Minkowski functionals are employed that provide the geometrical, topological, and morphological aspects of isosurfaces.
A previously created direct numerical simulation (DNS) database of mixing of species under supercritical pressure has been examined and analyzed for the purpose of understanding the modeling requirements in the context of large eddy simulation (LES). Of particular interest is reproducing in LES the feature of uphill species diffusion that is identified in DNS. The examination of the database was performed by employing Minkowski functionals that provide the geometrical, topological, and morphological aspects of isosurfaces that are extracted from a field through computing dimensionless shapefinders: genus, planarity, and filamentarity.
The analysis is restricted to simply connected isosurfaces having a null genus. Isosurfaces of the second invariant of the deformation tensor and of the dissipation calculated as a result of all transport processes were found to be quite different; those derived from the second invariant turned out to have more randomness when compared to those derived from the dissipation that had better defined volumetric extent. Upon filtering, at the same filter width, there were more structures of greater extent and with well-defined morphology resulting more from the dissipation than from the second invariant.
Independent of the filter width, the dissipation- related isosurfaces had more complex structure than those issued from the second invariant, as evidenced by larger planarity and filamentarity. In general, the structures originating from the second invariant were filamentary, a feature that was retained when filtering, whereas those originating from the dissipation had more comparable planarity and filamentary values. Having thus examined the template LES solution, the activity of terms in the differential LES equations was examined and, in addition to the classical subgridscale (SGS) terms issued from the convective terms of the original equations, other SGS terms were identified.
When evaluated on the database, some of these new terms were shown to have important contributions in the LES equations. The importance of the contribution of each term increased with increasing pressure. Several models were proposed and tested for these significant SGS terms with the goal of preserving, in future LES, the features observed in the template LES solution. The model that best reduced the error on all terms compared to the template values was based on an Approximate Deconvolution Model combined with explicit filtering that succeeded in reducing the error by more than a factor of two on terms occurring in the momentum, species, and energy equations. Particularly crucial was the effect of the model for recovering the flux of species experiencing uphill diffusion, a phenomenon identified for multi-species but not for binary-species mixing. Based on this study, caution is advised on simply extrapolating results from supercritical-pressure binaryspecies mixing to multi-species mixing.