Radial Flow Turbocompressors: Design, Analysis, and Applications

Cover
Half-title
Title page
Copyright information
Dedication
Contents
Credits
Introduction
Preface
Acknowledgements
Conventions and Nomenclature
Conventions
Nomenclature
Letters
Symbols
Subscripts
Superscripts
1 Introduction to Radial Flow Turbocompressors
1.1 Overview
1.1.1 Introduction
1.1.2 Learning Objectives
1.2 Definition of Turbomachinery
1.2.1 Open System
1.2.2 Continuous Energy Transfer by Flow over Blades Rotating around an Axis
1.2.3 Aerodynamic
1.2.4 Principle of Operation
1.3 Classification of Turbomachines
1.3.1 Power Consuming and Power Producing Machines
1.3.2 Thermal and Hydraulic Machines
1.3.3 Acceleration and Deceleration of the Flow
1.3.4 Flow Direction
1.3.5 Degree of Reaction
1.3.6 Boundary of the Flow Field
1.4 Short History of Thermal Turbomachines
1.4.1 The Prefix Turbo
1.4.2 Historical Overview
1.5 Components of Radial Flow Turbocompressors
1.5.1 The Single-Stage Radial Flow Turbocompressor Stage
1.5.2 Multistage Configurations
1.5.3 Impeller Types
1.5.4 Features of Multistage Radial Turbocompressors
1.6 Applications of Centrifugal Turbocompressors
1.6.1 Turbochargers and Superchargers
1.6.2 Compressed Air
1.6.3 Industrial Wastewater Treatment
1.6.4 Air Conditioning, Air Extraction and Building Ventilation Applications
1.6.5 Vacuum Compressors
1.6.6 Vapour Compression Refrigeration and Heat Pumps
1.6.7 Gas Turbines for Power Generation
1.6.8 Automotive Gas Turbines
1.6.9 Jet Propulsion Gas Turbines
1.6.10 The Auxiliary Power Unit
1.6.11 Oil, Gas and Chemical Applications
1.6.12 Fluid Catalytic Cracking Compressors
1.6.13 Air Separation Plants
1.6.14 Synthetic Fuels, Coal Liquefaction and Gas to Liquid
1.6.15 Carbon Capture and Storage (CSS)
1.6.16 Compressed Air Energy Storage
1.6.17 Centrifugal Steam Compressors for Mechanical Vapour Recompression
1.6.18 Fuel Cells
1.6.19 Microcompressors
1.6.20 Medical Applications
1.7 Some Other Publications
1.7.1 Books
1.7.2 Technical Conferences and Journals
2 Energy Transfer
2.1 Overview
2.1.1 Introduction
2.1.2 Learning Objectives
2.2 The Euler Turbine Equation
2.2.1 Newton's Laws of Motion
2.2.2 The Euler Turbine Equation
2.2.3 First Insights from the Euler Turbine Equation
2.2.4 Velocity Triangles
2.2.5 Centrifugal Effect and Degree of Reaction
2.3 The First Law of Thermodynamics
2.3.1 Thermodynamic Concepts
2.3.2 Definition of a System
2.3.3 Thermodynamic Properties
2.3.4 Quasiequilibrium and Reversible Processes
2.3.5 Sign Convention
2.3.6 The First Law Applied to a Fluid Element
2.3.7 First Law Applied to a Control Volume
2.4 The Steady Flow Energy Equation
2.4.1 Application of the SFEE
2.4.2 Definition of Static and Total Properties
2.4.3 Total Conditions
2.4.4 Special Cases of the Steady Flow Energy Equation
2.5 The Second Law of Thermodynamics
2.5.1 Entropy
2.5.2 The Gibbs Equation
2.6 Energy Transfer in Radial Turbocompressors
2.6.1 Combination of the First and Second Laws
2.6.2 The Reversible Steady Flow Shaft Work
2.6.3 Use of the First and the Second Laws in Efficiency Definition
2.6.4 Rothalpy
2.7 Different Ideal Compression Processes
2.7.1 The Isentropic Process
2.7.2 Diagrams Describing Changes of State in Radial Compressors
2.7.3 The Polytropic Process
2.7.4 Special Features of Polytropic Processes
2.8 The Aerodynamic Work
2.8.1 Flow Work, Aerodynamic Work and Displacement Work
2.8.2 Effect of the Gas Properties on the Aerodynamic Work
2.8.3 The Effect of the Efficiency on the Aerodynamic Work
2.9 The Compressor Stage as the Sum of Its Components
