[1] 包为民. 可重复使用运载火箭技术发展综述[J]. 航空学报, 2023, 44(23): 8-33+3.
BAO W M. A review of reusable launch vehicle tech-nology development[J]. Acta Aeronautica et Astro-nautica Sinica, 2023, 44(23): 8-33+3 (in Chinese).
[2] 张益荣, 张毅锋, 解静, 等. 典型高超声速翼身组合体粘性干扰效应模型研究[J]. 空气动力学学报, 2017, 35(02): 186-191.
ZHANG Y R, ZHANG Y F, XIE J, et al. Study of vis-cous interaction effect model for typical hypersonic wing-body figuration[J]. Acta Aerodynamica Sinica, 2017, 35(02): 186-191 (in Chinese).
[3] 潘利生, 郝亨隆, 姚子康, 等. 高速飞行器减阻降热研究进展[J]. 力学进展, 2023, 53(04): 793-818.
PAN L S, HAO H L, YAO Z K, et al. Current status of research on reducing drag and cooling of high-speed aircraft[J]. Advances in Mechanics, 2023, 53(04): 793-818 (in Chinese).
[4] 王长青. 空天飞行技术创新与发展展望[J]. 宇航学报, 2021, 42(07): 807-819.
WANG C Q. Technological innovation and develop-ment prospect of aerospace vehicle[J]. Journal of As-tronautics, 2021, 42(07): 807-819 (in Chinese).
[5] 罗振兵, 夏智勋, 王林, 等. 高超声速飞行器内外流主动流动控制[M]. 北京: 科学出版社, 2019.
LUO Z B, XIA Z X, WANG L, et al. Active flow con-trol of hypersonic vehicles[M]. Beijing: Science Press, 2019. (in Chinese).
[6] 黄红岩, 苏力军, 雷朝帅, 等. 可重复使用热防护材料应用与研究进展[J]. 航空学报, 2020, 41(12): 6-40.
HUANG H Y, SU L J, LEI C S, et al. Reusable ther-mal protective materials: application and research progress[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41(12): 6-40 (in Chinese).
[7] 丁明松, 刘庆宗, 江涛, 等. 磁控热防护系统在天地往返运载器上的应用仿真[J]. 航空学报, 2021, 42(07): 183-194.
DING M S, LIU Q Z, JIANG T, et al. Simulation of magnetohydrodynamic heat shield system on reusa-ble launch vehicles[J]. Acta Aeronautica et Astro-nautica Sinica, 2021, 42(07): 183-194 (in Chinese).
[8] 艾邦成, 陈思员, 韩海涛, 等. 疏导式热防护结构传热极限特性[J]. 航空学报, 2021, 42(02): 27-33.
AI B C, CHEN S Y, HAN H T, et al. Heat transfer limit characteristics of integrated dredging thermal protec-tion structure[J]. Acta Aeronautica et Astronautica Sinica, 2021, 42(02): 27-33 (in Chinese).
[9] 朱广生, 姚世勇, 段毅. 高速飞行器减阻降热流动控制技术研究进展及工程应用若干问题[J/OL]. 航空学报, (2023-06-07) [2024-12-08].
ZHU G S, YAO S Y, DUAN Y. Research progress and some issues in engineering application of flow control
technology for drag reduction and heat reduction of high-speed flight vehicles[J/OL]. Acta Aeronautica et Astronautica Sinica, (2023-06-07) [2024-12-08].
[10] 沈斌贤, 曾磊, 刘骁, 等. 高超声速飞行器主动质量引射热防护技术研究进展[J]. 空气动力学学报, 2022, 40(06): 1-13.
SHEN B X, ZENG L, LIU X, et al. Research progress of thermal protection technique by activemass injec-tion for hypersonic vehicle[J]. Acta Aerodynamica Sinica, 2022, 40(06): 1-13 (in Chinese).
[11] ZHANG J Z, ZHANG S C, WANG C H, et al. Recent advances in film cooling enhancement: A review[J]. Chinese Journal of Aeronautics, 2020, 33(4): 1119-1136.
[12] HWANG D. Review of research into the concept of the microblowing technique for turbulent skin friction reduction[J]. Progress in Aerospace Sciences, 2004, 40(8): 559-575.
[13] MI Q, YI S H, GANG D D, et al. Research progress of transpiration cooling for aircraft thermal protection[J]. Applied Thermal Engineering, 2024, 236: 121360.
[14] SHEN B X, LIU W Q, YIN L. Drag and heat reduc-tion efficiency research on opposing jet in supersonic flows[J]. Aerospace Science and Technology, 2018, 77: 696-703.
[15] 向树红, 商圣飞, 沈自才, 等. 高超声速气膜冷却技术研究进展及发展方向[J]. 宇航材料工艺, 2020, 50(03): 1-10.
XIANG S H, SHANG S F, SHEN Z C, et al. Research progress and development direction of hypersonic film cooling technology[J]. Aerospace Materials & Technology, 2020, 50(03): 1-10 (in Chinese).
[16] BERTIN J J, CUMMINGS R M. Critical hypersonic aerothermodynamic phenomena[J]. Annual Review of Fluid Mechanics, 2006, 38(1): 129-157.
[17] CHEN L, HE A, ZHAO J L, et al. Pore-scale modeling of complex transport phenomena in porous media[J]. Progress in Energy and Combustion Science, 2022, 88: 100968.
[18] WEI N E, HAN J Q ZHANG L F. Machine learning-assisted modeling[J]. Physics Today, 2021, 74(7): 36-41.
[19] CHEN X H, WANG Z C, DENG L, et al. Towards a new paradigm in intelligence-driven computational fluid dynamics simulations[J]. Engineering Applica-tions of Computational Fluid Mechanics, 2024, 18(1): 2407005.
[20] LENG C, TANG Z, ZHOU Y G, et al. Fifth paradigm in science: A case study of an intelligence-driven ma-terial design[J]. Engineering, 2023, 24: 126-137.
