Section: New Results

Numerical models and simulations applied to physics

Heat transfer modeling in saturated porous media

Participant : Édouard Canot.

This work is done in the context of the ARPHYMAT project (see 8.3.3 ) and the MODNUM project (see 8.3.2 ), in collaboration with Archeosciences, IPR and Lebanese International University (LIU), Lebanon. It was also done in the context of Caroline Thoux's internship (L3, INSA Rennes).

This work is published in [17] .

In this paper, the authors introduce a robust numerical strategy to estimate the temperature dependent heat capacity, thermal conductivity and porosity of a saturated porous medium, basing on the knowledge of heating curves at selected points in the medium. In order to solve the inverse problem, we use the least squares criterion (in which the sensitivity coefficients appear), leading to a system of ordinary differential equations (ODE). At the stage of numerical computations, we propose a new global approach, based on the method of lines and ordinary differential equations solvers, combined with a modified Newton method to deal with the nonlinearities presented in the system of coupled equations.

Concerning strong thermal transfer in saturated porous media, the LHA method (Latent Heat Accumulation) is able to take into account phase changes by considering heat accumulation at the local level. The explicit knowledge of the cells which are changing their state allows the build of the liquid-gas interface position. A 2D configuration has been considered, together with a structured mesh but without refinement. The validation of this new method has been checked by making comparison between numerical results and an analytical solution.

Granular materials

Participant : Édouard Canot.

This work is done in collaboration with IPR and is published in [11] .

We first studied the granular flows by the "discrete elements" method in silo geometries. By changing the micro-mechanical properties of the grains (restitution and friction) we showed that they had a significant influence on the flow discharge. Although models such as "discrete elements" provide access to all the individual properties of the grains, they have one major drawback: the computation time is very important that prohibits the modeling of geophysical and industrial situations. To overcome this problem, we used the "continuous medium" approach, which consider that the granular medium studied follows a rheology recently proposed in the literature. After discussing the numerical implementation, we have studied this rheology for steady and fully developed flows with a semi-analytical method in two configurations: a shear cell and a channel. This allowed us to highlight the differences between a granular medium and a Newtonian fluid.