Duct Termination Research Articles

Sound radiation from a circular duct with axial temperature gradients

An analytic analysis has been carried out to investigate the effects of temperature on the sound radiation from an unflanged circular duct by using a Wiener-Hopf technique. The wave equations were solved separately inside and outside the duct and the solutions were matched on the duct termination. Measured and computed results for uniform temperature in the duct are shown to be in close agreement. The results show that the radiation resistance is more affected than radiation reactance by the temperature difference between the gas and the ambient air. The radiation resistance is almost insensitive to, while radiation reactance decreases with, axial temperature gradients which increase the velocity potential in the duct as the wave propagates. At high frequency, the far field radiation pattern shows a second lobe as the temperature in the duct increases.

Active source cancellation of the blade tone fundamental and harmonics in centrifugal fans

In previous papers it has been shown that the aerodynamic noise of centrifugal fans can be controlled with active source cancellation methods. In particular, cancellation of a fan's blade tone fundamental was achieved by replacing a section of the fan's cut-off where the aerodynamic blade tones are generated with two appropriately driven secondary sources. In the present set of experiments, the method is extended to include cancellation of the harmonics of the blade tone. A special case is also examined where the frequency of the blade tone harmonic lies just above the cut-on frequency of the first higher order mode of the fan ducting. Results indicate that active control is effective at the harmonics of the blade tones as well as the fundamental for a variety of fan loading conditions and duct terminations. Further evidence has also been obtained with global measurements of the fan's radiated sound that supports the idea that the active control mechanism involves a local alteration of the aerodynamic source pressures.

Practical flow duct acoustics

Predictions of plane acoustic wave propagation through acoustically reactive flow duct systems are of practical relevance in design studies for industrial, transportation and environmental noise application. Acoustic conditions throughout the flow duct are described by the complex values of the incident and reflected wave amplitudes relative to that of the wave component incident at an open duct termination. Examples are given of the calculation of these relative component amplitudes with a comprehensive range of typical flow duct configurations. The practical consequences of wave attenuation and other losses are quantified, but consideration is restricted to plane wave propagation. In practical application the flux of acoustic energy from a prescribed source through some prescribed system will be governed by the acoustic characteristics of both. To maintain generality of application in this presentation, sources are represented simply by equivalent specified termination conditions. Thus modelling of source characteristics and its coupling with the system is not included here, neither is flow noise, nor is acoustic generation or amplification by flow processes acting as sources. Within these restrictions, effective methods are presented for quantifying and assessing acoustic performance, expressed in terms of realistic predictions for design application to practical situations. The emphasis throughout is based on fluid dynamic and acoustic principles and directed towards the development of physical insight with the identification of the relevant processes controlling wave propagation. Thus the methods described remain general enough for application to any relevant flow duct configuration, as well as those specifically considered here.

Reflection from an anechoic duct termination

A theoretical model was developed which describes the farfield reflection from various absorbent terminations of an acoustic duct with rigid walls. The absorbent termination is utilized to reduce the reflected sound from the ends of ducts and pipes. Such sound absorbing terminations can be used to minimize the shock wave (water hammer) travel in water pipes, reduce the flow noise at flow‐through pressure valves and at stations along the hydraulic lines where cross‐sectional changes occur. A parametric study of the terminations's geometry and material properties revealed the effects of longitudinal and shear wave resonances inside the termination on the frequency response of the reflection. A partially cemented lower boundary achieves much greater echo reduction than a uniform rigidly attached or stress‐free boundary. Peaks in the frequency response result not only from compressional thickness resonances, but also from shear and lateral compressional resonances induced by the discontinuity. A slight impedance mismatch promotes multiple reflections within the termination, hence increased resonance effects. [Work supported by the Naval Sea Systems Command.]

Spatial variation of phase in ducts and the measurement of acoustic energy reflection coefficients

The sound pressure in a one-dimensional duct contains amplitude and phase components, both of which vary with position. The spatial variation of phase is examined in this paper and is shown to be closely related to the relative flow of incident and reflected acoustic energy. A technique that determines the acoustic reflection coefficient of the duct termination by measuring the maximum rate change of phase with position is discussed. For the measurements of phase variation a single moveable probe microphone is used with a phasemeter. Good agreement has been obtained between this method and the more usual impedance tube method, which considers the amplitude component of sound pressure. The phase measurements, though, can be applied equally well to ducts of conical, rather than uniform, cross section, and require a relatively small length of duct in which to translate the probe (as little as 1/20 wavelength, for moderate reflectivities). Some preliminary measurements have been made in human ear canals. The eardrum reflection coefficients obtained in the 10- to 15-kHz range are between 0.6 and 0.85, somewhat higher than those obtained by other methods.

