INCOMPRESSIBLE FLOW TURBOMACHINES Design, Selection, Applications, George F. Round Professor Emeritus McMaster University Hamilton, Ontario Canada ELSEVIER BUTTERWORTH HEINEMANN Amsterdam Boston Heidelberg London New York Oxford Paris San Diego San Francisco Singapore Sydney Tokyo
CONTENTS Preface Nomenclature Dimensions of Fluid Mechanics Quantities Units Fundamental Definitions xiv xvi xviii xix xx Historical Background and Present State of Development, 1 1.1 Greek and Roman Machines 1 1.2 The Middle Ages 4 1.3 The Renaissance 4 1.4 The Post Renaissance 6 1.5 The Nineteenth Century to the Present 7 1.6 General Classification of Rotodynamic Turbines and Pumps 10 1.7 Theoretical Limitations 10 1.8 References 11 Theory of Turbomachines, 12 2.1 Equations Governing the Behavior of Turbomachines 12 2.2 Continuity Equation 12 2.3 Linear Momentum Theorem 13 2.4 Angular Momentum Equation 14 2.5 Euler Turbine Equation 15 2.6 Bernoulli Equation 17 2.6.1 Example: Use of Bernoulli Equation for Radial Flow 17 2.7 The Energy Equation 18 vii
VIII Contents 2.8 Similarity 19 2.9 Dimensional Analysis 20 2.10 Restrictions on Similarity Applications 21 2.11 Dimensionless Groups and Specific Speed 22 2.12 Scaling Discrepancies 22 2.13 Graphical Correlations for Specific Speed 24 2.14 General Geometry of Rotational, Radial, and Axial Flows 26 2.15 Circulation, Free Vortex Flow, and the Kutta-Joukowski Theorem 27 2.16 Forces Acting on an Axial-flow Turbine and Axial-flow Pump Blade... 31 2.17 Stream Function and Streamlines 37 2.18 Velocity Potential 38 2.19 Superposition of Streamlines 39 2.20 Axisymmetric Flows and Stokes's Stream Function 41 2.21 Meridional Streamlines and Velocities 43 2.22 Effects of Friction on Flows through Turbomachines 44 2.23 Solved Problems 45 2.24 References 54 3 Turbines, 55 3.1 Classification of Turbines 55 3.2 General Operating Conditions 55 3.3 Impulse Turbines-Pelton Wheels 56 3.3.1 Speed Factor, <t 57 3.3.2 Specific Speed of Pelton Wheels 59 3.3.3 Nozzles 60 3.3.4 Jet Force on Runner 60 3.3.5 Arrangement of Nozzles and Size of Jets 61 3.3.6 Jet Velocity and Diameter 63 3.3.7 Runner 64 3.3.8 Turgo Wheels 65 3.4 Radial-Flow Turbines Francis Turbines 67 3.4.1 Choice of Turbine Speed 70 3.4.2 Effect of Gate Opening 70 3.5 Axial-flow Turbines Propeller and Kaplan Turbines 71 3.5.1 Combinator.73 3.5.2 Effects of Rotor and Guide-vane Angle 75 3.5.3 Selection of Speed and Runner Dimensions 75 3.6 Other Turbines 79 3.6.1 Pump Turbines, 79 3.6.2 Deriaz Turbine 80 3.6.3 Bulb Turbine 81
Contents IX 3.6.4 Banki Turbine 82 3.6.5 Michell Turbine 82 3.7 Control and Governing of Turbines 84 3.7.1 Function of a Governor 84 3.7.2 Equations for Load Changes 84 3.7.3 Governors 86 3.7.4 Relief Valves 86 3.8 Solved Problems 87 3.9 References 102 4 Pumps, 103 4.1 Introduction 103 4.1.1 Theoretical Characteristics of Centrifugal Pumps 103 4.2 Classification of Rotary Pumps 105 4.3 Radial-flow Pumps 108 4.3.1 Geometry 108 4.3.2 Power 110 4.3.3 Theoretical Head 114 4.3.4 Energy Losses 114 4.3.5 Head Losses 114 4.3.6 Leakage Losses 115 4.3.7 Disk Friction Loss 117 4.3.8 Mechanical Losses 117 4.3.9 Specific Speed and Impeller Geometry 119 4.3.10 Modeling of Flow through an Impeller 119 4.3.11 Axisymmetric Flow 121 4.3.12 Net Positive Suction Head (NPSH) 122 4.3.13 Slip Factors 122 4.3.14 Effect of Blade Number, Outlet Blade Angle, and Circulation in Blade Passages 126 4.3.15 Choice of Blade Number and Blade Overlap 129 4.3.16 Energy Recovery 129 4.3.17 Examples of Radial-flow Pumps 130 4.3.18 Installation of a Typical Centrifugal Pump 130 4.3.19 Special-purpose Radial-flow Pumps 132 4.4 Mixed-flow Pumps Diagonal Impeller Pumps 133 4.5 Axial and Semiaxial Pumps 134 4.5.1 Unbounded Axial Impellers or Propellers 136 4.6 Pump Characteristics of Centrifugal Pumps 143 4.6.1 Single Centrifugal Pumps Radial- and Mixed-flow Impellers.. 143 4.6.2 Effect of Fluid Properties 145
