力学学报

Preface of Theme Articles on Computation Mechanics of Granular Materials

Ji Shunying

2021, 53(9): 2355-2356. doi: 10.6052/0459-1879-21-428

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A REVIEW OF SMOOTHED PARTICLE HYDRODYNAMICS FAMILY METHODS FOR MULTIPHASE FLOW

Chen Feiguo, Ge Wei

With meshfree and fully Lagrangian features of particle methods, smoothed particle hydrodynamics (SPH) is suitable to achieve high-accurate simulations of multiphase flows with large interfacial deformations, discontinuities, and multi-physics. Multiphase flow simulations with SPH methods have been reported abundantly and the specific implementations are much different. In this review, the basic SPH method and issues about fluid pressure, surface tension and solid boundary are discussed. And various implementations of SPH for multiphase flow simulation are mainly summarized as: (1) Lagrangian solver for the two-fluid model (TFM): The two phases are discreterized into two independent groups of SPH particles and coupled by the explicit interphase interaction; (2) multiphase SPH: The multiphase SPH method is considered as the natural extension of SPH method on multiphase flow simulation, and the interphase interaction is implicitly described by SPH parameters; (3) coupling of SPH and other discrete methods: The two phases with large differences each adopt different discrete methods to give play to the advantages of different Lagrangian methods; and (4) coupling of SPH and grid-based methods: The grid method handles the simple main-flow to obtain the balance between accuracy and efficiency. Also, some issues associated with SPH simulations of multiphase flows, such as the physicalization of simulation parameters and the improvement of accuracy and efficiency, are suggested as requiring attention.

2021, 53(9): 2357-2373. doi: 10.6052/0459-1879-21-270

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DISTRIBUTION AND EVOLUTION OF FREE VOLUME OF ELLIPSOIDAL PARTICLE SYSTEMS DURING SHEARING

Zou Yuxiong, Ma Gang, Li Yiao, Wang Di, Qiu Huanfeng, Zhou Wei

Granular material is a complex multi-body interaction system which is composed of a large number of discrete particles and their surrounding free volume. Although the correlation between free volume and the mechanical properties as well as the deformation characteristics of granular materials has been proved, the local free volume of non-spherical particles is not fully understood at present due to the difficulties in characterizing. In this paper, the combined finite and discrete element method (FDEM) is used to simulate the triaxial tests of ellipsoidal particles with different principal axis lengths, and the Set Voronoi tessellation method is applied to construct the Voronoi cells of the particles during shearing. The statistical distribution and evolution of the local free volume of the granular systems during shearing are analyzed, and the influence of particle shape on the evolution of free volume is studied. Our results show the anisotropy of Voronoi cells gradually increases during shearing, and the degree of anisotropy increase will be intensified with the increase of particle shape asphericity, which means the granular assembly with a larger asphericity will experience more intense rearrangement during shearing. The local void ratio of ellipsoidal particle systems with different asphericity statistically complies with a k−Γ distribution, which is controlled by the global void ratio of granular assembly and not affected by particle shape and shear state. The local void ratio fluctuations follow an asymmetric laplace distribution (ALD), and its asymmetric parameter which has a linear relationship with the global void ratio of granular assembly describes the competition between contraction and dilatation of local free volume.

2021, 53(9): 2374-2383. doi: 10.6052/0459-1879-21-255

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A NOVEL DISCRETE ELEMENT ROLLING RESISTANCE MODEL BASED ON HYSTERESIS SPRING ENERGY DISSIPATION

Gao Zhengguo, Dong Pengkun, Zhang Yajun, Sun Huizhu, Ndiaye Becaye Cissokho

The rolling resistance between particles plays an important role in the stability of the particulate systems. In a conventional discrete element method, the rolling resistance model between particles is usually made of springs, dashpots, and sliders in the rotational direction. The particles rolling kinetic energy is dissipated by the viscous (moment) and friction forces. With this model, the viscous force (moment) is directly related to the rolling velocity. Consequently, the dynamic dissipation capacity of particles close to the static state becomes weaker with the rolling velocity decreasing. It is known that the time required to simulate a particle rolling with a velocity close to zero by using the traditional discrete element method is longer than the experimental results. To solve this problem, the mechanism of rolling resistance caused by material hysteresis is analyzed based on tribological principle, and a new discrete element model of hysteresis rolling resistance (HDEM) is established. A hysteresis spring with velocity-independent kinetic energy dissipation is proposed, and its constitutive law’s formula is derived. To verify the new rolling resistance model, the free-rolling of a single round particle specimen on a flat surface is measured through a physical experiment. The measured data are compared with the results simulated by the new rolling resistance model HDEM and the conventional rolling resistance model. The results show that the results based on HDEM are more consistent with the experimental data, and the particle oscillation frequency is in better agreement with the experimental phenomenon observed.

