Hurst Exponents for Intra- and Intercycle Thermoacoustic Oscillations

Abstract

The detrended fluctuation analysis, a technique for detecting long-range correlations in fractal time series, is used to characterize thermoacoustic oscillations of impending combustion instabilities. The slope of the linear regime of the structure function with respect to the time scale in a logarithmic plot, referred to as the Hurst exponent, takes a different value across a critical time scale corresponding to one pressure cycle. The slope for pressure oscillations over one pressure cycle, termed as the intercycle Hurst exponent, is a power-law scaling parameter for long-range oscillations; however, the slope for pressure oscillations within one pressure cycle, termed as the “intracycle Hurst exponent,” is no longer a power-law scaling parameter but resultant from the nonstationary, local average of highly nonlinear (as a function of time), seemingly sinusoidal, nearly periodic pressure oscillations. Both parametric studies and analyses of experimental data show that the intracycle Hurst exponent consistently increases with the signal-to-noise ratio and peaks at 1.6, thus having potentials for assessments of the safety margin to the onset of combustion instabilities. Given the same observation window, the measurement error (or uncertainty) of the intracycle Hurst exponent is significantly lower than that of the intercycle Hurst exponent.