Temperature contour for the tank with the inlet at the bottom 19 Figure 2.5 Velocity vector plot for the tank with the inlet extended 50% into the tank and radial discharge at 450 from the axis 20 Figure 2.6 Streamline contour plot for the ta nk with the inlet extended 50% into the tank and radial discharge at 450 from the axis 21 Figure 2.7 Temperature contour plot for the tank with the inlet extended 50% into the tank and radial discharge at 450 from the axis 22 Figure 2.8 Velocity vector plot for the tank with the inlet at the bottom of the tank 23 Figure 2.9 Streamline contour plot for the tank with the inlet at the bottom of the tank 23 Figure 2.10 Temperature contour plot for the ta nk with the inlet at the bottom of the tank 24 Figure 2.11 Streamline contour for the tank with radial discharge from three openings of different widths 25 Figure 2.12 Streamline contour for the tank with radial discharge from three openings of equal widths 26 Figure 2.13 Temperature contour plot for the tank with radial discharge from three openings of equal widths 26
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v Figure 2.14 Streamline contour for the tank with inlet pipe extended into the tank and discharge at 450 from the axis. Inclin ed pipe length = 60 cm 27 Figure 2.15 Streamline contour for the tank with inlet pipe extended into the tank and discharge at 450 from the axis. Inclin ed pipe length = 30 cm 27 Figure 2.16 Streamline contour for the tank with inlet pipe extended into the tank and discharge at 600 from the axis 28 Figure 2.17 Temperature contour for the tank with inlet pipe extended into the tank and discharge at 600 from the axis 29 Figure 2.18 Streamline contour plot for the tank with radial flow in a Cchannel 30 Figure 2.19 Temperature contour plot for the tank with radial flow in a Cchannel 31 Figure 3.1 Schematic of a cylindrical tank with elliptical top and bottom 38 Figure 3.2 Graph showing the temperature at a particular section in the insulation 38 Figure 3.3 Velocity vector plot for the tank with the inlet at the bottom 40 Figure 3.4 Pressure contour plot for the tank with the inlet at the bottom 41 Figure 3.5 Temperature contour plot for the tank with the inlet at the bottom 42 Figure 3.6 Velocity vector plot for the tank with inlet at the bottom (Tank filled upto 25% of tank volume) 43 Figure 3.7 Velocity vector plot for the tank with inlet at the bottom (Tank filled upto 75% of tank volume) 44 Figure 3.8 Streamline contour plot for the ta nk with the Inlet at the bottom (Tank filled upto 75% of tank volume) 44 Figure 3.9 Pressure contour plot for the tank with the inlet at the bottom (Tank filled upto 75% of tank volume) 45 Figure 3.10 Temperature contour plot for the tank with the Inlet at the bottom (Tank filled upto 75% of tank volume) 46
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vi Figure 3.11 Velocity vector plot for radi al discharge from one opening 46 Figure 3.12 Streamline contour plot for the ta nk with radial di scharge from one opening 47 Figure 3.13 Streamline contour plot for the ta nk with radial discharge from three openings 47 Figure 3.14 Velocity vector plot for the tank with the extended inlet and radial discharge at 450 from the axis 49 Figure 3.15 Temperature contour plot for the tank with the extended inlet and radial discharge at 450 from the axis 50 Figure 3.16 Velocity vector plot for the tank with radial flow in a Cchannel 51 Figure 3.17 Streamline contour plot for the tank with radial flow in a smaller Cchannel 51 Figure 3.18 Streamline contour plot for the tank with radial flow in a greater Cchannel 53 Figure 3.19 Temperature contour plot for the tank with radial flow in a Cchannel 53 Figure 4.1 Schematic of a confined slot jet impinging on a uniformly heated solid plate 60 Figure 4.2 Dimensionless solidfluid interf ace temperature for different number of elements in x and z directions 62 Figure 4.3 Graph showing the variation of st agnation Nusselt number with jet Reynolds number 62 Figure 4.4 Dimensionless solidfluid interface temperature for varying Reynolds number 63 Figure 4.5 Nusselt number at the solidfluid interface for varying Reynolds number (Nonconjugate model) 63 Figure 4.6 Nusselt number at the solidfluid interface for varying Reynolds number (Conjugate model) 64
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vii Figure 4.7 Dimensionless temperature at the solidfluid interface for constant flow rate 65 Figure 4.8 Nusselt number at the solidfluid in terface for constant flow rate 66 Figure 4.9 Dimensionless solidfluid interface temperature for different nozzle widths 67 Figure 4.10 Local Nusselt number at the solidfluid interface for different nozzle widths 68 Figure 4.11 Comparison of local temperature at the interface for two different solid materials for two different solid thicknesses 69 Figure 4.12 Local Nusselt number at the solidfluid interface for different nozzle widths using silicon substrate 70 Figure 4.13 Local Nusselt number at the solidfluid interface for different nozzle widths using stainless steel substrate 70 Figure 4.14 Comparison of local heat transfer coefficient for three different impingement heights 72 Figure 4.15 Comparison of local heat transfer coefficient for four different impingement heights 73 Figure 4.16 Comparison of maximum temper ature and difference between maximum and minimum temperatures at the interface for different solids with various thicknesses 74 Figure 4.17 Comparison of maximum temperatur e within the solid for various thicknesses 75 Figure 4.18 Comparison of Nusselt number for different solids and plate thicknesses 75 Figure 4.19 Comparison of dimensionless solidfluid interface temperature for three different coolants 78 Figure 4.20 Comparison of local Nusselt numbe r for three different coolants using silicon substrate 79 Figure 4.21 Comparison of dimensionless solidfluid interface temperature for three different coolants 79
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viii Figure 4.22 Comparison of local Nusselt numbe r for three different coolants using stainless steel substrate 80 Figure 5.1 Schematic of a confined slot je t impinging on a so lid plate with discrete heat sources 86 Figure 5.2 Different combinations of locati on and magnitude of heat sources 87 Figure 5.3 Dimensionless temperature at the interface for different discrete heat sources with constant total power 89 Figure 5.4 Nusselt number at the interface for different discrete heat sources with total power constant (Nonconjugate model) 90 Figure 5.5 Dimensionless temperature at the interface for different discrete heat sources with total power constant 91 Figure 5.6 Isotherm plot for seven and three heat sources respectively with constant total power 92 Figure 5.7 Nusselt number at the interface for different discrete heat sources with total power constant using silicon substrate 92 Figure 5.8 Nusselt number at the interface for different discrete heat sources with total power constant using stainless steel substrate 93 Figure 5.9 Dimensionless temperature at the so lidfluid interface for different discrete heat sources with constant heat flux 94 Figure 5.10 Nusselt number at the solidfluid interface for different discrete heat sources with constant heat flux 95 Figure 5.11 Dimensionless temperature at the so lidfluid interface for different discrete heat sources with heat flux constant 96 Figure 5.12 Nusselt number at the solidfluid interface for different discrete heat sources with heat flux constant 97 Figure 5.13 Dimensionless temperature at the so lidfluid interface for different discrete heat sources with heat flux constant 97 Figure 5.14 Nusselt number at the solidfluid interface for different discrete heat sources with heat flux constant 98
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ix Figure 5.15 Comparison of maximum temper ature and difference between maximum and minimum temperatures at the interface for different solids with various heat sour ces with heat flux constant 99 Figure 5.16 Comparison of maximum temperature within the solid for different discrete heat sources with heat flux constant 100 Figure 5.17 Comparison of Nusselt number for different solids for different discrete heat sources with heat flux constant 100 Figure 5.18 Nusselt number at the solidfluid interface for different magnitudes of discrete heat sources and constant total power 102 Figure 5.19 Local Nusselt number at the solidfluid interface for different locations of discrete heat sources and constant total power 103 Figure 6.1 Schematic of a confined slot jet impinging on a uniformly heated solid plate 110 Figure 6.2 Dimensionless solidfluid interf ace temperature for different number of elements in x and z directions 111 Figure 6.3 Dimensionless temperature at the solidfluid interface with seven discrete heat sources and constant total power for varying Reynolds number 112 Figure 6.4 Nusselt number at the solidfluid in terface with seven discrete heat sources and constant total power for varying Reynolds number 113 Figure 6.5 Dimensionless temperature at the solidfluid interface with seven discrete heat sources and constant total power for varying Reynolds number 114 Figure 6.6 Nusselt number at the solidfluid in terface with seven discrete heat sources and constant total power for varying Reynolds number 114 Figure 6.7 Dimensionless temperature at the solidfluid interface with seven discrete heat sources and constant total power for same flow rate 115 Figure 6.8 Nusselt number at the solidfluid in terface with seven discrete heat sources and constant total power for same flow rate 116
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x Figure 6.9 Dimensionless temperature at the solidfluid interface with seven discrete heat sources and constant total power for different nozzle widths 117 Figure 6.10 Nusselt number at the solidfluid in terface with seven discrete heat sources and constant total power for different nozzle widths 118 Figure 6.11 Comparison of local temperatures at the interface with three discrete heat sources and constant total power for different solids 119 Figure 6.12 Comparison of local Nusselt number with three discrete heat sources and constant total power for different solid thicknesses 120 Figure 6.13 Comparison of local Nusselt number with three discrete heat sources and constant total power for different solid thicknesses 121 Figure 6.14 Comparison of maximum temper ature and difference between maximum and minimum temperatures at the interface for different solids with various thicknesses 122 Figure 6.15 Comparison of maximum temperat ure within the substrate for various thicknesses 123 Figure 6.16 Comparison of average Nusselt number for different solids and plate thicknesses 124 Figure 6.17 Dimensionless temperature at the in terface with three discrete heat sources and constant total power fo r different impingement heights 125 Figure 6.18 Local Nusselt number at the interface with three discrete heat sources and constant total power for different impingement heights 126 Figure 6.19 Dimensionless temperature at the in terface with three discrete heat sources and constant total power for different impingement heights 127 Figure 6.20 Local Nusselt number at the interface with three discrete heat sources and constant total power for different impingement heights 127 Figure 6.21 Dimensionless temperature at the in terface with three heat sources and constant total power for different fluids 128 Figure 6.22 Local Nusselt number at the interf ace with three heat sources and constant total power for different fluid 129
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xi Figure 6.23 Dimensionless temperature at the in terface with three heat sources and constant total power for different fluids 130 Figure 6.24 Local Nusselt number at the interf ace with three heat sources and constant total power for different fluids 130 Figure 6.25 Isotherms for stainless steel with three discrete heat sources and constant total power 131 Figure 6.26 Isotherms for stainless steel with three discrete heat sources and constant total power 131 Figure 6.27 Isotherms for silicon with thr ee discrete heat sources and constant total power 132
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xii LIST OF SYMBOLS b Thickness of the plate, [m] Cp Specific heat at consta nt pressure, [J / kg K] E Total applied thermal energy, [W/m] Fr Froude number, v/ gl g Acceleration due to gravity, [m / s2] h Heat transfer coefficient, qint/ (Tint Â– Tj), [W / m2K] H Height of the storage tank, [m] Hn Height of the nozzle from the plate, [m] k Thermal conductivity, [W / m K] k Turbulent kinetic energy, (for chapter 2 and 3) [W/m] L Length of the plate, [m] Nu Nusselt number, hW /k f p Pressure, [Pa] P Dimensionless Pressure, (ppout)/ vj 2 Pr Prandtl number, /
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xiii q Heat flux, [W / m2] Q Fluid flow rate per unit depth, [m2/s] r Radial coordinate, [m] Re Reynolds number, Wvj/ f T Temperature, [K] v Velocity, [m/s] V Dimensionless velocity, v/vj W Width of the slot nozzle, [m] x Coordinate parallel to the plate, [m] z axial coordinate, [m] (for chapter 2 and 3) Coordinate perpendicular to the pl ate, [m] (for chapter 4, 5, and 6) Greek Symbols Thermal diffusivity [m2/s], k/( Cp) Dimensionless vertical coordinate, z/L Thickness of the solid to le ngth of the plate ratio, b/L Turbulent kinetic ener gy dissipation rate, [m2/s3] Thermal conductivity ratio, ks/kf Dynamic viscosity of fluid [kg/ms]
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xiv Kinematic viscosity, [m2/s] Dimensionless horizontal coordinate, x/L Density [kg/m3] Dimensionless temperature, ((TTj) kf)/ (E) Jet impingement height to length of the plate ratio, Hn/L Density ratio, f/ s Width of the slot to leng th of the plate ratio, W/L Specific heat ratio, Cps/Cpf Dimensionless Energy, fvin 2/E t Eddy diffusivity, [m2/s] Subscripts av Average b Bulk f Fluid int Solid fluid interface j Jet max Maximum min Minimum out Outlet
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xv r Radial component s Solid x xcomponent z Axial direction (for chapter 2 and 3) zcomponent (for 4, 5 and 6)
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xvi COMPUTATION OF FLUID CIRCULATI ON IN A CRYOGENIC STORAGE TANK AND HEAT TRANSFER ANA LYSIS DURING JET IMPINGEMENT Santosh Kumar Mukka ABSTRACT The study presents a systematic single an d twophase analysis of fluid flow and heat transfer in a liquid hydr ogen storage vessel for both ea rth and space applications. The study considered a cylindrical tank with elliptical top and bo ttom. The tank wall is made of aluminum and a multilayered bla nket of cryogenic insulation (MLI) has been attached on the top of the aluminum. The tank is connected to a cryocooler to dissipate the heat leak through the insulation and tank wall into the fluid w ithin the tank. The cryocooler has not been modeled; only the flow in and out of the ta nk to the cryocooler system has been included. The primary emphas is of this research has been the fluid circulation within the tank for different fluid distribution scen ario and for different level of gravity to simulate all potential earth and space based applications. The equations solved in the liquid region included the conser vation of mass, conservation of energy, and conservation of momentum. For the solid re gion only the heat conduction equation was solved. The steadystate velocity, temperature and pressure distributi ons were calculated for different inlet positions, inlet opening sizes inlet velocities and for different gravity values. The above simulations were carried out for constant heat flux and constant wall temperature cases. It was observed from singlephase analysis that a good flow circulation can be obtained when the cold en tering fluid was made to flow in radial
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xvii direction and the inlet opening was placed close to the tank wall. For a twophase analysis the mass and energy balance at the evaporating interface was taken into account by incorporating the change in specific vol ume and latent heat of evaporation. A good flow circulation in the liquid region was observed when the co ld entering fluid was made to flow at an angle to the ax is of the tank or aligned to th e bottom surface of the tank. The fluid velocity in the vapor region was found to be higher compared to the liquid region. The focus of the study for the later part of the present investigation was the conjugate heat transfer during a confined liquid jet impingement on a uniform and discrete heating source. Equations governi ng the conservation of mass, momentum, and energy were solved in the fl uid region. In the solid region, the heat conduction equation was solved. The solidfluid interface temperature shows a strong dependence on several geometric, fluid flow, and heat transfer para meters. For uniform and discrete heat sources the Nusselt number increased with Reynolds num ber. For a given flow rate, a higher heat transfer coefficient was obtained with smalle r slot width and lower impingement height. The average Nusselt number and average heat transfer coefficient are greater for a lower thermal conductivity substrate. A higher heat transfer coefficient at the impingement location was seen at a smaller thickness, wh ereas a thicker plate or a higher thermal conductivity plate material pr ovided a more uniform dist ribution of heat transfer coefficient. Compared to Mil7808 and FC77, ammonia pr ovided much smaller solidfluid interface temperature and higher heat transfer coefficient whereas FC77 provided lower Nusselt number. In case of discrete he at sources calculations were done for two different physical conditions, namely, when th e total input power is constant and when the magnitude of heat flux at the sources ar e constant. There was a periodic rise and fall
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xviii of interface temperature along the heated and unh eated regions of the plate when the plate thickness was negligible. The average Nusselt number and average local heat transfer coefficient were highest for uniform heati ng case and it increased with number of heat sources during discrete heating.
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1 CHAPTER ONE INTRODUCTION AND LITERATURE REVIEW 1.1 Introduction An effective, affordable, and reliable st orage of cryogenic fluid is essential for propellant and life support systems in space vehicles. The extension of the human exploration of space from low earth orbit (L EO) into the solar sy stem is one of the NASAÂ’s challenges in the future. Without safe and efficient cryogenic storage, economically feasible long duration space missions will not be possible. The ZBO concept has recently evolved as an innovative means of storage tank pressure control, which reduces mass through a synergistic app lication of passive insulation, active heat removal, and forced liquid mixing. A cryoc ooler (with a power supply, radiator, and controls) is integrated into a traditional orbital cryogenic st orage subsystem to reject the storage system heat leak. With passive stor age, the storage tank size and insulation weight increase with days in orbit, wh ereas the ZBO storage system mass remains constant. In addition to space mission, the st orage and transportation of liquid hydrogen is important in several earth based engineering systems. The world energy crisis, coupled with the increasing ne ed to reduce air pollution, has placed important emphasis on developing new fuel sources for transportatio n systems. Experimental and theoretical studies in the literature have shown that hydrogen, with its al most unlimited supply potential and with its extraordinarily cl ean combustion properties, emerges as an
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2 operationally practical, economi cally feasible energy source Hydrogen has, for years, been recognized for its extremely high en ergy potential. But because of inherent difficulties in handling hydrogen in its gase ous form, technology has, emphasized the utilization of hydrogen in its liquid form. In cooling electronic components, incr eased power densities per device and smaller spacing between the devices have necessitated the search for innovative techniques of heat di ssipation. Jet impingement from a slot or axial nozzle is widely employed in industries for highly localized heating or cooling. In recent years, the demand for compactness and higher operational pr ocessors has led to high power density in electronic packages. An enhanced heat transfer method such as jet impingement will be required to provide the desired ther mal environment in electronic equipment. Alternative refrigerants suitable for refrigerat ion systems have been actively investigated owing to increasingly more regulations pl aced on the use of chlorofluorocarbonbased (CFC) refrigerants, as well as the scheduled phaseout of CFCs and hydrofluorocarbons (HCFCs) altogether. Ammonia has been c onsidered as an im portant alternative refrigerant for new and existing large central ized refrigerating, airconditioning systems, and thermal storage systems. Ammonia ha s a 0.00 value of ozone depletion potential (ODP) when released to atmosphere, and doe s not directly contribute to global warming. It also has a low boiling point and high latent heat of vaporization (about 9 times greater than R12 or R22). These characteristic s make ammonia a highly energyefficient refrigerant with minimal potential environmenta l problems. In order to take advantage of these benefits ammonia has been used as the coolant in the present investigation.
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3 1.2 Literature review (ZBO storage of cryogens) Mueller et al. [1] proposed that launc hing the space missions on smaller, less expensive launch vehicles would reduce the cost of space missions. For a Mars sample return mission, they considered using Mart ian carbondioxide, combined with hydrogen brought from earth, to generate oxygen and meth ane propellant for return to Earth. This eliminates the need to bring the propellant for the return trip and thereby reduces the spacecraft weight during its launch at earth. Spall [2] made a numerical study on natural stratification of turbulent flows in an axisymmetric, cylindrical, storage tank. His ca lculation involved th e injection of cold water through a slot at the base of an insulated tank. He employed both kmodel and the full Reynolds stress turbulence models a nd discussed the results. It was found that for a particular range of parameters, the inle t Reynolds number plays a little role in determining the stratification properties of th e fluid when the Archimedes number is held constant. Mueller and Durrant [3] presented an analysis of cryoge nic liquefaction and storage methods for insitu produced propella nts on Mars. They varied the insulation thickness and the cryocooler capacity to find optimum combinations for various insulation configurations, including multilayer insulation and microspheres. Their investigation showed that microsphere in sulation is preferre d for a human mission. Salerno and Kittel [4] presented a brief overview of Mars reference mission and the concomitant cryogenic fluid management technology. It was c oncluded that longterm cryogenic propellant stor age would minimize the mass re quired to get humans to Mars and assure that enough seed propellant remains so that cryogenic liquefiers on the Martian surface can produce the necessary prope llants to get humans back to earth. They
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4 observed that a mix of active and passive t echnologies would be needed to achieve a robust system at minimum cost. Kamiya et al. [5] developed a large e xperimental apparatus to measure the thermal conductance of vari ous insulations. Various sp ecimens with allowable dimensions: diameter 120cms and thickness up to 30cms could be tested. The structural analysis for the vessel structure of experime ntal apparatus was performed. The results of the deflection and stress of the vessels at room and the liquid nitrogen temperature were verified by the analytical models. Hastings et al. [6] made an e ffort to develop ZBO concepts for inspace storage of cryogenic propellants. Analytical modeling for the storage of 670 kgs of liquid hydrogen in lowearth orbit (LEO) was performed and it was observed that the ZBO system mass advantage, compared with passive storage begins at 60 days. Another important observation was that ZBO substantially adds operational flexibility as mission timelines can be extende d in real time with no propellant losses. Kittel [7] made a study on the parasitic heat loads on the propellant and he proposed an alternative approach of using a re liquefier to carry away the heat from the storage tank. He compared two schemes to remove the heat from the propellant. One scheme uses a sealed closed cycle cooler wi th a mixer. The mixer circulates propellant cooled by the refrigerator, isothermalizing th e tank. The other scheme uses a cooler that uses the propellant vapor as its working fluid. He concluded that the first scheme offers advantages in efficiency and the ability to test the cooler before integration while the second scheme is simpler to integrate a nd provides an emergency vent route that intercepts the parasitic heat of the cooler.
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5 Kamiya et al. [8] developed an experime ntal apparatus to measure the thermal conductance of different insulati on structures for large mass LH2 storage systems. The actual insulation structures comp rise not only the insulation ma terial but also reinforced members and joints. He tested two specimens, a vacuum multilayer insulation with a glass fiber reinforced plas tic (GFRP) and a vacuum so lid insulation. The thermal background test for verifying the thermal desi gn of the experimental apparatus showed that the background heat leak is 0.1 W, sm all enough to satisfy apparatus performance requirement and the thermal conductance measurements of specimens showed that the heat fluxes of MLI with a GFRP support a nd vacuum solid insulation are 8 and 5.4 W/m2 respectively. Van Dresar et al. [9] have reported the co rrelations for convective heat transfer coefficients for twophase flow of nitr ogen and hydrogen under low mass and heat flux conditions It has been observed that the Nusselt number exhibits peak values near transition from laminar to turbulent flow based on th e vapor Reynolds number The Nusselt number was correlated using components of the Mar tinelli parameter and a liquidonly Froude number. Zapke and Kroger [10] made an experimental investig ation of adiabatic gasliquid counterflow in inclined and vert ical rectangular ducts with a s quareedged gas inlet. It was observed that the flooding gas velocity is found to be strongly dependent on the duct height, the phase densities and duct inclination. Rousset et al [11] presented two different applications for twophase visu alization at low temp erature. They have conducted different experiments and showed that it is possible to visualize sample at cryogenic temperature without thermally perturbing the samples.
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6 From the above literature review, it may be noted that storag e of liquid hydrogen as well as other cryogenic fluids is needed fo r longterm space missions. Even though quite a few proof of concept studies have been done, a detailed simulation of fluid flow and heat transfer in cryogenic storage vessel has not been reported. 1.3 Literature review (Jet impingement) Jet impingement heat transfer (JIHT) has received considerable research attention due to it's potential application in the area of thermal heating and cooling processes. As computers and other electronic products su ch as cellular telephone s have become more sophisticated and smaller in size, the logistics of heat elimination have also become more difficult. Traditional methods such as the us e of fans because of their bulk size and noise are inadequate and inappropriate. Impinging jets are various types e.g. ai r jets, gas jets, and jets. This work focuses only on liquid jets. Also, impinging jets can be configured in vari ous ways. The most popular are circular (also know n as axisymmetric) and planar (also known as slot) jets. Slot jets typically impinge the heated plate in an axial manner. Circular jets however may be configured to impinge the heated surface e ither axially or radially. Furthermore, the liquid jets be they circular or planar ma y be configured as submerged or free surface. As described by Womac et al. [12], the flow and heat transfer phenomena in these two cases differ. In a submerged configuration, th e fluid exits a nozzle or orifice into a body of surrounding fluid that is the same as the jet itself. Submerged jets thus entrain surrounding fluid which may be at a different temperature. Vertical confinement of the submerged jet may also be important an d influence the heat transfer if the jet
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7 is formed by an orifi ce plate which bounds the flow. Gravitational effects are generally smaller in submerged jets. Free surface jets result when a liquid issues from a nozzle or orifice into a gas environment. Entrainment of surrounding fluid is therefore negligible. The shape of the free surface is gove rned by a balance of gravity, surface tension, and pressure forces. Gravity effects are obviously very dominant in this configuration. Extensive experimental work has been done for submerged liquid jets with various working fluids by Yamamoto et al [13], Elison and Webb [14], and Ma et al. [15]. They considered Reynolds number in the broad range of 55 2000. Elison Webb [14] studied circular jets with diameters of 0.584, 0.315, and 0.246 mm. They observed that Nusselt number co rrelated approxim ately with Re 0.8 for laminar jets. Heat flux was introduced through a thin metallic foil thus achieving a constant heat flux boundary condition. Ma et al. [15] measured heat transfer coefficients resulting from the impingement of transfor mer oil jets issui ng from tiny slot nozzles of 0.091, 0.146, and 0.234 mm in width. Fluid Prandtl numbers ranged from 200 to 270 while jet Reynolds number was between 55 and 415. They developed a correlation for heat transfer coefficient as a function of jet Reynolds number, nozzle to plate spacing, a nd slot width. Nusselt number correlated approximately with Re 0.8 and Pr 0.33. Garimella and Rice [ 16] carried out an experimental study on th e heat transfer from a small heat sour ce to a normally impinging, axisymmetric confined liquid jet us ing FC77 as the working fluid. Heat transfer was found to be sensitive to nozzle diameter, Reynolds number, and nozzle to heat source spacing.
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8 Submerged liquid jets find use in both ax isymmetric and planar configurations. Both configurations share the common feature of a very small stagnation zone at the impingement surface whose size is of the order of the jet dimension, with the subsequent formation of a wa ll jet region. Both are affected by viscous shear in the submerged configuration. Both may be configured in arrays in an attempt to achieve higher transport characteristics of the stagnation zone over a larger area. Both may also be oriented normal or oblique to the impingement plate. Oblique impingement obviously affects the hydrodynamics of the fl ow and consequently the heat and/or mass transfer. AbouZiyan and Ha ssan [17] made an experime ntal study of forced convection due to impingement of confined, submerged and fully turbulent jets in relation to the cooling of engine cylinder heads by water. They concluded that jet impingement can save between 50% and 92% of required cooling water compared to simple forced convection. Morr is et al. [18] made an an alytical investigation of flow fields in the orifice and confin ement regions of a normally impinging confined and submerged liquid jet. Predicted characteristics of the separation region at the orifice entrance agreed with pub lished experimental values for different orifice diameters and or ifice to target plate spacing. The pressure dr op across the orifice was predicted to be within 5% of their proposed empirical correlations based on published experimental data. They also found that computed flow patterns in the confinement region were in good qualitative agreement with experimental flow visualizations. Dinu et al. [19] made a numerical study of convective heat transfer from a confined submerged je t impinging on a moving surface. They considered both constant temperature as well as constant heat flux boundary
PAGE 30
9 conditions on the moving surface. With a constant temperature boundary condition, heat transfer distributions we re found to be se nsitive to the spee d of the heat transfer surface and to the jet inlet Re ynolds number. For a uniform heat flux boundary condition, Nusselt number on the m oving plate was more uniform than for a constant temperature boundary condition. Law and Masliyah [20] experimented w ith a twodimensional impingement jet discharging onto a flat plate. They used air as working fluid with a Reynolds number less than 400. They solved this pr oblem both numerically and expe rimentally to determine the heat transfer coefficient characteristics. A nother investigation of a twodimensional jet impinging on a flat plate was performed by Seyedein et a. [21]. In their analysis, the flow was also laminar, but it was discharged from multiple slot jets onto a heated flat plate. The Reynolds number was varied, as well as th e inclination of the plate receiving jet. They wanted to examine the effects that th e Reynolds number and inc line of the plate has on the Nusselt number. From their analysis, an incline surface created a level distribution of Nusselt number across the plate due to im proved exhaust of the fluid. Another group of people to investigate the same phenomena was Tzeng et al. [22]. They numerically examined a confine impingement jet with variations in its Reynolds number. Their experiment was performed so that a model coul d be constructed to accurately predict heat transfer performance of conf ined impingement jet discha rged onto a flat plate. Wang et al. [23] applied a previously deve loped analytical solution to predict the surface temperature and heat flux distributions over a chip cooled by a laminar impinging FC77 liquid or water jet. They presented results for two nozzle diameters. Wadsworth and Mudawar [24] performed an experiment to investigate singlephase heat transfer
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10 from a simulated chip to a twodimensional jet of dielectric flui d FC72 issuing from a thin rectangular slot into a confined channel. The main conclusion was that the jet maintained fairly isothermal surface conditi on and well suited for the packaging of large arrays of high power density electronics. Schaffe r et al. [25] presented the results of an experimental study measuring the average heat transfer coefficient for discrete sources located under a liquid jet issuing from a rect angular slot. The experiment was conducted for heat sources mounted on a channel (submer ged jet). They found th at a secondary peak is generated at a distance linked to the jet wi dth. Teuscher et al. [ 26] investigated FC77 impingement on an array of discrete heat source s with pin fins and parallel plate fins used as surface modifications. The former showed an increase in heat transfer coefficient by three times while the parallel plate fins re sulted in a three to five times increase. Garimella and Rice [16] experimentally inve stigated the local heat transfer from a small heat source to a normally impinging ax isymmetric and submerged liquid jet, in confined and unconfined configurations. Secondary peaks were more pronounced at smaller (confined) spacing and large nozzl e diameters for a given Reynolds number. Correlations were presented for the average he at transfer coefficient and Nusselt number. The heat transfer from discrete heat sources to single and multiple confined air jets was studied by Schroeder and Garimella [27]. The results were compared to those previously obtained for single air jet. A reduction in or ificetotarget spacing was found to increase the heat transfer coefficient in multiple jets with this effect being stronger at higher Reynolds numbers. With a ninejet arrangement, the heat transfer to the central jet was higher than for a corresponding single jet. The ef fectiveness of single and multiple jets in removing heat from a given heat source was compared at a fixed total flow rate. El
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11 Sheikh and Garimella [28] experimentally inve stigated the enhancemen t of heat transfer from a discrete heat source in confined air jet impingement. The enhancement in heat transfer was found to be a strong function of noz zle diameter and heat sink footprint area; at a given flow rate, the effectiveness decreased with decreasing nozzle diameter. Bula et al. [29] studied the impingement of axial free surface jet over a flat disc with discrete heat sources. Equations for the conservation of mass, momentum, and energy were solved taking into account the transport proce sses at the solidliquid and liquidgas interfaces. They found out that local heat transfer coefficient is maximum at the center of the disk and decreases graduall y with radius as the flow moves downstream. The other conclusion which they came to is the thickness of the plate and the location of discrete heat sources showed a greater impact on the maximum temperature and the average heat transfer coefficient. Wang and Mujumdar [30] made a comparative study of the heat transfer under a turbulent sl ot jet using five low Reynolds number k Â– models. They concluded that the jet inlet velocity pr ofile that provides slow jet spreading rate increases the heat transfer in and near impinging regions until a critical value of x / W is reached. Narayanan et. al [31] made an experime ntal study of flow field, surface pressure, and heat transfer rates of a submerged, turb ulent, slot jet impingi ng normally on a flat plate is presented. Two nozzletosurface sp acings of 3.5 and 0.5 nozzle exit hydraulic diameters, which correspond to transiti onal and potentialcore jet impingement, respectively, are considered. It was observed that for the transitional jet impingement, the mean and RMSaveraged fluctuating surface pre ssure, and local heat transfer coefficient peaked in the impingement region and decr eased monotonically in the wallbounded flow
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12 past impingement and for the potentialcore jet impingement, the primary peak in heat transfer, was observed in the impingement region, and it was followed by a region of local minimum and a secondary peak th at occurred at around 1.5 and 3.2 hydraulic diameters from the jet centerline, respectively. Alternative refrigerants suitable for refrigeration systems have been actively investigated owing to increasingly more regulations placed on the use of chlorofluorocarbonbased (CFC) refrigerants, as well as the scheduled phaseout of CFCs and hydrofluorocarbons (HCFCs) altogether. Ammonia has been co nsidered as an important alternative refriger ant for new and existing large centralized refrigerating, airconditioning systems, and thermal storage sy stems. Ammonia has a 0.00 value of ozone depletion potential (ODP) when released to atmosphere, and does not directly contribute to global warming. It also has a low boiling point and high latent heat of vaporization (about 9 times greater than R12 or R22). These character istics make ammonia a highly energyefficient refrigerant with minimal pot ential environmental problems. In order to take advantage of these benef its ammonia has been used as the coolant in the present investigation. 1.4 Objective To develop a simulation model for fluid fl ow and heat transfer in storage tank with constant heat flux and constant temperature applied on the tank wall. To investigate the geometric and flow parameters, optimizing the tank design for good fluid circulation and temperat ure uniformity within the tank. To develop a simulation model for fluid fl ow and heat transfer during a confined liquid jet impingement for uniform and discrete heat sources.
