Date/Time*/Room: Friday (3/30/2001) at 2:00 pm in 487 Pickard Hall
Thomas S. Lund,
Department of Mechanical and Aerospace Engineering,
University of Texas at Arlington
``A compact and complete tensor basis for use in turbulence modeling''Abstract: Statistically-based simulations methods for turbulent flow rely on "turbulence models" that account for transport associated with the fluctuations removed by the averaging operation. Due to the non-linear, stochastic nature of the Navier-Stokes equations, it is not possible to write closed equations for the missing transport terms. Thus turbulence modeling is often based on empiricism, physical insight, or on merely ad hoc assumptions. The majority of contemporary models are based on a gradient transport hypothesis that is derived from an analogy with molecular transport. These models postulate that the turbulent stress tensor is directly proportional to the strain rate tensor, which implies that they share the same principle directions. High resolution, direct numerical simulation data show that this condition is not met in actual turbulent flows. In order to remedy this defect, models have been proposed that are constructed from a tensor basis formed by various products of the strain and rotation rate tensors. Although the Caley-Hamilton theorem implies that the tensor basis should contain 11 independent terms, recent work has shown that more compact representations are possible. It will be shown that the minimum basis contains only 8 terms. Furthermore, it will be shown that bases containing as few as 6 terms can be constructed and that these will provide a complete representation except for one or two isolated highly-unusual strain and rotation rate configurations. The implications of the compact representation for turbulence modeling will be discussed and some computational results using the new models will be presented.