力学学报

REVIEW OF NEURAL NETWORK-BASED METHODS FOR SOLVING PARTIAL DIFFERENTIAL EQUATIONS

Zha Wenshu, Li Daolun, Shen Luhang, Zhang Wen, Liu Xuliang

Neural networks are widely used as a powerful information processing tool in the fields of computer vision, biomedicine, and oil-gas engineering, triggering technological changes. Due to the powerful learning ability, deep learning networks can not only discover physical laws but also solve partial differential equations (PDEs). In recent years, PDE solving based on deep learning has been a new research hotspot. Following the terms of traditional PDE analytical solution, this paper calls the method of solving PDE by neural network as PDE intelligent solution or PDE neural-network solution. This paper briefly introduces the development history of PDE intelligent solution, and then discusses the development of recovering unknown PDEs and solving known PDEs. The main focus of this paper is on a neural network solution method for a known PDE. It is divided into three categories according to the way of constructing loss functions. The first is data-driven method, which mainly learns PDEs from partially known data and can be applied to recovering physical equations, discovering unknown equations, parameter inversion, etc. The second is physical-constraint method, i.e., data-driven supplemented by physical constraints, which is manifested by adding physical laws such as governing equation to the loss function, thus reducing the network's reliance on labeled data and improving the generalization ability and application value. The third is physics-driven method (purely physical constraints), which solves PDEs by physical laws without any labeled data. However, such methods are currently only applied to solve simple PDEs and still need to be improved for complex physics. This paper introduces the research progress of intelligent solution of PDEs from these three aspects, involving various network structures such as fully-connected neural networks, convolutional neural networks, recurrent neural networks, etc. Finally, we summarize the research progress of PDE intelligent solutions, and outline the corresponding application scenarios and future research outlook.

2022, 54(3): 543-556. doi: 10.6052/0459-1879-21-617

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Preface of Theme Articles on Fluid Mechanics in Engines

Lian Huan

2022, 54(3): 557-558. doi: 10.6052/0459-1879-22-106

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RESEARCH PROGRESS OF ADAPTIVE CONTROL METHODS FOR COMPRESSOR FLOW STABILITY

Xu Dengke, Dong Xu, Xu Ruize, Li Jia, Sun Dakun, Sun Xiaofeng

Adaptive control of compressor flow stability is a key technology of intelligent aeroengine in the future. Basic research needs to answer three concerns. How to describe the system stability? How to change the system stability? How to monitor the system stability? Therefore, our team has carried out systematic and in-depth research work in three aspects: general theory of compressor flow stability, stability margin enhancement method based on wall impedance boundary and real-time stall warning technology. (1) The developed general theory of flow instability in turbomachinery not only can consider the flow non-uniformity and blade geometry, but also has high calculation efficiency and great prediction accuracy, which provides a reliable evaluation tool for the integrated design of compressor aerodynamics and stability. (2) The developed SPS (stall precursor-suppressed) casing treatment and foam metal casing treatment based on wall impedance boundary control strategy have made substantial progress in enhancing stability margin and reducing noise while maintaining the aerodynamic performance of the compressor system. Equivalent distributed source method is employed to establish the stall inception prediction model considering the effect of casing, which is able to make sensitivity analysis on crucial structural parameters of SPS casing treatment and foam metal casing treatment so as to provide the clear theoretical design criterion. The experimental results show that SPS casing treatment achieves the purpose of stability enhancement by restraining the nonlinear evolution of stall precursor wave, while maintaining the pressure ratio and efficiency characteristics of the compressor; Foam metal casing treatment has favorable engineering application prospects for its double effects of improving stability and reducing noise. (3) The developed real-time stall warning approach based on aeroacoustic principle increases the stall warning time to more than seconds, and can monitor the system stability online. Combining the above theoretical prediction method, stability enhancement technology and real-time stall warning approach, the closed-loop feedback adaptive control method is developed, which provides an adaptive stability control technology for the future intelligent aeroengine.

2022, 54(3): 559-576. doi: 10.6052/0459-1879-21-560

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AN ACOUSTIC ANALOGY MODEL FOR HELMHOLTZ RESONATORS WITH COOLING BIAS FLOW

Gan Zhenpeng, Yang Dong

Helmholtz resonators (HR), as a typical passive muffler device, are often installed in the combustor of aero engines and gas turbines to absorb noise and suppress combustion thermoacoustic oscillations. In practical applications, in order to prevent the high temperature gas in the combustion chamber from damaging the HR, a cooling airflow is often introduced from the back cavity of the HR into the combustor through its neck to protect the HR. The temperature of this cooling airflow is generally significantly lower than the temperature of the gas in the combustor. When such HR is installed on the combustor, the temperature difference may affect the relationship between the sound waves and entropy waves upstream and downstream of the HR in the combustor, and further affect the sound absorption performance of the HR. However, in previous models for studying the influence of HR on thermoacoustic oscillations in the combustor, the influence of this temperature difference is generally ignored. Based on the idea of acoustic analogy, we develop a theoretical model in this paper which can predict the acoustic performance of HR with cooling airflow. This HR is installed in a one-dimensional acoustic duct. The model is based on one-dimensional mass, momentum and energy conservation equations. Under the assumption of no viscous dissipation, ignoring volume forces, all external heat sources and thermal diffusion, we derived for the first time the wave equation with source term in a one-dimensional combustor with Helmholtz resonator with cooling airflow installed on the side wall.The source term on the right side of the equation reflects the effect of the resonator on the one-dimensional sound field in the combustor. It can be seen from this equation that the sound source/sink dissipation caused by the resonator is composed of entropy disturbance and mass disturbance terms. It can be further seen that the entropy disturbance generated by the temperature difference of the resonator will enter the one-dimensional sound wave equation in the combustor in the form of a sound source, significantly changing the effect of HR on the sound field in the combustor near its resonance frequency. By comparing with the existing jump condition model, we verified the accuracy of the model in predicting the effect of HR temperature difference on the sound field in the one-dimensional combustor.

