Local Wall Temperature Effects on the Second-Mode Instability

It has been shown that, in general, heating the wall beneath second-mode instabilities dampens them, whereas cooling the wall amplifies them. The purpose of this research was to determine the viability of localized wall temperature variations for controlling second-mode growth. In this paper, the results of a computational study were conducted where the wall temperature was varied locally and entirely along the Purdue flared cone at Mach 6. Such wall temperature variations could potentially be achieved actively by embedded heating/cooling systems or passively through vehicle material selection. It was found that heating the wall just downstream of the N1 neutral point amplifies second-mode growth, whereas heating the wall further downstream, toward the N2 neutral point, dampens second-mode growth. The opposite effect is found for wall cooling. It is shown by linear and nonlinear analyses that particular combinations of localized upstream cooling and downstream heating optimally dampen second-mode growth. Physically, this effect can be understood via modulation of the thermal boundary layer, which modifies the acoustic impedance well in which second modes resonate, and ultimately can be interpreted as a clockwise rotation of the stability diagram.