Multifractal Spectral Characteristics of Full-Scale Liquid Rocket Engines

Fractal-based methods are applied to three full-scale liquid engine combustors. The structure function is derived in each case, and it is found to have a single or dual slope, depending on whether the combustion oscillations are stable or unstable, respectively. The fractal spectrum, which is derived from the structure function, is characterized by four spectral characteristics, viz., the apex location, the mean width, the mean height, and the differential height. The evolution of these characteristics is tracked with respect to time and is shown to be correlated to the onset of instability. The variation of the apex location over a limited range of scales is studied as a novel metric to anticipate instability in lieu of the Hurst exponent. Another novel metric that is based on the variation of slope of the structure function across two different scale ranges is also formulated. It is found that the metrics can be used to provide universal thresholds for forewarning of instability in earth-storable and cryogenic liquid rocket engines. The metrics could be used in the design of shutdown and control systems for liquid engines operating near combustion stability boundaries.