力学学报

RESEARCH PROGRESS ON MULTIBODY AERODYNAMICS

Song Wei, Ai Bangcheng

Multibody vehicle widely exists in the fields of aerospace and weapon system. There are three main types for the multibody vehicle system. Firstly, multiple vehicles are in close proximity flight that do not touch each other, such as formation flight and towed flight. Secendly, multibody vehicle are in contact with each other or combined to flight as a whole, such as aircraft-store carriage, the booster-flight of multistage vehicles, etc. Finally, multibody vehicle is in the relative motion after recovery or separation, such as aircraft-store separation, stage separation of multistage vehicles, etc. Multibody interference or interaction universally exists in the flowfield of multibody vehicle during steady or unsteady flight and dynamic separation, which makes the flow physics or characteristics of multibody vehicle different from isolated-body vehicle, especially in supersonic and hypersonic flow. There are multiple shock-wave reflection and diffraction, interference or interaction between shock-wave and vortex, shock-wave and boundary layer among multibody vehicle, which can significantly change the aerodynamic characteristics of multibody vehicle. The concept of “multibody aerodynamics” is advocated to summarize the field of multibody vehicle, and its basic connotation, application fields and flow characteristics of typical multibody configurations are explained, in order to point out the direction and ideas on aerodynamics and separation dynamics of multibody vehicle for the future research.

2022, 54(6): 1461-1484. doi: 10.6052/0459-1879-22-096

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THREE-DIMENSIONAL SHOCK SEPARATED FLOW CORRECTIONS OF k-ω SST MODEL

Du Yiming, Gao Zhenghong, Shu Bowen, Qiu Fusheng, Song Chenxing

Shock/boundary-layer separation is a typical turbulence non-equilibrium flow in the field of aeronautical aerodynamics. Accurate simulation of shock separated flow is of great significance for aerodynamic performance evaluation and optimization of transonic aircraft. The definition of eddy viscosity coefficient in conventional eddy-viscosity turbulence models (EVM), however, is not suitable for non-equilibrium flow. The Bradshaw assumption introduced by k-ω SST turbulence model for this purpose instead restricts the generation of Reynolds stress when applied to three-dimensional flow with strong adverse pressure gradient and large separation, which results in the invalidity of k-ω SST model as well as other commonly used EVMs for this kind of flow. Moreover, the existing nonlinear constitutive relation of Reynolds stress cannot effectively improve the simulation accuracy. To this end, two shock separated flow correction methods respectively based on Bradshaw assumption and length scale are proposed for k-ω SST model. The former correction relaxes the limitation of Reynolds stress generation by increasing Bradshaw constant. While based on the concept of turbulence length scale, the latter correction constructs a modified function for the dissipation term of the ω equation by using the mixing length theory, the generation-dissipation ratio of turbulent kinetic energy and a newly defined ratio of length scale to improve the modeling length scale in three-dimensional shock separated flow. The two methods both get better simulation results for the transonic flow of ONERA M6 wing at high angle of attack than those of Reynolds stress model. Further Reynolds stress analysis reveals that the concept of "major Reynolds-stress component" in three-dimensional shock separated flow is no longer tenable since the magnitude of each Reynolds-stress component is close. The grid convergence analysis, and verifications on other angles of attack and the wall-function law of turbulent boundary layer on the flat plate further confirm the validity, applicability and universality of the proposed correction methods.

2022, 54(6): 1485-1501. doi: 10.6052/0459-1879-22-065

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DEVELOPMENT OF A NUMERICAL WAVE TANK WITH A CORRECTED SMOOTHED PARTICLE HYDRODYNAMICS SCHEME TO REDUCE NONPHYSICAL ENERGY DISSIPATION

Huang Xiaoting, Sun Pengnan, Lü Hongguan, Zhong Shiyun

So far, the smoothed particle hydrodynamics (SPH) method has been widely applied in the study of the interactions between water waves and structures. However, nonphysical energy dissipation is a still problem which challenges the simulation of wave-body interactions at large-scale and long duration. For example, in the SPH simulation of wave propagation to a long distance, the wave height could gradually become much smaller than the one generated near the wave maker. To tackle this problem, in this work a kernel correction algorithm is applied to the pressure gradient term in the SPH model, aiming to prevent nonphysical energy dissipation in long time simulations. The kernel correction algorithm is able to ensure the symmetry of the interaction between particle pairs, and therefore, compared with other corrective methods, the present corrected algorithm ensures the conservation of linear momentum and also avoids the complicated treatment at the free surface. Two numerical cases, i.e., the oscillating droplet and wave propagation in a numerical wave tank, are presented to test the accuracy and validity of present corrected SPH algorithm. For the oscillating droplet case, the corrected algorithm is shown to accurately simulate the evolution of the droplet shape, and the kinetic energy is dissipated much slower than traditional SPH models. Through the simulations of regular and irregular wave propagations as well as validations with experimental data, the capability of the corrected SPH algorithm to reduce nonphysical energy attenuation is demonstrated, even for wave propagation at long-term and long-distance conditions. In addition, this algorithm will be shown to be optimal for the SPH simulation at small smooth length, which contributes to save SPH computational cost significantly at three dimensional simulations.

