Prediction of flows in enclosed rotor–stator cavities

Abstract

A robust and fully predictive mathematical representation has been derived to predict the swirl ratio, pressure, and torque in enclosed rotor–stator cavities. For the flow regime of interest, turbulent boundary layers form on the rotor and stator, between which there is an inviscid fluid core. Utilizing the momentum-integral equations with suitable assumptions and the continuity of mass equation, governing equations are derived for the flow behavior, with the assumption that the swirl ratio is dependent on the radius. Predictive initial conditions are formulated, and a robust, computationally inexpensive numerical technique is implemented and predictions are shown to be in reasonable agreement with existing experimental data. The swirl ratio was proven to be highly dependent on the radius, with the distribution modified by the shroud and hub conditions. Additionally, the effects of two geometrical parameters were studied, namely, the gap ratio and non-dimensional inner radius. As the gap ratio increases from 0.05 to 0.5, the swirl ratio at the outer radius decreases from 0.56 to 0.35, leading to an increase in torque coefficient from 0.38 to 0.44. The swirl ratios for different inner radii differ at the inner part of the cavity while converging to a single value at the outer radius. The presented model can easily be integrated into the design code for gas turbine engines, contributing to the design of more efficient engines.