力学学报

RESEARCH PROGRESS ON HIGH-MACH-NUMBER SCRAMJET ENGINE TECHNOLOGIES

Yue Lianjie, Zhang Xu, Zhang Qifan, Chen Keting, Li Jinping, Chen Hao, Yao Wei, Zhong Fengquan, Li Fei, Wang Chun, Chen Hong

Hypersonic airbreathing flights are highly valued in both the fields of space transportation and national aerospace safety, and the scramjet engines are pivotal propulsion devices for these flights. The scramjet engines for flight Mach numbers within the range between 4.0 and 7.0 have been extensively studied and well developed in recent years, and the extension to the scramjet engines for higher flight Mach numbers within the range between 8.0 and 10.0 or even higher are sure to be a competing focus for near-space competitions in the following decades. The current paper analyzes and summarizes the recent research advances of scramjet engines with flight Mach numbers within the range between 8.0 and 10.0+ . First of all, the key scientific problems and technologies of the higher Mach number scramjet engines are highlighted, including the high-temperature dissociation and thermochemical nonequilibrium effects, mixing and combustion enhancement technologies in ultra-high-speed flows, the matching of hypersonic combustion and inflow compression and the operating modes, the high-enthalpy low Reynolds number boundary-layer flows and the boundary-layer flow control methods, the thermal protection technologies of high-enthalpy low-density combustion inflows, and the ground test facility technologies for high-Mach number scramjet engines, respectively. Second, the experimental apparatus related to high-enthalpy shock tunnels and the shock tunnel driving technologies and typical ground and flight experiments of the high-Mach number scramjet engines home and aboard in recent years are introduced. Third, research advances including overall performance analyses of thrusts and thermal protections, the prominent high-enthalpy dissociation and thermochemical nonequilibrium effects in high-Mach-number scramjet engines, and mixing and combustion enhancement technologies in the ultra-high-speed flows are reviewed, so as to assess the feasibilities of high-Mach-number scramjet engines, and to discuss the features of engines’ key technologies. Finally, the summary is presented and several suggestions are proposed for further studies of the higher Mach number scramjet engines.

2022, 54(2): 263-288. doi: 10.6052/0459-1879-21-547

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PREDICTION OF REYNOLDS STRESS ANISOTROPIC TENSOR BY NEURAL NETWORK WITHIN WIDE SPEED RANGE

Ren Haijie, Yuan Xianxu, Chen Jianqiang, Sun Dong, Zhu Linyang, Xiang Xinghao

Tensor based neural network (TBNN) is constructed based on Pope’s effective viscosity hypothesis, and it’s used to produces a mapping from the mean strain rate tensor, mean rotation rate tensor calculated by Reynolds averaged Navier-Stokes (RANS) to the high resolution Reynolds stress anisotropy tensor. The high resolution data is used to train TBNN, then TBNN will give prediction results of Reynolds stress anisotropic tensor from the RANS result. The prediction of TBNN will be compared with high resolution numerical simulation and wind tunnel results to evaluate the prediction ability of TBNN. This work expands the predictive ability of TBNN from the low speed domain to hypersonic conditions. Small sample training is performed on low speed channel flow, NACA0012 and hypersonic boundary layer and the prediction accuracy is satisfactory. In addition, the TBNN trained with channel flow accurately predicts the boundary layer of the low-speed flat plate, which verifies the generalization ability of the model. For the extrapolation channel flow at low-speed, TBNN can predict the Reynolds stress anisotropy tensor well in the range of y⁺ > 5, the error between direct numerical simulation (DNS), experiment and TBNN is inside 10%. Although the prediction accuracy of the low-speed airfoil is slightly lower than that of the channel flow, the cloud images predicted in the key area have significant improvement compared with RANS. For the hypersonic boundary layer, TBNN shows good predictive ability in the boundary layer, and the error between TBNN and DNS is also within 10% in the range of y⁺ > 5. Although Pope’s constitutive law is proposed for most incompressible flows, TBNN can still predict the Reynolds stress anisotropy tensor under hypersonic conditions. The predictive ability of this method in a wide speed range is confirmed and the generalization ability of the model has also been verified.

2022, 54(2): 347-358. doi: 10.6052/0459-1879-21-518

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MOMENTUM DECOMPOSITION AND ENERGY TRANSFER CHARACTERISTICS OF OPEN CAVITY FLOW

