Study of the Effect of Shape on the Aerodynamic Performance of Hyperloop Pod
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STUDY OF THE EFFECT OF SHAPE ON THE AERODYNAMIC PERFORMANCE OF HYPERLOOP POD By ANUP JAIN A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2019 © 2019 Anup Jain ACKNOWLEDGMENTS I would like to express my gratitude towards my supervisor, Dr. Bhavani Sankar, for his valuable guidance, help, and support. Without him, this project would not have been possible to be realized. It was great to have someone like him who was always available whenever I had any questions regarding the thesis. I want to thank my Co-chair, Dr. Ashok Kumar, for his valuable suggestions at every stage of the project and for all the discussions we had that helped me tremendously. I want to thank Dr. Siddharth Thakur for his guidance and consultation with the entire CFD process during the thesis. My special thanks, to the Support Engineers at Friendship Systems, for providing me free access to CAESES software and answering all my questions regarding it. Lastly, I want to thank all the people who directly or indirectly contributed to the successful completion of the Thesis 3 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................... 3 LIST OF TABLES ...................................... 6 LIST OF FIGURES ..................................... 7 LIST OF DEFINITIONS ................................... 8 ABSTRACT ......................................... 10 CHAPTER 1 INTRODUCTION ................................... 12 1.1 Objective ..................................... 12 1.2 Limitations .................................... 13 1.3 Thesis Outline .................................. 13 2 LITERATURE REVIEW ................................ 14 2.1 Background ................................... 14 2.2 Flow Field .................................... 15 2.3 Design Parameters and its effect on Drag .................... 17 2.4 Preliminary Shape Analysis ........................... 18 2.5 CFD Introduction ................................ 19 2.6 Turbulence Modeling .............................. 21 3 METHOD ....................................... 24 3.1 Geometry .................................... 24 3.2 Mesh ....................................... 26 3.3 Numerical Solver ................................. 28 3.3.1 Finite Volume Method .......................... 28 3.3.2 Pressure Based Solver and Density Based Solver ............ 29 3.4 Numerical Model ................................. 30 3.5 Boundary Conditions ............................... 31 3.6 K-omega SST Turbulence Model ........................ 32 3.7 Convergence and Verification .......................... 34 4 SURROGATE MODELING .............................. 39 4.1 Polynomial Regression Model .......................... 40 4.2 Kriging Regression Model ............................ 41 4.3 Surrogate Results ................................ 42 4 5 RESULTS ....................................... 45 5.1 Effect of Shape of Head ............................. 45 5.2 Effect of Shape of Tail .............................. 50 5.3 Sensitivity Analysis ................................ 55 6 CONCLUSION ..................................... 58 APPENDIX:ICEM CFD SCRIPT .............................. 59 REFERENCES ........................................ 69 BIOGRAPHICAL SKETCH ................................. 72 5 LIST OF TABLES Table page 3-1 Coordinates of the Control Points of the B-Spline .................. 26 3-2 Constraint of the variables of the control points ................... 27 4-1 Goodness of Fit for Polynomial and Kriging Regression Model ............ 43 5-1 Maximum Pressure Generated on Head for different Tail shapes ........... 52 6 LIST OF FIGURES Figure page 3-1 Parametric Pod Geometry ............................... 26 3-2 The Structured Grid around Pod with Semicircle head and Blunt tail ........ 28 3-3 Effect of Head shape on the drag for different operating pressures and velocity ... 34 3-4 Residuals ........................................ 36 3-5 Net Mass Flow Rate (across Inlet and Outlet) Vs Iterations ............. 36 3-6 Plot of Drag Coefficient Vs Iterations ......................... 37 3-7 Plot of Drag Vs Iterations ............................... 37 4-1 Plot of Drag obtained from the Response Surface vs Actual Observed Values. .... 43 5-1 Effect of Head shapes on drag for different Blockage ratio .............. 45 5-2 Effect of Head shapes on drag for different operating Pressures ........... 46 5-3 Distribution of Pressure Coefficient around the nose for different Head shapes ... 47 5-4 Pressure Distribution across the Semicircle shaped head ............... 48 5-5 Pressure Distribution across the Arched shaped head ................. 