Abstract
Unlike electric vehicles and electric aircrafts, hydrocarbon-fuelled (fossil) engine systems are much noisier. By conducting one-step chemical reaction-thermodynamics-acoustics coupling studies and experimental measurements, we explore the universal physics of how hydrocarbon-fuelled combustion is a noise maker. We also explain that how combustion-sustained noise at a particular frequency ω is intrinsically selected. These frequencies correspond to the acoustic resonance nature of the combustor. We find that a reacting gas in which the rate of chemical reacting increases with temperature is intrinsically and naturally unstable with respect to acoustic wave motion, since its modal growth rate α is greater than 0. Acoustic disturbances tend to exponentially i.e. exp(αt) increase first and then are limited by nonlinear effects and finally grow into limit cycle oscillations. The growth rate α is found to increase first and then decrease with the gradient of the heat release rate with respect to the temperature change, i.e. heat capacity. The maximum (α/ω)max depends on the specific heat ratio γ, which is related to the speed of sound. The unstable nature could be changed by introducing some acoustic dissipative/damping mechanisms, such as the boundary layer viscous drag and boundary losses. It is shown that such losses could lead to increased critical heat capacity, below which stable combustors can be designed. Finally, the acoustical energy consisting of both potential and kinetic energy is found to grow exponentially faster by 100% than the acoustic disturbance amplitude.
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References
Bragg S.L., Noise and oscillations in jet engines. Nature, 1964, 201(491): 123–124.
Rayleigh L., The explanation of certain acoustical phenomena. Nature, 1878, 18: 319–321.
Lieuwen T.C., Unsteady combustor physics, Cambridge University Press, Cambridge, 2012.
Park S., Choi G.M., Tanahashi M., Demonstration of a gas turbine combustion-tuning method and sensitivity analysis of the combustion-tuning parameters with regard to NOx emissions. Fuel, 2019, 239: 1134–1142.
Hashimoto T., Shibuya H., Gotoda H., Ohmichi Y., Matsuyama S., Spatiotemporal dynamics and early detection of thermoacoustic combustion instability in a model rocket combustor. Physical Review E, 2019, 99(3): 032208.
Sakaki K., Funahashi T., Nakaya S., Tsue M., Kanai R., Suzuki K., Inagawa T., Hiraiwa T., Longitudinal combustion instability of a pintle injector for a liquid rocket engine combustor. Combustion and Flame, 2018, 194: 115–127.
Xiong J., Morgan H., Krieg J., Liu F., Sirignano WA, Nonlinear Combustion Instability in a Multi-injector Rocket Engine. AIAA Journal, 2020, 58(1): 219–35.
Guan Y., Gupta V., Wan M., Li L.K., Forced synchronization of quasiperiodic oscillations in a thermoacoustic system. Journal of Fluid Mechanics, 2019, 879: 390–421.
Moon K., Jegal H., Gu J., Kim K.T., Combustion-acoustic interactions through cross-talk area between adjacent model gas turbine combustors. Combustion and Flame, 2019, 202: 405–416.
Magri L., Juniper M.P., Moeck J.P., Sensitivity of the Rayleigh criterion in thermoacoustics. Journal of Fluid Mechanics, 2020, 882. R1, DOI: https://doi.org/10.1017/jfm.2019.860.
Johnson M., Agrawal A.K., Effects of Porous versus Solid Inserts Pertaining to Instability Mitigation in Lean Direct Injection Combustion. AIAA SciTech 2019 Forum, 2019-0992, DOI: https://doi.org/10.2514/6.2019-0992.
Nagarajan B., Baraiya N.A., Chakravarthy S.R., Effect of inlet flow turbulence on the combustion instability in a premixed backward-facing step combustor. Proceedings of the Combustion Institute, 2019, 37(4): 5189–5196.
Sogaro F.M., Schmid P.J., Morgans A.S., Thermoacoustic interplay between intrinsic thermoacoustic and acoustic modes: non-normality and high sensitivities. Journal of Fluid Mechanics, 2019, 878: 190–220.
