Coalescence Prevention Algorithm for Level Set Method

Abstract

The application of interface tracking methods to bubbly flow modeling has grown in recent years due to improvements in computing performance and development of more efficient solvers. However, the standard formulation of most interface tracking methods is not designed to physically handle the interface interactions at reasonable grid sizes. Regardless of the method used, a high grid resolution is required in the liquid film region in order to properly model drainage process during bubble interaction, which in certain conditions prevents the coalescence. This makes large scale (many bubbles) simulations unaffordable. One of the popular interface tracking approached is the level-set (LS) method. To simulate realistic bubble coalescence behavior in the LS method an algorithm with the capability of delaying or preventing the process of multiple simultaneous coalescence events has been developed. Bubble interaction plays a significant role in high void fraction flow behavior and affects the transition to other flow regimes (e.g. churn-turbulent or slug flows). The described algorithm allows to improve the accuracy of predicting coalescence events in these relevant cases and has been tested in a variety of conditions and computational meshes. This novel algorithm uses the LS method field to detect when bubbles are in close proximity, indicating a potential coalescence event, and applies a subgrid scale force to simulate the unresolved liquid drainage force. The subgrid-model is introduced by locally modifying the surface tension force near the liquid film drainage area. The algorithm can also simulate the liquid drainage time of the thin film by controlling the length of time the increased surface tension has been applied. Thus a new method of modeling bubble coalescence has been developed. Several test cases were designed to demonstrate the capabilities of the algorithm. The simulations, including a mesh study, confirmed the abilities to identify and prevent coalescence as well as implement the time tracking portion, with an additional 10–25% computational cost. Ongoing tests aim to verify the algorithm’s functionality for simulations with different flow conditions, a ranging number of bubbles, and both structured and unstructured computational mesh types. Specifically, a bubble rising towards a free surface provides a test of performance and demonstrates the ability to consistently prevent coalescence. In addition, a two bubble case and a seven bubble case provide a more complex demonstration of how the algorithm performs for larger simulations. These cases are compared to much more expensive simulations capable of resolving the liquid film drainage (through very high local mesh resolution), to investigate how the algorithm replicates the liquid film drainage process.

A geometric mass control approach in level set method to simulate multiphase flows with complex interface topologies, case study: Oblique coalescence of gas bubbles in a liquid

“…Generally approaches to improve the mass dissipation in level set method increase computational time. 4,7 In Table 2 the Run time for a sample case (corresponding to case D in Figure 7) has been compared in two cases; conventional re-initialization approach of level set method with and without proposed geometric mass control scheme. Simulations in this research were performed on a 3.4 GHz Core i7-4930 k personal computer with 8-GB RAM.…”

“…However, when interface deformation is high and topology of interface thoroughly changes (re-connections or disconnections), such as bubble coalescence or break up problems, re-meshing procedure is computationally expensive and therefore this method is not applicable. [4][5][6] On the other hand, interface capturing methods such as level set are implemented in a fixed mesh. Hence, they can be applied in problems with high interface deformation after modification regarding mass conservation.…”

“…All of approaches cited above and many other studies conducted on improvement of mass conversation error have surcharged many additional computational costs. 4,7 In this research a geometric correction is applied to the level set method in order to mass conversation of this method in simulation of sharp changes of the interface occurring in most of gasliquid two-phase flows and capability of the proposed method is investigated by utilizing of the method to simulate oblique coalescence of the bubbles which is one of the cases with complex topologies and sharp changes of the interfaces.…”