2022, 54(3): 577-587. doi: 10.6052/0459-1879-21-561

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

Sun Mingbo, An Bin, Wang Hongbo, Wang Chenglong

Numerical flight of the scramjet engine has experienced extensive developments in recent years because of the advances in numerical method, physical modeling, and computer hardware. The numerical simulation of the internal and external coupling flow is gradually applied to the practical scenarios. With the rapid advances in combustion modeling, aerodynamics, structure design, material, and multi-physics coupling model, the “general numerical flight” that simultaneously resolves multiple physics fields might be available in the foreseeable future. Based on the latest developments of numerical flight and artificial intelligence (AI), the “intelligent numerical flight” is proposed in this study. On the one hand, intelligent numerical flight employs the artificial intelligence methodologies to address the conventional challenges in the field of numerical flight such as mesh generation and adaptation, high-fidelity physics modeling, data processing, and knowledge mining etc., which significantly promotes the accuracy and efficiency of numerical flight. On the other hand, intelligent numerical flight could be a breakthrough in the field of scramjet engine design. The artificial intelligence technique and massive data from multiple sources provide a solid foundation for building a high-fidelity digital twin of the scramjet engine. With the help of the digital twin, the full trajectory flight testing of a scramjet engine can be conducted in the virtual space, which may drastically speed up the design iteration. Moreover, the digital twin can run in parallel with the real scramjet engine during a ground test or a flight test. According to the experimental data, the digital twin rapidly generates multi-physics solutions of the scramjet engine. The status of the scramjet engine can be evaluated in a real-time manner. To facilitate the development of intelligent numerical flight, more effort should be spent on developing AI models that are both data-driven and physics informed, an intelligent software platform that resolves multiple physics fields, and a high-fidelity digital twin of the scramjet engine.

2022, 54(3): 588-600. doi: 10.6052/0459-1879-21-397

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DESIGN OF MULTISTAGE COMPRESSION WAVERIDER BASED ON THE LOCAL-TURNING OSCULATING CONES METHOD

Zheng Xiaogang, Zhu Chengxiang, You Yancheng

Due to its outstanding aerodynamic performance, the waverider is considered as one of the effective ways to break through the current “lift-to-drag barrier”. It has become the research hotspot for hypersonic vehicle design. However, the traditional waverider is widely generated by a single shock wave, which cause the lack of compression efficiency. To solve the aforementioned problem, a multistage compression waverider design method for non-axisymmetric shock waves, has been proposed in this paper based the local-turning osculating cones method. With the help of multiple non-axisymmetric shock waves, the pre-compression effect of the waverider forebody is able to be fully exerted, and new design ideas for the design of hypersonic vehicles under complicated geometric conditions can be provided as well. The double compression waverider with two elliptic cone shock waves was specified as an example to introduce the new proposed method in detail. Three types of double elliptic cone compression waveriders with different eccentricities were designed under the same conditions. The numerical results demonstrate that under the inviscid conditions, the wall pressure obtained by the proposed design method is basically consistent with the CFD result. The maximum error of the corresponding aerodynamic parameters is about 0.3%, which proves the reliability of this new proposed design method. Compared with the double conical compression waverider, the waverider with eccentricity larger than one has better compression performance and lift-drag characteristics, but lower total pressure recovery coefficient and volumetric efficiency. In contrast, the double compression waverider with eccentricity less than one has larger total pressure recovery coefficient and volumetric efficiency, but lower compression performance and lift-to-drag characteristics. Additionally, the shock structure of the waverider under the viscous conditions remain essentially the same, and the corresponding two elliptic cone shock waves basically intersect at the bottom section. It reveals that this kind of waverider still owns wonderful “wave-ride” characteristics when the viscosity is taken into consideration.

2022, 54(3): 601-611. doi: 10.6052/0459-1879-21-357

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INVESTIGATION OF FLOW CHARACTERISTICS AND FLAME STABILIZATION IN AN ETHYLENE-FUELED SCRAMJET COMBUSTOR

Shi Wen, Tian Ye, Guo Mingming, Liu Yuan, Zhang Chenlin, Zhong Fuyu, Le Jialing

To achieve successful ignition and stable combustion in an ethylene-fueled scramjet, the hydrogen is applied as the pilot fuel to ignite ethylene at low flight Mach numbers. Flow characteristics, flame propagation characteristics and combustion stability have been investigated in a scramjet combustor via various strategies of fuel injections, such as fuel injection of single hydrogen, single ethylene and combinations of fuels. The inflow conditions are Mach number of 2.0, a total temperature of 953 K and a total pressure of 0.82 MPa at the entrance of scramjet combustor. Multiple non-contact optical measurements, including the schlieren, CH luminosity images and OH-PLIF, have been applied to detect flow structures and flame propagation along with the 10 kHz pressure transducers monitoring the pressure of the centerline on the top wall of combustor. The results indicate that without fuel injection, the internal flow of scramjet would oscillate at a dominant frequency of approximately 450 Hz. With fuel injection, the oscillation is suppressed when the fuel is injected upstream of the cavity and there is no effect on the internal flow when the fuel is injected downstream of cavity step. OH-PLIF images reveal that the flame of pilot hydrogen is unstable. The flame mainly locates in the middle and posterior of cavity when the pilot hydrogen is injected upstream of cavity and OH radicals repeatedly gather and disperse in the middle of cavity. The flame of hydrogen cracks in shear layer and there is no chemical reaction around cavity ramp, when the pilot hydrogen is injected downstream of cavity step. Meanwhile, the combustion is also unstable with combined injection strategy. When the pilot hydrogen is closed, the flame transfers from the middle and posterior of cavity to the cavity ramp, then stabilizes, indicating that the combustion instability of combined injection strategy derives from the combustion instability of pilot hydrogen.

