Hybrid spatially-evolving DNS model of flow past a sphere

Direct numerical simulation in the form of a hybrid spatially-evolving model is used to simulate the turbulent wake behind a towed sphere at a subcritical Reynolds number, Re=U∞D/ν=3700, where U∞ is the free stream velocity, D is the diameter of the sphere, and ν is the viscosity. The sphere is not present in the model domain but realistic inflow conditions are obtained from a body-inclusive simulation. As such, the model is a hybrid of both body-inclusive and body-exclusive simulations which greatly reduces computational cost and allows for downstream study of wake dynamics. Inlet conditions are extracted from three locations in the streamwise, x1, direction namely x1/D=3,6, and 10, to investigate the sensitivity of the results to extraction position. Simulations are performed considering both unstratified and stratified fluids with Froude numbers, Fr=U∞/ND=∞,3, and 1 where N is the buoyancy frequency of the background, to explore the model effectiveness for varying levels of stratification. It is found that a strategic choice in extraction location is required in order to accurately capture the flow physics. Simulation results show less agreement with the body-inclusive simulations at extraction location x1/D=3 than with x1/D=6 or x1/D=10. Mean wake decay of the hybrid model simulations is consistent with the body-inclusive simulations. The layered flow structure of the stratified wake is captured well while phase lines indicating internal wave propagation are clearly observed in vorticity contours and are consistent with the body-inclusive simulations. Accurate turbulent kinetic energy (t.k.e.) capture is noted for all cases. Additional simulations with higher resolution grids were performed and analyzed to demonstrate the impact of grid resolution on turbulence statistics. Examination of t.k.e. budget terms indicates that improved grid resolution results in better agreement with the body-inclusive simulation near the inlet where the resolution disparity between the hybrid and body-inclusive simulations is most significant. The hybrid model is shown to be a robust tool for the study of turbulent wake dynamics.