Duct Modes Research Articles

First observations of low latitude whistlers using WHU ELF/VLF receiver system

The recently developed high-quality WHU ELF/VLF receiver system has been deployed in Suizhou, China (geomagnetic latitude 21.81°N, longitude 174.44°E, L=1.16) to detect low latitude extremely-low-frequency (ELF: 0.3‒3 kHz) and very-low-frequency (VLF: 3‒30 kHz) emissions originating from either natural or artificial sources since February 2016. During the first-month operation of the receiver system, a total of 3039 clear whistlers have been recorded at this low latitude station with the majority (97.0%) occurring on 28 February and 1 March 2016. Observed whistlers manifest various types including single one-hop, echo train, multi-flash, and multi-path. They tend to intensify after local midnight, reach the peak around 04‒05 LT, and then weaken quickly. Both features of lower cutoff frequencies of most whistlers below ∼1.6 kHz and almost uniform dispersion for many successive multi-flash whistlers suggest that these whistlers propagate along the geomagnetic field lines in the duct mode. The computed dispersion varies between ∼15 s1/2 and 23 s1/2 for observed one-hop whistlers and is greater than 50 s1/2 for three-hop echo train whistlers, indicating that the whistlers observed at the Suizhou station are low latitude whistlers.

Acoustic properties of multiple cavity resonance liner for absorbing higher-order duct modes.

This paper describes analytical and experimental studies conducted to investigate the acoustic properties of axially non-uniform multiple cavity resonance liner for absorbing higher-order duct modes. A three-dimensional analytical model is proposed based upon transfer element method. The model is assessed by making a comparison with results of a liner performance experiment concerning higher-order modes propagation, and the agreement is good. According to the present results, it is found that the performance of multiple cavity resonance liner is related to the incident sound waves. Moreover, an analysis of the corresponding response of liner perforated panel-cavity system is performed, in which the features of resonance frequency and dissipation of the system under grazing or oblique incidence condition are revealed. The conclusions can be extended to typical non-locally reacting liners with single large back-cavity, and it would be beneficial for future non-locally reacting liner design to some extent.

Generation of a single cylindrical duct mode using a mode synthesiser

The paper presents a method to generate a single user-selected waveguide cut-on mode by means of a mode synthesiser consisting of a set of point sources, each of them modelled by a thin pipe outlet and driven by a separate loudspeaker. Analysis of sound propagation in duct-like cylindrical facilities frequently needs considering the presence of higher cut-on modes together with mode reflection/coupling phenomena occurring on the duct outlet, impedance variations, etc. With increasing reduced frequency (Helmholtz number), description of the field becomes more and more complex. To avoid this complexity, at least in the case of tests carried out in laboratory conditions, the simplest approach seems to be able to generate a single cut-on mode by means of a properly constructed system, because to analyse the multi-mode wave, the contribution to the overall field from individual higher order modes must be established in advance. Based on in-duct field properties, the authors designed a mode synthesiser composed of N⩽13 point sources which was constructed and integrated into the measurement duct. Two methods were used to approach the problem of generating a single higher mode. In the first one, the amplitudes of the individual point sources were calculated by means of the in-duct Green’s function. In the second method, amplitudes of individual sources were calibrated based on sound pressure measurement data taken on the duct cross-section with only one source operating at a time. These measurements, fully automated at a given cross-section, were carried out for some reduced frequencies allowing for propagation of at least four cut-on modes. The advantages and disadvantages of the two methods and the causes of discrepancies between theoretical predictions and the results obtained were analysed.

Broadband noise suppression for turbofan inlet applications

Broadband noise in turbofan inlets is represented in a frequency domain analysis by a statistical distribution of propagating duct modes. The required number of modes is estimated by Rice’s approximation method. A brief overview of essential results from the theory of acoustic propagation in ducts is given, providing a starting point for Rice’s estimation of the distribution of propagating modes in a uniform unlined duct required to represent a broadband noise source. The relationship between mode cut-off ratio and attenuation in lined ducts is examined to connect cut-off ratio to modal attenuation, and it is shown by example that for arbitrary impedance at a specified frequency, modes with similar cut-off ratios have similar attenuation. It is then shown by example that the attenuation of a low-order circumferential mode, specifically the axially symmetric circumferential mode, with a large range of propagating radial mode cut-off ratios, is insensitive to impedance variations near the optimum impedance. Two models for estimating achievable attenuation for broadband noise attenuation, based on equipartition of acoustic power among propagating modes, are considered. One uses only the axially symmetric circumferential mode, and the second uses all propagating circumferential modes and their associated propagating radial modes. A new parallel architecture version of an established propagation code, designed to include all propagating modes on a statistical basis, is described. Examples for prediction of acoustic power attenuation of broadband noise at low frequency and at moderate frequency are used to compare the performance of the axially symmetric circumferential mode and the all circumferential mode models. It is shown by example that a broadband noise model based on the axially symmetric circumferential mode predicts lower attenuation than a model with all propagating circumferential modes. Rice’s correlation of mode cut-off ratio with attenuation justifies this observation.

