Non-universal transport mechanisms in vertical natural convection with dispersed light droplets

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, $\alpha = 5\times10^{-3}$ and $\alpha = 2\times 10^{-2}$, 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, $Nu$ retains the effective scaling exponents that are 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 is non-universal, 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) $Ra_d/Ra$, where $Ra_d$ is the droplet Rayleigh number, which we introduce in this paper. When $b \lesssim O(10^{-1})$ and $Ra_d/Ra \lesssim O(100)$, the $Nu$ scaling is expected to recover to the VC scaling without droplets, and comparison with $b$ and $Ra_d/Ra$ from our data supports this notion.