Fluid Mechanics and Thermodynamics of Turbomachinery

Fluid Mechanics and Thermodynamics of Turbomachinery
Copyright
Dedication
Preface to the Seventh Edition
Acknowledgments
List of Symbols
Subscripts
Superscripts
1 Introduction: Basic Principles
1.1 Definition of a turbomachine
1.2 Coordinate system
Relative velocities
Sign convention
Velocity diagrams for an axial flow compressor stage
1.3 The fundamental laws
1.4 The equation of continuity
1.5 The first law of thermodynamics
The steady flow energy equation
1.6 The momentum equation
Moment of momentum
The Euler work equation
Rothalpy and relative velocities
1.7 The second law of thermodynamics—entropy
1.8 Bernoulli’s equation
1.9 The thermodynamic properties of fluids
Ideal gases
Perfect gases
Steam
Commonly used thermodynamic terms relevant to steam tables
1.10 Compressible flow relations for perfect gases
Choked flow
1.11 Definitions of efficiency
Efficiency of turbines
Steam and gas turbines
Hydraulic turbines
Efficiency of compressors and pumps
1.12 Small stage or polytropic efficiency
Compression process
Small stage efficiency for a perfect gas
Turbine polytropic efficiency
Reheat factor
1.13 The inherent unsteadiness of the flow within turbomachines
References
2 Dimensional Analysis: Similitude
2.1 Dimensional analysis and performance laws
2.2 Incompressible fluid analysis
2.3 Performance characteristics for low-speed machines
2.4 Compressible flow analysis
Flow coefficient and stage loading
2.5 Performance characteristics for high-speed machines
Compressors
Turbines
2.6 Specific speed and specific diameter
The Cordier diagram
Compressible specific speed
2.7 Cavitation
Cavitation limits
References
3 Two-Dimensional Cascades
3.1 Introduction
3.2 Cascade geometry
Compressor blade profiles
Turbine blade profiles
3.3 Cascade flow characteristics
Streamtube thickness variation
Cascade performance parameters
Blade surface velocity distributions
3.4 Analysis of cascade forces
Lift and drag forces
Lift and drag coefficients
Circulation and lift
3.5 Compressor cascade performance
Compressor loss and blade loading
Fluid deviation
Incidence effects
Incompressible cascade analysis
Effects of Mach number
3.6 Turbine cascades
Turbine loss correlations
Correlation of Ainley and Mathieson
Reynolds number correction
Soderberg’s correlation
Mach number effects on loss
The Zweifel criterion
Flow exit angle
Turbine limit load
3.7 Cascade computational analysis
Calculation geometry
Method types
Boundary conditions
Transonic effects
Viscous effects
References
4 Axial-Flow Turbines: Mean-Line Analysis and Design
4.1 Introduction
4.2 Velocity diagrams of the axial turbine stage
4.3 Turbine stage design parameters
Design flow coefficient
Stage loading coefficient
Stage reaction
4.4 Thermodynamics of the axial turbine stage
4.5 Repeating stage turbines
4.6 Stage losses and efficiency
Turbine loss sources
Steam turbines
4.7 Preliminary axial turbine design
Number of stages
Blade height and mean radius
Number of aerofoils and axial chord
4.8 Styles of turbine
Zero reaction stage
50% Reaction stage
4.9 Effect of reaction on efficiency
4.10 Diffusion within blade rows
4.11 The efficiency correlation of
4.12 Design point efficiency of a turbine stage
Total-to-total efficiency of 50% reaction stage
Total-to-total efficiency of a zero reaction stage
Total-to-static efficiency of stage with axial velocity at exit
4.13 Stresses in turbine rotor blades
Centrifugal stresses
4.14 Turbine blade cooling
4.15 Turbine flow characteristics
Flow characteristics of a multistage turbine
References
5 Axial-Flow Compressors and Ducted Fans
5.1 Introduction
5.2 Mean-line analysis of the compressor stage
5.3 Velocity diagrams of the compressor stage
5.4 Thermodynamics of the compressor stage
5.5 Stage loss relationships and efficiency
Compressor loss sources
5.6 Mean-line calculation through a compressor rotor
