Assessment of the pseudopotential lattice-Boltzmann method for modeling multiphase fuel droplets

An improved pseudopotential lattice-Boltzmann model was proposed for simulating multiphase flow dynamics to describe fuel droplets, and its thermodynamic consistency was tested against the Peng-Robinson equation of state. The studied liquid fuels included paraffinic hydrocarbons with a different number of carbon atoms (C1-C10), methanol (CH3OH), hydrogen (H2), ammonia (NH3), and water (H2O). To improve accuracy and reduce the magnitude of the spurious currents, the multi-relaxation times collision operator was implemented and the forcing term was computed using the hybrid pseudopotential interaction force with an eighth-order isotropic degree. The pseudopotential lattice-Boltzmann model accurately predicted the equilibrium densities and captured satisfactorily the thermodynamic vapor-liquid coexistence curve given by the analytical solution of the Peng-Robinson equation of state for acentric factors ranging from -0.22 to 0.56, keeping the maximum average error for the liquid and vapor branches below 0.8% and 3.7%, respectively. Nevertheless, Peng-Robinson was found to be insufficiently accurate to replicate the actual thermodynamic state, especially for H2O and CH3OH, for which the results strongly deviated from the experimental vapor-liquid equilibrium densities and reached average errors for the vapor phase of nearly 28%. Furthermore, the surface tension (gamma) was retrieved using the multiphase pseudopotential lattice-Boltzmann results and served to verify the thermodynamic consistency of the pseudopotential lattice-Boltzmann with respect to the parachor model. Lastly, the pseudopotential lattice-Boltzmann model was also shown to predict accurately the transient behavior of oscillating droplets. Overall, the enhanced model satisfactorily predicted the properties and behavior of the substances for a wide range of conditions.