2022, 54(3): 612-621. doi: 10.6052/0459-1879-21-353

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FLOW FIELD AND COMBUSTION CHARACTERISTICS ANALYSIS OF SRAMJET UNDER Ma12 FLIGHT CONDITION

He Can, Xing Jianwen, Ouyang Hao, Deng Weixin, Xiao Baoguo

The compressibility correction of the calculation method is conducted to improve the simulation ability of high Mach number scramjet. The three-dimensional numerical simulations of the scramjet at Mach 12 flight condition are carried out. The shock system, parameters characteristics and combustion performance of the scramjet are analyzed. The results indicate that the position and intensity of shock wave calculated by the modified method are consistent with the experimental data. The modified method shows better ability in shock wave and high Ma scramjet simulation. The shock wave and reflected shock systems are formed in the scramjet. The basic structure of shock system through the flow path will not be changed by the combustion. The angle and number of shock waves will increase with the increase of equivalence ratio. The temperature rise and pressure rise induced by the intersection of shock waves are conducive to combustion heat release. The increase of wall heat flux caused by shock waves gradually reduces with the weakening of reflected shock waves along the flow direction. Most of the combustion is non-premixed in the flow field. The average temperature in the combustor exceeds 2500 K so that the efficiency of H₂-O₂ combustion deteriorates and the complete combustion product H₂O decreases. The available effective heat release increases in the forepart of the combustor and decreases in the rear section. O atom recombination mainly occurs in the nozzle. The chemical reactions are mainly conducted in the forepart of the combustor at the equivalence ratio of 0.5, while the reaction distance is longer at the equivalence ratio of 1.0. The difference between combustor drags of the two cases is small and the increase of total thrust coefficient is mainly contributed by the nozzle. Combustion will lead to the reduction of the combustor friction and whole model friction, while the changes of inlet friction and nozzle friction are not obvious.

2022, 54(3): 622-632. doi: 10.6052/0459-1879-21-496

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THE THEORETICAL METHOD TO INCREASE THE THRUST OF HIGH MACH NUMBER SCRAMJETS

Han Xin, Liu Yunfeng, Zhang Zijian, Zhang Wenshuo, Ma Kaifu

The oblique detonation engines and shock-induced combustion ramjets have been proved to be practicable for high flight Mach number air-breathing engines in recent years. However, whether the oblique detonation engines and shock-induced combustion ramjets have enough thrust or not is unknown yet. In this paper, the combustion characteristics and propulsive performance of scramjets are discussed theoretically. Firstly, the mechanism of engine unstart of scramjets is discussed from the point of view of shock/shock interaction and deflagration-to-detonation transition. The results show that engine unstart process is very similar to the deflagration-to-detonation transition process. In the combustor of scramjets, the maximum velocity of the deflagration wave is very close to the detonation velocity. Therefore, the C-J detonation velocity is defined as the stable operation boundary of scramjets. Secondly, the formula of thrust produced by the divergent nozzle is put forth and key parameters influencing thrust are obtained. According to the thrust formula, supersonic combustion is beneficial for increasing the thrust. The main way to increase the thrust is to increase the pressure of combustion products. The propulsive performance of scramjets is theoretically analyzed by using C-J detonation theory, which is the critical condition when the engine is thermally choked. Finally, the theoretical method to increase the thrust is discussed. For high flight Mach number scramjets Ma ≥ 12, the velocity in the isolator is much faster than the C-J detonation velocity in the combustor and the problem of engine unstart disappears. Therefore, extra fuel and oxidizer can be injected into the combustor to increase the thrust further as long as the shock wave generated by the high pressure combustion products is slower than the air velocity in the isolator. The theoretical results agree well with the existing experimental and numerical results, which can be used as a baseline for the development of high Mach number scramjets.

2022, 54(3): 633-643. doi: 10.6052/0459-1879-21-350

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NUMERICAL SIMULATION OF OLDROYD-B VISCOELASTIC DROPLET COLLISION

Guan Xinyan, Fu Qingfei, Liu Hu, Yang Lijun

The complex rheological properties make the atomization process of gel propellant difficult, which restricts its development. The addition of polymer gelling agent makes the gel propellant viscoelastic, so that viscoelastic droplets will be generated during atomization. Therefore, in order to further understand the atomization mechanism of gel propellant and improve the atomization performance of gel propellant , to carry out numerical simulation research on the collision behavior of viscoelastic droplets. Aiming at the droplet collision phenomenon in the atomization process of gel propellant, considering the viscoelastic effect of fluid, volume of fluid (VOF), adaptive mesh refinement (AMR), and log-conformation transformation were adopted. The Oldroyd-B constitutive model was used to describe the viscoelasticity of droplets, and a direct numerical simulation of the collision process of two viscoelastic droplets of equal volume was carried out. The head-on collision process of viscoelastic droplets is mainly concerned. The effect of relaxation time, viscosity ratio, Weber number on the head-on collision behavior was studied, the energy evolution of the droplet coalescence process under different physical properties was also calculated. In addition, the droplet collision behavior under different eccentricity was observed. By changing the collision velocity, the collision results of merging and bouncing are obtained. The results show that increasing the relaxation time is beneficial to the extrusion and retraction process of the coalesced droplet, and delaying the process of the droplet deformation, this is different from the results obtained by Newtonian fluids. Increasing the viscosity ratio can hinder the oscillation behavior of the coalesced droplet. As the eccentricity of the collision increases, extension and rotation occur, and the extensional distance increases with the degree of eccentricity. When the eccentricity decreases, the kinetic energy dissipation rate increases, and more kinetic energy is dissipated.