2022, 54(6): 1502-1515. doi: 10.6052/0459-1879-22-041

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INERTIAL RETRACTION OF LIQUID FILM ON MODERATELY WETTABLE PLATE

Wan Qiwen, Chen Xiaopeng, Hu Haibao, Du Peng

Spreading and rebounding of drop on solid substrate are of great significance in industry and scientific research, where the evolution of morphology of a drop is investigated frequently. It is normally believed that a spread drop retracts in inertia-capillary regime with a speed deduced by a Taylor-Culick procedure. Experimental and finite element method studies were conducted, which show that a drop retracts on moderately wettable plate with a low speed after the aforementioned inertia-capillary retraction. The speed has a value as low as 1/10 of the first retracting stage. The mechanism is explored according to the experiments and additional numerical simulations. It is found that the low-speed retraction depends on the density and capillary of the liquid, rather than the viscosity and wall condition (including the wettability and slip characters). It is revealed that the process is still dominated by capillary-inertial effects. The findings are also validated on the liquid with viscosity as high as 10 times of the original one in simulations. The research is valuable for studying droplet dynamics and relative industrial processes.

2022, 54(6): 1516-1522. doi: 10.6052/0459-1879-21-663

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DIRECT NUMERICAL SIMULATION OF SINGLE ABLATIVE PARTICLE DYNAMICS IN NEAR-WALL COUETTE FLOW UNDER AERODYNAMIC LOAD

Li Tingting, Li Qing, Tu Guohua, Yuan Xianxu, Zhou Qiang

When hypersonic vehicles reenter the atmosphere, the surface thermal protection materials will ablate under the action of high temperature airflow. In the process, the ablative particles will entrance the high temperature airflow and affect boundary-layer transition and turbulence characteristics downstream. Those phenomena will also happen in an arc-heated wind tunnel when conducting material thermal response experiments. Therefore, it is a significant basic scientific problem to study the transport behavior of inertial ablative particles under aerodynamic load. In this article, we analyzed the flow condition and particle exfoliation process very near a hypersonic vehicle wall with dimensional theory. After a series of reasonable assumptions and simplifications, we modelled the ablative particle exfoliation and transport process as one spherical inertial particle in Couette flow and adopted the particle resolved-direct numerical simulation (PR-DNS) method to study it. As a result, the particle exfoliation and transport characteristics were revealed and a normalized expression of particle start-up velocity was obtained, which would provide theoretical basis for accurate prediction of particle mass loss in the future. The research findings show that as the particle fluid density ratio$ {\rho _r} $increases, the particle inertia St increases, and the horizontal and normal velocities of particle decrease. The larger the particle diameter is, the larger the particle inertia St is, and the horizontal velocity of the particle decreases. However, the normal velocity and displacement of the larger particle are increased. The reason is maybe larger particles receive larger Saffman lift force. Besides, the normal displacement of ablative particles is much smaller than the horizontal displacement, so the particles are mainly transported horizontally. In order to find the unified law underlying all the regularities, we defined the start-up velocity and found that the normalized particle start-up velocity is a function of the particle and fluid inertia, i.e., the particle horizontal transport velocity is the velocity of fluid or neutral buoyant particle minus the inertia correction term.

2022, 54(6): 1523-1532. doi: 10.6052/0459-1879-21-604

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EXPERIMENTAL INVESTIGATION ON THE REGIMES OF HYDROCARBON SUPERSONIC COMBUSTION

Meng Fanzhao, Zhou Ruixu, Li Zhongpeng, Lian Huan

Numerical simulations of high-fidelity aerospace engines are usually based on the rapid chemical reaction flame surface assumption, that is, the characteristic scale of supersonic combustion reaction is smaller than the turbulent Kolmogorov scale. This model method has good simulation results for hydrogen fuel, but further research is needed for hydrocarbon fuels such as ethylene. Limited by the extreme environment special nonintrusive measurement techniques, experimental investigations on the discrimination of supersonic combustion flame mode have not been presented in literature. The applicability of the supersonic combustion flame surface model and understandings of the regimes of supersonic combustion restricts the development of high fidelity numerical simulation methods. Based on the in house designed MHz endoscope optical fiber sensor, experiments are designed to study the regimes of supersonic combustion of a dual-mode scramjet combustor. The minimum Shannon entropy of the chemiluminescence signal is used to define the characteristic time of supersonic combustion. The flow characteristic time of supersonic combustion is estimated according to the theoretical method and the incoming flow conditions. Combined with the partition combustion theory, the partition situation of hydrocarbon fuel combustion in a dual-mode scramjet is analyzed. Through combustion zoning and comparison with Taylor scale .The data presented in this paper suggests the supersonic combustion in the vortex framelet regime in a typical flight envelope (Re$\cong $50000; Da∈1.80-2.60, B zone), suggesting the strong influence of turbulence,With different sizes relative to the Taylor scale, vortex structures corresponding to different scales dominate the process. In addition, parametric evaluation on the influence of equivalence ratio, flux ratio and Mach number during a simulated acceleration is presented in this paper. The experiment found that the combustion gradually increased with the increase of the equivalence ratio within a certain range, and the enhancement effect was obviously stronger than that of the flux ratio; the change of the flux ratio would cause the combustion to bifurcate; the change of the incoming Mach number was important for The effect of combustion is more obvious, and it also shows that the effect mechanism of incoming flow is an important direction for future research on turbulent combustion theory.

