A numerical investigation on the flow effect over the Nusselt number in single droplet combustion

Numerical simulations of the combustion of isolated droplets, based on an interface capturing two-phase flow solver, are presented in this paper. The new numerical solver used is an extension of a classical evaporation solver based on a Level Set-Ghost Fluid Method to combustion applications. It is based on a variable density low Mach number solver for Navier–Stokes equations, and it accounts for complex thermo-physical variations of physical properties. After presenting a preliminary validation against experimental data for a $n$-decane static burning droplet, it is shown that the numerical simulations reproduce accurately different types of flame shapes. In particular, depending on the conditions, an envelope flame surrounding the droplet, a wake flame attached at the rear of the droplet or side flame, which is an intermediate state between the previous two regimes, are observed. The numerical results clearly demonstrate the strong effect of the different flame shapes on the Nusselt number of the evaporating droplet. The Nusselt number tends to decrease during the transition between the envelope flame to the wake flame, exhibiting a non-monotonic behavior for increasing Reynolds numbers. These results are significant since classical correlations on the Nusselt number assumes a monotonic increase for increasing Reynolds numbers, and thus miss the effect of the transition between the envelope flame to the wake flame. Finally, the solver developed for the sake of this study, presents many potentialities to explore more complex configurations than isolated and spherical droplets. Indeed, the overall numerical methodology enables to handle any interface shape and topology, and can be relevant to study collective effects, as the combustion of droplet groups, for instance.