A simplified v²–f model for near‐wall turbulence

Abstract

SUMMARYA simplified version of the v 2 -f model is proposed that accounts for the distinct effects of low-Reynolds number and near-wall turbulence. It incorporates modified C (1,2) coefficients to amplify the level of dissipation in non-equilibrium flow regions, thus reducing the kinetic energy and length scale magnitudes to improve prediction of adverse pressure gradient flows, involving flow separation and reattachment. Unlike the conventional v 2 -f , it requires one additional equation (i.e. the elliptic equation for the elliptic relaxation parameter f ) to be solved in conjunction with the k-model. The v 2 scaling is evaluated from k in collaboration with an anisotropic coefficient C and f . Consequently, the model needs no boundary condition on v 2 and avoids free stream sensitivity. The model is validated against a few flow cases, yielding predictions in good agreement with the direct numerical simulation (DNS) and experimental data.

Limiters and wall treatments in applied turbulence modeling

“…The same equation ( 27) was invoked with f playing the role of damping function for the k-ε model (Rahman and Siikonen 2007). Similar use of this equation has been made by others (Langer et al 2005).…”

Elliptic Blending with One-Equation Model

“…In particular, many turbulence models usually include the distance to the wall as an explicit parameter which hinders them from simulating complex flows involving multiple surfaces; the wall distance in this case becomes cumbersome to be defined accurately. The elliptic relaxation method is an excellent way to avoid the use of wall-distance in an eddy-viscosity turbulence model [1][2][3][4][5][6][7][8][9][10]. The wall blocking is governed by an elliptic partial differential equation (i.e., the Helmholtz-type equation) which accounts for non-local near-wall effects.…”