Early detection of combustion instabilities in liquid rocket engines: Assessment of statistical, recurrence, and fractal analyses for sub- and supercritical pressure conditions

Safe shutdown of a liquid rocket engine in ground testing prior to the onset of damaging combustion instabilities through reliable detection of instability precursors would translate to time and cost savings in engine development programmes. Methods derived from statistical, recurrence, and fractal analysis have been successfully applied in the literature to detect precursors in unsteady pressure signals from canonical combustion experiments, gas-turbine combustion experiments, and sub-scale rocket combustion experiments operated at low pressures. In the present work, several such methods were applied to data from two cryogenic oxygen-natural gas rocket experiments operated at higher pressures than previously reported; both sub- and supercritical with respect to oxygen. The goal was to identify methods that can discern limit-cycle instabilities from intermittently unstable operation and are sufficiently responsive to be applied as emergency shut-down criteria in engine tests. Among the methods applied were the standard deviation, variance of the auto-correlation, the second spectral moment, the ratio between determinism and recurrence rate, the Hurst-exponent, and the multifractal range. The second spectral moment, the Hurst-exponent, and a measure derived from the multifractal spectrum all have short detection delays for instability onset and short-lived could be discerned from self-sustaining instabilities with an appropriate choice of threshold value. They also have moderate computation cost which makes them of interest for potential real-time implementation. The Hurst-exponent has the additional advantage of a common threshold value for all test cases addressed, demonstrating its potential for broader application independent of combustion device or operating conditions.