Multiple-relaxation-time color-gradient lattice Boltzmann model for simulating two-phase flows with high density ratio

Abstract

In this paper we propose a color-gradient lattice Boltzmann (LB) model for simulating two-phase flows with high density ratio and high Reynolds number. The model applies a multirelaxation-time (MRT) collision operator to enhance the stability of the simulation. A source term, which is derived by the Chapman-Enskog analysis, is added into the MRT LB equation so that the Navier-Stokes equations can be exactly recovered. Also, a form of the equilibrium density distribution function is used to simplify the source term. To validate the proposed model, steady flows of a static droplet and the layered channel flow are first simulated with density ratios up to 1000. Small values of spurious velocities and interfacial tension errors are found in the static droplet test, and improved profiles of velocity are obtained by the present model in simulating channel flows. Then, two cases of unsteady flows, Rayleigh-Taylor instability and droplet splashing on a thin film, are simulated. In the former case, the density ratio of 3 and Reynolds numbers of 256 and 2048 are considered. The interface shapes and spike and bubble positions are in good agreement with the results of previous studies. In the latter case, the droplet spreading radius is found to obey the power law proposed in previous studies for the density ratio of 100 and Reynolds number up to 500.

Generalized three-dimensional lattice Boltzmann color-gradient method for immiscible two-phase pore-scale imbibition and drainage in porous media

“…As a more severe restriction, we point out that while the CGM can simulate high density ratios in simple test cases, in complex setups it appears to be impractical to simulate density ratios larger than approximately 20, as this would require very small time steps and consequently long simulation times. While it is still possible to simulate a high density ratio with the CGM, it is clear that it still remains a real challenge [42,47]. We believe that current state-of-the-art CGMs are mostly suited for simulating liquid-liquid interfaces in immiscible, incompressible, and isothermal Newtonian multiphase flows [41], and in a limited sense for liquid-gas interfaces at very low Reynolds numbers.…”

Three-dimensional lattice Boltzmann method benchmarks between color-gradient and pseudo-potential immiscible multi-component models

“…Approach to increase the Galilean invariance of the CGM has also been proposed. [28][29][30] The MRT has also been introduced to improve the stability of the CGM. [30][31][32] There are also approaches to model the static and dynamic contact angles accurately at a solid boundary.…”

“…[28][29][30] The MRT has also been introduced to improve the stability of the CGM. [30][31][32] There are also approaches to model the static and dynamic contact angles accurately at a solid boundary. [33][34][35] Recently, a generalized CGM with enhanced equilibrium for the D2Q9, D3Q15, D3Q19 and D3Q27 have been proposed.…”

Comparison of multiphase SPH and LBM approaches for the simulation of intermittent flows

“…The present LBM approach is the two-phase model introduced in [43] and completed with the improvements proposed in [52,51] for the recoloring operator and the color gradient. In addition, the contact angle ajustment is based on [56,57] and the corrective procedure to properly recover Navier-Stokes equations is borrowed from [58]. We work with 2 sets of distribution functions, one for each fluid, moving on a D2Q9 lattice.…”

“…Alternatively, for the first sub operator, (Ω k i ) (1) , one can use the Multiple Relaxation Time (MRT) operator instead of the BGK operator. The MRT approach is more stable than its BGK counterpart [61,58]. It reads as follows :…”