2021, 53(9): 2384-2394. doi: 10.6052/0459-1879-21-236

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ANALYSIS OF WAVE BEHAVIOR AND DEFORMATION CHARACTERISTICS OF GRANULAR MATERIALS IN PRO-BORDER ZONE UNDER IMPACT LOAD

Wang Jiao, Chu Xihua

The study of wave propagation in granular materials is of great significance in metamaterial manufacturing. The boundary design of wave-conducting metamaterials needs to consider the reflection and absorption of stress waves. First, the wave propagation behavior in a one-dimensional particle chain has been studied. According to the difference in the maximum kinetic energy that the particles can obtain at different positions from the boundary, the definition of the boundary area is given. Then the stress wave propagation behaviors of multiple sets of two-dimensional particle samples under impact load are analyzed. The influences of different boundary shapes and particle arrangement on the propagation behavior of stress waves in the pro-border zone have been considered. The results show that the arrangement of particles in the pro-border zone mainly affects the relative position and local porosity of particles near the boundary. The stress wave reflected by the boundary propagates directly in the pro-border zone in the shape of the boundary line. The more complicated the boundary situation (high local porosity, random arrangement of particles), the more accurate the conclusion. The wave velocity mainly determines the shape of the wave-front outside the pro-border zone, i.e., in the material center area. The convergence effect of the arc boundary on the wave reflection and the dispersion effect caused by the arrangement of the particles in the pro-border zone are two competing factors, which together determine the reflection process of the wave in the pro-border zone. Finally, the changes of the force chain network in the pro-border zone before and after reflection are analyzed. The distribution of kinetic energy intuitively reflects the phenomenon of reflection hysteresis. The process of particle contact and rebound in the boundary area corresponds to the storage and release of energy. This research will provide reference for the handling of boundary problems in metamaterial design.

2021, 53(9): 2395-2403. doi: 10.6052/0459-1879-21-242

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CONSTITUTIVE RELATIONS OF GRANULAR MATERIALS BY INTEGRATING MICROMECHANICAL KNOWLEDGE WITH DEEP LEARNING

Qu Tongming, Feng Yuntian, Wang Mengqi, Zhao Tingting, Di Shaocheng

Constitutive relations of granular materials are of great significance to many fields, such as geotechnical engineering. Different from traditional phenomenological constitutive theory, this study explores a micromechanics-informed data-driven constitutive modelling approach for granular materials via machine learning models. On the basis of Vogit’s homogenization assumption, an analytical small-strain stress-strain relation is established. This relation uniquely determines a group of micromechanical fabric variables associated with the constitutive behavior of granular materials. These recognized variables, together with principal strain and stress sequence pairs reflecting macroscopic properties of granular materials, are obtained via a series of discrete element models of triaxial compression tests. Considering the fact that these microscopic fabric tensors are internal variables, which cannot be directly used as inputs of a material constitutive model, a directed graph is introduced to incorporate microstructural information implicitly in the prediction of stress-strain responses. The gated recurrent unit (GRU) based recurrent neural networks are used as basic deep learning models to describe the mapping relation between nodes in the designed directed graph. In this study, the entire stress-strain prediction model can be assembled with two neural networks that are trained separately, after unfolding the directed graph from the target node to the source node. By testing the trained deep learning model based on brand new datasets, the results demonstrate that the proposed training approach can satisfactorily capture the multi-directional stress-strain responses with reversal loadings, such as conventional triaxial compression with unloading-reloading cycles, true-triaxial compression with constant intermediate principal stress (constant-b), and constant mean effective effective stress (constant-p) conditions with unloading-reloading cycles. The prediction results also show that the trained model possesses satisfactory interpolation and extrapolation capability. Considering the excellent ability of deep learning in terms of capturing the mechanical responses of granular materials and the unique features of open learning when new data is available, integrating a data-driven paradigm with theoretical constitutive models may be one of the important directions for constitutive research of granular materials.

