The contrived transient-explicit method for solving steady-state flows application to a rotating, recirculating flow文档.pdf

Compums F/uMs, Vol. 1, pp. 273-287. Pergamon Preu, 1973. Printed in Great Britain. THE CONTRIVED TRANSIENT-EXPLICIT METHOD FOR SOLVING STEADY-STATE FLOWS APPLICATION TO A ROTATING, RECIRCULATING FLOW L. M. DESOCIO, E. M. SPARROW,and E. R. G. ECKERT Department of Mechanical Engineering University of Minnesota, Minneapolis, Minnesota 55455, U.S.A. (Received 14 December 1972) Abstra..ct~A method is described for solving steady-state fluid flow and heat tranffex problems which are governed by elliptic-typediffexential equations. A contrived transient version of the steady-state problem is constructed by appending time derivativesto allthe parfl~ilmtingequa- tions, regardless of whether or not such terms have physical reality. ___ohtime dexivative is multiplied by a fictive diffusivity coefficient which is varied during the course of an explicit marching procedure in order to achieve rapid, stable convergence to the steady state. The solution method is applied to a three-component laminar flow in a cylindrical enclosure having one rotating wall and coolant throughtlow. Recirculation patterns are set up in the enclosure due to the shearing action of the throughflow and to the rotation of the disk. The surface heat transfer is found to decrease as the Reynolds number of the throughflow increases. N O M E N C L A T U R E a, b, ¢, d quantities defined in Table 1 k thermal conductivity L