Acoustic Duct Modes Research Articles

Sparse recovery by genetic algorithms for acoustic testing applications

Various acoustic testing applications involve solving inverse problems from acoustic measurements, such as acoustic imaging and duct mode identification. In these problems, the physical quantity to be inferred is sparse, which allows applications of certain sparse recovery techniques, such as the compressive sensing. But such methods usually involve very complex theory, which therefore set a high threshold for beginners. By contrast, this work proposes a similar but much simpler method based on the well-known genetic algorithm, which borrows only a few easily understood concepts from nature evolution and can rely on easily accessed software/toolboxes. The performance of the developed method is demonstrated by two acoustic testing experiments in an anechoic chamber, i.e., acoustic imaging and duct mode identification.

A scale model study of an engine test facility for alleviating low-frequency howl

A scale model experimental study is conducted addressing howl occurring during engine tests in the Propulsion Systems Laboratory (PSL) of NASA Glenn Research Center. The aim is to understand the sources of the howling noise and find possible remedies. It is shown that a jet discharged into the model of the PSL entrance duct gives rise to high levels of low frequency noise. This occurs apparently due to duct acoustic modes randomly excited by the jet. Wire-mesh screens of various mesh size and configuration as well as tabs, placed at the end of the model duct, are shown to affect the noise. Comparative effects of these configurations are studied, and some are found to alleviate the low-frequency noise significantly. Based on these results, the equivalent of a 4-mesh screen is recommended as the end treatment for the duct of the PSL facility.

Large-Eddy Simulation and Aeroacoustic Prediction of Supercritical Airfoil Side-Edge Noise

Airfoil self-noise is investigated on a cantilever wing with a supercritical profile with a compressible wall-resolved large-eddy simulation. The Reynolds number based on the chord is 620,000, and the angle of attack is 5°. The aerodynamic results reveal the development of a complex vortex system at the side edge, including primary, secondary, and tertiary vortices that govern aerodynamic noise production. The wall-pressure coefficient and root-mean-square pressure coefficient contours highlight the side-edge shear layer and flow impingement of the primary vortex at the pressure-side edge as important noise-generation mechanisms. Dynamic mode decomposition shows that the dominant pressure modes on the airfoil exist along primary and secondary vortex impingement lines. Far-field acoustic predictions based on both solid and porous Ffowcs-Willliams and Hawkings’ analogies demonstrate good agreement with experimental results between 1.5 and 9 kHz. Low-frequency tonal humps observed in the spectra result from duct acoustic modes excited by airfoil self-noise, a consequence of the installation effect. For this configuration, airfoil side-edge noise did not dominate over airfoil surface noise levels, suggesting that at low to moderate angles of attack, airfoil side-edge noise is not a significant contributor to the overall acoustic emissions.

On the acoustic wedge absorber design in underwater and its interior pressure computation in a chamber

This study presents a design of wedged shape absorber used in underwater in range of high frequency. The analysis of a set of periodical wedges, where each wedge is oriented 90 deg with other wedges. The set of periodical wedges is analyzed using finite element methods as a 3-D virtual impedance tube. The incident wave is on the normal direction of the tube. This 3-D model is able to simplify to a simple 2-D model and a two-point transfer function method is employed to compute reflection coefficient. The ation of frequencies higher than the cut-off plane wave frequency is addressed of that higher duct acoustic modes are excited by the wedge. These higher modes are recognized as stationary non-propagating waves, not contributing reflected waves away from the wedge. An impedance value associated with the reflection coefficient is identified based on plane wave condition. The impedance value is applied to surfaces of a closed space to computed interior pressures.

Spiral flow instability between a rotor and a stator in high-speed turbomachinery and its relation to fan noise

Hydrodynamic instabilities in the interstage of turbomachinery and their relation to fan broadband noise are investigated over wide operating conditions. By applying compressible linear stability analysis to the velocity profiles of NASA's high-speed fan rig, source diagnostic test (SDT), three distinct unstable regimes are found: the first mode amplifies disturbances over a wide frequency range including the rotor speed. The second mode rotates much slower and develops inside the outer-wall boundary layer. The third mode spins in the opposite direction. An approach equivalent to dynamic mode decomposition (DMD) successfully extracts these modes from a database of improved delayed detached-eddy simulation (IDDES) solving the SDT geometry at approach and cut-back conditions: the extracted DMD modes generally capture the characteristics of eigenfunctions predicted by the linear stability analysis. At the approach condition, the first two unstable modes seem to interact inside the outer-wall boundary layer, while at the cut-back condition, disturbances associated with the first regime migrate away from the wall. Moreover, outer-wall pressure fluctuations of the IDDES database are Fourier decomposed in the interstage: coherent structures extracted using proper orthogonal decomposition are found to be dominated by duct acoustic modes, and they can be mapped not only to interaction tones but also to broadband noise likely associated with the interaction between disturbances in the rotor wakes and quasi-stationary structures near the outer wall. This interaction noise appears to be radiated to both inlet and exhaust with similar azimuthal-mode distributions; however, the importance relative to other noise sources decreases with the engine speed.

