The Rise of Complexity in Describing Fluid Flow in Rotating Cavities

This paper is concerned with rotor-stator cavities in fluid machinery and contains a general survey explaining the fundamental effects and geometries. Starting with the free disk model the basic flow structure is shown. An attempt to derive the frictional moment for the free disk, using the Eulerian-equation of turbomachines, leads to the conclusion that 1D coherences are not sufficient to describe this type of flow. Next, a disk rotating in an enclosed housing is considered with respect to the appearance of a rotating fluid core, which mainly influences the static pressure distribution on the walls and the frictional resistance. Furthermore the inclusion of a superposed through-flow leads to a more realistic model that could be used as an example in the gap between an impeller and the stationary casing of a pump. In fact the core rotation is strongly influenced by the properties and direction of the incoming through-flow. As a consequence the pressure distribution is determined by the resulting core rotation, normally expressed in terms of the core rotation coefficient. For instance the pressure distribution acting on the back area of the impeller is a main part of the resulting axial force. The rise of complexity can be illustrated by considering the number of describing dimensionless parameters. The main parameters are derived using dimension analysis and their relevance is shown with respect to the flow physics.