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- 1. Design of a Tri-sonic Wind Tunnel A Graduate Project Report submitted to Manipal University in partial fulfilment of the requirement for the award of the degree of BACHELOR OF ENGINEERING In Aeronautical Engineering Submitted by Avik Arora (Reg no.: 100933063) Varun Adishankar (Reg no.: 100933003) Under the guidance of Jayakrishnan R Assistant Professor, Department of Aeronautical and Automobile Engineering DEPARTMENT OF AERONAUTICAL AND AUTOMOBILE ENGINEERING MANIPAL INSTITUTE OF TECHNOLOGY (A Constituent College of Manipal University) MANIPAL – 576104, KARNATAKA, INDIA May 2014
- 2. ii DEPARTMENT OF AERONAUTICAL AND AUTOMOBILE ENGINEERING MANIPAL INSTITUTE OF TECHNOLOGY (A Constituent College of Manipal University) MANIPAL – 576 104 (KARNATAKA), INDIA Manipal 23-05-2014 CERTIFICATE This is to certify that the project titled DESIGN OF A TRI-SONIC WIND TUNNEL is a record of the bonafide work done by Avik Arora (Reg. No. 100933063) and Varun Adishankar (Reg. No. 100933003) submitted in partial fulfilment of the requirements for the award of the Degree of Bachelor of Engineering (BE) in AERONAUTICAL ENGINEERING of Manipal Institute of Technology Manipal, Karnataka, (A Constituent College of Manipal University), during the academic year 2013 -14. Jayakrishnan R Project Guide Prof. Dr. Ramamohan S Pai B HOD, Aero & Auto M.I.T, MANIPAL
- 3. iii DECLARATION 23-05-2014 Manipal We, hereby declare that the project Design of a Tri-sonic Wind Tunnel and the associated report is our bonafide work submitted to Manipal Institute of Technology, Manipal University in fulfillment of requirements for the award of Degree of Bachelor of Engineering, Aeronautical Engineering. All work associated with this project has been done by us in Manipal Institute of Technology between January-May 2014. Avik Arora Varun Adishankar Reg. no. – 100933063 Reg. no. – 100933003 8th Semester, Aeronautical Engineering 8th Semester, Aeronautical Engineering MIT, Manipal MIT, Manipal
- 4. iv ACKNOWLEDGEMENTS Firstly, we would like to thank Prof. Dr. Ramamohan S Pai B (Head of Department, Aeronautical and Automobile Engineering, MIT, Manipal) and Mr. Kamlesh Kumar (Assistant Professor, Aeronautical and Automobile Engineering, MIT, Manipal) for providing us with the opportunity to work on our final semester project here in MIT. We would like to thank our guide, Mr. Jayakrishnan R (Assistant Professor, Aeronautical and Automobile Engineering, MIT, Manipal) for agreeing to provide his invaluable help and guidance in this project, without which it would have not been possible. We would like to thank Mr Shiva Prasad U (Assistant Professor, Aeronautical and Automobile Engineering, MIT, Manipal) for providing support and help regarding understanding of the software used for analysis. We would like to thank Dr. B Satish Shenoy (Professor, Aeronautical and Automobile Engineering, MIT, Manipal) for allowing us to carry out analyses in the CAD lab. We would like to thank Mr. Balbir Singh (Assistant Professor, Aeronautical and Automobile Engineering, MIT, Manipal) for staying after hours for us to complete our work and Mr. Manikandan M. (Assistant Professor, Aeronautical and Automobile Engineering, MIT, Manipal) for providing us with even more resources for us to gain more knowledge. We would like to thank rest of the aeronautical faculty who supported our work and inspired us to work better. We would like to thank Mr. Anchit Chandrashekar (Student, 8th semester Aeronautical Engg., 2014 Batch) for helping us out with implementation of moving geometry code. We would like to thank our families and friends in providing their advice and support during this period and also the systems used for analysis and other work which worked without fail during our project period. Avik Arora Varun Adishankar Reg no – 100933063 Reg no – 100933003 8th Semester, Aeronautical Engineering 8th Semester, Aeronautical Engineering MIT, Manipal MIT, Manipal
- 5. v ABSTRACT In the current world of obtaining excellence with the maximum cost saving any and almost all the aircrafts are designed using CAD software; then analysed for preliminary results. These designs however need to be verified and tested in real time which, given budget constraints cannot be done on a full scale. To obtain the aerodynamic properties and response of the plane under various conditions and orientations, wind tunnels are used. Aircrafts which particularly fly faster than the speed of sound encounter various kinds of flow, which can be classified as subsonic (slower than speed of sound), Transonic (very near to or equal to the speed of sound) and supersonic (faster than speed of sound). The complexity of flow involved while moving from a low subsonic regime to a supersonic regime are immense, including the crossing of sound barrier which offers immense amount of drag. Carrying out analysis of models of such aircrafts in different tunnels increases the testing time and in some cases, requires modification of the model to be accommodated in three separate tunnels. Such a problem can be overcome by design of a Tri-sonic wind tunnel which is capable of generating the three mentioned flow regimes. Such a tunnel can also be used to simulate the acceleration of the aircraft from subsonic to supersonic velocities and to study the transitional aerodynamic effects. The project focusses on aerodynamic design of a wind tunnel to simulate Subsonic, Transonic and supersonic flows. The proposed tunnel was designed based on flow theories to obtain a preliminary design of all the three types of wind tunnels. The tunnel is a closed type continuous wind tunnel. The design consists of CAD modelling of the nozzle, test section and diffuser for all the three types of wind tunnels. These three model designs were of similar lengths fixed by the length of the supersonic wind tunnel. The designs were analysed in CFD software individually to get the flow properties through the tunnels under steady state conditions. Then the mechanism for changing the geometry of the tunnel in order to get the geometry for the required flow regime and for different properties of the flow was designed and practically made for demonstration purposes. The design as mentioned above can generate different flow regimes and can help in study of transitional flow properties of the fluids. The variable geometry of the tunnel can obtain the required flow with better quality and a good pressure recovery reducing the cost of running of such a tunnel. The designs were made and analysed, resulting in various comparisons of different geometries, and providing the required data as expected from the designs. Various tools were used throughout the duration of the project, including MATLAB, ANSYS ICEM CFD, ANSYS FLUENT and SOLIDWORKS.
