# Aerothermodynamics of Turbomachinery

## Analysis and Design

1. Edition June 2010

480 Pages, Hardcover*Wiley & Sons Ltd*

**978-0-470-82500-6**

### Short Description

Although some books have been published in this field, there is no an advanced book focusing on turbomachinery aerothermodynamics with systematic introduction of fundamental theory, experimental methods, industrial applications and the latest developments. With his over 50 years' experience in the area, Chen's book fills the gap. The book focuses on four aspects: direct and inverse solutions, flow phenomena, and design optimization.

Computational Fluid Dynamics (CFD) is now an essential and effective tool used in the design of all types of turbomachine, and this topic constitutes the main theme of this book. With over 50 years of experience in the field of aerodynamics, Professor Naixing Chen has developed a wide range of numerical methods covering almost the entire spectrum of turbomachinery applications. Moreover, he has also made significant contributions to practical experiments and real-life designs.

The book focuses on rigorous mathematical derivation of the equations governing flow and detailed descriptions of the numerical methods used to solve the equations. Numerous applications of the methods to different types of turbomachine are given and, in many cases, the numerical results are compared to experimental measurements. These comparisons illustrate the strengths and weaknesses of the methods - a useful guide for readers. Lessons for the design of improved blading are also indicated after many applications.

* Presents real-world perspective to the past, present and future concern in turbomachinery

* Covers direct and inverse solutions with theoretical and practical aspects

* Demonstrates huge application background in China

* Supplementary instructional materials are available on the companion website

Aerothermodynamics of Turbomachinery: Analysis and Design is ideal for senior undergraduates and graduates studying in the fields of mechanics, energy and power, and aerospace engineering; design engineers in the business of manufacturing compressors, steam and gas turbines; and research engineers and scientists working in the areas of fluid mechanics, aerodynamics, and heat transfer.

Supplementary lecture materials for instructors are available at www.wiley.com/go/chenturbo

Preface.

Acknowledgments.

Nomenclature.

1 Introduction.

1.1 Introduction to the Study of the Aerothermodynamics of Turbomachinery.

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

1.3 Summary.

Further Reading.

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

2.1 Introduction.

2.2 Aerothermodynamics Governing Equations (Navier-Stokes Equations) of Turbomachinery.

2.3 Viscous and Heat Transfer Terms of Equations.

2.4 Examples of Simplification of Viscous and Heat Transfer Terms.

2.5 Tensor Form of Governing Equations.

2.6 Integral Form of Governing Equations.

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

2.8 Summary.

3 Introduction to Boundary Layer Theory.

3.1 Introduction.

3.2 General Concepts of the Boundary Layer.

3.2.1 Nature of Boundary Layer Flow.

3.3 Summary.

4 Numerical Solutions of Boundary Layer Differential Equations.

4.1 Introduction.

4.2 Boundary Layer Equations Expressed in Partial Differential Form.

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

4.4 Calculation Results and Validations.

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

4.6 Summary.

5 Approximate Calculations Using Integral Boundary Layer Equations.

5.1 Introduction.

5.2 Integral Boundary Layer Equations.

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

5.4 Laminar Boundary Layer Momentum Integral Equation.

5.5 Transitional Boundary Layer Momentum Integral Equation.

5.6 Turbulent Boundary Layer Momentum Integral Equation.

5.7 Calculation of a Compressible Boundary Layer.

5.8 Summary.

6 Application of Boundary Layer Techniques to Turbomachinery.

6.1 Introduction.

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

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

6.4 Summary.

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

7.1 Introduction.

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

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

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

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

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

7.7 Summary.

Appendix 7.A Formulas for Estimating the Coefficients of the Differential Equations of the 3D Two-Stream Function Coordinate Method.

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

8.1 Introduction.

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

8.3 Two-Dimensional Turbulent Flow Calculation Examples.

8.4 Three-Dimensional Turbulent Flow Calculation Examples.

8.5 Summary.

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

9.1 Introduction.

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

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

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

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

9.6 Summary.

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

10.1 Introduction.

10.2 Circumferential Blade-Bowing Study.

10.3 Axial Blade-Bowing Study.

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

10.5 Summary.

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

11.1 Introduction.

11.2 Post-Processing Algorithms.

11.3 Axial Turbine Secondary Vortices.

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

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

11.6 Summary.

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

12.1 Introduction.

12.2 Stream Function Method.

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

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

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

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

12.7 Summary.

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

13.1 Introduction.

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

13.3 Three-Dimensional Potential Function Hybrid Solution Method.

13.4 Summary.

14 Aerodynamic Design Optimization of Compressor and Turbine Blades.

14.1 Introduction.

14.2 Parameterization Method.

14.3 Response Surface Method (RSM) for Blade Optimization.

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

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

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

14.7 Summary.

References.

Index.