An unstructured conservative level-set algorithm coupled with dynamic mesh adaptation for the computation of liquid-gas flows

International audienceAccurate and efficient simulations of 3D liquid-gas flows are of first importance in many industrial applications, such as fuel injection in aeronautical combustion chambers. In this context, it is mandatory to handle complex geometries. The use of unstructured grids for two-phase flow modeling fulfills this requirement and paves the way to isotropic adaptive mesh refinement. This work presents a narrow-band conservative level-set algorithm implemented in the YALES2 incompressible flow solver, which is combined to dynamic mesh adaptation. This strategy enables resolving the small physical scales at the liquid-gas interface at a moderate cost. It is applied to predicting the outcome of a droplet collision with reflexive separation. In the accurate conservative level set framework, the interface is represented using a hyperbolic tangent profile, which is advected by the fluid, and then reshaped using a reinitialization equation. The classical signed-distance function is reconstructed at nodes in the narrow band around the interface using a geometric projection/marker method (GPMM), to calculate the smallest distance to the interface. The interface normal and curvature are computed using this signed-distance function. Within a mesh cell, the interface is approximated by a segment (2D) or one or several triangles (3D). The distance at the nodes is simply obtained by projection to the closest surface elements. If a node is connected to n elements containing interface fragments, it has a n-marker list (a marker contains the coordinates of the crossing points and the distance). To speed-up the algorithm, the markers stored at each node are sorted based on their distance. Markers are propagated from one band to another: each node compares its markers to its neighbors' and keeps the closest only. The GPMM approach for the reconstruction of the level-set signed-distance function used in conjunction with the reinitialization of Chiodi et al. (2017) leads to significant improvement in the interface quality and overall accuracy compared to the reinitialization of Desjardins et al. (2008) in the calculations performed on unstructured grids. Since the accuracy of the interface normal and curvature directly depends on the signed-distance function reconstruction, less spurious currents occur on the implicit surface. The improved level-set algorithm leads to accurate predictions of the outcome of a droplet collision with reflexive separation, and is validated against the experimental results of Ashgriz et al. (1990). Introduction Two-phase flows are ubiquitous in nature and in industrial systems. The understanding of the various phenomena occurring in liquid-gas flows is crucial for aeronautical combustors, in which a fuel is injected in liquid form, goes under an atomization process, evaporation, mixing with air and eventually combustion. Understanding the atomization process and the resulting droplet distribution is of first importance for aircraft engine performance and operability. The prediction of the atomization process is complex, due to many non-linear phenomena such as interface break-up, droplet convection, or droplet collision. Atomization also involves a wide range of time and space scales, which leads to important calculation costs. Thus, the use of dynamic mesh adaptation for unstructured meshes is particularly helpful for simulating industrial liquid-gas flow problems, as it allows implicit interface dynamics calculation in complex geometries at a reasonable cost [1]. To capture the interface, the conservative level set method is used, which accurately predicts the interface dynamics while conserving liquid mass [2]. This article presents a method to compute the signed-distance function on unstructured grids, and an implementation of the reinitialization of [3], adapted to unstructured meshes. Classic test cases are run to check the overall accuracy and robustness of the method, and a droplet collision case is simulated to validate the global algorithm with a front merging scenario against the experimental results of [4]