CFD MODELLING OF SUPERSONIC COMBUSTION

Transcription

1 DEPARTMENT OF ENGINEERING AUSTRALIAN NATIONAL UNIVERSITY 1998 CFD MODELLING OF SUPERSONIC COMBUSTION IN A SCRAMJET ENGINE FINAL REPORT BY PETER HYSLOP Supervisors: Dr Frank Houwing Aerophysics and Laser Diagnostics Research Laboratory Department of Physics and Theoretical Physics Australian National University Dr Keith Lovegrove Department of Engineering Australian National University

2 ABSTRACT This project was aimed at modelling the supersonic combusting flow inside the ANU s experimental Scramjet engine using the Computational Fluid Dynamics (CFD) program CFD-ACE. CFD models were initially verified with results from previous work and subsequently with results obtained in this project from experiments performed on the Scramjet in the T3 free-piston shock tunnel. In these experiments pressure measurements were obtained and compared with the CFD results. CFD results were then used to optimise the Scramjet for maximum thrust by varying two geometric parameters. Several investigations were firstly performed on Scramjet configurations used in previous work to develop an accurate CFD model of the flow. Turbulent and laminar flow, grid resolution, inlet conditions and a number of combustion models were all investigated. It was found that pressure trends along the floor of the Scramjet were well predicted for non-combusting flow, however for the associated combusting flows pressure was somewhat under-predicted. CFD models were then developed for Scramjet configurations investigated in the current project with a higher grid resolution and a more accurate calculation of the inlet conditions. CFD results showed a much better correlation with pressure measurements determined in the experimental phase of this project. Both the position and magnitude of shock and expansion waves and the general trends of pressure in the Scramjet duct were surprisingly well predicted. Values of the two geometric parameters were varied in both the CFD and experimental models. The range of parameters investigated was based on results found in previous work. For one of the parameters the values investigated were outside the range that produced maximum thrust. For the other, an optimum value was determined and the physical processes that cause the optimum identified Overall, CFD-ACE was found to be a flexible and accurate tool for modelling the supersonic, combusting flow in a Scramjet engine. While the initial development of CFD models was time consuming, once an accurate model was determined, modifications of flow conditions and geometric parameters could be easily and quickly made. i

3 ACKNOWLEDGMENTS There are a number of people that I would like to thank who have been associated with this project. Firstly, my supervisor Dr Frank Houwing for providing encouragement, valuable direction and the time for my numerous unscheduled meetings. I would also like to thank Matthew Gaston for his help with CFD-ACE, the setup of shock-tube experiments and general knowledge of Scramjets. Thankyou also to Sean O Byrne, Dr Paul Danehy, Phil Palmer and Jodie Fox and the rest of the ALDiR group for their encouragement and numerous queries answered. None of my work in the T3 shock tunnel would have been possible without the technical expertise of Paul Walsh and Paul Tant who helped with modifications of the Scramjet and ensured the smooth running of the tunnel. Thankyou also to mother nature, for providing a bad snow year surely without which I would have spent more time on the snow than in front of the computer and this thesis would have been ten pages shorter. Finally, thankyou to my parents for the years of encouragement and support. Thankyou all. ii

4 TABLE OF CONTENTS ABSTRACT i ACKNOWLEDGMENTS ii 1. INTRODUCTION Scramjet Engines ANU s Scramjet Aims 3 2. BACKGROUND ANU s Scramjet The T3 free-piston shock tunnel Previous work CFD Modelling Solution Methodology and Governing Equations Turbulence Models Reaction Models Supersonic flow theory Oblique shockwave relation Expansion waves Normal shockwaves Equivalence Ratio PROCEDURES Overview Verification of CFD-ACE with previous work Overall procedure Numerical procedures CFD model input parameters Optimisation of the Scramjet geometry using CFD-ACE Numerical procedures CFD model input parameters Post Processing Experimental verification of the optimum configuration Experimental Procedure Post processing EXPERIMENTAL SETUP Scramjet modifications Pressure transducers 24

5 4.3 Injection system Pressure Measurement system RESULTS AND PRELIMINARY ANALYSIS Verification of CFD-ACE with previous results Turbulent or laminar flow Grid resolution Combustion model Inlet pressure CFD image features Overall Results Comparison of CFD and previous experimental results Summary Comparison of CFD and experimental results RESULTS ANALYSIS AND DISCUSSION Comparison of experimental and CFD thrust calculations Effect of thrust surface angle Effect of flat duct length Effect of thrust surface length Effect of combustion SUMMARY AND CONCLUSIONS FURTHER WORK 48 APPENDIX A CFD-ACE GRIDS 51 APPENDIX B LIST OF SHOCK TUNNEL SHOTS 52 APPENDIX C SCRAMJET MODIFICATION DRAWINGS 53 APPENDIX D ADDITIONAL CFD AND EXPERIMENTAL RESULTS 62

6 LIST OF FIGURES Figure 1: Generic Scramjet engine...2 Figure 2: Schematic of ANU s Scramjet showing flat duct length, L and thrust surface angle, θ....4 Figure 3: Inner sections of ANU s Scramjet...5 Figure 4: T3 shock tunnel schematic (taken from ALDiR website)...5 Figure 5: Changing the effective flat duct length via (a) changing the flat duct length, (b) changing the injector length...7 Figure 6: Shock and expansion waves...11 Figure 7: Oblique shockwaves...12 Figure 8: Generation of a normal shockwave...13 Figure 9: Scramjet configurations used in verification of Doolans experiments...15 Figure 10: Sample grid (Note: for viewing purposes the grid resolution is half of what was generally used)...17 Figure 12: Modifications to the Scramjet example of the 200mm flat floor configuration...23 Figure 13: Typical injection pressure trace...25 Figure 14: Pressure data acquisition system...26 Figure 15: Grid comparison...28 Figure 16: Combustion comparison...29 Figure 17: Equilibrium combustion - water mass fraction...29 Figure 18: 2-step finite rate combustion water mass fraction...29 Figure 19: 7-step finite rate combustion water mass fraction...30 Figure 20: Pressure around the injection...30 Figure 21: Floor pressure long injector, 0mm flat duct...31 Figure 22: Floor pressure long injector, 50mm flat duct...32 Figure 23: Floor pressure long injector, 87mm flat duct...32 Figure 24: Floor pressure short injector, 80mm flat duct...33 Figure 25: Floor pressure short injector, 1170mm flat duct...33 Figure 26: Scramjet pressure 200 mm, 1.75 thrust surface...36 Figure 27: Scramjet pressure 150 mm flat floor, 7 thrust surface...36 Figure 28: Scramjet pressure 100 mm flat floor, 1.75 thrust surface...36 Figure 29: Scramjet Pressure 0 mm flat duct, 7 thrust surface...37 Figure 30: Comparison of CFD and experimental thrust calculations: (a) 7 thrust surface, (b) 1.75 thrust surface...39 Figure 31: Effect of thrust surface angle on thrust generated (combustion)...40 Figure 32: Thrust generated by 15 thrust surface...41 Figure 33: Effect of flat duct length on thrust generated (combustion)...41 Figure 34: Variation of flat duct length for 7 thrust surface angle...42 Figure 35: H 2 O mass fraction 50 mm flat duct, 7 thrust surface...42 Figure 36: H 2 O mass fraction 100 mm flat duct, 7 thrust surface...42 Figure 37: Temperature around the expansion region (50 mm flat duct, 7 thrust surface)...43 Figure 38: Incremental thrust / Thrust surface length...44 Figure 39: Scramjet floor pressure for 7 thrust surface: (a) 200 mm flat duct, (b) 100 mm flat duct.45 Figure 40: Incremental thrust...45

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8 CHAPTER ONE - INTRODUCTION 1. INTRODUCTION 1.1 SCRAMJET ENGINES One of the current interests in the space vehicle arena is in the development of aerospaceplanes reusable space vehicles with plane like characteristics. For these vehicles to be operationally viable an air breathing propulsion system is needed. Unlike current rocket powered space vehicles, an air breathing propulsion system does not require its own oxidiser to be carried. The obvious benefit is the minimization of the amount of oxidiser that must be carried on the vehicle by utilizing the oxygen available in the atmosphere. The weight of propellants that can be carried can be increased and, in principle, the gross takeoff weight of the vehicle can be reduced 1. Over the past 30 years considerable effort has been directed to the development of a functional airbreathing engine. The most viable engine to be studied is the Supersonic Combustion Ramjet engine (or Scramjet engine). Large scale projects to include the Scramjet engine design have included the British Aerospace HOTOL (Horizontal Take-Off and Landing) project and the NASA NASP (National Aerospace Project) project. The Scramjet engine design is an extension of the Ramjet. The difference between the two lies in flow state inside the engine. Both are designed to be used for supersonic flight, however a Scramjet allows the flow through the engine to remain supersonic, whereas in a Ramjet the flow is slowed to subsonic levels before it enters the combustor. Up to flight Mach numbers of 3 6 Ramjet engines are optimal. After Mach 6 various factors contribute to decreasing the efficiency of the engine. Slowing the flow to subsonic levels becomes unrealistic because this causes the combustor entrance temperature and pressure to become too high and causes the flow to dissociate. Combustion in dissociated flow is extremely inefficient because the heat released by exothermic combustion reactions is negated by the heat absorbed through endothermic dissociation reactions. The Scramjet engine is fundamentally simple in concept but surprisingly difficult in realization. Figure 1 shows a basic generic Scramjet design. At the most fundamental level it works by injecting fuel (typically hydrogen) into a flow of supersonic air. The air is at sufficiently high temperature and pressure for the fuel to combust, and the resulting mixture is expelled from the engine at a higher pressure 2. The Scramjet is composed of four main sections: the inlet, isolator, combustor and exhaust nozzle. These sections can be seen for the generic Scramjet shown in Figure 1. Chapter One Introduction 1

