On the Flow Behavior in Rotor-Stator System with Superposed Flow

Abstract

The flow between a rotor and a stator at high Reynolds number and small Ekman number is divided into three domains, two boundary layers adjacent to the discs separated by a central core. In the present work, a simple theoretical approach provides analytical solutions for the radial distribution of the core swirl ratio valid for a rotor-stator system with a superposed radial inflow rate. At first, the flow in the rotor boundary layer is assumed to behave as expressed by Owen and Rogers (1989) in the case of a turbulent flow on a rotating single disc. On the stator side, a necessary compensation flow rate must take place according to the conservation of mass. It is found that this compensation flow rate cannot be estimated with a good accuracy using the hypotheses of a stationary disc in a rotating fluid by Owen and Rogers (1989). Thus, two innovative weighting functions are tested, leading to new analytical laws relating the core swirl ratioKto the coefficient of flow rateCqrintroduced by Poncet et al. (2005). The adequacy between the theoretical solutions and numerous results of the literature is clearly improved and the discussion allows a better understanding of the flow behavior.