Radiation of cylindrical duct acoustic modes with flow mismatch

An analysis is presented for the radiation of spinning acoustic modes from a round duct. The model, based on a plug flow exhaust jet, allows for a flow temperature and velocity mismatch. Solutions to the convected wave equations within and outside the jet are devised, the continuity of acoustic pressure and particle displacement match at the jet interface being used. Formal solution is obtained by applying Fourier transforms, inversion being accomplished by using the Wiener-Hopf technique coupled with the Carrier-Koiter approximations. The analysis also is extended formally to include the inlet problem, but with a plug type inlet flow.The calculations suggest that the influence of the Mach number discontinuity is to offer a conflict between the effects of convection and refraction, the former becoming increasingly more significant at high subsonic Mach numbers by the presence of a strong lobe in the shadow zone. Effects of flight conditions are to weaken such conflicts so that in the limit of uniform Mach number, one recovers Carrier's well-known solution.The effect of a temperature mismatch is rather more dramatic, resulting in a sharp beaming of sound off to the side. This is consistent with the kinematic picture of a plane wave impinging on a temperature discontinuity.     

On the acoustic modes in a cylindrical duct with an arbitrary wall impedance distribution

The present paper considers the propagation of sound in a cylindrical duct, with a wall section of finite length covered by an acoustic liner whose impedance is an arbitrary function of position. The cases of (i) uniform wall impedance, and wall impedance varying along the (ii) circumference or (iii) axis of the duct, or (iv) both simultaneously, are explicitly considered. It is shown that a nonuniform wall impedance couples modes with distinct azimuthal l or axial m wave numbers, so that their radial wave numbers k can no longer be calculated separately for each pair (m,l). The radial wave numbers are the roots of an infinite determinant, in the case when the wall impedance varies either (i) circumferentially or (ii) radially. If the wall impedance varies (iv) both radially and circumferentially, then the radial wave numbers are the roots of a doubly infinite determinant, i.e., an infinite determinant in which each term is an infinite determinant. The infinite determinants specifying the radial wave numbers are written explicitly for sound in a cylindrical nozzle with a uniform axial flow, in which case the radial eigenfunctions are Bessel functions; the method of calculation of the radial wave numbers applies equally well to a cylindrical nozzle with shear flow and/or swirling flows, with the Bessel functions replaced by other eigenfunctions. The radial wave numbers are calculated by truncation of the infinite determinants, for several values of the aspect ratio, defined as the ratio of length to diameter. It is shown that a nonuniform wall impedance will give rise to additional modes compared with a uniform wall impedance. The radial wave numbers specify the eigenfrequencies for the acoustic modes in the duct; the imaginary parts of the eigenfrequencies specify the decay of the sound field with time, and thus the effectiveness of the acoustic liner.     

Energy flow measurements in acoustic waves in a duct

Where, how much and how efficiently the energy conversion takes place in a regenerator of a thermoacoustic engine are expressed using the axial distribution of acoustic work flow and heat flow. As a first step in determining the energy flows inside the regenerator, measuring methods of the work flow are briefly described and the experimental results in an acoustic resonator are shown. Applicability of these methods to the regenerator is discussed.     

The influence of a stationary uniform axial flow on the propagation of acoustic modes of vibration in a cylindrical duct

The propagation, in a cylindrical duct, of acoustic modes of vibration whose wavelength is smaller than the damping length, is studied in the presence of a stationary uniform axial flow.     

The influence of flow on the acoustic characteristics of a duct bend for higher order modes—A numerical study

A numerical technique was used to investigate the effects of flow on the acoustic transmission and reflection characteristics of a duct bend. The range of wave numbers examined extended to the cut-on value of the second cross-mode. Characteristics were studied in terms of the velocity potential, the acoustic pressure and the energy flux. The effects of locating a turning vane centrally in the bend were also examined in terms of the energy flux.     