2022, 54(3): 644-652. doi: 10.6052/0459-1879-22-020

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SINGLE DEGREE-OF-FREEDOM FLOW-INDUCED VIBRATION OF AN ELASTICALLY-SUPPORTED HARBOR SEAL WHISKER MODEL: AN EXPERIMENTAL STUDY

Song Liqun, Ji Chunning, Yuan Dekui, Xu Dong, Zhang Xiaona, Wei Yuhan, Yin Tong

Depending on its wave-shaped whiskers, the harbor seal can identify the vortex characteristics of the wake flow of its prey and trace them. Thus, it is of important scientific significance and practical value to investigate the identification mechanisms of the harbor seal whiskers. In this study, a 1:30 scaled experimental whisker model was fabricated based on the geometric parameters of a harbor seal whisker, and the one degree-of-freedom flow-induced vibrations of a single whisker model and an array of whisker models in uniform flow and wake flow were investigated. The correlation of the vibration responses of the whisker model and the vortex characteristics was analyzed. It was found that owing to the wavy shape of the whisker model, the vibration of the whisker model at the zero angle-of-attack is significantly suppressed in uniform flow, and the whisker model has a very low vibration amplitude in a certain range of the reduced velocity. However, when the angle-of-attack is relatively large ($\alpha \geqslant {30^ \circ }$), the vibration amplitude is significantly augmented. In the wake flow of a stationary circular cylinder, large-amplitude vibrations of the whisker model happen in a certain range of distance from the cylinder, and the vibration frequency locks on the vortex-shedding frequency of the wake flow. Different to the single-frequency vibration of the whisker model in uniform flow, the vibration frequency of the whisker model in wake flow shows a two-peak mode. In wake flow, the vibration amplitude of the whisker model is significantly affected by flow conditions, but the vibration frequency of the whisker model is relatively stable. In uniform flow and wake flow, the vibration amplitude and frequency of an array of whisker models are similar to those of a single whisker model, except at several reduced velocities, which indicates that the interference between the whisker models in a whisker array is not significant.

2022, 54(3): 653-668. doi: 10.6052/0459-1879-21-384

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MICRO IMPULSE MEASUREMENT METHOD AND EXPERIMENTAL RESEARCH BASED ON TORSION PENDULUM

Yang Chao, He Jianwu, Zhang Chu, Kang Qi, Duan Li

Satellite platforms with ultra-high microgravity levels play an important role in space gravitational wave detection and Earth’s gravitational field measurement. Pulsed micro-thrusters can help microgravity satellites achieve posture adjustment and control. The magnitude of the micro impulse is one of the important indicators to evaluate the propulsion performance of the pulsed micro thruster. There are two commonly used methods for measuring micro impulse based on torsion pendulum. The first method is to calculate the impulse based on the maximum angular displacement of the torsion pendulum after a single impulse element acts on the undamped torsion pendulum momentarily. The second method is to calculate the impulse based on the average angular displacement of the torsion pendulum rotation after the same high fixed frequency pulse is applied to the damped torsion pendulum. In order to realize the micro-impulse measurement of the pulse micro-thruster on the ground, the existing sub-micron-level thrust measurement system based on the torsion pendulum was used to conduct experimental research. We use the standard electrostatic force generated by the electrostatic comb to calibrate the existing torsion pendulum thrust measurement system, measure the torsion angular displacement through the capacitive displacement sensor, and obtain the relationship between thrust and angular displacement, as well as other torsion pendulum system parameters; Then, according to the two impulse measurement methods, the electromagnetic solenoid and the permanent magnet are used to generate the instantaneous magnetic force and the fixed frequency magnetic force to act on the torsion pendulum to study the micro impulse measurement capability of the thrust measurement system. The experimental results show that the impulse measurement range of the thrust measurement system is from 0.05 μN·s to 220 μN·s, and the impulse measurement resolution can reach 0.02 μN·s; Compared with method 1, using method 2 to measure micro-impulse can expand the impulse measurement range and improve the impulse resolution ability.

2022, 54(3): 669-677. doi: 10.6052/0459-1879-21-191

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NUMERICAL STUDY ON WATER ENTRY PROCESS OF SUPERCAVITATING PROJECTILE BY CONSIDERING BIDIRECTIONAL FLUID STRUCTURE INTERACTION EFFECT

Hao Changle, Dang Jianjun, Chen Changsheng, Huang Chuang

Supercavitating projectiles travel underwater at high speed and long distances through the supercavitation drag reduction technology, which is an effective means to counter close-range underwater threats. In order to expand the defense range and increase the lethality, the supercavitating projectile has a high launch speed. The high-speed supercavitating projectile is subjected to a great impact load during water entry process, and a significant structural deformation occurs on the projectile. There is an interaction between the structural deformation and the flow field. Resultantly, the regular simulation research method based on the rigid body assumption is no longer applicable. To study the structural deformation of the high-speed supercavitating projectile and its influence on the hydrodynamic characteristics, a bidirectional fluid-structurer interaction simulation model of the high-speed projectile is established by coupling the fluid dynamics solver and the structural dynamics solver. The accuracy of the numerical method to calculate the supercavitation flow field and the fluid structure interaction are validated by comparing with the published results. Numerical simulation investigations on the supercavitation flow field and the structural deformation characteristics of the high-speed projectile during water entry at different initial angles of attack are carried out with the bidirectional fluid-structure interaction method. By comparing the calculation results of the fluid-structure interaction model and the rigid body model, the influence of structural bending deformation of the supercavitating projectile on its hydrodynamic load is obtained. Research results show that the fluid-structure interaction effect has a significant influence on the supercavity and hydrodynamic load. When considering the fluid-structure interaction effect, there is positive feedback between the hydrodynamic load and the bending deformation of the supercavitating projectiles; the stress, strain and the hydrodynamic load of high-speed supercavitating projectiles increase significantly with the increase of the initial angle of attack. The structure of the projectile is safe when the initial velocity is 1400 m/s and the initial angle of attack is below 2°.

