On Turbulent Flow Between Rotating Cylinders

The present work had as its purpose the investigation of the velocity and turbulence distributions in the turbulent flow between two co-axial cylinders, the inner of which rotated. The radius of the inner cylinder was 7-7/8". Two aspect ratios were used, one 10" to 1-1/16", the other 10" to 17/32". All velocity and turbulence measurements were made with hot-wire technique, using a special holder which reduced spindle interference to a minimum. The circumferential velocity of the inner rotating cylinder was several hundred times the critical speed for instability of the laminar flow as given by G. I. Taylor. It was found that velocity distributions in which the circumferential velocity of the fluid increases outward actually exist and cannot be explained by the shadow effect of the measuring instrument as G. I. Taylor suggested. Also the flow between the rotating cylinders is three-dimensional. The mean velocity distribution depends on whether the transfer of shear is carried out by turbulent fluctuations or by secondary motion. The regions, where the secondary motion is negligible, the mean velocity distribution is logarithmic which was shown by Dr. von Karman to be the distribution in Couette's case of turbulent flow. The analysis of the measurements indicated that the secondary flow can be described by assuming ring-shaped vortices between the cylinders. It was known that such ring-shaped vortices introduce the instability of the laminar flow (see Ref. 1); but it was not known that such vortices exist at speeds as high as several hundred times the critical speed for instability, although their shapes are distorted. The sizes of the vortices and their numbers depend on the speed of the inner cylinder. The vortices can only exist in pairs, and at certain critical speeds the flow pattern may change suddenly due to the loss or gain of a pair of vortices. At high speeds the number of the vortices tends to decrease. The two-dimensional theories for turbulent flow between rotating cylinders are discussed. They can not even be taken as a first approximation for this three dimensional vortex-ring flow