2022, 54(6): 1533-1547. doi: 10.6052/0459-1879-21-686

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AUTO-IGNITION TABULATED METHOD FOR SUPERSONIC COMBUSTION AT HIGH MACH NUMBER

Zhang Jincheng, Wang Zhenguo, Sun Mingbo, Wang Hongbo, Wang Yanan, Liu Chaoyang

When the scramjet combustor works under high Mach number conditions, the total enthalpy of the inlet air is very high, and auto-ignition becomes an important physical and chemical process to maintain flame stability. This paper develops an auto-ignition tabulated method based on chemical kinetics, referring to the dimensions reduction means of the flamelet/progress variable model. The complex and multi-dimensional chemical reactions is reduced by defining the mixture fraction and progress variables, and the database method is successfully integrated into the existing large eddy simulation solver. After testing and verification, the method possesses the ability to simulate and describe the supersonic auto-ignition and flame. Numerical simulation is carried out for supersonic combustion induced by auto-ignition in two configuration. This method effectively reduces the amount of calculation in the process of solving chemical reactions by looking up the database. When the detailed chemical reaction mechanism is used, the auto-ignition behavior and flame structure can be accurately reproduced, and the predicted temperature and the distribution of important components are in good agreement with the experiment.

2022, 54(6): 1548-1556. doi: 10.6052/0459-1879-21-635

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NUMERICAL STUDY OF MULTISCALE CAVITATING FLOW AROUND A HYDROFOIL

Tian Beichen, Li Linmin, Chen Jie, Huang Biao, Cao Junwei

The multiscale effect of cavitation is a complex hydrodynamic phenomenon involving macroscale cavitation, microscale cavitation bubbles and transformation between scales. The cavitating flow around a NACA66 hydrofoil is simulated based on the established Euler-Lagrange algorithm. The macroscale cavitation vapor was captured through a large eddy simulation (LES) method and the volume of fluid (VOF) method in an Eulerian analysis. The motion, growth and collapse of sub-grid scale discrete bubbles were solved through discrete bubble model (DBM) in Lagrangian frame. Meanwhile, the solution model of different scale cavitation is selected through the comparison of scale between cavitation cavity and the local grid. The experimental results are compared with the numerical results to verify the accuracy of the numerical method. The results show that the number of discrete bubbles is closely related to the development of cloud cavitation. The number of discrete bubbles fluctuate little in the growth stage of attached sheet cavity with the bubbles mainly distributed at the interface of water and vapour. With the re-entrant jet occur at the trailing edge of attached cavity and develop to leading edgy of hydrofoil, the bubble number gradually increase and fill up the jet disturbance region. When the cavity detach, converge and shed downstream along with the hydrofoil, the discrete bubble number increase rapidly and the bubbles dispersed in the mixing region of water and vapour. Moreover, the probability density function of discrete bubble diameter conforms to Gamma distribution for the whole stage of cloud cavitation. With the increase of cavitation diameter, the number of cavitation first increases and then decreases. Additionally, the characteristics of the cavitation turbulent flow field have an important influence on the distribution of bubbles, and the discrete bubble is mainly distributed in the region of strong turbulence intensity, vortex and re-entrant flow.

2022, 54(6): 1557-1571. doi: 10.6052/0459-1879-22-022

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NUMERICAL SIMULATION OF FULL PHASES OF COLLAPSE OF THREE-DIMENSIONAL CYLINDRICAL GRANULAR PILE

Chen Fuzhen, Li Yaxiong, Shi Tengda, Yan Hong

The collapse of static granular pile under gravity is the basis for understanding many human processes and natural phenomena. There are some difficulties for the traditional simulation methods, such as large number of single particle tracking, obvious rheological characteristics, and complex phase evolution of macro simulation. Based on the physical mechanism of different phases in granular media, the concept of full phases is defined and divided into three regions. According to the stress-strain relationship and volume fraction of granular media, the existing theories describing each phase are effectively combined by determining the coupling relationship and transformation criteria between different phases, and the coupling model theory describing all phase states of granular media is established. Then the physical model of granular media is solved with the strategy of coupling smoothed discrete particle hydrodynamics and discrete element method. The coupling and transformation algorithm between different phase particles is clarified and the particle size independence of the diameter selection of the initial SDPH particles is tested. The numerical simulation of collapse process of granular pile under different aspect ratio is realized. The calculated results are in good agreement with the experimental results. At the same time, compared with the discrete element method, the amount of calculation is controlled. It not only captures the different phenomena of deposition after granular pile collapse under the influence of different parameters, but also obtains the effects of different conditions and parameters on the spreading characteristics of granular pile after collapse are obtained, which provides effective support for revealing the complex motion mechanism of granular media widely existing in industry and nature.

