Combined applications of analytic methods for detection of combustion instability triggering

https://doi.org/10.1016/j.ast.2021.106994Get rights and content

Abstract

Analytic methods are applied to investigate the dynamic behaviors of the model chambers with different lengths. They are dynamic mode decomposition (DMD), short-time Fourier transform (STFT), and recurrence plots (RPs), which are applied simultaneously to the chambers. The DMD can extract the dynamic modes in the chamber, their frequencies, and their growth rates, but can't find when the dynamic modes appear. Accordingly, the STFT is conducted to find the initiation of acoustic oscillations with specific frequencies and their evolution in real-time. Recurrence plots (RPs) are applied to see phase synchronization between oscillations of pressure and heat release rate and thereby, the triggering time of resonance is determined. In this study, the three methods are applied to the two model chambers, which are devised intentionally for stable and unstable combustion, respectively. The results showed that the present approach could extract unique stability characteristics in each chamber devised in terms of combustion instability. The combined applications can provide complete information on dynamic behaviors, including resonant frequencies, acoustic modes, sustainability of oscillations, the onset of instability triggering.

Introduction

Combustion-instability analysis is one of common subjects required for the development of liquid rocket engines. Frequently, combustion chambers of liquid rocket engines undergo severe problems of combustion instability accompanied with specific resonant modes. It is known that this phenomenon comes from the interaction between unsteady heat release from flames and acoustic pressure fluctuation [1], [2]. As a result, there are undesirable consequences such as thermal and mechanical damage on the injector faceplate and the chamber wall, intense mechanical vibration of the rocket body, the unpredictable malfunction of engines, etc. In order to understand and suppress this phenomenon, relevant characteristics of the dynamic system have been investigated and studied [3], [4], [5], [6], [7], [8], [9]. For combustion stabilization, harmful modes can be damped out by applying acoustic resonators such as Helmholtz and/or quarter-wave resonators [10], [11], [12] and by installing baffles inside a chamber [13], [14], [15], [16]. Acoustic resonators have the function to damp out or absorb pressure waves oscillating in a chamber. Accordingly, the resonator should be well-tuned to have high damping capacity [10], [17], [18]. For this purpose, information on in-chamber dynamic characteristics is required.

There are several analytic methods available in extracting dynamic characteristics inside a chamber, e.g., fast Fourier transform (FFT), dynamic mode decomposition (DMD) [16], [19], [20], flame transfer function (FTF) [21], [22], [23], [24], [25], flame describing function (FDF) [26], and so on. The Short-Time Fourier Transform (STFT) is one of the derivatives of FFT and is a reliable method in finding the specific frequency triggering combustion instability because it demonstrates the onset and transition of dominant frequency on a visible spectrogram map [27], [28], [29]. The STFT results show Fourier spectrum in a time series and are useful in monitoring the transition of both amplitudes and frequencies of pressure oscillations in a time domain. By applying the methods of STFT and DMD, information on dynamics of acoustic oscillations can be obtained, e.g., frequencies of the system, the spatial mode shapes, flame responses to the fluctuation of various inlet parameters, etc.

In testing a new chamber for stability rating, combustion instability may occur unexpectedly in real-time. Accordingly, the onset of instability, i.e., the instant time at which combustion instability is triggered, should be monitored to prevent engine failure or severe accidents.

One existing method to detect the triggering of combustion instability is the recurrence plots (RPs), which provide phase synchronization of pressure and heat release in a chamber [30], [31]. The appearance of phase synchronization indicates acoustic amplification in a chamber, resulting in combustion instability eventually. However, RPs can't provide the system frequencies at which the instability is caused and can't display the dynamic modes at the frequencies.

In this regard, analytic tools are adopted to detect the onset of combustion instability by combining the existing methods of DMD and STFT together with the method of RPs [30], [32]. The STFT results indicate when the dominant frequencies of the system come out, and the DMD results show the dominant acoustic modes and their acoustic fields. And, the RPs method is used to detect the onset of instability. Accordingly, to find out the onset of instability, the methods of RPs, STFT, and DMD are adopted at the same time. In this study, the methodology of combining these three methods is adopted for the first time to determine the triggering time of combustion instability. For their applications, two model chambers are selected, where stable and unstable combustion are intended, respectively, to see whether it can detect the onset of combustion instability successfully or not.

Section snippets

DMD algorithm

The dynamic mode decomposition (DMD) [33], [34] is a method developed to extract frequencies and damping coefficients (or growth rates) from linear fluctuations in a dynamic flow field. In order to perform the DMD analysis for a dynamic system, the instantaneous field data are taken to make m+1 snapshots and saved in the columns of two matrices in the form of Vm=[v1,,vm] and Vm+1=[v2,,vm+1], consecutively. Each column of matrices, Vm and Vm+1, has n rows that correspond to the number of

Numerical model of a chamber

For applications of the methods, a model chamber is adopted here. The 3-dimensional model chamber with a single injector adopted in the previous studies [25], [41] is simplified to the 2-dimensional model chamber for this purpose. The 2-dimensional model chambers with different chamber lengths, Lch, of 520 and 393 mm, respectively, have the same geometry of a cylinder and computational grids as shown in Fig. 4. Structured girds are applied for all domains. The grid number of cases with 520 mm

Conclusion

The post-processing methods have been applied to predict the combustion instability triggering in a combustion chamber by combining the methods of STFT, DMD, and the recurrence plots (RPs). For their applications, two model chambers have been adopted with different lengths. In terms of the longitudinal modes, one was devised for stable combustion and the other one for unstable combustion by adjusting the chamber length. From numerical simulations of reactive flow fields in the two chambers,

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

Present work was carried out with the support by the Space Core Technology Research Grants (2017M1A3A3A03015993) of the National Research Foundation of Korea (NRF), funded by the Ministry of Science, ICT (MSIT) of the Korean Government. YW, HSH, and CHS were partly supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korean government (MOTIE, 20206710100030, Development of Ecofriendly GT Combustor for 300 MWe-Class High-Efficiency Power

References (41)

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