A mathematical model has been developed to predict the behavior of mutually interacting drops of a first fluid surrounded by a second fluid, under quiescent conditions at supercritical temperature. The model has been specialized to represent the behavior of drops of liquid oxygen surrounded by hydrogen under supercritical conditions like those encountered in a rocket-engine combustion chamber.

The drops of liquid oxygen are formed by atomization from jets of liquid oxygen. There is considerable experimental evidence that the atomization process forms the drops in clusters, and that the drops interact within each cluster. The interaction among drops affects the stability of combustion process. Therefore, a model like the present one is needed for designing combustors, and for analyzing and controlling their operation.

These Plots Show Numerical Results from one of a number of example calculations performed by use of the model. The basic parameters in this example were an initial liquid-oxygen drop radius of 50 μm, initial sphere-of-influence radius of 100 μm, initial cluster radius of 2 cm, equivalent Nusselt number of 100, initial drop-surface temperature of 100 K, initial temperature of 1,000 K at the edge of the sphere of influence and outside the cluster, pressure of 20 MPa, and no oxygen outside the cluster. Times are indicated on the graphs in milliseconds.

The situation represented by the present interacting-drop model is that of a cluster of a finite number of drops of one fluid (which could be liquid oxygen) immersed in another fluid (a dense gas that could be hydrogen). All the drops are assumed to be spheres of same radius, and each drop is assumed to reside in a fictitious sphere of influence with a radius equal to half the distance to the nearest neighbor drop in the cluster. The interstitial region between the spheres of influence is assumed to be uniform and quiescent with respect to the cluster. Each sphere of influence contains one drop and its surrounding fluid, and has fixed mass; this means that the sphere of influence expands or contracts in response to variations in temperature.

The behavior of a drop within its sphere of influence is represented by the isolated-drop model described in the first of the two preceding articles – "Model of a Drop of O2 Surrounded by H2 at High Pressure" (NPO-20220). The interactions among drops and the resulting collective behavior of the drops are represented by using equations for the conservation of total mass, conservation of the mass of each fluid, and conservation of energy in the interstitial region to establish boundary conditions for the spheres of influence. Transfers of heat and mass to the cluster are modeled via a Nusselt-number formulation.

Numerical results from calculations for the liquid-oxygen/hydrogen system (see figure) show that the behavior of a cluster is insensitive to variations of the Nusselt number over 3 orders of magnitude. The results also show that at fixed pressure, the accumulation of oxygen in the interstitial region increases with decreasing distance between drops. At fixed initial distance between drops, the gradients of dependent variables become increasingly smeared as pressure increases; this behavior is qualitatively the opposite of that observed for isolated drops. From these observations it is inferred that clusters of drops might be desirable in supercritical combustion because they aid mixing of reactants.

This work was done by Josette Bellan and Kenneth Harstad of Caltech forNASA's Jet Propulsion Laboratory. NPO-20257

This Brief includes a Technical Support Package (TSP).
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Model of interacting O2 drops surrounded by H2 at a high pressure

(reference NPO20257) is currently available for download from the TSP library.

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