Dr. Chienchi Chao performed a series of calculations to assess the impact of azimuthal acoustic waves on the deformation of fuel jets exiting an impinging element injector such as that used in the F-1 engine which served as 1st stage propulsion in the Apollo launch vehicles. During development, the F-1 had many problems with tangential-mode instabilities as highlighted in the sketch below. Through changes in fuel jet sizes and additions of baffles on the injector face, an acceptable design was developed. However, this process was very time consuming and involved thousands of tests which raised program costs dramatically. Increasing the understanding of the role atomization plays in instabilities will hopefully reduce development costs for future engines.

In the figure above, the level of chamber pressure oscillations is correlated with frequency ratio. Here, the frequency ratio represents the ratio of the natural frequency of the chamber to that of the fuel jets. When the ratio is near unity there is great likelyhood that acoustic energy will cause large deformation in the fuel jets thereby affecting subsequent atomization, mixing, and combustion processes. The letters on the chart refer to various injector concepts used in the F-1 development program. The final Flight Rating Test (FRT) injector showed no instabilities, while the early Double Row Cluster (DRC) design showed pressure oscillations in excess of 400% of the mean.

Images of the actual fuel jet cross-sections for these two designs are compared at various times in the figure below. The DRC injector design shows very large deformation of the fuel jets, while the FRT design shows little response.