Quarter-wave Tube Research Articles

Pros and cons of equipping Harmonic Acoustic Pneumatic Sources (HAPS) with quarter wave tube: analytical model versus experimental validation

Pneumatic acoustic sources enable high Sound Pressure Levels (SPL). Harmonic Acoustic Pneumatic Sources (HAPS), utilizing airflow modulation to create precise acoustic pressure fields with controlled amplitude and phase, emerge as solutions for active harmonic-noise control at high SPLs. While theoretically capable of generating pure tones, HAPS appear to be non-linear sources with significant harmonic distortion in practice. Additionally, the mass airflow consumption of this source could be a drawback in certain applications. The aims of this study is to evaluate the advantages of a Quarter-Wave Tube (QWT) located at the HAPS output. A numerical analytical linear model has been developed to compute the radiated acoustic pressure and consumed mass air flow, according to the QWT and HAPS characteristics. For the cases of HAPS equipped with various QWT, this presentation will compare experimental results with the analytical model. This aims to highlight the advantages, including increased SPL of the radiated fundamental, reduced fundamental/harmonic distortion over a wide frequency range, and decreased airflow consumption. The disadvantage is related to the space required by the QWT because its diameters must be greater than the HAPS output. Whatever, this study demonstrate that HAPS can be improved when equipped with a dedicated exhaust.

Producing a High Level Harmonic Acoustic Pressure Field with Harmonic Acoustic Pneumatic Source (HAPS): Experimental Validation of the Harmonic Distortion Reduction

Applications such as active control of fane noise, require high Sound Pressure Levels (SPL). Pneumatic acoustic sources are usually used for that purpose (e.g. the WAS 3000 and the Mark VI and VII). The harmonic acoustic pneumatic sources (HAPS) - which use the chopping of an airflow to generate an acoustic pressure field - are being studied for applications requiring high-level harmonic acoustic pressure fields. A recent study has shown that the amplitude, phase, and frequency generated by HAPS are accurately controllable, and can reach 120 dBSPL. However, higher harmonics are also generated at high SPL and this could be detrimental to the intended applications (e.g. active control of tonal noise). An experimental campaign dedicated to understanding the harmonic distortion of HAPS has been conducted on a single HAPS in a semi-anechoic chamber. Measurements with quarter-wave tube at the output of the HAPS were also carried out to reduce this distortion. Levels of 120 to 130 dBSPL for the fundamental were reached, with a difference of 10 dB between the fundamental and the second harmonic (H1/H2 distorsion). Adding a quarter-wave tube increased the acoustic pressure level from 4 to 6 dBSPL, and the H1/H2 distorsion from 2 to 8 dBSPL.

Review on Resonator and Muffler Configuration Acoustics

Nowadays, resonators are widely used in automobile, industrial applications, aerospace engineering, and some other fields. One of the unique characteristics of resonators which made them highly convenient is their acoustic capability to attenuate noise without having to use any acoustic absorptive material. The device acts by manipulating the sound waves to create mismatch impedance. Recent studies also suggest that the typical bulk size resonator with narrow frequency bandwidth is not the only option anymore, since there are newly designed resonators that are capable of having wide attenuation bandwidth and are smaller in size. Numerical and experimental measures were executed accordingly with the same purpose to obtain efficient noise attenuation results from varying resonators’ and mufflers’ configuration in terms of quantity, types, and geometry. The aim of this review is to summarize recent developments on resonator study and to try highlighting some noteworthy issues that need to be unraveled by future research. Helmholtz resonator, Quarter wave tube, Herschel-Quincke tube and helicoidal resonator are part of the numerous resonator studies that will be covered in this paper.

Acoustic Optimization for Intake System of Commercial Bus

Based on simulation and test, a method for engine acoustical source characteristic extraction and acoustic optimization was presented. The intake noise of engine of commercial bus with four different acoustical loads was measured and the characteristic of the noise was extracted using the four-load method. The values of intake noise calculated by BEM were compared with the values measured in the vehicle intake noise test. The comparison result showed that the simulation values agreed with the experimental ones at most of the range which indicated that the extracted result was reliable. The anechoic frequency was determined by analyzing the intake noise spectrum measured in the vehicle intake noise test. Finally, an effective scheme adding a Helmholtz resonator and a quarter wave tube was proposed by simulation, applied to the real vehicle and verified in the test. The acoustic performance of the intake system was improved significantly.

