Higher Order Acoustic Modes Research Articles

Forced response of transverse reacting jet in vitiated crossflow to harmonic velocity disturbances

The orthogonally oriented injector configuration typically used in axial fuel staging-capable gas turbine combustors is known to produce complicated thermoacoustic interactions between two distinct reaction zones. Despite the fundamental importance of transfer functions of transverse reacting jets in vitiated crossflow, however, their distinctive properties remain unknown, and associated low-order modeling combined with two different flame transfer functions remains entirely undemonstrated. From detailed measurements of transfer functions of lean-premixed primary and secondary flames in response to harmonic velocity disturbances, here we show that the transfer function of a transverse reacting jet in high-temperature crossflow is described as having relatively larger gain without undulating patterns, near-linear slow decay in magnitude with respect to the forcing frequency, and remarkably shorter duration response time. By leveraging a reduced-order modeling approach to account for the finite time delay between the two distinct transfer functions and by validating the calculation results against velocity and pressure measurement data, we demonstrate that self-induced instabilities in an axial fuel-staged system can be simultaneously driven by the dynamics of primary and secondary flames, and that the triggering of second-stage-induced instability is characteristically connected to higher-order acoustic modes. Such non-axisymmetric intra-combustor interactions generate a cascade of spectral peaks, including the first and third longitudinal modes and their respective higher harmonics, and additional peaks at the sum and difference of two individual frequencies. While the primary flame's dynamics are capable of selectively exciting the first mode, the secondary jet flame exhibits more complicated modal dynamics, manifested as the L3 mode-coupled jet merging-related flame surface annihilation and the L1 mode-coupled lateral movements of the transverse jet column.

Shear flow effects in a 2D duct: Influence on wave propagation and direct impedance eduction

Impedance eduction of acoustic liners with flow is commonly performed under the assumption of a uniform velocity profile. In practice, the flow profile is not uniform and a significant mean flow shear is present close to the duct wall. The present paper aims to assess the validity of the uniform flow assumption, and more generally to study the effect of the mean flow shear on the impedance eduction process. This is particularly relevant when considering large ducts, high frequencies, high-order acoustic modes and flow velocities representative of aircraft engine nacelles. A numerical mode-matching model is used to compute the sound field in a 2D lined duct with different flow profiles. A detailed parametric study evaluates the influence of the mean flow shear on the axial wavenumbers of the acoustic modes and on the educed impedance. Various parameters are considered: the flow velocity profile (boundary layer thickness and mean Mach number), the direction of acoustic propagation relative to the flow, two different liner configurations and the presence of noise in the pressure data. A number of recommendations are given to achieve robust impedance eduction in large-duct facilities and at high-frequencies.

Analysis of acoustic modes induced by backward stimulated Brillouin scattering in acoustic wave-guided single mode optical fibers

In this work, the acoustic Helmholtz equation is derived, and its analytical solution and the characteristic equation of the uniform guide mode in single mode fibers are obtained by the method of separation of variables. The normalized frequency of the acoustic mode is defined. By combining the argument approximation of the Bessel function are analyzed the eigenvalue range of the acoustic mode, the cut-off frequency, far from the cut-off state of the acoustic mode induced by backward stimulated Brillouin scattering, the dispersion and the multi-peak Brillouin gain spectrum. The research results indicate that the longitudinal acoustic fundamental mode L<sub>01</sub> cannot be cut-off and is mainly confined in the fiber core, which is coupled with the optical fundamental mode LP<sub>01</sub> to form the main peak of the Brillouin gain spectrum. The other higher-order acoustic modes all have low cut-off frequencies and are distributed more in the fiber cladding than mode L<sub>01</sub> which couples with the optical fundamental mode LP<sub>01</sub> to form the subpeaks of the Brillouin gain spectrum. The transverse normalized phase constant and effective refractive index of the acoustic mode increase with normalized frequency increasing. Only longitudinal acoustic modes L<sub>0<i>n</i></sub> contribute to backward Brillouin gain spectrum in single mode fiber. When the GeO<sub>2</sub> concentration is less than 4% and core radius is 4.5 μm, the single mode characteristics of the fiber remain unchanged, but the maximum number of acoustic L<sub>0<i>n</i></sub> modes is 4. With the increase of GeO<sub>2</sub> concentration in the fiber core, the Brillouin gain spectrum is red-shifted and the number of acoustic modes increases, the Brillouin gain peak value of L<sub>01</sub> mode gradually increases, and the contributions of higher-order modes decrease. The single-mode fiber with a core’s germanium doped concentration of 3.65% and core radius of 4.3 μm has 4 L<sub>0<i>n</i></sub> modes and 16 L<sub><i>mn</i> </sub>(<i>m</i>>0) modes at a wavelength of 1.55 μm, with one main peak and two subpeaks in the Brillouin gain spectrum appearing due to the acousto-optic coupling of the acoustic L<sub>01</sub>, L<sub>03</sub>, and L<sub>04</sub> modes with the optical LP<sub>01</sub> mode. The single-mode fiber with a core’s germanium doped concentration of 15% and core radius of 1.3 μm has 3 L<sub>0<i>n</i></sub> modes and 7 L<sub><i>mn</i> </sub>(<i>m</i>>0) modes, with the Brillouin gain spectrum having 3 main peaks due to the acousto-optic coupling of the L<sub>01</sub>, L<sub>02</sub>, and L<sub>03</sub> modes with the LP<sub>01</sub> mode. These conclusions are well consistent with the reported experimental phenomena and provide theoretical references for studying and utilizing the SBS acoustic waveguide in optical fibers.

