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25 September 2020, Volume 37 Issue 5 Previous Issue    Next Issue

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Investigation of Normal Shock Structure by Using Navier-Stokes Equations with the Second Viscosity LI Xindong, ZHAO Yingkui, HU Zongmin, JIANG Zonglin 2020, 37(5): 505-513.  DOI: 10.19596/j.cnki.1001-246x.8121 Abstract ( )   HTML ( )   PDF (2299KB) ( )   To investigate influence mechanism of the second viscosity on internal flow of a normal shock wave, one-dimensional Navier-Stokes equations are numerically solved. It indicates that the second viscosity has a smoothing effect on density, heat flow and energy distribution in the shock wave, which results in a decrease of peak value of heat and entropy flows, and an increase of shock thickness. Due to the production of normal viscous dissipation, some lost mechanical energy is converted into internal energy. As considering the second viscosity, density distribution and shock thickness are greatly improved. They are in good agreement with experimental data. In addition, Knudsen number is obtained 0.12≤Kn≤0.4 within Mach number range from 1.2 to 10. It indicates that Navier-Stokes equations with the second viscosity simulate normal shock structure more accurately.

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Initial Value Conditions of Solutions of Riemann Problem for Elastic Perfectly Plastic Solid ZENG Zhiqiang, LIU Tiegang, GAO Si 2020, 37(5): 514-528.  DOI: 10.19596/j.cnki.1001-246x.8142 Abstract ( )   HTML ( )   PDF (5256KB) ( )   For a given solution of Riemann problem for elastic perfectly plastic solid Euler equations ignoring vacuum, we give condition that the initial physical quantity should be satisfied and prove completeness of the initial condition corresponding to a particular solution. That is, for any given initial physical quantity, it corresponds to only one solution of Riemann problem. Therefore, the solution of Riemann problem can be judged directly and accurately according to the initial condition in the design of exact or approximate Riemann solvers.

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A Godunov Method with Staggered Lagrangian Discretization Applicable to Isentropic Flows SUN Chen, LI Xiao, SHEN Zhijun 2020, 37(5): 529-538.  DOI: 10.19596/j.cnki.1001-246x.8144 Abstract ( )   HTML ( )   PDF (4941KB) ( )   In cell-centered Godunov method,unphysical overheating problem exists in rarefaction flows.We develop a Godunov method with staggered Lagrangian discretization which is applicable to isentropic flows. Velocity and thermodynamic variables are defined in staggered discretization. The velocity averaging process in a cell is avoided,so that the kinetic energy dissipation due to the momentum averaging process is removed. In contrast to the traditional von Neumann staggered grid method, the face flux is provided by a node multidimensional Riemann solver. The difficulty in selecting multidimensional artificial viscosity is overcome. In order to reduce unphysical entropy production of multidimensional Riemann solver in rarefaction problems,we give a reasonable criterion of rarefaction appearance to satisfy the thermodynamic relation. Numerical results show that the method removes overheating problem in rarefaction problems, and retains the property of accurate shock capturing of the original Lagrangian Godunov method as well.

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Numerical Simulation of One-dimensional Elastic-Perfectly Plastic Flow and Suppression of Wall Heating Phenomenon LI Xiao, SUN Chen, SHEN Zhijun 2020, 37(5): 539-550.  DOI: 10.19596/j.cnki.1001-246x.8141 Abstract ( )   HTML ( )   PDF (3643KB) ( )   An HLLC-type approximate Riemann solver is proposed to simulate one-dimensional elastic-perfectly plastic flow with Wilkins model. This Riemann solver introduces plastic wave and has the same wave number with actual physics. The wave speed is determined by characteristic analysis of wave system. The algorithm is simple to implement and does not need iteration. In order to reduce wall heating error in the simulation for strong shock (or rarefaction), wall heating viscosity is designed to effectively suppress the non-physical wall heating phenomenon.

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An iDdQ(q-1) Multiple-relaxation-time Lattice Boltzmann Model with External Force ZHU Qiaoli, ZHANG Wenhuan 2020, 37(5): 551-561.  DOI: 10.19596/j.cnki.1001-246x.8138 Abstract ( )   HTML ( )   PDF (1112KB) ( )   An iDdQ(q-1) MRT LB model with external force term is proposed with multi-scale expansion and inverse design method. It recovers to incompressible Navier-Stokes equation with external force term under low Mach number assumption. With simulations of Poiseuille flow, pulsatile flow in a three-dimensional square channel, and two-dimensional Taylor vortex flow in a square box, it is found that numerical results are in good agreement with analytical solutions. In addition, spatial accuracy of the model reaches second order, which verifies effectiveness of the model in simulating steady and unsteady incompressible flows driven by external forces.