- 6. vi LIST OF TABLES Table 1: Parabolic nozzle contour points..............................................................................................14 Table 2: List of simulations carried out (with boundary conditions)....................................................20
- 7. vii LIST OF FIGURES Figure 1: Characteristic lines – left running (CII) and right running characteristics (CI) [3] ....................5 Figure 2- Method to compute contour of divergent section of convergent-divergent nozzle [7] .............6 Figure 3: M=1 at first throat [13] ..............................................................................................................7 Figure 4: Starting shock [13] .....................................................................................................................7 Figure 5: Swallowed shock; tunnel start condition [13] ............................................................................7 Figure 6: Supersonic Wind tunnel 3-D with various sections...............................................................14 Figure 7: Subsonic wind tunnel 3-D with various sections...................................................................15 Figure 8: Subsonic wind tunnel with parabolic inlet (with lengths of each section) ............................16 Figure 9: Supersonic wind tunnel (with lengths of each section) .........................................................16 Figure 10: Mesh for subsonic wind tunnel showing parabolic inlet and test section junction..............16 Figure 11: Supersonic mesh showing the first nozzle throat and part of nozzle exit contour...............17 Figure 12: General boundary conditions for tunnel..............................................................................17 Figure 13: procedure for changing the geometry of the tunnel.............................................................19 Figure 14: Contours of static pressure ..................................................................................................21 Figure 15: Static pressure variation wrt position along center-line ......................................................22 Figure 16: Contours of Mach number...................................................................................................22 Figure 17: Mach number plot wrt position along center-line ...............................................................23 Figure 18: Contours of Static Pressure .................................................................................................23 Figure 19: Static Pressure plot wrt position along center-line ..............................................................24 Figure 20: Static Pressure plot wrt position along wall ........................................................................24 Figure 21: Contours of Mach number...................................................................................................25 Figure 22: Mach number plot wrt length along center-line ..................................................................25 Figure 23: Mach number plot wrt length along wall.............................................................................26 Figure 24: Contours of Static Pressure .................................................................................................26 Figure 25: Static Pressure plot wrt position along center-line ..............................................................27 Figure 26: Static Pressure plot wrt length along wall ...........................................................................27 Figure 27: Contours of Mach Number..................................................................................................28 Figure 28: Mach number plot wrt length along center-line ..................................................................28 Figure 29: Mach number plot wrt length along wall.............................................................................29 Figure 30: Contours of Static Pressure .................................................................................................29 Figure 31: Static Pressure plots wrt length along center-line ...............................................................30 Figure 32: Static Pressure plots wrt length along wall..........................................................................30 Figure 33: Contours of Mach number...................................................................................................31 Figure 34: Mach number plot wrt length along center-line ..................................................................31 Figure 35: Mach number plot wrt length along wall.............................................................................31 Figure 36: Contours of Static Pressure .................................................................................................32 Figure 37: Static Pressure plot wrt length along center-line.................................................................32 Figure 38: Static Pressure plot wrt length along wall ...........................................................................33 Figure 39: Contours of Mach number...................................................................................................33 Figure 40: Mach number plot wrt length along wall.............................................................................34 Figure 41: Mach number plot wrt length along center-line ..................................................................34 Figure 42: Contours of Static Pressure .................................................................................................35 Figure 43: Static Pressure plot wrt length along center-line.................................................................35 Figure 44: Static Pressure plot wrt length along wall ...........................................................................36 Figure 45: Contours of Mach number...................................................................................................36 Figure 46: Mach number plot wrt length along center-line ..................................................................37
- 8. viii Figure 47: Mach number plot wrt length along wall.............................................................................37 Figure 48: Contours of Static Pressure .................................................................................................38 Figure 49: Static Pressure plot wrt length along center-line.................................................................38 Figure 50: Static Pressure plot wrt length along wall ...........................................................................39 Figure 51: Contour Mach number.........................................................................................................39 Figure 52: Mach number plot wrt length along center-line ..................................................................40 Figure 53: Mach number plot wrt length along wall.............................................................................40 Figure 54: Contours of Static Pressure .................................................................................................41 Figure 55: Static Pressure plot wrt length along center-line.................................................................41 Figure 56: Static Pressure plot wrt length along wall ...........................................................................42 Figure 57: Contours of Mach number...................................................................................................42 Figure 58: Mach number plots wrt length along center-line.................................................................43 Figure 59 Mach number plot wrt length along wall..............................................................................43 Figure 60: Contours of Static Pressure .................................................................................................44 Figure 61: Static Pressure plot wrt length along center-line.................................................................44 Figure 62: Contours of Mach number...................................................................................................45 Figure 63: Mach number plot wrt length along center-line ..................................................................45 Figure 64: Contours of Velocity magnitude zoom................................................................................46 Figure 65: Contours of Static Pressure .................................................................................................46 Figure 66: Static Pressure plot wrt length along center-line.................................................................47 Figure 67: Contours of Mach Number..................................................................................................47 Figure 68: Mach number plot wrt length along center-line ..................................................................48 Figure 69: Contours of Static Pressure .................................................................................................48 Figure 70: Static Pressure plot wrt length along center-line.................................................................49 Figure 71: Contours of Mach number...................................................................................................49 Figure 72: Mach number plot wrt length along center-line ..................................................................50 Figure 73: Contours of Static Pressure .................................................................................................50 Figure 74: Static Pressure plot wrt length along center-line.................................................................51 Figure 75: Contours of Mach number...................................................................................................51 Figure 76: Mach number plot wrt length along center-line ..................................................................52 Figure 77: Stagnation to back pressure ratio vs. Mach number............................................................52 Figure 78: Reduction in pressure ratio (in %) vs. Mach number..........................................................53 Figure 79: Contours of Static Pressure .................................................................................................54 Figure 80: Static Pressure plot wrt length along center-line.................................................................54 Figure 81: Contours of Mach number...................................................................................................55 Figure 82: Mach number plot wrt length along center-line ..................................................................55 Figure 83: Contours of Static Pressure .................................................................................................56 Figure 84: Static Pressure plot wrt length along center-line.................................................................56 Figure 85: Contours of Mach number...................................................................................................57 Figure 86: Mach number plot wrt length along center-line ..................................................................57 Figure 87: Contours of Static Pressure .................................................................................................58 Figure 88: Static Pressure plot wrt length along center-line.................................................................58 Figure 89: Contours of Mach number...................................................................................................59 Figure 90: Mach number plot wrt length along center-line ..................................................................59 Figure 91: Contours of Static Pressure .................................................................................................60 Figure 92: Static Pressure plot wrt length along center-line.................................................................60 Figure 93: Contours of Mach number...................................................................................................61 Figure 94: Mach number plot wrt length along center-line ..................................................................61
- 9. ix Figure 95: Contours of Static Pressure .................................................................................................62 Figure 96: Static Pressure plot wrt length along center-line.................................................................62 Figure 97: Contours of Mach number...................................................................................................63 Figure 98: Mach number plot wrt length along center-line ..................................................................63 Figure 99: Contours of Static Pressure .................................................................................................64 Figure 100: Static Pressure plot wrt length along center-line...............................................................64 Figure 101: Contours of Mach numbers ...............................................................................................65 Figure 102: Mach number plot wrt length along center-line ................................................................65 Figure 103: Contours of velocity magnitude at local expansion corner ...............................................66 Figure 104: Contours of Static Pressure ...............................................................................................67 Figure 105: Static Pressure plot wrt length along center-line...............................................................67 Figure 106: Static Pressure plot wrt length along wall .........................................................................68 Figure 107: Contours of Mach number.................................................................................................68 Figure 108: Mach number plot wrt length along center-line ................................................................69 Figure 109: Mach number plot wrt length along wall...........................................................................69 Figure 110: Pressure-drop (shock close-up) .........................................................................................70 Figure 111: Contours of Static Pressure ...............................................................................................70 Figure 112: Static Pressure plot wrt length along center-line...............................................................71 Figure 113: Contours of Mach number.................................................................................................71 Figure 114: Mach number plot wrt length along center-line (lines indicate test section).....................72 Figure 115: Velocity magnitude contour (close-up at separation region).............................................72 Figure 116: Velocity vectors at separation region ................................................................................73 Figure 117: Velocity vectors indicating flow separation......................................................................73 Figure 118: Path lines showing separation of flow at diffuser throat ...................................................74 Figure 119: Contours of Static Pressure ...............................................................................................74 Figure 120: Static Pressure plot wrt length along center-line...............................................................75 Figure 121: Contours of Mach number.................................................................................................75 Figure 122: Mach number plot wrt length along center-line ................................................................76 Figure 123: Contours of Velocity magnitude, shock in nozzle zoomed ...............................................76 Figure 124: Variable geometry demonstration model with actuator mechanism and tunnel wall (currently under subsonic geometry alignment.....................................................................................77 Figure 125: Variable geometry mechanism showing diffuser section (current configuration - subsonic diffuser).................................................................................................................................................77 Figure 126: Variable geometry mechanism showing diffuser section (current configuration - supersonic diffuser)...............................................................................................................................78 Figure 127: Power requirements of scale 1:1 cross section..................................................................79 Figure 128: Power requirement of scale 1:49 cross section area..........................................................79
- 10. x List of Symbols dA Change in Area A Area of Cross Section A* Characteristic Area M Mach Number u Horizontal velocity component du Change in horizontal velocity component Γ Ratio of specific heats P0 Total pressure P Static pressure T0 Total temperature T Static temperature Ρ Density pb Back pressure P* Characteristic pressure At,1 Nozzle throat area At,2 Diffuser throat area Ti Inlet temperature pi Inlet pressure P0,2 Stagnation pressure after normal shock T0,2 Stagnation temperature after normal shock
- 11. xi Contents CERTIFICATE II DECLARATION III ACKNOWLEDGEMENTS IV ABSTRACT V LIST OF TABLES VI LIST OF FIGURES VII LIST OF SYMBOLS X CHAPTER 1 INTRODUCTION 1 CHAPTER 2 BACKGROUND THEORY 2 2.1 INTRODUCTION 2 2.2 WHAT ARE WIND TUNNELS?[5] 2 2.3 TYPES OF WIND TUNNELS [5] 2 2.4 COMPRESSIBLE FLOW THEORY [4][7] 3 2.5 NOZZLE FLOW PROPERTIES [4][7] 3 2.6 METHOD OF CHARACTERISTICS [3][4][7] 4 2.7 DIFFUSERS [4][7] 6 2.8 STARTING PROBLEM OF SUPERSONIC WIND TUNNEL [6][13] 6 CHAPTER 3 METHODOLOGY 8 3.1 INTRODUCTION 8 3.2 PROCEDURE CARRIED OUT 8 3.3 ANALYTICAL CALCULATIONS 8 3.3.1 Supersonic flow properties 8 3.3.2 Subsonic flow properties 10 3.4 TOOLS USED 11 3.4.1 Differential equations used in tools 11 3.5 TUNNEL DESIGN 12 3.6 MODEL GENERATION 12 3.7 MESH AND DETAILS 15 3.8 BOUNDARY CONDITIONS 17 3.9 MECHANISM OF VARIABLE GEOMETRY 18 CHAPTER 4 RESULTS 20 4.1 INTRODUCTION 20 4.2 SIMULATIONS CARRIED OUT 20 4.3 CONTOURS AND PLOTS 21 4.3.1 Subsonic 21 4.3.2 Transonic 53 4.3.3 Supersonic 66 4.4 VARIABLE GEOMETRY OUTCOME 77
- 12. xii 4.4.1 Sealing problem 78 4.5 POWER REQUIREMENTS 78 CHAPTER 5 CONCLUSION AND FUTURE SCOPE OF WORK 80 5.1 INTRODUCTION 80 5.2 BRIEF SUMMARY OF WORK 80 5.3 CONCLUSION 80 5.3.1 Supersonic 80 5.3.2 Subsonic 81 5.4 FUTURE SCOPE OF WORK 81 REFERENCES 82
- 13. 1 CHAPTER 1 INTRODUCTION The days of high speed aerodynamics and supersonic propulsion have entered a new era. Computational techniques available have reduced the workload dependencies on other means of testing. Still without experimental data and some physical validation, these may not hold much of a meaning. The wind tunnel for example was and is one of the best equipment for these applications. Although starting from the same computational bases in the designing phase for a wind tunnel due to cost considerations, a wind tunnel can be designed with a higher accuracy with numerical and theoretical approach as compared to only a theoretical approach. High speed aircrafts particularly supersonic aircrafts undergo radical changes as they move from low subsonic regime to high subsonic compressible regimes and further into transonic and supersonic flow regimes. These transitions pose majority of the design challenges to the aircraft manufacturers. Adhering to these challenges a wind tunnel capable of accelerating from subsonic, transonic and supersonic regimes of flow is probably inevitable equipment in terms of testing parameters and cost. It can provide closest possible results for aircraft designers for the final design of a supersonic aircraft and to obtain the values and parameters for effect of varied flow as the aircraft accelerates from subsonic to supersonic regimes.
