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Abstract
A three-dimensional color-fluid lattice Boltzmann model for immiscible two-phase flows is developed in the framework of a three-dimensional 27-velocity (D3Q27) lattice. The collision operator comprises the D3Q27 versions of three suboperators: a multiple-relaxation-time (MRT) collision operator, a generalized Liu-Valocchi-Kang perturbation operator, and a Latva-Kokko-Rothman recoloring operator. A D3Q27 version of an enhanced equilibrium distribution function is also incorporated into this model to improve the Galilean invariance. Three types of numerical tests, namely, a static droplet, an oscillating droplet, and the Rayleigh-Taylor instability, show a good agreement with analytical solutions and numerical simulations. Following these numerical tests, this model is applied to liquid-jet-breakup simulations. The simulation conditions are matched to the conditions of the previous experiments. In this case, numerical stability is maintained throughout the simulation, although the kinematic viscosity for the continuous phase is set as low as 1.8×10^{-4}, in which case the corresponding Reynolds number is 3.4×10^{3}; the developed lattice Boltzmann model based on the D3Q27 lattice enables us to perform the simulation with parameters directly matched to the experiments. The jet's liquid column transitions from an asymmetrical to an axisymmetrical shape, and entrainment occurs from the side of the jet. The measured time history of the jet's leading-edge position shows a good agreement with the experiments. Finally, the reproducibility of the regime map for liquid-liquid systems is assessed. The present lattice Boltzmann simulations well reproduce the characteristics of predicted regimes, including varicose breakup, sinuous breakup, and atomization.
Highlights
Multiphase and multicomponent flows appear in many natural and industrial processes
The collision operator comprises the D3Q27 versions of three suboperators: a multiple-relaxation-time (MRT) collision operator, a generalized Liu–Valocchi– Kang perturbation operator, and a Latva-Kokko–Rothman recoloring operator
A D3Q27 version of an enhanced equilibrium distribution function is incorporated into this model to improve the Galilean invariance
Summary
Multiphase and multicomponent flows appear in many natural and industrial processes. A liquid jet injected into another fluid is an interesting example of such a flow. McCracken and Abraham [61] successfully introduced an MRT operator to the multiphase lattice Boltzmann model and performed liquid-jet breakup simulations [31] They assumed that the flow was axisymmetric in two dimensions. Matsuo et al [32] used the three-dimensional two-phase lattice Boltzmann model, which was developed by Ebihara and Watanabe [62] based on the model of He et al [41] They compared their simulation results with experiments and investigated the effect of the Froude number upon the jet-breakup length. Saito et al [33] incorporated the MRT operator into the three-dimensional 19-velocity (D3Q19) color-fluid model proposed by Liu et al [53] and applied this model to liquid-jet-breakup simulations They could simulate liquid-jet breakup with the Reynolds number up to O(103), the kinematic-viscosity ratio was set to unity to avoid numerical instability.
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