应用数学和力学

Internal Mechanical Shock Wave: an Explanation of the Ocean Shock Current

WU Feng, ZHONG Wanxie

2019, 40(8): 823-839. doi: 10.21656/1000-0887.400138

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Abstract:
With the Lagrangian coordinate and the Hamiltonian principle, the 2D displacement internal wave equation was derived. Based on the 2D displacement internal wave equation, the 2D internal mechanical shock wave in the 2-layer shallow water system was analyzed numerically and analytically. In terms of the numerical examples, it is found that the internal mechanical shock wave have 4 characteristics, i.e., high velocity, short duration, narrow space range and shock change of water surface, which means the ocean shock current is essentially an internal mechanical shock wave. The internal mechanical shock wave also provides an explanation for the ocean cliffs.

Problems and Improved Methods of 3D Ocean Hydrodynamic Calculation With the σ Coordinate Transformation

BAI Yuchuan, WEN Zhichao, XU Haijue, LIAO Shizhi, CAO Yonggang, XIA Huayong

2019, 40(8): 840-855. doi: 10.21656/1000-0887.390344

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Abstract:
The 3D hydrodynamic model plays an important role in accurate simulation of the physical characteristics of the ocean. The complex highorder terms are discarded in the traditional σ coordinate transformation due to the limitation of the computer ability, which causes certain errors or calculation distortions for actual complex terrains (or water depth variations). Therefore, the existent σ coordinate 3D hydrodynamic model was modified in order to meet the needs for highprecision calculation results. In the improved model, the complex highorder terms related to the flow velocity, the water level and the terrain introduced through the σ coordinate transformation were comprehensively considered. The specific interpolation function and the combination of the FEM and the FDM were used to solve the complete 3D shallow water model equations in the σ coordinate system. Compared with the existent model, the improved model has a wider range of applications for changes in the bottom slope, the water depth and the tidal amplitude, which could improve the simulation of the vertical flow distribution characteristics under complex water depth changes and promote the accuracy of the calculation results. The calculation error can be kept in a small range in the improved model under some extreme water conditions (with a tidal amplitude to water depth ratio greater than 0.15), and the improved model can reach a steady state in a short time.

Linear Stability Analysis on Thermo-Bioconvection of Gyrotactic Microorganisms in a Horizontal Porous Layer Saturated by a Power-Law Fluid

DAI Dexuan, WANG Shaowei

2019, 40(8): 856-865. doi: 10.21656/1000-0887.390298

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Abstract:
To study the stability of bioconvection in a non-Newtonian fluid-saturated porous medium, the linear stability analysis with the model for gyrotactic microorganisms and power-law fluids was carried out. Based on the Galerkin method, the governing equation was solved to get the numerical solution of the biological Rayleigh number, which represents the stability of bioconvection. The effects of various parameters on the change of power-law indexes were studied in detail. It is concluded that, as the fluid velocity increases, the influence of the power-law index on the stability of the bioconvection will change, and this change will be affected by the thermal Rayleigh number and the biological Lewis number. The results also show that, as the gyrotactic capability of microorganisms increases, the bioconvection stability will decrease, and properly increasing the power-law index is conducive to the stability.

An Experimental Study of Leakage Effects on Flexible Pipelines

GUO Shihao, LI Ye

2019, 40(8): 866-879. doi: 10.21656/1000-0887.390296

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Abstract:
Based on the model experiment, the leakage effects introduced by the leaking hole on the flexible pipeline with a constant internal flow velocity were studied. It is found that the leakage effect can change the critical value, so that the deformation increases linearly with the flow velocity. The leakage effect can also increase the deformation amplitude, and at the same time excite different vibration modes of the pipeline system, causing the vibration responses of multiple frequencies. The research provides a basis for the leakage location in pipelines and an experimental reference for numerical simulation.

Numerical Simulation of Fluid-Solid Coupling Collision Based on the Finite Element Immersed Boundary Method

YANG Ming, LIU Jubao, YUE Qianbei, DING Yuqi, YAO Liming

2019, 40(8): 880-892. doi: 10.21656/1000-0887.400053

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Abstract:
A direct numerical simulation method was developed for solid-solid collision in fluid. The sharp interface immersed boundary method was used to simulate the dynamic boundary problems in fluids, which avoids the negative volume error in the body-conforming mesh method. The finite element method based on the penalty function was used to simulate the motion and collision of the solids. The coupling solution of the fluid domain and the solid domain was realized in the partitioned coupling approach. Comparison of the experimental data of normal collision and oblique collision between spherical particles and the wall verifies the validity of the numerical simulation method. The variation of the flow field before and after the collision was obtained. The contact force and stress in the solid domain were also got with the numerical simulation method. This model is applicable to fluid-flow environments such as the abrasion of solid particles on pipes, the fluid-induced collision between ocean risers, the impact of falling objects on submarine pipelines and so on.

