Cone-and-plate apparatus: a compact system for studying well-characterized turbulent flow fields

Abstract

We have investigated the turbulent flow field inside a cone-and-plate Couette flow apparatus (CPA). The CPA presents a compact, easily varied and easily measured flow system with well-characterized turbulent and laminar flow fields and a good full turbulent spectrum. The CPA can also produce the same time-average stress for both laminar and turbulent regimes. The apparatus consisted of a shallow 2° cone of 0.75 m radius rotating above a flat plate in air. A high-resolution X-wire probe was used to measure the turbulent and time-mean flow properties. A single parameter \(\tilde R = (r^2 \omega \alpha ^2 )/(12v)\), which is a measure of the centrifugal forces acting on the moving fluid, governs the degree of secondary flow and turbulence in the device. In the fully turbulent region, R > 4, the mean velocity profile has steep gradients near each surface and is nearly uniform in the central core; and the normalized azimuthal velocity closely follows the ubiquitous law of the wall near the plate. The turbulence intensity exhibits two peaks at the edges of the core flow, and the frequency spectrum of velocity fluctuations near the plate resembles that found in isotropic turbulence. This study also suggests that the rotational symmetry with the stationary bottom plate is a much more convenient experimental geometry than a circular Couette flow.