Stability analysis of continuous rotating detonation in hollow combustor
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摘要:
在空桶燃烧室中开展了不同流量下（142.7～493.9 g/s）的连续旋转爆震试验。流量为493.9 g/s时，爆震波的传播速度接近Chapman-Jouguet（CJ）理论参考值。随着流量的减小，爆震波的传播速度和压力逐渐降低。当流量降至142.7 g/s，爆震波演化为双波模态，并伴有熄灭-再起爆现象。而且，爆震波的压力和速度周期性波动，平均传播速度仅为76.8%的CJ爆震速度。随后，采用非线性时间序列分析法讨论了不同工况下爆震波的稳定性。结果表明：流量大于300 g/s时，燃烧室的高频压力序列在相空间中的吸引子收敛为极限环模式。减小流量后导致吸引子趋于混乱，表明爆震传播稳定性降低，系统趋于无序状态。该研究讨论了流量对爆震波稳定性的影响，并探索了非线性时间序列分析在旋转爆震稳定性研究中的应用，为复杂工况下爆震波稳定性判断提供了方法参考。
Abstract:Rotating detonation experiments were conducted with various mass flow (i.e., 142.7−493.9 g/s) in a hollow combustor. The propagation velocity of the detonation wave was close to the Chapman-Jouguet (CJ) detonation speed when the mass flow reached 493.9 g/s. With the decrease of mass flow, the velocity and pressure of the detonation waves decreased. When it dropped to 142.7 g/s, the detonation waves evolved into a two-wave mode, accompanied by extinction and re-initiation phenomenon. Moreover, the pressure and velocity of the detonation waves fluctuated periodically, and the average propagation velocity was only 76.8% of CJ detonation velocity. Further, the nonlinear time-series analysis was adopted to reveal the stabilities of detonation waves. Results showed that when the mass flow was greater than 300 g/s, the attractor of the pressure time series in the phase space converged to the limit cycle mode. Decreasing the flow led to the disorder of the attractor. It indicated that the stability of the detonation wave decreased, and the system was prone to disorder. This study proved the effectiveness of nonlinear time-series analysis in studying the stabilities of rotating detonation, providing a methodological reference for the judgment of detonation wave stability under complex working conditions.
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图 3 工况1～工况5中高频压力和爆震速度轨迹
Figure 3. History of the high-frequency pressures and detonation velocities of case 1−case 5
图 9 关于爆震波压力的二维相位图（工况1）
Figure 9. Two-dimensional phase portrait of detonation waves’ pressure （case 1）
图 10 关于爆震波压力的二维相位图（工况2 ～工况5）
Figure 10. Two-dimensional phase portrait of detonation waves’ pressure for case 2−case 5
表 1 设计条件和统计参数
Table 1. Design conditions and statistical parameters
工况编号 $ \dot{m} $/（g/s） 波数 $ {f}_{\text{FFT}} $/kHz $ {V}_{\text{FFT}} $/（m/s） $ \overline{V} $/（m/s） $ {S}_{V} $ $ \overline{p} $/MPa $ {S}_{p} $ （$ \overline{V}/{V}_{\text{CJ}} $）/% 1 142.7 双波 9.77 1535.3 1482.1 87.16 0.246 0.132 76.8 2 188.1 单波 4.98 1563.3 1565.9 24.50 0.335 0.120 81.1 3 300.3 单波 5.67 1781.3 1784.6 15.73 0.923 0.104 92.4 4 384.8 单波 5.99 1880.8 1874.5 15.63 1.138 0.163 97.1 5 493.9 单波 6.14 1929.4 1932.6 11.34 1.597 0.198 100.1 
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