ALBERT

Description: Measurements have been made of the Couette flow in the annular space between concentric cylinders with a radius ratio of 1.5, the outer cylinder being held stationary and the inner one rotated at speeds to give Taylor numbers in the range 1.0 × 104−2.3 × l06 times the critical value for first instability of the steady viscous flow. Mean velocities have been measured both with Pitot tubes and with linearized hot-wire anemometers, and turbulent intensities and stresses, frequency spectra and space-time correlations have been obtained using single hot-wire anemometers of X-form and linear arrays of eight single-wire anemometers. For Taylor-number ratios to the critical number less than 3 × l05, the most prominent feature of the flow is a system of toroidal eddies, encircling the inner cylinder and uniformly spaced in the axial direction with nearly the separation of the Taylor vortices of the viscous instability. They are superimposed on a background of irregular motion and, except within the thin wall layers, the toroidal eddies contribute more to the total intensity. With increase of rotation speed, the toroidal eddies lose their regularity, and they cannot be clearly distinguished at Taylor-number ratios beyond 5 × l05.The change of flow type from quasi-regular toroidal to fully irregular turbulent takes place over an extensive range of Taylor-number ratio centred near 3 × l05, and it may be linked with changes in the thin wall layers that separate the flow boundaries from the central region of nearly constant circulation. For ratios over 5 × l05, an appreciable part of the wall layers is comparatively unaffected by flow curvature and has a logarithmic distribution of mean velocity similar to that found in channel flows. It is suggested that the motion in the wall layers changes from a set of Gortler vortices characteristic of curved-wall flow to the more irregular motion found on plane walls, causing the toroidal eddies to break into sections of length ranging from a considerable fraction of the flow perimeter to nearly the separation of the cylinders. Changes in the frequency spectra of the radial and azimuthal velocit'y fluctuations are consistent with such a change.

Description: Measurements have been made in flow between concentric cylinders with only the inner one rotating, for Reynolds numbers (based on flow gap) from 17000 to 120000, corresponding to Taylor numbers from 8x107to 4x109. At the lower speeds (Reynolds numbers less than 30000), the large scale motion consists of toroidal eddies, highly uniform in spacing and intensity and convected by a slow axial flow past fixed sensors. By synchronizing an external oscillator with the passage frequency, flow velocity and small scale turbulent intensity may be sampled at defined stages of the passage cycle and averaged to provide maps of the velocity fields and the associated distributions of small scale intensity and Reynolds stress. At higher speeds, the passage of toroidal eddies becomes too irregular to establish the passage cycle, but, by comparing the velocity fluctuations from four inclined hot wires placed near the outer cylinder, the current location of large scale flow separation from the outer cylinder can be approximately determined. Statistics of the temporal variations of the location show that the large scale motion still approximates to the toroidal form, but that there are azimuthal variations of separation position and velocity that indicate a change from toroidal to helical eddies. Conditional averages of flow velocity and small scale turbulent intensity, based on relative distance from the position of flow separation, are very similar in form and magnitude to phase selected averages obtained at lower speeds. The considerable changes in the large scale motion that occur as the Reynolds number increases from 300 to 1200 times the critical value are believed to arise from increase in the ‘turbulent Taylor number’ of the central flow, based on variation of angular momentum and on the eddy diffusion coefficients for linear and angular momentum. Effects on the motion of the slow axial flow, always less than 1 % of the peripheral flow velocity, are also discussed. © 1984, Cambridge University Press. All rights reserved.