2022, 54(3): 678-687. doi: 10.6052/0459-1879-21-510

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RESEARCH ON INTELLIGENT IDENTIFICATION ALGORITHMS FOR SHORT-TERM AERODYNAMICS OF HYPERSONIC WIND TUNNELS

Wang Qinchao, Li Shichao, Gao Hongli, Ma Guilin, Wu Guang, Duan Zhiqin

Pulse combustion wind tunnel force measurement is an important step in the research and development process of hypersonic aircraft, and with the development of hypersonic aircraft technology, large-scale and heavy-load aircraft test models has become the trend of hypersonic pulse combustion wind force test. During the effective test time of several hundred milliseconds, large-scale force measurement system stiffness weakened and other issues will seriously lead to poor aerodynamic identification accuracy. The large-scale measurement model poses a challenge to the accurate aerodynamic identification of the short-term pulse combustion wind tunnel. To solve this problem, a new intelligent aerodynamic identification algorithm based on traditional signal processing combined with deep learning is presented in this paper. The algorithm framework is mainly divided into two stages for signal processing: (1) signal decomposition, (2) data training. In the signal decomposition stage, the original data is decomposed into different modal sub-signals through variational modal decomposition (VMD). In the training stage, the effective features in the remaining datasets containing characteristic sub-signals are extracted by deep learning model, and the real aerodynamic signals are obtained. In addition, in order to enhance the robustness and applicability of the algorithm, different optimization methods are used to optimize the hyperparameters in the algorithm at different stages of the algorithm framework to obtain the optimal parameter combination. This algorithm model has obtained relatively ideal results in terms of aerodynamic recognition accuracy and anti-interference. Finally, the algorithm is validated on a suspended force test bench, and the results show that the algorithm model can effectively identify and filter out the interference components that are difficult to eliminate by the traditional methods brought by the large-scale model. Finally, the algorithm is successfully applied to the large scale model force measurement system of pulse combustion wind tunnel. Accuracy of aerodynamic identification of large-scale model force measurement system is effectively improved.

2022, 54(3): 688-696. doi: 10.6052/0459-1879-21-484

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THREE-DIMENSIONAL NUMERICAL ANALYSIS OF SPONTANEOUS LARGE-DEFORMATION OF PLATE-LIKE STRUCTURES

Zhang Mohan, Li Luxian

Plate-like structures in nature, such as flowers and leaves, tend to have a curvaceous shape as a result of a large deformation process. Similar phenomena can also be observed in plate-like structures in various engineering fields. Here, plate-like structure signifies a special three-dimensional structure that is the stack of identical planar structures and the thickness size is hence far less than the planar ones. Stimulated by the incompatible deformation due to factors such as growth and external stimuli, a plate-like structure possesses internal stresses. In this paper, a spontaneous deformation behavior produced by the existing internal stresses is studied. To this end, the strain energy of the plate-like structure is firstly decomposed into two contents, that is, the stretch-like deformation energy and the remaining deformation energy, respectively. To evaluate these two different energies, we suggest a numerical approach based on a three-dimensional (3D) large-deformation finite element analysis (FEA). A condition for buckling instability of such a plate-like structure is then proposed to be the crossover point at which the remaining deformation energy goes beyond the stretch-like deformation energy from none. With this condition, the concept of threshold thickness is further introduced in order to characterize the crossover point, which is verified by comparing the values from the FEA with those from the classical plate theory for a simply-supported square plate. Finally, several spontaneous large-deformation problems modeled by typical power-law thermal expansions are studied through a 3D large-deformation FEA, and the effects of incompatible factors such as the magnitude and the power index on internal stress fields and the threshold thickness are also examined. Our present work shows that the large deformation of plate-like structures is a spontaneous process such that the remaining deformation energy increases from zero to a value larger than the stretch-like deformation energy. In particular, the 3D large-deformation FEA is an effective method to solve the buckling instability of plate-like structures stimulated by a complex internal stress field.

2022, 54(3): 697-706. doi: 10.6052/0459-1879-21-593

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DILATANCY ANALYSIS OF GRANULAR MATERIALS BASED ON MESOSCOPIC TOPOLOGICAL EVOLUTIONS

