Lattice Boltzmann Solver for Multiphase Flows: Application to High Weber and Reynolds Numbers.

The lattice Boltzmann method, now widely used for a variety of applications, has also been extended to model multiphase flows through different formulations. While already applied to many different configurations in low Weber and Reynolds number regimes, applications to higher Weber/Reynolds numbers or larger density/viscosity ratios are still the topic of active research. In this study, through a combination of a decoupled phase-field formulation-the conservative Allen-Cahn equation-and a cumulant-based collision operator for a low-Mach pressure-based flow solver, we present an algorithm that can be used for higher Reynolds/Weber numbers. The algorithm was validated through a variety of test cases, starting with the Rayleigh-Taylor instability in both 2D and 3D, followed by the impact of a droplet on a liquid sheet. In all simulations, the solver correctly captured the flow dynamics andmatched reference results very well. As the final test case, the solver was used to model droplet splashing on a thin liquid sheet in 3D with a density ratio of 1000 and kinematic viscosity ratio of 15, matching the water/air system at We = 8000 and Re = 1000. Results showed that the solver correctly captured the fingering instabilities at the crown rim and their subsequent breakup, in agreement with experimental and numerical observations reported in the literature.

Consistent simulation of droplet evaporation based on the phase-field multiphase lattice Boltzmann method.

In the present article, we extend and generalize our previous article [H. Safari, M. H. Rahimian, and M. Krafczyk, Phys. Rev. E 88, 013304 (2013)] to include the gradient of the vapor concentration at the liquid-vapor interface as the driving force for vaporization allowing the evaporation from the phase interface to work for arbitrary temperatures. The lattice Boltzmann phase-field multiphase modeling approach with a suitable source term, accounting for the effect of the phase change on the velocity field, is used to solve the two-phase flow field. The modified convective Cahn-Hilliard equation is employed to reconstruct the dynamics of the interface topology. The coupling between the vapor concentration and temperature field at the interface is modeled by the well-known Clausius-Clapeyron correlation. Numerous validation tests including one-dimensional and two-dimensional cases are carried out to demonstrate the consistency of the presented model. Results show that the model is able to predict the flow features around and inside an evaporating droplet quantitatively in quiescent as well as convective environments.

Extended lattice Boltzmann method for numerical simulation of thermal phase change in two-phase fluid flow.

In this article, a method based on the multiphase lattice Boltzmann framework is presented which is applicable to liquid-vapor phase-change phenomena. Both liquid and vapor phases are assumed to be incompressible. For phase changes occurring at the phase interface, the divergence-free condition of the velocity field is no longer satisfied due to the gas volume generated by vaporization or fluid volume generated by condensation. Thus, we extend a previous model by a suitable equation to account for the finite divergence of the velocity field within the interface region. Furthermore, the convective Cahn-Hilliard equation is extended to take into account vaporization effects. In a first step, a D1Q3 LB model is constructed and validated against the analytical solution of a one-dimensional Stefan problem for different density ratios. Finally the model is extended to two dimensions (D2Q9) to simulate droplet evaporation. We demonstrate that the results obtained by this approach are in good agreement with theory.