- 14. 2 CHAPTER 2 BACKGROUND THEORY 2.1 Introduction This chapter discusses about the literature survey carried out in order to obtain the required design parameters. The chapter contains the formulae used for various calculations. 2.2 What are Wind Tunnels? [5] Wind tunnels are an extremely useful tool to conduct aerodynamic tests on aircraft models and other related components of aircrafts. Wind tunnels are not just limited to aircraft design alone, they are also used in design of automobiles, wind turbines, buildings, bridges etc. They are a very integral part of testing and analysis when computational analysis is not feasible. Also, wind tunnels enable easy testing of scaled models of aircrafts so as to understand their behaviour during various phases of flight, and at various flight speeds, before performing a flight test, so that any noticeable defects can be corrected, and the design can be improved. Wind tunnels give us the flexibility to vary the flow conditions like pressure, temperature, speed etc. for a wider range of tests that can be performed. 2.3 Types of Wind Tunnels [5] Wind tunnels can be classified in various ways. Most notably they can be classified on the basis of the speed of the flow in test section, and on the circuit of air flow. Based on speed of flow in test section, they can be classified as follows – Subsonic – Wherein the flow in the test section is limited to speeds below Mach 0.8. They can be further classified as low subsonic (generally known as Low Speed Wind tunnels), for flows below Mach 0.3, and high subsonic, for flows up to Mach 0.8 Transonic – In these tunnels, test section flow is in the transonic regime, i.e., between Mach 0.8 and Mach 1.2. Transonic flows are generally very complex to analyse, and as a result, it is difficult to design transonic wind tunnels, and there are not as many transonic wind tunnels as subsonic or supersonic wind tunnels. Supersonic – These tunnels involve flow beyond Mach 1. Hypersonic – Flows above Mach 4 are tested in these wind tunnels. Based on the circuit of air flow, they can be classified as – Open Circuit Wind Tunnels – These consist of a straight long tube consisting of the settling chamber, nozzle, test section, diffuser and fan in a straight section. Closed Circuit Wind Tunnels – These consist of a recirculating tube with corners, and the various sections in an open circuit wind tunnel are also present in this type of tunnel.
- 15. 3 2.4 Compressible Flow Theory [4][7] Since this project involved the design of a tri-sonic wind tunnel, it meant extensive use of compressible flow principles, as most of the flow taking place is compressible in nature. Incompressible flow principles are no longer valid in this type of flow. The high velocities used in this project involve large pressure gradients, which lead to changes in local density at various points in the flow. Discontinuous large variations in pressure can lead to formation of shock waves. For the purpose of theoretical calculations, the flow is assumed to be isentropic, thus isentropic flow relations and shock relations were used during the theoretical design phase. 2.5 Nozzle Flow properties [4][7] A nozzle is essentially a variable area, converging duct, mainly used to accelerate flow. They are of two main types, subsonic and supersonic. The analysis of isentropic flows across nozzles can be studied and analysed based on the area-velocity relation (derived from the compressible continuity equation), given as follows – ( ) [2.1] For the design of supersonic (convergent-divergent) nozzles, the following formula is obtained from the above relation – ( ) ( ) [2.2] This relation tells us that the Mach number at any location in the duct is a function of the ratio of local duct area to the sonic throat area (A* ). Isentropic relations were used for the determination of properties of the flow. These isentropic relations are as follows – ( ) [2.3] ( ) [2.4] ( ) [2.5]
- 16. 4 Also, the following normal shock relations were used – ( ) [2.6] ( ) ( ) [2.7] ( )( ) [2.8] [2.9] Where, subscripts 2 and 1 represent quantity after shock and quantity before shock respectively. 2.6 Method of Characteristics [3][4][7] Method of characteristics is a numerical method which is generally used to plot the contour of a convergent-divergent supersonic nozzle. It uses non-linear differential equations of velocity potential equations. Characteristic lines are unique lines in the flow where the derivatives of the flow properties become indeterminate and discontinuous, though the flow properties themselves exist as finite values. General procedure of method of characteristics involves the following steps – Step 1 Characteristic lines are determined in the flow, i.e., particular directions in the xy space where flow variables are continuous but their derivatives are indeterminate, and sometimes even discontinuous.
- 17. 5 Figure 1: Characteristic lines – left running (CII) and right running characteristics (CI) [3] Step 2 Partial differential conservation equations are combined in such a fashion that ODEs are obtained which hold only along the characteristic lines. These ODEs are called compatibility equations. Step 3 These compatibility equations are then solved step-by-step along the characteristic lines, starting from the given initial condition at some point or region in the flow. In this manner, the complete flow field can be mapped out along the characteristics. By following the above iterative procedure, we can obtain the contour of the supersonic nozzle such that no expansion waves or shock waves are formed.