9 inlet combustor fuel thrust surface isolator exhast nozzle Figure 1: Generic Scramjet engine The inlet heats and slows the flow through a series of oblique shockwaves. This ram portion of the cycle means the engine cannot be operated statically. The isolator serves to separate the combustor from the inlet of the engine, allowing further slowing of the flow. Combustion is achieved through the continuous injection of fuel (usually hydrogen) into the supersonic flow. In the above diagram the fuel is injected streamwise, however, other injection techniques (eg. wall mounted or transverse) can be used. The fuel mixes and combusts, increasing the pressure and temperature of the flow. Finally the flow is expanded via the nozzle. This serves two purposes: to allow the flow to accelerate to the external speed, and to provide a mechanism by which the increase in pressure can be converted into forward thrust. It should be noted that although the above engine is symmetric, this is only one possible configuration, the design may also be asymmetric. One of the major differences of Scramjets from conventional engines is that they have no moving parts. Also, because of their very high flow speeds, proposed designs are much longer than conventional engines and must be integrated into the airframe, rather than a separate attachment. This allows the fuel/air mixture sufficient time to mix and combust. As an example, the thrust surface usually includes the entire rear of the aircraft. It should be noted that the uniqueness of the Scramjet engine lies in its supersonic combustion other air-breathing engines can propel a vehicle to supersonic speeds but none maintains the supersonic flow throughout the engine. At present no aerospace vehicles use the Scramjet engine for propulsion. Most research to date has been conducted in ground based research facilities. More recently small scale test engines have been mounted to larger conventionally powered vehicles. One of the main difficulties in the development of the Scramjet engine is the reproduction of a Scramjet s operating conditions. Free piston shock tunnel facilities, such as the one at the ANU, generate the required test conditions for very short periods of time (1 4 ms). This short test time is a disadvantage in producing steady state real world conditions, however they are the only facilities capable of producing the required pressure and temperature. (Shock tunnel facilities use shock waves and a number of pressurised phases to develop the desired pressure, temperature and flow speed). Blow down facilities generate flow for longer periods of time, but cannot generate the high pressure and high temperature required at high Mach numbers. One hindrance to Scramjet engine concept lies in the fact that they are only operational when above a Mach number of 6. This means that a dual phase propulsion system is required for flight up to Mach Chapter One Introduction 2

10 6. Kerrebrock 3 suggests the possibility of using a turbine engine followed by a Ramjet and finally a Scramjet. Another suggestion for outer orbit aerospace applications involves the initial use of a conventional rocket, then Scramjet and again a rocket when upper atmosphere is reached. The eventual configuration would depend on the specific application of the vehicle. In addition to the space launch applications, air-breathing propulsion is also being considered for hypersonic cruise vehicle applications (Moore and Ronald (1996)). Currently only satellite-servicing concepts are on the horizon, however commercial vehicles with speeds double and triple those of the Concorde are still the dream of many. 1.2 ANU S SCRAMJET The ANU s Scramjet is a small scale version of the generic Scramjet with the inlet removed. It s design is based on a Scramjet used at the University of Queensland and has been in use for research at the ANU since The Scramjet is designed to be used in the ANU s T3 Free Piston Shock Tunnel. It has been designed so that study can be performed on different supersonic flow processes and properties. Previous work with the Scramjet has involved investigation of the effect of Mach number, fuel fraction and other inlet properties on combustion; investigation of a number of different injector shapes; and flow visualisation. 1.3 AIMS This project was very much a continuation of work performed at the ANU in the T3 free piston shock tunnel since Its aims were twofold: To model the flow inside the ANU s model Scramjet engine using the Computational Fluid Dynamics (CFD) program, CFD-ACE, and To optimise the combustor geometry of the ANU s Scramjet engine for maximum thrust at a single operating condition (Mach number and equivalence ratio * ). The configuration of the Scramjet was optimised by varying two geometric parameters: the length of the flat section downstream of the fuel injector and the angle of the thrust surface. The optimisation was performed both experimentally and using CFD. Pressure measurements on the walls of both the physical and computation models were then compared. This project stems from the Department of Physics recent purchase of the CFD-ACE program. In a concise form, the overall goal of this project was to gain confidence with the use of a CFD program for modelling supersonic flow and to apply this program to optimise the Scramjet for maximum thrust. * equivalence ratio is a measure of the richness of the fuel-air mixture.(see section 2.6) Chapter One Introduction 3

11 CHAPTER TWO - BACKGROUND 2. BACKGROUND 2.1 ANU S SCRAMJET ANU s Scramjet is designed to be used in the T3 Free Piston Shock Tunnel 4. This shock tunnel is capable of producing supersonic flow at a high temperature, the conditions that would be prevalent at the inlet of a real Scramjet. The ANU s Scramjet is a duct approximately 500mm long, 25 mm high and 52 mm wide. It has a plane base injector (flat ended) injecting fuel parallel to the flow and thrust surface on the bottom side. The two geometric parameters, flat duct length, L and thrust surface angle, θ should be noted. For the purposes of this thesis the flat duct length is defined as the distance between the end of the injector and the start of the thrust surface. Twelve pressure transducers are mounted on the floor of the Scramjet. Figure 2 shows a schematic of the ANU s Scramjet. Several modification were made to the Scramjet during this project. These are outline in section 4.1 Figure 2: Schematic of ANU s Scramjet showing flat duct length, L and thrust surface angle, θ. It should be noted that the ANU s Scramjet differs from the generic Scramjet, shown in Figure 1, in two ways. Firstly, the ANU s Scramjet does not have a converging inlet and therefore only simulates the flow downstream of the inlet. The second difference is that the ANU s Scramjet is not symmetric, there is a thrust surface on only one side of the duct. The injector has a leading edge as designed by the National Aerospace Laboratory in Japan. It is a double wedge with a 10 half angle, rounded at the leading edge with a 0.5 mm radius. Chapter Two Background 4

12 flat floor sections pressure transducers side plates Figure 3: Inner sections of ANU s Scramjet The Scramjet was originally based on a design used in the University of Queensland s shock tunnel T4, but since then has had numerous modifications. Figure 3 shows the inside sections of the Scramjet. The inner sections of the Scramjet is used to modify the geometry of the combustor and thrust surface. Different sized and shaped plates can be placed in this section to change the geometry. Different style injectors can also be inserted by removing the front section. Pressure transducers are mounted in the floor of the duct. The transducers mountings in the unconfined region behind the end of the roof were not used. The injection system was contained in the bottom of the Scramjet. Pressurised hydrogen (1400 kpa for this project) is stored in a coiled copper tube (called a Ludweig tube) which is connected to a solenoid. When the solenoid is triggered, it activates a fast acting valve system contained in the front section of the Scramjet and the hydrogen is injected into the flow. 2.2 THE T3 FREE-PISTON SHOCK TUNNEL All experimental work was performed in the T3 free-piston shock tunnel at the ANU physics department. The shock tunnel can generate supersonic flow for 1 4 ms at high pressure and temperature. This short duration is one of the disadvantages of a shock tunnel, however it is the only type of facility capable of producing supersonic flow with real world Scramjet operating conditions. Figure 4: T3 shock tunnel schematic (taken from ALDiR website) Chapter Two Background 5

