High-dimensional multi-objective optimization of aero-engine based on POD-PCE-Kriging model
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摘要:
针对于传统的航空发动机燃烧室设计过程计算周期长，加工和试验成本高，制约发动机设计周期的问题，基于航空发动机燃烧室模型，结合POD-PCE-Kriging（本征正交分解-多项式混沌展开-Kriging）模型和粒子群优化（PSO）算法开展了燃烧性能代理模型的构建和多目标优化设计。通过试验，应用POD-PCE-Kriging模型预测结果与一维程序计算结果进行对比分析，针对于燃烧效率和总压损失预测值的方均根误差分别为0.0063%和0.1227%。对设计变量参数开展寻优，并对获取的Pareto最优解集进行了分析，为满足性能指标的先进航空发动机燃烧室设计提供了物理见解，可以快速准确获得满足最优性能的设计参数，缩短航空发动机的研制周期。
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关键词:
- 航空发动机燃烧室设计 /
- 代理模型 /
- POD-PCE-Kriging模型 /
- 粒子群优化算法 /
- 多目标优化
Abstract:In view of the traditional aero-engine combustor design process with long calculation cycle, high processing test and cost which restricts the engine design cycle, based on the aero-engine combustor model, POD-PCE-Kriging (proper orthogonal decomposition-polynomial chaotic expansion-Kriging) model and particle swarm optimization (PSO) algorithms were combined to construct the combustion performance surrogate model and carry out multi-objective optimization design. Through the test, the predicted results of POD-PCE-Kriging model were compared with the calculated results of one-dimensional program, and the root mean square errors of the predicted values of combustion efficiency and total pressure loss were 0.0063% and 0.1227%, respectively. Optimization search was carried out for the design variables, and the obtained Pareto optimal solution set was analyzed to provide physical insight into the design of advanced aero-engine combustor to meet the performance specifications, which can quickly and accurately obtain the design parameters to meet the optimal performance and accelerate the development cycle of aero-engine.
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图 1 双旋流燃烧室主燃孔中心截面轴向速度分布数值模拟与试验结果对比
Figure 1. Comparison between numerical simulation and test results of axial velocity distribution on the center section of the main combustion hole in a twin-swirl combustor
图 2 双旋流燃烧室沿轴向流量分配对比
Figure 2. Comparison of axial flow distribution in twin-swirl combustor
图 5 燃烧效率及总压损失全局灵敏度分析结果图
Figure 5. Global sensitivity analysis of combustion efficiency and total pressure loss
图 6 代理模型燃烧效率预测对比图
Figure 6. Comparison of predictions of surrogate models on combustion efficiency
图 7 代理模型总压损失预测对比图
Figure 7. Comparison of predictions of surrogate models on total pressure loss
图 9 燃烧效率随影响参数变化情况图
Figure 9. Variation of combustion efficiency with influential parameters
图 10 总压损失随影响参数变化情况图
Figure 10. Variation of total pressure loss with influential parameters
表 1 双旋流燃烧室出口总温计算结果对比
Table 1. Comparison of the calculated results of total temperature at the outlet of the twin-swirl combustor
计算方法 燃烧室出口总温/K 一维计算（Case1） 1721.3 一维计算（Case2） 1773.4 CFD三维计算 1720.9 
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表 2 双旋流燃烧室性能参数对比
Table 2. Comparison of performance parameters of twin-swirl combustor
性能参数 一维计算
（Case1）一维计算
（Case2）CFD
三维计算燃烧效率 0.9994 0.9994 0.9974 总压恢复系数 0.9601 0.9565 0.9604
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表 3 燃烧室设计要求
Table 3. Combustor design requirements
参数 设计状态 慢车状态 进口总温/K 850 492.9 油气比 0.0430 0.0106 燃烧效率 > 0.99 > 0.98 总压损失 < 0.06 < 0.07 出口温度分布系数（OTDF） < 0.20 出口径向温度分布系数（RTDF） < 0.12
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表 4 设计变量
Table 4. Design variable
设计变量 数值范围 进口总温${T}_{{\rm{t}}}$/K 427.55～1070.33 进口总压${p}_{{\rm{t}}}$/kPa 500～3200 进口流量$\dot m_{\rm{in}}$/(kg/s) 19.01～82.398 油气比$\varphi$ 0.0106～0.0430 主燃孔数量${N}_{{\rm{m}}}$/个 2～4 主燃孔直径${D}_{{\rm{m}}}$/mm 12.1～16.8 每排冷却孔数量${N}_{{\rm{c}}}$/个 10～20 冷却孔直径${D}_{{\rm{c}}}$/mm 0.5～1.5
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