A New Formulation of the V2F Model using Elliptic Blending and its Application to Heat Transfer Prediction

The present paper proposes a new uncoupled formulation of the v2-f model that addresses numerical issues usually arising with such models without any loss in prediction accuracy. The model is based on elliptic blending, and unlike its “code-friendly” predecessors, it correctly predicts near-wall asymptotic behaviours without impairing its overall robustness, which brings it to the same level of stability as most standard eddy viscosity models used in industrial applications. The model is tested in cases featuring heat transfer when buoyant forces strongly influence the turbulence regime, and its anisotropy. The case of air flowing upwards inside a heated infinite pipe and a heated channel are studied. The different formulations of the v2-f model are compared with the Direct Numerical Simulations given in You et al. (2003) and Kasagi and Nishimura (1997), respectively for the pipe and the channel. With the new formulation, not only the overall predictions are improved, but also turbulence damping due to buoyancy is remarkably well predicted. Moreover, in case of relaminarisation induced by mixed convection regime, numerical robustness of the computation strongly depends on the formulation used for the v2 and f equations, and the way near-wall balance of the leading order terms is handled. The new formulation presented herein proved robust and more capable of reproducing the relaminarisation.