On the turbulent heat flux and temperature variance in supersonic shock-wave boundary-layer interaction

Abstract

The direct numerical simulation of an impinging oblique shock wave interacting with a spatially evolving turbulent boundary layer on a flat plat at Mach number 2.25 is used to investigate the characteristics of turbulent heat flux and temperature variance. Downstream of the interaction, the turbulent heat flux and temperature variance attain very large values in the outer region. The observed amplification of the turbulent heat flux is independent of the pressure–velocity correlation and is mainly characterized by mass flux. The coupling between temperature variance and turbulent kinetic energy is analyzed by examining the turbulent time-scale ratio. Across the interaction, the nearly constant time-scale ratio found in most parts of the boundary layer is generally smaller than the commonly accepted value of 0.5. The near-wall asymptotic behavior of the temperature variance is verified. Bidimensional empirical mode decomposition is adopted to analyze the contributions of different scale structures to the turbulent heat flux and temperature variance. This scale-decomposed analysis reveals that, compared with the upstream boundary layer, the shock interaction leads to increasingly pronounced contributions of the greatly enhanced outer large-scale structures and decreased contributions associated with the near-wall small-scale structures. In addition, an analysis of the primary budget terms in the transport of turbulent heat flux and temperature variance was performed. Unlike the upstream budget, the balance of production, destruction, and redistribution changes significantly in the downstream region.