Drop heating and evaporation in CFD spray simulations are predicted by analytical models (like [1]), which were derived and validated for single drops and they may become questionable when used to model dense sprays. However, the effect of interaction among neighbouring droplets cannot be ignored when the drop mutual distance becomes comparable with their size [2], and it is known that increasing the number of droplets per unit volume reduces the evaporation rate [3]. Analytical models for a couple of interacting drop, under the assumption of constant thermophysical properties, are available in the open literature [4]. The effect of more complex droplet distribution and variable gas properties was numerically investigated [5], and recently an exact analytical solution of conservation equations for the drop pair case, considering the explicit dependence on gas density of temperature ad composition, was reported [6]. More complex arrays of interacting droplets were also studied [7]. Exact analytical solutions of the energy and species equations are not available for complex drop dispositions, but a method based on the use of point mass sources to model the evaporating droplets was proposed [8], for drop array of any complexity, under the assumption of constant gas properties, although it was shown [9] that the solution for multi-drop structures does not respect the exact boundary conditions on the drop surface.

The present work reports an analytical approach to evaluate the effects of droplet neighbouring on heating and evaporation, solving the conservation equations through the point source method, accounting for the dependence on temperature and composition of gas thermophysical properties. The previously mentioned inherent approximation, related to the boundary conditions on the drop surface, was deepened and a method to mitigate the effect is proposed.

The analytical solutions for different arrays of droplets were compared with exact analytical solution in bispherical coordinates, for the drop pair case, and with numerical solution of the conservation equations for the drop array, to assess the model accuracy.

References:

[1] Int. J. Heat Mass Transfer 32(9) (1989) 1605-1618.

[2] Int. J. Heat Mass Transfer 93 (2016) 788 – 802.

[3] Int. J. Heat Mass Transfer 96 (2016) 20 – 28.

[4] Combust. Flame 43 (1981) 111–119.

[5] Int. J. Heat Mass Transfer 36 (1993) 875.

[6] Int. J. Heat Mass Transfer 127 (2018) 485–496

[7] Int. J. Heat Mass Transfer 48 (2005) 4354–4366

[8] Combust. Flame 57 (1984) 237-245.

[9] Combust. Flame 65 (1984) 367-369.