Chen N. Aerothermodynamics of Turbomachinery: Analysis and Design

John Wiley & Sons (Asia) Pte Ltd, 2, 2010. 461 p. — ISBN: 978-0-470-82500-6 (cloth).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.Nomenclaturentroduction to the Study of the Aerothermodynamics of Turbomachinery
Brief Description of the Development of the Numerical Study of the Aerothermodynamics of TurbomachineryFurther ReadingGoverning Equations Expressed in Non-Orthogonal Curvilinear Coordinates to Calculate 3D Viscous Fluid Flow in TurbomachineryAerothermodynamics Governing Equations (Navier–Stokes Equations) of Turbomachinery
Viscous and Heat Transfer Terms of Equations
Viscous Stress Tensor
Strain Tensor
Viscous Force
Rates of Work Done by the Viscous Stresses and Dissipation Function
Heat Transfer Term
Examples of Simplification of Viscous and Heat Transfer Terms
Three-Dimensional Flow in Turbomachinery Expressed by Using Arbitrary Non-Orthogonal Coordinates
S1 Stream-Surface Flow
S2 Stream-Surface Flow
Annulus Wall Boundary Layer
Three-Dimensional Boundary Layer on Rotating Blade Surface
Tensor Form of Governing Equations
Continuity Equation
Momentum Equation
Energy Equation
Entropy Equation
Integral Form of Governing Equations
Continuity Equation
Momentum Equation
Energy Equation
A Collection of the Basic Relationships for Non-Orthogonal CoordinatesIntroduction to Boundary Layer TheoryGeneral Concepts of the Boundary Layer
Nature of Boundary Layer Flow
Boundary Layer Thicknesses
Transition of the Boundary Layer Regime
Boundary Layer Separation
Thermal Boundary LayerNumerical Solutions of Boundary Layer Differential EquationsBoundary Layer Equations Expressed in Partial Differential Form
Two-Dimensional Laminar Boundary Layer Equations
Laminar Boundary Layer Equations of Axisymmetrical Flow
Turbulent Boundary Layer Equations
Boundary Conditions of Solution
Numerical Solution of the Boundary Layer Differential Equations for a Cascade on the Stream Surface of Revolution
Boundary Layer Equations of S1 Stream Surface Flow of Revolution and Their Solution
Turbulence Modeling
Calculation Results and Validations
Laminar Boundary Layer Calculation Example
Turbulent Boundary Layer with Favorable Pressure Gradient
Turbulent Boundary Layer with Adverse Pressure Gradient (Ludweig and Tillmann)
Turbulent Boundary Layer with Favorable Pressure Gradient (Bell)
Turbulent Boundary Layer with Adverse Pressure Gradient (Schubauer and Spangenberg)
Application to Analysis of the Performance of Turbomachinery Blade Cascades
Boundary Layer Momentum Thickness (Bammert’s Experiment)
Laminar Boundary Layer Prediction (Turbine and Compressor Blade Profiles)
Laminar-Turbulent Boundary Layer Prediction
Turbulent Viscosity Prediction
Stagger Angle Effect (C4)
Effect of Incidence Angle on Blade Loss Coefficient (C4)
Effect of Reynolds Number on the Loss Coefficient of Compressor Blade Cascades (C4)
Effect of Stream Sheet Thickness on Boundary Layer Momentum Thickness (Turbine Blade)Approximate Calculations Using Integral Boundary Layer EquationsIntegral Boundary Layer Equations
Boundary Layer Momentum Integral Equation of the Flow on the Stream Surface of Revolution
Momentum and Energy Integral Equations of the Boundary
Layer for Different Flow Cases
Generalized Method for Approximate Calculation of the Boundary Layer Momentum Thickness
Laminar Boundary Layer Momentum Integral Equation
Transitional Boundary Layer Momentum Integral Equation
Velocity Distribution in the Boundary Layer Region
Wall Shear Stress Prediction in the Transitional Region
An Approximate Momentum Integral Equation for the Transitional Region