13 As seen in Figure 4, the T3 shock tunnel is composed of a number of sections. The main section are: the compression tube, in which the high pressure driver gas is generated; the shock tube, in which the test gas is situated and shockwaves are developed; the nozzle, which accelerates the flow to the desired test conditions; the test section, in which the apparatus being tested is placed; and the dump tank. A steel diaphragm is situated between the compression and shock tubes and a Mylar diaphragm is placed between the shock tube and nozzle. Prior to a shot in the tunnel, the test section, compression tube and shock tube are evacuated. The shock tube, compression tube and high pressure reservoir are then filled with gases determined by the desired flow conditions at the nozzle exit. The high pressure reservoir is air and the driver gas in the compression tube is a mixture of helium and argon. The shock tube is filled with either air or nitrogen depending on whether combustion or non-combustion is being tested in the Scramjet. To produce supersonic flow in the tunnel the following events occur: 1. A high pressure is built up in the high pressure reservoir 2. The piston is released, driving it into the compression tube and compressing the driver gas. 3. The diaphragm bursts and a shockwave propagates through the shock tube increasing the pressure and temperature of the test gas. The driver gas pushes the test gas in front of it. 4. The shockwave reflects from the end wall of the shock tube, raising the pressure and temperature further and causing the Mylar diaphragm to burst. 5. The test gas exits through the nozzle which is shaped to produce the desired Mach number. 6. The test gas travels through the Scramjet, mounted in the test section, and into the dump tank. 2.3 PREVIOUS WORK Investigation in Scramjet design and related activity has been performed for thirty years since the research interest in supersonic combustion was first expressed. A review of the previous research is given in Heiser and Pratt 2,5. Much of the previous work on the Scramjet at the ANU has involved flow visualisation, for which the Aerophysics and Laser Diagnostic Research Laboratory (ALDiR) at the Department of Physics, is well known. Various visualisation techniques have been used. These include Schlieren, shadowgraph and Planar Laser Induced Fluorescence (PLIF) systems 6. In addition to visualising the flow with the above techniques, static pressure measurements have also been made inside the Scramjet. The most relevant work to this project is the work performed in 1997 by Doolan 7 in his Engineering Honours Project, Optimising the Combustor Geometry in a Supersonic Combustion Ramjet. In this project the flat duct length in the Scramjet was varied for a single thrust surface angle of 3.5. The angle of 3.5 was proposed by researchers at the Japanese National Aerospace Laboratories (NAL) for the condition: Mach number, M = 2.5 Temperature, T = 1100 K Pressure, P = 1.4 atm Chapter Two Background 6

14 Their value of thrust surface angle was not determined on the basis of optimising thrust but on other considerations which are discussed in detail by O Byrne 4. Essentially, this value was the minimum value necessary to avoid an undesirable phenomena known as thermal choking, which reduces the Mach number inside the combustor to subsonic values so that it no longer operates as a true Scramjet engine. The flat duct length was varied in two ways: by increasing the distance between the injector and start of the thrust surface; and by decreasing the injector length (effectively increasing the distance between the end of injector and the thrust surface). L L L L (a) (b) Figure 5: Changing the effective flat duct length via (a) changing the flat duct length, (b) changing the injector length This second method of increasing flat duct length had several shortcomings, the most significant of these being that different shockwave patterns and flow conditions were obtained in the duct using the different length injectors. Decreasing the injector length could not therefore be considered equivalent to increasing the flat floor length. Regardless of this problem, the conclusion of this project was that, for a given total length of Scramjet, increasing the flat duct length produced an increase in thrust. The maximum flat duct length investigated (87 mm) was found to produce the greatest thrust. Several different configurations of flat duct length and injector length were investigated. The pressure on the floor of the Scramjet was measured using 12 PCB pressure transducers. From these pressure measurements one dimensional calculations were performed using a Visual Basic program, Scramjet. This program calculated several parameters including: Mach number, temperature and fraction of fuel burnt. The results were used to compare the flow properties at the different configurations and to calculate the thrust generated. Additionally, images of the flow in the region just behind the injector were developed using the Shadowgraph technique 4 and used for a qualitative analysis of the flow. This project continued directly from Doolan s work. It is aimed at determining to what extent increasing flat duct length increases thrust and combining this with an investigation of thrust surface angle. It also extends the previous work through the use of Computational Fluid Dynamics. Other recent Scramjet studies at the ANU (by other Physics and Engineering students) have included: comparison of transverse and parallel injection schemes, investigation of parallel injector geometry on mixing performance and the investigation of a transient pressure rise in the duct 8,9,10. Chapter Two Background 7

15 2.4 CFD MODELLING Computational Fluid Dynamics (CFD) packages are very powerful tools for analysing any type of fluid flow. They are capable of calculating a large number of flow parameters that are often difficult or impossible to determine experimentally. For optimisation purposes, they allow easy manipulation of geometry and flow conditions. The program used in this project was CFD-ACE 11. CFD-ACE can be used to model a large variety of different types of flow: subsonic or supersonic; turbulent or laminar; incompressible or compressible; mixing and reacting; and steady state or transient. It should be noted that other programs exist that model supersonic flows better than CFD-ACE (in particular shockwaves) but due to price, ease of use and software support CFD-ACE was preferred for the current project. Also, CFD-ACE was currently being used by Gaston 12 to model a number of Scramjet injectors, and so advice could be given on its use. CFD-ACE actually consists of 3 modules; CFD-GEOM 13, used to generate the geometry and the grid; CFD-ACE, used to define the remainder of the model conditions and control the solver; and CFD- VIEW 14, used to analyse the results. All these modules are controlled using user friendly Graphical User Interfaces (GUIs), although more powerful controls can be invoked using a command language Solution Methodology and Governing Equations CFD-ACE uses a control volume approach in calculating flow parameters. The region of interest in the flow is divided into a grid. Each grid element is considered as a control volume with the properties constant over its volume. For each control volume, fluid flow is simulated by numerically solving partial differential equations that govern the transport of flow quantities, also know as flow variables. The variables include mass, momentum, energy, turbulence quantities, mixture fractions and species concentrations. The variables for which transport equations have to be solved will depend on the nature of the flow problem. The three equations common to all fluid dynamics problems are the conservation of mass, momentum and energy equations. In differential form these are: Conservation of mass: ρ t + x j ( ρu ) j = 0 (2.1) where u j is the jth Cartesian component of the instantaneous velocity and ρ is the fluid density. Conservation of momentum: p τ ij ( ρ ui ) + ( ρuiu j ) = + + ρfi (2.2) t x x x j k j Chapter Two Background 8

16 where p is the static pressure, τ ij is the viscous stress tensor and f i is the body force. Conservation of energy: t q p p j ( ρh) + ( ρu jh) = + + u j + τ ij x j x j t x j ui x j i (2.3) where q j is the j-component of the heat flux and h is the static enthalpy. The three Partial Differential Equations (PDE s), along with any others dependant on the specific flow problem, are discretized on the computational grid, a set of algebraic equations are formed, and the solution of the algebraic equations determined. This method generates the flow variables at each grid point. An iterative solution scheme is used by CFD-ACE to solve the algebraic equations. The equations are solved sequentially and repeatedly with the goal of improving the solution at each iteration. The solution is monitored by viewing global residuals (the difference between the current and previous solution average over the entire domain). A solution is generally considered converged when the residuals have decrease by 4-5 orders of magnitude. The most important point to consider when using CFD-ACE (or any CFD program) is that the quality of its output is only as good as the quality of its input so care has to be taken to make sure that inputs, such as boundary conditions, fluid properties and fluid models are as accurate for (or applicable to) the specific problem, as possible Turbulence Models The turbulence model used for the CFD models analysed in this project was the standard k-ε model. It was used because it is well known and applicable to high Reynolds number flows 15. The model equations can be found in the CFD-ACE theory manual 16. The parameters associated with this model are k and L. The physical significance of these parameters is discussed in the CFD-ACE theory manual 16. k can be calculated using the equation: µ laminar k = Lρ 2 (2.4) where µ laminar is the laminar viscosity and ρ the density. For all CFD models L was 25 mm, the height of the Scramjet duct Reaction Models Chapter Two Background 9

17 During this project three different reaction models were used. The fundamental concepts behind these are outlined below. The instantaneous model The instantaneous reaction model assumes that a single chemical reaction occurs and proceeds instantaneously to completion. The reaction used for the Scramjet was the hydrogen-water reaction: 2H 2 + O 2 2H 2 O. The equilibrium model The equilibrium model requires the specification of all the chemical species that might exist in the reacting mixture. No specific reactions need to be specified. This reaction model calculates the species concentrations at its equilibrium condition. The species specified for the reaction mixture were: H 2, O 2, N 2, H 2 O, OH, O and NO. The multi-step finite rate model The multi-step finite rate reaction model uses chemical rate equations to model any number reaction occurring in the system. The reaction rates are calculated using the Arrhenius equation: k = A T p e n ( Ea/RT ) (2.5) where: k is the reaction rate coefficient A p is the pre-exponential constant E a /R is the activation temperature n is the temperature exponent A p, E a /R and n are determine experimentally for a particular reaction. Two different reaction sets were used during the course of this project, a two-step model and a sevenstep model. The reactions and rate coefficients are shown in the tables below. 2-step finite rate reaction No. Reaction Ap [m 3 /kmol s] n Ea/R [K] 1 H 2 + O 2 OH + OH OH +H 2 2H 2 O Note: this 2 step chemical rate equation was taken from Rogers and Chinitz step finite rate reaction Chapter Two Background 10