Han Shuaibin, Luo Yong, Li Hu, Wu Conghai, Zhang Shuhai

Cavity structure is extensively employed in the aerospace vehicle components and ground vehicles. The complex characteristics of the flow and acoustic fields is one of the key problems that must be considered in the design of the associated practical engineering. In the cavity flow, the hydro-acoustic interaction plays an important role in the self-sustained oscillation. Accurate identification and decomposition of the hydrodynamic and acoustic mode is the key to improving the understanding of the hydro-acoustic interaction and the associated energy transfer mechanism. In this paper, the two-dimensional Navier-Stokes equation is directly solved to conduct numerical simulation of open cavity flow with inflow Mach number of 0.8 to obtain the high-order accuracy unsteady flow field. Adopting Doak’s momentum potential theory, the momentum of the flow is decomposed into three parts of the hydrodynamic vortical component, the hydrodynamic entropic component and the acoustic component. The physical properties and the associated energy transfer characteristics of each component are analyzed. The results show that the hydrodynamic vortical and entropic components exist only in the near field, which are convected downstream with the main flow at the speed of shear layer convection. The spatial distribution of the vortical and entropic components are concentrated in the shear layer and resembles each other. The hydrodynamic energy carried by the vortical component is transported from the inside of the shear layer to the outside of the shear layer and to the rear-end of the cavity while the energy carried by the entropic component is continuously transported to the shear layer and then dissipated there. The acoustic component exists in both the near and far field, and the spatial distribution of the acoustic component exhibits a classical compression-divergence pattern. The acoustic energy is radiated from the rear-end of the cavity and propagates to the upstream and the far field at the speed of sound.

2022, 54(2): 359-368. doi: 10.6052/0459-1879-21-569

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INSTABILITY ANALYSIS OF INVISCID DROPLET SUBJECT TO VERTICAL VIBRATION

Liu Dehua, Li Yikai

Faraday instability on the droplet surface due to external periodic oscillation is widely used in ultrasonic atomization, spraying processing and other applications. The analysis of Faraday instability is of great significance to the study of the surface dynamics of vibrating droplet. In this paper, the Faraday instability problem is extended from radial vibration to vertical vibration, and the instability of inviscid droplet surface wave in vertical vibration is studied. The vertical vibration makes the droplet momentum equation a Mathieu equation with spatial correlation term and time periodic coefficient. The dispersion relations between the growth rate, the mode number and flow parameters of vertically vibrating droplet surface waves are obtained by using Floquet theory. The neutral stable boundary of vertically vibrating inviscid droplet under Faraday instability is obtained by solving an eigenvalue problem of surface deformation modes. The difference of droplet neutral stability boundary between vertical vibration and radial vibration is compared. The influence of elevation angle θ on the neutral instability boundary is obtained by the approximate calculation under the assumption of large mode number. The results show that the difference between vertically vibrating droplets and radially vibrating droplets is obvious. The differences are as follows: in the case of harmonic, the unstable region of droplet surface wave becomes smaller, and the droplet will be more difficult to destabilize under external excitation; In the case of subharmonic, the neutral stable boundaries of the droplet surface wave coincide, and the droplet unstable wave will not appear subharmonic mode. Besides, for vertically vibrating droplets, the larger the elevation angle θ, the smaller the neutral instability region, and the easier it is for the droplet surface to remain stable under external excitation.

2022, 54(2): 369-378. doi: 10.6052/0459-1879-21-483

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STUDY ON THE DROPLET SIZE OF LIQUID JET IN A COAXIAL AIRFLOW

Guo Limei, Lü Ming, Ning Zhi

In view of the lack of prediction model of droplet size of the liquid jet in a coaxial airflow, combined with the linear stability theory of the liquid jet, the mathematical expression of droplet size of the liquid jet in a coaxial airflow based on the critical modulus is established in this paper. On this basis, the effects of surrounding gas twisting (the surrounding airflow has both axial and circumferential motion) and fluid physical parameters (gas compressibility, liquid viscosity, gas liquid density ratio, and surface tension) on droplet size of liquid let are studied respectively. The research results show that: (1) both the axial ejection and coaxial rotation of the surrounding airflow will lead to the droplet size increasing first and then decreasing. When there is only rotation motion of the surrounding airflow, the surrounding airflow rotation has little effect on the droplet size of liquid jet under the same critical modulus. (2) Within the range of parameters studied in this paper, the droplet size of liquid jet decreases with the increasing of the surrounding gas compressibility and the gas liquid density ratio, and the droplet size of liquid jet increases with the increasing of the liquid viscosity and surface tension. The effect of gas compressibility on droplet size of liquid jet is stronger when the surrounding airflow rotates coaxially, while the effect of liquid viscosity on droplet size of liquid jet is more significant when the surrounding airflow ejects coaxially. The research results have certain theoretical significance and engineering application value for the droplet size prediction of liquid jet in a coaxial airflow.

2022, 54(2): 405-413. doi: 10.6052/0459-1879-21-375

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GENERALIZED FINITE DIFFERENCE METHOD FOR BENDING AND MODAL ANALYSIS OF FUNCTIONALLY GRADED CARBON NANOTUBE-REINFORCED COMPOSITE PLATES

