SUMMARYThis paper presents a general methodology for studying instabilities of natural convection flows enclosed in cavities of complex geometry. Different tools have been developed, consisting of time integration of the unsteady equations, steady state solving, and computation of the most unstable eigenmodes of the Jacobian and its adjoint. The methodology is validated in the classical differentially heated cavity, where the steady solution branch is followed for vary large values of the Rayleigh number and most unstable eigenmodes are computed at selected Rayleigh values. Its effectiveness for complex geometries is illustrated on a configuration consisting of a cavity with internal heated partitions. We finally propose to reduce the Navier-Stokes equations to a differential system by expanding the unsteady solution as the sum of the steady state solution and of a linear combination of the leading eigenmodes. The principle of the method is exposed and preliminary results are presented.

Global characterization of hydrodynamics and gas-liquid transfer in a 2D column with a 4 mm thickness is carried out with water and aqueous glycerol solutions. This new design can be used as a photobioreactor of low thickness to intensify the volumetric productivity by increasing microalgae concentration. To mimic the presence of algae cultures, the liquid viscosity is adjusted with glycerol. Focuses are made on flow regimes and their transitions, mixing, and gas-liquid transfer at the scale of the reactor. In comparison with conventional bubble columns lower terminal velocities are obtained. So, in homogeneous regime, the residence time of bubbles is greater than in conventional bubble columns and the gas holdup is slightly higher. However, regime transitions appear at relatively low superficial gas velocities in the confined bubble column. In addition, two transition regimes are visible and have macroscopic flow structures very similar to the ones observed for conventional columns. For the mixing time, a dependence on the viscosity is observed and whatever the solution tested, this parameter decreases very quickly with the increase of the gas superficial velocity. Finally, global gas-liquid mass transfer coefficients measurements show lower values than in classical bubble columns at the same superficial gas velocity.

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