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

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 ) = C K E 2 3 k - 5 3 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 C K = E ( k ) k 5 3 / E 2 3 ≈ 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 S 2 ( 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 S2(r) ∝ r2 has been detected and the numerically simulated S2(r) in the resolved “dissipation range” was fitted as S2 ∝ r1.93.