Liu Jiaying, Zhou Wei, Ji Xiang, Wei Gang, Yuan Siying, Li Xinjun

Dilatancy is one of the most important characteristics for frictional granular materials, especially for geo materials. It is widely accepted that the mechanism of dilatancy could be related to the evolution of the internal topological structure within the granular system. Based on meso-structural data of granular assemblies, features of the internal topological structure evolution in the granular system can be captured, which could further help to correlate the mesoscopic topological evolution and the macroscopic deformation properties including dilatancy. In this paper, the discrete element method (DEM) was used to conduct biaxial tests on dense, medium-dense and loose frictional granular materials, respectively. According to those DEM data from macroscopic to microscopic levels, the topological mechanism for dilatancy of granular materials are investigated in terms of network parameters (e.g., coordination number and clustering coefficient) and deformation features of 3 types of mesoscopic structures induced by topological exchanges. The results show that the significant strain softening and dilatancy occur for dense granular samples under biaxial loading, which is related to the topological and geometric changes of mesoscopic structures. The medium dense sample also exhibits dilatancy features but the degree is less evident, and the loose sample only shows contractancy and strain hardening during the shearing process. The contact network could be tessellated to force loop structures with the polygon shapes, and further classified into new, lost and constant categories by considering the topological exchanges. The anisotropy and composition evolutions of three groups of force loop structures are different, and loops with larger size could exhibit higher geometrical anisotropy. Under deviatoric loads, the new loop structures are easily related to higher dilatancy, and the dilatancy mechanism of the overall granular system could be influenced by the comprehensive effects of the topological evolutions of new meso structures and geometrical evolutions of constant meso structures.

2022, 54(3): 707-718. doi: 10.6052/0459-1879-21-521

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MULTISCALE SIMULATION OF MECHANICAL DEFORMATION EFFECTS ON CRITICAL PROPERTIES OF Nb₃Sn HIGH FIELD COMPOSITE SUPERCONDUCTORS

Yang Xujia, He Yuxin, Zhang Xin, Yang Xiaomin, Wang Tao, Qiao Li

A15 superconducting Nb₃Sn has shown great promise for applications in the international thermonuclear experimental reactor, and high energy physics. In these high field applications, the stress/strain arises from the cool-down and operation process of the superconducting magnet, inducing the performance degradation of the Nb₃Sn cable-in-conduit conductors, which is a critical issue in the superconductivity applications and developments. Due to the complex multi-scale structure of Nb₃Sn composite, the electromechanical coupling responses at different scales are intrinsically interrelated. On the basis of the micro-meso-macro frame analysis, this paper intends to study the effects of strain induced variations of the characteristic parameters of material microstructure on the superconducting properties of Nb₃Sn and establish the constitutive model which accounts for the multiscale coupling in strained Nb₃Sn. A framework for micro-to-macro transitions for multi-scale analysis of multifilamentary superconducting composites is developed. Using this model, we respectively predict the critical properties degradation responses of Nb₃Sn polycrystal under hydrostatic pressure and Nb₃Sn composite under axial loading, the predicted results are in qualitative agreement with the experimental observations.. This study reveals the multiscale coupling mechanism of electromechanical effects in Nb₃Sn high-field superconducting composite.With the aid of the study, the multiscale features in electromechanical coupling behavior in Nb based A15-type compounds are identified. The study will promote the material engineering application process, and the results of which are promising to engineer optimized large-scale superconducting high magnetic field systems. It is helpful to improve the understanding and description of the strain sensitivity of Nb₃Sn, and to provide a solid theoretical support for the manufacture of high-field superconducting magnets. The developed simulation model provides a basis for the detailed description of strain effects on the superconducting properties of Nb₃Sn. Furthermore, the developed multiscale model lays foundation for understanding the empirical relation given by the experiment and opens the way for the parameterization of the strain effects on the superconducting Nb₃Sn.

2022, 54(3): 719-731. doi: 10.6052/0459-1879-21-491

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5/6 DOFS CB SHELL ELEMENTS BASED ON THE LOCAL FRAME OF SE(3) GROUP

Zhang Teng, Liu Cheng, Zhang Zhijuan, Liu Shaokui

The modeling method based on the local frame of Lie group (LFLG) for flexible multibody dynamics can naturally eliminate the geometric nonlinearity of the overall rigid motion, so that the generalized internal forces and inertial forces as well as their Jacobian matrices are invariant under the arbitrary rigid body motion. In this paper, a novel 5 Dofs continuum-based (CB) shell element based on the LFLG is proposed by integrating the idea of the LFLG and the CB shell theory. Compared with the geometrically exact shell element based on the LFLG, the proposed shell element greatly simplifies the complexity caused by the interpolation, and the discretized strain tensors naturally satisfy the objectivity. At the same time, the finite element discretization and variational operations are commutative, which further simplifies the computation of the generalized internal forces and their Jacobian matrices. To deal with the composite structure conveniently, the relationship between the mid-surface motion and the drilling Dofs is established by the polar decomposition of the mid-surface deformation gradient tensor on the basis of the 5 Dofs CB shell element. Then, a 6 Dofs CB shell element based on the LFLG is proposed. To improve the convergence accuracy of the proposed elements, the two-field Hellinger-Reissner variational principle and the assumed natural strain (ANS) method are used to alleviate the in-plane and transverse shear locking, respectively. Several static examples are presented to verify the convergence accuracy of the 6 Dofs CB shell element. A dynamic example is presented to demonstrate that the 6 Dofs CB shell element can eliminate the geometric nonlinearity of the overall rigid motion.

