Similarities between the quasi‐bubble and the generalized wave continuity equation solutions to the shallow water equations

Two common strategies for solving the shallow water equations in the finite element community are the generalized wave continuity equation (GWCE) reformulation and the quasi‐bubble velocity approximation. The GWCE approach has been widely analysed in the literature. In this work, the quasi‐bubble equations are analysed and comparisons are made between the quasi‐bubble approximation of the primitive form of the shallow water equations and a linear finite element approximation of the GWCE reformulation of the shallow water equations. The discrete condensed quasi‐bubble continuity equation is shown to be identical to a discrete wave equation for a specific GWCE weighting parameter value. The discrete momentum equations are slightly different due to the bubble function. In addition, the dispersion relationships are shown to be almost identical and numerical experiments confirm that the two schemes compute almost identical results. Analysis of the quasi‐bubble formulation suggests a relationship that may guide selection of the optimal GWCE weighting parameter. Copyright © 2004 John Wiley & Sons, Ltd.     

nfluence of exciting parameters on the vibration of single cavitation bubble driven by intensive sound

根据考虑了液体可压缩性的改进的微气泡动力学方程,采用改进的初始半径对单泡超声空化现象进行了数值计算研究. 结果表明,微气泡振动对一些参量很敏感：微气泡振动半径与初始半径的比值随振动频率的增大而减小;提高声场声压会加剧气泡崩塌程度,但过高的声压又不能使微气泡崩塌;微气泡崩塌速率随气泡初始半径的增加而增大,在一定范围内能保证空化泡稳定振动,在初始半径为1.6\,$\mu$m 处空化程度最强,如果继续增大初始半径则空化程度减弱、甚至消失;微气泡崩塌程度随黏滞系数和表面张力的增大而减弱,过大的黏滞系数和表面张力会使微气泡崩塌难以发生. 计算结果与他人的实验数据相比,发现液体的可压缩性使单泡空化强度增强, 对最佳空化区域范围的确定有较大的影响.     

装药量及水深对水下爆炸气泡动态特性的影响

以气泡体积加速度模型为基础研究水下爆炸气泡运动的初始条件,采用MSC.DYTRAN 非线性 有限元软件,结合开发的定义流场初始条件与边界条件的子程序,研究水下爆炸气泡运动特性,包括气泡的脉 动、坍塌以及射流等运动特性,并将气泡脉动体积计算结果与实验及边界积分方法计算结果进行对比,验证了 有限元模型的正确性与有效性。以此为基础,得到初始水深、装药量与气泡的脉动体积、最大半径、周期以及 射流速度之间的关系,计算结果与经验公式具有较好的一致性。得到一些有规律性的曲线,可为相关水下爆 炸气泡动态特性研究提供参考。     

Propagation of nonlinear waves in an inhomogeneous gas-liquid medium. Derivation of wave equations in the Korteweg-de Vries approximation

Equations describing the propagation of waves of small but finite amplitude in a liquid with gas bubbles are derived. The bubble distribution density is a continuous function of bubble size and spatial coordinates. It is found that, for a uniform bubble distribution, the obtained equations become the Korteweg-de Vries, Kadomtsev-Petviashvili and Khokhlov-Zabolotskaya equations. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 188–197, March–April, 2009.     

水下爆炸气泡运动的理论研究

在适当深度的无黏、无旋的流体中对水下爆炸气泡运动特性进行理论研究。综合运用势流理论、能量方程以及拉格朗日方程建立气泡在不可压缩流体中的运动方程。并以此为基础,考虑重力、浮力以及阻力等多种因素对气泡运动特性的影响,通过引入新的边界积分方程,结合分析力学中完整非保守系统的Hamilton原理建立气泡在可压缩流体中的运动微分方程,并对微分方程进行求解。将方程的数值解与MSC.DYTRAN非线性有限元软件的计算结果以及经验公式进行对比,方程数值解与二者都具有较好的一致性。结果表明,基于非保守系统可压缩流体建立的气泡运动方程正确、可行,相关的理论研究和计算具有一定参考价值。     

静水中气泡上升运动及阻力系数研究

采用模型计算法与实验法结合的方式对静水中气泡上升运动行为进行研究。通过牛顿运动定律,基于不同物理模型,建立气泡在水中运动的微分方程;假设气泡在运动过程中的关键参数取值,推导小气泡在水中浮升过程中的气泡行为预测公式;针对不同流态下的气泡上升关键参数进行适应性分析和算例计算。通过设计气泡上升运动实验,对气泡上升运动公式进行适应性分析,修正关键参数的取值。据此提出一种小气泡上升运动规律的计算方法以及关键参数取值方式及参考区间。     

小当量炸药深水爆炸气泡脉动模拟实验

为在实验室内开展深水爆炸气泡脉动规律研究, 通过增加水面大气压强来模拟水中静水压的方法, 建立可模拟深水环境的爆炸容器。开展不同模拟水深条件下的3种当量炸药的水下爆炸实验, 得到了气泡脉动过程图像, 验证小当量深水爆炸模拟实验与自由场实验的等效性, 分析气泡脉动周期与最大半径同模拟水深的关系。实验结果表明:容器壁面反射效应对气泡脉动过程的影响可以忽略不计, 模拟实验可等效为自由场实验; 深水爆炸气泡脉动周期及最大半径随流体静力深度增加的衰减系数分别为-0.83和-0.364。     