Schulze M., Sattelmayer T., Eigenvalue Analysis for the Prediction of Initial Growth Rates of Thermoacoustic Instability in Rocket Motors. 53rd AIAA Aerospace Sciences Meeting, 2015, pp. 1606.
Nagaraja S., Kedia K., Sujith R.I., Characterizing energy growth during combustion instabilities: Singularvalues or eigenvalues? Proceedings of the Combustion Institute, 2009, 32(2): 2933–2940.
Schulze M., Sattelmayer T., Linear stability assessment of a cryogenic rocket engine. International Journal of Spray and Combustion Dynamics, 2017, 9(4): 277–298.
Nicoud F., Benoit L., Sensiau C., Poinsot T., Acoustic modes in combustors with complex impedances and multidimensional active flames. AIAA Journal, 2007, 45(2): 426–441.
Bigongiari A., Heckl M.A., A Green’s function approach to the rapid prediction of thermoacoustic instabilities in combustors. Journal of Fluid Mechanics, 2016, 798: 970–996.
Pant T., Wang H., Transported PDF modeling of thermo-acoustic instability in a self-excited model rocket combustor using Eulerian Monte Carlo Fields method. AIAA SciTech 2019 Forum, 2019, pp. 1496.
Kraus C., Selle L., Poinsot T., Coupling heat transfer and large eddy simulation for combustion instability prediction in a swirl burner. Combustion and Flame, 2018, 191: 239–251.
Silva C.F., Magri L., Runte T., Polifke W., Uncertainty quantification of growth rates of thermoacoustic instability by an adjoint Helmholtz solver. Journal of Engineering for Gas Turbines and Power, 2017, 139(1): 011901.
Mejia D., Miguel-Brebion M., Selle L., On the experimental determination of growth and damping rates for combustion instabilities. Combustion and Flame, 2016, 169: 287–296.
Ghirardo G., Boudy F., Bothien M.R., Amplitude statistics prediction in thermoacoustics. Journal of Fluid Mechanics, 2018, 844: 216–246.
Bothien M.R., Noiray N., Schuermans B., A novel damping device for broadband attenuation of low-frequency combustion pulsations in gas turbines. Journal of Engineering for Gas Turbines and Power, 2014, 136(4): 041504.
Noiray N., Denisov A., A method to identify thermoacoustic growth rates in combustion chambers from dynamic pressure time series. Proceedings of the Combustion Institute, 2017, 36(3): 3843–3850.
Kim K.T., Hochgreb S., Measurements of triggering and transient growth in a model lean-premixed gas turbine combustor. Combustion and Flame, 2012, 159(3): 1215–1227.
Fleifil M., Annaswamy A.M., Ghoneim Z.A., Ghoniem A.F., Response of a laminar premixed flame to flow oscillations: A kinematic model and thermoacoustic instability results. Combustion and Flame, 1996, 106(4): 487–510.
Schulze M., Sattelmayer T., A comparison of time and frequency domain descriptions of high frequency acoustics in rocket engines with focus on dome coupling. Aerospace Science and Technology, 2015, 45: 165–173.
Balusamy S., Li L.K., Han Z., Hochgreb S., Extracting flame describing functions in the presence of self-excited thermoacoustic oscillations. Proceedings of the Combustion Institute, 2017, 36(3): 3851–3861.
Juniper M.P., Triggering in the horizontal Rijke tube: non-normality, transient growth and bypass transition. Journal of Fluid Mechanics, 2011, 667: 272–308.
Su W., Wang N., Li J., Zhao Y., Yan M., Improved method of measuring pressure coupled response for composite solid propellants. Journal of Sound and Vibration, 2014, 333(8): 2226–2240.
Morgans A.S., Dowling A.P., Model-based control of combustion instabilities. Journal of Sound and Vibration, 2007, 299(1–2): 261–282.
Blonbou R., Laverdant A., Zaleski S., Kuentzmann P., Active control of combustion instabilities on a Rijke tube using neural networks. Proceedings of the Combustion Institute, 2000, 28(1): 747–755.
