FUNDAMENTALS OF TURBOMACHINES.

Description

Preface Contents About the Author Symbols Subscripts Superscripts 1 Working Principles 1.1 Definition of a Turbomachine 1.2 Examples of Axial Turbomachines 1.2.1 Axial Hydraulic Turbine 1.2.2 Axial Pump 1.3 Mean Line Analysis 1.4 Basic Laws for Stationary Duct Parts 1.4.1 Conservation of Mass 1.4.2 Conservation of Momentum 1.4.3 Conservation of Energy 1.4.4 Forms of Energy: Mechanical Energy and Head 1.4.5 Energy Dissipation: Head Loss 1.5 Basic Laws for Rotating Duct Parts 1.5.1 Work and Energy Equations in a Rotating Frame with Constant Angular Velocity 1.5.2 Moment of Momentum in the Absolute Frame: Rotor Work 1.5.3 Rotor Work in the Mean Line Representation of the Flow 1.5.4 Moment of Momentum in the Relative Frame: Forces Intervening in the Rotor Work 1.5.5 Energy Component Changes Caused by the Rotor Work 1.6 Energy Analysis of Turbomachines 1.6.1 Mechanical Efficiency and Internal Efficiency 1.6.2 Energy Analysis of an Axial Hydraulic Turbine 1.6.3 Energy Analysis of an Axial Pump 1.7 Examples of Radial Turbomachines 1.8 Performance Characteristics 1.9 Exercises 2 Basic Components 2.1 Aerofoils 2.1.1 Force Generation 2.1.2 Performance Parameters 2.1.3 Pressure Distribution 2.1.4 Boundary Layer Separation 2.1.5 Loss Mechanism Associated to Friction: Energy Dissipation 2.1.6 Profile Shapes 2.1.7 Blade Rows with Low Solidity 2.2 Linear Cascades 2.2.1 Relation with the Real Machine 2.2.2 Cascade Geometry 2.2.3 Flow in Lossless Cascades: Force Components 2.2.4 Significance of Circulation 2.2.5 Flow in Lossless Cascades: Work 2.2.6 Flow in Cascades with Loss: Force Components 2.2.7 Flow in Cascades with Loss: Energy Dissipation and Work by Drag Force 2.2.8 The Zweifel Tangential Force Coefficient 2.2.9 The Lieblein Diffusion Factor 2.2.10 Performance Parameters of Axial Cascades 2.3 Channels 2.3.1 Straight Channels 2.3.2 Bends and Curved Channels 2.4 Diffusers 2.4.1 Dump Diffusers 2.4.2 Inlet Flow Distortion 2.4.3 Flow Separation 2.4.4 Flow Improvement 2.4.5 Representation of Diffuser Performance 2.4.6 Deceleration in a Bend 2.5 Exercises References 3 Fans 3.1 Fan Applications and Fan Types 3.1.1 Fan Applications 3.1.2 Large Radial Fans 3.1.3 Small Radial Fans 3.1.4 Large Axial Fans 3.1.5 Small Axial Fans 3.1.6 Cross-Flow Fans 3.2 Idealised Mean Line Analysis of a Radial Fan 3.2.1 Idealised Flow Concept: Infinite Number of Blades 3.2.2 Degree of Reaction 3.2.3 Relation Between Rotor Blade Shape and Performance Parameters 3.2.4 Performance Characteristics with Idealised Flow 3.3 Lossless Two-Dimensional Flow Through a Radial Rotor with a Finite Number of Blades 3.3.1 Relative Vortex in Blade Channels 3.3.2 Velocity Difference Across a Rotating Channel 3.3.3 Pressure Difference Across a Rotating Channel 3.3.4 Slip: Reduction of Rotor Work 3.3.5 Number of Blades and Solidity: Pfleiderer Moment Coefficient 3.3.6 Number of Blades: Examples 3.4 Internal Losses with Radial Fans 3.4.1 Turning Loss in the Rotor Eye 3.4.2 Incidence Loss at the Rotor Entry 3.4.3 Displacement by Blade Thickness 3.4.4 Rotor Friction Loss and Rotor Diffusion Loss 