Batchelor versus Stewartson flow structures in a rotor-stator cavity with throughflow

Abstract

The present work considers the turbulent flow inside a high-speed rotor-stator cavity with or without superimposed throughflow. New extensive measurements made at IRPHE by a two-component laser Doppler anemometer technique and by pressure transducers are compared to numerical predictions based on one-point statistical modeling using a low-Reynolds-number second-order full stress transport closure (Reynolds stress model). The advanced second-order model provides good predictions for the mean flow as well as for the turbulent field and so is the adequate level of closure to describe such complex flows. A better insight into the dynamics of such flows is also gained from this study. Indeed the transition between a Batchelor type of flow with two boundary layers separated by a central rotating core and a Stewartson type of flow with only one boundary layer on the rotating disk is characterized in the (r*,Ro) plane, where r* is the dimensionless radial location and Ro a modified Rossby number. The 5∕7 power-law of Poncet et al. [“Turbulent rotating disk with inward throughflow,” J. Fluid Mech. 522, 253 (2005)] describing the mean centripetal flow in a rotor-stator system is extended to different aspect ratios and to the case of centrifugal Batchelor type of flows.