2022, 54(6): 1572-1589. doi: 10.6052/0459-1879-22-001

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PROBING INTO THE CREEP MECHANISM OF AMORPHOUS ALLOY BASED ON QUASI-POINT THEORY

Xu Zongrui, Hao Qi, Zhang Langting, Qiao Jichao

As a typical multi-body interaction and non-equilibrium system, how to clarify the deformation mechanism under multi-field coupling stimuli and then establish the intrinsic correlation among the deformation behavior, flow characteristics and microstructure evolution of amorphous alloys keep the fundamental topic. In the current work, a prototypical La_56.16Ce_14.04Ni_19.8Al₁₀ amorphous alloy which shows a pronounced slow $ \;\beta $ relaxation process was selected as the model system. Series of creep experiments of the amorphous alloy over wide temperature and stress range were carried out. Evolution of creep compliance $ J $, quasi steady-state strain rate $ \dot{{\varepsilon }_{s}} $, characteristic relaxation time $ \tau $, stress index $ n $along with the apparent activation energy for creep ${Q}_{{\rm{app}}}$were systematically investigated in order to probe into the deformation mechanism involved in the creep process of amorphous alloys. In parallel, a gradual transition of deformation mode from elasticity to viscoelasticity and viscoplasticity of amorphous alloys during creep was analyzed. In the framework of the quasi-point defects theory, a complete picture delineating the deformation process of amorphous creep was probed from the perspective of microstructure evolution. The results demonstrated that the creep deformation of amorphous alloy is a typical thermo-mechanical coupling and nonlinear mechanics process, which could be affected by experimental temperature, applied stress and loading time. The creep mechanism of amorphous alloy is dominated by the diffusion which is related to thermal particle flow when the applied stress is lower. On the other hand, when the stress is higher, the creep mechanism corresponds to more complicated synergistic actions consisting of both stress-induced collective rearrangements of atoms and temperature-induced thermal activation. In addition, the underlying physical background of the elastic-plastic transition of the amorphous alloy during creep deformation was described, which is correlated to the initiation of quasi-point defects as well as the formation, expansion and coalescence process of sheared micro-domains under thermo-mechanical stimuli.

2022, 54(6): 1590-1600. doi: 10.6052/0459-1879-22-059

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THERMOELASTIC DAMPING IN FUNCTIONALLY GRADED MINDLIN RECTANGULAR MICRO PLATES

Li Shirong

Accurately modelling and evaluating of thernoelastic damping (TED) in functionally graded material (FGM) micro plates are challenging novel topics in the study on the responses of thermoelastic coupled vibration of this kind of new type micro resonators. In this paper, TED in a simply supported FGM rectangular micro plate with moderate thickness is investigated by means of mathematical analysis. Based on the Mindlin plate theory and the one-way coupled heat conduction theory, differential equations governing the thermal-elastic free vibration of the FGM micro plates with the material properties varying continuously along with the thickness direction are established. Under the adiabatic boundary conditions at the top and the bottom surfaces, analytical solution of the temperature field expressed by the kinematic parameters is obtained by using layer-wise homogenization approach. As a result, the structural vibration equation including the thermal membrane force and moment is transformed into a partial differential equation only in terms of the amplitude of the deflection. Then, by using the mathematical similarity between the eigenvalue problems an analytical solution of the complex frequency for an FGM Mindlin micro plate with the four edges simply supported is arrived at, from which the inverse quality factor representing the TED is extracted. Finally, numerical results of TED for the FGM rectangular micro plate made of ceramic-metal constituents with the material properties varying in the thickness as power functions are presented. Effects of the transverse shear deformation, the gradient of the material property and the geometric parameters on the TED are quantitatively investigated in detail. The numerical results show that the TED evaluated by the Mindlin plate theory is smaller than that by the Kirchhoff plate theory and that the difference in the values predicted by the two plate theories becomes significant along with the increase of the thickness-to-side length ratio.

2022, 54(6): 1601-1612. doi: 10.6052/0459-1879-22-055

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ENERGY BALANCE SIZE EFFECT MODEL OF COMPRESSIVE STRENGTH FOR QUASI-BRITTLE MATERIALS

Liu Xiaoyu, Yang Zheng, Zhang Huimei

To address the problem of existing size effect models cannot reflect complete size effect of compressive strength and internal mechanism of quasi-brittle materials. In this paper, by analyzing energy input, storage, global-local energy dissipation during the failure process of quasi-brittle materials under uniaxial compression, mechanical model and bilinear nominal and true stress-strain curves are established to reflect global and local damage and describe the above energy evolution process respectively. On this basis, the expressions of input energy, stored elastic energy and global-local energy dissipation are determined when the nominal stress is the maximum. Finally, size effect model of compressive strength is established with energy balance principle. The energy balance size effect model of compressive strength can completely reflect the size effect of nominal compressive strength, namely with the increase of sample size, nominal compressive strength is the real strength when sample size is less than or equal to the size of local damage zone, and then gradually decreases, eventually tends to the elastic ultimate strength when the sample size approaches infinity. High to diameter ratio together with sample diameter can be taken into account in the energy balance size effect model of compressive strength. Its parameters, which can reflect the effect of real strength, elastic ultimate strength, nonlinear of nominal damage modulus, size and direction of local damage zone on nominal compressive strength size effect of quasi-brittle materials, have clear physical meaning. Experiment and numerical simulation data of various materials are utilized to validate and evaluate the energy balance size effect model of compressive strength and existing size effect models. The results indicate that the energy balance size effect model of compressive strength can well describe the nonlinear variation and internal mechanism of size effect of experiment and numerical simulation, and compared with the existing size effect models, its total average error is the smallest and less than 5%.

