Finite element fluid flow computations through porous media employing quasi-linear and nonlinear viscoelastic models

Mathematical modeling involving porous heterogeneous media is important in a number of composite manufacturing processes, such as resin transfer molding (RTM), injection molding and the like. Of interest here are process modeling issues as related to composites manufacturing by RTM, because of the ability of the method to manufacture consolidated net shapes of complex geometric parts. In this research, we propose a mathematical model by utilizing the local volume averaging technique to establish the governing equations and therein provide finite element computational developments to predict the flow behavior of a viscous and viscoelastic fluid through a porous fiber network. The developments predict the velocity, pressure, and polymeric stress by modeling the conservation laws (e.g. mass and momentum) of the flow field coupled with constitutive equations for polymeric stress field. The governing equations of the flow are averaged for the fluid phase. Furthermore, the simulations target a variety of viscoelastic models (e.g. Newtonian model, Upper-Convected-Maxwell Model, Oldroyd-B model and Giesekus model) to provide a fundamental understanding of the elastic effects on the flow field. To solve the complex coupled nonlinear equations of the mathematical model described above, a combination of Newton linearization and the Galerkin and Streamline-Upwinding-Petrov-Galerkin (SUPG) finite element procedures are employed to accurately capture the representative physics. The formulations are first validated with available test cases of viscoelastic flows without porous media. Therein, the simulations are described for viscoelastic flow through porous media and the comparative results of different constitutive models are presented and discussed at length.