A new methodology for turbulencemodelers using DNS database analysisBy

1. Motivation and objectives Many industrial applications in such elds as aeronautical, mechanical, thermal, and environmental engineering involve complex turbulent ows containing global separations and subsequent reattachment zones. Accurate prediction of this phenomena is very important because separations innuence the whole uid ow and may have an even bigger impact on surface heat transfer. In particular, reattaching ows are known to be responsible for large local variations of the local wall heat transfer coeecient as well as modifying the overall heat transfer. For incompress-ible, non-buoyant situations, the uid mechanics have to be accurately predicted in order to have a good resolution of the temperature eld. Much previous work on such phenomena has used the case of the backward facing step. The sudden expansion of a channel ow indeed gives rise to a simple geometry, but one that contains complex aerodynamic features such as separation, a spreading shear layer, interaction of this shear layer with a wall, recirculation, and recovery of the reattached boundary layer. Moreover, a lot of databases are available from physical experiments to numerical simulations (DNS and LES): this makes for a good test case on which to validate turbulence models. In past years, various two-equation turbulence models have been tested and compared with the available experiments. The principal feature of models using wall functions is an underprediction of the recirculation length by about 15%. In fact, recent simulations or experiments show an important departure of the velocity pro-les from the law of the wall, not only in the recirculation, but also in the recovery region. A bad prediction of aerodynamics near the wall would have dramatic effects on predictions of heat transfer. The low-Reynolds number cases show strong anisotropies, not only in the boundary layer, but also in the spreading shear layer and in the recirculation; any linear two-equation model would fail to reproduce this important feature of the ow. For this reason, and with the aim of future studies of ows involving buoyancy, curvature, or rotation, we decided to use a Second Moment Closure (SMC) approach, which intrinsically can take into account these phenomena. The closure of the Reynolds-stress equations consists partially in nding a model for the pressure-strain correlation which acts as a redistribution term between the Reynolds-stress components. Since the Launder, Reece and Rodi, 1975 (LRR) paper , a number of models have been proposed especially to take into account speciic wall-behavior. However, all …