Interaction of droplet dispersion and evaporation in a polydispersed spray

Abstract

The interaction between droplet dispersion and evaporation in an acetone spray evaporating under ambient conditions is experimentally studied with an aim to understand the physics behind the spatial correlation between the local vapour mass fraction and droplets. The influence of gas-phase turbulence and droplet–gas slip velocity of such correlations is examined, while the focus is on the consequence of droplet clustering on collective evaporation of droplet clouds. Simultaneous and planar measurements of droplet size, velocity and number density, and vapour mass fraction around the droplets, were obtained by combining the interferometric laser imaging for droplet sizing and planar laser induced fluorescence techniques (Sahuet al.,Exp. Fluids, vol. 55, 1673, 2014b, pp. 1–21). Comparison with droplet measurements in a non-evaporating water spray under the same flow conditions showed that droplet evaporation leads to higher fluctuations of droplet number density and velocity relative to the respective mean values. While the mean droplet–gas slip velocity was found to be negligibly small, the vaporization Damköhler number ($Da_{v}$) was approximately ‘one’, which means the droplet evaporation time and the characteristic time scale of large eddies are of the same order. Thus, the influence of the convective effect on droplet evaporation is not expected to be significant in comparison to the instantaneous fluctuations of slip velocity, which refers to the direct effect of turbulence. An overall linearly increasing trend was observed in the scatter plot of the instantaneous values of droplet number density ($N$) and vapour mass fraction ($Y_{F}$). Accordingly, the correlation coefficient of fluctuations of vapour mass fraction and droplet number density ($R_{n\ast y}$) was relatively high (${\approx}0.5$) implying moderately high correlation. However, considerable spread of the$N$versus$Y_{F}$scatter plot along both coordinates demonstrated the influence on droplet evaporation due to turbulent droplet dispersion, which leads to droplet clustering. The presence of droplet clustering was confirmed by the measurement of spatial correlation coefficient of the fluctuations of droplet number density for different size classes ($R_{n\ast n}$) and the radial distribution function (RDF) of the droplets. Also, the tendency of the droplets to form clusters was higher for the acetone spray than the water spray, indicating that droplet evaporation promoted droplet grouping in the spray. The instantaneous group evaporation number ($G$) was evaluated from the measured length scale of droplet clusters (by the RDF) and the average droplet size and spacing in instantaneous clusters. The mean value of$G$suggests an internal group evaporation mode of the droplet clouds near the spray centre, while single droplet evaporation prevails near the spray boundary. However, the large fluctuations in the magnitude of instantaneous values of$G$at all measurement locations implied temporal variations in the mode of droplet cloud evaporation.