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13 To explore the effects of slot width, jet impingement height, plate thickness, solid and fluid properties, and nozzle Reynolds number on the fluid flow and heat transfer characteristics within the channel.
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14 CHAPTER TWO COMPUTATION OF FLUID (LIQUID HYDROGEN) CIRCULATION IN A HYDROGEN STORAGE TANK 2.1 Mathematical model The mathematical model for which the simulations are performed is represented by figure 2.1. The physical structure of the mo del comprises of a cylindrical body with an elliptical top and bottom. A twodimensional axisymmetric jet enters the tank from the bottom and exits from the top. The diameter of both inlet and outlet are 0.15m. The height of the tank is 2.6m. The major and minor axes of the elliptical portion are 3m and 1.3m. The tank wall is made of alum inum and is 0.0127m thick. The tank is surrounded by an insulation of 0.1m thickness. Heat flux or temperature was applied at the outer wall. The working fluid in this problem is liquid hydrogen. Different ideas for channeling the flow in the tank were implemented. Assuming the fluid to be incompressible, the equations describing the conservation of mass, momentum, and energy in cylindrical coordinates can be written as: rz1 r0 rrz (1)
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15 Figure 2.1 Schematic diagram of the liquid hydrogen cylindrical tank 0 50 100 150 200 250 300 350 00.511.522.533.5 Distance (x 10E2 m)Temperature (K) Outer surface = 305 K (Numerical) 305 K (Experimental) Outer surface = 235 K (Numerical) 235 K (Experimental) Outer surface = 164 K (Numerical) 164 K (Experimental) Figure 2.2 Graph showing the temperature at a particular section in the insulation with elliptical top and bottom
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16 rrrrzzr rztt fp 112 r2 rzrrr3rrzzrz (2) zzrzzrr rztt fp 112 gr2 rzzrrzrz3zrr (3) tt ffff rz ttTTTT 1 r rzrrprrzprz (4) The effects of turbulence in the flow field were determined by using the kmodel. In this model, the turbulent kinetic energy and its dissipation rate were calculated by using the following equations. 2222 2 t rrzrz rrzt 2 kkkk1kk r2 rrzrrrrrzzr z (5) k C r z z r r k C z r r r r z r rz r z r r t k t z r r 2 2 2 2 2 2 1 2 22 1 (6) 2k Ct. (7) The empirical constants appearing in equatio ns (57) are given the following values (Kays [32]): C=0.09, C1=1.44, C2=1.92, k =1, =1.3, Prt=1. The equation used for the conservation of energy within th e solid can be written as follows:
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17 2 ss 2TT 1 r0 rrr z (8) The boundary conditions needed to solve the above equations included uniform axial velocity at the inlet, no slip condition at th e solidfluid interface and constant heat flux or constant temperature at the outer surface of the tank. 2.2 Numerical simulation The above governing equations along with the boundary conditions were solved using the finiteelement method. The solid an d fluid regions were both divided into a number of quadrilateral elements. After the Ga lerkin formulation was used to discretize the governing equations, the NewtonRaphson method was used to solve the ensuing algebraic equations. NewtonRaphson method is based on the principle that if th e initial guess of the root of f(x) = 0 is at xi, then if one draws the ta ngent to the curve at f(xi), the point xi+1 where the tangent crosses the xaxis is an improved estimate of the root. Using the definition of th e slope of a function, at ix x ) = (x fitan 10 i i ix x ) f(x = which gives ) f'(x ) f(x = x xi i i i1 The above equation is called the NewtonRaphson formula for solving nonlinear equations of the form0 x f. The finite element program called FIDAP was used for this computation. Convergence is based on tw o criteria being satisfied simultaneously.
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18 One criterion is the relative change in field values from one iteration to the next; the other is the residual for each conservation e quation. In this problem a tolerance of 0.1 percent (or 0.001) for both conve rgence criteria was applied. 2.3 Results and discussion In order to validate the numerical mode l, the test conditi ons used by NASA was input as the boundary condition for the si mulation. Figure 2.2 shows a comparison of LH2 experiment at NASA Marshall with the numerical simulations performed for the respective cases. Numerical simulations were performed for the same tank with the outer surface maintained at 164K, 235K, and 305K. The results matched reasonably well with experimental data. Figure 2.3 Streamline contour for the tank with the inlet at the bottom (Velocity=10m/s, g=9.81m/s2, q=2.35W/m2)
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19 Figure 2.4 Temperature contour for the tank with the inlet at the bottom (Velocity=10m/s, g=9.81m/s2, q=2.35W/m2) Figures 2.3 and 2.4 show the stream line and temperature contour plots respectively for the tank, which has inlet at the bottom. As the fluid enters the tank it moves upward as a submerged jet and expands. Due to heat transfer, the temperature of the fluid near the wall incr eases and it rises upward as a wall plume due to buoyancy and this causes circulation in the tank. Fina lly, the fluid streams moving upward due to buoyancy and that due to forced convection mi xes and exits from th e outlet at the top. It was observed that as the inlet velocity increases, the momentum of the incoming jet surpasses the buoyant force and that reduces ci rculation within the tank which results in a more direct flow from inlet to outlet. Th e temperature of the fluid decreases rapidly from the tank wall to the center of the ta nk. Large amount of temperature reduction is seen in the insulation and this is because of much lower thermal conductivity of the
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20 insulation compared to the fluid or tank wall. An almost linear variation in the pressure within the tank was observed from the inlet to the outlet. Figure 2.5, 2.6, and 2.7 show the velocit y, streamline and the temperature contour plots in the tank with the inlet exte nded axially about 50% into the tank and the fluid is discharged at an angle of 450 to the axis. It was observed that the fluid moves towards the tank wall because of the mome ntum. When the fluid impinges the tank wall, some fluid moves down towards the bo ttom of the tank al ong the wall and some fluid moves towards the exit. The fluid that has moved down towards the bottom encounters the upward moving flow due to buoyancy and makes a complex circulation in the lower portion of the tank. The fluid in the upper portion also makes a circulation and then mixes with the fluid coming from the lower portion and then exits from the outlet. The idea of this type of channeling was to improve the circulation within the Figure 2.5 Velocity vector plot for the tank with the inlet extended 50% into the tank and radial discharge at 450 from the axis (Velocity=10m/s, g=9.81m/s2, q=2.35W/m2)
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21 Figure 2.6 Streamline contour plot for the tank with the inlet extended 50% into the tank and radial discharge at 450 from the axis (Velocity=10m/s, g=9.81m/s2, q=2.35W/m2) tank. It can be seen that circulation is improved in the tank wh en compared to the previous design of inlet at the bottom because the fluid is made to divide into parts and circulate in each part and th en exits from the outlet. This idea also proves a better prospect to reduce temperature nonuniformity in the fluid. This can be clearly seen from table 2.1. The average temperature of the fluid at the outlet is more when the fluid is discharged at an angle into the tank. It was observed that as the number of openings increase, the fluid is discharg ed at different locations in the tank and this makes the fluid to circulate at respective discharg ed locations. This also provided better temperature uniformity compared to the case of inlet at the bottom. The temperature contour shows a large drop within the insula tion. An almost linear pressure variation was observed within the tank from the inlet to the outlet.
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22 Simulations were also carried out at a zero gravity condition. Figures 2.8, 2.9 and 2.10 show the velocity, streamline and th e temperature contour plots for the tank, which has the inlet at the bottom. In order to get a better picture of fluid temperature variation, no insulation was provided and the tank wall is maintain ed at a constant temperature (30 K). There is no buoyancy force in this case as the gravity is zero. The circulation that is taking place in this situ ation is only because of the momentum, which is carried by the incoming fluid. The incomi ng fluid jet expands and impinges at the top wall of the tank. Then the fluid moves downw ard along the wall carrying heat with it. The hot and cold fluids mix at the bottom portion of the tank where more changes of temperature is seen in the temperature contour plot. The fluid circulates within the tank and exits from the outlet at the top. Figure 2.7 Temperature contour plot for the tank with the inlet extended 50% into the tank and radial discharge at 450 from the axis (Velocity=10m/s, g=9.81m/s2, q=2.35W/m2)
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23 Figure 2.8 Velocity vector plot for the tank with the inlet at the bottom of the tank (Velocity=0.01m/s, g=0, Tw = 30K) Figure 2.9 Streamline contour plot for the tank w ith the inlet at the bottom of the tank (Velocity=0.01m/s, g=0, Tw = 30K)
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24 Figure 2.10 Temperature contour plot for the tank with the inlet at the bottom of the tank (Velocity=0.01m/s, g=0, Tw = 30K) Figures 2.11 shows the streamline contour in the tank when the inlet is extended axially into the tank and the fluid is discharg ed radially at three openings with different widths. The openings are placed at 0.25H, 0.5 H, and 0.75H distances. The sizes of the openings are 0.05m, 0.075m a nd 0.10m respectively. Figures 2.12 shows the streamline contour for the same scenario but with same opening widths. It can be seen from figure 2.12 that large amount of the fluid enters the ta nk from first two openings without using the third opening., whereas in the tank where the openi ngs are of different wi dths fluid uses all the three openings to en ter that tank. This can be clearly seen in figure 2.11. It can also be observed that the fluid from the third opening doesnÂ’t involve much in the circulation and all the fluid entering the tank through the thir d opening makes it way directly to the exit. This is the main reason for a decrease in the average temperature of the fluid at the outlet which is 26.67 K when compared to the average temperature of the fluid at the outlet for a
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25 tank with equal opening widths which is 28.82 K. The temperature distribution within the tank for this case is shown in figure 2.13. As ci rculation takes place ne ar to lower portion of the tank more changes of temper ature are observed in that region. Figure 2.11 Streamline contour for the tank with ra dial discharge from three openings of different widths (Velocity=0.01m/s, g=0, Tw = 30K)
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26 Figure 2.12 Streamline contour for the tank with ra dial discharge from three openings of equal widths (Velocity=0.01m/s, g=0, Tw = 30K) Figure 2.13 Temperature contour plot for the tank with radial discharge from three openings of equal widths (Velocity=0.01m/s, g=0, Tw = 30 K)
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27 Figure 2.14 Streamline contour for the tank with inlet pipe extended into the tank and discharge at 450 from the axis (Velocity=0.01m/s, g=0, Tw = 30K, Inclined pipe length = 60 cm) Figure 2.15 Streamline contour for the tank with inlet pipe extended into the tank and discharge at 450 from the axis (Velocity=0.01m/s, g=0, Tw = 30K, Inclined pipe length = 30 cm)
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28 Figure 2.14 shows the streamline contour for the tank with inlet pipe extended into the tank and the fluid being discharged at 450 from the axis. The overall circulation was improved in this case. It can be seen that the bottom porti on of the tank along the inclined pipe shows no considerable circula tion. This can be reduced by using a smaller inclined pipe. Figure 2.15 show s the streamline contour for the same scenario but with a shorter incline pipe. It can be observed that the two circulations formed for a larger incline pipe combine when the incline pi pe length is reduced thereby efficiently utilizing the tank volume for the fluid circulation. This would be an additional advantage to this design. Table 2.1 shows the average outlet temperatures for both the designs. It was observed that the average out let temperature of the fluid was less when a shorter incline pipe is used for discharging the fluid into the tank. Figure 2.16 Streamline contour for the tank with inlet pipe extended into the tank and discharge at 600 from the axis (Velocity=0.01m/s, g=0, Tw = 30K)
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29 Figure 2.17 Temperature contour for the tank with inlet pipe extended into the tank and discharge at 600 from the axis (Velocity=0.01m/s, g=0, Tw = 30K) Figure 2.16 shows the streamline contour fo r the tank when the inlet is extended radially into the tank and the fluid is discharged at 600 to the axis of the tank. A similar scenario, which occurred when the fluid is discharged at 450 to the axis of the tank, is observed here. Two separate circulations ar e formed in the lower an upper portion of the tank. Fluid from these circulations combin es and exits from the outlet at th e outlet. The circulation within the ta nk has slightly improved when compared to the previous case. This can be clearly seen from the ta ble 2.1. The average outlet temperature for a 600 angle discharge is slightly greater (27.35 K) when compared to the average outlet temperature for a 450 angle discharge which is 27.24 K. Temperature changes are seen in the upper and lower portion of the tank this is because of the formation of the circulations in those portions. This can be seen from figure 2.17 which gives the
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30 temperature contour within the tank for the pr esent situation. A deve loped stage of this channeling is the Cchannel, which is presente d in figure 2.18. In this case, the inlet is extended along the circumference of the ellip tical wall to a certain length. A very good amount of circulation is observed in this de sign. There are two circulations formed one right at the Cchannel opening and the other at the exit. An efficient way to utilize the Cchannel would be to increase the length of the channel along the el liptical wall; this forces more fluid to flow and circulate along the tank boundary all the way to the exit. Figure 2.19 shows the temperature distribution within the tank. The fluid that comes in contact with the tank wall gets heated up as it rises upward. Since the fluid is forced to flow along the tank wall large amount of fluid is heated in relatively small time unlike the other channeling designs. The temperature of the fluid decreases from the tank wall Figure 2.18 Streamline contour plot for the tank with radial flow in a Cchannel (Velocity=0.01m/s, g=0, Tw = 30K).
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31 Figure 2.19 Temperature contour plot for the tank with radial flow in a Cchannel (Velocity=0.01m/s, g=0, Tw = 30K). to the tank axis. It can be concluded that flow through Cchannel and flow through openings of same diameters prov ide a better heat transfer. A quantitative analysis of the results can be made as follows: The fifth column in table 2.1 gives the diffe rence factor DF. It is defined as the percentage of the ratio of difference between the maximum temperature within the tank and average outlet temperature to the maxi mum temperature within the tank. A lower DF value is because of the lower differen ce between the maximum temperature within the tank and the average outlet temperature th is implies that better circulation within the tank has allowed to increase the average outlet temperature thereby reducing the difference. Hence lower the DF vale better is the design performa nce. For g = 9.81 m/s2 DF value is observed to be lower(11.4%) wh en the inlet is extended axially about 50% into the tank and the fluid is discharged at an angle of 450 to the axis when compared to the inlet at the bottom of the tank(13.01%). Th is implies that angular discharge model
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32 has allowed more circulation within the tank thus allowing even distribution of heat. The performance is improved by 12.4% for angular discharge design. For g = 0 case the DF factor for the in let at the bottom is observed to be 10.91. The DF factors for all other models has b een observed to be less except for the case when the inlet is extended into the tank and the fluid is discharged from three openings of unequal diameters, thus implying a better ci rculation in all the designs has allowed a even distribution of heat. Lower values are observed when fluid is discharged through greater Cchannel length and when inlet is extended into the tank and fluid is discharged from three openings of equal diameters. The performance is improved by 64.3% and 73.7% respectively when compared to the inlet at the bottom case.
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33 Table 2.1 Average outlet temperature of the fl uid and maximum fluid temperature obtained for different positions of the inlet pipe for liquid Hydrogen (Diameter of the inlet = 0.15 m) Sl. No Type of Opening (Tavg)out = A (Tf)max = B DF= 100 B A B g = 9.81 m/s2 1 Inlet at the bottom of the tank. 27.2 31.27 13.01 2 Inlet pipe extended ax ially about 50% into the tank and the fluid is discharged at an angle 45o to the axis. 28.2 31.83 11.4 g = 0 1 Inlet at the bottom of the tank. 26.71 29.98 10.91 2 Inlet pipe extended axially and the fluid is discharged radially from an opening of diameter 0.01 m 27.34 29.9 8.56 3 Inlet pipe extended axially and the fluid is discharged radially fr om three openings of diameters 0.05 m, 0.075 m, and 0.1 m respectively and placed equidistant from one another. 26.67 30.0 11.1 4 Inlet pipe extended axially and the fluid is discharged radially fr om three openings of diameters 0.05 m each placed equidistant from one another 28.82 29.99 3.9 5 Inlet pipe extended axially into the tank and the fluid is discharged at an angle 45o to the axis. Gun length = 0.7 m. 27.24 29.98 9.14 6 Inlet pipe extended axially into the tank and the fluid is discharged at an angle 45o to the axis. Gun length = 0.35 m 27.77 29.99 7.4
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34 Table 2.1 (continued) 7 Inlet pipe extended axially into the tank and the fluid is discharged at an angle 60o to the axis Inclined pipe length 27.35 30 8.83 8 Radial flow of fluid in a smaller CChannel length 28.44 30 5.2 9 Radial flow of fluid in a greater CChannel length 29.14 30 2.87
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35 CHAPTER THREE COMPUTATION OF FLUID (LIQUID AND VAPOR HYDROGEN) CIRCULATION IN A HYDROGEN STORAGE TANK 3.1 Mathematical model The mathematical model shown in the Fig. 1 represents the basic structure of the tank. The physical structure of the model comprises of a cylindrical body with an elliptical top and bottom. A twodimensional axisymmetric jet enters the tank from the bottom and exits from the top. The diameter of the inlet and ou tlet are 0.15m. The height of the tank is 2.6m. The major and minor axes of the e lliptical portion are about 3m and 1.3cm. The tank wall is 0.0127m thick. The tank is surr ounded by an insulation of 0.1m thickness. Heat sources are applied at th e outer wall. The working fluid in this problem is hydrogen. Different ideas for channeling the flow were implemented. Assuming the fluid in both th e states (liquid and vapor) to be incompressible, the equations describing the conservation of ma ss, momentum, and energy in cylindrical coordinates can be written as: rz1 r0 rrz (1) rrrrzzr rztt fp 112 r2 rzrrr3rrzzrz (2)
PAGE 57
36 zzrzzrr rztt fp 112 gr2 rzzrrzrz3zrr (3) tt ffff rz ttTTTT 1 r rzrrprrzprz (4) The effects of turbulence in the flow field were determined by using the kmodel. In this model, the turbulent kinetic energy and its dissipation rate were calculated by using the following equations. 2222 2 t rrzrz rrzt 2 kkkk1kk r2 rrzrrrrrzzr z (5) k c r v z v z v r v r v k v c z r r r r z v r v r vz r z r r t t z r r 2 2 2 2 2 2 1 2 22 1 (6) 2k Ct (7) The empirical constants appearing in equatio ns (57) are given the following values (Kays [32]): C=0.09, C1=1.44, C2=1.92, k =1, =1.3, Prt=1. It may be noted that the governing equations (17) are applicable to both liquid and vapor regions in the tank. For simplicity, th e liquidvapor interface was assumed to be a perfect horizontal surface. The liquid region underneath this surface was assigned liquid properties, whereas the vapor region above this surface was assigned vapor properties at the saturation temperature corresponding to the mean tank pressure In both liquid and vapor regions, the kmodel was used for the simulation of turbulence. Due to large size,
PAGE 58
37it will be impossible to maintain perfectly laminar flow in any region of the tank. Therefore the turbulent flow was assumed over the entire fluid region of the tank. This approach is believed to be adequate since th e value of the turbulent viscosity will be negligibly small if a region of the tank is somewhat stagnant. The choice of kmodel for the simulation of turbulence was done so mewhat arbitrarily. It will be useful to explore other models for future work. The equation used for the conservation of en ergy within the solid can be written as follows: ss ssTT 1 krk0 rrrzz (8) The boundary conditions needed to solve th e above equations included uniform axial velocity at the inlet, no slip condition at the solidfluid interface and constant heat flux at the outer surface of the tank. In addition, conservation of mass and energy during the evaporation process at the liquidvapor in terface had to be satisfied. These can be expressed as: zv fv zl flv v (9) z T k h v z T kfv fv lv zv fv fl fl (10)
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38 Figure 3.1 Schematic of a cylindrical tank with elliptical top and bottom 0 50 100 150 200 250 300 350 00.511.522.533.5 Distance (cm)Temperature (K) Outer surface = 305 K (Numerical) 305 K (Experimental) Outer surface = 235 K (Numerical) 235 K (Experimental) Outer surface = 164 K (Numerical) 164 K (Experimental) Figure 3.2 Graph showing the temperature at a particular section in the insulation
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39Here the subscript Â‘lÂ’ represents the liquid si de of the interface and Â‘vÂ’ the vapor side of the interface. The symbol Â‘kÂ’ stands for th e thermal conductivity and the latent heat of vaporization is expressed by hlv. 3.2 Numerical simulation The above governing equations along with the boundary conditions were solved using the finiteelement method. The solid an d fluid regions were both divided into a number of quadrilateral elements. After the Galerkin formulation was used to discretize the governing equations, the NewtonRaphson method was used to solve the ensuing algebraic equations. NewtonRaphs on method is based on the principle that if the initial guess of the root of f(x) = 0 is at xi, then if one draws the tangent to the curve at f(xi), the point xi+1 where the tangent crosses the xaxis is an improved estimate of the root. Using the definition of th e slope of a function, at ix x ) = (x fitan 10 i i ix x ) f(x = which gives ) f'(x ) f(x = x xi i i i 1 The above equation is called the Newt onRaphson formula for solving nonlinear equations of the form0 x f. Convergence is based on two criteria being satisfied simultaneously. One criterion is the relative cha nge in field values fr om one iteration to the next; the other is the residual for each conservation equation. In this problem a tolerance of 0.1 percen t (or 0.001) for both convergence crit eria was applied. In order to make sure that the results are going to be correct an initial run was made for the
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40experiments which were conduc ted at NASA Marshall. Figure 2 shows a comparison of LH2 experiment at NASA Marshall with the numerical simulations performed for the respective cases. Numerical simulations were performed for the same tank with the outer surface maintained at 164K, 235K, and 305K. Th e results matched reasonably well with experimental data. 3.3 Results and discussion Figure 3.3 shows the velocity vector pl ot for the tank, which has inlet at the bottom of the tank. The evaporating interface is located at the middle of the tank. It is assumed that the fluid gets va porized as it crosses the evap orating interface and all the fluid above the evaporating interface is in vapor form. As the fluid enters the tank it moves upwards as a submerged jet and expands. As the fluid reaches the upper portion of the tank it vaporizes. Due to heat transfer, the temperature of the fluid near the wall increases and it rises upward as a wall plume due to buoyancy and this causes circulations in the liquid regi on. A portion of the circulati ng liquid evaporates at the liquidvapor interface. The temper ature of the vapor near to the wall increases due to the heat transfer and this rises upward as a wall plume due to buoyancy and circulates in the vapor region. Finally the circulating vapor formed in the vapor region and the vapor emerging from the evaporating interface mixes a nd exits from the outlet at the top. It is observed that the fluid circulates with higher velocity in vapor regi on when compared to liquid region. This is because of the extra velocity gained by the fluid during its evaporation. It is observed that as the in let velocity increases, the momentum of the Figure 3.3 Velocity vector plot for the tank with the inlet at th e bottom (Flowrate = 0.000177m3/s, g=9.81m/s2, q=308W/m2)
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41incoming jet surpasses the buoyant force and that modifies circulation patterns within the liquid and vapor regions. Figure 3.4 shows the pressure contour plot for the above case. An almost linear variation in the pressure within the tank was observed from the inlet to the outlet. Greater pressure reduction is observed in the liquid region when co mpared to the vapor region. Figure 3.4 Pressure contour plot for th e tank with the inlet at the bottom (Flowrate = 0.000177m3/s, g=9.81m/s2, q=308W/m2)
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42 Figure 3.5 shows the temperatur e contour plot for the above case. The temperature of the fluid increases from the inlet to the outlet and this is because of the constant heat flux, which enters the tank through the tank wall. The temperature of the fluid across the evaporating surface is observed to be the same showing that the phase change has occurred at the sa turation temperature. As the fluid ve locity increases, the amount of time the fluid remains in contact with the wall decreases and hence the maximum temperature attained by the fl uid reduces. The temperature of the fluid decreases as we move away from the tank wall. Simulations were performed for different fill conditions in the tank. Three different fill conditions for which the simulations were performed are 25%, 50% and 75% of the tank volume. Figure 3.6 and 3.7 show the veloci ty vector plots for 25% and 75% liquid conditions. It can be ob served from figure 3.6 that when the liquid level is low, no significant circulation is obs erved in liquid region. As th e liquid level increases the Figure 3.5 Temperature contour plot for the tank with the inlet at the bottom (Flow rate = 0.000177m3/s, g=9.81m/s2, q=308W/m2)
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43circulation of the incoming fluid in the liquid region increases. In figure 3.7, more number of smaller circulations are observe d in the vapor region when compared to a single large circulation as in the previous case when the evaporating interface is in the middle of the tank. This can be clearly seen in the figure 3.8. which shows the streamline contour plot for the above situation. The developing circulation in the vapor region splits into smaller circulations because of the smalle r volume available to mix the fluid streams. Figure 3.6 Velocity vector plot for the ta nk with inlet at the bottom (Tank filled upto 25% of tank volume) (Flowrate = 0.000177m3/s, g=9.81m/s2, q=308 W/m2)
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44 Figure 3.8 Streamline contour plot for the tank with the inlet at the bottom (Tank filled upto 75% of tank volume) (Flowrate = 0.000177m3/s, g=9.81m/s2, q=308W/m2) Figure 3.7 Velocity vector plot for the tank w ith inlet at the bottom (Tank filled upto 75% of tank volume) (Flowrate = 0.000177m3/s, g=9.81m/s2, q=308W/m2)
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45 Figure 3.9 shows the pressure distributi on within the tank. An almost linear pressure reduction is observed with a great er reduction in the liquid region when compared to the vapor. Figure 3.10 shows the temperature distribution within the tank when it is filled upto 75% with liquid. Maximu m temperature always occurs in the vapor region. As the vapor region is small, the maximum temperature attained in the tank is less when compared to the maximum temperature a ttained when evaporating interface is at the middle of the tank. This can be clearly seen from the table 3.1. The maximum fluid temperature within the tank reduces as the va por level decreases. The highest temperature is observed when the vapor level is 75% of the tank volume and the lowest is observed when the vapor level is 25% of the tank volume. This is because the vapor is heated for a relatively smaller time when the evaporating in terface is towards the outlet of the tank. Figure 3.9 Pressure contour plot for the tank with the inlet at the bottom (Tank filled upto 75% of tank volume) (Flowrate = 0.000177m3/s, g=9.81m/s2, q=308W/m2)
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46 Figure 3.10 Temperature contour plot for the tank with the Inlet at the bottom (Tank filled upto 75% of tank volume) (Flowrate = 0.000177m3/s, g=9.81m/s2, q=308W/m2) Figure 3.11 Velocity vector plot for radial di scharge from one opening (Flowrate = 0.000177m3/s, g=9.81m/s2, q=308W/m2)
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47 Figure 3.13 Streamline contour plot for the tank with radial discharge from three openings. (Flowrate = 0.000177m3/s, g=9.81m/s2, q=308W/m2) Figure 3.12 Streamline contour plot for the tank with radial discharge from one opening ( Flowrate = 0.000177m3/s, g=9.81m/s2, q=308W/m2)
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48Radial discharge, inclined discharge, a nd discharge along the wall of the tank were three different ideas implemented to improve the channeling of th e flow in the tank. Figure 11 shows the velocity vector plot within the tank when the fluid is discharged radially into the tank from an opening at 80cm height away from the bottom of the tank. This was done by extending the intake pipe into the liquid medium and discharging the liquid from the cryocooler through holes along th e periphery of the pi pe. Fluid circulation in liquid region increases in this type of design. This can be seen from the values of maximum temperature attained within the tank. The maximum temperature attained within the tank is 72.45 K, which is less comp ared to the maximum temperature attained when inlet is at the bottom of the tank (81.61 K). As the fluid circ ulation increases the incoming heat is more evenly distributed because the heated fluid is constantly replaced by the cold fluid. This thereby decreases the nonuniformity of the temperature within the liquid region. Figures 3.12 and 3.13 show the streamline contours within the tank when the inlet is extended into the tank and the flui d is discharged from one and three openings respectively. It was observed th at the fluid from three openi ngs combine in to a single large circulation as the available space is li mited. Hence not much variation in the fluid flow pattern is observed when the fluid is discharged from one or three openings. This can be clearly seen from table 3.1. The maximu m temperature values within the tank for a three opening case (72.09 K) is slightly less than that of one opening case (72.45 K).
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49 Figures 3.14 and 3.15 show the velocity ve ctor plot, and temper ature contour plot for the tank which has the inlet extended axially into the tank and the fluid is discharged at an angle of 450 to the axis. When a high velocity fluid enters into the tank it moves towards the tank wall because of the mo mentum possessed by it. When the fluid impinges the tank wall, some fluid moves dow n towards the bottom of the tank along the wall and some fluid moves to wards the upper portion of the tank. The fluid that has moved down towards the bottom encounters the upward moving flow due to buoyancy and makes a circulation in th e liquid portion of the tank. Th e vapor in the upper portion also makes a circulation and then mixes with the vapor which is formed from the liquid coming from the lower portion and then exits through the outlet. Figure 3.14 Velocity vector plot for the tank with the extended inlet and radial discharge at 450 from the axis (Flowrate = 0.000177m3/s, g=9.81m/s2, q=308 W/m2)
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50 The idea of this type of channeling was to improve the circulation within the tank. It was observed that the fluid in liq uid region is split into two parts and it circulates in each part. It can be seen that circulation is improved in the tank when compared to the previous design of inlet at the bottom because the liquid is made to divide into parts and circulate in each part. This liquid after circul ating in the liquid region moves towards the vapor region. It gets vaporized and mixes with the circulating vapor in that region and then exits through the outlet. As the fluid circulation increases within the tank the incoming heat is more evenly distributed within the fluid; and hence this idea also proves a better prospect to reduce temperature nonuniformity in the fluid. This can be clearly seen from the table 3.1. The average ou tlet temperature was observed to be 50.43 K which is very less when compared to the pr evious designs. An almost linear pressure variation was observed within the tank from the inlet to the outlet. Figure 3.15 Temperature contour plot for the tank with the extended inlet and radial discharge at 450 from the axis (Flowrate = 0.000177m3/s, g=9.81m/s2, q=308 W/m2)
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51 Figure 3.17 Streamline contour plot for the tank with radial flow in a smaller Cchannel (Flowrate = 0.000177m3/s, g=9.81m/s2, q=308W/m2) Figure 3.16 Velocity vector plot for the tank with radial flow in a Cchannel (Flowrate = 0.000177m3/s, g=9.81m/s2, q=308W/m2)
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52It is observed that a small portion of the tank volume near to the inclined pipe has much smaller circulation. The portion that ha s smaller circulation is considerably less when compared to the larger inclined pipe length case. A developed stage of this channeling is the Cchannel, which is presente d in figure 3.16; in th is case, the inlet is extended along the circumference of the ellip tical wall to a certain length. Figures 3.17 and 3.18 show the streamline contours within the tank for a shorter and longer Cchannel length. It can be observed that circulations in the liquid region are formed right at the exit of the Cchannel. This design helps in completely utilizing the tank volume thereby circulation is improved in this design. Circul ations are seen in th e liquid and the vapor regions. Since the liquid is forced to flow along the tank wall large amount of liquid is heated in relatively small time unlike the other channeling designs. Simulations were performed for different lengths of Cchanne l. It was observed that as the Cchannel length increases the average outlet temper ature and the maximum fluid temperature within the tank have increased. This is because the fluid in a greater Cchannel length is forced to remain in contact with the tank wall for a longer time when compared to the shorter Cchannel length. The values of average outlet temperature and maximum temperature of the fluid are gi ven in table 3.1. The temper ature of the fluid decreases from the tank wall to the tank axis.
