Numerical Simulation and Subgrid-Scale Modeling of Mixing and Wall-Bounded Turbulent Flows

Abstract

We extend the idea of multiscale large-eddy simulation (LES), the underresolved fluid dynamical simulation that is augmented with a physical description of subgrid-scale (SGS) dynamics. Using a vortex-based SGS model, we consider two areas of specialization: active (buoyant) scalar mixing and wall-bounded turbulence. First, we develop a novel method to perform direct numerical simulation (DNS) of statistically stationary buoyancy-driven turbulence by using the fringe-region technique within a triply periodic domain, in which a mixing region is sandwiched between two fringes that supply the flow with unmixed fluids---heavy on top of light. Spectra exhibit small-scale universality, as evidenced by collapse in inner scales. A comparison with high-resolution DNS spectra from Rayleigh--Taylor turbulence reveals some similarities. We perform LES of this flow to show that a passive scalar SGS model can also be used in an unstably stratified environment. LES spectra, including subgrid extensions, show good agreement with DNS data. For stably stratified flows, we develop an active scalar SGS model by performing a perturbation expansion in small Richardson numbers of the passive scalar SGS model to obtain an expression for the SGS scalar flux that contains buoyancy corrections. We then develop a wall model for LES in which the near-wall region is unresolved. A special near-wall SGS model is constructed by averaging the streamwise momentum equation together with an assumption of local--inner scaling, giving an ordinary differential equation for the local wall shear stress that is coupled with the LES. An extended form of the stretched-vortex SGS model, which incorporates the production of near-wall Reynolds shear stresses due to the winding of streamwise momentum by near-wall attached SGS vortices, then provides a log relation for the off-wall LES boundary conditions. A Karman-like constant is calculated dynamically as part of the LES. With this closure we perform LES of turbulent channel flow for friction-velocity Reynolds numbers $Rey_ au=2, extrm{k}$--$20, extrm{M}$. Results, including SGS-extended spectra, compare favorably with DNS at Rey_ au=2, extrm{k}$, and maintain an $O(1)$ grid dependence on $Rey_ au$. Finally, we apply the wall model to LES of long channels to capture effects of large-scale structures. Computed correlations are found to be consistent with recent experiments.