Li Yudong, Fu Zhuojia, Tang Zhuochao

Composite plates have always received much attention. In view of excellent mechanical properties of functionally graded carbon nanotube-reinforced composite (FG-CNTRC), it is particularly important to study the mechanical behavior of FG-CNTRC plates by scholars. Based on the first order shear deformation theory, a novel meshless collocation method, generalized finite difference method (GFDM), is applied to the bending and modal analysis of FG-CNTRC plates. Based on the multivariate Taylor series expansion and the moving least-squares theory, the partial derivatives of the underdetermined displacements at a certain node can be represented by a linear combination of the displacements of its neighboring nodes in the GFDM implementation. The proposed GFDM not only has the advantages of avoiding meshing generation and numerical integration, but also provides the sparse system, which overcomes the highly ill-conditioned assembled matrix issue existed in most of meshless collocation methods. Hence the method has advantages of simple-form, easy-to-use and -implement, which is generally used in a variety of scientific and engineering problems. The numerical model for the bending and modal analysis of FG-CNTRC plates in the GFDM implementation is firstly proposed. Then the computational validity and convergence of the GFDM are analysed by some benchmark cases. Finally, the influences of different distributional types, volume fraction, rotational angle of CNTs, inclination angle of plate, thickness to span ratio, length-width ratio and boundary conditions on the structural bending and modal are investigated in details.

2022, 54(2): 414-424. doi: 10.6052/0459-1879-21-439

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EFFECT COMPARISON OF GLOBALIZATION BLEND BASED-METHODS FOR STESS TOPOLOGY OPTIMIZATION

Peng Xirong, Sui Yunkang, Ye Hongling, Tie Jun

Because of the local characteristics of element stresses, the corresponding structural topology optimization model has too many constraints. Although a globalization method can dramatically reduce the number of constraints in the optimization model, there exist a few elements whose stresses exceeds the allowable stress of materials in the optimized topology. For stress topology optimization problems of continuum structures, this paper aims to overcome the problems of stress over-limit and to improve the solve efficiency. The multiplier method and sequence quadratic programming (SQP) method are proposed. And an aggregation model, called as the m-model in the globalization blend method (named by the globalization-aggregation method), is solved by the two proposed methods. And the solve efficiency of the two proposed methods are compared with the moving asymptote method (MMA) which solves a series of first-order approximated model. On this basis, the SQP method, the most effective method of solving m-model, is adopted to blend with globalization method to form the globalization blend method, which is adopted to solve the structural volume minimization model under stress constraints (named by the s-model). The globalization blend method is compared with the previous globalization method. The results show that: (1) among the three methods of solving the m-model, the solve efficiency of the multiplier method and SQP method is much higher than that of the MMA method. And the solve efficiency of the SQP method is slightly higher than that of the multiplier method. (2) Although the solve efficiency of the globalization blend method is similar to that of the globalization method, the globalization blend method completely avoids the phenomenon of element stress over-limit. In the condition that all stress constraints are satisfied, the resulting optimized topology obtained by the globalization blend method is lighter than that of the globalization method. The globalization blend method has stronger ability to find the optimal solution.

2022, 54(2): 459-470. doi: 10.6052/0459-1879-21-499

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EXTENSION OF MULTI-SCALE METHOD AND ITS APPLICATION TO NONLINEAR VISCOELASTIC SYSTEM

Fan Shutong, Shen Yongjun

Viscoelastic materials have broad application prospects in aviation, machinery, civil engineering and other fields, and the nonlinear Zener model with 1.5 degrees of freedom can better describe their characteristics. Therefore, it is of great significance to study the extension and application of multi-scale method. Based on the traditional multi-scale method, the multi-scale method is extended to approximate the analytical solution of the nonlinear odd-order differential equation, and the dynamic problems of the nonlinear odd-order system are solved. Taking the nonlinear Zener model as an example, its dynamic behavior and stability condition under harmonic excitation are analyzed. Firstly, the approximate analytical solution of the nonlinear Zener model is obtained through the extended multi-scale method, and the analytical solution is verified by the numerical method. The results are in good agreement, which proves the correctness of the extended method. Then, the amplitude-frequency equation and phase-frequency equation of steady-state response are derived from the analytical solution, and it is found that there are multi-valued characteristics in a certain frequency range for weakly damped systems. Moreover, the stability condition of steady-state periodic solutions is obtained based on Lyapunov first method, and the system stability is analyzed by using this condition. Finally, the effects of nonlinear term, external excitation and the stiffness and damping coefficients of Maxwell elements on the dynamic behavior and system stability are analyzed by simulation. It is found that whether the stiffness is hardened or softened, the resonance amplitude can be gradually reduced and the multi-solution region can be expanded. The amplitude of external excitation has little influence on the backbone curve of amplitude frequency characteristics, but has a great influence on the shape of amplitude frequency curve. With the increase of the stiffness coefficient of Maxwell element, the resonance amplitude increases slightly. The increase of the damping of Maxwell element can reduce the resonance amplitude and the multi-solution region, and finally the multi-solution phenomenon can disappear. These results are of great significance to the study on dynamic characteristics of nonlinear viscoelastic systems in the future.

