Effect of expansion on the wall heat flux in a supersonic turbulent boundary layer

Abstract

Direct numerical simulation of a spatially developing supersonic turbulent boundary layer at a Mach number of 2.25 and a friction Reynolds number of Reτ = 769 subjected to an expansion corner with a deflection angle of 12° is performed to investigate the effect of expansion on the characteristics of the wall heat flux (WHF). The effect of expansion on the statistical and structural properties of the fluctuating WHF is analyzed systematically in terms of probability density function, frequency spectra, and space-time correlations. Normalization using the local root mean square value yields good collapse of the probability density function curves. Unlike with wall pressure frequency spectra, it is found that expansion has little influence on the low-frequency components of the WHF spectrum. The correlation results show that the main effect of expansion is to increase the characteristic length scales and convection velocity of the WHF fluctuation in the post-expansion region. Furthermore, a direct comparison between the conditionally averaged flow fields and those presented in the authors' previous work [Tong et al., Phys. Fluids 34, 015127 (2022)] is performed to uncover the effect of expansion on the flow structures associated with extreme positive and negative WHF fluctuation events. We highlight that the extreme positive event emerges below a small hot spot under the action of a strong Q4 event, whereas the extreme negative event is relatively insensitive to expansion and still occurs between a pair of strong oblique vortices. In addition, we decompose the mean WHF into seven physics-informed contributions and quantify the effect of expansion on the dominating components with the aid of the bidimensional empirical mode decomposition method. The scale-decomposed results demonstrate quantitatively that expansion decreases the contribution of the large-scale structures in the outer region but the small-scale structures in the near-wall region contribute heavily to the mean WHF generation in the downstream region.