Silva, A.T.G.; Fernandes, C.; Organista, J.; Souza, L.; Castelo, A. Validation of HiG-Flow Software for Simulating Two-Phase Flows with a 3D Geometric Volume of Fluid Algorithm. Mathematics2023, 11, 3900.
Silva, A.T.G.; Fernandes, C.; Organista, J.; Souza, L.; Castelo, A. Validation of HiG-Flow Software for Simulating Two-Phase Flows with a 3D Geometric Volume of Fluid Algorithm. Mathematics 2023, 11, 3900.
Silva, A.T.G.; Fernandes, C.; Organista, J.; Souza, L.; Castelo, A. Validation of HiG-Flow Software for Simulating Two-Phase Flows with a 3D Geometric Volume of Fluid Algorithm. Mathematics2023, 11, 3900.
Silva, A.T.G.; Fernandes, C.; Organista, J.; Souza, L.; Castelo, A. Validation of HiG-Flow Software for Simulating Two-Phase Flows with a 3D Geometric Volume of Fluid Algorithm. Mathematics 2023, 11, 3900.
Abstract
This study reports the development of a numerical method to simulate two-phase flows of Newtonian fluids that are incompressible, immiscible, and isothermal. The interface in the simulation was located and reconstructed using the geometric volume of fluid (VOF) method. The implementation of the Piecewise-Linear Interface Calculation (PLIC) scheme of the VOF method was performed to solve the three-dimensional (3D) interface transport during the dynamics of two-phase flows. In this method, the interface is approximated by a line segment in each interfacial cell. The balance of forces at the interface was accounted for using the continuum interfacial force (CSF) model. To solve the Navier-Stokes equations, meshless finite difference schemes from the HiG-Flow computational fluid dynamics software were employed. The 3D PLIC-VOF HiG-Flow algorithm was used to simulate several benchmark two-phase flows for the purpose of validating the numerical implementation. First, the performance of the PLIC implementation was evaluated by conducting two standard advection numerical tests: the 3D shearing flow test and the 3D deforming field test. Good agreement is obtained for the 3D interface shape using both the 3D PLIC-VOF HiG-Flow algorithm and those found on the scientific literature. In addition, the absolute error of the volume tracking advection calculation obtained by our 3D PLIC-VOF HiG-Flow algorithm was found to be smaller than the one found in the scientific literature for both the 3D shearing and 3D deforming flow tests. Lastly, the 3D bubble rising problem was simulated for different fluid densities and viscosity’s ratios. Again, good agreement is obtained for the 3D interface shape using both the newly implemented algorithm and the OpenFOAM, DROPS and NaSt3D software. The bubble’s rise velocity and evolution of the bubble’s center of mass is also computed with the 3D PLIC-VOF HiG-Flow algorithm and found to be in agreement with these software.
Computer Science and Mathematics, Applied Mathematics
Copyright:
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