Lattice Boltzmann Simulations of Multiple Droplet Interactions During Impingement on the Substrate

Studying material interface evolution in the course of multiple droplet interactions is critical for understanding the material additive process in inkjet deposition. In this paper, we have developed a novel numerical model based on the Lattice Boltzmann Method (LBM) to simulate the interface dynamics during impingement and interaction of multiple droplets. A lattice Boltzmann formulation is proposed to solve the governing equations of the continuous phasefield model that are used in commercial software COMSOL. The LBM inter-particle force is derived by comparing the recovered macroscopic equations from LBM equations with the governing equations of the phase-field model. In addition, a new set of boundary conditions for the LBM formulation is proposed based on conservation of mass and momentum to ensure correct evolution of contact line dynamics. The results of LBM simulations are compared with those of COMSOL and experimental data from literature. The comparison shows the proposed LBM model not only yields a significant improvement in computational speed, but also results in better accuracy than COMSOL as validated against the experiments. We have also demonstrated the capability of the developed LBM numerical solver for simulating interactions between multiple droplets impinging on the substrate, which is critical for development and optimization of inkjet manufacturing.Mechanical Engineerin

A multi-component discrete Boltzmann model for nonequilibrium reactive flows

We propose a multi-component discrete Boltzmann model (DBM) for premixed, nonpremixed, or partially premixed nonequilibrium reactive flows. This model is suitable for both subsonic and supersonic flows with or without chemical reaction and/or external force. A two-dimensional sixteen-velocity model is constructed for the DBM. In the hydrodynamic limit, the DBM recovers the modified Navier-Stokes equations for reacting species in a force field. Compared to standard lattice Boltzmann models, the DBM presents not only more accurate hydrodynamic quantities, but also detailed nonequilibrium effects that are essential yet long-neglected by traditional fluid dynamics. Apart from nonequilibrium terms (viscous stress and heat flux) in conventional models, specific hydrodynamic and thermodynamic nonequilibrium quantities (high order kinetic moments and their departure from equilibrium) are dynamically obtained from the DBM in a straightforward way. Due to its generality, the developed methodology is applicable to a wide range of phenomena across many energy technologies, emissions reduction, environmental protection, mining accident prevention, chemical and process industry

Godunov-Type Upwind Flux Schemes of the Two-Dimensional Finite Volume Discrete Boltzmann Method

A simple unified Godunov-type upwind approach that does not need Riemann solvers for the flux calculation is developed for the finite volume discrete Boltzmann method (FVDBM) on an unstructured cell-centered triangular mesh. With piecewise-constant (PC), piecewise-linear (PL) and piecewise-parabolic (PP) reconstructions, three Godunov-type upwind flux schemes with different orders of accuracy are subsequently derived. After developing both a semi-implicit time marching scheme tailored for the developed flux schemes, and a versatile boundary treatment that is compatible with all of the flux schemes presented in this paper, numerical tests are conducted on spatial accuracy for several single-phase flow problems. Four major conclusions can be made. First, the Godunov-type schemes display higher spatial accuracy than the non-Godunov ones as the result of a more advanced treatment of the advection. Second, the PL and PP schemes are much more accurate than the PC scheme for velocity solutions. Third, there exists a threshold spatial resolution below which the PL scheme is better than the PP scheme and above which the PP scheme becomes more accurate. Fourth, besides increasing spatial resolution, increasing temporal resolution can also improve the accuracy in space for the PL and PP schemes