Drop-Laden Rayleigh-Bénard Convection
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In this work, we investigate the complex behavior of a swarm of deformable droplets suspended in Rayleigh–B{\'e}nard convection, where thermal forcing drives continuous interactions between the dispersed and carrier phases. The drops can deform, coalesce, and break as they are advected by the flow. To describe the system evolution, we couple direct numerical simulations (DNS) of the Navier–Stokes equations (used to describe the flow field), the energy equation (used to describe the temperature field) with a phase-field method based on the accurate diffuse-interface (ACDI) formulation (used to describe the dispersed phase). The computational domain has a unitary aspect ratio, and the Prandtl number is fixed to unity to isolate the influence of buoyancy. By varying the thermal expansion coefficient, we systematically explore Rayleigh numbers from Ra=10^5 to Ra=10^8. The introduction of a dispersed phase modifies the global heat-transfer properties of the system. In particular, we observe pronounced fluctuations in the Nusselt number relative to the classical single-phase Rayleigh–Bénard configuration, indicating strong coupling between droplet dynamics and thermal transport. Analysis of the flow topology reveals that droplets preferentially cluster in regions where the flow-topology parameter Q is positive, corresponding to vortex-dominated structures. Furthermore, large positive values of $Q$ correlate with large deformations, leading to elongated droplets.
