力学学报

RESEARCH PROGRESS ON ORBITAL DYNAMICS ABOUT THE BINARY ASTEROID SYSTEM EXPLORATION

Wang Yue, Fu Tao, Zhang Ruikang

The binary asteroid systems, consisting of two asteroids orbiting each other through the mutual gravitation, are of great significance for studying the origin of our solar system and the evolution of planetary systems, as well as for the planetary defense. Therefore, binary asteroid systems have become a hot research topic of the planetary science and astrodynamics, and several in situ exploration missions will be launched in the near future. The unique configurations and complex dynamical environments of binary asteroid systems have brought about new challenges for orbital dynamics and the mission design. The studies devoted to the new challenges have greatly promoted the development of basic theories of orbital mechanics. In this paper, we review and summarize the research progress on orbital dynamics about the binary asteroid system exploration. We first introduce the background and significance of the binary asteroid system exploration, and briefly review the formation theory and the research status of orbital dynamics about binary asteroid systems. Secondly, the modeling methods for the irregular gravity field and the mutual gravitational potential of binary asteroid systems are introduced. The coupled orbit-attitude motion of two members of the binary system, i.e., the full two-body problem, including the equilibrium configurations and their stability, is also discussed. Thirdly, the concept and applications of the restricted full three-body problem about binary asteroid systems are introduced, including the libration points and associated periodic orbits, general periodic orbits, transfer orbits, and station-keeping strategies. In the fourth part, the secular orbital evolution around one member of a binary asteroid system is focused from viewpoint of the perturbed two-body problem. The perturbation theory and applications in planetary systems are illustrated first, and then some recent research on the semi-analytical orbital model and stability analysis around the primary of a binary asteroid system is presented. Fifthly, the orbital dynamics analyses and the mission design for near future exploration missions, considering mission objectives and practical constraints, are summarized. Finally, based on the current research progress, challenges and prospects of orbital dynamics and related technologies about the binary asteroid system exploration are discussed.

2022, 54(5): 1155-1185. doi: 10.6052/0459-1879-21-637

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BIFURCATION ANALYSIS OF THERMOCAPILLARY CONVECTION BASED ON POD-GALERKIN REDUCED-ORDER METHOD

Guo Ziyi, Zhao Jianfu, Li Kai, Hu Wenrui

Thermocapillary convection is driven by surface tension gradient caused by temperature gradient. The flow is subject to nonlinear interactions between convection and heat transfer, so it has complex transition behaviors. It is significant to investigate the flow bifurcation phenomenon as parameters in the governing equations change. The POD-Galerkin reduced-order method is a fast fluid computational method, based on proper orthogonal decomposition and Galerkin projection. The numerical bifurcation method finds the parameter values at which bifurcation exists by computing the asymptotic flow states and bifurcation points directly. In order to tackle flow transition problems in a more efficient way, a combination of direct numerical simulation, POD-Galerkin reduced-order method and numerical bifurcation method is applied to investigate the transition behavior of thermocapillary convection in a liquid layer. The POD reduced-order model of thermocapillary convection in a 2D cavity under different volume ratios is established and its bifurcation diagram is obtained by numerical bifurcation method. The validity of such a model for Reynolds numbers and volume ratios that are different from those for which the model is derived is studied and the possibility of modelling thermocapillary flow in a simple geometry over a range of flow parameters is assessed. Compared with the results obtained by direct numerical simulation, the accuracy and robustness of the low-order model are verified. The results show that the reduced-order model reflects qualitatively similar flow characteristics to the original high-order system, and quantitively, the relative error of frequency of periodic solution of the reduced-order model to that obtained by the direct numerical simulation is around 5%. Hence, the feasibility of the POD-Galerkin reduced-order method on thermocapillary convection is confirmed.

2022, 54(5): 1186-1198. doi: 10.6052/0459-1879-21-642

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VORTEX DYNAMICS OF A PITCHING HYDROFOIL BASED ON THE VORTICITY MOMENT THEORY

Hao Huiyun, Liu Yunqing, Wei Haipeng, Zhang Mengjie, Huang Biao

In this paper, the unsteady vortical structures and corresponding hydrodynamic characteristics of the pitching NACA66 hydrofoil are numerically simulated with the standard k-ω SST turbulence model and dynamic mesh technology. And the influence of local vortical structures on the transient lift is quantitatively obtained based on the finite-domain vorticity moment theory. The results show that during the upstroke stage, transition of laminar flow to turbulence moves from the trailing edge to the leading edge of the hydrofoil at small angle of attack. At relatively higher angle of attack, a clockwise trailing edge vortex ( defined as −TEV)appears on the suction surface firstly. It gradually increases in size and develops towards the leading edge to be fused with the clockwise leading edge vortex (defined as −LEV) there. Then the new developed −LEV interacts with the counterclockwise trailing edge vortex (defined as +TEV) until it falls off completely, which directly leads to the dynamic stall of the hydrofoil. Meanwhile, quantitative analysis based on the finite-domain vorticity moment theory shows that the attached −LEV and −TEV in the finite domain provide positive lift, while +TEV provides negative lift. At the moment when −LEV covers almost the whole suction surface, it contributes the most to the transient total lift which accounts for about 50%. It is also found that different parts of a vortex provide positive or negative lift. As for shedding vortices escaping from the finite domain, all regions of a vortex provide only consistent contribution instead, which means that a clockwise vortex provides positive lift, while a counterclockwise vortex provides negative lift. During the fluctuating stall stage, the overall contribution from the vortices out of the finite domain is quite little and has slight fluctuation, which reflects the unsteady characteristics of the vortical flow caused by the shedding and convection of large-scale vortices

