Heat transfer in drop-laden low-Prandtl-number channel turbulence

In this work, we numerically investigate heat transfer in low-Prandtl-number drop-laden wall-bounded turbulence. These flows are characteristic of nuclear and fusion technologies, where liquid metals – known for their high thermal conductivity – are laden with drops or bubbles of another liquid or pressurised gas. To this end, we consider forced convection turbulence between two differentially heated parallel plates. The carrier phase (i.e. liquid metal) is characterised by a low Prandtl number $Pr_c=0.013$ , while for the dispersed phase, we explore a range of Prandtl numbers from $Pr_d=0.013$ (matched case) to $Pr_d=7$ (super-unitary Prandtl number in the dispersed phase). Simulations are conducted at constant friction Reynolds number $Re_\tau =300$ , and for each dispersed phase Prandtl number, two volume fractions are examined: $\alpha =5.4\,\%$ and $\alpha =10.6\,\%$ . The simulation framework relies on direct numerical simulation of the Navier–Stokes equations, coupled with a phase-field method and the energy equation. Results show that an increase of the dispersed phase Prandtl number reduces heat transfer, leading to a lower Nusselt number for both volume fractions. To explain this behaviour, we analyse how the drops modify the temperature field, and demonstrate that the heat transfer reduction stems from a decreased diffusive heat flux within the dispersed phase. Finally, we propose a phenomenological model to predict the Nusselt number as a function of both the dispersed phase volume fraction and Prandtl number.