Numerical Study of Geometry and Rotation Dependence on the Flow in Labyrinth Seals

A computational study was conducted on the flow, both compressible and incompressible, in a labyrinth seal at various geometries and rotation rates. The computations were performed using the commercial software Fluent® which solves the k-ε model to predict the flow field in the seal. Various clearance-pitch ratios were used to study the effect of clearance on the flow. The aspect ratio, which is defined as the pitch-height ratio was varied to study the influence of the depth of the cavity on the flow as a whole. These studies span a range of Taylor's number that is defined accordingly, while fixing the Reynolds number at 1000. \n\tThe effects of clearance, aspect ratio and rotational rates are studied using carry-over coefficient and discharge coefficient. It is observed that a secondary recirculation zone (SRZ) occurs inside a seal cavity at above certain Taylor's number. This significantly changes the flow field in the seal and the cavity which results an increases in pressure drop across the seal for a given flow boundary condition. This formation of SRZ's is more evident in incompressible flow and occur at prohibitively high rotational speeds in case of air (compressible flow). It is also observed that flow with teeth on rotor are characterized by SRZ's while it's not case with teeth on stator. A flow map which shows the onset and presence of SRZ's is shown. \n\tThe ratio of tangential velocity of the shaft to the average of the swirl velocity in a cavity at various geometries of the cavities are presented. They seem to be decreasing with decreasing depth and follow a linear pattern with the aspect ratios of the cavity.