Turbine aerodynamics : axial-flow and radial-inflow turbine design and analysis

404 Pages·2006·12.05 MB·English

by  Aungier

TURBINE
AERODYNAMICS
AXIAL-FLOW AND RADIAL-INFLOW TURBINE DESIGN
AND ANALYSIS
Ronald H. Aungier
NEW YORK ASME PRESS 2005
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To my wife Anne, with love
My companion and partner in everything worthwhile
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TABLE OF CONTENTS
PREFACE xiii
1. INTRODUCTION 1
1.1 Basic Turbine Confi gurations. . . . . . . . . . . . . . . . . . . . . . . .2
1.2 Radial-Infl ow and Axial-Flow Turbine Features. . . . . . . . .5
1.3 Velocity Diagrams for a Stage . . . . . . . . . . . . . . . . . . . . . . .7
1.4 Similitude and Performance Characteristics. . . . . . . . . . .10
1.5 Units and Conventions. . . . . . . . . . . . . . . . . . . . . . . . . . . .16
2. THERMODYNAMICS 17
2.1 First and Second Laws of Thermodynamics . . . . . . . . . . .18
2.2 Effi ciency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20
2.3 Fluid Equation-of-State Fundamentals . . . . . . . . . . . . . . .22
2.4 The Caloric Equation of State . . . . . . . . . . . . . . . . . . . . . .24
2.5 Entropy and the Speed of Sound . . . . . . . . . . . . . . . . . . .25
2.6 The Thermal Equation of State for Real Gases. . . . . . . . .26
2.7 Thermodynamic Properties of Real Gases . . . . . . . . . . . .31
2.8 Thermally and Calorically Perfect Gases. . . . . . . . . . . . . .32
2.9 The Pseudoperfect Gas Model. . . . . . . . . . . . . . . . . . . . . .33
2.10 Liquid-Phase Properties . . . . . . . . . . . . . . . . . . . . . . . . . . .34
2.11 Gas Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .36
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2.12 Component Performance Parameters. . . . . . . . . . . . . . . .36
2.13 A Computerized Equation of State Package. . . . . . . . . . .40
3. FLUID MECHANICS 43
3.1 Flow in a Rotating Coordinate System . . . . . . . . . . . . . . .45
3.2 Adiabatic Inviscid Compressible Flow. . . . . . . . . . . . . . . .48
3.3 Adiabatic Inviscid Compressible Flow Applications. . . . .50
3.4 Boundary Layer Analysis . . . . . . . . . . . . . . . . . . . . . . . . . .52
3.5 Two-Dimensional Boundary Layer Analysis. . . . . . . . . . .54
3.6 Axisymmetric Three-Dimensional Boundary
Layer Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .57
3.7 Vector Operators in Natural Coordinates. . . . . . . . . . . . .59
4. EMPIRICAL PERFORMANCE MODELS FOR
AXIAL-FLOW TURBINE BLADE ROWS 61
4.1 Blade Row Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . .63
4.2 Fluid Deviation Angle. . . . . . . . . . . . . . . . . . . . . . . . . . . . .65
4.3 Overview of the Loss System. . . . . . . . . . . . . . . . . . . . . . .68
4.4 Profi le Loss Coeffi cient. . . . . . . . . . . . . . . . . . . . . . . . . . . .69
4.5 Secondary Flow Loss Coeffi cient. . . . . . . . . . . . . . . . . . . .79
4.6 Trailing-Edge Loss Coeffi cient . . . . . . . . . . . . . . . . . . . . . .81
4.7 Shock Loss Coeffi cient . . . . . . . . . . . . . . . . . . . . . . . . . . . .81
4.8 Supersonic Expansion Loss Coeffi cient. . . . . . . . . . . . . . .82
4.9 Blade Clearance Loss Coeffi cient. . . . . . . . . . . . . . . . . . . .83
4.10 Lashing Wire Loss Coeffi cient . . . . . . . . . . . . . . . . . . . . . .83
4.11 Leakage Bypass Loss. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .83
4.12 Partial Admission Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . .87
4.13 Disk Friction Loss. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .88
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TABLE OF CONTENTS (cid:127) vii