Broadband noise reduction by circular multi-cavity mufflers operating in multimodal propagation conditions

In this study, sound propagation through a circular duct with non-locally lining is investigated both numerically and experimentally. The liner concept is based on perforated screens backed by air cavities. Dimensions of the cavity are chosen to be of the order or bigger than the wavelength so acoustic waves within the liner can propagate parallel to the duct surface. This gives rise to complex scattering mechanisms among duct modes which renders the muffler more effective over a broader frequency range. This work emanates from the Cleansky European HEXENOR project which aim is to identify the best multi-cavity muffler configuration for reduction of exhaust noise from helicopter turboshaft engines. Here, design parameters are the cavity dimensions in both longitudinal and azimuthal directions. The best cavity configuration must in addition fit weight specifications which implies that the number of walls separating each cavity should be chosen as small as possible. To achieve these objectives, the scattering matrix of the lined duct section is obtained experimentally for two specific muffler configurations operating in multimodal propagation conditions. The good agreement with numerical predictions serves to validate the perforate plate impedance model used in our calculation. Finally, given an incident acoustic pressure which is representative of typical combustion noise spectrum, the best cavity configuration achieving the maximum overall acoustic Transmission Loss is selected numerically. The study also illustrates how the acoustic performances are dependent on the nature of the incident field.

Investigation of Fan-Wake/Outlet-Guide-Vane Interaction Broadband Noise

Fan-wake/outlet-guide-vane interaction broadband noise in turbofan jet engines is studied. The mechanism and some issues are first discussed using a two-dimensional gust-prediction model. An oblique gust-prediction model is then developed. Quasi-three-dimensional unsteady lift is calculated using a two-dimensional equivalence method. It is coupled with annular duct modes to obtain the sound power spectrum density. Spanwise turbulence integral length scales and their impact on power spectrum density predictions are investigated. A spanwise integration limit suitable for the complete frequency range is proposed. The model is validated using the NASA Source Diagnostic Test data. Sound power scaling with vane count is examined. If solidity is maintained, the cascade response does not converge on the single-airfoil response, even for low vane counts. The sound power varies inversely with at low frequency; it scales with at very high frequency. The power spectrum density trend with the fan tip Mach number is also identified. It scales with if turbulence intensity in the fan wake scales “ideally” with . At offdesign conditions, fan wakes are not ideal; therefore, different speed trends apply. scaling is found to best fit the Source Diagnostic Test data and the prediction.

Near-field sound radiation of fan tones from an installed turbofan aero-engine.

The development of a distributed source model to predict fan tone noise levels of an installed turbofan aero-engine is reported. The key objective is to examine a canonical problem: how to predict the pressure field due to a distributed source located near an infinite, rigid cylinder. This canonical problem is a simple representation of an installed turbofan, where the distributed source is based on the pressure pattern generated by a spinning duct mode, and the rigid cylinder represents an aircraft fuselage. The radiation of fan tones can be modelled in terms of spinning modes. In this analysis, based on duct modes, theoretical expressions for the near-field acoustic pressures on the cylinder, or at the same locations without the cylinder, have been formulated. Simulations of the near-field acoustic pressures are compared against measurements obtained from a fan rig test. Also, the installation effect is quantified by calculating the difference in the sound pressure levels with and without the adjacent cylindrical fuselage. Results are shown for the blade passing frequency fan tone radiated at a supersonic fan operating condition.

