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

Abstract

Lattice Boltzmann two equation K–E turbulence model is applied to investigation of “inertial-range” velocity fluctuations in high Reynolds number flow (Re=DU/ν=1.25×106) past three-dimensional circular cylinder of diameter D. A detailed study of sensitivity of simulated flow features to variation of computational mesh size Δ revealed an almost two decades of the Kolmogorov inertial range spectrum E(k)=CKE23k-53 for the resolutions D/Δ=256 and D/Δ=128. The mean (“sub grid”) dissipation rate E calculated from the K–E 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 CK=E(k)k53/E23≈1.5-1.7 agreed well with experimental data. The quality of the low resolution simulations (D/Δ≈64) was somewhat poorer. The simulated structure functions S2(r)=(u(x+r)-u(x))2¯ and s3=|u(x+r)-u(x)|3¯ obeyed the expected scaling behavior. No clean analytic range of the second-order structure function S2(r)∝r2 has been detected and the numerically simulated S2(r) in the resolved “dissipation range” was fitted as S2∝r1.93.