[21] MALITSKY N, CASTAIN R, COWAN M. Spark-mpi: Approaching the fifth paradigm of cognitive applica-tions[J]. arXiv preprint arXiv: 1806.01110, 2018.
[22] HAN J Q, ZHANG L F, CAR R. Deep potential: A general representation of a many-body potential en-ergy surface[J]. arXiv preprint arXiv: 1707.01478, 2017.
[23] LI J H, HUANG W L. Paradigm shift in science with tackling global challenges[J]. National Science Re-view, 2019, 6(6): 1091-1093.
[24] 杨小康, 许岩岩, 陈露, 等. AI for Science：智能化科学设施变革基础研究[J]. 中国科学院院刊, 2024, 39(01): 59-69.
YANG X K, XU Y Y, CHEN L, et al. AI for Science: Al enabled scientific facility transforms fundamental research[J]. Bulletin of Chinese Academy of Sciences 2024, 39(01): 59-69 (in Chinese).
[25] 陈云霁, 郭崎. AI for Technology：技术智能在高技术领域的应用实践与未来展望[J]. 中国科学院院刊, 2024, 39(01): 34-40.
CHEN Y J, GUO Q. Al for Technology: Applied prac-tices and future perspectives of technological intelli-gence in high tech areas[J]. Bulletin of Chinese Academy of Sciences, 2024, 39(01): 34-40 (in Chi-nese).
[26] 鄂维南. AI助力打造科学研究新范式[J]. 中国科学院院刊, 2024, 39(01): 10-16.
ER W N. AI helps to establish a new paradigm for scientifie research[J]. Bulletin of Chinese Academy of Sciences, 2024, 39(01): 10-16 (in Chinese).
[27] BHARDWAJ G, O’CONNOR J, RETTIE S, et al. Ac-curate de novo design of membrane-traversing mac-rocycles[J]. Cell, 2022, 185(19): 3520-3532. e26.
[28] DAVIES A, VELI?KOVI? P, BUESING L, et al. Ad-vancing mathematics by guiding human intuition with AI[J]. Nature, 2021, 600(7887): 70-74.
[29] JUMPER J, EVANS R, PRITZEL A, et al. Highly ac-curate protein structure prediction with AlphaFold[J]. Nature, 2021, 596(7873): 583-589.
[30] DEGRAVE J, FELICI F, BUCHLI J, et al. Magnetic control of tokamak plasmas through deep reinforce-ment learning[J]. Nature, 2022, 602(7897): 414-419.
[31] 吴智, 范德威, 周裕. 人工智能控制湍流进展:系统、算法、成就、数据分析方法[J]. 力学进展, 2023, 53(02): 273-307.
WU Z, FAN D W, ZHOU Y. Advances in control of turbulence by artificial intelligence:Systems, algo-rithms, achievements and data analysis methods[J]. Advances in Mechanics, 2023, 53(02): 273-307 (in Chinese).
[32] KRAMER B, PEHERSTORFER B, WILLCOX K E. Learning nonlinear reduced models from data with operator inference[J]. Annual Review of Fluid Me-chanics, 2024, 56(1): 521-548.
[33] 李道伦, 沈路航, 查文舒, 等. 基于神经算子与类物理信息神经网络智能求解新进展[J]. 力学学报, 2024, 56(04): 875-889.
LI D L, SHEN L H, ZHA W S, et al. New progress in intelligent solution of neural operators and physics-informed-based methods[J]. Chinese Journal of Theo-retical and Applied Mechanics, 2024, 56(04): 875-889 (in Chinese).
[34] 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[J]. 航空学报, 2021, 42(04): 231-250.
WANG Y X, HAN R K, LIU Z Y, et al. Progress of deep learning modeling technology for fluid mechan-ics[J]. Acta Aeronautica et Astronautica Sinica, 2021, 42(04): 231-250 (in Chinese).
[35] 张伟伟, 寇家庆, 刘溢浪. 智能赋能流体力学展望[J]. 航空学报, 2021, 42(04): 26-71.
ZHANG W W, KOU J Q, LIU Y L. Prospect of artifi-cial intelligence empowered fluid mechanics[J]. Acta Aeronautica et Astronautica Sinica, 2021, 42(04): 26-71 (in Chinese).
[36] BRUNTON S L, NOACK B R, KOUMOUTSAKOS P. Machine learning for fluid mechanics[J]. Annual Re-view of Fluid Mechanics, 2020, 52(1): 477-508.
[37] MOFFAT R J, KAYS W M. The turbulent boundary layer on a porous plate: experimental heat transfer with uniform blowing and suction[J]. International Journal of Heat and Mass Transfer, 1968, 11(10): 1547-1566.
[38] SIMPSON R L, MOFFAT R J, KAYS W M. The turbu-lent boundary layer on a porous plate: experimental skin friction with variable injection and suction[J]. In-ternational Journal of Heat and Mass Transfer, 1969, 12(7): 771-789.
[39] KAYS W M. Heat transfer to the transpired turbulent boundary layer[J]. International Journal of Heat and Mass Transfer, 1972, 15(5): 1023-1044.
[40] THIELBAHR W H, KAYS W M, Moffat R J. The tur-bulent boundary layer on a porous plate: Experi-mental heat transfer with uniform blowing and suc-tion, with moderately strong acceleration[J]. ASME Journal of Heat and Mass Transfer, 1972, 111-118.
[41] KEARNEY D W, KAYS W M, MOFFAT R J. Heat transfer to a strongly accelerated turbulent boundary layer: Some experimental results, including transpira-tion[J]. International Journal of Heat and Mass Trans-fer, 1973, 16(6): 1289-1305.
[42] 孟丽燕, 姜培学, 蒋方帅, 等. 烧结多孔壁面发汗冷却换热的实验研究[J]. 清华大学学报(自然科学版), 2005, (11): 97-99.
