The stability of parallel, quasi-parallel and stationary flows
Date
1973-09
Authors
Kahawita, Rene A., author
Meroney, Robert N., author
Fluid Dynamics and Diffusion Laboratory, College of Engineering, Colorado State University, publisher
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Abstract
The methods of linear perturbation theory have been used to study the stability of various flows, among them being (i) The stability of boundary layers along concave heated walls; (ii) The stability of boundary layers along concave walls with suction; (iii) The stability of wall jets along concave and convex walls; (iv) The spin up of a two-dimensional cylinder in an infinite medium; (v) The stability of stationary layers of fluid with arbitrary temperature stratification; (vi) The stability of natural convection flow along inclined plates. During the course of this work, three different solution techniques were employed; one of them was an approximate analytic technique, the remaining two were numerical. Three-dimensional spatially and temporally amplifying disturbances were considered in this study. The results indicated that the normal velocity component of the mean flow in a boundary layer, although much smaller than the stream wise component had a profound effect in reducing the stability of the flow. On the other hand, suction at the wall improved the stability characteristics. For the flow of parallel layers of fluid along heated walls with small curvature, it was found that a unique stability curve for neutral disturbances may be obtained if the quantity plotted along the abscissa is Ra + KsNg2 where Ra is the Rayleigh number, Ng is the Goertler number and Ks is a constant which expresses the relative importance of the mean temperature and velocity profiles. It was demonstrated also that wall jets are unstable on concave as well as convex walls. The results obtained for the stability of the spin up of a cylinder in an infinite medium are in qualitative agreement with experiment. The dependence of the onset of convective overturning in an unstable layer of fluid with a nonlinear basic temperature profile and bounded above by fluid of varying stability on Rayleigh number was established. The angle at which the two-dimensional wave instability passes into the three-dimensional mode in natural convection along an inclined plate was calculated. The result was found to be in good agreement with experiment. Other results obtained for this flow were in good qualitative agreement with experiment. Finally, some simple wind tunnel experiments with boundary layers along curved heated walls were performed. Photographic evidence of longitudinal vortices was obtained together with some qualitative data.
Description
CER73-74-RK-RNM12.
Prepared under Office of Naval Research, project no. NR 062-414/6-6-68 (Code 438), U.S. Department of Defense.
Includes bibliographical references.
Prepared under Office of Naval Research, project no. NR 062-414/6-6-68 (Code 438), U.S. Department of Defense.
Includes bibliographical references.
Rights Access
Subject
Air flow
Boundary layer
Fluid mechanics