Horns as particle velocity amplifiers

Preliminary measurements and numerical predictions reveal that simple, and relatively small, horns generate remarkable amplification of acoustic particle velocity. For example, below 2 kHz, a 2.5 cm conical horn has a uniform velocity amplification ratio (throat-to-mouth) factor of approximately 3, or, in terms of a decibel level, 9.5 dB. It is shown that the velocity amplification factor depends on the horn's mouth-to-throat ratio as well as, though to a lesser degree, the horn's flare rate. A double horn configuration provides limited additional gain, approximately an increase of up to 25%.     

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。      

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.     

Finite element simulation of non-linear acoustic generation in a horn loudspeaker

The loudspeaker is an electro-acoustic device for sound reproduction which requires the distortion as small as possible. The distortion may arise from the magnetic non-linearity of the york, the uneven magnetic field distribution, the mechanical non-linearity at the diaphragm suspension and the acoustic non-linearity due to the high sound pressure and velocity in the duct-radiation system. A horn is sometimes provided in front of the vibrating diaphragm radiator, which plays an important role to increase the efficiency by matching the acoustic impedance between the radiator and the ambient medium. The horn is in many cases folded twice or three times to shorten the length, which further degrades the reproduction quality. The sound intensity and velocity are apt to attain very high in the small cross-sectional area in the throat and in the folded regions, which may cause the distortion due to the non-linear effect of the medium. The present paper is to investigate the frequency characteristics of the loudspeaker numerically evaluating the generation of the harmonics and sub-harmonics. An axisymmetric folded horn is considered for which the wave equation with the non-linear term retained is solved by the finite element method. The solution is made in time domain in which the sound pressure calculated at the opening end of the horn is Fourier-transformed to the frequency domain to evaluate the distortion, while the wave marching in the horn is visualized.     

A nonrational B-spline profiled horn with high displacement amplification for ultrasonic welding

A new horn with high displacement amplification for ultrasonic welding is developed. The profile of the horn is a nonrational B-spline curve with an open uniform knot vector. The ultrasonic actuation of the horn exploits the first longitudinal displacement mode of the horn. The horn is designed by an optimization scheme and finite element analyses. Performances of the proposed horn have been evaluated by experiments. The displacement amplification of the proposed horn is 41.4% and 8.6% higher than that of the traditional catenoidal horn and a Bézier-profile horn, respectively, with the same length and end surface diameters. The developed horn has a lower displacement amplification than the nonuniform rational B-spline profiled horn but a much smoother stress distribution. The developed horn, the catenoidal horn, and the Bézier horn are fabricated and used for ultrasonic welding of lap-shear specimens. The bonding strength of the joints welded by the open uniform nonrational B-spline (OUNBS) horn is the highest among the three horns for the various welding parameters considered. The locations of the failure mode and the distribution of the voids of the specimens are investigated to explain the reason of the high bonding strength achieved by the OUNBS horn.     

AN ACOUSTIC TRANSFORMER COMPOSED OF HORNS AND ITS APPLICATION

A new acoustic transformer was developed by connecting three horns to improve radiation performance in the frequency region below 500 Hz. The proposed acoustic transformer was evaluated by numerical analysis using the commercial computer program SYSNOISE and by experiment. The acoustic transformer is composed of three horns, one of which was used in an inverted form. A design model was developed by use of Webster's horn equation and showed that the transformer can improve radiation efficiency. This was confirmed by numerical calculation using SYSNOISE. An acoustic projector was designed by use of the developed transformer and a piezoelectric unimorph-type actuator. The sound pressure measured at the mouth of the constructed acoustic projector was compared with the sound pressures evaluated at the same location by numerical calculation to investigate the differences between the numerical simulation model and the actual acoustic projector. Sound pressures generated by several acoustic radiators were calculated numerically and compared with the measured and calculated sound pressures of the developed acoustic projector to evaluate the effects of use of the proposed acoustic transformer. The comparative evaluation shows that the proposed acoustic transformer can provide up to a 10 dB gain over use of a horn in the narrow band low-frequency region from 100 to 200 Hz.     

Matching a transducer to water at cavitation: acoustic horn design principles

High-power ultrasound for several decades has been an integral part of many industrial processes conducted in aqueous solutions. Maximizing the transfer efficiency of the acoustic energy between electromechanical transducers and water at cavitation is crucial when designing industrial ultrasonic reactors with large active volumes. This can be achieved by matching the acoustic impedances of transducers to water at cavitation using appropriately designed ultrasonic horns. In the present work, a set of criteria characterizing the matching capabilities of ultrasonic horns is developed. It is shown that none of the commonly used tapered-shape horns can achieve the necessary conditions. An analytical method for designing five-element acoustic horns with the desirable matching properties is introduced, and five novel types of such horns, most suitable for practical applications, are proposed. An evaluation of the horns' performance is presented in a set of experiments, demonstrating the validity of the developed theoretical methodology. Power transfer efficiency increase by almost an order of magnitude is shown to be possible with the presented horn designs, as compared to those traditionally utilized.     

