Acoustic Instability of the Slab Rocket Motor
Acoustic Instability of the Slab Rocket Motor
复制标题
板式火箭发动机的声学不稳定性
DOI：
10.2514/1.14794
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发表时间：
2004
影响因子：
1.9
通讯作者：
G. Flandro
中科院分区：
文献类型：
--
作者：
S. Fischbach;J. Majdalani;G. Flandro
本文提供了严格的数学细节，从而改进了固体火箭发动机声不稳定性的公式。用数值方法和渐近方法对稳定增长率因子进行了估计。在广泛的工作参数范围内，得到了稳定系数的解析表达式。对于正在调查的所有有代表性的火箭发动机，分析估计的误差为5%或更小。数值和渐近在预测明显低于经典稳定性理论所预测的稳定系统时是收敛的。这种显著的差异可以归因于在以前的公式中忽略了时间相关的旋转耦合。目前的研究揭示了六个额外的增长率修正的细节，这些修正以前没有考虑到。这些因素包括旋转流量、平均涡量、粘度、伪声、伪涡量和非定常喷管增长率等。第四项和第五项是由于声学和涡旋与通常被忽略的伪压力的相互作用。第六是由于与流出喷嘴的非定常流相关联的能量。这项研究使我们能够分离出各种流动属性对稳定性的影响。这些参数包括电机展弦比、表面马赫数、粘性参数、振荡模态形状数和表面导纳。根据板坯电机的几何形状，我们发现流动转向修正被另一个先前未考虑的旋转项完全抵消。我们还发现，非定常喷管阻尼效应被另一个由伪压力引起的不稳定源所抵消。
This article provides rigorous mathematical details leading to an improved formulation of acoustic instability in solid rocket motors. The evaluation of stability growth rate factors is carried out both numerically and asymptotically. Analytical expressions for the stability factors are obtained over a broad spectrum of operating parameters. For all representative rocket motors under investigation, the analytical estimates exhibit an error of 5% or less. Both numerics and asymptotics converge in predicting markedly less stable systems than projected by classic stability theory. The dramatic differences can be ascribed to the dismissal of time-dependent rotational coupling in the previous formulation. The current study unravels the details of six additional growth rate corrections not accounted for previously. These include the rotational flow, mean vorticity, viscosity, pseudo acoustic, pseudo vorticity and unsteady nozzle growth rate factors. The fourth and fifth terms are due to acoustical and vortical interactions with the often neglected pseudopressure. The sixth is due to the energy associated with the unsteady rotational flow exiting the nozzle. This study enables us to isolate the impact of various flow attributes on stability. These involve the motor aspect ratio, surface Mach number, viscous parameter, oscillation mode shape number, and surface admittance. Based on the slab motor geometry, we find that the flow turning correction is cancelled identically by another rotational term not accounted for previously. We also find that the unsteady nozzle damping effect is offset by another source of instability due to the pseudopressure.