EI、Scopus 收录
中文核心期刊

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

超燃冲压发动机仿真: 从数值飞行到数智飞行

孙明波 安彬 汪洪波 王成龙

孙明波, 安彬, 汪洪波, 王成龙. 超燃冲压发动机仿真: 从数值飞行到数智飞行. 力学学报, 2022, 54(3): 588-600 doi: 10.6052/0459-1879-21-397
引用本文: 孙明波, 安彬, 汪洪波, 王成龙. 超燃冲压发动机仿真: 从数值飞行到数智飞行. 力学学报, 2022, 54(3): 588-600 doi: 10.6052/0459-1879-21-397
Sun Mingbo, An Bin, Wang Hongbo, Wang Chenglong. Numerical simulation of the scramjet engine: from numerical flight to intelligent numerical flight. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(3): 588-600 doi: 10.6052/0459-1879-21-397
Citation: Sun Mingbo, An Bin, Wang Hongbo, Wang Chenglong. Numerical simulation of the scramjet engine: from numerical flight to intelligent numerical flight. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(3): 588-600 doi: 10.6052/0459-1879-21-397

超燃冲压发动机仿真: 从数值飞行到数智飞行

doi: 10.6052/0459-1879-21-397
基金项目: 国家自然科学基金资助项目(11925207)
详细信息
    作者简介:

    孙明波, 教授, 主要研究方向: 高超声速推进技术. E-mail: sunmingbo@nudt.edu.cn

  • 中图分类号: V211.3

NUMERICAL SIMULATION OF THE SCRAMJET ENGINE: FROM NUMERICAL FLIGHT TO INTELLIGENT NUMERICAL FLIGHT

  • 摘要: 数值计算方法、物理模型和计算硬件的进步极大地促进了超燃冲压发动机仿真的发展, 基于内外流一体化仿真的数值飞行技术已日渐成熟并逐步应用于工程实践, 伴随燃烧、气动、结构、材料以及传热多物理场耦合模型和计算方法的发展, 叠加多场计算的广义数值飞行技术有望近期得到突破. 目前人工智能技术的快速发展, 将赋能于数值飞行技术, “数智飞行”这一新的研究模式应运而生. 一方面, 数智飞行将利用人工智能突破传统数值飞行技术在网格生成与自适应、高保真物理模型、数据处理与知识挖掘等方面的发展瓶颈, 全面提升数值飞行的精度、准度和效能; 另一方面, 数智飞行将突破传统发动机研发模式, 通过构建智能化发动机数字孪生体, 实现发动机在虚拟空间中的全弹道飞行考核, 加快发动机设计迭代. 此外, 数字孪生体在试验中可与实体发动机同步运行, 根据感知数据快速预测多物理场, 实现对实体发动机工作状态的实时评估. 为促进数智飞行技术的发展, 未来需要重点针对数据驱动与物理约束的有机结合、智能化多物理场联合仿真平台、发动机数字孪生体构建等方面开展研究.

     

  • 图  1  超燃冲压发动机示意图[12]

    Figure  1.  Scramjet engine concept[12]

    图  2  超燃冲压发动机内外流一体化仿真典型结果

    Figure  2.  Representative numerical results of internal and external coupling flow

    图  3  两种内外流一体化仿真平台

    Figure  3.  Two software platforms for numerical simulation of internal and external coupling flow

    图  4  超燃冲压发动机中的多物理场耦合

    Figure  4.  Multi-physics coupling in a scramjet engine

    图  5  TX-V结构响应与寿命预测[30]

    Figure  5.  Structural response and life prediction of TX-V[30]

    图  6  基于卷积神经网络的网格分类器[36]

    Figure  6.  A mesh classifier based on convolutional neural network[36]

    图  7  基于神经网络的流场快速预测[42]

    Figure  7.  Fast flow field prediction based on neural network[42]

    图  8  构建数据驱动湍流模型的流程图[47]

    Figure  8.  Flow chart for building a data-driven turbulence model[47]

    图  9  Shock-Net和Tecplot软件识别的激波[60]

    Figure  9.  Shock waves detected by Shock-Net and Tecplot[60]

    图  10  基于本征正交分解和长短时记忆神经网络的混合模型降阶方法[64]

    Figure  10.  A hybrid model order reduction method based on proper orthogonal decomposition and long short-term memory neural network[64]