浅层水中爆炸冲击波对混凝土墩斜碰撞作用试验研究

通过含铝炸药JHL-3的实爆试验,得到混凝土墩在单个装药浅层水中爆炸、两个装药浅层水中对称及不对称设置同步起爆爆炸作用下、混凝土墩迎爆面上的冲击波压力响应数据;获得了迎爆面中心反射压力峰值计算模型;分析了两个装药浅层水中爆炸冲击波对混凝土墩绕射及透射作用效应。     

坑道内爆炸条件下水的消波效应研究

内爆炸对坑道内的人员、装备、结构都具有巨大的毁伤效应,内爆炸的防护技术已成为研究的热点。本文就炸药在坑道内爆炸情况下水的消波效应,开展了坑道模型爆炸试验、实际坑道爆炸试验、数值模拟研究,结果表明:坑道内爆炸条件下水具有显著的消波效应。文中还给出了不同置水工况下坑道空气冲击波超压的衰减率范围,并对水消波效应的机理进行了初步探讨。     

自由场水中爆炸气泡的物理特性

将水中爆炸气泡运动阶段周围流场假设为无粘、无旋、不可压缩的理想流体,运用边界元法模拟自由场中气泡的运动,在气泡运动模拟过程中引入数值光顺技术及弹性网格技术,避免因网格扭曲而导致的数值发散,并开发计算程序。计算值与实验值吻合良好,误差小于10%。从自由场水中爆炸气泡的基本现象入手,基于本文中开发的程序系统地研究了自由场中气泡的动力学特性。对流场中不同方位的压力进行分析,得出气泡中心的迁移方向及射流的攻击方向压力载荷比其他方向均大,说明气泡射流的攻击方向压力载荷最大,对水中结构造成严重毁伤,表明了气泡载荷的不对称性。计算了流场中不同位置的速度变化曲线,结果表明随着距气泡中心距离的增大,气泡运动引起的滞后流的速度迅速减小,且随着气泡的膨胀和坍塌,滞后流的方向逆转,总结了滞后流的衰减及变化规律。     

The effects of blood viscoelasticity on the pulse wave in arteries

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SH波对一维六方准晶中直裂纹的散射

分析了SH波对一维六方准晶中直裂纹的散射问题。利用积分变换技术,结合Copson方法,通过求解对偶积分方程,得到声子场和相位子场应力、位移及裂纹尖端动应力强度因子的解析表达式。通过数值算例讨论了裂纹长度、入射角和入射波频率对标准动应力强度因子的影响,此研究在工程材料应用中有一定的参考价值。     

水中爆炸激波对水泥试样作用的数值模拟分析

通过对水中爆炸激波在水泥净浆试样中传播的数值模拟,再现了爆炸激波的传播过程,采用对典型单元受到的激波作用和应力进行分析的方法,得出了水泥试样各个区域损伤破坏的成因,数值模拟结果和实验现象吻合。     

Spheroidal wave solutions for sound radiation problems in the near-field of planar structures

Current research in active noise control and in the reconstruction of vibrating sources often requires knowledge of the independent source–field components that best represent the complex acoustical transfer paths observed between a radiating structure and a given control or observation domain. In this paper, closed-form solutions are provided for the singular value expansion of the radiation operator that maps the boundary velocity of a baffled rectangular structure onto the acoustic pressure observed in the half-space domain over a hemi-spheroidal surface located at an arbitrary separation distance from the radiator, including in the near-field zone. Independent contributions of the evanescent and propagating wave components to the complex power are examined for a baffled beam when varying the frequency and the source–field distance parameter. It is shown that the reactive-to-active power ratio induced by each singular mode follows an inverse power law that scales on the product between the reduced frequency and the source–field distance parameter. A transitional region is defined in the space-frequency domain within which the reactive power components are preponderant and should be accounted for when controlling or imaging the near-field zone of a planar radiator. The optimality of the singular source modes is found to be of interest to actively reduce the active and reactive power components in the near-field zone of a radiator with a limited number of independent control channels.     

浅层水中沉底的两个装药爆炸的数值模拟研究

根据试验模型和试验结果,进行了浅层水中沉底的两个装药爆炸的数值模拟;通过与水中单个装药爆炸,以及无限水中两个装药同时爆炸的数值模拟结果的对比分析,研究了水底水面对沉底的两个装药同时爆炸产生的冲击波传播与相互作用的影响。结果表明:水底对冲击波压力峰值有削弱作用,水面使冲击作用冲量明显减小,冲击波相互作用压力叠加或多次冲击作用可提高爆炸威力。     

Numerical and experimental study on the motion characteristics of single bubble in a complex channel

This paper is an extended study from previous work. In this study, the focus is paid to the dynamics of bubble rising and deformation in a complex channel, while the previous work is in straight channel. For this purpose, a three-dimensional lattice Boltzmann method (LBM) is employed to simulate the dynamics behaviour of a bubble rising in a complex channel consisting of three half-round throats. To validate the numerical method, a visual experiment was carried out by means of a high-speed digital camera and computer image processing technology. The behaviour of the rising bubble through glycerine solution in a complex channel was recorded. Some physical parameters such as rising velocities, trajectory and shapes of the bubble were calculated and processed based on the experimental data. In the same conditions, the trajectory, shapes and rising velocities of the bubble were simulated during its rising process by the proposed LBM. The numerical results are in good agreement with the experimental results. It demonstrates that LBM used in this work is feasible for simulating two-phase flow in such a complex channel.     

