Studying the effect of wall cooling in supersonic boundary layer flow using resolvent analysis

Abstract

Analysis of the resolvent operator is used to study the properties of high-speed turbulent boundary layers for cooled walls. Previous study [1] shows that the resolvent response modes in the relatively subsonic region of high-speed turbulent boundary layers with adiabatic wall boundary conditions follow the same scaling law as those of the incompressible boundary layer case, validating Morkovin’s hypothesis on a mode-by-mode basis. Here, we study the effect of the cooled-wall boundary condition on the individual resolvent response modes to understand the underlying mechanisms that cause the failure of Morkovin’s hypothesis and velocity transformations for increasingly non-adiabatic walls. In particular, we show that the density and temperature resolvent mode shapes for the cooled-wall case exhibit a secondary peak in the inner and logarithmic layer, which is a result of the non-monotonic mean temperature profile that is absent in adiabatic cases. We also show that the secondary peak becomes more prominent with decreasing surface temperature ratio. The deviation of the mean velocity profiles is attributed to the change in the response modes in the near-wall region, the effect of which is propagated further away from the wall through nonlinear interactions.