2022, 54(2): 495-502. doi: 10.6052/0459-1879-21-487

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FRACTURING DEGREE AND PREDICTION OF PERFORATION CLUSTER SPACING FOR EFFICIENT EXPLOITATION OF SHALE GAS

Wang Tao, Liu Zhanli, Zhuang Zhuo

The fracturing property of shale reservoirs is a key factor affecting shale gas production. Based on fracture mechanics theory, taking the shear failure of rock bedding weak plane under high confining pressure as the main research object, the concept of fracturing degree is proposed according to the ratio between tensile strength of rock and shear strength of bedding plane. The dimensionless qualitative curve is given, which covers the comprehensive geological and engineering factors of brittle mineral content, viscosity-dominated and toughness-dominated fracture tip fluid pressure and perforation cluster distribution spacing. Then, a new dimensionless parameter is proposed to characterize the fracturing degree of shale under high confining pressure, which can be used as a reference index for engineering. In this paper, fracture mechanics theory is combined with hydraulic fracturing for efficient shale gas production, which has mechanics theoretical significance and engineering application prospects.

2022, 54(2): 517-525. doi: 10.6052/0459-1879-21-197

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NUMERICAL INVESTIGATION ON SAFE STAGE SEPARATION PROBLEM OF A TSTO MODEL AT MACH 7

Wang Yue, Wang Yunpeng, Xue Xiaopeng, Jiang Zonglin

Stage separation of two-stage-to-orbit (TSTO) vehicle under hypersonic inflow conditions will produce complex unsteady aerodynamic interference between the two stages, which directly increases the risk of TSTO separation. This complex aerodynamic interference is accompanied by the combined action of shock wave and boundary layer interaction, horseshoe vortex, shock wave, and wake interference between the two stages. In the current study, the complex models of the TSTO booster and orbiter are simplified into two three-dimensional (3-D) wedges. Based on the overset dynamic grid technology, the Navier-Stokes equations coupled with six-degree-of-freedom rigid body dynamic equations are solved to simulate and analyze the stage separation process, to explore the flow characteristics and physical mechanism of stage separation. In the numerical analysis, static and dynamic numerical simulations were carried out for the three-dimensional flowfield of TSTO under different orbiter’s lifting angles (β), and the flow patterns and interference characteristics with varying β were analyzed and discussed in detail. Combined with the flowfield structure and wall pressure distribution, as well as separated flow, the mechanism of the aerodynamic interference between the two stages during the TSTO separation, were clarified, and the effects of the lifting angle condition of the orbiter on the safe separation for the current TSTO model was discussed. The numerical results show that the interstage aerodynamic interference increases with the increase of the lifting angle of the orbiter, and decreases with the increase of the interstage clearance during stage separation. Before the release of the orbiter, the interstage aerodynamic interference and 3-D separated flow topology become more complex with the increase of β, and separation area increases, as well as the number of critical points. In the process of stage separation, the variation amplitude of the aerodynamic characteristics of both stages increases with the increase of β, and the separation time decreases. Moreover, the lifting angle of the orbiter is 6° ~ 8° would be conducive to the safe stage separation for the current TSTO model.

2022, 54(2): 526-542. doi: 10.6052/0459-1879-21-423

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Preface of theme articles on microgravity fluid physic

Duan Li

2022, 54(2): 289-290. doi: 10.6052/0459-1879-22-070

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INSTABILITY IN THE SOLUTAL-THERMOCAPILLARY LIQUID LAYER WITH TWO FREE SURFACE

Zhao Chengzhuo, Hu Kaixin

Solute-thermocapillary convection is a flow driven by a surface tension gradient caused by uneven concentration and temperature distribution at the fluid interface. It mainly appears in microgravity environment space or small-scale flow where the surface tension dominates, such as crystal growth, microfluidic, alloy pouring and solidification, organic thin liquid film growth, etc. The stability of this flow is of great significance of these applications. In the present work, the convective instability in the solutal-thermocapillary liquid layer with two free surfaces is examined by linear stability analysis. The relation between the critical Marangoni number and the Prandtl numbers (Pr) is obtained at different capillary ratio (η). The critical modes of solute-thermocapillary flow and pure thermocapillary flow are quite different. The former are downstream streamwise wave, upstream streamwise wave, spanwise stationary mode and upstream oblique waves, but the latter are upstream oblique waves and upstream streamwise wave. When Pr is larger, the flow stability will be weaker when Pr increases. At other parameters, the flow stability will be stronger when Pr increases. In the middle or low Pr, solute capillary force makes the flow more unstabler; at high Pr, solute capillary force may make the flow more stable. Flow stability does not change monotonously from η. In most cases, the distributions of perturbation concentration field and temperature field are similar. The energy analysis shows the main energy source of perturbation kinetic energy is the surface capillary force, but the work done by solute capillary force and thermal capillary force may be either positive or negative.