2022, 54(5): 1199-1208. doi: 10.6052/0459-1879-21-543

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LARGE EDDY SIMULATION OF FLOW PAST TWO CONICAL CYLINDERS IN TANDEM ARRANGEMENT

Liu Jian, Zou Lin, Tao Fan, Zuo Hongcheng, Xu Hanbin

In order to explore the time-averaged drag coefficient, fluctuating lift coefficient characteristics and flow field mechanism of two conical cylinders in tandem arrangement, large eddy simulation is used to simulate two conical cylinders in tandem arrangement with a spacing ratio of 2−10 at Re = 3900. The two spanwise asymmetric reflux zones formed behind the upstream conical cylinder make the en dash pressure distribution behind it asymmetric. The upwash, downwash and side shear layers developed by the upstream conical cylinder are the main reasons for the variation of the time-averaged drag coefficient and the fluctuating lift coefficient of the upstream and downstream conical cylinders. The flow structure between tandem two conical cylinders can be divided into three states with the change of spacing ratio: in the shear layer wrapping state, transition state and wake impact state. Shear layer wrapping state, the dominant incoming flow at the free ends of the upstream conical cylinder has a wide range of influence on the windward side of the downstream conical cylinder. The shear layer of the upstream conical cylinder completely wraps the downstream conical cylinder, inhibiting the formation of the backflow zone behind the downstream conical cylinder, causing a decrease in the time-averaged drag coefficient of the downstream conical cylinder. In the wake impact state, the wake of the upstream conical cylinder is fully developed, and the size of the recirculation zone does not change with the spacing ratio. The wake of the upstream conical cylinder periodically falls off and hits the surface of the downstream conical cylinder, which greatly increases the pulsating lift coefficient. The maximum fluctuating lift coefficient is about 20.7 times higher than that of a single straight cylinder. In the transition state, the time-averaged drag coefficient and the fluctuating lift coefficient will both increase compared with the shear layer wrapped state. This research can provide theoretical support for the layout of wind energy harvesting structures.

2022, 54(5): 1209-1219. doi: 10.6052/0459-1879-21-653

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FLIGHT TEST OF AIRCRAFT THREE-AXIS ATTITUDE CONTROL WITHOUT RUDDERS BASED ON DISTRIBUTED DUAL SYNTHETIC JETS

Zhao Zhijie, Luo Zhenbing, Liu Jiefu, Deng Xiong, Peng Wenqiang, Li Shiqing

The autonomous and controllable dual synthetic jet actuators were integrated into an aircraft with a conventional layout and then, the three-axis flight tests without rudders were carried out to verify the ability of distributed three-axis dual synthetic jet actuators to control the attitudes of the aircraft during the cruising. First of all, the dual synthetic jet actuators were improved, and the distributed three-axis attitude control dual synthetic jet actuators were created. Moreover, roll circulation control actuators were installed on the trailing edge of both-side wings close to the wingtips, where their jet outlets were close to the pressure surface. Yaw reverse dual synthetic jet actuators, evenly arranged on the upper and lower surfaces along the span direction, were respectively installed at the 20% chord of the wing close to the wingtips on both sides. Pitch circulation control actuators, whose outlets were also close to the pressure surface, were installed on the trailing edge of the in-house flat tail under the V tail. Then, for an aircraft with a cruising speed of 30 m/s, the three-axis attitude control flight tests without rudders have been carried out during the cruising. Relevant flight attitude information shows that distributed dual synthetic jets could realize the three-axis attitude control of the aircraft without rudders during the cruising. What’s more, the coupling has been shown between the lateral and heading control. The two-way roll control of the aircraft could be realized by the roll circulation control actuators, and the maximum roll angular velocity that can be generated is 16.87°/s. In addition, yaw reverse dual synthetic jet actuators could achieve the two-way yaw control, and the maximum yaw angular velocity that can be generated is 9.09°/s. Pitch circulation control actuators could realize the longitudinal control of the aircraft, and the maximum pitch angular velocity that can be generated is 7.68°/s.

2022, 54(5): 1220-1228. doi: 10.6052/0459-1879-21-586

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ANALYSIS OF GAS MODEL’S INFLUENCE ON AERODYNAMIC CHARACTERISTICS FOR HYPERSONIC VEHICLE OVER HOT JET INTERACTION FLOW FIELD

Fu Yang’aoxiao, Liu Qingzong, Ding Mingsong, Jiang Tao, Li Peng, Dong Weizhong, Xu Yong, Gao Tiesuo