18 No. Reaction Ap [m 3 /kmol s] n Ea/R [K] 1 H 2 + O 2 OH + OH H + O 2 OH + O OH + H 2 H 2 O + H O + H 2 OH + H OH + OH H 2 O + O H + OH H 2 O + M H + H H 2 + M SUPERSONIC FLOW THEORY The most important consideration with supersonic flow is that the flow is compressible. A compressible flow is one for which the density cannot be considered constant (for flow below M = 0.3 the fluid can be considered to have a constant density). Compressibility leads to two phenomena unique to supersonic flow - shockwaves and expansion waves (see Figure 6). There are two types of shockwaves: oblique and normal. Oblique shockwaves and expansion waves are generated when a supersonic flow changes direction a shockwave when the flow converges and an expansion wave when the flow expands. shock wave expansion wave normal shock wave M 2<M 1 M 3>M 2 M 4<M 3<1 M 1 Figure 6: Shock and expansion waves Oblique shockwave relation An oblique shockwave is generated when the direction of a supersonic flow changes in a convergent way. The relative conditions after a oblique shock are the same as for the normal shock - Mach number decreases and pressure, temperature, density and entropy increase. The flow can however remain supersonic. The simplest case is flow over a half wedge. Chapter Two Background 11

19 shockwave M 1 β M 2 θ Figure 7: Oblique shockwaves The angle of the resulting shockwave is a function of both the wedge angle and free stream Mach number and is given by the relation 18 : M tanθ = 2 cot β 2 M1 ( γ sin β 1 + cos 2β ) + 2 (2.6) If this function is viewed graphically, it becomes apparent that for a fixed deflection angle θ, as the free stream Mach number is decreased the shockwave angle, β increases Expansion waves The overall effect of an expansion wave is the opposite of a shockwave: Mach number increases and temperature, pressure and density decrease. Entropy, however remains constant. Unlike a shockwave, the flow condition across an expansion wave change gradually and they are represented schematically as an expansion fan Normal shockwaves Shockwaves are established in supersonic flow as a solution to the problem of disturbance propagating through a flow. The properties of a flow such as pressure, temperature and density propagate through a flow at the speed of sound, a, which for an ideal gas is given by: a = γrt (2.7) where γ is the ratio of specific heats c p /c v, R is the universal gas constant and T the temperature. Consider the flow around a blunt body such as the one shown below. When the flow is subsonic, disturbances or information may be transmitted upstream since the speed of sound is greater than the flow velocity. The flow can be warned about the upcoming body and the flow condition varied accordingly. Chapter Two Background 12

20 Figure 8: Generation of a normal shockwave For the case where the flow is supersonic, the speed of sound is less than the velocity of the fluid. Flow disturbances cannot therefore be transmitted upstream and they tend to coalesce a short distance in front of the body. Since these disturbances cannot propagate upstream, ahead of the normal shock the flow has no idea about the upcoming body and acts as if the body is not there. After the shock the flow becomes subsonic and moves around the object. Both normal and oblique shockwaves can be considered as discontinuities in the flow. Flow condition change across them over a very small distance (typically 10-5 m for air at standard conditions). Across a normal shockwave, the Mach number decreases (to below 1 (subsonic)) and pressure, temperature, density and entropy increase. 2.6 EQUIVALENCE RATIO When referring to the Scramjet engine the term equivalence ratio is often used. The equivalence ratio is a measure of the richness of the air-fuel mixture. It is defined as the mass flux of fuel divided by the mass flux of air, all divided by this same ratio for a stoichiometric mixture. m& fuel m& air φ = m& fuel m& air stoic. (2.8) Chapter Two Background 13

21 CHAPTER THREE PROCEDURES 3. PROCEDURES 3.1 OVERVIEW Due to the multiple aims associated with this project it was divided into three phases: 1. Verification of CFD-ACE with previous work 2. Optimisation of the Scramjet geometry using CFD-ACE 3. Experimental verification of the optimum configuration In the first phase, experimental results obtained by Doolan 7 in 1997 were compared with models generated using CFD-ACE. Pressure measurements on the thrust surface of the Scramjet provided a basis for this comparison. This phase took approximately half the time allocated for the project. It involved a building a CFD model gradually - from the simplest case, to an increasing level of complexity. When this was done, this model was used as a basis for the remaining configurations. The second phase was to model the Scramjet at a particular operating condition (free stream pressure, temperature, Mach number and equivalence ratio) and to vary the two geometric parameters to find the maximum thrust. The models generated in phase one were used as a basis for these models. The final phase was to perform experiments in the T3 free piston shock tunnel using the ANU s Scramjet. Several of the configurations modelled using CFD were investigated by measuring the pressure inside the Scramjet combustor. This involved several modification to the Scramjet to accommodate new configurations and pressure transducer mounting positions. It should be noted that the phases in this project were not performed consecutively. Phase one was completed first, however components of phases two and three were performed simultaneously. There were several reasons for this. First of all, work using the T3 shock tunnel had to fit in with other work in the tunnel. The work was scheduled in the tunnel mid-way through second semester and this time had to be adhered to. Ideally CFD modelling would have been finished before this time but as the project proceeded this became unrealistic. The second reason was that the CFD modelling in phase one took longer than expected and so the other phases were pushed back. 3.2 VERIFICATION OF CFD-ACE WITH PREVIOUS WORK Before using CFD-ACE to model new configurations of the Scramjet, the program was used to model experiments that were performed in 1997 by Doolan 7. Pressure measurements on the thrust surface of the Scramjet were compared for these experiments with the CFD results obtained in this project. Five different configurations of the Scramjet were investigated by Doolan. In three of the conditions, a 78 mm long injector was used with 0, 50 and 87 mm flat duct sections. In the other two, a shorter 48 mm long injector was used with 80 and 117 mm flat duct sections. In all configurations, a thrust surface angle of 3.5 was used. Chapter Three Procedures 14

22 Figure 9: Scramjet configurations used in verification of Doolans experiments Pressure was measured at twelve positions on the thrust surface of the Scramjet. The positions with respect to the end of the injector are shown below: Transducer Position (mm) Transducer Position (mm) Experiment were performed for two different flow condition: combustion and non-combustion. In the combustion cases the free stream gas was air, in the non-combustion case the free stream was nitrogen. Nitrogen has a molecular mass similar to air and does not cause the hydrogen fuel to combust. The flow condition used were as follows: Mach number Pressure - 90 kpa Temperature K Equivalence Ratio Overall procedure Two dimensional CFD models of all 5 configurations were constructed. There were several reasons why three dimensional models were not used. Firstly, CFD had not been used to model the flow in the ANU s Scramjet and it was thought best to start from the simplest case - two dimensions. Secondly, 3D models require significantly more computational time and finally it is easier to analyse the results in only two dimensions. The approach taken in building the five models was to start from the simplest possible configuration and flow conditions and to gradually build on this, increasing complexity until the desired level of detail and accuracy was achieved. Two models were gradually constructed using this procedure and Chapter Three Procedures 15

23 the remaining 3 configurations based on these. As the models increased in complexity and different features were added, pressure measurements along the floor were monitored and compared with experimental results. The results can be found in section In building up an accurate first model the following issues were addressed: What grid resolution is required? Should a turbulent or laminar flow model be used? What mixing model should be used? What reaction model should be used? To address these issues the model was built up with the following configurations: 1. flat, empty Scramjet duct with laminar flow 2. flat, empty duct with turbulent flow 3. empty duct (no injector) with thrust surface and turbulent flow 4. duct with thrust surface, injector and turbulent flow 5. duct with thrust surface, injector, turbulent flow and injection and mixing 6. duct with thrust surface, injector, turbulent flow, injection, mixing and instantaneous combustion 7. duct with thrust surface, injector, turbulent flow, injection, mixing and equilibrium combustion 8. duct with thrust surface, injector, turbulent flow, injection, mixing and 2-step finite-rate combustion 9. duct with thrust surface, injector, turbulent flow, injection, mixing and 7-step finite-rate combustion Also, for step 5 a grid analysis was performed to see what effect grid resolution had on results. 48 different models were generated during this phase. This large number was due to the variety of different flow conditions that were experimented with Numerical procedures For each model generated in this phase there were several common steps. These steps are outlined below: 1. Generate the grid The grids were generated using CFD-GEOM. This program first requires the definition of the overall geometry. The geometry is divided into several domains which depend on the geometry of the model. For each wall of a domain the number of grid points are defined. After all the walls are defined the internal cells are generated. Grid points can be distributed according to a power law so that changes in grid resolution occur gradually (grid spacing should not change between two cells by more than a factor of 0.3). The output of this program is used by the program CFD-ACE. Chapter Three Procedures 16

