有限长号筒中非线性声传播的数值模拟研究

研究了大振幅活塞声源经有限长号筒向外辐射声波的非线性声学问题。采用具有频散保持特性的高精度计算格式求解了适用于变截面管道的一维非线性声场模型,并考虑到声波的非线性畸变及管口处的声反射,加入了宽频时域声阻抗边界条件。宽频阻抗模型的共轭复数系数采用优化拟合方法近似求解,并采用递推卷积算法快速求解出时域声阻抗。在弱非线性条件下模拟指数形号筒中的声传播取得了与已有实验相一致的结果,表明模型能够描述声波非线性畸变带来的宽频特性。进而采用本模型数值模拟了大振幅活塞声源在双曲形、锥形、指数形和正弦形号筒中的非线性声传播问题,结果表明号筒出口声压级受活塞振动速度、频率以及号筒形状的影响,并分析讨论了波形畸变与号筒几何形状之间的关系。     

管内声传播非线性效应及反声影响的数值研究

本文提出了包括考虑反声效应的一种数值方法来计算跨声速变截面硬壁管道内无声激波非线性声传播问题。通过许多算例,详细讨论了管道形状,喉部流动马赫数,入口声源强度及反声源强度对非线性声传播影响。算例表明,确实存在最佳反声强度,这时管道出口可得到明显的声衰减效果。     

锥型热声谐振管内非线性声场的数值模拟研究

从声学角度出发,考虑粘性耗散、非线性效应及管型结构变化的影响,利用伽辽金法,对锥型热声谐振管内的一维声场进行了数值模拟研究,对谐振管结构参数对声场的影响进行了分析,给出了锥型管内压比随谐振管结构参数变化的规律,通过与圆柱型直管的比较,揭示了锥型管在抑制谐波及提高压比等方面的优越性。     

声边界层外非线性声流旋涡的理论及数值模拟

非线性声流旋涡在加速热、质传输过程和清除固体表面积灰等方面具有显著的优势。为探究换热管声边界层外非线性声流旋涡的流场特性,采用Nyborg极限滑移速度法数值模拟了平面驻波声场和行波场中二维换热管周围的非线性声流现象。与经典Rayleigh声流的解析解对比,验证了数值方法的可行性。数值计算表明,在驻波场中,换热管处于声压波节和声压波腹位置时,换热管外分别呈现出4个和8个轴对称分布的声流旋涡结构;当换热管偏离声压波节或声压波腹位置时,换热管外的声流旋涡结构不再呈轴对称分布。滑移速度分布的波峰和波腹总个数决定了声流旋涡的个数。在行波场中,声流旋涡的流场特性与声波频率f和声压级L呈现出强的非线性依赖关系,声流强度满足：U_{2 max}=6.95388e^-72L^33.50669f^-0.98828。     

岩石中爆炸波传播的数值模拟

采用一维球对称流体弹塑性模型模拟了一系列ＴＮＴ填实爆炸引起的周围岩石动力学参量的变化,根据计算结果拟合了岩石中峰值应力、粒子速度、加速度及位移的近似公式,并与一些文献中提供的实测结果进行了比较,说明数值模拟可为爆破工程、安全评估提供参考。     

岩石中爆炸波传播的数值模拟

采用一维球对称流体弹塑性模型模拟了一系列TNT填实爆炸引起的周围岩石动力学参量的变化,根据计算结果拟合了岩石中峰值应力、粒子速度、加速度及位移的近似公式。并与一些文献中提供的实测结果进行了比较。说明数值模拟可为爆破工程、安全评估提供参考。     

有限入射声束在液固界面声反射的数值研究

采用将有限声束分解为一系列平面波的方法，对液固界面声束的声反射问题进行了数值研究，结果表明，当声束入射角为瑞利疲激角时，反射声速有明显位移；当声束在液固界面“掠射”时，反射声速显著变宽，文中还讨论了束宽对反射声速横截面上声场分布的影响。     

基于有限体积法数值模拟双撕裂模非线性演化

以磁流体理论为基础,采用基于有限体积法的通量差分分裂格式数值求解具有双曲保守律形式的电阻磁流体方程组。编写C++程序对平板几何位形下的等离子体双撕裂模进行了长时间数值模拟,得到双撕裂模不稳定性的演化图景,捕捉到了双撕裂模非线性发展过程中磁场重联的几个典型阶段,讨论了等离子体电阻和两个有理面之间的距离对双撕裂模不稳定性非线性发展的影响。为研究磁流体动力学提供了一种可行的高精度数值算法。     

有限振幅声波非线性传播畸变消除的研究

在高声强情况下建立一个无畸变（或低畸变）的声场是非线性声学的一个颇有兴趣的问题。本文讨论了频率分别为f₁,f₂和f₃三列声波的非线性相互作用,其中f₁为有限报幅声波的频率,而f₂=2f₁,f₃=3f₁。基于Fenlon关于多频率有限振幅声波传播的理论,作者指出,如果适当控制频率为f₂及f₃声波的初始位相和振幅,就有可能在某些接收点上抑制有限振幅声波的二次及三次谐波,从而使其传播畸变有极明显的降低。     

Numerical simulation of nonlinear propagation of sound waves in a finite horn

Nonlinear acoustic propagation generated by a piston in a finite horn is numerically studied.A quasi-one-dimensional nonlinear model with varying cross-section uses high-order low-dispersion numerical schemes to solve the governing equation.Because of the nonlinear wave distortion and reflected sound waves at the mouth,broadband time-domain impedance boundary conditions are employed.The impedance approximation can be optimized to identify the complex-conjugate pole-residue pairs of the impedance functions,which can be calculated by fast and efficient recursive convolution.The numerical results agree very well with experimental data in the situations of weak nonlinear wave propagation in an exponential horn,it is shown that the model can describe the broadband characteristics caused by nonlinear distortion.Moreover,finite-amplitude acoustic propagation in types of horns is simulated,including hyperbolic,conical,exponential and sinusoidal horns.It is found that sound pressure levels at the horn mouth are strongly affected by the horn profiles,the driving velocity and frequency of the piston.The paper also discusses the influence of the horn geometry on nonlinear waveform distortion.     