Turbulent Boundary Layer Momentum Integral Equation
The Law of Velocity Distribution
Shape Parameters, H and H
Wall Shear Stress Coefficient
Boundary Layer Momentum Thickness Prediction
An Approximate Formula for Prediction of the Shape Parameter H of the Turbulent Boundary Layer
Empirical Constants for the Generalized Method for Approximate Calculation of Turbulent Boundary Layer Momentum Thickness Proposed by Different Authors
Calculation of a Compressible Boundary Layer
Compressibility Transformation of the Integral Equation of the Boundary Layer
Calculation Method for a Compressible Boundary Layer
Without Heat Transfer
Boundary Layer Calculation Method for a Blade Cascade on the Stream Surface of RevolutionApplication of Boundary Layer Techniques to TurbomachineryFlow Rate Coefficient and Loss Coefficient of Two-Dimensional Blade Cascades
Flow Rate Coefficient of a Blade Cascade
Loss Coefficient of a Blade Cascade
Studies on the Velocity Distributions Along Blade Surfaces and Correlation
Analysis of the Aerodynamic Characteristics of Plane Blade Cascades
Influence of Blade Surface Velocity Distribution on Boundary Layer Momentum Loss Thickness
The Loss Coefficient of a Theoretical Optimum Plane Turbine
Profile Cascade
Correlations of the Loss Coefficient of a Plane Turbine Profile Cascade (Using the Geometrical Convergence Gradient of
Blade Passage, G)
Correlations of the Loss Coefficient of a Plane Turbine Profile Cascade (Using the Convergence Gradient of Blade Passage G**
Expressed by Flow Angles)
Correlations of the Loss Coefficient of a Plane Compressor Blade Cascade (Using Diffusion Factor D)Stream Function Methods for Two- and Three-Dimensional Flow Computations in TurbomachineryThree-Dimensional Flow Solution Methods with Two Kinds of Stream Surfaces
Three-Dimensional Solution
Quasi-Three-Dimensional Solution
Two- Stream Function Method for Three-Dimensional Flow Solution
Coordinate System and Metrical Tensors
Three-Dimensional Governing Equations of Steady Inviscid Fluid Flow
Definition of Stream Functions and Coordinate-Transformation
Boundary Conditions and Calculation Examples
Stream Function Methods for Two-Dimensional Viscous Fluid Flow Computations
Navier–Stokes Equation Solution for Rotating Blade Cascade Flow on an S1 Stream Surface of Revolution
Boundary Conditions
Solution Procedure
Calculation Examples
Stream Function Method for Numerical Solution of Transonic Blade Cascade Flow on the Stream Surface of Revolution
Stream Function Equation and Artificial Compressibility
Stone’s Strongly Implicit Procedure (SIP) and its Improvement
Numerical Solution Procedure
Calculation Examples
Finite Analytic Numerical Solution Method (FASM) for Solving the Stream Function Equation of Blade Cascade Flow
Governing Equation and its Solution
Linearization of Equation Solution for a Rectangular Region
Non-Orthogonal Coordinate System and Discretized Difference Equation
Adaptability of the Coefficients to Compressibility
Numerical Solution Procedure
Calculation Examples7.A Formulas for Estimating the Coefficients of the Differential Equations of the 3D Two-Stream Function
Coordinate MethodPressure Correction Method for Two-Dimensional and Three-Dimensional Flow Computations in TurbomachineryGoverning Equations of Three-Dimensional Turbulent Flow and the Pressure Correction Solution Method
Governing Equations
Two-Equation (k – e) Turbulence Model
Coordinate Transformation and Generalized Form of Governing Equations with Body-Fitted Coordinates for Calculating Orthogonal Coordinate Components of the Velocity Vector
Discretized Algebraic Equations
