Statistical Model of Multicomponent-Fuel Drop Evaporation for Many-Drop Flow Simulations

Abstract

A statistical formulation is developed describing the composition in an evaporating multicomponent-fuel liquid drop and in the gas phase surrounding it. When a complementary discrete-component model is used, it is shown that, when drops are immersed in a carrier gas containing fuel vapor, condensation of species onto the drop results in the development of a minor peak in the liquid composition probability distribution function (PDF). This peak leads to a PDF shape that can be viewed as a combination of two gamma PDFs, which is determined by ve parameters. A model is developed for calculating the parameters of the two combined gamma PDFs. Extensive tests of the model for both diesel and gasoline show that the PDF results replicate accurately the discrete model predictions. Most important, the mean and variance of the composition at the drop surface are in excellent agreement with the discrete model. Results from the model show that although the second peak is minor for the liquid PDF, its corresponding peak for the vapor distribution at the drop surface has a comparable magnitude to and sometimes exceeds that corresponding to the rst peak. Four-parameter models are also exercised, and it is shown that they are unable to capture the physics of the problem. Superscripts.s/ = drop surface conditions .1/ = far-eld conditions

Modeling evaporation of Jet A, JP-7, and RP-1 drops at 1 to 15 bars

“…as shown in [24], where µ is the variable used as a species tag (e.g., the molar mass) in a distribution and p (∞) is the far field pressure. This means that to unify the representation of homologous class properties, attention should be focused on modeling p sat in a general manner that is simple enough to be functionally usable and that also introduces the needed dependency on µ.…”

“…(4) where T bn ∝ m 0.5 , suggests that the Γ -PDF should no longer be a function of m, but instead should be primarily a function of m 0.5 , neglecting additional minor dependencies in m. This conclusion is reinforced by the dependency of the kerosene fuel properties with m, as listed in Table 1. Therefore, we use here the model developed by Harstad et al [24], but with a new dependency of the Γ -PDF…”

“…Clearly, the single-Γ -PDF inherently cannot accommodate substantial condensation onto the drop that may create a second peak in the mixture distribution. This limitation was quantified by Harstad et al [24] who derived a more general model, based on two added Γ -PDFs, called the double-Γ -PDF, which can accommodate a wide range of drop far field conditions. Thus, the double-Γ -PDF is…”

“…To determine P l as a function of time, one needs to solve for the vector η ≡ (α 1 , β 1 , α 2 , β 2 , ε) at each time step. A method for obtaining this vector has been developed [24] and the accuracy of the double-Γ -PDF model to portray a discrete distribution was verified by comparing its predictions with statistics from a discrete species model.…”

“…With this new representation, the Γ -PDF becomes a function of m 0.5 rather than m [11,12,18,[22][23][24]. Then, we briefly recall the double-Γ -PDF model of Harstad et al [24] in the context of the new m 0.5 dependency of the Γ -PDF. Results are presented for three kerosenes, whose composition, provided by Edwards [26] as a discrete bar chart, was fitted to portray a double-Γ -PDF.…”