A numerical formulation for nonlinear ultrasonic waves propagation in fluids

A finite-difference algorithm is developed for analysing the nonlinear propagation of pulsed and harmonic ultrasonic waves in fluid media. The time domain model allows simulations from linear to strongly nonlinear plane waves including weak shock. Effects of absorption are included. All the harmonic components are obtained from only one solving process. The evolution of any original signal can be analysed. The nonlinear solution is obtained by the implicit scheme via a fast linear solver. The numerical model is validated by comparison to analytical data. Numerical experiments are presented and commented. The effect of the initial pulse shape on the evolution of the pressure waveform is especially analysed.     

次声波在非均匀运动大气中非线性传播特性的研究

基于有限时域差分方法将大气中近似到二阶的非线性波动方程进行离散化,得到了数值模拟所采用的差分方程. 在此基础上,对线阵列辐射的脉冲声波在非均匀运动大气中的垂直和斜向传播进行了二维数值模拟,模拟了武汉地区(114:20°E, 30:37°N)在夏季和冬季UT=29000 s时开始传播的脉冲声波在不同时刻的声压分布. 模拟时通过采用Msise00和HWM93 两个大气模型,考虑了由于大气温度和密度变化以及大气风场存在所引起的大气不均匀性和运动性. 通过研究上述两季有风与无风条件下的声压差值p_r,可以发现:风场对次声波在传播中声压分布的影响较大;由于不同季节和不同传播距离上"有效声速"的不同,导致了两季p_r分布波形存在差异;风场对声波非线性传播的影响要远大于其对线性传播的影响. 关键词： 次声波传播 非均匀运动大气 有效声速     

Modelling the pressure field in the vicinity of a microphone membrane using PIV

A new approach for estimating the acoustic pressure in the near field of a microphone based on non-intrusive direct measurement of acoustic particle velocity is proposed.This method enables the estimation of the acoustic pressure inside a domain located in front of the microphone membrane. The acoustic pressure is calculated using the acoustic particle velocity on the frontiers of this domain and a physical model based on the Green function of the system.Results are obtained using the acoustic velocity measured with Particle Image Velocimetry (PIV) in front of a microphone excited with a plane wave inside a rectangular waveguide. They show that the diffraction of the plane wave by the microphone leads to an increase of the acoustic pressure on the microphone edge in the order of magnitude of 0.1 dB.     

Landau electron in a rotating environment: A general factorization of time evolution

For the Landau problem with a rotating magnetic field and a confining potential in the (changing) direction of the field, we derive a general factorization of the time evolution operator that includes the adiabatic factorization as a special case. The confining potential is assumed to be of a general form and it can correspond to nonlinear Heisenberg equations of motion. The rotation operator associated with the solid angle Berry phase is used to transform the problem to a rotating reference frame. In the rotating reference frame, we derive a natural factorization of the time evolution operator by recognizing the crucial role played by a gauge transformation. The major complexity of the problem arises from the coupling between motion in the direction of the magnetic field and motion perpendicular to the field. In the factorization, this complexity is consolidated into a single operator which approaches the identity operator when the potential confines the particle sufficiently close to a rotating plane perpendicular to the magnetic field. The structure of this operator is clarified by deriving an expression for its generating Hamiltonian. The adiabatic limit and non-adiabatic effects follow as consequences of the general factorization which are clarified using the magnetic translation concept.     

匹配垂直质点振速的浅海地声参数反演

海底声学参数对海洋波导中的声场特性研究和相关应用具有重要意义。针对一次夏季黄海声传播实验,分析了浅海负跃层环境下垂直质点振速的传播特性和简正波结构,说明当声源和接收器均位于负跃层下时,除海底附近外的大部分深度上垂直质点振速能量较高,且与声压相比,号数高的简正波对垂直质点振速的贡献更大,利用垂直质点振速进行匹配场反演能获得更高的海底参数敏感性。分析了海底吸收系数对垂直质点振速匹配场反演的影响,结果表明只有当进行匹配场反演时设置的海底吸收系数接近真实值时,才能获得准确的海底声速、密度和海深反演结果。利用实验中矢量水听器获取的垂直质点振速信号进行匹配场反演,将海底吸收系数在变化范围内取不同值对海底声速、密度和平均海深进行全局搜索,根据代价函数值最大确定了海底声速、密度及平均海深的反演结果,并利用不同距离上的声压传播损失反演出不同频率下的海底吸收系数。根据反演得到的海底声学参数计算声压传播损失,与实验中声压水听器测量结果符合较好。     

Simulation of the nonlinear vibration of a string using the Cellular Automata based on the reflection rule

In this study, the nonlinear dynamic responses of a string are simulated using the Cellular Automata method based on the reflection rule. In the case of nonlinear systems, the velocity of wave propagation is not constant and depends on the amplitude. A new treatment of the dynamic time step is proposed for the Cellular Automata method considering the effect of the propagation velocity. As numerical examples, first, the dynamic responses of a string with linear characteristic are simulated using the Cellular Automata method. A typical resonance curve can be obtained. Second, the dynamic responses of a string with nonlinear characteristic are simulated using the proposed method. Some characteristic types of vibration can be obtained. It is concluded that the linear and nonlinear dynamic responses of a string may be obtained by simulation using the Cellular Automata method.     