2022, 54(3): 746-761. doi: 10.6052/0459-1879-21-584

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REACTIONLESS TERMINAL SLIDING MODE CONTROL OF SPACE ROBOT WITH JOINT DEAD-ZONE

Zhang Zhihao, Yu Xiaoyan

As the present reaction null space planning for the incomplete kinematic properties of the space manipulator during the general operation involvesn either the impact of joint dead-zones on the system nor the relationship between the manipulator and the target to be grasped, it can not ensure the effectiveness of the tracking control in the presence of joint dead-zone. In this paper, the study of reaction null space planning and control in the final period before intercepting a target of a free-floating three-link space manipulator with joint dead-zone is focused. First, the dynamic model of a free-floating three-link space manipulator with joint dead-zone is established by the second Lagrange equation, in which the position and attitude of the carrier are uncontrolled. Then, the reaction null space mathematical model of the free-floating three-link space manipulator with joint dead-zone is derived, and the vector norm constraint algorithm of the reaction null space is studied. Furthermore, a nonsingular fast terminal sliding mode control algorithm with anti-interference and high convergence is proposed, in which it combines the double power reaching rate of variable coefficient with the nonsingular fast terminal sliding mode surface to improve the convergence speed and interference immunity. The dead-zone of the joint may reduce the control accuracy of the space robot system. In order to eliminate the influence of the free-floating three-link space manipulator’s joint dead-zone, an adaptive dead-zone compensator is designed. This compensator can approach the upper bound of dead-zone characteristics by self-adaptive control to eliminate the effect of the joint dead-zone on the system and to ensure the effectiveness of the tracking control. Finally, based on the Lyapunov function method the stability of the system is proved, and numerical simulation is carried out. The simulation results show the desired reactionless trajectories are tracked with the base’s attitude reactionless and the effectiveness of the proposed planning and control algorithm is demonstrated.

2022, 54(3): 778-786. doi: 10.6052/0459-1879-21-494

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NEIGHBORING PERIODIC MOTION AND ITS IDENTIFICATION FOR SPUR GEAR PAIR WITH SHORT-PERIOD ERRORS

Liu Pengfei, Zhu Lingyun, Gou Xiangfeng, Shi Jianfei, Jin Guoguang

The pitch deviation and other errors as the short-period error in spur gear pair lead to complex periodic motion which affects the transmission stationarity of gear systems. The complex periodic motion is defined as the neighboring periodic motion. It is identified by using the multi-time scale Poincaré mapping sections. A nonlinear dynamics model of the spur gear pair with pitch deviation is introduced in order to study the neighboring periodic motion of the gear pair. Backlash, time-varying contact ratio and other parameters are considered. The dynamics model is numerically calculated by the variable step 4-order Runge-Kutta method. The proposed identification method is used to analyze the neighboring periodic motion of the system under different parameters. The information of attractors and the basin of attraction in the state plane can be obtained by the improved cell mapping theory. The multi-stable neighboring periodic motions of the system under the variation of torque and meshing frequency are investigated by typical nonlinear dynamics analysis methods, such as multi-initial values bifurcation diagrams, phase diagrams, Poincaré maps, basin of attraction and bifurcation dendrogram. Results show that the short-period error in the spur gear pair leads to the complex periodic motion of the system. In the micro time scale, Poincaré mapping points of the system show the form of point clusters. The number of point clusters and actual motion period of the system are the number of Poincaré mapping points in the macro time scale. The short-period error leads to the increase of the number of attractors in the micro time scale which makes the motion transition process of the system more complex. The reasonable range of parameters and initial values can improve the transmission stationarity of the gear pair. The identification and analysis methods provide a theoretical basis for the study of the neighboring periodic motion in nonlinear systems.

2022, 54(3): 787-800. doi: 10.6052/0459-1879-21-556

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A RECURRENT CONVOLUTIONAL NEURAL NETWORK SURROGATE MODEL FOR DYNAMIC MESHFREE ANALYSIS

Chen Jian, Wang Dongdong, Liu Yuxiang, Chen Jun

In addition to the complexity of meshfree approximation that needs extra computational effort, the dynamic meshfree analysis requires the computation of dynamic response recursively at each time step, which significantly lowers the overall computational efficiency. In this work, the intrinsic relationships are established between meshfree discrete data and machine learning training samples, and recursive computational procedure of dynamic meshfree analysis and temporal sequence information transmission mode of recurrent convolution neural networks. With the aid of these intrinsic links, a recurrent convolutional neural network structure design method for meshfree discretization is proposed, which is then used to develop a recurrent convolution neural network surrogate model for dynamic meshfree analysis. This surrogate model takes full advantage of the flexibility of meshfree discretization. Meanwhile, meshfree analysis can provide versatile and highly accurate numerical samples, which then enhance the generality and applicability of the proposed surrogate model for dynamic meshfree analysis. Besides, the unique historical memory characteristics of the recurrent module embedded in the recurrent convolution neural network surrogate model enable an effective processing of the sequence information, and then accelerate the dynamic meshfree computational procedure with accuracy guarantee. The efficiency and accuracy of the recurrent convolution neural network surrogate model for dynamic meshfree analysis are validated through representative examples.

2022, 54(3): 732-745. doi: 10.6052/0459-1879-21-565

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BENCHMARK SOLUTIONS OF RANDOM VIBRATION RESPONSES FOR MODERATELY THICK CYLINDRICAL SHELLS UNDER STATIONARY/NONSTATIONARY EXCITATIONS