Predictions of Fan Broadband Noise Using Lifting Surface Method

This paper adopts the three-dimensional lifting surface method as a new cascade-response function to predict fan broadband interaction noise. The stator is modeled as an annular cascade, and the vanes are assumed to be zero-thickness plates with no stagger angle. The unsteady loading spectrum on the stator vanes is considered under a fully three-dimensional condition rather than calculated by the strip theories that are widely used in the existing analytical broadband fan noise models. The sound power spectrum is calculated in an annular duct using numerical integration weighted by statistical turbulence spectrum. The present theory is verified by calculating the category 4 benchmark problem of the Third Computational Aeroacoustics Workshop for the response function and by comparing the predictions of a benchmark test for the broadband formulations of the sound power spectra. Then, the predictions of the inlet and exhaust sound power spectra for the NASA source diagnostic test are presented, which both show good agreement with the experimental results. The discrepancies indicate the importance of further corrections for stagger and swirling mean flow effects in realistic predictions. In the end, the variation trend of the sound power with different vane numbers is well captured, which indicates that this effect mainly refers to the propagation of cut-on acoustic modes in an annular duct. This model has the capability for further studies on the vane swept or lean effects.

On Certain Practical Issues Relating to Construction of the In-duct Single Mode Synthesizer

Abstract It is convenient to have a device and a method of generating single cut-on modes in cylindrical hard-walled waveguides or at least in laboratory models of such systems. This allows to examine, among other things, properties of various active and/or passive elements inserted in a cylindrical duct by testing them in conditions when the incident (input) wave comprises only one cut-on mode and determining the reflection and transmission coefficients for single selected incident modes. As it has been already demonstrated by the present authors, it is possible to generate single cut-on modes in a circular duct using a small (although increasing with mode order) number of acoustic monopoles arranged properly on a duct cross-section and driven with appropriate acoustic volume amplitudes and phases. Laboratory models of such sources are proposed in this paper and results of tests verifying their directional properties are presented. The other technical issue relating to practical utilization of the proposed method is the possible error introduced by the apparatus used for scanning the acoustic field inside the duct model. It is shown that insertion of the measuring probe changes the total energy radiated into the free space only by a fraction of a decibel.

Mitigation of wind tunnel wall interactions in subsonic cavity flows

The flow over an open aircraft bay is often represented in a wind tunnel with a cavity. In flight, this flow is unconfined, though in experiments, the cavity is surrounded by wind tunnel walls. If untreated, wind tunnel wall effects can lead to significant distortions of cavity acoustics in subsonic flows. To understand and mitigate these cavity–tunnel interactions, a parametric approach was taken for flow over an L/D = 7 cavity at Mach numbers 0.6–0.8. With solid tunnel walls, a dominant cavity tone was observed, likely due to an interaction with a tunnel duct mode. An acoustic liner opposite the cavity decreased the amplitude of the dominant mode and its harmonics, a result observed by previous researchers. Acoustic dampeners were also placed in the tunnel sidewalls, which further decreased the dominant mode amplitudes and peak amplitudes associated with nonlinear interactions between cavity modes. This indicates that cavity resonance can be altered by tunnel sidewalls and that spanwise coupling should be addressed when conducting subsonic cavity experiments. Though mechanisms for dominant modes and nonlinear interactions likely exist in unconfined cavity flows, these effects can be amplified by the wind tunnel walls.

Multi-Modal Acoustic Flow Decomposition Examined in a Hard Walled Cylindrical Duct

Abstract Flow fields could be of great interest in the study of sound propagation in aeroengines. For ducts with rigid boundaries, the fluid-resonant category may contribute significantly to unwanted noise. An understanding of the multi-modal propagation of acoustic waves in ducts is of practical interest for use in the control of noise in, for example, aero-engines, automotive exhaust and heating or ventilation systems. The purpose of our experiments was to test the acoustic energy transmission of duct modes based on studies carried out by the sound intensity technique. Sound intensity patterns in circular duct are discussed of modal energy analysis with particular reference to proper orthogonal decomposition and dynamic mode decomposition. The authors try to justify some advantages of the sound intensity experimental research in this area. In the paper, the wide-band sound signal propagated from source approximated with loudspeaker in hard-walled duct is imaged using a sound intensity - based approach. For a simple duct geometry, the sound intensity field is examined visually and by performing a modal decomposition greater insight into the acoustic structures is obtained. The image of sound intensity fields below and above “cut-off” frequency region are found to compare acoustic modes which might resonate in duct.

