Flow and Heat Transfer in a Co-Rotating Cavity with Tubes: A Coupled Prediction Model

In previous studies, researchers established mathematical models for predicting the pressure coefficient in simple cavities and tubed vortex reducers based on the assumptions of incompressibility and adiabatic reversibility. However, these mathematical models are not suitable for engineering design and cannot predict the internal pressure and temperature. In this study, we first derived mathematical equations for predicting the pressure drop and temperature change in a tubed vortex reducer, by considering the irreversible loss at the tube inlet. To compensate for the shortcomings of the incompressibility assumption, we developed an iterative alternating calculation method that revises the density. Subsequently, we established a coupled prediction model based on the aforementioned equations and methods. The verified Reynolds stress model results proved that the coupled prediction model and the single prediction model, which represents the incompressible case, yield similar results in predicting pressure under low-rotating-speed conditions. However, as the rotating speed was increased, the error of the single prediction model gradually increased, whereas the coupled prediction model still had good prediction accuracy. With an increase in the length and number of tubes, the pressure drop showed a decreasing trend, whereas the temperature change did not fluctuate significantly.