- 18. 6 Figure 2- Method to compute contour of divergent section of convergent-divergent nozzle [7] 2.7 Diffusers [4][7] Diffuser is the section of the wind tunnel responsible for reducing the speed of the flow and to recover pressure. Different wind tunnels employ different kinds of diffusers based on flow velocity, power consumption etc. Following classification can be done based on flow velocities for subsonic or supersonic diffusers: For subsonic diffusers the area Mach number relation dictates that the velocity decreases as area increases for Mach number less than 1. For supersonic diffusers, the area Mach number relation dictates that the velocity decreases as area decreases for Mach number greater than 1. This suggests that the supersonic diffuser should have convergent divergent section to decelerate the flow from supersonic to subsonic flow again with the diffuser throat Mach number nearing 1. 2.8 Starting problem of supersonic wind tunnel [6][13] During tunnel start-up, there is zero flow velocity, and constant pressure exists throughout the tunnel. The starting of the tunnel is enabled by changing the back pressure, and consequently the pressure ratio po/pb, by using the compressor. Initially, there will be subsonic flow everywhere. As we keep increasing ratio of inlet total pressure to back pressure po/pb, the flow velocity keeps increasing, and at a certain point, normal shock formation takes place in the throat of
- 19. 7 the convergent-divergent nozzle. With subsequent increase in pressure ratio, normal shock gradually moves backward in the test section. To have the shock to completely disappear from test section, it must completely pass through the second throat. Thus, initially, the second throat area needs to be high (for starting), and once the shock wave is pushed behind, the area of second throat can be reduced for optimal operating conditions. A variable area throat of the diffuser would be most useful in this case. This variation can be achieved by increasing the diffuser throat area using normal shock relations as given above. Figure 3: M=1 at first throat [13] Figure 4: Starting shock [13] Figure 5: Swallowed shock; tunnel start condition [13]
- 20. 8 CHAPTER 3 METHODOLOGY 3.1 Introduction This section discusses the design and analysis carried out for the wind tunnel. Since it is not possible to analyze the complete wind tunnel, therefore the detailed analyses were carried out on the nozzle, test section and diffuser regions, and the preliminary calculations for other components were carried out. The method of changing geometry and its demonstration was also carried out. 3.2 Procedure carried out The methodology adopted is primarily based on quasi-one dimensional flow theories. The air flow for the calculation is assumed to be inviscid and the changes that take place are isentropic. As the major aim to obtain steady state subsonic, transonic and supersonic flow in the wind tunnel, three different tunnels of same length will be designed and analyzed. A mechanism will be designed which is required to change the geometry of the wind tunnel as the flow accelerates from subsonic to supersonic velocities. The wind tunnels would be designed and analyzed using software while the mechanism for varying the geometry would either be made practically as a demonstration or if possible will also be simulated. 3.3 Analytical Calculations Principles of compressible flow, nozzle flow and isentropic flow equations were used to design the shape of the wind tunnel and calculate the pressure ratios, temperature ratios, and the area ratios, for each case – supersonic and subsonic. 3.3.1 Supersonic flow properties 3.3.1.1 Nozzle and Test section calculations An inlet Mach number of 0.4 was assumed in the initial calculations. Based on that, using the following formula for Area-Mach number relation, the inlet-throat area ratio was calculated (from equation 2.2). ( ) ( ) The area ratio was found to be For a test section Mach number of 2.0, the respective pressure and temperature ratios were calculated and the following values obtained (from equation 2.3 to 2.5) –
- 21. 9 Now, to design the test section dimensions, sea-level conditions were assumed in the test section for a Mach number of 2.0. Accordingly, the following values of pressures and temperatures were obtained – Assuming the throat area of convergent-divergent nozzle to be 1 m2 , the rest of the dimensions can be calculated with this reference. 3.3.1.2 Diffuser calculations [7] A diffuser is a very important part of a supersonic wind-tunnel, as most of the pressure recovery takes place in this section. The most optimal diffuser possible in a supersonic wind tunnel is a convergent-divergent diffuser with a throat, which is designed to minimize the reflected shock waves and combine them into one single normal shock at the end of the diffuser throat. This is done so as to minimize the total pressure losses across the shock waves as much as possible. The presence of a normal shock at the end of the diffuser throat means that the flow after the normal shock will be subsonic and thus subsequently there will not be many problems faced in trying to slow down the flow (to speeds that can be comfortably handled by the fan/compressor), rather than when the speed of flow after diffuser throat is supersonic. Also, for isentropic flow in a supersonic wind tunnel, the following relation is valid:
- 22. 10 [3.1] This relation states that ratio of diffuser throat to nozzle throat is equal to the ratio of the total pressure of the flow before and after the normal shock in the diffuser. Since the total pressure after the normal shock is higher than the total pressure preceding it, the second (diffuser) throat area is always greater than the first (nozzle) throat area. Thus, using normal shock relations and the earlier total pressure values obtained, the following values were obtained – For all practical cases, the second throat must be larger than the first throat related by the above ratio. Assuming first throat area as 1 m2 , area of second throat is 1.387 m2 , thus, to obtain proper flow in the test section, any diffuser throat with area greater than this will suffice. Thus, an area of At,2 = 1.4 m2 was chosen. From the above relation, the total pressure and total temperature behind the normal shock were calculated to be the following – 3.3.2 Subsonic flow properties To estimate the subsonic flow properties, a design test section Mach number of 0.7 was chosen and the area ratios were designed appropriately. In this case, test section area is equal to the throat area of the duct. Also, since the test section area has to be same for all three wind tunnel configurations (subsonic, transonic and supersonic), the test section area was fixed to 1.6875 m2 as obtained from supersonic calculations. Considering an inlet Mach number of 0.3, using compressible flow properties, the following value was obtained for inlet area to throat area ratio– And the throat to exit area ratio is – Using the isentropic flow relations, the rest of the flow properties were calculated and obtained as follows –
- 23. 11 For inlet Mach number 0.3 and throat Mach number 0.7 (from equation 2.6 to 2.8) – The above calculations were made for the assumption that flow is adiabatic and isentropic. Test section conditions are sea-level, atmospheric conditions. 3.4 Tools Used Three major tools were used in the initial calculations and design phase. ANSYS ICEM CFD ANSYS FLUENT MATLAB SOLIDWORKS ANSYS ICEM CFD was used to make a 2-D CAD model of the tunnels and mesh them for analysis. The analyses were carried out in ANSYS Fluent. The complete wind tunnel was designed using CAD software to give an idea about the complete final geometry of the whole tunnel. MATLAB was used to design a contour for the divergent section of the convergent-divergent nozzle in the supersonic wind tunnel using a code [11] implementing Method of Characteristics. K-epsilon viscous model was used on FLUENT for viscous analysis. The standard K-epsilon is valid only for turbulent flows. The eddy viscosity is determined from a single turbulence length scale, and all scales of motion are not included. This has a limitation with separated flows. This model is valid and usable for high Reynolds number flows. For lower Reynolds number flows, K-Omega model tends to perform better. [12] 3.4.1 Differential equations used in tools Continuity Equation [14] The continuity equation is obtained from the law of conservation of mass: ( ) Where, is density of the fluid
- 24. 12 u is the velocity vector in Cartesian coordinates. Navier-Stokes Equations [14] Navier-Stokes equations describe the conservation of momentum in a fluid flow, in three dimensions. The following are the basic Navier-Stokes equations used: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Where, = Pressure, = Effective viscosity Energy Equations [14] ( ) ( ) ( ) Where, = Internal Energy = Thermal conductivity T = temperature = Viscous heat generation term 3.5 Tunnel Design Initially the convergent sections of the subsonic and transonic wind tunnels were tested with linearly inclined geometry from the inlet to the test section. After this further tests were carried out with parabolic contour from inlet to test section, to check the difference in flow quality. 3.6 Model Generation Depending on the area and pressure ratios calculated, a simple CAD geometry was made in order to mimic the tunnel with the following parameters – Supersonic Throat area = 1 m2 Test section area = 1.6875 m2
- 25. 13 Inlet area (for Mach 0.4 entry flow) = 1.5904 m2 Diffuser exit area (for assumed exit Mach flow of 0.7) = 1.67 m2 The exit geometry for the nozzle of the supersonic wind tunnel was made using Method of Characteristics. A MATLAB script [11] was utilized in order to generate the required geometry. Later on, the half-angles for the nozzle inlet and the exit diffuser were changed to 2o for supersonic wind tunnel. The final length obtained from above conditions was calculated to be 15.92 m. The geometry of the wind tunnel could have possibility of being a circular or a rectangular one. Circular geometry having the advantages of smoother transition and no shock corners has several disadvantages compared to a rectangular cross-section. The following are the advantages offered by the rectangular cross-section: Better test section visibility Easier to form a variable geometry Easier manufacture Easier nozzle design Can accommodate wider models Following were the parameters calculated for subsonic case of the wind tunnel: Subsonic Test section area = 1.6875 m2 Inlet area = 3.2603 m2 Diffuser exit area = 2.491 m2 The geometry for generating sonic and near-sonic flows will be same as that for subsonic. The final length of the tunnel (nozzle, test section, diffuser) was selected as that of the supersonic wind tunnel and the same length was used for other configurations as well. Another geometry having parabolic intake for flow quality comparison was made for subsonic and transonic flow conditions, using the following equations – With “a” being the constant value of 0.0265, obtained from the above given data of test section and inlet. Nozzle height was obtained by subtracting the obtained value from inlet height. The following points were obtained for different locations on the wind tunnel.