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53 Figure 3.18 Streamline contour plot for the tank with radial flow in a greater Cchannel (Flowrate = 0.000177m3/s, g=9.81m/s2, q=308W/m2) Figure 3.19 Temperature contour plot for the tank with radial flow in a Cchannel (Flowrate = 0.000177m3/s, g=9.81m/s2, q=308W/m2)
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54The results from the simulations can be summarized as follows: The incoming fluid from the cryocooler penetrates the fluid in the tank as a submerged jet and diffuses into the fluid me dium as it loses its momentum. The fluid adjacent to the wall rises due to buoyancy and also mixes with the colder fluid due to forced circulation. The temperat ure of the fluid is highest at the wall and it decreases rapidly towards the axis of the tank. Discharge of fluid from the cryocooler at different locations within the tank results in better mixing compared to the single inlet at the bottom of the tank. Greater circulation is observed in vapor region when compared to liquid region. Larger pressure reduction is observed in liq uid region. For a given tank geometry and insulation structure, the Zero Boiloff (ZBO) condition can be maintained by controlling the cryocooler operation and the fluid mixing within the tank. A quantitative analysis of the results can be made as follows: The fifth column in Table 3.1 gives the di fference factor DF. It is defined as the percentage of the ratio of difference betw een the maximum temperature within the tank and average outlet temperature to the maximu m temperature within the tank. A lower DF value is because of the lower difference between the maximum temperature within the tank and the average outlet temperature this implies that better circulation within the tank has allowed to increase the av erage outlet temperature thereby reducing the difference. It can be observed that though the discharge through Cchannel a nd discharge at an angle to the tank axis show highe r DF value it can be noticed th at the maximum temperature value within the tank and the average outlet temperature are considerably less for these cases when compared to all other cases. Hence evaluating the design performance depending
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55upon the DF factor doesnÂ’t yield correct resu lts. Since lower temperatures are observed for discharge through Cchannel and for discharge at an angle to the tank axis these models are more preferable compared to other models.
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56Table 3.1 Average outlet temperature of th e fluid and maximum fluid temperature obtained for different positions of the inle t pipe for liquidvapor hydrogen (Diameter of the inlet = 0.15 m, g = 9.81 m/s2) Sl. No Type of Opening (Tavg)out (oC) = A (Tf)max (oC) = B DF = 100 B A B 1 Inlet at the bottom of the tank. (Tank filled upto 25% of tank volume) 82.74 87.11 5.02 2 Inlet at the bottom of the tank. (Tank filled upto 50% of tank volume) 80.06 84.70 5.48 3 Inlet at the bottom of the tank. (Tank filled upto 75% of tank volume) 76.99 81.61 5.66 4 Inlet pipe extended axia lly and the fluid is discharged radially from an opening of diameter 0.01 m 71.73 72.45 0.99 5 Inlet pipe extended axia lly and the fluid is discharged radially from three openings of diameter 0.01 m each. 71.17 72.09 1.28 6 Inlet pipe extended axially into the tank and the fluid is discharged at an angle 45o to the axis. 50.43 65.81 23.37 7 Radial flow of fluid in a smaller CChannel length 36.36 42.74 14.59 8 Radial flow of fluid in a greater CChannel length 41.68 45.66 8.72
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57 CHAPTER FOUR COMPUTATION OF HEAT TRANSFER DURING CONFINED LIQUID JET IMPINGEMENT WITH UNI FORM HEAT SOURCE 4.1 Mathematical model We consider an axisymmetric jet di scharging from a nozzle and impinging perpendicularly at the center of a solid plate subjected to a c onstant heat flux. If the fluid is considered to be incompressible and have constant properties, e quations describing the conservation of mass, momentum, and energy in Cartesian coordinate s can be written as [33]: 0 z xV V (1) 2 2 2 2Re X X z z x xV V P V V V V (2) 2 2 2 2 2Re 1 z z z z z xV V P Fr V V V V (3) 2 2 2 2Pr Re f f f z f xV V (4)
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58The equation describing the conservation of energy inside the solid can be written as: 02 2 2 2 s s (5) To complete the physical model, equations (1) to (5) are subjected to the following boundary conditions: At 0 : 0 0 s (6) At 0 0 0 : 0 f z xV V (7) At 0 : 0 1 s (8) At 0 0 : 1 fP (9) At 1 : 0 s (10) At f s z x f sV V 1 ; 0 0 : (11) At 0 , 0 : 2 / 0 f j z xV V V (12) At 0 0 0 : 1 2 f z xV V (13) 4.2 Numerical simulation The governing equations along with the boundary conditions described in the previous section were solved by using the finite element me thod. The dependent variables, i.e., velocity, pressure, and temp erature were interpolated to a set of nodal points that defined the finite element. Four node quadr ilateral elements were used. In
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59each element, the velocity, pressure, and temp erature fields were approximated which led to a set of equations that defined the con tinuum. The continuum was discretized using an unstructured grid, which allowed finer meshes in areas of steep variations such as the solidfluid interface. After the Galerkin form ulation was used to discretize the governing equations, the NewtonRaphson method was us ed to solve the ensuing algebraic equations. NewtonRaphson method is based on th e principle that if the initial guess of the root of f(x) = 0 is at xi, then if one draw s the tangent to the curve at f(xi), the point xi+1 where the tangent crosses the xaxis is an improved estimate of the root. Using the definition of th e slope of a function, at ix x ) = (x fitan 10 i i ix x ) f(x = which gives ) f'(x ) f(x = x xi i i i 1 The above equation is called the Newt onRaphson formula for solving nonlinear equations of the form0 x f. Convergence is based on two criteria being satisfied simultaneously. One criterion is the relative cha nge in field values fr om one iteration to the next; the other is the residual for each conservation equation. In this problem a tolerance of 0.1 percent (or 0.001) for both convergence criteria was applied.
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604.3 Results and discussion q L b HnxOutflow Confinement plate Nozzle InflowAxis of symmetryZ Impingement plate Fluid W/2 Figure 4.1 shows the simulated geometry. The simulation was carried out for two different materials, namely silicon, and stainl ess steel. The length of the plate (L = 0.008 m) and the temperature of the jet at the nozzle exit (Tj = 293 K) were kept constant during the simulation. Ammonia was used as the primary working fluid for the simulation, which is an emerging coolant for space based thermal management systems. In order to determine the number of el ements for accurate numerical solution, computations were performed for several comb inations of number of elements in the x and z directions covering the solid and fl uid regions. The dimensionless solidfluid interface temperature for these simulations is plotted in figure 4.2. It was observed that the numerical solution becomes grid independent when the number of divisions in the x and z directions are increased over 80. Co mputations with 80x80 grids gave almost Figure 4.1 Schematic of a confined slot jet impinging on a uniformly heated solid p late
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61identical results when compared to those obt ained using 160x160 grids. In order to save computer time while retaining accuracy, 80 x 80 divisions were chosen for all final computations. In order to validate the numerical model, th e test conditions used by Ma et al. [34] were input as the boundary condition for th e simulation. Figure 4.3 shows a comparison of the experimental results reported by Ma et al. [34], and the present numerical simulation results for the same assembly. The plot shows the variati on of stagnation heat transfer coefficient resulting from the impinge ment of transformer oil jet issuing from slot nozzle for different Reynolds number. The width of the nozzle used was 0.091 mm. the nozzle to plate spacing was 20. It may be noted that numerical predictions compared with experimental measurements reasonabl y well for the entire range of Reynolds number tested by the Ma et al. [34]. Th e difference is in the range of 26%. Both the conjugate and nonconjugate mode ls have been simulated with varying Reynolds number. Figures 4.4 and 4.5 show the variations in dimensionless temperature and Nusselt number respectively along the solidfluid interface for a nonconjugate model. These simulations are performed at = 0.4 and at an aspect ratio of 0.4. As the nozzle slot width is maintained constant th e flow rate increases with the jet Reynolds number. It is observed that the higher veloc ity fluid carries away greater amount of heat from the interface leaving it at a lower te mperature. Hence the solidfluid interface temperature decreases as the jet Reynolds num ber increases. As the fluid moves along the plate it gets heated up and the am ount of heat carried away by it at the trailing end is less when compared to the leading end of the plate.
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62 0 5 10 15 20 25 00.20.40.60.81 NX x NZ = 160 x160 NX x NZ = 80 x 80 NX x NZ = 40 x40 NX x NZ = 20 x20 0 1 2 3 4 5 6 7 150250350450550650750 Series1 Present Simulation Experimental (Ma et al) Figure 4.2 Dimensionless solidfluid interface temperature for different number of elements in x and z directions (Re = 1645, = 0, = 0.4, = 0.4) Dimensionless solidfluid interface temperature, in t Dimensionless distance from the axis of the nozzle, ( ) Nuo/Pr1/3 Reynolds number (Re) Figure 4.3 Graph showing the variation of stagnation Nusselt number with jet Reynolds number
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63 0 2 4 6 8 10 12 00.20.40.60.81 Re = 445 Re = 668 Re = 890 Re = 1115 0 5 10 15 20 25 30 35 00.20.40.60.81 Re = 445 Re = 668 Re = 890 Re = 1115 Figure 4.4 Dimensionless solidfluid interface temperature for varying Reynolds number ( = 0.4, = 0.4, =0) Dimensionless distance from the axis of the nozzle, ( ) Dimensionless solidfluid interface temperature, in t Figure 4.5 Nusselt number at the solidfluid interface for varying Reynolds Number ( Noncon j u g ate model ) ( = 0.4 = 0.4 = 0 ) Dimensionless distance from the axis of the nozzle, ( ) Local Nusselt Number, Nu
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64 10 12 14 16 18 20 22 00.20.40.60.81 Re = 445 Re = 668 Re = 890 Re = 1115 This causes the increase in the temperature of the interface along the length of the plate. The overall values of the local heat tr ansfer coefficient and hence the local Nusselt number increases with jet inle t Reynolds number over the entire solidÂ–fluid interface. The usual bell shaped profile typical for impinging jets with a peak at the stagnation line is obtained in the numerical study. The heat tr ansfer coefficient increases with Reynolds number because of higher velocity of the fluid impinging on the plate. For any given Reynolds number the local Nusselt number d ecreases smoothly along the length of the plate this is because of the increase in th e interface temperature. It was observed that when the flowrate is increas ed from 445 to 1115 a 58% incr ease in the heat transfer coefficient is observed. Figure 4.6 shows the variation in the Nusselt number along the solidfluid interface for a conjugate model. It can be observed that the overall Nusselt number values decreases along the length of the plate. The Nusselt number distribution Dimensionless distance from the axis of the nozzle, ( ) Local Nusselt Number, Nu Figure 4.6 Nusselt number at the solidfluid interface for varying Reynolds number ( Con j u g ate model ) ( = 0.4 = 0.4 = 0.3125 Solid material =Silicon )
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65for a conjugate model is observed to be more uniform when compared to the nonconjugate model. This is because the overa ll transport is affected by the conduction within the solid. It was observed that when the flowrate is in creased 445 to 1115 a 60.13% increase in the heat transf er coefficient is observed. M odels showing the effect of the solid thickness on the Nusselt number have been shown in the future sections. Figures 4.7, and 4.8 show the variations of dimensionless temperature, and Nusselt number, respectively along the solidfluid interf ace for various slot widths maintaining a constant Reynolds number of 890. It may be noted that the flow rate is directly proportional to Reynolds number and therefore th e flow rate is also the same in these simulations. The nozzle slot widths considered are 0.8mm, 1.6mm, 3.2mm and 6.4mm. For the local heat transfer coefficient and Nusse lt number, the same ha lf bell shaped 0 1 2 3 4 5 6 7 8 9 00.20.40.60.81 = 0.8 = 0.4 = 0.2 = 0.1 Figure 4.7 Dimensionless temperature at the solidfluid interface for constant flow rate ( = 0.4, = 0) Dimensionless distance from the axis of the nozzle, ( ) Dimensionless solidfluid interface temperature, in t
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66 10 20 30 40 50 60 70 80 00.10.20.30.40.50.60.70.80.91 = 0.8 = 0.4 = 0.2 = 0.1 curves (considering only one axisymmetric half) are present. The interface temperature increases outwardly with radial distance and the lo west temperature is found at the stagnation line undern eath the center of the slot opening. It may be observed in figure 4.7 that the interface temp erature decreases with decrease in the slot opening all along the plate. The lower interface temperatur e is the result of larger convective heat transfer rate caused by higher jet velocity. Wh en the flow rate (or Reynolds number) is kept constant, a smaller slot opening results in larger impingement velocity which consequently contributes to larger velocity of fluid moving along the plate (within the boundary layer as well as in the wall jet). As the heat transfer coefficient and Nusselt number vary in the same manner it can be no ticed from figure 4.8 that the heat transfer rate at the impingement region can be augmen ted by a great extent if the nozzle width is reduced. For an eightfold reductio n in slot opening width, th e peak value of local heat Figure 4.8 Nusselt number at the solidflui d interface for constant flow rate ( = 0.4, = 0) Dimensionlessdistan cefromtheaxisofthenozzle,( ) Local Nusselt Number, Nu
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67transfer coefficient as well as the Nusselt number increases by almost 4 times. Due to more rapid decrease from the peak in th e case of smaller opening, the average heat transfer coefficient does not increase as muc h, but still of the orde r of 2.5 times for the length of the plate considered in the present investigation. The average values of heat transfer coefficient and Nusse lt number for these cases are listed in Table 1. The above observation suggests that a smaller slot opening is more desirable in nozzle design because of larger convective heat transfer ra te at the solidfluid interface for any given fluid flow rate. However, further study incl uding the pressure drop characteristics at the nozzle may be needed to arrive at the optimum slot opening. It was observed that when the slot width is increased from 0.0008m to 0.0032m the heat transfer coefficient is 0 2 4 6 8 10 12 00.20.40.60.81 = 0.1 = 0.2 = 0.4 = 0.8 Figure 4.9 Dimensionless solidfluid inte rface temperature for different nozzle widths ( = 0.4, = 0) Dimensionless solidfluid interface temperature, in t Dimensionlessdistancefromtheaxisofthenozzle,( )
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68 0 5 10 15 20 25 30 35 40 00.20.40.60.81 = 0.1 = 0.2 = 0.4 = 0.8 increased by 2.8%, but when it is increased to 0.0064m a 25% increase in the heat transfer coefficient is seen. Figure 4.9 and 4.10 show the variations in the dimensionless temperature and the Nusselt number along the so lidfluid interface fo r various slot widths and for a constant jet velocity. Since the slot width is used as the length scale for Reynolds number, the Reynolds number also varied in these runs. Th ere is a crossover of local distributions of temperature as well as the Nusselt number as the nozzle width is varied. The minimum temperature and highest local values of heat transfer co efficient and Nusselt number are still obtained for a nozzle width of 0.08 cm, th e lowest width considered in the present investigation. However, this run also results in the lowest heat transfer coefficient at the exit end of the plate. The lo cal values of Nusselt number at the downstream locations increase with nozzle width because of larger impingement region as well as larger flow Figure 4 .10 Local Nusselt number at the soli dfluid interface for different nozzle widths ( = 0.4, = 0) Dimen sionlessdistancefromtheaxisofthenozzle,( ) Local Nusselt Number, Nu
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69rate to carry away the heat. It can be also noticed that when the nozzle width is increased from 0.32 cm to 0.64 cm, the heat transfer perf ormance improves everywhere in the plate. Looking at the average values of heat transfer coefficien t and Nusselt number listed in Table 1, it can be observed that the lowest values are for W=0.16 cm and it increases in both directions. A more significa nt increase is seen when the width is increased, even though that increase is at the expense of a larg er flow rate. It was observed that when the slot width is increased by 0.0008m to 0.0064m th e heat transfer coef ficient is decreased by 25.02%. Figure 4.11 shows a plot of dimensi onless solidfluid interface temperature versus distance from the axis of impingement for two different metals at two different values of 0.125 and 0.25. 2.5 3 3.5 4 4.5 5 5.5 00.20.40.60.81 Silicon, = 0.125 Stainless Steel, = 0.125 Silicon, = 0.25 Stainless Steel, = 0.25 Dimensionless solidfluid interface temperature, in t Dimensionless distance from the axis of the nozzle, ( ) Figure 4.11 Comparison of local temperature at the interface for two different solid materials for two different solid thicknesses (Re = 1545, = 0.4, = 0.4)
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70 21.5 22 22.5 23 23.5 24 24.5 25 25.5 00.20.40.60.81 = .125 = 0.25 = .5 = 0.75 = 1.125 = 1.5 15 17 19 21 23 25 27 29 31 33 00.20.40.60.81 = 0.125 = 0.25 = 0.5 = 0.75 = 1.125 = 1.5 Local Nusselt Number, Nu Figure 4. 12 Local Nusselt number at the solidfluid interface for different nozzle widths using silicon substrate (Re = 1545, = 0.4, = 0.4, Solid material = Silicon) Dimensionlessdistancefromtheaxisofthenozzle,( ) Figure 4. 13 Local Nusselt number at the solidfluid interface for different nozzle widths using stainl ess steel substrate (Re = 1545, = 0.4, = 0.4, Solid material = Stainless Steel) Local Nusselt Number, Nu Dimensionlessdistancefromtheaxisofthenozzle,( )
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71The temperature values are found to be sensitive to thermal conductivity of the solids with stainless steel giving the lowe st temperature at the stagnation point and the highest temperature at the outlet. This is consistent with the fact that it has the lowest thermal conductivity of th e two (13.6 W/mK). Silicon, which has the highest thermal conductivity of the two, (140 W/mK ) behaves in the opposite manner in that it has the highest stagna tion point temperature and the lowest outlet temperature, implying that a larger thermal conductivity allows a better distribution of heat within the solid. The crossover of the curves for the two materials seen in figure 4.11 is also expected because the fluid flow rate and heat flux at the bottom of the plate remain constant. It can also be observed that distribu tion of the temperature along the interface is more uniform when is 0.25 for both the metals compared to the temperatures at at 0.125. This behavior is clearl y seen in figures 4.12 and 4.13. Figures 4.12 and 4.13 compare the local Nusselt number along the solidfluid interface for silicon and stainless steel at different values of 0.125, 0.25, 0.5, 0.75, 1.125, and 1.5. A higher variation is seen for a plate with smaller th ickness. As the thickness increases, the Nusselt number distribution become s more uniform. Beyond the plate thickness of 4 mm ( = 0.5), the distribution does not change very significantly indicating that the overall transport is dominated by convection at the solidfluid interface and not by conduction within the solid. The values of average heat transfer coefficient and average Nusselt number for these cases are also listed in Table 1. It may be noticed that for both the materials, the average Nusselt number decreas es with plate thickness. The increment, however, is small in magnitude and practically disappears at large thickness. For any particular value of the plate thickness the av erage local heat transf er coefficient and the
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72average Nusselt number of stainless steel is great er than that of silic on. This is because of the lower thermal conductivity of the stainless steel. Computations were performed to e xplore the effects of impingement height on the solidfluid interface temperature. Fo ur different aspect ratios of = 0.4, 0.8, 1.6, and 2.0 were modeled using ammonia as the working fluid and at a value of 0.625 thickness as the solid. Figure 4.14 and 4.15 show s the results for local Nusse lt number for silicon and stainless steel. = 0.4 gives the highest interface temperature and consequently the lowest heat transfer coefficient and Nusselt number. As the distance from the nozzle to the plate increases, the heat transfer coef ficient and the Nusselt number decrease. The difference between the average Nusselt numbe r and the average local heat transfer 20 22 24 26 28 00.20.40.60.81 = 0.4 = 0.8 = 1.8 = 2.0 Figure 4.14 Comparison of local heat tran sfer coefficient for three different impingement heights (Re=1545, = 0.625, Solid material = Silicon) Dimensionless distance from the axis of the nozzle, ( ) Local Nusselt number, Nu
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73 18 20 22 24 26 28 30 32 00.20.40.60.81 = 0.4 = 0.8 = 1.6 = 2.0 coefficients reduce as the value increases. More fluctuation in the Nusselt number and heat transfer coefficient are seen for stainle ss steel. This is because of the lower thermal conductivity of the material. Figure 4.16 shows a plot of maximum temperature and maximum to minimum temperature difference at the interface as a function of for both silicon and stainless steel. Stainless steel exhibits more sensitivity to solid thickness than silicon. Also, since it has the lowest thermal conductivity, it has overall higher va lues of temperature indicating that the model is sensitive to solid thermal conduc tivity. Both the solids show higher maximum temperature and high er temperature range at the smallest thickness. As the thickness increases, the conduction within the solid results in more uniformity of temperature at the interface and reduces down the value of highest Local Nusselt number, Nu Figure 4.15 Comparison of local heat transf er coefficient for four different impingement heights (Re=1545, = 0.625, Solid material = Stainless Steel) Dimensionless distance from the axis of the nozzle, ( )
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74temperature which is encountered at the outlet end of the plate next to the heat source. It may be also noticed that be yond a thickness of 0.006 m, there is hardly any variation of temperatures plotted in this figure, indicat ing that an optimum design condition has been reached. Figure 4.17 presents the maximum temp eratures attained in silicon and stainless steel substrates for different thicknesses. The graph gives an idea of the temperature range for which the substrates can be use d. It was observed that for any particular thickness of a substrate the maximum temperature is attained at the outer end of the plate. Both the solids show higher maximum temperature at the largest thickness. Since stainless steel has less thermal conductivity comp ared to silicon it has higher values of temperature all over the plate. 0 2 4 6 8 10 12 14 16 18 20 0.1250.250.50.751.1251.5 0 0.5 1 1.5 2 2.5 max, Silicon max, Stainless Steel maxmin, Silicon maxmin, Stainless Steel Dimensionless Maximum Temp erature at the Interface, maxsol Figure 4.16 Comparison of maximum temp erature and difference between maximum and minimum temperatures at the interface for different solids with various thicknesses (Re = 1545, = 0.4, = 0.4) Dimensionless thickness of the plate, Dimensionless Maximum to Minimum Interface Temperature Difference maxin t minin t
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75 0 2 4 6 8 10 12 14 16 18 20 0.1250.250.50.751.1251.5 max, Silicon max, Stainless Steel 22.5 23 23.5 24 24.5 25 25.5 26 26.5 0.1250.250.50.751.1251.5 Nuav, Stainless Steel Nuav, Silicon Figure 4.18 Comparison of Nusselt number for different solids and plate thicknesses ( Re = 1545, = 0.4, = 0.4 ) Average Nusselt Number, Nuav Dimensionless thickness of the plate, Dimensionless thickness of the plate, Dimensionless Maximum Temperature in the solid, maxisolid Figure 4.17 Comparison of maximum temp erature within the solid for various thicknesses ( Re = 1545 = 0.4 = 0.4 )
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76Figure 4.18 presents the va riation of average Nusselt number for both silicon and stainless steel for different plate thicknesses. It can be noticed that the maximum value is obtained at the smallest thickness and it gradua lly decreases with thickness. Also, there is a large variation for stainless steel, which has the lowest thermal conductivity of both the materials considered in this investigation. It may be also noticed that the variation of average Nusselt number diminishes with thic kness and there is no noticeable change at high thickness and high thermal conductivity. Th e average Nusselt number, which is an indicator of overall performance, settles to a constant value when enough thickness is provided because the maximum redistribution of heat by conduction within the plate has already been taken place. Figures 4.19 and 4.20 compare the results of present work ing fluid (ammonia) with two other coolants that have been consider ed in previous thermal management studies, namely FC77 and Mil7808 for a silicon substrat e. It may be noticed that ammonia gives much lower interface temperatur e and much higher heat transfer coefficient compared to both FC77 and Mil7808. Figure 4.19 shows th e dimensionless solidfluid interface temperature for a silicon substrate. Though am monia shows a lower so lidfluid interface temperature the dimensionless interface te mperature and the Nusselt number, however, are highest for FC77, primarily because of its lower ther mal conductivity compared to the other two fluids. The superior thermal pe rformance of ammonia may be useful for its application as a working fluid in thermal mana gement systems for aircraft and spacecraft. A similar scenario is observed when stainless steel plate is used instead of silicon plate. Figures 4.21 and 4.22 shows the results for dimensionless solidfluid interface temperature and the local Nusselt number al ong the plate length fo r a stainless steel
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77substrate. The average Nusselt number and av erage local heat transfer coefficient of stainless steel are observed to be slightly greate r than that of silicon for any coolant. For a silicon substrate it was observe d that the average Nusselt nu mber at the interface was increased by 80.88% when ammo nia is used as coolant in stead of FC77 and it was 80.41% more when compared to the averag e Nusselt number obtained using Mil7808. For a stainless steel substrate it was observed that the average Nusselt number at the interface was increased by 81.38% when ammonia is used as coolant instead of FC77 and it was 81.09% more when compared to the average Nusselt number obtained using Mil7808. The results gathered from the simula tions can be analyzed as follows: The solidfluid interface temperature as well as the heat transfer coefficient shows a strong dependence on several geometric, fluid flow, and heat transfer parameters such as jet Reynolds number, nozzle slot width, impingement height, plate thickness, plate material, and fluid prope rties. The inlet Reynolds numbe r was kept at values where laminar flow could be obtained. The heat tr ansfer coefficient increased with Reynolds number. For a constant Reynolds number and je t impingement height heat distribution is more uniform for a conjugate model when comp ared to a non conjugate model. The heat transfer coefficient decreased with slot widt h for a given flowrate. At the stagnation line, local values of heat transfer coeffici ent was highest because of the pronounced convective effects. Heat tran sfer then reduced gradually towards the outflow boundary. For a constant jet velocity, a higher heat transfer coefficien t at the impingement location was seen for a small slot wi dth but a higher average heat transfer coefficient was observed for larger slot width. A lower impi ngement height result ed in higher heat
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78transfer coefficient. A higher heat transfer coefficient at the im pingement location was seen at a smaller thickness, wh ereas a thicker plate provided a more uniform distribution of heat transfer coefficient. Plate material s with a higher thermal conductivity provided a more uniform distribution of interface temperatur e as well as the heat transfer coefficient. Compared to Mil7808 and FC77, ammonia provi ded much smaller so lidfluid interface temperature and higher heat transfer coeffi cient. The average lo cal heat transfer coefficient and average Nusselt number of st ainless steel are observed to be slightly greater than th at of silicon. 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 00.20.40.60.811.2 Ammonia FC77 Mil7808 Figure 4.19 Comparison of dimensionless solid fluid interface te mperature for three different coolants (Re=1545, = 0.4, = 0.4, = 0.0625, Solid material = silicon) Dimensionless distance from the axis of the nozzle, ( ) Dimensionless solidfluid interface temperature, in t
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79 0 5 10 15 20 25 30 35 40 45 00.20.40.60.811.2 Ammonia Fc77 Mil7808 1 2 3 4 5 6 7 8 00.20.40.60.811.2 Ammonia FC77 Mil7808 Figure 4.21 Comparison of dimensionless solidfluid interface temperature for three different coolants (Re=1545, = 0.4, = 0.4, = 0.0625, Solid material = stainless steel) Figure 4.20 Comparison of local Nusselt num ber for three different coolants usin g silicon substrate ( Re=1545, = 0.4, = 0.4, = 0.0625, Solid material = silicon ) Local Nusselt Number, Nu Dimensionless distance from the axis of the nozzle, ( ) Dimensionless solidfluid interface temperature, in t Dimensionless distance from the axis of the nozzle, ( )
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80 0 10 20 30 40 50 60 00.20.40.60.811.2 Ammonia Mil7808 FC77 Figure 4.22 Comparison of local Nusse lt number for three different coolants using stainless steel substrate (Re=1545, = 0.4, = 0.4, = 0.0625, Solid material = Stainless steel) Local Nusselt Number, Nu Dimensionless distance from the axis of the nozzle, ( )
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81Table 4.1 Average heat transfer coefficient and average Nusselt number for an uniformly heated plate Material Fluid Re W(cm) b(cm) Vin(cm/sec)Hn(cm) hav(w/m2K) Nuav ammonia 445 0.32 4.836 0.32 2286.18 14.104 ammonia 668 0.32 7.259 0.32 2803.08 17.296 ammonia 890 0.32 9.672 0.32 3234.69 19.963 ammonia 1115 0.32 12.117 0.32 3619.00 22.338 ammonia 222.5 0.08 9.672 0.32 3121.73 19.903 ammonia 445 0.16 9.672 0.32 3103.78 19.789 ammonia 890 0.32 9.672 0.32 3234.19 20.452 ammonia 1780 0.64 9.672 0.32 3903.54 24.888 ammonia 890 0.64 4.836 0.32 2740.50 17.128 ammonia 890 0.32 9.672 0.32 3239.97 20.312 ammonia 890 0.16 19.344 0.32 4419.09 27.780 ammonia 890 0.08 38.688 0.32 6606.43 40.489 Silicon ammonia 445 0.32 0.1 4.836 0.32 1977.68 12.39 Silicon ammonia 668 0.32 0.1 9.672 0.32 2435.48 15.25 Silicon ammonia 890 0.32 0.1 19.344 0.32 2820.94 17.67 Silicon ammonia 1115 0.32 0.1 38.688 0.32 3166.86 19.84 Silicon ammonia 1545 0.32 0.1 16.78 0.32 3865.35 24.043 Silicon ammonia 1545 0.32 0.2 16.78 0.32 3836.06 23.860 Silicon ammonia 1545 0.32 0.4 16.78 0.32 3824.45 23.788 Silicon ammonia 1545 0.32 0.6 16.78 0.32 3822.48 23.776 Silicon ammonia 1545 0.32 0.9 16.78 0.32 3822.01 23.773 Silicon ammonia 1545 0.32 1.2 16.78 0.32 3821.92 23.772 Stainless steel ammonia 1545 0.32 0.1 16.78 0.32 4151.64 26.00 Stainless steel ammonia 1545 0.32 0.2 16.78 0.32 4010.44 25.11 Stainless steel ammonia 1545 0.32 0.4 16.78 0.32 3957.31 24.77 Stainless steel ammonia 1545 0.32 0.6 16.78 0.32 3917.62 24.54 Stainless steel ammonia 1545 0.32 0.9 16.78 0.32 3914.86 24.52 Stainless steel ammonia 1545 0.32 1.2 16.78 0.32 3914.86 24.52 Silicon ammonia 1545 0.32 0.5 16.78 0.32 4174.04 26.14 Silicon ammonia 1545 0.32 0.5 16.78 0.64 3632.9 23.25 Silicon ammonia 1545 0.32 0.5 16.78 1.28 3523.72 22.55 Silicon ammonia 1545 0.32 0.5 16.78 1.60 3437.46 22.00 Stainless steel ammonia 1545 0.32 0.5 16.78 0.32 4059.28 25.42 Stainless steel ammonia 1545 0.32 0.5 16.78 0.64 3736.56 23.04 Stainless steel ammonia 1545 0.32 0.5 16.78 1.28 3610.06 22.61 Stainless steel ammonia 1545 0.32 0.5 16.78 1.60 3543.12 22.19 Silicon ammonia 1545 0.32 0.05 16.78 0.32 3920.56 25.09 Silicon FC77 1545 0.32 0.05 16.78 0.32 749.30 38.06 Silicon Mil7808 1545 0.32 0.05 16.78 0.32 768.17 16.42 Stainless steel ammonia 1545 0.32 0.05 16.78 0.32 4227.19 26.95 Stainless steel FC77 1545 0.32 0.05 16.78 0.32 787.15 39.98 Stainless steel Mil7808 1545 0.32 0.05 16.78 0.32 799.22 17.05
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82 CHAPTER FIVE ANALYSIS OF FLUID FLOW DURI NG CONFINED LIQUID JET IMPINGEMENT FOR DIFFERENT NUMBER OF DISCRETE HEAT SOURCES 5.1 Mathematical model We consider an axisymmetric jet di scharging from a nozzle and impinging perpendicularly at the center of a solid plate subjected to heating by discrete heat sources on the opposite surface of the plat e as shown in figure 1. If the fluid is considered to be incompressible and its properties (density, viscosity, thermal conductivity, and specific heat) are dependent on temperature, the dimensionless equations describing the conservation of mass, momentum, and energy in Cartesian coordinates can be written as [33]: 0 z xV V (1) z x z x x z x xV V V V p V V V V Re 1 2 Re 3 2 (2) x z z x z z z xV V V V P Fr V V V V 2 Re 3 2 Re 1 12 (3)
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83 f f f z f xV V 1 1 Pr Re 1 P V P Vx zPr 1 ) ( 2 2 2 23 2 2 Pr Re 1 z x z x z xV V V V V V (4) Considering variable therma l conductivity, the equation desc ribing the conservation of energy inside the solid can be written as: 0 s s (5) To complete the physical model, equations (1) to (5) are subjected to the following boundary conditions: At 0 ; 0 ; 0 s (6) At 0 0 0 ; ; 0 f x xV V (7) At 0 ; 0 ; 1 s (8) At 0 ) ( 0 ; ; 1 fP (9) At f s z x f sV V 1 0 0 ; (10) At j f j z xV V V , 0 2 0 ; (11) At 0 0 0 1 2 ; f z xV V (12) In order to simulate the discrete heat sources, localized heat fluxes were introduced at several locations and their magn itudes were varied. Figure 2 demonstrates
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84the boundary condition at the bottom of the plat e for different problems considered in the present investigation. For exam ple, for case (a), equations (1 ) to (5) are subjected to the following boundary conditions: At 5 9 ; 9 1 0 ; 0 s (13) At 0 ; 3 1 9 1 ; 0 s (14) At 5 9 ; 9 5 3 1 ; 0 s (15) At 0 ; 9 7 9 5 ; 0 s (16) At 5 9 ; 1 9 7 ; 0 s (17) 5.2 Numerical simulation The governing equations along with the boun dary conditions were solved by using the finite element method. Fournode qu adrilateral elements were used. In each element, the velocity, pressure, and temperat ure fields were approximated which led to a set of equations that defined the continuum. After the Galerkin form ulation was used to discretize the governing equations, the Newt onRaphson method was used to solve the ensuing algebraic equations. Ne wtonRaphson method is based on the principle that if the initial guess of the root of f(x) = 0 is at xi, then if one draws the tangent to the curve at f(xi), the point xi+1 where the tangent crosses the xaxis is an improved estimate of the root. Using the definition of th e slope of a function, at ix x ) = (x fitan
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85 10 i i ix x ) f(x = which gives ) f'(x ) f(x = x xi i i i 1 The above equation is called the NewtonRaphson formula for solving nonlinear equations of the form 0 x f. Convergence is based on two criteria being satisfied simultaneously. One criterion is th e relative change in fi eld values from one iteration to the next; the other is the resi dual for each conservation equation. In this problem a tolerance of 0.1 percent (or 0.001) for both convergence criteria was applied. Figure 5.1 shows the simulated geometry. The simulation was carried out for two different materials, namely si licon and stainless steel. The length of the plate (L = 0.008 m) and the temperature of the jet at the nozzle exit (Tj = 293 K) were kept constant during the simulation. Ammonia was used as the working fluid for the simulation, which is an emerging coolant for space based thermal management systems. The properties of Ammonia are temperature de pendent and for any give n temperature, thermal conductivity, viscosity, specific heat, and dens ity can be calculated using equations (18) to (21). k = 69912.953 Â– 1026.449T + 6.0828125T2 Â– 0.018005208T3 + 2.65625E05T4 Â– 1.5625E08T5 (18) = 78411.526 + 1209.4674T Â– 7.3773828T2+ 0.022323698T3 Â– 3.3554687E05T4 + 2.00652083E08T5 (19)
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86cp = 14633.163 + 222.04991T Â– 1.345077T2 + 0.0040670703T3 Â– 6.1386719E06T4 + 3.7005208E09T5 (20) = 161497.37 Â– 2416.6952T + 14.514766T2 Â– 0.043544271T3 + 6.5234375E05T4 Â– 3.90625E08T5 (21) Here Â‘TÂ’ is the absolute temperature in K. These equations were developed by fitting tabulated data for Ammonia for the temper ature range of 290 Â– 370 K as presented by Carey [35]. b HnxOutflow Confinement plate Nozzle InflowAxis of symmetryZ Impingement plate Fluid W/2 q"q"q" L 2L2L2L2L Figure 5.1 Schematic of a confined slot jet impinging on a solid plate with discrete heat sources
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87 Discrete heat sources locati on at the bottom of the plate Heat energy combinations. Figure 5.2 Different combin ations of location and magnitude of heat sources
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88It was observed that the numerical solu tion becomes grid independent when the number of divisions in the x and z directi ons are increased over 80. Therefore 80 x 80 divisions were chosen for all final com putations in the present investigation. 5.3 Results and discussion Figure 5.3 presents the dimensionless interface temperature distribution for different number of heat sources when the solid thickness is negligible (b = 0). In this case, the total applied heat energy was kept constant. The heat flux was obtained by dividing the total energy by the to tal heated area of the plate. For continuous heating (one heat source), the value of heat flux was 250 kW/m2. The value of heat flux for three heat sources was 450 kW/m2. Similarly for four he at sources and seven he at sources cases, the heat fluxes applied were 464 kW/m2 and 480 kW/m2, respectively. It can be observed that for a single heat source case, the minimum temperature is present at the stagnation point. For multiple heat sources case, the temperature increased as the fluid moved downstream along the heater. The temperature dropped in th e region where heat is not applied. The drastic change in temperature through out th e interface for multiple sources of heat is because of the mixing of low density hot fluid near the plate with high density cold fluid away from the plate (outside the thermal boundary laye r). It is observed that the temperature at the stagnation point is highest for the seven heat sources because of the application of larger amount of heat flux wh en compared to other three cases. As the number of heat sources reduced, the temperat ure at the stagnation point also decreased. The discrete heating resulted in periodic rise and fall of interface temperature along the heated and unheated regions of the pl ate. It can also be observed that for all the different cases considered, the temperature varied ar ound the curve for con tinuous heating (heat sources = 1) because the total therma l energy input was kept constant.
