WOLAŃSKI P . Detonative propulsion [J ] . Proceedings of the Combustion Institute , 2013 , 34 ( 1 ): 125 - 158 . DOI: 10.1016/j.proci.2012.10.005 http://doi.org/10.1016/j.proci.2012.10.005 https://linkinghub.elsevier.com/retrieve/pii/S1540748912004014 https://linkinghub.elsevier.com/retrieve/pii/S1540748912004014

李宝星 , 翁春生 . 气体与液体两相连续旋转爆轰发动机爆轰波传播特性三维数值模拟研究 [J ] . 兵工学报 , 2017 , 38 ( 7 ): 1358 - 1367 . DOI: 10.3969/j.issn.1000-1093.2017.07.014 http://doi.org/10.3969/j.issn.1000-1093.2017.07.014 为了研究气体与液体两相连续旋转爆轰波的传播特性，基于三维守恒元和求解元方法，在圆柱坐标系下采用带化学反应的气体与液体两相爆轰模型，对连续旋转爆轰发动机进行三维数值模拟。通过计算获得了爆轰波起爆及其稳定传播时的流场结构，分析了流场在燃烧室径向方向的变化以及发动机的推力性能，揭示了两相爆轰波的传播特性。研究结果表明：燃烧室内流场结构与文献\[4\]中的实验研究结果定性一致；由于环形燃烧室外壁面的收敛和内壁面的发散，爆轰强度沿着燃烧室的径向方向逐渐增强，实现了爆轰波的自持旋转传播；以汽油为燃料、富氧空气为氧化剂，在填充总压为0.2 MPa、总温为288.15 K、燃料液滴半径为25 μm的条件下，连续旋转爆轰发动机所获得的平均推力约为880 N，爆轰波的传播频率约为4 390 Hz.

LI B X , WENG C S . Three-dimensional numerical simulation on the propagation characteristicsof detonation wave in gas-liquid two-phase continuous rotating detonation engine [J ] . Acta Armamentarii , 2017 , 38 ( 7 ): 1358 - 1367 . (in Chinese)

SATO T , CHACON F , WHITE L , et al . Mixing and detonation structure in a rotating detonation engine with an axial air inlet [J ] . Proceedings of the Combustion Institute , 2021 , 38 ( 3 ): 3769 - 3776 . DOI: 10.1016/j.proci.2020.06.283 http://doi.org/10.1016/j.proci.2020.06.283 https://linkinghub.elsevier.com/retrieve/pii/S1540748920303758 https://linkinghub.elsevier.com/retrieve/pii/S1540748920303758

FOTIA M L , HOKE J , SCHAUER F . Study of the ignition process in a laboratory scale rotating detonation engine [J ] . Experimental Thermal and Fluid Science , 2018 , 94 : 345 - 354 . DOI: 10.1016/j.expthermflusci.2017.11.002 http://doi.org/10.1016/j.expthermflusci.2017.11.002 https://linkinghub.elsevier.com/retrieve/pii/S0894177717303473 https://linkinghub.elsevier.com/retrieve/pii/S0894177717303473

XIA Z J , MA H , LIU C , et al . Experimental investigation on the propagation mode of rotating detonation wave in plane-radial combustor [J ] . Experimental Thermal and Fluid Science , 2019 , 103 : 364 - 376 . DOI: 10.1016/j.expthermflusci.2019.01.032 http://doi.org/10.1016/j.expthermflusci.2019.01.032 https://linkinghub.elsevier.com/retrieve/pii/S0894177718305272 https://linkinghub.elsevier.com/retrieve/pii/S0894177718305272

孟豪龙 , 翁春生 , 武郁文 , 等 . 环形燃烧室中凹腔对C2H4/Air旋转爆轰流场影响的数值模拟 [J ] . 兵工学报 , 2022 , 43 ( 5 ): 1063 - 1074 .

