Tangential and radial mean momentum and stress analysis of rotating disk turbulent boundary layers

Abstract

Abstract

Turbulence statistics of a three-dimensional boundary layer over a rotating disk are measured using molecular tagging velocimetry and laser Doppler velocimetry up to a friction Reynolds number of asymptotically equals ≃ $\simeq$ 3000. The present new water-based facility results in the achievement of relatively high Reynolds numbers, and we overcome the challenges associated with mimicking an infinite disk scenario using a finite tank. For the first time, the mean momentum balance and mean stress budget of this flow are investigated in the tangential/streamwise direction and are contrasted with those in a zero-pressure-gradient turbulent boundary layer over a flat plate. Furthermore, the mean momentum and stress balance in the radial direction are examined to better understand the cross-flow effects on the structure of the rotating disk turbulent flow. The tangential and radial mean momentum equations both contribute at leading order to the mean flow dynamics. Analytical approximations for the tangential and radial friction velocities are found using the mean equations and well-supported similarity assumptions. Furthermore, an analytical estimation for the variations of the mean wall-normal velocity across the boundary layer is derived, which shows a good agreement with present measurements. Independent of Reynolds number, the log layer in the rotating disk turbulent boundary layer is seen to extend to the boundary layer edge with an ostensibly negligible wake. This is similar to observations in the turbulent sink flow under equilibrium conditions and channel flow. Through quadrant analysis, it is evidenced that the Reynolds-shear-stress-producing events are weakened in the rotating disk boundary layer.