Small-Scale Dissipation in Binary-Species Transitional Mixing Layers
- Created: Tuesday, 01 March 2011
This method enables cost-effective modeling for supercritical conditions prevailing in gas-turbine and liquid-rocket engines.
Motivated by large eddy simulation (LES) modeling of supercritical turbulent flows, transitional states of databases obtained from direct numerical simulations (DNS) of binary-species supercritical temporal mixing layers were examined to understand the subgrid-scale dissipation, and its variation with filter size. Examination of the DSN-scale domain-averaged dissipation confirms previous findings that, out of the three modes of viscous, temperature and species-mass dissipation, the species-mass dissipation is the main contributor to the total dissipation. The results revealed that the percentage of species-mass by total dissipation is nearly invariant across species systems and initial conditions. This dominance of the species-mass dissipation is due to high-density-gradient magnitude (HDGM) regions populating the flow under the supercritical conditions of the simulations; such regions have also been observed in fully turbulent supercritical flows. The domain average being the result of both the local values and the extent of the HDGM regions, the expectations were that the response to filtering would vary with these flow characteristics. All filtering here is performed in the dissipation range of the Kolmogorov spectrum, at filter sizes from 4 to 16 times the DNS grid spacing. The small-scale (subgrid scale, SGS) dissipation was found by subtracting the filtered-field dissipation from the DNS-field dissipation.
In contrast to the DNS dissipation, the SGS dissipation is not necessarily positive; negative values indicate backscatter. Backscatter was shown to be spatially widespread in all modes of dissipation and in the total dissipation (25 to 60 percent of the domain). The maximum magnitude of the negative sub-grid-scale dissipation was as much as 17 percent of the maximum positive sub-grid-scale dissipation, indicating that, not only is backscatter spatially widespread in these flows, but it is considerable in magnitude and cannot be ignored for the purposes of LES modeling. The Smagorinsky model, for example, is unsuited for modeling SGS fluxes in the LES because it cannot render backscatter. With increased filter size, there is only a modest decrease in the spatial extent of backscatter. The implication is that even at large LES grid spacing, the issue of backscatter and related SGS-flux modeling decisions are unavoidable.
As a fraction of the total dissipation, the small-scale dissipation is between 10 and 30 percent of the total dissipation for a filter size that is four times the DNS grid spacing, with all OH cases bunched at 10 percent, and the HN cases spanning 24–30 percent. A scale similarity was found in that the domain-average proportion of each small-scale dissipation mode, with respect to the total small-scale dissipation, is very similar to equivalent results at the DNS scale. With increasing filter size, the proportion of the small-scale dissipation in the dissipation increases substantially, although not quite proportionally. When the filter size increases by four-fold, 52 percent for all OH runs, and 70 percent for HN runs, of the dissipation is contained in the sub-grid-scale portion with virtually no dependence on the initial conditions of the DNS.
The indications from the dissipation analysis are that modeling efforts in LES of thermodynamically supercritical flows should be focused primarily on mass-flux effects, with temperature and viscous effects being secondary. The analysis also reveals a physical justification for scale-similarity type models, although the suitability of these will need to be confirmed in a posteriori studies.