We are concerned with the chaotic flow fields of turbulent mixing. Chaotic flow is found in an extreme form in multiply shocked Richtmyer-Meshkov unstable flows. The goal of a converged simulation for this problem is twofold: to obtain converged solutions for macro solution features, such as the trajectories of the principal shock waves, mixing zone edges, and mean densities and velocities within each phase, and also for such micro solution features as the joint probability distributions of the temperature and species concentration or a chemical reaction rate. We introduce parameterized subgrid models of mass and thermal diffusion, to define the large eddy simulation (LES) that replicate the micro features observed in the direct numerical simulation (DNS). The Schmidt numbers and Prandtl numbers are chosen to represent typical liquid, gas and plasma parameter values. Our main result is to explore the variation of the Schmidt, Prandtl and Reynolds numbers by three orders of magnitude, and the mesh by a factor of 8 per linear dimension (up to 3200 cells per dimension), to allow exploration of both DNS and LES regimes and verification of the simulations for both macro and micro observables. We study mesh convergence for key properties describing the molecular level of mixing, including chemical reaction rates between the distinct fluid species.
Methodologically, the results are also new. In common with the shock capturing community, we allow and maintain sharp solution gradients, and we enhance these gradients through use of front tracking. In common with the turbulence modeling community, we include subgrid scale models with no adjustable parameters for LES. These two methodologies have not been previously combined. In contrast to both of these methodologies, our use of Front Tracking, with DNS or LES resolution of the momentum equation at or near the Kolmogorov scale, but without resolving the Batchelor scale, allows a feasible approach to the modeling of high Schmidt number flows.
Key words. Turbulence, Subgrid models, Large eddy simulation, Direct numerical simulation, Mass diffusion, Thermal diffusion, Schmidt numbers, Prandtl numbers.
|School:||State University of New York at Stony Brook|
|School Location:||United States -- New York|
|Source:||DAI-B 71/04, Dissertation Abstracts International|
|Subjects:||Applied Mathematics, Plasma physics, Nuclear physics|
|Keywords:||Front tracking, Large eddy simulation, Mixing flows, Thermal diffusion, Turbulent flows|
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