Weak nonlinear propagation of sound in a finite exponential horn.

This article presents an approximate solution for weak nonlinear standing waves in the interior of an exponential acoustic horn. An analytical approach is chosen assuming one-dimensional plane-wave propagation in a lossless fluid within an exponential horn. The model developed for the propagation of finite-amplitude waves includes linear reflections at the throat and at the mouth of the horn, and neglects boundary layer effects. Starting from the one-dimensional continuity and momentum equations and an isentropic pressure-density relation in Eulerian coordinates, a perturbation analysis is used to obtain a hierarchy of wave equations with nonlinear source terms. Green's theorem is used to obtain a formal solution of the inhomogeneous equation which takes into account linear reflections at the ends of the horn, and the solution is applied to the nonlinear horn problem to yield the acoustic pressure for each order, first in the frequency and then in the time domain. In order to validate the model, an experimental setup for measuring fundamental and second harmonic pressures inside the horn has been developed. For an imposed throat fundamental level, good agreement is obtained between predicted and measured levels (fundamental and second harmonic) at the mouth of the horn.     

Numerical simulation of three-dimensional nonlinear water waves

We present an accurate and efficient numerical model for the simulation of fully nonlinear (non-breaking), three-dimensional surface water waves on infinite or finite depth. As an extension of the work of Craig and Sulem [19], the numerical method is based on the reduction of the problem to a lower-dimensional Hamiltonian system involving surface quantities alone. This is accomplished by introducing the Dirichlet–Neumann operator which is described in terms of its Taylor series expansion in homogeneous powers of the surface elevation. Each term in this Taylor series can be computed efficiently using the fast Fourier transform. An important contribution of this paper is the development and implementation of a symplectic implicit scheme for the time integration of the Hamiltonian equations of motion, as well as detailed numerical tests on the convergence of the Dirichlet–Neumann operator. The performance of the model is illustrated by simulating the long-time evolution of two-dimensional steadily progressing waves, as well as the development of three-dimensional (short-crested) nonlinear waves, both in deep and shallow water.     

应用非线性薛定谔方程模拟深海内波的传播

本文选取东沙岛以东深海区域,应用描述深海内波的非线性薛定谔方程,采用啁啾的思想,研究了频散和非线性效应之间的关系,模拟了深海内波的传播.数值模拟内波演变趋势与MODIS影像拍摄到的内波演变趋势基本符合,从而验证了应用非线性薛定谔方程模拟深海弱非线性内波传播的合理性. 关键词： 深海内波 啁啾 非线性薛定谔方程 频散和非线性     

Waveguide propagation of sound beams in a nonlinear medium

A possibility of a waveguide propagation of sound beams in the case of compensation of the diffraction divergence by the nonlinear refraction is demonstrated theoretically. A stationary (with respect to the longitudinal coordinate) solution is obtained to the nonlinear equation for a sound beam (the Khokhlov—Zabolotskaya equation); the solution describes the characteristic bow-shaped profile of the beam and the self-localized (with respect to the transverse coordinate) distribution of the peak values of this profile. The physical and mathematical features of this phenomenon belonging to nonlinear acoustics are discussed and compared with those of the well-known analog from nonlinear optics. A scheme of an experimental realization of the waveguide propagation of acoustic beams is proposed.     

Numerical simulation of the transformation of a nonlinear wave at a finite depth

The shallow-water propagation of a nonlinear wave formed in deep water has been numerically analyzed based on the conformal model of surface waves. The lifetime of wave until its collapse is investigated. The parameters at which extreme waves may occur are found. An example of practical application of the simulation results is presented.     

Shallow water sound propagation with surface waves

The theory of wavefront modeling in underwater acoustics is extended to allow rapid range dependence of the boundaries such as occurs in shallow water with surface waves. The theory allows for multiple reflections at surface and bottom as well as focusing and defocusing due to reflection from surface waves. The phase and amplitude of the field are calculated directly and used to model pulse propagation in the time domain. Pulse waveforms are obtained directly for all wavefront arrivals including both insonified and shadow regions near caustics. Calculated waveforms agree well with a reference solution and data obtained in a near-shore shallow water experiment with surface waves over a sloping bottom.     

Numerical simulations of random sound waves

We perform one-dimensional numerical simulations of both driven and impulsively generated sound waves propagating through a medium whose mass density admits time-independent, random fluctuations. While the amplitude of both types of wave is always attenuated, driven sound waves can be either retarded or speeded up depending on their wavenumber and amplitude and on the strength of the random field. The speed of a pulse propagating in the random medium is also altered, in agreement with the findings for the driven waves. The concomitant action of nonlinearity and randomness results in wave speeding for wavenumbers which are of the order of the size of an average random density fluctuation, whereas it gives retardation for larger wavenumbers.