We present an improved method to reproduce the behavior of the contact line on solid walls in the simulation of 3D unsteady interfacial flows characterized by large density ratios. The method has been implemented in a numerical code based on a second-order projection method to solve the Navier-Stokes equations, a level set method to describe the interface evolution and an adaptive grid refinement based on an octree data structure. Although the level set method is widely used in the simulation of interfacial flows, it poses a particular difficulty, related to the reinitialization procedure, when used in flows in which the interface intersects a solid wall. The reinitialization procedure is required to maintain the level set function as the signed distance function to the interface and is typically based on solving a Hamilton-Jacobi equation, whose characteristics are perpendicular to the interface. When the interface intersects a solid wall at an angle other than 90º, a blind zone appears in the domain that is not reached by the characteristic lines, making it necessary to introduce a boundary condition for the level let function on the solid surface in that zone. Different approaches have been proposed in the literature, most of them for 2D problems. A procedure similar to that proposed in \[Xu, S., & Ren, W. (2016). Commun. Comput. Phys., 20(5), 1163-1182\] for tridimensional problems is used in this work. This procedure is based on the normal extension of the contact angle from the interface along the solid wall. This extension is done by solving a hyperbolic equation with a propagation velocity vector equal to the signed normal to the interface. This equation is discretized using an upwind scheme to improve the efficiency of the method.  The extended contact angle allows a Neumann boundary condition to be obtained for the level set function along the solid wall in the blind zone. In addition, to improve accuracy in modeling the behavior of the contact line, we impose a similar boundary condition at the solid wall to calculate the curvature of the interface. To assess the accuracy and robustness of the proposed method, we have conducted several preliminary numerical tests in three dimensions, whose results are compared with analytical solutions and other results available in the literature.


On the Boundary Condition for the Level Set Function in the Numerical Simulation of Moving Contact Lines

Division / Sponsors: 
Heat Transfer Division (HTD), Fluids Engineering Division (FED)

Heat Transfer Summer Conference
Paper Proceedings: https://asmedigitalcollection.asme.org/HT/HT2020/volume/83709

18th International Conference on Nanochannels, Microchannels, and Minichannels
Paper Proceedings: https://asmedigitalcollection.asme.org/ICNMM/ICNMM2020/volume/83693

Fluids Engineering Division Summer Meeting
Paper Proceedings: https://asmedigitalcollection.asme.org/FEDSM/FEDSM2020/volume/83716

HT-ICNMM2020 - Virtual Conference, SHTC - Virtual Conference, FEDSM2020 - Virtual Conference

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