Euler‐Lagrange Simulations of Turbulent Two‐phase Flows with an Advanced Deterministic Bubble Coalescence Model

Abstract

The present paper is concerned with an advanced version of the deterministic coalescence model [1] and its application to turbulent bubble-laden flows. The major drawback of this film drainage model -its incapability to handle large numbers of coalescence processes -is avoided by an a-priori determination of a parametric relation for the transition time between the main drainage mechanisms. The comparison with experimental results yields a good overall agreement, while the application to a downward pipe flow demonstrates the ability of the model to efficiently handle large numbers of coalescence processes.Turbulent two-phase flows containing dispersed bubbles with the ability to coalesce are encountered in a variety of natural and industrial processes, e.g., bubble columns used for many chemical applications. Euler-Lagrange predictions are a promising ansatz for the prediction of such flow phenomena, since all bubbles are tracked individually through the flow field by solving Newton's second law [2] providing detailed information about the evolution of the dispersed phase. On the other hand, the Eulerian fluid can be treated both accurately and cost-efficiently by a large-eddy simulation (LES) [3].The present bubble coalescence model is based on the approach by Jeelani and Hartland [1], where the coalescence process is determined by the temporarily evolving deformation of the colliding bubbles and the simultaneous drainage of the liquid film trapped between the bubbles. Coalescence occurs if the film thickness is reduced within the collision time t c below a critical value [4], otherwise a rebound takes place. The varying contact area between the bubbles is found by a force balance acting on the bubbles during the collision. In the present approach a radial pressure gradient in the liquid is considered, which was neglected in the original model, thereby, making the model consistent with the assumption of a radial outflow [5,6]. The expression of the varying contact time can be inserted into the drainage equations describing the inertia-dominated [6] and the viscous-dominated [5] reduction of the film thickness, thus, allowing to treat the distinctive cases of the coalescence of clean and contaminated bubbles. In the case of clean bubbles, coalescence is solely inertia-dominated making the determination of the final film thickness easy. However, for the case of contaminated bubbles, the drainage is initially inertia-dominated and then changes to the viscous-dominated regime [7]. Consequently, it is necessary to determine the corresponding transition time t j for each individual collision by solving a conditional equation [1]. Unfortunately, this requires a numerical root-finding scheme rendering the approach unfeasible for the estimation of flows containing a large number of (contaminated) bubbles.The proposed solution to this challenge is to determine the transition time for a pre-defined range of collision velocities u rel,0 and diameters d eq providing a map of t j /t c . Subsequently, a regression function of ...