Surface Signature of Flow Past a Sphere at Moderate Reynolds Numbers

The incompressible viscous flow past a sphere is investigated numerically at moderate Reynolds numbers. Periodic vortex shedding happens at these Reynolds numbers. The primary objective is to identify the surface signature when the wake reaches the surface. The numerical method is a direct numerical simulation based on finite volume method using open-sourced code OpenFOAM. This work can contribute to the detection of underwater obstacles. The unsteady flow is calculated at Reynolds number of 300. The flow shows a planar symmetric pattern with vortex shedding. When Reynolds number increases to 500, the flow becomes more chaotic and loses its planar symmetry. At Reynolds number of 500, highly organized periodic surface signatures appear on the shear-free surface when the sphere is near the surface. The signatures are identified as the cold regions with hot edges when constant heat flux is performed on the surface. There is a pair of vortices with opposite rotating directions inside the signature, which can be visualized by passive Lagrangian particles. The incompressible flow acts like compressible flow on the surface because the surface divergence and convergence happen. At Reynolds number of 500, the cylindrical vortex sheet is reorganized into vortex rings due to complex instabilities effects. The periodic vortex rings attach the surface to form the periodic thermal surface signatures