xxii
Contents
7 Dynamic Similitude ................................................................................. 247
7.1 Principles of Dynamic Similitude .................................................... 247
7.1.1 Definition of Dynamic Similitude ........................................ 247
7.1.2 Dimensionless Parameter Groups ........................................ 248
7.1.3 Similitude Conditions ........................................................... 248
7.1.4 Purpose of Similitude Analysis ............................................ 250
7.1.5 Dimensional Analysis ........................................................... 251
7.1.6 Independent and Dependent Parameter Groups ................... 252
7.1.7 Dimensionless Parameter Groups in Turbomachines
with a Constant Density Fluid .............................................. 252
7.1.8 Strong and Weak Similitude Conditions .............................. 254
7.2 Characteristic Numbers of Turbomachines ...................................... 254
7.2.1 Definition of a Characteristic Number ................................. 254
7.2.2 Specific Speed and Specific Diameter ................................. 255
7.2.3 Relation Between Characteristic Numbers
and Machine Shape .............................................................. 257
7.2.4 Design Diagrams .................................................................. 259
7.2.5 Shape of Characteristic Curves ............................................ 261
7.2.6 Power Specific Speed ........................................................... 262
7.3 Application Example of Similitude: Variable Rotational
Speed with a Pump ........................................................................... 263
7.4 Imperfect Similitude ......................................................................... 266
7.4.1 Effect of Reynolds Number with the Same Fluid ................ 266
7.4.2 Effect of Relative Roughness ............................................... 267
7.4.3 Effect of Viscosity ................................................................ 268
7.4.4 Rotor Diameter Reduction: Impeller Trimming ................... 270
7.4.5 Reduced Scale Models ......................................................... 271
7.5 Series and Parallel Connection ......................................................... 272
7.5.1 Parallel Connection of Fans ................................................. 272
7.5.2 Parallel Connection of Pumps .............................................. 273
7.5.3 Series Connection of Fans .................................................... 274
7.6 Turbomachine Design Example: Centrifugal Fan ............................ 276
7.7 Exercises .......................................................................................... 279
References ................................................................................................. 282
8 Pumps ....................................................................................................... 283
8.1 Cavitation ......................................................................................... 283
8.1.1 Cavitation Phenomenon and Cavitation Consequences ....... 283
8.1.2 Types of Cavitation .............................................................. 284
8.1.3 Cavitation Assessment: Cavitation Number and
Required Net Positive Suction Height ................................. 286
8.1.4 Optimisation of the Inlet of a Centrifugal Pump Rotor ........ 289
8.1.5 Net Positive Suction Head of the Installation ...................... 291
8.1.6 Increasing the Acceptable Suction Height ........................... 292
Contents
7 Dynamic Similitude ................................................................................. 247
7.1 Principles of Dynamic Similitude .................................................... 247
7.1.1 Definition of Dynamic Similitude ........................................ 247
7.1.2 Dimensionless Parameter Groups ........................................ 248
7.1.3 Similitude Conditions ........................................................... 248
7.1.4 Purpose of Similitude Analysis ............................................ 250
7.1.5 Dimensional Analysis ........................................................... 251
7.1.6 Independent and Dependent Parameter Groups ................... 252
7.1.7 Dimensionless Parameter Groups in Turbomachines
with a Constant Density Fluid .............................................. 252
7.1.8 Strong and Weak Similitude Conditions .............................. 254
7.2 Characteristic Numbers of Turbomachines ...................................... 254
7.2.1 Definition of a Characteristic Number ................................. 254
7.2.2 Specific Speed and Specific Diameter ................................. 255
7.2.3 Relation Between Characteristic Numbers
and Machine Shape .............................................................. 257
7.2.4 Design Diagrams .................................................................. 259
7.2.5 Shape of Characteristic Curves ............................................ 261
7.2.6 Power Specific Speed ........................................................... 262
7.3 Application Example of Similitude: Variable Rotational
Speed with a Pump ........................................................................... 263
7.4 Imperfect Similitude ......................................................................... 266
7.4.1 Effect of Reynolds Number with the Same Fluid ................ 266
7.4.2 Effect of Relative Roughness ............................................... 267
7.4.3 Effect of Viscosity ................................................................ 268
7.4.4 Rotor Diameter Reduction: Impeller Trimming ................... 270
7.4.5 Reduced Scale Models ......................................................... 271
7.5 Series and Parallel Connection ......................................................... 272
7.5.1 Parallel Connection of Fans ................................................. 272
7.5.2 Parallel Connection of Pumps .............................................. 273
7.5.3 Series Connection of Fans .................................................... 274
7.6 Turbomachine Design Example: Centrifugal Fan ............................ 276
7.7 Exercises .......................................................................................... 279
References ................................................................................................. 282
8 Pumps ....................................................................................................... 283
8.1 Cavitation ......................................................................................... 283
8.1.1 Cavitation Phenomenon and Cavitation Consequences ....... 283
8.1.2 Types of Cavitation .............................................................. 284
8.1.3 Cavitation Assessment: Cavitation Number and
Required Net Positive Suction Height ................................. 286
8.1.4 Optimisation of the Inlet of a Centrifugal Pump Rotor ........ 289
8.1.5 Net Positive Suction Head of the Installation ...................... 291
8.1.6 Increasing the Acceptable Suction Height ........................... 292