Direct and Large-Eddy Simulations of Spatially Evolving Supercritical Turbulent Shear Layers
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Purushotham, Dhruv
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Abstract
A given pure component supercritical fluid at a thermodynamic state in the vicinity of its critical point exhibits significant susceptibility to perturbations in the state. The variation of the thermodynamic and transport properties at these loci are strongly nonlinear as a result of non-negligible intermolecular forces in the fluid. These nonlinearities stress the formulations of existing LES subfilter closures, which are derived based on assumptions that break down at these states. The performance of certain subfilter closures under these conditions is largely unclear and the extension of this argument to multi-component settings adds further uncertainty. The research in this dissertation aims to address a judiciously selected subset of these concerns through a multi-faceted approach based on the joint application of the DNS and LES techniques.
Specific outcomes of the research are as follows. First, the DNS data set produced for this work shows that Lagrangian enstrophy is amplified by baroclinicity in an instantaneous sense, and is likely associated with highly-strained local vortical structures. At certain times, the baroclinic contribution can be as much as roughly half the dominant vortex stretching contribution. However, the importance of baroclinicity in the mean diminishes. Enstrophy generation through elemental dilatation is also instantaneously significant, but diminishes in the mean. A detailed analysis of turbulence anisotropy shows that some select points within the shear layer are subject to statistically two, or even one-component turbulence, implying attenuation likely stemming from regions of high density gradient magnitude which are known to appear in systems at these conditions. This is a particular manifestation of the thermo-fluid coupling present in such flows.
Comparisons between three LES calculations indicate that coarser grids result in higher shear layer growth rates relative to that predicted by the reference DNS data. An evaluation of turbulent kinetic energy spectra and transport property ratios indicates that this could be a result of over-active subfilter models. Mean molecular transport properties are found to rival their corresponding turbulent analogs, and this is likely a unique behavior due to the thermodynamic setting. The rough equivalence of the molecular transport properties to their turbulent counterparts essentially doubles the action of the diffusive operator in the filtered system of equations, thus imparting additional diffusion to the field. This helps correct for amplified field anisotropies which likely arise not only naturally from the lack of grid resolution at the coarse limit, but also from the presence of regions of high density gradient magnitude which attenuate turbulent fluctuations and inhibit mixing. In this light, the extra diffusion imparted by the models serves as a corrective mechanism, however, it appears that in this thermodynamic setting in the coarse grid limit, the specific models employed ought to be attenuated to some level, given the mismatch in shear layer growth rates.
Finally, to isolate and analyze subfilter model performance in a rigorous fashion, an a priori analysis of three classes of subfilter closures is performed. The results indicate that, as expected, the dynamic mixed class of closure performs best. However, quantitative data from this analysis indicates that performing LES using the mixed dynamic closures at grid resolutions 4-5x coarser in each coordinate direction than the required DNS resolution at a given Reynolds number yields acceptable performance. At these resolutions, modeled subfilter stresses remain well correlated with the true subfilter stresses, however, the coarsening represents significant computational savings which can aid engineering design in practical settings. The specific resolution guideline here in particular represents a novel outcome of this research in the area of subfilter modeling for LES.
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2024-04-27
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Dissertation