Modeling and Simulation of Single Ethanol/Water Droplet Evaporation in Dry and Humid Air

ABSTRACT

The modeling and simulation of the heating and evaporation of a spherically symmetric single, bi-component ethanol/water droplet in convective air is studied which allows for an improved understanding of the different heating and evaporation characteristics of the two components of the bi-component droplet. The concentration inside the droplet interior is considered to be uniform and the temperature is modeled with the distillation-limit model. The Abramzon–Sirignano model is used for describing the convective droplet heating and evaporation, and Brenn’s extension for multicomponent droplets is used for modeling the ethanol/water droplet. The UNIFAC method is employed to describe the activity coefficients to account for the non-ideal behavior of the ethanol/water mixture. The numerical results corresponding to non-ideal and ideal mixing are compared with experimental data from the literature. Moreover, a parameter study of the ethanol/water droplet evaporation in both dry and humid air for combustion conditions is performed where both the initial gas temperature and velocity and the initial droplet size and composition are varied. The evolution of the droplet surface area, the mass fractions, the mass evaporation rate, and the surface temperature are analyzed for the different conditions. In general, the UNIFAC method initially leads to a somewhat faster evaporation rate and slows down after the higher volatile component has almost completely evaporated; however, its effect on the droplet lifetime is small. Humidity strongly affects the bi-component droplet heating and evaporation because of the condensation of water on the droplet surface which retards the water evaporation but enhances the initial ethanol evaporation for high relative humidity. Also, in humid conditions, the droplet lifetime is strongly increased compared to evaporation in dry air. The parametric dependencies of droplet lifetime and the evaporation characteristics of the bi-component ethanol/water droplet evaporation in both dry and humid convective air may be used in more complex simulations of non-reacting and reacting spray flows.

KEYWORDS:

• Bi-component droplet evaporation
• ethanol/water
• dry and humid air
• UNIFAC method
• droplet lifetime

Acknowledgments

EG would like to express her great appreciation to W.A. Sirignano for two very inspiring years in his research group in 1993–94 and valuable discussions beyond. The authors acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - Projektnummer 374463455 and through HGS MathComp.

Nomenclature/Notation

Symbols

$a$	=	group interaction parameter
$B_M$	=	Spalding mass transfer number
$B_T$	=	Spalding heat transfer number
$c_p$	=	specific heat capacity
$D$	=	diffusivity
$\lambda$	=	thermal conductivity
$L_{\mathrm{v}}$	=	latent heat of vaporization
$m$	=	droplet mass
$\dot{m}$	=	mass evaporation rate
$M$	=	number of different groups
$N$	=	number of components
$\widetilde{\mathrm{N}\mathrm{u}}$	=	modified Nusselt number
Pe	=	Peclet number
Pe${ }_{\mathrm{m}}$	=	liquid mass Peclet number
Pe${ }_{\mathrm{t}}$	=	liquid thermal Peclet number
$p$	=	pressure
$q$	=	relative Van-der-Waals surface area
$r$	=	relative Van-der-Waals volume
$r_{\mathrm{d}}$	=	droplet radius
$\widetilde{\mathrm{S}\mathrm{h}}$	=	modified Sherwood number
$t$	=	time
$T$	=	temperature
$u$	=	velocity
$X$	=	mole fraction
$Y$	=	mass fraction

Greek Symbols

$\gamma$	=	activity coefficient
$\mathrm{\Gamma }$	=	group activity coefficient
$\rho$	=	density
$\nu$	=	number of structural groups

Subscripts

g	=	gas
l	=	liquid
s	=	surface
d	=	droplet
EtOH	=	ethanol
$\mathrm{\infty }$	=	condition in the ambience
f	=	film
atm	=	atmospheric
vap	=	vapor
$i$	=	component
0	=	initial value

Superscripts

C	=	combinatorial
R	=	residual