MENG L Y, JIANG P X, JIANG F S, et al. Experi-mental investigation of the heat transfer for transpira-tion cooling through a sintered porous plate[J]. Jour-nal of Tsinghua University (Science and Technology), 2005, (11): 97-99 (in Chinese).
[43] LIU Y Q, JIANG P X, XIONG Y B, et al. Experi-mental and numerical investigation of transpiration cooling for sintered porous flat plates[J]. Applied Thermal Engineering, 2013, 50(1): 997-1007.
[44] LANGENER T, WOLFERSDORF V J, Laux T, et al. Experimental investigation of transpiration cooling with subsonic and supersonic flows at moderate tem-perature levels[C]//44th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit. 2008: 5174.
[45] LANGENER T, WOLFERSDORF V J, Selzer M, et al. Experimental investigations of transpiration cooling applied to C/C material[J]. International Journal of Thermal Sciences, 2012, 54: 70-81.
[46] HWANG D P. Skin-friction reduction by a micro-blowing technique[J]. AIAA Journal, 1998, 36(3): 480-481.
[47] NOWAK R, WIETING A, HOLDEN M. Shock/shock interference on a transpiration cooled hemispherical model[C]//21st Fluid Dynamics, Plasma Dynamics and Lasers Conference. 1990: 1643.
[48] HOLDEN M, RODRIGUEZ K, NOWAK R. Studies of shock/shock interaction on smooth and transpiration-cooled hemispherical nosetips in hypersonic flow[C]//22nd Fluid Dynamics, Plasma Dynamics and Lasers Conference. 1991: 1765.
[49] 熊宴斌. 超声速主流条件发汗冷却的流动和传热机理研究[D]. 北京: 清华大学, 2013.
XIONG Y B. Study of the mechanism of flow and heat transfer on supersonic transpiration cooling[D]. Beijing: Tsinghua University, 2013 (in Chinese).
[50] CASTIGLONE L A, NORTHAM G B, BAKER N R, et al. Wall drag in internal Mach-2 flow with cavity and transpiration injection[J]. Journal of Propulsion and Power, 2000, 16(3): 472-477.
[51] 黄拯, 祝银海, 熊宴斌, 等. 激波对超音速平板发汗冷却的影响[J].工程热物理学报, 2014, 35(11): 2288-2293.
HUANG Z, ZHU Y H, XIONG Y B, et al. Investiga-tion of shock wave infuence on supersonic transpira-tion cooling[J]. Journal of Engineering Thermophys-ics, 2014, 35(11): 2288-2293 (in Chinese).
[52] 黄干, 廖致远, 祝银海, 等. 高温主流条件下相变发汗冷却实验研究[J]. 工程热物理学报, 2017, 38(04): 817-821.
HUANG G, LIAO Z Y, ZHU Y H, et al. Change in high temperature flow experimental investigation of transpiration cooling with phase[J]. Journal of Engi-neering Thermophysics, 2017, 38(04): 817-821 (in Chinese).
[53] 马杰, 林佳, 王建华. 液态水相变发散冷却的实验[J]. 航空动力学报, 2014, 29(03): 556-562.
MA J, LIN J ,WANG J H. Experiment on transpiration cooling with phase change of liquid water[J]. Journal of Aerospace Power, 2014, 29(03): 556-562 (in Chi-nese).
[54] LIAO Z Y, ZHU Y H, HUANG G, et al. Experimental investigation of transpiration cooling on a porous plate with phase change in supersonic flow tunnel[J]. Journal of Propulsion Technology, 2019, 40(5): 1058.
[55] Huang G, Zhu Y H, Liao Z Y, et al. Experimental in-vestigation of transpiration cooling with phase change for sintered porous plates[J]. International Journal of Heat and Mass Transfer, 2017, 114: 1201-1213.
[56] CHOI S H, SCOTTI S J, SONG K D, et al. Transpiring cooling of a scram-jet engine combustion cham-ber[C]//32nd Thermophysics Conference. 1997: 2576.
[57] SONG K D, CHOI S H, SCOTTI S J. Transpiration cooling experiment for scramjet engine combustion chamber by high heat fluxes[J]. Journal of propulsion and Power, 2006, 22(1): 96-102.
[58] 吴亚东, 朱广生, 高波, 等. 多孔介质相变发汗冷却主动热防护试验研究[J]. 宇航学报, 2017, 38(02): 212-218.
WU Y D, ZHU G S, GAO B, et al. An experimental study on the phase-changed transpiration cooling for active thermal protection[J]. Journal of Astronautics, 2017, 38(02): 212-218 (in Chinese).
[59] 陈星宇, 王丽燕, 陈伟华, 等. 真空条件下多孔平板发汗冷却试验研究[J]. 北京航空航天大学学报, 2021, 47(08): 1594-1604.
CHEN X Y, WANG L Y, CHEN W H, et al. Transpira-tion cooling test of porous plate in vacuum environ-ment[J]. Journal of Beijing University of Aeronautics and Astronautics, 2021, 47(08): 1594-1604 (in Chi-nese).
[60] OTSU H, FUJITA K, ITO T. Application of the tran-spiration cooling method for reentry vehicles[C]//45th AIAA Aerospace Sciences Meeting and Exhibit. 2007: 1209.
[61] FROHLKE K, HAIDN O, SERBEST E. New experi-mental results on transpiration cooling for hydro-gen/oxygen rocket combustion chambers[C]//34th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit. 1998: 3443.
[62] SOLLER S, KIRCHBERGER C, KUHN M, et al. Ex-perimental investigation of cooling techniques and materials for highspeed flight propulsion sys-tems[C]//16th AIAA/DLR/DGLR International Space Planes and Hypersonic Systems and Technologies Conference. 2009: 7374.
