Automotive Aerodynamics

The automobile is an icon of modern technology because it includes most aspects of modern engineering, and it offers an exciting approach to engineering education. Of course there are many existing books on introductory fluid/aero dynamics but the majority of these are too long, focussed on aerospace and don’t adequately cover the basics. Therefore, there is room and a need for a concise, introductory textbook in this area.

Automotive Aerodynamics fulfils this need and is an introductory textbook intended as a first course in the complex field of aero/fluid mechanics for engineering students. It introduces basic concepts and fluid properties, and covers fluid dynamic equations. Examples of automotive aerodynamics are included and the principles of computational fluid dynamics are introduced. This text also includes topics such as aeroacoustics and heat transfer which are important to engineering students and are closely related to the main topic of aero/fluid mechanics.

This textbook contains complex mathematics, which not only serve as the foundation for future studies but also provide a road map for the present text. As the chapters evolve, focus is placed on more applicable examples, which can be solved in class using elementary algebra. The approach taken is designed to make the mathematics more approachable and easier to understand.

Key features:

• Concise textbook which provides an introduction to fluid mechanics and aerodynamics, with automotive applications
• Written by a leading author in the field who has experience working with motor sports teams in industry
• Explains basic concepts and equations before progressing to cover more advanced topics
• Covers internal and external flows for automotive applications
• Covers emerging areas of aeroacoustics and heat transfer

Automotive Aerodynamics is a must-have textbook for undergraduate and graduate students in automotive and mechanical engineering, and is also a concise reference for engineers in industry.