MENG H L , WENG C S , WU Y W , et al . Numerical simulation of cavity influence on c2h4/air rotating detonation flow field in annular combustor [J ] . Acta Armamentarii , 2022 , 43 ( 5 ): 1063 - 1074 . (in Chinese)

魏万里 , 翁春生 , 武郁文 , 等 . 氧化剂喷注面积对连续旋转爆轰波传播特性影响的实验研究 [J ] . 兵工学报 , 2018 , 39 ( 12 ): 2345 - 2353 . DOI: 10.3969/j.issn.1000-1093.2018.12.008 http://doi.org/10.3969/j.issn.1000-1093.2018.12.008 为了研究氧化剂喷注面积对连续旋转爆轰波传播特性的影响，以H₂为燃料、空气为氧化剂，在喷孔-环缝式连续旋转爆轰发动机上开展了一系列试验研究。基于燃烧室内高频压力信号和氧化剂集气腔内的压力信号，分析了氧化剂喷注面积对连续旋转爆轰波传播过程、速度亏损和稳定性以及爆轰波波头高度的影响。试验结果表明：当推进剂质量流量不变时，增大氧化剂喷注面积，爆轰波传播速度亏损增大，爆轰波稳定性变差，同时爆轰波波头高度减小；在氧化剂喷注面积为217.1 mm²、当量比为0.9时，爆轰波平均速度达到1 800 m/s，为理论Chapman-Jouguet速度的93%，同时爆轰波表现最为稳定；当氧化剂喷注面积不变时，随着当量比的增大，爆轰波传播的稳定性先升高、后降低。

WEI W L , WENG C S , WU Y W , et al . Experimental research on influence of oxidant injection area on the propagation characteristics of continuous rotating detonation wave [J ] . Acta Armamentarii , 2018 , 39 ( 12 ): 2345 - 2353 . (in Chinese)

ZHOU R , WU D , WANG J P . Progress of continuously rotating detonation engines [J ] . Chinese Journal of Aeronautics , 2016 , 29 ( 1 ): 15 - 29 . DOI: 10.1016/j.cja.2015.12.006 http://doi.org/10.1016/j.cja.2015.12.006 https://linkinghub.elsevier.com/retrieve/pii/S1000936115002356 https://linkinghub.elsevier.com/retrieve/pii/S1000936115002356

刘世杰 , 刘卫东 , 林志勇 , 等 . 连续旋转爆震波传播过程研究(Ⅰ):同向传播模式 [J ] . 推进技术 , 2014 , 35 ( 1 ): 138 - 144 .

LIU S J , LIU W D , LIN Z Y , et al . Research on continuous rotating detonation wave propagation process(Ⅰ): one direction mode [J ] . Journal of Propulsion Technology , 2014 , 35 ( 1 ): 138 - 144 . (in Chinese)

刘世杰 , 林志勇 , 刘卫东 , 等 . 连续旋转爆震波传播过程研究(Ⅱ):双波对撞传播模式 [J ] . 推进技术 , 2014 , 35 ( 2 ): 269 - 275 .

LIU S J , LIU W D , LIN Z Y , et al . Research on continuous rotating detonation wave propagation process(Ⅱ): two-wave collison propagation mode [J ] . Journal of Propulsion Technology , 2014 , 35 ( 2 ): 269 - 275 . (in Chinese)

ZHANG H L , LIU W D , LIU S J . Experimental investigations on H2/air rotating detonation wave in the hollow chamber with laval nozzle [J ] . International Journal of Hydrogen Energy , 2017 , 42 ( 5 ): 3363 - 3370 . DOI: 10.1016/j.ijhydene.2016.12.038 http://doi.org/10.1016/j.ijhydene.2016.12.038 https://linkinghub.elsevier.com/retrieve/pii/S0360319916335844 https://linkinghub.elsevier.com/retrieve/pii/S0360319916335844

YANG X K , SONG F L , WU Y , et al . Investigation of rotating detonation fueled by a methane-hydrogen-carbon dioxide mixture under lean fuel conditions [J ] . International Journal of Hydrogen Energy , 2020 , 45 ( 41 ): 21995 - 22007 . DOI: 10.1016/j.ijhydene.2020.05.225 http://doi.org/10.1016/j.ijhydene.2020.05.225 https://linkinghub.elsevier.com/retrieve/pii/S0360319920320802 https://linkinghub.elsevier.com/retrieve/pii/S0360319920320802

ZHDAN S A , BYKOVSKII F A , VEDERNIKOV E F . Mathematical modeling of a rotating detonation wave in a hydrogen-oxygen mixture [J ] . Combustion, Explosion, and Shock Waves , 2007 , 43 ( 4 ): 449 - 459 . DOI: 10.1007/s10573-007-0061-y http://doi.org/10.1007/s10573-007-0061-y http://link.springer.com/10.1007/s10573-007-0061-y http://link.springer.com/10.1007/s10573-007-0061-y