2021, 53(9): 2404-2415. doi: 10.6052/0459-1879-21-221

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RESEARCH ON THE EFFECTS OF ROLLER-SPREADING PARAMETERS FOR NYLON POWDER SPREADABILITY IN ADDITIVE MANUFACTURING

Zhang Jiangtao, Tan Yuanqiang, Ji Caiyuan, Xiao Xiangwu, Jiang Shengqiang

The powder spreading process is one of the key processes in the powder-bed-based additive manufacturing (AM) technology. The roller-spreading parameters include the powder spreading layer thickness H, roller’s diameter D, roller’s rotational speed ω and translational velocity V, which have a major impact on the powder spreadability in AM processes. In this paper, the nylon powder was taken as the research object, and the discrete element method (DEM) was deployed to simulate the nylon powder spreading process by a roller. The three powder spreadability indicators including the deposition fraction, percent coverage and deposition rate were established. The central composite design (CCD) model was used to generate 30 groups of simulation cases. The regression models of three powder spreadability indicators were fitted by the response surface method (RSM). The analysis of variance was used to prove the accuracy and predicting effectiveness of regression models. In addition, the effect of process parameters on powder spreadability indicators was analyzed in detail. The results showed that the powder spreading layer thickness H was a leading influencing factor. The roller’s translational velocity V was a less important influencing factor. The roller’s diameter D and rotational speed ω had a slight influence on powder spreadability indicators. Both the H and D with V were determined as the main interactive factors on powder spreadability indicators. The three powder spreadability indicators were taken as the optimization goal, and the multi-objective optimization of roller-spreading parameters was carried out by the expectation method. The predicted optimal combination of powder spreading parameters and powder spreadability indicators were obtained. Moreover, the optimal results were verified through the experiments. The results showed that the predicted results of powder spreadability indicators were in good agreement with experimental results. The research results in this paper can provide guidance for the optimization of roller-spreading parameters in AM.

2021, 53(9): 2416-2426. doi: 10.6052/0459-1879-21-240

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NUMERICAL ICE TANK FOR ICE LOADS BASED ON MULTI-MEDIA AND MULTI-SCALE DISCRETE ELEMENT METHOD

Ji Shunying, Tian Yukui

The investigation of ice loads on polar ships and offshore engineering structures is very important for anti-ice structure design, safe operation and structural integrity management in ice-covered regions. Recently, the rapid developments on high-performance computing techniques and multi-media, multi-scale numerical methods provide an effective improvement on the determination of ice loads on polar ships and offshore engineering structures. The numerical methods represented by the discrete element method (DEM) achieved excellent contributions on the ice load predictions. Therefore, considering the engineering demands to forecast ice loads and mechanical responses of polar ships and offshore structures, and also based on the present state-of-the-art of the multi-media and multi-scale numerical methods for coupling of sea ice, engineering structures and fluid, the concept, frame and technique of numerical ice tank are discussed based on DEM simulations. The numerical ice tank has significant advantages in reliability, economy, rapidity, expansibility and scenario in determining the ice load on hulls and offshore engineering structures. Based on the concept and experience of numerical tank, this paper illustrates the feasibility and engineering application prospects of numerical ice tank with the DEM simulations on ice loads and structural mechanical responses of typical ship and offshore platform. The computational parameters in DEM simulations were calibrated with the mechanical properties of sea ice obtained with physical experiments. The ice loads on ship hull and jacket platforms simulated with DEM were compared with the model tests and filed measurements. Finally, the interaction between ice cover and structures of model tests in ice tank are repeated numerically with DEM. With the numerical ice tank, ice loads on ships and offshore structures can be simulated with DEM under various ice conditions on different scales. The necessity of combination of theoretical analysis, field measurement and model test with the numerical ice tank is also elaborated. The research above can be aided to develop the numerical software for ice load determination for polar ships and offshore engineering structures, and to promote the implementation of the polar ocean strategy in China.

2021, 53(9): 2427-2453. doi: 10.6052/0459-1879-21-243

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DIRECT NUMERICAL SIMULATION OF DRAG REDUCTION IN TURBULENT BOUNDARY LAYERS CONTROLLED BY INCLINED BLOWING AND SUCKING

Xia Qianjin, Lian Long, Qu Jianxiong, Wang Yongsheng, Xue Yuan, Wang Qiang, Zhao Lihao