Gas model can have significant influence on the efficiency and accuracy of hypersonic vehicle’s reaction control system (RCS) hot jet interaction flow field simulation, the choice of gas model in numerical simulation is an important issue remains to be solved. Based on reaction jet hot gas’s physical and chemical reaction model and by solving three dimensional Navier-Stokes equation with chemical reaction source term, numerical simulation method of hypersonic vehicle’s reaction control system hot jet interaction flow field is established, by using chemical reacting flow, chemical frozen flow, binary gas model and simplified air jet model, numerical simulation of typical configuration’s hot jet interaction flow field is carried out, based on the simulation results, the influence of different gas model on hot jet interaction flow field structure and hypersonic vehicle’s aerodynamic characteristics is studied, the influences under various flight altitude and flight speeds are also discussed in detail. The result shows that: among the above four different gas models, chemical reacting flow model has higher precision, its result agrees better with wind tunnel experiment data than other three simplified models. In this paper’s low flight altitude conditions, using simplified model for hot jet interaction flow field simulation will underestimate the boundary layer separation length, which will introduce error to the prediction of vehicle’s aerodynamic characteristics, it will also underestimate the surface heat flux near nozzle exit, which is unfavorable for the design of thermal protection system. As the flight Mach number increases, the error introduced by simplified models increases, while the discrepancy between different simplified models also increases. In this paper’s high flight altitude conditions, the discrepancy between different gas models decrease, for these cases, simplified models are good to use for their high computation efficiency. These results can provide reference for future numerical simulation of hypersonic vehicle’s hot jet interaction flow field and the design of hypersonic vehicle’s reaction control system.

2022, 54(5): 1229-1241. doi: 10.6052/0459-1879-21-685

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EXPERIMENTAL STUDY ON THE EVOLUTION OF LIQUID NITROGEN CAVITATING FLOWS THROUGH CONVERGING-DIVERGING NOZZLE

Chen Jiacheng, Chen Tairan, Liang Wendong, Tan Shulin, Geng Hao

The objective of this paper is to investigate the unsteady characteristics of liquid nitrogen cavitating flow in a converging-diverging (C-D) nozzle via a cryogenic experimental facility. A high-speed camera with high resolution was employed to study the evolution of cavity with varying cavitation numbers σ under T_throat ≈ 77 K. In order to quantitatively analyze the unsteady characteristics and temporal-spatial evolution, processed data such as the length and area of cavitation based on experimental images were obtained. The results show that: (1) As the cavitation number decreases and under similar free-stream velocity and temperature, the liquid nitrogen cavitation shows four typical flow patterns, with the cavitation length within 2.5 h for incipient cavitation, between 2.5 h and 7.5 h for sheet cavitation, between 7.5 h and 15 h for large-scale cloud cavitation, and over 15 h for double-cloud cavitation, Additionally, a significant phenomenon of re-entrant jet is captured in the large-scale cloud cavitation and double-cloud cavitation; (2) as the liquid nitrogen cavitating flow evolves from incipient cavitation to double-cloud cavitation, the scale of shedding cavity increases gradually, meanwhile, the amplitude and quasi-period of cavity area pulsation is getting longer. In addition, it is observed that the blockage effect on the cavitation flow at the throat is significantly enhanced in the large-scale cloud cavitation and double-cloud cavitation; (3) compared with incipient cavitation, the travel distance of shedding cavities increases by 0.97, 2.65 and 2.68 times in sheet cavitation, large-scale cloud cavitation and double-cloud cavitation, and the collapse time increases by 1.18, 3.59 and 4.47 times, respectively. For the double-cloud cavitation, there are two significantly different evolutions of shedding cavity.

2022, 54(5): 1242-1256. doi: 10.6052/0459-1879-21-614

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EXPERIMENTAL STUDY ON DRAG REDUCTION CHARACTERISTICS OF DIUTAN GUM SOLUTION BY SLIT INJECTION

Shi Pengfei, Du Wei, Hu Haibao, Feng Jiaxing, Xie Luo

Diutan gum (DG) is a new type of polymer additive that can greatly reduce turbulence resistance. Compared with PEO, PAM and other flexible polymers, DG has significant shear resistance. However, there are relatively few studies on its drag reduction performance at present. In this paper, the relationship between the rheological characteristics of DG and its drag reduction behavior is analyzed by testing the rheological characteristics of DG, the law of drag reduction by in-tube injection and the process of spray diffusion, and the reasons for the change of its drag reduction law are explained from the perspective of spray diffusion. The results show that DG solution is a shear thinning fluid. The viscosity - elastic transition occurs and the transition point is independent of temperature, only moves forward with the increase of concentration. The drag reduction effect of DG increases firstly and then decreases with The Reynolds number, and increases monotonically with the injection rate. Compared with pure water injection, DG solution diffuses slowly in the flow field, and the higher the injection rate, the more obvious the agglomeration near the wall surface. Combined with the observation of jet diffusion of DG solution, it can be seen that when the flow rate is small, DG solution is not fully diffused, but in an uneven aggregation state, which does not give full play to its turbulence inhibition effect and has weak drag reduction. With the increase of flow velocity, the flow shear rate increases, the diffusion of DG is gradually uniform, the turbulence inhibition effect is enhanced, and the drag reduction rate increases. However, when the flow rate is too high, the concentration of DG is seriously diluted, and the shear rate in the near wall area is too high, which may cause the fracture of long chain molecules, resulting in the decrease of drag reduction effect.

