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Purpose <p>Thermo-acoustic instability (TAI) in gas turbines induces severe operational challenges, including excessive noise, structural damage, and catastrophic failures. Current methods for modeling and suppressing TAI often rely on solving nonlinear transcendental equations, resulting in the loss of analysis results and limiting their practicality.</p> Method <p>An energy-based analytical framework for thermo-acoustic tubes integrated with passive control devices is developed, using Helmholtz resonators (HRs) as a case study. A modified Fourier series expansion with boundary smoothing polynomials is introduced to handle arbitrary impedance boundary conditions. Thermo-acoustic coupling dynamics are described through energy-based equations, enabling multi-device control by additive energy terms. Matrix characteristic equations replace conventional nonlinear transcendental equations to derive modal parameters.</p> Results <p>Experimental and numerical validations confirm the framework’s accuracy in predicting TAI suppression. Critical parameters (e.g., HR frequency, geometry) and their matching relationships with target chambers are quantified.</p> Conclusion <p>The framework provides a predictive tool for designing HRs and other passive control devices in thermoacoustic systems. Its energy-based approach simplifies multi-device integration and offers insights for industrial applications, advancing stable gas turbine operation.</p>

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An Energy-Based Solution for Modal Characteristics Analysis of an Impedance Ended Thermo-Acoustic Tube Coupled with Helmholtz Resonator

  • 期刊论文

  • 发表日期：

    2025年4月7日

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  • Xue Xing,
  • Jiaqi Wang,
  • Shunan Wang,
  • Bingjie Ma,
  • Zhigang Wang

摘要

Purpose

Thermo-acoustic instability (TAI) in gas turbines induces severe operational challenges, including excessive noise, structural damage, and catastrophic failures. Current methods for modeling and suppressing TAI often rely on solving nonlinear transcendental equations, resulting in the loss of analysis results and limiting their practicality.

Method

An energy-based analytical framework for thermo-acoustic tubes integrated with passive control devices is developed, using Helmholtz resonators (HRs) as a case study. A modified Fourier series expansion with boundary smoothing polynomials is introduced to handle arbitrary impedance boundary conditions. Thermo-acoustic coupling dynamics are described through energy-based equations, enabling multi-device control by additive energy terms. Matrix characteristic equations replace conventional nonlinear transcendental equations to derive modal parameters.

Results

Experimental and numerical validations confirm the framework’s accuracy in predicting TAI suppression. Critical parameters (e.g., HR frequency, geometry) and their matching relationships with target chambers are quantified.

Conclusion

The framework provides a predictive tool for designing HRs and other passive control devices in thermoacoustic systems. Its energy-based approach simplifies multi-device integration and offers insights for industrial applications, advancing stable gas turbine operation.