Phase-reduction analysis of periodic thermoacoustic oscillations in a Rijke tube

Phase-reduction analysis captures the linear phase dynamics with respect to a limit cycle subjected to weak external forcing. We apply this technique to study the phase dynamics of the self-sustained oscillations produced by a Rijke tube undergoing thermoacoustic instability. Through the phase-reduction formulation, we are able to reduce these dynamics to a scalar equation for the phase, which allows us to efficiently determine the synchronisation properties of the system. For the thermoacoustic system, we find the conditions for which $m:n$ frequency locking occurs, which sheds light on the mechanisms behind asynchronous and synchronous quenching. We also reveal the optimal placement of pressure actuators that provide the most efficient route to synchronisation.

On the Effect of Noise Induced Dynamics on Linear Growth Rates of Oscillations in an Electroacoustic Rijke Tube Simulator

Suppressing self-excited thermoacoustic oscillations in combustion chambers is essential for gas turbine system stability. Passive acoustic damping devices such as Helmholtz resonators are commonly employed in modern combustors to address the problem of thermoacoustic instabilities. The estimation of deterministic parameters characterizing flame-acoustic coupling, specifically the stability margins and linear growth/decay rates, is a prerequisite for designing these devices. As gas turbine combustors are typically noisy systems due to the presence of highly turbulent flows and unsteady combustion, it is essential to understand the role of noise and its impact on the estimated system stability. Recently several new results on the stochastic dynamics of thermoacoustic systems and the use of noise-induced dynamics to estimate system stability characteristics have been reported. In the present work, we study the different approaches previously reported on the estimation of linear growth/decay rates from noise-induced dynamics on an electroacoustic Rijke tube (a prototypical thermoacoustic system) simulator. We estimate the growth rates from noisy data obtained from the subthreshold, bistable, and linearly-unstable regions of the observed subcritical Hopf bifurcation and investigate the effect of additive noise intensity. We find that the noise intensity affects the stability boundaries and the estimated growth rates.

Numerical simulation of thermoacoustic instability in Rijke tube

The influence of three different states on the thermoacoustic instability characteristics of Rijke tube was compared in order to reseach the influencing factors of thermoacoustic oscillation by using the Rijke tube model with stack as the heat source. The thermoacoustic oscillations are numerically simulated from the start-up to the saturation state, and the effects of the temperature on the dynamic viscosity and the thermal conductivity are compared. The results show gravity has a greater influence than the thermoacoustic oscillation caused by thermal buoyancy, and it is related to the inner balance of the tube after the gravity and the temperature gradient caused by the protrusion and the temperature gradient caused by the reduction of the amplitude dissipation. For the comprehensive comparison of the two variable parameters, it is found that when the viscosity coefficient changes with temperature and the thermal conductivity is a fixed value, both of them decrease by 49.5% with the temperature change rate. This result far exceeds the viscosity coefficient itself influences.

Transfer Learning for Detection of Combustion Instability via Symbolic Time Series Analysis

Transfer learning (TL) is a machine learning (ML) tool where the knowledge, acquired from a source domain, is 'transferred' to perform a task in a target domain that has (to some extent) a similar setting. The underlying concept does not require the ML method to analyse a new problem from the beginning, and thereby both the learning time and the amount of required target-domain data are reduced for training. An example is the occurrence of thermoacoustic instability (TAI) in combustors, which may cause pressure oscillations, possibly leading to flame extinction as well as undesirable vibrations in the mechanical structures. In this situation, it is difficult to collect useful data from industrial combustion systems, due to the transient nature of TAI phenomena. A feasible solution is the usage of prototypes or emulators, like a Rijke tube, to produce largely similar phenomena. This paper proposes symbolic time series analysis (STSA)-based transfer learning, where the key idea is to develop a capability of discrimination between stable and unstable operations of a combustor, based on the time series of pressure oscillations from a data source that contains sufficient information, even if it is not the target regime, and then transfer the learnt models to the target regime. The proposed STSA-based pattern classifier is trained on a previously validated numerical model of a Rijke-tube apparatus. The knowledge of this trained classifier is 'transferred' to classify similar operational regimes in: (i) an experimental Rijke-tube apparatus and (ii) an experimental combustion system apparatus. Results of the proposed transfer learning have been validated by comparison with those of two shallow neural networks (NN)-based TL and another NN having an additional long-short-term-memory (LSTM) layer, which serve as benchmarks, in terms of classification accuracy and computational complexity.

Shape Optimization of Thermoacoustic Systems Using a 2D Adjoint Helmholtz Solver

Thermoacoustic instabilities, which arise due to the interaction between flames and acoustics, are sensitive to small changes to the system parameters. In this paper, we apply adjoint-based shape optimization to a 2D finite element Helmholtz solver to find accurately and inexpensively the shape changes that most stabilise a 2D thermoacoustic system in the linear regime. We examine two cases: a Rijke tube and a turbulent swirl combustor. Both systems exhibit an unstable longitudinal mode and we suppress the instability by slightly modifying the geometry. In the case of the turbulent swirl combustor, the sensitivities are higher in the plenum and in the burner than in the combustion chamber, mainly due to the effect of the mean temperature. In the cooler regions, the local wavelength is shorter, which means that geometry changes of a given distance have more influence than they do where the local wavelength is longer. This is the first time adjoint-based shape optimization is applied to 2D Helmholtz solvers in thermoacoustics, after being previously applied to low-order thermoacoustic networks. But Helmholtz solvers have an intrinsic advantage: they can handle complex geometries. The easy scalability of this method to complex 3D geometries make this tool a strong candidate for the iterative design of thermoacoustically stable combustors.