Bloxsidge G.J., Dowling A.P., Langhorne P.J., Reheat buzz: an acoustically coupled combustion instability. Part 2. Theory. Journal of Fluid Mechanics, 1988, 193: 445–473.
Heckl M.A., Active control of the noise from a Rijke tube. Journal of Sound and Vibration, 1988, 124(1): 117–133.
Yu Y.C., Sisco J.C., Rosen S., Madhav A., Anderson W.E., Spontaneous longitudinal combustion instability in a continuously-variable resonance combustor. Journal of Propulsion and Power, 2012, 28(5): 876–887.
Gulati A., Mani R., Active control of unsteady combustion-induced oscillations. Journal of Propulsion and Power, 1992, 8(5): 1109–1115.
Burnley V.S., Culick F.E., Influence of random excitations on acoustic instabilities in combustion chambers. AIAA Journal, 2000, 38(8): 1403–1410.
Eckstein J., Sattelmayer T., Low-order modeling of low-frequency combustion instabilities in aeroengines. Journal of Propulsion and Power, 2006, 22(2): 425–432.
Motheau E., Nicoud F., Poinsot T., Mixed acoustic-entropy combustion instabilities in gas turbines. Journal of Fluid Mechanics, 2014, 749: 542–576.
Zhao D., Gutmark E., Reinecke A., Mitigating self-excited flame pulsating and thermoacoustic oscillations. Science Bulletin, 2019, 64: 941–952.
Raun R.L., Beckstead M.W., Finlinson J.C., Brooks K.P., A review of Rijke tubs, Rijke burners and related devices. Progress in Energy and Combustion Science, 1993, 19: 313–364.
Feldman Jr K.T., Reivew of the literature on Rijke thermoacoustic phenomena. Journal of Sound and Vibration, 1968, 7(1): 83–89.
Dowling A.P., Williams Ffowcs J. E., Sound and Sources of Sound. John Wiley & Sons Inc, 2000, Chister, UK, pp. 18–23.
Hashimoto T., Shibuya H., Gotoda H., Ohmichi Y, Matsuyama S, Spatiotemporal dynamics and early detection of thermoacoustic combustion instability in a model rocket combustor. Physical Review E, 2019, 99 (3): 032208.
Backhaus S., Swift G.W., A thermoacoustic Stirling heat engine, Nature, 1999, 399 (6734): 335–338.
Barinaga M., Acoustic fridge takes to space. Science, 1992, 255(5044): 534–535.
Yazaki T., Sugioka S., Mizutani F., Mamada H., Nonlinear dynamics of a forced thermoacoustic oscillation. Physical Review Letters, 1990, 64(21): 2515.
Kryuchkov N.P., Yakovlev E.V., Gorbunov E.A., Couëdel L., Lipaev A.M., Yurchenko S.O., Thermoacoustic instability in two-dimensional fluid complex plasmas. Physical Review Letters, 2018, 121(7): 075003.
Cengel Y.A., Boles M.A., Thermodynamics: An engineering approach. 7th Edition, McGraw Hill, New York, USA, 2011.
Bai X., Cheng P., Li Q., Sheng L., Kang Z., Effects of self-pulsation on combustion instability in a liquid rocket engine. Experimental Thermal and Fluid Science, 2020, 114: 110038.
Zhou H., Tao C., Liu Z., Meng S., Cen K., Optimal control of turbulent premixed combustion instability with annular micropore air jet. Aerospace Science and Technology, 2020, 98: 105650.
Acknowledgements
We gratefully acknowledge the financial support from the University of Canterbury, New Zealand (Grant No. 452STUPDZ) and Singapore National Research Foundation (Grant No. NRF2016 NRF-NSFC001-102), and National Natural Science Foundation of China (11661141020).
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Zhao, D. Thermodynamics-Acoustics Coupling Studies on Self-Excited Combustion Oscillations Maximum Growth Rate. J. Therm. Sci. 31, 1591–1603 (2022). https://doi.org/10.1007/s11630-020-1361-8
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DOI: https://doi.org/10.1007/s11630-020-1361-8