Compressible case
Incompressible case
5.7 Preliminary compressor stage design
Stage loading
Flow coefficient
Reaction
Interstage swirl
Blade aspect ratio
5.8 Off-design performance
5.9 Multistage compressor performance
Overall pressure ratio and efficiency
Off-design operation and stage matching
Stage stacking
Annulus wall boundary layers
5.10 High Mach number compressor stages
5.11 Stall and surge phenomena in compressors
Casing treatment
Control of flow instabilities
5.12 Low speed ducted fans
Lift and drag coefficients
Blade element theory
Blade element efficiency
Lift coefficient of a fan aerofoil
References
6 Three-Dimensional Flows in Axial Turbomachines
6.1 Introduction
6.2 Theory of radial equilibrium
6.3 The indirect problem
Free-vortex flow
Compressor stage
Forced vortex
Variable vortex design
Mixed vortex design
First power stage vortex design
6.4 The direct problem
Some special cases
The general solution of the radial equilibrium equation
A special case
6.5 Compressible flow through a fixed blade row
6.6 Constant specific mass flow
6.7 Off-design performance of a stage
6.8 Free-vortex turbine stage
6.9 Actuator disc approach
Blade row interaction effects
Application to compressible flow
6.10 Computational through-flow methods
6.11 3D flow features
Secondary flow
Leakage flows
6.12 3D design
Sweep
Lean
Endwall profiling
Leakage paths, seals, and gaps
6.13 The application of 3D computational fluid dynamics
Single-passage steady computations
Multiple blade row steady computations
Unsteady computations
Current and future application of CFD to turbomachinery
References
7 Centrifugal Pumps, Fans, and Compressors
7.1 Introduction
7.2 Some definitions
7.3 Thermodynamic analysis of a centrifugal compressor
The impeller
The diffuser
7.4 Inlet velocity limitations at the compressor eye
7.5 Design of a pump inlet
7.6 Design of a centrifugal compressor inlet
Case A 넀㄀㴀　뀀
Case B 넀㄀─㌀攀　뀀
Some remarks on the use of prewhirl vanes at entry to the impeller
7.7 The slip factor
Introduction
The relative eddy concept
Slip factor correlations
7.8 A unified correlation for slip factor
Comparison of the new slip factor theory with experimental results
Method of Calculating the Shape Factor F
Illustrative exercise
Results
7.9 Head increase of a centrifugal pump
7.10 Performance of centrifugal compressors
Determining the pressure ratio
Effect of backswept vanes
Illustrative exercise
Kinetic energy leaving the impeller
Illustrative exercise
7.11 The diffuser system
Vaneless diffusers or volutes
Vaned diffusers
7.12 Diffuser performance parameters
Diffuser design calculation
7.13 Choking in a compressor stage
Inlet
Impeller
Diffuser
References
8 Radial-Flow Gas Turbines
8.1 Introduction
8.2 Types of IFR turbine
Cantilever turbine
The 90° IFR turbine
8.3 Thermodynamics of the 90° IFR turbine
8.4 Basic design of the rotor
Nominal design
Spouting velocity
8.5 Nominal design point efficiency
8.6 Some Mach number relations
8.7 The scroll and stator blades
Stator loss models
Effects of varying the vaneless space and the vane solidity
Loss coefficients used in 90° IFR turbines
Nozzle
Rotor loss coefficients
8.8 Optimum efficiency considerations
Design for optimum efficiency
Solution of Whitfield’s design problem
8.9 Criterion for minimum number of blades
8.10 Design considerations for rotor exit
8.11 Significance and application of specific speed
8.12 Optimum design selection of 90° IFR turbines
8.13 Clearance and windage losses
8.14 Cooled 90° IFR turbines
References
9 Hydraulic Turbines
9.1 Introduction
Tidal power
Wave power
Features of hydropower plants
9.2 Hydraulic turbines
Early history of hydraulic turbines
Flow regimes for maximum efficiency
Capacity of large Francis turbines
9.3 The Pelton turbine
A simple hydroelectric scheme
Controlling the speed of the Pelton turbine
Sizing the penstock diameter