24 Figure 10: Sample grid (Note: for viewing purposes the grid resolution is half of what was generally used) A more detailed figure of a typical grid can be found in Appendix A. 2. Generate the model CFD-ACE is used to generate and modify the CFD model. There are two sections to this program: model and solve. The model section is used to define fluid properties, mixing, reacting and turbulence models and the boundary conditions. The solve section is used the control the iteration, relaxation, output and to start the solver. The first step in defining a model is to import the grid. The different option of fluid models are then selected (these can include: compressible, incompressible, turbulence, heat transfer, mixing and reacting flows). Fluid properties are then defined. For each of the flow models specified, associated parameter are also defined. The boundary conditions and overall initial conditions are then defined (initial conditions generated from previously run models can be used). In the solver section of the program, parameters such as the number of iterations, relaxation and limits are specified. Also, the parameters that are to be recorded are selected. Finally the model is submitted and the residuals can be viewed. Generally the solution was deemed to be converged when the residuals had decreased by 4 5 orders of magnitude. 3. View the results After the solution has converged and the run stopped, the results can be viewed using CFD-VIEW. Two methods of representing the data were used in this project: viewing a particular property over the entire duct using a specified colour palette, and graphing a property along a particular cell line. The first of these gives an overall, qualitative analysis of the flow, the second a quantitative analysis CFD model input parameters For a larger number of the models generated in this phase the parameters input to CFD-ACE were the same. A summary of these are shown below. Fluid properties Density - Ideal gas law Viscosity - Sutherland s law Specific heat - JANNAF method Conductivity - Prandtl Number, 0.7 Mass diffusion - Schmidt Number, 0.9 Chapter Three Procedures 17

25 Air composition - mass fraction Boundary conditions O N Inlet (free stream) Pressure - 70 kpa Temperature K Velocity m/s k L m Injector Pressure kpa Temperature K Velocity m/s k L m Wall Isothermal - T = 298 K Outlet Extrapolated Models Turbulence k-ε - Prandtl number 0.9 Schmidt number 0.5 Reaction Instantaneous Reaction - 2H 2 + O 2 2H 2 O Reaction - Equilibrium Species present - H 2, O 2, N 2, H 2 O, OH, O, NO Reaction 2-step finite rate See section for reaction rate coefficients. Reaction 7-step finite rate See section for reaction rate coefficients. Chapter Three Procedures 18

26 3.3 OPTIMISATION OF THE SCRAMJET GEOMETRY USING CFD-ACE The second phase of this project was the optimisation of the Scramjet combustor geometry for maximum thrust using CFD-ACE. This phase was dependant on the completion of phase one since the correct operation of the CFD-ACE program and models had to be verified before any subsequent models could be made. The effect on thrust was investigated by varying the flat floor length, L and thrust surface angle, θ (see Figure 2) for a given total length of Scramjet. Previous work by Doolan showed that in his configuration the thrust increased as flat floor length increased (for a given total length of duct). The increase in thrust is due to an increase in pressure as the floor length is increased. The pressure increases because there is more time (distance) for the flow to mix and combust before the cooling and quenching effects of the expansion are caused by the angled thrust surface. For Doolan s configurations, no limit to this increase was found. It was anticipated that there would be a limit to the increase in thrust since an increasing flat floor length (producing increasing thrust) would be counteracted by a short length of thrust surface for which the pressure can be converted into thrust. Also, variation of thrust surface angle should have some effect on the maximum thrust attainable. It was anticipated there would be some trade-off between the effects of pressure decrease due to a larger θ (larger expansion) and more efficient conversion of pressure into thrust at larger θ (due to a larger component of the thrust surface being perpendicular to the flow) Numerical procedures A total length of Scramjet of 500 mm was considered. This corresponds to the maximum length of the ANU Scramjet. The free stream conditions used were as follows: Mach number Pressure kpa Temperature K Equivalence Ratio The Scramjet models were all based on the ANU s Scramjet with the longer 78 mm strut injector. Flat duct length was varied between 50 and 200 mm and thrust surface angle between 1.75 and 7 degrees. The flat duct limits were chosen based on Doolan s conclusions. The thrust surface angles were chosen based on an angle determined by the National Aerospace Laboratory (NAL), Japan. This angle was 3.5. Angles were chosen at increments above and below this angle. All the limits were also chosen such that the ANU s Scramjet could be modified to accommodate the changes. Initially a matrix of configurations within these limits was investigated. These are shown in the table below. Chapter Three Procedures 19

27 Flat duct length Thrust surface angle mm 50, , , , mm 100, , , , mm 150, , , , 7 200mm 200, , , , 7 Due to time constraints a number of these configurations were not modelled. These are shown in italics. Two other configurations not shown, one with 0 mm flat duct at 7 thrust surface angle and one with 100 mm flat duct and 15 thrust surface angle, were also modelled. All configurations were modelled for both combustion and non-combustion cases CFD model input parameters Numerous different parameters and properties were input to CFD-ACE. For all the models these were the same, the only changes were to the geometry. The model properties and parameters input to the program are listed below. Fluid properties Density - Ideal gas law Viscosity - Sutherland s law Specific heat - JANNAF method Conductivity - Prandtl Number, 0.7 Mass diffusion - Schmidt Number, 0.9 Air composition - mass fraction O N Ar NO O Boundary conditions Inlet (free stream) Pressure kpa Temperature K Velocity m/s k L m Injector Pressure kpa Temperature K Velocity m/s Chapter Three Procedures 20

28 Wall Outlet k L m Isothermal - T = 298 K Extrapolated Models Turbulence k-ε - Prandtl number 0.9 Schmidt number 0.5 Reaction - 7 step finite rate Post Processing See section for details CFD data was collected in the form of pressure traces along the floor of the Scramjet and colour images of pressure and H 2 O mass fraction in the duct. H 2 O mass fraction gives an indication of where and to what degree combustion is occurring in the duct. A pressure force summary was also generated for each model. This contained pressure and shear forces resolved into x and y components for each of the walls and boundaries in the models. These forces could be summed to give the total thrust generated by the Scramjet. 3.4 EXPERIMENTAL VERIFICATION OF THE OPTIMUM CONFIGURATION The third phase of this project was the verification of the optimum configuration of the combustor geometry by performing experiments using the ANU s Scramjet in the T3 shock tunnel. This phase served to both further verify the operation of CFD-ACE and to determine how the optimum condition predicted from CFD-ACE results compared with actual experimental results. Before experiments could be performed a number of modifications to the Scramjet were made so that the different configurations could be tested and so pressure transducers could be placed in appropriate sections. These modifications are outlined in section 4.1. A total of 33 shots in the T3 shock tunnel were used in this project for the testing of 14 different configurations (see Appendix B for shot details). The configurations tested ranged from mm in flat duct length and from 1.75 to 7 thrust surface angle. Originally the 50 mm flat duct length was going to be tested as well (as was modelled using CFD) however time constraints prevented this. Additionally 2 configurations at 0 and 50 mm flat duct length and 7 thrust surface angle were tested. For each configuration both combustion and non-combustion cases were investigated by using air and nitrogen in the free stream respectively. Chapter Three Procedures 21

29 3.4.1 Experimental Procedure Before the experiments were started, the injection system (see section 4.3) was calibrated by firing the shock tunnel (with Scramjet mounted in the test section) and measuring the injector pressure trace. The delay on the injector timing system was adjusted so that the correct equivalence ratio was obtained. These shots were also used to see if the pressure acquisition system was working. The first configuration tested was the 200 mm flat floor, 1.75 thrust surface angle. This had the most constrictive geometry and was tested first to see if the flow choked * - which it did not. The remaining configuration were then tested. For each of the flat floor configurations the thrust surface angle was modified from to 1.75, 3.5, 5.25 and 7. The flat floor length was then reduced to the next increment. After all these configurations were tested the two additional configurations of 0 and 50 mm flat floor with 7 angle were tested. For each of the configurations 2 shots were fired. After every two shots the test section side plates were removed, the Scramjet disassembled and the configuration changed. Pressure transducer positions were changed every time the flat duct length was decreased. This process usually took between 1½ and 2 hours. For each shot there was also 1 2 hours to pump down and then pressurise the shock tunnel. Shock tunnel operation was performed by Paul Walsh and Paul Tant. An average of 3 shots were performed each day over a period of 14 days Post processing Pressure data was recorded over a period of 10 ms. The pressure measurements used in this project were taken at 1.4 ms after the flow began. This figure has been determined as the time at which the flow is steady in previous experiments 4. The pressures at this time were smoothed over a period of 0.2 ms. Thrust was calculated by fitting a linear spline to the pressure data and integrating this pressure over the distance of the thrust surface using Simpson s rule (up to a total Scramjet length of 500 mm). The force was then resolved to the x direction. Experimental error was determined by calculating thrust for several configurations using the trapeziodal rule and Simpson s rule. This yielded values consisted to within 10%. By allowing 3% accuracy for the pressure measurements the accuracy of the thrust measurements is estimated as ±13%. * A choked flow is a subsonic flow that has been caused by too much heat being released in combustion. It can be avoided by expanding and thus cooling the flow. Chapter Three Procedures 22

