Mathematics (Sep 2023)
Validation of HiG-Flow Software for Simulating Two-Phase Flows with a 3D Geometric Volume of Fluid Algorithm
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 is 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 is 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 is 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 are employed. The 3D PLIC-VOF HiG-Flow algorithm is used to simulate several benchmark two-phase flows for the purpose of validating the numerical implementation. First, the performance of the PLIC implementation is 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 in the scientific literature, specifically, the piecewise-constant flux surface calculation, the volume of fluid method implemented in OpenFOAM, and the high-order finite-element software FEEL. In addition, the absolute error of the volume tracking advection calculation obtained by our 3D PLIC-VOF HiG-Flow algorithm is found to be smaller than the one found in the scientific literature for both the 3D shearing and 3D deforming flow tests. The volume fraction conservation absolute errors obtained using our algorithm are 4.48×10−5 and 9.41×10−6 for both shearing and deforming flow tests, respectively, being two orders lower than the results presented in the scientific literature at the same level of mesh refinement. Lastly, the 3D bubble rising problem is simulated for different fluid densities (ρ1/ρ2=10 and ρ1/ρ2=1000) and viscosity ratios (μ1/μ2=10 and μ1/μ2=100). Again, good agreement is obtained for the 3D interface shape using both the newly implemented algorithm and OpenFOAM, DROPS, and NaSt3D software. The 3D PLIC-VOF HiG-Flow algorithm predicted a stable ellipsoidal droplet shape for ρ1/ρ2=10 and μ1/μ2=10, and a stable cap shape for ρ1/ρ2=1000 and μ1/μ2=100. The bubble’s rise velocity and evolution of the bubble’s center of mass are also computed with the 3D PLIC-VOF HiG-Flow algorithm and found to be in agreement with those software. The rise velocity of the droplet for both the ellipsoidal and cap flow regime’s is found, in the initial stages of the simulation, to gradually increase from its initial value of zero to a maximum magnitude; then, the steady-state velocity of the droplet decreases, being more accentuated for the cap regime.
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