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Vorticity dynamics



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J Fluid Mech 2000 vol 421 pp 185 227 c 2000 Cambridge University Press Printed in the United Kingdom 185 Vorticity dynamics of dilute two way coupled particle laden mixing layers By E M E I B U R G1 2 E W A L L N E R1 3 A P A G E L L A1 4 A R I A Z1 C H A R T E L2 A N D F N E C K E R2 1 Department of Aerospace and Mechanical Engineering University of Southern California Los Angeles CA 90089 1191 USA 2 Institute of Fluid Dynamics Swiss Federal Institute of Technology ETH Zentrum CH 8092 Zu rich Switzerland 3 Present address Institute of Flight Mechanics and Flight Control University of Stuttgart Pfaffenwaldring 7a D 70550 Stuttgart Germany 4 Present address Institute of Aero and Gasdynamics University of Stuttgart Pfaffenwaldring 21 D 70550 Stuttgart Germany Received 20 August 1999 and in revised form 22 May 2000 The two way coupling mechanisms in particle laden mixing layers are investigated with and without particle settling and with an emphasis on the resulting modifications to the fluid vorticity field The governing equations are interpreted with respect to the production and cancellation of vorticity These mechanisms are shown to be related to the misalignment of the concentration gradient and the slip velocity as well as to the difference in fluid and particle vorticities Preliminary insight into the physics is obtained from an analysis of the unidirectional base flow For this model problem the conditions are established under which the particle velocity remains a single valued function of space for all times The resulting simplified set of twoway coupled equations governing the vorticity of the fluid and particulate phases respectively is solved numerically The formation of a decaying travelling wave solution is demonstrated over a wide range of parameters Interestingly the downward propagation of the fluid vorticity field is not accomplished through convection but rather by the production and loss of vorticity on opposite sides of the mixing layer For



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