TURBINE AERODYNAMICS AXIAL-FLOW AND RADIAL-INFLOW TURBINE DESIGN AND ANALYSIS Ronald H. Aungier NEW YORK ASME PRESS 2005 Downloaded From: http://ebooks.asmedigitalcollection.asme.org/ on 01/06/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded From: http://ebooks.asmedigitalcollection.asme.org/ on 01/06/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use To my wife Anne, with love My companion and partner in everything worthwhile Downloaded From: http://ebooks.asmedigitalcollection.asme.org/ on 01/06/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded From: http://ebooks.asmedigitalcollection.asme.org/ on 01/06/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use 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 Downloaded From: http://ebooks.asmedigitalcollection.asme.org/ on 01/06/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use vi (cid:127) TABLE OF CONTENTS 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 Downloaded From: http://ebooks.asmedigitalcollection.asme.org/ on 01/06/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use 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 Downloaded From: http://ebooks.asmedigitalcollection.asme.org/ on 01/06/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use viii (cid:127) TABLE OF CONTENTS 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 Downloaded From: http://ebooks.asmedigitalcollection.asme.org/ on 01/06/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use TABLE OF CONTENTS (cid:127) ix 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 Downloaded From: http://ebooks.asmedigitalcollection.asme.org/ on 01/06/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use x (cid:127) TABLE OF CONTENTS 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 Downloaded From: http://ebooks.asmedigitalcollection.asme.org/ on 01/06/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use