Analysis of Effects on Shock Initiation Performances for Booster Charge Structure Parameters

LIANG Bin, SHI Xiaohai, YU Cunxiang, LI Huimin, LI Juncheng

2019, 40(8): 893-909. doi: 10.21656/1000-0887.390306

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Abstract:
The booster charge structure has direct effects on the detonation wave propagation, the driven flyers and the shock initiation performance. To analyze the influence of the booster charge structure on the performance parameters of the flyer power, a numerical simulation scheme was designed based on the orthogonal test principle in view of the 3 structural parameters, including the flyer thickness, the charge diameter and the flyer height. The AUTODYN3D finite difference program was used to establish the corresponding numerical model, and the main charge structure parameters influencing the flyer velocity, momentum and kinetic energy indexes were obtained through statistical analysis of the simulation results. The analyses and results provide a theoretical basis for the design of similar booster charges.

Global Smooth Solutions With Exponential Growth to 2D Inviscid Boussinesq Equations Without Heat Conduction and 3D Axisymmetric Incompressible Euler Equations on Smooth Domains

MENG Dejia, DENG Dawen

2019, 40(8): 910-916. doi: 10.21656/1000-0887.390245

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Abstract:
The growth of smooth solutions to 2D inviscid Boussinesq equations without heat conduction and the 3D axisymmetric Euler equations was investigated, to find regions where these systems have fast growing solutions. Through appropriately choosing the initial temperature and the velocity component, the Boussinesq system was decoupled into 2 parts. From the part involving only the vorticity, the vorticity and velocity can be solved and the smooth regions determined. From the part involving the temperature, one can see that the growth of temperature derivatives depends only on the velocity component. Through choosing that component appropriately, solutions with temperature derivatives of exponential growth were constructed on certain unbound smooth regions. The same method was applied to the axisymmetric Euler equations. Through choosing the radial velocity component appropriately, the system can be decoupled and one can ultimately find a class of smooth domains, and on them smooth global solutions of exponential growth. This investigation extends the results of Chae, Constantin and Wu on the inviscid Boussinesq system without heat conduction on a 2D cone to a class of smooth domains. Their method was also applied to the 3D axisymmetric Euler equations to obtain a similar result.

Study on Lightning Induced Voltages in Transmission Lines Under Soil Conductivity Stratified Structures

GAO Jinge, LI Jingxiao

2019, 40(8): 917-925. doi: 10.21656/1000-0887.390093

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Abstract:
To solve the contradiction between the ideal hypothesis and the real situation in solution of the lightning induced voltage model, the Rusck model was improved through replacement of the actual line height with the equivalent line height. This method enables fast solution of lightning induced voltages in transmission lines under soil conductivity stratified structures. The effectiveness and superiority of the improved Rusck model were verified through comparison with the FDTD results. The simulation results show that, for a single soil layer with a conductivity less than 0.1 S/m, the influence of the conductivity should be considered in solution of the induced voltage, and the peak voltage will increase with the decrease of the conductivity. For a stratified structure, the induced voltage will increase with the thickening of the upper soil layer with a less conductivity; on the contrary, the induced voltage will decrease with the thickening of the upper layer, and the effects of soil stratification can be ignored for the case of an upper soil layer with a thickness exceeding 5 m.

Computation of Total Stress Fields for Cracked Bi-Material Structures With the Extended Boundary Element Method

LI Cong, NIU Zhongrong, HU Zongjun, HU Bin, CHENG Changzheng

2019, 40(8): 926-937. doi: 10.21656/1000-0887.400013

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Abstract:
According to the theory of linear elasticity, the conventional numerical methods are difficult to calculate the singular stress fields of cracked bi-material structures. An extended boundary element method (XBEM) was proposed to calculate the singular stress fields near crack tips. Firstly, a small sector around the crack tip was removed from the cracked structure. The displacement and stress components in the small sector were expressed as asymptotic series expansions with respect to the radial coordinate from the tip. The amplitude coefficients in the asymptotic series expansions were taken as the basic unknowns. Secondly, the boundary element method was used to analyze the cracked structure without the small sector. Consequently, the complete displacement and stress fields of the cracked structure were solved through combination of the boundary element analysis and the asymptotic series expansions near the tip. For the 2 domains near the crack tip of a bonded bi-material, reasonable terms shall be chosen in the asymptotic series expansions respectively. The computation results show the accuracy and effectiveness of the XBEM for determining the stress fields of the cracked bi-material structures.

A Reproducing Kernel Interpolation Method for Axisymmetric Elastodynamic Problems

CHEN Shenshen, ZENG Jiawei

2019, 40(8): 938-944. doi: 10.21656/1000-0887.390242

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Abstract:
The reproducing kernel interpolation method (RKIM) is a novel type of meshless method emerging in recent years. Because the shape functions of the RKIM have point interpolation property and high-order smoothness, the essential boundary conditions can be imposed directly and high computational accuracy is ensured as well. In order to solve the elastodynamic problems for 3D axisymmetric solids more effectively, a novel numerical method based on the RKIM was presented and discussed. Due to axial symmetry of geometry and boundary conditions, only a set of discrete nodes on a cross section are required in the computation and therefore the preprocessing of this method is very simple. The Newmark-β algorithm was employed for time integration. Numerical examples show that, the proposed method for solving axisymmetric elastodynamic problems possesses the advantages of meshless methods and high accuracy.

2019 Vol. 40, No. 8