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Shape Optimization of Stratosphere Airship with Propeller CHEN Hao, CAI Ruming 2020, 37(5): 562-570.  DOI: 10.19596/j.cnki.1001-246x.8146 Abstract ( )   HTML ( )   PDF (15435KB) ( )   A design platform for airship shape optimization with propeller is established with computational fluid dynamics and optimization techniques. Firstly, Hicks-Henne shape functions were used to parameterize hull of the airship. Then,a hybrid dynamic mesh generation method was presented based on inverse distance weighting (IDW) interpolation and transfinite interpolation (TFI). An actuator disk model of propeller was employed to simulate viscous flow around the airship. LOTTE airship was chosen as the initial shape, and drag coefficient was chosen as the objective function. Airship volume was selected as a constraint. The optimized shape based on non-linear programming by quadratic lagrangian (NLPQL) algorithm was obtained. It shows that afterbody shape of the optimized airship is relatively flat and location of the maximum diameter moves forward. Aerodynamic performance of the new shape is significantly improved. Compared with that of the LOTTE hull,drag coefficient of the optimized shape is reduced by 26.88%.

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Microscopic Mechanism of Nonlinear Gas Alternating Oscillation in Microchannel Pulse Tube: Molecular Dynamics Study CHE Yanjin, QI Yingxia, PAN Shuai, WANG Yuhe, ZHANG Hua 2020, 37(5): 571-580.  DOI: 10.19596/j.cnki.1001-246x.8149 Abstract ( )   HTML ( )   PDF (2038KB) ( )   Molecular dynamics simulation is used to simulate response of nonlinear sinusoidal alternation flow of helium gas oscillation in a pulse tube. Formation of axial pressure wave and temperature field inducted by gas oscillation was studied.Influence of length to diameter ratio on temperature difference and phase of cold and hot ends of the pulse tube is shown. It shows that the pressure wave,speed wave and mass flow wave accompanying by driving force are similar to a sinusoidal function while the temperature wave is similar to a half-sinusoidal function. The oscillation period is shortened with increase of the diameter of the tube and prolonged with increase of the length of the tube. The maximum temperature difference between hot end and cold end increases with the length of the tube but independent of diameter. It is predicted that there is an optimal aspect ratio and oscillation period for pulse tube with different diameter, which increases with increasing of the diameter. It provides a theoretical basis for optimizing efficiency of pulse tube.

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Inhomogeneous Swelling of Core-Shell Composite Gels: Chain Entanglement Effect YAN Huixian, SU Hengdi 2020, 37(5): 581-588.  DOI: 10.19596/j.cnki.1001-246x.8128 Abstract ( )   HTML ( )   PDF (4434KB) ( )   As gel molecules form a gel network, molecular chain segments are intertwined to form physical crosslinking, which affects significantly their mechanical behavior. To study effect of entanglement formed by physical cross-linking on deformation behavior and solvent distribution of core-shell composite gels, a mathematical model is developed in finite elasticity of core-shell composite gels based on tensor derivation. And a slip-link chain entanglement model was introduced. It shows that under the influence of rigid core, tensile behavior of gel shell is anisotropy. Distribution of solvent in the gel shell is non-uniform. It increases nonlinearly from inside to outside. Solvent diffusion in gel does not satisfy Ficks law. The higher the degree of chain entanglement is, the lower the radial and circumferential extension ratio of gel shell, and the lower the swelling ratio are.

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Interfacial Interaction and Diffusion Properties of Functionalized CNT/Polymer Systems: Molecular Dynamics Simulations WANG Xuemei, DONG Bin, ZHU Ziliang, YANG Junsheng 2020, 37(5): 589-594.  DOI: 10.19596/j.cnki.1001-246x.8135 Abstract ( )   HTML ( )   PDF (5226KB) ( )   Molecular dynamics simulations are used to study interfacial interaction and diffusion properties of CNT/polymer chains. It shows that —CH3 decreases interfacial interaction energies of PE/CNT and PP/CNT systems. However, interfacial interaction energy of CNT/PEO modified with —CH3 is increased. Compare interaction energies between pure CNT and PE, PP and PEO, we found that the interfacial interaction energy increased as CNT modified with —OH and —COOH. And the strength satisfies —COOH<—OH. Besides, total energies of PE/CNT, PP/CNT and PEO/CNT modified with —CH3, —OH and —COOH are reduced. The decrease rate follows rule: —COOH < —OH < —CH3. Coulomb energy plays the main role in the non-bond energies rather than vdW energy. Moreover, diffusion coefficient of functional CNT/PE, CNT/PP and CNT/PEO are obviously reduced by the impose of function groups, and the diffusion coefficient of the polymer chains satisfy —COOH<—OH<—CH3.

