This talk presents a setup that we have designed to particularly investigate the effects regarding the free rotation of a spherical object in a flow channel in 2D and 3D.
The interaction between a fluid flow and rigid bodies appears in many physical applications. The flow around a free rigid body causes both displacement and rotation of that body, via the forces and torque exerted from the fluid onto the body. Conversely, the motion of the body causes changes in the flow. The complexity that comes with coupling models for fluid and elastic or rigid bodies and the numerical challenges due to evolving geometrical domains make reliable and benchmark computations very necessary though difficult to perform. This talk presents a setup that we have designed to particularly investigate the effects regarding the free rotation of a spherical object in a flow channel in 2D and 3D. This setup connects to the well known benchmark of flow past a cylinder  and is accessible to standard CFD software.
Figure 1: Spatial configuration of the 3D setup.
In this setup the flow applies a torque force on the object. The induced rotation then couples back to the flow via the boundary conditions. We discuss the governing equations of this fluid structure interaction problem; namely the incompressible Navier-Stokes equations and the relevant realizations of Newton’s second law that relates the rotation of the rigid body to the forces acting on it. The proposed benchmark configurations comprise two and three spatial dimensions and quasi-stationary (low Reynolds-number) and periodic (high Reynolds-number) regimes. For a discretization independent comparison of the results, we also propose significant, nondimensionalized characteristic values.
The benchmark cases were solved numerically with various approaches and software tools so that the computed characteristic values could be reported within in a reasonable confidence interval.
In this talk, we introduce the mathematical model, discuss the characteristic and challenges of the benchmark cases, and present the various implementation and their particular advantages. The codes that were reported on in our work  as well as the raw data and postprocessing routines are available  for further exploration and reproduction.
M Schäfer and S Turek: Benchmark computations of laminar flow around a cylinder. (With support by F. Durst, E. Krause and R. Rannacher) Flow Simulation with High-Performance Computers II. DFG priority research program results 1993-1995, 1996.
H von Wahl et al.: Numerical benchmarking of fluid-rigid body interactions. Computers & Fluids, 2019.