A mathematical model describes the evaporation of drops of a hydrocarbon liquid composed of as many as hundreds of chemical species. The model is intended especially for application to any of several types of kerosenes commonly used as fuels. Like evaporating- multicomponent- fuel-drop models described in several previous NASA Tech Briefs articles, the present model invokes the concept of continuous thermodynamics, according to which the chemical composition of the evaporating multicomponent liquid is described by use of a probability distribution function (PDF). However, as described below, the present model is more generally applicable than is its immediate predecessor.
The present model is built on the one reported in "Statistical Model of Evaporating Multicomponent Fuel Drops" (NPO-30886), which appears elsewhere in this issue. To recapitulate: The PDF in that model is a superposition of two functions and, accordingly, is denoted a double PDF. It is a function of the molecular weight plus five other parameters. Unfortunately, some of those other parameters depend on the class of homologous hydrocarbon species, so that it becomes necessary to have a double PDF for each such class entering the fuel composition. The introduction of multiple double PDFs would make the computation very cumbersome, negating the advantage of the continuous- thermodynamics formulation. The derivation of the present model is driven by the concept of a unified thermodynamic representation of three classes of homologous hydrocarbons (alkanes, naphthenes, and aromatics) that constitute the principal components of kerosenes. Somewhat more specifically, it is sought to characterize the hydrocarbons in each homologous series by unified reference temperatures, pressures, and other parameters that depend only on molecular weights and thermodynamic quantities.
The derivation leads to a new version of the double PDF, in which the square root of the molecular weight occupies the position previously occupied by the molecular weight and other parameters are modified accordingly. By design, this version of the double PDF applies to the three major homologous series in kerosene; hence, it is not necessary to use multiple double PDFs. An additional advantage of this formulation is that it is valid over the subcritical region in the pressure range from 1 to 15 bars (0.1 to 1.5 MPa).
The model has been tested on three kerosenes used as aircraft and rocket fuels: Jet A, JP-7, and RP-1. The present version of the double PDF has been fitted to the discrete species distributions of these kerosenes and extensive calculations of evaporation of isolated drops performed. The results show that under the assumption of a quasi-steady gas phase, a relation known in the literature as the D2 law (pertaining to the rate of decrease of the square of the drop diameter) is recovered after an initial dropheating transient. A related quantity known in the literature as the asymptotic evaporation rate constant has been found to be an increasing function of the far-field temperature and pressure, a complex function of far-field composition, and a weak function of the difference between the drop-surface and farfield vapor molar fractions. In a comparison between results obtained (a) under the assumption that the interior of the drop is well mixed (the "wm" assumption) and (b) under the assumption that the drop can evaporate either in a wellmixed mode or at unchanging (frozen) composition (the "wm-fc" assumption), it was found that the differences between the asymptotic evaporation rate constants under the two assumptions is within the range of uncertainty in the transport properties (see figure).
This work was done by Josette Bellan and Kenneth Harstad of Caltech for NASA's Jet Propulsion Laboratory. For more information, download the Technical Support Package (free white paper) at www.techbriefs.com/tsp under the Information Sciences category. NPO-40437