interface tracking algorithm

In the present study, for the first time, a finite volume coupled solver is developed for the simultaneous numerical solving of two-phase incompressible fluid flow equations at low Reynolds numbers, and for solving the the interface position equation by applying interface boundary conditions using the foam-extend platform. The studied flows with interface and mesh motion are considered to be laminar and in the range of Reynolds numbers less than 100. The Foam-extend is a fork of OpenFOAM, an opensource object-oriented C++ library for computational continuum mechanics. This solver is based on the interface tracking algorithm, which is developed using an innovative technique called zero-thickness cell. This technique removes the distance effect for the cell adjacent to the interface, and the interface is modeled with zero thickness cells. The main advantage of the present coupled solver compared to the previously developed solvers is that in this solver, all the equations in both phases are coupled with each other by cells adjacent to the interface and with an the interface position equation. All the governing equations and the interface position equation are assembled in a single linear system of equations and simultaneously solved. In fact, unlike the usual segregated procedure of solving two phase flows, where the phases are solved with lagged value boundary conditions, in the present solver, the phases are solved simultaneously with the interface conditions in an implicit manner and in the same block matrix system. The movement of the interface was done separately, and in another step. For this purpose, the kinematic condition was implemented. The computational performance of the coupled solver was evaluated by solving the equations of two-phase fluid flow inside a channel and on a backward-facing step. In the beginning, a preliminary investigation was done for the case, where both phases were completely independent and decoupled. Matching the interface with the streamlines, as well as the reasonable and justifiable movement of the surface, has been observed from the physical point of view. Also, the damping of the numerical oscillations generated on the interface and changing the flow variables will be investigated. The present results are in excellent agreement with other results reported in the literature.

The present paper introduces the implementation of a concurrent solver for pressure and velocity to solve free surface flows within the foam-extend framework. Integrating pressure and velocity fields with interface tracking algorithm has led to the development of a solver equivalent to the base foam-extend solver, named interTrackFoam. The current algorithm is entirely implemented using the structures, classes, and functions available in the foam-extend framework, and all the capabilities of this framework remain usable. Additionally, this solver utilizes libraries related to block matrices in foam-extend along with parallel solving capabilities. The block matrix system serves as the foundation for the concurrent solver. Notably, reducing the number of inner loops and performing one-step pressure and velocity solving are among the primary differences from the recognized default solver. Essentially, this solver represents the initial step towards a concurrent solver for velocity, pressure, temperature, and constituents with heat and mass transfer capabilities. The solver's capability is demonstrated through solving various experimental cases, including three-dimensional reservoirs, free surface flow around airfoils, and flow over sloping surfaces. With the concurrent solving capability of pressure and velocity, this solver holds significant potential in addressing complex physics and geometries. The ability for simultaneous solving enables reducing iterations or considering relatively higher time steps for flow computation.

The vapour absorption into the liquid falling film has occurred in various natural phenomena and its application has spread in various industries, such as the dehumidification and desalination industry. The complexity of flow dynamics, mass transfer, heat, and small dimensions of a liquid film has made its modeling and numerical simulation a key role in the investigation and studying of the effectiveness and improvement of the absorption process in a liquid film absorbent. In the present work, the effects of Reynolds number, wall temperature, and wall shape on the interfacial heat and mass transfer have been investigated. Numerical modeling has been performed using an unsteady Arbitrary Lagrangian-Eulerian interface tracking method by Fortran. The simulation results show that the deformation of the wall surface and the cooling of the wall temperature has a significant effect on the rate of gas vapor absorption into the laminar liquid film in comparison with the flat wall