Model for Predicting the Head Shape of a Taylor Bubble Rising through Stagnant Liquids in a Vertical Tube

Abstract

Dumitresku’s model is a classic model for predicting the shape of a Taylor bubble head. Since the model consists of two equations, there is a discontinuity in predicting Taylor bubble surfaces when two equations are switched. A proposed model is derived from Euler’s equation and based on the Dumitresku’s model. It can predict the whole shape of a Taylor bubble head, similar to the Dumitresku’s model. However, this model reduces the discontinuity which regularly occurs in the Dumitresku’s model due to the equations switching. Similarities between the Dumitresku’s model and the proposed model are investigated through a numerical simulation of flow fields around a Taylor bubble head. Simulation results show that the geometric and kinematic similarities between the two models are extremely ensured while the dynamic similarity is acceptably ensured with less confidence. However, the proposed model can partially reduce the discontinuities in the simulation results as desired.

Keywords: Computation; Dumitresku’s model; Euler’s equation; Similarity; Taylor bubble.