3 Equations of State
3.1 Overview
3.1.1 Introduction
3.1.2 Learning Objectives
3.2 Equations of State for Perfect Fluids
3.2.1 Terminology
3.2.2 Perfect Gas
3.2.3 Idealised Incompressible Fluid
3.3 Equations of State for Real Gases
3.3.1 Real Gases with a Constant Compressibility Factor Z
3.3.2 Principle of Corresponding States
3.3.3 Van der Waals Equation
3.3.4 Cubic Equations of State
3.3.5 Virial Equations of State
3.3.6 Multiple Variable Equations of State
3.3.7 Real Gas Mixtures
3.3.8 Software Packages for Real Gases
3.4 The Aungier-Redlich-Kwong Cubic Equation of State
3.4.1 Aungier-Redlich-Kwong
3.4.2 Departure Functions for the Caloric Equation of State
3.4.3 Temperature Dependence of the Specific Heat
3.5 Isentropic and Polytropic Processes with Real Gases
3.5.1 Isentropic Process
3.5.2 Polytropic Process
3.6 The Aerodynamic Work with Real Gases
3.6.1 Schultz Method for the Polytropic Head
3.6.2 Mallen and Saville Method for the Polytropic Head
3.6.3 Huntington Method for the Polytropic Head
3.6.4 International Standards
4 Efficiency Definitions for Compressors
4.1 Overview
4.1.1 Introduction
4.1.2 Learning Objectives
4.2 Compressor Efficiency
4.2.1 Issues with the Definition of Efficiency
4.2.2 The Ideal Reversible Reference Process
4.2.3 The Minimum Work of Compression
4.3 Isentropic Efficiency
4.3.1 The Static-Static Isentropic Efficiency
4.3.2 The Total-Total Isentropic Efficiency
4.3.3 The Total-Static Isentropic Efficiency
4.3.4 Comparison of Total-Total and Total-Static Isentropic Efficiencies
4.3.5 Evolution of the Isentropic Efficiency in the Compressor
4.3.6 Divergence of Constant Pressure Lines
4.4 Polytropic Efficiency
4.4.1 The Polytropic Process
4.4.2 Preheat Effect
4.4.3 Polytropic Efficiency in Terms of Entropy Changes
4.4.4 Static-Static Polytropic Efficiency
4.4.5 Total-Total Polytropic Efficiency
4.4.6 Total-Static Polytropic Efficiency
4.4.7 Stage and Component Polytropic Efficiencies
4.5 The Impeller Wheel Efficiency
4.6 External Losses and Sideloads
4.7 Efficiency in Diabatic Processes
4.7.1 Diabatic Compression Processes
4.7.2 The Effect of Heat Transfer in Turbocharger Compressors
4.7.3 Diabatic Polytropic Efficiency
4.7.4 Isothermal Efficiency
4.8 Efficiency Definitions for Real Gases
5 Fluid Mechanics
5.1 Overview
5.1.1 Introduction
5.1.2 Learning Objectives
5.2 The Laws of Fluid Mechanics
5.2.1 Internal Flows in Compressors
5.2.2 Fundamentals of Fluid Motion
5.2.3 Continuity Equation
5.2.4 Momentum Equation
5.2.5 Moment of Momentum Equation
5.2.6 Navier-Stokes and Euler Equations
5.2.7 Average Values of Complex Flows
5.3 Pressure Gradients in Fluid Flows
5.3.1 Euler Equation of Motion along a Streamline
5.3.2 Euler Equation of Motion Normal to a Streamline
5.3.3 Swirling Flow in an Annulus
5.3.4 The Simple Radial Equilibrium Equation for an Axial Flow
5.3.5 Radial Equilibrium for the Inlet of a Radial Impeller
5.3.6 Pressure Gradients in the Circumferential Direction
5.4 Coriolis and Centrifugal Forces in Impellers
5.4.1 Coriolis and Centrifugal Forces
5.4.2 Effect of the Coriolis Force on Pressure Gradients
5.4.3 The Relative Eddy
5.4.4 Slip Velocity in Radial Compressors
5.5 Boundary Layers and End-Wall Flows
5.5.1 The Boundary Layers
5.5.2 Boundary Layer Thickness
5.5.3 Displacement Thickness and Boundary Layer Blockage
5.5.4 Mass-Flow Thickness, Momentum Thickness and Energy Thickness
5.5.5 Boundary Layer Structure in the Meridional Direction
5.5.6 Boundary Layer Transition
5.5.7 Boundary Layer Separation
5.5.8 Laminar Separation Bubble