    图  11  航空发动机的数字孪生体

    Figure  11.  Digital twin of an aero engine

    图  12  超燃冲压发动机的数字孪生体

    Figure  12.  Digital twin of a scramjet engine

    图  13  数字孪生体在超燃冲压发动机设计中的应用

    Figure  13.  Application of digital twin in the field of scramjet engine design

  • [1] Duraisamy K, Iaccarino G, Xiao H. Turbulence modeling in the age of data. Annual Review of Fluid Mechanics, 2019, 51: 357-377 doi: 10.1146/annurev-fluid-010518-040547
    [2] Gonzalez-Juez ED, Kerstein AR, Ranjan R, et al. Advances and challenges in modeling high-speed turbulent combustion in propulsion systems. Progress in Energy and Combustion Science, 2017, 60: 26-67 doi: 10.1016/j.pecs.2016.12.003
    [3] 周铸, 黄江涛, 黄勇等. CFD技术在航空工程领域的应用、挑战与发展. 航空学报, 2017, 38(3): 020891 (Zhou Zhu, Huang Jiangtao, Huang Yong, et al. CFD technology in aeronautic engineering field: Applications, challenges and development. Acta Aeronautica et Astronautica Sinica, 2017, 38(3): 020891 (in Chinese)
    [4] 赵钟, 何磊, 何先耀. 风雷(PHengLEI)通用CFD软件设计. 计算机工程与科学, 2020, 42(2): 210-219 (Zhao Zhong, He Lei, He Xianyao. Design of general CFD software PHengLEI. Computer Engineering and Science, 2020, 42(2): 210-219 (in Chinese) doi: 10.3969/j.issn.1007-130X.2020.02.004
    [5] Urzay J. Supersonic combustion in air-breathing propulsion systems for hypersonic flight. Annual Review of Fluid Mechanics, 2018, 50: 593-627 doi: 10.1146/annurev-fluid-122316-045217
    [6] Zhang S, Chen F, Liu H. Integrated fluid-thermal-structural analysis for predicting aerothermal environment of hypersonic vehicles// 52nd Aerospace Sciences Meeting, National Harbor, Maryland, 2014
    [7] Fujiyoshi H, Hirakawa T, Yamashita T. Deep learning-based image recognition for autonomous driving. IATSS Research, 2019, 43(4): 244-252 doi: 10.1016/j.iatssr.2019.11.008
    [8] Dou Z, Wang X, Shi S, et al. Exploiting deep representations for natural language processing. Neurocomputing, 2020, 386: 1-7 doi: 10.1016/j.neucom.2019.12.060
    [9] Ahamed NN, Karthikeyan P. A reinforcement learning integrated in heuristic search method for self-driving vehicle using blockchain in supply chain management. International Journal of Intelligent Networks, 2020, 1: 92-101 doi: 10.1016/j.ijin.2020.09.001
    [10] 张伟伟, 朱林阳, 刘溢浪等. 机器学习在湍流模型构建中的应用进展. 空气动力学学报, 2019, 37(3): 444-454 (Zhang Weiwei, Zhu Linyang, Liu Yilang, et al. Progresses in the application of machine learning in turbulence modeling. Acta Aerodynamica Sinica, 2019, 37(3): 444-454 (in Chinese)
    [11] Brunton SL, Noack BR, Koumoutsakos P. Machine learning for fluid mechanics. Annual Review of Fluid Mechanics, 2020, 52: 477-508 doi: 10.1146/annurev-fluid-010719-060214
    [12] Peebles C. Road to Mach 10: Lessons learned from the X-43A flight research program. Reston: Library of Flight Series, AIAA, 2008: 36-78
    [13] McQuade PD, Eberhardt S, Livne E. CFD-based aerodynamic approximation concepts optimization of a two-dimensional scramjet vehicle. Journal of Aircraft, 1995, 32(2): 262-269 doi: 10.2514/3.46711
    [14] 王德鑫, 褚佑彪, 刘难生等. 高背压进气道中内外流耦合作用的大涡模拟研究. 航空学报, 2021, 42(9): 625754 (Wang Dexin, Chu Youbiao, Liu Nansheng, et al. Large-eddy simulations of the external and internal coupling flow in an inlet of high back pressure. Acta Aeronautica et Astronautica Sinica, 2021, 42(9): 625754 (in Chinese)
    [15] Bisek NJ. Influence of the external aeroshell on the HIFiRE-6 using high-fidelity simulations//55th AIAA Aerospace Sciences Meeting, Grapevine, Texas, 2017
    [16] 何良俊, 张兵, 尤厚丰等. 吸气式高超声速飞行器机体/推进一体化内外流非定常耦合方法. 气体物理, 2020, 5(6): 52-59 (He Liangjun, Zhang Bing, You Houfeng, et al. Unsteady coupling method of internal and external flows for airbreathing hypersonic vehicle with airframe/propulsion integration. Physics of Gases, 2020, 5(6): 52-59 (in Chinese)
    [17] Barth JE, Wise DJ, Wheatley V, et al. Tailored fuel injection for performance enhancement in a Mach 12 scramjet engine. Journal of Propulsion and Power, 2019, 35(1): 72-86 doi: 10.2514/1.B36794
    [18] 陈兵, 仇理宽, 龚春林等. 流-固-推进耦合下的机体/推进一体化性能分析. 推进技术, 2020, 41(4): 729-739 (Chen Bing, Qiu Likuan, Gong Chunlin, et al. Airframe-propulsion integrated performance under fluid-structure-propulsion coupling. Journal of Propulsion Technology, 2020, 41(4): 729-739 (in Chinese)
    [19] 牛东圣, 侯凌云, 潘鹏飞等. 超燃冲压发动机内外流场三维燃烧数值模拟. 航空动力学报, 2014, 29(4): 763-769 (Niu Dongsheng, Hou Lingyun, Pan Pengfei, et al. Three-dimensional combustion numerical simulation of scramjet internal and external flow fields. Journal of Aerospace Power, 2014, 29(4): 763-769 (in Chinese)
    [20] 孙明波, 汪洪波, 李佩波等. 超燃冲压发动机计算燃烧学, 北京: 科学出版社, 2021