[63] SERBEST E, HAIDN O, HALD H, et al. Effusion cooling in rocket combustors applying fibre rein-forced ceramics[C]//35th Joint Propulsion Conference and Exhibit. 1999: 2911.
[64] FOREEST V A, SIPPEL M, GüLHAN A, et al. Tran-spiration cooling using liquid water[J]. Journal of Thermophysics and Heat Transfer, 2009, 23(4): 693-702.
[65] GüLHAN A . RESPACE-Key technologies for reusa-ble space systems [M]. Berlin: Springer-Verlag Berlin Heidelberg, 2008.
[66] HOLDEN M. Experimental studies in the LENS shock tunnel and expansion tunnel to examine real-gas ef-fects in hypervelocity flows[C]//42nd AIAA Aero-space Sciences Meeting and Exhibit. 2004: 916.
[67] WANG J H, ZHAO L J, WANG X C, et al. An exper-imental investigation on transpiration cooling of wedge shaped nose cone with liquid coolant[J]. Inter-national Journal of Heat and Mass Transfer, 2014, 75: 442-449.
[68] DING L, WEI K, ZHANG Q, et al. An experimental investigation on transpiration cooling of porous flat plate[C]//2011 International Conference on Remote Sensing, Environment and Transportation Engineer-ing. IEEE, 2011: 5692-5696.
[69] WEIHS H, LONGO J, TURNER J. The sharp edge flight experiment SHEFEX II, a mission overview and status[C]//15th AIAA International Space Planes and Hypersonic Systems and Technologies Conference. 2008: 2542.
[70] B?HRK H. Transpiration-cooled hypersonic flight experiment: setup, flight measurement, and recon-struction[J]. Journal of Spacecraft and Rockets, 2015, 52(3): 674-683.
[71] BOEHRK H. Transpiration cooling at hypersonic flight-AKTiV on SHEFEX II[C]//11th AIAA/ASME Joint Thermophysics and Heat Transfer Conference. 2014: 2676.
[72] WEIHS H. Sounding rockets for entry research: SHEFEX flight test program[C]//Proceedings of the 21st ESA Symposium on Rocket and Balloon Pro-grammes. ESA Communications, 2013: 143-152.
[73] TURNER J, ETTL J, H?RSCHGEN-EGGERS M, et al. Shefex II vehicle and subsystem design, flight per-formance and their application to future hypersonic missions[C]//Proceedings of the ESA-PAC 21st Sym-posium, Thun, Switzerland. 2013: 9-13.
[74] GüLHAN A, SIEBE F, THIELE T, et al. Sharp edge flight experiment-II instrumentation challenges and selected flight data[J]. Journal of Spacecraft and Rockets, 2014, 51(1): 175-186.
[75] WEIHS H. Wall thickness optimization of a transpira-tion-cooled sharp leading edge at atmospheric re-entry[C]. //International Conference on Porous Media & Their Applications in Science.2014.
[76] 靳旭红, 黄飞, 张俊, 等. 上层大气层飞行器研究进展及气动技术挑战[J]. 航空学报, 2024, 45(22): 6-21.
JIN X H, HUANG F, ZHANG J, et al. Spacecraft in upper atmosphere: Research development and aero-dynamic challenges[J]. Acta Aeronautica et Astro-nautica Sinica, 2024, 45(22): 6-21 (in Chinese).
[77] 张俊, 蒋亦凡, 陈松, 等. 超低轨卫星气动阻力计算与减阻设计研究综述[J]. 航空学报, 2024, 45(21): 159-180.
ZHANG J, JIANG Y F, CHEN S, et al. Overview of aerodynamic drag calculation and reduction design for very low Earth orbit satellites[J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(21): 159-180 (in Chinese).
[78] PICONE J M, HEDIN A E, DROB D P, et al. NRLMSISE‐00 empirical model of the atmosphere: Statistical comparisons and scientific issues[J]. Jour-nal of Geophysical Research: Space Physics, 2002, 107(A12): SIA 15-1-SIA 15-16.
[79] LOCKERBY D A, REESE J M, GALLIS M A. Captur-ing the Knudsen layer in continuum-fluid models of nonequilibrium gas flows[J]. AIAA Journal, 2005, 43(6): 1391-1393.
[80] MOHAMAD A A. Lattice boltzmann method[M]. London: Springer, 2011.
[81] 黄飞, 沈清, 程晓丽, 等. 一种DSMC分子仿真下的权因子预定义方法[J]. 航空学报, 2014, 35(08): 2174-2181.
HUANG F, SHEN Q, CHENG X L, et al. A New Pre-defined Method of Particle Weight in DSMC Molecu-lar Simulation[J]. Acta Aeronautica et Astronautica Sinica, 2014, 35(08): 2174-2181 (in Chinese).
[82] JINDAL P, AGRWAL S, SHARMA R P. A brief review on numerical studies on film cooling effectiveness[J]. Applied Mechanics and Materials, 2016, 852: 699-706.
[83] AHN J. Large eddy simulation of film cooling: A review[J]. Energies, 2022, 15(23): 8876.
[84] 刘汉儒, 陈南树, 刘宇, 等. 多孔介质流动控制及气动降噪研究进展[J]. 航空学报, 2023, 44(16): 6-26.
LIU H R, CHEN N S, LIU Y, et al. Review of porous media used in flow control and aerodynamic noise reduction[J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(16): 6-26 (in Chinese).
[85] WHITAKER S. The Forchheimer equation: a theoreti-cal development[J]. Transport in Porous media, 1996, 25(1): 27-61.
[86] ABRIOLA L M, PINDER G F. A multiphase approach to the modeling of porous media contamination by organic compounds: 1. Equation development[J]. Wa-ter resources research, 1985, 21(1): 11-18.
[87] WANG C Y, BECKERMANN C. A two-phase mixture model of liquid-gas flow and heat transfer in capillary porous media—I. Formulation[J]. International Jour-nal of Heat and Mass Transfer, 1993, 36(11): 2747-2758.