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First-principles Study of Hydrogen Behaviors in Plutonium Oxides ZHANG Le, SUN Bo, SONG Haifeng 2020, 37(5): 595-602.  DOI: 10.19596/j.cnki.1001-246x.8118 Abstract ( )   HTML ( )   PDF (9461KB) ( )   In-depth investigation of hydrogen behaviors in Pu-oxide overlayers (mainly PuO2 and α-Pu2O3) is critical for modeling complex induction period of Pu hydriding. Within DFT+U and DFT-D3 schemes, systematic first-principles calculations and ab initio thermodynamic evaluations reveal that hydrogen absorption, dissolution behaviors, and diffusion mechanism in PuO2 are quite different from those in α-Pu2O3, among which highly endothermic absorption and dissolution of hydrogen are primary hydrogen resistance mechanism of PuO2. Since its difficult recombination, atomic H is preferred existence state in PuO2, but H will recombine spontaneously in α-Pu2O3. In PuO2, H diffusion is always clinging to O anions, whereas in α-Pu2O3, H2 prefers to migrate along O vacancies with higher barriers. Based on a series of theoretical studies, we conclude that the main interactions between hydrogen and Pu-oxide overlayers are not involved with chemical reactions and intact PuO2 can effectively inhibit hydrogen permeation.The hydrogen dissolution in α-Pu2O3 can be reasonably described by an ideal solid solution model.

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First-principles Study on Structures and Mechanical Properties of Ternary Layered Ceramics M-Al-N (M=Ti, Zr, Hf) PENG Junhui 2020, 37(5): 603-611.  DOI: 10.19596/j.cnki.1001-246x.8108 Abstract ( )   HTML ( )   PDF (3301KB) ( )   Based on first-principles method, structural stability of M-Al-N (M=Ti, Zr, Hf) was investigated and mechanical properties were calculated. Firstly, enthalpies of M-Al-N compounds were calculated, and M2AlN and M4AlN3 were found to be thermodynamically stable. Except for experimental structures Ti2AlN, Ti4AlN3, Zr2AlN and Hf2AlN, two stable structures Zr4AlN3 and Hf4AlN3 were found. Mechanically and dynamically stable were verified by calculation of elastic constants and phonon spectrum. Mechanical properties of M2AlN and M4AlN3 were calculated. It was found that they had high bulk modulus, shear modulus, elastic modulus, Vickers hardness and brittleness. Variation of mechanical properties of M-Al-N compounds with composition was analyzed, which provided theoretical basis for selection and application of this kind of materials. At last, electron density of states and partial DOS, electron density, Mulliken population analysis of M-Al-N (M=Ti, Zr, Hf) compounds were calculated.

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Mechanism of Spontaneous Formation of Spiral Wave in Neuronal Network with Unidirectional Coupling HUANG Zhijing, BAI Jing, TANG Guoning 2020, 37(5): 612-622.  DOI: 10.19596/j.cnki.1001-246x.8134 Abstract ( )   HTML ( )   PDF (10960KB) ( )   A two-dimensional neuronal network with unidirectional coupling is constructed, and information transmission entropy is introduced to describe the directed information transmission. Hindmarsh-Rose neuron model is used to study mechanism of spontaneous generation of ordered waves such as spiral waves in the network. Numerical simulation shows that the network can appear spontaneously spiral wave, traveling wave, target wave and plane wave with appropriately selected strength of coupling and distance of unidirectional coupling. It is found that generation of various ordered waves is related to intermittently directed information transmission in the network. Entropy resonance occurs as single or multiple spiral waves appear in the network. Intermittently directed information transmission is also observed in the network with noise, inhibitory coupling and repulsive coupling when spiral wave and multiple spiral waves are spontaneously appeared. Self-sustaining long plane waves are observed for the first time. It is due to persistent strong directed information transmission in the network.

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Optimization of Synchronization Performance and Robustness Analysis in Power Grids Based on Power Tracing ZOU Yanli, GAO Zheng, LIANG Mingyue, LI Zhihui, HE Ming 2020, 37(5): 623-630.  DOI: 10.19596/j.cnki.1001-246x.8137 Abstract ( )   HTML ( )   PDF (4755KB) ( )   Kuramoto-like model is adopted to model a power grid reasonably. And critical synchronization coupling strength and average synchronization error are used to describe synchronization ability and robustness of a power grid, respectively. It is found that power distribution of generators has a great influence on transmission power of lines, and the more high-load lines in power grid, the more difficult the network synchronization. Based on the discovery, we calculate transmission power of each line under uniform power distribution method of generators (EG mode). Then, based on a power flow tracking algorithm, an non-uniform power distribution method (TG mode) of the generators is further proposed. With this method, as the total amount of power generated is given, power of the hub generator node is increased and power of the edge generator node is reduced. It shows that the new power distribution strategy reduces effectively critical synchronization coupling strength and average synchronization error. Thus the method improves synchronization performance and robustness of a power grid.