[1]BORRVALL T, PETERSSON J.Topology optimization of fluids in Stokes flow[J].International Journal for Numerical Methods in Fluids, 2003, 41(1):77-107
[2]GERSBORG-HANSEN A, SIGMUND O, HABER R B.Topology optimization of channel flow problems[J].Structural and Multidisciplinary Optimization, 2005, 30(3):181-192
[3]ALEXANDERSEN J, SIGMUND O, AAGE N.Large scale three-dimensional topology optimisation of heat sinks cooled by natural convection［J］.International Journal of Heat and Mass Transfer, 2016, 100:876-891.[J].International Journal of Heat and Mass Transfer, 2016, 100:876-891
[4]CHALLIS V J, GUEST J K.Level set topology optimization of fluids in Stokes flow[J].International Journal for Numerical Methods in Engineering, 2009, 79(10):1284-1308
[5]ZHOU S, LI Q.A variational level set method for the topology optimization of steady-state Navier–Stokes flow[J].Journal of Computational Physics, 2008, 227(24):10178-10195
[6]DENG Y, ZHANG P, LIU Y, et al.Optimization of unsteady incompressible Navier–Stokes flows using variational level set method[J].International Journal for Numerical Methods in Fluids, 2013, 71(12):1475-1493
[7]GARCKE H, HECHT C, HINZE M.Numerical Approximation of Phase Field Based Shape and Topology Optimization for Fluids[J].SIAM Journal on Scientific Computing, 2015, 37(4):A2077-A2100
[8]DENG Y, LIU Z, ZHANG P, et al.Topology optimization of unsteady incompressible Navier–Stokes flows[J].Journal of Computational Physics, 2011, 230(17):6688-6708
[9]KREISSL S, PINGEN G, MAUTE K.Topology optimization for unsteady flow[J].International Journal for Numerical Methods in Engineering, 2011, 87(13):1229-1253
[10]YOON G H.Topology optimization for turbulent flow with Spalart–Allmaras model [J]. Computer Methods in Applied Mechanics and Engineering, 2016, 303: 288-311.[J].Computer Methods in Applied Mechanics and Engineering, 2016, 303:288-311
[11]DILGEN S B, DILGEN C B, FUHRMAN D R, et al.Density based topology optimization of turbulent flow heat transfer systems[J].Structural and Multidisciplinary Optimization, 2018, 57(5):1905-1918
[12]Padhy R, Suresh K, Chandrasekhar A. Topology optimization of multiscale fluid devices using variational autoencoders and super-shapes[DB/OL]. arXiv prep.[J].rXiv:2309.08435, 2023., rint, :-
[13]KOU C, YIN Y, ZHU M, et al. Efficient neural topology optimization via active learning for enhancing turbulent mass transfer in fluid channels[DB/OL].arXiv prep.[J].rXiv:2503.03997, 2025., rint, :-
[14]Sá L F N, OKUBO JR C M, SILVA E C N.Topology optimization of subsonic compressible flows[J].Structural and Multidisciplinary Optimization, 2021, 64(1):1-22
[15]Maffei F S, de Sá L F N, Moscatelli E, et al.Integer programming topology optimization for subsonic compressible flows with geometry trimming. International Journal of Heat and Mass Transfer, 2023; 201:123614.[J].International Journal of Heat and Mass Transfer, 2023, 201:123614-123614
[16]GARCIA-RODRIGUEZ L F, ALONSO D, SILVA E C N.Turbulence effects in the topology optimization of compressible subsonic flow[J].International Journal for Numerical Methods in Fluids, 2025, 97(1):44-68
[17]Sá L F N, MAFFEI F S, RIBEIRO L N B S, et al.Topology optimization design of labyrinth seal-type devices considering subsonic compressible turbulent flow conditions [J]. Computers & Mathematics with Applications, 2024, 176: 306-323.[J].Computers & Mathematics with Applications, 2024, 176:306-323
[18]张 敏，杨金广，刘 艳.流体拓扑优化方法及其在叶轮机械中的应用[J].推进技术, 2021, 42(11):2401-2416
[19]ZHANG Min，YANG Jin-guang，LIU Yan.Fluid Topology Optimization Method and Its Application in Turbomachinery[J].Journal of Propulsion Technology, 2021, 42(11):2401-2416
[20]张敏.涡轮动叶叶顶间隙泄漏控制及结构优化研究[D].大连理工大学, 2019.
[21]Zhang Min.Turbine Rotor Blade Tip Clearance Leakage Control and Structural Optimization Research[D]. Dalian University of Technology, 2019(in Chinese).
[22]Zhang M, Du J, Zhang H, et al.Fluid topology optimization of gas-turbine-related components[C]//1st International Conference on Mechanical System Dynamics (ICMSD 2022). IET, 2022, 2022: 943-949.