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89Figure 5.4 shows the local Nusselt number along the interface. It may be noted that unlike continuous h eating, the discrete heating does no t give the highes t heat transfer coefficient at the stagnation point. Because of the absence of heat flux in certain regions during discrete heating, the heat transfer co efficient in those regions is zero. In each heated region, the local Nusselt number is highest at the leading edge of the heat source, and it gradually decreases as the flow m oves downstream. This behavior is expected because of repeated growth of thermal boundary layer in the fluid adjacent to the heater. As the number of heat sources increased, the value of maximum local Nusselt number increased. It was found that th e average heat transfer coe fficient value is highest for uniform heating case. The average heat transf er coefficient increased with the number of heat sources for the discrete heating case wh en the total applied heat energy was kept constant. The average Nusselt number at the solidfluid interface for uniform heating case 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 00.20.40.60.81 Heat Sources = 1 Heat Sources = 3 Heat Sources = 4 Heat Sources = 7 Figure 5.3 Dimensionless temperature at the interface for different discrete heat sources with constant total power (E = 2 kW/m, Re = 890, = 0.4, = 0.4, = 0) Dimensionless distance from the axis of the nozzle, ( ) Dimensionless solidfluid interface temperature, int
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90 0 5 10 15 20 25 30 35 40 0.00.20.40.60.81.0 Heat Sources = 1 Heat Sources = 3 Heat Sources = 4 Heat Sources = 7 Figure 5.4 Nusselt number at the interface for di fferent discrete heat sources with total power constant (Nonconjugate m odel) (E = 2 kW/m, Re = 890, = 0.4, = 0.4, = 0) was observed to be 172.15%, 170.19%, a nd 168.25% more when compared to 3, 4, and 7 heat sources respectively. Figure 5.5 presents the dimensionles s solidfluid interface temperature distribution for different number of heat sources with solid (silicon) of finite thickness. It may be noted that the inte rface temperature is minimum at the stagnation point and maximum at the edge of the plate. This is due to the development of the thermal boundary layer. The interface temperature at the axis of impingement (x = 0) is maximum for uniformly heated plate (one heat source). This is opposite to that seen in the nonconjugate model (figure 3). This is because of the distribution of heat by conduction within the solid. For three heat sources case, even t hough heat is not applied in some regions, because of the high th ermal conductivity of silicon, th e heat distribution inside the solid is more uniform. Also, because of the larger distance between the heat sources, minimum temperature at the interface was obs erved for three heat sources case. As the Dimensionless distance from the axis of the nozzle, ( ) Local Nusselt Number, Nu
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91number of heat sources increased, the dist ance between the consecutive heat sources decreased, its effect on the interface temperature decreased and became negligible after certain number. In the present investigation, when the number of heat sources was seven, the interface temperature was approaching the values at the interf ace when the plate is heated uniformly. This can be explained by looking at the isotherms in the solid presented in figure 5.6. The isotherms were developed around the area where heat was applied and became more and more uniformly distributed in the solid as the number of heat sources increased showing the same trend as in the case of uniform heat application. Figure 5.7 shows the variations in local Nusselt number along the solidfluid interface for different number of heat sources. The total en ergy calculated at the solidfluid interface 2 2.5 3 3.5 4 4.5 5 5.5 6 00.10.20.30.40.50.60.70.80.91 Heat Sources = 1 Heat Sources = 3 Heat Sources = 4 Heat Sources = 7 Figure 5.5 Dimensionless temperature at the interface for different discrete heat sources with total power constant (E = 2 kW/m, Re = 890, = 0.4, = 0.4, = 0.125, Solid = Silicon) Dimensionless distance from the axis of the nozzle, ( ) Dimensionless solidfluid interface tem p erature int
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92 Figure 5.6 Isotherm plot for seven and three h eat sources respectively with constant total power (E =2 kW/m, Re = 890, = 0.4, = 0.25, Material = Silicon) was 1.978 kW/m. In these simulations, a cons tant nozzle slot wi dth of 3.2 mm and Hn/W ratio of 1 was used. The overall values of the local Nusselt number have shown almost the same variation over the entire solidfluid interface. The lo cal heat transfer coefficient is highest at the stagnation point. The averag e value of Nusselt number increased slightly with the increase in number of heat sources. But it remained highest for uniform heating case. 10 12 14 16 18 20 22 24 26 28 30 32 00.20.40.60.81 Heat Sources = 1 Heat Sources = 3 Heat Sources = 4 Heat Sources = 7 Figure 5.7 Nusselt number at the interface for di fferent discrete heat sources with total power constant using silicon subs trate (E = 2 kW/m, Re = 890, = 0.4, = 0.4, = 0.125, Solid = Silicon) Dimensionless distance from the axis of the nozzle, ( ) Local Nusselt Number, Nu
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93 10 12 14 16 18 20 22 24 26 28 30 32 00.20.40.60.811.2 Heat Sources = 1 Heat Sources = 3 Heat Sources = 4 Heat Sources = 7 Figure 5.8 Nusselt number at the interface for di fferent discrete heat sources with total power constant using st ainless steel substrate (E = 2 kW/m, Re = 890, = 0.4, = 0.4, = 0.125, Solid =Stainless Steel) To study the effect of thermal conductivity of the solid, the anal ysis was repeated using stainless steel as the solid applying exactly the same physical boundary conditions as we have applied in case of silicon. Tota l heat energy applied was kept constant. Figure 5.8 presents the variations of local Nusselt number. Due to lower thermal conductivity of stainless steel compared to silicon, the redistr ibution of heat within the solid is lower. A gradual decrease downstream is seen for both 1 and 7 heat sources. In the case of 3 and 4 heat sources, the heat transfer coefficient tend s to remain constant or increase slightly in the unheated region. Due to larger spacing of heat sources in these two cases, the interfacial heat flux as well as temperature distribution in that region play a more significant role in the overall distribution of heat transfer coefficient. The average heat transfer coefficient increased with the increase in the number of heat sources. The average Nusselt number and the average heat transfer coefficient were found to be Local Nusselt Number, Nu Dimensionless distance from the axis of the nozzle, ( )
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94highest for uniform heating case and they in creased with the increase in the number of heat sources. Figures 5.9 and 5.10 show the variations of dimensionless temperature and the Nusselt number at the solidfluid interface for different number of heat sources when the heat flux at the sources were ke pt at a constant value. As we have applied same heat flux, it can be observed that the temperature at th e stagnation point is same for all single and multiple heat source cases. But for multiple he at source cases, because of the absence of heat at particular regions and also because of the mixing of hot fluid with the cold fluid, the temperature gradually decreased, reached minimum and then increased to a maximum value where heat is applied. In figure 5.10, for multiple heat sources case, it can be clearly seen that wherever heat is not appl ied the heat transfer coefficient dropped to zero, raised to a value at the beginning of the heated region and then gradually decreased 0 1 2 3 4 5 6 7 8 9 10 00.20.40.60.81 heat sources = 1 heat sourcse = 3 heat sources = 4 heat sources = 7 Figure 5.9 Dimensionless temperature at the so lidfluid interface fo r different discrete heat sources with constant heat flux (Re = 890, = 0.4, = 0.4, = 0) Dimensionless solidfluid interface tem p erature int Dimensionless distance from the axis of the nozzle, ( )
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95 0 10 20 30 40 50 60 70 00.20.40.60.81 Heat Sources = 1 Heat Sources = 3 Heat Sources = 4 Heat Sources = 7 Figure 5.10 Nusselt number at the solidfluid in terface for different discrete heat sources with constant heat flux (Re = 890, = 0.4, = 0.4, = 0) throughout the heated region due to the de velopment of thermal boundary layer. The highest local Nusselt number is obt ained for seven heat sources, the maximum number of sources used in this investigation. Because of the application of constant heat flux, the variation in average va lues of heat transfer coefficient and Nusselt number for multiple heat sources is very significant. Highest average heat transfer coefficient value is observed for uniform heating. The value of Nusselt number for continuous heating is about 1.5 times that of Nusselt number for three heat sources case. There is not much variation in averag e Nusselt number for discrete heating. Figures 5.11 and 5.12 show the variation of solidfluid interface temperature and the local Nusselt number for a silicon substrate. Since the heat flux at the sources were kept at a constant value, the temperature at the stagnation point is higher when the plate is uniformly heated. As the number of heat sources increased, the temperature at the stagnation point decreased. The average Nusselt number is more for uniformly heated case and the variations small in case of multiple heat sources case. A similar scenario is Local Nusselt Number, Nu Dimensionless distance from the axis of the nozzle, ( )
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96observed when a stainless steel substrate is us ed instead of silicon. Figure 5.13 shows the variation of solidfluid interface temperature wi th solid (stainless steel). Since the thermal conductivity of stainless steel is much lower when compar ed to that of silicon, the periodic distribution of solid fluid interface temperature can be observed from the figure 5.13 for three and four heat source cases. But as the number of heat sources increases, the distribution of heat becomes more and more uniform because of the reduced distance between the heat sources. Fi gure 5.14 shows the va riation of local Nusselt number. The average Nusselt number is more for the uniform ly heated case and th e variation is small in case of multiple heat sources cases. This trend can be related to total heat energy applied to the plate. There is only a very small difference between total energy for different cases of discrete heating consid ered here, whereas the total energy for 2 2.5 3 3.5 4 4.5 5 5.5 6 00.20.40.60.81 Heat Sources = 1 Heat Sources = 3 Heat Sources = 4 Heat Sources = 7 Figure 5.11 Dimensionless temperature at the solidfluid interface for different discrete heat sources with heat flux constant (Re = 890, = 0.4, = 0.4, = 0.125, Solid = Silicon) Dimensionless solidfluid interface tem p erature int Dimensionless distance from the axis of the nozzle, ( )
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97 10 15 20 25 30 00.20.40.60.81 Heat Sources = 1 Heat Sources = 3 Heat Sources = 4 Heat Sources = 7 Figure 5.12 Nusselt number at the solidfluid in terface for different discrete heat sources with heat flux constant (Re = 890, = 0.4, = 0.4, = 0.125, Solid = Stainless Steel) 1 2 3 4 5 6 7 00.20.40.60.81 Heat Sources = 1 Heat Sources = 3 Heat Sources = 4 Heat Sources = 7 Figure 5.13 Dimensionless temperature at the solidfluid interface for different discrete heat sources with heat flux constant (Re = 890, = 0.4, = 0.4, = 0.125, Solid = Stainless Steel) Dimensionless solidfluid interface tem p erature int Dimensionless distance from the axis of the nozzle, ( ) Local Nusselt Number, Nu Dimensionless distance from the axis of the nozzle, ( )
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98 10 12 14 16 18 20 22 24 26 28 30 32 00.10.20.30.40.50.60.70.80.91 Heat Sources = 1 Heat Sources = 3 Heat Sources = 4 Heat Sources = 7 Figure 5.14 Nusselt number at the solidfluid in terface for different discrete heat sources with heat flux constant (Re = 890, = 0.4, = 0.4, = 0.125, Solid = Stainless Steel) continuous heating (heat source = 1) is signifi cantly higher. The value of E for the cases of 1, 3, 4, and 7 sources were 20 00 W/m, 1111 W/m, 1077 W/m, and 1040 W/m, respectively. Figure 5.15 compares the maximum dimens ionless interface temperature and the difference between maximum to minimum di mensionless interface temperature using silicon and stainless steel substrates for different number of heat sources. Both the materials show maximum interface temperatur e for uniform heating case. The maximum interface temperature reduces as the number of heat sources increase however the difference is negligible when the heat sources are greater than three. Since the maximum temperature remains almost the same the temp erature difference reduces as the number of heat sources increase. This is because the peri odic fluctuation of heat distribution reduces as the number of heat sources increase. The temperature values for stainless steel were Local Nusselt Number, Nu Dimensionless distance from the axis of the nozzle, ( )
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99greater than that of silicon for any number of heat sources. This is because of the lower thermal conductivity of stainless steel when compared to silicon. Figure 5.16 compares the dimensionless ma ximum temperatures for stainless steel and silicon substrates for di fferent number of heat sour ces. The maximum temperature attained within the substrate reduces as the number of heat sources increase and settles down to an almost same value when the number of heat sources is greater than three. This is obvious with the fact that the energy values reduce as the number of heat sources increase. Stainless steel has shown higher te mperature values when compared to silicon this is because of its lower thermal conductivity when compared to si licon. This trend is observed of average Nusselt number too. Figure 5.17 compares the average Nusselt number for silicon and stainless steel s ubstrates for different heat sources. 0 1 2 3 4 5 6 7 8 9 10 1347 0 5 10 15 20 25 30 35 40 max, Silicon max min, Silicon max, Stainless Steel max min, Stainless Steel N umber of discrete heat sources Dimensionless Maximum Temp erature at the Interface, max int Dimensionless Maximum to Minimum Interface Temperature Difference maxin t minin t Figure 5.15 Comparison of maximum temperat ure and difference between maximum and minimum temperatures at the interface for diffe rent solids with various heat sources with heat flux constant (Re = 890, = 0.4, = 0.4, = 0.125)
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100 0 1 2 3 4 5 6 7 8 1347 Silicon Stainless Steel 17 17.5 18 18.5 19 19.5 20 20.5 21 1347 Stainless Steel Silicon N umber of discrete heat sources Number of discrete heat sources Average Nusselt Number, Nuav Dimensionless Maximum Temperature in the solid, maxisolid Figure 5.16 Comparison of maxi mum temperature within the solid for different discrete heat sources with heat flux constant (Re = 890, = 0.4, = 0.4, = 0.125) Figure 5.17 Comparison of Nusselt number for di fferent solids for different discrete heat sources with heat flux constant (Re = 890, = 0.4, = 0.4, = 0.125)
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101Average Nusselt number is more for unifo rm heating case and it reduces as the number of heat sources increase. Figure 5.18 shows the variations in Nusselt number with different magnitudes of discrete heat sources. Three heat sources were considered in this case. Magnitude of the total heat energy appl ied was kept constant. Pictorial description of all cases considered here is shown in figur e 2. It was observed that the values of local Nusselt number are greater at places where heat flux is applied. It can be seen that the local Nusselt number values are greater for ca se M1 at the stagnation point. This is because of the application of greater heat flux (300 KW/m2) at that point when compared to the other cases. The Nusselt number values for case M1 then decreased at a greater rate. This is because of the lower heat flux applied over the rest of the plate. As same amount of heat flux was applie d at the stagnation point th e Nusselt number values for cases M and M2 differ by a negligible amount at stagnation point. The second heat source provided the same amount of heat in case M and greater amount in case M2 hence the Nusselt number values for case M2 were sl ightly higher at that location though the difference was negligible. Towards the exit end of the plate the Nusselt number values for case M2 differed by a considerable am ount with case M having higher values. However, there is no significant variation in lo cal heat transfer coefficient values at the stagnation point. At the exit end of the plat e, M3 has shown the highest heat transfer coefficient value and M1 has shown the lowest This could be because of the application of high heat flux at the exit end of the plate in case of M3. The average Nusselt number differed by a slight amount w ith case M being higher. Figure 5.19 shows the variation of Nusselt number for different locations of the heat sources. The objective of these computatio ns was to explore the variations in heat transfer coefficient and Nusselt number for diffe rent heat input locations. Please note that
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102case (b) is exactly oppos ite to case (a) where we swappe d the heat input locations and hence for case (b) there was no heat source at the center of the plate. The local heat transfer coefficient was minimum for the case (b). Average heat transfer coefficient and average Nusselt number were almost the same for case (a) and case (c) and were more than those of case (b) showing that better resu lts can be achieved using case (a) and case (c) designs. 0 10 20 30 40 50 60 00.10.20.30.40.50.60.70.80.91 M M1 M2 M3 Figure 5.18 Nusselt number at the solidfluid interface for different magnitudes of discrete heat sources and constant total power (E = 1.1 kW/m, Re = 890, = 0.4, = 0.4, = 0.0625, Solid =Silicon) Local Nusselt Number, Nu Dimensionless distance from the axis of the nozzle, ( )
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103 0 5 10 15 20 25 30 35 00.10.20.30.40.50.60.70.80.91 a b c Figure 5.19 Local Nusselt number at the solidfluid interface for different locations of discrete heat sources and constant total power (E = 1.1 kW/m, Re = 890, = 0.4, = 0.4, = 0.0625, Solid =Silicon) The results gathered from the simula tions can be analyzed as follows: The solidfluid interface temperature as well as the heat transfer coefficient shows a strong dependence on number, magnitude, and location of heat sources and plate material properties. For a given constant to tal heat energy, the fo llowing conclusions can be drawn from the numerical results: (1) Th e temperature at the stagnation point reduced with the decrease in number of heat sources. (2) The average heat transfer coefficient and the average Nusselt number values increased with increase in number of heat sources in both conjugate and nonconjugate models. (3) The effect of nu mber of heat sources is negligible when the solid conducti vity is high. (4) Th e average heat transf er coefficient is highest for uniform heating when compared to discrete heating. (5) The isothermal lines inside the solid showed that beyond cri tical thickness, the pl ate presented a one dimensional heat conduction in regions away from the impingement plane and the heated Local Nusselt Number, Nu Dimensionless distance from the axis of the nozzle, ( )
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104surface, and therefore did not exert much infl uence in convection heat transfer process. When the heat flux at the sour ces was kept at a c onstant value, the highest average heat transfer coefficient was observed for uni form heating in both conjugate and nonconjugate models. For discrete heating, the magnitude and the geometric location of heat sources influenced the maximum temperature as well as local distribution of heat transfer coefficient.
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105 Table 5.1 Average heat transfer coefficien t and Nusselt number for a varying number of heat sources Material Fluid Re W (cm) b (cm) Vj (cm/s) Number of Heat Sources Heat source type Position/ Magnitude of heat sources Hn (cm) hav (W/m2K) Nuav Ammonia 890 0.32 0 9.672 1 Constant power a/M 0.32 3525.58 22.48 Ammonia 890 0.32 0 9.672 3 Constant power a/M 0.32 1289.46 8.26 Ammonia 890 0.32 0 9.672 4 Constant power a/M 0.32 1305.53 8.32 Ammonia 890 0.32 0 9.672 7 Constant power a/M 0.32 1314.29 8.38 Silicon Ammonia 890 0.32 0.1 9.672 1 C onstant power a/ M 0.32 3004.7 18.82 Silicon Ammonia 890 0.32 0.1 9.672 3 C onstant power a/ M 0.32 2975.99 18.64 Silicon Ammonia 890 0.32 0.1 9.672 4 C onstant power a/ M 0.32 2950.78 18.67 Silicon Ammonia 890 0.32 0.1 9.672 7 C onstant power a/ M 0.32 2991.96 18.74 Stainless Steel Ammonia 890 0.32 0.1 9.672 1 Constant power a/M 0.32 3287.32 20.59 Stainless Steel Ammonia 890 0.32 0.1 9.672 3 Constant power a/M 0.32 3231.44 20.24 Stainless Steel Ammonia 890 0.32 0.1 9.672 4 Constant power a/M 0.32 3245.81 20.33 Stainless Steel Ammonia 890 0.32 0.1 9. 672 7 Constant power a/M 0.32 3280.9 20.55 Ammonia 890 0.32 0 9.672 3 Constant heat fluxa/M 0.32 2423.27 15.45 Ammonia 890 0.32 0 9.672 4 Constant heat fluxa/M 0.32 2377.81 15.16 Ammonia 890 0.32 0 9.672 7 Constant heat fluxa/M 0.32 2445.87 15.59 Silicon Ammonia 890 0.32 0.1 9.672 3 Constant heat fluxa/M 0.32 2945.66 18.55 Silicon Ammonia 890 0.32 0.1 9.672 4 Constant heat fluxa/M 0.32 2940.87 18.42 Silicon Ammonia 890 0.32 0.1 9.672 7 Constant heat fluxa/M 0.32 2936.08 18.39 Stainless Steel Ammonia 890 0.32 0.1 9.672 3 Constant heat fluxa/M 0.32 3218.67 20.16 Stainless Steel Ammonia 890 0.32 0.1 9.672 4 Constant heat fluxa/M 0.32 3231.44 20.14 Stainless Steel Ammonia 890 0.32 0.1 9.672 7 Constant heat fluxa/M 0.32 3226.65 20.11 Silicon Ammonia 890 0.32 0. 05 9.672 3 Constant power a/M 0.32 3206.12 20.08 Silicon Ammonia 890 0.32 0. 05 9.672 3 Constant power a/M1 0.32 3172.02 19.87 Silicon Ammonia 890 0.32 0. 05 9.672 3 Constant power a/M2 0.32 3066.42 19.21 Silicon Ammonia 890 0.32 0. 05 9.672 3 Constant power a/M3 0.32 3150.28 19.73 Silicon Ammonia 890 0.32 0. 05 9.672 3 Constant power a/M 0.32 3156.21 19.77 Silicon Ammonia 890 0.32 0. 05 9.672 3 Constant power b/M 0.32 2993.19 18.75 Silicon Ammonia 890 0.32 0. 05 9.672 3 Constant power c/M 0.32 3156.23 19.77
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106 CHAPTER SIX HEAT TRANSFER COMPUTATION DURING CONFINED LIQUID JET IMPINGEMENT WITH DISCRETE HEAT SOURCES 6.1 Mathematical model We consider an axisymmetric jet di scharging from a nozzle and impinging perpendicularly at the center of a solid plate subjected to heating by discrete heat sources on the opposite surface of the plat e as shown in figure 1. If the fluid is considered to be incompressible and its properties (density, viscosity, thermal conductivity, and specific heat) are dependent on temperature, the dimensionless equations describing the conservation of mass, momentum, and energy in Cartesian coordinates can be written as [33]: 0 z xV V (1) z x z x x z x xV V V V p V V V V Re 1 2 Re 3 2 (2) x z z x z z z xV V V V P Fr V V V V 2 Re 3 2 Re 1 12 (3)
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107 f f f z f xV V 1 1 Pr Re 1 P V P Vx zPr 1 ) ( 2 2 2 23 2 2 Pr Re 1 z x z x z xV V V V V V (4) Considering variable thermal conductivity, th e equation describing the conservation of energy inside the solid can be written as: 0 s s (5) To complete the physical model, equations (1) to (5) are subjected to the following boundary conditions: At 0 ; 0 ; 0 s (6) At 0 0 0 ; ; 0 f x xV V (7) At 0 ; 0 ; 1 s (8) At 0 ) ( 0 : 1 fP (9) At f s z x f sV V 1 0 0 ; (10) At j f j z xV V V , 0 2 0 ; (11) At 0 0 0 1 2 ; f z xV V (12) In order to simulate the discrete heat sources, localized heat fluxes were introduced at several locations and their magn itudes were varied. Figure 2 demonstrates
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108the boundary condition at the bottom of the plate for different problems considered in the present investigation. For exampl e, for case (a), equations (1) to (5) are subjected to the following boundary conditions: At 5 9 ; 9 1 0 ; 0 s (13) At 0 ; 3 1 9 1 ; 0 s (14) At 5 9 ; 9 5 3 1 ; 0 s (15) At 0 ; 9 7 9 5 ; 0 s (16) At 5 9 ; 1 9 7 ; 0 s (17) 6.2 Numerical simulation The governing equations along with the boundary conditions described in the previous section were solved by using the finite element me thod. The dependent variables, i.e., velocity, pressure, and temp erature were interpolated to a set of nodal points that defined the finite element. Four node quadr ilateral elements were used. In each element, the velocity, pressure, and temp erature fields were approximated which led to a set of equations that defined the conti nuum. After the Galerkin formulation was used to discretize the governing equations, the NewtonRaphson method was used to solve the ensuing algebraic equations. Ne wtonRaphson method is based on the principle that if the initial guess of the root of f(x) = 0 is at xi, then if one draws the tangent to the curve at f(xi), the point xi+1 where the tangent crosses the xax is is an improved estimate of the root. Using the definition of th e slope of a function, at ix x
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109 ) = (x fitan 10 i i ix x ) f(x = which gives ) f'(x ) f(x = x xi i i i 1 The above equation is called the Newt onRaphson formula for solving nonlinear equations of the form0 x f. The continuum was discretized using an unstructured grid which allowed finer meshes in areas of steep variations such as the solidfluid interface. Due to nonlinear nature of the governing transport equations, an iterative procedure was used to arrive at the soluti on for the velocity and temperature fields. Convergence is based on two criteria being sa tisfied simultaneously. One criterion is the relative change in field values from one iteration to the next; the other is the residual for each conservation equation. In this problem a tolerance of 0.1 percent (or 0.001) for both convergence criteria was applied. 6.3 Results and discussion Figure 6.1 shows the simulated geometr y. The simulation was carried out for two different substrate materials, namely silicon, a nd stainless steel. The length of the plate (L = 0.008 m) and the temperature of the jet at the nozzle exit (Tj = 293 K) were kept constant during the simulations. Ammonia was used as the primary working fluid for the simulation, which is an emerging coolant for space based thermal management systems. The properties of Ammonia ar e temperature dependent and for any given temperature, thermal conductivity, viscosity, specific heat and density can be calculated using equations (18) to (21).