5.5.9 Boundary Layer Structure Normal to the Blade Surface
5.5.10 Law of the Wall
5.5.11 End-Wall Boundary Layer
5.5.12 Turbulent Boundary Layers on Rough and Smooth Surfaces
5.5.13 Friction Factor for Fully Developed Pipe Flow with Roughness
5.6 Secondary Flows
5.6.1 Generation of Secondary Flows
5.6.2 Secondary Flows in Radial Compressors
5.7 Tip Clearance Flows
5.7.1 Structure of the Leakage Flow Pattern
5.7.2 Effect of Blade-to-Blade Loading
5.8 Jet-Wake Flow in Impellers
5.8.1 Early Descriptions of the Jet-Wake Flow
5.8.2 Breakthrough in Understanding through Laser Measurements
5.8.3 A Modern Synthesis
5.8.4 Conclusions
6 Gas Dynamics
6.1 Overview
6.1.1 Introduction
6.1.2 Learning Objectives
6.2 Gas Dynamics of Ideal Gases
6.2.1 Background
6.2.2 One-Dimensional Flow in Variable Area Ducts
6.2.3 The Continuity Equation in Compressible Flow
6.2.4 Corrected Flow per Unit Area
6.2.5 Choked Flow
6.2.6 Variation of Pressure in a Nozzle at Different Back Pressures
6.3 Shock and Expansion Waves
6.3.1 Normal Shock Waves
6.3.2 Oblique Shock Waves
6.3.3 Prandtl-Meyer Expansion Waves
6.4 Shock Structure in Transonic Compressors
6.4.1 Detached Curved Shock on a Leading Edge of a Blade Row
6.4.2 Unique Incidence
6.4.3 Variation of Shock Structure with Operating Point
6.5 Gas Dynamics of Real Gases
6.5.1 Background
6.5.2 Ratio of Specific Heats in a Real Gas
6.5.3 Isentropic Exponents
6.5.4 Speed of Sound in a Real Gas
6.5.5 Isentropic Flow Process in a Real Gas
6.5.6 Corrected Mass Flow per Unit Area
7 Aerodynamic Loading
7.1 Overview
7.1.1 Introduction
7.1.2 Learning Objectives
7.2 Isolated Aerofoils
7.2.1 Lift and Drag
7.2.2 Aerofoil Profile Shape
7.2.3 Leading and Trailing Edges
7.2.4 Incidence and Angle of Attack
7.2.5 Effect of Incidence
7.2.6 Effect of Mach Number
7.3 Profiles in Cascade
7.3.1 Loss Coefficient and Deviation
7.3.2 Profile Types
7.3.3 Alpha-Mach Diagram
7.3.4 The Effect of Solidity on Loading
7.3.5 The Compressor as a Diffusing Flow Channel
7.3.6 Cascade Loading Limits
7.4 Diffusers
7.4.1 Functionality and Applications
7.4.2 Performance Coefficients of Diffusers
7.4.3 Diffusers in Compressible Flow
7.4.4 Flow Regimes in Planar Diffusers
7.4.5 Reneau Diffuser Performance Charts
7.4.6 Step Diffusers
7.4.7 Diffusers in Series
7.5 Blade Loading Parameters
7.5.1 Limits to Operation of Blade Rows
7.5.2 Incidence
7.5.3 Stage Work Coefficient: ? = ?ht/
7.5.4 De Haller Criterion, DH = w2/w1
7.5.5 Mach Number Ratio in the Isentropic Core Flow: MR2 = Mrel1t/Mrel2j
7.5.6 Ideal Static Pressure Rise Coefficient: Cpid = (p2 - p1)/(?)
7.5.7 Maximum Static Pressure Recovery Coefficient of Koch (1981)
7.5.8 Equivalent Diffuser Opening Angle
7.5.9 Zweifel Tangential Force Coefficient
7.5.10 The Lieblein Diffusion Factor
7.5.11 Modified Diffusion Factor for Radial Impellers
7.5.12 Aungier Diffusion Factor and Blade Loading Parameter
7.5.13 Limits to Blade-to-Blade and Hub-to-Casing Loading
8 Similarity
8.1 Overview
8.1.1 Introduction
8.1.2 Learning Objectives
8.2 Similarity of Fluid Flows
8.2.1 Nondimensional Parameters
8.2.2 Newton or Euler Number
8.2.3 Strouhal Number
8.2.4 Reynolds Number
8.2.5 Mach Number
8.3 Geometric Similarity
8.3.1 Scaling
8.3.2 Surface Roughness
8.4 Fluid Dynamic Similarity
8.4.1 Flow Coefficients
8.4.2 Work Coefficients
8.4.3 Pressure Rise or Head Rise Coefficients
8.4.4 Reynolds Number
8.5 Thermodynamic Similarity
8.5.1 Tip-Speed Mach Number
8.5.2 Polytropic, Isentropic and Incompressible Analysis
8.5.3 Normalised Nondimensional Parameters
8.6 Applications of Similarity Parameters
