Thermo-acoustic instability explained

Thermo-acoustic instability refers to an instabiltiy arising due to acoustics field and unsteady heat release process. This instability is very relevant in combustion instabilities in systems such as rocket engines, etc.^{[1] [2] [3]}

Rayleigh criterion

A very simple mechanism of acoustic amplication was first identified by Lord Rayleigh in 1878.^{[4] [5]} In simple terms, Rayleigh criterion states that amplification results if, on the average, heat addition occurs in phase with the pressure increases during the oscillation.. That is, if

p' is the pressure perturbation (with respect to its mean value \langle p\rangle ) and • q' is the rate of heat release per unit volume (with respect to its mean value \langle • q\rangle ), then the Rayleigh criterion says that acoustic amplification occurs if \langle p' • q' \rangle > 0 .

Rayleigh criterion is used to many explain phenomena such as singing flames in tubes, sound amplification in Rijke tube and others. In complex systems, Rayleigh criterion, may not ne strictly valid, as there exists many damping factors such as viscous/wall/nozzle/relaxation/homogeneous/particle damping, mean-flow effects, et, that are not accounted in Rayleigh's analysis.

See also

• Darrieus–Landau instability
• Diffusive–thermal instability
• Rijke tube

Notes and References

1. Williams, F. A. (2018). Combustion theory. CRC Press.
2. Clavin, P., & Searby, G. (2016). Combustion waves and fronts in flows: flames, shocks, detonations, ablation fronts and explosion of stars. Cambridge University Press.
3. Forman A. Williams, Marcel Barrère, N. C. Huang (1969). Fundamental aspects of solid propellant rockets. Technivision Services
4. Rayleigh, L. (1878). The explanation of certain acoustical phenomena. Roy. Inst. Proc., 8, 536-542.
5. Rayleigh, J. W. S. B. (1896). The theory of sound (Vol. 2). Macmillan.