Development of wall models for LES of separated flows using statistical evaluations

Wall models are the key technology making possible the application of large eddy simulation to flows of engineering interest. In this paper, a new approach to the development of wall models is presented, which, in contrast to classical wall models, relies on a strong physical background and therefore is considered to be able to predict separated flows reliably. The idea is based on the concept of artificial viscosity. It requires definitions of the distribution of the eddy viscosity in the outer layer and the thickness of the viscous sublayer. The second issue is the critical aspect. Applying the artificial viscosity approach to the needs of LES wall modeling is discussed in detail and promising wall models are derived analytically. Statistical evaluations using nonlinear stochastic estimation are carried out in order to determine an important physical dependence involved in the new wall models, namely the ratio of the thickness of the viscous sublayer to the height of the wall-nearest cell. As test cases, the flow in plane channels and over a periodic arrangement of hills is considered. A posteriori results show clearly the advantages of the wall models developed, especially for separated flows.