Simulation analysis of low-frequency combustion stability of a hydrogen oxygen gas generator
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摘要:
针对某氢氧火箭发动机燃气发生器热试车参数存在约200～230 Hz较明显脉动的现象，建立了低频燃烧稳定性仿真数学模型，来分析是否发生了燃烧时滞相关的极限循环低频不稳定燃烧。不同燃烧时滞、喷注器压降和燃烧室容积条件下的仿真结果显示：由燃烧时滞引起的低频不稳定燃烧频率显著低于试验结果，试验中低频脉动可能是受到了供应管路声学频率的扰动。进一步分析表明：决定燃烧系统稳定性的关键参数是燃烧时滞与燃气停留时间的比值，当该比值大于临界值时系统趋于不稳定，相反系统趋于稳定。基于仿真数据拟合形成了系统固有频率计算的半经验公式，系统固有频率随着燃烧时滞与燃气停留时间之和增大而降低。获取了在不同压降占比下的稳定边界，随着喷注器压降占比的增大，系统由稳定转为不稳定的燃烧时滞与燃气停留时间的临界比值越大。
Abstract:In view of the obvious pressure oscillations of 200−230 Hz in the hot test of a hydrogen oxygen rocket engine gas generator, a low frequency combustion stability simulation mathematical model was established to analyze whether there is low-frequency unstable combustion phenomenon of limit cycle related to combustion delay. Simulation results under different combustion time delay, pressure drop of injector and combustion chamber volume showed that the oscillations frequency related to the combustion time delay was significantly lower than the test data. The low-frequency fluctuation in the test data may be excited by the acoustic frequency of the feed line. Further analysis showed that the key parameter to determine the stability of the system is the ratio of combustion delay to gas residence time. When the ratio was greater than a critical value, the system became unstable, otherwise the system became stable. Based on the simulation data fitting, a semi empirical formula for calculating the inherent frequency of the system was formed. The inherent frequency of the system decreased with the increase of the sum of combustion delay and gas residence time. The stable boundary of the system under different injector pressure drops was obtained. With the increase of pressure drop ratio, the critical ratio of combustion delay and gas residence time from stable to unstable became larger.
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图 2 不同喷注器模型燃气生成速率对比
Figure 2. Comparison of gas generation rate under different injector models
图 3 不同喷注器模型燃烧室压力对比
Figure 3. Comparison of combustion chamber pressure under different injector models
图 5 燃烧时滞对压力振荡频率与幅值的影响
Figure 5. Influence of combustion delay on frequency and amplitude of pressure oscillation
图 6 喷注器压降对不稳定的抑制效果
Figure 6. Inhibitory effect of injector pressure drop on instability
图 7 喷注器压降对压力振荡频率与幅值的影响
Figure 7. Influence of injector pressure drop on frequency and amplitude of pressure oscillation
图 9 增大容积对压力振荡频率与幅值的影响
Figure 9. Influence of increasing volume on frequency and amplitude of pressure oscillation
图 10 不同扰动频率压力响应频谱
Figure 10. Pressure response spectrum of different disturbance frequencies
图 11 不同喷注器压降条件下210 Hz扰动压力响应
Figure 11. Pressure response to 210 Hz disturbance under different nozzle pressure drop conditions
图 12 燃气发生器试验压力振荡频谱
Figure 12. Pressure oscillation frequency spectrum of gas generator in test
图 13 燃烧室容积对固有频率影响（τ=3 ms）
Figure 13. Influence of combustion volume on inherent frequency of system （τ=3 ms）
图 14 特定压降下系统的稳定边界（τ/θg=0.51）
Figure 14. Stability boundary of system under a certain injector pressure drop （τ/θg=0.51）
图 15 同步变化容积与燃烧时滞的系统固有频率（τ/θg=0.51, τ=kvt, Vc=kvtVc,0）
Figure 15. Inherent frequency of system with synchronously varying volume and combustion delay（τ/θg=0.51, τ=kvt, Vc=kvtVc,0）
图 17 不同压降下系统的稳定边界
Figure 17. Stability boundary of system under different injector pressure drop
图 18 不同喷注器压降下系统稳定边界的固有频率
Figure 18. Inherent frequency of system on stability boundary under different injector pressure drop
表 1 模型几何参数
Table 1. Geometric parameters of the model
参数 数值 原始燃烧室容积$ {V}_{\text{c},\text{0}} $/ 10−3 m3 3.93 喷嘴长度$ {L_{\text{i}}} $/m 0.04 喷嘴出口面积$ {A_{\text{i}}} $/10−5 m2 7.85 燃烧室喉部面积$ {A_{\text{t}}} $/10−4 m2 3.42 
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表 2 燃气发生器工况参数
Table 2. Working condition parameters of gas generator
参数 数值 平均室压$ {\bar p_{\text{c}}} $/MPa 3.2 推进剂平均流量$ {\bar q_{m{\text{,i}}}} $/（kg/s） 0.45 混合比$ \gamma $/1 0.9 燃气温度$ {T_{\text{g}}} $/K 896 燃气绝热指数$ k $/1 1.36 喷注器流量系数$ \mu $/1 0.482 原始喷注器压降室压占比$ \Delta {p_{\text{0}}} $/1 0.174 原始燃气停留时间$ {\theta }_{\text{g},\text{0}} $/ms 13.6 初始燃烧时滞 $ {\tau _{\text{0}}} $/ms 3
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表 3 液氧管路声学频率与试验频率对比
Table 3. Comparison between acoustic frequency of the liquid oxygen pipe and test data
参数 试验1 试验2 试验 3 氧头腔压力/MPa 3.88 4.35 4.02 液氧温度/K 89.08 88.09 87.71 声速/（m/s） 930.9 940.7 942.2 管道长度/m 2.047 2.047 2.047 管路声学频率/Hz 227.4 229.8 230.2 试验频率/Hz 224.4 225.5 221.4
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