Wall Confinement Effects for Spheres in the Reynolds Number Range of 30–2000

The paper studies in detail the time history of formation, evolution, and instability of the vortex ring, associated with a family of spheres in the Reynolds number range of 30–2000 and with a blockage ratio of 3–30 percent. The flow visualization results are obtained using the classical dye injection procedure. Simultaneous measurements of pressure distribution on the surface of the sphere help establish correlation between the onset of instability of the vortex ring and the surface loading. The results suggest that the influence of the Reynolds number on the surface pressure distribution is primarily confined to the range R_n < 1000. However, for the model with the highest blockage ratio of 30.6 percent, the pressure continues to show Reynolds number dependency for R_n as high as 2300. In general, effect of the Reynolds number is to increase the minimum as well as the wake pressures. On the other hand, the effect of an increase in the blockage ratio is just the opposite. The wall confinement tends to increase the drag coefficient, however, the classical dependence of skin friction on the Reynolds number C_d,f ∝ R^−1/2, is maintained. The paper also presents useful information concerning location of the separating shear layers as affected by the Reynolds number and blockage. For comparison, available analytical and experimental results by other investigators are also included. Results show that for a given blockage, separation points may move upstream by as much as 20 deg over a Reynolds number range of 100–600. In general, for a given Reynolds number, the wall confinement tends to move the separation position downstream.