High amplitude acoustic transmission through duct terminations: Theory

Recent experimental measurements have demonstrated that net acoustic energy dissipation can occur when sound waves interact with free shear layers, which are produced either by boundary layer separation in mean fluid flow at sharp edges, or by separation of the boundary layer in the acoustic flow at an edge in the absence of mean flow. This paper presents theoretical results which are offered in an attempt to explain these observations quantitatively. Comparison is made between the predicted and measured net energy loss which occurs upon transmission of high amplitude impulsive acoustic waves through various duct terminations, and also between calculated and measured reflection coefficients in the duct. The agreement is generally at least qualitatively good, and would appear to justify the physical assumptions on which the theoretical arguments are based.

Acoustic power dissipation on radiation through duct terminations: Experiments

This paper describes the acoustic transmission characteristics of ducts, nozzles, orifices, and perforated plates, studied under an experimental program using an acoustic impulse technique. In this technique high intensity pulses, generated by discharging a capacitor across a spark gap, were used as the sound source. The test conditions include heated and unheated flows, with and without simulated flight. Results for a straight round duct, three convergent nozzles, a suppressor nozzle, 12 orifice plates, and 10 perforated plates are presented. A low frequency acoustic power loss phenomenon was observed for all configurations at all test conditions including the no flow condition. It was suspected that the power loss phenomenon at the no flow condition could be due to the conversion of acoustic energy into vortical energy due to non-linear propagation of high intensity pulses. However, a small amount of low frequency power loss was noticed even when tests were repeated with low intensity sound. Detailed flow visualization results were also obtained to complement the acoustic results.

Multi-station VLF direction-finding measurements in eastern Canada

The directions of propagation, in the earth-ionosphere waveguide, of multi-component two-hop whistlers recorded on 10 July 1972 by four VLF goniometer receivers in eastern Canada have been determined. Using the bearings of these great circle paths, triangulation of several whistler exit-points has been accomplished. The L-values of the whistler exit-points determined by this method are systematically lower than those expected from their nose frequencies, by ~ 0.6. Various explanations are discussed for this effect. The most satisfactory is that the whistler waves leave through the side of the ducts (in which they had propagated for most of their path through the magnetosphere) at an altitude of a few thousand kilometres, and then are refracted to lower L-values before exiting from the lower ionosphere. The results are consistent with both the duct termination altitude predicted by Bernhardt and Park (1977) for the appropriate conditions and also with the observed upper cut-off frequency of the whistlers.

Trapping of whistler-mode waves in ducts with tapered ends

The trapping of whistler-mode waves in field-aligned electron density enhancements (ducts) with tapered bases is investigated by ray-tracing for ducts terminating above 1600 and 900 km corresponding to summer day and summer night conditions respectively. This complements previous ray-tracing calculations made for ducts extending down to 300 km (Spstrangeways, 1981). The position and size of whistler exit-points is estimated for the model ducts employed. These are found to vary from 15 to 90 km in size and are located equatorwards of the foot of the field line of the duct. Two trapping modes are generally operative, corresponding to trapping through the base region and side of a duct and can result in two separated exit-points for a single duct. The variation of the trapping properties of a duct with the altitude above which it terminates is investigated in detail for both summer day and winter night conditions for altitudes of termination between 200 and 1900 km. The altitude of duct termination has a very marked effect on the proportion of waves trapped by each of the trapping modes. It also influences the range of initial latitude from which rays can become trapped in the duct, the effect being greatest for the winter night model.

Multimodal Far-Field Acoustic Radiation Pattern Using Mode Cutoff Ratio

The far-field sound radiation theory for a circular duct was studied for both single-mode and multimodal inputs. The investigation was intended to develop a method to determine the acoustic power produced by turbofans as a function of mode cutoff ratio. This information is essential for the design of acoustic suppressors in engine ducts. With reasonable simplifying assumptions, the single-mode radiation pattern was shown to be reducible to a function of mode cutoff ratio only (modal indices removed). With modal cutoff ratio as the dominant variable, multimodal radiation patterns can be reduced to a simple explicit expression. This approximate expression provides excellent agreement with an exact calculation of the sound radiation pattern using equal acoustic power per mode. Radiation patterns for cases other than equal modal power are presented using the approximate radiation equation. An approximate expression for the duct termination losses as a function of cutoff ratio also is included.

