(320d) Beyond Boussinesq: A Realizable Closure Model for the Reynolds Stress

The Reynolds-averaged Navier-Stokes (RANS-) equation for constant property Newtonian fluids is unclosed due to the explicit appearance of the normalized Reynolds (NR-) stress and the turbulent kinetic energy. A closure model for the normalized Reynolds stress (either algebraic or differential) must produce non-negative operators for all turbulent flows, including flows in rotating frames-of-reference. In this presentation, a recently developed algebraic closure for the NR-stress, referred to as the URAPS-closure (see Koppula et al., 2009, 2011), is used to calculate the influence of frame rotation on the components of the NR-stress for homogeneous and for inhomogeneous flows. The URAPS closure is formulated as a mapping of the NR-stress into itself and is, thereby, a non-negative operator for all turbulent flows. Unlike closure models based on an eddy-viscosity theory, the new closure predicts the redistribution of the turbulent kinetic energy among the three components of the fluctuating velocity for statistically stationary rotating channel flows.

Koppula, K.S., A. Bénard, and C. A. Petty, 2009, “Realizable Algebraic Reynolds Stress Closure”, 2009, Chemical Engineering Science, 64, 22, 16 November 2009, 4611-4624.

Koppula, K. S., A. Bénard, and C. A. Petty, 2011, “Turbulent Energy Redistribution in Spanwise RotatingChannel Flows”, Ind. Eng. Chem. Res., pubs.acs.org/IECR, dx.doi.org/ 10.1021/ie1020409.