2022, 54(2): 291-300. doi: 10.6052/0459-1879-21-148

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EFFECT OF ASPECT RATIO ON THERMOCAPILLARY CONVECTION INSTABILITY OF GaAs MELT LIQUID BRIDGE

Zhou You, Zeng Zhong, Liu Hao, Zhang Liangqi

In this paper, we explore the effect of aspect ratio on the instability of thermocapillary convection in GaAs melt (Pr = 0.068) liquid bridge by using the linear stability analysis in the context of spectral element method. Besides, we provide physical insight on the underlying instability mechanism via energy analysis. Differing from the cases of typical low Prandtl number (such as Pr = 0.011) and typical high Prandtl number (such as Pr > 1), which correspond to stationary instability and oscillatory instability respectively, the instability of the thermocapillary convection of GaAs melt (Pr = 0.068) is of note due to its noticeable dependence on the aspect ratio (As). In particular, we observe two instability modes for the flow considered here with the variation of the aspect ratio. When the aspect ratio As ranges from 0.4 to 1.18, thermocapillary flow transits from two-dimensional axisymmetric steady convection to three-dimensional periodic oscillatory convection (oscillatory instability). While for 1.20 ≤ As ≤ 2.5, the stationary instability appears and the two-dimensional axisymmetric steady flow transits to three-dimensional steady flow. As for the instability mechanism of the thermocapillary convection, the liquid bridge of high Prandtl number is characterized by thermocapillary mechanism, while the case of low Prandtl number features the hydrodynamic inertia mechanism. Based on disturbance energy analysis, it is shown that the instability of the present thermocapillary convection arises from the combined action of the hydrodynamic inertial instability and thermocapillary instability, in which the hydrodynamic inertial instability mechanism is dominant, and the specific proportion of these two contributions varies with the aspect ratio.

2022, 54(2): 301-315. doi: 10.6052/0459-1879-21-227

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MECHANISTIC STUDY OF LASER-DRIVEN DROPLET MIGRATION

Ye Zhijun, Duan Li, Kang Qi

Droplet thermocapillary migration is a typical scientific problem in microgravity fluid science, and the study of microgravity droplet dynamics not only has the theoretical significance of fluid mechanics, but also has important practical value. A two-dimensional axisymmetric laser-driven droplet migration model was established. The laser-driven droplet migration process in microgravity environment is studied by simulation calculations, and the effects of droplet diameter and mother liquor parameters on droplet migration speed and behavior are investigated. Firstly, the migration of the droplets was studied when the mother liquor and the droplets have smaller laser coefficients and the initial positions of the droplets are different; then the migration of the droplets was studied the mother liquor has a smaller laser absorption coefficient and the droplets have a larger laser absorption coefficient and the ratios of the diameter to the width of the mother liquor are different. Simulation results show that when the absorption coefficients of both mother liquor and droplet for laser are small, the direction of droplet migration is mainly influenced by the initial position of the droplet. When the absorption coefficient of the mother liquor to the laser is small and the absorption coefficient of the droplet to the laser is large, the droplet will move toward the laser. The initial position of the droplet has less influence on the migration direction, but the ratio of the droplet diameter to the width of the mother liquor will affect the droplet migration behavior. By comparing with the YGB theory, the simulation results are consistent with the trend of the theoretical results. The physical mechanism of laser-driven droplet migration is studied, the mechanism of interfacial tension effect is explored, the law of laser-driven droplet migration is obtained, and the driving control method for droplets is explored.

2022, 54(2): 316-325. doi: 10.6052/0459-1879-21-522

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CAPILLARY RISE OF LIQUID BETWEEN PLATES WITH A CERTAIN ANGLE UNDER MICROGRAVITY

Chen Shangtong, Wu Di, Wang Jia, Duan Li, Kang Qi

In space, because the gravity basically disappears and the secondary forces such as surface tension force play a major role, fluid behavior is quite different from that of the ground. Therefore, it is necessary to deeply explore the laws and characteristics of fluid behavior in microgravity environment. The plate-type tank uses plate-type components to manage the fluid in microgravity environment, so as to provide the thruster with gas-free propellant, which is of great significance for the precise attitude control and orbit adjustment of the spacecraft. Plate-type components often include plates with a certain included angle, such as liquid storage blades. The capillary rise of liquid between plates with a certain angle under microgravity is explored in this paper. The influences of the dynamic contact angle between the liquid and the plates wall, the pressure loss caused by convection, the viscous resistance, and the curved liquid surface in the reservoir are all considered. A second order differential equation of the capillary-driven flow is derived, which can be solved with forth-order Runge−Kutta method. By considering two dominant forces at the same time, the flow can be divided into three regions, and approximate equations of climbing height in different regions are obtained. Six kinds of numerical models are created, three kinds of silicone oil is chonsen and Volume of Fluid(VOF) method is used to carry out numerical simulation. Numerical results are in good agreement with theoretical results, which verifies theoretical analysis. This research can be theoretical basis for plate tanks’ design and fluid management in space.