2022, 54(5): 1257-1263. doi: 10.6052/0459-1879-21-567

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THE FINITE THICKNESS MODEL CALIBRATES THE BIMODAL-AFM YOUNG'S MODULUS MEASUREMENTS OF THE TWO-DIMENSIONAL MoS₂

Chen Shan, Peng Jinfeng, Huang Le, Zeng Xin, Li Lihao, He Wenyuan, Zheng Xuejun

Because the two-dimensional (2D) materials possesses unique crystal structures, novel physical properties and excellent mechanical properties, the 2D materials is of broad application prospects in many fields including micro- and nano-electromechanical systems and flexible electronic devices, etc. The elastic modulus is one of the basic mechanical parameters for 2D materials, which is of an important influence on its device application and strain regulation. However, restricted by the characteristics of two-dimensional structure and atomic thickness, it is difficult to measure the accurate elasticity modulus of 2D materials. Amplitude modulation and frequency modulation within the bimodal atomic force microscopy is an efficient method for measuring Young's modulus of 2D materials, but the influence of rigid substrates cannot be ignored for the measurement results. In this work, the Young's modulus distribution of the substrate and 2D molybdenum sulfide were directly measured by the bimodal atomic force microscopy. Based on the finite thickness model, the intrinsic Young's modulus value of the sample was obtained after corrected the substrate effect. The elastic coefficient and Young's modulus of 2D molybdenum disulfide were calculated by the first principles calculation. The experimental results are consisted with the calculation results. That’s to say, the bimodal atomic force microscopy is a reliable direct characterization method for Young's modulus of 2D materials. This method does not require tedious steps like preparing suspended 2D materials, and can avoid shortcomings of conventional characterization methods. For thin films of large area two-dimensional materials, this work provides a reliable experimental basis for the programmed characterization analysis of their mechanical properties. Meanwhile, it provides firm experimental basis for future mechanistic statistical analysis of high throughput experimental data.

2022, 54(5): 1264-1273. doi: 10.6052/0459-1879-22-034

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BIDIRECTIONAL HOMOGENIZATION METHOD FOR ACCURATE ANALYSIS OF MECHANICAL BEHAVIORS OF Nb₃Sn SUPERCONDUCTING COILS

He An, Li Jianbo, Xue Cun

Nb₃Sn superconducting magnets can produce high magnetic fields during operation, and the Nb₃Sn superconducting coils subjected to strong electromagnetic force can result in great mechanical strain. The strain sensitivity of Nb₃Sn superconducting material will degrade the critical performance of the Nb₃Sn magnet coil, which has a significant impact on the safety and stability of magnets. Therefore, it is of great scientific significance to accurately calculate the mechanical behavior of superconducting magnets under electromagnetic force. Nb₃Sn superconducting magnets are mainly made of superconducting wires wound into coil structure and solidified by epoxy resin. Nb₃Sn superconducting wire is a composite structure mainly made of multiple microfilament embedded in a copper matrix. Therefore, the size from superconducting filaments to superconducting magnets spans several orders of magnitude, which brings challenges for accurate analysis of the mechanical deformation of superconducting coils. Firstly, the representative element (RVE) homogenization method is used to analyze the equivalent mechanical parameters of the whole coil. By comparing the results of the equivalent homogenization model and the actual structure of the coil, it is found that there are significant errors in the equivalent homogenization model. Therefore, we propose a bidirectional homogenization analysis method with high accuracy and low computational cost to study the stress-strain distribution of each component material (Nb₃Sn filament, copper, and epoxy resin) in the superconducting coil. This method does not require large-scale numerical modeling and the results of this method are in good agreement with that of the actual composite coils, which verifies the effectiveness and accuracy of this method. Finally, based on the proposed multi-scale method, we discuss the stress-strain variations of each layer of the Nb₃Sn superconducting coil versus turns and layers under the electromagnetic force in detail.

2022, 54(5): 1274-1290. doi: 10.6052/0459-1879-22-033

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DESIGN OF ELASTICALLY ISOTROPIC PLA LATTICE STRUCRURE IN FUSED FILAMENT FABRICATION CONSIDERING MATERIAL ANISOTROPY

Wang Shuheng, Dai Shi, Wu Xinwei, Ma Yongbin, Deng Zichen

The rise of additive manufacturing technology stimulates researchers' enthusiasm for structural innovative design. However, the anisotropy of additive manufactured materials poses certain difficulties for the prediction and design of structural mechanical properties. To accurately predict the elastic properties of polylactic acid (PLA) materials and lattice structures made in fused filament fabrication and realize the elastically isotropic design of lattice structures, firstly, this paper adopts an orthogonal anisotropic elastic model to describe the elastic behavior of the PLA materials, and obtains the nine independent elastic constants needed for the orthogonal anisotropic model through experiments and calculations. Then, a 2D compound truss lattice structure with tunable mechanical properties is designed, and its analytical expressions for the in-plane effective elastic properties and elastic isotropy condition are derived based on the representative volume element (RVE) method without considering the material anisotropy. Finally, the elastic modulus and thickness of the struts in the lattice structure are adjusted according to the anisotropy of the PLA material, and the analytical expressions of the in-plane elastic properties and elastic isotropy condition of the lattice structur are derived based on the RVE method. The results show that the orthogonal anisotropic elastic model is suitable for describing the elastic behavior of fused filament fabricated PLA materials, and the elastic modulus of PLA materials in arbitrary direction can be accurately predicted based on this model. The anisotropy of the material needs to be fully considered when predicting and designing the mechanical properties of the fused filament fabricated lattice structures. After considering the material anisotropy, the elastic isotropy design of part of lattice structures can be realized by adjusting their geometric sizes based on the RVE method.

