The near wall mixing length formulation revisited

The calculation of transport phenomena in boundary layers, pipe or duct ̄ows can be easily accomplished by a simple, zero order, mixing length formulation. The application of this model in simple engineering ̄ows, i.e., ̄ows without recirculation or asymmetry, is still widely extended because of its simplicity and its ability to match experimental results at the same degree than more elaborated models. Most of the mixing-length formulations for near-wall ̄ows use a damping factor to decrease rapidly the characteristic length as the wall is approached. The most popular damping factor is the one suggested by van Driest [1], which has been modi®ed extensively to accommodate di€erent wall conditions [2±6]. A yet unresolved and apparently intrinsic shortcoming of the mixing length model is that it cannot predict properly the turbulent viscosity pro®le …ntAy† in the near-wall region. The purpose of the current study is to demonstrate that the mixing length theory can be formulated consistently with available information of the turbulent viscosity pro®les near the wall and to propose a mixing length equation valid for momentum and heat transfer across turbulent wall-bounded ̄ows. This formulation could also improve large-eddy simulations (LES) carried out with subgrid models, where the length scale in the direction normal to the wall is modi®ed with a damping factor to improve numerical predictions (see for example [7]).