激发圆形管道内多阶声模态的扬声器阵列控制方法

声模态发生器是通过控制扬声器阵列在管道内激发声模态波的一种装置。为了解决在管道内同时激发多个声模态的问题,研究了激发圆形管道内多阶声模态的扬声器阵列控制方法。采用轴向多圈布置的声源阵列,并调节各个声源的幅值和相位,实现同时激发包括径向声模态在内的多个声模态。同时考虑声源的周向位置和轴向位置信息,建立各个声源与多个目标模态系数之间的线性关系,运用最小二乘法求解得到激发目标多模态所需各个声源的复强度（包括幅值和相位）,所研制的高阶模态发生器以计算的声源复强度为输入量,采用数字信号系统控制扬声器输出的幅值和相位,用于实现管道内声源激发,该模态激发过程无需针对特定模态优化声源的位置。实验结果表明,所研制的模态发生器可精确激发单个或多个声模态,且目标模态系数信噪比几乎都大于10 dB。     

A numerical method for acoustic normal modes for shear flows

The normal modes and their propagation numbers for acoustic propagation in wave guides with flow are the eigenvectors and eigenvalues of a boundary value problem for a non-standard Sturm-Liouville problem. It is non-standard because it depends non-linearly on the eigenvalue parameter. (In the classical problem for ducts with no flow, the problem depends linearly on the eigenvalue parameter.) In this paper a method is presented for the fast numerical solution of this problem. It is a generalization of a method that was developed for the classical problem. A finite difference method is employed that combines well known numerical techniques and a generalization of the Sturm sequence method to solve the resulting algebraic eigenvalue problem. Then a modified Richardson extrapolation method is used that dramatically increases the accuracy of the computed eigenvalues. The method is then applied to two problems. They correspond to acoustic propagation in the ocean in the presence of a current, and to acoustic propagation in shear layers over flat plates.     

The acoustic modes of a rectangular cavity containing a rigid,incomplete partition

A theoretical and experimental study of the acoustic modes of a rectangular cavity containing a rigid, incomplete partition is presented. The theoretical results are obtained by using finite element techniques. It is shown that component mode synthesis techniques, developed for dynamic structural analysis, can be used for acoustic analysis to increase efficiency. The experimental measurements were made on a Perspex model. Good agreement is shown between theory and experiment.     

On acoustic waves generated in a rectangular basin by low-frequency gravity modes

Summary Sound waves generated by low-frequency gravity modes are further examined. In this consideration, the study is extended to a closed inland body of water. By the use of the appropriate Green's function and traditional shallow water approximations, the mean response is completely evaluated. The result suggests that this response function is inversely proportional to fourth power of the exciting wave number.

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Riassunto Si esaminano ulteriormente onde sonore generate da modi di gravità a bassa frequenza. In questa considerazione, lo studio è esteso ad un bacino d'acqua chiuso nell'entroterra. Mediante la funzione di Green appropriata e le approssimazioni tradizionali dell'acqua bassa, si valuta completamente la risposta media. Il risultato suggerisce che questa funzione di risposta è inversamente proporzionale alla quarta potenza del numero d'onda di eccitazione.

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Резюме Исследуются звуковые волны, образованные гравитационными модами низкой частоты. В этой работе рассматривается случай замкнутого прямоугольного бассейна. Используя соответствующую функцию Грина и традиционные приближения мелкой воды, полностью определяется средний отклик. Полученный результат предполагает, что функция отклика обратно пропорцоинальна четвертой степени возбуждающего волнового числа.

     

Temperature dependence of the soft acoustic shear modes in h.c.p. zirconium

Neutron measurements of the dispersion curve v(q) for [10·0] phonons polarized in [11·0] are presented for hexagonal close-packed Zr at 300°, 773°, and 1073°K. Given that the crystal transforms to b.c.c. at 1135°K and demonstrates a pronounced softening in the C₆₆ elastic constant, v(q) shows only a uniform lowering of the entire branch, consistent with the behavior of C₆₆(T) but fractionally smaller for large wave vectors. No anomalous phonon linewidths are observed.     

