An Improved Low-Reynolds-Number k – ϵ Model for Aerodynamic Flows

Abstract

Abstract A low-Reynolds-number k – ∈ model based on a new turbulent structure parameter a 1 _ N C = − u ′ v ′ ‾ / u ′ v ′ ‾ k k ${a_{1\_{\rm{NC}}}}\left({= - \left| {{{\overline {u^' v^'}} \mathord{\left/ {\vphantom {{\overline {u^' v^'}} k}} \right.} k}} \right|} \right)$ and a recalibrated wall-damping function (WDF) f μ ${f_\mu}$ is proposed and evaluated. In order to account for the effect of variation of Reynolds number on maximum value of the WDF, a ratio between two different turbulent Reynolds numbers is involved in the WDF. In addition, instead of using a constant ratio between Reynolds shear stress and turbulent kinetic energy, e. g. a 1 = 0.31, the new turbulent structure parameter a 1_NC is proposed based on several sets of direct numerical simulation (DNS) data. The deduction of near-wall asymptotic behavior is performed to prove that the new proposed model can yield a correct wall value for turbulent viscosity. The new model is validated with several well-documented flow cases, and the yielding results are in good agreement with experimental data. Moreover, three frequently used turbulence models are also involved into the comparisons and the results indicate that the new model offers remarkable improvement on the nonequilibrium flows, e. g. separated and adverse pressure gradient flows.