Beam and phase effects in angle-beam-through-transmission method of ultrasonic velocity measurement

The accuracy of a plane wave approximation for phase velocity measurements in isotropic and anisotropic material using the angle-beam-through-transmission method has been investigated numerically and experimentally. In this method the velocity is measured in different propagation directions as a function of incidence angle. The effect of two factors on the measurement accuracy have been discussed: intrinsic phase shift of the transmitted signal through a fluid-solid interface and beam diffraction due to the finite beam size of receiver and transmitter. It is shown that the interface-induced phase shift can introduce an error in time delay measurements of the shear wave after the first critical angle and that this time delay error can be accurately corrected for. Numerical results obtained by a time-domain beam model show that except at the critical angles, the finite width of the transmitter and receiver only affects the amplitudes of the transmitted signals and has almost no effect on the measured zero-cross time delay; therefore the plane wave approximation for obtaining phase velocity from the measured time delay data by this method and the plane wave interface-induced phase correction are fully applicable.     

二维晶格中激波的传播和自由面反射的分子动力学数值研究

本文用分子动力学方法研究和计算了面心晶体中沿(1、0、0)面或休心晶体中沿(1、1、0)面上激波的传播和自由面反射现象。在所研完的范围内(u_p=10~75×10⁴cm/sec)粒子速度沿平均值的振动是不衰减的,激皮的传播速度和波后粒子速度的平均值呈线性关系。激波在自由面反射后,自由表面附近的粒子速度为活塞速度的二倍,这和宏观力学结果相同。此外,还出现最外层分子不断地以更高的速度被抛离的现象,这和宏观测量的微物质喷射现象亦类似。在稍后的阶段,还显示出内部粒子间被拉开的"微断裂"现象。     

Simulation of the nonlinear vibration of a string using the cellular automation method

In this study, the nonlinear dynamic responses of a string were simulated using the cellular automaton (CA) method. The local rules were set for the amplitude of vibration and the decay rate of amplitude. In the case of nonlinear systems, the velocity of wave propagation is not constant and depends on the amplitude. Thus, a new treatment of the time step was proposed, i.e., the time step in the CA method is adjusted to real time by considering the effect of the propagation velocity. As numerical examples, first, the dynamic responses of a string with linear characteristic were simulated and a typical resonance curve could be obtained. Secondly the dynamic responses of a string with nonlinear characteristic were simulated. Some characteristic types of vibration could be obtained. It was concluded that the linear and nonlinear dynamic responses of a string could be simulated using the CA method.     

高声压级时多孔金属板的吸声特性研究

针对高声压级下有限厚度多孔金属板在线性阻抗背衬条件下(背衬表面声压与声质点速度为线性关系)的吸声问题,提出了一个描述不同声压级下材料层法向吸声性能的一维模型,并给出求解材料层内部声质点速度的线化与差分方法,以预测多孔金属板在高声压级下的非线性吸声特性。在阻抗管中对两块多孔金属板进行了声学测试,得到了材料层法向表面阻抗和吸声系数随入射声压级变化的实验结果。研究表明:实验与理论预测符合良好,验证了模型与数值方法的正确性。本文所提原理和方法,可用于一般硬质多孔材料。      

Relations between matrix elements of the nonlinear Boltzmann collision integral in the axisymmetric case

The properties of the nonlinear Boltzmann collision integral for the axisymmetric velocity distribution are studied. Expansions in spherical Hermitian polynomials orthogonal to the Maxwellian weighting function are employed. It is shown that the nonlinear matrix elements of the collision operator are related to each other by simple relations, which are valid for arbitrary cross sections of particle interaction even if a preferential direction exists. The relations are derived from the invariance of the collision operator under the choice of basis functions or, more precisely, under both temperature and the mean velocity of the Maxwellian weighting function. The recurrent relations found allow one to calculate the matrix elements at large values of indices. This makes it possible to construct exact solutions to complicated kinetic problems.     

Magnetohydrodynamic shock waves in a gas mixture

The properties of the non-relativistic propagation of a plane shock wave in a gas mixture of charged particles in the presence of an external uniform magnetic field, oriented in a direction transverse to the direction of propagation, are studied. Expressions for the pressure, density and velocity ratios are obtained. It is shown that the presence of a transverse magnetic field narrows down the range of values of the density ratio.     

Elastic waves in suspensions

A model of heterogeneous medium taking into account the friction between the particles and liquid, as well as the relaxation of the small-size particles to the equilibrium on the stress, has been proposed to describe the propagation of the elastic waves in a suspension. A system of wave equations describing the propagation of a plane longitudinal wave has been formulated for the components of the medium. Analytical expressions for the sound velocity in a suspension has been obtained in the approximation in which the particles are completely carried away by liquid in the limiting cases in which the particles are in equilibrium under stress with the liquid or equilibrium is absent. The dependence of the sound velocity in the medium on the volumetric portion and the size of the inclusions has been studied. The obtained results agree with the experimental data and obtained analytical expressions for the sound velocity. The dynamics of the components of the medium at the propagation of the plane longitudinal monochromatic wave has been studied.     