4.14 Clearance Gap Windage Loss. . . . . . . . . . . . . . . . . . . . . . .90
4.15 Moisture Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .91
5. AERODYNAMIC PERFORMANCE ANALYSIS
OF AXIAL-FLOW TURBINES 93
5.1 The Meridional Coordinate System. . . . . . . . . . . . . . . . . .95
5.2 The Approximate Normal Equilibrium Model. . . . . . . . . .97
5.3 Inviscid Adiabatic Flow on A Quasi-Normal. . . . . . . . . .101
5.4 Linking Quasi-Normals. . . . . . . . . . . . . . . . . . . . . . . . . . .104
5.5 The Flow Profi les on a Quasi-Normal . . . . . . . . . . . . . . .106
5.6 Turbine Performance Analysis. . . . . . . . . . . . . . . . . . . . . 111
5.7 Typical Performance Analysis Results. . . . . . . . . . . . . . . 121
5.8 Diaphragm-Disk Rotor Leakage Flows . . . . . . . . . . . . . .125
5.9 Blade Forces and Rotor Thrust. . . . . . . . . . . . . . . . . . . . .127
5.10 Concluding Remarks. . . . . . . . . . . . . . . . . . . . . . . . . . . . .130
6. PRELIMINARY AERODYNAMIC DESIGN OF
AXIAL-FLOW TURBINE STAGES 133
6.1 Preliminary Aerodynamic Design Strategy. . . . . . . . . . .135
6.2 Velocity Triangles at the Design Radius . . . . . . . . . . . . .136
6.3 The Vortex Type and Swirl Velocity Distributions . . . . .138
6.4 Stage Effi ciency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .139
6.5 The Optimum Pitch-to-Chord Ratio. . . . . . . . . . . . . . . . .143
6.6 Initializing the Total Thermodynamic Conditions . . . . .145
6.7 The Stage Inlet Flow Profi les. . . . . . . . . . . . . . . . . . . . . .146
6.8 Sizing the Annulus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
6.9 Selecting the Blade Row Geometry. . . . . . . . . . . . . . . . .149
6.10 A Computerized Preliminary Design System . . . . . . . . .150
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6.11 Selection of the Dimensionless Performance
Parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .153
6.12 Selection of the Swirl Velocity Vortex Type. . . . . . . . . .157
6.13 Concluding Remarks. . . . . . . . . . . . . . . . . . . . . . . . . . . . .165
7. D ETAILED AIRFOIL DESIGN FOR
AXIAL-FLOW TURBINES 167
7.1 Defi nition of the Airfoil Geometry . . . . . . . . . . . . . . . . .168
7.2 The Airfoil Profi le Model . . . . . . . . . . . . . . . . . . . . . . . . . 171
7.3 Determining the Polynomial Coeffi cients. . . . . . . . . . . . 173
7.4 Leading and Trailing Edge Profi les . . . . . . . . . . . . . . . . . 175
7.5 The Passage Throat Calculation. . . . . . . . . . . . . . . . . . . . 176
7.6 Adjusting the Uncovered Turning . . . . . . . . . . . . . . . . . . 178
7.7 Design of a Complete Blade. . . . . . . . . . . . . . . . . . . . . . . 179
7.8 The Optional Defi ning Points. . . . . . . . . . . . . . . . . . . . . .180
7.9 Evaluation of the Airfoil Design . . . . . . . . . . . . . . . . . . .180
7.10 A Computerized Airfoil Design System. . . . . . . . . . . . . .182
8. INDUSTRIAL AXIAL-FLOW TURBINE
APPLICATION PROCEDURES 185
8.1 Stage Performance Rating Curves. . . . . . . . . . . . . . . . . .187
8.2 Reynolds Number Effects. . . . . . . . . . . . . . . . . . . . . . . . .191
8.3 Reaction Rating Curves. . . . . . . . . . . . . . . . . . . . . . . . . . .193
8.4 Application Procedures Based on Rating Curves. . . . . .194
9. A ERODYNAMIC PERFORMANCE ANALYSIS
OF RADIAL-INFLOW TURBINES 197
9.1 Radial-Infl ow Turbine Stage Geometry. . . . . . . . . . . . . .200
9.2 Boundary Layer Analysis . . . . . . . . . . . . . . . . . . . . . . . . .201
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9.3 The Boundary Layer Loss Coeffi cient . . . . . . . . . . . . . . .203
9.4 Inlet Volute Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . .205