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110 b HnxOutflow Confinement plate Nozzle InflowAxis of symmetryZ Impingement plate Fluid W/2 q"q"q" L 2L2L2L2L k = 69912.953 Â– 1026.449T + 6.0828125T2 Â– 0.018005208T3 + 2.65625E05T4 Â– 1.5625E08T5 (18) = 78411.526 + 1209.4674T Â– 7.3773828T2+ 0.022323698T3 Â– 3.3554687E05T4 + 2.00652083E08T5 (19) cp = 14633.163 + 222.04991T Â– 1.345077T2 + 0.0040670703T3 Â– 6.1386719E06T4 + 3.7005208E09T5 (20) = 161497.37 Â– 2416.6952T + 14.514766T2 Â– 0.043544271T3 + 6.5234375E05T4 Â– 3.90625E08T5 (21) Here Â‘TÂ’ is the absolute temperature in K. These equations were developed by fitting tabulated data for Ammonia for the te mperature range of 290 Â– 370 K as presented by Carey [35]. In order to determine the number of el ements for accurate numerical solution, computations were performed for several comb inations of number of elements in the x and z directions covering the solid and fl uid regions. The dimensionless solidfluid Figure 6.1 Schematic of a confined slot jet impinging on a uniformly heated solid plate
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111interface temperature for these simulations ar e plotted in figure 6.2. It was observed that the numerical solution becomes grid independent when the number of divisions in the x and z directions are increased over 80. Co mputations with 80x80 grids gave almost identical results when compared to those obt ained using 160x160 grids. In order to save computer time while retaining accuracy, 80 x 80 divisions was chosen for all final computations. Figure 6.3 presents the dimens ionless solidfluid interface temperature distribution for different Reynolds number using silicon substrate. It can be observed that 0 5 10 15 20 25 00.20.40.60.81 NX x NZ = 160 x160 NX x NZ = 80 x 80 NX x NZ = 40 x40 NX x NZ = 20 x20 Figure 6.2 Dimensionless solidfluid interface temperature for different number of elements in x and z directions (Re = 1645, = 0, = 0.4, = 0.4) Dimensionless solidfluid interface temperature, in t Dimensionless distance from the axis of the nozzle, ( )
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112 0.01 0.015 0.02 0.025 0.03 0.035 00.20.40.60.81 Re = 445 Re = 668 Re = 890 Re = 1115 the minimum temperature was present at th e stagnation point and the maximum at the edge of the plate. As expected, the interf ace temperature, as well as the minimumtomaximum temperature difference at the interface decreases with Reynolds number because of more fluid flow rate to carry aw ay the heat. Figure 6.4 shows the variations in the Nusselt number along the solidfluid in terface for different Reynolds numbers. In these simulations, a constant no zzle slot width of 3.2 mm and Hn/W ratio of 1 have been used. The overall values of the local heat tr ansfer coefficient and hence the local Nusselt number increases with jet inle t Reynolds number over the entire solidÂ–fluid interface. The usual bell shaped profile typical for impinging jets with a peak at the stagnation line is obtained in the numerical study. The heat tr ansfer coefficient increases with Reynolds number because of higher velo city of the fluid impinging on the plate. It was observed that the average Nusselt number increased by 50.59% when the Reynolds number is increased from 445 to 1115. Figu res 6.5 and 6.6 show the variat ions in the solidfluid Figure 6.3 Dimensionless temperature at the so lidfluid interface w ith seven discrete heat sources and constant total power for varying Reynolds number (E = 1.04 kW/m, = 0.4, = 0.4, = 0.625, Solid material =Silicon) Dimensionless distance from the axis of the nozzle, ( ) Dimensionless solidfluid interface temperature, in t
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113interface temperature and the local Nusselt number for a st ainless steel substrate at different Reynolds numbers. A similar phenomenon was observed. The interface temperature and the maximum to minimum te mperature difference at the interface decrease with the Reynolds number. The wa ve pattern in the temperature distribution graph shows that a non uniform heat distribut ion has taken place. This is because of the lower thermal conductivity of stainless stee l when compared to silicon. The average nusselt number and average heat transfer coef ficient increased with the Reynolds number. It was observed that the average Nusselt number increased by 52.7% when the Reynolds number is increased from 445 to 1115. For a given Reynolds number, stainless steel substrate has greater heat transfer coeffi cient and nusselt number all over the plate. 5 10 15 20 25 30 35 00.20.40.60.81 Re = 445 Re = 668 Re = 890 Re = 1115 Figure 6.4 Nusselt number at the solidfluid interface with seven discrete heat sources and constant total power for varying Reynolds number (E = 1.04 kW/m, = 0.4, = 0.4, = 0.625, Solid material =Silicon) Dimensionless distance from the axis of the nozzle, ( ) Local Nusselt Number, Nu
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114 0.01 0.015 0.02 0.025 0.03 0.035 0.04 00.10.20.30.40.50.60.70.80.91 Re = 445 Re = 668 Re = 890 Re = 1115 5 10 15 20 25 30 35 00.10.20.30.40.50.60.70.80.91 Re = 445 Re = 668 Re = 890 Re = 1115 Figure 6.5 Dimensionless temperature at the so lidfluid interface w ith seven discrete heat sources and constant total power for varying Reynolds number (E = 1.04 kW/m, = 0.4, = 0.4, = 0.625, Solid material =Stainless steel) Dimensionless distance from the axis of the nozzle, ( ) Dimensionless solidfluid interface temperature, in t Figure 6.6 Nusselt number at the solidfluid interface with seven discrete heat sources and constant total power for varying Reynolds number (E = 1.04 kW/m, = 0.4, = 0.4, = 0.625, Solid material =Stainless steel) Dimensionless distance from the axis of the nozzle, ( ) Local Nusselt Number, Nu
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115 0 0.005 0.01 0.015 0.02 0.025 0.03 00.10.20.30.40.50.60.70.80.91 = 0.8 = 0.4 = 0.2 = 0.1 Figures 6.7, and 6.8 show the variations of dimensionless so lidfluid interface temperature, and Nusselt number, respectively with dimensionless radial distance for various slot widths maintaining a constant Reynolds number of 890. It may be noted that the flow rate is directly proportional to Reynol ds number and therefore the flow rate is also the same in these simulati ons. The nozzle slot widths considered are 0.8mm, 1.6mm, 3.2mm and 6.4mm. For the local heat transfer coefficient and Nusselt number, the same half bell shaped curves (considering only one axisymmetric half) are present. The interface temperature incr eases outwardly with radial distance and the lowest temperature is found at the stagnati on line underneath the center of the slot opening. It may be observed in figure 6.7 that the interface temper ature decreases with decrease in the slot opening all along the pl ate. The lower interfac e temperature is the result of larger convective heat transfer ra te caused by higher jet velocity. When the flow Dimensionless distance from the axis of the nozzle, ( ) Dimensionless solidfluid interface temperature, in t Figure 6.7 Dimensionless temperature at th e solidfluid interface with seven discrete heat sources and constant total power for same flow rate (E = 1.04 kW/m, Re = 890, = 0.4, = 0.625, Solid material =Silicon)
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116rate (or Reynolds number) is kept constant, a smaller slot opening results in larger impingement velocity, which cons equently contributes to larger velocity of fluid moving along the plate (within the boundary layer as we ll as in the wall jet). From the graph between heat transfer coefficient and the radi al distance from the axis of the nozzle it was observed that the heat transfer rate at th e impingement region can augmented by a great extent if the nozzle width is reduced. The same can be seen in figure 6.8. This is because heat transfer coefficient and the Nusselt numbe r vary in a same manner. For an eightfold reduction in slot opening width, the peak value of local heat transfer coefficient increased by almost 2.5 times. Due to more rapid decrea se from the peak in the case of smaller opening, the average heat transfer coefficient in creased only to the order of 2.2 times for 0 10 20 30 40 50 00.20.40.60.81 = 0.8 = 0.4 = 0.2 = 0.1 Figure 6.8 Nusselt number at the solidfluid interface with seven discrete heat sources and constant total power for same flow rate (E = 1.04 kW/m, = 0.4, = 0.625, Solid material =Silicon) Dimensionless distance from the axis of the nozzle, ( ) Local Nusselt Number, Nu
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117 0 0.005 0.01 0.015 0.02 0.025 0.0300.20.40.60.81 = 0.2 = 0.4 = 0.8 The interesting thing to be observed is that the Nusselt number does not vary in a the length of the plate considered whereas it is of the order of 2.5 times in uniformly heated plate case. The interesting thing to be observed is that the Nusselt number does not vary in a similar manner as the heat transfer coefficient this is because in calculating Nusselt number, slot width is used as the length scale; so as the slot width decreases the Nusselt number too decreased. Though heat transfer coefficient is used in calculating the Nusselt number the rate of increas e of heat transfer coefficient is small when compared to the rate decrease of slot width. Hence Nusselt number decreased. The average values of heat transfer coefficient and Nusselt number for these cases are listed in Table 6.1. It was observed that the average heat transfer coefficient is incr eased by 58.77% when the slot width is reduced from 0.0064 m to 0.0008 m. The above observation suggests that a smaller slot opening is more desirable in no zzle design because of larger convective heat Dimensionless solidfluid interface temperature, in t Dimensionless distance from the axis of the nozzle, ( ) Figure 6.9 Dimensionless temperatur e at the solidfluid interface with seven discrete heat sources and constant to tal power for different nozzle widths (E = 1.04 kW/m, Inlet velocity = 9.672cm/s, = 0.4, = 0.625, Solid material=Silicon)
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118transfer rate at the solidflu id interface for any given fluid flow rate. However, further study including the pressure dr op characteristics may be need ed to arrive at the optimum slot opening. Figure 6.9 and 6.10 show the variations of dimensionless interface temperature and the Nusselt number with radial distance fo r various slot widths for a constant jet velocity. Since the slot width was used as the length scale for Reynolds number, the Reynolds number also varied in these ru ns. A very small difference of interface temperature was observed when the slot width was 0.16cm and 0.32cm. The minimum temperature and highest local values of heat transfer coefficient and Nusselt number were obtained for a nozzle width of 0.64 cm, the highest width considered in the present investigation. This run also resulted in the highest heat transfer coefficient through out the plate. The local values of Nusselt number at the downstream locations increase with 0 10 20 30 40 50 60 70 00.20.40.60.81 = 0.2 = 0.4 = 0.8 Figure 6.10 Nusselt number at the solidfluid interface with seven discrete heat sources and constant total power for diff erent nozzle widths (E = 1.04 kW/m, Inlet velocit y = 9.672cm/s = 0.4 = 0.625 Solid material =Silicon ) Local Nusselt Number, Nu Dimensionless distance from the axis of the nozzle, ( )
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119 0 0.01 0.02 0.03 0.04 0.05 0.06 00.10.20.30.40.50.60.70.80.91 Silicon, = 0.125 Silicon, = 0.25 Stainless Steel, = 0.125 Stainless Steel, = 0.25 nozzle width because of larger impingement regi on as well as a larger flow rate to carry away the heat. It can also be noticed that when the nozzle width was increased from 0.32 cm to 0.64 cm, the heat transfer performan ce improved everywhere in the plate. Looking at the average values of heat transfer coeffici ent and Nusselt number li sted in Table 6.1, it can be observed that the lowest values are for W=0.16 cm. The average Nusselt number is approximately 5 times more when the slot width is incr eased from 0.0016 m to 0.0064m. A more significant increase can be seen when the width was increased, even though that increase was at the e xpense of a larger flow rate. Figures 6.11 shows the plot of dimensi onless temperature at the solidfluid interface against dimensionless distance from the axis of impingement for silicon, and stainless steel respectively and for two different values of solid thickness. In both the cases, it is evident that th e interface temperature is se nsitive to the solid thickness Figure 6.11 Comparison of local temperatur es at the interf ace with three discrete heat sources and constant total power for different solid thicknesses ( E = 2kW/m Re = 890 = 0.4 = 0.4 ) Dimensionless solidfluid interface temperature, in t Dimensionless distance from the axis of the nozzle, ( )
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120especially at the stagnation point where rather significantly lower temperatures were observed as the solid wafe rÂ’s thickness reduced to 1 mm ( = 0.125). The temperature values are also found to be sensitive to thermal conductivity of the solids with stainless steel giving the lowest temperature at the stagnation point and the highest temperature at the outlet. This is consistent with the fact that it has the lower thermal conductivity of th e two (13.4 W/mK). Silicon, which has the highest thermal con ductivity of the both, (140 W/mK ) behaves in the opposite manner in that it has the highest stagna tion point temperature and the lowest outlet temperature, implying that a larger thermal conductivity allows a better distribution of heat within the solid. In case of stai nless steel, fluctuations in temperature were observed wherever heat is not applied thus showing its high sensitivity 10 15 20 25 30 35 00.20.40.60.81 = 0.125 = 0.25 = 0.5 = 0.75 = 1.125 = 1.5 Local Nusselt Number, Nu Dimensionless distance from the axis of the nozzle, ( ) Figure 6.12 Comparison of local Nusselt number with three discrete heat sources and constant total power for different solid thicknesses (E = 2kW/m, Re = 890, = 0.4, = 0.4, Solid material = Silicon)
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121 10 15 20 25 30 35 00.20.40.60.81 = 0.125 = 0.25 = 0.5 = 0.75 = 1.125 = 1.5 to the location of heat sources Such behavior of stainless steel is be cause of its lower thermal conductivity. This trend in stainles s steel disappeared at higher thickness beyond 1 mm. At higher values of thickness in the range of 4 mm to 12 mm ( = 0.51.5), the changes in stagnation point temperat ure are relatively lower. Also apparent is the fact that when stagnation temperatures are lower, the outflow temperature tends to be relatively higher which is quite expected because both flow rate and heat energy at the bottom surface of the plate we re kept constant. Similar trend can be seen when the plate is uniformly heated. This phenomenon has been documented by Lachefski et al. (1995) and is the main drawback of axially impinging jets as opposed to radial jets which give s better uniformity of temperature. It can also be noted that a thicker plate provides more uniform interface temperature be cause of radial Local Nusselt Number, Nu Dimensionless distance from the axis of the nozzle, ( ) Figure 6.13 Comparison of local Nusselt number with three discrete heat sources and constant total power for different solid thicknesses (E = 2kW/m, Re = 890, = 0.4, = 0.4, Solid material = Stainless Steel)
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122distribution of heat within the solid due to conduction. Figures 6.12 and 6.13 compares the local Nusselt number for different plate thicknesses for silicon and stainless steel substrates. The total energy calculate d at the solidfluid interface was 1.978 kW/m. In these simulations, a constant nozzle slot widt h of 3.2 mm and Hn/W ratio of 1 was used. The overall values of the local Nu sselt number have shown almost the same variation over the entire solidfluid interface. The local heat transfer coefficient is highest at the stagnation point. The values of average heat transfer coefficient and average Nusselt number for these cases are also listed in Table 6.1. It may be noticed that for both the materials, the average Nusselt number decreases with increase in plate thickness and has become almost the same for all the solid thickness beyond 4 mm. The increment, however, is small in magnitude a nd practically disappears at large thickness. The average heat transfer coefficient and average Nusselt number we re observed to be 0 0.01 0.02 0.03 0.04 0.05 0.06 0.1250.250.50.751.1251.5 0 0.005 0.01 0.015 0.02 0.025 0.03 max, Silicon max, Stainless Steel maxmin, Silicon maxmin, Stainless Steel Dimensionless Maximum Temp erature at the Interface, maxint Dimensionless Maximum to Minimum Interface Temperature Difference maxin t minin t Dimensionless thickness of the p late ,( ) Figure 6.14 Comparison of maximum te mperature and difference between m aximum and minimum temperatures at the in terface for different solids with various thicknesses ( E = 2kW/m Re = 890 = 0.4 = 0.4 )
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123 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.1250.250.50.751.1251.5 Silicon Stainless Steel greater for a stainless steel substrate when co mpared to a silicon s ubstrate. Figure 6.14 shows a plot for dimensionless maximu m temperature and difference between dimensionless maximum and minimum temperat ure at the solidfl uid interface as a function of solid thicknesses fo r silicon and stainless steel. Stainless steel exhibits more sensitivity to solid thickne ss than silicon. Also, since it has the lowest thermal conductivity, it has higher overall values of te mperature indicating that the model is sensitive to solid therma l conductivity. Both the solids show higher maximum temperature and higher temperature range at the smallest thickness. As the thickness increases, the conduction within the solid resu lts in more uniformity of temperature at the interface and reduces down the value of highest temperature, which is encountered at the outlet end of the plate next to the heat source. It may al so be noticed that beyond a Dimensionless Maximum Temperat ure within the substrate, max sol Dimensionless thickness of the p la t e ,( ) Figure 6.15 Comparison of maximum temp erature within the substrate for various thicknesses (E = 2kW/m, Re = 890, = 0.4, = 0.4)
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124thickness of 0.006 m, there is hard ly any variation of temperature plotted in this figure, indicating that an optim um design condition has been reache d. It can also be noticed that the difference between maximum and minimum te mperatures at the solidfluid interface decreases as the plate thickness increases. This is because of more uniform heat distribution within the solid as the plate thickness increases. Figure 6.15 compares the maximum temperat ures attained within the silicon and stainless steel substrates for different plate thicknesses. The graph gives an idea of the temperature range for which th e substrates can be used. It was observed that for any particular thickness of a substr ate the maximum temperature is attained at the outer end of the plate. Both the substrates show hi gher maximum temperature at larger thickness. Since stainless steel has less th ermal conductivity compared to si licon it has higher values of temperature all over the plate. 18 18.5 19 19.5 20 20.5 21 21.5 22 0.1250.250.50.751.1251.5 Nuav, Silicon Nuav, Stainless Steel Figure 6.16 Comparison of average Nusselt number for different solids and plate thicknesses (E = 2kW/m, Re = 890, = 0.4, = 0.4) Dimensionless thickness of the plate, ( ) Average Nusselt number, Nuav g
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125 0.009 0.01 0.011 0.012 0.013 0.014 0.015 0.016 0.017 0.018 00.20.40.60.81 Hn = 3.2mm Hn = 6.4mm Hn = 9.6mm Figure 6.16 shows the variation of aver age Nusselt number with plate thickness for different materials. It can be noticed that the maximum value is obtained at the smallest thickness and it gradually decreases with thickness. Also, there is a larger variation for stainless steel, which has the lowest thermal conductivity among the materials considered in this investigation. It may be also noticed that the variation of average Nusselt number diminishes with thic kness and there is no noticeable change at high thickness and high thermal conductivity. The average Nusselt number, which is an indicator of overall performance, settles to a constant value when enough thickness is provided because the maximum redistribution of heat by conduction within the plate has already been taken place. Dimensionless solidfluid interface temperature, in t Dimensionless distance from the axis of the nozzle, ( ) Figure 6.17 Dimensionless temperature at th e interface with thr ee discrete heat sources and constant total power for different impingement heights (E = 2 kW/m, Re=890, = 0.625, Solid material = Silicon)
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126 Computations are also done to explore the effects of impingement height on the solidfluid interface temperature. Three di fferent jet height to plate lengths of = 0.4, 0.8, and 1.2 were modeled for silicon and stainl ess steel substrates of 0.5 mm thickness using ammonia as the working fluid. Fi gure 6.17 and 6.18 show the variations of dimensionless temperature and Nusselt num ber along the solidfluid interface for different jet impingement heights. = 0.4 gives the lowest interface temperature and consequently the highest heat transfer coe fficient and Nusselt number. As the distance from the nozzle to the plate increases, th e heat transfer coefficient and the Nusselt number decreases. However, there is practica lly small difference in distributions between = 0.8 and 1.2, thus indicating that the effect of jet imp ingement height becomes negligible after it reaches certain limit. Averag e heat transfer heat transfer coefficient and the average Nusselt number values are shown in the Table 6.1. It was observed that the average Nusselt number is increased by 28% when the impingement height is decreased 0 5 10 15 20 25 30 35 00.20.40.60.81 = 0.4 = 0.8 = 1.2 Local Nusselt number, Nu Figure 6.18 Local Nusselt number at the interface w ith three discrete heat sources and constant total power for different impingement heights (E = 2 kW/m, Re=890, = 0.625, Solid material = Silicon) Dimensionless distance from the axis of the nozzle, ( )
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127 0 0.005 0.01 0.015 0.02 0.025 00.20.40.60.81 = 0.4 = 0.8 = 1.2 0 5 10 15 20 25 30 35 00.20.40.60.81 = 0.4 = 0.8 = 1.2 Dimensionless solidfluid interface temperature, in t Figure 6.19 Dimensionless temperature at th e interface with thr ee discrete heat sources and constant total power for different impingement heights (E = 2 kW/m, Re=890, = 0.625, Solid material = Stainless Steel) Dimensionless distance from the axis of the nozzle, ( ) Dimensionless distance from the axis of the nozzle, ( ) Local Nusselt number, Nu Figure 6.20 Local Nusselt number at the interface w ith three discrete heat sources and constant total power for different impingement heights (E = 2 kW/m, Re=890, = 0.625, Solid material = Stainless Steel)
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128 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 00.20.40.60.81 Ammonia FC77 Mil7808 from 0.0096m to 0.0032m. A similar variation was performed for stainless steel substrate. Figures 6.19 and 6.20 show the variations of dimensionless interface temperature and Nusselt number along the plate length for a stai nless steel substrate. A similar trend as above was observed. The solidfluid interface te mperature increased with increase in the impingement height and the local heat tran sfer coefficient and local Nusselt number values decreased as the impingement height increased. Non uniform heat distribution was observed for a stainless steel substrate this is because of the lower thermal conductivity of the stainless steel when compared to silic on. It was observed that the average Nusselt number was increased by 46.9% when the impi ngement height is reduced from 0.0096m to 0.0032m. Figure 6.21 compare the results of pres ent working fluid (ammonia) with two other coolants that have been considered in previous thermal management studies, Dimensionless solidfluid interface temperature, in t Dimensionless distance from the axis of the nozzle, ( ) Figure 6.21 Dimensionless temperature at th e interface with three heat sources and constant total power for different fluids (E = 1.1 kW/m, Re=890, = 0.4, = 0.4, = 0.625, Solid material = silicon)
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129namely FC77 and Mil7808 for a silicon substr ate. It has been observed that ammonia gives much lower interface temperature and much higher heat transfer coefficient compared to both FC77 and Mil7808. Figu re 6.21 shows the va riations in the dimensionless solidfluid interface temperatur e. The figures show that FC77 has lower dimensionless interface temperature; this is because the calculation of dimensionless temperature involves thermal conductivity of the fluid. Since FC77 has lower thermal conductivity the dimensionless interface temperature was observed to be less for FC77. The Nusselt number, however, is highest fo r FC77, primarily because of its lower thermal conductivity compared to the other two fluids. This can be seen from figure 6.22. The superior thermal performance of ammoni a may be useful for its application as a working 0 10 20 30 40 50 60 70 00.20.40.60.81 Ammonia FC77 Mil7808 Figure 6.22 Local Nusselt number at the in terface with thr ee heat sources and constant total power for different fluids (E = 1.1 kW/m, Re=890, = 0.4, = 0.4, = 0.625, Solid material = silicon) Dimensionless distance from the axis of the nozzle, ( ) Local Nusselt Number, Nu
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130 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 00.20.40.60.81 Ammonia FC77 Mil7808 0 10 20 30 40 50 60 70 00.20.40.60.81 Ammonia FC77 Mil7808 Local Nusselt Number, Nuav Figure 6.24 Local Nusselt number at the in terface with thr ee heat sources and constant total power for different fluids (E = 1.1 kW/m, Re=890, = 0.4, = 0.4, = 0.625, Solid material = Stainless Steel) Dimensionless distance from the axis of the nozzle, ( ) Dimensionless solidfluid interface temperature, in t Dimensionless distance from the axis of the nozzle, ( ) Figure 6.23 Dimensionless temperature at th e interface with three heat sources and constant total power for different fluids (E = 1.1 kW/m, Re=890, = 0.4, = 0.4, = 0.625, Solid material = silicon)
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131 Figure 6.25 Isotherms for stainl ess steel with three disc rete heat sources and constant total power (E = 1.04 kW/m, Re = 890, = 0.25, = 0.4) Figure 6.26 Isotherms for stainl ess steel with three disc rete heat sources and constant total power (E = 1.04 kW/m, Re = 890, = 0.75, = 0.4)
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132 fluid in thermal management systems for airc raft and spacecraft. A similar scenario is observed when stainless steel plate is used instead of silicon plate. Figures 6.23 and 6.24 show the variations in dimensionless solidfluid interface temperature and local Nusselt number along the plate length fo r a stainless steel substrat e. The average Nusselt number and average local heat transfer coefficient of stainless steel are observed to be slightly greater than that of silicon fo r any coolant. It can be obser ved that the heat distribution along the solidfluid interface is more uniform for silicon substrate when compared to stainless steel substrate. This is because of the higher therma l conductivity of silicon when compared to stainless steel. For a si licon substrate the average heat transfer coefficient at the solidfluid interface usi ng ammonia as coolant was observed to be 363.12% more when compared to the one fo r FC77 and it was obs erved to be 379.33% more when compared to Mil7808. For a stai nless steel substrate it was observed to 380.03% more when compared to FC77 and it was 405.13% more when compared to the average heat transfer coefficient ob tained using Mil7808 as coolant. Figures 6.25, 6.26, and 6.27 show isotherm cont our plots within the solid for stainless steel at thickness of 2mm and 6mm and silicon with 2 mm respectively. The Figure 6.27 Isotherms for silicon with three discrete heat sources and constant total power (E = 1.04 kW/m, Re = 890, = 0.25, = 0.4)
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133isotherms tend to be more concentric ar ound the stagnation point The effect of nonuniform heating is felt only at the bottom of the plate. The shapes of the isotherms are not really affected by the therma l conductivity of the solids. Th e minimum temperature in all the cases was observed at the stagnation point while the maximum was at the outer end of the bottom surface of the plate (heat flux surf ace). For the thicker solid, the isotherms exhibit better uniformity as indi cated by the fact that th ey are more parallel to the interface and plate bottom surfaces. The maximum temperature difference within the silicon is less than that for stainless steel implying that a larger thermal conductivity allows a better distribu tion of heat within the solid. The results gathered from the simula tions can be summarized as follows: The solidfluid interface temperature as well as the heat transfer coefficient shows a strong dependence on several geometric, fluid flow, and heat transfer parameters such as jet Reynolds number, nozzle slot width, impingement height, plate thickness, plate material, and fluid prope rties. The inlet Reynolds numbe r was kept at values where laminar flow could be obtained. The heat tr ansfer coefficient increased with Reynolds number. The heat transfer coefficient decrease d with slot width for a given flowrate. At the stagnation line, local values of heat transfer coefficient were highest because of the pronounced convective effects. Heat transfer then reduced gradually towards the outflow boundary. For a constant jet ve locity, a higher heat transfer coefficient was observed all over the plate for larger slot width. A lower impingement height resulted in higher heat transfer coefficient. The average heat transf er coefficient was obser ved to be higher for a smaller plate thickness, whereas a thicker pl ate provided a more uni form distribution of heat transfer coefficient. Plate material s with a higher thermal conductivity provided a
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134more uniform heat distribution. Compared to Mil7808 and FC77, ammonia provided much smaller solidfluid interface temperature and higher heat transf er coefficient. The Nusselt number was observed to greater for FC77. The average local heat transfer coefficient and average Nusselt number for stai nless steel substrate were observed to be greater than th at of silicon.
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135Table 6.1 Average heat transfer coefficient and Nusselt number for a discretely heated plate Material Fluid Re W (cm) b (cm) Vj (cm/s) Number of Heat Sources Heat source type Hn (cm) hav (W/m2K) Nuav Silicon Ammonia 445 0.320.054.8 7 Constant power0.32 2313.53 14.49 Silicon Ammonia 668 0.320.057.259 7 Constant power0.32 2591.94 16.23 Silicon Ammonia 890 0.320.059.672 7 Constant power0.32 3017.07 18.9 Silicon Ammonia 1115 0.320.0512.11 7 Constant power0.32 3484.18 21.82 Silicon Ammonia 890 0.080.0538.7 7 Constant power0.32 6034.13 9.45 Silicon Ammonia 890 0.160.0519.3 7 Constant power0.32 4027.64 12.61 Silicon Ammonia 890 0.320.059.672 7 Constant power0.32 3017.07 18.9 Silicon Ammonia 890 0.640.054.8 7 Constant power0.32 2487.43 31.16 Silicon Ammonia 445 0.160.059.672 7 Constant power0.32 2981.16 9.34 Silicon Ammonia 890 0.320.059.672 7 Constant power0.32 3017.07 18.9 Silicon Ammonia 1780 0.640.059.672 7 Constant power0.32 3807.20 47.7 Silicon Ammonia 890 0.320.1 9.672 3 Constant power0.32 3130.55 19.6 Silicon Ammonia 890 0.320.2 9.672 3 Constant power0.32 3084.49 19.32 Silicon Ammonia 890 0.320.4 9.672 3 Constant power0.32 3062.67 19.18 Silicon Ammonia 890 0.320.6 9.672 3 Constant power0.32 3057.15 19.15 Silicon Ammonia 890 0.320.9 9.672 3 Constant power0.32 3054.72 19.13 Silicon Ammonia 890 0.321.2 9.672 3 Constant power0.32 3054.04 19.13 Stainless Steel Ammonia 445 0.320.054.8 7 Constant power0.32 2538.77 15.90 Stainless Steel Ammonia 668 0.320.057.259 7 Constant power0.32 2878.47 18.03 Stainless Steel Ammonia 890 0.320.059.672 7 Constant power0.32 3354.51 21.01 Stainless Steel Ammonia 1115 0.320.0512.11 7 Constant power0.32 3876.97 24.28 Stainless Steel Ammonia 890 0.320.1 9.672 3 Constant power0.32 3407.5 21.34 Stainless Steel Ammonia 890 0.320.2 9.672 3 Constant power0.32 3327.22 20.84 Stainless Steel Ammonia 890 0.320.4 9.672 3 Constant power0.32 3250.84 20.36 Stainless Steel Ammonia 890 0.320.6 9.672 3 Constant power0.32 3224.47 20.20 Stainless Steel Ammonia 890 0.320.9 9.672 3 Constant power0.32 3211.39 20.11 Stainless Steel Ammonia 890 0.321.2 9.672 3 Constant power0.32 3207.48 20.09 Silicon Ammonia 890 0.320.059.672 3 Constant power0.32 3018.65 18.9 Silicon Ammonia 890 0.320.059.672 3 Constant power0.64 2659.19 16.66 Silicon Ammonia 890 0.320.059.672 3 Constant power0.96 2357.06 14.76 Stainless Steel Ammonia 890 0.320.059.672 3 Constant power0.32 3463.34 21.69 Stainless Steel Ammonia 890 0.320.059.672 3 Constant power0.64 3063.56 19.19
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136 Table 6.1 (continued) Stainless Steel Ammonia 890 0.32 0.05 9.672 3 Constant power 0.96 2357.06 14.76 Silicon Ammonia 890 0.32 0.05 9.672 3 Constant power 0.32 3078.77 19.28 Silicon FC77 890 0.32 0.05 9.672 3 Constant power 0.32 664.78 33.77 Silicon Mil7808 890 0.32 0.05 9.672 3 Constant power 0.32 642.45 13.71 Stainless Steel Ammonia 890 0.32 0.05 9.672 3 Constant power 0.32 3463.34 21.69 Stainless Steel FC77 890 0.32 0.05 9.672 3 Constant power 0.32 720.96 36.62 Stainless Steel Mil7808 890 0.32 0.05 9.672 3 Constant power 0.32 685.63 14.63
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137 CHAPTER SEVEN CONCLUSIONS 7.1 Cryogenic storage The conclusions gathered from the results of single phase analysis of cryogenic storage can be summarized as follows: The incoming fluid from the cryocooler penetrates the fluid in the tank as a submerged jet and diffuses into the flui d medium as it loses its momentum. When the gravity is present, the fluid ad jacent to the wall rises upward due to buoyancy and also mixes with the colder fl uid due to the forced circulation. In the absence of gravity, the incoming fluid jet expands and impinges on the top wall of the tank and then the fluid moves downward along the tank wall and carry heat with it. The mixing of hot and cold fluids takes place at the bottom portion of the tank. The temperature of the fluid is highest at the wall and it decreases rapidly towards the axis of the tank. The discharge of the incoming fluid from the cryocooler at several locations and/or at an angle to the axis results in better mixing compared to single inlet at the bottom of the tank. The Cchannel ge ometry proposed here provides a better heat transfer from the tank wall to the cold fluid.
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138 The conclusions gathered from the results of two phase analysis of cryogenic storage can be summarized as follows: The incoming fluid from the cryocooler pe netrates the fluid in the tank as a submerged jet and diffuses into the flui d medium as it loses its momentum. The fluid adjacent to the wall rises due to buoyancy and also mixes with the colder fluid due to forced circulation. The temperature of the fluid is highes t at the wall and it decreases rapidly towards the axis of the tank. Discharge of fluid from the cryocooler at different locations within the tank results in better mixing compared to th e single inlet at the bottom of the tank. Greater circulation is observed in va por region when compared to liquid region. Larger pressure reduction is observed in liquid region. For a given tank geometry and insulation structure, the Zero Boiloff (ZBO) condition can be maintained by controll ing the cryocooler operation and the fluid mixing within the tank. 7.2 Jet impingement The conclusions gathered from the result s of heat transfer computation during confined liquid jet impingement with uniform heat source can be summarized as follows: The solidfluid interface temperature as well as the heat transfer coefficient shows a strong dependence on several geomet ric, fluid flow, and heat transfer parameters such as jet Reynolds number, nozzle slot width, impingement height,
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139 plate thickness, plate material, and flui d properties. The inlet Reynolds number was kept at values where lami nar flow could be obtained. The heat transfer coefficient in creased with Reynolds number. For a constant Reynolds number and jet im pingement height he at distribution is more uniform for a conjugate model when compared to a non conjugate model. The heat transfer coefficient decreased with slot width for a given flowrate. At the stagnation line, local values of heat transfer coefficient was highest because of the pronounced convective e ffects. Heat transfer then reduced gradually towards the outflow boundary. For a constant jet velocity, a higher heat transfer coefficient at the impingement location was seen for a small slot width but a higher average heat transfer coefficient was observed fo r larger slot width. A lower impingement height resulted in higher heat transfer coefficient. A higher heat transfer coefficient at the impingement location was seen at a smaller thickness, whereas a thicker plate provided a more unif orm distribution of heat transfer coefficient. Plate materials with a higher therma l conductivity provided a more uniform distribution of interface temp erature as well as the heat transfer coefficient. The average local heat transfer coefficient and average Nusselt number of stainless steel are observed to be slig htly greater than that of silicon. Compared to Mil7808 and FC77, ammoni a provided much smaller solidfluid interface temperature a nd higher heat transfer coefficient.
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140 The conclusions gathered from the fluid flow analysis during confined liquid jet impingement for different number of discre te heat sources can be summarized as follows: The solidfluid interface temperature as well as the heat transfer coefficient shows a strong dependence on number, magnitude, an d location of heat sources and plate material properties. For a given constant total heat energy, the following conclu sions can be drawn from the numerical results: (1) The temperature at the stagnation point reduced with the decrease in number of heat sources. (2) The average heat transfer coe fficient and the average Nusselt number values increased with increase in number of heat sources in both conjugate and nonconjugate models. (3) The effect of number of heat s ources is negligible when the solid conductivity is high. (4) The average heat transfer coeffi cient is highest for uniform heating when compared to discrete heating. (5) The isothermal lines inside th e solid showed that beyond critical thickness, the plate presented a one dimensional heat conduction in regions away from the impingement plane and the heated surface, and therefore did not exert much influence in convection heat transfer process.