8.6.1 Idealised Performance of Compressors
8.6.2 Similarity of Pressure Ratio
8.6.3 Compressor Performance Maps
8.6.4 Stage Characteristic Curves
8.6.5 Similarity in Performance Testing
8.6.6 Scaling and Power Density of Small Machines
8.6.7 Corrected Flow
8.7 Performance Corrections for Deviation from Similarity
8.7.1 Generalised Approach
8.7.2 Corrections for Geometrical Changes on Performance
8.7.3 Correction for the Effect of the Reynolds Number
8.7.4 Correction for the Effect of the Isentropic Exponent
9 Specific Speed
9.1 Overview
9.1.1 Introduction
9.1.2 Learning Objectives
9.2 Specific Speed and Specific Diameter
9.2.1 Background
9.2.2 Definitions
9.2.3 Other Definitions of These Parameters
9.2.4 Physical Significance of Specific Speed and Diameter
9.2.5 The Range of Parameter Variation
9.3 The Cordier Diagram
9.3.1 Background
9.3.2 Usefulness of the Cordier Diagram
9.3.3 The Effect of Compressibility
10 Losses and Performance
10.1 Overview
10.1.1 Introduction
10.1.2 Learning Objectives
10.2 The Definition of Losses
10.2.1 Estimation of Losses
10.2.2 Loss Coefficient Definitions for a Component
10.2.3 Component Losses Defined by Efficiency
10.3 Viscous Loss Mechanisms
10.3.1 A Modern Understanding
10.3.2 Profile and End-Wall Loss
10.3.3 Losses in Viscous Boundary Layers
10.3.4 Dissipation Coefficients in Radial Compressors
10.3.5 Reynolds-Dependent and Reynolds-Independent Losses
10.4 Other Aerodynamic Losses
10.4.1 Trailing-Edge Loss
10.4.2 Leading-Edge Loss
10.4.3 Mach Number Loss
10.4.4 Tip Leakage Loss
10.4.5 Leakage Loss over Shrouded Impellers
10.5 Loss Correlations in Centrifugal Stages
10.5.1 Correlations
10.6 Parasitic Losses
10.6.1 Entropy Losses or Additional Work
10.6.2 Disc Friction Loss
10.6.3 Leakage Loss over Shrouds
10.6.4 Recirculation Loss
10.6.5 The Effect of Parasitic Losses on Performance
10.7 Global Estimate for Aerodynamic Efficiency at the Design Point
10.7.1 Efficiency as a Function of the Duty and Size
10.7.2 Initial Sizing of the Compressor
10.8 Mean-Line Calculation of the Flow Conditions through the Stage
10.8.1 The Process of Compression
10.8.2 The Local Flow Conditions through the Stage
10.8.3 The Stage as the Sum of Two Components
11 Impeller Design
11.1 Overview
11.1.1 Introduction
11.1.2 Learning Objectives
11.2 Impeller Design
11.3 Impeller Types
11.3.1 Open Impellers
11.3.2 Shrouded Impellers
11.3.3 Impeller Tip Speeds
11.4 Flow Conditions at the Impeller Inlet
11.4.1 Optimisation of the Inlet Velocity Triangle
11.4.2 Variation of the Flow Angle with Radius
11.4.3 Inlet Relative Mach Number
11.4.4 Splitter Blades
11.5 Flow Conditions at the Impeller Throat
11.6 Flow Conditions at Impeller Outlet
11.6.1 Backsweep
11.6.2 The Influence of Backsweep on the Compressor Characteristic
11.6.3 Effect of Work Coefficient on the Steepness of the Characteristic
11.6.4 The Link between the Inlet and Outlet Velocity Triangles
11.6.5 The Outlet Width Ratio of the Impeller
11.6.6 The Influence of Various Parameters on the Outlet Velocity Triangle
11.6.7 Selection of Impeller Blade Number
11.6.8 One-Dimensional Impeller Preliminary Design in a Nutshell
11.6.9 Effect of the Impeller Outlet Velocity Triangle on the Diffuser
11.7 The Compressor Characteristic as Influenced by Losses and Work
11.7.1 The Influence of the Work Coefficient
11.7.2 Influence of the Losses
11.8 Guidelines to Detailed Impeller Design
11.8.1 Blade Loading Distribution in the Meridional Direction
11.8.2 The Wrap, Rake and Lean Angles
11.8.3 Effect of Lean
11.8.4 Control of Clearance Flows