3.4.5 Dump Diffusion Loss at the Rotor Exit 3.4.6 Deceleration Loss in the Rotor Eye 3.4.7 Flow Separation at Rotor Entry and Rotor Exit 3.4.8 Incidence Loss at the Volute Entry 3.4.9 Friction Loss Within the Volute 3.4.10 Applicability of the Loss Models 3.4.11 Optimisation of the Rotor Entry of a Centrifugal Fan 3.4.12 Characteristics Taking Losses into Account 3.5 Overall Performance Evaluation 3.5.1 Mechanical Loss 3.5.2 Leakage Loss 3.5.3 Overall Efficiency with Power Receiving Machines 3.5.4 Overall Efficiency with Power Delivering Machines 3.5.5 Detailed Efficiency Analyses 3.5.6 Total-to-Total and Total-to-Static Efficiencies 3.6 Rotor Shape Choices with Radial Fans 3.7 Axial and Mixed-Flow Fans 3.7.1 Degree of Reaction with Axial Fans 3.7.2 Free-Vortex and Non-free-vortex Types 3.7.3 Axial Fan Characteristics 3.7.4 Mixed-Flow Fans 3.8 Flow Rate Control of Fans 3.9 Exercises References 4 Compressible Fluids 4.1 Basic Laws 4.2 Compressibility and Velocity of Sound 4.3 Compressibility Effect on the Velocity–Pressure Relation 4.4 Shape of a Nozzle 4.5 Expansion and Compression 4.6 Nozzle with Initial Velocity 4.7 Nozzle with Losses: Infinitesimal Efficiency 4.8 Isentropic and Polytropic Efficiencies 4.9 Effect of Heat Transfer 4.10 Exercises References 5 Performance Measurement 5.1 Pressure Measurement 5.1.1 Metal Manometer 5.1.2 Pressure Transducer 5.1.3 Digital Manometer 5.1.4 Calibration of Pressure Meters 5.2 Temperature Measurement 5.2.1 Glass Thermometer 5.2.2 Temperature Transducer 5.2.3 Digital Thermometer 5.3 Flow Rate Measurement 5.3.1 Reservoir 5.3.2 Flow Over a Weir 5.3.3 Pressure Drop Devices 5.3.4 Industrial Flow Rate Meters 5.3.5 Positioning of Flow Rate Meters in Ducts 5.4 Torque Measurement 5.4.1 Swinging Suspended Motor or Brake 5.4.2 Calibrated Motor 5.4.3 Torque Transducer 5.5 Rotational Speed Measurement 5.5.1 Optical Tachometer 5.5.2 Electrical Tachometer 5.5.3 Rotational Speed Transducer 5.6 Laboratory Test of a Pelton Turbine 5.6.1 Test Rig 5.6.2 Measurements 5.6.3 Measurement Procedure 5.6.4 Calculations 5.6.5 Measurement Example 5.7 Laboratory Test of a Centrifugal Fan 5.7.1 Test Rig 5.7.2 Measurements 5.7.3 Measurement Procedure 5.7.4 Calculations 5.7.5 Measurement Example 5.8 Laboratory Test of a Centrifugal Pump 5.8.1 Test Rig 5.8.2 Measurements 5.8.3 Measurement Procedure 5.8.4 Calculations 5.8.5 Measurement Example 6 Steam Turbines 6.1 Applications of Steam Turbines 6.2 Working Principles of Steam Turbines 6.3 The Steam Cycle 6.4 The Single Impulse Stage or Laval Stage 6.4.1 Velocity Triangles 6.4.2 Work and Energy Relations 6.4.3 Stage Efficiency Definitions 6.4.4 Blade Profile Shape 6.4.5 Loss Representation 6.4.6 Optimisation of Total-to-Static Efficiency 6.5 The Pressure-Compounded Impulse Turbine or Rateau Turbine 6.5.1 Principle 6.5.2 Efficiency 6.6 The Velocity-Compounded Impulse Turbine or Curtis Turbine 6.7 The Reaction Turbine 6.7.1 Degree of Reaction 6.7.2 Efficiency 6.7.3 Axial Inflow and Outflow 6.8 Steam Turbine Construction Forms 6.8.1 Large Steam Turbines for Coal-Fired Power Stations 6.8.2 Large Steam Turbines for Nuclear Power