An adaptive quarter-wave tube that uses the sliding-Goertzel algorithm for estimation of phase

This paper describes an adaptive quarter wave tube used to attenuate a tone from the exhaust noise of a large diesel engine. A sliding-Goertzel algorithm was used to calculate the phase angle of the transfer function between a microphone in the adaptive quarter wave tube and in the main exhaust duct. The control system adjusted the length of the adaptive quarter wave tube until the phase angle was −90° and caused the sound pressure level at the cylinder firing frequency in the exhaust duct to be minimized. The system was able to adapt to changes in engine speed, exhaust gas temperature, and load applied to the engine. The results demonstrate that the sliding-Goertzel algorithm can be used effectively to estimate the phase angle in an adaptive–passive acoustic control system.

Noise reduction using a quarter wave tube with different orifice geometries

It is well known that the acoustic performance of silencing elements decreases with an increase in exhaust gas flow. Tests were conducted on three orifice geometries of side-branches on an adaptive quarter-wave tube to determine which was the least compromised by the high-speed exhaust gas passing over the side-branch. The side-branch geometries that were tested were a sharp edge, a backward inclined branch, and a bell mouth. The experimental results show that the side-branch with a bell-mouth geometry resulted in the greatest noise reduction by an adaptive quarter-wave tube.

Experimenting with end-correction and the speed of sound

What follows is an alternative to the standard tuning fork and quarter-wave tube speed ofsound experiment. Rather than adjusting the water level in a glass or plastic tube to varythe length of an air column, a set of resonance tubes of different lengths is used. Theexperiment still demonstrates the principles of standing waves in air columns and can alsobe used to study end-correction as well as determining the speed of sound in air.

Thermoacoustic oscillations in ducted domestic heating systems

Thermoacoustic oscillation is a significant problem in ducted domestic heating systems fitted with fully premixing burners as well as in combustion systems of industrial scale. This paper reports experiments using a burner closely representative of practical designs in which high-intensity free-field sound has been used to simulate the feedback which may be excited naturally in installations with different acoustic properties. This experimental approach facilitates study of the non-linear response of the burner/flame sub-system to feedback of different frequencies and direct measurement of the acoustic impedance of the burner under operational conditions. A function proportional to the Rayleigh integral has been evaluated directly from the experimental results. It is found that the head of this type of burner divides the typical installation into a quarter-wave tube and a Helmholtz resonator which must couple unstably for thermoacoustic oscillations to be autoexciting. It is further found that there is a strong interaction between the acoustic field and the mean flow which modifies significantly the behaviour of the burner as a Helmholtz resonator and thus the stability of the whole system.

Technical Note: Effects Due to Exhaust and Tail Pipes on Insertion Loss of Mufflers

(Submitted 28 September 2010; revised 13 August 2010; accepted 18 February 2011) In this study, the influence of exhaust pipe lengths on insertion loss(IL) which has not been analyzed in previous studies is investigated. IL is calculated analytically for a simple expansion chamber including source impedance, exhaust and tail pipe lengths. The prediction of frequencies based on models of quarter wave tube and half wave tube for exhaust and tail pipe resonances agree well with the effects seen in experimentally measured IL.

Measuring End Correction for a Quarter-Wave Tube

The values for the speed of sound calculated in a standard quarter-wave tube experiment are generally too low because the measured length of the air-column is less than one-quarter of the wavelength of the sound. This is because the antinode of the standing wave generated by the tuning fork is in reality beyond the actual end of the tube. This error can be reduced by adding a standard “end correction” to the air-column length, generally considered to be about one-third the diameter of the tube.

Exact Solution for One-Dimensional Acoustic Fields in Ducts With Polynomial Mean Temperature Profiles

The purpose of this paper is to present closed form expressions for sound propagation in ducts with polynomial mean temperature profiles. It is shown that using appropriate transformations, the one-dimensional wave equation for ducts with an axial mean temperature gradient can be reduced to a standard differential equation whose form depends upon the specific mean temperature profile in the duct. The solutions are obtained in terms of Bessel and Neumann functions. The analysis neglects the effects of mean flow and therefore the solutions obtained are valid only for mean mach numbers that are less than 0.1. The developed solution is used to investigate the sound propagation in a quarter wave tube with an axial mean temperature gradient. The expressions for the four pole parameters are also presented.

