In turbulent combustors, the transition from stable combustion (i.e. combustion noise) to thermoacoustic instability occurs via intermittency. During stable combustion, the acoustic power production happens in a spatially incoherent manner. In contrast, during thermoacoustic instability, the acoustic power production happens in a spatially coherent manner. In the present study, we investigate the spatiotemporal dynamics of acoustic power sources during the intermittency route to thermoacoustic instability using complex network theory. To that end, we perform simultaneous acoustic pressure measurement, high-speed chemiluminescence imaging and particle image velocimetry in a backward-facing step combustor with a bluff body stabilized flame at different equivalence ratios. We examine the spatiotemporal dynamics of acoustic power sources by constructing time-varying spatial networks during the different dynamical states of combustor operation. We show that as the turbulent combustor transits from combustion noise to thermoacoustic instability via intermittency, small fragments of acoustic power sources, observed during combustion noise, nucleate, coalesce and grow in size to form large clusters at the onset of thermoacoustic instability. This nucleation, coalescence and growth of small clusters of acoustic power sources occurs during the growth of pressure oscillations during intermittency. In contrast, during the decay of pressure oscillations during intermittency, these large clusters of acoustic power sources disintegrate into small ones. We use network measures such as the link density, the number of components and the size of the largest component to quantify the spatiotemporal dynamics of acoustic power sources as the turbulent combustor transits from combustion noise to thermoacoustic instability via intermittency.

We present a novel and an efficient way to mitigate oscillatory instability in turbulent reactive flows. First, we construct weighted spatial correlation networks from the velocity field obtained from high-speed particle image velocimetry. Using network measures, we identify the optimal location for implementing passive control strategies. By injecting micro-jets at this optimal location, we are able to reduce the amplitude of the pressure oscillations to a value comparable to what is observed during the state of stable operation. This approach opens up new avenues to control oscillatory instabilities in turbulent flows.

Abstract

We use complex network theory to investigate the dynamical transition from stable operation to thermoacoustic instability via intermittency in a turbulent combustor with a bluff body stabilized flame. A spatial network is constructed, representing each of these three dynamical regimes of combustor operation, based on the correlation between time series of local velocity obtained from particle image velocimetry. Network centrality measures enable us to identify critical regions of the flow field during combustion noise, intermittency, and thermoacoustic instability. We find that during combustion noise, the bluff body wake turns out to be the critical region that determines the dynamics of the combustor. As the turbulent combustor transitions to thermoacoustic instability, during intermittency, the wake of the bluff body loses its significance in determining the flow dynamics and the region on top of the bluff body emerges as the most critical region in determining the flow dynamics during thermoacoustic instability. The knowledge about this critical region of the reactive flow field can help us devise optimal control strategies to evade thermoacoustic instability.

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Many complex systems exhibit periodic oscillations comprising slow–fast timescales. In such slow–fast systems, the slow and fast timescales compete to determine the dynamics. In this study, we perform a recurrence analysis on simulated signals from paradigmatic model systems as well as signals obtained from experiments, each of which exhibit slow–fast oscillations. We find that slow–fast systems exhibit characteristic patterns along the diagonal lines in the corresponding recurrence plot (RP). We discern that the hairpin trajectories in the phase space lead to the formation of line segments perpendicular to the diagonal line in the RP for a periodic signal. Next, we compute the recurrence networks (RNs) of these slow–fast systems and uncover that they contain additional features such as clustering and protrusions on top of the closed-ring structure. We show that slow–fast systems and single timescale systems can be distinguished by computing the distance between consecutive state points on the phase space trajectory and the degree of the nodes in the RNs. Such a recurrence analysis substantially strengthens our understanding of slow–fast systems, which do not have any accepted functional forms.

Capturing the complex spatiotemporal flame dynamics inside a rocket combustor is essential to validate high-fidelity simulations for developing high-performance rocket engines. Utilizing tools from a complex network theory, we construct positively and negatively correlated weighted networks from methylidyne (CH*) chemiluminescence intensity oscillations for different dynamical states observed during the transition to thermoacoustic instability (TAI) in a subscale multi-element rocket combustor. We find that the distribution of network measures quantitatively captures the extent of coherence in the flame dynamics. We discover that regions with highly correlated flame intensity oscillations tend to connect with other regions exhibiting highly correlated flame intensity oscillations. This phenomenon, known as assortative mixing, leads to a core group (a cluster) in the flow-field that acts as a “reservoir” for coherent flame intensity oscillations. Spatiotemporal features described in this study can be used to understand the self-excited flame response during the transition to TAI and validate high-fidelity simulations essential for developing high-performance rocket engines.

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