Numerical simulation of mass transfer dynamics in Taylor flows
Résumé
Direct Numerical Simulations of mass transfer within Taylor flows are carried out using the periodic unit-cell approach by means of the Level-Set method, under the axisymmetric assumption. The considered cases are based on the experimental study of Butler et al. (2018) (absorption of gaseous species) for bubbles of Reynolds numbers Re_b>200 and capillary numbers Ca>10^{-3}. Firstly, the hydrodynamics of five cases are calculated up to steady state, after which the bubble shape, lubrication film thickness and velocity profiles are compared to experimental and theoretical results. Using these converged hydrodynamics, the transient mass transfer between the gas and liquid phases is then simulated, assuming no change in bubble volume. The Péclet number $Pe$ is varied between 10 and 900 by changing the diffusion coefficient, allowing for new insight into local phenomena of mass transfer. In this way, the maximal transfer fluxes at the interface are observed to be (i) close to the stagnation point at the film entrance, and (ii) at the rear cap where the tangential velocity is greatest. As once as the mass transfer coefficient becomes constant, the fluxes across the part of the interface in contact with the film and around the bubble caps are each characterised by a local Sherwood number. The latter evolves by Pe_{film}^{1/2} across the film and is found to be predictable by a simple model when Pe_{film} > 1, where Pe_{film} is the film Péclet number. Concerning the caps, it evolves by Pe^{1/2} but only in a finite range of Pe, contrary to the common assumption of similarity of transfer around the caps with that around a rising unconfined spherical bubble. Such local analyses could be further used in multizone models of mass transfer for Taylor flows.
Finally, a correlation is proposed to scale the global Sherwood number Sh_{\infty} far from channel inlet, defined as a function of both a Péclet number Pe_R based on the relative velocity between the bubble and the two-phase flow and the gas volume fraction in the unit cell. Its predictions are discussed against experimental results at much higher Péclet numbers, after showing that Sh_{\infty} is independent on the initial concentration distribution in the liquid (the latter being sensitive to the injection conditions in experiments).
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