Reynolds shear stress (RSS) is an important source of high frictional resistance in wall turbulence. A theory suggests that the distribution of Reynolds shear stress in turbulent flow fields can be weakened through negative Reynolds stress (net positive) on walls in order to achieve drag reduction. However, integrals of the Reynolds−averaged Navier−Stokes equations indicate that the positive Reynolds stress (net negative) generated on a wall has a negative contribution to the skin friction coefficient of the wall. In this study, a series of inclined slits are being set up at the bottom of the control region for the turbulent boundary layer flow. Positive or negative wall Reynolds stress is generated by periodic blowing and sucking achieved by this device. Direct numerical simulation method is used to validate and explore the drag reduction theory described above. The turbulent boundary flow model used here has a Reynolds number (based on the outer flow velocity and momentum loss thickness) from 300 to 860. Through multiple sets of numerical simulations, the influences of jet strength and frequency on skin friction coefficient have been explored and the effects of positive and negative wall-generated Reynolds stress on the flow have been compared. Results show that the drag reduction rate associated with positive wall-generated Reynolds stress can reach 3.26, which is higher than that associated with negative Reynolds stress. It is concluded that the positive wall-generated Reynolds stress has a negative contribution to the skin friction, while the negative Reynolds stress has a positive contribution to the skin friction. Based on the gain-loss ratio, this control strategy is not able to obtain a net energy gain.

2021, 53(9): 2454-2467. doi: 10.6052/0459-1879-21-223

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STABILITY ANALYSIS OF VISCOELASTIC LIQUID DROPLETS EXCITED BY RADIAL OSCILLATIONS

Yao Muwei, Fu Qingfei, Yang Lijun

When a liquid drop is periodically excited by an external radial oscillation force, the instability of standing wave mode will be formed on its surface, which is known as the spherical Faraday instability problem. The oscillation frequency of the instability surface wave will render as a harmonic or sub-harmonic mode according to the different fluid physical parameters and the forced excitation conditions. Based on the linear small perturbation theory, this paper studies the instability behavior of the viscoelastic droplet surface wave subjected to the radial oscillating force. The oscillating radial force causes the momentum equations to be Mathieu equations which included time period coefficients. Therefore, the system becomes a parametric instability problem, which can be solved by Floquet theory. In this model, the characteristics of viscoelasticity are treated as an effective viscosity which related to the rheological model of the fluid, which simplifies the solving process of the problem. Based on the analysis of the neutral stability curve and growth rate of the surface wave, the influence of viscoelastic parameters on the stability of droplets were studied. The results showed that the increase of zero-shear viscosity (μ₀) as well as deformation retardation time (λ₂) can inhibit the growth of droplet surface wave, therefore increased the excitation amplitude which made the droplet unstable at a harmonic mode.With the increase of oscillation amplitude, the regions of unstable growth rate decrease, and as the oscillation frequency increase, the value of droplet surface wave growth rate decrease. Through the analysis of the growth rate, it can be concluded that the increase of the stress relaxation time (λ₁) increases the growth rate, thereby promoting the growth of surface wave on the droplet.

2021, 53(9): 2468-2476. doi: 10.6052/0459-1879-20-416

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NUMERICAL STUDY ON TWO-DIMENSIONAL ELECTRO-THERMAL CONVECTION IN A PARTIALLY HEATED CAVITY

Liu Zhentao, Xiao Li, He Kun, Wang Lei

In recent years, the active enhancement of heat transfer with electric field has drawn a wide attention in the field of heat transfer. Since the complex mathematical model as well as the strong nonlinear couplings between multi-physics, the theoretical analysis and experimental studies on this field are relatively few. In this paper, the lattice Boltzmann method is adopted to studied the two-dimensional electro-thermal convection in a partially heated cavity. The effects of dimensionless parameters such as Rayleigh number $Ra$, electric Rayleigh number $T$, length of electrode plate $h$, and the distance from the center of electrode plate to the lower wall $\delta$, on the heat transfer efficiency are investigated, and the bifurcation structure of the electro-thermal convection is also analyzed. Numerical results show that as the number of electric Rayleigh number $T$ increases, the heat transfer efficiency gradually increases, and the bifurcation type for electric Rayleigh number $T$ is usually subcritical. while the bifurcation type for the Rayleigh number $Ra$ is supercritical. In addition, when the electric Rayleigh number $T$ is larger enough, the coulomb force is dominant over the buoyancy force, and the effect of the Rayleigh number $Ra$ on heat transfer coefficient is insignificant. Further, a comparison of the heat transfer efficiency of the various electrode positions shows that the heat transfer efficiency is optimal when the electrode plate is in the middle of the left sidewall, and the smaller the length of the electrode plate, the more efficient of the heat transfer. The results of this article extend the existing two-dimensional electro-thermal convection model, and it can provide a reference for theoretical analysis of other electro-thermal convection problems with non-uniform temperature boundary.

