Aerothermodynamics of Turbomachinery: Analysis and Design

Preface xvii

Acknowledgments xix

Nomenclature xxi

1 Introduction 1

1.1 Introduction to the Study of the Aerothermodynamics of Turbomachinery 1

1.2 Brief Description of the Development of the Numerical Study of the Aerothermodynamics of Turbomachinery 2

1.3 Summary 6

2 Governing Equations Expressed in Non-Orthogonal Curvilinear Coordinates to Calculate 3D Viscous Fluid Flow in Turbomachinery 9

2.1 Introduction 9

2.2 Aerothermodynamics Governing Equations (Navier–Stokes Equations) of Turbomachinery 10

2.3 Viscous and Heat Transfer Terms of Equations 11

2.4 Examples of Simplification of Viscous and Heat Transfer Terms 15

2.5 Tensor Form of Governing Equations 20

2.6 Integral Form of Governing Equations 21

2.7 A Collection of the Basic Relationships for Non-Orthogonal Coordinates 22

2.8 Summary 24

3 Introduction to Boundary Layer Theory 25

3.1 Introduction 25

3.2 General Concepts of the Boundary Layer 25

3.3 Summary 35

4 Numerical Solutions of Boundary Layer Differential Equations 37

4.1 Introduction 37

4.2 Boundary Layer Equations Expressed in Partial Differential Form 37

4.3 Numerical Solution of the Boundary Layer Differential Equations for a Cascade on the Stream Surface of Revolution 41

4.4 Calculation Results and Validations 45

4.5 Application to Analysis of the Performance of Turbomachinery Blade Cascades 49

4.6 Summary 57

5 Approximate Calculations Using Integral Boundary Layer Equations 59

5.1 Introduction 59

5.2 Integral Boundary Layer Equations 59

5.3 Generalized Method for Approximate Calculation of the Boundary Layer Momentum Thickness 64

5.4 Laminar Boundary Layer Momentum Integral Equation 66

5.5 Transitional Boundary Layer Momentum Integral Equation 68

5.6 Turbulent Boundary Layer Momentum Integral Equation 70

5.7 Calculation of a Compressible Boundary Layer 81

5.8 Summary 84

6 Application of Boundary Layer Techniques to Turbomachinery 87

6.1 Introduction 87

6.2 Flow Rate Coefficient and Loss Coefficient of Two-Dimensional Blade Cascades 87

6.3 Studies on the Velocity Distributions Along Blade Surfaces and Correlation Analysis of the Aerodynamic Characteristics of Plane Blade Cascades 92

6.4 Summary 101

7 Stream Function Methods for Two- and Three-Dimensional Flow Computations in Turbomachinery 103

7.1 Introduction 103

7.2 Three-Dimensional Flow Solution Methods with Two Kinds of Stream Surfaces 104

7.3 Two- Stream Function Method for Three-Dimensional Flow Solution 106

7.4 Stream Function Methods for Two-Dimensional Viscous Fluid Flow Computations 118

7.5 Stream Function Method for Numerical Solution of Transonic Blade Cascade Flow on the Stream Surface of Revolution 127

7.6 Finite Analytic Numerical Solution Method (FASM) for Solving the Stream Function Equation of Blade Cascade Flow 131

7.7 Summary 140

8 Pressure Correction Method for Two-Dimensional and Three-Dimensional Flow Computations in Turbomachinery 145

8.1 Introduction 145

8.2 Governing Equations of Three-Dimensional Turbulent Flow and the Pressure Correction Solution Method 146

8.3 Two-Dimensional Turbulent Flow Calculation Examples 157

8.4 Three-Dimensional Turbulent Flow Calculation Examples 169

8.5 Summary 198

9 Time-Marching Method for Two-Dimensional and Three-Dimensional Flow Computations in Turbomachinery 199

9.1 Introduction 199

9.2 Governing Equations of Three-Dimensional Viscous Flow in Turbomachinery 201

9.3 Solution Method Based on Multi-Stage Runge-Kutta Time-Marching Scheme 205

9.4 Two-Dimensional Turbulent Flow Examples Calculated by the Multi-Stage Runge–Kutta Time-Marching Method 216

9.5 Three-Dimensional Flow Examples Calculated by the Multi-Stage Runge–Kutta Time-Marching Method 226

9.6 Summary 249

10 Numerical Study on the Aerodynamic Design of Circumferentialand Axial-Leaned and Bowed Turbine Blades 251

10.1 Introduction 251

10.2 Circumferential Blade-Bowing Study 252

10.3 Axial Blade-Bowing Study 266

10.4 Circumferential Blade-Bowing Study of Turbine Nozzle Blade Row with Low Span-Diameter Ratio 277

10.5 Summary 286

11 Numerical Study on Three-Dimensional Flow Aerodynamics and Secondary Vortex Motions in Turbomachinery 287

11.1 Introduction 287

11.2 Post-Processing Algorithms 288

11.3 Axial Turbine Secondary Vortices 289

11.4 Some Features of Straight-Leaned Blade Aerodynamics of a Turbine Nozzle with Low Span-Diameter Ratio 310

11.5 Numerical Study on the Three-Dimensional Flow Pattern and Vortex Motions in a Centrifugal Compressor Impeller 317

11.6 Summary 326

12 Two-Dimensional Aerodynamic Inverse Problem Solution Study in Turbomachinery 329

12.1 Introduction 329

12.2 Stream Function Method 331

12.3 A Hybrid Problem Solution Method Using the Stream Function Equation with Prescribed Target Velocity for the Blade Cascades of Revolution 336

12.4 Stream-Function-Coordinate Method (SFC) for the Blade Cascades on the Surface of Revolution 343

12.5 Stream-Function-Coordinate Method (SFC) with Target Circulation for the Blade Cascades on the Surface of Revolution 350

12.6 Two-Dimensional Inverse Method Using a Direct Solver with Residual Correction Technique 353

12.7 Summary 359

13 Three-Dimensional Aerodynamic Inverse Problem Solution Study in Turbomachinery 361

13.1 Introduction 361

13.2 Two-Stream-Function-Coordinate-Equation Inverse Method 362

13.3 Three-Dimensional Potential Function Hybrid Solution Method 364

13.4 Summary 372

14 Aerodynamic Design Optimization of Compressor and Turbine Blades 375

14.1 Introduction 375

14.2 Parameterization Method 377

14.3 Response Surface Method (RSM) for Blade Optimization 387

14.4 A Study on the Effect of Maximum Camber Location for a Transonic Fan Rotor Blading by GPAM 395

14.5 Optimization of a Low Aspect Ratio Turbine by GPAM and a Study of the Effects of Geometry on the Aerodynamics Performance 401

14.6 Blade Parameterization and Aerodynamic Design Optimization for a 3D Transonic Compressor Rotor 412

14.7 Summary 426

References 429

Index 441