The Effect of Mass Flow Rate on the Reflection Behaviour of Small-Amplitude Pressure Waves from Duct Terminations

This paper describes an investigation of the reflection characteristics of small-amplitude pressure waves in the presence of steady flow in a duct. A correlation technique employing pseudo-random binary-sequence (p.r.b.s.) pulses is introduced. A theoretical model of the process is presented together with considerations of correlation analysis. The results show agreement between the experimental results and the model; they further indicate that, in the presence of a steady flow component, there is a significant effect on the reflection behaviour of plane pressure waves for a reduction in the area terminating a duct. The experimental technique is effective at very low flow velocities (Mach number = 0·02, Reynolds number = 30 times 103) and establishes a linear relationship between a reflection coefficient and a non-dimensional mass flow number. A reflection coefficient of flow is introduced as an appropriate parameter for such conditions. The procedure could be applied to a wide range of industrial processes to determine flow coefficients of duct elements in situ, to optimize flow processes and to locate leakage flows.

High frequency sound attenuation in short flow ducts

Traditionally, sound propagation in flow ducts has been analyzed using modal theory. However, for high-frequency (duct height divided by free-space wavelength much greater than unity) sources near (the order of the duct height or less) the duct termination, mode theory may be unnecessarily burdensome and seems to obscure the basic simplicity of the propagation phenomenon. In this paper, geometric acoustics is employed to develop absorbent liner design procedures for the case of high frequency sources in short ducts. Point and line sources in a two-dimensional parallel plate duct are utilized to develop basic concepts, which are then extended to the point and distributed sources in a cylindrical duct. In each case, an optimal impedance distribution (or segmentation) is found for subsonic plug flow. The applicability of this approach to the design of inlet and exhaust noise suppressors for aircraft turbomachinery is discussed.

High temperature effects on the radiation impedance of an unflanged duct exit

The results of a series of measurements, of the radiation impedance of an unflanged duct termination with high temperature airflow at very low velocity, are presented. The principal difference between these results and the impedance in the absence of temperature gradients is a progressive increase in radiation resistance with increasing jet temperature.

Method of acoustic modules

Most theoretical studies in duct acoustics involve idealized conditions. Thus, sound propagation in semi-infinite absorbent ducts is considered and radiation from a rigid duct termination is analyzed. Very little consideration is given, in general, to matching these subproblems together to solve a specific practical problem. The method of the acoustic modules is a first step towards resolution of such discrepancies. Both these problems are analyzed in terms of the same (rigid duct) eigenfunctions. Each module has au input (pressure and velocity distributions) which uniquely determines its output. Thus, a cascade of modules could be analyzed if the source impedance of the first module and the termination impedance of the last module are known. The paper includes analysis of a rectangular module by means of a finite-length Green's function and a discussion of the applications of this method to various practical problems. [Work supported by NASA Lewis under Contract No. NAS 3-18010.]

Acoustic energy flow in lined ducts containing uniform or “plug” flow

In connection with the method (used in simple insertion loss models) of relating, approximately, the perturbed duct field to the acoustic field radiated from the duct termination, expressions have been formulated for the energy flows associated with individual modes, according to certain definitions. It has been shown that the axial energy flow in a uniform flow duct can only be strictly equated with the radiated energy if the radiation is from an “inlet flow” termination, if the axial energy flow is calculated according to the energy flux defined by Cantrell and Hart and if the duct walls are non-absorptive. If the duct walls are absorptive the duct and radiated energy flows are approximately identical if the duct energy flow is primarily due to the existence of well “cut-on” modes.

Experimental determination of three-dimensional liquid rocket nozzleadmittances.

The three-dimensional nozzle admittance, an important parameter in combustion instability studies, was experimentally measured for several nozzle configurations. The admittance values were obtained using a modification of the classical impedance tube technique. The modified impedance tube method measures the admittance of a duct termination in the presence of one-dimensional mean flow and three-dimensional oscillations. Values of the nozzle admittance were obtained from pressure amplitude measurements taken at discrete points along the length of the tube. To determine the effects of nozzle geometry, nozzles were tested with half-angles of 15, 30, and 45 deg and entrance Mach numbers of 0.08, 0.16, and 0.20. The admittance results are presented as functions of nondimensional frequency for mixed first tangential-longitudinal modes. These results are compared with available theoretical predictions, and good agreement between theory and experiment is shown.