Velocity Profiles in Steady and Unsteady Rotating Flows for a Finite Cylindrical Geometry

Experimental determinations have been made of tangential velocity profiles in liquid water under conditions of steady and unsteady rotating flows for low (4 to 5) and high (1000) Reynolds numbers. Velocity measurements were performed by using the laser-Doppler velocimeter in various finite cylindrical arrangements with one stationary and one rotating disk. The steady velocity profiles (at appreciable distances from the cylindrical wall) have been found to be in excellent agreement with theoretical predictions based on solutions of the requisite boundary-value problems for cylinders of infinite radius. The observed unsteady velocity profiles (at appreciable distances from the cylindrical wall) for impulsive slow-down and impulsive start-up at small Reynolds numbers (R) are well accounted for by using a linearized theory for an axisymmetric configuration of infinite radial extent. For large values of R, no large differences were observed in the characteristic slow-down times at different radial locations (away from the cylindrical wall). The experimentally observed tangential velocity profiles for impulsive start-up show characteristic development times that are sensitive functions of the finite radial extent used in the geometric arrangement. Speed-up times decrease as the radial distance from the point of observation to the confining cylinder is reduced. In geometric arrangements in which only the cylinder radius was varied, characteristic development times for tangential motion were found to be a function of the dimensionless ratio measuring the radial distance to the wall divided by the cylinder radius.