RANS and LES/RANS Simulations of Flow Over an Dynamically Pitching Naca0012 Airfoil

Abstract

The hybrid Large-Eddy/Reynolds-Averaged Navier-Stokes (LES/RANS) and RANS simulations are used to investigate the properties of subsonic flow over NACA 0012 airfoils undergoing static and dynamic stall conditions (M=0.1, α=16.7°, Re c =1.0×10 6 ). In the simulations of NACA 0012 airfoil at static stall case, Menter's SST model predicts an attached flow at the leading edge, whereas the Gieseking's LES/RANS model on a coarser mesh predicts a massively separated flow characterized by the stabilization of a detached leading edge vortex near the trailing edge. The predictions by Gieseking's model on a coarse mesh agree closely with PIV measurements of mean velocity, the Reynolds axial stress and the Reynolds normal stress, but over-predict the magnitude of the Reynolds shear stress. However, Gieseking's model on a fine mesh predicts a more attached flow because the under-resolved LES on the fine mesh (but not fine enough as required in a wall-resolved LES) fails to reproduce the cascade process at the smaller scale and results in an overlyenergetic boundary layer near leading edge which resists and delays the separation. In 3D simulations of dynamic stall case where the NACA 0012 airfoil is dynamically pitching about its quarter-chord at a reduced frequency, k r =0.1, Gieseking's model on a coarse mesh in spanwise direction correctly predicts response of the massive separation at static stall angle of 16.7° during downstroke pitching, but it also predicts some leading edge separation which is not present in the experiment during upstroke pitching. Mesh refinement in the spanwise direction helps reducing the level of leading edge separation during upstroke pitching, but results in an under-separated flow solution for downstroke response, which is consistent with what happens in the static stall case and the reason is also similar. By introducing a grid correction function in the definition of outer layer turbulence length scale, Salazar's fix takes grid resolution into consideration while determining the RANS to LES transition. The inclusion of Salazar's fix to Gieseking's model delays the leading edge separation during upstroke pitching, but it also introduces a too-attached flow for downstroke response. Nomenclature c = airfoil chord C N = model constant for blending function in Gieseking's model C s = model constant (sharpening factor) in Gieseking's model  C = model constant in Menter SST turbulence f = pitching frequency k = turbulent kinetic energy k r = reduced frequency L = representative length scale l inner = inner layer turbulent length scale l outer = outer layer turbulent length scale M = Mach number = freestream pressure Re c = chord Reynolds number S = magnitude of strain rateAIAA SciTech T = temperature u, v, w = velocity in x, y, z directions = freestream velocity x/c = axial distance over axial chord = angle of attack = blending function for LES/RANS eddy viscosity = density = ratio of turbulence length scale = molecular viscosity = eddy viscosity = specific turbulence dissipation rate = magnitude of...

Development of a new LES/RANS formulation

“…Static-stall predictions for the Aerospatiale 'A-Airfoil' [27], reported in [24], were quite reasonable and similar to those obtained by Mary and Sagaut [35] using a wall-resolved LES. Dynamic stall calculations [25,26], performed for an experiment of Pruski, et al [29] involving pitching of a NACA 0012 airfoil, never achieved this level of success. While other factors (spanwise domain extent, grid resolution, tunnel blockage effects) certainly influenced predictive capability, the fact that the ensemble-averaging strategies employed (variants of weighted exponential time-averaging methods) could not operate properly for a pitching airfoil led to additional uncertainties that could not be completely resolved…”

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