Small-Scale Dissipation in Supercritical, Transitional Mixing Layers

Abstract

The dissipation and small-scale dissipation is calculated for transitional states obtained elsewhere from Direct Numerical Simulations (DNS) of temporal, supercritical mixing layers for two species systems, O₂/H₂ and C₇H₁₆/N₂, so as to understand their species-independent and species-dependent aspects. The effect of filter size on the results was also investigated, with filtering exclusively performed in the dissipation regime of the energy spectrum. Both domain-average dissipation and the small-scale dissipation were analyzed in terms of the three mode contributions to them due to the viscous, heat and species-mass fluxes. The species-mass flux originated contribution dominates both the dissipation and the small-scale dissipation for all simulations and its percentage of the total dissipation or of the small-scale dissipation varies in a very small range across the species system, the initial Reynolds number and the perturbation wavelength used to excite the layer. For a filter size that is four times the DNS grid size, the proportion of each small-scale dissipation mode in the total small-scale dissipation is similar to that obtained at the DNS scale, indicating a scale similarity. It was also found that the percentage of total small-scale dissipation in the total DNS dissipation is only species-system and filter size dependent but nearly independent of the initial conditions. With filter size increase, the increase in the small-scale dissipation portion of the DNS dissipation has similar functional variation for both species systems, although the fraction reached by C₇H₁₆/N₂ layers is much larger than for O₂/H₂ ones. Normalization by the results obtained at the smallest filter size led to highlighting several aspects that are only species-system dependent with increasing the filter size. Backscatter was shown to occur over a substantial percentage of the computational domain, and its magnitude was found to be a substantial fraction of the positive small-scale dissipation. A four fold increase in filter size decreased the spatial extent of backscatter by only at most 32%, 13% and 7.5% for the viscous, heat and species-mass flux originated modes. The implications or these results for Larger Eddy Simulation modeling are discussed.

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