Stations 6.8.3 Mid-Size Steam Turbines 6.8.4 Industrial Steam Turbines 6.9 Blade Shaping 6.9.1 HP and IP Blades 6.9.2 LP Blades 6.10 Exercises References 7 Dynamic Similitude 7.1 Principles of Dynamic Similitude 7.1.1 Definition of Dynamic Similitude 7.1.2 Dimensionless Parameter Groups 7.1.3 Similitude Conditions 7.1.4 Purpose of Similitude Analysis 7.1.5 Dimensional Analysis 7.1.6 Independent and Dependent Parameter Groups 7.1.7 Dimensionless Parameter Groups for Turbomachines with a Constant-Density Fluid 7.1.8 Strong and Weak Similitude Conditions 7.2 Characteristic Numbers of Turbomachines 7.2.1 Definition of a Characteristic Number 7.2.2 Specific Speed and Specific Diameter 7.2.3 Relation Between Characteristic Numbers and Machine Shape 7.2.4 Design Diagrams 7.2.5 Shape of Characteristic Curves 7.2.6 Power Specific Speed 7.3 Application Example of Similitude: Variable Rotational Speed with a Pump 7.4 Imperfect Similitude 7.4.1 Effect of Reynolds Number with the Same Fluid 7.4.2 Effect of Relative Roughness 7.4.3 Effect of Viscosity 7.4.4 Rotor Diameter Reduction: Impeller Trimming 7.4.5 Reduced Scale Models 7.5 Series and Parallel Operation 7.5.1 Parallel Operation of Fans 7.5.2 Parallel Operation of Pumps 7.5.3 Series Operation of Fans 7.6 Turbomachine Design Example: Centrifugal Fan 7.7 Exercises References 8 Pumps 8.1 Cavitation 8.1.1 Cavitation Phenomenon and Cavitation Consequences 8.1.2 Types of Cavitation 8.1.3 Blade Pressure Distribution in Presence of Cavitation 8.1.4 Cavitation Assessment: Required Net Positive Suction Height 8.1.5 Optimisation of a Rotor Entry 8.1.6 Net Positive Suction Head of the Installation 8.1.7 Avoidance of Cavitation 8.1.8 Increasing the Acceptable Suction Height 8.2 Priming of Pumps: Self-priming Types 8.2.1 Side Channel Pump 8.2.2 Peripheral Pump (Regenerative Pump) 8.2.3 Self-priming Centrifugal Pump 8.2.4 Jet Pump 8.3 Unstable Operation 8.4 Component Shaping 8.4.1 Simply and Doubly-Curved Blades in Radial Rotors 8.4.2 Blade Shapes of Mixed-Flow and Axial Pumps 8.4.3 Pump Inlet 8.4.4 Pump Outlet 8.4.5 Vaneless Diffuser Rings 8.4.6 Vaned Diffuser Rings 8.4.7 Volute (Spiral Case) 8.4.8 Return Channels 8.5 Internal Parallel or Series Arrangements 8.5.1 Reasons for Internal Parallel or Series Arrangements 8.5.2 Internal Parallel Arrangement 8.5.3 Internal Series Arrangement: Multistage Pumps 8.6 Constructional Aspects 8.6.1 Shaft Sealing 8.6.2 Bearings 8.6.3 Axial Force Balancing with Single-Stage Pumps 8.6.4 Axial Force Balancing with Multistage Pumps 8.6.5 Wear Rings 8.7 Pump Examples 8.7.1 Norm Pumps or Standard Pumps 8.7.2 Sealless Pumps: Circulation Pumps, Chemical Pumps 8.7.3 High-Pressure Pumps 8.7.4 Borehole Pumps 8.7.5 Vertical Submerged Pumps 8.7.6 Slurry Pumps 8.7.7 Pumping of Solid Materials 8.7.8 Partial Emission Pumps 8.7.9 Pumps for Viscous Fluids 8.7.10 Vertical Propeller Pumps 8.8 Determination of Main Dimensions and Performance Prediction 8.8.1 Main Dimensions 8.8.2 Performance Evaluation 8.9 Exercises References 9 Hydraulic Turbines 9.1 Hydraulic Energy 9.2 Hydraulic Turbine Types 9.2.1 Large Turbines (> 10 MW) 9.2.2 Small