2022, 54(6): 1613-1629. doi: 10.6052/0459-1879-21-460

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RESEARCH ON DYNAMIC CRUSHING AND MECHANISM OF MITIGATION AND ENERGY ABSORPTION OF CELLULAR SACRIFICIAL LAYERS

Fan Dongyu, Su Binhao, Peng Hui, Pei Xiaoyang, Zheng Zhijun, Zhang Jianxun, Qin Qinghua

In this paper, the dynamic crushing behavior and the mechanism of mitigation and energy absorption of the cellular sacrificial layers subjected to the intensive dynamic loading are investigated theoretically and numerically. Based on the rigid, perfectly plastic, locking (R-PP-L) and the rigid, plastic hardening (R-PH) constitutive models of the cellular materials, a theoretical model of the dynamic response of the cellular sacrificial layers subjected to the intensive dynamic loading is developed. The one-dimensional shock wave propagation in the cellular sacrificial layers is analyzed further. Finite element model is established by employing the Voronoi method and the numerical simulations are carried out to obtain the deformation modes and the response curves whilst the effect of interface on the mitigation and the energy absorption of the cellular sacrificial layers is discussed in detail. It is shown that the theoretical model considering the plastic hardening of cellular materials (R-PH model) can effectively predict the reflection of incident wave at the distal end and the secondary compression process of the cellular sacrificial layers as well as the enhancement phenomenon of the end stress than the R-PP-L model. Comparisons between the continuous and discontinuous interface models demonstrate that the continuous design of the cellular sacrificial layers can enhance the mitigation and the energy absorption while the interfaces separated by the rigid plates can decrease the effect of the incompleteness of interface cells. The peak stresses at the ends subjected to the same momentum increase with the increase of impact energy. It is possible that the reflection of the shock wave at the ends results in the stress enhancement at the ends.

2022, 54(6): 1630-1640. doi: 10.6052/0459-1879-22-047

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A NUMERICAL SIMULATION METHOD FOR THE ELASTIC ANISOTROPY OF SINGLE CRYSTAL ICE BASED ON PERIDYNAMICS

Huang Yan, Wang Jianping, Sun Jianqiao

The anisotropy in the deformation and failure of natural ice, originating from the anisotropy of single crystal ice, is the main reason of the complex loading process during the ice-structure interaction. However, studies on the numerical simulation method of the anisotropy of single crystal ice are still rare in the academic community. To simulate such mechanical property of ice, a numerical simulation method for the elastic anisotropy of single crystal ice is proposed in this paper based on the theory of peridynamics. In the present method, the variation of Young's modulus of single crystal ice along different loading directions with respect to the c-axis obtained from published experimental results is adopted in the influence function of the force density vector in the state-based peridynamic model. Based on the numerical simulations of the uniaxial compression of single crystal ice along the loading directions of 0°, 45° and 90° with respect to the c-axis, correction method for the influence function of the peridynamic model, as well as the calibration procedure for the related auxiliary parameters, are proposed in this paper. Furthermore, validations of the Young's modulus for other loading directions including 15°, 30°, 60° and 75° are made, and good agreement has been achieved according to the comparison between the numerical and the reference experimental values. The results show that the correction method and calibration procedure presented in this paper can efficiently find the optimal solution to the influence function for the consistency between the Young's modulus of the numerical model and the reference Young's modulus from the published experiments, which indicates that the proposed numerical method based on peridynamic theory can sensibly simulate the elastic anisotropy behavior of single crystal ice. The main findings in this paper can provide basic reference for the future development of the numerical simulation method for the anisotropy of polycrystalline ice.

2022, 54(6): 1641-1650. doi: 10.6052/0459-1879-22-064

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ISOTROPICALLY TRANSFORMED STRESS METHOD FOR THE ANISOTROPY OF SOILS

Yao Yangping, Tang Kesong

The anisotropy of the material refers to the differences in mechanical parameters, structural characteristics and stress-strain relationships of different directions. Establishment of proper strength criteria and reasonable constitutive models which can accurately illustrate this complex characteristic of materials is a huge contribution to the theoretical studies of constitutive relations of materials. However, the anisotropy of materials has always been a major difficulty for researchers in determining the mechanical properties of materials. In order to demonstrate the abstract affection of the materials’ anisotropy, professor Quanshui Zheng proposed the isotropicization theorem, providing valuable thoughts and referential ideas for subsequent researchers to deal with the anisotropy problem. Building on these ideas, the authors proposed the transformed stress (TS) method. The TS method focused on the stress-induced anisotropy of granular geotechnical materials, introduced another train of thought to describe the anisotropy of materials. The TS method followed the theory of professor Zheng about isotopicizing the anisotropy of the materials, which can be considered as a development of the isotropicization theorem. The aim of this article is to clarify the internal connection between the isotropicization theorem and the transformed stress method through the analysis of the deduction progress of transformed stress method. Also, the practical problems faced in the anisotropy treatment process of specific materials and how these problems can be solved with TS method was illustrated with an example of the stress-induced anisotropy treatment of soil materials. In this paper, three reasonable assumptions in practical application of the TS method have been raised, and the specific stress transformation formula is deduced. Also, the significance of applying the TS method even when knowing the specific functions considering the anisotropy of geotechnical materials has been delivered, and the necessity of application of TS method in the progress of constructing soil elastic-plastic constitutive models has also been proved.

