Statistical Model of Evaporating Multicomponent Fuel Drops

The statistical aspect of the model enters through invocation of the concept of continuous thermodynamics, according to which the chemical composition of a fuel is described probabilistically, by use of a probability distribution function (PDF). This concept was summarized in two prior NASA Tech Briefs articles: “Model of Mixing Layer With Multicomponent Evaporating Drops” (npo-30505), Vol. 28, No. 3 (March 2004), page 55, and “Simulations of Evaporating Multicomponent Fuel Drops” (npo-30641), Vol. 29, No. 3 (March 2005), page 72. However, the present statistical model differs from the model of the cited prior articles.

In the prior model, the PDF is a single- peaked Gamma distribution, which is a function of the molar weight and of several parameters. However, the prior model does not generate a second peak at the low-molar-weight end of the dropcomposition PDF that emerges when condensation of vapor onto drops occurs.

The present model generates the needed second peak. The PDF in the present model is a superposition of two Γ-PDFs and, accordingly, is denoted a double-Γ-PDF. It is a function of the molar weight plus five parameters.

Formally, the calculation prescribed by this model can be reduced to an inverse mapping from (1) the first five distribution moments, which can be calculated by use of the conservation equations, to (2) the five parameters of the double-Γ-PDF. The complexity of the inverse mapping, and the fact that the statistics of a discrete-chemical-species model may not be represented exactly by the double-Γ-PDF, make this calculation only approximate.

In a practical calculation, one makes a further approximation by utilizing only the first four moments and four parameters plus a fifth parameter that is determined empirically. Despite these approximations, extensive tests of the model on both diesel oil and gasoline show that the double-Γ-PDF accurately represents the predictions of the discrete-chemicalspecies model (see figure). Moreover, the mean and variation of composition at the drop surface as computed by use of the double-Γ-PDF are in excellent agreement with those computed by use of the discrete-chemical-species model: this is an important result because these mean and variance determine the composition of the gas mixture.

This work was done by Kenneth Harstad, Patrick Le Clercq, and Josette Bellan 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 Physical Sciences category. NPO-30886

This Brief includes a Technical Support Package (TSP).

Statistical Model of Evaporating Multicomponent Fuel Drops (reference NPO-30886) is currently available for download from the TSP library.

Download it now!

 

This Brief includes a Technical Support Package (TSP).

Statistical Model of Evaporating Multicomponent Fuel Drops (reference NPO-30886) is currently available for download from the TSP library.

Login first to download.