Quantitative comparison of Taylor flow simulations based on sharp‐interface and diffuse‐interface models

Abstract

SUMMARYA pressure‐driven flow of elongated bullet‐shaped bubbles in a narrow channel is known as Taylor flow or bubble‐train flow. This process is of relevance in various applications of chemical engineering. In this paper, we describe a typical simplified experimental setting, with surface tension, density and viscosity as prescribed input parameters. We compare a sharp‐interface model based on a moving grid aligned with the bubble boundary (ALE coordinates) and a diffuse‐interface model where the bubble shape is implicitly given by a phase‐field function. Four independent implementations based on the two modeling approaches are introduced and described briefly. Besides the simulation of the bubble shapes, we compare some resulting quantities such as pressure difference and film widths within the implementations and to existing analytical and experimental results. The simulations were conducted in 2D and 3D (rotationally symmetric). Good accordance of the results indicate the applicability and the usability of all approaches. Differences between the models and their implementations are visible but in no contradiction to theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.

Accuracy of two‐phase flow simulations: The Taylor Flow benchmark

“…The first project focused on 2D numerics, and was therefore limited to experimental data obtained from a round capillary (since the surface tension in all experimental setups is relatively high, rotational symmetry of the bubble can then be safely assumed) [12]. Participating numerical codes were based both on a classical sharp-interface approach and also on a diffuseinterface model.…”

“…Advantages include www.gamm-proceedings.com the experimental accessibility and comparability, the sensitivity to a large range of surface tensions and the practical relevance of the proposed setup. The first two studies have been performed [12,13] and showed that it was possible yet demanding to obtain agreement between the codes and the experimental data. It is planned to put detailed data of the different codes and experiments online as supplementary material to the corresponding papers as well on the SPP homepage (www.dfg-spp1506.de/taylor-bubble).…”

“…Diffuse interface models are also used to numerically simulate the two-phase flow situation. The corresponding equations are specified in [12] and can be seen as an approximation to the above sharp interface formulation (under the assumption of small mobility and interface thickness).…”

On Convergent Schemes for Diffuse Interface Models for Two-Phase Flow of Incompressible Fluids with General Mass Densities

“…Various numerical experiments underline the full practicality of this approach-see [19]. In the benchmark paper [5] on Taylor flow, the method of [19] was successfully validated by comparison with physical experiments and different numerical approaches. Diffuse interface models for two-phase flow of incompressible viscous fluids began to interest mathematicians some 10 years ago, while the basic concept of coupling momentum equations with the Cahn-Hilliard equation had been suggested much earlier-see the famous "Model H" of Hohenberg and Halperin [22].…”

An efficient and energy stable scheme for a phase‐field model for the moving contact line problem

“…We thus demonstrate a practical approximation procedure for the phase-field model of the moving contact line problem. Encouraged by the good agreement of the diffuse interface methods with non-wetting two-phase flow experiments [32], we shall compare the method with experimental data in the near future.…”