Insights of Transitions to Thermoacoustic Instability in Inverse Diffusion Flame using Multifractal Detrended Fluctuation Analysis

TL;DR

This work uses multifractal detrended fluctuation analysis (MFDFA) to characterize parameter-driven transitions to thermoacoustic instability in inverse diffusion flames (IDF). By examining two control strategies—varying Reynolds number at fixed power input and varying power input at near-constant Reynolds number—the study shows that IDF dynamics are highly multifractal in chaotic states, progressively lose multifractality in mixed or weakly ordered states, and become nearly monofractal at fully developed thermoacoustic instability, with the generalized Hurst exponent $H(q)$, spectrum width $\omega$, and singularity strength $\alpha$ serving as robust indicators of dynamical state and onset of instability. Comparisons with recurrence-network metrics indicate MFDFA provides clearer inter-state switching signals and stable behavior once instability is established. The findings offer practical, parameter-dependent indicators for early detection and prediction of thermoacoustic transitions in IDF, with potential for real-time monitoring and physics-inspired learning approaches.

Abstract

The inverse diffusion flame (IDF) can experience thermoacoustic instability due to variations in power input or flow conditions. However, the dynamical transitions in IDF that lead to this instability when altering control parameters have not been thoroughly investigated. In this study, we explore the control parameters through two different approaches and employ multifractal detrended fluctuation analysis to characterize the transitions observed prior to the onset of thermoacoustic instability in the inverse diffusion flame. Our findings reveal a loss of multifractality near the region associated with thermoacoustic instability, which suggests a more ordered behavior. We determine that the singularity exponent, the width of the multifractal spectrum, and the Hurst exponent are reliable indicators of thermoacoustic instability and serve as effective classifiers of dynamical states in inverse diffusion flames.

Figures (10)

• Figure 1: Here, we introduce the experimental setup of Rijke tube in which the experiments of inverse diffusion flame (IDF) are conducted. The setup features a co-flow tube, with air supplied through the inner tube and fuel through the outer tube. A quartz tube serves as the wall of the combustion zone. Additionally, an acoustic signal from the combustor is recorded using a data acquisition system.
• Figure 2: The temporal oscillations of acoustic signal (plots (I) a-d), Fast Fourier transform of the corresponding fluctuations (plots (II) a-d) and reconstructed phase space portraits (plots (III) a-d) are presented at various flow conditions for a constant power input at 0.39 KW which are: (a) $Re$ = 1566, (b) $Re$ = 3132, (c) $Re$ = 5220, and (d) $Re$ = 5950. The root mean square of the acoustic oscillations (i.e., $p^{\prime}_{rms}$) is also shown in the figure.
• Figure 3: The performance of 0-1 test on C-1 dataset is shown in the figure. The asymptotic growth rate ($K_c$) is found to be almost 1 at $Re$ = 1566 and 2088, confirming the presence of chaotic dynamics. On the other side, $K_c$ shows lower values during $Re$ = 4176 to 5533, supporting that the system has regular dynamics. However, since the value of $K_c$ during mixed mode oscillations also shows 1 or near 1, the measure may not be helpful for understanding the subtle difference between chaotic and mixed mode state.
• Figure 4: The temporal oscillations of the acoustic signal (plots (I) a-c), Fast fourier transform of the corresponding fluctuations (plots (II) a-c) and the reconstructed phase space portraits (plots (III) a-c) are presented at following power inputs while $Re$ is almost constant: (a) $PI = 0.546$ KW, (b) $PI = 0.6279$ KW and (c) $PI = 0.6825$ KW.
• Figure 5: We vary the generalized Hurst exponent ($H_q$) and multifractal scaling or mass exponent ($H_q$) as a function of $q$ for C-1 (a1 and b1) and C-2 (a2 and b2) cases. Using these two measures ($H_q$ and $H_q$), we identify the multifractal behavior, a typical characteristic of a complex state and the monofractal behavior, indication of self similar structure at different magnification of scale for different dynamical regimes of IDF subjected to the variation of $Re$ and $PI$. Further, we plot the singularity spectrum ($f(\alpha)$ over a wide range of $\alpha$ to identify the transition between multifratal and monofractal behavior of the system (see plots c1 and c2).