Analytical and numerical studies on a single-droplet evaporation and combustion under forced convection

Abstract

Existing droplet evaporation/combustion models in computational fluid dynamics (CFD) simulation of spray combustion are based on simplified 1-D models. Both these models and recently developed 3-D models of singledroplet combustion do not give the conditions for the different existing droplet combustion modes. In this paper, droplet evaporation and combustion are studied both analytically and numerically. In the analytical solution, a 2-D axisymmetric flow surrounding an evaporating and combusting droplet was considered. The governing equations were solved using an integral method, similar to the Karman-Pohlhausen method for solving boundary-layer flows with pressure gradient. The results give a local evaporation rate and flame radius in agreement with experimental results. In numerical simulation, 3-D combusting gas flows surrounding an ethanol droplet were studied. The prediction results show three modes of droplet combustion under different relative velocities, explaining the change in the evaporation constant with an increase in relative velocity observed in experiments. This implies that different droplet combustion models should be developed in simulating spray combustion. The predicted local evaporation rate and flame radius by numerical simulation are in agreement with the analytical solution in the range of azimuthal angles 0 • < θ < 90 • . The numerical results indicate that the drag force of an evaporating and combusting droplet is much smaller than that of a cold solid particle, and thus the currently used drag models should be modified.

Studies on Two-Mode Spray Combustion

“…Recent high-speed photography [2] confirms these phenomena. These experimental results tell us that the spray flame may take different modes: unignited droplets evaporating in gas flames or a group of ignited droplets with diffusion flames, which is also in agreement with different combustion modes of a single droplet under different relative gas velocities [3], this is because the droplets of different sizes may be ignited (form enveloped flames) or un-ignited (form non-enveloped flames) under different gas temperatures, relative gas velocities. However, up to now in the simulation of spray combustion, including RANS modeling, LES and point-particle DNS, only the mode of unignited droplets evaporating in hot gas flames is taken into account.…”

Studies on the flame structure and drag of a combusting droplet group

“…Figure 3 shows three combustion modes of the droplet group. There are fully-enveloped flame, partially-enveloped flame and wake flame under different gas relative velocity, similar to the numerical results of a single droplet [26], and the PLIF measurement results obtained by Mercier et al [27]. However, in case of the droplet group, different combustion modes may exist in the same region, since there are different droplet sizes in a computation domain.…”

“…Obviously, velocities ahead of droplets are larger than those behind droplets due to the Stefan flow, leading to the change of drag. The similar phenomenon was observed in the velocity vectors surrounding a single droplet [26]. The streamlines are distorted due to the interaction between droplets.…”

“…The drag coefficient of a droplet in its group is still smaller than that of a single droplet, as shown in Table 3. Figure 9 gives the drag coefficient of the single combusting droplet vs droplet Reynolds number, reported in [26]. It is seen that as the droplet Reynolds number increases to be greater than 280, the reduction effect of drag gradually diminishes.…”

Research Progress on the Ocean Estuary and its Enlightenment to the Study of the Tributary in Three Gorges Reservoir

“…However, the computation of a three-dimensional model is very huge for practical problems. Therefore, application of two-dimensional or quasi-three-dimensional models are still used commonly [24,25,35].…”