- 26. 14 Table 1: Parabolic nozzle contour points X 0 1 2 3 3.5 4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.7 5.8 5.848 Nozzle height 1.63 1.305 1.17 1.07 1.02 0.978 0.96 0.95 0.93 0.91 0.90 0.89 0.87 0.86 0.85 0.846 0.844 The final geometry of the whole tunnel (excluding the propulsion system) was designed in 3D using the CAD software to depict how the complete wind tunnel would look like. The following figures depict the 3D geometry of the wind tunnel (both supersonic and subsonic geometries) and also show the other components of the final wind tunnel and how it would look like. Figure 6: Supersonic Wind tunnel 3-D with various sections A B C D E F
- 27. 15 Figure 7: Subsonic wind tunnel 3-D with various sections For both the figures 6, 7, we have – A : Corner D : Nozzle B : Settling Chamber E : Test Section C : Lofted section F : Diffuser 3.7 Mesh and Details The mesh was formed using ANSYS ICEM CFD commercial meshing software. Several meshes were made in order to check for mesh dependency. Different mesh sizes varying from 0.01 to 0.002 were tested with no significant changes beyond mesh size of 0.006. The mesh type was selected to be quad-dominant in order to provide the best geometry capture and low flow distortion. Half of the wind tunnel was meshed for analysis in order to save time. Symmetry conditions were used. A B C D E F
- 28. 16 Figure 8: Subsonic wind tunnel with parabolic inlet (with lengths of each section) Figure 9: Supersonic wind tunnel (with lengths of each section) The meshes displayed above (in figure 8, 9) were used for subsonic and supersonic analysis. The mesh size was kept small enough to capture the geometry properly. Figure 10: Mesh for subsonic wind tunnel showing parabolic inlet and test section junction 8.042 m 3.374 m 2.474 m 2 m 4.073 m 4 m 5.848 m 2 m Nozzle Test section Diffuser Nozzle inlet Nozzle exit Test section Diffuser inlet Diffuser exit
- 29. 17 Figure 11: Supersonic mesh showing the first nozzle throat and part of nozzle exit contour Figure 9 and 10 represent the corner points in geometry which has been captured in both subsonic and supersonic cases. Intermittent tri-elements exist along with quad-elements to subdivide the mesh for better distribution of mesh along the edges. 3.8 Boundary Conditions Pressure inlet and outlet boundary conditions were used for analysis of the wind tunnel: Figure 12: General boundary conditions for tunnel Following were test section parameters assumed: Pressure = 101325 Pa Temperature = 300 K Density = 1.225 Kg/m2 From the above values and obtained area ratios, inlet boundary conditions were calculated from isentropic relations for supersonic flows. Supersonic conditions: o Pressure inlet Wall Pressure Inlet Internal Fluid Symmetry Pressure outlet
- 30. 18 Gauge pressure = 792812.3672 Pa initial gauge pressure = 710054.1 Pa Total temperature = 540 K These values were obtained from the relations as mentioned previously in section 3.3. Similarly for subsonic wind tunnel, following were the parameters obtained: Pressure inlet o Gauge pressure = 140550.8 Pa o Initial gauge pressure = 132034.6 Pa o Total temperature = 329.374 K For the outlet conditions, maximum pressure recovery was calculated using isentropic relations and further iterations were performed to get the required pressure recovery for the given conditions. For supersonic case, maximum diffuser pressure recovery = 571602.2835 Pa The wall conditions were given as no-slip, stationary wall for all cases. 3.9 Mechanism of variable geometry The tri-sonic wind tunnel design has a characteristic feature to modify the area ratios in order to generate the specific flow conditions for subsonic, transonic or supersonic. A nozzle design algorithm from method of characteristics was used in order to obtain the required exit geometry of the nozzle for supersonic flows over various Mach numbers. For subsonic flows, parabolic inlet geometry was formed using the equations stated in section 3.6. These particular coordinates were fed into servo-motors located at specific positions in order to modify the geometry as and when the flow conditions changed from subsonic through transonic to higher supersonic flows (up to Mach 2.0). Servo mechanisms can be used as a demonstrator which could be replaced by high-powered hydraulic devices in actual scenario to produce the contour shape for the required flow conditions. The following procedure was followed to modify the geometry as deemed necessary for the flow conditions:
- 31. 19 Figure 13: procedure for changing the geometry of the tunnel Check whether an increase to the compressor input has been provided or not. If no, then no change, if yes, continue with procedure. Measurement of stagnation and test section pressures Calculation of static to stagnation pressure ratios Determination of Mach no. using isentropic relations Check whether Mach number close to 1 If Mach no. >1 Check if geometry is as required by the flow. If so, no change, otherwise continue to next step. Calculate nozzle values from MOC by keeping test section area constant Multiply nozzle throat value with the required factor (1.4) to get diffuser throat height Send the required coordinates to the actuators located at various positions to obtain a required geometry If Mach no. <1 Check if geometry is as required by the flow. If so, no change, otherwise continue to next step. Calculate nozzle inlet values using parabolic equation by keeping test section and inlet height constant. Modify diffuser geometry into a linearly tapered section. Send the required coordinates to the actuators located at various positions to obtain a required geometry
- 32. 20 CHAPTER 4 RESULTS 4.1 Introduction The following chapter discusses about the simulations carried out and the results obtained. It also includes the comparison between various cases for different conditions. A section for mechanism of variable geometry is included which explains how the transitions of the wind tunnel take place. 4.2 Simulations carried out Table 2: List of simulations carried out (with boundary conditions) S no Geometry name Po(Pa) Pi(Pa) To(K) Pb(Pa) Tout(K) Dh in Dh out Iin (%) Iout (%) 1 2d_Subsonic 140550.8 132034.6 329.38 123600 315.61 - - - - 2 2d_Subsonic 140550.8 132034.6 329.38 125000 315.61 - - - - 3 2d_Subsonic 140550.8 132034.6 329.38 125800 315.61 - - - - 4 2d_Subsonic 140550.8 132034.6 329.38 126000 315.61 - - - - 5 2d_Subsonic_para 140550.8 132034.6 329.38 125000 315.61 - - - - 6 2d_Subsonic_para 140550.8 132034.6 329.38 125800 315.61 - - - - 7 2d_Subsonic_para 140550.8 132034.6 329.38 123600 315.61 - - - - 8 2d_Subsonic_para 140550.8 132034.6 329.38 126000 315.61 - - - - 9 2d_Subsonic_para_vis 140550.8 132034.6 329.38 123264 315.61 4.92 3.99 2.5 2.5 10 2d_Subsonic_para_vis 140550.8 132034.6 329.38 123893 315.61 4.92 3.99 2.5 2.5 11 2d_Subsonic_para_vis 140550.8 132034.6 329.38 124191 315.61 4.92 3.99 2.5 2.5 12 2d_Subsonic_para_vis 140550.8 132034.6 329.38 121845 315.61 4.92 3.99 2.5 2.5 13 2d_Transonic 140550.8 132034.6 329.38 122000 315.61 - - - - 14 2d_Transonic_para 140550.8 132034.6 329.38 122000 315.61 - - - - 15 2d_Transonic_para 140550.8 132034.6 329.38 122800 315.61 - - - - 16 2d_Transonic_para_vis 140550.8 132034.6 329.38 121200 315.61 4.92 3.99 3 3 17 2d_Transonic_para_vis 140550.8 132034.6 329.38 121060 315.61 4.92 3.99 3 3 18 2d_Transonic_para_vis 140550.8 132034.6 329.38 120800 315.61 4.92 3.99 3 3 19 2d_supersonic 792812.4 710054.1 540 453000 491.81 - - - -
- 33. 21 20 2d_supersonic_vis 792812.4 710054.1 540 400000 491.81 2.74 2.87 5 5 21 2d_supersonic_strt_vis 792812.4 710054.1 540 400000 491.81 2.74 2.87 5 5 The above table lists out some of the analyses carried out in order to obtain the required results. The name in the table gives the type of geometry used in the following representation: 1st label_2nd label_ (other labels separated by underscores) 1st Label – Dimensions of the wind tunnel 2nd Label – Speed of flow in test section Other labels – Any special condition o Para – parabolic inlet o Vis – viscous o Strt – Straight section of supersonic diffuser after the convergent section 4.3 Contours and Plots Following are the contours and plots obtained for above mentioned analyses. 4.3.1 Subsonic For the subsonic case, two geometries were designed, analyzed and compared in order to obtain the best possible flow quality in the test section. The graphs near the walls for the sections should be as smooth as possible with minimal adverse pressure gradients. Following are the analyses done for the subsonic wind tunnels. 4.3.1.1 Analyses carried out 1. Inviscid case - For Back pressure of 123600 Pa: a. Straight tapered inlet: Figure 14: Contours of static pressure
- 34. 22 Figure 15: Static pressure variation wrt position along center-line Here (figure 14 and 15) as it can be seen that there seems to be a sudden pressure drop near the wall of the contour of the wind tunnel. Figure 16: Contours of Mach number
- 35. 23 Figure 17: Mach number plot wrt position along center-line The graph above (figure 17) represents the Mach number distribution along the center line. The distribution of the flow is nearly ideal as expected. But as the flow is observed closer towards the wall, there is a lot of disturbance and localized sonic flow regions. b. Parabolic inlet: Figure 18: Contours of Static Pressure
- 36. 24 Figure 19: Static Pressure plot wrt position along center-line Figure 20: Static Pressure plot wrt position along wall The contours and plots above (Figure 18, 19, 20) display a trend similar to the ones for the linear nozzle section as discussed before, though the sudden pressure drops observed are considerably lower in case of parabolic nozzle.
