Influence of the initial boundary layer on base pressure

Abstract

The base pressure p_b, for an initial turbulent boundary layer, is determined for supersonic nonisothermal flow about a two-dimensional backward-facing step. This problem has been considered previously. In solving it in [1, 2], use was made of the Korst condition [3], which assumes equality of the total pressure p_j ^* on the line of constant mass to the pressure behind the closing oblique shock. However the pressure at the reattachment section p_* is lower than that behind the closing shock by 30–40% [4], and consequently the Korst condition is inaccurate. Therefore in the references cited only qualitative agreement with experiment was obtained. In contrast with [1, 3], Nash [5] introduces p_*; however, it is defined by an empirical coefficient. In the present study, to find p_b we make use of the condition of conservation of mass in the base region, written in the form of the equality p_j ^*=p_*, where p_* is defined from the assumption of minimum thickness δ of the dissipative layer at the reattachment section.

Satisfactory agreement with the available experimental data is obtained without the use of correction factors. In the simplest case, when the thickness of the oncoming boundary layer δ₁=0, the proposed method is no more complex than that of Korst. The determination of the base pressure with δ₁=0 is considered in §1, and the determination with δ₁>0 is considered in §2.