Disturbed boundary layer flow with local time-dependent surface heating

Abstract

Local flows in a laminar boundary layer flowing over surface heating elements are investigated. Mathematical models of disturbed flows are constructed on the basis of an asymptotic analysis and the similarity parameters are determined. The time-dependent local heating regimes ensuring control of separation and flow stability in the boundary layer are studied. The results of a numerical and analytic analysis are obtained.

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

“…The present work continues the studies started in Lipatov (2006) and Koroteev & Lipatov (2009), which were devoted to the construction of asymptotic solutions of Navier-Stokes equations in the regions containing local heating elements which are situated on the surface of the body. In our previous work (Koroteev & Lipatov 2009), we demonstrated how this problem can be solved analytically for small temperature perturbations.…”

“…The sizes of these regions are proportional to powers of the parameter Re = −2 . For the problem under consideration the detailed analysis of equations corresponding to each region was fulfilled in Lipatov (2006) and Koroteev & Lipatov (2009) and therefore is not described here. Note that the effect of perturbations is defined by scales of terms in Navier-Stokes equations.…”

“…Local perturbations of the temperature generate an effective local hump (Lipatov 2006) and produce an additional displacement of stream lines. The resulting displacement is described by the function A 1 (x b ).…”

“…The problems M. V. Koroteev and I. I. Lipatov of perturbations generated by small humps located on the surface in the bottom of the boundary layer have been the subject of studies during past several decades (Bogolepov & Neiland 1971;Smith 1974;Bogolepov & Neiland 1976). Lipatov (2006) presented a general description of problems emerging when local heating elements are located on the surface. In the same work an important similarity between the problems in question and those of flows over the surface with small humps was demonstrated.…”

“…Localization of the perturbations and their influence on the flow functions made it possible to employ asymptotic analysis based on a triple-deck structure (Neiland 1969;Stewartson & Williams 1969;Messiter 1970) to derive equations for different asymptotic regions in the vicinity of the thermal element (Lipatov 2006). Stationary solutions which are described in terms of free interaction of the boundary layer with the inviscid flow for the supersonic case corresponding to small perturbations of temperature T T ∼ O(1) were found in Koroteev & Lipatov (2009) and were also obtained for the subsonic case in Koroteev & Lipatov (2011).…”