Abstract

Steady, incompressible turbulent sink flows that develop between two stationery discs with and without swirl were investigated numerically using the software FLUENT 6.1 with the Reynolds Stress Model (RSM) employed to approximate turbulence. The main purpose of the work is to validate the method and then elaborate on some key features of these types of flows. Both problems studied here were characterized by severe streamline bending. Exploratory tests using the k - [varepsilon] methodology reconfirmed that it is not suitable for flows of these type. Instead, the Reynolds Stress Model (RSM) with five equations for 2D geometry and 7 equations for 3D to accurately resolved the physics of the problems well. Furthermore, the continuative rather the pressure boundary condition yielded stable solutions. Care however had to be applied in selecting the length of the outlet manifold. The basic idea was to avoid the vena contracta after the ninety-degree bend by increasing the length of the exit pipe. The obtained numerical results are shown to be in accord with past experiments throughout the entire domain. The technique is able to resolve, at a satisfactory level, the flow development even at known problematic areas such as for example near the sink exit. Acceleration was found to be the primary controlling factor for both purely radial and swirling inflow where monotonic changes of pressure gradient are a common manifestation. For uni-radial sink flow, inertia increase either due to inlet velocity augmentation or decrease of the local area produces flatter velocity profiles thus suggesting that inertia reigns over the viscous forces. In the case of swirling inflow, the overpowering centrifugal force field forced almost all of the fluid to be drained through the Ekman's boundary layers developed on each of the disk surface. It now becomes clear that the growth of flow near the disk or spikes in the radial velocity is due to the combined action of boundary layer development and local reduction of the flow area. The numerical algorithm was also able, for the first time, to successfully capture the toroidal recirculation zone that is known to inhabit the central portion of the flow. The latter is also responsible for the development of a reversed flow, which causes the saddle-like behavior of the radial velocity near the mid-plane. The tangential velocity peaks near the disks known from previous experiments and numerical formulations appeared also in the current solutions. Therefore, the present study has validated a tool that can now be used to provide answers to some outstanding questions. It can be employed to provide an insight into the stabilizing effects of acceleration which encourages the flow to remain laminar even at very high inlet Reynolds numbers, or to laminarize in case that the entering flow is turbulent. It could also provide the limits of validity of the previous simple models