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141 When the heat flux at the sources was ke pt at a constant value, the highest average heat transfer coefficient was observed for uniform heating in both conjugate and nonconjugate models. For discrete heating, the magnitude and the geometric location of heat sources influenced the maximum temperature as well as local distribution of heat transfer coefficient. The conclusions gathered from the heat tran sfer computation during confined liquid jet impingement with discrete heat sources can be summarized as follows: The solidfluid interface temperature as well as the heat transfer coefficient shows a strong dependence on several geometric, fluid flow, and heat transfer parameters such as jet Reynolds number, nozzle slot width, impingement height, plate thickness, pl ate material, and fluid properties. The inlet Reynolds number was kept at values where laminar flow could be obtained. The heat transfer coefficient in creased with Reynolds number. The heat transfer coefficient decreased w ith slot width for a given flowrate. At the stagnation line, local values of heat transfer coefficient were highest because of the pronounced convective eff ects. Heat transfer then reduced gradually towards the outflow boundary. For a constant jet velocit y, a higher heat transfer co efficient was observed all over the plate for larger slot width. A lower impingement height resulted in higher heat transfer coefficient.
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142 The average heat transfer coefficient was observed to be higher for a smaller plate thickness, whereas a thicker plat e provided a more uniform distribution of heat transfer coefficient. Plate materials with a higher thermal conductivity provided a more uniform heat distribution. For a constant jet impingement height an d slot width: the average local heat transfer coefficient and average Nusse lt number for stainless steel substrate were observed to be greater than that of silicon at any plate thickness. Compared to Mil7808 and FC77, a mmonia provided much smaller solidfluid interface temperature and higher he at transfer coefficient. The Nusselt number was observed to greater for FC77. 7.3 Recommendations for future research Further research can be done using different tank materi al and different shapes of the tank for cryogenic storage. For jet im pingement different substrate and coolant combinations can be done for better results. In addition, other e nhancement mechanisms such as transient analysis, turbulence and ro tation of the plate can be included in future investigations.
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143 REFERENCES [1] P. J. Muller, J. C. Batty, and R. M. Zurbin, HighPressure cryogenic hydrogen storage system for a Mars sample return mission, Cryogenics, vol. 36, pp. 815822, 1996. [2] R. E. Spall, A numerical study of tran sient mixed convection in cylindrical thermal storage tanks, International jour nal of heat and ma ss transfer, vol.41, pp.20032011, 1998. [3] P. Muller, and T. Durrant, Cryogenic pr opellant liquefaction and storage for a precursor to a human Mars mission, Cryogenics, vol.39, pp.10211028, 1999. [4] L. J. Salerno, and P. Kittel, Cryogenic s and the human exploration of Mars, Cryogenics, vol.39, pp.381388, 1999. [5] S. Kamiya, K. Onishi, and E. Nishigak i, A large experimental apparatus for measuring thermal conductance of LH2 storage tank insulations, Cryogenics, vol, 40, pp. 3544, 2000. [6] L. J. Hastings, D. W. Plachta, L. Sale rno, and P. Kittel, An overview of NASA efforts on zero boiloff storage of cryoge nic propellants, Cryogenics, vol. 41, pp. 833839, 2002. [7] P. Kittel, Propellant preservation usi ng reliquifiers, Cryogenics, vol. 41, pp.841844, 2001. [8] S. Kamiya, K. Onishi, N. Konshima, a nd K. Nishigaki, Thermal test of the insulation structure for LH2 tank by usi ng the large experimental apparatus, Cryogenics, vol. 40, pp.737748, 2001. [9] N. T, Van Dresar, J. D. Siegwarth, M. M. Hasan, Convectiv e heat transfer coefficients for nearhorizontal twopha se flow of nitrogen and hydrogen at low mass and heat flux, Cryogeni cs, vol. 41, no. 1112, pp. 805811. [10] A. Zapke, D.G. Kroger, Countercurrent gasliquid flow in inclined and vertical ductsI: Flow patterns, pressure drop ch aracteristics and flooding, International journal of multiphase flow, vol. 26, no.9, pp. 14391455.
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144 [11] B. Rousset, D. Chatain, D. Beysens, B. Jager, Twophase visualization at cryogenic temperature, Cryoge nics, vol. 41, no.56, pp. 443451, 2001. [12] D. J. Womac, F. Incropera, and S. Ramadhyani, Correlating equations for impingement cooling of small heat sources with single circular liquid jets, Journal of heat transfer, 115, pp. 106114, 1993. [13] H. Yamamoto, Y. Udugawa, and M. Su zuki, Cooling system for FACOM M780 large scale computer, Proceedings of th e international symposium on cooling technology for electronic equipment, pp. 701714, 1987. [14] B. Elison, and B. Webb, Local heat transf er to impinging jets in the intially laminar, transitional and turbulent regime s, International journal of heat and mass transfer, vol. 37, no. 8, pp. 12071216, 1994. [15] C. F. Ma, Q. Zheng, and S. C. Lee, Im pingement heat transfer and recovery effect with submerged jets of large pr andtl number liquids, International journal of heat and mass transfer, vol. 40, pp. 14811490, 1996. [16] V. Garimella, and R. Rice, 1995, Conf ined and submerged liquid jet heat transfer, Journal of heat transfer, 117, no. 4, pp. 871877, 1995. [17] A. B. AbouZiyan, and F. Hassan, Effect of jet characteristics on heat transfer by impingement of submerged confine water jets, ASME heat transfer division, vol3611, pp. 211218, 1998. [18] G. K. Morris, K. S. Garimella, and J. A. Fitzgerald, Improved predictions of the flow field in submerged and confined impinging jets using the reynolds stress model, Thermomechanical phenomena in electronic systems Proceedings of the intersociety conference, IEEE, NJ98CH36208, pp. 362370, 1998. [19] C. A. Dinu, D. E. Beasely, and J. A. Liburdy, Heat tran sfer from a moving plate to confined impinging jet, ASME h eat transfer divi sion, vol.3574, pp.192205, 1998. [20] H. S. Law, and J. H. Masliyah, Mass transfer due to a confined laminar impinging jet, International journal of heat and mass transfer, vol. 27, no. 4, pp. 529539, 1984. [21] S. H. Seyedein, M. Hasan, and A. S. Mu jumdar, Laminar flow and heat transfer from multiple impinging slot jets with an inclined confinement surface, International journal of heat a nd mass transfer, vol. 37, no. 13, pp. 18671875, 1994.
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145 [22] P. Y. Tzeng, C. Y. Soong, and C. D. Hseih, Numerical investigation of heat transfer under confined impinging turbulen t slot jets, Numerical heat transfer, part A, vol. 35, pp. 903924, 1999. [23] X. S. Wang, Z. Dagan, and L. M. Jiji, Prediction of surface te mperature and heat flux of a microelectronic chip with jet impingement cooling, Journal of electronic packaging, vol. 112, pp. 5762, 1990. [24] D. C. Wadsworth, and I. Mudawar, Coo ling of a multiple electronic module by means of confined twodimensional jets of dielectric liquid, Journal of heat transfer, vol. 112, pp. 891898, 1990. [25] D. Schaffer, F. P. Incropera, and S. Ramadhyani, Planar liquid jet impingement cooling of multiple discrete heat sources, Journal of electronic packaging, vol. 113, pp. 359366, 1991. [26] K. L. Teuscher, S. Ramadhyani, and F. P. Incropera, Jet impingement cooling of an array of discrete heat sources with extended su rfaces, Enhanced cooling techniques for electronic applic ations, ASME/HTDvol. 263, pp. 110, 1993. [27] V. P. Schroeder, and S. V. Garimella, Heat transfer from a discrete heat source in confined air jet impingement, Proceedings of 11th international heat transfer conference, vol. 5, pp. 451456, 1998. [28] H. A. Sheikh, and S. V. Garimella, Enha ncement of air jet impingement heat transfer using pinfin heat sinks, IEEE transactions on components and packaging technology, vol. 23, no. 2, pp. 300388, 1998. [29] A. J. Bula, M. M. Rahman, and J. E. Leland, Axial steady free surface jet impinging over flat disc with discrete heat sources, International journal of heat and fluid flow, vol. 21, pp. 1121, 2000. [30] S. J. Wang, and A. S. Mujumdar, A comparative study of five low Reynolds number kmodels for impingement heat tran sfer, Applied thermal engineering, vol. 25, no. 1, pp. 3144, 2005. [31] V. Narayanan, J. SeyedYagoobi, and R. H. Page, An experimental study of fluid mechanics and heat transfer in an impinging slot jet flow International journal of heat and mass transfer, vol. 47, n.89, pp. 18271845, 2004. [32] W. M. Kays, and M. E. Crawford, C onvective heat and mass transfer, Third edition, McGraw Hill, New York, 1993.
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146 [33] L. C. Burmeister, Convective h eat transfer, Wiley, New York, 1993. [34] F. C. Ma, Y. Zhuang, C. S. Lee, and T. Gomi, Impingement Heat Transfer and Recovery Effect with Submerged Jets of Large Prandtl Number LiquidII. Initially Laminar Confined Slot Jets, In ternational journal of heat and mass transfer, vol. 40, n.6, pp. 14911500, 1997. [35] V. P. Carey, Liquidvapor phasechange phe nomena, Taylor & Francis, Bristol, PA 1992.
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147 APPENDICES
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148 Appendix A: Computation of fluid (liquid hydrogen) circulation in a hydrogen storage tank FIGEN( 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 ) POINT( ADD, COOR, X = 0, Y = 0 ) POINT( ADD, COOR, X = 65, Y = 0 ) POINT( ADD, COOR, X = 195, Y = 0 ) POINT( ADD, COOR, X = 260, Y = 0 ) POINT( ADD, COOR, X = 360, Y = 0 ) POINT( ADD, COOR, X = 100, Y = 0 ) POINT( ADD, COOR, X = 100, Y = 7.5 ) POINT( ADD, COOR, X = 0, Y = 7.5 ) POINT( ADD, COOR, X = 65, Y = 7.5 ) POINT( ADD, COOR, X = 195, Y = 7.5 ) POINT( ADD, COOR, X = 260, Y = 7.5 ) POINT( ADD, COOR, X = 360, Y = 7.5 ) POINT( ADD, COOR, X = 65, Y = 150 ) POINT( ADD, COOR, X = 195, Y = 150 ) POINT( SELE, LOCA, WIND = 1 ) 0.0639881, 0.474206 / ID = 6 0.0699405, 0.569444 / ID = 7 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.0684524, 0.472222 / ID = 6 0.833333, 0.482143 / ID = 1 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.833333, 0.482143 / ID = 1 0.825893, 0.56746 / ID = 8 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.0669643, 0.571429 / ID = 7 0.831845, 0.575397 / ID = 8 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 )
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149 Appendix A: (Continued) 0.0848214, 0.43254 / ID = 1 0.931548, 0.436508 / ID = 2 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.931548, 0.436508 / ID = 2 0.925595, 0.573413 / ID = 9 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.0833333, 0.448413 / ID = 1 0.077381, 0.583333 / ID = 8 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.241071, 0.329365 / ID = 1 POINT( SELE, NEXT = 1 ) / ID = 8 POINT( SELE, LOCA, WIND = 1 ) 0.364583, 0.35119 / ID = 9 CURVE( ADD ) CURVE( SELE, PWIN, WIND = 1 ) 0.330357, 0.345238, 0.394345, 0.269841 CURVE( DELE ) POINT( SELE, LOCA, WIND = 1 ) 0.125, 0.430556 / ID = 4 0.921131, 0.448413 / ID = 5 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.114583, 0.539683 / ID = 11 0.940476, 0.525794 / ID = 12 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.928571, 0.452381 / ID = 5 0.927083, 0.539683 / ID = 12
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150 Appendix A: (Continued) CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.147321, 0.452381 0.111607, 0.46627 / ID = 4 0.123512, 0.539683 / ID = 11 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.55506, 0.472222 / ID = 2 POINT( DELE ) POINT( SELE, LOCA, WIND = 1 ) 0.424107, 0.472222 / ID = 3 POINT( DELE ) POINT( SELE, LOCA, WIND = 1 ) 0.0669643, 0.462302 / ID = 1 0.974702, 0.464286 / ID = 4 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.0595238, 0.531746 / ID = 8 0.962798, 0.539683 / ID = 11 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.373512, 0.329365 / ID = 9 0.21875, 0.343254 / ID = 8 0.36756, 0.700397 / ID = 13 CURVE( ADD, ELLI, ANG2 = 90 ) POINT( SELE, LOCA, WIND = 1 ) 0.642857, 0.329365 / ID = 10 0.770833, 0.34127 / ID = 11 0.63244, 0.694444 / ID = 14 CURVE( ADD, ELLI, ANG2 = 90 ) POINT( SELE, LOCA, WIND = 1 ) 0.376488, 0.728175
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151 Appendix A: (Continued) / ID = 13 0.650298, 0.706349 / ID = 14 CURVE( ADD ) CURVE( SELE, LOCA, WIND = 1 ) 0.517857, 0.349206 / ID = 13 CURVE( DELE ) POINT( SELE, LOCA, WIND = 1 ) 0.366071, 0.339286 / ID = 9 0.61756, 0.345238 / ID = 10 POINT( DELE ) CURVE( SELE, LOCA, WIND = 1 ) 0.450893, 0.333333 / ID = 2 0.188988, 0.456349 / ID = 1 0.340774, 0.642857 / ID = 4 CURVE( SELE, LOCA, WIND = 1 ) 0.412202, 0.587302 / ID = 3 SURFACE( ADD, WIRE, EDG1 = 1, EDG2 = 1, EDG3 = 1, EDG4 = 1 ) CURVE( SELE, LOCA, WIND = 1 ) 0.665179, 0.420635 / ID = 8 0.227679, 0.521825 / ID = 11 0.391369, 0.666667 / ID = 9 CURVE( SELE, LOCA, WIND = 1 ) 0.397321, 0.396825 / ID = 10 SURFACE( ADD, WIRE, EDG1 = 1, EDG2 = 1, EDG3 = 1, EDG4 = 1) CURVE( SELE, PWIN, WIND = 1 ) 0.400298, 0.31746, 0.383929, 0.240079 CURVE( SELE, PWIN, WIND = 1 ) 0.21875, 0.305556, 0.264881, 0.30754 CURVE( SELE, PWIN, WIND = 1 ) 0.199405, 0.394841, 0.293155, 0.43254 CURVE( SELE, PWIN, WIND = 1 ) 0.470238, 0.757937, 0.489583, 0.654762
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152 Appendix A: (Continued) CURVE( SELE, PWIN, WIND = 1 ) 0.55506, 0.609127, 0.818452, 0.56746 CURVE( SELE, PWIN, WIND = 1 ) 0.75, 0.311508, 0.796131, 0.305556 SURFACE( ADD, WIRE, EDG1 = 1, EDG2 = 2, EDG3 = 1, EDG4 = 2) CURVE( SELE, PWIN, WIND = 1 ) 0.495536, 0.329365, 0.486607, 0.251984 CURVE( SELE, PWIN, WIND = 1 ) 0.215774, 0.305556, 0.293155, 0.301587 CURVE( SELE, PWIN, WIND = 1 ) 0.183036, 0.414683, 0.303571, 0.456349 CURVE( SELE, PWIN, WIND = 1 ) 0.516369, 0.771825, 0.535714, 0.626984 CURVE( SELE, PWIN, WIND = 1 ) 0.577381, 0.595238, 0.815476, 0.563492 CURVE( SELE, PWIN, WIND = 1 ) 0.745536, 0.305556, 0.796131, 0.301587 SURFACE( ADD, WIRE, EDG1 = 1, EDG2 = 2, EDG3 = 1, EDG4 = 2) SURFACE( SELE, LOCA, WIND = 1 ) 0.522321, 0.684524 SURFACE( DELE ) CURVE( SELE, LOCA, WIND = 1 ) 0.537202, 0.710317 / ID = 16 CURVE( DELE ) CURVE( SELE, LOCA, WIND = 1 ) 0.339286, 0.678571 / ID = 14 CURVE( DELE ) CURVE( SELE, LOCA, WIND = 1 ) 0.699405, 0.672619 / ID = 15 CURVE( DELE ) CURVE( SELE, LOCA, WIND = 1 ) 0.376488, 0.587302 0.407738, 0.581349 / ID = 11 CURVE( DELE ) CURVE( SELE, LOCA, WIND = 1 ) 0.299107, 0.650794 / ID = 3 CURVE( DELE ) CURVE( SELE, LOCA, WIND = 1 ) 0.494048, 0.597222 / ID = 12 CURVE( DELE )
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153 Appendix A: (Continued) POINT( SELE, LOCA, WIND = 1 ) 0.477679, 0.422619 / ID = 1 0.473214, 0.65873 / ID = 8 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.46875, 0.31746 / ID = 1 POINT( SELE, LOCA, WIND = 1 ) 0.488095, 0.363095 / ID = 4 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.354167, 0.702381 / ID = 13 0.630952, 0.702381 / ID = 14 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.520833, 0.482143 / ID = 4 0.525298, 0.736111 / ID = 11 CURVE( ADD ) POINT( ADD, COOR, X = 6.27, Y = 7.5 ) POINT( ADD, COOR, X = 75, Y = 7.5 ) POINT( ADD, COOR, X = 195, Y = 7.5 ) POINT( SELE, LOCA, WIND = 1 ) 0.380952, 0.34127 / ID = 17 POINT( SELE, LOCA, WIND = 1 ) 0.43006, 0.14881 / ID = 8 POINT( SELE, LOCA, WIND = 1 ) 0.447917, 0.595238 / ID = 13 CURVE( ADD, ELLI, ANG2 = 90 ) CURVE( SELE, LOCA, WIND = 1 ) 0.19494, 0.482143 / ID = 15 CURVE( DELE ) POINT( SELE, LOCA, WIND = 1 ) 0.471726, 0.464286 / ID = 16 POINT( DELE )
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154 Appendix A: (Continued) POINT( SELE, LOCA, WIND = 1 ) 0.636905, 0.355159 0.629464, 0.331349 / ID = 18 0.63244, 0.694444 / ID = 14 0.770833, 0.35119 / ID = 11 CURVE( ADD, ELLI, ANG2 = 90 ) POINT( SELE, LOCA, WIND = 1 ) 0.394345, 0.331349 / ID = 17 POINT( DELE ) POINT( ADD, COOR, X = 65, Y = 7.5 ) POINT( SELE, LOCA, WIND = 1 ) 0.376488, 0.337302 / ID = 19 0.22619, 0.345238 / ID = 8 0.360119, 0.698413 / ID = 13 CURVE( ADD, ELLI, ANG2 = 90 ) CURVE( SELE, LOCA, WIND = 1 ) 0.4375, 0.297619 / ID = 12 CURVE( SELE, LOCA, WIND = 1 ) 0.40625, 0.196429 / ID = 7 0.388393, 0.414683 / ID = 16 CURVE( SELE, LOCA, WIND = 1 ) 0.50744, 0.712302 / ID = 13 0.733631, 0.589286 / ID = 15 CURVE( SELE, LOCA, WIND = 1 ) 0.443452, 0.496032 / ID = 14 SURFACE( ADD, WIRE, EDG1 = 1, EDG2 = 2, EDG3 = 1, EDG4 = 2) CURVE( SELE, PWIN, WIND = 1 ) 0.547619, 0.799603, 0.572917, 0.212302 MEDGE( ADD, SUCC, INTE = 30, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, PWIN, WIND = 1 ) 0.175595, 0.492063, 0.886905, 0.52381 MEDGE( ADD, SUCC, INTE = 25, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, PWIN, WIND = 1 )
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155 Appendix A: (Continued) 0.209821, 0.305556, 0.796131, 0.301587 MEDGE( ADD, SUCC, INTE = 8, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, PWIN, WIND = 1 ) 0.956845, 0.303571, 1, 0.311508 CURVE( SELE, PWIN, WIND = 1 ) 0.0133929, 0.303571, 0.0729167, 0.303571 MEDGE( ADD, SUCC, INTE = 8, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, PWIN, WIND = 1 ) 0.0892857, 0.355159, 0.122024, 0.240079 CURVE( SELE, PWIN, WIND = 1 ) 0.880952, 0.388889, 0.885417, 0.25 MEDGE( ADD, SUCC, INTE = 15, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, LOCA, WIND = 1 ) 0.38244, 0.428571 / ID = 2 0.241071, 0.525794 / ID = 1 0.327381, 0.746032 / ID = 4 CURVE( SELE, LOCA, WIND = 1 ) 0.473214, 0.392857 / ID = 7 MLOOP( ADD, MAP, VISI, NOSH, EDG1 = 1, EDG2 = 1, EDG3 = 1, EDG4 = 1 ) CURVE( SELE, LOCA, WIND = 1 ) 0.745536, 0.21627 / ID = 8 0.366071, 0.343254 / ID = 14 0.46131, 0.507937 / ID = 9 CURVE( SELE, LOCA, WIND = 1 ) 0.526786, 0.321429 / ID = 10 MLOOP( ADD, MAP, VISI, NOSH, EDG1 = 1, EDG2 = 1, EDG3 = 1, EDG4 = 1 ) CURVE( SELE, LOCA, WIND = 1 ) 0.425595, 0.311508 / ID = 12 CURVE( SELE, LOCA, WIND = 1 ) 0.482143, 0.200397 / ID = 7 0.465774, 0.456349 / ID = 16 CURVE( SELE, LOCA, WIND = 1 ) 0.526786, 0.71627
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156 Appendix A: (Continued) / ID = 13 0.706845, 0.599206 / ID = 15 CURVE( SELE, LOCA, WIND = 1 ) 0.526786, 0.186508 / ID = 14 MLOOP( ADD, MAP, VISI, NOSH, EDG1 = 1, EDG2 = 1, EDG3 = 1, EDG4 = 1 ) CURVE( SELE, LOCA, WIND = 1 ) 0.483631, 0.295635 / ID = 12 CURVE( SELE, LOCA, WIND = 1 ) 0.477679, 0.168651 / ID = 7 0.455357, 0.422619 / ID = 16 CURVE( SELE, LOCA, WIND = 1 ) 0.528274, 0.718254 / ID = 13 0.720238, 0.623016 / ID = 15 CURVE( SELE, LOCA, WIND = 1 ) 0.53869, 0.375 / ID = 14 MLOOP( ADD, MAP, VISI, NOSH, EDG1 = 1, EDG2 = 2, EDG3 = 1, EDG4 = 2 ) CURVE( SELE, LOCA, WIND = 1 ) 0.724702, 0.369048 / ID = 8 0.340774, 0.505952 / ID = 14 0.511905, 0.638889 / ID = 9 CURVE( SELE, LOCA, WIND = 1 ) 0.514881, 0.478175 / ID = 10 CURVE( SELE, LOCA, WIND = 1 ) 0.55506, 0.140873 / ID = 2 0.428571, 0.331349 / ID = 1 0.540179, 0.517857 / ID = 4 CURVE( SELE, LOCA, WIND = 1 ) 0.421131, 0.255952 / ID = 7
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157 Appendix A: (Continued) MFACE( WIRE, EDG1 = 1, EDG2 = 1, EDG3 = 1, EDG4 = 1 ) CURVE( SELE, LOCA, WIND = 1 ) 0.485119, 0.299603 / ID = 12 CURVE( SELE, LOCA, WIND = 1 ) 0.410714, 0.230159 / ID = 7 0.400298, 0.454365 / ID = 16 CURVE( SELE, LOCA, WIND = 1 ) 0.47619, 0.706349 / ID = 13 0.754464, 0.579365 / ID = 15 CURVE( SELE, PWIN, WIND = 1 ) 0.755952, 0.305556, 0.796131, 0.303571 MFACE( WIRE, EDG1 = 1, EDG2 = 2, EDG3 = 1, EDG4 = 2 ) MFACE( SELE, PWIN, WIND = 1 ) 0.21131, 0.367063, 0.261905, 0.240079 MFACE( SELE, PWIN, WIND = 1 ) 0.809524, 0.365079, 0.840774, 0.259921 MFACE( MESH, MAP, ENTI = "h2" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.014881, 0.303571, 0.0431548, 0.299603 ELEMENT( SETD, EDGE, NODE = 2 ) MEDGE( MESH, MAP, ENTI = "inlet" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.962798, 0.305556, 0.991071, 0.303571 MEDGE( MESH, MAP, ENTI = "outlet" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.136905, 0.30754, 0.142857, 0.28373 MEDGE( SELE, PWIN, WIND = 1 ) 0.313988, 0.303571, 0.315476, 0.28373 MEDGE( SELE, PWIN, WIND = 1 ) 0.84375, 0.299603, 0.846726, 0.277778 MEDGE( MESH, MAP, ENTI = "axis" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.233631, 0.549603, 0.263393, 0.549603 MEDGE( SELE, PWIN, WIND = 1 ) 0.431548, 0.767857, 0.450893, 0.680556 MEDGE( SELE, PWIN, WIND = 1 ) 0.584821, 0.636905, 0.813988, 0.579365 UTILITY( UNSE, ALL ) MEDGE( SELE, PWIN, WIND = 1 ) 0.191964, 0.59127, 0.303571, 0.575397 MEDGE( MESH, MAP, ENTI = "w1" )
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158 Appendix A: (Continued) MEDGE( SELE, PWIN, WIND = 1 ) 0.491071, 0.748016, 0.494048, 0.686508 MEDGE( MESH, MAP, ENTI = "w2" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.644345, 0.517857, 0.806548, 0.484127 MEDGE( MESH, MAP, ENTI = "w3" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.139881, 0.305556, 0.14881, 0.337302 MEDGE( MESH, MAP, ENTI = "a" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.828869, 0.309524, 0.839286, 0.335317 MEDGE( MESH, MAP, ENTI = "b" ) END( ) FIPREP( ) ENTITY( ADD, NAME = "h2", FLUI, PROP = "h2" ) ENTITY( ADD, NAME = "w1", WALL ) ENTITY( ADD, NAME = "w2", WALL ) ENTITY( ADD, NAME = "w3", WALL ) ENTITY( ADD, NAME = "a", WALL ) ENTITY( ADD, NAME = "b", WALL ) ENTITY( ADD, NAME = "inlet", PLOT ) ENTITY( ADD, NAME = "outlet", PLOT ) ENTITY( ADD, NAME = "axis", PLOT ) CONDUCTIVITY( ADD, SET = "h2", CONS = 0.000236616 ) DENSITY( ADD, SET = "h2", CONS = 0.05895 ) SPECIFICHEAT( ADD, SET = "h2", CONS = 4.45 ) VISCOSITY( ADD, SET = "h2", CONS = 7.52e06 ) BCFLUX( ADD, HEAT, ENTI = "w1", CONS = 0.000056281 ) BCFLUX( ADD, HEAT, ENTI = "w2", CONS = 0.000056281 ) BCFLUX( ADD, HEAT, ENTI = "w3", CONS = 0.000056281 ) BCFLUX( ADD, HEAT, ENTI = "a", CONS = 0 ) BCFLUX( ADD, HEAT, ENTI = "b", CONS = 0 ) BCNODE( ADD, VELO, ENTI = "w1", CONS = 0 ) BCNODE( ADD, VELO, ENTI = "w2", CONS = 0 ) BCNODE( ADD, VELO, ENTI = "w3", CONS = 0 ) BCNODE( ADD, VELO, ENTI = "a", CONS = 0 ) BCNODE( ADD, VELO, ENTI = "b", CONS = 0 ) BCNODE( ADD, URC, ENTI = "inlet", CONS = 0 ) BCNODE( ADD, URC, ENTI = "axis", CONS = 0 ) BCNODE( ADD, UZC, ENTI = "inlet", CONS = 1 ) BCNODE( ADD, TEMP, ENTI = "inlet", CONS = 25 ) CLIPPING( ADD, MINI ) 0, 0, 0, 0, 25, 0 / ***If the flow is turbulent and kmodel is used then add the following lines of code VISCOSITY( ADD, SET = "h2", TWO, CONS = 7.52e6 )
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159 Appendix A: (Continued) ICNODE( KINE, CONS = 0.003, ALL ) ICNODE( DISS, CONS = 0.00045, ALL ) BCNODE( KINE, CONS = 0.001, ENTI = "inlet" ) BCNODE( DISS, CONS = 0.00045, ENTI = "inlet" ) /**** DATAPRINT( ADD, CONT ) EXECUTION( ADD, NEWJ ) OPTIONS( ADD, UPWI ) POSTPROCESS( ADD, ALL, NOPT, NOPA ) PRESSURE( ADD, PENA = 1e07, DISC ) PRINTOUT( ADD, NONE, BOUN ) PROBLEM( ADD, AXI, INCO, STEA, TURB, NONL, NEWT, MOME, ENER, FIXE, SING ) RENUMBER( ADD, PROF ) SOLUTION( ADD, N.R. = 10000, ACCF = 0 ) TURBOPTIONS( ADD, STAN ) UPWINDING( ADD ) 1, 1, 0, 0, 2, 0, 1, 1 END( ) CREATE( FISO )
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160 Appendix B: Computation of fluid (liqui d and vapor hydrogen) circulation in a hydrogen storage tank FIGEN( 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) POINT( ADD, COOR, X = 0, Y = 0 ) POINT( ADD, COOR, X = 65, Y = 0 ) POINT( ADD, COOR, X = 195, Y = 0 ) POINT( ADD, COOR, X = 260, Y = 0 ) POINT( ADD, COOR, X = 260, Y = 7.5 ) POINT( ADD, COOR, X = 195, Y = 150 ) POINT( ADD, COOR, X = 65, Y = 150 ) POINT( ADD, COOR, X = 0, Y = 7.5 ) POINT( SELE, LOCA, WIND = 1 ) 0.0269058, 0.125561 / ID = 1 0.958146, 0.13154 / ID = 4 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.964126, 0.135526 / ID = 4 0.971599, 0.163428 / ID = 4 0.982063, 0.187344 / ID = 5 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.278027, 0.860987 / ID = 7 0.738416, 0.858994 / ID = 6 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.0313901, 0.13154 / ID = 1 0.0224215, 0.203288 / ID = 8 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.269058, 0.13154 / ID = 2 0.0254111, 0.107623 / ID = 1 0.261584, 0.841056 / ID = 7
