Vortical flow. Part 2. Flow past a sphere in a constant-diameter pipe

This paper describes an experimental and numerical investigation of concentrated vortex flow past a sphere in a constant-diameter pipe. As the swirl was increased at a fixed sphere Reynolds number of approximately 1100, the length of the mean downstream separation bubble decreased. For a small range of swirl intensity, an almost stagnant separation bubble formed on the upstream hemisphere. A further increase in swirl caused the bubble to become unstable and develop into an unsteady spiral disturbance. At very high swirl the downstream separation bubble was eliminated and an unsteady separation zone extended far upstream. Calculations of the vorticity field from surface fits to azimuthal and axial velocity data suggest that upstream separation is caused by the distortion of vortex filaments in the diverging flow approaching the sphere. Numerical solutions of steady inviscid axisymmetric flow past a sphere exhibit a fold in the vicinity of upstream separation. It is suggested that this accounts for the extreme sensitivity encountered in the experiments.