11.8.5 Design of Transonic Inducers
11.8.6 Multipoint Design and Design Compromises
11.9 Three-Dimensional Features
11.9.1 Ruled Surface Impellers
11.9.2 Free-Form versus Ruled-Surface Impeller
11.9.3 Leading-Edge Sweep
11.10 Impeller Families
11.10.1 Industrial and Process Applications
11.11 Impeller Trim
11.11.1 Shroud Cutting
11.11.2 Hub Cutting
11.11.3 Parameterised Geometry Definition of Intermediate Stages
11.11.4 Determination of Contours for Hub or Shroud Cutting
11.11.5 Impeller Outlet or Inlet Blade Cutback
11.11.6 Overfile and Underfile
11.11.7 Other Issues Related to Stage Adaptation
11.12 Comparison with Rotors of Other Machine Types
11.12.1 Comparison with Axial Compressor Stages
11.12.2 Comparison with Mixed Flow Compressors
11.12.3 Comparison with Centrifugal Pump Impellers
11.12.4 Comparison with Radial Turbine Impellers
12 Diffuser Design
12.1 Overview
12.1.1 Introduction
12.1.2 Learning Objectives
12.2 Effect of the Flow at the Impeller Outlet
12.2.1 The Effect of the Impeller Velocity Triangle at the Design Point
12.2.2 The Effect of the Flow Nonuniformity at the Impeller Outlet
12.2.3 The Effect of the Diffuser Inlet Flow Angle
12.2.4 The Effect of the Meridional Flow Channel at Diffuser Inlet
12.2.5 The Effect of the Impeller Outlet Mach Number
12.3 Vaneless Diffusers
12.3.1 Ideal Pressure Recovery of an Incompressible Vaneless Diffuser
12.3.2 Surge or Rotating Stall in a Vaneless Diffuser
12.3.3 Effect of Mach Number and Losses in a Vaneless Diffuser
12.3.4 Choke in a Vaneless Diffuser
12.4 Vaned Diffusers
12.4.1 Comparison of Vaned and Vaneless Diffusers
12.4.2 Types of Vaned Diffusers
12.4.3 Design of Vaned Diffusers
12.5 Ideal Pressure Recovery in a Vaned Diffuser
12.6 Zones of Pressure Recovery in a Vaned Diffuser
12.6.1 Pressure Recovery
12.6.2 The Vaneless Space
12.6.3 The Semivaneless Space
12.6.4 The Diffuser Channel Downstream of the Throat
12.6.5 The Exit SemiVaneless Space
12.6.6 The Exit Vaneless Space
12.7 Vaneless Space and Semivaneless Space
12.8 Blockage at the Throat in Diffuser Channels
12.9 Matching the Diffuser Throat with the Impeller
12.10 Wedge Diffuser Channels
12.11 Cascade Diffuser Channels
12.11.1 Cascade Diffuser Performance
12.11.2 Cascade Diffuser Design Guidelines
12.11.3 Low-Solidity Cascade Diffuser Channels
12.12 Pipe Diffusers
12.13 Downstream Semivaneless Space and Vaneless Space
12.14 Special Cases
13 Casing Component Design
13.1 Overview
13.1.1 Introduction
13.1.2 Learning Objectives
13.2 Casing and Rotor Configurations
13.3 Inlet or Suction Nozzle
13.4 Intermediate Inlet Nozzles
13.4.1 Inlet Volutes in Multistage Compressors
13.4.2 Side-Stream Inlet
13.5 Inlet Guide Vanes
13.6 Outlet Volute
13.6.1 Design of the Scroll or Volute
13.6.2 Shape of the Volute Cross Sections
13.6.3 Design and Off-Design Performance
13.6.4 Volute Pressure Distortion
13.7 Return Channel System
13.7.1 Crossover Bend
13.7.2 The Return Channel Outlet Width
13.7.3 Schedule of Width Ratio
13.7.4 Return Channel Vanes
13.8 Deswirl Vanes
13.8.1 Axial Deswirl Vanes
13.8.2 Deswirl Vanes for Compressors with Integral Coolers
13.9 Axial Thrust
13.9.1 Balance of Forces
13.9.2 Balance Piston
13.9.3 Bulk Model for Swirling Flow in Cavities
13.9.4 Swirling Flow in the Rotor-Stator Cavities of a Shrouded Impeller
13.9.5 Swirl Brakes
14 Geometry Definition
14.1 Overview
14.1.1 Introduction
14.1.2 Learning Objectives
14.2 Coordinate Systems for Turbomachinery
14.3 Axisymmetric and Blade-to-Blade Stream Surfaces in Radial Compressors
14.4 Geometry Definition of Flow Channels