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161 Appendix B: (Continued) CURVE( ADD, ELLI, ANG2 = 90 ) POINT( SELE, LOCA, WIND = 1 ) 0.748879, 0.111609 / ID = 3 0.982063, 0.115595 / ID = 4 0.736921, 0.864973 / ID = 6 CURVE( ADD, ELLI, ANG2 = 90 ) CURVE( SELE, LOCA, WIND = 1 ) 0.0224215, 0.169407 / ID = 1 CURVE( SELE, NEXT = 1 ) / ID = 4 CURVE( DELE ) CURVE( SELE, LOCA, WIND = 1 ) 0.961136, 0.1714 / ID = 1 CURVE( SELE, NEXT = 1 ) / ID = 2 CURVE( DELE ) CURVE( SELE, ALL ) CURVE( DELE ) POINT( ADD, COOR, X = 65, Y = 7.5 ) POINT( ADD, COOR, X = 195, Y = 7.5 ) POINT( SELE, LOCA, WIND = 1 ) 0.0328849, 0.119581 / ID = 1 0.0298954, 0.179372 / ID = 8 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.267564, 0.878924 / ID = 7 0.736921, 0.858994 / ID = 6 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.974589, 0.113602 / ID = 4 0.980568, 0.181365 / ID = 5 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.0224215, 0.115595 / ID = 1
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162 Appendix B: (Continued) 0.970105, 0.111609 / ID = 4 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.251121, 0.197309 / ID = 9 0.019432, 0.193323 / ID = 8 0.263079, 0.851021 / ID = 7 CURVE( ADD, ELLI, ANG2 = 90 ) POINT( SELE, LOCA, WIND = 1 ) 0.7429, 0.199302 / ID = 10 0.735426, 0.851021 / ID = 6 0.967115, 0.207275 / ID = 5 CURVE( ADD, ELLI, ANG2 = 90 ) POINT( ADD, COOR, X = 130, Y = 0 ) POINT( ADD, COOR, X = 130, Y = 7.5 ) POINT( ADD, COOR, X = 130, Y = 150 ) POINT( SELE, LOCA, WIND = 1 ) 0.497758, 0.117588 / ID = 11 0.502242, 0.851021 / ID = 13 CURVE( ADD ) CURVE( SELE, LOCA, WIND = 1 ) 0.668161, 0.868959 / ID = 2 POINT( SELE, LOCA, WIND = 1 ) 0.512706, 0.870952 / ID = 13 CURVE( SPLI ) CURVE( SELE, LOCA, WIND = 1 ) 0.674141, 0.117588 / ID = 4 POINT( SELE, LOCA, WIND = 1 ) 0.497758, 0.119581 / ID = 11 CURVE( SPLI ) CURVE( SELE, LOCA, WIND = 1 ) 0.5142, 0.296961 / ID = 7 POINT( SELE, LOCA, WIND = 1 )
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163 Appendix B: (Continued) 0.512706, 0.199302 / ID = 12 CURVE( SPLI ) CURVE( SELE, LOCA, WIND = 1 ) 0.363229, 0.860987 / ID = 8 0.499253, 0.667663 / ID = 13 0.506726, 0.203288 / ID = 12 0.402093, 0.15147 / ID = 10 0.038864, 0.173393 / ID = 1 0.0373692, 0.211261 / ID = 5 SURFACE( ADD, WIRE, EDG1 = 1, EDG2 = 2, EDG3 = 1, EDG4 = 2) CURVE( SELE, LOCA, WIND = 1 ) 0.597907, 0.831091 / ID = 9 0.896861, 0.623817 / ID = 6 0.989537, 0.187344 / ID = 3 0.914798, 0.155456 / ID = 11 0.511211, 0.173393 / ID = 12 0.502242, 0.209268 / ID = 13 SURFACE( ADD, WIRE, EDG1 = 1, EDG2 = 2, EDG3 = 1, EDG4 = 2) CURVE( SELE, PWIN, WIND = 1 ) 0.0852018, 0.613852, 0.935725, 0.542103 CURVE( SELE, PWIN, WIND = 1 ) 0.0941704, 0.675635, 0.130045, 0.617838 MEDGE( ADD, SUCC, INTE = 30, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, PWIN, WIND = 1 ) 0.301943, 0.815147, 0.331839, 0.0976582 CURVE( SELE, PWIN, WIND = 1 ) 0.593423, 0.884903, 0.690583, 0.0976582 CURVE( SELE, PWIN, WIND = 1 ) 0.342302, 0.908819, 0.364723, 0.773293 MEDGE( ADD, SUCC, INTE = 25, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, PWIN, WIND = 1 ) 0.019432, 0.149477, 0.985052, 0.149477 MEDGE( ADD, SUCC, INTE = 8, RATI = 0, 2RAT = 0, PCEN = 0 )
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164 Appendix B: (Continued) CURVE( SELE, LOCA, WIND = 1 ) 0.252616, 0.129547 / ID = 10 0.0403587, 0.159442 / ID = 1 0.0313901, 0.245142 / ID = 5 0.376682, 0.860987 / ID = 8 0.499253, 0.673642 / ID = 13 0.508221, 0.19133 / ID = 12 MLOOP( ADD, MAP, VISI, NOSH, EDG1 = 1, EDG2 = 2, EDG3 = 1, EDG4 = 2 ) CURVE( SELE, LOCA, WIND = 1 ) 0.669656, 0.125561 / ID = 11 0.503737, 0.153463 / ID = 10 0.502242, 0.193323 / ID = 12 UTILITY( UNSE, LAST ) UTILITY( UNSE, LAST ) CURVE( SELE, LOCA, WIND = 1 ) 0.506726, 0.169407 / ID = 10 CURVE( SELE, NEXT = 1 ) / ID = 12 CURVE( SELE, LOCA, WIND = 1 ) 0.494768, 0.386647 / ID = 13 0.659193, 0.878924 / ID = 9 0.856502, 0.691579 0.925262, 0.516193 / ID = 6 0.974589, 0.175386 / ID = 3 MLOOP( ADD, MAP, VISI, NOSH, EDG1 = 1, EDG2 = 2, EDG3 = 1, EDG4 = 2 ) CURVE( SELE, LOCA, WIND = 1 ) 0.38565, 0.847035 / ID = 8 0.509716, 0.564026 / ID = 13
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165 Appendix B: (Continued) 0.4858, 0.155456 / ID = 10 CURVE( SELE, NEXT = 1 ) / ID = 11 CURVE( SELE, NEXT = 1 ) / ID = 12 CURVE( SELE, LOCA, WIND = 1 ) 0.400598, 0.119581 / ID = 10 0.0418535, 0.159442 / ID = 1 0.038864, 0.251121 / ID = 5 MFACE( WIRE, EDG1 = 1, EDG2 = 2, EDG3 = 1, EDG4 = 2 ) CURVE( SELE, LOCA, WIND = 1 ) 0.639761, 0.866966 / ID = 9 0.899851, 0.695566 / ID = 6 0.979073, 0.159442 / ID = 3 0.908819, 0.159442 / ID = 11 0.503737, 0.163428 / ID = 10 0.499253, 0.243149 / ID = 13 UTILITY( UNSE, LAST ) UTILITY( UNSE, LAST ) CURVE( SELE, LOCA, WIND = 1 ) 0.515695, 0.167414 / ID = 10 CURVE( SELE, NEXT = 1 ) / ID = 13 CURVE( SELE, NEXT = 1 ) / ID = 12 CURVE( SELE, LOCA, WIND = 1 ) 0.502242, 0.45441 / ID = 13 MFACE( WIRE, EDG1 = 1, EDG2 = 2, EDG3 = 1, EDG4 = 2 ) POINT( ADD, COOR, X = 100, Y = 0 ) POINT( ADD, COOR, X = 100, Y = 7.5 ) POINT( ADD, COOR, X = 360, Y = 7.5 ) POINT( ADD, COOR, X = 360, Y = 0 ) POINT( SELE, LOCA, WIND = 1 ) 0.0179372, 0.269058
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166 Appendix B: (Continued) / ID = 14 0.0269058, 0.348779 / ID = 15 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.0239163, 0.267065 / ID = 14 0.215247, 0.273044 / ID = 1 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.0224215, 0.330842 / ID = 14 POINT( SELE, NEXT = 1 ) / ID = 15 POINT( SELE, LOCA, WIND = 1 ) 0.224215, 0.3428 / ID = 8 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.77429, 0.273044 / ID = 4 0.971599, 0.269058 / ID = 17 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.971599, 0.269058 / ID = 17 0.974589, 0.340807 / ID = 16 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.77429, 0.334828 / ID = 5 0.983558, 0.332835 / ID = 16 CURVE( ADD ) CURVE( SELE, LOCA, WIND = 1 ) 0.0747384, 0.294968 / ID = 15 0.0134529, 0.300947 / ID = 14 0.0523169, 0.306926 / ID = 16 0.22272, 0.296961 / ID = 1
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167 Appendix B: (Continued) SURFACE( ADD, WIRE, EDG1 = 1, EDG2 = 2, EDG3 = 1, EDG4 = 2) CURVE( SELE, LOCA, WIND = 1 ) 0.116592, 0.285002 / ID = 15 0.0239163, 0.304933 / ID = 14 0.0463378, 0.312905 / ID = 16 0.213752, 0.296961 / ID = 1 SURFACE( ADD, WIRE, EDG1 = 1, EDG2 = 1, EDG3 = 1, EDG4 = 1) CURVE( SELE, LOCA, WIND = 1 ) 0.853513, 0.283009 / ID = 17 0.77728, 0.304933 / ID = 3 0.798206, 0.318884 / ID = 6 CURVE( SELE, NEXT = 1 ) / ID = 19 CURVE( SELE, LOCA, WIND = 1 ) 0.983558, 0.298954 / ID = 18 SURFACE( ADD, WIRE, EDG1 = 1, EDG2 = 1, EDG3 = 1, EDG4 = 1) CURVE( SELE, PWIN, WIND = 1 ) 0.121076, 0.350772, 0.140508, 0.267065 CURVE( SELE, PWIN, WIND = 1 ) 0.862481, 0.320877, 0.884903, 0.283009 MEDGE( ADD, SUCC, INTE = 15, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, PWIN, WIND = 1 ) 0.973094, 0.300947, 0.985052, 0.300947 CURVE( SELE, PWIN, WIND = 1 ) 0.0239163, 0.30294, 0.0373692, 0.304933 CURVE( SELE, PWIN, WIND = 1 ) 0.0298954, 0.30294, 0.0104634, 0.30294 MEDGE( ADD, SUCC, INTE = 8, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, LOCA, WIND = 1 ) 0.112108, 0.27703 / ID = 15 0.0373692, 0.296961 / ID = 14 0.0538117, 0.318884 / ID = 16 0.239163, 0.312905 / ID = 1
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168 Appendix B: (Continued) MLOOP( ADD, MAP, VISI, NOSH, EDG1 = 1, EDG2 = 1, EDG3 = 1, EDG4 = 1 ) CURVE( SELE, LOCA, WIND = 1 ) 0.87145, 0.298954 / ID = 17 0.763827, 0.310912 / ID = 3 0.801196, 0.32287 / ID = 19 0.956652, 0.310912 / ID = 18 MLOOP( ADD, MAP, VISI, NOSH, EDG1 = 1, EDG2 = 1, EDG3 = 1, EDG4 = 1 ) CURVE( SELE, LOCA, WIND = 1 ) 0.0896861, 0.273044 / ID = 15 0.0298954, 0.304933 / ID = 14 0.044843, 0.32287 / ID = 16 0.230194, 0.300947 / ID = 1 MFACE( WIRE, EDG1 = 1, EDG2 = 1, EDG3 = 1, EDG4 = 1 ) CURVE( SELE, LOCA, WIND = 1 ) 0.890882, 0.286996 / ID = 17 0.747384, 0.318884 / ID = 3 0.829596, 0.316891 / ID = 19 0.971599, 0.300947 / ID = 18 MFACE( WIRE, EDG1 = 1, EDG2 = 1, EDG3 = 1, EDG4 = 1 ) MFACE( SELE, LOCA, WIND = 1 ) 0.139013, 0.312905 / ID = 3 MFACE( MESH, MAP, ENTI = "liq" ) MFACE( SELE, LOCA, WIND = 1 ) 0.328849, 0.304933 / ID = 1 MFACE( MESH, MAP, ENTI = "liq" ) MFACE( SELE, LOCA, WIND = 1 ) 0.587444, 0.306926 / ID = 2 MFACE( MESH, MAP, ENTI = "vap" ) MFACE( SELE, LOCA, WIND = 1 )
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169 Appendix B: (Continued) 0.838565, 0.296961 / ID = 4 MFACE( MESH, MAP, ENTI = "vap" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.167414, 0.300947, 0.174888, 0.27703 MEDGE( SELE, PWIN, WIND = 1 ) 0.298954, 0.298954, 0.315396, 0.271051 MEDGE( SELE, PWIN, WIND = 1 ) 0.571001, 0.300947, 0.578475, 0.283009 MEDGE( SELE, PWIN, WIND = 1 ) 0.860987, 0.296961, 0.863976, 0.269058 ELEMENT( SETD, EDGE, NODE = 2 ) MEDGE( MESH, MAP, ENTI = "axis" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.971599, 0.30294, 0.985052, 0.300947 MEDGE( MESH, MAP, ENTI = "outlet" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.0224215, 0.30294, 0.0284006, 0.304933 MEDGE( MESH, MAP, ENTI = "inlet" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.127055, 0.306926, 0.136024, 0.338814 MEDGE( MESH, MAP, ENTI = "1" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.874439, 0.326856, 0.883408, 0.298954 MEDGE( MESH, MAP, ENTI = "2" ) MEDGE( MESH, MAP, ENTI = "2" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.239163, 0.570005, 0.281016, 0.506228 MEDGE( MESH, MAP, ENTI = "w1" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.411061, 0.725461, 0.409567, 0.651719 MEDGE( MESH, MAP, ENTI = "w2" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.566517, 0.741405, 0.588939, 0.62581 MEDGE( MESH, MAP, ENTI = "w3" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.727952, 0.512207, 0.850523, 0.500249 MEDGE( MESH, MAP, ENTI = "w4" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.476831, 0.458396, 0.523169, 0.416542 MEDGE( SELE, PWIN, WIND = 1 ) 0.494768, 0.304933, 0.511211, 0.308919 MEDGE( MESH, MAP, ENTI = "joint" ) END( ) FIPREP( )
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170 Appendix B: (Continued) ENTITY( ADD, NAME = "liq", FLUI, PROP = "liq", MDEN = "liq", MVIS = "liq", MSPH = "liq", MCON = "liq" ) ENTITY( ADD, NAME = "vap", FLUI, PROP = "vap", MDEN = "vap", MVIS = "vap", MSPH = "vap", MCON = "vap" ) ENTITY( ADD, NAME = "axis", PLOT ) ENTITY( ADD, NAME = "outlet", PLOT ) ENTITY( ADD, NAME = "inlet", PLOT ) ENTITY( ADD, NAME = 1, PLOT ) ENTITY( ADD, NAME = 2, PLOT ) ENTITY( ADD, NAME = "w1", WALL ) ENTITY( ADD, NAME = "w2", WALL ) ENTITY( ADD, NAME = "w3", WALL ) ENTITY( ADD, NAME = "w4", WALL ) ENTITY( ADD, NAME = "joint", PLOT, ATTA = "vap", NATT = "liq" ) CONDUCTIVITY( ADD, SET = "liq", CONS = 0.000255 ) CONDUCTIVITY( ADD, SET = "vap", CONS = 9.56e05 ) DENSITY( ADD, SET = "liq", CONS = 0.066105 ) DENSITY( ADD, SET = "vap", CONS = 0.0075 ) SPECIFICHEAT( ADD, SET = "liq", CONS = 3.0087 ) SPECIFICHEAT( ADD, SET = "vap", CONS = 3.5 ) VISCOSITY( ADD, SET = "vap", CONS = 2.25e05 ) VISCOSITY( ADD, SET = "liq", CONS = 9.99e05 ) BCNODE( ADD, VELO, ENTI = "w1", CONS = 0 ) BCNODE( ADD, VELO, ENTI = "w2", CONS = 0 ) BCNODE( ADD, VELO, ENTI = "w3", CONS = 0 ) BCNODE( ADD, VELO, ENTI = "w4", CONS = 0 ) BCNODE( ADD, VELO, ENTI = "1", CONS = 0 ) BCNODE( ADD, VELO, ENTI = "2", CONS = 0 ) BCNODE( ADD, URC, ENTI = "inlet", CONS = 0 ) BCNODE( ADD, URC, ENTI = "axis", CONS = 0 ) BCNODE( ADD, UZC, ENTI = "inlet", CONS = 1 ) BCNODE( ADD, TEMP, ENTI = "inlet", CONS = 25 ) CLIPPING( ADD, MINI ) 0, 0, 0, 0, 25, 0 / ***If the flow is turbulent and kmodel is used then add the following lines of code VISCOSITY( ADD, SET = "liq", TWO, CONS = 9.99e5 ) VISCOSITY( ADD, SET = "vap", TWO, CONS = 2.25e5 ) ICNODE( KINE, CONS = 0.003, ALL ) ICNODE( DISS, CONS = 0.00045, ALL ) BCNODE( KINE, CONS = 0.001, ENTI = "inlet" ) BCNODE( DISS, CONS = 0.00045, ENTI = "inlet" )
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171 Appendix B: (Continued) /**** DATAPRINT( ADD, CONT ) EDDYVISCOSITY( ADD, SPEZ ) EXECUTION( ADD, NEWJ ) GRAVITY( ADD, MAGN = 980, THET = 270, PHI = 0 ) OPTIONS( ADD, UPWI ) POSTPROCESS( ADD, ALL, NOPT, NOPA ) PRESSURE( ADD, PENA = 1e07, DISC ) PRINTOUT( ADD, NONE, BOUN ) PROBLEM( ADD, AXI, INCO, STEA, TURB, NONL, NEWT, MOME, BUOY, FIXE, SING ) RELAXATION( ADD, RADI = 0.1, VELO = 0.1, TEMP = 0.1, SPEC = 0, STRU = 0.1 ) RENUMBER( ADD, PROF ) TURBOPTIONS( ADD, STAN ) UPWINDING( ADD, STRE ) 1, 1, 0, 0, 2, 0, 1, 1 BCNODE( ADD, UZC, ENTI = "joint", CONS = 0.1 ) BCFLUX( ADD, HEAT, ENTI = "w1", CONS = 0.007366 ) BCFLUX( ADD, HEAT, ENTI = "w2", CONS = 0.007366 ) BCFLUX( ADD, HEAT, ENTI = "w3", CONS = 0.007366 ) BCFLUX( ADD, HEAT, ENTI = "w4", CONS = 0.007366 ) BCNODE( ADD, UZC, ENTI = "joint", CONS = 0.022 ) BCFLUX( ADD, HEAT, ENTI = "1", CONS = 0 ) BCFLUX( ADD, HEAT, ENTI = "2", CONS = 0 ) SOLUTION( ADD, N.R. = 1000, VELC = 0.015, RESC = 0.015, PREC = 21, ACCF = 0,NOLI, PPRO ) END( ) CREATE( FISO )
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172 Appendix C: Computation of heat transfer during confin ed liquid jet impingement with uniform heat source FIGEN( 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 ) 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 POINT( ADD, COOR, X = 0, Y = 0 ) POINT( ADD, COOR, X = 0.8, Y = 0 ) POINT( ADD, COOR, X = 0.8, Y = 0.32 ) POINT( ADD, COOR, X = 0, Y = 0.32 ) POINT( ADD, COOR, X = 0.16, Y = 0.32 ) POINT( ADD, COOR, X = 0, Y = 0.05 ) POINT( ADD, COOR, X = 0.16, Y = 0.05 ) POINT( ADD, COOR, X = 0.224, Y = 0.05 ) POINT( ADD, COOR, X = 0.288, Y = 0.05 ) POINT( ADD, COOR, X = 0.352, Y = 0.05 ) POINT( ADD, COOR, X = 0.416, Y = 0.05 ) POINT( ADD, COOR, X = 0.48, Y = 0.05 ) POINT( ADD, COOR, X = 0.544, Y = 0.05 ) POINT( ADD, COOR, X = 0.608, Y = 0.05 ) POINT( ADD, COOR, X = 0.672, Y = 0.05 ) POINT( ADD, COOR, X = 0.736, Y = 0.05 ) POINT( ADD, COOR, X = 0.8, Y = 0.05 ) WINDOW( CHAN = 1, MATR ) 1, 0, 0, 0 0, 1, 0, 0 0, 0, 1, 0 0, 0, 0, 1 0.02, 0.82, 0.18, 0.45, 0.84, 0.84 45, 45, 45, 45 POINT( SELE, LOCA, WIND = 1 ) 0.0298954, 0.19133 / ID = 11 0.0328849, 0.296961 / ID = 1 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.0328849, 0.296961 / ID = 1 0.0373692, 0.787245 / ID = 4 CURVE( ADD )
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173 Appendix C: (Continued) POINT( SELE, LOCA, WIND = 1 ) 0.995516, 0.197309 / ID = 7 0.96562, 0.296961 / ID = 2 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.971599, 0.286996 / ID = 2 0.970105, 0.7713 / ID = 3 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.0343797, 0.183358 / ID = 11 0.0657698, 0.187344 / ID = 8 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.0657698, 0.187344 / ID = 8 0.13154, 0.201295 / ID = 10 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.133034, 0.203288 / ID = 10 0.22272, 0.189337 / ID = 12 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.224215, 0.189337 / ID = 12 0.286996, 0.187344 / ID = 13 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.286996, 0.187344 / ID = 13 0.382661, 0.183358 / ID = 14 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.382661, 0.185351 / ID = 14 0.464873, 0.175386 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.361734, 0.195316 / ID = 14 0.469357, 0.19133 / ID = 15 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.449925, 0.197309
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174 Appendix C: (Continued) / ID = 15 0.532138, 0.197309 / ID = 16 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.532138, 0.197309 / ID = 16 0.594918, 0.199302 / ID = 17 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.596413, 0.199302 / ID = 17 0.668161, 0.193323 / ID = 18 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.668161, 0.195316 / ID = 18 0.7429, 0.195316 / ID = 19 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.745889, 0.195316 / ID = 19 0.843049, 0.19133 / ID = 20 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.843049, 0.19133 / ID = 20 0.899851, 0.187344 / ID = 21 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.899851, 0.187344 / ID = 21 0.967115, 0.179372 / ID = 7 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.044843, 0.279023 / ID = 1 0.953662, 0.286996 / ID = 2 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.0239163, 0.787245 / ID = 4 0.209268, 0.789238 / ID = 5 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.210762, 0.791231 / ID = 5
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175 Appendix C: (Continued) 0.976084, 0.783259 / ID = 3 CURVE( ADD ) CURVE( SELE, LOCA, WIND = 1 ) 0.524664, 0.308919 / ID = 18 0.0284006, 0.562033 / ID = 2 0.0911809, 0.77728 / ID = 19 0.310912, 0.775286 / ID = 20 0.962631, 0.512207 / ID = 4 SURFACE( ADD, WIRE, EDG1 = 1, EDG2 = 1, EDG3 = 2, EDG4 = 1 ) CURVE( SELE, LOCA, WIND = 1 ) 0.0418535, 0.245142 / ID = 1 0.130045, 0.279023 / ID = 18 0.967115, 0.251121 / ID = 3 0.949178, 0.189337 / ID = 17 0.862481, 0.185351 / ID = 16 0.783259, 0.173393 / ID = 15 0.693572, 0.187344 / ID = 13 UTILITY( UNSE, LAST ) CURVE( SELE, LOCA, WIND = 1 ) 0.732436, 0.173393 / ID = 14 0.64275, 0.189337 / ID = 13 0.571001, 0.181365 / ID = 12 0.484305, 0.179372 / ID = 11 0.42003, 0.187344 / ID = 10 0.337818, 0.181365 / ID = 9 0.282511, 0.189337 / ID = 8 0.19432, 0.173393 / ID = 7 0.124066, 0.195316 / ID = 6 0.0523169, 0.175386 / ID = 5 SURFACE( ADD, WIRE, EDG1 = 1, EDG2 = 1, EDG3 = 1, EDG4 = 13 ) CURVE( SELE, PWIN, WIND = 1 ) 0.656203, 0.281016, 0.656203, 0.281016
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176 Appendix C: (Continued) CURVE( SELE, PWIN, WIND = 1 ) 0.656203, 0.281016, 0.663677, 0.332835 MEDGE( ADD, SUCC, INTE = 125, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, PWIN, WIND = 1 ) 0.58296, 0.821126, 0.587444, 0.725461 MEDGE( ADD, SUCC, INTE = 100, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, PWIN, WIND = 1 ) 0.155456, 0.83707, 0.153961, 0.707524 MEDGE( ADD, SUCC, INTE = 25, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, PWIN, WIND = 1 ) 0.125561, 0.227205, 0.955157, 0.169407 MEDGE( ADD, SUCC, INTE = 10, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, PWIN, WIND = 1 ) 0.0403587, 0.223219, 0.044843, 0.181365 MEDGE( ADD, SUCC, INTE = 5, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, PWIN, WIND = 1 ) 0.0134529, 0.546089, 1, 0.476333 MEDGE( ADD, SUCC, INTE = 50, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, PWIN, WIND = 1 ) 0.0119581, 0.249128, 1, 0.233184 MEDGE( ADD, SUCC, INTE = 10, RATI = 0, 2RAT = 0, PCEN = 0 ) MEDGE( SELE, PWIN, WIND = 1 ) 0.00896861, 0.2571, 1, 0.21724 MEDGE( MODI, SUCC, INTE = 8, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, LOCA, WIND = 1 ) 0.445441, 0.275037 / ID = 18 0.0313901, 0.504235 / ID = 2 0.103139, 0.783259 / ID = 19 0.35426, 0.77728 / ID = 20 0.983558, 0.466368 / ID = 4 MLOOP( ADD, MAP, VISI, NOSH, EDG1 = 1, EDG2 = 1, EDG3 = 2, EDG4 = 1 ) CURVE( SELE, LOCA, WIND = 1 ) 0.038864, 0.23717 / ID = 1 0.125561, 0.269058 / ID = 18 0.971599, 0.251121 / ID = 3 CURVE( SELE, PWIN, WIND = 1 ) 0.935725, 0.223219, 0.935725, 0.175386 CURVE( SELE, PWIN, WIND = 1 ) 0.86846, 0.21724, 0.857997, 0.175386 CURVE( SELE, PWIN, WIND = 1 ) 0.77429, 0.179372, 0.77728, 0.239163 CURVE( SELE, PWIN, WIND = 1 ) 0.727952, 0.227205, 0.723468, 0.175386 CURVE( SELE, PWIN, WIND = 1 ) 0.647235, 0.179372, 0.647235, 0.231191 CURVE( SELE, PWIN, WIND = 1 ) 0.55157, 0.227205, 0.55157, 0.197309
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177 Appendix C: (Continued) CURVE( SELE, PWIN, WIND = 1 ) 0.487294, 0.185351, 0.4858, 0.213254 CURVE( SELE, PWIN, WIND = 1 ) 0.411061, 0.225212, 0.399103, 0.177379 CURVE( SELE, PWIN, WIND = 1 ) 0.328849, 0.187344, 0.327354, 0.225212 CURVE( SELE, PWIN, WIND = 1 ) 0.245142, 0.225212, 0.234679, 0.179372 CURVE( SELE, PWIN, WIND = 1 ) 0.165919, 0.189337, 0.165919, 0.221226 CURVE( SELE, PWIN, WIND = 1 ) 0.0926756, 0.221226, 0.0896861, 0.179372 CURVE( SELE, PWIN, WIND = 1 ) 0.0433483, 0.219233, 0.044843, 0.185351 MLOOP( ADD, MAP, VISI, NOSH, EDG1 = 1, EDG2 = 1, EDG3 = 1, EDG4 = 13 ) CURVE( SELE, LOCA, WIND = 1 ) 0.982063, 0.452417 / ID = 4 0.892377, 0.292975 / ID = 18 0.044843, 0.542103 / ID = 2 0.0687593, 0.759342 / ID = 19 0.315396, 0.773293 / ID = 20 MFACE( WIRE, EDG1 = 1, EDG2 = 1, EDG3 = 1, EDG4 = 2 ) CURVE( SELE, LOCA, WIND = 1 ) 0.0343797, 0.233184 / ID = 1 0.152466, 0.265072 / ID = 18 0.962631, 0.243149 / ID = 3 0.958146, 0.205282 / ID = 17 0.838565, 0.177379 / ID = 15 UTILITY( UNSE, LAST ) CURVE( SELE, LOCA, WIND = 1 ) 0.901345, 0.169407 / ID = 16 0.829596, 0.169407 / ID = 15 0.732436, 0.175386 / ID = 14 0.662182, 0.175386 / ID = 13 0.599402, 0.173393 / ID = 12 0.509716, 0.169407 / ID = 11 0.437967, 0.173393 / ID = 10 0.361734, 0.173393
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178 Appendix C: (Continued) / ID = 9 0.284006, 0.183358 / ID = 8 0.203288, 0.183358 / ID = 7 0.13154, 0.181365 / ID = 6 0.0463378, 0.177379 / ID = 5 MFACE( WIRE, EDG1 = 1, EDG2 = 1, EDG3 = 1, EDG4 = 13 ) MFACE( SELE, LOCA, WIND = 1 ) 0.807175, 0.785252 / ID = 1 MFACE( MESH, MAP, ENTI = "fluid" ) MFACE( SELE, LOCA, WIND = 1 ) 0.650224, 0.227205 / ID = 2 MFACE( MESH, MAP, ENTI = "solid" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.0956652, 0.841056, 0.0896861, 0.701545 ELEMENT( SETD, EDGE, NODE = 2 ) MEDGE( MESH, MAP, ENTI = "inlet" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.428999, 0.843049, 0.437967, 0.745391 MEDGE( MESH, MAP, ENTI = "cp" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.0463378, 0.5999, 0, 0.595914 MEDGE( MESH, MAP, ENTI = "ax1" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.940209, 0.490284, 1, 0.480319 MEDGE( MESH, MAP, ENTI = "outlet" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.615845, 0.269058, 0.626308, 0.30294 MEDGE( MESH, MAP, ENTI = "inter" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.0179372, 0.247135, 0.0597907, 0.249128 MEDGE( MESH, MAP, ENTI = "ax2" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.964126, 0.2571, 1, 0.255107 MEDGE( MESH, MAP, ENTI = "sside" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.0418535, 0.221226, 0.0418535, 0.175386 MEDGE( MESH, MAP, ENTI = "h1" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.0986547, 0.233184, 0.0986547, 0.153463 MEDGE( MESH, MAP, ENTI = "i1" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.168909, 0.225212, 0.173393, 0.197309 MEDGE( MESH, MAP, ENTI = "h2" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.236173, 0.225212, 0.239163, 0.183358 MEDGE( MESH, MAP, ENTI = "i2" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.328849, 0.225212, 0.328849, 0.183358
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179 Appendix C: (Continued) MEDGE( MESH, MAP, ENTI = "h3" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.397608, 0.23717, 0.397608, 0.167414 MEDGE( MESH, MAP, ENTI = "i3" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.488789, 0.241156, 0.48281, 0.159442 MEDGE( MESH, MAP, ENTI = "h4" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.54559, 0.245142, 0.556054, 0.181365 MEDGE( MESH, MAP, ENTI = "i4" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.627803, 0.221226, 0.626308, 0.203288 MEDGE( MESH, MAP, ENTI = "h5" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.71151, 0.229198, 0.71151, 0.179372 MEDGE( MESH, MAP, ENTI = "i5" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.778774, 0.231191, 0.786248, 0.185351 MEDGE( MESH, MAP, ENTI = "h6" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.860987, 0.229198, 0.862481, 0.193323 MEDGE( MESH, MAP, ENTI = "i6" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.932735, 0.23717, 0.940209, 0.1714 MEDGE( MESH, MAP, ENTI = "h7" ) END( ) FIPREP( ) ENTITY( ADD, NAME = "solid", SOLI, PROP = "si" ) ENTITY( ADD, NAME = "fluid", FLUI, PROP = "ammonia" ) ENTITY( ADD, NAME = "inlet", PLOT ) ENTITY( ADD, NAME = "cp", PLOT ) ENTITY( ADD, NAME = "ax1", PLOT ) ENTITY( ADD, NAME = "outlet", PLOT ) ENTITY( ADD, NAME = "inter", PLOT ) ENTITY( ADD, NAME = "ax2", PLOT ) ENTITY( ADD, NAME = "sside", PLOT ) ENTITY( ADD, NAME = "h1", PLOT ) ENTITY( ADD, NAME = "h2", PLOT ) ENTITY( ADD, NAME = "h3", PLOT ) ENTITY( ADD, NAME = "h4", PLOT ) ENTITY( ADD, NAME = "h5", PLOT ) ENTITY( ADD, NAME = "h6", PLOT ) ENTITY( ADD, NAME = "h7", PLOT ) ENTITY( ADD, NAME = "i1", PLOT ) ENTITY( ADD, NAME = "i2", PLOT ) ENTITY( ADD, NAME = "i3", PLOT ) ENTITY( ADD, NAME = "i4", PLOT ) ENTITY( ADD, NAME = "i5", PLOT ) ENTITY( ADD, NAME = "i6", PLOT ) ENTITY( SELE, ENTR = "inter", NAME = "i6", PLOT ) ENTITY( DELE, ENTR = "inter", NAME = "inter", PLOT ) ENTITY( ADD, NAME = "inter", PLOT, ATTA = "fluid", NATT = "solid" ) CONDUCTIVITY( ADD, SET = "ammonia", CURV = 11 )