2022, 54(5): 1291-1302. doi: 10.6052/0459-1879-22-031

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RESEARCH ON THE FORMATION MECHANISM OF ADDITIONAL BENDING MOMENT AND BEARING CAPACITY OF BOLT OF TYPICAL CONNECTED STRUCTURE AND STRUCTURAL OPTIMIZATION DESIGN

Fan Gang, Zhang Hongyu, Wang Jiebing, Xue Zheng, Liu Xiaohua

Considering the problem that the bearing capacity of the high-strength bolt is greatly weakened by the additional bending moment in the tensile condition of the typical connection structure, a mechanism study on the generation of additional bending moment of the bolt is carried out, and a structural optimization design method is proposed to effectively reduce the additional bending moment of the bolt. The analytical solution of the additional bending moment of the bolt is derived based on the established equivalent mechanical model of the typical connection structure. The correctness of the analytical solution is verified by numerical simulation. Considering that the bolt is subjected to tensile and bending coupled loads at the same time, the interaction of various stress distributions on the bolt across-section under different tensile and bending combinations is studied by introducing the plastic bending theory of the beam, and the plastic reduction coefficient of bending moment considering the influence of axial force is given. Based on the maximum stress failure criterion, a study on the failure criterion of bolts considering additional bending moment and bending plasticity is carried out, which has more engineering application value. Based on the mechanism, the optimization design of typical connection structure is carried out to reduce the additional bending moment of the bolt and thus improve bolt’s bearing capacity. The working mechanism of the hinged ball joint is expounded by analytical method. The sensitivity analysis of the additional bending moment of the bolt is carried out based on numerical simulation, which verifies the effectiveness of the optimization design method. The test research is then carried out and the additional bending moment of the bolt in different connection status are obtained. The test results verify the correctness and feasibility of the optimization design method. This method is capable of greatly reducing the additional bending moment of the high-strength bolt, maximizing the bearing capacity of the bolt, and improving the reliability of the connection structure.

2022, 54(5): 1303-1321. doi: 10.6052/0459-1879-21-644

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RESEARCH ON STRESS FIELD OF SURROUNDING ROCK AND LINING STRUCTURE OF DEEP-BURIED SUBSEA TUNNEL CONSIDERING SEEPAGE EFFECT

Jin Bo, Hu Ming, Fang Qihong

Deep-buried subsea tunnels are often under high water pressure condition and therefore groundwater seepage exerts a great impact on the surrounding rock and lining structure safety. In this paper, a mechanical model of deep-buried subsea tunnel with lining is proposed to study the influence mechanism of groundwater seepage on the surrounding rock and lining structure stability during the service stage of subsea tunnel. Firstly, a conformal mapping method is adopted to map the semi-infinite domain which includes seawater and surrounding rock elastic zone into an annular domain, and the seepage equation in polar coordinates between interfaces is established according to the seepage boundary conditions. Thus, the analytical solution of the seepage field of the subsea tunnel is obtained. Secondly, the seepage field is applied to the stress field in the form of volume force, the stress balance equation is established according to the stress boundary conditions, and based on the Drucker-Prager (D-P) criterion which takes account of the effect of the intermediate principal stress, an elastoplastic analytical solution is derived for the surrounding rock and lining structure under the influence of seepage effect. Finally, taking Shenzhen Mawan Sea-Crossing Passage as an engineering example, the analytical solution is compared with the finite element numerical solution, which verifies the accuracy of the theoretical solution in this paper, the influence law of seepage effect on the stress field of tunnel surrounding rock and lining structure is studied, and the factors influencing the radius of surrounding rock plastic zone are analyzed. The results show that: the seepage effect has a significant influence on the hoop stress in surrounding rock and lining structure, and the radial stress increases nonlinearly with the increase of $\rho $. As the seawater goes deeper, the water pressure on tunnel continues to increase, and the surrounding rock plastic zone increases significantly. An increase in the internal water head can effectively limit the development of the surrounding rock plastic zone, with the initial limiting effect being obvious while the subsequent effect being gradually weakened.

2022, 54(5): 1322-1330. doi: 10.6052/0459-1879-21-670

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STUDY ON NATURAL CHARACTERISTICS OF FLUID-CONVEYING PIPES WITH ELASTIC SUPPORTS AT BOTH ENDS

Yan Xiong, Wei Sha, Mao Xiaoye, Ding Hu, Chen Liqun

Fluid-conveying pipes have been widely used in aerospace, petrochemical, offshore and other important engineering fields. The vibration characteristics of the fluid-conveying pipes, especially the natural characteristics of the system, have been an important issue in the research of scholars around the world. This study investigates the natural characteristics of transverse vibration of a fluid-conveying pipe with elastic supports at both ends. In particular, the natural characteristics of the fluid-conveying pipe with asymmetric elastic supports at both ends are discussed. The governing equation and boundary conditions of the fluid-conveying pipe system are derived by the Hamilton’s principle. The modal functions of the static pipe are obtained by the complex modal method, and then they are used as the potential function and weight function for the Galerkin method to truncate the control equation of the linear derived system. The effects of symmetrical support stiffness at both ends, asymmetric support stiffness at both ends, pipe length and fluid mass ratio on the natural frequencies of the system are discussed. The discussion focuses on the variation of natural frequencies under the condition of asymmetric supports that may happen at both ends of the pipe. Results show that a fast decrease in the first natural frequency for large symmetrical support stiffness. When the support stiffness at both ends of the pipe changes, the natural frequencies of each order of the pipe obtain the maximum or minimum value when the support stiffness at both ends is equal. For the pipe with asymmetric supports at both ends, the closer the support stiffness at both ends, the faster the first natural frequency decreases, and the smaller the corresponding critical flow velocity. The greater the flow velocity of the fluid, the more significant is the effect on the natural frequency of the pipe supported by asymmetric supports at both ends.