2021, 53(9): 2477-2492. doi: 10.6052/0459-1879-21-205

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THEORETICAL ANALYSIS ON HYPERSONIC MHD SHOCK STAND-OFF DISTANCE OF BLUNT BODY

Li Yixiang, Wang Qiu, Luo Kai, Li Jinping, Zhao Wei

High speed and shock compression behind the bow shock of an aircraft head result in very high temperature, which would subsequently lead to a conductivity plasma flowfield around the vehicle. The plasma gas provides a direct working environment for the application of magnetic field. The magnetohydrodynamic (MHD) flow control, which uses the magnetic field to alter the trajectory of ions or electrons, can improve the aerodynamic characteristics of hypersonic vehicles effectively. As an intuitive aerodynamic phenomenon in the field of hypersonic MHD flow control, shock stand-off distance has attracted close attention from researchers. Under the influence of the applied magnetic field, the shock stand-off distance will change with it, of which the value can directly reflect the effect of the MHD flow control. However, the relevant theoretical models are still limited, and further development in this field is consequently needed. Focusing on dealing with this problem, MHD hypersonic shock stand-off distance of the spherical model is theoretically studied in this paper. By means of radially integrating the continuity equation and applying mathematical method of variable separation to the momentum equation, the analytical expression of MHD shock stand-off distance is obtained. The theoretical analysis was performed under the assumption of low magnetic Reynolds number, and the common-used dipole distribution of magnetic field as applied. The results show that the MHD stand-off distance of shock increases with the increase of magnetic interaction parameter. Moreover, the regularity can be found that as the speed of inflow becomes higher, magnetic interaction parameter can be viewed as the primary impact factor of shock stand-off distance under hypersonic condition. The theoretical model in this work can rapidly evaluate the effect of MHD control, and it can provide theoretical guidance to the design of experiment scheme and the analysis of results.

2021, 53(9): 2493-2500. doi: 10.6052/0459-1879-21-127

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THE STUDY ABOUT THE IMPACT OF THE FREE-SURFACE ON THE PERFORMANCE OF THE PROPELLER ATTACHED AT THE STERN OF A SUBMARINE

Li Peng, Wang Chao, Han Yang, Kuai Yunfei, Wang Shimin

The performance of the propeller attached at the stern of the submarine navigating under limited depths is affected obviously by the free-surface, duo to the changes of the flow field characteristics around this vehicle. And what mentioned above will greatly threaten the security of the maneuverability of the submarine. To figure out the effect of the free-surface on the performance of the propeller attached at the stern of the submarine. In this paper, the URANS (unsteady Reynold average Navier−Stokes) equations coupled with $ k - \omega $ turbulence model are used for the numerical simulations about performance of the self-propulsion model (the standard Sub-off geometry and the E1619 propeller). At first, the experimental data available including the resistance tests of the submarine with all appendages under total submergence, the resistance tests of the revolution with different navigating depths and the OWC (open water curve) of the propeller, is used for the validation of the numerical method adopted in this paper. Next, the correctness of the numerical method is acquired based on three sets of grids with different spatial resolutions. Finally, the performance of the self-propulsion model navigating under two depths and three different velocities is simulated carefully to figure out the effect of the free-surface on the performance of the self-model. The numerical results show that the exitance of the free surface increases the rotational speed of the propeller at a specific navigating speed, which corresponds to the self-propulsion point. The increment mentioned above is related to the wave pattern induced by the submarine. The wave pattern will cause the nozzle-like flow between submarine and free-surface. The nozzle-like flow and the suction of the propeller change the angle of attack of the blade profile at different radial sections. Meanwhile, approaching and getting away from free surface will also significantly change the hydrodynamic loads of the propeller.

2021, 53(9): 2501-2514. doi: 10.6052/0459-1879-21-063

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HYDRODYNAMICS OF A DUAL-CHAMBER OWC WAVE ENERGY CONVERTER IN HEAVING MOTION