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.     

Some general properties of the exact acoustic fields in horns and baffles

The propagation of the fundamental, longitudinal acoustic mode in a duct of variable cross-section is considered, and the “Webster” wave equations for the sound pressure and velocity are used to establish some general properties of the exact acoustic fields. The equipartition of kinetic and compression energies is shown (section 2.1) to hold at all stations only for (i) a duct of constant cross-section and (ii) an exponential horn; these are the two cases for which the wave equations for the acoustic velocity and pressure coincide. It is proved (section 2.3) that there are only five duct shapes, forming two dual families, which have constant cut-off frequency(ies): namely, (I) the exponential duct, which is self-dual, and is the only shape with constant (and coincident) cut-offs both for the velocity and pressure; (II) the catenoidal horns, of cross-section S～cosh², sinh², which, with their duals (III) the inverse catenoidal ducts S～sech², csch², have one constant cut-off frequency, respectively, for the acoustic pressure and velocity. The existence of at least one constant cut-off frequency implies that the corresponding wave equation can be transformed into one with constant coefficients, and thus the acoustic fields calculated exactly in terms of elementary (exponential, circular and hyperbolic) functions; this property also applies to the imaginary transformations of the above shapes, viz., the sinusoidal S～sin² and inverse sinusoidal S～csc² ducts, that have no cut-off frequency, i.e., are acoustically “transparent”. It is shown that elementary exact solutions of the Webster equation exist only (section 3.1) for these seven shapes: namely, the exponential, catenoidal, sinusoidal and inverse ducts; it is implied that for all other duct shapes the exact acoustic fields involve special functions, in infinite or finite terms, e.g., Bessel and Hermite functions respectively for power-law and Gaussian horns. Examples of the method of analysis are given by calculating, in elementary form, the exact acoustic fields in inverse catenoidal ducts, for all cases of (a) propagating waves above, (b) non-oscillating modes below and (c) transition fields at the cut-off frequency. The inverse catenoidal ducts consist of (A) the horn of cross-section S～sech², ressembling the “soliton” of non-linear water wave fame, and (B) the baffle of cross-section S～csch², which also matches two exponentially converging ducts, but has infinite, instead of finite, flare at the origin. The geometrical and acoustic properties of these ducts are illustrated by sets of six plots, in Figure 1(a) for the sech-horn and in Figure 1(b) for the csch-baffle; the exact acoustic fields are described by amplitude and phase decompositions of the sound velocity and pressure, plotted as functions of position along the duct, for four frequencies ranging from the cut-off condition to the ray limit (or W.K.B.J. approximation).     

Model and estimation method for predicting the sound radiated by a horn loudspeaker - With application to a car horn

This paper deals with a new car horn device made of a sound synthesizer and an electrodynamic horn loudspeaker. It presents an one-dimensional model allowing to predict the loudspeaker efficiency and a specific method to estimate experimentally the model parameters. First, this model aims at reducing the time spent in the design process. Second it aims at correcting the sound emitted by the sound synthesizer in order that the listener hears the sound designed for creating the warning message. The study gives a survey of the vast loudspeaker literature. It is based on the conventional electroacoustic approach used for electrodynamic loudspeakers and on wave propagation models used for characterizing acoustic horns. The estimation of the model parameter values is performed using measurements of the electrical impedance of the loudspeaker and of the acoustic impedance of the horn. The model is assessed by comparing the calculated and measured electrical impedances and horn efficiencies. Results show that the model predicts well the horn efficiency up to 2500 Hz, the limitation being due to the horn radiation impedance modelization.     

Design of a Bézier-profile horn for high displacement amplification

A new horn for high displacement amplification is developed. The profile of the horn is a cubic Bézier curve. The ultrasonic actuation of the horn exploits the first longitudinal displacement mode of the horn. A design method of the horn using an optimization scheme and finite element analyses is developed. Prototypes of the horns are manufactured by a numerical control machining process. Performances of the proposed horn have been evaluated by experiments. Experimental results of the harmonic response of the fabricated horn confirm the effectiveness of the design method. The displacement amplification of the proposed horn is 71% higher than that of the traditional catenoidal horn with the same length and end surface diameters.     