SUN J , ZHOU J , LIU S J , et al . Plume flowfield and propulsive performance analysis of a rotating detonation engine [J ] . Aerospace Science and Technology , 2018 , 81 : 383 - 393 . DOI: 10.1016/j.ast.2018.08.024 http://doi.org/10.1016/j.ast.2018.08.024 https://linkinghub.elsevier.com/retrieve/pii/S1270963818306692 https://linkinghub.elsevier.com/retrieve/pii/S1270963818306692

孟豪龙 , 翁春生 , 武郁文 , 等 . 基于OpenFOAM的三维H2/Air连续旋转爆轰流场数值模拟 [J ] . 推进技术 , 2020 , 41 ( 6 ): 1351 - 1360 .

MENG H L , WENG C S , WU Y W , et al . Three-dimensional numerical simulation of h2/air continuous rotating detonation flow field based on openfoam [J ] . Journal of Propulsion Technology , 2020 , 41 ( 6 ): 1351 - 1360 . (in Chinese)

KATTA V R , CHO K Y , HOKE J L , et al . Effect of increasing channel width on the structure of rotating detonation wave [J ] . Proceedings of the Combustion Institute , 2019 , 37 ( 3 ): 3575 - 3583 . DOI: 10.1016/j.proci.2018.05.072 http://doi.org/10.1016/j.proci.2018.05.072 https://linkinghub.elsevier.com/retrieve/pii/S1540748918300737 https://linkinghub.elsevier.com/retrieve/pii/S1540748918300737

COCKS P A , HOLLEY A T , GREENE C B , et al . Development of a high fidelity rde simulation capability [C ] // Proceedings of the 53rd AIAA Aerospace Sciences Meeting. Kissimmee,FL,US:AIAA , 2015 .

刘朋欣 , 郭启龙 , 赵炜 , 等 . 基于旋转爆震三维流场结构分析的计算模型对比研究 [J ] . 推进技术 , 2020 , 41 ( 12 ): 2757 - 2765 .

LIU P X , GUO Q L , ZHAO W , et al . Computational models based on analysis of three dimensional flow field structures in rotating detonation [J ] . Journal of Propulsion Technology , 2020 , 41 ( 12 ): 2757 - 2765 . (in Chinese)

LIU P X , GUO Q L , SUN D , et al . Wall effect on the flow structures of three-dimensional rotating detonation wave [J ] . International Journal of Hydrogen Energy , 2020 , 45 ( 53 ): 29546 - 29559 . DOI: 10.1016/j.ijhydene.2020.07.196 http://doi.org/10.1016/j.ijhydene.2020.07.196 https://linkinghub.elsevier.com/retrieve/pii/S0360319920328068 https://linkinghub.elsevier.com/retrieve/pii/S0360319920328068

ZHANG L F , ZHANG S J , WANG J P . A direct simulation ofcontinuous detonation engine with the navier-stokes equations [C ] // Proceedings of the 21st AIAA International Space Planes and Hypersonics Technologies Conference.Reston,VA,US:AIAA , 2017 .

HIRSCHFELDER J O , CURTISS C F . Theory of detonations. irreversible unimolecular reaction [J ] . The Journal of Chemical Physics , 1958 , 28 ( 6 ): 1130 - 1147 . DOI: 10.1063/1.1744357 http://doi.org/10.1063/1.1744357 https://pubs.aip.org/jcp/article/28/6/1130/77903/Theory-of-Detonations-I-Irreversible-Unimolecular https://pubs.aip.org/jcp/article/28/6/1130/77903/Theory-of-Detonations-I-Irreversible-Unimolecular The composition, temperature, and pressure as functions of distance in a steady-state, plane gaseous detonation wave are studied. The effects of the coefficients of viscosity, diffusion, and thermal conductivity are included. The basic equations are set up for a gas in which the irreversible unimolecular reaction A→B takes place with the release of energy. The topological nature of the solutions is discussed and some detailed numerical solutions are given. The numerical calculations (obtained by a point-by-point integration of the detonation equations) indicate a strong probability that there is a highest ambient pressure above which a steady-state detonation cannot take place, and indicate a possibility that there is an ambient pressure below which a detonation cannot occur. In the examples considered, there is strong coupling between the reaction zone and the shock zone so that the solutions never come close to the von Neumann ``spike.'' If the Mach number is greater than unity, the solutions have an entirely different nature and exist for only a single ambient pressure rather than for a range of pressures. However, from hydrodynamical considerations, a detonation wave initiated from either a point or a fixed wall can become equivalent to the steady-state solutions only if the Mach number is greater than or equal to unity.

