燃烧室非线性压力振荡及其产生机理研究
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摘要
当燃烧不稳定现象发生时,燃烧室内部往往伴随有较大幅值的压力振荡,其表现形式是非线性的。为了加深对其产生机理的认识,在能量平衡方法的基础上,通过求解包含高阶非线性项的各阶能量平衡方程,模拟了燃烧室非线性压力振荡曲线,给出了不稳定状态下,燃烧室压力的陡峭化过程以及各阶模态的"极限环"幅值分布。在此基础上,进一步对初始线性增长率α以及非线性效应对"极限环"幅值的影响规律进行了参数化研究,获得相应的分布规律曲线。最后,作为验证,对不同稳定工况下的"爆炸弹"压力振荡过程进行了数值模拟。研究表明,不稳定燃烧过程中,各阶模态之间存在相互作用,且随着α的增加,"极限环"幅值呈线性递增趋势,而非线性效应对"极限环"幅值的影响规律则相反。此外,"爆炸弹"数值实验表明,在进一步完善非线性项后,能量平衡方法具有模拟非线性燃烧不稳定现象的潜力。
When the combustion instable phenomenon happens, the high amplitude pressure oscillation often occurs simultaneously in combustion chamber, which behaves in nonlinear form. In order to make it more clear about the mechanism of production, the nonlinear oscillating curve for chamber pressure was simulated based on the energy balance method through solving the energy equations including high-order nonlinear term of each mode. The pressure steepening process and the distribution of "limited cycle" amplitudes in the unstable status are also presented. Based on this, the parameterized study is conducted on the influence of initial linear growth rate α and the nonlinear effect on "limited cycle" amplitude, and the corresponding distribution curves are also showed in this paper.Then, as a validation, the pressure oscillating process of "bomb" under different stable conditions are simulated as well. It indicates that during the unbalanced combustion, interactive effects exist between the oscillating modes. Although "limited cycle" amplitude assumes progressive increase tendency with the increase of α the nonlinear effect on "limited cycle" amplitude has the opposite tendency. Except for this, the numerical experiment results show that if the nonlinear term can be further perfect properly, the energy balance method can be applied to the simulation of nonlinear combustion instable.
When the combustion instable phenomenon happens, the high amplitude pressure oscillation often occurs simultaneously in combustion chamber, which behaves in nonlinear form. In order to make it more clear about the mechanism of production, the nonlinear oscillating curve for chamber pressure was simulated based on the energy balance method through solving the energy equations including high-order nonlinear term of each mode. The pressure steepening process and the distribution of "limited cycle" amplitudes in the unstable status are also presented. Based on this, the parameterized study is conducted on the influence of initial linear growth rate α and the nonlinear effect on "limited cycle" amplitude, and the corresponding distribution curves are also showed in this paper.Then, as a validation, the pressure oscillating process of "bomb" under different stable conditions are simulated as well. It indicates that during the unbalanced combustion, interactive effects exist between the oscillating modes. Although "limited cycle" amplitude assumes progressive increase tendency with the increase of α the nonlinear effect on "limited cycle" amplitude has the opposite tendency. Except for this, the numerical experiment results show that if the nonlinear term can be further perfect properly, the energy balance method can be applied to the simulation of nonlinear combustion instable.
引文
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[12]FLANDRO G A,PERRY E H,FRENCH J C.Nonlinear rocket motor stability computations:understanding the brownlee-marble observations[C]//44th AIAA Aerospace Sciences Meeting and Exhibit.Fort Lauderdale,Florida:AIAA,2006:539-546.
[13]FLANDRO G A,JACOB E J.Irregular burning:on the origin of the DC shift[C]//43rd AIAA Joint Propulsion Conference.Las Vegas,USA:AIAA,2007:146-153.
[14]GLOYER P W,RICE T M,FLANDRO G A.Ares I thrust oscillation mitigation via motor modifications[C]//56th JANNAF Propulsion Meeting.USA:AIAA,2009:1110-1118.
[15]FLANDRO G,JACOB E.Finite amplitude waves in liquid rocket combustion chambers[C]//46th AIAA Aerospace Sciences Meeting.USA:AIAA,2008:111-119.
[16]FLANDRO G,FISCHBACH S.Effects of wave incidence on combustion instability driving mechanisms[C]//AIAA Joint Propulsion Conference.Cincinatti,OH:AIAA,2007:22-28.
[2]FLANDRO G A,SIMS J D.On nonlinear combustion instability in liquid propellant rocket engines:AIAA-2004-3516[R]Cincinatti,USA:AIAA,2004.
[3]KIRCHHOFF G.Vorlesungen uber mathematische physik:mechanik[M].Germany:Leibzig,1877.
[4]CANTRELL R H,HART R W.Interaction between sound and flow in acoustic cavities:mass,momentum,and energy considerations[J].Journal of the acoustical society of America,1964,36(4):697-706.
[5]HART R W,MCCLURE F T,Combustion instability:acoustic interaction with a burning propellant surface[J].The journal of chemical physics,1959,10(6):1501-1514.
[6]HART R W,MCCLURE F T,Theory of acoustic instability in solid propellant rocket combustion[C]//Tenth Symposium(International)on Combustion.Las Vegas,USA:AIAA,1964:1047-1066.
[7]SANDHAM N D,MORFEY C L,HU Z W.Nonlinear mechanisms of sound generation in a perturbed parallel jet flow[J].Journal of fluid mach,2006,565(2):1-23.
[8]MORFEY C L.Acoustic energy in non-uniform flows[J].Journal of sound and vibrations,1971,14(4):159-169.
[9]MYERS M K.Transport of energy by disturbances in arbitrary steady flows[J].Journal of fluid mechanics,1991,226(3):383-400.
[10]MYERS M K.An exact energy corollary for homentropic flow[J].Journal of sound and vibrations,1986,109(3):277-284.
[11]MYERS M K.Generalization and extension of the law of acoustic energy conservation in a nonuniform flow[C]//AIAA 24th Aerospace Sciences Meeting.Sacramento,California:AIAA,1986:86-0471.
[12]FLANDRO G A,PERRY E H,FRENCH J C.Nonlinear rocket motor stability computations:understanding the brownlee-marble observations[C]//44th AIAA Aerospace Sciences Meeting and Exhibit.Fort Lauderdale,Florida:AIAA,2006:539-546.
[13]FLANDRO G A,JACOB E J.Irregular burning:on the origin of the DC shift[C]//43rd AIAA Joint Propulsion Conference.Las Vegas,USA:AIAA,2007:146-153.
[14]GLOYER P W,RICE T M,FLANDRO G A.Ares I thrust oscillation mitigation via motor modifications[C]//56th JANNAF Propulsion Meeting.USA:AIAA,2009:1110-1118.
[15]FLANDRO G,JACOB E.Finite amplitude waves in liquid rocket combustion chambers[C]//46th AIAA Aerospace Sciences Meeting.USA:AIAA,2008:111-119.
[16]FLANDRO G,FISCHBACH S.Effects of wave incidence on combustion instability driving mechanisms[C]//AIAA Joint Propulsion Conference.Cincinatti,OH:AIAA,2007:22-28.