Turbulence modeling for flows around convex features giving rapid eddy distortion

Abstract

Reynolds averaged Navier–Stokes model performances in the stagnation and wake regions for turbulent flows with relatively large Lagrangian length scales (generally larger than the scale of geometrical features) approaching small cylinders (both square and circular) is explored. The effective cylinder (or wire) diameter based Reynolds number, Re W ⩽ 2.5 × 10 3. The following turbulence models are considered: a mixing-length; standard Spalart and Allmaras (SA) and streamline curvature (and rotation) corrected SA (SARC); Secundov’s ν t-92; Secundov et al.’s two equation ν t– L; Wolfshtein’s k– l model; the Explicit Algebraic Stress Model (EASM) of Abid et al.; the cubic model of Craft et al.; various linear k– ε models including those with wall distance based damping functions; Menter SST, k– ω and Spalding’s LVEL model. The use of differential equation distance functions (Poisson and Hamilton–Jacobi equation based) for palliative turbulence modeling purposes is explored. The performance of SA with these distance functions is also considered in the sharp convex geometry region of an airfoil trailing edge. For the cylinder, with Re W ≈ 2.5 × 10 3 the mixing length and k– l models give strong turbulence production in the wake region. However, in agreement with eddy viscosity estimates, the LVEL and Secundov ν t-92 models show relatively little cylinder influence on turbulence. On the other hand, two equation models (as does the one equation SA) suggest the cylinder gives a strong turbulence deficit in the wake region. Also, for SA, an order or magnitude cylinder diameter decrease from Re W = 2500 to 250 surprisingly strengthens the cylinder’s disruptive influence. Importantly, results for Re W ≪ 250 are virtually identical to those for Re W = 250 i.e. no matter how small the cylinder/wire its influence does not, as it should, vanish. Similar tests for the Launder–Sharma k– ε, Menter SST and k– ω show, in accordance with physical reality, the cylinder’s influence diminishing albeit slowly with size. Results suggest distance functions palliate the SA model’s erroneous trait and improve its predictive performance in wire wake regions. Also, results suggest that, along the stagnation line, such functions improve the SA, mixing length, k– l and LVEL results. For the airfoil, with SA, the larger Poisson distance function increases the wake region turbulence levels by just under 5%.