Development and Application of Rotation and Curvature Correction to Wray-Agarwal Turbulence Model

Computational Fluid Dynamics (CFD) is increasingly playing a significant role in the analysis and design of aircrafts, turbomachines, automobiles, and in many other industrial applications. In majority of the applications, the fluid flow is generally turbulent. The accurate prediction of turbulent flows to date remains a challenging problem in CFD. In almost all industrial applications, Reynolds-Averaged Navier-Stokes (RANS) equations in conjunction with a turbulence model are employed for simulation and prediction of turbulent flows. Currently the one-equation (namely the Spalart-Allmaras (SA) and Wray-Agarwal (WA) and two-equation (namely the k-ε and Shear Stress Transport k-ω) turbulence models remain the most widely used models in industry. However, improvements and new developments are needed to improve the accuracy of the turbulence models for wall bounded flows with separation in the presence of adverse pressure gradients, and for flows with rotation and curvature (RC) such as those encountered in turbomachinery, centrifugal pumps and the rotating machinery in other industrial devices. The goal of this research is to enable the eddy-viscosity type turbulence models to accurately account for the rotation and curvature effects. To date, there have been two approaches for inclusion of RC effects in turbulence models, which can be categorized as the “Modified Coefficients Approach” which parameterizes the model coefficients such that the growth rate of turbulent kinetic energy is either suppressed or enhanced depending upon the effect of system rotation and streamline curvature on the pressure gradient in the flow and the “Bifurcation Approach” which parameterizes the eddy-viscosity coefficient such that the equilibrium solution bifurcates from the main branch to decaying solution branches. In this research, the uncertainty quantification (UQ) is applied to examine the sensitivity of RC correction coefficients and the coefficients are modified based on the UQ analysis to improve the model’s behavior. Both these approaches are applied to the widely used turbulence models (SA, SST k-ω and WA) and they show some improvement in predictions of turbulent flow in all benchmark test cases considered, namely the flow in a 2D curved duct, flow in a 2D U-turn duct, fully developed turbulent flow in a 2D rotating channel, fully developed turbulent flow in a 2D rotating backward-facing step, flow in a rotating cavity, flow in a stationary and rotating serpentine channel, flow in a rotor-stator cavity and in a hydrocyclone as well as two wall-unbounded turbulent flow cases. All the simulations are conducted using the commercial software ANSYS Fluent and the open source CFD software OpenFOAM. The success of this research should enhance the ability of the RANS modeling for more accurate prediction of complex turbulent flows with rotation and curvature effects. In addition to the RANS modeling of RC effects, a new DES model incorporating the WA2017m-RC turbulence model (referred to as the WA2017m-RC-DES model) is developed and validated against experimental and DNS data. Further improvements are obtained with the DES model in some test cases