Experimental investigation of multimodal noise generation by ducted low Mach number flows through orifice plates

Noise generation by low Mach number air flows through circular orifices in rectangular ducts is investigated. In particular, the influence of the number and position of the orifices maintaining a constant flow area is addressed. A review of the available theories suggests a certain importance of such parameters in the excitation of higher-order acoustic duct modes. A qualitative coefficient is proposed for a first characterization of the ability to enhance or lessen a given higher-order acoustic mode by the plate geometry. An experimental campaign is performed to measure the total emitted acoustic power by different plate geometries as well as its modal composition. It is found that the orifices' numbers and positions greatly influence the acoustic emissions while the flow pressure drop caused by the obstacles is similar. The proposed qualitative coefficient shows good agreement with the experimental results. A particle image velocimetry measurement campaign is performed to visualize the near-field average flow behavior upstream and downstream of the orifice plates. An increase in the turbulent velocity fluctuations in the vicinity of the orifices is observed on both sides, further validating previous studies on the subject.

Acoustic energy balances for sound radiated from duct exit with mean flow

An old model problem for the exchange of energy between sound field and mean flow by vortex shedding has been worked out in numerical detail. The analytically exact solution of the problem of reflection, diffraction and radiation of acoustic modes in a semi-infinite annular duct with uniform subsonic mean flow, including shedding of unsteady vorticity from the duct exit, allows a precise formulation of Myers’ energy for perturbations of an inviscid mean flow. The transmitted power [Formula: see text] in the duct and the radiated power [Formula: see text] in the far field differ by the amounts of hydrodynamic far field powers [Formula: see text] inside and [Formula: see text] outside the wake (vortex sheet) emanating from the duct edge, plus the power [Formula: see text] that disappears into the vortex sheet. This last component represents the source term in Myers’ energy equation. This is evidence of the non-conserved character of acoustic energy in mean flow, owing to the coupling of the acoustic field with the mean flow. [Formula: see text], [Formula: see text] and [Formula: see text] are always positive. This is normally the case too for [Formula: see text] and [Formula: see text]. But for not too high frequencies or other circumstances where shed vorticity produces more sound than was necessary for its creation, [Formula: see text] and even [Formula: see text] may also be negative.

Numerical Simulation of Acoustic Resonance in a Duct Containing a Flat Plate

This work is about numerical simulations of vortex induced acoustic resonance in a duct, experimentally investigated by Welsh et al. Vortex shedding of low-speed flow over a flat plate excites an acoustic duct mode, leading to a lock-in of shedding and acoustic resonance frequency over a wide range of flow velocities. This study shows that a state-of-the-art compressible Navier–Stokes flow solver is able to capture the lock-in phenomenon. The focus is on the numerical parameters required to precisely recover the experimental results in terms of lock-in range and acoustic pressure levels. Complete and reliable physical data are thereby obtained, which can aid in developing a systematic understanding of the complex flow interactions. Furthermore, hysteresis behavior is discovered and numerically explored.

Numerical and Asymptotic Solutions of the Pridmore-Brown Equation

A study is made of acoustic duct modes in two-dimensional and axisymmetric three-dimensional lined ducts with an isentropic inviscid transversely nonuniform mean flow and sound speed. These modes are described by a one-dimensional eigenvalue problem consisting of a Pridmore-Brown equation complemented by hard-wall or impedance-wall boundary conditions. A numerical solution, based on a Galerkin projection and an efficient method for the resulting nonlinear eigenvalue problem, is compared with analytical approximations for low and high frequencies. A collection of results is presented and discussed. Modal wave numbers are traced in the complex plane for varying impedance, showing the usual regular modes and surface waves. A study of a vanishing boundary layer (the Ingard limit) showed that, in contrast to the smoothly converging acoustic modes and downstream running acoustic surface wave, the convergence of the other surface waves is numerically more difficult. Effects of (transverse) turning points and exponential decay are discussed. Especially the occurrence of modes insensitive to the wall impedance is pointed out. Cut-on wave numbers of hard-wall modes are presented as a function of frequency. A strongly nonuniform mean flow gives rise to considerable differences between the modal behavior for low and for high frequencies.

