Abstract: The cavity has a great influence on the performance of supersonic combustors， such as combustion efficiency， drag characteristics and flame stability. The impact of the cavity parameter variation on the performance of combustors is complex coupled. A surrogate model based optimization and parameter analysis of the cavities in three-dimensional supersonic combustors with transverse fuel injection upstream were performed. The length， depth and sweepback angle of cavities were first designed by orthogonal experiment. Numerical simulations were applied to analyze the performance and flow fields of the test cases. Surrogate models of the combustion efficiency and total pressure recovery coefficient with the design variables were constructed. Based on the complex system optimization strategy， optimization of the cavity parameters were carried out twice to provide the Pareto front by the non-dominated sorting genetic algorithm (NSGA-Ⅱ). The results show that the optimal cavity configurations can be divided into narrow deep type， shallow long type and medium deep and long type， which correspond to rapid change section， gentle change section and extraordinary change section in the Pareto front. The combustion efficiency has a negative correlation with the length of cavities and a positive correlation with the depth of cavities. Whereas， the total pressure recovery coefficient has the opposite situations. Both combustion efficiency and total pressure recovery coefficient have few positive correlations with the sweepback angle. The combustors in the gentle change section have more uniform pressure distribution and higher total pressure recovery coefficient， which should be preferred when there is no need of high combustion efficiency. The length-to-depth ratio of the cavities in this section is about 2.67 to 8.

Key words: Supersonic combustors；Cavity configuration；Surrogate models；Optimization

摘要： 凹腔构型对超声速燃烧室的燃烧效率、阻力特性、火焰稳定等性能都有重要的影响，且凹腔构型各参数变化产生的影响存在复杂的耦合作用。因此，针对横向喷射燃料的三维超声速燃烧室凹腔构型进行了基于代理模型的优化设计及参数分析研究。首先对凹腔的长度、深度和后壁倾角进行正交试验设计，数值仿真用以对凹腔燃烧室进行流场与性能分析，建立燃烧室燃烧效率和总压恢复系数与设计变量间的代理模型，根据基于替代模型的复杂系统优化策略，采用带精英策略的非支配排序遗传算法(NSGA-Ⅱ)对凹腔构型进行二次优化设计，得到Pareto前沿面。结果分析表明，优化凹腔构型可分为窄深型、浅长型和中深中长型，分别对应Pareto前沿面的急变段、平缓段和巨变段；凹腔燃烧室的燃烧效率与凹腔长度呈负相关，与凹腔深度呈正相关，总压恢复系数反之；后壁倾角对总压恢复系数和燃烧效率影响均较小。平缓区的燃烧室压力幅度变化小且总压恢复系数高，其长深比在2.67～8，在不需要极高的燃烧效率情况下，可以优先选择平缓区凹腔构型。

关键词: 超声速燃烧室；凹腔构型；代理模型；优化