Boundary Conditions and Wall-Function Treatment
Two-Dimensional Turbulent Flow Calculation Examples
A Symmetric Airfoil
Low Speed Subsonic Turbine Blade Cascade (NACA TN-3802)
Turbine Blade Cascade (VKI-LS59)
Transonic Turbine Blade Cascade with Large Round Leading Edges (T12)
Supersonic Turbine Blade Cascade
Compressor Blade Cascade (T1)
Three-Dimensional Turbulent Flow Calculation Examples
Linear Turbine Blade Cascade
Annular Turbine Blade Cascade
High Turning Turbine Blade Cascade for an Annular Blade Cascade Wind Tunnel
Linear Compressor Cascade
BUAA Single Rotor Test Compressor
Centrifugal ImpellerTime-Marching Method for Two-Dimensional and Three-Dimensional Flow Computations in TurbomachineryGoverning Equations of Three-Dimensional Viscous Flow in Turbomachinery
Relative Motion in Turbomachinery
Governing Equations Written in Differential Equation Formulation
Governing Equations Written in Integral Form
Solution Method Based on Multi-Stage Runge-Kutta Time-Marching Scheme
Discretization of Governing Equations
Method for Prediction of Parameters on Boundary Surfaces and Fluxes
Adaptive Dissipation Term
Modified Multi-Stage Runge–Kutta Time-Marching Scheme
Turbulence Modeling and Wall Function
Multi-Grid Scheme
Two-Dimensional Turbulent Flow Examples Calculated by the Multi-Stage Runge–Kutta Time-Marching Method
A Grid Generation Method Based on Analogy with the Staff–Spring System
Turbine Blade Cascade (VKI-LS59)
Transonic Steam Turbine Blade Cascade (VKI-LS59 ST)
Supersonic Inlet Flow Compressor Blade Cascade
Three-Dimensional Flow Examples Calculated by the Multi-Stage Runge–Kutta Time-Marching Method
Numerical Solution for Three-Dimensional Inviscid Flow in a Transonic Single Rotor Compressor
Numerical Solution for Three-Dimensional Turbulent Flow in a Single Rotor Compressor
Numerical Solution for Three-Dimensional Turbulent Flow in a Turbine Stage
Three-Dimensional Turbulent Flow in a Centrifugal Impeller by the Modified Multi-Stage Runge–Kutta Time-Marching MethodNumerical Study on the Aerodynamic Design of Circumferential-and Axial-Leaned and Bowed Turbine BladesCircumferential Blade-Bowing Study
Circumferential Blade-Bowing Procedure
Effect on the Pressure Distributions of the Surfaces of Revolution at Different Span Heights
Effect on Parameter Contours of the Meridian Surfaces (x2¼ const)
Effect on Pressure Contours of the Coordinate Surfaces (x1¼ const)
The Bowing Effect for Restraining Boundary-Layer Separation from the End-Wall
Circumferential Bowing Effect on Pitch-Wise
Mass-Averaged Parameters at Station
Suggestion of Applying a New Circumferentially Bowed Blading
Axial Blade-Bowing Study
Axial Blade-Bowing Procedure
Effect on Static Pressure Contours of the Meridian Surfaces (x2¼ const)
Effect on Pressure Distributions of the Surfaces of Revolution at Different Span Heights
Effect on Static Pressure Contours of the Surfaces of x1 ¼ const
Effect on Circumferentially Averaged Parameters at the Vertical Measuring Plane (Just at the Exit from the Blade
Channel, that is, Station No. 3)
Axial Bowing Effect on Secondary Flow
Axial Bowing Effect on Global Adiabatic Efficiency and Flow Rate
Circumferential Blade-Bowing Study of Turbine Nozzle Blade Row with Low Span-Diameter Ratio
Leaning Effect on Adiabatic Efficiency and Exit Flow Angle
Generation of a Radial Stacking Form Close to Optimal
An Attempt at a Blade ModificationNumerical Study on Three-Dimensional Flow Aerodynamics and Secondary Vortex Motions in TurbomachineryPost-Processing Algorithms
Relative Velocity Vector Schemes, Surface Trace and Volume Trace
Vortex Intensity