Energy losses in the Pelton turbine
Optimum jet diameter
Exercise
9.4 Reaction turbines
9.5 The Francis turbine
Basic equations
The pump turbine
9.6 The Kaplan turbine
Basic equations
9.7 Effect of size on turbomachine efficiency
9.8 Cavitation in hydraulic turbines
Connection between Thoma’s coefficient, suction specific speed, and specific speed
Exercise
Avoiding Cavitation
Peripheral velocity factor
Selecting the right turbine
9.9 Application of CFD to the design of hydraulic turbines
9.10 The Wells turbine
Introduction
Operating principles
Two-dimensional flow analysis
Design and performance variables
Effect of flow coefficient
Effect of blade solidity
Effect of hub–tip ratio
The starting behavior of the Wells turbine
Pitch-controlled blades
A turbine with self-pitch-controlled blades
Further work
9.11 Tidal power
Categories of tidal power
Tidal stream generators
The SeaGen tidal turbine
References
10 Wind Turbines
10.1 Introduction
Wind characteristics and resource estimation
Historical viewpoint
10.2 Types of wind turbine
Large HAWTs
Small HAWTs
Effect of tower height
10.3 Performance measurement of wind turbines
Wind speed probability density function
Storing energy
Calculating the maximum possible power production of a wind turbine
10.4 Annual energy output
10.5 Statistical analysis of wind data
Basic equations
Wind speed probability distributions
10.6 Actuator disc approach
Introduction
Theory of the actuator disc
An alternative proof of Betz’s result
The power coefficient
The axial force coefficient
Correcting for high values of a¯
Estimating the power output
10.7 Blade element theory
Introduction
The vortex system of an aerofoil
Wake rotation
Forces acting on a blade element
Lift and drag coefficients
Connecting actuator disc theory and blade element theory
Tip–speed ratio
Turbine solidity
Solving the equations
10.8 The BEM method
Spanwise variation of parameters
Evaluating the torque and axial force
Correcting for a finite number of blades
Prandtl’s correction factor
Performance calculations with tip correction included
10.9 Rotor configurations
Blade planform
Effect of varying the number of blades
Effect of varying tip–speed ratio
Rotor optimum design criteria
10.10 The power output at optimum conditions
10.11 HAWT blade section criteria
10.12 Developments in blade manufacture
10.13 Control methods
Blade-pitch control
Passive or stall control
Aileron control
10.14 Blade tip shapes
10.15 Performance testing
10.16 Performance prediction codes
BEM theory
Lifting surface, prescribed wake theory
Comparison with experimental data
Peak and postpeak power predictions
Enhanced performance of turbine blades
10.17 Environmental matters
Visual intrusion
Acoustic emissions
10.18 The largest wind turbines
Appendix A: Preliminary Design of an Axial-Flow Turbine for a Large Turbocharger
Design requirements
Mean radius design
Determining the mean radius velocity triangles and efficiency
Determining the root and tip radii
Variation of reaction at the hub
Choosing a suitable stage geometry
Estimating the pitch/chord ratio
Blade angles and gas flow angles
Additional information concerning the design
Postscript
References
Appendix B: Preliminary Design of a Centrifugal Compressor for a Turbocharge
Design requirements and assumptions
Determining the blade speed and impeller radius
Design of impeller inlet
Efficiency considerations for the impeller
Design of impeller exit
Flow in the vaneless space
An iterative procedure
The vaned diffuser
The volute
Determining the exit stagnation pressure, p03, and overall compressor efficiency, ηC
References
Appendix C: Tables for the Compressible Flow of a Perfect Gas
Appendix D: Conversion of British and American Units to SI Units
Appendix E: Mollier Chart for Steam
Appendix F: Answers to Problems
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Index