Guo Quanshi, Deng Zhengzhi, Wang Xiaoliang, Cheng Pengda

The oscillating water column (OWC) wave energy conversion device have been recognized as the most promising wave energy conversion technology due to the advantages of its simple structure, convenient assembly and easy maintenance. A heave-only dual-chamber OWC device was numerically investigated by a well-developed open source software OpenFOAM coupled with a wave generation and absorption toolbox Waves2Foam. The volume of fluid (VOF) method tracking the water-air interface and the six-degree-freedom (6DOF) Dynamic Mesh solver duplicating the heave motion of the OWC device were employed to examine the influences of the relative width of the front and rear chambers and the spring elastic coefficient on the energy capture width ratio and hydrodynamic characteristics of the device under the actions of different incident regular waves. Through comparing the present results with the existing ones of a fixed dual-chamber OWC wave energy converter, and examining the free-decay motion of a cylinder, the rationality and effectiveness of the present numerical model has been revealed. The results show that the wider rear chamber can make for the extraction of wave energy of the dual-chamber OWC in heave motion. The heave-only dual-chamber OWC device can improve the device performance as the relative width ratio of the front and rear chambers is 1/2, and the rear chamber has larger capture width ratio in the middle and high frequency wave bands, compared with that of the fixed one. Multiple-peak values of the relative water surface elevation and the relative pressure occur in the whole test wave frequency bands due to the phase gap between the dual-chamber OWC device and the water columns in the front and rear chambers. In addition, it is found that by adjusting the spring stiffness coefficient, the wave-frequency bandwidth of high-efficiency can be significantly broadened and larger energy capture width ratio can be achieved.

2021, 53(9): 2515-2527. doi: 10.6052/0459-1879-21-072

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IMPACT ENERGY RELEASE AND DAMAGE CHARACTERISTICS OF TWO HIGH-ENTROPY ALLOYS

Hou Xianwei, Xiong Wei, Chen Haihua, Zhang Xianfeng, Wang Haiying, Dai Lanhong

In order to explore the impact energy release characteristics regularities of two typical high-entropy alloy materials, using the Φ14.5 mm ballistic gun launcher, the quasi-sealed test chamber system, two typical high-entropy alloy fragments, the FeNiMoW and the FeNiCoCr, were carried out the release energy effect tests at different impact velocities. Furthermore, the test platform was used to study the penetration and damage effect of two high-entropy alloy fragments to multi-layered targets, which were placed to the bottom of the test chamber. By changing the thickness of the steel target fixed in front of the test chamber, the impact release energy characteristics and damage regularities of two high-entropy alloy fragments to the subsequent multi-layered targets were studied. The study found that FeNiMoW and FeNiCoCr high-entropy alloy fragments began to react releasing chemical energy at around 1356 m/s and 1217 m/s, respectively. There was no chemical reaction reacted below this velocity. It was obvious that the impact velocities had a great influence to the release energy of the two high-entropy alloy fragments. As the velocity increased, the energy release response of the fragments became more intense, the peak overpressure showed a rising trend and the rising velocity became faster. As the thickness of the front steel target increased from 1 mm to 5 mm at an impact velocity of approximately 1600 m/s, it could be seen that the peak overpressures of FeNiMoW fragments showed a rise trend, and the peak overpressures of FeNiCoCr fragments showed a downward trend. In the process of the fragments perforating the front steel target and penetrating the multi-layered aluminum targets, the reduction of the release energy reaction degree will contribute to the enhancement of the penetration effect of the fragments, and the more increasing thickness of the front steel target will reduce the penetration and damage effect of the fragments to the multi-layered aluminum targets. On the other hand, as the thickness of the front steel target increases, the area of the first layer of aluminum target damaged by the fragments first increases and then decreases.

2021, 53(9): 2528-2540. doi: 10.6052/0459-1879-21-327

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DEFLECTION-BENDING MOMENT COUPLING NEURAL NETWORK METHOD FOR THE BENDING PROBLEM OF THIN PLATES WITH IN-PLANE STIFFNESS GRADIENT

Huang Zhongmin, Xie Zhen, Zhang Yishen, Peng Linxin

A neural network method is developed to solve the bending problems of functionally graded thin plates with in-plane stiffness gradient in this paper. The partial differential equation (PDE) of the bending of thin plates with in-plane stiffness gradient is a complex fourth-order PDE. The conventional neural network solution based on strong form, may face the problem of slow convergence and the boundary conditions are difficult to handle when solving the PDE. According to the Kirchhoff thin plate bending theory, a neural network solution to the bending problem of thin plates with any in-plane stiffness gradient in rectangular coordinate system is proposed in this paper. The neural network model includes deflection network and bending moment network, which are used to predict the deflection and bending moment of the thin plate respectively. Thus, the solution of the fourth-order PDE is transformed into a series of second-order PDEs. By constructing trial function of the deflection and bending moment, the results of neural network calculation can be strictly satisfied the boundary conditions. In the back propagation process, training error is calculated according to the error function formula proposed in this paper and combining Adam optimization algorithm to update the internal parameters of the neural networks. In this paper, the bending problems of thin plate with in-plane stiffness gradient with different boundary conditions and shapes are solved, and the calculated results are compared with theoretical solutions or those of finite element solutions. It shows that the proposed method is suitable for solving the bending problem of thin plate with in-plane stiffness gradient. And the convergence of bending moment network is slower than the deflection network. However, it is robust and easier in dealing with boundary conditions.