2022, 54(5): 1341-1352. doi: 10.6052/0459-1879-21-566

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TWO GENERALIZED INCREMENTAL HARMONIC BALANCE METHODS WITH OPTIMIZATION FOR ITERATION STEP

Huang Jianliang, Zhang Bingxu, Chen Shuhui

As a semi-analytial and semi-numerical method, the incremental harmonic balance (IHB) method is capable of dealing with strongly nonlinear systems to any desired accuracy. However, as it is often in case numerical method, there exists initial value problem that can cause divergence with using the IHB method. To solve the initial value problem, two generalized IHB method are presented in this work. The first one (GIHB1) is combined with backtracking line search (BLS) optimization algorithm, which adjust the iteration step to decrease for the convergence of the solutions. The second one (GIHB2) is combined with BLS optimization algorithm and the dogleg method, which is an iterative optimization algorithm for the solution of non-linear least squares problems. The GIHB2 method is adopted for the Newton-Raphson iteration with gradient descent such that the convergence of the solutions increases monotonically along the path with gradient descent way with two parameters. At the end, two examples are presented to show the efficiency and the advantages of the two GIHB methods for initial value problem.

2022, 54(5): 1353-1363. doi: 10.6052/0459-1879-22-042

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DISCRETE TIME TRANSFER MATRIX MODELING OF FlEXIBLE WHEELSET AND VERTICAL VIBRATION

Liu Pengfei, Yang Shaopu, Liu Yongqiang, Gu Xiaohui, Liu Zechao

For the dynamic simulation problems of elastic vibration and high-frequency exciting test for railway wheelset, the discrete time transfer matrix method is applied to establish the flexible wheelset vibrating model. The discrete time transfer matrixes of distributed mass elastic axle, lumped mass wheel and spring-damping element in wheelset are derived based on the Newmark-β integration formula. Both the Riccati method and Newmark-β method are applied to solve the vertical vibrating accelerations, velocities and displacements of wheelset system. The wheelset dynamic model is then introduced into the bogie frame and rail roller submodels to form an integrated dynamic system, in which the latter submodels are solved by the new explicit integration method. The single-wheelset rolling and vibration dynamic model of railway vehicle is then completed. The solution flow of dynamic simulation in the mixed integral modes is presented subsequently. Based on the vibrating and rolling test rig, the high-speed running test within the speeds of 300 ~ 400 km/h is carried out in the conditions of surface initial roughness, grinded polygon and local depression for rail rollers. The corresponding dynamic simulation under the same running conditions is carried out simultaneously. Both the simulation and test results are compared in time-frequency domains to verify the theoretical model. Viewed from the perspective of time-frequency characteristics and amplitude distribution of vibration accelerations, the results indicate that, the flexible wheelset dynamics model can well reflect the medium-high frequency vibration rules for the system vibrations below the frequency of 500 Hz. The dynamic excitations such as wheel out of round, polygonal wear and local depression can be captured effectively. The amplitude errors of calculated axle-box accelerations under the above three roller surface conditions are lower than 9% in general. The model has good adaptability and precision. However, the application of relevant modeling methods in the complex spatial structures needs further exploration.

2022, 54(5): 1375-1386. doi: 10.6052/0459-1879-22-008

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RESEARCH ON DAMPING RATIO IDENTIFICATION OF BEAM BRIDGE BASED ON VEHICLE BRIDGE COUPLING THEORY

Yang Yang, Xu Wenming, Lu Huicheng, Yuan Aipeng, Tan Xiaokun, Bi Hesheng, Fang Guangjun, Tang Yan

A damping ratio identification method of the simply supported beam based on the vehicle bridge coupling dynamics theory is proposed. Firstly, the test vehicle is designed as a single degree of freedom system according to the dynamic theory, and then the signal of the simply supported beam bridge response is obtained from the response signal of the contact point between the test vehicle and the simply supported bridge by using the sensor installed on the test vehicle. The signal including the first-order frequency of the simply supported beam bridge is filtered based on the principle of vehicle bridge coupling dynamics. Finally, the damping ratio of the simply supported beam bridge is assumed, The assumed first-order vibration mode of the simply supported beam bridge is obtained through the assumed damping ratio of the simply supported beam bridge, and the cycle is continued until the maximum value point of the first-order vibration mode calculated under the assumed damping ratio is in the middle, that is the identified real damping ratio of the simply supported beam bridge. This paper first explains the feasibility of this method from the theoretical derivation of vehicle bridge coupling dynamics, and then analyzes the vehicle bridge coupling dynamics model under the influence of different vehicle speed and unsteady vehicle speed, road roughness, environmental noise and other factors. Finally, it is preliminarily verified by real bridge test. The results show that this method can overcome the influence of external adverse factors to a certain extent, achieve the purpose of identifying the damping ratio of beam bridge, and provide a better method for identifying the damping ratio of simply supported beam bridge. It has the advantages of less parameter setting, simple and convenient operation and higher test accuracy, At the same time, it is helpful to promote the practical engineering application of the vehicle bridge coupling dynamics theory and technology based on vehicle bridge coupling in beam bridge modal parameter identification.

