TY - JOUR
T1 - A Volume-of-Fluid method for multicomponent droplet evaporation with Robin boundary conditions
AU - Zamani Salimi, Salar
AU - Scapin, Nicolò
AU - Popescu, Elena Roxana
AU - Costa, Pedro
AU - Brandt, Luca
PY - 2024
Y1 - 2024
N2 - We propose a numerical method tailored to perform interface-resolved simulations of evaporating multicomponent two-phase flows. The novelty of the method lies in the use of Robin boundary conditions to couple the transport equations for the vaporized species in the gas phase and the transport equations of the same species in the liquid phase. The Robin boundary condition is implemented with the cost-effective procedure proposed by Chai et al. [1] and consists of two steps: (1) calculating the normal derivative of the mass fraction fields in cells adjacent to the interface through the reconstruction of a linear polynomial system, and (2) extrapolating the normal derivative and the ghost value in the normal direction using a linear partial differential equation. This methodology yields a second-order accurate solution for the Poisson equation with a Robin boundary condition and a first-order accurate solution for the Stefan problem. The overall methodology is implemented in an efficient two-fluid solver, which includes a Volume-of-Fluid (VoF) approach for the interface representation, a divergence-free extension of the liquid velocity field onto the entire domain to transport the VoF, and the temperature equation to include thermal effects. We demonstrate the convergence of the numerical method to the analytical solution for multicomponent isothermal evaporation and observe good overall computational performance for simulating non-isothermal evaporating two-fluid flows in two and three dimensions.
AB - We propose a numerical method tailored to perform interface-resolved simulations of evaporating multicomponent two-phase flows. The novelty of the method lies in the use of Robin boundary conditions to couple the transport equations for the vaporized species in the gas phase and the transport equations of the same species in the liquid phase. The Robin boundary condition is implemented with the cost-effective procedure proposed by Chai et al. [1] and consists of two steps: (1) calculating the normal derivative of the mass fraction fields in cells adjacent to the interface through the reconstruction of a linear polynomial system, and (2) extrapolating the normal derivative and the ghost value in the normal direction using a linear partial differential equation. This methodology yields a second-order accurate solution for the Poisson equation with a Robin boundary condition and a first-order accurate solution for the Stefan problem. The overall methodology is implemented in an efficient two-fluid solver, which includes a Volume-of-Fluid (VoF) approach for the interface representation, a divergence-free extension of the liquid velocity field onto the entire domain to transport the VoF, and the temperature equation to include thermal effects. We demonstrate the convergence of the numerical method to the analytical solution for multicomponent isothermal evaporation and observe good overall computational performance for simulating non-isothermal evaporating two-fluid flows in two and three dimensions.
KW - Multicomponent liquid droplet
KW - Phase change
KW - Robin boundary condition
KW - Volume-of-Fluid method
UR - http://www.scopus.com/inward/record.url?scp=85196727074&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2024.113211
DO - 10.1016/j.jcp.2024.113211
M3 - Article
AN - SCOPUS:85196727074
SN - 0021-9991
VL - 514
JO - Journal of Computational Physics
JF - Journal of Computational Physics
M1 - 113211
ER -