Numerical modeling and analysis of gas entrainment for the ventilated cavity in vertical pipe

A semi-empirical gas entrainment model was proposed for the ventilated cavity in vertical pipe, based on which, a complete numerical scheme was established by coupling with the Eulerian-Eulerian two-fluid model to predict the multiscale flow field created by ventilated cavity. Model predictions were validated against experimental measurements on void fraction and bubble size distributions. Simulations were carried out to explore the effect of ventilation rate and inlet turbulence intensity on the macroscale cavity shape and the bubbly flow downstream of the ventilated cavity. As the ventilation rate increasing, a reverse trend was observed for the void fraction and bubble size distributions. It is concluded that the average void fraction in the pipe flow region is determined by the volumetric ratio between liquid and gas. However, the bubble size evolution is dominated by the breakage effect induced by turbulence in the vortex region. Furthermore, simulations were conducted to analyze geometric scale effect based upon Froude similitude. The results imply that the velocity distributions were properly scaled. Slight scale effect was seen for the void fraction caused by faster dispersion of bubbles in the larger size model. The comparatively greater bubble size was predicted in the smaller model, implying significant scale effects in terms of turbulence and surface tension effect. It reveals that empirical correlations valid in wide range are required for the extrapolation from small-size laboratory models.