Evaluation of a Cascade-Based Acoustic Model for Fan Tonal Noise Prediction

This study aims at evaluating an analytical model for the prediction of tonal fan noise created by the rotor–stator interaction. The methodology consists of comparing unsteady flow simulations with the cascade-based acoustic model to quantify the influence of some technological effects not included in the model. The simulations are performed with a dedicated turbomachinery flow solver Turb’Flow on a simplified stator vane cascade. They allow discussing the effects of both model assumptions of no vane thickness and inviscid flow on the predictions of the acoustic sources as well as on the modal acoustic powers radiated within the duct. The Kutta condition is found to be efficient to locally represent the viscosity effects, and the vane thickness tends to moderately modify the distributions of the sources and the amplitudes of the duct modes. Moreover, a three-dimensional decomposition of the aerodynamic excitation is proposed and coupled with the three-dimensional analytical cascade response. This fully three-dimensional acoustic model is evaluated by comparisons with an unsteady simulation of a realistic axial compressor stage. An improvement in the prediction of the acoustic sources and powers is clearly shown with respect to the previously used two-dimensional version of the model.

Acoustics flow analysis in circular duct using sound intensity and dynamic mode decomposition

Sound intensity generation in hard-walled duct with acoustic flow (no mean-flow) is treated experimentally and shown graphically. In paper, numerous methods of visualization illustrating the vortex flow (2D, 3D) can graphically explain diffraction and scattering phenomena occurring inside the duct and around open end area. Sound intensity investigation in annular duct gives a physical picture of sound waves in any duct mode. In the paper, modal energy analysis are discussed with particular reference to acoustics acoustic orthogonal decomposition (AOD). The image of sound intensity fields before and above "cut-off" frequency region are found to compare acoustic modes which might resonate in duct. The experimental results show also the effects of axial and swirling flow. However acoustic field is extremely complicated, because pressures in non-propagating (cut-off) modes cooperate with the particle velocities in propagating modes, and vice versa. Measurement in cylindrical duct demonstrates also the cut-off phenomenon and the effect of reflection from open end. The aim of experimental study was to obtain information on low Mach number flows in ducts in order to improve physical understanding and validate theoretical CFD and CAA models that still may be improved.

Shear Layer Driven Acoustic Modes in a Cylindrical Cavity

This paper describes the interior acoustic pressure of a cylindrical cavity driven by a shear layer. Existing cavity flow literature is generally focused on rectangular cavities, where the resonance is either longitudinal or the result of excited depth modes inside the cavity. The design of the present circular cavity is such that azimuthal duct modes can be excited in various combinations with depth modes depending on free stream velocity. An acoustic simulation of the system was used to identify the modes as a function of frequency when the system is driven by an acoustic point source. With appropriate manipulation of the free stream flow, abrupt mode switching and mode oscillation were both observed, and a condition with a dominant azimuthal mode was found. The strength of the lock-on was documented for the various resonance conditions, and the effects of the cavity opening size and location were studied.

Acoustic scattering in flexible waveguide involving step discontinuity.

In this paper, the propagation and scattering of acoustic waves in a flexible wave-guide involving step discontinuity at an interface is considered. The emerging boundary value problem is non-Sturm-Liouville and is solved by employing a hybrid mode-matching technique. The physical scattering process and attenuation of duct modes versus frequency regime and change of height is studied. Moreover, the mode-matching solution is validated through a series of numerical experiments by testifying the power conservation identity and matching interface conditions.

Indirect acoustic impedance eduction in presence of flow based on an analytical two-port formulation

In order to assess the performance of advanced acoustic absorbing materials the acoustic impedance should be determined with high accuracy, especially, in presence of a grazing flow. This paper presents an analytical methodology for the grazing flow acoustic impedance eduction, based on a two-port representation of an acoustic system. This procedure is dedicated to the frequency range below the cut-on frequency of the transversal duct modes and its major appeal refers to a reduced number of microphones and the experimental rig simplicity. The methodology is verified by comparison with acoustic finite element simulations. Experiments are performed on two liner configurations and the educed impedance is compared with reference results obtained with a different approach at another test rig, and shows good agreement. A sensitivity analysis on the influence of the input parameters is carried out showing the influence of the rigid-/impedance wall transition effects, flow Mach number, number of microphones and microphone positioning accuracy.