2022, 54(6): 1651-1659. doi: 10.6052/0459-1879-21-651

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STUDY ON THE EVOLUTION OF LIQUID BRIDGE FORCE BETWEEN FLAKY PARTICLES

Liu Fengyin, Jiang Jingxi, Li Dongdong

Studying the liquid bridging force between particles can help reveal the internal mechanism of the water-holding properties of unsaturated soils. In order to explore the evolution law of the liquid bridge force between flaky particles and study the hydraulic characteristics of unsaturated soils from a meso-scale scale, the Surface Evolver software was used to construct a three-dimensional liquid bridge model between two parallel flaky particles, and the tension of the liquid bridge was analyzed. The influence of contact angle, liquid bridge volume, separation distance and the pinning effect of the solid-liquid contact line on the law of the change of the liquid bridge force during the process. Based on the arc assumption, calculate the liquid bridge force and the size of the contact radius under the corresponding conditions, and compare and analyze the results with the above simulation results. The results show that the liquid bridge force between flake particles increases with the increase of the liquid bridge volume, decreases with the increase of the separation distance, and first increases and then decreases or decreases with the increase of the solid-liquid contact angle; when the liquid bridge volume is constant In the pinning state, the force first increases rapidly with the increase of the separation distance, reaches the peak value, and then gradually decreases; the Surface Evolver simulation is compared with the calculation result of the annular approximation of the liquid bridge interface, when the solid-liquid contact angle is large (θ = 60° and θ = 80°), the relative error of the two is within 6%, and when the solid-liquid contact angle is reduced to 30° and below, the relative error increases, and the particles The greater the separation distance, the greater the relative error.

2022, 54(6): 1660-1668. doi: 10.6052/0459-1879-21-628

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A NUMERICAL STUDY ON FLAPPING DYNAMICS OF A COMPOSITE LAMINATED BEAM IN SHEAR FLOW

Liu Hao, Qu Yegao, Meng Guang

We present a numerical study of the large deflection flapping dynamics of a composite laminated beam in a shear axial flow. A higher-order shear deformation zig-zag theory combined with von Kármán strains is adopted to characterize the geometrical nonlinearity of the composite laminated beam. The finite volume method based on an arbitrary Lagrangian-Eulerian (ALE) approach is employed to solve the Navier-Stokes equation of incompressible viscous fluid. A strongly coupled, partitioned fluid-structure interaction method is adopted to accommodate the dynamic coupling of the two-dimensional shear flow and the laminated beam. The validity of the present method is confirmed by analysing the flapping characteristics of composite laminated beams, which with difference in elasticity between the two layers, subjected to a uniform axial flow. We investigate the effects of shear velocity profile on the flapping characteristics (including limit-cycle oscillation, vortex shedding frequency, and flow pattern) of single isotropic beams and composite laminated beams in a shear axial flow. It is found that with the increase of shear velocity slope, the deflection of the flapping motion neutral axis increases, the standard deviation and dominant frequency of transverse flapping displacement at the beam tip first decrease and then increase. In addition, the differences in the wake vortex modes are discussed. The flapping characteristics of laminated beams with difference in elastic modulus, thickness and ply angle between the two layers are studied. The increase of the difference in elastic modulus changes the symmetry of the laminated beam flapping motion trajectory. Three distinct response regimes are observed depending on the difference in thickness and ply angle between the two layers: fixed-point stable regime, periodic limit-cycle oscillations regime, and aperiodic oscillations regime. The change of thickness ratio of laminated beams makes its vibration regime change from periodic limit cycle oscillations regime to fixed-point stable regime. The increase of the ply angle of laminated beams changes the flapping regime from periodic limit cycle oscillations regime to aperiodic oscillations regime.

2022, 54(6): 1669-1679. doi: 10.6052/0459-1879-22-114

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NOETHER SYMMETRIES AND CONSERVED QUANTITIES OF WALL CLIMBING ROBOT SYSTEM

