Numerical implementation of interfacial drag force for one-dimensional, two-way bubble tracking method

A two-way bubble tracking method, in which each bubble is individually tracked on the Lagrangian coordinates, is one of the most promising two-phase flow models to partly take the place of a fully-averaged two-fluid model. In this method, conservation equations on different coordinate systems must be solved simultaneously, so that construction of the phase coupling models becomes particularly important. In the present study, taking into account the downward liquid flow formed around a bubble rising in a vertical pipe and using the bubble shape function proposed by Trapp et al. at the same time, we developed simple phase coupling models for one-dimensional, two-way bubble tracking method. The calculated results of a single bubble rising in a circular pipe filled with stagnant liquid showed that the proposed model not only successfully mitigates the numerical fluctuation of the bubble rising velocity but also naturally predicts the effect of containing wall on the terminal bubble velocity; the present model would therefore be reasonable from both numerical and physical points of view. It was also revealed that the mean void fraction in bubbly two-phase flow is reasonably to be predicted if the effect of other bubbles on the downward liquid flow is appropriately evaluated. (author)