Joseph Katz, San Diego State University, USA

Series Preface xii

Preface xiv

1 Introduction and Basic Principles 1

1.1 Introduction 1

1.2 Aerodynamics as a Subset of Fluid Dynamics 2

1.3 Dimensions and Units 3

1.4 Automobile/Vehicle Aerodynamics 5

1.5 General Features of Fluid Flow 9

1.5.1 Continuum 10

1.5.2 Laminar and Turbulent Flow 11

1.5.3 Attached and Separated Flow 12

1.6 Properties of Fluids 13

1.6.1 Density 13

1.6.2 Pressure 14

1.6.3 Temperature 14

1.6.4 Viscosity 16

1.6.5 Specific Heat 19

1.6.6 Heat Transfer Coefficient, k 19

1.6.7 Modulus of Elasticity, E 20

1.6.8 Vapor Pressure 22

1.7 Advanced Topics: Fluid Properties and the Kinetic Theory of Gases 23

1.8 Summary and Concluding Remarks 26

Reference 27

Problems 27

2 The Fluid Dynamic Equations 35

2.1 Introduction 35

2.2 Description of Fluid Motion 36

2.3 Choice of Coordinate System 38

2.4 Pathlines, Streak Lines, and Streamlines 39

2.5 Forces in a Fluid 40

2.6 Integral Form of the Fluid Dynamic Equations 43

2.7 Differential Form of the Fluid Dynamic Equations 50

2.8 The Material Derivative 57

2.9 Alternate Derivation of the Fluid Dynamic Equations 59

2.10 Example for an Analytic Solution: Two-Dimensional, Inviscid Incompressible, Vortex Flow 62

2.10.1 Velocity Induced by a Straight Vortex Segment 65

2.10.2 Angular Velocity, Vorticity, and Circulation 66

2.11 Summary and Concluding Remarks 69

References 72

Problems 72

3 One-Dimensional (Frictionless) Flow 81

3.1 Introduction 81

3.2 The Bernoulli Equation 82

3.3 Summary of One-Dimensional Tools 84

3.4 Applications of the One-Dimensional Friction-Free Flow Model 85

3.4.1 Free Jets 85

3.4.2 Examples for Using the Bernoulli Equation 89

3.4.3 Simple Models for Time-Dependent Changes in a Control Volume 93

3.5 Flow Measurements (Based on Bernoulli’s Equation) 96

3.5.1 The Pitot Tube 96

3.5.2 The Venturi Tube 98

3.5.3 The Orifice 100

3.5.4 Nozzles and Injectors 101

3.6 Summary and Conclusions 102

3.6.1 Concluding Remarks 103

Problems 104

4 Dimensional Analysis, High Reynolds Number Flows, and Definition of Aerodynamics 122

4.1 Introduction 122

4.2 Dimensional Analysis of the Fluid Dynamic Equations 123

4.3 The Process of Simplifying the Governing Equations 126

4.4 Similarity of Flows 127

4.5 High Reynolds Number Flow and Aerodynamics 129

4.6 High Reynolds Number Flows and Turbulence 133

4.7 Summary and Conclusions 136

References 136

Problems 136

5 The Laminar Boundary Layer 141

5.1 Introduction 141

5.2 Two-Dimensional Laminar Boundary Layer Model – The Integral Approach 143

5.3 Solutions using the von Kármán Integral Equation 147

5.4 Summary and Practical Conclusions 156

5.5 Effect of Pressure Gradient 161

5.6 Advanced Topics: The Two-Dimensional Laminar Boundary Layer Equations 164

5.6.1 Summary of the Exact Blasius Solution for the Laminar Boundary Layer 167

5.7 Concluding Remarks 169

References 170

Problems 170

6 High Reynolds Number Incompressible Flow Over Bodies: Automobile Aerodynamics 176

6.1 Introduction 176

6.2 The Inviscid Irrotational Flow (and Some Math) 178

6.3 Advanced Topics: A More Detailed Evaluation of the Bernoulli Equation 181

6.4 The Potential Flow Model 183

6.4.1 Methods for Solving the Potential Flow Equations 183

6.4.2 The Principle of Superposition 184

6.5 Two-Dimensional Elementary Solutions 184

6.5.1 Polynomial Solutions 185

6.5.2 Two-Dimensional Source (or Sink) 187

6.5.3 Two-Dimensional Doublet 190

6.5.4 Two-Dimensional Vortex 193

6.5.5 Advanced Topics: Solutions Based on Green’s Identity 196

6.6 Superposition of a Doublet and a Free-Stream: Flow Over a Cylinder 199

6.7 Fluid Mechanic Drag 204

6.7.1 The Drag of Simple Shapes 205

6.7.2 The Drag of More Complex Shapes 210

6.8 Periodic Vortex Shedding 215

6.9 The Case for Lift 218

6.9.1 A Cylinder with Circulation in a Free Stream 218

6.9.2 Two-Dimensional Flat Plate at a Small Angle of Attack (in a Free Stream) 222

6.9.3 Note About the Center of Pressure 224

6.10 Lifting Surfaces: Wings and Airfoils 225

6.10.1 The Two-Dimensional Airfoil 226

6.10.2 An Airfoil’s Lift 228

6.10.3 An Airfoil’s Drag 229

6.10.4 An Airfoil Stall 231

6.10.5 The Effect of Reynolds Number 232

6.10.6 Three-Dimensional Wings 233

6.11 Summary of High Reynolds Number Aerodynamics 248

6.12 Concluding Remarks 249

References 249

Problems 250

7 Automotive Aerodynamics: Examples 262

7.1 Introduction 262

7.2 Generic Trends (For Most Vehicles) 263

7.2.1 Ground Effect 264

7.2.2 Generic Automobile Shapes and Vortex Flows 265

7.3 Downforce and Vehicle Performance 269

7.4 How to Generate Downforce 274