Fu Jingli, Lu Xiaodan, Xiang Chun

The wall climbing robot's motion is a kind of imitation gecko's crawling motion. The wall climbing robot's motion can be divided into four limbs driving the body's movement. The previous research is based on Newton's mechanics. In this paper, Lagrange mechanics method is used to establish the motion equation of the wall climbing robot system, and the Noether symmetry theory of the system is established by using the Lie group analysis method, and the motion law of the wall climbing robot is obtained. Firstly, the kinetic energy, potential energy, Lagrange functions and nonholonomic constraints of nonholonomic wall climbing robot system are given, and the Lagrange equation of nonholonomic wall climbing robot system is established. Secondly, by introducing infinitesimal transformation of time and generalized coordinates, the basic variational formulas of Hamilton action and Hamilton action of nonholonomic wall climbing robot system are proposed. Thirdly, the wall climbing robot system is given The definition, criterion and existing Noether conserved quantity of Noether symmetry transformation and generalized quasi symmetry transformation are introduced. The Noether theorem of non conservative holonomic system and non conservative nonholonomic wall climbing robot system is proposed. Finally, taking the wall climbing robot on the conic surface as an example, the given conserved quantity is directly integrated, and the exact solution of the whole motion of the wall climbing robot on the conical surface and the motion of the limbs are given The numerical results show that the motion law of the wall climbing robot is found and the Noether symmetry theory of the nonholonomic wall climbing robot system is well verified. This paper proposes a new symmetry solution method for Lie group analysis method applied to other complex robot systems and flexible robot systems.

2022, 54(6): 1680-1693. doi: 10.6052/0459-1879-22-084

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INTERVAL UNCERTAINTY ANALYSIS METHODS FOR MULTIBODY SYSTEMS BASED ON SIGNAL DECOMPOSITION AND CHEBYSHEV POLYNOMIALS

Jiang Xin, Bai Zhengfeng, Ning Zhiyuan, Wang Siyu

Uncertainty inherited in the parameters of multibody systems will induce significant deviation on the dynamic responses. The interval analysis method, which only need the information of lower and upper bounds of the interval uncertain parameters, can efficiently consider uncertainties in the dynamics analysis of multibody systems. The bounds of responses obtained by the CIM (Chebyshev interval method) for multibody systems in the presence of interval uncertainty would deteriorate with the increase of time history. To circumvent this problem, two novel methods CIM-HHT (Hilbert-Huang transform) and CIM-LMD (local mean decomposition), which combine signal decomposition technique and Chebyshev polynomials, are developed in this paper to accurately envelope the long period interval responses of system under interval uncertainty. The HHT and LMD are combined, respectively, with the Chebyshev polynomials to approximate the instantaneous amplitude and phase obtained by signal decomposition. HHT and LMD can decompose the multicomponent responses of multibody system into the sum of several monocomponent and a trend component. Then, the instantaneous amplitude and instantaneous phase of the monocomponent, and the trend component can be employed to construct corresponding surrogate model by the Chebyshev polynomials, respectively. Based on the surrogate models for the instantaneous amplitude, instantaneous phase and trend component, the coupling entire surrogate model for the system can be established and the upper bound and lower bound of the system responses can be calculated subsequently. To verify the accuracy and effectiveness of the proposed methods, a simple pendulum and a crank slider under interval uncertainty are presented. Numerical results demonstrated that the CIM-HHT and CIM-LMD present desirable computational accuracy in the procedure of long period interval dynamic analysis of multibody systems. Furthermore, compared with CIM-HHT, the CIM-LMD is characterized with weaker end effect and high computational accuracy in the long period interval dynamic analysis of multibody systems.

2022, 54(6): 1694-1705. doi: 10.6052/0459-1879-22-092

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ENERGY SAVING MECHANISM OF HYDRODYNAMIC COLLECTIVE BEHAVIOR OF MULTIPLE FLEXIBLE BEAMS IN V FORMATION

Zhang Lei, Ao Lei, Pei Zhiyong

The phenomenon of aggregation of animals in V formation is ubiquitous in our daily life, such as bird flocks in migration. It is commonly recognized that this collective mode helps to save energy of the group. However, little direct evidence is given. Research on the energy saving mechanism of this collective behavior can not only help to improve the understanding of nature secret, but also lay a foundation for its bionic application. In this paper, a simulation method developed based on Fluent is adopted to solve this fluid-structure interaction problem of hydrodynamic collective behavior of multiple flexible beams in V formation. Specifically, finite volume method is used to simulate the flow field, governing equations of Euler-Bernoulli beam are complemented through user-defined function, and then solved by the mode superposition method and fourth-order Runge-Kutta method. Dynamic mesh technique is adopted to trace the coupling interface between flow field and structural field. The hydrodynamic aggregations of multiple (three or five) self-propelled 2D flexible beams in V configuration are simulated. Three propulsive properties (mean velocity, input power and efficiency) of beams in V formation are compared with the corresponding data of single self-propelled beam. It is found that not only the following beams in V formation possess the promotion of mean velocity and propulsive efficiency, the performance of leading beam also increases, and the growing rate surpasses 14%. Those data provide the direct evidence of energy saving in the collective behavior of V formation. In addition, in order to find out the mechanism of the formation of hydrodynamic aggregation behavior and the reason of the energy saving of beams (especially the leading beam) in V formation, the obtained flow details (vortices contour and pressure contour) are analyzed.

