Combustion noise is scale-free: transition from scale-free to order at the onset of thermoacoustic instability

Abstract

We investigate the scale invariance of combustion noise generated from turbulent reacting flows in a confined environment using complex networks. The time series data of unsteady pressure, which is the indicative of spatiotemporal changes happening in the combustor, is converted into complex networks using the visibility algorithm. We show that the complex networks obtained from the low-amplitude, aperiodic pressure fluctuations during combustion noise have scale-free structure. The power-law distributions of connections in the scale-free network are related to the scale invariance of combustion noise. We also show that the scale-free feature of combustion noise disappears and order emerges in the complex network topology during the transition from combustion noise to combustion instability. The use of complex networks enables us to formalize the identification of the pattern (i.e. scale-free to order) during the transition from combustion noise to thermoacoustic instability as a structural change in topology of the network.

Visibility Graphs for Image Processing

“…Theoretical research on visibility graphs has elaborated on mathematical methods [8][9][10][11] and some rigorous results on the properties of these graphs when associated to canonical models of complex dynamics have been obtained [12][13][14][15]. From a practical point of view, this method has been used as a feature extraction procedure to construct feature vectors from time series for statistical learning purposes (see [16][17][18][19][20][21][22] for just a few examples in the life sciences or [23][24][25][26][27][28][29][30] for other applications in the physical sciences). Very recently [31], this paradigm has been theoretically extended to handle scalar fields.…”

Experimental investigation of vertical turbulent transport of a passive scalar in a boundary layer: Statistics and visibility graph analysis

“…Although different research fields have taken advantage of network science during last decades (e.g., social, biological, or technological networks [15]), only recently complex networks have emerged as an effective framework also to study fluid flows. The main applications of network science to fluid flows involve the study of two-phase flows [16,17], turbulent jets [18,19], isotropic and wall-bounded turbulence [20][21][22], reacting flows [23,24], Lagrangian mixing [25,26] and geophysical flows [27,28]. Among several techniques that have been developed so far to study time-series by means of complex networks [29], the visibility graph approach [30] was here adopted since it is a simple but powerful tool to extract non-trivial insights into the non-linear process from which the time-series are obtained [29].…”

Randomized methods to characterize large-scale vortical flow networks

“…Low-order nonlinear models may be obtained by Galerkin projection of the Navier Stokes equations onto POD modes, and these models have had great success for uncovering underling mechanisms that drive flows [4]. Regardless, there are issues with Galerkin models, such as instability and mode deformation with changing parameters and boundary conditions [12][13][14], limiting the success of POD-Galerkin modeling for turbulence.Recently, network theoretic approaches have been increasingly leveraged to analyze complex, fluid flow systems [15][16][17][18][19][20][21]. Network science [22] characterizes the structure and dynamics on a graph consisting of nodes and the edges connecting them.…”

“…Recently, network theoretic approaches have been increasingly leveraged to analyze complex, fluid flow systems [15][16][17][18][19][20][21]. Network science [22] characterizes the structure and dynamics on a graph consisting of nodes and the edges connecting them.…”