On acoustic radiation by a rigid object in a fluid flow

A problem of sound radiation by an absolutely rigid object, moving with respect to the surrounding fluid, is considered on the basis of the Lighthill's equation for aerodynamic sound. An integral representation of the radiated acoustic field is utilized, where the field is characterized as the sum of three fields, generated by a volume distribution of monopoles and by distributions of monopoles and dipoles on the surface of the rigid object. It is shown that, due to a discontinuity of Lighthill's stress tensor on the rigid boundary, a layer of surface divergence of hydrodynamic stresses on the boundary must be taken into account when evaluating the volume integral over Lighthill's quadrupole sources. When the contribution of the surface divergence is included in the solution of Lighthill's equation, amplitudes of the monopole and dipole sound radiated by the rigid object are shown to depend on the potential components of the normal velocity and the pressure on the rigid surface. The obtained solution is compared with Curle's solution for this problem, which establishes that the sound radiation by a rigid object is determined by the force exerted by the object upon the fluid. Both solutions are applied to two known problems of sound scattering and radiation by a rigid sphere in variable pressure and velocity fields. It is shown that predictions based on the obtained solution are equivalent to the results known from literature, whereas Curle's solution gives predictions contradicting the known results. It is also shown that the Ffowcs Williams and Hawkings equation, which coincides with Curle's equation for an immoveable rigid object, does not lead to the correct predictions as well.     

利用声辐射模态对声场进行重构

声辐射模态是定义在振动表面上的一组互相独立的基函数,描绘了振动表面的多极子辐射模式。本文利用声辐射模态对平板辐射的声场进行重构，并同时就频率和模态数对误差的影响进行了分析。针对复杂振动表面幅射的声场，重构时需正则化处理。数值计算结果和对应的理论值达到很好的吻合。     

Effect of shear equilibrium flow in Tokamak plasma on resistive wall modes

A code named LARWM with non-ideal magnetohydrodynamic equations in cylindrical model is used to describe the instability in Tokamak plasma surrounded by a conducting wall with finite resistivity. We mainly take three factors related to the shear equilibrium plasma flow into consideration to study the stabilizing effect of the shear flow on the resistive wall modes (RWMs). The three factors are the velocity amplitude of flow, the shear rate of flow on plasma surface, and the inertial energy of equilibrium plasma flow. In addition, a local shear plasma flow is also calculated by the LARWM code. Consequently, it is found that the inertial energy of the shear equilibrium plasma flow has an important role in the stabilization of the RWMs.     

On flame extinction by a spatially periodic shear flow

It is shown that the adiabatic high Lewis number premixed gas flame spreading through a large-scale zero-mean time-independent periodic shear flow constitutes a bistable system with a hysteretic transition between stable propagation modes. A mildly non-adiabatic flame may be quenched provided the flow-field intensity exceeds a certain critical value. The study is motivated by the experimentally known phenomenon of flame extinction by turbulence.     

Effect of flow on quasi-one-dimensional acoustic wave propagation in a variable area duct of finite length

The general equation for the velocity potential of quasi-one-dimensional acoustic wave motion in a variable area, finite duct with one-dimensional flow is derived by using a perturbation technique. The non-linear second-order partial differential equation is linearized and then solved, by either a power series expansion method or the Runge-Kutta fourth-order method, for harmonic time dependence. The boundary condition taken at the duct mouth is that of matching the impedance of the duct sound field to that of the radiation field at the duct opening. Three axial Mach number variations along the duct axis are considered and the results obtained are compared with those for the case of constant Mach number, to determine the influence of the axial velocity gradient on sound propagation. The effect of flow on the radiation impedance is also considered.     

On the acoustic boundary condition in the presence of flow

The boundary condition on the acoustic perturbation velocity at an impermeable surface in a flow is considered for the cases in which the surface generates a sound field by vibration or is acoustically deformed by an incident sound field. It is shown that in general the condition is not equivalent to the requirement of continuity of acoustic particle displacement in the direction normal to the unperturbed surface.