Turbulent flow between a rotating and a stationary disk

Turbulent how between a rotating and a stationary disk is studied. Besides its fundamental importance as a three-dimensional prototype flow, such flow fields are frequently encountered in rotor-stator configurations in turbom achinery applications. A direct numerical simulation is therefore performed by integrating the time-dependent Navier-Stokes equations until a statisti cally steady state is reached and with the aim of providing both long-time statistics and an exposition of coherent structures obtained by conditional sampling. The simulated flow has local Reynolds number r(2)omega/nu = 4 x 10(5) and local gap ratio s/r = 0.02, where omega is the angular velocity o f the rotating disk, r the radial distance from the axis of rotation, nu th e kinematic viscosity of the fluid, and s the gap width. The three components of the mean velocity vector and the six independent Re ynolds stresses are compared with experimental measurements in a rotor-stat or flow configuration. In the numerically generated how field, the structur al parameter a(1) (i.e, the ratio of the magnitude of the shear stress vect or to twice the mean turbulent kinetic energy) is lower near the two disks than in two-dimensional boundary layers. This characteristic feature is typ ical for three-dimensional boundary layers, and so are the misalignment bet ween the shear stress vector and the mean velocity gradient vector, althoug h the degree of misalignment turns out to be smaller in the present flow th an in unsteady three-dimensional boundary layer flow. It is also observed t hat the wall friction at the rotating disk is substantially higher than at the stationary disk. Coherent structures near the disks are identified by means of the lambda (2 ) vortex criterion in order to provide sufficient information to resolve a controversy regarding the roles played by sweeps and ejections in shear str ess production. An ensemble average of the detected structures reveals that the coherent structures in the rotor-stator flow are similar to the ones f ound in two-dimensional flows. It is shown, however, that the three-dimensi onality of the mean flow reduces the inter-vortical alignment and the tende ncy of structures of opposite sense of rotation to overlap. The coherent st ructures near the disks generate weaker sweeps (i.e. quadrant 4 events) tha n structures in conventional two-dimensional boundary layers. This reductio n in the quadrant 4 contribution from the coherent structures is believed t o explain the reduced efficiency of the mean flow in producing Reynolds she ar stress.