2022, 54(2): 326-335. doi: 10.6052/0459-1879-21-261

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DEM SIMULATION OF ORDERING OF CUBES WITH ROUNDED CORNERS BY ROTATION DRIVEN

Zhang Qi, Qiao Ting, Ji Shunying, Hou Meiying

The study of the orderly packing of macroscopic particle can not only provide a research model for the self-assembly of microscopic particles in thermal systems but also help to imcrease the packing fraction of granular materials in industry. Experimental results showed that cubic particles with rounded corners subjected to alternating rotation of the cylinder would achieve orderly packing. In order to investigate the internal structure evolution and mechanism of the orderly packing process of cubic particles with rounded corners in rotational cylinders, the cubic particles with rounded corners are constructed by the superquadric surface equation. Numerical simulations are carried out to investigate the orderly packing process of cubic particles with rounded corners in the rotation cylinder based on discrete element method. The simulation reproduces the transition of cubic particles from the random packing state to the ordered dense packing state in the experiment, and gives the variation of packing fraction and cubatic order parameter with the increase of rotation number under different motion. The results show that the packing fraction and the cubatic order parameter to increase gradually with the increase of the number of rotation until a stable value. The orderly packing process of the system starts from the external particles to the inner particles gradually. By regulating the angular displacement of the cylinder, it is found that the characteristic number of alternating rotation for the particles to complete the orderly packing process is inversely proportional to the angular displacement of the cylinder. If the angular displacement is too low, the system will only form a structure with clusters of particles whose sides are parallel to the horizontal plane and clusters of particles whose diagonal of the face parallel to gravity. It is also found that cubic particles in a sub-gravity environment can also achieve orderly packing through the alternating rotation of the cylinder. The reduction of gravitational acceleration inhibits the transition from disordered to ordered packing of cubic particles.

2022, 54(2): 336-346. doi: 10.6052/0459-1879-21-341

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SUBSONIC UNSTEADY AERODYNAMIC CHARACTERISTICS ON SLENDER REVOLUTIONARY BODY AT EXTRA-WIDE ANGLE-OF-ATTACK

Wang Fangjian, Wang Hongwei, Li Xiaohui, Dong Lei, Huang Zhan, Chen Lan

As the main means of attack in modern air combat, air-to-air missile requires higher maneuverability and agility than target aircraft. What’s more, in the face of the new generation of aircraft, the new air-to-air missile must possess all-round attack capability, especially to the threat from the rear target. Therefore, advanced and efficient maneuver methods such as higher turning rate and larger maneuver envelope are needed. In order to ensure the successful completion of efficient maneuvering, the new advanced air-to-air missile is required to have flight and maneuvering control capability within the range of extra-wide angle-of-attack (α = 0° ~ 180°). In the past, most of the observation and research on unsteady flow with extra-wide large angle-of-attack were concentrated in the range α = 40° ~ 60°, and the maximum angle-of-attack was less than 90°. In this paper, numerical simulation (delayed detached eddy simulation, DDES) and wind tunnel test in FD-12 (oil-flow visualization experiment) are used to study the transient flow characteristics and unsteady characteristics in Mach number 0.6 at the angle-of-attack of α = 0° ~ 180° of the slender revolutionary body. At the angle-of-attack of α = 0° ~ 90°, the flow on the leeward side of the slender revolutionary body is mainly dominated by concentrated vortices caused by cylindrical segments, which are characterized by asymmetric vortice, unsteady vortice and vortex shedding. At the angle-of-attack of α = 90° ~ 180°, the bottom of the slender revolutionary body is forward, which leads to a large separation area, and many small-scale eddy interaction in the separation area. As the flow gradually develops backward along the axial direction, the leeward flow is gradually dominated by asymmetric vortex flow. The frequency St number of surface fluctuating pressure induced by asymmetric vortices ranges from 0.19 to 0.33, and the frequency St number of surface fluctuating pressure induced by bottom separation region ranges from 1.55 to 1.64.

2022, 54(2): 379-395. doi: 10.6052/0459-1879-21-415

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EXPERIMENTAL STUDY OF GALLIUM DROPLET IMPACTING ON SOLID WALL UNDER THE STRONG MAGNETIC FIELD

Meng Xu, Wang Zenghui, Cai Zhiyang, Zhang Dengke

In the electromagnetic metallurgy processing of materials and the magnetic confinement fusion device, the impact process of metal droplet under the influence of magnetic field and substrate temperature shows complex dynamic characteristics. The spread and rebound characteristics of liquid gallium droplet impacting isothermal and sub-cooled substrate under horizontal magnetic field were studied experimentally. High speed camera is used to capture the change of droplet profile during impact. The maximum spreading factor under different magnetic field strength, impact velocities and substrate temperatures, the maximum height in rebound process, the radius and velocity of secondary droplet are obtained through image processing. The impact velocity increases from 0.45 m/s to 1.8 m/s, and the magnetic field intensity increases from 0 T to 1.6 T. The substrate temperature is 30 °C, −20 °C and −10 °C. The effects of magnetic field and substrate temperature on droplet spread and rebound are analyzed. The experimental results show that the variation of the maximum spreading factor of droplet impacting on the isothermal and sub-cooled substrate is in good agreement with the theoretical prediction. Under the condition that the droplet impacts the isothermal wall, different rebound phenomena occur under different We numbers. The magnetic field inhibits the droplet spreading parallel to the magnetic field and the generation of secondary droplet, while the magnetic field has a elongation effect on the droplet spreading parallel to the magnetic field direction in the rebound process. When the droplet impacts the sub-cooled substrate, within a certain range of We number, the secondary droplet separation will also happen. At this time, the velocity of secondary droplets is smaller. The enhancement of magnetic field and the increase of We number will weaken the oscillation of the droplet in the height direction, accelerating the solidification process.

