Heat transport in two-phase vertical natural convection using an Euler–Lagrange approach

We present numerical results of dispersed droplets in vertical natural convection (VNC) flow, which is a buoyancy driven flow between differentially heated vertical walls. Our focus is to study the effects of droplets on the local statistics of heat transport in natural convection, where heat transport enhancement due to bubbles has recently been reported [5]. Our numerical simulations are fully-resolved and based on an Euler–Lagrange approach with two phases: the first is the carrier phase (liquid), which is solved by a second-order accurate finite-difference scheme and marched in time using a fractional-step approach; the second is the dispersed phase (droplets) that are much larger than the Kolmogorov length scale. The interfacial droplet boundaries and deformations are modelled by an immersed boundary method and an interaction potential approach, respectively. We show that the heat flux is slightly enhanced for the Rayleigh number range 1.3×10⁸–2.3×10⁹ and Prandtl number of 7, which can be attributed to droplet induced mixing.