## 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.

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