9.5 Nozzle Row Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . .207
9.6 Rotor Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
9.7 Vaneless Annular Passage Analysis. . . . . . . . . . . . . . . . .218
9.8 Exhaust Diffuser Analysis. . . . . . . . . . . . . . . . . . . . . . . . . 219
9.9 Imposed Total Pressure Loss . . . . . . . . . . . . . . . . . . . . . .222
9.10 Inlet Station Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . .222
9.11 The Performance Analysis Strategy. . . . . . . . . . . . . . . . .222
9.12 Mass Balance Procedures. . . . . . . . . . . . . . . . . . . . . . . . .223
9.13 Subcritical Performance Analysis. . . . . . . . . . . . . . . . . . .224
9.14 Supercritical Performance Analysis. . . . . . . . . . . . . . . . .227
9.15 Typical Performance Analysis Results. . . . . . . . . . . . . . .229
10. P RELIMINARY AERODYNAMIC DESIGN OF
RADIAL-INFLOW TURBINE STAGES 233
10.1 Preliminary Aerodynamic Design Strategy. . . . . . . . . . .235
10.2 Rotor Tip Sizing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .238
10.3 Rotor Design Specifi cations. . . . . . . . . . . . . . . . . . . . . . .239
10.4 Rotor Sizing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .241
10.5 Evaluating the Rotor Design . . . . . . . . . . . . . . . . . . . . . .243
10.6 Rotor End-Wall Contours . . . . . . . . . . . . . . . . . . . . . . . . .244
10.7 Straight-Line Element Rotor Blade Camberlines . . . . . .247
10.8 Radial Element Rotor Blade Camberlines . . . . . . . . . . . .249
10.9 Nozzle Blade Geometry . . . . . . . . . . . . . . . . . . . . . . . . . .250
10.10 Nozzle Row Sizing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .254
10.11 Evaluating the Nozzle Design . . . . . . . . . . . . . . . . . . . . .255
10.12 Initial Estimates of the Nozzle Design
Specifi cations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .256
10.13 Volute Preliminary Design . . . . . . . . . . . . . . . . . . . . . . . .257
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10.14 Exhaust Diffuser Sizing . . . . . . . . . . . . . . . . . . . . . . . . . .259
10.15 A Typical Preliminary Design Example . . . . . . . . . . . . . .260
10.16 A Computerized Preliminary Design System . . . . . . . . .262
11. DETAILED AERODYNAMIC DESIGN OF
RADIAL-INFLOW TURBINE COMPONENTS 265
11.1 Nozzle Blade Detailed Design . . . . . . . . . . . . . . . . . . . . .267
11.2 A General Approach to Gaspath Detailed Design . . . . .270
11.3 Useful Curve Forms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .273
11.4 Constructing the Annulus and Quasi-Normals. . . . . . . .280
11.5 Constructing the Blade Camberline. . . . . . . . . . . . . . . . .282
11.6 Constructing the Blade Surfaces . . . . . . . . . . . . . . . . . . .283
11.7 The Blade Passage Throat Geometry . . . . . . . . . . . . . . .286
11.8 An Effective Gaspath Design System . . . . . . . . . . . . . . .287
11.9 Application to Impeller Design . . . . . . . . . . . . . . . . . . . .290
12. A ERODYNAMIC DESIGN AND PERFORMANCE
ANALYSIS OF EXHAUST DIFFUSERS 295
12.1 Basic Diffuser Technology . . . . . . . . . . . . . . . . . . . . . . . .297
12.2 An Approximate Performance Analysis . . . . . . . . . . . . .298
12.3 Sizing the Exhaust Diffuser . . . . . . . . . . . . . . . . . . . . . . .299
12.4 A Detailed Aerodynamic Performance Analysis. . . . . . .302
13. TWO-DIMENSIONAL ANALYSIS OF THE FLOW
IN THE BLADE-TO-BLADE PLANE 309
13.1 The Blade-to-Blade Flow Problem. . . . . . . . . . . . . . . . . . 311
13.2 Coordinate System and Velocity Components. . . . . . . . 314
13.3 The Potential Flow Solution Procedure. . . . . . . . . . . . . . 315
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