(312h) Realizable Algebraic Reynolds Stress Model for Single Phase and Multiphase Turbulent Flows

The ability to predict the low-order statistical properties of single-phase and multiphase turbulent flows is critical for engineering processes such as mixing and separation of immiscible phases. Although instantaneous phase-averaged equations have been successfully developed over the past thirty years for multiphase fluids (Drew and Passman, 1999), the ensemble-averaged equations for turbulent flows are statistically unclosed. Many researchers use a multiphase "eddy" viscosity model to relate the Reynolds stress to the local mean strain rate (see Manninen et al., 1996), but this approach is unsuitable for processes where phase separation and mixing by local pressure differences is a significant phenomena. Parks et al. (1998) and Weispfennig et al. (1999) have identified a closure for the Reynolds stress that is realizable for a wide class of turbulent flows, which is fundamentally different than the algebraic realizable closure of Shih et al. (1995). The new approach, yields a non-linear algebraic relationship between the turbulent momentum flux and a non-negative, symmetric dyadic-valued operator that depends on the mean velocity gradient and a relaxation time associated with the local space-time structure of the turbulence. Benchmark experimental and computational data for single-phase fluids are used to determine the closure parameters in the theory. The presentation will summarize the new approach and its extension to multiphase turbulent flows.

Drew, D.A. and S. L. Passman, 1999, Theory of Multicomponent Fluids, Applied Mathematical Series, Volume 135, Springer, New York.

Manninen, M., V. Taivassalo, and S. Kallio, 1996, ?On the Mixture Model for Multiphase Flow?, Technical Research Center of Finland, VTT Publications 288, 67 pages.

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

Shih, T-H, W.W. Liou, A. Shabbir, Z. Yang, and J. Zhu, 1995, "A New k- Eddy Viscosity model for high Reynolds Number Turbulent Flows", Computers Fluids, Vol 24, No.3, 227-238.

Weispfennig, K., S. M. Parks, and C. A. Petty, 1999, ?Isotropic Prestress for Fully Developed Channel Flows?, Physics of Fluids, 11(5), 1262-1271.