49 5-6 Pressure Distribution across the Splined Elliptic shaped head ............ 50 5-7 Effect of Head shape on the drag for different operating pressures and velocity ... 51 5-8 Effect of Tail shapes on drag for different Blockage ratio ............... 51 5-9 Maximum Pressure generated on the head due to different shapes of Tail ...... 52 5-10 Velocity Distribution across the pod with Blunt Tail ................. 53 5-11 Velocity Distribution across the pod with Elliptic Tail ................ 53 5-12 Velocity Distribution across the pod with Splined shaped Tail ............ 54 5-13 Effect of Head shape on the drag for different operating pressures and velocity ... 54 5-14 Effect of Tail shape on Drag for different operating Pressures ............ 55 5-15 Effect of Tail shape on Drag for different Velocity .................. 56 5-16 Sensitivity based on Polynomial Regression Model .................. 56 5-17 Sensitivity based on Kriging Regression Model .................... 57 7 LIST OF DEFINITIONS 2D Two-Dimensional 3D Three-Dimensional CFD Computational Fluid Dynamics COD Coefficient of Determination DBS Density Based Solver DNS Direct Numerical Simulation DOE Design of Experiment FVM Finite Volume Method LHS Latin Hypercube Sampling Maglev Magnetic levitation NURBS Non-Uniform Rational Basis Spline OSF Optimal Space Filling PBS Pressure Based Solver PRG Polynomial Regression Model RANS Reynolds-average Navier-Stokes equations SST Shear Stress Transport i ith vector element j jth vector element a Acceleration β Blockage ratio Kb Boltzmann constant ρ Density µ Dynamic viscosity νT Eddy viscosity R Gas constant g Gravitational constant 8 q Heat flux vector δ Kronecker delta < Less than M Mach number λ Molecular mean free path << Much smaller than y+ Non-dimensional wall distance ∼ Of the order of ∂ Partial derivative p Pressure Cp Pressure coefficient Re Reynolds number ω Specific turbulence dissipation rate T Temperature k Turbulence kinetic energy ▽ Vector differential operator − Vector notation 9 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science STUDY OF THE EFFECT OF SHAPE ON THE AERODYNAMIC PERFORMANCE OF HYPERLOOP POD By Anup Jain December 2019 Chair: Bhavani V. Sankar Major: Mechanical Engineering The Hyperloop is a new form of a ground transportation system that consists of pods carrying passengers or cargo traveling through a partially evacuated tube. Hyperloop, in a nutshell, is about eliminating two factors that slow down traditional vehicles, friction, and air resistance. To tackle the former, we levitate the pod using electromagnets and propel it using linear induction motor, whereas to address the later, we remove the air inside the tube such that we have a low-pressure environment. However, this motion of the hyperloop pod through a confined space, at transonic speeds imposes unique fluid dynamic challenges such aschoked flow, Kantrowitz Limit. These factors have a substantial impact on the performance ofthe vehicle and hence investigating the aerodynamics becomes of paramount importance while analyzing such systems. This master’s thesis aims to investigate the effect of the different head and tail shapeson the aerodynamic drag under varying blockage ratios, pressure, and velocity. We perform 2D steady-state simulations on three distinct heads and tail shapes, respectively. The blockage ratio differs from 0.25 - 0.6, pressure ranges from 10 Pa to 100 KPa, and velocity changes from 50 m/s to 300 m/s. The shape of the head is found to have no pronounced effect on the drag for any value of the blockage ratio. On the contrary, it is the shape of the tail that has a significant impact on the aerodynamic drag regardless of the pressure, velocity, and blockage ratio. For a given value of pressure in the tube, there is a limiting velocity above which the 10 shape of the head has a substantial effect on the aerodynamic drag. The lower the pressure in the tube, the higher the limiting velocity and viceversa. Sensitivity analysis is performed to verify the accuracy of the results,on 2D parametric geometry constructed using B-splines. Two surrogate models, the second-order polynomial and Kriging are used to compute the sensitivities. The results obtained are in line with our previous findings and confirm that the aerodynamic drag is more sensitive to the shape of thetailthan to the shape of the head. 11 CHAPTER 1 INTRODUCTION Hyperloop is a new form of transportation method that consists of passenger pods traveling through a partially evacuated tube. The pressure inside the tube is about 0.1%- 1% SpaceX (2013) of the atmospheric pressure obtained by removing the air inside the tube. The pods are levitated using electromagnets,