Computation of the Flow Over a Sphere at Re = 3700: A Comparison of Uniform and Turbulent Inflow Conditions

Abstract

A highly resolved computation o f the flow past a sphere at Reynolds number Re = 3700 using a finite element method (FEM)-based residual-based variational multiscale (RBVMS) formulation is performed. Both uniform and turbulent inflow conditions are considered with the uniform flow case validated against a previous direct numerical sim ulation (DNS) study. We find that, as a result o f adding free-stream turbulence o f moder ate intensity, the drag force on the sphere is increased, the length o f the recirculation bubble is reduced dramatically, and the near-wake turbulence is significantly more ener getic than in case o f uniform inflow. In the case o f uniform inflow, we find that the solu tion exhibits low temporal frequency modes, which necessitate long-time simulations to obtain high-fidelity statistical averages. Subjecting the sphere to turbulent inflow removes the low-frequency modes from the solution and enables shorter-time simulations to achieve converged flow statistics.

Immersogeometric analysis of compressible flows

“…The flow around a sphere at Reynolds numbers Re = 100 and 300 for laminar flow and Re = 3700 for turbulent flow constitute canonical test cases, for which a large number of reference results are available in the literature (see, e.g., [130][131][132][133][134] for laminar flow and [135][136][137] for turbulent flow).…”

“…The shedding. For the turbulent case, we record the drag history over time, and use the Lomb-Scargle periodogram technique to extract the frequency (see [137] for details).…”

“…For the turbulent case at Re = 3700, we consider only one mesh resolution design for generating the immersogeometric and corresponding boundary-fitted meshes. The mesh design is based on the experience reported by Bazilevs et al [137], in which the same VMS formulation with weakly enforced boundary conditions presented in Section 2.1.3 was employed. Note that prismatic elements were used for the boundary layer mesh in [137].…”

“…The mesh design is based on the experience reported by Bazilevs et al [137], in which the same VMS formulation with weakly enforced boundary conditions presented in Section 2.1.3 was employed. Note that prismatic elements were used for the boundary layer mesh in [137]. In our cases, for the sake of consistency between immersogeometric and boundary-fitted meshes, only tetrahedral elements are considered and we keep the element heights in the boundary layer comparable to those reported in [137].…”

“…Note that prismatic elements were used for the boundary layer mesh in [137]. In our cases, for the sake of consistency between immersogeometric and boundary-fitted meshes, only tetrahedral elements are considered and we keep the element heights in the boundary layer comparable to those reported in [137].…”