The analysis of forming the bulge in a spilling water wave

The early stages of a spilling breaking water wave leading to the formation of a bulge on the forward face of the wave are investigated. In this study, simultaneous space-time measurements of the free-surface elevation of a spilling breaking water wave are recorded and analyzed. The analysis, carried out in the frame of reference moving with the crest of the wave, reveals that the formation of the bulge is due to the presence of a shock-like mode. In the previous frame of reference, the shock itself is unsteady but its (spatial) location is time independent and coincides with the “toe” of the bulge. As time increases, the shock undergoes a flip (a reflection symmetry) with respect to the midpoint of our time interval. Such a flip is responsible for an abrupt increase of the wave steepness, which will lead to wave breaking at later times. Following these observations, we present a two-dimensional quantitative model which reproduces both the formation of the bulge and the sudden increase of the wave steepness. Supported by the Foundation of the State Education Commission of China     

Influence of elastic material compressibility on parameters of an expanding spherical stress wave

We investigated the influence of elastic material compressibility on parameters of an expanding spherical stress wave. The material compressibility is represented by Poisson’s ratio, ν, in this paper. The stress wave is generated by a pressure produced inside a spherical cavity surrounded by the isotropic elastic material. The analytical closed form formulae determining the dynamic state of the mechanical parameters (displacement, particle velocity, strains, stresses, and material density) in the material have been derived. These formulae were obtained for surge pressure p(t) = p ₀ = const inside the cavity. From analysis of these formulae, it is shown that the Poisson’s ratio substantially influences the course of material parameters in space and time. All parameters intensively decrease in space together with an increase of the Lagrangian coordinate, r. On the contrary, these parameters oscillate versus time around their static values. These oscillations decay in the course of time. We can mark out two ranges of parameter ν values in which vibrations of the parameters are “damped” at a different rate. Thus, Poisson’s ratio in the range below about 0.4 causes intense decay of parameter oscillations. On the other hand in the range 0.4 < ν < 0.5, i.e. in quasi-incompressible materials, the “damping” of parameter vibrations is very low. In the limiting case when ν = 0.5, i.e. in the incompressible material, “damping” vanishes, and the parameters harmonically oscillate around their static values. The abnormal behaviour of the material occurs in the range 0.4 < ν < 0.5. In this case, an insignificant increase of Poisson’s ratio causes a considerable increase of the parameter vibration amplitude and decrease of vibration “damping”.      

Gas bubble oscillations in a fluid in the presence of 2:1 resonance between the radial and deformation oscillation frequencies

Small nonlinear oscillations of an ellipsoidal bubble in a fluid in the presence of 2:1 frequency resonance between the radial and ellipsoidal modes are considered. The equations of motion are reduced to Hamiltonian form. The quadratic and cubic terms are taken into account in the expansion of the Hamiltonian. The Hamilton function is transformed to the normal form using the invariant normalization method in the first approximation. This makes it possible to construct an analogy between the system considered and the well-known problem of a pendulous spring. The radial and ellipsoidal bubble oscillation modes correspond to the vertical and horizontal coordinates of a material point, respectively. In the absence of resonance the solution of the nonlinear equations differs from the solution of the linear equations by only a small (quadratic in the amplitude) change in the oscillation frequency. In the resonance case the radial and ellipsoidal oscillation modes periodically change places and the energy of one mode is converted into that of the other. The interest in the system in resonance is associated with precisely this fact. The question of the dissipation effect in real media is considered. The decay rate depends significantly on the physical properties of the material and, in certain special cases, can be small enough for the energy transfer effect to manifest itself.     

Numerical study on wave propagation in a low-rigidity elastic medium considering the effects of gravity

We discuss the effects of vertical gravity force on wave propagation when a material is intermediate between solid and fluid, especially we focus on what kinds of phase are generated and how it propagates on the surface. We introduce gravity terms into the 2D linear finite element method in order to account for the contribution from the gravity. Numerical simulations are conducted for a half-space model and a two-layered, single horizontal layer overlain on a half-space, model. Both models are compared between the results including and excluding the viscosity. The fastest phase propagating from a surface point source, a leaking Rayleigh wave for usual elastic material, is transformed into an interesting phase including some common features to the gravity wave when the gravity effect becomes significant. The viscosity does not affect the fastest phases, whereas it affects other latter phases appearing only for the two-layered model.