2021, 53(9): 2541-2553. doi: 10.6052/0459-1879-21-273

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VIBRATION ANALYSIS OF ELECTRIC VEHICLE-ROAD COUPLING SYSTEM CONSIDERING TIRE-ROAD MULTI-POINT CONTACT

Li Shaohua, Feng Guizhen, Ding Hu

The unsprung mass of the electric vehicle driven by the hub motor is large, which makes the tire dynamic load increase, and the motor excitation further aggravates the wheel vibration. Meanwhile, the dynamic calculation results of the simplified model of single point contact between tire and road are different from the actual. Thus, considering the electromagnetic excitation of the motor, nonlinear foundation and multi-point contact between tire and road, the electromechanical coupling dynamic model of the electric vehicle-road system is established. The vertical vibration of the nonlinear foundation beam is derived by the Galerkin method, and the accurate expression of the nonlinear integral term in the nonlinear foundation beam is derived by using the integral sum formula. A simple method to select the truncation order of the road is proposed, which is verified with the convergence of road response. Accordingly, the effects of multi-point contact between tire and road, nonlinear foundation, motor excitation, vehicle speed and road roughness amplitude on vehicle response are studied. The results show that among the effects of nonlinear foundation and multi-point contact on the vehicle response, the tire dynamic load has the largest influence, and the vehicle body acceleration and suspension dynamic displacement have a small effect. Moreover, when the motor excitation is considered, the influence of the two on the vehicle response increases. From the perspective of the influence on the road response, the motor excitation has the greatest, the nonlinear foundation has the second influence, and the multi-point contact has the less. The established model and research method provide a new idea for vertical dynamics analysis of electric vehicles.

2021, 53(9): 2554-2568. doi: 10.6052/0459-1879-21-239

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HOPF BIFURCATION STUDY OF WHEELSET SYSTEM

Wu Shijiang, Zhang Jiye, Sui Hao, Yin Zhonghui, Xu Qi

Aiming at the problem of nonlinear dynamics in the wheelset system, this paper analyzes the Hopf bifurcation point of the system based on the Hopf bifurcation algebraic criterion of the wheel considering the gyroscopic action, that is, the expression of the linear critical speed of the serpentine instability of the wheelset system. Based on the bifurcation theory, the first and second Lyapunov coefficient expressions of the wheelset system are obtained. Combining with the shooting method, the bifurcation diagrams of the wheelset system with and without the gyroscopic action under different longitudinal stiffness are also obtained. Through comparison with the bifurcation diagrams of the wheelset system with and without gyroscopic action, it is found that under the same longitudinal stiffness, both the linear critical speed and the nonlinear critical speed of the wheelset system considering the gyroscopic action are greater than those of the wheelset system without considering the gyroscopic action, that is to say, the gyroscopic action can improve the motion stability of the wheelset system. Based on the Bautin bifurcation theory, this paper takes the longitudinal stiffness and longitudinal velocity as parameters. In this way, wheelset systems with and without gyroscopic action are obtained, as well as the topological diagrams of the migration mechanism from subcritical Hopf bifurcation to supercritical Hopf bifurcation, and then from supercritical Hopf bifurcation to subcritical Hopf bifurcation. By comparing the Bautin bifurcation topological diagrams of the wheelset system with and without gyroscopic action, it is found that the gyroscopic action will change the degenerate Hopf bifurcation of the wheelset system, which, however, has little action on the Bautin bifurcation topology of the wheelset system.

2021, 53(9): 2569-2581. doi: 10.6052/0459-1879-21-321

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CONSTRUCRION AND ANALYSIS OF A NEW COMPUTABLE MODEL FOR BOLTZMANN EQUATION