    Sun Mingbo, Wang Hongbo, Li Peibo, et al. Computational Combustion Dynamics of Scramjet. Beijing: Science Press, 2021 (in Chinese))
    [21] 吴颖川, 贺元元, 贺伟等. 吸气式高超声速飞行器机体推进一体化技术研究进展. 航空学报, 2015, 36(1): 245-260 (Wu Yingchuan, He Yuanyuan, He Wei, et al. Progress in airframe-propulsion integration technology of air-breathing hypersonic vehicle. Acta Aeronautica et Astronautica Sinica, 2015, 36(1): 245-260 (in Chinese)
    [22] 时圣波, 唐硕, 梁军. 临近空间飞行器防隔热/承载一体化热结构设计及力/热行为. 装备环境工程, 2020, 17(1): 36-42 (Shi Shengbo, Tang Shuo, Liang Jun. Design and thermomechanical behavior of full-composite structurally integrated thermal protection structure for near space vehicles. Equipment Environmental Engineering, 2020, 17(1): 36-42 (in Chinese)
    [23] 桂业伟, 刘磊, 代光月等. 高超声速飞行器流-热-固耦合研究现状与软件开发. 航空学报, 2017, 38(7): 020844 (Du Yewei, Liu Lei, Dai Guangyue, et al. Research status of hypersonic vehicle fluid-thermal-solid coupling and software development. Acta Aeronautica et Astronautica Sinica, 2017, 38(7): 020844 (in Chinese)
    [24] 王梓伊, 张伟伟, 刘磊. 高超声速飞行器热气动弹性仿真计算方法综述. 气体物理, 2020, 5(6): 1-15 (Wang Ziyi, Zhang Weiwei, Liu Lei. Review of simulation methods of hypersonic aerothermoelastic problems. Physics of Gases, 2020, 5(6): 1-15 (in Chinese)
    [25] Liu L, Dai G, Zeng L, et al. Experimental model design and preliminary numerical verification of fluid-thermal-structural coupling problem. AIAA Journal, 2019, 57(4): 1715-1724 doi: 10.2514/1.J056398
    [26] Blades EL, Miskovish RS, Nucci M, et al. Towards a coupled multiphysics analysis capability for hypersonic vehicle structures//52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Denver, Colorado, 2011
    [27] 代光月, 贾洪印, 曾磊等. 多场耦合效应对高超声速进气道入口参数影响. 推进技术, 2018, 39(6): 1267-1274 (Dai Guangyue, Jia Hongyin, Zeng Lei, et al. Effects of fluid-thermal-structural coupling on inlet parameters of hypersonic intake. Journal of Propulsion Technology, 2018, 39(6): 1267-1274 (in Chinese)
    [28] 戎毅, 朱剑琴, 戴武昊等. 超燃冲压发动机冷却通道与燃烧室耦合传热数值研究[J]. 推进技术, 2021, 出版中

