v2¯/k−f Turbulence Model and Its Application to Forced and Natural Convection

We present the rationale and some validation of a version of Durbin’s elliptic relaxation eddy-viscosity model, which solves a transport equation for the velocity scale ratio v 2 ¯ / k instead of v 2 ¯ . The new model, developed independently at TU Delft and UMIST (in two variants, shows improved robustness, faster convergence and less sensitivity to grid nonuniformities. The two variants differ insignificantly in the formulation of the v 2 ¯ / k and f equations: the UMIST model endeavours to remain close to Durbin’s original one, while TUD variant introduces quasi-linear pressure strain formulation but with some further numerically beneficial simplifications. The model validation in a range of attached, separating and impinging flows with heat transfer, as well as in natural convection in a tall cavity, showed satisfactory predictions in all cases considered.