Effects of Central Tube on Shape of Modal Duct of a Helicoid in a Simple Expansion Chamber

The shape of the modal duct of an acoustic wave propagating in a muffling system varies with the internal geometry. This shape can be either as a result of plane wave propagation or three-dimensional wave propagation. These shapes depict the distribution of acoustic pressure that may be used in the design or modification of mufflers to create resonance at cut-off frequencies and hence achieve noise attenuation or special effects on the output of the noise. This research compares the shapes of acoustic duct modes of two sets of four pitch configurations of a helicoid in a simple expansion chamber with and without a central tube. Models are generated using Autodesk Inventor modeling software and imported into ANSYS 18.2, where a fluid volume from the complex computer-aided-design (CAD) geometry is extracted for three-dimensional (3D) analysis. Mesh is generated to capture the details of the fluid cavity for frequency range between 0 and 2000Hz. After defining acoustic properties, acoustic boundary conditions and loads were defined at inlet and outlet ports before computation. Postprocessed acoustic results of the modal shapes and transmission loss (TL) characteristics of the two configurations were obtained and compared for geometries of the same helical pitch. It was established that whereas plane wave propagation in a simple expansion chamber (SEC) resulted in a clearly defined acoustic pressure pattern across the propagation path, the distribution in the configurations with and without the central tube depicted three-dimensional acoustic wave propagation characteristics, with patterns scattering or consolidating to regions of either very low or very high acoustic pressure differentials. A difference of about 80 decibels between the highest and lowest acoustic pressure levels was observed for the modal duct of the geometry with four turns and with a central tube. On the other hand, the shape of the TL curve shifts from a sinusoidal-shaped profile with well-defined peaks and valleys in definite multiples of π for the simple expansion chamber, while that of the other two configurations depended on the variation in wavelength that affects the location of occurrence of cut-on or cut-off frequency. The geometry with four turns and a central tube had a maximum value of TL of about 90 decibels at approximately 1900Hz.

Comparison of two low-order models for the prediction of fan broadband noise

Two low-order methods for predicting the broadband noise downstream of a fan exit guide vane (FEGV) due to interaction with rotor wake turbulence are compared. The noise is predicted with a two-step approach in each method. The methods share the exact same first step. The unsteady vane surface pressure is computed using a strip approach. At each strip, the 2D flat-plate cascade response to a gust in the wave-number, frequency domain is calculated. An integral approach is used for this calculation. The two methods then differ in the second step. One method integrates the unsteady surface pressure together with the Green's function for a cylindrical annulus to obtain the downstream duct acoustic pressure modes. The other method computes rectilinear acoustic modes relevant to the cascade at each strip. In the second method, the total power is obtained by adding the acoustic power downstream of each strip. Both methods neglect mean flow swirl effects on acoustic propagation. The fan broadband noise workshop RC1 and FC2 cases are used as a platform to compare the two methods. When the FEGV inflow turbulent parameters are taken from different sources (e.g. hot-wire, CFD) the predictions from both methods respond similarly. The trends predicted with both methods based on turbulence level or rotor speed are similar. The trends with vane count predicted by the two methods do not match and it is unclear which prediction is correct. The actual spectrum predicted by the Green's function method for all of the cases is shown to be slightly closer to experimental results.

Tones Encountered with a Coannular Nozzle and a Method for Their Suppression

With multistream coannular exhaust flows, sometimes tones occur that may fail the nozzle hardware meeting noise regulation standards. A two-stream nozzle was studied experimentally and numerically in an attempt to identify the sources of such tones and explore remedies. Sharp tones occurred in a range of low jet Mach numbers . The source was investigated by parametric variations that included inner nozzle lip thickness, lip-to-lip distance between the inner and outer nozzles, and the length and geometry of the inner nozzle duct. Ultimately, it was inferred that the tones occurred due to a coupling between vortex shedding from the struts, which held the nozzles and the centerbody together, and various duct acoustic modes. Thus, with a thicker strut geometry, the tones occurred in a higher range (up to 0.85) because a given shedding frequency occurred at a higher , and vice versa. A leading-edge treatment of the struts was shown to eliminate the tones via disruption of the vortex shedding.

