Formulation of the k-omega Turbulence Model Revisited

David C. Wilcox President DCW Industries, Inc. La Cañada, CA With the rapidly developing field of Detached Eddy Simulation (DES) has come renewed interest in classical Reynolds-averaged (RANS) models of turbulence. DES solves the exact Navier-Stokes equation for the largest eddies and uses a conventional turbulence model to determine Reynolds stresses in thin shear layers. The quality of the DES, of course, depends critically upon how accurate the RANS model is. This seminar presents a new version of the author's k-omega model of turbulence, which is the most widely used turbulence model of its type for Computational Fluid Dynamics applications. The revisions include addition of just one new closure coefficient and a minor adjustment to the dependence of eddy viscosity on turbulence properties. The result is a model that applies to both boundary layers and free shear flows for all speed ranges from incompressible to hypersonic. The modifications to the new k-omega model have been made using the methodology developed by Wilcox in his popular textbook entitled "Turbulence Modeling for CFD." In this methodology, boundary layers and free shear flows are first dissected and analyzed using perturbation methods and similarity solutions. All aspects of the model, including boundary conditions for rough surfaces and surfaces with mass injection, are then developed and validated. Finally, a series of computations is performed for approximately 100 different applications including free shear flows, attached boundary layers, backward-facing steps and separated flows. The test cases include flows from incompressible speeds to Mach numbers in excess of 10. All computations have been done with state-of-the-art numerical flow solvers. The improvements to the k-omega model represent a significant expansion of its range of applicability. The new model, like preceding versions, provides accurate solutions for mildly-separated flows and simple geometries such as that of a backward-facing step. The model's improvement over earlier versions lies in its accuracy for even more complicated separated flows. This seminar demonstrates the enhanced capability for supersonic flow into compression corners and hypersonic shock/boundary-layer interactions. The excellent agreement is achieved without introducing any compressibility modifications to the turbulence model.

Location: Seaver Science Library (SSL) Room 150

Audiences: Everyone Is Invited

Contact: April Mundy