Axisymmetric flow near a spherical obstacle placed in a spherical cavity

An attempt to model the waves near a prosthetic spherical cardiac Starr valve placed in the aorta is presented. The laminar flow is considered incompressible and Newtonian, and of fixed form. Volumetric forces are neglected, and equations for stationary flow are written, considering stagnation flow at the wall, the axial symmetry of the problem, and the hydrodynamic conditions upstream and downstream from the singularity. The calculations were made by using a finite element method. The numerical results were compared with experimental results obtained from laser velocimetry of liquid flow (vaseline) in a transparent tank with a spherical obstacle. A good match was found for Re in the range 5-100.