Interaction and scattered mode measurement in a mixed bypass/core duct with multiple rotating sources

The rotating rake mode measurement system was developed and implemented at the NASA Glenn Research Center in the 1990s to measure turbofan duct acoustic modes. The system is a radial rake with distributed microphones that is inserted into the duct and continuously rotates about the centerline. The rotating rake mode measurement system provides a complete map of the acoustic duct modes present in a ducted fan and has been used on a variety of test articles: from a low-speed concept test rig to full-scale production turbofan engines. Prior rotating rake mode measurement system measurements have occurred in environments with a single rotating source interacting with a stationary source to produce duct modes at the fan rotor harmonics. A recent test of a scale model high-speed research fan in the NASA 9 × 15 ft Low Speed Wind Tunnel had two rotating sources, a rotor fan and a booster fan, on the same shaft. The interaction of the two rotating sources generated scattering at the harmonic sum and difference tones, and modal scattering at a given fan harmonic. Rotating rake mode measurement system data were acquired from this high-speed fan model which provided a database to allow for validation of the duct mode analysis technique expansion and experimental evidence of the scattering phenomenon. In this paper, modes from the two different sources and associated stationary surfaces from a sample fan condition were reported and compared to analytical predictions, in order to validate the ability of the rotating rake mode measurement system to measure scattered modes. Sample modal content of the booster fan tone and its harmonics tones are presented as well as the sum and difference interaction between the rotor and booster fans.

Sound Radiation Characteristics of a Rectangular Duct with Flexible Walls

Acoustic breakout noise is predominant in flexible rectangular ducts. The study of the sound radiated from the thin flexible rectangular duct walls helps in understanding breakout noise. The current paper describes an analytical model, to predict the sound radiation characteristics like total radiated sound power level, modal radiation efficiency, and directivity of the radiated sound from the duct walls. The analytical model is developed based on an equivalent plate model of the rectangular duct. This model has considered the coupled and uncoupled behaviour of both acoustic and structural subsystems. The proposed analytical model results are validated using finite element method (FEM) and boundary element method (BEM). Duct acoustic and structural modes are analysed to understand the sound radiation behaviour of a duct and its equivalence with monopole and dipole sources. The most efficient radiating modes are identified by vibration displacement of the duct walls and for these the radiation efficiencies have been calculated. The calculated modal radiation efficiencies of a duct compared to a simple rectangular plate indicate similar radiation characteristics.

Numerical Investigation of Flow Acoustic Coupling in a Half-Dump Combustor

This paper reports on the investigation of combustion instabilities in a methane–air non-premixed half-dump combustor for different flow Reynolds number () using computational aero-acoustic (CAA) simulation. To simulate the flow physics under turbulent flow conditions, detached-eddy simulation in conjunction with generalized eddy-dissipation model is adopted, while a CAA formulation based on Lighthill’s acoustic analogy is used for computing the acoustic field. It is observed that the unsteady pressure signals predominantly arise from either the natural acoustic modes of the duct or the local flow fluctuations in the vortex shedding process downstream of the dump plane, giving rise to different dominant frequencies at different spatial locations at lower and a single dominant locked-on frequency at higher . The nondimensional numbers, that is, Helmholtz and Strouhal numbers, are used to characterize the duct acoustic modes from the vortex shedding modes. Under reacting flow conditions, unsteady heat release and pressure oscillations are monitored to compute Rayleigh index in order to verify if the instability is driving (positive net value) or damping (negative net value) at different frequency levels. Moreover, the predicted Helmholtz and Strouhal numbers are found to be in excellent agreement with the experimental data available in the open literature for a wide range of .