The Design of Potter Horns for THz Applications Using a Genetic Algorithm

We describe the design and performance of Potter horns at millimetre and submillimetre wavelength employing a novel software package that we have developed, using Genetic Algorithm. The horn is easy to fabricate and exhibits excellent beam circularity and low cross polarization over a 15% bandwidth which is sufficient for many applications. Excitation of the required higher order modes is done by either a step or a flare discontinuity at the horn throat. In each case we provide design curves that give the optimum parameters of the horn geometry as a function of frequency and beamwidth. The range of values provided covers the parameters required for the design of horns for telescope feeds and various other instruments. The design curves show clearly that the flare-step performance is superior to the traditional groove-step Potter horn. The simulations for designing these horns were carried out at millimetre and submillimetre wavelengths but the results can be scaled to lower or higher frequencies. A key component in the design method is the optimization software that searches for the correct magnitude and location of the flare discontinuities. We have developed a software package based on the combination of modal matching, a genetic algorithm (GA) and downhill simplex optimization. The genetic code is first used to locate the proximity of the global minimum. The set of parameters obtained are then used as a starting point for the simplex method, which refines the parameters to the required accuracy.     

Reflectance of acoustic horns and solution of the inverse problem

A method is described for solving the inverse problem of determining the profile of an acoustic horn when time-domain reflectance (TDR) is known only at the entrance. The method involves recasting Webster's horn equation in terms of forward and backward propagating wave variables. An essential feature of this method is a requirement that the backward propagating wave be continuous at the wave-front at all locations beyond the entrance. Derivation of the inverse solution raises questions about the meaning of causality in the context of wave propagation in non-uniform tubes. Exact reflectance expressions are presented for infinite exponential, conical and parabolic horns based on exact solutions of the horn equation. Diameter functions obtained with the inverse solution are a good match to all three horn profiles.     

An experimental and analytical study of a new flap valve for generating simulated sonic booms

The design, operation, and performance of a sonic boom simulator, featuring a radically new dual-flap valve and electromechanical control system, are described. This new flap valve with its large maximum throat area (160 cm²) was designed to regulate the air flow from a low pressure reservoir (up to 0·2 atm overpressure) into the apex of a large pyramidal horn (25 m long, 3 m × 3 m base), where the incoming low speed air flow (up to 150 m/s) produces a travelling simulated sonic boom or N-wave with relatively little superposed high frequency noise. As a consequence, the full scale simulated sonic boom is virtually free of superposed jet noise, a major advance over past work with such horn-type simulators. Additionally, an advanced gasdynamic analysis of the reservoir coupled with an advanced acoustic analysis of the wave motion in the horn is presented to predict the characteristics of the simulated sonic boom—wave form, amplitude, duration, and rise time. Predicted and measured overpressure signatures are shown to be in excellent agreement.     

Combining COMSOL modeling with acoustic pressure maps to design sono-reactors

Scaled-up and economically viable sonochemical systems are critical for increased use of ultrasound in environmental and chemical processing applications. In this study, computational simulations and acoustic pressure maps were used to design a larger-scale sono-reactor containing a multi-stepped ultrasonic horn. Simulations in COMSOL Multiphysics showed ultrasonic waves emitted from the horn neck and tip, generating multiple regions of high acoustic pressure. The volume of these regions surrounding the horn neck were larger compared with those below the horn tip. The simulated acoustic field was verified by acoustic pressure contour maps generated from hydrophone measurements in a plexiglass box filled with water. These acoustic pressure contour maps revealed an asymmetric and discrete distribution of acoustic pressure due to acoustic cavitation, wave interaction, and water movement by ultrasonic irradiation. The acoustic pressure contour maps were consistent with simulation results in terms of the effective scale of cavitation zones (∼10 cm and <5 cm above and below horn tip, respectively). With the mapped acoustic field and identified cavitation location, a cylindrically-shaped sono-reactor with a conical bottom was designed to evaluate the treatment capacity (∼5 L) for the multi-stepped horn using COMSOL simulations. In this study, verification of simulation results with experiments demonstrates that coupling of COMSOL simulations with hydrophone measurements is a simple, effective and reliable scientific method to evaluate reactor designs of ultrasonic systems.     

