Note on Porous Rotating Disk Flow
by
N. Kelson
CiSSaIM, QUT
Coauthors: A. Desseaux (Institut Universitaire de Technologie, Valenciennes, France)

In this work, we revisit the classical Kármán rotating disk problem. This problem has a long history, with von Kármán originally describing similarity transformations for which the Navier-Stokes equations reduce to a system of coupled ordinary differential equations. Subsequently, an extensive literature has built up on this and closely related flows, especially with regard to apparent non-uniqueness of solutions of the governing equations.

Here we re-examine the flow of a porous heated rotating disk, motivated by the view that this problem can serve as a prototype for practical swirl flows. In combustors, for example, the swirl is often generated by a fan or rotating honeycomb so that the upstream flow is close to solid-body rotation with a nearly uniform axial velocity profile. A shooting method is used to compute solutions to the resulting two-point asymptotic boundary value problem, where estimates for the unknown boundary conditions at the surface are needed to initiate the iterative process. The dependence of the computations on the latter is investigated, and for strong injection, we find that the success of the procedure depends very sensitively on these initial guesses. Thus, the purpose of this communication is to point out basic results relating to the flow and the numerical scheme. A series solution is developed for mass transfer through the disk, and is compared with existing analyses to obtain approximate boundary conditions for high suction or injection. Sample computations using the derived boundary conditions are then presented to demonstrate their efficacy, particularly for high injection rates. Finally, the relevance of the results to practical flows will be briefly discussed.

Date received: July 30, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadk-88.