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180 Appendix C: (Continued) 1e+10, 270, 290, 293, 310, 330, 350, 370, 390, 400, 1e+10 0.00136, 0.00136, 0.00116, 0.0011487, 0.00109, 0.0009824, 0.0008724, 0.0007649, 0.0006573, 0.0006023, 0.0006023 SPECIFICHEAT( ADD, SET = "ammonia", CURV = 10 ) 1e+10, 270, 290, 293, 310, 330, 350, 370, 390, 1e+10 1.099, 1.099, 1.11127, 1.123, 1.16, 1.21, 1.29, 1.4, 1.849, 1.849 VISCOSITY( ADD, SET = "ammonia", CURV = 11 ) 1e+10, 270, 290, 293, 310, 330, 350, 370, 390, 400, 1e+10 0.00192, 0.00192, 0.00152, 0.00148, 0.00125, 0.00105, 0.000885, 0.000702, 0.000507, 0.000395, 0.000395 DENSITY( ADD, SET = "ammonia", CONS = 0.59525, TEMP = 0 ) VOLUMEXPANSION( ADD, SET = "ammonia", CONS = 0.0015, REFT = 293 ) GRAVITY( ADD, MAGN = 981, THET = 90, PHI = 0 ) CONDUCTIVITY( ADD, SET = "si", CONS = 0.334 ) DENSITY( ADD, SET = "si", CONS = 2.33 ) SPECIFICHEAT( ADD, SET = "si", CONS = 0.239 ) ICNODE( ADD, VELO, STOK, NODE, X, Y, Z ) ICNODE( ADD, TEMP, CONS = 293, ENTI = "inlet" ) ICNODE( ADD, TEMP, CONS = 293, ENTI = "fluid" ) BCFLUX( ADD, HEAT, ENTI = "h1", CONS = 5.97 ) BCFLUX( ADD, HEAT, ENTI = "h2", CONS = 5.97 ) BCFLUX( ADD, HEAT, ENTI = "h3", CONS = 5.973 ) BCFLUX( ADD, HEAT, ENTI = "h4", CONS = 5.973 ) BCFLUX( ADD, HEAT, ENTI = "h5", CONS = 5.973 ) BCFLUX( ADD, HEAT, ENTI = "h6", CONS = 5.973 ) BCFLUX( ADD, HEAT, ENTI = "h7", CONS = 5.973 ) BCFLUX( ADD, HEAT, ENTI = "i1", CONS = 0 ) BCFLUX( ADD, HEAT, ENTI = "i2", CONS = 0 ) BCFLUX( ADD, HEAT, ENTI = "i3", CONS = 0 ) BCFLUX( ADD, HEAT, ENTI = "i4", CONS = 0 ) BCFLUX( ADD, HEAT, ENTI = "i5", CONS = 0 ) BCFLUX( ADD, HEAT, ENTI = "i6", CONS = 0 ) BCFLUX( ADD, HEAT, ENTI = "ax2", CONS = 0 ) BCFLUX( ADD, HEAT, ENTI = "sside", CONS = 0 ) BCFLUX( ADD, HEAT, ENTI = "cp", CONS = 0 ) BCNODE( ADD, VELO, ENTI = "cp", CONS = 0 ) BCNODE( ADD, VELO, ENTI = "inter", CONS = 0 ) BCNODE( ADD, VELO, ENTI = "ax2", CONS = 0 ) BCNODE( ADD, VELO, ENTI = "sside", CONS = 0 ) BCNODE( ADD, UX, ENTI = "ax1", CONS = 0 ) BCNODE( ADD, UX, ENTI = "inlet", CONS = 0 ) BCNODE( ADD, UY, ENTI = "inlet", CONS = 4.9 ) BCNODE( ADD, TEMP, ENTI = "inlet", CONS = 293 ) DATAPRINT( ADD, CONT ) EXECUTION( ADD, NEWJ ) OPTIONS( ADD, UPWI ) POSTPROCESS( ADD, ALL, NOPT, NOPA ) PRESSURE( ADD, PENA = 1e07, DISC ) PRINTOUT( ADD, NONE, BOUN )
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181 Appendix C: (Continued) PROBLEM( ADD, 2D, INCO, STEA, LAMI, NONL, NEWT, MOME, BUOY, FIXE, NOST, NORE, SING ) RENUMBER( ADD, PROF ) SOLUTION( ADD, N.R. = 25, VELC = 0.01, RESC = 0.01, ACCF = 0 ) END( )
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182 Appendix D: Analysis of fl uid flow during confined liquid jet impingement for different number of discrete heat sources FIGEN( 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 ) 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 POINT( ADD, COOR, X = 0, Y = 0 ) POINT( ADD, COOR, X = 0.8, Y = 0 ) POINT( ADD, COOR, X = 0.8, Y = 0.32 ) POINT( ADD, COOR, X = 0, Y = 0.32 ) POINT( ADD, COOR, X = 0, Y = 0.05 ) POINT( ADD, COOR, X = 0.8, Y = 0.05 ) 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 0.02000 0.82000 0.18000 0.45000 0.84000 0.84000 45.000000 45.000000 45.000000 45.000000 POINT( ADD, COOR, X = 0.089, Y = 0.05 ) POINT( ADD, COOR, X = 0.267, Y = 0.05 ) POINT( ADD, COOR, X = 0.444, Y = 0.05 ) POINT( ADD, COOR, X = 0.622, Y = 0.05 ) 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 0.02000 0.82000 0.18000 0.45000 0.84000 0.84000 45.000000 45.000000 45.000000 45.000000 POINT( ADD, COOR, X = 0.16, Y = 0.32 ) POINT( SELE, LOCA, WIND = 1 ) 0.0328849, 0.215247 / ID = 5 0.118087, 0.195316 / ID = 7 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.119581, 0.195316 / ID = 7 0.337818, 0.183358 / ID = 8 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.361734, 0.199302 / ID = 8
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183 Appendix D: (Continued) 0.550075, 0.219233 / ID = 9 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.550075, 0.219233 / ID = 9 0.744395, 0.209268 / ID = 10 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.745889, 0.211261 / ID = 10 0.971599, 0.19133 / ID = 6 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.0179372, 0.19133 / ID = 5 0.0313901, 0.314898 / ID = 1 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.0418535, 0.300947 / ID = 1 0.019432, 0.795217 / ID = 4 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.989537, 0.205282 / ID = 6 0.980568, 0.283009 / ID = 2 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.980568, 0.283009 / ID = 2 0.976084, 0.77728 / ID = 3 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.0298954, 0.785252 / ID = 4 0.201794, 0.787245 / ID = 11 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.201794, 0.787245 / ID = 11 0.979073, 0.781266 / ID = 3 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.019432, 0.290982 / ID = 1 0.976084, 0.275037
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184 Appendix D: (Continued) / ID = 2 CURVE( ADD ) CURVE( SELE, LOCA, WIND = 1 ) 0.295964, 0.283009 / ID = 12 0.0358744, 0.534131 / ID = 7 0.119581, 0.781266 / ID = 10 0.310912, 0.787245 / ID = 11 0.982063, 0.464375 / ID = 9 SURFACE( ADD, WIRE, EDG1 = 1, EDG2 = 1, EDG3 = 2, EDG4 = 1 ) CURVE( SELE, LOCA, WIND = 1 ) 0.559043, 0.285002 / ID = 12 0.973094, 0.243149 / ID = 5 CURVE( SELE, NEXT = 1 ) / ID = 8 CURVE( SELE, LOCA, WIND = 1 ) 0.901345, 0.1714 / ID = 5 0.738416, 0.177379 / ID = 4 0.556054, 0.179372 / ID = 3 0.330344, 0.187344 / ID = 2 0.119581, 0.169407 / ID = 1 0.0463378, 0.229198 / ID = 6 SURFACE( ADD, WIRE, EDG1 = 1, EDG2 = 1, EDG3 = 5, EDG4 = 1 ) CURVE( SELE, PWIN, WIND = 1 ) 0.316891, 0.231191, 0.914798, 0.129547 MEDGE( ADD, SUCC, INTE = 28, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, PWIN, WIND = 1 ) 0.0971599, 0.241156, 0.0926756, 0.175386 MEDGE( ADD, SUCC, INTE = 14, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, PWIN, WIND = 1 ) 0.727952, 0.265072, 0.733931, 0.32287 MEDGE( ADD, SUCC, INTE = 126, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, PWIN, WIND = 1 ) 0.107623, 0.825112, 0.115097, 0.713503 MEDGE( ADD, SUCC, INTE = 25, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, PWIN, WIND = 1 ) 0.511211, 0.858994, 0.524664, 0.715496 MEDGE( ADD, SUCC, INTE = 101, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, LOCA, WIND = 1 ) 0.690583, 0.279023 / ID = 12 UTILITY( UNSE, ALL ) CURVE( SELE, PWIN, WIND = 1 )
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185 Appendix D: (Continued) 0.0164425, 0.613852, 1, 0.552068 MEDGE( ADD, SUCC, INTE = 50, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, PWIN, WIND = 1 ) 0.00896861, 0.247135, 1, 0.233184 MEDGE( ADD, SUCC, INTE = 15, RATI = 0, 2RAT = 0, PCEN = 0 ) MEDGE( SELE, LOCA, WIND = 1 ) 0.00896861, 0.255107 / ID = 6 UTILITY( UNSE, ALL ) MEDGE( SELE, PWIN, WIND = 1 ) 0.0119581, 0.243149, 0.998505, 0.233184 MEDGE( MODI, SUCC, INTE = 12, RATI = 0, 2RAT = 0, PCEN = 0 ) MEDGE( SELE, PWIN, WIND = 1 ) 0.964126, 0.247135, 1, 0.255107 MEDGE( SELE, PWIN, WIND = 1 ) 0.0149477, 0.247135, 0.0792227, 0.245142 MEDGE( MODI, SUCC, INTE = 10, RATI = 0, 2RAT = 0, PCEN = 0 ) 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 0.02000 0.82000 0.18000 0.45000 0.84000 0.84000 45.000000 45.000000 45.000000 45.000000 CURVE( SELE, LOCA, WIND = 1 ) 0.575486, 0.286996 / ID = 12 0.0179372, 0.568012 / ID = 7 0.0896861, 0.781266 / ID = 10 0.294469, 0.801196 / ID = 11 0.976084, 0.512207 / ID = 9 MLOOP( ADD, MAP, VISI, NOSH, EDG1 = 1, EDG2 = 1, EDG3 = 2, EDG4 = 1 ) CURVE( SELE, LOCA, WIND = 1 ) 0.532138, 0.273044 / ID = 12 CURVE( SELE, PWIN, WIND = 1 ) 0.961136, 0.245142, 0.988042, 0.245142 CURVE( SELE, LOCA, WIND = 1 ) 0.857997, 0.187344 / ID = 5 0.675635, 0.173393 / ID = 4 0.508221, 0.177379 / ID = 3 0.312407, 0.173393 / ID = 2 0.110613, 0.1714 / ID = 1 0.019432, 0.243149 / ID = 6
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186 Appendix D: (Continued) MLOOP( ADD, MAP, VISI, NOSH, EDG1 = 1, EDG2 = 1, EDG3 = 5, EDG4 = 1 ) CURVE( SELE, LOCA, WIND = 1 ) 0.620329, 0.294968 / ID = 12 0.0313901, 0.556054 / ID = 7 0.112108, 0.77728 / ID = 10 0.295964, 0.793224 / ID = 11 0.962631, 0.500249 / ID = 9 MFACE( WIRE, EDG1 = 1, EDG2 = 1, EDG3 = 2, EDG4 = 1 ) CURVE( SELE, LOCA, WIND = 1 ) 0.886398, 0.27703 / ID = 12 CURVE( SELE, PWIN, WIND = 1 ) 0.956652, 0.253114, 0.982063, 0.247135 CURVE( SELE, PWIN, WIND = 1 ) 0.898356, 0.231191, 0.892377, 0.159442 CURVE( SELE, PWIN, WIND = 1 ) 0.715994, 0.187344, 0.715994, 0.23717 CURVE( SELE, PWIN, WIND = 1 ) 0.526158, 0.235177, 0.505232, 0.169407 CURVE( SELE, PWIN, WIND = 1 ) 0.278027, 0.189337, 0.279522, 0.231191 CURVE( SELE, PWIN, WIND = 1 ) 0.0866966, 0.235177, 0.0762332, 0.179372 CURVE( SELE, PWIN, WIND = 1 ) 0.0179372, 0.23717, 0.0403587, 0.23717 MFACE( WIRE, EDG1 = 1, EDG2 = 1, EDG3 = 5, EDG4 = 1 ) MFACE( SELE, LOCA, WIND = 1 ) 0.943199, 0.791231 / ID = 1 MFACE( MESH, MAP, ENTI = "fluid" ) MFACE( SELE, LOCA, WIND = 1 ) 0.835575, 0.203288 / ID = 2 MFACE( MESH, MAP, ENTI = "solid" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.0822123, 0.829098, 0.0911809, 0.765321 MEDGE( SELE, PWIN, WIND = 1 ) 0.795217, 0.522172, 0.793722, 0.520179 ELEMENT( SETD, EDGE, NODE = 2 ) MEDGE( MESH, MAP, ENTI = "inlet" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.45142, 0.843049, 0.458894, 0.709517 MEDGE( MESH, MAP, ENTI = "cp" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.0508221, 0.585949, 0.00298954, 0.591928 MEDGE( MESH, MAP, ENTI = "ax1" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.971599, 0.56004, 1, 0.56004 MEDGE( MESH, MAP, ENTI = "outlet" ) MEDGE( SELE, PWIN, WIND = 1 )
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187 Appendix D: (Continued) 0.403587, 0.267065, 0.41704, 0.298954 MEDGE( MESH, MAP, ENTI = "inter" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.962631, 0.239163, 1, 0.239163 MEDGE( MESH, MAP, ENTI = "sside" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.00896861, 0.255107, 0.0597907, 0.249128 MEDGE( MESH, MAP, ENTI = "ax2" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.0672646, 0.227205, 0.0687593, 0.19133 MEDGE( MESH, MAP, ENTI = "h1" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.180867, 0.227205, 0.186846, 0.173393 MEDGE( MESH, MAP, ENTI = "i1" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.446936, 0.213254, 0.45142, 0.165421 MEDGE( MESH, MAP, ENTI = "h2" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.647235, 0.233184, 0.653214, 0.183358 MEDGE( MESH, MAP, ENTI = "i2" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.866966, 0.223219, 0.869955, 0.189337 MEDGE( MESH, MAP, ENTI = "h3" ) END( ) FIPREP( ) ENTITY( ADD, NAME = "fluid", FLUI, PROP = "ammonia" ) ENTITY( ADD, NAME = "solid", SOLI, PROP = "si" ) ENTITY( ADD, NAME = "inlet", PLOT ) ENTITY( ADD, NAME = "cp", PLOT ) ENTITY( ADD, NAME = "ax1", PLOT ) ENTITY( ADD, NAME = "outlet", PLOT ) ENTITY( ADD, NAME = "sside", PLOT ) ENTITY( ADD, NAME = "ax2", PLOT ) ENTITY( ADD, NAME = "h1", PLOT ) ENTITY( ADD, NAME = "h2", PLOT ) ENTITY( ADD, NAME = "h3", PLOT ) ENTITY( ADD, NAME = "i1", PLOT ) ENTITY( ADD, NAME = "i2", PLOT ) ENTITY( ADD, NAME = "inter", PLOT, ATTA = "fluid", NATT = "solid" ) CONDUCTIVITY( ADD, SET = "ammonia", CURV = 11 ) 1e+10, 270, 290, 293, 310, 330, 350, 370, 390, 400, 1e+10 0.00136, 0.00136, 0.00116, 0.0011487, 0.00109, 0.0009824, 0.0008724, 0.0007649, 0.0006573, 0.0006023, 0.0006023 SPECIFICHEAT( ADD, SET = "ammonia", CURV = 10 ) 1e+10, 270, 290, 293, 310, 330, 350, 370, 390, 1e+10 1.099, 1.099, 1.11127, 1.123, 1.16, 1.21, 1.29, 1.4, 1.849, 1.849 VISCOSITY( ADD, SET = "ammonia", CURV = 11 ) 1e+10, 270, 290, 293, 310, 330, 350, 370, 390, 400, 1e+10 0.00192, 0.00192, 0.00152, 0.00148, 0.00125, 0.00105, 0.000885, 0.000702, 0.000507, 0.000395, 0.000395 DENSITY( ADD, SET = "ammonia", CONS = 0.59525, TEMP = 0 )
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188 Appendix D: (Continued) VOLUMEXPANSION( ADD, SET = "ammonia", CONS = 0.0015, REFT = 293 ) DENSITY( ADD, SET = "si", CONS = 2.33 ) CONDUCTIVITY( ADD, SET = "si", CONS = 0.334 ) SPECIFICHEAT( ADD, SET = "si", CONS = 0.239 ) BCFLUX( ADD, HEAT, ENTI = "h1", CONS = 5.97 ) BCFLUX( ADD, HEAT, ENTI = "h2", CONS = 5.97 ) BCFLUX( ADD, HEAT, ENTI = "h3", CONS = 5.97 ) BCFLUX( ADD, HEAT, ENTI = "i1", CONS = 0 ) BCFLUX( ADD, HEAT, ENTI = "i2", CONS = 0 ) BCNODE( ADD, VELO, ENTI = "cp", CONS = 0, X, Y, Z ) BCNODE( ADD, VELO, ENTI = "inter", CONS = 0, X, Y, Z ) BCNODE( ADD, VELO, ENTI = "sside", CONS = 0, X, Y, Z ) BCNODE( ADD, VELO, ENTI = "ax2", CONS = 0, X, Y, Z ) BCNODE( ADD, UX, ENTI = "inlet", CONS = 0, X, Y, Z ) BCNODE( ADD, UX, ENTI = "ax1", CONS = 0, X, Y, Z ) BCNODE( ADD, UY, ENTI = "inlet", CONS = 9.672, X, Y, Z ) BCNODE( ADD, TEMP, ENTI = "inlet", CONS = 293, X, Y, Z ) BCFLUX( ADD, HEAT, ENTI = "cp", CONS = 0 ) BCFLUX( ADD, HEAT, ENTI = "sside", CONS = 0 ) BCFLUX( ADD, HEAT, ENTI = "ax2", CONS = 0 ) ICNODE( ADD, TEMP, CONS = 293, ENTI = "inlet" ) ICNODE( ADD, TEMP, CONS = 293, ENTI = "fluid" ) ICNODE( ADD, VELO, STOK, NODE, X, Y, Z ) DATAPRINT( ADD, CONT ) EXECUTION( ADD, NEWJ ) GRAVITY( ADD, MAGN = 981, THET = 90, PHI = 0 ) OPTIONS( ADD, UPWI ) POSTPROCESS( ADD, ALL, NOPT, NOPA ) PRESSURE( ADD, PENA = 1e07, DISC ) PRINTOUT( ADD, NONE, BOUN ) PROBLEM( ADD, 2D, INCO, STEA, LAMI, NONL, NEWT, MOME, BUOY, FIXE, NOST, NORE,SING ) RENUMBER( ADD, PROF ) SOLUTION( ADD, N.R. = 25, VELC = 0.01, RESC = 0.01, ACCF = 0 ) END( )
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189 Appendix E: Heat transfer co mputation during confine li quid jet impingement with discrete heat sources FIGEN( 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 ) 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 POINT( ADD, COOR, X = 0, Y = 0 ) POINT( ADD, COOR, X = 0.8, Y = 0 ) POINT( ADD, COOR, X = 0.8, Y = 0.32 ) POINT( ADD, COOR, X = 0, Y = 0.32 ) POINT( ADD, COOR, X = 0, Y = 0.05 ) POINT( ADD, COOR, X = 0.8, Y = 0.05 ) 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 0.02000 0.82000 0.18000 0.45000 0.84000 0.84000 45.000000 45.000000 45.000000 45.000000 POINT( ADD, COOR, X = 0.089, Y = 0.05 ) POINT( ADD, COOR, X = 0.267, Y = 0.05 ) POINT( ADD, COOR, X = 0.444, Y = 0.05 ) POINT( ADD, COOR, X = 0.622, Y = 0.05 ) 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 0.02000 0.82000 0.18000 0.45000 0.84000 0.84000 45.000000 45.000000 45.000000 45.000000 POINT( ADD, COOR, X = 0.16, Y = 0.32 ) POINT( SELE, LOCA, WIND = 1 ) 0.0328849, 0.215247 / ID = 5 0.118087, 0.195316 / ID = 7 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.119581, 0.195316 / ID = 7 0.337818, 0.183358 / ID = 8 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.361734, 0.199302 / ID = 8
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190 Appendix E: (Continued) 0.550075, 0.219233 / ID = 9 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.550075, 0.219233 / ID = 9 0.744395, 0.209268 / ID = 10 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.745889, 0.211261 / ID = 10 0.971599, 0.19133 / ID = 6 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.0179372, 0.19133 / ID = 5 0.0313901, 0.314898 / ID = 1 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.0418535, 0.300947 / ID = 1 0.019432, 0.795217 / ID = 4 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.989537, 0.205282 / ID = 6 0.980568, 0.283009 / ID = 2 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.980568, 0.283009 / ID = 2 0.976084, 0.77728 / ID = 3 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.0298954, 0.785252 / ID = 4 0.201794, 0.787245 / ID = 11 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.201794, 0.787245 / ID = 11 0.979073, 0.781266 / ID = 3 CURVE( ADD ) POINT( SELE, LOCA, WIND = 1 ) 0.019432, 0.290982 / ID = 1 0.976084, 0.275037
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191 Appendix E: (Continued) / ID = 2 CURVE( ADD ) CURVE( SELE, LOCA, WIND = 1 ) 0.295964, 0.283009 / ID = 12 0.0358744, 0.534131 / ID = 7 0.119581, 0.781266 / ID = 10 0.310912, 0.787245 / ID = 11 0.982063, 0.464375 / ID = 9 SURFACE( ADD, WIRE, EDG1 = 1, EDG2 = 1, EDG3 = 2, EDG4 = 1 ) CURVE( SELE, LOCA, WIND = 1 ) 0.559043, 0.285002 / ID = 12 0.973094, 0.243149 / ID = 5 CURVE( SELE, NEXT = 1 ) / ID = 8 CURVE( SELE, LOCA, WIND = 1 ) 0.901345, 0.1714 / ID = 5 0.738416, 0.177379 / ID = 4 0.556054, 0.179372 / ID = 3 0.330344, 0.187344 / ID = 2 0.119581, 0.169407 / ID = 1 0.0463378, 0.229198 / ID = 6 SURFACE( ADD, WIRE, EDG1 = 1, EDG2 = 1, EDG3 = 5, EDG4 = 1 ) CURVE( SELE, PWIN, WIND = 1 ) 0.316891, 0.231191, 0.914798, 0.129547 MEDGE( ADD, SUCC, INTE = 28, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, PWIN, WIND = 1 ) 0.0971599, 0.241156, 0.0926756, 0.175386 MEDGE( ADD, SUCC, INTE = 14, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, PWIN, WIND = 1 ) 0.727952, 0.265072, 0.733931, 0.32287 MEDGE( ADD, SUCC, INTE = 126, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, PWIN, WIND = 1 ) 0.107623, 0.825112, 0.115097, 0.713503 MEDGE( ADD, SUCC, INTE = 25, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, PWIN, WIND = 1 ) 0.511211, 0.858994, 0.524664, 0.715496 MEDGE( ADD, SUCC, INTE = 101, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, LOCA, WIND = 1 ) 0.690583, 0.279023 / ID = 12 UTILITY( UNSE, ALL ) CURVE( SELE, PWIN, WIND = 1 )
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192 Appendix E: (Continued) 0.0164425, 0.613852, 1, 0.552068 MEDGE( ADD, SUCC, INTE = 50, RATI = 0, 2RAT = 0, PCEN = 0 ) CURVE( SELE, PWIN, WIND = 1 ) 0.00896861, 0.247135, 1, 0.233184 MEDGE( ADD, SUCC, INTE = 15, RATI = 0, 2RAT = 0, PCEN = 0 ) MEDGE( SELE, LOCA, WIND = 1 ) 0.00896861, 0.255107 / ID = 6 UTILITY( UNSE, ALL ) MEDGE( SELE, PWIN, WIND = 1 ) 0.0119581, 0.243149, 0.998505, 0.233184 MEDGE( MODI, SUCC, INTE = 12, RATI = 0, 2RAT = 0, PCEN = 0 ) MEDGE( SELE, PWIN, WIND = 1 ) 0.964126, 0.247135, 1, 0.255107 MEDGE( SELE, PWIN, WIND = 1 ) 0.0149477, 0.247135, 0.0792227, 0.245142 MEDGE( MODI, SUCC, INTE = 10, RATI = 0, 2RAT = 0, PCEN = 0 ) 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 0.02000 0.82000 0.18000 0.45000 0.84000 0.84000 45.000000 45.000000 45.000000 45.000000 CURVE( SELE, LOCA, WIND = 1 ) 0.575486, 0.286996 / ID = 12 0.0179372, 0.568012 / ID = 7 0.0896861, 0.781266 / ID = 10 0.294469, 0.801196 / ID = 11 0.976084, 0.512207 / ID = 9 MLOOP( ADD, MAP, VISI, NOSH, EDG1 = 1, EDG2 = 1, EDG3 = 2, EDG4 = 1 ) CURVE( SELE, LOCA, WIND = 1 ) 0.532138, 0.273044 / ID = 12 CURVE( SELE, PWIN, WIND = 1 ) 0.961136, 0.245142, 0.988042, 0.245142 CURVE( SELE, LOCA, WIND = 1 ) 0.857997, 0.187344 / ID = 5 0.675635, 0.173393 / ID = 4 0.508221, 0.177379 / ID = 3 0.312407, 0.173393 / ID = 2 0.110613, 0.1714 / ID = 1 0.019432, 0.243149 / ID = 6
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193 Appendix E: (Continued) MLOOP( ADD, MAP, VISI, NOSH, EDG1 = 1, EDG2 = 1, EDG3 = 5, EDG4 = 1 ) CURVE( SELE, LOCA, WIND = 1 ) 0.620329, 0.294968 / ID = 12 0.0313901, 0.556054 / ID = 7 0.112108, 0.77728 / ID = 10 0.295964, 0.793224 / ID = 11 0.962631, 0.500249 / ID = 9 MFACE( WIRE, EDG1 = 1, EDG2 = 1, EDG3 = 2, EDG4 = 1 ) CURVE( SELE, LOCA, WIND = 1 ) 0.886398, 0.27703 / ID = 12 CURVE( SELE, PWIN, WIND = 1 ) 0.956652, 0.253114, 0.982063, 0.247135 CURVE( SELE, PWIN, WIND = 1 ) 0.898356, 0.231191, 0.892377, 0.159442 CURVE( SELE, PWIN, WIND = 1 ) 0.715994, 0.187344, 0.715994, 0.23717 CURVE( SELE, PWIN, WIND = 1 ) 0.526158, 0.235177, 0.505232, 0.169407 CURVE( SELE, PWIN, WIND = 1 ) 0.278027, 0.189337, 0.279522, 0.231191 CURVE( SELE, PWIN, WIND = 1 ) 0.0866966, 0.235177, 0.0762332, 0.179372 CURVE( SELE, PWIN, WIND = 1 ) 0.0179372, 0.23717, 0.0403587, 0.23717 MFACE( WIRE, EDG1 = 1, EDG2 = 1, EDG3 = 5, EDG4 = 1 ) MFACE( SELE, LOCA, WIND = 1 ) 0.943199, 0.791231 / ID = 1 MFACE( MESH, MAP, ENTI = "fluid" ) MFACE( SELE, LOCA, WIND = 1 ) 0.835575, 0.203288 / ID = 2 MFACE( MESH, MAP, ENTI = "solid" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.0822123, 0.829098, 0.0911809, 0.765321 MEDGE( SELE, PWIN, WIND = 1 ) 0.795217, 0.522172, 0.793722, 0.520179 ELEMENT( SETD, EDGE, NODE = 2 ) MEDGE( MESH, MAP, ENTI = "inlet" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.45142, 0.843049, 0.458894, 0.709517 MEDGE( MESH, MAP, ENTI = "cp" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.0508221, 0.585949, 0.00298954, 0.591928 MEDGE( MESH, MAP, ENTI = "ax1" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.971599, 0.56004, 1, 0.56004 MEDGE( MESH, MAP, ENTI = "outlet" ) MEDGE( SELE, PWIN, WIND = 1 )
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194 Appendix E: (Continued) 0.403587, 0.267065, 0.41704, 0.298954 MEDGE( MESH, MAP, ENTI = "inter" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.962631, 0.239163, 1, 0.239163 MEDGE( MESH, MAP, ENTI = "sside" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.00896861, 0.255107, 0.0597907, 0.249128 MEDGE( MESH, MAP, ENTI = "ax2" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.0672646, 0.227205, 0.0687593, 0.19133 MEDGE( MESH, MAP, ENTI = "h1" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.180867, 0.227205, 0.186846, 0.173393 MEDGE( MESH, MAP, ENTI = "i1" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.446936, 0.213254, 0.45142, 0.165421 MEDGE( MESH, MAP, ENTI = "h2" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.647235, 0.233184, 0.653214, 0.183358 MEDGE( MESH, MAP, ENTI = "i2" ) MEDGE( SELE, PWIN, WIND = 1 ) 0.866966, 0.223219, 0.869955, 0.189337 MEDGE( MESH, MAP, ENTI = "h3" ) END( ) FIPREP( ) ENTITY( ADD, NAME = "fluid", FLUI, PROP = "ammonia" ) ENTITY( ADD, NAME = "solid", SOLI, PROP = "si" ) ENTITY( ADD, NAME = "inlet", PLOT ) ENTITY( ADD, NAME = "cp", PLOT ) ENTITY( ADD, NAME = "ax1", PLOT ) ENTITY( ADD, NAME = "outlet", PLOT ) ENTITY( ADD, NAME = "sside", PLOT ) ENTITY( ADD, NAME = "ax2", PLOT ) ENTITY( ADD, NAME = "h1", PLOT ) ENTITY( ADD, NAME = "h2", PLOT ) ENTITY( ADD, NAME = "h3", PLOT ) ENTITY( ADD, NAME = "i1", PLOT ) ENTITY( ADD, NAME = "i2", PLOT ) ENTITY( ADD, NAME = "inter", PLOT, ATTA = "fluid", NATT = "solid" ) CONDUCTIVITY( ADD, SET = "ammonia", CURV = 11 ) 1e+10, 270, 290, 293, 310, 330, 350, 370, 390, 400, 1e+10 0.00136, 0.00136, 0.00116, 0.0011487, 0.00109, 0.0009824, 0.0008724, 0.0007649, 0.0006573, 0.0006023, 0.0006023 SPECIFICHEAT( ADD, SET = "ammonia", CURV = 10 ) 1e+10, 270, 290, 293, 310, 330, 350, 370, 390, 1e+10 1.099, 1.099, 1.11127, 1.123, 1.16, 1.21, 1.29, 1.4, 1.849, 1.849 VISCOSITY( ADD, SET = "ammonia", CURV = 11 ) 1e+10, 270, 290, 293, 310, 330, 350, 370, 390, 400, 1e+10 0.00192, 0.00192, 0.00152, 0.00148, 0.00125, 0.00105, 0.000885, 0.000702, 0.000507, 0.000395, 0.000395 DENSITY( ADD, SET = "ammonia", CONS = 0.59525, TEMP = 0 )
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195 Appendix E: (Continued) VOLUMEXPANSION( ADD, SET = "ammonia", CONS = 0.0015, REFT = 293 ) DENSITY( ADD, SET = "si", CONS = 2.33 ) CONDUCTIVITY( ADD, SET = "si", CONS = 0.334 ) SPECIFICHEAT( ADD, SET = "si", CONS = 0.239 ) BCFLUX( ADD, HEAT, ENTI = "h1", CONS = 5.97 ) BCFLUX( ADD, HEAT, ENTI = "h2", CONS = 5.97 ) BCFLUX( ADD, HEAT, ENTI = "h3", CONS = 5.97 ) BCFLUX( ADD, HEAT, ENTI = "i1", CONS = 0 ) BCFLUX( ADD, HEAT, ENTI = "i2", CONS = 0 ) BCNODE( ADD, VELO, ENTI = "cp", CONS = 0, X, Y, Z ) BCNODE( ADD, VELO, ENTI = "inter", CONS = 0, X, Y, Z ) BCNODE( ADD, VELO, ENTI = "sside", CONS = 0, X, Y, Z ) BCNODE( ADD, VELO, ENTI = "ax2", CONS = 0, X, Y, Z ) BCNODE( ADD, UX, ENTI = "inlet", CONS = 0, X, Y, Z ) BCNODE( ADD, UX, ENTI = "ax1", CONS = 0, X, Y, Z ) BCNODE( ADD, UY, ENTI = "inlet", CONS = 9.672, X, Y, Z ) BCNODE( ADD, TEMP, ENTI = "inlet", CONS = 293, X, Y, Z ) BCFLUX( ADD, HEAT, ENTI = "cp", CONS = 0 ) BCFLUX( ADD, HEAT, ENTI = "sside", CONS = 0 ) BCFLUX( ADD, HEAT, ENTI = "ax2", CONS = 0 ) ICNODE( ADD, TEMP, CONS = 293, ENTI = "inlet" ) ICNODE( ADD, TEMP, CONS = 293, ENTI = "fluid" ) ICNODE( ADD, VELO, STOK, NODE, X, Y, Z ) DATAPRINT( ADD, CONT ) EXECUTION( ADD, NEWJ ) GRAVITY( ADD, MAGN = 981, THET = 90, PHI = 0 ) OPTIONS( ADD, UPWI ) POSTPROCESS( ADD, ALL, NOPT, NOPA ) PRESSURE( ADD, PENA = 1e07, DISC ) PRINTOUT( ADD, NONE, BOUN ) PROBLEM( ADD, 2D, INCO, STEA, LAMI, NONL, NEWT, MOME, BUOY, FIXE, NOST, NORE,SING ) RENUMBER( ADD, PROF ) SOLUTION( ADD, N.R. = 25, VELC = 0.01, RESC = 0.01, ACCF = 0 ) END( )