[23]李信卿，赵清海，龙凯，等.考虑瞬态效应的周期性多材料传热结构拓扑优化[J].航空学报, 2022, 43(12):425964-
[24]LI X Q, ZHAO Q H, LONG K, et al.Topology optimization of periodic multi-material heat conduction structures considering transient effects[J].Acta Aeronautica et Astronautica Sinica, 2022, 43(12):425964-
[25]Song Z, Wang J, Tang S, et al.Dual-objective topology optimization design for latent heat storage systems using composite phase change materials [J]. Energy, 2025; 319:135069.[J].Energy, 2025, 319:135069-135069
[26]Zhang T, Jing T, Qin F, et al.Topology optimization of regenerative cooling channel in non-uniform thermal environment of hypersonic engine [J]. Applied Thermal Engineering, 2023, 219: 119384.[J].Applied Thermal Engineering, 2023, 219:119384-119384
[27]李新磊, 吴坤, 赵林英, 范学军.面向发动机再生冷却的流热耦合拓扑优化[J].力学学报, 2023, 55(11):2661-2674
[28]Li Xinlei, Wu Kun, Zhao Linying, Fan Xuejun.Topology optimization of coupled thermal-fluid problems for regenerative cooling engines[J].Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(11):2661-2674
[29]Yeranee, K., Rao, Y., Yang, L., et al. (2022). Enhanced thermal performance of a pin-fin cooling channel for gas turbine blade by density-based topology optimization. International journal of thermal sciences, 181, 107783.[J].International journal of thermal sciences, 2022, 181:107783-107783
[30]Yeranee, K., Rao, Y., Zuo, Q., et al. (2024). Thermal performance enhancement for gas turbine blade trailing edge cooling with topology-optimized printable diamond TPMS lattice. International Journal of Heat and Fluid Flow, 110, 109649.[J].International Journal of Heat and Fluid Flow, 2024, 110:109649-109649
[31]Svanberg K.The method of moving asymptotes—a new method for structural optimization[J].International journal for numerical methods in engineering, 1987, 24(2):359-373
[32]Bear J.Dynamics of fluids in porous media[M]. Courier Corporation, 2013.
[33]STOLPE M, SVANBERG K.An alternative interpolation scheme for minimum compliance topology optimization[J].Structural and Multidisciplinary Optimization, 2001, 22(2):116-124
[34]ZYMARIS A S, PAPADIMITRIOU D I, GIANNAKOUGLOU K C, et al.Continuous adjoint approach to the Spalart–Allmaras turbulence model for incompressible flows[J].Computers & Fluids, 2009, 38(8):1528-1538
[35]STRELETS M.Detached eddy simulation of massively separated flows[J].39th Aerospace Sciences Meeting and Exhibit, , 2001(879):-
[36]BASSI F, CRIVELLINI A, REBAY S, et al.Discontinuous Galerkin solution of the Reynolds-averaged Navier–Stokes and k-ω turbulence model equations[J].Computers & Fluids, 2005, 34(4-5):507-540
[37]LANGTRY R B, MENTER F R.Correlation-based transition modeling for unstructured parallelized computational fluid dynamics codes[J].AIAA Journal, 2009, 47(12):2894-2906
[38]HOLKA Q, TOUBIANA E, CORTIAL J, et al.Density-based topology optimization of a surface cooler in turbulent flow using a continuous adjoint turbulence model[J].Structural and Multidisciplinary Optimization, 2022, 65(8):223-
[39]吴望一.流体力学上册[M]. 北京大学出版社, 1982.
[40]Wu Wangyi.Fluid Mechanics Volume 1[M]. Peking University Press, 1982(in Chinese).
[41]彭泽琰, 刘刚.航空燃气轮机原理[M]. 国防工业出版社, 2000.
[42]Peng Zeyan, Liu Gang.Principles of Aircraft Gas Turbines[M]. National Defense Industry Press, 2000(in Chinese).
[43]MARCK G, NEMER M, HARION J L, et al.Topology optimization using the SIMP method for multiobjective conductive problems[J].Numerical Heat Transfer, Part B: Fundamentals, 2012, 61(6):439-470
[44]GALANOS N, PAPOUTSIS-KIACHAGIAS E M, et al.The Cut-Cell Method for the Conjugate Heat Transfer Topology Optimization of Turbulent Flows Using the " Think Discrete–Do Continuous" Adjoint[J].Energies, 2024, 17:1817-
[45]OLESEN L H, OKKELS F, BRUUS H.A high-level programming-language implementation of topology optimization applied to steady-state Navier-Stokes flow[J].International Journal for Numerical Methods in Engineering, 2006, 65(7):975-1001
[46]吴仲华.可压缩气体流过位于任意回转面上叶栅的解法和这种叶栅的设计方法[J].机械工程学报, 1956, 4(1):21-46
[47]Wu Zhonghua.Solution for compressible gas flow through cascades on arbitrary surfaces of revolution and design method of such cascades[J].Journal of Mechanical Engineering, 1956, 4(1):21-46
[48]BEHR T.Control of Rotor Tip Leakage and Secondary Flow by Casing Air Injection in Unshrouded Axial Turbines[D]. Zurich: SWISS FEDERAL INSTITUTE OF TECHNOLOGY ZURICH, 2007.
[49]高杰，郑群，许天帮，等.叶顶泄漏涡破裂对涡轮损失的影响[J].航空学报, 2014, 35(5):1257-1264
[50]GAO J, ZHENG Q, XU T B, et al.Effect of tip leakage vortex breakdown on losses in turbine[J].Acta Aeronautica et Astronautica Sinica, 2014, 35(5):1257-1264
[51]高杰，郑群，岳国强，等.燃气轮机涡轮叶顶气动与热技术研究进展[J].航空学报, 2017, 38(9):521019-
[52]GAO J, ZHENG Q, YUE G Q, et al.Research progress on turbine blade tip aerodynamics and heat transfer technology for gas turbines[J].Acta Aeronautica et Astronautica Sinica, 2017, 38(9):521019-
[53]Goodfellow I, Bengio Y, Courville A, et al.Deep learning[M]. Cambridge: MIT press, 2016.
[54]Kalyanmoy D.A fast and elitist multi-objective genetic algorithm: NSGA-II[J].IEEE Trans. on Evolutionary Computation, 2002, 6(2):182-197
[55]Wennerstrom A J.Design of highly loaded axial-flow fans and compressors[J].Compresseur Axial, 2000[J].Compresseur Axial, 2000, :-
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