7.5 Tools used for Aerodynamic Evaluations 274

7.5.1 Example for Aero Data Collection: Wind Tunnels 276

7.5.2 Wind Tunnel Wall/Floor Interference 279

7.5.3 Simulation of Moving Ground 281

7.5.4 Expected Results of CFD, Road, or Wind Tunnel Tests (and Measurement Techniques) 283

7.6 Variable (Adaptive) Aerodynamic Devices 286

7.7 Vehicle Examples 291

7.7.1 Passenger Cars 292

7.7.2 Pickup Trucks 298

7.7.3 Motorcycles 299

7.7.4 Competition Cars (Enclosed Wheel) 302

7.7.5 Open-Wheel Racecars 306

7.8 Concluding Remarks 312

References 314

Problems 314

8 Introduction to Computational Fluid Mechanics (CFD) 316

8.1 Introduction 316

8.2 The Finite-Difference Formulation 317

8.3 Discretization and Grid Generation 320

8.4 The Finite-Difference Equation 321

8.5 The Solution: Convergence and Stability 324

8.6 The Finite-Volume Method 326

8.7 Example: Viscous Flow Over a Cylinder 328

8.8 Potential-Flow Solvers: Panel Methods 331

8.9 Summary 335

References 337

Problems 337

9 Viscous Incompressible Flow: “Exact Solutions” 339

9.1 Introduction 339

9.2 The Viscous Incompressible Flow Equations (Steady State) 340

9.3 Laminar Flow between Two Infinite Parallel Plates: The Couette Flow 340

9.3.1 Flow with a Moving Upper Surface 342

9.3.2 Flow between Two Infinite Parallel Plates: The Results 343

9.3.3 Flow between Two Infinite Parallel Plates – The Poiseuille Flow 347

9.3.4 The Hydrodynamic Bearing (Reynolds Lubrication Theory) 351

9.4 Flow in Circular Pipes (The Hagen-Poiseuille Flow) 359

9.5 Fully Developed Laminar Flow between Two Concentric Circular Pipes 364

9.6 Laminar Flow between Two Concentric, Rotating Circular Cylinders 366

9.7 Flow in Pipes: Darcy’s Formula 370

9.8 The Reynolds Dye Experiment, Laminar/Turbulent Flow in Pipes 371

9.9 Additional Losses in Pipe Flow 374

9.10 Summary of 1D Pipe Flow 375

9.10.1 Simple Pump Model 378

9.10.2 Flow in Pipes with Noncircular Cross Sections 379

9.10.3 Examples for One-Dimensional Pipe Flow 381

9.10.4 Network of Pipes 391

9.11 Free Vortex in a Pool 394

9.12 Summary and Concluding Remarks 397

Reference 397

Problems 397

10 Fluid Machinery 411

10.1 Introduction 411

10.2 Work of a Continuous-Flow Machine 415

10.3 The Axial Compressor (The Mean Radius Model) 417

10.3.1 Velocity Triangles 421

10.3.2 Power and Compression Ratio Calculations 424

10.3.3 Radial Variations 429

10.3.4 Pressure Rise Limitations 431

10.3.5 Performance Envelope of Compressors and Pumps 434

10.3.6 Degree of Reaction 441

10.4 The Centrifugal Compressor (or Pump) 446

10.4.1 Torque, Power, and Pressure Rise 447

10.4.2 Impeller Geometry 450

10.4.3 The Diffuser 454

10.4.4 Concluding Remarks: Axial versus Centrifugal Design 457

10.5 Axial Turbines 458

10.5.1 Torque, Power, and Pressure Drop 459

10.5.2 Axial Turbine Geometry and Velocity Triangles 461

10.5.3 Turbine Degree of Reaction 464

10.5.4 Turbochargers (for Internal Combustion Engines) 473

10.5.5 Remarks on Exposed Tip Rotors (Wind Turbines and Propellers) 474

10.6 Concluding Remarks 478

Reference 478

Problems 478

11 Elements of Heat Transfer 485

11.1 Introduction 485

11.2 Elementary Mechanisms of Heat Transfer 486

11.2.1 Conductive Heat Transfer 486

11.2.2 Convective Heat Transfer 489

11.2.3 Radiation Heat Transfer 491

11.3 Heat Conduction 495

11.3.1 Steady One-Dimensional Heat Conduction 497

11.3.2 Combined Heat Transfer 499

11.3.3 Heat Conduction in Cylinders 502

11.3.4 Cooling Fins 506

11.4 Heat Transfer by Convection 515

11.4.1 The Flat Plate Model 516

11.4.2 Formulas for Forced External Heat Convection 520

11.4.3 Formulas for Forced Internal Heat Convection 526

11.4.4 Formulas for Free (Natural) Heat Convection 529

11.5 Heat Exchangers 534

11.6 Concluding Remarks 536

References 539

Problems 539

12 Automobile Aero-Acoustics 544

12.1 Introduction 544

12.2 Sound as a Pressure Wave 546

12.3 Sound Loudness Scale 549

12.4 The Human Ear Perception 552

12.5 The One-Dimensional Linear Wave Equation 553

12.6 Sound Radiation, Transmission, Reflection, Absorption 556

12.6.1 Sound Wave Expansion (Radiation) 556

12.6.2 Reflections, Transmission, Absorption 559

12.6.3 Standing Wave (Resonance), Interference, and Noise Cancellations 560

12.7 Vortex Sound 561

12.8 Example: Sound from a Shear Layer 564

12.9 Buffeting 568

12.10 Experimental Examples for Sound Generation on a Typical Automobile 574

12.11 Sound and Flow Control 576

12.12 Concluding Remarks 577

References 578

Problems 578

Appendix A 581

Appendix B 583

Index 589

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