Measured distortion of a laminar circular Couette flow by end effects

Abstract

Measurements at moderately large Reynolds numbers in a finite laminar circular Couette flow show that the tangential motion near the axial plane of symmetry is two-dimensional, within experimental accuracy, but is nevertheless strongly modified by end conditions. During the course of an experimental investigation of transition in circular Couette flow (Van Atta 1966) it became necessary to measure very accurately the laminar velocity profile midway between the ends of a finite rotating-cylinder apparatus. The formal object of the measurements was to establish a known flow for calibration of a hot-wire probe array for response to changes in pitch angle, yaw angle, and speed. The simplest laminar motion which could conveniently be set up in the apparatus at hand was a flow with the inner cylinder a t rest and with the outer cylinder and end plates rotating together. The measurements were made at relatively high laminar Reynolds numbers, and they showed the influence of the end plates on the tangential flow field to be unexpectedly large. The experiment is therefore reported here for its intrinsic interest as an example of a three-dimensional secondary flow in a rotating fluid.The experimental technique was to carry out a simultaneous flow survey and probe calibration by holding the cylinder speed constant and traversing a hot-wire probe radially in the initially unknown flow. Electrical signals from the probe were then extrapolated to the far wall, where the fluid velocity with respect to the probe was accurately known. Several such extrapolations at different fixed cylinder speeds provided a relationship between velocity and voltage for use away from the wall. To keep the relative velocity at the probe as large as possible, the outer half of the flow was surveyed from the stationary inner cylinder, and the inner half of the flow was surveyed from the rotating outer cylinder. In both cases, however, the wires were supplied with current through slip rings. The same hot wires, slip rings, cables, and instrumentation were used through the measurements, which extended over a period of several weeks.The platinum-rhodium hot wires used had a diameter of 0.0001in. and a length of about 0.04 in, and were operated in the constant-temperature mode (hot resistance/cold resistance about 1.15). All wires were mounted parallel to the axis of rotation of the cylinders. Two wires on a single probe were traversed t Now at University of California at San Diego. 33Fluid Mech. 25

Stability and turbulent transport in Taylor–Couette flow from analysis of experimental data

“…This puzzling aspect has been explained by Coles and Van Atta [10]; in absence of circulation, in stationary state, the torque exerted at the inner and outer cylinder must balance. In the presence of circulation, the transport of fluid toward or away from the plane of symmetry induces an imbalance of the two torques, which ceases to be equal.…”

“…This circulation depends on the ratio of radii and velocities, and on the top and bottom boundary conditions [2,9]. Its signature is easy to detect by profile monitoring, or by measuring the difference between the torque at the inner and outer cylinder [10]. Of course this circulation is both radial and vertical and it varies along the cylinders axis.…”

Highly turbulent Taylor-Couette turbulence

“…For laminar flow e.g. for purely outer cylinder rotation this clearly is the case (Coles & van Atta [74], Hollerbach & Fournier [89]). However, we argue that the strong turbulence destroys such an axial dependence of the flow field.…”

“…for pure outer cylinder rotation -this clearly is not the case, as has been known since G. I. Taylor, see e.g. the classical experiments by Coles & van Atta [74], the numerical work by Hollerbach & Fournier [89], or the review by Tagg [90]. For such weakly rotating systems, profile distortions from the plates propagate into the fluid and dominate the whole laminar velocity field.…”

“…2 A clear deviation is found between the measurement results with the laminar profile. The reason for this deviation is due to end-plate effects [72,74,75] -the laminar flow profile of type (2.1) only exists when the aspect ratio of TC is infinite. More measurements are upcoming for studying velocity profiles in high-Reynolds-number Taylor-Couette flow.…”