Soutenance de Florencia Falkinhoff

This thesis presents an experimental and numerical study focused on the hydrodynamics in fixed beds of spherical particles that are randomly distributed inside a cylindrical container (e.g. a reactor), so that border effects are not negligible. Fixed beds are a particular example of a porous medium, and we are particularly motivated by the use of fixed beds in the context of AA-CAES technologies as a thermal energy storage unit. Fixed beds, as porous media in general, present a multi-scale problem: the hydrodynamics at the smallest scales can be very different from those at the largest scales. In order to bridge this scale hierarchy upscale techniques are usually used such as volume averaging, that link the small-scale fluctuations with the large-scale dynamics. These techniques are typically applied at a mesoscale. However, the equations involved at this scale do not form a closed system, so that a closure model is needed.

Moreover, the flows that saturate fixed beds can get incredibly complex, as the spheres distri- bution and the walls produce tortuous paths and local changes in porosity, and there are solid-fluid interactions that also drive and affect the hydrodynamics. In order to explore how these effects can affect upscaling techniques, we studied the behavior of an inertial confined flow at all three scales: the macro, the micro and the meso. We did this by computing numerical simulations and doing two different experimental campaigns. Both the experimental and numerical methods allowed us to study hydrodynamical effects of the three non-dimensional parameters involved in the system: the Reynolds number Re, the porosity ε and the sphere-to-reactor diameter ratio D/d.

The first experimental and numerical campaigns were dedicated to the study of the flow past fixed beds from the global (macro) point of view. We studied the variability of the pressure field and pressure gradient and how they are affected by confinement effects.

The second experimental campaign consisted on studying the hydrodynamics at the pore (micro) scale by using refractive index-matching Particle Tracking Velocimetry. We observed that even though the flow is globally laminar, its behavior at the microscale is comparable to that of a fully turbulent flow. We then complemented the experiments with numerical data, which allowed us to study the local homogeneity and isotropy of the flow.

We finally linked the results obtained at the global and pore scales to the mesoscale using numerical results, which reflected the multi-scale nature of the system. We explored the different terms involved in the non-closed volume-averaged equations in order to help find a closure model that takes into account the wall effects, which include the local solid-fluid interactions and the Reynolds stress tensor.