Performance of subgrid-scale models in coarse large eddy simulations of a laminar separation bubble

Abstract

The flow over many blades and airfoils at moderate angles of attack and Reynolds numbers ranging from 104 to 105 undergoes separation due to the adverse pressure gradient generated by surface curvature. In many cases, the separated shear layer then transitions to turbulence and reattaches, closing off a recirculation region—the laminar separation bubble. An equivalent problem is formulated by imposing suitable boundary conditions for flow over a flat plate to avoid numerical and mesh generation issues. Recent work demonstrated that accurate large eddy simulation (LES) of such a flow is possible using only O(1%) of the direct numerical simulation (DNS) resolution but the performance of different subgrid-scale models could not be properly assessed because of the effects of unquantified numerical dissipation. LES of a laminar separation bubble flow over a flat plate is performed using a pseudo-spectral Navier-Stokes solver at resolutions corresponding to 3% and 1% of the chosen DNS benchmark by Spalart and Strelets (2000). The negligible numerical dissipation of the pseudo-spectral code allows an unambiguous assessment of the performance of subgrid-scale models. Three explicit subgrid-scale models—dynamic Smagorinsky, σ, and truncated Navier-Stokes (TNS)—are compared to a no-model simulation (under-resolved DNS) and evaluated against benchmark DNS data focusing on two quantities of critical importance to airfoil and blade designers: time-averaged pressure (Cp) and skin friction (Cf) predictions used in lift and drag calculations. Results obtained with explicit subgrid-scale models confirm that accurate LES of laminar separation bubble flows is attainable with as low as 1% of DNS resolution, and the poor performance of the no-model simulation underscores the necessity of subgrid-scale modeling in coarse LES with low numerical dissipation.

An implicit turbulence model for low-Mach Roe scheme using truncated Navier–Stokes equations

“…According to [17], this ratio ER obtained from the theoretical dissipation, inertial, and Batchelor energy spectra should be in the range 0.007-0.009. This range has been also validated in [31] and [32] for laminar separation bubble flows. An ER larger than 0.009 indicates that the energy at small scales is excessive and should be dissipated by increasing  .…”

Wall-Modeled Large Eddy Simulation of Laminar and Turbulent Separation Bubble Flows

“…2,3 However, wall-resolved LES is limited to problems with low to moderate Reynolds numbers due to the strong scaling requirements of resolving the viscous sublayer within the boundary layer. 4 In contrast, wall-modeled LES near-wall resolution requirements scale much more weakly (if at all) with Reynolds number, extending the reach of LES to a wider range of engineering problems and aircraft configurations.…”