    Rong Y, Zhu J, Dai W, et al. Numerical study on coupled heat transfer between cooling channel and combustor of scramjet [J]. Journal of Propulsion Technology, 2021, in press (in Chinese))
    [29] Tzong G, Jacobs R, Liguore S. Air vehicle integration and technology research (AVIATR) task order 0015: Predictive capability for hypersonic structural response and life prediction: Phase I-identification of knowledge gaps. The Boeing Company, 2010
    [30] Quiroz R, Embler J, Jacobs R, et al. Air vehicle integration and technology research (AVIATR) task order 0023: Predictive capability for hypersonic structural response and life prediction: Phase II-detailed design of hypersonic cruise vehicle hot-structure. The Boeing Company, 2012
    [31] Chedid R, Najjar N. Automatic finite-element mesh generation using artificial neural networks-Part I: Prediction of mesh density. IEEE Transactions on Magnetics, 1996, 32(5): 5173-5178 doi: 10.1109/20.538619
    [32] Alfonzetti S, Coco S, Cavalieri S, et al. Automatic mesh generation by the Let-It-Grow neural network. IEEE Transactions on Magnetics, 1996, 32(3): 1349-1352 doi: 10.1109/20.497496
    [33] Alfonzetti S. A neural network generator for tetrahedral meshes. IEEE Transactions on Magnetics, 2003, 39(3): 1650-1653 doi: 10.1109/TMAG.2003.810325
    [34] Zhang Z, Jimack PK, Wang H. MeshingNet3 D: Efficient generation of adapted tetrahedral meshes for computational mechanics. Advances in Engineering Software, 2021, 157-158: 103021 doi: 10.1016/j.advengsoft.2021.103021
    [35] 王年华, 鲁鹏, 常兴华等. 基于机器学习的非结构网格阵面推进生成技术初探. 力学学报, 2021, 53(3): 740-751 (Wang Nianhua, Lu Peng, Chang Xinghua, et al. Preliminary investigation on unstructured mesh generation technique based on advancing front method and machine learning methods. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(3): 740-751 (in Chinese) doi: 10.6052/0459-1879-20-402
    [36] Patel A, Safdari M. Smart adaptive mesh refinement with NEMoSys//AIAA Scitech 2021 Forum, Virtual Event, 2021
    [37] Fukami K, Fukagata K, Taira K. Super-resolution reconstruction of turbulent flows with machine learning. Journal of Fluid Mechanics, 2019, 870: 106-120 doi: 10.1017/jfm.2019.238
    [38] Liu B, Tang J, Huang H, et al. Deep learning methods for super-resolution reconstruction of turbulent flows. Physics of Fluids, 2020, 32: 025105 doi: 10.1063/1.5140772
    [39] Carlberg KT, Jameson A, Kochenderfer MJ, et al. Recovering missing CFD data for high-order discretizations using deep neural networks and dynamics learning. Journal of Computational Physics, 2019, 395: 105-124 doi: 10.1016/j.jcp.2019.05.041
    [40] Kim B, Azevedo VC, Thuerey N, et al. Deep fluids: A generative network for parameterized fluid simulations. Eurographics, 2019, 38(2): 59-70
    [41] Thuerey N, Weißenow K, Prantl L, et al. Deep learning methods for Reynolds-averaged Navier-Stokes simulations of airfoil flows. AIAA Journal, 2020, 58: 25-36 doi: 10.2514/1.J058291
    [42] An J, Wang H, Liu B, et al. A deep learning framework for hydrogen-fueled turbulent combustion simulation. International Journal of Hydrogen Energy, 2020, 45: 17992-18000 doi: 10.1016/j.ijhydene.2020.04.286
    [43] 张珍, 叶舒然, 岳杰顺等. 基于组合神经网络的雷诺平均湍流模型多次修正方法. 力学学报, 2021, 53(6): 1532-1542 (Zhang Zhen, Ye Shuran, Yue Jieshun, et al. A combined neural network and multiple modification strategy for Reynolds-Averaged Navier-Stokes turbulence modeling. Chinese Journal of Theoretical and Applied Mechanic, 2021, 53(6): 1532-1542 (in Chinese) doi: 10.6052/0459-1879-21-073
