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

Abstract

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 Rn < 1000. However, for the model with the highest blockage ratio of 30.6 percent, the pressure continues to show Reynolds number dependency for Rn 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 Cd,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.

The formation mechanism and shedding frequency of vortices from a sphere in uniform shear flow

“…There are six parameters which govern the vortex shedding frequency of a sphere in a uniform shear flow: the diameter of the sphere d, the approach velocity at the sphere centre U, the transverse velocity gradient of the shear flow G, the kinematic viscosity of the fluid v, the projected area of the sphere S and the cross-sectional area of the test section C. Therefore, the functional relationship for the frequency& of vortex shedding from a sphere in uniform shear flow can be written as dimensional body (Modi & Akutsu 1984). By introducing the Reynolds number Re and the shear parameter K, which are defined by…”

Numerical investigation of three-dimensionally evolving jets under helical perturbations

“…Whereas inviscid mechanisms have been demonstrated to dominate the jet's large-scale evolution, the Reynolds number does have crucial importance in determining the resulting organized motions of the wake. For Reynolds numbers lower than 400, the vortex sheet coming off a sphere has been observed to roll up into ring-like vortices (Taneda 1956;Modi & Akatsu 1984). With increasing Reynolds number, a breakdown in the individuality of vortex structures occurs while the roll-up occurs closer to the sphere.…”

Drag and wakes of freely falling 60° cones at intermediate Reynolds numbers

“…11. It may be noted that unlike the freely falling 60°cones, the singlesided shedding of hairpin vortices was observed for both fixed 13,17,18,30,[34][35][36] and freely falling 21 solid spheres.…”

“…The cones were machined and polished carefully so as to be regarded as hydraulically smooth. The dimensions of the cones were sufficiently small so that the effect of wall confinement will be insignificant in the drag measurement 9-12 and flow visualization, 13 respectively. About an hour was spent to settle the water in the tank before each test.…”