- 37. 25 Figure 21: Contours of Mach number Figure 22: Mach number plot wrt length along center-line
- 38. 26 Figure 23: Mach number plot wrt length along wall As it can be seen, in the above plots and contours (figure 21, 22, 23), the flow approaches higher Mach numbers (close to sonic speeds) for the nozzle with tapered section inlet; while under same conditions, the parabolic nozzle has no such sudden rise in the Mach number. This is due to the sudden expansion corner which the flow temporarily experiences as it goes from a convergent section to the test section. This particular trend highlights the fact that a gradual area variation provides a much smoother flow and less disruption. This also affects the analysis as such effects might disrupt the flow around the model and near the walls. 2. Inviscid case - For back pressure of 125000 Pa: a. Straight tapered inlet: Figure 24: Contours of Static Pressure
- 39. 27 Figure 25: Static Pressure plot wrt position along center-line Figure 26: Static Pressure plot wrt length along wall The above static pressure contours and plots (figure 24, 25, 26) are obtained for a lower Mach number in the previous case, although the localized sonic flow is reduced near the expansion corners but can still considerably disturb the flow.
- 40. 28 Figure 27: Contours of Mach Number Figure 28: Mach number plot wrt length along center-line
- 41. 29 Figure 29: Mach number plot wrt length along wall Again the Mach number plots above (figure 27, 28, 29) tend to be near ideal near the center-line, but then again, they get disrupted near the wall due to localized sonic flows. b. Parabolic inlet Figure 30: Contours of Static Pressure
- 42. 30 Figure 31: Static Pressure plots wrt length along center-line Figure 32: Static Pressure plots wrt length along wall In this case (figure 30, 31, 32), there is also a pressure drop just before the test section, but is considerably lower than the case with the straight section nozzle under same conditions.
- 43. 31 Figure 33: Contours of Mach number Figure 34: Mach number plot wrt length along center-line Figure 35: Mach number plot wrt length along wall
- 44. 32 Here (in Figure 33, 34, 35) there is again a localized increase in Mach number due to a very gradual expansion corner. This results in a rise of Mach number just at the extremities of test section, but the geometry prevents the Mach number from rising up to sonic flows under the same conditions, as for a linearly tapered nozzle. 3. Inviscid case - For back pressure of 125800 Pa: a. Straight tapered inlet Figure 36: Contours of Static Pressure Figure 37: Static Pressure plot wrt length along center-line
- 45. 33 Figure 38: Static Pressure plot wrt length along wall Here (in figure 36, 37, 38), a similar trend as observed in previous cases is apparent. Figure 39: Contours of Mach number
- 46. 34 Figure 40: Mach number plot wrt length along wall Figure 41: Mach number plot wrt length along center-line Due to the pressure ratio for the operation of the wind tunnel, the Mach number, though suddenly increases, does not reach sonic flow (refer figure 39, 40, 41).
- 47. 35 b. Parabolic inlet Figure 42: Contours of Static Pressure Figure 43: Static Pressure plot wrt length along center-line
- 48. 36 Figure 44: Static Pressure plot wrt length along wall In the above graphs (figure 43, 44), the drop in pressure is again a lot lower at the test section inlet in comparison with the linearly tapered nozzle under same conditions. Figure 45: Contours of Mach number
- 49. 37 Figure 46: Mach number plot wrt length along center-line Figure 47: Mach number plot wrt length along wall Here (in figure 45, 46, 47), apart from the earlier trend between parabolic and straight tapered nozzle, it can also be seen that the pressure or Mach number in the test section varies greatly with the pressure ratio applied. As the back pressure recovery will always be a factor of the inlet pressures and other viscous losses, thus it is obtained rather than provided. The above plots and contours depict that for varying pressure ratios, it is possible to achieve different Mach numbers in the test section. 4. Inviscid case - For back pressure of 126000 Pa: a. Straight tapered inlet
- 50. 38 Figure 48: Contours of Static Pressure Figure 49: Static Pressure plot wrt length along center-line
- 51. 39 Figure 50: Static Pressure plot wrt length along wall Here (in figure 48, 49, 50), the pressure ratio allows for the near-design condition working of the wind tunnel. It is observed from the above graphs that a design static pressure of 1 atm exists in the test section. Figure 51: Contour Mach number
- 52. 40 Figure 52: Mach number plot wrt length along center-line Figure 53: Mach number plot wrt length along wall Here (refer figure 51, 52, 53), the near design Mach number of 0.7 is achieved in the test section. Near the walls, there is again localized high speed flow, but of lower intensity.
- 53. 41 b. Parabolic inlet: Figure 54: Contours of Static Pressure Figure 55: Static Pressure plot wrt length along center-line
- 54. 42 Figure 56: Static Pressure plot wrt length along wall Here (figure 54, 55, 56), the pressure drop is minimal as compared to the previous cases, and the flow quality is better than the linearly tapered nozzle. Figure 57: Contours of Mach number
- 55. 43 Figure 58: Mach number plots wrt length along center-line Figure 59 Mach number plot wrt length along wall Here (in figure 57, 58, 59), the wind tunnel is working near its design conditions of Mach 0.70 for a test section pressure of 1 atm. The change in pressure ratios depicts the change in Mach number. Here, a considerable increase in Mach number (as highlighted in the above contours for test section) can be seen for the change in geometry of the nozzle from a linear curve to a parabolic curve. This in turn solidifies the assertions made previously. The viscous cases were analyzed only for parabolic geometries as it had better flow quality during inviscid analyses.
- 56. 44 5. Viscous case - Back Pressure of 123264 Pa: Figure 60: Contours of Static Pressure Figure 61: Static Pressure plot wrt length along center-line Here (in figure 60, 61), viscous loss of nearly 1.4% of the back pressure (to obtain Mach flow of 0.78) was obtained. This gave a particular pressure ratio including the losses.
- 57. 45 Figure 62: Contours of Mach number Figure 63: Mach number plot wrt length along center-line This was the initial viscous case (refer figure 60, 61, 62, 63), run for subsonic viscous flows. The pressure ratio has resulted in a 0.77 Mach flow. In this case, the viscous losses are calculated to be 1.42 % of the back pressure recovery obtained for inviscid case for a similar Mach number flow in a test section.
- 58. 46 Figure 64: Contours of Velocity magnitude zoom The above contour (figure 64) is a magnified view of the test section wall of the wind tunnel. It is observed that the no-slip condition of the wall is causing the flow nearby to slow down, as the flow velocity is zero at the wall. 6. Viscous case - Back Pressure of 123893 Pa Figure 65: Contours of Static Pressure
- 59. 47 Figure 66: Static Pressure plot wrt length along center-line The above case (refer figure 65, 66) depicts the viscous flow through wind tunnel under the given pressure ratios (Stagnation pressure of 140550.8 Pa). Figure 67: Contours of Mach number
- 60. 48 Figure 68: Mach number plot wrt length along center-line The case above (refer figures 65-68) was run to generate a 0.73 Mach flow. After the calculations converged, the test section was found to have a Mach number of 0.75, which depicted that the extra losses assumed for viscous flows were more than the losses obtained. Therefore, the viscous losses were found to be less than 1.5 % of the total back-pressure recovery. 7. Viscous case - Back Pressure of 124191 Pa: Figure 69: Contours of Static Pressure
- 61. 49 Figure 70: Static Pressure plot wrt length along center-line Here (refer figure 69, 70), localized pressure drops near the wall of the contour can be seen due to a gradual expansion corner. Figure 71: Contours of Mach number
- 62. 50 Figure 72: Mach number plot wrt length along center-line Here (in figure 71,72), we get a converged Mach number of 0.73 in the test section, against a predicted 0.72, after assuming viscous losses of 1.4 % of total back pressure recovery. This particular case indicates that, even though the Mach number achieved is higher than expected, the viscous losses have increased with the increase in flow Mach number. 8. Viscous case - Back Pressure of 121845 Pa: Figure 73: Contours of Static Pressure
- 63. 51 Figure 74: Static Pressure plot wrt length along center-line This is the case (figure 73, 74) of near-sonic flow, where the flow tends to exceed Mach 0.85 in the test section. A disturbance in the contour is observed near the corners where there is a localized pressure drop. Figure 75: Contours of Mach number
- 64. 52 Figure 76: Mach number plot wrt length along center-line In above contour and plot (figure 75, 76), the pressure losses were assumed to be 1.4 % of the total back pressure recovery for an expected flow of Mach 0.88. Mach number of 0.86 was achieved in the test section against the predicted value. This indicates that the assumed viscous losses of 1.4 % were not valid and the actual losses were higher. 4.3.1.2 Comparison of viscous losses Figure 77: Stagnation to back pressure ratio vs. Mach number
- 65. 53 Figure 78: Reduction in pressure ratio (in %) vs. Mach number It is depicted in the graphs above (figures 77, 78), as the flow velocity increases, the amount of viscous losses also tend to increase. 4.3.2 Transonic For transonic analyses, the subsonic geometry was used. The flow quality obtained was extremely bad with Mach numbers varying very steeply between 0.98 and 1.10. Thus, the geometry was modified to include a straight portion before the test section, keeping the tunnel length same but reducing the nozzle length by half. This was done in order to allow the shocks to die down. 4.3.2.1 Analyses carried out 1. Inviscid case - Back Pressure 122000 Pa The cases here depict the flow in two different geometries - the first one having a linear nozzle section and the second one having a parabolic nozzle. a. Linearly tapered inlet:
- 66. 54 Figure 79: Contours of Static Pressure Figure 80: Static Pressure plot wrt length along center-line The above pressure plot and contour (figures 79, 80) depict sonic flow in the tunnel resulting in various shock reflections and interactions. Localized pressure rise can also be observed after the shocks.