[88] WANG C Y, BECKERMANN C. A two-phase mixture model of liquid-gas flow and heat transfer in capillary porous media—II. Application to pressure-driven boiling flow adjacent to a vertical heated plate[J]. In-ternational Journal of Heat and Mass Transfer, 1993, 36(11): 2759-2768.
[89] ALOMAR O R, MENDES M A A, TRIMIS D, et al. Simulation of complete liquid–vapour phase change process inside porous evaporator using local thermal non-equilibrium model[J]. International Journal of Thermal Sciences, 2015, 94: 228-241.
[90] WANG M, WANG J H, PU J, et al. Transient heat dissipation performances of transpiration cooling with coolant phase change[J]. International Communica-tions in Heat and Mass Transfer, 2022, 135: 106082.
[91] HE F, WANG J H, XU L C, et al. Modeling and simu-lation of transpiration cooling with phase change[J]. Applied Thermal Engineering, 2013, 58(1-2): 173-180.
[92] LIU T L, SU H, CHEN Z W, et al. Numerical investi-gation on the transient transport and heat transfer characteristics of transpiration cooling with liquid phase change during coolant adjustment[J]. Applied Thermal Engineering, 2022, 209: 118277.
[93] DONG W J, WANG J H, CHEN S Y, et al. Modelling and investigation on heat transfer deterioration during transpiration cooling with liquid coolant phase-change[J]. Applied Thermal Engineering, 2018, 128: 381-392.
[94] HU H W, JIANG P X, OUYANG X L, et al. A modi-fied energy equation model for flow boiling in porous media and its application to transpiration cooling at low pressures with transient effect[J]. International Journal of Heat and Mass Transfer, 2020, 158: 119745.
[95] SU H, HE F, WANG J H, et al. Numerical investiga-tion on the effects of porous cone parameters on liq-uid transpiration cooling performance[J]. Internation-al Journal of Thermal Sciences, 2021, 161: 106743.
[96] SU H, WANG J H, HE F, et al. Numerical investiga-tion on transpiration cooling with coolant phase change under hypersonic conditions[J]. International Journal of Heat and Mass Transfer, 2019, 129: 480-490.
[97] DONG W J, WANG J H. A new model and its applica-tion to investigate transpiration cooling with liquid coolant phase change[J]. Transport in Porous Media, 2018, 122: 575-593.
[98] LEE D Y, VAFAI K. Analytical characterization and conceptual assessment of solid and fluid temperature differentials in porous media[J]. International Journal of Heat and Mass Transfer, 1999, 42(3): 423-435.
[99] MARAFIE A, VAFAI K. Analysis of non-Darcian effects on temperature differentials in porous media[J]. International Journal of Heat and Mass Transfer, 2001, 44(23): 4401-4411.
[100] WANG J H, WANG H N. A Discussion of transpira-tion cooling problems through an analytical solution of local thermal nonequilibrium model[J]. Journal of Heat Transfer, 2006, 128(10): 1093-1098.
[101] 黄拯. 高温与超音速条件下发汗冷却基础问题研究[D]. 北京: 清华大学, 2015.
HUANG Z. Research on the transpiration cooling in supersonic and high temperature flow[D]. Beijing: Tsinghua University, 2015 (in Chinese).
[102] 苏浩. 发散冷却系统冷却能力和流动换热特性的数值研究[D]. 合肥: 中国科学技术大学, 2020.
SU H. Numerical investigations on the cooling capac-ity and characteristics of flow and heat transfer of transpiration cooling[D]. Hefei: University of Science and Technology of China, 2020 (in Chinese).
[103] MINKOWYCZ W J, HAJI-SHEIKH A, VAFAI K . On departure from local thermal equilibrium in porous media due to a rapidly changing heat source: the Sparrow number[J]. International Journal of Heat and Mass Transfer, 1999, 42(18): 3373-3385.
[104] PALLARES J, GRAU F X. A modification of a Nusselt number correlation for forced convection in porous media[J]. International Communications in Heat and Mass Transfer, 2010, 37(9): 1187-1190.
[105] ACHENBACH E. Heat and flow characteristics of packed beds[J]. Experimental Thermal and Fluid Sci-ence, 1995, 10(1): 17-27.
[106] 胥蕊娜, 姜培学. 流体在微多孔介质内对流换热实验研究[J]. 工程热物理学报, 2008, (08): 1377-1379.
XU R N, JIANG P X. Experimental investigations of convection heat transfer in microporous media[J]. Journal of Engineering Thermophysics, 2008, (08): 1377-1379 (in Chinese).
[107] XU R N, HUANG Y L, JIANG P X, et al. Internal heat transfer coefficients in microporous media with rarefaction effects[J]. Science China Technological Sciences, 2012, 55: 2869-2876.
[108] CERMINARA A, DEITERDING R, SANDHAM N. A mesoscopic modelling approach for direct numerical simulations of transition to turbulence in hypersonic flow with transpiration cooling[J]. International Jour-nal of Heat and Fluid Flow, 2020, 86: 108732.
[109] LIU X, ZHOU W X, YU W L. Numerical simulation study of transpiration cooling with hydrocarbon fuel as coolant[J]. Applied Thermal Engineering, 2023, 221: 119687.
[110] JIANG P X, LIAO Z Y, HUANG Z, et al. Influence of shock waves on supersonic transpiration cooling[J]. International Journal of Heat and Mass Transfer, 2019, 129: 965-974.
[111] HUANG Z, ZHU Y H, XIONG Y B, et al. Investiga-tion of transpiration cooling for sintered metal porous struts in supersonic flow[J]. Applied Thermal Engi-neering, 2014, 70(1): 240-249.
[112] XIAO X F, ZHAO G B, ZHOU W X, et al. Large-eddy simulation of transpiration cooling in turbulent channel with porous wall[J]. Applied Thermal Engi-neering, 2018, 145: 618-629.