Scholte波与含泥沙两相流介质属性关系的分析及仿真验证

基于四种超声悬浮液模型Urick, Urick-Ament, HT, Mcclements分析了Scholte波在两相流体与多孔介质固体界面处的传播特性. 结合各模型的复波数表达式建立含泥沙流体-多孔介质固体界面波特征方程, 分析了Scholte波速与两相流体积含量、粒径等介质属性的关系. 通过仿真实验获得界面波信号, 运用时延估计获得Scholte波速与泥沙含量、粒径的关系, 发现所得的波速与Urick-Ament和HT理论有相对好的一致性. 关键词： Scholte波 两相流体 多孔介质 泥沙含量     

Energy and momentum of sound pulses

The energy and momentum of three-dimensionally localized sound pulses are shown to be constant in time for propagation in fluids of negligible viscosity. Further, the energy always exceeds the product of the momentum and the speed of sound. This property follows from the fact that three-dimensionally localized pulses are necessarily converging or spreading (they have a focal region). A consequence of this convergence/divergence is that the associated pressure gradient, density gradient and particle velocity are not purely longitudinal, as they are for pulses localized in only one dimension. The velocity remains curl-free up to second order, however. Analytic values of energy and momentum are obtained from a particular localized solution of the wave equation.     

圆孔非线性声阻抗三维时域仿真与特性分析

为研究有限振幅声波作用下圆孔的非线性声学特性,提出了基于三维时域计算流体动力学(CFD)仿真的圆孔非线性声阻抗提取方法,通过求解层流方程来模拟声信号在圆孔及上下游的传播,以及采用横向周期性边界条件来考虑高穿孔率时圆孔之间相互作用的影响。研究了不同幅值声波作用下孔径、厚度和穿孔率对声阻抗的影响规律,通过对质点振速幅值、频率和板厚等组成的无量纲参量进行非线性回归分析,得到了圆孔非线性声阻抗的拟合公式,并将其转换为可考虑多频声波影响的时域模型。最后结合声阻抗时域模型和有限差分方法计算了直通穿孔管消声器在小振幅和有限振幅声波作用下的传递损失,通过与实验测量结果的比较,验证了拟合公式的准确性和实用性。     

弛豫媒质中有限束超声波的非线性传播畸变理论

文中提出弛豫媒质中有限束非线性声波方程,并采用微扰法求得由非线性传播畸变产生的高次谐波的一般解.研究表明,对高斯型声波,其谐波畸变解可以解析给出,而且其径向分布始终维持高斯函数.虽然其频散量大小会影响各次谐波的振幅,但其相速的变化却仍与对在频率的小振幅波相同.文中还用Blackstock算子将所得的结果应用于任何吸收-频散媒质,包括只能从经验得到其吸收与频率关系的一些生物媒质.     

Spherical turbulent flame propagation of pulverized coal particle clouds in an O2/N2 atmosphere

The present study aims to clarify the effects of turbulence intensity and coal concentration on the spherical turbulent flame propagation of a pulverized coal particle cloud. A unique experimental apparatus was developed in which coal particles can be dispersed homogeneously in a turbulent flow field generated by two fans. Experiments on spherical turbulent flame propagation of pulverized coal particle clouds in a constant volume spherical chamber in various turbulence intensities and coal concentrations were conducted. A common bituminous coal was used in the present study. The flame propagation velocity was obtained from an analysis of flame propagation images taken using a high-speed camera. It was found that the flame propagation velocity increased with increasing flame radius. The flame propagation velocity increases as the turbulence intensity increases. Similar trends were observed in spherical flames using gaseous fuel. The coal concentration has a weak effect on the flame propagation velocity, which is unique to pulverized coal combustions in a turbulent field. These are the first reports of experimental results for the spherical turbulent flame propagation behavior of pulverized coal particle clouds. The results obtained in the present study are obviously different from those of previous pulverized coal combustion studies and any other results of gaseous fuel combustion research.     

迭代重加权时域平面波叠加法的非稳态声场重建

提出了迭代重加权时域平面波叠加法,并应用于非稳态声场重建。该方法首先通过时域离散卷积得到全息面时域声压与虚源面时域波数谱离散状态公式;然后根据稀疏表示和迭代重加权,得到残差范数与加权解范数最小化问题表达式;最后将每一对波数下虚源面时域波数谱与时域传播核卷积叠加得到重建面上的时域声压。为了验证该方法的有效性,给出了激励板声源的仿真验证,并在半消声室内进行了实验验证。讨论了一些参数对该方法的影响,并通过与基于Tikhonov正则化的时域平面波叠加法比较,突出该方法的重建优势。仿真和实验结果表明,该方法对非稳态声场重建具有很好的效果,并且重建精度高。