14.4.1 Geometry Definition
14.4.2 Bernstein Polynomials
14.4.3 Bezier Curves
14.4.4 Bezier Surfaces and Bezier Patches
14.4.5 Meridional Channel as a Series of Bezier Patches
14.5 Geometry Definition of Blades and Vanes
14.5.1 Ruled Surface
14.5.2 Camber Angle and Thickness Distribution
14.5.3 Circular Arc Blades
15 Throughflow Code for Radial Compressors
15.1 Overview
15.1.1 Introduction
15.1.2 Learning Objectives
15.2 A Preliminary Overview of the Throughflow Method
15.2.1 Quasi 3D Flow on S1 and S2 Stream Surfaces
15.2.2 The Streamline Curvature Throughflow Method
15.2.3 Design and Analysis Mode
15.2.4 Losses and Deviation
15.2.5 Blade Surface Velocities
15.2.6 Spanwise Mixing
15.3 Notation for the Blade Angles of the Velocity Gradient Equation
15.3.1 The Radial Lean Angle, γr
15.3.2 The Axial Lean Angle, γz
15.3.3 The Meridional Streamline Inclination Angle or Pitch Angle, ε
15.3.4 The Radius of Curvature, rc
15.3.5 The Meridional Blade Angle, β
15.3.6 The Lean Angle of the Blade in Direction of the q-o, γ
15.4 The Throughflow Equation of Motion
15.4.1 Derivation from the Momentum Equation
15.4.2 Body Force Term
15.4.3 The Dissipation Force Term
15.4.4 Classical Radial Equilibrium Equation
15.5 Streamline Curvature Velocity Gradient Equation
15.5.1 Different Forms of the Equation
15.5.2 Centrifugal Acceleration Due to Swirl
15.5.3 Centrifugal Acceleration Due to Curvature
15.5.4 Normal Acceleration along the q-o
15.5.5 Pressure Force Term
15.5.6 Body Force Term
15.5.7 Dissipation Force Term
15.5.8 Modification of the Meridional Velocity Gradient
15.5.9 Integration of the Velocity Gradient Equation
15.5.10 Update of Streamline Positions
15.6 The Iterative Scheme
15.6.1 Iteration to Mass Flow
15.6.2 Iteration to Pressure Ratio
15.7 Empirical Modifications
15.7.1 Deviation and Incidence
15.7.2 Losses
15.7.3 Blockage
15.8 Spanwise Mixing
15.8.1 Denton Mixing Model
15.8.2 Diffusion Equation Mixing
15.8.3 Trailing-Edge Mixing at the Outlet of a Compressor Radial Impeller
15.9 Pressure Gradient from Blade Force
15.9.1 Circumferential Pressure Gradient
15.9.2 Linear Blade-to-Blade Approximation
15.10 Choking
15.10.1 Choking in a Throughflow Code
15.10.2 Choking in Compressor Blade Rows
15.10.3 Choking of an Individual Stream-Tube in an Annulus
15.10.4 Choking at a Virtual Throat
15.10.5 The Choke Limit of the Meridional Velocity, cm
15.10.6 Choking in Q3D Isentropic Flow
15.10.7 Choking of an Individual Stream-Tube in an Unbladed Annulus
15.10.8 Choking of the Annulus as a Whole
15.10.9 Choking by Unique Incidence
15.10.10 Losses in a Choked Compressor Blade Row
15.10.11 Choking of a Stream-Tube at a Turbine Blade Row Outlet
15.10.12 Supersonic Deviation at Turbine Outlet
15.11 Use of Throughflow in Design
16 Computational Fluid Dynamics
16.1 Overview
16.1.1 Introduction
16.1.2 Learning Objectives
16.2 Historical Background to Turbomachinery CFD
16.2.1 The Revolution in Design Tools
16.2.2 Emergence of CFD for Compressor Design
16.2.3 Academic Codes
16.2.4 Codes from Government Organisations and Large Turbomachinery Companies
16.2.5 Difficulties in the Early Years
16.2.6 Commercial CFD Software
16.3 The Governing Equations
16.3.1 Navier-Stokes Equations
16.4 The Modern Numerical Method
16.4.1 The Finite Volume Method
16.4.2 Pressure-Based versus Density-Based
16.4.3 Computational Grid
16.4.4 Some Aspects of the Internal Methods of the Code
16.4.5 Boundary Conditions
16.5 Stage Calculations with Interface Planes
16.5.1 Steady-State Interface Planes
16.5.2 Unsteady Calculations
16.6 Turbulence Models