Sound Generated by Fan Wakes and Validation with Experiments

This paper presents a validation of the rotor-wake/stator interaction code, CAAT-S, with NASA Source Diagnostic Test (SDT) experiments. CAAT-S is a computationally efficient three-dimensional code based on the Euler equations linearized about a nonlinear rotational mean flow. It accounts for the flow swirl, the blade and fan 3D geometry and loading, and yields directly the radiated sound in terms of the duct acoustic modes. Two exit guide vane configurations, three power levels, and three blade passing frequencies (BPF) are considered. The power levels presented are taken at approach, cutback, and takeoff conditions for (a) the SDT low vane count (LVC) stator and (b) the SDT low noise (LN) stator. The mean flow and wake profiles are taken from the SDT experiments and exhibit strong radial dependencies. The reduced frequencies, based on the blade tip and speed of sound, associated with SDT data range from 15 for the 1BPF at approach power to 72 for 3 BPF at takeoff power. This produces a large number of propagating acoustic modes and makes the prediction of the vane forces and the radiated sound power a real computational challenge. Improved nonreflecting boundary conditions are developed extending the capability of CAAT-S to resolve the large number of high frequency modes, and making it suitable for turbofan engine noise prediction. CAAT-S calculated sound power level (PWL) underpredicts data by about 3 dB for both LVC and LN configurations. However, CAAT-S trend predictions are within the scatter of the experimental data. These results validate CAAT-S for moderate to high subsonic Mach numbers and over a broad range of blade passing frequencies.

Acoustically Consistent Investigation of Combustion Instabilities in a Dump Combustor

An acoustically consistent, linear modal analysis-based analytical method is presented to predict the longitudinal and transverse combustion instabilities in a two-dimensional Cartesian dump combustor. At first, rigorous acoustical analysis (without combustion) is performed of two duct configurations with one and two discontinuities in the cross-sectional area. Novel, acoustically consistent jump or matching conditions are developed and applied at the duct cross-sectional interface(s), with distinct forms for the purely axial and nonaxial modes. The effects of uniform and nonuniform mean flows, cross-sectional area ratio, as well as of different types of boundary conditions on the duct acoustic modes are investigated. Acoustic modal frequency predictions are in excellent agreement with the analytical and numerical results of Meissner (“Effect of Cross-Sectional Area Discontinuities in Closed Hard-Walled Ducts on Frequency of Longitudinal Modes,” Archives of Acoustics, Vol. 35, No. 3, 2010, pp. 421–435). In the second part, combustion instabilities of a two-dimensional Cartesian dump combustor are investigated. The instability analysis employs the developed acoustically consistent jump conditions instead of the conventional mass, momentum, and energy balance-based conditions. Effects of the fluctuating heat-release source term in the acoustic wave equation are incorporated directly into the longitudinal wave number, obviating the need for a separate energy matching condition across the flame. A detailed investigation of the parametric space and boundary conditions affecting combustion instabilities is undertaken, and the consistency of the modal analysis with the Rayleigh criterion is explicitly demonstrated. Further, the present approach enables the consideration of arbitrary mean flame shapes in determining the unstable modes. Instabilities are demonstrated for the fundamental longitudinal mode and its harmonics, as well as for the fundamental transverse mode. The effects of the cross-sectional area ratio and flow Mach number on the unstable-mode growth rates are also presented.

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.

Physical processes influencing acoustic radiation from jet engine inlets

AbstractNumerical simulations of acoustic radiation from a jet engine inlet are performed using advanced computational aeroacoustics algorithms and high-quality numerical boundary treatments. As a model of modern commercial jet engine inlets, the inlet geometry of the NASA Source Diagnostic Test is used. Fan noise consists of tones and broadband sound. This investigation considers the radiation of tones associated with upstream-propagating duct modes. The primary objective is to identify the dominant physical processes that determine the directivity of the radiated sound. Two such processes have been identified. They are acoustic diffraction and refraction. Diffraction is the natural tendency for an acoustic duct mode to follow a curved solid surface as it propagates. Refraction is the turning of the direction of propagation of a duct mode by mean flow gradients. Parametric studies on the changes in the directivity of radiated sound due to variations in forward flight Mach number, duct mode frequency, azimuthal mode number and radial mode number are carried out. It is found there is a significant difference in directivity for the radiation of the same duct mode from an engine inlet when operating in static condition versus one in forward flight. It will be shown that the large change in directivity is the result of the combined effects of diffraction and refraction.

Research on the Method to Decompose Propagation Sound Wave in Annular Duct

There are many benchmark problems which have exact solutions or experiment data to gauge the simulation of aeroacoustic problems. Annular duct acoustic modes are good benchmark problems of this kind. The waves propagated along the duct can be considered as the summation of infinite Fourier modes. The energy relations of a single Fourier mode are deduced from governing equations in this paper. To investigate the properties of acoustic wave propagating along the duct, it’s necessary to decompose acoustic waves in the duct into multiple Fourier modes; the decomposition methods are presented.