Automotive Aerodynamics

Joseph Katz, San Diego State University, USA

"This is where the book by Katz excels and the fundamental fluid principles are extensively covered undera vehicle aerodynamics title"...."Katz’s book will make a prime choice textbook for an undergraduate Automotive Engineering course, as fluid related modules in various academic years can cover the topicspresented in various chapters of the book" Remus Cîrstea, Course Director MSc Automotive Engineering, Lecturer in Fluid Dynamics, Coventry University on behalf of The Aeronautical Jornal, Oct 2017

• Series Preface xiiPreface xiv1 Introduction and Basic Principles 11.1 Introduction 11.2 Aerodynamics as a Subset of Fluid Dynamics 21.3 Dimensions and Units 31.4 Automobile/Vehicle Aerodynamics 51.5 General Features of Fluid Flow 91.5.1 Continuum 101.5.2 Laminar and Turbulent Flow 111.5.3 Attached and Separated Flow 121.6 Properties of Fluids 131.6.1 Density 131.6.2 Pressure 141.6.3 Temperature 141.6.4 Viscosity 161.6.5 Specific Heat 191.6.6 Heat Transfer Coefficient, k 191.6.7 Modulus of Elasticity, E 201.6.8 Vapor Pressure 221.7 Advanced Topics: Fluid Properties and the Kinetic Theory of Gases 231.8 Summary and Concluding Remarks 26Reference 27Problems 272 The Fluid Dynamic Equations 352.1 Introduction 352.2 Description of Fluid Motion 362.3 Choice of Coordinate System 382.4 Pathlines, Streak Lines, and Streamlines 392.5 Forces in a Fluid 402.6 Integral Form of the Fluid Dynamic Equations 432.7 Differential Form of the Fluid Dynamic Equations 502.8 The Material Derivative 572.9 Alternate Derivation of the Fluid Dynamic Equations 592.10 Example for an Analytic Solution: Two-Dimensional, Inviscid Incompressible, Vortex Flow 622.10.1 Velocity Induced by a Straight Vortex Segment 652.10.2 Angular Velocity, Vorticity, and Circulation 662.11 Summary and Concluding Remarks 69References 72Problems 723 One-Dimensional (Frictionless) Flow 813.1 Introduction 813.2 The Bernoulli Equation 823.3 Summary of One-Dimensional Tools 843.4 Applications of the One-Dimensional Friction-Free Flow Model 853.4.1 Free Jets 853.4.2 Examples for Using the Bernoulli Equation 893.4.3 Simple Models for Time-Dependent Changes in a Control Volume 933.5 Flow Measurements (Based on Bernoulli’s Equation) 963.5.1 The Pitot Tube 963.5.2 The Venturi Tube 983.5.3 The Orifice 1003.5.4 Nozzles and Injectors 1013.6 Summary and Conclusions 1023.6.1 Concluding Remarks 103Problems 1044 Dimensional Analysis, High Reynolds Number Flows, and Definition of Aerodynamics 1224.1 Introduction 1224.2 Dimensional Analysis of the Fluid Dynamic Equations 1234.3 The Process of Simplifying the Governing Equations 1264.4 Similarity of Flows 1274.5 High Reynolds Number Flow and Aerodynamics 1294.6 High Reynolds Number Flows and Turbulence 1334.7 Summary and Conclusions 136References 136Problems 1365 The Laminar Boundary Layer 1415.1 Introduction 1415.2 Two-Dimensional Laminar Boundary Layer Model – The Integral Approach 1435.3 Solutions using the von Kármán Integral Equation 1475.4 Summary and Practical Conclusions 1565.5 Effect of Pressure Gradient 1615.6 Advanced Topics: The Two-Dimensional Laminar Boundary Layer Equations 1645.6.1 Summary of the Exact Blasius Solution for the Laminar Boundary Layer 1675.7 Concluding Remarks 169References 170Problems 1706 High Reynolds Number Incompressible Flow Over Bodies: Automobile Aerodynamics 1766.1 Introduction 1766.2 The Inviscid Irrotational Flow (and Some Math) 1786.3 Advanced Topics: A More Detailed Evaluation of the Bernoulli Equation 1816.4 The Potential Flow Model 1836.4.1 Methods for Solving the Potential Flow Equations 1836.4.2 The Principle of Superposition 1846.5 Two-Dimensional Elementary Solutions 1846.5.1 Polynomial Solutions 1856.5.2 Two-Dimensional Source (or Sink) 1876.5.3 Two-Dimensional Doublet 1906.5.4 Two-Dimensional Vortex 1936.5.5 Advanced Topics: Solutions Based on Green’s Identity 1966.6 Superposition of a Doublet and a Free-Stream: Flow Over a Cylinder 1996.7 Fluid Mechanic Drag 2046.7.1 The Drag of Simple Shapes 2056.7.2 The Drag of More Complex Shapes 2106.8 Periodic Vortex Shedding 2156.9 The Case for Lift 2186.9.1 A Cylinder with Circulation in a Free Stream 2186.9.2 Two-Dimensional Flat Plate at a Small Angle of Attack (in a Free Stream) 2226.9.3 Note About the Center of Pressure 2246.10 Lifting Surfaces: Wings and Airfoils 2256.10.1 The Two-Dimensional Airfoil 2266.10.2 An Airfoil’s Lift 2286.10.3 An Airfoil’s Drag 2296.10.4 An Airfoil Stall 2316.10.5 The Effect of Reynolds Number 2326.10.6 Three-Dimensional Wings 2336.11 Summary of High Reynolds Number Aerodynamics 