An exact solution for one-dimensional acoustic fields in ducts with an axial temperature gradient

Abstract In this paper an approach is presented for obtaining exact analytical solutions for sound propagation in ducts with an axial mean temperature gradient. The one-dimensional wave equation for ducts with an axial mean temperature gradient is derived. The analysis neglects the effects of mean flow, and therefore the solutions obtained are valid only for mean Mach numbers that are less than 0.1. The derived wave equation is then transformed to the mean temperature space. It is shown that by use of suitable transformations, the derived wave equation can be reduced to analytically solvable equations (e.g., Bessel’s differential equation). The applicability of the developed technique is demonstrated by obtaining a solution for ducts with a linear temperature profile. This solution is then applied to investigate the dependence of sound propagation in a quarter wave tube upon the mean temperature profile. Furthermore, the developed analytical solution is used to extend the classical impedance tube technique to the determination of admittances of high temperature systems (e.g., flames). The results obtained using the developed analytical solution are in excellent agreement with experimental as well as numerical results. Analytical solutions were also obtained for a duct with an exponential temperature profile and also for a temperature profile that corresponds to a constant convective heat transfer coefficient at the wall.

Oscillations in Axisymmetric Dump Combustors

Combustion instability in axisymmetric dump combustors with uniform ducts on either side of the dump plane and with fully open as well as constricted exits is examined, and flammability and stability limits established as a function of upstream and downstream duct lengths. With the exit fully open, the oscillations depend mainly on the downstream length, while the upstream length affects the strength of the oscillations in combustors with a large downstream to upstream diameter ratio. For small diameter ratios, the upstream length has a decisive influence on the occurrence of instability, The use of a strategically located orifice in the upstream duct and of a coaxial annular quarter-wave tube to suppress oscillations in combustors with acoustically closed and acoustically open upstream ends is demonstrated. Combustion instability is not observed with long downstream ducts constricted at the exit and the possible reasons are discussed. Oscillations observed in short ducts are associated with the acoustic ...

Resonant frequencies of cylindrical Helmholtz resonators

A simple analysis predicts the Helmholtz and higher modes of cylindrical resonators. Formulas for the quarter-wave tube, the closed tube, and the classic Helmholtz resonator are special cases. It is found that the classic Helmholtz formula begins to lose accuracy for resonator lengths L≳λ/16. A corrected Helmholtz equation is given as an approximation to the exact result. The analysis requires values of inside and outside orifice end corrections. Rayleigh’s model of a piston in an infinite wall and Ingard’s calculations for a piston radiating into a tube give satisfactory results when the theory is compared to experiments. Resonator experiments were performed with k0L in the range π/8 to 3π/8 and orifice to cavity diameter ratios from 0.1 to 0.8. Subject Classification: 20.40.

Theory of a generalized Helmholtz resonator

Based on the jet-flow model which is manifested in the nonlinearity of the orifice flow upon the passage of a high intensity wave, the theory of a generalized Helmholtz resonator has been developed. The results for some special devices, such as the conventional Helmholtz resonator and the quarter-wave tube, can be obtained through this general approach. The performance of the acoustic damper is characterized by a quantity known as the real part of the admittance coefficient. It is known that the conventional Helmholtz resonator has the lowest peak performance but the response is quite flat over a certain frequency range. On the other hand, a quarter-wave tube offers the largest peak in energy absorption with rather poor off-resonance behavior. Once the orifice length goes beyond the quarter-wave tube configuration, the performance of the so-called long damping device is even less attractive away from resonance.

Experimental verification of the energy dissipation mechanism in acoustic dampers

An experimental program is described which verifies the theoretical model that acoustic damping devices undergoing high intensity oscillations dissipate energy via jet kinetic losses. Pressure measurements within the damping devices and flow duct together with detailed surveys of the jet velocities provide the experimental confirmation. The theory accounts for duct flow effects, both steady and unsteady, as well as the jet dissipation. Discrepancies between theory and experiment can be traced to neglect of higher order terms or ignoring the difficult wall friction term in the case of the quarter-wave tube.

Suppression of Burner Oscillations by Acoustical Dampers

Abstract Tests on the suppression of burner oscillations are described. The work was not all inclusive but did produce several positive conclusions which may help in quieting particular combustion installations, or may be of help in preventing waste of effort in trying ineffective methods. The effectiveness of a quarter-wave tube was found to be critically dependent on length, but relatively insensitive to location, as long as the tube is placed in the region of the pressure antinode. Similarly, the effectiveness of a Helmholtz resonator depended critically on volume for a particular neck, but is quite insensitive to location. In neither case did the suppressor have to be placed near the particular antinode where energy was fed into the oscillation. The degree of suppression obtained was approximately proportional to the cross-sectional area of the tube; the same conclusion appears to be warranted with regard to the cross-sectional area of the throat of a Helmholtz resonator. Almost complete suppression was obtained with holes drilled in the side of the tube and placed within 10 per cent of a wave length from a pressure antinode. It was found that the diameter of the hole need not be greater than about 1/10 to 1/15 of the diameter of the combustion chamber, but should be greater than the wall thickness for best suppression.