Rotating Flow

by Childs, Peter R. N.

• ISBN13: 9780123820983
• ISBN10: 0123820987
• Format: Hardcover
• Copyright: 2010-10-25
• Publisher: Butterworth-Heinemann

Summary

Rotating flow is critically important across a wide range of scientific, engineering and product applications, providing design and modeling capability for diverse products such as jet engines, pumps and vacuum cleaners, as well as geophysical flows. Developed over the course of 20 years' research into rotating fluids and associated heat transfer at the University of Sussex Thermo-Fluid Mechanics Research Centre (TFMRC), Rotating Flow is an indispensable reference and resource for all those working within the gas turbine and rotating machinery industries. Traditional fluid and flow dynamics titles offer the essential background but generally include very sparse coverage of rotating flows-which is where this book comes in. Beginning with an accessible introduction to rotating flow, recognized expert Peter Childs takes you through fundamental equations, vorticity and vortices, rotating disc flow, flow around rotating cylinders and flow in rotating cavities, with an introduction to atmospheric and oceanic circulations included to help deepen understanding. Whilst competing resources are weighed down with complex mathematics, this book focuses on the essential equations and provides full workings to take readers step-by-step through the theory so they can concentrate on the practical applications. A detailed yet accessible introduction to rotating flows, illustrating the differences between flows where rotation is significant and highlighting the non-intuitive nature of rotating flow fields Written by world-leading authority on rotating flow, Peter Childs, making this a unique and authoritative work Covers the essential theory behind engineering applications such as rotating discs, cylinders, and cavities, with natural phenomena such as atmospheric and oceanic flows used to explain underlying principles Provides a rigorous, fully worked mathematical account of rotating flows whilst also including numerous practical examples in daily life to highlight the relevance and prevalence of different flow types Concise summaries of the results of important research and lists of references included to direct readers to significant further resources

Table of Contents

Preface	p. xi
About the Author	p. xv
Notation and Units	p. xvii
Introduction to Rotating Flow
Introduction	p. 1
Geometric Configurations	p. 3
Geophysical Flow	p. 7
Conclusions	p. 14
References	p. 15
Laws of Motion
Introduction	p. 17
Navier-Stokes Equations	p. 19
Surface Forces	p. 20
Body Forces	p. 24
Inertia Forces	p. 25
Equilibrium	p. 26
Continuity Equation	p. 31
Solution of the Governing Equations of Fluid Mechanics	p. 33
Equations of Motion in a Rotating Coordinate System	p. 33
Dimensional Analysis and Similarity	p. 38
Conclusions	p. 51
References	p. 51
Vorticity and Rotation
Introduction	p. 53
Vortex Flow	p. 58
Free Vortex	p. 59
Forced Vortex	p. 65
Compound Vortex	p. 69
Free Spiral Vortex	p. 70
Helmholtz's Theorems	p. 71
Toroidal Vortex	p. 71
The Bathtub Vortex	p. 72
Taylor-Proudman Theorem	p. 75
Conclusions	p. 78
References	p. 78
Introduction to Rotating Disc Systems
Introduction	p. 81
The Free Disc	p. 83
Laminar Flow over the Free Disc	p. 85
A Rotating Fluid above a Stationary Disc	p. 97
Turbulent Flow over a Single Disc	p. 102
Momentum Integral Equations for Turbulent Flow over a Rotating Disc	p. 104
Ekman Integral Equations	p. 121
Impinging Flow on a Rotating Disc	p. 123
Conclusions	p. 125
References	p. 126
Rotor-Stator Disc Cavity Flow
Introduction	p. 127
Enclosed Rotor-Stator Disc Systems	p. 130
Inviscid Equations of Motion	p. 138
Rotor-Stator with Radial Outflow	p. 139
Rotor-Stator with Radial Inflow	p. 148
Rotor-Stator with Stationary Shroud and Radial Outflow	p. 152
Rotor-Stator with Stationary Shroud and External Flow	p. 158
Static and Rotating Protrusions	p. 165
Thrust on a Disc	p. 168
Conclusions	p. 172
References	p. 172
Rotating Cylinders, Annuli, and Spheres
Introduction	p. 177
Rotating Cylinder Flow	p. 179
Rotating Couette Flow	p. 185
Flow Instabilities and Taylor Vortex Flow	p. 193
Journal Bearings	p. 203
Boundary-Lubricated Bearings	p. 207
Design of Full Film Hydrodynamic Bearings	p. 208
Rotating Cylinders and Spheres with Cross-flow	p. 236
Conclusions	p. 244
References	p. 244
Rotating Cavities
Introduction	p. 249
Closed Rotating Cylindrical and Annular Cavities	p. 251
Rotating Cavity with Radial Outflow	p. 253
Rotating Cavity with Radial Inflow	p. 255
Rotating Cavities with Axial Throughflow	p. 258
Characterization of Cavity Flow and Modeling	p. 259
Boundary Layer Approximation for Rotating Cavity Flows	p. 260
Linear Ekman Layer Equations	p. 265
Integral Equations	p. 271
Modeling of Selected Rotating Cavity Applications	p. 275
Closed Rotating Cavities	p. 275
Rotating Cavity with Radial Outflow	p. 281
Rotating Cavity with Radial Outflow and Axial Inlet	p. 284
Radial Inflow	p. 285
Rotating Cavities with Axial Throughflow	p. 287
Conclusions	p. 295
References	p. 296
Atmospheric and Oceanic Circulations
Introduction	p. 299
Coordinate System	p. 305
Earth, Sun, and Moon Dynamics	p. 307
Structure and Composition of the Atmosphere	p. 310
The Energy Cycle	p. 315
Atmospheric Circulation	p. 322
Rossby Waves and Jet Streams	p. 329
Pressure Systems and Fronts	p. 335
Pressure Systems	p. 335
Fronts	p. 340
Anticyclones	p. 344
Weather Maps	p. 345
Intense Atmospheric Vortices	p. 351
Thunderstorms	p. 351
Tornadoes and Waterspouts	p. 351
Whirlwinds and Dust Devils	p. 354
Hurricanes and Typhoons	p. 355
Oceanic Circulation	p. 359
Conclusions	p. 365
References	p. 365
Properties of Air	p. 367
The Vector Cross Product	p. 373
Glossary	p. 377
Index	p. 383
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