An unstructured conservative level-set algorithm coupled with dynamic mesh adaptation for the computation of liquid-gas flows
Romain Janodet  1@  , Geoffroy Vaudor  1@  , Ghislain Lartigue  1@  , Pierre Benard  1@  , Vincent Moureau  1@  , Renaud Mercier  2@  
Centre National de la Recherche Scientifique : UMR6614
Site Universitaire du Madrillet, BP 12, 76801 St Etienne du Rouvray Cedex -  France
2 : SAFRAN Tech
Rue des Jeunes Bois, Châteaufort - CS 80112, Magny-Les-Hameaux 78772, France -  France

Accurate 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 be able 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 flow solver, and its application for predicting the outcome of a droplet collision with reflexive separation on a dynamically adapted unstructured mesh, in order to resolve the small physical scales at the liquid-gas interface at a moderate cost.

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 estimate the smallest distance to the interface. The interface normal and curvature are computed using this signed-distance function. An interpolation is first performed to find the interface position on each crossing node pair. Within a cell, the interface is then approximated by a line (2D) or a plane (3D) connecting the intersection points. The distance at the nodes in the first band level is obtained by projection. 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). The markers are then sorted based on the distance. For further band levels, data are propagated and 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 Nashgriz et al. (1990).

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