Numerical Study of Flow Past Circular Cylinder Using Hybrid Turbulence Formulations

Two multiscale-type turbulence models are implemented in the PAB3D solver. The models are based on modifying Reynolds-averaged Navier-Stokes equations. The first scheme is a hybrid Reynolds-averaged Navier-Stokes and large eddy simulation model using the two-equation k epsilon model with a Reynolds-averaged Navier-Stokes and large eddy simulation transition function dependent on grid spacing and the computed turbulence length scale. The second scheme is a modified version of the partially averaged Navier-Stokes model, where the unresolved kinetic energy parameter f(k) is allowed to vary as a function of grid spacing and the turbulence length scale. Solutions from these models are compared to Reynolds-averaged Navier-Stokes results and experimental data for a stationary and rotating cylinder. The parameter f(k) varies between zero and one and has the characteristic to he equal to one in the viscous sublayer, and when the Reynolds-averaged Navier-Stokes turbulent viscosity becomes smaller than the large eddy simulation viscosity. The formulation, usage methodology, and validation example are presented to demonstrate the enhancement of PAB3D's time-accurate and turbulence modeling capabilities. The models are compared to Reynolds-averaged Navier-Stokes results and experimental data for turbulent separated flows and laminar separated flows around stationary and rotating cylinders. For a stationary cylinder, the turbulent separated case is accurately simulated using the general two-equation k epsilon turbulence model (eddy-viscosity model). PAB3D accurately predicts the drag coefficient C-D, lift coefficient C-L, and the Strouhal number St. The laminar separated case was a challenge for the Reynolds-averaged Navier-Stokes computation with an eddy-viscosity turbulence model. The Reynolds-averaged Navier-Stokes with large eddy simulation and partially averaged Navier-Stokes performed well and showed marked improvements over the Reynolds-averaged Navier-Stokes solution. The modified partially averaged Navier-Stokes model was the most accurate. For the rotating cylinder, the spin ratio varied from zero to one, and the partially averaged Navier-Stokes results were in good agreement with published experimental data. Reynolds-averaged Navier-Stokes with large eddy simulation and partially averaged Navier-Stokes capture both temporal and spatial fluctuations and produce large-scale structures that do not occur in the Reynolds-averaged Navier-Stokes simulation. The current results show promise for the capability of partially averaged Navier-Stokes in simulating unsteady and complex flow phenomena.