Instabilities in Elliptical Jets

Problem Statement
Jet mixing has important implicatons in the design of combustors and the design of propulsion systems from the standpoint of minimizing their thermal and acoustic detectability.

In such applications, experiments have shown that elliptical jets mix much more rapidly than circular ones. The reasons for this lie in the generaton and evolution of vortical structures produced along the boundary of the jet as a result of the Kelvin-Helmholtz instability. Experiments have not yet produced a definitive description of this process. This is at least partially due to the rich spectral content of elliptical jets which produces jitter which makes it difficult to interpret the results of experimental measurements.

Consequently, direct numerical simulations of the mixing process which provide "jitter-free" visualizatoins of the mixing process offer to provide important insight into the reasons for the superior mixing properties of elliptical jets.

Visual Insight
The two visualizations shown here are the result of calculations performed by the authors on the Connection machine of the Naval Research Laboratory using the Flux Corrected Transport (FCT) algorithm. The variable being plotted is the concentration of a convected passive scalar.

The first visualization shows the jet in an early stage of development (250 time steps) in a horizontal perspective with the flow direction beign from left to right. The vortical structure along the periphery of the jet is a result of the influence of the Kelvin-Helmholtz instability. The kinking of the surface of the ellipse is the beginning of the helical mode of the instability. The wiggles seen along the circumference of the jet at the outflow boundary are believed to be a result of the Widnall instability which is known to appear in circular jets. To the authors' knowledge, this is the first time that mixing of an elliptical jet has been seen.

The second visualization shows the jet at 750 time steps with the jet in a vertical orientation and the flow from the bottom to the top of the screen. Here at a late stage in the mixing process the geometrical integrity of the ellipse has been almost completely lost and all that can be seen of the previous structure is a remnant of the helical instability.

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