On two-phase flow solvers in irregular domains with contact line

Abstract

International audienceWe present numerical methods that enable the direct numerical simulation of two-phase flows in irregular domains. A method is presented to account for surface tension effects in a mesh cell containing a triple line between the liquid, gas and solid phases. Our numerical method is based on the level-set method to capture the liquid–gas interface and on the single-phase Navier–Stokes solver in irregular domain proposed in [35]to impose the solid boundary in an Eulerian framework. We also present a strategy for the implicit treatment of the viscous term and how to impose both a Neumann boundary condition and a jump condition when solving for the pressure field. Special care is given on how to take into account the contact angle, the no-slip boundary condition for the velocity field and the volume forces. Finally, we present numerical results in two and three spatial dimensions evaluating our simulations with several benchmarks

Direct numerical simulation of nucleate pool boiling at large microscopic contact angle and moderate Jakob number

“…This preliminary work has instigated many other numerical methods which have been developed keeping the guidelines of this first paper [11][12][13]15,22,29,33,34,38,39,43,45,[56][57][58]. All these studies present new developments of numerical methods allowing a sharp description of discontinuous terms in the framework of a welldefined numerical theory.…”

“…That can be done by imposing the following Neumann boundary condition on the / function, such as it is proposed in [33] …”

“…(9) and (11), are solved with an explicit temporal discretization, this boundary condition can be imposed by populating ghost cells outside of the computational field. If an immersed solid domain is considered inside the computational field, solving an iterative PDE is required, such as in [1,8,33], to build an extrapolated field that maintains the suitable boundary condition on the / function for imposing the contact angle. In the simulations presented in this paper, as a horizontal wall in the x-direction with a normal vector in the y direction is considered, the following simple relation allows imposing this boundary condition:…”

An energy-preserving level set method for multiphase flows

“…In particular, we prove that equation (9) is still valid when we replace A byÃ, which is defined over the volumes and thus much more convenient to compute. First, as a preliminary stage, we take the gradient of the transport equation (5) in the pursue of a relation between the marker function and the smoothed surface…”

“…Multiphase flows are ubiquitous in industrial applications. They are present in a rich variety of physical phenomena such as vaporization [1], atomization [2], electrohydrodynamics [3] or boiling [4], among others [5,6].…”