Lattice Boltzmann two-equation model for turbulence simulations:High-Reynolds number flow past circular cylinder

摘要

Lattice Boltzmann two equation K-S turbulence model is applied to investigation of "inertial-range" velocity fluctuations in high Reynolds number flow (Re = DU/v = 1.25 × 10~6) past three-dimensional circular cylinder of diameter D. A detailed study of sensitivity of simulated flow features to variation of computational mesh size A revealed an almost two decades of the Kolmogorov inertial range spectrum E(k) = C_Kε~(2/3)k-_(3/5) for the resolutions D/△ = 256 and D/△ = 128. The mean ("sub grid") dissipation rate ε calculated from the κ-ε equations and the one directly from the numerically resolved velocity field were close to each other. Thus, the model automatically satisfies the constant-energy-flux-constraint in inertial range. The computed Kolmogorov constant Cκ = E(K)k_(5/3)/ε_(2/3) 1.5 - 1.7 agreed well with experimental data. The quality of the low resolution simulations (D/A ≈ 64) was somewhat poorer. The simulated structure functions S2( r) = (u(x + r) - u(x))~2 and s_3 = |u(x + r) - u(x)|~3 obeyed the expected scaling behavior. No clean analytic range of the second-order structure function S_2(r) α r~2 has been detected and the numerically simulated S_2( r) in the resolved "dissipation range" was fitted as S_2 α r~(1.93).