Local temperature perturbations of the boundary layer in the regime of free viscous–inviscid interaction

Abstract

We analyse the disturbed flow in the subsonic laminar boundary layer, disturbances being generated by local heating elements, which are placed on the surface. It is exhibited that these flows are described in terms of free interaction theory for specific sizes of thermal sources. We construct the numerical solution for the case of a flat subsonic stream in the viscous asymptotic layer, in which the flow is described by nonlinear equations for vorticity, temperature and an interaction condition which provides the influence of perturbations to the pressure in the main order. The obtained solutions are compared with those for corresponding linear problems with small perturbations. It is demonstrated that strong temperature perturbations in some situations allow us to obtain the flow close to the separated flow.

Subsonic flow past localised heating elements in boundary layers

“…The main difference between the present work and that of Koroteev & Lipatov (2012), Koroteev & Lipatov (2013) is that H(x b ) = 0 in the latter.…”

“…The wall-shear distribution in figure 2b decreases initially but there is a sharp rise and drop on entering and leaving the heated region. The discontinuous changes forh = 0 at the start and end of the heated region are also seen in the results of Koroteev & Lipatov (2012). The main difference between the flat plate case withh = 0 and the hump shape is that the presence of the hump creates a larger pressure drop and much larger rise in the wall shear stress across the heated part as compared to the flat plate case.…”

“…We also introduce the free-stream Mach Neiland (1971) has discussed the arguments leading to the triple-deck scales and Lipatov (2006), Koroteev & Lipatov (2012), Koroteev & Lipatov (2013) in particular have explained how small changes in the surface temperature lead to a nonlinear interaction within the triple-deck. The interested reader is referred to these and other papers for more details of the governing equations and expansions.…”

“…Based on triple deck theory, we investigate subsonic flow past MEMS type heating elements placed on a flat surface in which the heating element has a hump shape. The current work reduces to the problem investigated by for example Koroteev & Lipatov (2012), Koroteev & Lipatov (2013) when the MEMS devices have zero hump height. Apart from MEMS devices, another motivation for the current work is to try and understand how local hot spots or cold bumps affect separation.…”

“…The triple deck problem is formulated and the linear and non-linear analysis and results are presented. The current work is a generalisation of the problem discussed by (Koroteev & Lipatov 2012, 2013 where the MEMS devices have flat shaped surfaces. The results show the hump-shaped heating elements enhance large drops in pressure and peaks and troughs in the skin-friction over the centre of the hump as compared to the flat shaped devices which may be useful for controlling the flow.…”