2486.12 Concluding Remarks 249References 249Problems 2507 Automotive Aerodynamics: Examples 2627.1 Introduction 2627.2 Generic Trends (For Most Vehicles) 2637.2.1 Ground Effect 2647.2.2 Generic Automobile Shapes and Vortex Flows 2657.3 Downforce and Vehicle Performance 2697.4 How to Generate Downforce 2747.5 Tools used for Aerodynamic Evaluations 2747.5.1 Example for Aero Data Collection: Wind Tunnels 2767.5.2 Wind Tunnel Wall/Floor Interference 2797.5.3 Simulation of Moving Ground 2817.5.4 Expected Results of CFD, Road, or Wind Tunnel Tests (and Measurement Techniques) 2837.6 Variable (Adaptive) Aerodynamic Devices 2867.7 Vehicle Examples 2917.7.1 Passenger Cars 2927.7.2 Pickup Trucks 2987.7.3 Motorcycles 2997.7.4 Competition Cars (Enclosed Wheel) 3027.7.5 Open-Wheel Racecars 3067.8 Concluding Remarks 312References 314Problems 3148 Introduction to Computational Fluid Mechanics (CFD) 3168.1 Introduction 3168.2 The Finite-Difference Formulation 3178.3 Discretization and Grid Generation 3208.4 The Finite-Difference Equation 3218.5 The Solution: Convergence and Stability 3248.6 The Finite-Volume Method 3268.7 Example: Viscous Flow Over a Cylinder 3288.8 Potential-Flow Solvers: Panel Methods 3318.9 Summary 335References 337Problems 3379 Viscous Incompressible Flow: “Exact Solutions” 3399.1 Introduction 3399.2 The Viscous Incompressible Flow Equations (Steady State) 3409.3 Laminar Flow between Two Infinite Parallel Plates: The Couette Flow 3409.3.1 Flow with a Moving Upper Surface 3429.3.2 Flow between Two Infinite Parallel Plates: The Results 3439.3.3 Flow between Two Infinite Parallel Plates – The Poiseuille Flow 3479.3.4 The Hydrodynamic Bearing (Reynolds Lubrication Theory) 3519.4 Flow in Circular Pipes (The Hagen-Poiseuille Flow) 3599.5 Fully Developed Laminar Flow between Two Concentric Circular Pipes 3649.6 Laminar Flow between Two Concentric, Rotating Circular Cylinders 3669.7 Flow in Pipes: Darcy’s Formula 3709.8 The Reynolds Dye Experiment, Laminar/Turbulent Flow in Pipes 3719.9 Additional Losses in Pipe Flow 3749.10 Summary of 1D Pipe Flow 3759.10.1 Simple Pump Model 3789.10.2 Flow in Pipes with Noncircular Cross Sections 3799.10.3 Examples for One-Dimensional Pipe Flow 3819.10.4 Network of Pipes 3919.11 Free Vortex in a Pool 3949.12 Summary and Concluding Remarks 397Reference 397Problems 39710 Fluid Machinery 41110.1 Introduction 41110.2 Work of a Continuous-Flow Machine 41510.3 The Axial Compressor (The Mean Radius Model) 41710.3.1 Velocity Triangles 42110.3.2 Power and Compression Ratio Calculations 42410.3.3 Radial Variations 42910.3.4 Pressure Rise Limitations 43110.3.5 Performance Envelope of Compressors and Pumps 43410.3.6 Degree of Reaction 44110.4 The Centrifugal Compressor (or Pump) 44610.4.1 Torque, Power, and Pressure Rise 44710.4.2 Impeller Geometry 45010.4.3 The Diffuser 45410.4.4 Concluding Remarks: Axial versus Centrifugal Design 45710.5 Axial Turbines 45810.5.1 Torque, Power, and Pressure Drop 45910.5.2 Axial Turbine Geometry and Velocity Triangles 46110.5.3 Turbine Degree of Reaction 46410.5.4 Turbochargers (for Internal Combustion Engines) 47310.5.5 Remarks on Exposed Tip Rotors (Wind Turbines and Propellers) 47410.6 Concluding Remarks 478Reference 478Problems 47811 Elements of Heat Transfer 48511.1 Introduction 48511.2 Elementary Mechanisms of Heat Transfer 48611.2.1 Conductive Heat Transfer 48611.2.2 Convective Heat Transfer 48911.2.3 Radiation Heat Transfer 49111.3 Heat Conduction 49511.3.1 Steady One-Dimensional Heat Conduction 49711.3.2 Combined Heat Transfer 49911.3.3 Heat Conduction in Cylinders 50211.3.4 Cooling Fins 50611.4 Heat Transfer by Convection 51511.4.1 The Flat Plate Model 51611.4.2 Formulas for Forced External Heat Convection 52011.4.3 Formulas for Forced Internal Heat Convection 52611.4.4 Formulas for Free (Natural) Heat Convection 52911.5 Heat Exchangers 53411.6 Concluding Remarks 536References 539Problems 53912 Automobile Aero-Acoustics 54412.1 Introduction 54412.2 Sound as a Pressure Wave 54612.3 Sound Loudness Scale 54912.4 The Human Ear Perception 55212.5 The One-Dimensional Linear Wave Equation 55312.6 Sound Radiation, Transmission, Reflection, Absorption 55612.6.1 Sound Wave Expansion (Radiation) 55612.6.2 Reflections, Transmission, Absorption 55912.6.3 Standing Wave (Resonance), Interference, and Noise Cancellations 56012.7 Vortex Sound 56112.8 Example: Sound from a Shear Layer 56412.9 Buffeting 56812.10 Experimental Examples for Sound Generation on a Typical Automobile 57412.11 Sound and Flow Control 57612.12 Concluding Remarks 577References 578Problems 578Appendix A 581Appendix B 583Index 589