Numerical analysis and flow visualization of unsteady viscous flows with separation regions
by
Dan Mateescu
Aeronautical Program, Mechanical Engineering Department, McGill University
Coauthors: Eddy Zuppel

Unsteady flows with oscillating boundaries are encountered in many aeronautical and other engineering applications. In many of these problems, the unsteady flows (as well as the steady ones) often display separation regions, which are generated by sharp geometric changes of the fixed and/or oscillating walls bounding the fluid flows. The resulting flows are complex and there is a need for special numerical methods capable of accurately solving these unsteady flows with separation regions.

This paper presents an efficient numerical method for the nonlinear analysis of unsteady flows with oscillating boundaries and separation regions. This method uses a three-point-backward discretization in real time and a pseudo-time relaxation procedure with artificial compressibility to advance the solution from one real time step to the next. The method uses a central differencing scheme on a stretched staggered grid in the computational domain, a factored alternate direction implicit (ADI) scheme, and a special decoupling procedure to reduce the numerical problem to the solution of several scalar tridiagonal systems of equations.

The method is first validated for steady flows by comparison with previous computational and experimental results; the present solutions were found in good agreement with the previous results.

The method is then used to obtain unsteady flow solutions for several benchmark unsteady flow problems, such as the unsteady flows past downstream-facing steps with oscillating walls. Detailed flow visualizations, depicting the unsteady pattern of the streamlines and the velocity magnitude contours, are presented for several specific flow problems, analyzing the effect of various physical parameters, such as the Reynolds number, the oscillation amplitude and the oscillation frequency.

Date received: March 12, 2004

Copyright © 2004 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 # canw-07.