2022, 54(2): 396-404. doi: 10.6052/0459-1879-21-513

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DYNAMIC MECHANICAL BEHAVIOR OF ADDITIVE MANUFACTURING TC4 ALLOY

Xi Yu, Zhang Qiang, Zhang Xinyue, Liu Xiaochuan, Guo Yazhou

Additive manufacturing TC4 alloy is a kind of metal material with excellent mechanical properties and process properties. It has been widely used in the aerospace field. In recent years, the effect of stress state on the deformation and failure behavior of metal materials has been widely concerned in the research field of plastic mechanics. However, most of these studies were performed considering quasi-static state only, but few of them took into account the high strain rates. In this paper, the effects of stress state on the deformation and failure behavior of additive manufacturing TC4 alloy were systematically investigated. Starting from the basic mechanical properties of additive manufacturing TC4 alloy, the stress triaxiality $ \eta $ and Lode angle parameters $ \overline \theta $ are used to characterize the stress state. Using electronic universal testing machine, high-speed hydraulic servo testing machine and split Hopkinson bar, combined with digital image correlation analysis, the mechanical properties of additive manufacturing TC4 alloy under different strain rates and different stress states were tested. The deformation and failure characteristics of the material under various working conditions are obtained. In order to obtain the internal stress state history parameters and strain field of the sample, this article passes ABAQUS performs numerical simulation to obtain the stress state history parameters and failure strain at the maximum strain of the specimen. Based on the results of experimental testing and simulation analysis, the traditional MMC failure model was revised, and the failure model of material was established that fully considered the strain rate, stress triaxiality and Lode angle effect. At the same time, a Johnson-Cook failure model considering the effects of stress triaxiality η and strain rate is established. A high-speed impact experiment was carried out on the additive manufacturing TC4 alloy plate, and numerical simulation was carried out for the experiment, which verified the usability of the established constitutive model and failure model.

2022, 54(2): 425-444. doi: 10.6052/0459-1879-21-418

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ANALYTICAL APPROACH TO THE VISCOELASTO-PLASTIC MECHANICAL RESPONSE OF DEEP SOFT ROCK TUNNEL CONSIDRING THE ROCKBOLT REINFORCEMENT EFFECT

Zhao Nannan, Shao Zhushan, Zheng Xiaomeng, Wu Kui, Qin Su

The surrounding rock of deep soft rock tunnel shows significant plastic softening and dilatancy characteristics. The ignorance of the coupling influences of these two characteristics in current studies leads to the inaccurate prediction results of tunnel deformation. In order to solve the problem, a viscoelasto-plastic calculation model of deep soft rock tunnel is established, based on the Kelvin-Voigt model and Mohr-Coulomb strength criterion. In this model, the plastic softening and dilatancy of surrounding rock are considered and the restriction effect of tunnel face is introduced as well. Furthermore, a mechanical model of rockbolt-reinforced surrounding rock is established by using the equivalent stiffness method, which takes the rockbolt reinforcement into account. Considering the relationship between plastic radius of surrounding rock and bolt length, analytical solutions for tunnel responses under the six conditions are provided. In addition, the reliability and effectiveness of the theoretical derivation are well validated by comparing numerical and analytical results. Finally, the reinforcement effect of rockbolt is discussed based on the analytical solution and a comprehensive parametric investigation is carried out, including the installation time and stiffness of rockbolt and tunnel excavation rate. Results indicate that without considering the rockbolt reinforcement effect, the excavation rate only poses the influence on the development law of early deformation of tunnel, and its influence on the final tunnel displacement can be ignored. The tunnel deformation will be greatly underestimated without considering the plastic deformation of surrounding rock, resulting in a large gap between the predicted and actual results. When the excavation rate is large, the rockbolt should be installed as earlier as possible, to ensure that the rockbolt can play an effective role inmiting surrounding rock deformation. There exists a sub-linear relationship between bolt stiffness and tunnel displacement, and the increase of rockbolt stiffness can prolong the time required for surrounding rock entering plastic deformation. The results of this paper can provide useful guidance for the similar projects.