2022, 54(6): 1706-1719. doi: 10.6052/0459-1879-21-688

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HIGH-SPEED TRAIN TREAD WEAR PREDICTION MODEL BASED ON I-ML-ELM

Wang Meiqi, Wang Yi, Chen Enli, Liu Yongqiang, Liu Pengfei

For purpose of solving the problem that a single model of high-speed train wheel tread wear cannot be used for quantitative calculation of train wheel tread wear under various complicated working conditions, we propose a feasible measurement method of wheel tread wear of high-speed trains based on the multilayer extreme learning machine with identity mapping. Firstly, we introduce the identity mapping into the multilayer extreme learning machine, then we propose an identity multilayer extreme learning machine (I-ML-ELM) model. In order to test the I-ML-ELM validity, it is applied to four multivariate regression data sets which are from machine learning public data sets. And experimental results show that the I-ML-ELM can achieve a perfect generalization performance and stability at a fast training speed and a quick reaction of the trained network to new observations. Secondly, based on the vehicle-track coupled dynamics theory, we establish the vehicle-track coupling dynamics model of high-speed trains. By simulating different working conditions, we observe the wheel tread wear of high-speed trains, and the I-ML-ELM prediction model is used to learn and predict the wheel tread wear of high-speed trains. Finally, in order to further test the effectiveness of I-ML-ELM prediction model, it is applied to the actual measurement value of wheel tread wear of high-speed train. The results show that compared with those five learning machines (extreme learning machine, fast learning machine, multilayer extreme learning machine, multilayer kernel extreme learning machine and derived least square fast learning network), the performance parameters of I-ML-ELM prediction model are the best as a whole and the model achieves a very good prediction precision and generalization ability. The further verification of the measured data of high-speed train lines show that the prediction model based on I-ML-ELM can not only reflect the influence of different operating parameters on the wheel tread wear value of high-speed trains better, but also realize the prediction of wheel tread wear.

2022, 54(6): 1720-1731. doi: 10.6052/0459-1879-21-692

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SOLUTION INTERPOLATION FOR HIGH-ORDER ACCURATE ADAPTIVE FLOW SIMULATION

Zhou Shuai, Xiao Zhoufang, Fu Lin, Wang Dingshun

Mesh adaptation and high order numerical methods are regarded as effective techniques to improve the adaptability of computational fluid dynamics (CFD) to complex problems. The combination of these two techniques requires solving a series of technical challenges, one of which is the flow field interpolation for high order numerical methods among different adaptation steps. A high-order accurate solution interpolation method is proposed for the high-order accurate adaptive flow simulation. In this method, it interpolates the numerical flow solution from the mesh in the previous iteration step into the mesh of the current iteration step, to allow the simulation to be restarted from the previous state. To realize the conservation of physical quantities in the process of flow field interpolation, the method first computes the overlapping regions of the new and old meshes and then transfers the physical quantities from the old mesh to the new mesh in the overlapping regions. To achieve high-order accuracy, the k-exact least-squares method is first used to reconstruct the numerical solution on the old mesh, and as a result, a polynomial with the required order that represents the distribution of the physical quantity is obtained over each element of the background mesh. Then Gaussian numerical integration is used to integrate the physical quantities over each element of the new mesh, which accurately transfers the physical quantities from the background mesh to each element of the new mesh. Finally, the effectiveness of the proposed algorithm is verified by a numerical example with an exact solution and an example of high-order accurate adaptive flow simulation. The results of the first example show that a smaller interpolation error exists when higher-order accurate interpolation is adopted, and the second example shows that the method in this paper can effectively shorten the iterative convergence time of high order accurate flow simulation.

2022, 54(6): 1732-1740. doi: 10.6052/0459-1879-22-060

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ANALYSIS OF VORTEX-INDUCED VIBRATION FOR A CANTILEVER RISER IN A DEEP-SEA MINING SYSTEM

Jin Guoqing, Zou Li, Zong Zhi, Sun Zhe, Wang Hao

Different from the traditional marine riser, the vertical lifting pipeline in the deep-sea mining system can be regarded as a flexible cantilever riser with an unconstrained bottom end. Likewise, problems in terms of vortex-induced vibrations (VIVs) and flexible deformations can be encountered during operation. In this paper, a quasi-three-dimensional time-domain numerical model coupled with the discrete vortex method (DVM) and finite element method (FEM) is employed in the time domain. Systematic simulations have been carried out to investigate the VIVs of a cantilever riser under different current speeds. The results indicate that, for a cantilever riser, the transverse vibration mode number rises with increasing the reduced velocity. In a certain range of reduced velocities, the dominant vibration modes remain unchanged. When the modal transition occurs, the corresponding vibration amplitudes can abruptly drop. However, when the new high-order mode is excited, vibration amplitudes of the riser again gradually increase with increasing the incoming velocities. In the same vibration mode, the root-mean-squared values for the bottom displacements of the riser linearly rise with the reduced velocities. When vibration mode changes, a jump phenomenon for the dominant vibration frequencies can be observed. Especially, the present work discusses the vibration responses of the cantilever riser in the three-order dominant mode. It can be found that the unconstrained bottom end of the riser exhibits relatively large vibration energy. The standing wave characteristics of the vibration amplitudes gradually enhance with the increase of the reduced velocities. The VIV response characteristics of a two-ends hinged riser and a cantilever riser are compared in this investigation, both of which exhibit the same variation tendency in terms of amplitude and dominant vibration frequency.

2022, 54(6): 1741-1754. doi: 10.6052/0459-1879-21-679

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2022 Vol. 54, No. 6

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