Peng Aoping, Li Zhihui, Wu Junlin, Pi Xingcai, Jiang Xinyu

Due to large differences of geometric scale between the components of near space vehicles, the multi-scale complex non-equilibrium flow phenomenon will appear in many flow field regions when vehicles flying at high Mach number and high altitudes. In those regions the gas molecular velocity distribution functions are related to the local molecular velocities and macroscopic parameters, such as velocities, temperatures, heat flux vectors and stress tensors. By analyzing the first-order Chapman−Enskog approximate solution of Boltzmann equation, a new computable collision relaxation model is constructed, which considers the influence of heat flux vector and stress tensor, and satisfies the high-order collision moments of Boltzmann equation. The basic properties such as conservation law and H theorem are analyzed mathematically. The compatibility between the new model equation and Boltzmann equation is proved. The relationships between the new model and old models such as Shakhov and Belyi models are given. The expression of the collision relaxation parameter is determined by using molecular collision dynamics. As examples, one dimensional shock profiles and two dimensional flows around a flat plate and two side-by-side cylinders in near space environments are simulated by gas kinetic unified algorithm with different models. By comparing with results of DSMC method, it shows that in one dimensional problems the results of Shakhov model with heat flux is better than the new model because of smaller 1D shear stress, but in two dimension the new model can capture the position of shock wave better than the other two models due to higher dimensional shear stresses leading to more distinct viscosity effect. Especially for macro parameters in shock waves, the results of the new model accord with those of DSMC better. Then the validity and reliability of the new model is verified. These results illuminate that the collision relaxation model is influenced by multi-parameters together in the flow field when the non-equilibrium effects are quite distinct.

2021, 53(9): 2582-2594. doi: 10.6052/0459-1879-21-104

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DATA-DRIVEN GLOBAL DYNAMICS OF THE INDIAN OCEAN

Li Zigang, Yan Wang, Kang Jiaqi, Jiang Jun, Hong Ling

The inherent law and mechanism, underlying the complex ocean currents in sea, can offer scientific support for marine engineering, such as search and rescue at sea, pollutant diffusion forecast, shipping route design. In this paper, the generalized cell mapping method based on the idea of space discretization is proposed to carry out the global analysis for finding long-term and short-term dynamic structures underlying the Indian Ocean. Taking the typical monsoon and climate features in the ocean region into account, the one step transition probability matrices in different interval levels are created based on the drifter database from 1979—2019 to describe the evolutions of state of the system. Then, the long-term and short-term profiles of attraction (vortex core) and its region of influence (vortex area) are revealed and characterized by means of topological analysis. In comparison, the predicted distributions and features of responses are highly consistent with real observations of drifters to verify the rationality and validity of the proposed method and results. It is shown that the long-term vortex area is obviously presented in the region of latitude 20° to 45° south, longitude 40° to 96° east, which causes the dynamic concentration of drifters on the region, while the repellency for drifter trajectories is also observed both near the south of latitude 40° south and the equator. Meanwhile, the short-term dynamic vortices can dominate transient paths and tendency of drifters to induce the counterclockwise circulation of current in the southern Indian Ocean.

2021, 53(9): 2595-2602. doi: 10.6052/0459-1879-21-218

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EXPERIMENTAL RESEARCH ON QUANTIFICATION OF COUNTERCURRENT IMBIBITION DISTANCE FOR TIGHT SANDSTONE

Qi Songchao, Yu Haiyang, Yang Haifeng, Wang Yang, Yang Zhengming

China has an unbelievable number of tight oil reserves in storage, but a large majority of the tight oil reservoirs are in low sweep efficiency and in poor depletion development. Countercurrent imbibition is an important recovery mechanism for enhancing oil recovery during water injection development of tight oil reservoirs. At present, a large number of scholars have mainly conducted research on the imbibition recovery of tight oil reservoirs as well as the factors that may have influences on that, but actually there are few research on the imbibition distance that characterizes the range of imbibition effect in tight oil reservoirs. In this paper, the CT online scanning device is employed to establish a quantification method for countercurrent imbibition distance (CID) of tight cores, determining the range of countercurrent imbibition, and it also can make a further study on the influence of fluid pressure, water saturation, core permeability and surfactant on CID. In addition, it can be utilized to determine the relationship between CID and imbibition recovery. As a result, this study also provides theoretical guidance for enhancing oil recovery of tight oil reservoirs. The research results show that the CID scale of tight core with the permeability of about 0.3 mD is only 1.25 ~ 1.625 cm, and CID of the tight core with 0.302 mD under the condition of 5 MPa is 1.375 cm. Under the experimental conditions in this article, fluid pressure and initial water saturation have little effect on the CID of tight cores, while permeability and surfactant have significant effect on the CID of tight cores. What’s more, the CID of the core with 0.784 mD is 2.63 times higher than that of the core with 0.302 mD. In conclusion, the CID is a crucial parameter for the characterization of imbibition recovery, and it determines the range of countercurrent imbibition.

2021, 53(9): 2603-2611. doi: 10.6052/0459-1879-21-298

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2021 Vol. 53, No. 9

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