Modelagem Lattice Boltzmann multicomponente para o escoamento de fluidos imiscíveis com altas razões de viscosidade

Abstract

The present work proposes the development of a multicomponent lattice Boltzann model for the representation of high viscosity ratios in immiscible flows, using as reference in its development the models described by Shan e Chen (1993) and Philippi et al. (2012). The proposed model is based on the use of high-order discretization schemes and on the adaptation of a moments-based collision model. Through Chapman-Enskog analyses, which recover the balance equations of the numerically discretized model, it is demonstrated that the balance equations of the developed model eliminate discretization and modeling errors present in the model proposed by Shan e Chen (1993). Verification results of the moments-based collision model were conducted to verify the Stokes hypothesis in incompressible flows, being observed that the model increases numerical stability and reduces the compressibility effects characteristic of LBM, both while maintaining the second-order grid convergence rate. The multicomponent model validation is done through problems of static bubble, Poiseuille flow for two-components and fluid-fluid displacement, analyzing the numerical stability limit behaviors, accuracy, and magnitude of spurious currents. The results demonstrate numerical stability limits for the viscosity ratio tending to infinity in the problems of static bubble and Poiseuille flow for two-components, while in the fluid-fluid displacement problem were reached stability in the order of 104 . In the other analyzes of spurious currents and accuracy, the results were consistent with those presented by the other models in the literature. Finally, the present model is employed in the representation of the fluid-fluid displacement problem in porous media, being observed a good capacity to represent the behaviors of distinct displacement states, as well as a high numerical stability of the viscosity ratio in the order of 10−6 to 106 , depending on the capillary number.