ZHAO M J , ZHANG H W . Large eddy simulation of non-reacting flow and mixing fields in a rotating detonation engine [J ] . Fuel , 2020 , 280 : 118534 . DOI: 10.1016/j.fuel.2020.118534 http://doi.org/10.1016/j.fuel.2020.118534 https://linkinghub.elsevier.com/retrieve/pii/S0016236120315301 https://linkinghub.elsevier.com/retrieve/pii/S0016236120315301

LIU X Y , LUAN M Y , CHEN Y L , et al . Propagation behavior of rotating detonation waves with premixed kerosene/air mixtures [J ] . Fuel , 2021 , 294 : 120253 . DOI: 10.1016/j.fuel.2021.120253 http://doi.org/10.1016/j.fuel.2021.120253 https://linkinghub.elsevier.com/retrieve/pii/S0016236121001290 https://linkinghub.elsevier.com/retrieve/pii/S0016236121001290

PAL P , XU C , KUMAR G , et al . Large-eddy simulations and mode analysis of ethylene/air combustion in a non-premixed rotating detonation engine [C ] // Proceedings of AIAA Propulsion and Energy Forum and Exposition. Reston,VA,US:AIAA , 2020 .

PAL P , XU C , KUMAR G , et al . Large-eddy simulation and chemical explosive mode analysis of non-ideal combustion in a non-premixed rotating detonation engine [C ] // Proceedings of AIAA SciTech 2020 Forum. Reston,VA,US:AIAA , 2020 .

WELLER H G , TABOR G , JASAK H C , et al . A tensorial approach to computational continuum mechanics using object orientated techniques [J ] . Computers in Physics , 1998 , 12 ( 6 ): 620 - 631 . DOI: 10.1063/1.168744 http://doi.org/10.1063/1.168744 https://pubs.aip.org/cip/article/12/6/620/510187/A-tensorial-approach-to-computational-continuum https://pubs.aip.org/cip/article/12/6/620/510187/A-tensorial-approach-to-computational-continuum In this article the principles of the field operation and manipulation (FOAM) C++ class library for continuum mechanics are outlined. Our intention is to make it as easy as possible to develop reliable and efficient computational continuum-mechanics codes: this is achieved by making the top-level syntax of the code as close as possible to conventional mathematical notation for tensors and partial differential equations. Object-orientation techniques enable the creation of data types that closely mimic those of continuum mechanics, and the operator overloading possible in C++ allows normal mathematical symbols to be used for the basic operations. As an example, the implementation of various types of turbulence modeling in a FOAM computational-fluid-dynamics code is discussed, and calculations performed on a standard test case, that of flow around a square prism, are presented. To demonstrate the flexibility of the FOAM library, codes for solving structures and magnetohydrodynamics are also presented with appropriate test case results given. © 1998 American Institute of Physics.

MCGOUGH D A . Detonation modeling in openfoam using adaptive mesh refinement [D ] . Boulder,CO,US : University of Colorado Boulder , 2020 .

WANG Y H . Rotating detonation in a combustor of trapezoidal cross section for the hydrogen-air mixture [J ] . International Journal of Hydrogen Energy , 2016 , 41 ( 12 ): 5605 - 5616 . DOI: 10.1016/j.ijhydene.2016.02.028 http://doi.org/10.1016/j.ijhydene.2016.02.028 https://linkinghub.elsevier.com/retrieve/pii/S0360319915312696 https://linkinghub.elsevier.com/retrieve/pii/S0360319915312696

ZHANG L , MA J Z , ZHANG S J , et al . Three-dimensional numerical study on rotating detonation engines using reactive navier-stokes equations [J ] . Aerospace Science and Technology , 2019 , 93 : 105271 . DOI: 10.1016/j.ast.2019.07.004 http://doi.org/10.1016/j.ast.2019.07.004 https://linkinghub.elsevier.com/retrieve/pii/S1270963819300604 https://linkinghub.elsevier.com/retrieve/pii/S1270963819300604