Confined wakes: A numerical solution of the Navier-Stokes equations

✍ Scribed by Jean Paris; Stephen Whitaker

• Publisher: American Institute of Chemical Engineers
• Year: 1965
• Tongue: English
• Weight: 866 KB
• Volume: 11
• Category: Article
• ISSN: 0001-1541
• DOI: 10.1002/aic.690110616

✦ Synopsis

A numerical solution of the two-dimensional Navier-Stokes equations is presented for the confined wake formed by the merging of two-plane Poiseuille flow streams. The system of finitedifference equations for the stream function and vorticity i s solved by the Peaceman-Rachford elimination method for Reynolds numbers of 1, 50, 387, and 647. While the stability of the numerical method i s not a probiem for this range of Reynolds numbers, the number of points in the finite-difference network (and hence the computation time) does become burdensome.

At high Reynolds numbers, the primary boundary-layer simplification is imposed t o yield a set of parabolic equations for the vorticity ond stream function. These equations are solved by a straightforward "marching" technique, thus providing a solution with a minimum of computational effort. The "boundary-layer equations" presented in this paper are not subject to the order of magnitude analysis which leads to the neglect of one of the momentum equations in order t o obtain the Prandtl boundary-layer equations. The method outlined here represents an approximote solution for high Reynolds numbers, which gives surprisingly good agreement with the complete solution.

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