Small-scale dissipation in binary-species, thermodynamically supercritical, transitional mixing layers

Abstract

The irreversible entropy production (i.e. the dissipation) has three distinct modes due to viscous, heat and species-mass fluxes. Computations of the dissipation and its modes are conducted using transitional states obtained from Direct Numerical Simulations (DNS) of O2/H2 and C7H16/N2 temporal mixing layers at thermodynamically supercritical pressure. A non-dimensionalization of the mathematical expression for each dissipation mode is first performed and representative reference values computed using the DNS database are utilized to highlight the order of magnitude of each mode and their relative importance. For more quantitative results, the importance of each dissipative mode is assessed both at the DNS scale and at scales determined by filter sizes from four to sixteen times the DNS grid spacing. The subgrid-scale (SGS) dissipation is computed by subtracting the filtered-field dissipation from the DNS-field dissipation. For each species system, three layers are considered having different initial Reynolds number and perturbation wavelength. For all layers, it is found that the species-mass flux contribution dominates both the DNS and SGS dissipation due to high density-gradient-magnitude (HDGM) regions which are a distinctive physical aspect of these layers. Backscatter, indicated by regions of negative SGS dissipation, is found in a substantial portion (15–60%) of the domain, and decreases only slightly with increasing filter width. Regions of the most intense negative and positive SGS dissipation strongly correlate with the HDGM regions. On a domain-average basis, the proportional contribution of each dissipation mode to the total is similar at the DNS and SGS scales, indicating scale-similarity. The proportion of the species-mass dissipation mode to the total is remarkably similar in value across all simulations whether at the DNS or SGS scale. For each mode and the total, the SGS contribution to the DNS-field dissipation is only species-system and filter-size dependent but nearly independent of the initial Reynolds number and perturbation wavelength. The SGS contribution is smaller for O2/H2 layers than for C7H16/N2 ones, but increases more rapidly with increasing filter width. The implications of these results for Larger Eddy Simulation modeling are discussed.