    [44] Singh AP, Medida S, Duraisamy K. Machine-learning-augmented predictive modeling of turbulent separated flows over airfoils. AIAA Journal, 2017, 55(7): 2215-2227 doi: 10.2514/1.J055595
    [45] Yang M, Xiao Z. Improving the k-ω-γ-Ar transition model by the field inversion and machine learning framework. Physics of Fluids, 2020, 32: 064101 doi: 10.1063/5.0008493
    [46] Ling J, Jones R, Templeton J. Machine learning strategies for systems with invariance properties. Journal of Computational Physics, 2016, 318: 22-35 doi: 10.1016/j.jcp.2016.05.003
    [47] Zhu L, Zhang W, Kou J, et al. Machine learning methods for turbulence modeling in subsonic flows around airfoils. Physics of Fluids, 2019, 31: 015105 doi: 10.1063/1.5061693
    [48] Wang Z, Luo K, Li D, et al. Investigations of data-driven closure for subgrid-scale stress in large-eddy simulation. Physics of Fluids, 2018, 30: 125101 doi: 10.1063/1.5054835
    [49] Xie C, Wang J, Li H, et al. Artificial neural network mixed model for large eddy simulation of compressible isotropic turbulence. Physics of Fluids, 2019, 31: 085112 doi: 10.1063/1.5110788
    [50] Lapeyre CJ, Misdariis A, Cazard N, et al. Training convolutional neural networks to estimate turbulent sub-grid scale reaction rates. Combustion and Flame, 2019, 203: 255-264 doi: 10.1016/j.combustflame.2019.02.019
    [51] Yellapantula S, Perry BA, Grout RW. Deep learning-based model for progress variable dissipation rate in turbulent premixed flames. Proceedings of the Combustion Institute, 2021, 38: 2929-2938 doi: 10.1016/j.proci.2020.06.205
    [52] 任嘉豪, 王海鸥, 邢江宽等. 湍流火焰切向应变率的低维近似模型. 浙江大学学报(工学版), 2021, 55(7): 1-8 (Ren Jiahao, Wang Haiou, Xin Jiangkuan, et al. Lower-dimensional approximation models of tangential strain rate of turbulent flames. Journal of Zhejiang University (Engineering Science), 2021, 55(7): 1-8 (in Chinese)
    [53] Wan K, Barnaud C, Vervisch L, et al. Chemistry reduction using machine learning trained from non-premixed micro-mixing modeling: Application to DNS of a syngas turbulent oxy-flame with side-wall effects. Combustion and Flame, 2020, 220: 119-129 doi: 10.1016/j.combustflame.2020.06.008
    [54] Pulga L, Bianchi G, Falfari S, et al. A machine learning methodology for improving the accuracy of laminar flame simulations with reduced chemical kinetics mechanisms. Combustion and Flame, 2020, 216: 72-81 doi: 10.1016/j.combustflame.2020.02.021
    [55] Chung WT, Mishra AA, Perakis N, et al. Data-assisted combustion simulations with dynamic submodel assignment using random forests. Combustion and Flame, 2021, 227: 172-185 doi: 10.1016/j.combustflame.2020.12.041
    [56] Xiao H, Cinnella P. Quantification of model uncertainty in RANS simulations: A review. Progress in Aerospace Sciences, 2019, 108: 1-31 doi: 10.1016/j.paerosci.2018.10.001
    [57] Ling J, Templeton J. Evaluation of machine learning algorithms for prediction of regions of high Reynolds averaged Navier-Stokes uncertainty. Physics of Fluids, 2015, 27: 085103 doi: 10.1063/1.4927765
    [58] 叶舒然, 张珍, 王一伟等. 基于卷积神经网络的深度学习流场特征识别及应用进展. 航空学报, 2021, 42(4): 524736 (Ye Shuran, Zhang Zhen, Wang Yiwei, et al. Progress in deep convolutional neural network based flow field recognition and its applications. Acta Aeronautica et Astronautica Sinica, 2021, 42(4): 524736 (in Chinese)