[113] XIAO X F, ZHAO G B, ZHOU W X. Numerical in-vestigation of transpiration cooling for porous nose cone with liquid coolant[J]. International Journal of Heat and Mass Transfer, 2018, 121: 1297-1306.
[114] BETCHEN L, STRAATMAN A G, THOMPSON B E. A nonequilibrium finite-volume model for conjugate fluid/porous/solid domains[J]. Numerical Heat Trans-fer, Part A: Applications, 2006, 49(6): 543-565.
[115] ALBERTO J. Momentum jump condition at the boundary between a porous medium and a homoge-neous fluid: inertial effects[J]. Journal of Porous Me-dia, 1998, 1(3): 201-217.
[116] PHANIKUMAR M S, MAHAJAN R L. Non-Darcy natural convection in high porosity metal foams[J]. International Journal of Heat and Mass Transfer, 2002, 45(18): 3781-3793.
[117] ALAZMI B, VAFAI K. Analysis of variants within the porous media transport models[J]. ASME Journal of Heat and Mass Transfer, 2000, 122(2): 303-326.
[118] WOLFERSDORF V J. Effect of coolant side heat transfer on transpiration cooling[J]. Heat and Mass Transfer, 2005, 41: 327-337.
[119] KOVENSKII V I, TEPLITSKII Y S. Modelling of heat transfer in an infiltrated granular bed in view of the difference of phase temperatures[J]. International Journal of Heat and Mass Transfer, 2006, 49(1-2): 359-365.
[120] 董文杰. 发散冷却基础问题的理论与数值研究[D]. 合肥: 中国科学技术大学, 2018.
DONG W J. Theoretical and numerical investigations on basic problems of transpiration cooling[D]. Hefei: University of Science and Technology of China, 2018 (in Chinese).
[121] DING R, WANG J H, HE F, et al. Numerical investi-gation on a double layer combined cooling structure for aerodynamic heat control of hypersonic vehicle leading edge[J]. Applied Thermal Engineering, 2020, 169: 114949.
[122] SU H, HE F, WANG J H, et al. Numerical investiga-tion on the characteristics of coolant flow, heat ab-sorption and phase change in transpiration cooling process[J]. International Journal of Thermal Sciences, 2019, 142: 68-76.
[123] LEE S, YOU D. Data-driven prediction of unsteady flow over a circular cylinder using deep learning[J]. Journal of Fluid Mechanics, 2019, 879: 217-254.
[124] WANG R, KASHINATH K, MUSTAFA M, et al. To-wards physics-informed deep learning for turbulent flow prediction[C]//Proceedings of the 26th ACM SIGKDD international conference on knowledge dis-covery & data mining. 2020: 1457-1466.
[125] WANG R, WALTERS R, YU R. Incorporating sym-metry into deep dynamics models for improved gen-eralization[J]. arXiv preprint arXiv:2002.03061, 2020.
[126] WANG R, WALTERS R, YU R. Approximately equivariant networks for imperfectly symmetric dy-namics[C]//International Conference on Machine Learning. PMLR, 2022: 23078-23091.
[127] PFAFF T, FORTUNATO M, SANCHEZ-GONZALEZ A, et al. Learning mesh-based simulation with graph networks[C]//International conference on learning representations. 2020.
[128] BRANDSTETTER J, WORRALL D, WELLING M. Message passing neural PDE solvers[J]. arXiv pre-print arXiv:2202.03376, 2022.
[129] WANG H X, LI J X, DWIVEDI A, et al. Beno: Boundary-embedded neural operators for elliptic pdes[J]. arXiv preprint arXiv:2401.09323, 2024.
[130] HE X D, WANG Y N, LI J. Flow completion network: Inferring the fluid dynamics from incomplete flow in-formation using graph neural networks[J]. Physics of Fluids, 2022, 34(8).
[131] BRYUTKIN A, HUANG J H, DENG Z Y, et al. Ham-let: Graph transformer neural operator for partial dif-ferential equations[J]. arXiv preprint arXiv:2402.03541, 2024.
[132] BOUSSIF O, BENGIO Y, BENABBOU L, et al. MAgnet: Mesh agnostic neural PDE solver[J]. Ad-vances in Neural Information Processing Systems, 2022, 35: 31972-31985.
[133] YIN Y, KIRCHMEYER M, FRANCESCHI J Y, et al. Continuous pde dynamics forecasting with implicit neural representations[J]. arXiv preprint arXiv:2209.14855, 2022.
[134] HAN X, GAO H, PFAFF T, et al. Predicting physics in mesh-reduced space with temporal attention[J]. arXiv preprint arXiv:2201.09113, 2022.
[135] LU L, JIN P Z, PANG G F, et al. Learning nonlinear operators via DeepONet based on the universal ap-proximation theorem of operators[J]. Nature machine intelligence, 2021, 3(3): 218-229.
[136] WANG S F, WANG H W, PERDIKARIS P. Learning the solution operator of parametric partial differential equations with physics-informed DeepONets[J]. Sci-ence advances, 2021, 7(40): eabi8605.
[137] JIN P Z, MENG S, LU L. MIONet: Learning multiple-input operators via tensor product[J]. SIAM Journal on Scientific Computing, 2022, 44(6): A3490-A3514.
[138] JIANG Z Y, ZHU M, LU L. Fourier-MIONet: Fourier-enhanced multiple-input neural operators for multi-phase modeling of geological carbon sequestration[J]. Reliability Engineering & System Safety, 2024, 251: 110392.
[139] SEIDMAN J, KISSAS G, PERDIKARIS P, et al. NOMAD: Nonlinear manifold decoders for operator learning[J]. Advances in Neural Information Pro-cessing Systems, 2022, 35: 5601-5613.