- 67. 55 Figure 81: Contours of Mach number Figure 82: Mach number plot wrt length along center-line Here (refer figures 81, 82), the shock formation results in a lot of disturbance in the test section and a huge variation in the Mach number over very small distances.
- 68. 56 b. Parabolic inlet: Figure 83: Contours of Static Pressure Figure 84: Static Pressure plot wrt length along center-line In figures 83, 84, it is observed the shocks are much weaker in the test section as compared to linearly tapered nozzle (as discussed for figures 79-81).
- 69. 57 Figure 85: Contours of Mach number Figure 86: Mach number plot wrt length along center-line In figures 85, 86, it is observed that, although the shocks do tend to die down as the flow approaches test section, the flow still has strong enough shocks to render the test section flow useless. In case of parabolic inlet, the shock still exists, but the flow is closer to the required sonic region and the variation due to the shocks is extremely low compared to the previous geometry, for similar boundary conditions.
- 70. 58 2. Inviscid case - Back Pressure of 122800 Pa Figure 87: Contours of Static Pressure Figure 88: Static Pressure plot wrt length along center-line Here in figures 87, 88, the pressure variation across the test section is lower as compared to the previous parabolic case.
- 71. 59 Figure 89: Contours of Mach number Figure 90: Mach number plot wrt length along center-line For the above figures 89, 90, it can be seen that the flow variation for sonic conditions is better than the flow conditions for the previous case, as in the previous case, the flow seemed to be choked. In this particular case, sonic conditions have been achieved without the complete choking of the flow.
- 72. 60 3. Viscous case - Back Pressure of 121200 Pa: Figure 91: Contours of Static Pressure Figure 92: Static Pressure plot wrt length along center-line Here from figure 91 and figure 92, a transonic flow exists in the test section. Linear pressure gradients can be observed as the flow passes through the test section. These variations are low due to a very slight thickening of boundary layer which might take place due to the flow velocity.
- 73. 61 Figure 93: Contours of Mach number Figure 94: Mach number plot wrt length along center-line For the pressure ratio in this particular case (refer figures 91-94), a transonic flow Mach number of 0.9 was achieved in the test section.
- 74. 62 4. Viscous case - Back Pressure of 121060 Pa: Figure 95: Contours of Static Pressure Figure 96: Static Pressure plot wrt length along center-line In the above figures, 95, 96, it can be seen that a localized pressure drop near the walls exists, along with a minor pressure gradient through the test section.
- 75. 63 Figure 97: Contours of Mach number Figure 98: Mach number plot wrt length along center-line Here in figure 97 and figure 98, a Mach number of 0.93 was achieved in the test section. As it can be seen in the graph, for Mach number vs position, there is a gradual increase in the test section Mach number over the length of the test section. This particular finding leads to the conclusion that the boundary tends to, very gradually, increase in thickness, thus producing a secondary nozzle in the test section, accelerating the flow. The thickness, however, does not change very drastically, and is low enough to not have a considerable change in the Mach number.
- 76. 64 5. Viscous case - Back Pressure of 120800 Pa: Figure 99: Contours of Static Pressure Figure 100: Static Pressure plot wrt length along center-line The pressure contour and graph above (figures 99, 100) depict the variation of the pressure gradient through test section to be much steeper than the previous cases.
- 77. 65 Figure 101: Contours of Mach numbers Figure 102: Mach number plot wrt length along center-line As explained before, there is a Mach number rise in the test section itself, after the nozzle has ended (refer figure 101 and figure 102), due to slight increase in boundary layer thickness across the test section. In this particular case, due to a higher flow velocity, the boundary layer tends to have a higher thickness (though negligibly) than the previous case. Even this negligible increase in thickness is enough to cause the test section to act as a nozzle, and have a higher Mach number towards its end.
- 78. 66 Figure 103: Contours of velocity magnitude at local expansion corner This particular velocity contour (figure 103), near the wall of the tunnel depicts a local expansion corner formed as the nozzle ends into the test section. 4.3.3 Supersonic For supersonic analyses, various geometries were considered, initially starting with circular sections geometries. But they were replaced by rectangular sections wind tunnels, given their advantages as mentioned previously. Two separate geometries, both containing nozzles designed by method of characteristics, were made. Both had identical overall lengths, nozzles, and test sections. The difference was made in the diffuser section where one of the tunnels had the diffuser half-angles of 2o , while the other had diffuser half-angles of 4o . But the nozzle with 4o half angle accommodated a straight diffuser throat section before the expansion cone. This was to allow for shock reflections and smoother deceleration of the flow.
- 79. 67 4.3.3.1 Analyses carried out 1. Inviscid case – Back Pressure of 453000 Pa (Diffuser half-angle 2o ): Figure 104: Contours of Static Pressure Figure 105: Static Pressure plot wrt length along center-line
- 80. 68 Figure 106: Static Pressure plot wrt length along wall Here in figures 104, 105, 106, a very smooth pressure drop is observed across the convergent section of the nozzle. A near constant static pressure exists along the center-line in the expansion section of the nozzle. This proves that a nozzle exit contour has been successfully generated using method of characteristics, which prevents reflected shocks. The distribution of pressure near the wall has a smooth drop in the contour designed by method of characteristics. After the method of characteristics, the pressure is nearly constant in the test section. Figure 107: Contours of Mach number
- 81. 69 Figure 108: Mach number plot wrt length along center-line Figure 109: Mach number plot wrt length along wall In figure 107, 108, 109, the Mach number distribution along center-line is very smooth in the test section. Also, as it can be seen from the graphs, there are minimal disturbances as the Mach number rises to supersonic in the expansion part of the nozzle. A flow of Mach number 2.0 is obtained with a good distribution from the center-line to the wall. Here it is also observed that the Mach number drops to subsonic values as it reaches the end of the wind tunnel, which depicts the diffuser performs as expected, for the given length.
- 82. 70 Figure 110: Pressure-drop (shock close-up) This is a close-up image (figure 110) of the exit of diffuser where a high Mach number gradient is observed. This particular case depicts the back pressure causes the flow to decelerate to subsonic values before it exits the diffuser. 2. Viscous case - Back pressure 400000 Pa (Diffuser half-angle 2o ): Figure 111: Contours of Static Pressure The above pressure contour (figure 111) depicts the pressure variation along the wind tunnel. The contour depicts a design pressure of 1 atm being achieved in the test section. Also a sudden pressure gradient is observed in the diffuser section of the tunnel depicting a shock.
- 83. 71 Figure 112: Static Pressure plot wrt length along center-line This static pressure graph (figure 112) depicts a smooth drop in pressure along the center-line of the wind tunnel until the test section where it is consistent as with the flow. The sudden rise as observed is due to the shock being formed at that particular position in the diffuser section of the wind tunnel. Figure 113: Contours of Mach number This Mach number contour (figure 113) as depicted above shows a uniform distribution of flow in the test section. There is a gradual decrease in flow velocity as it nears the wall reaching 0 as there is a no slip condition on the wall.
- 84. 72 Figure 114: Mach number plot wrt length along center-line (lines indicate test section) The graph above (figure 114) shows a smooth increase in Mach number smoothly through the nozzle into the test section, where there is very little variation. The plot depicts that there is a drop in the diffuser as expected and Mach number drops from 1.8 to nearly Mach 0.6. Figure 115: Velocity magnitude contour (close-up at separation region) Figure 115 is a close-up of contour of velocity magnitude depicting the shock occurring in the diffuser. The slight deviation from normal shock occurs due to boundary layer giving it a lambda shape.
- 85. 73 Figure 116: Velocity vectors at separation region Figure 116 is a vector contour of the flow in the diffuser. The vectors are colour by velocity magnitude. The vectors are observed to turn inwards towards the flow due to boundary layer separation. Figure 117: Velocity vectors indicating flow separation Figure 117 is magnified to display the flow separation after the shock in the diffuser. The vectors are observed to have an eddy formation near the wall.
