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.

Turbulence modeling of the Von Kármán flow: Viscous and inertial stirrings

“…This tendency for relaminarization of the RSM model has already been noticed by Poncet et al [34,35] in the rotor-stator configuration. As a conclusion, there is no significant effect of the Reynolds number on the mean flow for Re ≥ 10 5 , which confirms the results of Cadot et al [16] and Ravelet [21].…”

“…A refined mesh 160 × 160 is necessary to model flows with straight blades. It is to be compared to the 140 × 80 mesh used by Elena and Schiestel [32,33] and Poncet et al [34,35] in rotor-stator systems. The calculation is initialized using realistic data fields, which satisfy the boundary conditions.…”

“…The predictions of the Reynolds Stress Model (RSM) used in the present work have already been validated in the rotor-stator configuration (Γ = 0) [32][33][34][35] for a wide range of aspect ratio G and Reynolds number Re. It showed that this level of closure is adequate in such flow configurations, while the usual k − ǫ model, which is blind to any rotation effect presents serious deficiencies.…”

“…Blevins [42] proposed some values for the drag coefficient (expected errors of ±20%) in an The reader is thus referred to [32][33][34][35] for more details about the RSM model and the numerical method.…”

Turbulent Von Kármán Swirling Flows

“…In the following, G = 1.8 and Γ = −1. Our numerical approach is based on one-point statistical modeling using a low Reynolds number second-order full stress transport closure (Reynolds Stress Model, RSM) sensitized to rotation effects and already validated for Γ = 0 and a wide range of G and Re [1]. To model straight blade effects, we add a volumic drag force in the equation of V θ the tangential velocity component:…”