[140] LANTHALER S, MOLINARO R, HADORN P, et al. Nonlinear reconstruction for operator learning of PDEs with discontinuities[J]. arXiv preprint arXiv:2210.01074, 2022.
[141] LEE J Y, CHO S W, HWANG H J. HyperDeepONet: learning operator with complex target function space using the limited resources via hypernetwork[J]. arXiv preprint arXiv:2312.15949, 2023.
[142] LIN G, MOYA C, ZHANG Z C. B-DeepONet: An enhanced Bayesian DeepONet for solving noisy par-ametric PDEs using accelerated replica exchange SGLD[J]. Journal of Computational Physics, 2023, 473: 111713.
[143] VENTURI S, CASEY T. SVD perspectives for aug-menting DeepONet flexibility and interpretability[J]. Computer Methods in Applied Mechanics and Engi-neering, 2023, 403: 115718.
[144] KONTOLATI K, GOSWAMI S, KARNIADAKIS G E, et al. Learning in latent spaces improves the predic-tive accuracy of deep neural operators[J]. arXiv pre-print arXiv:2304.07599, 2023.
[145] LI Z Y, KOVACHKI N, AZIZZADENESHELI K, et al. Multipole graph neural operator for parametric partial differential equations[J]. Advances in Neural Infor-mation Processing Systems, 2020, 33: 6755-6766.
[146] CAO Q Y, GOSWAMI S, KARNIADAKIS G E. La-place neural operator for solving differential equa-tions[J]. Nature Machine Intelligence, 2024, 6(6): 631-640.
[147] RAONIC B, MOLINARO R, ROHNER T, et al. Con-volutional neural operators[C]//ICLR 2023 Workshop on Physics for Machine Learning. 2023.
[148] XIONG W, HUANG X M, ZHANG Z Y, et al. Koopman neural operator as a mesh-free solver of non-linear partial differential equations[J]. Journal of Computational Physics, 2024, 513: 113194.
[149] FENG M Q, HUANG Y X, LIAO W X, et al. SINGER: Stochastic Network Graph Evolving Operator for High Dimensional PDEs[C]//The Thirteenth Interna-tional Conference on Learning Representations.
[150] GENEVA N, ZABARAS N. Transformers for model-ing physical systems[J]. Neural Networks, 2022, 146: 272-289.
[151] LI Z J, SHU D L, BARATI FARIMANI A. Scalable transformer for pde surrogate modeling[J]. Advances in Neural Information Processing Systems, 2023, 36: 28010-28039.
[152] YANG L, LIU S T, MENG T W, et al. In-context oper-ator learning with data prompts for differential equa-tion problems[J]. Proceedings of the National Acade-my of Sciences, 2023, 120(39): e2310142120.
[153] WU H X, LUO H K, WANG H, et al. Transolver: A fast transformer solver for pdes on general geome-tries[J]. arXiv preprint arXiv:2402.02366, 2024.
[154] LI Z Y, KOVACHKI N, AZIZZADENESHELI K, et al. Neural operator: Graph kernel network for partial dif-ferential equations[J]. arXiv preprint arXiv:2003.03485, 2020.
[155] LI Z Y, KOVACHKI N, AZIZZADENESHELI K, et al. Fourier neural operator for parametric partial differen-tial equations[J]. arXiv preprint arXiv:2010.08895, 2020.
[156] LI Z Y, ZHENG H K, KOVACHKI N, et al. Physics-informed neural operator for learning partial differen-tial equations[J]. ACM/JMS Journal of Data Science, 2024, 1(3): 1-27.
[157] LI Z Y, HUANG D Z, LIU B, et al. Fourier neural operator with learned deformations for pdes on gen-eral geometries[J]. Journal of Machine Learning Re-search, 2023, 24(388): 1-26.
[158] LI Z Y, KOVACHKI N, CHOY C, et al. Geometry-informed neural operator for large-scale 3d pdes[J]. Advances in Neural Information Processing Systems, 2023, 36: 35836-35854.
[159] LIU N, JAFARZADEH S, YU Y. Domain agnostic fourier neural operators[J]. Advances in Neural In-formation Processing Systems, 2023, 36: 47438-47450.
[160] RAHMAN M A, ROSS Z E, AZIZZADENESHELI K. U-no: U-shaped neural operators[J]. arXiv preprint arXiv:2204.11127, 2022.
[161] TRAN A, MATHEWS A, XIE L X, et al. Factorized fourier neural operators[J]. arXiv preprint arXiv:2111.13802, 2021.
[162] XIAO X Y, CAO D F, YANG R C, et al. Coupled mul-tiwavelet neural operator learning for coupled partial differential equations[J]. arXiv preprint arXiv:2303.02304, 2023.
[163] BRANDSTETTER J, BERG R, WELLING M, et al. Clifford neural layers for PDE modeling[J]. arXiv preprint arXiv:2209.04934, 2022.
[164] ZHANG R, MENG Q, ZHU R C, et al. Monte Carlo Neural PDE Solver for Learning PDEs via Probabilis-tic Representation[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2025.
[165] ZHAO X Y, CHEN X Q, GONG Z Q, et al. RecFNO: A resolution-invariant flow and heat field reconstruc-tion method from sparse observations via Fourier neural operator[J]. International Journal of Thermal Sciences, 2024, 195: 108619.
[166] HELWIG J, ZHANG X, FU C, et al. Group equivari-ant fourier neural operators for partial differential equations[J]. arXiv preprint arXiv:2306.05697, 2023.
[167] TIWARI K, KRISHNAN N M, et al. Cono: Complex neural operator for continuous dynamical systems[J]. arXiv preprint arXiv:2310.02094, 2023.
[168] RAISSI M, PERDIKARIS P, KARNIADAKIS G E. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations[J]. Journal of Computational physics, 2019, 378: 686-707.
[169] CHEN Z, LIU Y, SUN H. Physics-informed learning of governing equations from scarce data[J]. Nature communications, 2021, 12(1): 6136.