30 CHAPTER FOUR EXPERIMENTAL SETUP 4. EXPERIMENTAL SETUP 4.1 SCRAMJET MODIFICATIONS There were several modification made to the Scramjet. The drawings for these can be found in Appendix C. The section after the injector is composed of two sections, the flat floor and the thrust surface. In order to change the geometry to the desired configurations flat floor sections and side plates to hold these up were constructed. To change the thrust surface angle, side plates that hold the long, thrust surface section were made. A B C D flat floor sections E F G side plates Figure 11: Modifications to the Scramjet example of the 200mm flat floor configuration In order to change the Scramjet geometry over equal floor increments, 50 and 25 mm floor sections were fabricated. These sections contained 2 and 1 PCB pressure transducer mountings respectively. A 100 mm floor section already existed, so 4 transducer mounts were incorporated in this (D). A single 50 mm floor section also existed. This mount had been constructed is such a way so that it could fit immediately behind the injector, the other sections could not (B). With the 50, 100 and 50 mm sections the configurations with flat floor length between 100 and 200 mm could be constructed. The 25 mm section was made in anticipation of smaller increments of floor length being investigated but time constraints prevented this. For each of the floor section made, two side plates were fabricated to serve as structural supports. These are shown as E and F in Figure 11. Side plates for the 3.5 degree thrust surface already existed. Plates for 1.75, 5.25 and 7 were constructed. A 7 side plate is shown as G in Figure 11. Modifications were also made to the roof section of the Scramjet to accommodate two pressure transducers immediately behind the injector (A). Ideally these transducers would have been placed on the floor behind the injector however they would have interfered with another pressure transducer that Chapter Four Experimental Setup 23

31 is mounted in the injector and has a lead that exits just below the first floor section. Consequently they were placed in the roof, and since the Scramjet is symmetric up until the thrust surface, the readings should be the same as if they were placed on the floor. 4.2 PRESSURE TRANSDUCERS Twelve PCB transducers were used to measure the pressure in the duct. One other PCB was used to record the pressure just after the injector fast-acting valve. The PCB details are shown in the table below. Transducer Type Calibration [mv/kpa] Transducer Type Calibration [mv/kpa] 1 113M M M M M M M M M M M AA Injector 112A The positions of the pressure transducers on the Scramjet roof and floor varied depending on the flat floor length used. The positions are shown in the table below. 100 mm floor 150 mm floor 200 mm floor Transducer Position [mm] Transducer Position [mm] Transducer Position [mm] INJECTION SYSTEM The injection system is configured so that the injection is initiated well before the supersonic flow reaches the Scramjet and finished well after the flow has past. Hydrogen fuel is stored in a coiled copper Ludweig tube. When a solenoid, situated inside the Scramjet, is triggered a fast acting valve is activated injecting the hydrogen into the flow via the injector. A pressure transducer is mounted in a cavity behind the valve which measures the static pressure. Chapter Four Experimental Setup 24

32 Injector Stagnation Pressure [kpa] Time [ms] Pressure [Pa] Figure 12: Typical injection pressure trace Figure 12 shows a typical injection pressure trace. The red line shows the time at which the flow passes through the Scramjet (for 1 ms) and the blue the injector pressure. The mass flow rate of hydrogen out of the injector, and therefore the equivalence ratio, is based on the static pressure in the injector. Even though this pressure is decreasing over time, during the short period that flow passes through the Scramjet, it can be considered constant. To calibrate the injection to the correct equivalence ratio, both the initial reservoir pressure and the timing of the injector can be modified. A He-Ne laser attached to the side of the shock tunnel is used to trigger the injection solenoid valve. When the shock tunnel is fired the whole tube, from the high pressure reservoir to the nozzle, moves backward approximately 3 cm. When this occurs the laser moves out of line from a photo-diode which is stationary and a ve pulse is produced. This pulse is isolated, attenuated and delayed and sent to the solenoid power supply to start injection. 4.4 PRESSURE MEASUREMENT SYSTEM The pressure measurement system is outlined in Figure 13. There were a total of 15 PCB pressure transducers 12 measuring pressure in the Scramjet, one measuring pressure just before the injector and two measuring the timing of the shockwave (stagnation and timing PCB s). Data was recorded on one LeCroy waveform digitizer and 3 Tektronix digital oscilloscopes. Eight of the pressure channels were recorded on the LeCroy and the remaining 4 on the 4-channel oscilloscope. Data was stored on the LeCroy and could be downloaded later via a Macintosh computer. Data from the cro could be recorded directly to floppy disk. The LeCroy and cro had a sampling rates of 20 µs and 10 µs respectively (this data was later smoothed). The first of the 2-channel oscilloscope s was used to record the injection pressure trace and the stagnation pulse. The stagnation pulse showed at what time the flow passed through the Scramjet and from this the injector pressure, and thus equivalence ratio, could be determined (see section 4.3). The second of the 2-channel oscilloscope s was used to record the timing and stagnation PCB traces. These showed the relative time at which the shockwave passed. They were used to determine the consistency of the shock speed. Chapter Four Experimental Setup 25

33 The order of events involved in a single acquisition was as follows. The shockwave in the shock tube generated two signals one from the timing PCB and one from the stagnation PCB. These two signal caused the timer to start and stop respectively (measuring the time between the two PCB and thus the shock speed). The stagnation signal was also passed to a pulse generator, the output of which triggered both the LeCroy and 4-channel oscilloscope. Data was recorded on the LeCroy and the oscilloscope as the supersonic flow passed through the Scramjet. Scramjet nozzle shock tube stagnation PCB timing PCB PCB pressure transducers Injector PCB PCB power supply PCB power supply Group 3 attenuation unit timer PCB s 1-8 PCB s 9-12 Lecroy Bank 4 Waveform digitizer Farnell Pulse Generator stagnation pulse injector stagnation Tektronix Tektronix Tektronix 4 channel CRO 2 channel CRO 2 channel CRO timing Figure 13: Pressure data acquisition system Chapter Four Experimental Setup 26

34 CHAPTER FIVE RESULTS AND PRELIMINARY ANALYSIS 5. RESULTS AND PRELIMINARY ANALYSIS 5.1 VERIFICATION OF CFD-ACE WITH PREVIOUS RESULTS Results in this section are in the form of pressures along the Scramjet floor and CFD colour images of pressure and H 2 O mass fraction. H 2 O mass fraction gives an indication of where and to what degree combustion is occurring in the duct Turbulent or laminar flow The first two CFD models generated where flat, straight ducts, 350 mm long with no injector and with turbulent and laminar flow respectively. The boundary layer thickness in each of these models was measured at the outlet by determining the point at which the flow velocity was 99% of the free stream velocity (this was easily determined using CFD-VIEW). The results were: laminar model, boundary layer thickness - 1 mm turbulent model, boundary layer thickness - 6 mm The boundary layer thickness was also calculated using 1-D isentropic flow theory and pressures at the inlet and outlet of the duct (obtained from an empty duct shot in the Scramjet) to calculate the effective area reduction in the flow (as the flow travels downstream the boundary layer grows and effectively reduces the area of the duct). The result was a boundary layer thickness of 7 mm. This thickness corresponds most closely to the turbulent model. As a result, turbulent flow was selected for the remainder of the models Grid resolution For a Scramjet duct with thrust surface, an injector injecting hydrogen, and mixing (no combustion), a model was constructed and a test performed to determine the effect of grid resolution on the pressures on the floor of the duct. The grids were based on the grid that was used for all other models. The grid at the original resolution (11294 cells) was compared with two other grids, one with the number of grid points halved (2618 cells) and one with the grid points doubled (45664 cells). The results of this test can be found below. Chapter Five Results and Preliminary Analysis 27

35 Fine Grid Medium Grid Coarse Grid Pressure [Pa] Distance from SCRAMJET inlet [m] Figure 14: Grid comparison Figure 14 shows that the higher the grid resolution, the better the model resolves the shock and expansion waves (peaks and troughs). The overall trends for all grids however are the same and on the thrust surface floor, where the shock waves have weakened, the pressures are very similar. The shock and expansion waves are generally in the same place (position in the flow) for all grids. Apart from result accuracy, the other important issue in this test was the computational time. The coarse grid took approximately 15 minutes to converge, the medium 45 minutes and the fine 3 hours. Considering the accuracy of the three grids and the computational time it was decided the medium grid was most appropriate Combustion model For the two long injector configurations with 0 and 50 mm flat ducts, instantaneous, equilibrium, 2- step finite rate and 7-step finite rate combustion models were used. A comparison of these reaction models can be found below. Figure 15 shows the pressures along the floor of the Scramjet. It is apparent that the instantaneous and equilibrium combustion models produce very similar results and that the pressure rise associated with combustion for both occurs soon after the fuel exits the injector. This is also seen in Figure 16 where the water combustion product is visible from immediately behind the injector. Figure 17 and Figure 18 show that, for the finite rate models, there is a delay in the ignition. This ignition delay is apparent in experimental pressure results (see later) and is a well documented phenomena for the hydrogen oxygen reaction. The hydrogen oxygen reaction actually occurs in two stages: the first step, where the temperature does not change substantially but production of radicals (O, H and OH) occurs; and the second step, where heat is released and the temperature rises rapidly. The time involved in the first step is significant and is called the ignition delay time. Figure 18 shows that for the 7-step model the ignition delay is longer than the 2-step. Chapter Five Results and Preliminary Analysis 28