Faisabilité d’un observatoire de cancers ciblés sur le département des Bouches-du-Rhône

An experimental laboratory study was performed to measure the effect of acoustic noise on the magnitude of tube vibrations in a staggered tube array and to measure the effectiveness of baffles on suppressing transverse duct modes. The acoustically induced tube vibration was experimentally determined for a flexible tube in three different transverse locations in the tube array. It was found that a tube located in the center of the duct, where a nodal point of the acoustic pressure resided, was most influenced by the transverse mode. On the other hand, a tube located near the duct side wall, where the acoustic pressure oscillation was highest, was not affected by the acoustic standing wave since it produced almost imperceptible vibration. It is shown that the acoustic pressure gradient across a tube is the cause of the tube vibration. Experiments were also performed to determine the effect of baffles for reducing the noise of acoustic resonance. The results showed that a single baffle substantially reduced the first mode resonance, as long as it was located close to the center of the bundle. The insertion of two baffles, in various locations, effectively eliminated acoustic resonance in the 1st and 2nd transverse duct modes. It is seen that the third acoustic mode is not significantly affected by either one or two baffles.

Fine-tuning of nonBragg bandgaps in axisymmetric ducts via arbitrary periodic walls

We investigate the nonBragg bandgap (NBBG) resulting from interference between two transverse guided wave modes in an axisymmetric duct with periodic walls. We find that the NBBG bandwidth is proportional to both the height and shape factor of the wall undulations. The shape factor is defined as the norm of the major Fourier component of the periodic wall profile. Varying the height directly tunes the bandwidth, while manipulating the wall profile results in a slight change in the shape factor, which leads to fine-tuning of the bandgap. We also find that for a fixed height, the NBBG width is related to the area under the curve for the product of the wall profile and a half-period sine or cosine function. We propose an area estimation method according to which a larger area results in a wider NBBG. A numerical example reveals that NBBG fine-tuning can be achieved by carefully varying the shape factor. The results will benefit the design of band structures, especially subtle modifications by selecting suitable wall undulations.

Comparative study on mode-identification algorithms using a phased-array system in a rectangular duct

To identify multiple acoustic duct modes, conventional beam-forming, CLEAN as well as L2 (i.e. pseudo-inverse) and L1 generalized-inverse beam-forming are applied to phased-array pressure data. A tone signal of a prescribed mode or broadband signal is generated upstream of a curved rectangular duct, and acoustic fields formed in both upstream and downstream stations of the test section are measured with identical wall-mounted microphone arrays. Sound-power distributions of several horizontal and vertical modes including upstream- and downstream-propagating waves can be identified with phased-array techniques, and the results are compared among the four approaches. The comparisons using synthetic data demonstrate that the L2 generalized-inverse algorithm can sufficiently suppress undesirable noise levels and detect amplitude distributions accurately in over-determined cases (i.e. the number of microphones is more than the number of cut-on modes) with minimum computational cost. As the number of cut-on modes exceeds the number of microphones (i.e. under-determined problems), the L1 algorithm is necessary to retain better accuracy. The comparison using test data acquired in the curved duct test rig (CDTR) at NASA Langley Research Center suggests that the L1/L2 generalized-inverse approach as well as CLEAN can improve the dynamic range of the detected mode by as much as 10dB relative to conventional beam-forming even with mean flow of M=0.5.

Effect of Rotor Shielding on Fan-Outlet Guide Vanes Broadband Noise Prediction

An analytical model for the rotor–stator broadband noise is improved by accounting for the rotor acoustic shielding. Both the analytical models for the stator broadband noise and for the rotor scattering are strip-theory approaches based on previously published formulations of the three-dimensional unsteady blade loading for a rectilinear cascade. Specific treatment is introduced to address the behavior around the cut on frequency of the duct modes both in the noise generation and in the noise scattering. A simple effect of the swirl between the rotor and the stator is considered using a Doppler shift in frequency. The power spectral density of the acoustic power and the sound pressure level at the duct wall are studied for the NASA source diagnostic test fan rig. The separate effects of the shielding by a cascade of the rotation of the rotor and of the swirl are investigated. Corotating modes dominate in the inlet. The rotor shielding decreases the acoustic power at intermediate frequencies but increases it at higher frequencies because of the frequency scattering and of the scattering in radial mode orders, which does not exist in a fully rectilinear model. The swirl has a strong effect that must be included.