[170] JIN X W, CAI S Z, LI H, et al. NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations[J]. Journal of Computational Physics, 2021, 426: 109951.
[171] GAO H, SUN L N, WANG J X. PhyGeoNet: Physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state PDEs on irregular domain[J]. Journal of Computational Physics, 2021, 428: 110079.
[172] ZENG Q, KOTHARI Y, BRYNGELSON S H, et al. Competitive physics informed networks[J]. arXiv preprint arXiv:2204.11144, 2022.
[173] GNANASAMBANDAM R, SHEN B, CHUNG J, et al. Self-scalable tanh (stan): Faster convergence and bet-ter generalization in physics-informed neural net-works[J]. arXiv preprint arXiv:2204.12589, 2022.
[174] WANG Y F, ZHONG L L. NAS-PINN: Neural archi-tecture search-guided physics-informed neural net-work for solving PDEs[J]. Journal of Computational Physics, 2024, 496: 112603.
[175] YOU R Q, ZHANG S M, KONG T L, et al. High-order discontinuity detection physics-informed neural network[J]. arXiv preprint arXiv:2307.15877, 2023.
[176] TOLOUBIDOKHTI M, YE Y B, MISSEL R, et al. Dats: Difficulty-aware task sampler for meta-learning physics-informed neural networks[C]//The Twelfth International Conference on Learning Repre-sentations. 2023.
[177] DUARTE D H G, DE LIMA P D S, De Araújo J M. Outlier-resistant physics-informed neural network[J]. Physical Review E, 2025, 111(2): L023302.
[178] CHEN N X, CUI C J, MA R J, et al. Sharp-PINNs: staggered hard-constrained physics-informed neural networks for phase field modelling of corrosion[J]. arXiv preprint arXiv:2502.11942, 2025.
[179] SUN J, LIU Y H, WANG Y Z, et al. BINN: A deep learning approach for computational mechanics prob-lems based on boundary integral equations[J]. Com-puter Methods in Applied Mechanics and Engineering, 2023, 410: 116012.
[180] GAFOOR CTP A, KUMAR BOYA S, JINKA R, et al. A physics-informed neural network for turbulent wake simulations behind wind turbines[J]. Physics of Fluids, 2025, 37(1).
[181] OLDENBURG J, BOROWSKI F, WOLLENBERG W, et al. Augmentation of experimentally obtained flow fields by means of Physics Informed Neural Networks (PINN) demonstrated on aneurysm flow[C]//Current Directions in Biomedical Engineer-ing. De Gruyter, 2023, 9(1): 519-523.
[182] SIRIGNANO J, SPILIOPOULOS K. DGM: A deep learning algorithm for solving partial differential equations[J]. Journal of computational physics, 2018, 375: 1339-1364.
[183] ARISTOTELOUS A C, MITCHELL E C, MAROULAS V. ADLGM: An efficient adaptive sam-pling deep learning Galerkin method[J]. Journal of Computational Physics, 2023, 477: 111944.
[184] DU Y F, ZAKI T A. Evolutional deep neural net-work[J]. Physical Review E, 2021, 104(4): 045303.
[185] CHEN H L, WU R D, GRINSPUN E, et al. Implicit neural spatial representations for time-dependent pdes[C]//International Conference on Machine Learn-ing. PMLR, 2023: 5162-5177.
[186] XUE T J, BEATSON A, ADRIAENSSENS S, et al. Amortized finite element analysis for fast PDE-constrained optimization[C]//International Conference on Machine Learning. PMLR, 2020: 10638-10647.
[187] BRUNA J, PEHERSTORFER B, Vanden-Eijnden E. Neural Galerkin schemes with active learning for high-dimensional evolution equations[J]. Journal of Computational Physics, 2024, 496: 112588.
[188] LIU X Y, ZHU M, LU L, et al. Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamics[J]. Communications Physics, 2024, 7(1): 31.
[189] WU T L, MARUTAMA T, ZHAO Q Q, et al. Learning controllable adaptive simulation for multi-resolution physics[J]. arXiv preprint arXiv:2305.01122, 2023.
[190] CAO Y D, CHAI M, LI M C, et al. Efficient learning of mesh-based physical simulation with bi-stride mul-ti-scale graph neural network[C]//International con-ference on machine learning. PMLR, 2023: 3541-3558.
[191] LINO M, FOTIADIS S, BHARATH A A, et al. Multi-scale rotation-equivariant graph neural networks for unsteady Eulerian fluid dynamics[J]. Physics of Flu-ids, 2022, 34(8).
[192] ZHANG X, HELWIG J, LIN Y C, et al. Sinenet: Learning temporal dynamics in time-dependent par-tial differential equations[J]. arXiv preprint arXiv:2403.19507, 2024.
[193] HAO Z K, WANG Z Y, SU H, et al. Gnot: A general neural operator transformer for operator learn-ing[C]//International Conference on Machine Learn-ing. PMLR, 2023: 12556-12569.
[194] SERRANO L, LE BOUDEC L, KASSA? KOUPA? A, et al. Operator learning with neural fields: Tackling pdes on general geometries[J]. Advances in Neural Information Processing Systems, 2023, 36: 70581-70611.
[195] VLACHAS P R, ARAMPATZIS G, UHLER C, et al. Multiscale simulations of complex systems by learn-ing their effective dynamics[J]. Nature Machine Intel-ligence, 2022, 4(4): 359-366.
[196] LYU Y F, ZHAO X Y, GONG Z Q, et al. Multi-fidelity prediction of fluid flow based on transfer learning us-ing Fourier neural operator[J]. Physics of Fluids, 2023, 35(7).
[197] FANG S K, COOLEY M, LONG D, et al. Solving high frequency and multi-scale pdes with gaussian processes[J]. arXiv preprint arXiv:2311.04465, 2023.
CJA