36 For the remainder of the configurations only the 7-step finite rate model was used. This was because it better represented the actual reactions occurring in the flow. Also, in some configurations, the two step model was quite difficult to converge and required a stiff reaction solver, which took longer to converge than the 7-step. Floor Pressure - Long injector, 50mm flat duct (li-50f) Instantaneous Combustion Equilibrium Combustion 7-step finite rate combustion 2-step finite rate combustion Non-combustion Pressure [Pa] Distance from duct entrance [m] Figure 15: Combustion comparison Figure 16: Equilibrium combustion - water mass fraction Figure 17: 2-step finite rate combustion water mass fraction Chapter Five Results and Preliminary Analysis 29

37 Figure 18: 7-step finite rate combustion water mass fraction Inlet pressure Originally the inlet pressure used was 90 kpa. This figure was determined in a previous project 19. As more configurations were modelled it became apparent that overall the pressures were too high (when compared with experimental results). The inlet pressure was therefore gradually reduced until the CFD non-combustion results matched up with experimental non-combustion result. (It was thought that the non-combustion model were predicting the flow more accurately than the combustion models). This was further justified by analysing the pressure at the inlet and around the injector. The 90 kpa inlet pressure was based on a PCB pressure transducer measurement (positioned above the injector) of 140 kpa. This difference is due to the flow passing through a shockwave before it reaches the transducer. When a inlet pressure of 90 kpa was used the CFD model predicted a pressure of 180 kpa at an equivalent position. When the inlet pressure was reduced to 70 kpa this pressure was 140 kpa CFD image features Pressure is one of the better flow parameter from which to visualise the different processes occurring in the Scramjet. The figure below shows the flow around the injector section. Figure 19: Pressure around the injection Clearly visible are the shock waves (red and yellow) caused initially by the injector leading edge. Not so clear are the expansion waves (blue/green) originating from the back of the leading edge and rear Chapter Five Results and Preliminary Analysis 30

38 of the injector. Behind the injector, recompression shocks are visible after the flow has expanded around the back of the injector. The shock and expansion waves can be seen to reflect off the walls and injector of the Scramjet. The shock and expansion wave become noticeably smeared as they travel downstream. The first shock waves are clearer than those downstream. This is one of the problems with any finite element method and can only be partially improved by increasing the grid density. After the injector the flow becomes more complex, with increasing interactions between the reflecting shock and expansion waves Overall Results The figures below show the comparison of CFD and experimental results for each of the 5 configurations. The images below each plot show where on the Scramjet the pressure measurement were taken. It should be noted that for the configuration li-0f, the grid resolution was double the other configurations. Floor Pressures - Long injector, 0mm flat duct (li-0f) High grid density models Pressure [Pa] Experiment - Combustion (9942) Experiment - Non-combustion (9943) CFD - Non-combustion CFD - Combustion - 7 step finite rate Distance from duct entrance [m] Figure 20: Floor pressure long injector, 0mm flat duct Chapter Five Results and Preliminary Analysis 31

39 Floor Pressure - Long injector, 50mm flat duct (li-50f) Experiment - Combustion (9946) Experiment - Non-combustion (9947) CFD - Non-combustion CFD - Combustion - 7 step finite rate Pressure [Pa] Distance from duct entrance [m] Figure 21: Floor pressure long injector, 50mm flat duct Floor Pressure - Long injector, 87mm flat duct (li-87f) Experiment - Combustion (9951) CFD - Instantaneous Combustion (choked) CFD - Combustion - 7-step finite rate CFD - Non-combustion Pressure [Pa] Distance from duct entrance [m] Figure 22: Floor pressure long injector, 87mm flat duct Chapter Five Results and Preliminary Analysis 32

40 Floor Pressure - Short Injector, 80mm flat duct (si-80f) Experiment CFD - Non-combustion CFD - Combustion - 7-step finite rate Pressure [Pa] Distance from duct entrance [m] Figure 23: Floor pressure short injector, 80mm flat duct Floor Pressure - Short injector, 117mm flat duct (si-117f) Experiment - Combustion (9949) Experiment - Non-combustion (9950) CFD - Non-combustion CFD - Combustion - 7-step finite rate Pressure [Pa] Distance from duct entrance [m] Figure 24: Floor pressure short injector, 1170mm flat duct Chapter Five Results and Preliminary Analysis 33

41 It should be noted that for the configurations where no experimental results are shown for the noncombustion cases, data was unavailable Comparison of CFD and previous experimental results The most obvious difference between the experimental and CFD results, for all the configurations, is that the large fluctuations in the experimental results are not present in the CFD results. These fluctuations are due to reflected shock and expansion waves in the duct. CFD-ACE is not particularly good at resolving shock waves. The grid often is not of a high enough resolution to pick up the large changes in fluid properties across them. Increasing the grid resolution does increase their sharpness, (as shown in Figure 14) but at the expense of computational time. Figure 14 also shows that no matter what grid resolution, the shock waves are smeared as they travel downstream. This cannot be avoided using CFD-ACE. In reality, shock waves decrease in strength as they are reflected off the walls, but to a much lesser degree than apparent in CFD-ACE. All 5 CFD configuration show there is an increase in pressure when comparing the combustion and non-combustion cases. This is as expected and is due to the temperature rise associated with the combustion reaction. The CFD result using instantaneous combustion for the long injector with 87 mm flat duct configuration shows a very large increase in pressure. This is due to the Scramjet choking (choking occurs when flow in the Scramjet becomes subsonic). The experimental results show that the flow did not choke, however this has been attributed to transient effects - it takes a finite time before the flow chokes and the test times were too short to observe the final state of the flow. This was the only case where the CFD results differed to such a large extent from the experimental. For the non-combustion cases, CFD results show a good correlation with experimental results, in terms of both overall trends (decreasing pressure as the floor diverges) and magnitude. This can be partially attributed to the modification of the inlet pressure (see section 5.1.4). The CFD combustion models show significantly less correlation with experimental results. Overall the pressures are lower than the experiments would indicate. There are two likely reasons for this: grid resolution and inlet conditions. In all of the experimental combustion results, there is an initial sharp rise in the pressure in the duct. In Figure 20 this can be seen approximately half-way along the thrust surface, in the remaining configurations it can be seen toward the beginning of the thrust surface. This increase is due to the pressure rise associated with combustion. It is thought that the combustion is initiated by the flow passing through a shock wave. The shock wave increases the pressure and temperature above the ignition conditions and combustion occurs rapidly. The ignition temperature is between K. Changes over this range have a significant effect on the reaction rate. For the medium grid resolution used in the above configurations, the pressure and temperature rise associated with the shock waves was not sharp enough (as seen in Figure 14) to reach the ignition temperature and so the flow did not fully ignite. The difference in pressure between the non-combustion and combustion CFD cases does show that combustion is occurring, however by doubling the grid resolution, as was Chapter Five Results and Preliminary Analysis 34

42 the case for long injector, 0mm flat duct configuration (Figure 20), the full pressure rise associated with combustion can be seen. The pressure for the combusting mixture is still however lower than experiments suggest. If the grid resolution was increased for the remaining configurations it is thought that the larger pressure rise would be seen. Due to time constraints these models were not generated. The other possible explanation for the difference in combustion results could lie in the inlet conditions input to CFD. Since combustion is highly sensitive to temperature in the range K, a slight change in the inlet temperature could have a significant effect on combustion in the duct. Inlet pressure was changed from the original values in order to reproduce the non-combustion results, which could suggest that other parameters may not be correct. Uncertainty was also associated with the inlet conditions, since for Doolan s experiments the flow passed through a diffuser (a set of converging plates) to slow the flow before it entered the Scramjet. The pressure and Mach number were verified after the diffuser, but there was more uncertainty with the Scramjet inlet conditions than if no diffuser was used (as was the case for this project) Summary The lessons learnt in this phase were very important for the subsequent CFD modelling. Turbulent and laminar flows were investigated to see which was most appropriate; several different combustion models were tested and the most appropriate chosen; and problem with low grid resolution identified. The models used in the next phase of the project where based on the combustion and non-combustion models shown above. The most important modifications to these were a doubling of the grid resolution and more accurate predictions for the inlet conditions. 5.2 COMPARISON OF CFD AND EXPERIMENTAL RESULTS In this section results obtained from CFD and experiments perform in this project are compared. For conciseness, results from four representative configurations are shown below. Pressure measurements for all configurations modelled and tested can be found in Appendix C. 300 Combustion 300 Non-Combustion Pressure [kpa] Experiment 50 Experiment CFD Distance from front of Scramjet [m] CFD Distance from front of Scramjet [m] Chapter Five Results and Preliminary Analysis 35

43 Figure 25: Scramjet pressure 200 mm, 1.75 thrust surface 300 Combustion 300 Non-Combustion Pressure [kpa] Experiment CFD Distance from front of Scramjet [m] 50 Experiment CFD Distance from front of Scramjet [m] Figure 26: Scramjet pressure 150 mm flat floor, 7 thrust surface 300 Combustion 300 Non-Combustion Pressure [kpa] Experiment CFD Distance from front of Scramjet [m] 50 0 Experiment CFD Distance from front of Scramjet [m] Figure 27: Scramjet pressure 100 mm flat floor, 1.75 thrust surface Chapter Five Results and Preliminary Analysis 36

