Two-dimensonal numerical simulation and computation of the flow between a rotating and a stationary disk - 5

Abstract

The flow between a rotating and stationary disk represents an important problem for many turbomachinery applications. We used a direct numerical simulation (DNS) by integrating the time dependent Navier-Stokes equations until a steady state was reached. There were investigated two cases with both rotating disks in shroud and with one rotating and one stationary disk. The local Reynolds number r2Ω/ν=3.1.104 and gap aspect ratio α=h/r=0.066; Ω represents here angular velocity of the rotating disk, r tha radial coordinate, ν the kinematic viscosity and h the gap width. In our solution one can good observe that the wall friction at the rotating disk is substantially higher than at the stationary one. Also was considered time dependent behaviour of such dynamic system and pictured as a Recurrence Plot (RP) and bifurcation diagram. As a second part of our study was considered more simplified stationary numerical model defined by a system of nonlinear differential equations. Von Kármán, 1921 modified Navier - Stokes equations to get only rotating disk infinitely far from a stationary disk. A similar progress used also later Batchelor (1951) and Stewartson (1953) for two rotating disks. In our system is embodied constant pressure condition.