2022, 54(5): 1387-1402. doi: 10.6052/0459-1879-21-691

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SHOCK-TUNNEL EXPERIMENTAL STUDY OF COMBUSTION ENHANCEMENT METHODS FOR A HIGH-MACH-NUMBER SCRAMJET

Zhang Xu, Zhang Qifan, Yue Lianjie, Meng Dongdong, Luo Weihang, Yu Jiangpeng, Zhang Xiaoyuan, Li Jinping, Chen Hong, Li Fei

Based on the JF-24 high-enthalpy shock tunnel in Institute of Mechanics, Chinese Academy of Sciences, the current paper performed direct-connect combustion tests of a high-Mach-number scramjet engine to study high-Mach-number combustion enhancement methods and fuel types’ effects. The test-section was a circular cross-section scramjet combustor with cavity structures, and fuel injectors were arranged in the isolator. Hydrogen and ethylene fuels were severally used in current tests at the same equivalence ratio of 0.7. Fuel injection utilized two different test-section configurations without and with small struts, respectively. Some injection holes of the latter configuration were located on the strut tops. For each configuration, two adjacent rings of injecting holes were arranged for single-ring and dual-rings injections, respectively. Test results demonstrated that stabilized combustion performances of hydrogen and ethylene fuels in hypersonic flows under a Mach number $ M{a_{\text{f}}}{\text{ = }}10 $ flight condition. Meanwhile, compared to the single-ring fuel injection method, dual-rings fuel injections and adding injections on small-strut tops were beneficial for combustion enhancements. The reason was speculated that interactions of adjacent fuel jets and shock/separation structures probably could improve fuel-air mixing, and additional fuel injection on small-strut tops meant more available air for mixing. Under the same combustion enhancement methods of dual-ring injections and additional small-strut top injections, hydrogen fuel generated better thrust performance than ethylene fuel, while their combustion efficiencies were similar. This was possibly because that the hydrogen fuel had a higher caloricity, and thus it could generate more heat release. Besides, test also verified that under the current high-enthalpy high-speed inflow condition, combustion heat release was controlled by fuel-air mixing processes, and meanwhile the upper limits of heat release was limited by high-temperature dissociation effects. This was because that heat release led to decreases of local flow speeds and increase flow temperatures. Consequently, high-temperature dissociation endothermic reactions would be more remarkable, resulting in decrease of heat release.

2022, 54(5): 1403-1413. doi: 10.6052/0459-1879-21-348

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DESIGN AND OPTIMIZATION FOR HYPERSONIC CONE-DERIVED WAVERIDER WITH BLUNTED LEADING-EDGE

Guo Shuaiqi, Liu Wen, Zhang Chen’an, Wang Famin

The waverider configuration has a broad application in hypersonic vehicles due to its high lift-to-drag ratio (L/D). In actuality, the sharp leading edge must be blunted because of the serious aerothermal heating problem, which can lead to significant loss of aerodynamic performance. Thus, the optimum configuration with sharp leading-edge cannot guarantee that it is still optimum after being blunted. To solve the problem, this paper first studies the influence and mechanism of leading-edge bluntness on the lift and drag characteristics of different configurations. The results show that the bluntness causes the lift to decrease slightly, the drag to increase greatly, and the L/D to decrease significantly. The wave drag of the blunted leading-edge plays a dominant role in the total drag increment, and the friction drag of the blunted leading-edge is very close to the friction drag reduction of the upper and lower surface. Based on the above results, this paper evaluates the wave drag of the blunted leading-edge by the modified Newton theory, and combines the aerodynamic models of sharp leading-edge waverider and genetic algorithm to obtain the optimum configurations with blunted leading-edge. The aerodynamic forces of the optimum configurations are evaluated via CFD simulation. The results show that under the constraints of different flight altitudes, different lift, and different blunt radii, compared with the optimum configurations with sharp leading-edge, the blunted optimized waveriders have the characteristics that the width is smaller, the sweep angle at the same longitudinal position is larger, and the L/D is higher. At the design condition of M_∞ = 15, H = 50 km and CL = 0.3, the L/D of the optimum blunted configuration with R = 10 mm can be improved by 9.32%. What’s more, as the constraint of the lift coefficient increases, blunt radius increases, and the flight altitude decreases, the advantage of L/D for the blunted optimized waveriders become more evident.

