Vortex Dominated Flows: A Volume Celebrating Lu Ting's 80th Birthday

by Blackmore, Denis L.; Krause, Egon; Tung, Chee; Ting, L.

• ISBN13: 9789812563200
• ISBN10: 9812563202
• Format: Hardcover
• Copyright: 2005-08-08
• Publisher: World Scientific Pub Co Inc

Summary

Honoring the contributions of one of the field's leading experts, Lu Ting, this indispensable volume contains important new results at the cutting edge of research. A wide variety of significant new analytical and numerical results in critical areas are presented, including point vortex dynamics, superconductor vortices, cavity flows, vortex breakdown, shock/vortex interaction, wake flows, magneto-hydrodynamics, rotary wake flows, and hypersonic vortex phenomena. The book will be invaluable for those interested in the state of the art of vortex dominated flows, both from a theoretical and applied perspective. Professor Lu Ting and Joe Keller have worked together for over 40 years. In their first joint work entitled ?Periodic vibrations of systems governed by nonlinear partial differential equations?, perturbation analysis and bifurcation theory were used to determine the frequencies and modes of vibration of various physical systems. The novelty was the application to partial differe

Table of Contents

Preface	xiii
Foreword	xxix
Joeseph B. Keller
Circular Discrepancy and a Monte Carlo Algorithm for Generating a Low Circular Discrepancy Sequence	1	(20)
Introduction	1	(2)
Circular discrepancy	3	(1)
Measuring Δ[P]	3	(4)
The vortex points	7	(2)
Other sequences	9	(4)
Mapping the square to a disc	10	(1)
Hammersley sequence	11	(1)
Antonov-Saleev variant of the Sobol sequence	11	(1)
Example	12	(1)
Numerical results 1	13	(1)
Numerical results 2	14	(1)
Conclusion	15	(6)
Periodic and Quasiperiodic Motion of Point Vortices	21	(22)
Introduction	22	(2)
Symplectic preliminaries	24	(2)
Fixed point theorems	26	(1)
Hamiltonian formulation of point vortex dynamics	27	(6)
Decomposition of the Hamiltonian	33	(2)
Estimates of the non-integrable perturbations	35	(1)
Application of KAM and fixed point theorems	36	(3)
Concluding remarks	39	(4)
Experiments on Heave/Pitch Limit-Cycle Oscillations of a Supercritical Airfoil Close to the Transonic Dip	43	(24)
Introduction	44	(3)
Test set-up	47	(1)
Equations of motion	48	(4)
Structural-dynamic parameters	50	(1)
Method of flutter calculations	50	(2)
Results and discussion	52	(11)
Transonic dip	52	(4)
Limit-cycle oscillations	56	(3)
Energy exchange in limit-cycle oscillations	59	(4)
Concluding remarks	63	(4)
Vortices in Superconductors	67	(20)
Introduction	68	(1)
The Ginzburg-Landau model	69	(6)
The time-dependent Ginzburg-Landau equations	72	(2)
A simplified GL model valid for high values of κ	74	(1)
The vortex state in non-ideal superconductors	75	(12)
Pinning of vortices	76	(2)
Josephson junctions	78	(2)
Surface superconductivity in high fields	80	(2)
Thermal fluctuations	82	(5)
Accurate Numerical Simulation of Three-dimensional Lid-driven Cavity Flows with Different Span Lengths	87	(12)
Introduction	88	(1)
Formulation and numerical method	88	(5)
Governing equations	88	(1)
Numerical method	89	(4)
Results	93	(3)
Concluding remarks	96	(3)
Geometric, Stochastic and Algebraic Vortices	99	(20)
Introduction	99	(4)
Geometric vortices	103	(3)
Conservation laws	103	(1)
Slender vortices	104	(1)
Diffusive vortices	105	(1)
Stochastic vortices	106	(4)
Proper orthogonal decomposition	106	(1)
A de-noising definition of coherent vortices	107	(2)
A probabilistic version of the vorticity equation	109	(1)
Algebraic vortices	110	(5)
Numerical vortex methods	110	(3)
Adaptive wavelet method for the vorticity equation	113	(2)
Conclusions	115	(4)
Experimental Investigation & Numerical Simulation of Oblique Shock/Vortex Interaction	119	(16)
Dedication to Professor Lu Ting	119	(1)
Introduction	119	(2)
Experimental investigation	121	(5)
Experimental setup	122	(1)
Measurement techniques	123	(1)
Experimental program	124	(2)
Numerical investigation	126	(1)
Computational setup and boundary conditions	126	(1)
Results	127	(3)
Experimental results	127	(1)
Weak/moderate interaction	127	(2)
Numerical results	129	(1)
Conclusions	130	(5)
Breakdown of Slender Vortices: The State of the Art	135	(22)
Introduction	136	(2)
Inviscid incompressible flow	138	(7)
Viscous incompressible flow	145	(8)
Concluding remarks	153	(4)
A Numerical Analysis of Vortex Dislocation in Wake-type Flow with Different Spanwise Nonuniformity	157	(12)
Introduction	158	(1)
Numerical simulation and method	159	(3)
Numerical results	162	(4)
Local spanwise nonuniformity	162	(3)
Stepped spanwise nonuniformity	165	(1)
Concluding remarks	166	(3)
Vortex Dipole Coordinates on the Sphere	169	(14)
Introduction	169	(3)
The dipole coordinate system	172	(2)
One and two dipoles	174	(3)
The fundamental interactions	177	(3)
Concluding remarks	180	(3)
Magneto-Fluid-Dynamic Flow Control	183	(16)
Dedication	183	(1)
Abstract	183	(1)
Introduction	184	(1)
Governing equations	185	(2)
Plasma models	187	(1)
Electro-fluid-dynamic interaction	188	(2)
Magneto-fluid-dynamic interaction	190	(2)
Concluding remarks	192	(7)
Interaction between Longitudinal Vortices and Normal and Oblique Shocks	199	(30)
Introduction	199	(2)
Governing equations	201	(2)
Computational setup and boundary conditions	203	(8)
Numerical method and vortex identification	211	(2)
Results	213	(8)
Conclusions	221	(8)
Analysis of Rotor Vortex Wake Structure Using 3-C PIV Measurements	229	(22)
Introduction	229	(2)
Test set-up and 3-C PIV measurements	231	(1)
PIV data process	231	(2)
Rotation of PIV measuring plane	233	(2)
Concluding remarks	235	(16)
Typical Vortex Phenomena in Flow Fields Past Space Vehicles	251
Introduction	252	(1)
Numerical simulation tool	253	(3)
Vortical flow effects on space vehicles	256	(1)
General	256	(1)
Influence on lift	256	(1)
Influence on drag	257	(1)
Influence on heat flux	258	(1)
Hot wall effects	259	(1)
Conclusions	260