Numerical Study of Flow Past a Circular Cylinder Using Hybrid Turbulence Formulations

Abstract

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 ke 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 be 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 ke 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.