- 86. 74 Figure 118: Path lines showing separation of flow at diffuser throat The path lines in the above contour (figure 118) depict the flow separation right after the shock and then it re attaches as the flow progresses further. This trend is as expected for the diffuser and reattachment is necessary for diffuser to work properly. 3. Viscous case - Back Pressure of 400000 Pa (Diffuser half-angle 4o ): Figure 119: Contours of Static Pressure There is a sudden pressure gradient in the nozzle of the wind tunnel (refer figure 119) indicating a shock and unstart condition of wind tunnel. The flow is completely subsonic the test section.
- 87. 75 Figure 120: Static Pressure plot wrt length along center-line There is a smooth drop in Pressure across the nozzle (refer figure 120) due to the design of the nozzle. The shock in the nozzle causes a sudden rise in pressure causing low velocity flow conditions in the test section. Figure 121: Contours of Mach number
- 88. 76 Figure 122: Mach number plot wrt length along center-line The Mach number contour and graph in figure 121 and figure 122 depicts a trend expected during an unstart condition of the wind tunnel. The flow through the test section is subsonic and there is a very high gradient disrupting the flow after a normal shock in the diffuser. Figure 123: Contours of Velocity magnitude, shock in nozzle zoomed Figure 123 is a close-up view of the shock which occurs in the nozzle. A flow separation can be seen right after the shock. This is the unstart condition of wind tunnel. The possible reason for this is expected to be change in the diffuser inlet angle which was increased to be 4 degrees in this case.
- 89. 77 4.4 Variable geometry outcome The change in geometry using various actuators is possible and can be done using high powered hydraulic actuators in case of real wind tunnels. The code which was made in order to change the geometry by calculating the Mach number from the static to stagnation pressure ratio determines the shape of the geometry for the nozzle and the diffuser. The code works in such a manner that the exit area of the nozzle is fixed at the test section and throat area varies depending on the Mach number (for supersonic flows). For subsonic and transonic flows, the geometry has a parabolic nozzle with exit area equal to area of the test section. The throat area of the diffuser changes depending upon the nozzle throat area as calculated from the method of characteristics code (nozzle exit has constant area). For subsonic cases, the diffuser has linearly tapered section inclined at a half angle of 2.8o due to the length. Figure 124: Variable geometry demonstration model with actuator mechanism and tunnel wall (currently under subsonic geometry alignment Figure 125: Variable geometry mechanism showing diffuser section (current configuration - subsonic diffuser)
- 90. 78 Figure 126: Variable geometry mechanism showing diffuser section (current configuration - supersonic diffuser) 4.4.1 Sealing problem The variation in geometry could cause a problem regarding proper sealing of the tunnel (in order to prevent pressure leaks). This problem could be mitigated by either using high friction sealing techniques which can prevent the pressure leak and would only allow the geometry to move under the actuation force. Another method of sealing is suggested to have a flexible wall at the sides of the wind tunnel fixed on top and bottom walls. The flexible walls would result in change of internal volume as the geometry moves. These particular corrections can be included in the initial calculations itself to prevent any adverse variation from the expected results. 4.5 Power Requirements The maximum power requirements for a wind tunnel occur during start-up (for a supersonic case). For continuous operation, these power requirements drastically reduce. Therefore, the power calculations done for start-up would suffice for providing the maximum power required in order to operate the wind tunnel. A MATLAB script was used to calculate the required power for 1:1 scale wind tunnel and the following results were obtained.
- 91. 79 Figure 127: Power requirements of scale 1:1 cross section It is observed from the graph in figure 127 that power requirements are extremely high. This is due to the fact that at 1:1 scale, there is a huge amount of mass of air to be moved through the tunnel, as the cross section area is 1.6875×8.4375 m2 . For practical purposes, the test section area needs to be reduced. Thus, the lengths are scaled down by a factor of 7, to give a cross section area of 0.2411×1.2054 m2 . The following was the graph obtained for the smaller test section. Figure 128: Power requirement of scale 1:49 cross section area It is observed from figure 128 that the more realistic value of 12 MW is required for running the wind tunnel when the lengths are scaled down by a factor of 7.
- 92. 80 CHAPTER 5 CONCLUSION AND FUTURE SCOPE OF WORK 5.1 Introduction The analyses carried out for various cases have produced various results, highlighting certain observations which lead to several conclusions. These conclusions are listed in this chapter, along with the future work which could be carried out. 5.2 Brief Summary of work The objective of the project was to design a tri-sonic wind tunnel capable of generating subsonic, transonic and supersonic flows in the test section. The designs were made and analyses were carried out for several conditions and geometries. The geometries were designed based on different conditions and various equations were used for designing the contours. The boundary conditions were theoretically calculated using isentropic relations. The maximum value of back pressure recovery (in case of supersonic Mach 2.0 tunnel) was obtained to be 0.721 times the stagnation pressure at inlet. Therefore, any back pressure value obtained will be lesser than the above mentioned pressure ratio. 5.3 Conclusion The objective of designing a tri-sonic wind tunnel was met with designs of subsonic, transonic and supersonic tunnels providing the required results. Following were the conclusions derived from the results obtained: 5.3.1 Supersonic The method of characteristics (for supersonic nozzle exit geometry) produced better results than linearly tapered nozzles. A stable Mach number of 2.0 was obtained in the supersonic wind tunnel for both viscous and inviscid cases, with the following conclusions made from observations: For inviscid cases, the normal shock was stabilized near the exit of the diffuser. In case of viscous flow through the supersonic tunnel, very little boundary layer thickening was observed. The flow quality wasn’t much affected by it. In case of 2o diffuser inlet geometry, for viscous flows, the shock was existent just behind the diffuser throat, rather than the exit of the diffuser. A lambda shock seemed to have formed due to viscous effects near the wall. Also, in the diffuser, there was a region of flow separation right after the shock, which resulted in eddy formations. This flow was reattached to the wall as the flow progressed further downstream. In case of geometry with 4o diffuser inlet half-angle (with straight throat section of 2 m length), the tunnel remained in unstart condition with subsonic flow throughout the test section.
- 93. 81 5.3.2 Subsonic Different Mach numbers were achieved for various cases designed for subsonic flow by changing the pressure ratio across the tunnel. There seemed to be a trend where the viscous losses increased with the Mach number in the wind tunnel. This is due to the fact that, with the increase in flow speeds, the viscous energy dissipation also increases. The boundary layer thickening in case of transonic wind tunnel resulted in increasing the Mach number of the flow even through the test section. This particular condition was obtained due to the increase in the boundary layer thickness as the flow progressed through the test section. This thickening of boundary layer would be extremely low but it resulted in a slight convergent section in the test section. The parabolic geometry produced much better flow quality and lesser adverse pressure gradients. 5.4 Future scope of work Analysis on complete wind tunnel including all sections could be carried out. Complete propulsion system design can be carried out. Model tolerances for the tunnel can also be calculated and different geometries analyzed in order to get the required result. Vanes for turning sections also can be designed, with the flow straightener system. Instrumentation system can be designed in order to get the measurements and readings from the wind tunnels.
- 94. 82 REFERENCES Journal / Conference Papers [1] J. C. Crown and W. H. Heybey, “Supersonic nozzle design (project NOL 159”, NAVAL ORDNANCE LABORATORY MEMORANDUM, 10594, 1950, Pg. 2-19. [2] MILAN VLAJINAC, “Design construction and evaluation of a subsonic wind tunnel”, Massachusetts Institute of Technology, U.S.A, June 1970, Pg. 1 to 13 [3] Kelly Butler, David Cancel, Brian Earley, Stacey Morin, Evan Morrison, Michael Sangenario, “Design and construction of a Supersonic Wind Tunnel Reference / Hand Books [4] John D. Anderson, Jr., “Modern compressible flow with historical perspective”, McGraw-Hill Publishers, 3rd Edition, ISBN-13: 978-1-25-902742-0. [5] Alan Pope, “Wind Tunnel Testing”, John Wiley and Sons, Inc, New York, 2nd Edition November 1958. [6] Alan Pope, Kenneth Goin, “High-speed Wind Tunnel testing”, John Wiley and Sons, Inc, 1965 [7] John D. Anderson, Jr., “Fundamentals of Aerodynamics”, McGraw-Hill Publishers, 5th Edition Web/Other [8] Trying to achieve supersonic flow in a pipe, www.cfd-online.com [9] Nozzles and diffusers, www.wiley.com [10] Diffusers, www.navier.stanford.edu [11] 2-D Nozzle design, www.mathworks.in [12] Use of K-Epsilon and K-Omega models, www.cfd-online.com [13] Starting Problem of Supersonic Wind Tunnels, Georgia Tech College of Aerospace Engineering course [14] Navier-Stokes equations, ANSYS 14.0 Help section

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