Turbulent flow 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 turbomachinery applications. A
direct numerical simulation is therefore performed by integrating the time-dependent
Navier–Stokes equations until a statistically 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
r2ω/v = 4 × 105
and local gap ratio s/r = 0.02, where ω is the angular velocity of the
rotating disk, r the radial distance from the axis of rotation, v the kinematic viscosity
of the fluid, and s the gap width.
The three components of the mean velocity vector and the six independent Reynolds
stresses are compared with experimental measurements in a rotor–stator flow configuration.
In the numerically generated flow field, the structural parameter a1 (i.e. the
ratio of the magnitude of the shear stress vector to twice the mean turbulent kinetic
energy) is lower near the two disks than in two-dimensional boundary layers. This
characteristic feature is typical for three-dimensional boundary layers, and so are the
misalignment between the shear stress vector and the mean velocity gradient vector,
although the degree of misalignment turns out to be smaller in the present flow than
in unsteady three-dimensional boundary layer flow. It is also observed that 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 λ2 vortex criterion
in order to provide sufficient information to resolve a controversy regarding the roles
played by sweeps and ejections in shear stress production. An ensemble average of
the detected structures reveals that the coherent structures in the rotor–stator flow are
similar to the ones found in two-dimensional flows. It is shown, however, that the three-dimensionality of the mean flow reduces the inter-vortical alignment and the tendency
of structures of opposite sense of rotation to overlap. The coherent structures near the
disks generate weaker sweeps (i.e. quadrant 4 events) than structures in conventional
two-dimensional boundary layers. This reduction in the quadrant 4 contribution from
the coherent structures is believed to explain the reduced efficiency of the mean flow
in producing Reynolds shear stress.