Um método computacional para modelagem de problemas de fluidos carregados com partículas.

Abstract

In this work, a study is presented on Fluid-Particle interaction problems and the methods and formulations used to solve them. In addition, is proposed a new method for solving coupled problems of fluid mechanics and particle mechanics. The idea is based on previous works by (Gomes e Pimenta 2015) and (Campello 2016), and the goal is to develop an efficient computational model suited to simulate problems involving flowing fluid media laden with solid particles. The fluid problem is resolved by an Eulerian finite element approach using local element velocity-pressure pairs satisfying the LBB compatibility condition, with the resulting nonlinear system of equations being iteratively solved by the Newton-Raphson method. As an important feature, the fluid mesh remains fixed during the flow, just as in classical Eulerian approaches. The particles´ problem, in turn, is resolved in a Lagrangian discrete element approach, wherein both particle-to-particle and particle-to-wall (fixed boundaries) contacts are freely permitted and resolved. The influence of the fluid on the motion of the particles is represented by means of forces and moments, which are computed from the fluid flow and imposed on the particles in a coupled, iterative and explicit way. The fluid-particles´ interfaces are treated by means of immersed boundary technique, in which the fluid interface conditions with the (nonmatching) particles´ boundaries are imposed through discontinuous piecewise constant Lagrange multipliers interpolating functions along the interfaces. An explicit, staggered and interactive scheme is adopted to achieve convergence within each time step of the problem. In order to illustrate the potentialities of the proposed scheme, particle-laden fluid flow simulations are presented.