Boundary Layer Separation

Flow separation is a phenomenon of widespread interest in boundary layer theory and its understanding was advanced considerably by Stewartson and Williams (1969) who showed that regular separation could occur by an interactive process; see also Neiland (1969) and Messiter (1970). Since then, triple deck theory has contributed much to the understanding of boundary layer separation.

Excellent reviews may be found in Stewartson (1981), Messiter (1983) and Smith (1986). Finally, Sychev et al. (1997) is the translation of the first textbook (Sychev, 1990) on this fascinating subject. Two book chapters have been written by Rothmayer and Smith (1998). More recently, an introductory book on interactive boundary layer theory has been written by Ian Sobey (2000).

Thermal boundary layer separation

There are many examples of fluid flows in technology and engineering where imposed boundary conditions or geometries results in flow separation. In applications where thermal effects are significant, such as cooling or insulating systems, such separations can have important consequences for the heat transfer properties of the system.

Currently we are considering the manner in which a thermal jet flow, such as that driven by buoyancy along a heated vertical wall, can separate resulting in a drastic reduction in heat transfer through the wall. Such separations may be relevant, for example, where the jet encounters a corner, obstruction or sudden change in thermal boundary conditions.

One important aspect of such flows is the role of the Prandtl number. Present work aims to investigate the flow development at high Prandtl numbers where inertial effects are suppressed at the expense of buoyancy, leading to the possibility of the thermal field playing a significant role in the local separation process. Results have been presented for the separation zone at finite Prandtl numbers, where locally the flow is controlled by viscosity and inertia, independent of thermal effects. Nevertheless the resulting temperature field is of some interest and its calculation is a natural first step in the analysis of high Prandtl number separating flows.


A computational challenge

The last three papers demonstrate why the free interaction of a separating thermal boundary layer is a formidable computational problem. In a nutshell, a forward-backward parabolic partial differential equation over an unbounded domain needs to be solved. The following strategy could confirm the asymptotic results reported in Daniels & Ratnanather (2001):
J Tilak Ratnanather

Associate Research Professor
Center for Imaging Science and
Institute for Computational Medicine,
Department of Biomedical Engineering,
The Johns Hopkins University

Campus address: Clark 308B;
Phone number: (410) 516-2927;
E-mail: tilak AT cis DOT jhu DOT edu