    [59] Ströfer CM, Wu J, Xiao H, et al. Data-driven, physics-based feature extraction from fluid flow fields using convolutional neural networks. Communications in Computational Physics, 2019, 25(3): 625-650
    [60] Liu Y, Lu Y, Wang Y, et al. A CNN-based shock detection method in flow visualization. Computers & Fluids, 2019, 184: 1-9
    [61] Han J, Tao J, Wang C. FlowNet: A deep learning framework for clustering and selection of streamlines and stream surfaces. IEEE Transactions on Visualization and Computer Graphics, 2020, 26(4): 1732-1744
    [62] Li H, Tan J. Cluster-based Markov model to understand the transition dynamics of a supersonic mixing layer. Physics of Fluids, 2020, 32: 056104 doi: 10.1063/1.5145276
    [63] 王怡星, 韩仁坤, 刘子扬等. 流体力学深度学习建模技术研究进展. 航空学报, 2021, 42(4): 524779 (Wang Yixing, Han Renkun, Liu Ziyang, et al. Progress of deep learning modeling technology for fluid mechanics. Acta Aeronautica et Astronautica Sinica, 2021, 42(4): 524779 (in Chinese)
    [64] Pawar S, Ahmed SE, San O, et al. Data-driven recovery of hidden physics in reduced order modeling of fluid flows. Physics of Fluids, 2020, 32: 036602 doi: 10.1063/5.0002051
    [65] Agostini L. Exploration and prediction of fluid dynamical systems using auto-encoder technology. Physics of Fluids, 2020, 32: 067103 doi: 10.1063/5.0012906
    [66] Regazzoni F, Dedè L, Quarteroni A. Machine learning for fast and reliable solution of time-dependent differential equations. Journal of Computational Physics, 2019, 397: 108852 doi: 10.1016/j.jcp.2019.07.050
    [67] 张智超, 高太元, 张磊等. 基于径向基神经网络的气动热预测代理模型. 航空学报, 2021, 42(4): 524167 (Zhang Zhichao, Gao Taiyuan, Zhang Lei, et al. Aeroheating agent model based on radial basis function neural network. Acta Aeronautica et Astronautica Sinica, 2021, 42(4): 524167 (in Chinese)
    [68] 李左飙, 温风波, 唐晓雷等. 基于深度学习的单排孔气膜冷却性能预测. 航空学报, 2021, 42(4): 524331 (Li Zuobiao, Wen Fengbo, Tang Xiaolei, et al. Prediction of single-row hole film cooling performance based on deep learning. Acta Aeronautica et Astronautica Sinica, 2021, 42(4): 524331 (in Chinese)
    [69] 胡伟杰, 黄增辉, 刘学军等. 基于自动核构造高斯过程的导弹气动性能预测. 航空学报, 2021, 42(4): 524093 (Hu Weijie, Huang Zenghui, Liu Xuejun, et al. Missile aerodynamic performance prediction of Gaussian process through automatic kernel construction. Acta Aeronautica et Astronautica Sinica, 2021, 42(4): 524093 (in Chinese)
    [70] 刘魁, 刘婷. 数字孪生在航空发动机可靠性领域的应用探索. 航空动力, 2019, 4: 61-64 (Liu Kui, Liu Ting. Digital twin and its potential application in the field of aero engine reliability. Aerospace Power, 2019, 4: 61-64 (in Chinese)
    [71] 刘永泉, 黎旭, 任文成等. 数字孪生助力航空发动机跨越发展. 航空动力, 2021, 2: 24-29 (Liu Yongquan, Li Xu, Ren Wencheng, et al. Digital twin boosting leap-forward development of aero engine. Aerospace Power, 2021, 2: 24-29 (in Chinese)
    [72] 刘婷, 张建超, 刘魁. 基于数字孪生的航空发动机全生命周期管理. 航空动力, 2018, 1: 52-56 (Liu Ting, Zhang Jianchao, Liu Kui. Aero engine life cycle management based on digital twin. Aerospace Power, 2018, 1: 52-56 (in Chinese)
    [73] Raissi M, Perdikaris P, Karniadakis GE. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 2019, 378: 686-707 doi: 10.1016/j.jcp.2018.10.045
  • 加载中
图(13)
计量
  • 文章访问数:  1718
  • HTML全文浏览量:  558
  • PDF下载量:  318
  • 被引次数: 0
出版历程
  • 收稿日期:  2021-08-15
  • 录用日期:  2022-02-13
  • 网络出版日期:  2022-02-14
  • 刊出日期:  2022-03-18

目录

    /

    返回文章
    返回