A two-layer calculation for the initial interaction region of an unseparated supersonic turbulent boundary layer with a ramp

Abstract

The interaction of an unseparated supersonic turbulent boundary layer with a compression corner produces an extremely rapid rise in pressure at the corner, followed by a more gradual increase to the final pressure. In this paper, the flow in the corner region is analyzed by an integral method with the objective of predicting the initial pressure rise. Comparisons with experimental pressure rise data are presented for cases covering supersonic and hypersonic flows of practical interest. Also presented are sone calculations and comparisons of downstream pressure distributions obtained by using the predicted corner rise as the first point in an existing inviscid method.

Cylindrical and conical flow regimes of three-dimensional shock/boundary-layer interactions

“…It is difficult to verify this range on independent grounds, since the nature of M slip is not well understood. However, Rosen et al 14 have developed a 2D calculation method based on the above inviscid-flow reasoning, and their results indicate that 2.1 <M slip <2.3 is not unreasonable for the present test conditions.…”

“…Some progress has recently been made in modeling 2D shock/turbulent boundary-layer interactions by treating most of the incoming boundary layer as a nonuniform inviscid field. 14 ' 15 (In fact, this is the basis of the well-known "tripledeck" theory.) These analytical schemes recognize that the decreasing Mach number toward the wall in the supersonic turbulent boundary layer, although a result of turbulent momentum transfer, can be modeled largely as an inviscid rotational flow.…”

“…For present purposes this philosophy dictates that M^ is not the Mach number at which shock detachment first occurs in a swept compression corner interaction. Rather, it is some effective Mach number near the wall (also called M slip 14 ' 15 ) which marks the boundary between viscous and inviscid rotational domains, and is presumably responsible for the onset of shock detachment.…”

Turbulent boundary-layer interaction with a shock wave at a compression corner

“…Reflected disturbances reaching the surface typically lead to a more gradual pressure increase, which continues for a distance of perhaps a few boundary-layer thicknesses, depending on the external-flow Mach number. At lower Mach numbers a pressure overshoot has been observed very close to the corner, followed by a gradual decrease toward the inviscid-flow value (Roshko & Thomke 1969).…”

“…Roshko & Thomke 1969;Elfstrom 1972) that, if effects of separation are negligible, the mean flow changes in the boundary layer might be described approximately by inviscid-flow equations, except in regions very close to the corner and very close to the surface downstream of the corner. The accuracy of this approximation has been confirmed by numerical calculation of surface pressures by the method of characteristics (Roshko & Thomke 1969;Rosen, Roshko & Pavish 1981). In particular cases these results show close agreement with measured values for the gradual part of the pressure increase.…”