SEGREGATED PREDICTION OF 3-D COMPRESSIBLE SUBSONIC FLUID FLOWS USING COLLOCATED GRIDS

Abstract

A segregated approach for the prediction of three-dimensional, compressible, subsonic flows is presented. The method uses a collocated finite volume scheme in body-fitted coordinates. For computational expediency and ease of implementation of high-order schemes, the continuity, momentum, and state equations are decoupled and solved sequentially. In order to eliminate potential “checkerboard” pressure distributions due to the decoupling of the pressure-velocity terms in conjunction with a collocated grid, a novel method of nonlinear cell-face interpolation is adopted. The high-order QUICK scheme is implemented for discretizing convective terms, while the central difference scheme is used for discretizing diffusion terms. A four-stage Runge-Kutta explicit scheme is employed to time-march the solution of the governing equations toward steady state. The finite volume code is applied to the prediction of three-dimensional, laminar flows in a straight duct of square cross section, a cubic driven cavity, a strongly curved duct of square cross section and a two-dimensional airfoil. The ability of the method to eliminate checkerboard pressure distribution and achieve convergence is demonstrated. The method yields accurate results, while at the same time utilizing efficiently the architecture of a vector machine. Finally, the ability of the method to perform satisfactorily near the low Mach number limit is demonstrated through comparisons with incompressible flow measurements.

Notes

Address correspondence to Professor Dennis Assanis, Department of Mechanical Engineering and Applied Mechanics, University of Michigan, 321 W. E. Lay Automotive Laboratory, 1231 Beal Avenue, Ann Arbor, MI 48109-2121, USA.