Modification to the k-Omega Turbulence Model for Vortically Dominated Flows

Abstract

[Abstract] Vortically dominated flows (wingtip, vortex-fin interaction, jet into cross-flow) have traditionally been difficult to accurately model using two-equation RANS (Reynolds Averaged NavierStokes) CFD tools. However RANS models provide the “workhorse” for many aerodynamic simulations. Hence, modifying/extending classical RANS turbulence models to provide the best possible vortex simulation capability is highly desirable. Here we derive by examination and asymptotic solution of a local line vortex problem a modification to the k-�& model to be more accurate for curvature/vortex dominated flows. As with other vortex/rotation sensitization approaches, e.g. Spalart and Shur (1997) 1 the modification pertains to the turbulence model source terms, however, here we suggest that both production and dissipation should be enhanced; implying that vortical flows should honor local equilibrium. That both formulations will yield similar results follows from the fact that the effective viscosity is formulated as a ratio of k/�& and for equilibrium an attendant increase in turbulent kinetic energy is accompanied by an attendant increase in �& . Using a perturbation solution for the wall layer (log-law) with curvature problems, we show that the modification derived here correctly recovers law-ofthe-wall with curvature. Tensor generalizations are suggested for the modification and limiting behavior, i.e. no effect for minimal curvature is shown. Finally the magnitude of the modification term is estimated by consideration of a closed form and simple numerical solutions for the classical driven lid cavity problem. Though preliminary, this discussion provides a more formal mathematical/physical basis for a class of turbulence model curvature sensitization modifications.