Huo Hui, Chen Guohai, Wang Wenpei, Yang Dixiong

Cylindrical shell structures are frequently adopted in aerospace, ship, automobile and other engineering fields. Due to the complexity of service environments, cylindrical shells are unavoidably subjected to various random excitations, resulting in stochastic dynamic responses. Considering the moderately thick cylindrical shells with transverse shear deformation and moment of inertia effect, the pseudo excitation method is extended to the continuum structure, and the exact benchmark solutions of root mean squares of responses under various random excitations are efficiently obtained. Firstly, the exactly analytical natural frequencies and modal functions of moderately thick cylindrical shells with shear diaphragm boundary conditions are given. Then, according to the random excitation form, by using pseudo excitation method and mode superposition technique, the analytical and exact frequencies and modal functions and the constructed pseudo excitation are introduced into random vibration analysis. The power spectral density functions of stochastic responses of moderately thick cylindrical shells under stationary and nonstationary excitations are derived analytically, and the corresponding root mean squares are achieved via integration. The integral computation involves integration operations in the spatial, frequency and time domains. Analytical integration can obtain the closed-form exact solutions, while the difficulty and efficiency increase with increasing number of participated modes. To take full advantage of the merit of matrix operation of PEM, the discrete analytical method (DAM), with analytical spatial integral as well as numerical integral in the frequency and time domains, is proposed to obtain the exact stochastic responses of moderately thick cylindrical shells in closed and open forms. This procedure can ensure the accuracy of spatial integral, and efficiently obtain the exact distribution of random response, which provides the benchmark solutions for other numerical methods. Comparing the results with those of ABAQUS software and Monte Carlo simulation with as well as related literature illustrates the high accuracy and efficiency of the proposed DAM. Finally, the significant effects of ratio of thickness to radius, load distribution form, and time-modulated function on stochastic dynamic responses of cylindrical shell are revealed.

2022, 54(3): 762-776. doi: 10.6052/0459-1879-21-538

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MESOSCOPIC NUMERICAL SIMULATION ON DYNAMIC BIAXIAL TENSION-COMPRESSION FAILURE CRITERION OF CONCRETE

Jin Liu, Li Jian, Yu Wenxuan, Du Xiuli

Concrete structures in normal service are often subject to complex stresses and are inevitably subject to the sporadic dynamic loads. The failure criterion is the foundation for the study of mechanical properties of concrete under complex loads. Limited by the test equipment and other conditions, the existing dynamic biaxial tension-compression strength failure criterion has a complex form, lacks of higher strain rate and lateral stress ratio range and has not yet considered the coupling effect of strain rate and lateral stress ratio comprehensively. In order to further propose a more applicable and accurate failure criterion of concrete dynamic biaxial tension-compression strength, a 3D random numerical model of cubic concrete is established on a mesoscale in this study. The dynamic tension-compression failure behavior of concrete materials under different strain rates and lateral stress ratios are simulated. The influence of strain rate and lateral stress ratio on the failure modes and dynamic biaxial strengths of concrete are discussed respectively. The failure criterion of dynamic biaxial tension-compression strength of concrete is put forward. The simulation results indicated that with the increase of strain rate and lateral stress ratio, the internal damage of concrete specimen increases and the number of cracks increase. Under dynamic biaxial tension-compression loads, with the increasing strain rate, the dynamic spindle compressive strength and dynamic lateral tensile strength of concrete increase gradually. With the increasing lateral stress ratio, the dynamic spindle compressive strength decreases while the dynamic lateral tensile strength increases. The dynamic biaxial Tension-Compression failure criterion of concrete proposed in this paper has the advantages of wide range of applicable strain rate and lateral stress ratio, concise form, no longer restricted by physical test conditions and considering the coupling effect of strain rate and lateral stress ratio, etc. The established failure criterion of concrete has been verified from different angles.

2022, 54(3): 800-809. doi: 10.6052/0459-1879-21-563

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FLUID FEATURE ANALYSIS BASED ON TIME HISTORY DEEP LEARNING

Zhan Qingliang, Bai Chunjin, Ge Yaojun

Flow feature analysis is an important research area of fluid mechanics. Traditional feature analysis methods, which mainly based on magnitude of the flow parameter, is greatly affected by the parameter form and subjective threshold. In this paper, a new flow field feature analysis method is proposed based on flow time history deep learning, and flow time history feature extraction analysis framework based on autoencoder is established; The unsupervised training method is used to recognize the hidden complex features in the flow time history signal, and realize the low-dimensional representation and feature analysis of the complex time history features in the flow field. The flow field feature analysis of cylinder with Re_D = 200 was carried out, and the low-dimensional characterization of periodic laminar flow field data was obtained. Flow feature distribution was directly obtained according to the latent code, and results obtained proved to be reasonable. The proposed method can provide new methods and references for solving problems such as flow field feature extraction, flow feature analysis and flow feature representation.

2022, 54(3): 822-828. doi: 10.6052/0459-1879-21-524

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NUMERICAL RESEARCH ON INTERIOR BALLISTICS OF THE TWO-STAGE LIGHT GAS GUN DRIVEN BY GASEOUS DETONATION

Shang Jiahao, Xing Haoyun, Wang Qiu, Li Jinping, Zhao Wei, Wei Bingchen

Two-stage light gas gun is one of the most widely used equipment in hypervelocity projectile launching technology, which plays an important role in a various of engineering fields such as hypersonic aerodynamics and material mechanical in high velocity impact. A two-stage light gas gun driven by gaseous detonation was designed and constructed at Institute of Mechanics, Chinese Academy of Sciences, which eliminated the disadvantages like deficient driving capability of high-pressure gas and low maintainability of gunpower. A one-quasi-dimensional numerical method was used to investigate the interior ballistic process and launching performance of detonation driving mode and pressure gas mode, the effect that the change of ignition tube position has on light gas gun and the effect of various parameters on launching performance. The result showed that the launching performance of detonation driving was superior to that of high-pressure gas driving. The contrast of forward and backward detonation driving mode showed that the change of detonation driving mode had slight influence on launching performance, but the strength design of the whole equipment had to take into consideration the driving mode. The research of various loading parameters showed the increase of detonation tube filling pressure enhanced the launching performance, beside, piston mass had complex effect on launching velocity. But the design index of light gas gun and the material performance of piston and projectile restrict the adjusting range of loading parameters. Due to the limitation, the parameters should adjust together in order to optimize the launching performance during the practical process.

2022, 54(3): 811-822. doi: 10.6052/0459-1879-21-437

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2022 Vol. 54, No. 3

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