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Abstract

We present results on the effect of dispersed droplets in vertical natural convection (VC)
using direct numerical simulations based on a two-way fully coupled Euler–Lagrange
approach with a liquid phase and a dispersed droplets phase. For increasing thermal
driving, characterised by the Rayleigh number, Ra, of the two analysed droplet volume fractions, α = 5×10−3 and α = 2×10−2, we find non-monotonic responses to the overall heat fluxes, characterised by the Nusselt number, Nu. The Nu number is larger
when the droplets are thermally coupled to the liquid. However, Nu values remain close
to the 1/4-laminar VC scaling, suggesting that the heat transport is still modulated
by thermal boundary layers. Local analyses reveal the non-monotonic trends of local
heat fluxes and wall-shear stresses: whilst regions of high heat fluxes are correlated
to increased wall-shear stresses, the spatio-temporal distribution and magnitude of the
increase are non-monotonic, implying that the overall heat transport is obscured by
competing mechanisms. Most crucially, we find that the transport mechanisms inherently
depend on the dominance of droplet driving to thermal driving that can quantified by
(i) the bubblance parameter b, which measures the ratio of energy produced by the
dispersed phase and the energy of the background turbulence, and (ii) Rad/Ra, where Rad is the droplet Rayleigh number, which we introduce in this paper. When b O(10−1) and Rad/Ra O(100), the Nu scaling is expected to recover to the VC scaling without droplets, and comparison with b and Rad/Ra from our data supports this notion.