Lattice Boltzmann methods for multiphase flow and phase-change heat transfer

Owing to its conceptual simplicity and computational efficiency, the pseudopotential multiphase lattice Boltzmann (LB) model has attracted significant attention since its emergence. In this work, we aim to extend the pseudopotential LB model to simulate multiphase flows at large density ratio and relatively high Reynolds number. First, based on our recent work [Q. Li, K. H. Luo, and X. J. Li, Phys. Rev. E 86, 016709 (2012)], an improved forcing scheme is proposed for the multiple-relaxation-time pseudopotential LB model in order to achieve thermodynamic consistency and large density ratio in the model. Next, through investigating the effects of the parameter a in the Carnahan-Starling equation of state, we find that the interface thickness is approximately proportional to 1/√a. Using a smaller a will lead to a wider interface thickness, which can reduce the spurious currents and enhance the numerical stability of the pseudopotential model at large density ratio. Furthermore, it is found that a lower liquid viscosity can be gained in the pseudopotential model by increasing the kinematic viscosity ratio between the vapor and liquid phases. The improved pseudopotential LB model is numerically validated via the simulations of stationary droplet and droplet oscillation. Using the improved model as well as the above treatments, numerical simulations of droplet splashing on a thin liquid film are conducted at a density ratio in excess of 500 with Reynolds numbers ranging from 40 to 1000. The dynamics of droplet splashing is correctly reproduced and the predicted spread radius is found to obey the power law reported in the literature.

Lattice Boltzmann modeling of multiphase flows at large density ratio with an improved pseudopotential model.

The impact of liquid drops on solid surfaces is ubiquitous in nature, and of practical importance in many industrial processes. A drop hitting a flat surface retains a circular symmetry throughout the impact process. Here we show that a drop impinging on Echevaria leaves exhibits asymmetric bouncing dynamics with distinct spreading and retraction along two perpendicular directions. This is a direct consequence of the cylindrical leaves that have a convex/concave architecture of size comparable to the drop. Systematic experimental investigations on mimetic surfaces and lattice Boltzmann simulations reveal that this novel phenomenon results from an asymmetric momentum and mass distribution that allows for preferential fluid pumping around the drop rim. The asymmetry of the bouncing leads to ∼40% reduction in contact time.

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Symmetry breaking in drop bouncing on curved surfaces.

Over the last two decades, lattice Boltzmann methods have become an increasingly popular tool to compute the flow in complex geometries such as porous media. In addition to single phase simulations allowing, for example, a precise quantification of the permeability of a porous sample, a number of extensions to the lattice Boltzmann method are available which allow to study multiphase and multicomponent flows on a pore scale level. In this article we give an extensive overview on a number of these diffuse interface models and discuss their advantages and disadvantages. Furthermore, we shortly report on multiphase flows containing solid particles, as well as implementation details and optimization issues.

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Multiphase lattice Boltzmann simulations for porous media applications : a review

Lattice Boltzmann simulations of micron-scale drop impact on dry surfaces

Wall boundary conditions for the lattice Boltzmann equation (LBE) method for nonideal gases proposed by Lee and Fischer [Phys. Rev. E 74, 046709 (2006)] are examined. The LBE simulations of the contact line are typically contaminated by small but strong counter-rotating parasitic currents near solid surfaces. We find that these currents can be eliminated to round-off if the potential form of the intermolecular force is used with the boundary conditions based on the wall energy approach and the bounce-back rule. Numerical tests confirm the elimination of the parasitic currents in the vicinity of the contact line and the agreement of the calculated density, excess mass, and contact angle at the solid surfaces with theory.

Wall boundary conditions in the lattice Boltzmann equation method for nonideal gases.

In the non-ideal gas lattice Boltzmann equation (LBE), the intermolecular forces between solid and uid can be represented by the inclusion of the wall free energy in the expression of the total free energy. We derived and investigated three types of polynomial (linear, quadratic, and cubic) wall free energy based boundary conditions for the non-ideal gas LBE method. Static cases with a liquid drop sitting on solid surfaces are examined. All the proposed boundary conditions are able to predict the equilibrium states very well in the range of moderate contact angles by incorporating the potential form of the intermolecular forces and the bounce-back rule that guarantees mass conservation. Simulations with dieren t boundary conditions are carried out and the results are compared concerning the accuracy as well as the applicability of dieren t polynomial boundary conditions.

Lin Liu

Papers

Lattice Boltzmann simulations of micron-scale drop impact on dry surfaces

Wall boundary conditions in the lattice Boltzmann equation method for nonideal gases.

Wall free energy based polynomial boundary conditions for non-ideal gas lattice boltzmann equation