Model for classical and ultimate regimes of radiatively driven turbulent convection. - Archive ouverte HAL Access content directly
Journal Articles Journal of Fluid Mechanics Year : 2020

Model for classical and ultimate regimes of radiatively driven turbulent convection.

Abstract

In a standard Rayleigh-Bénard experiment, a layer of fluid is confined between two horizontal plates and the convection regime is controlled by the temperature difference between the hot lower plate and the cold upper plate. The effect of direct heat injection into the fluid layer itself, for example by light absorption, is studied here theoretically. In this case, the Nusselt number (N u) depends on two non-dimensional parameters: the Rayleigh number (Ra) and the ratio between the spatial extension of the heat source (l) and the height of the fluid layer (h). For both the well-known classical and ultimate convection regimes, the theory developed here gives an analytical formula for the variations of the Nusselt number as a function of Ra and the l/h ratio. For large Rayleigh numbers and in the classical convection regime, by increasing l/h from 0 to 1/2, the Ra-dependent Nusselt number gradually changes from the standard scaling N u ∼ Ra 1/3 to the asymptotic scaling N u ∼ Ra 2/3. For the ultimate convection regime, N u gradually changes from N u ∼ Ra 1/2 scaling to an asymptotic behaviour seen only at very high Ra for which N u ∼ Ra 2. This theory is validated by the recent experimental results given by Bouillaut et al. (2019), at least in the classical regime. The predictions for the ultimate regime cannot be confirmed at this time due to the absence of experimental or numerical works on Rayleigh-Bénard convection both driven by internal sources and for very large Ra.
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Dates and versions

hal-02299927 , version 1 (29-09-2019)
hal-02299927 , version 2 (15-06-2020)

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Mathieu Creyssels. Model for classical and ultimate regimes of radiatively driven turbulent convection.. Journal of Fluid Mechanics, 2020, 900, ⟨10.1017/jfm.2020.521⟩. ⟨hal-02299927v2⟩
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