16.6.1 The Chief Outstanding Difficulty
16.6.2 Turbulent or Eddy Viscosity
16.6.3 Algebraic (or Zero-Equation) Models
16.6.4 One-Equation Models
16.6.5 Two-Equation Models
16.6.6 Other Models
16.7 Quality and Trust
16.7.1 Errors and Uncertainties
16.7.2 Round-Off Errors
16.7.3 Iteration or Convergence Error
16.7.4 Discretisation or Numerical Error
16.7.5 Model Uncertainty
16.7.6 Application Uncertainties
16.7.7 User Errors
16.7.8 Code Errors
16.8 Checklists for the Design Process with CFD
16.8.1 Design Rules
16.8.2 Assessing a Design with CFD
16.8.3 Interpretation of the CFD Data
17 Compressor Instability and Control
17.1 Overview
17.1.1 Introduction
17.1.2 Learning Objectives
17.2 Instabilities in Compressors
17.2.1 Instability
17.2.2 Differences between Axial and Radial Compressor Characteristics
17.2.3 Surge
17.2.4 Rotating Stall
17.2.5 Inlet Recirculation
17.2.6 Other Instability Mechanisms in Compressors
17.2.7 Conditions for Compression System Instability
17.2.8 The Greitzer B Parameter
17.2.9 Stability of Components
17.2.10 Rotating Stall Inception in Axial Compressors
17.2.11 Stall Inception in Radial Compressors
17.2.12 The Effect of Impeller and Diffuser Matching on Stability
17.3 Off-Design Operation of Radial Compressors
17.3.1 Types of System Requirements
17.3.2 Safety Margin Definitions
17.4 Typical Operating Range of Single-Stage Radial Turbocompressors
17.4.1 Field Experience
17.5 Stability Control and Enhancement
17.5.1 The Power Relative to That at Design
17.5.2 Variable Speed Control
17.5.3 Suction and Discharge Throttling
17.5.4 Adjustable Inlet Guide Vanes
17.5.5 Adjustable Diffuser Vanes
17.5.6 Bypass and Bleed Regulation
17.5.7 Impeller Recirculating Bleed
17.5.8 Variable Trim
17.5.9 Passive Control Systems with Slots and Chambers
17.5.10 Bleed or Injection within the Diffuser
17.5.11 Active Control Systems
18 Maps and Matching
18.1 Overview
18.1.1 Introduction
18.1.2 Learning Objectives
18.2 Methods of Map Prediction
18.2.1 Different Map Generation Methods
18.3 Map Prediction for Single Stages
18.3.1 Normalised Efficiency Characteristics
18.3.2 Variation of Efficiency with Flow Coefficient and Tip-Speed Mach Number
18.3.3 Equations for the Variation in Efficiency from Surge to Choke
18.3.4 Variation of the Peak Efficiency with Mach Number
18.3.5 Variation of the Flow Coefficient at Peak Efficiency with Mach Number
18.3.6 Location of the Surge Line and the Choke Line
18.3.7 Variation of the Work Coefficient with Flow and Mach Number
18.3.8 Validation of Maps Predicted with This Method
18.3.9 The Difference in the Characteristics of Vaned and Vaneless Stages
18.4 Apparent Efficiency Due to Heat Transfer Effects
18.5 Extrapolation of a Measured Map
18.5.1 Extrapolation to Low Pressure Ratio
18.5.2 Extrapolation to Negative Flow
18.6 Map Prediction for Multiple Stages
18.6.1 Basic Equations for Stage Stacking
18.6.2 Interpolation in the Stage Characteristics
18.6.3 Determination of Surge, Choke and Peak Efficiency Points
18.7 Matching of the Diffuser with the Impeller
18.7.1 The Effect of Impeller and Diffuser Matching on Choke
18.7.2 The Effect of Impeller and Diffuser Matching on Surge
18.8 Matching in Multistage Compressors
18.8.1 Idealised Example of Multistage Compressor Matching
18.9 Matching of the Compressor to a Turbine in a Gas Turbine
18.9.1 Efficiency of a Gas Turbine
18.9.2 Off-Design Performance
18.10 Matching Issues of a Compressor in a Turbocharger
18.10.1 Turbocharger Efficiency
18.10.2 The Compressor Boost Pressure Ratio
18.10.3 The Engine Operation in the Compressor Map