Turbines (< 10 MW) 9.3 Pelton Turbines: Impulse Turbines 9.3.1 Performance Characteristics 9.3.2 Specific Speed 9.3.3 Determination of the Main Dimensions 9.3.4 Flow Rate Control and Over-Speed Protection 9.4 Francis and Kaplan Turbines: Reaction Turbines 9.4.1 Shape of the Velocity Triangles: Kinematic Parameters 9.4.2 Optimisation of the Velocity Triangles 9.4.3 Degree of Reaction and Speed Ratio 9.4.4 Examples 9.4.5 Velocity Triangles with Varying Degree of Reaction 9.4.6 Specific Speed and Meridional Shape of Francis Turbines 9.4.7 Efficiency Related to Specific Speed 9.4.8 Flow Rate Control with Reaction Turbines 9.5 Bulb and Tube Turbines 9.6 Reversible Pump-Turbines 9.7 Pumps Functioning as Turbine 9.8 Cavitation in Hydraulic Turbines 9.9 Exercises References 10 Wind Turbines 10.1 Wind Energy 10.2 Types of Wind Energy Conversion Systems 10.2.1 Drag Machines 10.2.2 High-Speed Horizontal-Axis Wind Turbines 10.2.3 Large Horizontal-Axis Wind Turbines for Electricity Generation 10.2.4 Mid-Size and Small Horizontal-Axis Wind Turbines for Electricity Generation 10.2.5 Low-Speed Horizontal-Axis Wind Turbines 10.2.6 Vertical-Axis Wind Turbines 10.3 Wind Turbine Performance Analysis 10.3.1 Single-Streamtube Momentum Analysis 10.3.2 Multiple-Streamtube Momentum Analysis 10.3.3 Blade-Element Momentum Analysis 10.3.4 Optimisation of a Rotor Blade 10.4 Adaptation to a Wind Regime 10.5 Exercises References 11 Power Gas Turbines 11.1 General Concept and Components 11.1.1 Definition of a Gas Turbine 11.1.2 Comparison with Other Thermal Engines 11.1.3 Example of a Power Gas Turbine 11.1.4 Compressor Part 11.1.5 Turbine Part 11.1.6 Combustion Chamber 11.2 Thermodynamic Modelling 11.2.1 Isentropic Efficiency with Adiabatic Compression or Expansion 11.2.2 Reheat Effect 11.2.3 Infinitesimal Efficiency; Polytropic Efficiency 11.2.4 Thermodynamic Properties of Air and Combustion Gas 11.2.5 Heat Capacity Representation 11.2.6 Cooled Expansion 11.2.7 Compression with Extraction 11.3 Performance of Simple-Cycle Power Gas Turbines 11.3.1 Idealised Simple Cycle 11.3.2 Simple Cycle with Component Efficiencies and Different Heat Capacities of Air and Combustion Gas 11.3.3 Simple Cycle with Component Efficiencies, Cooling and Variable Gas Properties 11.4 Performance of Power Gas Turbines with Enhanced Cycles 11.4.1 Compression with Intercooling 11.4.2 Expansion with Reheat 11.4.3 Recuperator 11.4.4 Combined Gas and Steam Cycles 11.4.5 Steam Injection 11.5 Classification of Power Gas Turbines 11.6 Exercises References 12 Thrust Gas Turbines 12.1 Thrust Generation 12.1.1 Propeller 12.1.2 Reactor or Jet Engine 12.1.3 Rocket 12.2 Overview of Aircraft Gas Turbine Engines 12.2.1 Turbojet 12.2.2 Turboprop and Turbo-Shaft 12.2.3 Bypass Turbojet 12.2.4 Turbofan 12.2.5 Prop-Fan and Unducted Fan 12.2.6 Geared Turbofan 12.3 Performance Parameters of Aircraft Propulsion Systems 12.3.1 Specific Thrust 12.3.2 Dynamic Power 12.3.3 Gas Power and Dynamic Efficiency 12.3.4 Thermal Power, Thermodynamic and Thermal Efficiencies 12.3.5 Propulsive Power and Propulsive Efficiency 12.3.6 Overall Efficiency 12.3.7 Generalisation