Entropy Increment
An Approximate Formula for Predicting the Secondary Flow Velocity Vector
Axial Turbine Secondary Vortices
Saddle Point and Horseshoe Vortex
Bowing Effect on the Location of the Saddle Point
Passage Vortex
Bowing Effect on the Development of the Passage Vortex
Bowing Effect on the Passage Vortex for Different Incidence Angles
Corner Vortex in Straight and Saber-Shaped Blade Cascades
Tip Clearance Vortex
Blade Bowing Effect in Blades with Tip Clearance
Mechanism of Loss Reduction by Bowed Blades
Some Features of Straight-Leaned Blade Aerodynamics of a Turbine Nozzle with Low Span-Diameter Ratio
Leaning Effect on Static Pressure Contours on the Blade Surfaces and on the Exit Coordinate Plane
Leaning Effect on Limiting Streamlines on Blade Surfaces
Leaning Effect on Entropy Contours at the Exit Plane from the Blade Channel
Numerical Study on the Three-Dimensional Flow Pattern and Vortex Motions in a Centrifugal Compressor Impeller
Complexity of the Flow in an Impeller
Limiting Streamlines on the Pressure/Hub and Suction/Hub Surfaces
Secondary Vortices in the Centrifugal Impeller
Topology of the Passage Vortex in the Centrifugal Compressor Impeller
Separation Vortex in a Vaneless Diffuser
aneless Diffuser Design ImprovementTwo-Dimensional Aerodynamic Inverse Problem Solution Study in TurbomachineryStream Function Method
S2 Meridional Stream Surface Flow
S1 Stream Surface Flow of Revolution
A Hybrid Problem Solution Method Using the Stream Function Equation with Prescribed Target Velocity for the Blade Cascades of Revolution
Circumferentially Geometric Proportional Curvilinear Coordinate System
Stream Function Equation and its Coefficients
Solution Procedure
Calculation Examples
Stream-Function-Coordinate Method (SFC) for the Blade Cascades on the Surface of Revolution
Stream-Function-Coordinate Equation
Artificial Compressibility Technique
Boundary Conditions
Numerical Examples
Stream-Function-Coordinate Method (SFC) with Target Circulation for the Blade Cascades on the Surface of Revolution
Blade Circulation and its Derivative
Blade Thickness Distribution
Two-Dimensional Inverse Method Using a Direct Solver with Residual Correction Technique
Residual Correction Equation
A Calculation ExampleThree-Dimensional Aerodynamic Inverse Problem Solution Study in TurbomachineryTwo-Stream-Function-Coordinate-Equation Inverse Method
Two-Stream-Function-Coordinate Differential Equations
Inverse Problem Solution Procedure
A Calculation Example
Three-Dimensional Potential Function Hybrid Solution Method
Governing Equations
Potential Function Equation
Solution Procedure
Calculation ExampleAerodynamic Design Optimization of Compressor and Turbine BladesParameterization Method
Parameterization of Blade Profile and Stacking Line
D Blade Reconstruction (Rebuilding)
Parameter Effects on the Geometry of a Blade Profile
Response Surface Method (RSM) for Blade Optimization
Response Surface Creation
Principle Scheme of the Response Surface Method
A Study on the Effect of Maximum Camber Location for a Transonic Fan Rotor Blading by GPAM
Brief Description
Optimization Procedure
Optimization of a Low Aspect Ratio Turbine by GPAM and a Study of the Effects of Geometry on the Aerodynamics Performance
Geometry Effect on Blade Performance
Optimal Turbine Nozzle Blades
Blade Parameterization and Aerodynamic Design Optimization for a 3D Transonic Compressor Rotor
Calculation Example
Brief Description of Methodologies
Optimization with Response Surface Method (RSM)
Optimization by Gradient-Based Parameterization Method (GPAM)
Simple Gradient Method (SGM)
Final Results