2022, 54(2): 445-458. doi: 10.6052/0459-1879-21-447

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STUDY ON NONLINEAR COUPLED VIBRATIONS OF DAMAGED SUSPENDED CABLES WITH SYMMETRY-BREAKING

Zhao Yaobing, Zheng Panpan, Chen Lincong, Kang Houjun

Symmetry is one of the five aesthetic characteristics in the vibration theory, but the symmetry-breaking is also inevitable. This paper takes a common vulnerable structure in engineering-the suspended cable-as an example, and the influences of symmetry-breaking on the planar coupled vibrations have been investigated when the asymmetric damage is occurred. Firstly, the in-plane nonlinear dynamical model of damaged suspended cable has been established, and the nonlinear infinite dimensional differential equations have been obtained by using the Galerkin method. The method of multiple scales has been adopted to obtain the modulation equations of the nonlinear systems’ in-plane coupled vibrations. The resonant curves of undamaged and damaged suspended cables including the first nine modes have been obtained by using the numerical methods, and the stabilities of solutions have also been determined. The largest Lyapunov exponent has been calculated to determine the system’s chaotic motions. The numerical results show that the classical parabolic curves have been often adopted to simulate the suspended cables’ static configurations. However, when the asymmetric damage occurs, the piecewise functions should be used to accurately describe the damaged cables’ static configurations. The symmetry-breaking causes crossover points between two natural frequencies of suspended cables to turn into veering points, and the symmetric/anti-symmetric mode shapes before damage are changed into the asymmetric ones after damaged. The nonlinear interaction coefficients are changed significantly, resulting in significant changes in internal resonant responses. When the excitation is directly applied to the higher-order modes, the single-mode solutions and internal resonant ones are obvious in the undamaged system, while the damaged system does not present the obvious single-mode solutions. The bifurcations and chaos of the damaged system are also changed obviously, and some chaotic motions around the period-doubling bifurcation are observed as to the damaged system.

2022, 54(2): 471-481. doi: 10.6052/0459-1879-21-542

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CODIMENSION-2 BIFURCATION ANALYSIS OF MACROSCOPIC TRAFFIC FLOW MODEL

Fan Shuangshuang, Liu Danyang, Duan Lixia

The traffic flow characteristics are an important factor in mixed traffic flow modeling. The bifurcation in the traffic flow model is one of the issues related to the complex traffic phenomena. The bifurcation phenomenon of traffic flow models involves complex dynamic characteristics and is rarely studied. Therefore, an optimal velocity model is proposed to study the effects of driver’s memory on driving behavior. Based on the optimal velocity continuous traffic flow model with memory, we analyze and predict complex traffic phenomena by using nonlinear dynamics. The conditions for the existence of LP bifurcation are derived. We numerically obtain codim-1 Hopf (H) bifurcation, LP bifurcation and homoclinic (HC) bifurcation, and codim-2 generalized Hopf (GH) bifurcation, cusp (CP) bifurcation and Bogdanov-Takens (BT) bifurcation. According to the characteristics of two-parameter bifurcation regions, the influence of memory parameters on the one-parameter bifurcation structures is studied, and the influence of different bifurcation structures on traffic flow is analyzed. The phase plane is used to describe the variational characteristics of the trajectories near the equilibrium point. Selecting the Hopf bifurcation and saddle-node bifurcation as the starting point of density evolution, we describe the uniform flow, stable and unstable crowded flow and stop-and-go phenomena. Further, these outcomes can improve the understanding of go-and-stop waves and local clusters observed on highways. The results show that the driver’s memory plays an important role in the stability of the traffic flow. Dynamic behavior can well explain the complex phenomenon of congested traffic. The source of traffic congestion can be better understood by considering the impact of codim-2 bifurcation. The results in this paper can provide some theoretical methods for the suppress traffic congestion.

2022, 54(2): 482-494. doi: 10.6052/0459-1879-21-509

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EFFICIENT NUMERICAL METHOD FOR ORBIT DYNAMIC FUNCTIONS WITH INITIAL VALUE AND TWO-POINT BOUNDARY-VALUE CONSTRAINTS

Zhang Zhe, Dai Honghua, Feng Haoyang, Wang Xuechuan, Yue Xiaokui

It is a fundamental problem to efficiently solve the orbit dynamic systems occurred in the process of orbit design, space capture, deep space exploration and many other aerospace engineering missions. The traditional numerical integration methods, which are based on finite difference method, can hardly meet the requirement of low-latency computation in aerospace missions for their strict needs of small integration step size. In this paper, the high performance local collocation feedback iteration (LCFI) method is presented for orbit dynamic functions with initial value and two-point boundary-value constraints. LCFI does not need to estimate Jacobian matrix during the calculation process for that it is based on Picard iteration method, and it is able to save convergence time via combining error-feedback strategy. Besides, time domain collocation method is used to transfer the symbolic operations into algebraic operations, thus make the iterative formula of LCFI concise. In addition, LCFI is able to solve Lambert’s problem efficiently via combining quasi linearization method and superposition method, and its parameters can be adaptively adjusted via an adopted ph mesh refinement method to better play its ability of calculating with large step size. The validity of LCFI is verified via solving the orbit propagation problem, the perturbed Lambert’s problem, and the transfer trajectory in the circular restricted three-body model. Simulation results show that the computational efficiency of LCFI is higher than 1.5 times that of quasi linearization local variational iteration method, and the parameter adjustment method based on ph mesh refinement method is able to further increase the calculation speed of LCFI by more than 6 times.

2022, 54(2): 503-516. doi: 10.6052/0459-1879-21-336

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2022 Vol. 54, No. 2

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