Numerical Analysis of Combustion Instability in Hybrid Rockets

建立了固液火箭发动机内弹道和燃烧不稳定等瞬态特性的计算模型。数值模型进行了验证，对实验预测的稳态回归率。在非稳态时变模拟中，非稳态对流热通量通过将稳态形式的壁热通量的时间边界层延迟应用于回归率的变化来建模。类比一个简单的非线性振荡系统，它示出，这样的延迟可以导致在系统中的负阻尼引起自激振荡。在这个模型上，一个不稳定的区域包围。首先，观察到回归速率和腔室压力的振荡周期性增加（线性区域），然后进入非线性极限循环。还观察到腔室压力的正DC偏移。用该模型预测的不同固有模态（包括本征混合振荡模态）的频率与理论预测值吻合较好。参数分析已进行了不同的电机配置。他们的DC移位和RMS幅度的预测值的效果报告。与文献中的实验数据的非线性极限环振幅的预测进行比较，显示出良好的一致性。它的结论是，使用这种新的方法，混合火箭发动机的设计者可以研究正在设计的发动机的稳定性特性。

A computational model of a hybrid rocket motor has been developed for the purpose of simulation of internal ballistics and transient behavior such as combustion instabilities. The numerical model is validated against experiments for prediction of steady state regression rates. In the unsteady time-dependent simulation, the unsteady convective heat flux is modelled by the application of a temporal boundary layer delay of the steady state form of wall heat flux to the changes in the regression rate. With analogy to a simple non-linear oscillating system, it is shown that such a delay can result in negative damping in the system causing self-excited oscillations. Upon this modelling, an unstable region ensues. At first an oscillating periodic increase in the regression rate and chamber pressure is observed (linear regime), which then proceeds into a non-linear limit cycle. A positive DC shift in the chamber pressure is also observed. The frequencies of different natural modes (including the intrinsic hybrid oscillation mode) predicted by the model are found to be in good agreement with theoretical prediction. Parametric analyses have been carried out with different motor configurations. Their effect on the predicted values of DC shift and RMS amplitude is reported. Comparison against the prediction of non-linear limit cycle amplitude is performed for experimental data in literature, showing good agreement. It is concluded that using such a novel approach, a hybrid rocket motor designer can study the stability characteristics of the motor being designed.