为了构建适用于燃烧室冷态流动混合过程的代理模型(surrogate model,SM)的方法,该文研究了构建过程中的关键步骤,通过使用Latin超立方抽样(Latin hypercube sampling,LHS)方法进行样本选取,在完成数值模拟后使用本征正交分解提取样本间的主要特征进行降维,再通过Kriging插值法完成工况插值。结果表明：该构建方法能够处理冷态高速、高湍流度、强旋流动和燃料/空气掺混,精度高于国际平均水平。同时,该文提出了构建方法的应用准则,为后续更复杂、包含燃烧反应过程以及结构变化的燃烧室SM构建奠定基础。
[Objective] Numerical simulation of a gas turbine combustor is an important step in its design process. Due to the complexity of the physical and chemical processes, the calculation cost is high. The calculation cost can be reduced by constructing surrogate model of combustor. This paper focuses on the key steps in the construction of a surrogate model suitable for cold gas flow and the mixing process of combustor. Furthermore, this paper proposes a surrogate model for the central nozzle and the subsequent combustor space of a heavy-duty gas turbine. [Methods] The construction of the surrogate model includes several key steps: design of experiments (DOE), numerical simulation, dimensionality reduction, and an interpolation process. Two parameters are selected as the input parameters for the surrogate model: The fuel mass flow rate Gf and the combustor inlet air pressure p2. Latin hypercube sampling is used in the DOE to determine 12 operating conditions for computational fluid dynamics (CFD) simulations, and the results are used to build the surrogate model. Proper orthogonal decomposition is used for dimensionality reduction, wherein a set of basis functions and corresponding coefficients are extracted. The basis functions reflects the main characteristics of the combustor flow field. Moreover, the data dimensionality is reduced from the number of grid nodes of the combustor to the number of basis functions, which do not exceed the number of operating conditions. The Kriging model is used to interpolate the coefficients of the basis function with the input parameters of the surrogate model. Four verification conditions are set up to determine the accuracy of the surrogate model through a comparison of the surrogate model results with the CFD simulation results. The outlet cross section of the central nozzle and the longitudinal section of the combustor are selected to compare multiple key parameter distributions, including axial velocity, radial velocity, tangential velocity, CH4 concentration, turbulent kinetic energy, and pressure. The vector operations are used to compare the distributions of various parameters, which can simultaneously reflect the differences in the numerical and spatial distributions of various parameters. [Results] The results showed that the error in most parameters was ~1%. The results also revealed that the construction method of the surrogate model could be applied to cold high-speed and high-turbulence strong rotational flow and fuel/air mixing. The accuracy was higher than the international average level, and the application criteria of the construction method were proposed. The influences of interpolation methods, sample numbers, and basis function numbers on the accuracy of the surrogate model were analyzed. The accuracy of SM was higher than extrapolation. Increasing the number of sample operations and basis functions could improve the accuracy of the surrogate model, but also increased the computational cost. [Conclusions] The SM construction method (POD & Kriging) is suitable for the cold gas flow and mixing process in the combustor. The paper lays the foundation for subsequent research on the construction method of combustor SM, which includes combustion reactions and geometric structure changes.
[1] 焦树建.燃气轮机燃烧室[M].北京:机械工业出版社, 1981. JIAO S J. Gas turbine combustor[M]. Beijing:China Machine Press, 1981.(in Chinese)
[2] MAK S, SUNG C L, WANG X J, et al. An efficient surrogate model for emulation and physics extraction of large eddy simulations[J]. Journal of the American Statistical Association, 2018, 113(524):1443-1456.
[3] WANG X J, YEH S T, CHANG Y H, et al. A high-fidelity design methodology using LES-based simulation and POD-based emulation:A case study of swirl injectors[J]. Chinese Journal of Aeronautics, 2018, 31(9):1855-1869.
[4] YEH S T, WANG X J, SUNG C L, et al. Common proper orthogonal decomposition-based spatiotemporal emulator for design exploration[J]. AIAA Journal, 2018, 56(6):2429-2442.
[5] 朱新奇.飞行器外形优化设计方法及多输出代理模型研究[D].西安:西北工业大学, 2019. ZHU X Q. Research on flight vehicle shape optimization design algorithms and multi-output surrogate model[D]. Xi'an:Northwestern Polytechnical University, 2019.(in Chinese)
[6] 吕利叶.先进代理模型方法与应用研究[D].大连:大连理工大学, 2020. Lü L Y. On advanced surrogate models and application[D]. Dalian:Dalian University of Technology, 2020.(in Chinese)
[7] 夏陈超.基于CFD的飞行器高保真度气动外形优化设计方法[D].杭州:浙江大学, 2016. XIA C C. High-fidelity aerodynamic shape optimization method of aircraft based on computational fluid dynamics[D]. Hangzhou:Zhejiang University, 2016.(in Chinese)
[8] 李俊芳,张步涵.基于进化算法改进拉丁超立方抽样的概率潮流计算[J].中国电机工程学报, 2011, 31(25):90-96. LI J F, ZHANG B H. Probabilistic load flow based on improved Latin hypercube sampling with evolutionary algorithm[J]. Proceedings of the CSEE, 2011, 31(25):90-96.(in Chinese)
[9] WANG X J, CHANG Y H, LI Y X, et al. Surrogate-based modeling for emulation of supercritical injector flow and combustion[J]. Proceedings of the Combustion Institute, 2021, 38(4):6393-6401.
[10] 冯俞楷. POD降维算法在传热与流动数值模拟中的应用[D].北京:华北电力大学, 2017. FENG Y K. Application of POD reduced-order algorithm on heat transfer and flow simulation[D]. Beijing:North China Electric Power University, 2017.(in Chinese)
[11] 黄煌.风资源评估后处理系统的实现与并行优化[D].北京:清华大学, 2015. HUANG H. The implementantion and optimization of post-processing system for wind resource assessment[D]. Beijing:Tsinghua University, 2015.(in Chinese)
[12] 本杰明.基于遥感和机器学习从地表特征对地下水深度的预测方法研究[D].北京:清华大学, 2019. BEN J M. Predicting groundwater depth from surface features using remote sensing and machine learning[D]. Beijing:Tsinghua University, 2019.(in Chinese)
[13] 邹林君.基于Kriging模型的全局优化方法研究[D].武汉:华中科技大学, 2011. ZOU L J. Research on global optimization algorithm based on kriging model[D]. Wuhan:Huazhong University of Science and Technology, 2011.(in Chinese)
[14] 胡和敏.火电空冷系统跨尺度热质传递的数值模拟研究[D].北京:华北电力大学, 2014. HU H M. Cross scale simulation on heat and mass transfer of air-cooled condenser in power plant[D]. Beijing:North China Electric Power University, 2014.(in Chinese)
[15] 祁海鹰,田园,耿俊杰. X重型燃机联合研制低排放燃烧室模拟计算项目报告[R].北京:清华大学, 2021. QI H Y, TIAN Y, GENG J J. Report on simulation of low emission combustor for a heavy gas turbine[R]. Beijing:Tsinghua University, 2021.(in Chinese)
[16] SACKS J, WELCH W J, MITCHELL T J, et al. Design and analysis of computer experiments[J]. Statistical Science, 1989, 4(4):409-423.