Contents 4.7 Series and Parallel Connections 145 4.7.1 Multistage Centrifugal Pumps 149 4.8 Displacement Rotary Pumps 149 4.8.1 Vane Pumps 149 4.8.2 Peristaltic Pump 150 4.8.3 Lobe Pumps 151 4.8.4 RVP Pump 151 4.8.5 Water Ring Pumps 152 4.9 Flow Control 153 4.9.1 Throttling of the Flow at Inlet or Outlet 155 4.9.2 Pump Disconnection 157 4.9.3 Regulated Flow Bypass 158 4.9.4 Speed Regulation 159 4.9.5 Impeller Blade Adjustment 160 4.9.6 Inlet Guide-vane Adjustment 160 4.9.7 Air Locking 161 4.10 Automatic Priming 161 4.11 Fluid Couplings 165 4.12 Solved Problems 170 4.13 References 187 Some Aspects of Design, 188 5.1 General Remarks 188 5.2 Application to Flow 188 5.2.1 Axial-flow Design 188 5.3 Axial and Radial Thrusts in Pumps and Turbines 189 5.3.1 Axial 189 5.3.2 Closed Single-entry Centrifugal Impellers 189 5.3.3 Multistage Balancing of Single-entry Stages 191 5.3.4 Radial 191 5.4 Critical Speeds 192 5.4.1 Lateral Critical Speed of an Unbalanced Simple Rotor 193 5.4.2 Multiple Disks 195 5.4.3 Use of Singularity Functions 198 5.4.4 Solution by Numerical Integration 199 5.4.5 Torsional Critical Speed r 200 5.5 Seals 201 5.6 Cooling Seals 203 5.7 Glands 204 5.8 Solved Problems 204 5.9 References 208
Contents XI 6 Design of Impellers and Runners of Single and Double Curvature, 210 6.1 General Remarks on Design of Runners and Impellers 210 6.2 Single-Curvature Design 210 6.2.1 Meridional Velocities, Inlet Diameter, and Inlet Angle 210 6.2.2 Tip Impeller Velocity, U2, and Outlet Diameter, d2 211 6.2.3 Inlet Areas and Impeller Widths 212 6.2.4 Dimension Calculations, Continuity Adjustments 213 6.3 Example of Design Blade of Single Curvature 213 6.4 Design of Blades of Double Curvature 224 6.4.1 Impeller Blades with Double Curvature 224 6.5 Design of Double-curvature Blades by Conformal Mapping 228 6.6 References 230 7 Inlet and Outlet Elements, 231 7.1 Inlet Elements of Turbines 231 7.1.1 Surge Tanks 231 7.1.2 Basic Equations for Differential Surge Tanks 232 7.1.3 Instability of the Surge Tank 233 7.2 Inlet Elements of Pumps 233 7.3 Outlet Elements of Turbines 235 7.3.1 Draft Tubes 235 7.4 Outlet Elements of Pumps 237 7.4.1 Volute Design 239 7.4.2 Velocity Distributions in Different Volute Cross Sections 241 7.4.3 Design of a Volute 242 7.4.4 Relation between Volute Velocity and Specific Speed 244 7.5 Solved Problem 244 7.6 References 246 8 Head Losses in Components of Turbine and Pump Systems, 247 8.1 Pipes 247 8.1.1 Friction Factor 247 8.1.2 Hydraulic Diameter 249 8.2 Losses through Other Elements 249 8.2.1 Discharge, Velocity, and Contraction Coefficients 249 8.2.2 Nozzle Loss 253 8.2.3 Fittings, Valves, and Joints 253
XII Contents 8.2.4 Expansions and Contractions 254 8.2.5 Losses in Pipe Branches 254 8.3 Total Frictional Loss in a Pipe System 254 8.4 Solved Problems 255 8.5 References 268 9 Cavitation, 269 9.1 Causes of Cavitation and Parts Affected 269 9.1.1 Methods of Detecting Cavitation 270 9.2 Cavitation in Turbines 270 9.2.1 Thoma Number, a 272 9.3 Cavitation in Pumps 273 9.3.1 Cavitation and Specific Speed 274 9.4 Determination of Limits of Cavitation 275 9.5 Limitations of Similarity Laws 278 9.6 Methods of Prevention of Cavitation 279 9.7 Conclusions about Cavitation 279 9.8 References 280 10 Water Hammer, 281 10.1 Introduction 281 10.2 Equations Describing Wave Generation and Propagation 282 10.2.1 Valve Opening or Closure Position as a Function of Time 284 10.3 Graphical Solution 287 10.4 Other Wave Reflections 291 10.4.1 Reflection at the Closed End of a Pipe 291 10.4.2 Effect of Change of Area Cross Section 291 10.4.3 Junctions and Branches 292 10.4.4 Pump Failure 293 10.5 Solved Problems 293 10.6 References 298 71 Corrosion, 299 11.1 Introduction 299 11.2 Thermodynamics of the Corrosion Process 299 11.3 Corrosion of Iron and Steel 302 11.3.1 Effect of Temperature 303 11.3.2 Effect of ph 303 11.3.3 Action of Anaerobic Bacteria 303 11.3.4 Pitting and Crevice Corrosion 303 11.4 Corrosion Resistance of Steel Alloys 304
Contents XIII 11.5 Stress Corrosion Cracking and Corrosion Fatigue 306 11.6 Galvanic or Bimetallic Corrosion 306 11.7 Cathodic Protection 307 11.7.1 Sacrificial Anodes 307 11.7.2 Protection and Overprotection 308 11.8 Effect of Flow Rate of the Environmental Fluid 308 11.9 References 309 Appendices 310 Al Equations 310 A2 Specific Gravity and Viscosity of Water at Atmospheric Pressure 313 A3 Vapor Pressure Chart for Various Liquids 315 A4 Densities of Various Liquids 316 A5 Mathematical and Physical Constants 317 A6 Conversion Factors 318 A7 Beam Formulas and Figures 321 A8 Charts for Flows through Fittings 324 A9 Friction Factor: Reynolds Number Chart (Moody Diagram) 334 A10 Values of Pipe Roughness, e for Various Materials 335 All Characteristic Values of Water in the Saturation States 336 Index 338