A definitive guide to mastering flow and heat transfer in rotating disc systems for aerospace and turbomachinery applications
Rotating Disc Cavity Flow and Heat Transfer by John W. Chew, Professor of Mechanical Engineering at the University of Surrey and internationally recognized authority on turbomachinery internal air systems, consolidates over four decades of expertise in fluid mechanics and heat transfer in rotating environments. The book addresses one of the most complex challenges in aerospace and power generation: predicting and controlling flow and thermal behavior inside rotating disc cavities. Prof. Chew distills cutting-edge analytical, computational, and experimental knowledge into practical methods engineers and researchers can apply directly to design and analysis.
This resource is organized into two parts. The first details the fundamental theory, analytical solutions, and computational methods – ranging from boundary layer models to advanced CFD approaches – across laminar, transitional, and turbulent regimes. The second presents a systematic classification of rotating cavity flows in turbomachinery, including rotor-stator systems, corotating discs, and rim sealing applications, supported by many examples and extensive comparisons with experimental data. Together, they provide a unique, authoritative reference point for both academic research and industrial practice.
Key features include:
- Comprehensive treatment of analytical and computational models with clear explanations of their assumptions, limits, and applications
- Formulae, correlations, and graphs designed for direct use in engineering design and performance evaluation
- Critical comparisons of theoretical and computational predictions against experimental results, highlighting best practices for model validation
- Structured coverage of practical cases in aeroengines, power generation gas turbines, and industrial compressors
- Modular chapter design enabling selective reading tailored to research or applied engineering needs
Rotating Disc Cavity Flow and Heat Transfer is essential for practicing engineers, researchers, and designers engaged in turbomachinery internal air systems, as well as graduate students specializing in fluid mechanics, heat transfer, or aerospace propulsion. Readers will gain both a consolidated knowledge base and actionable engineering guidance, making it a critical addition to professional and academic libraries.
Table of Contents:
Preface xi
Frequently Used Notation xiii
1 Introduction 1
References 4
Part I Theory and Modelling Methods 7
2 Essential Theory 9
2.1 Mass, Momentum and Energy Balances 9
2.1.1 Mass Conservation 11
2.1.2 Angular Momentum 12
2.1.3 Axial and Radial Momentum 13
2.1.4 Energy Conservation 14
2.1.5 Total Temperature and Total Pressure 16
2.1.6 Euler Work Equation and Rothalpy 17
2.1.7 Navier–Stokes Equations 17
2.1.8 Vorticity and Q-Criterion 19
2.2 Rotating Coordinate Systems 20
2.2.1 Governing Differential Equations 20
2.2.2 Relative Total Temperature and Pressure 21
2.2.3 Rotary Stagnation Temperature and Pressure 22
2.3 Dimensional Analysis 23
2.3.1 Nondimensional Governing Equations 23
2.3.2 Buckingham Pi Theorem 26
2.4 Reynolds-Averaged Equations and Eddy Viscosity 28
2.5 Heat Transfer 31
2.5.1 Forced Convection 31
2.5.2 Centrifugal Free Convection 32
2.5.3 Similarity Between Heat and Momentum Transfer 35
2.6 Rotating Waves and Fourier Analysis 38
2.7 Concluding Remark 40
References 41
3 Analytical Solutions for Inviscid and Laminar Flow 43
3.1 Exact Solutions of the Navier–Stokes Equations 43
3.1.1 One-Dimensional Solutions (Free, Forced and Mixed Vortices) 43
3.1.2 Axisymmetric Laminar Viscous Flow 45
3.1.2.1 The Free Rotating Disc 45
3.1.2.2 Rotating Flow Above a Stationary Disc 47
3.1.2.3 Flow Between Infinite Discs 48
3.2 Axisymmetric Laminar Boundary Layer Flow 49
3.3 Further Approximate Solutions 51
3.3.1 Steady Inviscid Flow 52
3.3.2 Laminar Ekman Boundary Layers 53
3.3.3 Laminar Ekman Layer Heat Transfer 56
3.3.4 Inertial Waves 58
3.3.5 Acoustic Waves 60
3.4 Concluding Remark 62
References 63
4 Laminar–Turbulent Transition 65
4.1 The Free Disc 65
4.2 BEK Flows (Bödewadt, Ekman, von Kármán) 67
4.3 Enclosed Rotor–Stator Disc Cavities 68
4.4 Corotating Disc Cavities with Radial Flow 69
4.5 Rotating Cones 70
4.6 Rotating Cylinders 71
4.7 Centrifugal Free Convection 72
