Investigation of dynamic subgrid-scale and wall models for turbulent boundary layers

Most turbulent flows cannot be calculated by direct numerical simulation (DNS) of the Navier-Stokes equations because the range of scales of motions is so large that the computational cost becomes prohibitive. In large-eddy simulation (LES), only the large eddies are resolved and the effect of the small scales on the larger ones is modeled through a subgrid-scale (SGS) model. Given that accurate representation and prediction of turbulence is needed in many engineering and scientific applications, development of accurate yet computationally efficient SGS models is an important task. Additionally, wall models are necessary to overcome the prohibitive near-wall resolution requirements for the large scales in high-Reynolds-number turbulent flows. This study investigates a new SGS model, the anisotropic minimum-dissipation (AMD) model, which is constructed to provide the minimum eddy viscosity required to avoid energy pile-up in the smallest resolved scales. The AMD model is successfully applied in simulations of decaying grid turbulence for isotropic grids, and temporal mixing layer and turbulent channel flow for anisotropic grids. This model is more cost-effective than the dynamic Smagorinsky model (DSM) and appropriately switches off in laminar and transitional flows. The formulation of the AMD model is extended to the transport equation for scalar concentration to model the subfilter scalar flux. The performance of the model is tested in the simulation of high-Reynolds-number rough-wall boundary-layer flow with a constant and uniform surface scalar flux. The simulation results obtained from the scalar model show good agreement with well-established empirical correlations and theoretical predictions of the resolved flow statistics. The accuracy of the SGS models is tested by studying the convergence properties in the outer region of a channel flow at moderate to high Reynolds numbers. As LES requires scale separation of the resolved and subgrid scales, the convergence study must be conducted in high-Reynolds-number flows. However, the analysis shows that the errors from the near-wall region are dominant for SGS models in usual LES grid resolutions, where the grid is not refined in the wall-parallel directions. For evaluation of SGS models, in order to overcome the grid requirements imposed by the near-wall turbulent eddies as well as the errors accumulated near the wall, a possible solution is to isolate the outer region of wall-bounded flows. This is made possible by one of two ways: suppressing the near-wall dynamics through a modified wall, or supplying the correct mean stress at the wall with a wall model. Theoretical analysis of the error scaling of SGS models for the mean velocity profile, turbulence intensities, and energy spectra is performed. The numerical convergence studies of the DSM and AMD models show that both models are first-order accurate in terms of the mean velocity profile, which is consistent with the theoretical assessments. Lastly, a new dynamic wall model based on the slip boundary condition is proposed. The use of the slip boundary condition for wall-modeled LES is motivated through theoretical analysis and a priori study of DNS data. The effect of the slip boundary condition on the one-point statistics of the flow is investigated in LES of turbulent channel and flat-plate turbulent boundary layer. The slip boundary condition provides a framework to compensate for the deficit or excess of mean momentum at the wall. The requirements for the slip lengths to be used in conjunction with wall models are discussed, and the equation that connects the slip boundary condition with the stress at the wall is derived. A dynamic procedure based on the invariance of wall stress under test filtering is formulated for the slip condition, providing a dynamic slip wall model free of any a priori specified coefficients. The performance of the proposed dynamic wall model is tested in a series of LES of turbulent channel flow at varying Reynolds numbers, non-equilibrium three-dimensional transient channel flow, and zero-pressure-gradient flat-plate turbulent boundary layer. The results show that the dynamic wall model is able to accurately predict mean and turbulence intensities for various flow configurations, Reynolds numbers, and grid resolutions.

Advisor: Moin Parviz 
Bose Sanjeeb
Lele Sanjiva K. (Sanjiva Keshava)