Koji Maeta, Takenao Ohkawa

Abstract:

This study proposes a low-dimensional thermoacoustic model for predicting pressure fluctuations in lean-burn combustion systems. Traditional monitoring approaches based solely on experimental data or physical models lack accuracy and responsiveness for real-time applications. To address this limitation, a linearized acoustic wave equation incorporating heat release fluctuations and flow-induced acoustic sources was formulated using conservation laws. A finite element Analysis (FEA) model was developed and implemented in the time domain via the Newmark-β scheme. A simplified Rijke tube model was constructed, with input data such as temperature distribution derived from high-speed flame image analysis, enabling computational efficiency and near-real-time prediction without CFD. Experimental validation was conducted with a premixed combustor under various air flow rates and burner positions. The predicted and observed pressure signals showed increasing amplitude with leaner mixtures. The correlation coefficients for the peak frequencies of the first and second modes were 0.77 and 0.67, respectively. Damping ratios estimated using Hilbert transform and curve fitting yielded a correlation coefficient of 0.73. The most unstable flame location corresponded to the position of maximum acoustic pressure gradient, consistent with the theoretical forcing term formulation. These results demonstrate the model’s capability to capture combustion instability trends and its potential for future integration with data assimilation and machine learning techniques.

Keywords: Combustion instability, Mathematical Model, Low-dimensional model, Data Assimilation, Finite Element Method

Date Published: May 5, 2025
DOI: 10.11159/jffhmt.2025.016

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