Abstract
A recently developed forcing scheme has allowed the pseudopotential multiphase lattice Boltzmann method to correctly reproduce coexistence curves, while expanding its range to lower surface tensions and arbitrarily high density ratios [Lycett-Brown and Luo, Phys. Rev. E 91, 023305 (2015)PLEEE81539-375510.1103/PhysRevE.91.023305]. Here, a third-order Chapman-Enskog analysis is used to extend this result from the single-relaxation-time collision operator, to a multiple-relaxation-time cascaded collision operator, whose additional relaxation rates allow a significant increase in stability. Numerical results confirm that the proposed scheme enables almost independent control of density ratio, surface tension, interface width, viscosity, and the additional relaxation rates of the cascaded collision operator. This allows simulation of large density ratio flows at simultaneously high Reynolds and Weber numbers, which is demonstrated through binary collisions of water droplets in air (with density ratio up to 1000, Reynolds number 6200 and Weber number 440). This model represents a significant improvement in multiphase flow simulation by the pseudopotential lattice Boltzmann method in which real-world parameters are finally achievable.
Highlights
The lattice Boltzmann method (LBM) is a mesoscopic simulation approach that provides an attractive alternative to traditional computational fluid dynamics
We have shown that the surface tension parameter, σc, can be varied with only slight effects on the gas density, and that with the newly introduced correction accounting for the cascaded collision operator, this result is unaffected by varying the associated additional relaxation rates
While the results presented here are a significant advance for the pseudopotential multiphase LBM, it should be noted that other methods such as that by Lee and Fischer [42] have successfully reduced spurious velocities for comparable interface widths and density ratios
Summary
The lattice Boltzmann method (LBM) is a mesoscopic simulation approach that provides an attractive alternative to traditional computational fluid dynamics. The method of Guo et al [17] performs better than the EDM for the exponential form of the equation of state proposed by Shan and Chen This had previously resulted in some confusion over which forcing scheme is the most appropriate to use. Lycett-Brown et al [19,33] provided an alternative derivation of the cascaded LBM and extended it to a pseudopotential multiphase scheme, resulting in increased stability at low viscosity, and the reduction of spurious velocities by tuning the relaxation rates of the higher-order moments.
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