Low-Reynolds-number k-ε models for separated and reattaching flows

Abstract

Two versions of k-ε turbulence model are proposed to compute turbulent separated and reattaching flows. In the first version, a nonlinear low-Reynolds-number $k-ε$ model is developed. In this model, the limiting near-wall behavior and nonlinear Reynolds stress representations are incorporated. Emphasis is placed on the adoption of $R_y (\equiv \sqrt{k} y /ν)$ instead of $y^+ (\equiv u_{τ}y /ν)$ in the low-Reynolds-number model for predicting turbulent separated and reattaching flows. The non-equilibrium effect is examined to describe the recirculating flows away from the wall. In the second version, a new $k-ε-f_{μ}$ turbulence model is proposed, which can be applied to complex flows involving multiple surfaces. The wall-damping function $f_{μ}$ is obtained by solving the elliptic $f_{μ}$ equation. Emphasis is placed on the formulation of the $f_{μ}$ equation in a general coordinate system. The near-wall effect, without reference to distance, is fully incorporated in this model. The non-equilibrium effect is examined to describe recirculating flows away from the wall. A modified model of the ε-equation is developed to account for the local anisotropy in strongly strained turbulent flows. A finite volume code based on SIMPLEC is developed for calculation of steady and incompressible flows with complex irregular boundaries. In this code, a third-order accurate convective scheme is implemented for non-uniform grid and three-dimensional version of strongly implicit procedure (SIP) is developed. The present models are validated by solving the benchmark problem of turbulent flow behind a backward-facing step and other complex turbulent flow. The predictions of the present model are cross-checked with the existing measurements and DNS data. The model performances are shown to be generally satisfactory.