Bubble coalescence in turbulent flows: A mechanistic model for turbulence-induced coalescence applied to microgravity bubbly pipe flow

Abstract

A mechanistic model for bubble coalescence in turbulent flow is presented. The model is developed in two steps, which are essentially separable. In the first, expressions put forward earlier for the collision frequency and coalescence probability of equal bubbles during turbulence-driven, high-Reynolds-number collisions are extended to unequal bubbles and to take account of bubble–turbulence and bubble–bubble interactions. In the second, the resulting expression for the coalescence rate is used to derive source terms in the transport equations for the moment densities of the bubble-diameter distribution, which can readily be evaluated locally within a CFD code. The result is an extremely compact framework capable of providing predictions of the evolution of bubble size distributions in space and time at the expense of only two additional scalar transport equations. To provide an experimental validation of the model, some data on the bubble size evolution along a pipe flow under microgravity conditions have been used. Microgravity experiments on gas–liquid bubbly pipe flows have been carried out during parabolic flights in aircraft. Bubble diameter distributions have been determined from high speed video recording and image processing. In the absence of gravity, collisions between bubbles smaller than the integral length scale of turbulence are primarily due to turbulence. The results from the calculation are in good agreement with the experimental data. The model is then used to predict the influence of the void fraction, the bubble size at the pipe inlet and the liquid mean velocity on the coalescence rate.