In high-speed flight, film cooling can protect optical windows from the hot external flow. However, the resulting mixing layer over the window will introduce aero-optical distortions, which detrimentally affect airborne optical sensors or systems at supersonic and hypersonic speeds. Wall-modeled large-eddy simulations of a supersonic turbulent mixing-layer flow over an optical window, recessed into a shallow cavity, were conducted for a fixed Mach 2 freestream and for freestream total temperatures of 300, 450, and 650 K. The total temperature of the subsonic cooling flow was 300 K. The simulations revealed a faster spreading of the mixing layer as the freestream total temperature increased, which was explained by an increase in the shear stress and baroclinic torque. The overall levels of the aero-optical distortions were calculated and are in general agreement with experimental results. For the 450 K case, both the boundary layer and mixing layer contributed to the aero-optical distortions. For the other two cases, the mixing-layer contribution dominated. A density kernel-based proper orthogonal decomposition revealed streamwise coherent structures related to the incoming boundary layer for the 450 K case. For the two other cases, a two-dimensional mixing-layer mode contributed to the total optical path differences.
Andrade et al. (Mon,) studied this question.