4.7.1 Radial Convection 72
4.7.2 Axial Convection 73
4.8 Concluding Remark 75
References 75
5 Integral Boundary-Layer Methods for Turbulent Flow 79
5.1 Axisymmetric Integral Boundary-Layer Equations 79
5.1.1 Mass and Momentum Equations 79
5.1.2 The Energy Equation 82
5.2 Free and Enclosed Rotating Disc Flows 83
5.2.1 A Disc Rotating in a Quiescent Environment 83
5.2.2 Forced Vortex Flow Above a Rotating Disc or Cone with 0 ≤ kδ < 1 87
5.2.3 Forced Vortex Flow Above a Rotating Disc or Cone with 1 < kδ ≤ ∞ 89
5.2.4 Free Vortex Flow Above a Rotating Disc or Cone 90
5.2.5 Rotor-Stator Cavity Flow 93
5.3 Turbulent Ekman Layers and Corotating Disc Cavity Flows 96
5.3.1 The Turbulent Ekman Layer Solution 96
5.3.2 Corotating Disc Cavities with Radial Outflow 98
5.3.3 Corotating Disc Cavities with Radial Inflow 100
5.3.4 Buoyancy Effects 103
5.4 Concluding Remark 103
References 104
6 Computational Fluid Dynamics 107
6.1 Computational Fluid Dynamics (CFD) Solution Methods 107
6.2 Reynolds-Averaged Navier–Stokes (RANS) Models 109
6.2.1 The Eddy Viscosity Hypothesis 109
6.2.2 Mixing Length Models 109
6.2.3 The k − ε Model 111
6.2.3.1 Model Description 111
6.2.3.2 Model Evaluations for Rotating Disc Flows 112
6.2.4 The k − ω SST Model 115
6.2.5 Other Eddy Viscosity Models 117
6.2.6 Other Reynolds-Averaged Navier–Stokes (RANS) Models 118
6.3 Large Eddy Simulation (LES) 121
6.3.1 Modelling Approach 121
6.3.2 Performance for Boundary Layer Dominated Disc Cavity Flows 123
6.3.3 Performance for More Complex Disc Cavity Flows 126
6.4 Direct Numerical Simulation (DNS) 129
6.5 Fluid–Solid Coupling 132
6.6 Concluding Remark 134
References 135
Part II Examples and Applications 139
7 Rotor–Stator Disc Cavities 141
7.1 Flow in Plane Disc Cavities 141
7.1.1 Closed Cavities 141
7.1.2 Simple Radial Outflow 144
7.1.3 Simple Radial Inflow 147
7.1.4 Open Cavities and Rotating Flow Modes 151
7.1.5 Transient Flow 151
7.2 Flow in More Complex Geometries 152
7.2.1 Axisymmetric Geometries or Approximations 152
7.2.2 Effects of Boltheads and Other Features 155
7.3 Preswirl Systems 161
7.3.1 System Description 161
7.3.2 System Performance Parameters 162
7.3.3 Elementary Modelling 164
7.3.4 Examples 166
7.4 Heat Transfer 167
7.5 Concluding Remark 171
References 171
8 Corotating Disc Cavities 175
8.1 Radial Outflow 175
8.1.1 Integral Solutions for the Flow Field 176
8.1.2 CFD Solutions for the Flow Field 178
8.1.3 Heat Transfer 179
8.2 Radial Inflow 183
8.2.1 Integral Solutions for Inlet Swirl Fractions ≥ 1 184
8.2.2 Integral Solutions for Inlet Swirl Fractions < 1 186
8.2.3 CFD and Heat Transfer 187
8.2.4 Non-Unique Solutions and Hysteresis 191
8.3 Buoyant Flow in Closed Cavities 193
8.3.1 Axial Convection 193
8.3.2 Radial Convection 195
8.3.3 Mixed Axial/Radial Convection 200
8.4 Rotating Cavities with Axial Throughflow 201
8.4.1 Flow Structure 201
8.4.2 Elementary Modelling 203
8.4.3 Computational Fluid Dynamics 205
8.4.4 Parametric Dependencies 208
8.5 Concluding Remark 211
References 211
9 Rim Sealing 217
9.1 Flow Mechanisms 218
9.1.1 Disc Pumping 219
9.1.2 Pressure-driven Ingestion 221
9.1.3 Mainstream, Seal and Cavity Flow Interactions 222
9.2 Dimensional Analysis and Elementary Modelling 225
9.3 Sealing Effectiveness 227
9.3.1 Measurements with No or Weak Annulus Flow 227
9.3.2 Measurements with Annulus Flow 230
9.3.3 Effectiveness Distribution in the Cavity 232
9.3.4 Density Ratio Effects 234
9.3.5 Computational Fluid Dynamics (CFD) 235
9.4 Seal Design 239
9.4.1 Seal Geometry 239
9.4.2 Effect of Engine Configuration and Operating Conditions 242
9.4.3 Flow Conditioning 244
9.5 Concluding Remark 244
References 245
Index 253
About the Author :
John W. Chew, Ph.D., CEng., FRAeS, FASME is Emeritus Professor of Mechanical Engineering at the University of Surrey, UK. and was previously a Corporate Specialist in Aeroelasticity and Heat Transfer at Rolls-Royce plc, Derby, UK. An internationally recognized leader in turbomachinery internal air systems, he has pioneered research on computational and mathematical modeling of rotating flows for over 40 years. As an academic he has advised industry on bespoke design methods, published extensively, regularly served as organizer at the annual ASME TURBO EXPO, and delivered invited lectures around the world. He is also Editor of the Proceedings of the IMechE Journal of Mechanical Engineering Science.
