xix
Contents
3.3 Radial Fan Analysis for Lossless Two-Dimensional Flow
with Finite Number of Rotor Blades ................................................ 106
3.3.1 Relative Vortex in Blade Channels ....................................... 106
3.3.2 Velocity Difference over a Rotating Blade .......................... 107
3.3.3 Slip: Reduction of Rotor Work ............................................. 112
3.3.4 Number of Blades and Solidity: Pfleiderer Moment
Coefficient ............................................................................ 115
3.3.5 Number of Blades: Examples ............................................... 118
3.4 Internal Losses with Radial Fans ..................................................... 120
3.4.1 Turning Loss at Rotor Entrance ........................................... 120
3.4.2 Incidence Loss at Rotor Entrance ........................................ 120
3.4.3 Displacement by Blade Thickness ....................................... 122
3.4.4 Rotor Friction Loss and Rotor Diffusion Loss ..................... 123
3.4.5 Dump Diffusion Loss at Volute Entrance ............................. 123
3.4.6 Incidence Loss at Volute Entrance ....................................... 125
3.4.7 Friction Loss Within the Volute ........................................... 126
3.4.8 Diffusion at the Rotor Inlet .................................................. 126
3.4.9 Flow separation at Rotor Inlet and Rotor Outlet .................. 127
3.4.10 Applicability of the Loss Models ....................................... 129
3.4.11 Optimisation of the Rotor Inlet of a Centrifugal Fan ......... 129
3.4.12 Characteristics Taking Losses into Account ....................... 131
3.5 Overall Performance Evaluation ...................................................... 134
3.5.1 Mechanical Loss ................................................................... 134
3.5.2 Leakage Loss ........................................................................ 135
3.5.3 Overall Efficiency with Power Receiving Machines ........... 135
3.5.4 Overall Efficiency with Power Delivering Machines .......... 136
3.6 Rotor Shape Choices with Radial Fans ............................................ 136
3.7 Axial and Mixed-Flow Fans ............................................................. 140
3.7.1 Degree of Reaction with Axial Fans .................................... 140
3.7.2 Free Vortex and Non-Free Vortex Types .............................. 141
3.7.3 Axial Fan Characteristics; Adjustable Rotor Blades ............ 143
3.7.4 Mixed-Flow Fans ................................................................. 144
3.8 Exercises .......................................................................................... 146
3.8.1 Centrifugal Pump (Idealised Flow) ...................................... 146
3.8.2 Rotor of a Centrifugal Fan (Finite Number of Blades
and Internal Losses) ............................................................. 146
3.8.3 Number of Blades of a Rotor of a Centrifugal Fan .............. 147
3.8.4 Volute of a Centrifugal Fan .................................................. 147
3.8.5 Leakage Flow Rate with Centrifugal Fan ............................ 147
3.8.6 Centrifugal Pump (Finite Number of Blades and
Internal Losses) .................................................................... 148
3.8.7 Axial Fan (Idealised Flow): Analysis on Average
Diameter ............................................................................... 148
3.8.8 Axial Fan (Idealised Flow): Free Vortex and NonFree Vortex ........................................................................... 149
Contents
3.3 Radial Fan Analysis for Lossless Two-Dimensional Flow
with Finite Number of Rotor Blades ................................................ 106
3.3.1 Relative Vortex in Blade Channels ....................................... 106
3.3.2 Velocity Difference over a Rotating Blade .......................... 107
3.3.3 Slip: Reduction of Rotor Work ............................................. 112
3.3.4 Number of Blades and Solidity: Pfleiderer Moment
Coefficient ............................................................................ 115
3.3.5 Number of Blades: Examples ............................................... 118
3.4 Internal Losses with Radial Fans ..................................................... 120
3.4.1 Turning Loss at Rotor Entrance ........................................... 120
3.4.2 Incidence Loss at Rotor Entrance ........................................ 120
3.4.3 Displacement by Blade Thickness ....................................... 122
3.4.4 Rotor Friction Loss and Rotor Diffusion Loss ..................... 123
3.4.5 Dump Diffusion Loss at Volute Entrance ............................. 123
3.4.6 Incidence Loss at Volute Entrance ....................................... 125
3.4.7 Friction Loss Within the Volute ........................................... 126
3.4.8 Diffusion at the Rotor Inlet .................................................. 126
3.4.9 Flow separation at Rotor Inlet and Rotor Outlet .................. 127
3.4.10 Applicability of the Loss Models ....................................... 129
3.4.11 Optimisation of the Rotor Inlet of a Centrifugal Fan ......... 129
3.4.12 Characteristics Taking Losses into Account ....................... 131
3.5 Overall Performance Evaluation ...................................................... 134
3.5.1 Mechanical Loss ................................................................... 134
3.5.2 Leakage Loss ........................................................................ 135
3.5.3 Overall Efficiency with Power Receiving Machines ........... 135
3.5.4 Overall Efficiency with Power Delivering Machines .......... 136
3.6 Rotor Shape Choices with Radial Fans ............................................ 136
3.7 Axial and Mixed-Flow Fans ............................................................. 140
3.7.1 Degree of Reaction with Axial Fans .................................... 140
3.7.2 Free Vortex and Non-Free Vortex Types .............................. 141
3.7.3 Axial Fan Characteristics; Adjustable Rotor Blades ............ 143
3.7.4 Mixed-Flow Fans ................................................................. 144
3.8 Exercises .......................................................................................... 146
3.8.1 Centrifugal Pump (Idealised Flow) ...................................... 146
3.8.2 Rotor of a Centrifugal Fan (Finite Number of Blades
and Internal Losses) ............................................................. 146
3.8.3 Number of Blades of a Rotor of a Centrifugal Fan .............. 147
3.8.4 Volute of a Centrifugal Fan .................................................. 147
3.8.5 Leakage Flow Rate with Centrifugal Fan ............................ 147
3.8.6 Centrifugal Pump (Finite Number of Blades and
Internal Losses) .................................................................... 148
3.8.7 Axial Fan (Idealised Flow): Analysis on Average
Diameter ............................................................................... 148
3.8.8 Axial Fan (Idealised Flow): Free Vortex and NonFree Vortex ........................................................................... 149