Wall-modelled large-eddy simulation of turbulent flow past airfoils

Abstract

We present large-eddy simulation (LES) of flow past different airfoils with$Re_{c}$, based on the free-stream velocity and airfoil chord length, ranging from$10^{4}$to$2.1\times 10^{6}$. To avoid the challenging resolution requirements of the near-wall region, we develop a virtual wall model in generalized curvilinear coordinates and incorporate the non-equilibrium effects via proper treatment of the momentum equations. It is demonstrated that the wall model dynamically captures the instantaneous skin-friction vector field on arbitrary curved surfaces at the resolved scale. By combining the present wall model with the stretched-vortex subgrid-scale model, we apply the wall-modelled LES approach to three different airfoil cases, spanning different geometrical parameters, different attack angles and low to high$Re_{c}$. The numerical results are verified with direct numerical simulation (DNS) at low$Re_{c}$, and validated with experiment data at higher$Re_{c}$, including typical aerodynamic properties such as pressure coefficient distributions, velocity components and also more challenging measurements such as skin-friction coefficient and Reynolds stresses. All comparisons show reasonable agreement, providing a measure of validity that enables us to further probe simulation results into aspects of flow physics that are not available from experiments. Two techniques to quantify hitherto unexplored physics of flows past airfoils are employed: one is the construction of the anisotropy invariant map, and the second is skin-friction portraits with emphasis on flow transition and unsteady separation along the airfoil surface. The anisotropy maps for all three$Re_{c}$cases, show clearly that a portion of the flow field is aligned along the axisymmetric expansion line, corresponding to the turbulent boundary layer log-law behaviour and the appearance of turbulent transition. The instantaneous skin-friction portraits reveal a monotonic shrinking of the near wall structure scale. At$Re_{c}=10^{4}$, the interaction between the primary separation bubble and the secondary separation bubble contributes to turbulent transition, similar to the case of flow past a cylinder. At higher$Re_{c}=10^{5}$, the primary separation breaks into several small separation bubbles. At even higher$Re_{c}=2.1\times 10^{6}$, near the turbulent separation, the skin-friction lines show small-scale reversal flows that are similar to those observed in DNS of the flat plate turbulent separation. A notable feature of turbulent separation in flow past an airfoil is the appearance of turbulence structures and small-scale reversal flows in the spanwise direction due to the vortex shedding behaviour.

Large-eddy simulation and modelling of Taylor–Couette flow

“…The spatial discretization of the nonlinear term utilizes a fourth-order energy-conservative scheme of the skew-symmetric form by Morinishi et al (1998), while for all other terms are discretized using a fourth-order central difference scheme. The present code framework has been verified and validated for several flows that include flow over an airfoil using both DNS (Zhang et al 2015) and wall-modeled LES (Gao et al 2019) and wallresolved LES of flow over a circular cylinder in different configurations (Cheng et al 2017 . All LES described presently were performed on the Cray XC40 supercomputer Shaheen at KAUST.…”

Large-eddy simulations of turbulent flow in a channel with streamwise periodic constrictions

“…The virtual wall model in generalized curvilinear coordinates developed by Gao et al (2019), coupled with the stretched vortex SGS model, has been strongly verified and validated in various airfoil flows. We briefly describe the essential idea of the wall model with details relegated to appendix B.…”

“…In this section, the flow configuration is described, and following that we present the essential set of equations including the boundary conditions at the virtual wall required to perform WMLES in a wall-bounded domain. The detailed derivations for the wall model in the generalized curvilinear coordinates were given by Gao et al (2019). We include the details of the wall model, the SGS model and the numerical methods in appendices for the sake of completeness.…”

“…In the present investigation, we emphasize three main objectives. First, the extended virtual wall model developed by Gao et al (2019) is applied in a periodic channel flow (both bottom and top walls). All the WMLES results are validated with experimental data wherever available.…”

Ferrofluid thin films for aerofoil lift enhancement and delaying flow separation

“…Refs. [1][2][3][4][5][6][7][8][9][10]). Suction and blowing, turbulence promoters, vortex generators, and moving walls are just some examples of the various techniques that can be found in literature.…”