Inviscid–viscous interaction on triple-deck scales in a hypersonic flow with strong wall cooling

Abstract

Inviscid–viscous interaction in a high supersonic flow is studied on the triple-deck scales to delineate the wall-temperature influence on the flow structure in a region near a laminar separation. A critical wall-temperature rangeO(Tw*) is identified, in which the pressure–displacement relation governing the lower deck departs from that of the classical (Stewartson, Messiter, Neiland) formulation, and below which the pressure–displacement relation undergoes still greater changes along with drastic scale changes in the triple deck. The reduced lower-deck problem falls into three domains: (i) supercritical (Tw* [Lt ]Tw), (ii) transcritical (Tw=O(Tw*)) and (iii) subcritical (Tw[Lt ]Tw*). Readily identified is a parameter domain overlapping with the Newtonian triple-deck theory of Brown, Stewartson & Williams (1975), even though the assumption of a specific-heat ratio approaching unity is not required here. Computational study of the compressive free-interaction solutions and solutions for a sharp-corner ramp are made for the three wall-temperature ranges. Finite-difference equations for primitive variables are solved by iterations, employing Newton linearization and a large-band matrix solver. Also treated in the program is the sharp-corner effect through the introduction of proper jump conditions. Comparison with existing numerical results in the supercriticalTwrange reveals a smaller separation bubble and a more pronounced corner behaviour in the present numerical solution. Unlike an earlier comparison with solutions by interactive-boundary-layer methods for ramp-induced pressure with separation, the IBL results do approach closely the triple-deck solution atRe= 108in a Mach-three flow, and the differences atRe= 106may be attributed in part to the transcritical temperature effect. Examination of the numerical solutions indicates that separation and reattachment on a compressive ramp cannot be effectively eliminated/delayed by lowering the wall temperature, but loweringTwdrastically reduces the triple-deck dimension, and hence the degree of upstream influence.