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RESEARCH PAPERS

Consistent Boundary Conditions for Reduced Navier-Stokes (RNS) Scheme Applied to Three-Dimensional Viscous Flows

[+] Author and Article Information
D. R. Reddy

Turbomachinery Analysis Section, Sverdrup Technology, Inc., Lewis Research Center Group, Cleveland, Ohio 44135

S. G. Rubin

Department of Aerospace Engineering and Engineering Mechanics, University of Cincinnati, Cincinnati, Ohio 45221

J. Fluids Eng 110(3), 306-314 (Sep 01, 1988) (9 pages) doi:10.1115/1.3243549 History: Received September 24, 1987; Online October 26, 2009

Abstract

A consistent and efficient set of boundary conditions are developed for the multi-sweep space marching pressure-elliptic Reduced Navier-Stokes (RNS) scheme as applied for three-dimensional internal viscous flow problems. No-slip boundary conditions are directly imposed on the solid walls. There is no iteration procedure required in the cross plane to ensure mass conservation across each marching plane. The finite difference equations forming the coefficient matrix are ordered such that the surface normal velocity is specified on all the solid walls; unlike external flows, a pressure boundary condition in the cross plane is not required. Since continuity is directly satisfied at all points in the flow domain, the first order momentum equations can be solved directly for the pressure without the need for a Poisson pressure correction equation. The procedure developed herein can also be applied with periodic boundary conditions. The analysis is given for general compressible flows. Incompressible flow solutions are obtained, for straight and curved ducts of square cross section, to validate the procedure. The solutions of these test cases are used to demonstrate the applicability of the RNS scheme, with the improved boundary conditions, for internal flows with strong interaction as would be encountered in ducts and turbomachinery geometries.

Copyright © 1988 by ASME
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