Turbulent heat transport regimes in a channel

Abstract

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Buoyancy-driven bubbly flows: scaling of velocities in bubble columns operated in the heterogeneous regime

“…As for long channels or pipes, the translational invariance observed along the bubble column axis implies that the only characteristic length is the column diameter, provided that the column is high enough. Besides, and owing to that translational invariance, a uniform density gradient develops along the channel (Cholemari & Arakeri 2009;Castaing et al 2017). That expectation is corroborated in bubble columns.…”

“…Such large-scale organization is reminiscent of turbulent buoyancy-driven flows in confined channels with zero mean flow where density gradients are due to solute concentration (Cholemari & Arakeri 2009) or to temperature (Castaing et al. 2017). As for long channels or pipes, the translational invariance observed along the bubble column axis implies that the only characteristic length is the column diameter, provided that the column is high enough.…”

“…Besides, and owing to that translational invariance, a uniform density gradient develops along the channel (Cholemari & Arakeri 2009; Castaing et al. 2017). That expectation is corroborated in bubble columns.…”

“…where ρ/ρ is evaluated at a large length scale. In turbulent buoyancy-driven flows in confined channels, the constant axial gradient of the mean density is used to evaluate ρ (Cholemari & Arakeri 2009;Castaing et al 2017). In bubble columns, as the flow destabilization arises from lateral differences in density and thus in buoyancy, we sought a relevant scale from the radial void fraction profile.…”

Convection driven by internal heat sources and sinks: Heat transport beyond the mixing-length or “ultimate” scaling regime

“…Interestingly, the data then displays a square-root relation between the heat flux and the internal temperature gradient [22,23]. However, the associated Rayleigh and Nusselt numbers need be built using the width of the channel [24][25][26]. The resulting scaling relation between the heat flux and the internal temperature gradient explicitly involves the width of the domain, which challenges its applicability to the arbitrarily wide domains characteristic of astrophysical and geophysical flows.…”