18.10.4 A Conventional Turbocharger with Fixed Turbine Geometry
18.10.5 A Turbocharger with a Wastegate (Turbine Bypass Valve)
18.10.6 A Turbocharger with a Variable Geometry Turbine
19 Structural Integrity
19.1 Overview
19.1.1 Introduction
19.1.2 Learning Objectives
19.2 Open or Closed Impellers
19.3 Impeller Manufacturing and Materials
19.3.1 Manufacturing of Open Impellers
19.3.2 Manufacturing of Shrouded Impellers
19.3.3 Materials
19.3.4 Heat Treatment
19.4 Introduction to Static Blade Loading of Impellers
19.4.1 Static Radial Force and Stresses Due to Rotation
19.4.2 Stresses in a Blade Due to Lean and Bending
19.4.3 Stresses in a Rotating Disc
19.4.4 Effect of Mechanical Forces on the Blade Shape
19.5 Introduction to Dynamic Blade Loading of Impellers
19.5.1 Source of Vibrations
19.5.2 A Brief Introduction to Mechanical Vibrations
19.5.3 Vibrations of a Blade
19.5.4 Vibrations of Circular Discs
19.5.5 Vibrations of Bladed-Disc Structures
19.5.6 Mistuning
19.5.7 Achieving Safe Designs Due to Vibrations
19.6 Computational Methods
19.7 Design Data for Mechanical Analysis
19.7.1 Design Cycles
19.7.2 Design Life
19.7.3 Design Speed
19.7.4 Design Temperature
19.7.5 Design Stresses
19.7.6 Yield Stress
19.7.7 Disc Burst
19.7.8 Creep
19.7.9 Fouling, Corrosion and Erosion
19.8 Assessment of Fatigue
19.8.1 Definitions
19.8.2 The Goodman Diagram
19.9 Vibrational Considerations
19.9.1 Mode Shapes of Rotationally Periodic Structures
19.9.2 Centrifugal Stress Stiffening
19.9.3 Avoidance of Dangerous Resonances in Centrifugal Stages
19.9.4 Campbell Diagram
19.9.5 Interference Diagrams
19.9.6 High-Order Resonances
19.9.7 Experimentally Determined Campbell Diagrams
19.10 Disc Design
19.10.1 Introduction
19.10.2 Impeller Hub Disc
19.10.3 Impeller Shroud
19.10.4 Thermal Stresses
19.11 Assembly Designs
19.11.1 Axial Tie Bolt
19.11.2 Shrink Fit
19.12 Rotordynamics
19.12.1 An Introduction to Compressor Rotordynamics
19.12.2 Rotor Instability
19.12.3 Unbalance Response Analysis
19.12.4 The Jeffcott Single Mass Rotor
19.13 Rotor Modelling
19.13.1 Theoretical Model Development
19.13.2 Rotor Stability
19.13.3 Rotordynamic Modelling
19.13.4 Rotordynamic Specifications for Compressors
20 Development and Testing
20.1 Overview
20.1.1 Introduction
20.1.2 Learning Objectives
20.2 Design and Development for Centrifugal Compressors
20.2.1 Design Process
20.2.2 Conceptual Design
20.2.3 Preliminary Design of Centrifugal Compressors
20.2.4 Geometry Specification
20.2.5 Throughflow and Blade-to-Blade Design
20.2.6 Preliminary Structural Analysis
20.2.7 3D CFD and FE Design
20.2.8 Optimisation and Inverse Methods
20.2.9 Prototype Testing
20.3 Compressor Testing
20.3.1 Types of Tests
20.3.2 Acceptance Tests for Industrial Compressors
20.3.3 Acceptance Tests for Turbochargers
20.3.4 Prototype Tests
20.4 Basic Research and Development Tests
20.4.1 Dedicated Research Rigs
20.4.2 Industrial Compressor Test Rigs
20.4.3 Rigs for Open Impellers
20.4.4 Determination of Impeller and Diffuser Efficiencies
20.4.5 Simplified Research Rigs
20.5 Instrumentation and Measurements
20.5.1 General
20.5.2 Measurement of Gas Mass-Flow Rate
20.5.3 Measurement of Torque
20.5.4 Measurement of Rotational Speed
20.5.5 Measurement of Steady Pressure
20.5.6 Rakes or Combs
20.5.7 Measurement of Flow Angle
20.5.8 Measurement of Temperature
20.5.9 Measurement of Unsteady Parameters
20.5.10 Tip Clearance Measurement Techniques
20.5.11 Typical Internal Instrumentation Assemblies
20.6 Determination of Stall and Surge
References
Index