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Asymptotic approach to combustion instability.

Xuesong Wu1

  • 1Department of Mathematics, Imperial College, London SW7 2BZ, UK. x.wu@ic.ac.uk

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|August 18, 2005
PubMed
Summary

This study investigates combustion instability in premixed flames using an asymptotic approach. Researchers found that enthalpy fluctuations can generate sound waves, leading to parametric flame instability and mutual coupling with acoustic modes.

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Area of Science:

  • Fluid dynamics
  • Chemical kinetics
  • Acoustics

Background:

  • Combustion instability in premixed flames is a critical phenomenon.
  • Understanding the interplay between flame dynamics and acoustics is essential for safety and efficiency.
  • Previous models often simplify the complex interactions within the combustion process.

Purpose of the Study:

  • To develop an asymptotic approach for analyzing combustion instability in premixed flames.
  • To investigate the coupling between flame behavior and acoustic waves.
  • To study the nonlinear interaction between Darrieus-Landau instability and acoustic modes.

Main Methods:

  • Utilized an asymptotic approach with assumptions of large activation energy and small Mach number.
  • Modeled the flow as four interactive sub-regions: chemical reaction, heat transport, hydrodynamics, and acoustics.

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  • Derived a reduced system to describe flame-acoustics coupling and analyzed weakly nonlinear interactions.

    • Main Results:

    • A reduced system accurately describes the coupling between flame and acoustics.
    • One-dimensional enthalpy fluctuations in the oncoming mixture generate sound waves.
    • Enthalpy fluctuations can induce parametric instability in the flame.

    Conclusions:

    • The asymptotic approach provides a robust framework for studying combustion instability.
    • Enthalpy fluctuations play a significant role in generating sound and causing flame instability.
    • The mutual coupling between sound waves and parametric instability is crucial at instability thresholds.