for Double-Flow Engines 12.3.8 Specific Fuel Consumption 12.4 Performance of the Gas Generator and the Single-Jet Engine 12.4.1 Analysis with Loss-Free Components 12.4.2 Analysis with Component Losses 12.5 Performance of Double-Flow Engines 12.5.1 Unmixed Flows (Double-Jet Engine: Turbofan, Turboprop) 12.5.2 Mixed Flows (Bypass Engine) 12.5.3 Intercooling and Recuperation 12.6 Technological Aspects of the Turbofan Engine 12.6.1 Discs and Shafts 12.6.2 Vanes and Blades 12.6.3 Combustion Chamber 12.6.4 Mixer, Nozzles and Thrust Reverser 12.7 Exercises References 13 Axial Compressors 13.1 Mean Line Analysis 13.1.1 Velocity Triangles 13.1.2 Fundamental Equations 13.1.3 Kinematic Parameters 13.1.4 Total-To-Total Efficiency and Loss Representation 13.1.5 Average Density 13.1.6 Force Components 13.1.7 Diffusion Factor and Loss Correlations 13.1.8 Secondary Flow: Principle 13.1.9 Radial Variation of Flow: Principle 13.1.10 Optimisation of a Stage 13.1.11 Blade Shape 13.1.12 Attainable Pressure Ratio 13.2 Secondary Flow 13.2.1 Definition of Secondary Flow 13.2.2 Passage Vortex and Trailing Vortices 13.2.3 Corner Vortices 13.2.4 Horseshoe Vortex 13.2.5 Leakage Vortex and Scraping Vortex 13.2.6 Loss Assessment 13.3 Radial Flow Variation 13.3.1 S1–S2 Decomposition 13.3.2 Radial Equilibrium 13.3.3 Free-Vortex Blades 13.3.4 Forcing of the Vortex Distribution 13.3.5 Effect of End Wall Boundary Layers 13.3.6 Three-Dimensional Blade Design 13.4 Compressor Blade Profiles 13.4.1 Subsonic and Supercritical Cascades 13.4.2 Transonic Cascades 13.4.3 Supersonic Cascades and Transonic Cascades with High Inlet Mach Number 13.5 Performance Characteristics and Operating Range 13.5.1 General Shape of a Characteristic Curve 13.5.2 Rotating Stall 13.5.3 Choking 13.5.4 Surge 13.5.5 Operating Range 13.6 Exercises References 14 Radial Compressors 14.1 Construction Forms and Applications 14.1.1 Rotor Types 14.1.2 General Shape of a Radial Compressor 14.1.3 Comparison Between Radial and Axial Compressors 14.1.4 Examples of Radial Compressors 14.2 Kinematic Parameters 14.3 Pressure Ratio 14.4 Rotor Shape 14.4.1 Number of Blades 14.4.2 Rotor Entry and Exit 14.4.3 Secondary Flow in the Rotor 14.5 Diffusers 14.5.1 Mixing Zone 14.5.2 Vaneless Diffusers 14.5.3 Vaned Diffusers 14.6 Three-Dimensional Blade Shaping 14.7 Performance Characteristics 14.7.1 Flow Instability 14.7.2 Choking 14.7.3 Operating Characteristics and Operating Range 14.8 Exercises References 15 Axial and Radial Turbines for Gases 15.1 Axial Turbines 15.1.1 Kinematic Parameters 15.1.2 Radial Variation of Flow Parameters 15.1.3 Secondary Flow 15.1.4 Blade Profiles 15.1.5 Three-Dimensional Blade Shaping 15.1.6 Vane and Blade Clocking 15.1.7 Operating Characteristic of Axial Turbines 15.2 Radial Turbines 15.2.1 Shape and Functioning 15.2.2 Kinematic Parameters 15.2.3 Operating Characteristic of Radial Turbines 15.2.4 Radial Turbine Applications 15.3 Dimensional Analysis with Compressible Fluids 15.3.1 Independent and Dependent Π-groups 15.3.2 Dimensionless Compressor and Turbine Characteristics 15.3.3 Corrected Quantities 15.4 Exercises References Index