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摘要:
针对变循环发动机非线性部件模型共同工作方程组求解时初值选取对收敛速度和精度的影响问题，提出一种基于量子粒子群优化（QPSO）算法与Broyden拟牛顿法混合的求解思路。首先，对变循环发动机（VCE）进行变几何特性分析以及反向传播（BP）神经网络下的外涵道稳态特性分析基础上，建立反映变几何特性以及模式切换等全状态部件模型。其次，以该模型性能计算为基准，提出了一种基于QPSO的Broyden拟牛顿混合算法来达到发动机共同工作平衡要求，通过发散系数实现混合算法的切换，以改善单一Broyden拟牛顿法对初值选取的依赖性同时提高QPSO算法的求解效率。通过高阶非线性方程组的仿真验证了算法的有效性、求解效率以及精度。最后，进行VCE部件模型稳态、动态仿真计算，结果表明：与GasTurb性能计算结果对比可以看出发动机速度特性、高度特性等变化趋势与GasTurb基本一致，且误差均小于2%；基于QPSO的Broyden拟牛顿混合算法可有效快速地完成VCE部件模型的求解；所建VCE部件模型能够有效实现该新型发动机的性能模拟分析。
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关键词:
- 变循环发动机(VCE) /
- 变几何特性 /
- 外涵道 /
- 非线性方程组求解 /
- 量子粒子群优化(QPSO) /
- Broyden拟牛顿法
Abstract:A new hybrid algorithm which is based on quantum particle swarm optimization (QPSO) algorithm and Broyden quasi-Newton algorithm was proposed to reduce the effect of initial value selection on convergence speed and accuracy in solving the variable cycle engine (VCE) model. Firstly, based on the analysis of the VCE geometrical characteristics and the analysis of the steady-state characteristics of the external duct through backpropagation(BP) neural network method, a component model was established which can reflect variable geometry property and mode switching and other states of the VCE. Secondly, based on the model performance calculation, a QPSO based Broyden quasi-Newton hybrid algorithm was used to solve the VCE model cooperating equations, which improved the convergence and calculation efficiency of the hybrid algorithm by introducing the divergence coefficient to combine the two single algorithms. The effectiveness, efficiency and accuracy of the algorithm were verified by the simulation of high-order nonlinear equations. Finally, the steady state and dynamic simulation of VCE component model were carried out. The results of VCE model show that, compared with the results of GasTurb performance calculation, the trends of velocity characteristics and altitude characteristics are basically the same with those of GasTurb, the error between VCE model and GasTurb is less than 2%. The hybrid algorithm based on QPSO and Broyden quasi-Newton algorithm can solve the VCE model efficiently and quickly. The established VCE model can be used for performance simulation and analysis.
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图 1 初值选取对Broyden拟牛顿法求解收敛性的影响
Figure 1. Influence of initial value selection on solving convergence of Broyden quasi-Newton method
图 2 初值选取对Broyden拟牛顿法收敛一致性的影响
Figure 2. Influence of initial value selection on convergence consistency of Broyden quasi-Newton method
图 3 可调静子叶片角度为10°时，变几何特性修正计算与传统方法结果对比
Figure 3. Comparison of variable geometry characteristic correcting calculation results with results of traditional method when adjustable stator blade angle is 10°
图 4 变循环航空发动机外涵道结构示意图
Figure 4. Schematic diagram of external duct structure of variable cycle aero-engine
图 5 模式选择活门为5°时，进口总压分别为356.24和351.091 kPa工况时，副外涵道与CDFS涵道流场计算结果
Figure 5. Flow field calculation results of vice external duct and CDFS duct at total import pressure of 356.24 and 351.091 kPa when mode of valve 5° is selected
图 8 高阶非线性方程组求解结果对比
Figure 8. Comparison of solving results of high-order nonlinear equations
图 9 双涵及单涵模式下不同高度及马赫数的速度及高度特性仿真结果对比
Figure 9. Comparison of simulation results of velocity and height characteristics at different height and Mach numbers in double-duct and single-duct modes
图 10 单、双涵模式工作VCE稳态特性对比
Figure 10. Comparison of steady-state characteristics of variable-cycle engines between single-duct and double-duct working modes
图 11 H=8 km，Ma=0.9的双涵工作模式动态仿真结果
Figure 11. Dynamic simulation results of double-duct working mode when H=8 km and Ma=0.9
图 12 H=12 km，Ma=1.5的单涵工作模式动态仿真结果
Figure 12. Dynamic simulation results of single-duct working mode when H=12 km and Ma=1.5
表 1 设计点参数
Table 1. Design point parameters
参数 参数值 双涵模式 单涵模式 低压转子转速PCNF 100 100 高压转子转速PCNC 100 100 风扇叶尖压比PRF_tip 3.5 3.5 风扇叶根压比PRF_root 3.2 3.2 CDFS压比PRCDFS 1.3 1.3 压气机压比PRC 6 6 燃烧室总温T4/K 1850 1850 高压涡轮落压比PRHT 2.763489 2.795642 低压涡轮落压比PRLT 1.915404 1.703737 前涵道比BYPASS1 0.3 0 后涵道比BYPASS2 0.3 0.4 
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