(325f) Realizable Reynolds Stress Closures for Turbulent Flows

Direct
numerical simulations of the instantaneous Navier-Stokes equation for constant
property fluids as well as direct experimental evidence clearly show that the
Reynolds stress cannot be represented as an algebraic dyadic-valued function of
the mean strain rate, as suggested by Boussinesq more than 100 years ago. However,
the governing equation for turbulent fluctuations does show that under certain
conditions the normalized Reynolds stress can be related to a non-negative
prestress operator by an algebraic preclosure equation (Parks et al., 1998).

A
self-consistent argument supports the idea that the normalized prestress can be
expressed as an explicit algebraic function of the normalized Reynolds stress.
This hypothesis together with the preclosure equation yields a non-linear
algebraic equation for the Reynolds stress, which can be solved by successive
substitution.  In this presentation, the efficacy of the new closure for the
Reynolds stress will be illustrated for a class of benchmark flows in inertial
and non-inertial frames. The results will be compared with a realizable
algebraic closure previously developed by Shih et al., 1994.  

Parks,
S.M., K. Weispfennig, and C.A. Petty, 1998, ?An Algebraic Preclosure Theory for
the Reynolds Stress?, Phys. Fluids, 10(3), 645-653.

Shih
T.H., J. Zhu and J.L. Lumley, 1994, ?A New Reynolds Stress Algebraic Equation
Model?, NASA TM-106644.