2022, 54(5): 1414-1428. doi: 10.6052/0459-1879-21-611

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STUDY ON SNAP-OFF MECHANISM AND SIMULATION DURING GAS-LIQUID IMMISCIBLE DISPLACEMENT

Zhang Shengting, Li Jing, Chen Zhangxing, Zhang Tao, Wu Keliu, Feng Dong, Bi Jianfei, Li Xiangfang

Studying the mechanism of phase interface snap-off during gas liquid immiscible displacement and its influencing factors have great significance in the field of enhanced oil and gas recovery such as gas driving, gas water alternation and foam driving. In this work, based on the original pseudopotential lattice Boltzmann model, we improved the fluid-fluid force scheme, added the fluid-solid force, coupled the Redlich-Kwong (RK) equation of state, and used the exact difference method (EDM) to add the external forces to the LBM framework. As well as verified the accuracy of the model by calibrating the thermodynamic consistency of the model and simulating a series of two phase systems such as testing the interfacial tension, static equilibrium contact angle and retention of the liquid phase at the corner. Based on the modified pseudopotential lattice Boltzmann model, we have carried out gas-liquid immiscible displacement simulations in a pore-throat-pore system, and the results have shown that: the snap-off phenomenon is related to the displacement pressure difference, pore-throat length ratio and pore-throat width ratio, and the snap-off phenomenon occurs only when the displacement pressure difference is within a certain range. When the displacement pressure difference is larger than the upper limit of the critical displacement pressure difference, the snap-off will be inhibited even if the snap-off condition predicted by the classical static rule has been reached; When the displacement pressure difference is less than the lower limit of the critical displacement pressure difference, it cannot overcome the "pinning" effect of the capillary tube and results in ineffective displacement. For the pore-throat structure with constant pore-throat width ratio, the displacement pressure difference range in which the snap-off phenomenon occurs increases as the pore-throat length ratio increases; For the pore-throat structure with constant pore-throat length ratio, the displacement pressure difference range in which the snap-off phenomenon occurs increases as the pore-throat width ratio decreases.

2022, 54(5): 1429-1442. doi: 10.6052/0459-1879-21-576

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MULTIBODY DYNAMICAL MODELING AND ANALYSIS OF MARINE NUCLEAR POWER PLATFORM POSITIONING SYSTEM

Guo Chongchong, Wu Wenhua, Wu Guodong, Cao Guangming, Lü Baicheng

Marine nuclear power platform can provide a stable energy supply for oil and gas exploitation, remote islands and desalination of sea water. It is an important marine equipment with potential. As the core part of the nuclear power platform, the positioning system is mainly composed of a single-point turret, YOKE, mooring legs and mooring bracket, which is a typical multi-rigid body dynamic system. The multi-body dynamic analysis of the positioning system can improve the long-term operation reliability of nuclear power platform. Based on the theory of multi-body dynamics and the topology of multi-hinge connection of positioning system, a multi-body dynamic simulation model of positioning system is established. Then, considering the marine environment of nuclear power platform operation, the 6-DOF motion time history of nuclear power platform under multi-year return periods is obtained through spectral analysis and the theory of linear superposition. Taking the first marine nuclear power platform in China as an example, the mooring restoring force of the positioning system and the mechanical behavior of each hinge joint are calculated under the sea conditions of 1-year return period, 10-year return period and 100-year return period by using multi-body dynamic model. Compared with the quasi-static mechanical model and Kane dynamic model, the mooring restoring stiffness curve of the positioning system is calculated, and the dynamic amplification factor of the mooring restoring force is proposed. The research can provide a reference for the evaluation of the mooring capacity of the positioning system and the mechanical analysis of each hinge structure.

2022, 54(5): 1443-1455. doi: 10.6052/0459-1879-21-690

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A REVIEW OF THE FOURTH NATIONAL SYMPOSIUM ON BIOMECHANICS FOR YOUNG SCHOLARS

Wu Yu, Li Dechang, Ji Baohua

This review briefly introduces the Fourth National Symposium on Biomechanics for Young Scholars. It summarizes the scientific presentations delivered by the invited experts and young scholars.

2022, 54(5): 1456-1460. doi: 10.6052/0459-1879-22-012

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STRUCTURAL ELASTOGRAPHY METHOD BASED ON TOPOLOGY OPTIMIZATION

Fu Junjian, Li Shuaihu, Li Hao, Gao Liang, Zhou Xiangman, Tian Qihua

Elastic modulus is an important performance parameter of engineering materials, which can measure the ability of an object to resist elastic deformation. Elastography is a medical imaging method that characterizes the physical properties of biological tissues through elastic modulus. To apply the elastography method to the damage identification of mechanical equipment structures and improve the local characterization and the global identification capabilities of elastography, a structural elastography method based on the topology optimization method is proposed. Inspired by the topology optimization theory, the relative densities or elastic modulus coefficients of the discrete elements of the structure are used as the elastography parameters to characterize the degree of damage. The interpolation model of imaging parameters and elastic modulus is then established. The mapping relationship between damage characterization, structural model, and physical response is constructed based on the finite element model. The least-square of the displacement responses of the damaged structure and the undamaged structure is taken as the optimization objective function. The upper and lower limits of imaging parameters are taken as constraints. The optimization model of the structural elastography is established based on the objective and constraints. The sensitivity of the imaging problem is derived based on the adjoint method. The numerical implementation for the inverse solution of the elastography problem is given in detail. Two 2D cantilever beam and Michell beam numerical examples are firstly conducted. The imaging results show that the topology optimization based elastography method can obtain high-quality elastic modulus images of structures with homogeneous and heterogeneous materials without any prior information. The elastography method is also effective for the imaging of structures with single damage and multi-damages. And the imaging results do not depend on specific boundary conditions. The elastography method is further extended to a 3D cantilever beam problem to verify the generalization of the proposed method.

2022, 54(5): 1331-1340. doi: 10.6052/0459-1879-21-672

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2022 Vol. 54, No. 5

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