Localized dynamic kinetic-energy model for compressible wavelet-based adaptive large-eddy simulation

Wavelet-based adaptive large-eddy simulation (WA-LES) is an extension of the LES method where wavelet threshold filtering is used to separate resolved (more energetic) from residual (less energetic) turbulent flow motions. The effect of unresolved less energetic coherent structures is approximated through deterministic closure models. The method has been recently extended to compressible flows, where the governing equations are expressed in terms of wavelet-based density-weighted Favre-filtered variables. In this study, a novel localized dynamic model for compressible WA-LES of inhomogeneous flows is developed and tested for wall-bounded turbulence. The proposed model, which is based on the solution of the additional evolution equation for the subgrid-scale turbulent kinetic energy, extends the original incompressible formulation in De Stefano et al. [Phys. Fluids 20, 045102 (2008)] to compressible flows. The new modeling procedure is successfully validated for a classical benchmark case that is the supersonic turbulent flow in a plane channel.

Figure 1

Instantaneous adaptive mesh colored by normalized temperature (top) and streamwise velocity (bottom) contours, for four different equispaced cross-sections of the channel.

Figure 2

Normalized mean streamwise velocity (left), temperature (middle) and density (right) for WA-LES solutions, compared to reference DNS [35].

Figure 3

Normalized RMS values of streamwise velocity (left), temperature (middle), and density (right) fluctuations for WA-LES solutions, compared to reference DNS [35].

Figure 4

Resolved turbulent normal stresses for WA-LES solutions, compared to reference DNS [35].

Figure 5

Turbulent shear stress, compared to reference DNS [35].

Figure 6

Resolved turbulent heat flux for WA-LES solutions, compared to reference DNS [35].

Figure 7

Instantaneous contour maps of viscosity (top) and conductivity (bottom) ratios, for four different equispaced cross-sections of the channel.

Figure 8

Instantaneous contour maps of the dynamic model coefficients that are $C_{\nu }$, $C_{\lambda }$, $C_J$, $C_{\mathrm{\Pi }}$, $C_{{\varepsilon }_{\mathrm{s}}}$, and $C_{{\varepsilon }_d}$ at the channel midplane.