The identification of tyre induced vehicle interior noise

Sound transmission into a vehicle is classified as either airborne or structure borne sound. From the point view of noise control, the reduction of noise transferred by different paths requires different solutions. Coherence function analysis is often used to identify transmission paths. However it can be difficult to separate the airborne from structure borne components. The principle of acoustic reciprocity offers a convenient method for overcoming this difficulty. The principal states that the transfer function between an acoustic volume velocity source and an acoustic receiver is independent of a reversal of the position of source and receiver. The work done on this study involves exciting a stationary tyre and measuring the surface velocity of the tyre at a number of discrete points. The acoustic transfer functions between each point on the tyre and a receiver point are measured reciprocally. Two sets of measurements are then combined to yield a measure of the sound pressure due to a point force on the tyre via the acoustic transmission path only. This technique also provides information on the relative contributions of various regions of the tyre wall to the resultant noise. Also the sound radiation characteristics, the horn effect, and resonance at the wheel housing are identified through the reciprocal measurement.     

纵-扭复合振动模式指数型复合超声变幅杆的研究

本文对指数型纵－扭复合振动模式的复合超声变幅杆进行了理论及实验研究，该变幅杆由均匀截面直棒及指数型截面杆组成。文中推出了变幅杆中纵向振动及扭转振动的共振频率方程，通过发迹指数型变截面棒的截面变化规律，实现了同一变幅杆中纵向振动与扭转振动的同频共振。     

液体材料超声处理过程中声场和流场的分布规律研究

针对合金熔体等液体材料的超声处理过程,选取水作为透明模型材料,采用数值模拟计算和示踪粒子实验方法,研究了20和490 kHz两种频率超声作用下水中的声场和流场分布.结果表明,增大变幅杆半径能够提高水中声压水平,扩大空化效应的发生区域.当超声频率为20 kHz时,水中声压最大值出现在超声变幅杆下端面处,且声压沿传播距离的增大而显著减小.如果超声频率增加至490 kHz,水中的声压级相比于20 kHz时明显提高,且声压沿着超声传播方向呈现出周期性振荡特征.两种频率超声作用下水中的流场呈现相似的分布特征,且平均流速均随着变幅杆半径增大表现出先升高后降低的趋势.变幅杆半径相同时,20 kHz频率超声作用下水中的平均流速高于490 kHz频率超声.采用示踪粒子图像测速技术实时观察和测定了水中的流速分布,发现其与计算结果基本一致.     

Enhanced vibration performance of ultrasonic block horns

Block horns are tuned components designed to vibrate in a longitudinal mode at a low ultrasonic frequency. Reliable performance of such horns is normally associated with the amplitude of vibration, uniformity of vibration amplitude at the working surface and the avoidance of modal participation by non-tuned modes at the operating frequency. In order to maximise vibration amplitude uniformity, standard slotting configurations are included in the horn design. However, defining a slotted block geometry which guarantees sufficient tuned frequency isolation from nearby modes as well as high amplitude and amplitude uniformity, is not straightforward. This paper discusses horn configurations which satisfy these criteria and investigates the design requirements of block horns which operate as intermediate components in ultrasonic systems, where the block horn dominates the vibration behaviour of the system. The importance of mode shape characterisation is discussed and modes are classified using experimental data from 3D laser Doppler vibrometer measurements and finite element analysis. In particular, the role of additional fine slots and castellations are studied with reference to two distinct ultrasonic applications involving a similar block horn.     

Understanding the ultrasound field of high viscosity mixtures: Experimental and numerical investigation of a lab scale batch reactor

In this work, mixtures of increasing viscosity (from 0.9 to ≈720 mPas) are sonicated directly using an ultrasonic horn at 30 kHz to investigate the effect of viscosity on the ultrasound field both from an experimental and numerical point of view. The viscosity of the mixtures is modified by preparing water-polyethylene glycol solutions. The impact of the higher viscosity on the acoustic pressure distribution is studied qualitatively and semi-quantitatively using sonochemiluminescence. The velocity of light scattering particles added in the mixtures is also explored to quantify acoustic streaming effects using Particle Image Velocimetry (PIV). A numerical model is developed that is able to predict cavitationally active zones accounting for both thermoviscous and cavitation based attenuation. The results show that two cavitation zones exist: one directly under the horn tip and one around the part of the horn body that is immersed in the liquid. The erosion patterns on aluminum foil confirm the existence of both zones. The intensity of the cavitationally active zones decreases considerably with increasing viscosity of the solutions. A similar reduction trend is observed for the velocity of the particles contained in the jet directly under the tip of the horn. Less erratic flow patterns relate to the high viscosity mixtures tested. Finally, two numerical models were made combining different boundary conditions related to the ultrasonic horn. Only the model that includes the radial horn movements is able to qualitatively predict well the location of the cavitation zones and the decrease of the zones intensity, for the highest viscosities studied. The current findings should be taken into consideration in the design and modelling phase of horn based sonochemical reactors.