Swirl Ratio Prediction Model in Rotor-Stator Cavity With Superposed Outward Radial Throughflow Based on Region Partition

Abstract

The Rotor-Stator cavity (R-S cavity) is a prototype model in many engineering applications such as gas turbine secondary air systems. The flow characteristics of the R-S cavity are relatively complex considering the rotation effect. A radial through flow is usually superposed in the R-S cavity, further complicating the fluid motion. The flow inside an R-S cavity with a superposed radial throughflow can be divided into four regions based on flow characteristics: a source region, a rotor entrainment layer, a rotating core, and a mixing region. In the present work, a one-dimensional (1-D) radial swirl ratio predictive model is built and verified based on computational fluid dynamics (CFD) results in the rotor entrainment layer and rotating core region. A swirl ratio gradient governing equation is deduced at first. The equation involves two scale factors CS and CR which are related to the stator and rotor friction correspondingly. The governing equation in the rotor entrainment layer is further simplified by neglecting the stator friction factor CS where the rotor friction prevails. Then, based on the discretized governing equation, CR and CS are determined via approximation with CFD results. Correlations between CR, CS, and nondimensional radial through flowrate cw are determined and verified. The obtained correlations and the discretized governing equation together form the complete swirl ratio, predictive model. The model accuracy is described by cross-correlation coefficients, which show a good agreement. The 1-D model is then implemented to different rotating speed cases, based on which the model portability is discussed.