Droplet combustion experiments were conducted in reduced gravity to investigate how various mass and energy transport mechanisms affect overall droplet combustion behaviors. In one study, individual heptane and methanol droplets in the $1.2-5.0$ \unit{mm} diameter range were burned in reduced gravity and in a controlled chamber, with air-inert mixtures at 0.1 and 0.07 MPa and about 298 K, where the monatomic gases helium and xenon were separately used as the added inert. Xenon is about 32 times heavier than helium, however, the thermal conductivity of helium is about 26 times higher compared to xenon at 300 K, 1 bar. Because the molecular weights and thermodynamic properties between xenon and helium are significantly different, the choice of these two gasses would be appropriate in order to investigate transport property effects, such as Lewis number variations on combustion phenomena. Xenon and helium flame suppressant effectiveness are also evaluated. The results indicate that ambient gas transport properties play an important role in determining limiting oxygen indices as well as burning rates and radiant heat output histories of flames.
In the second study, the effects of liquid mixing on droplet combustion behaviors were investigated. To this end, reduced gravity combustion experiments were performed with individual propanol-glycerol and heptane-hexadecane mixture droplets. In the case of propanol-glycerol mixture droplets, the initial n-propanol mass fraction was $Y=0.95$ and droplets had initial diameters in the $2-5$ \unit{mm} range. Some droplets were fiber supported while others were free floating, and the environment was either an oxygen/nitrogen mixture at $1$ atm or an oxygen/helium mixture at pressures of $1$ and $3$ atm. In the case of heptane-hexadecane mixture droplets, the initial heptane mass fractions was either $Y=0.95$ or $Y=0.8$ with initial droplet diameters in the $1.7-4.8$ \unit{mm} range.
The ambient in which heptane/hexadecane droplets were burned consisted of oxygen mixed with either helium or nitrogen at $1$ atm. The goals of these experiments are to evaluate the relationships between liquid mixing and droplet burning rates. Propanol is several orders of magnitude more volatile compared to glycerol. Likewise, heptane is also significantly more volatile compared to hexadecane. Differences in volatilities in these mixtures are related to liquid transport rates through theory developed using asymptotic analysis. Liquid diffusivities have been calculated from experimentally measured variables, and are used as a metric to quantify the degree of liquid mixing within droplets. Influences of the inert, initial droplet diameter, support fiber, and the delay time before droplet ignition on liquid diffusivities are also reported. Studies of bi-component droplets can potentially yield new insights on behaviors of droplets in sprays composed of practical fuels, which are generally mixtures.
In the third study, the Nusselt number, $\Nu$, was evaluated for an isothermal fluid sphere immersed in a Stokes flow. The dimensionless convective-diffusive conservation equation is solved asymptotically for the case where the Peclet number based on the sphere radius, $\varepsilon$, is small relative to unity. The Nusselt number is evaluated by integrating the derivative of the asymptotic solution over the surface of the sphere. The conservation equation is also solved numerically. A comparison of the numerical and asymptotic solutions shows that the asymptotic expression for $\Nu$ is valid only for the Peclet number being small relative to unity. An alternative asymptotic expression for $\Nu$ is also developed, and it is shown that this expression is valid for Peclet numbers of order unity. The current work improves and corroborates prior correlations for $\Nu$, particularly those developed by Acrivos and Taylor (1962), as well as those by Brunn (1982), and may have application to evaporating droplets (e.g., as a numerical sub-model).