44 300 Combustion 300 Non-Combustion Pressure [kpa] Experiment CFD Distance from front of Scramjet [m] 50 0 Experiment CFD Distance from front of Scramjet [m] Figure 28: Scramjet Pressure 0 mm flat duct, 7 thrust surface The CFD results above show a much better correlation with experimental results than for comparisons with Matthew Doolan s results. As was mentioned previously this was most likely due to the increased grid resolution and better estimate for the inlet conditions. The above results show a much better prediction of the shock and expansion waves. All the major pressure increases and decreases are predicted and the variations in pressures associated with the shock and expansion waves are much greater in magnitude than in the previous results. The overall magnitudes and trends associated with combustion, non-combustion and expansion around the thrust surface are also well predicted. In CFD results, the large step down in pressure occurs over the initial change in geometry around the thrust surface. The most obvious difference between results is the position of the shock waves. For the combustion cases CFD-ACE consistently predicted the shock wave downstream (to the right) of experimental results. For the non-combustion cases CFD-ACE consistently predicted the shock wave upstream (to the left) of experiments. Overall the positioning of the shock waves was better predicted in the CFD combustion models than the non-combustion models. The logical explanation for these differences is that the shock and expansion wave angles are wrongly predicted. There could be several reasons for this: 1. The Mach number of the free stream is not right. As seen in section 2.5.1, the angle of an oblique shock generated from a change in direction of the flow is dependant on the Mach number. An increase in Mach number will produce a decrease in the shock angle and thus a change in the position of the shock waves. This explanation would not however explain why there are differences in position between the combustion and non-combustion models. 2. The other possibility is that the conditions in the hydrogen fuel stream are incorrect. Shock and expansion waves are reflected and transmitted at varying angles as they pass through the hydrogen stream. The angle that they are reflected and transmitted is dependant on the Mach numbers of Chapter Five Results and Preliminary Analysis 37

45 both the free stream air and the hydrogen stream. The combustion process would change the Mach number in the hydrogen stream. 3. The third possibility is that for the non-combustion cases the nitrogen and air results cannot be compared (Nitrogen was used in the free stream in experiments while air was used in CFD). Using Nitrogen, which has a fractionally lower molecular weight, in the CFD models would have the effect of increasing the shock wave angle and shifting the shock waves further to the left, however it may have some other effect that could not be forseen. Regardless of these differences, the above results show CFD predicts the flow in the Scramjet surprisingly well. Shock and expansion waves are predicted accurately in magnitude (but not so well in position) and overall pressures and trends are well predicted. Chapter Five Results and Preliminary Analysis 38

46 CHAPTER 6 - RESULTS ANALYSIS AND DISCUSSION 6. RESULTS ANALYSIS AND DISCUSSION 6.1 COMPARISON OF EXPERIMENTAL AND CFD THRUST CALCULATIONS 300 Combustion Non-Combustion Experiment CFD Experiment CFD 140 Combustion Non-Combustion Experiment CFD Experiment CFD Thrust [N] Thrust [N] Flat floor length [mm] Flat floor length [mm] (a) (b) Figure 29: Comparison of CFD and experimental thrust calculations: (a) 7 thrust surface, (b) 1.75 thrust surface Figure 29 shows the comparison between thrust determined from CFD and from experiments for two thrust surface angles. It shows that for the combustion cases, CFD thrust calculations are higher than the experimental calculations while for the non-combustion cases the CFD results are consistently lower than experiments. This is consistent with the comparison of pressure measurements (see Appendix C). The remaining analyses in this chapter are based on the CFD results. 6.2 EFFECT OF THRUST SURFACE ANGLE Chapter Six Results Analysis and Discussion 39

47 Total Thrust [N] mm 150 mm 100 mm 50 mm Thrust Surface angle [deg] Figure 30: Effect of thrust surface angle on thrust generated (combustion) Figure 30 shows the total thrust in the Scramjet as a function of the thrust surface angle. These values are plotted for all four of the flat duct lengths. The thrust generated is actually negative since the shear forces generated on the walls of the Scramjet are greater than the thrust developed by the thrust surface. This is not surprising due to the low equivalence ratio used (0.5). Clearly shown in Figure 30 is the trend of increasing thrust as the thrust surface angle is increased. This is because as the angle is increased the component of the pressure force in the x direction is increased. The maximum thrust is generated for the 7 degree case, however the limit to this increase is undetermined. In hindsight larger thrust surface angles should have been investigated. The angles used where based on the 3.5 degree angle used in previous experiments by Doolan and proposed by researchers at the Japanese National Aerospace Laboratories (NAL). There was however some confusion about this angle which resulted in the incorrect assumption that it would be appropriate to investigate angles around this value for use as the thrust surface angle. A single configuration with 15 thrust surface and 100 mm flat duct length was investigated after the above results were found. The results of this are shown in Figure 31. Chapter Six Results Analysis and Discussion 40

48 50 Total Thrust [N] Thrust Surface angle [deg] 200 mm 100 mm Figure 31: Thrust generated by 15 thrust surface This shows that a 15 thrust surface generates positive 30 N of thrust. It transpired that previous investigations have occurred for thrust surface angles around this value. Further investigation of thrust surface angles above and below this value would be required to determine the maximum thrust obtainable 6.3 EFFECT OF FLAT DUCT LENGTH Total Thrust [N] Flat duct length [mm] Figure 32: Effect of flat duct length on thrust generated (combustion) Figure 32 shows that varying the flat duct length has much less effect than varying the thrust surface angle. It also shows that the thrust surface length (which is dependant on the length of the flat duct Chapter Six Results Analysis and Discussion 41

49 length since the total length of the Scramjet is not varied) does not have as large an effect on the thrust generated as the thrust surface angle. For the 7 thrust surface maximum thrust is produced for a flat duct length of 100 mm. This is shown in more detail in Figure 33. Total Thrust [N] Flat duct length [mm] Figure 33: Variation of flat duct length for 7 thrust surface angle The decreasing thrust at lower flat duct lengths is due to a lack of combustion in the duct. When the duct is expanded too close to the injector, the expansion reduces the pressure and temperature before the fuel has time to ignite. This can be seen in Figure 34 below. Figure 34: H 2 O mass fraction 50 mm flat duct, 7 thrust surface Figure 34 shows that the bottom side of the fuel stream does not combust until near the end of the duct. Figure 35 shows the water mass fraction for the next longest flat floor configuration with both sides of the fuel stream combusting. Figure 35: H 2 O mass fraction 100 mm flat duct, 7 thrust surface In this configuration the flat duct is sufficiently long to allow the ignition delay to occur before the pressure and temperature is decreased by the expansion. For the zero flat duct configuration virtually no combustion occurs (This can also be seen in Appendix C where the pressures from the combustion and non-combustion cases are almost the same). Chapter Six Results Analysis and Discussion 42

50 Expanding the flow too early causes the temperature to decrease below the ignition temperature (between 1100 and 1200 K). Figure 36 shows the temperature over the range K in the region immediately after the expansion, for the 50 mm flat duct case. This highlights the subtle but important temperature differences between the upper and lower sections of the duct. The upper red/purple section just after the expansion (caused by a reflected shock wave) causes the upper boundary of the fuel stream to ignite and combust. In the lower section, the expansion causes the temperature to decrease below the ignition temperature and so the lower boundary of the fuel stream does not combust. Figure 36: Temperature around the expansion region (50 mm flat duct, 7 thrust surface) For configurations with longer flat duct lengths, the temperature also drops below the ignition temperature after the expansion, however the combustion process can sustains itself since the length is such that it has already begun to combust further upstream. These results highlight the important relationship between ignition delay time (or ignition delay length) and flat duct length. They show that for combustion to occur in the duct the thrust surface must not begin before ignition of the fuel-air mixture. The length of duct required for combustion, using the free stream conditions investigated in this project, is 100 mm. For different free stream conditions this value would be most dependant on free stream Mach number and temperature. This length could also be reduced when using other injectors that increase the mixing efficiency in the duct 12. As the thrust surface angle is decreased the flat duct length has less effect on the combustion in the duct. This can be seen for the 1.75 case in Figure 32 where thrust produced increases until 0 mm of flat floor. In this case the thrust surface begins before the mixture begins to combust, however the expansion is not large enough to cause the temperature to decrease below the ignition value. For the 3.5 and 5.25 cases the optimum flat duct length is undefined. The optimum flat duct length may vary for the thrust surface cases between 1.75 and 7 depending on the effect of the expansion process, however thrust surface angles above 7 would all have an optimum value of 100 mm (since regardless of the angle, combustion begins before the thrust surface begins). 6.4 EFFECT OF THRUST SURFACE LENGTH Chapter Six Results Analysis and Discussion 43