(510a) Turbulent Flows of Complex Fluids

Turbulent multiphase flows are encountered ubiquitously in the process industry. The potential for simulating these flows has primarily occurred because of advancements in computational hardware and software. However, longstanding deficiencies in low-order turbulence closure models continue to limit the practical utility of computational methods as an enabling technology. This presentation will extend a recently developed Reynolds stress closure model to an interpenetrating continua (see Manninen et al., 1996, On the Mixture Model for Multiphase Flow, Espoo, Technical Research Centre of Finland, VTT Publication 288). The normalized Reynolds stress by definition is a non-negative operator for all turbulent flows. Consequently, the eigenvalues of this operator must be non-negative in inertial frames of reference as well as in non-inertial frames-of-reference. This fundamental mathematical property cannot be compromised if turbulence modeling is to attain its full potential in predicting flows in complex geometries (see Koppula, et al. 2009, “Realizable Algebraic Reynolds Stress Closure”, Chem. Eng. Sci., 64, 4611-4624; and, Koppula, et al. , “Turbulent Energy Redistribution in Spanwise Rotating Channel Flows”, Ind. Eng. Chem. Res., 50 (15), 8905-8916). Although current CFD technology can simulate benchmark flows, the ability to predict low-order statistical properties beyond a calibrating flow is presently not possible. This weakness of turbulence modeling can be traced to the incorrect closure hypothesis that velocity fluctuations are objective vector fields. This assumption is embedded in the sub-grid closures associated with large-eddy simulations; the pressure/strain rate closures, and the class of eddy viscosity models associated with the closure of the Reynolds averaged Navier-Stokes equation. The ad hoc assumption that the Reynolds stress is an objective operator similar to the Cauchy stress is not supported by physical principles of thermodynamics and turbulence.