Flow in a Concentric Annulus with Inner- or Outer-Cylinder Rotation: A Conventional and Sensitized RANS Modelling Study

A conventional differential, near-wall Reynolds stress model (RSM) and its eddy-resolving version, sensitized appropriately to account for the turbulence unsteadiness (termed as Improved Instability- Sensitized RSM model - IIS-RSM), are applied within the unsteady Reynolds-Averaged Navier Stokes (RANS) computational framework to simulate the annular flow formed by two concentrically arranged cylinders. Two characteristic situations, in which the rotation of the inner cylinder by a constant angular velocity and that of the outer cylinder were considered individually, were studied in a range of rotational intensities. The corresponding Reynolds numbers based on the hydraulic diameter and axial bulk velocity of amount to 8900 and 12500 for the inner and outer cylinder rotations, respectively. The scale-supplying equation governing the inverse turbulent time scale relies on the ’homogeneous dissipation’ rate ( \(\omega _h=\varepsilon ^h/k\) ). The eddy-resolving capability of the IIS-RSM is enabled by a selective enhancement of the turbulence production by introducing an additional production term in the length-scale determining transport equation, in accordance with the Scale-Adaptive Simulation (SAS) strategy. The results for the cases with inner cylinder rotation obtained by both model versions show substantial mutual agreement and agree well with the reference LES data. The flow driven by the outer cylinder rotation at higher rotational rates is correctly predicted by the IIS-RSM model, in contrast to the conventional RANS approach resulting in premature relaminarization.