Sound radiation control of an unbaffled long enclosure using wavy micro-perforated panel absorbers

The sound radiation control of an unbaffled long enclosure using wavy micro-perforated panel absorbers (WMPPAs) was numerically and experimentally investigated. First, a hybrid model based on the finite element method (FEM) and the Wiener-Hopf (W-H) technique was established to calculate the sound pressure level (SPL) radiated from an unbaffled long enclosure lined with MPPAs. Then, the hybrid model was validated, and the sound suppression performance of a single WMPPA was evaluated. The results demonstrate that the WMPPA exhibits better sound absorption properties than the flat and corrugated micro-perforated panel absorber (FMPPA and CMPPA), especially in the middle- to high-frequency range. To further enhance the sound attenuation performance, an array of WMPPAs was subsequently proposed to absorb higher-order acoustic modes inside the long enclosure so that broadband-radiated noise could be suppressed. The comparison results demonstrate that the WMPPAs can reduce the radiated SPL within a wide frequency range which is favourable for the suppression of environmental noise. In addition, the WMPPA array shifts the sound reduction curve towards a low-frequency range by approximately 500 Hz compared with that of a single WMPPA, which is promising for the reduction of broadband noise. After that, a mechanistic study was conducted to explain the sound reduction performance of WMPPAs from the perspective of modal contributions. In addition, the diffraction effect of sound waves at the sharp edge of a long enclosure was illustrated. Besides, the contribution of the wavy structure's scattering effect to the sound reduction performance of WMPPAs was analysed. Finally, the sound absorption abilities of the WMPPAs were examined using a quasi-two-dimensional (quasi-2D) experiment. The results show that the WMPPAs exhibit good sound reduction performance in the middle- to high-frequency range, which verifies the feasibility of applying WMPPAs to suppress the broadband noise radiated from long enclosures.

Multi-parameter distributed fiber optic sensing using double-Brillouin peak fiber in Brillouin optical time domain analysis.

In this paper, we demonstrate a multi-parameter fiber sensing system based on stimulated Brillouin scattering in a double-Brillouin peak specialty fiber with enhanced Brillouin gain response. The amplitude level of the second Brillouin gain peak, which originated from the higher-order acoustic modes, has been improved with an approximately similar amplitude level to the first Brillouin gain peak from the fundamental acoustic mode. Compared to other multi-Brillouin peak fibers presented in the literature, the proposed fiber significantly reduces the measured Brillouin frequency shift error, thus improving strain and temperature accuracies. By utilizing the sensitivity values of the strain and temperature associated with each Brillouin gain spectrum (BGS) peak, a successful discriminative measurement of strain and temperature is performed with an accuracy of ±13 μɛ, and ±0.5 °C, respectively. The proposed double-Brillouin peak fiber appears to be a possible alternative to other multi-BGS peak fibers, for instance, large effective area fiber and dispersion compensating fibers, which are inherently accompanied by large measurement errors due to the weak Brillouin gain values originating from the higher-order acoustic modes. The demonstrated results show different strain and temperature coefficients of 47 kHz/µɛ, 1.15 MHz/°C for peak 1 and 51 kHz/µɛ, 1.37 MHz/°C for peak 2. Moreover, the enhanced BGS peak gains having nearly the same amplitude levels enable the discriminative measurement of strain and temperature. Such fibers in Brillouin interrogation eliminate the need for complex monitoring setups and reduce measurement errors. We recommend that for long-distance natural gas pipeline monitoring, where discriminative strain and temperature measurement is crucial, the proposed double-Brillouin peak fiber can be highly beneficial.

Higher-order mode filtering by a resistive layer.

A method for filtering higher-order acoustic modes using a resistive layer is proposed and applied to a two-dimensional rectangular waveguide with a quiescent fluid. An analogue of Cremer's criterion is discussed and used to obtain the optimal modal attenuation of the non-planar waves while the plane wave is preserved. Numerical validation of the concept is performed for a straight waveguide and an abrupt expansion in a waveguide.

Simultaneous sensing of temperature and strain with enhanced performance using forward Brillouin scattering in highly nonlinear fiber.

Simultaneous temperature and strain sensing has been demonstrated for the first time to our knowledge by using forward Brillouin scattering (FBS) in a highly nonlinear fiber (HNLF). It is based on different responses of radial acoustic modes R0,m and torsional-radial acoustic modes TR2,m to the temperature and strain. High-order acoustic modes with large FBS gain in an HNLF are chosen to improve the sensitivity. To reduce the measurement error, a method to select the best mode combination with the lowest measurement errors is proposed and demonstrated by both simulation and experiment. Three mode combinations have been used for both temperature and strain sensing, and by using the mode combination (R0,18, TR2,29), the lowest temperature and strain errors of 0.12°C/39 µɛ have been achieved. Compared with sensors using backward Brillouin scattering (BBS), the proposed scheme only requires frequency measurement around 1 GHz, which is cost-effective without the need for a ∼10-GHz microwave source. Moreover, the accuracy is enhanced since the FBS resonance frequency and spectrum linewidth are much smaller than those of BBS.

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.

Intramode Brillouin Scattering Properties of Single-Crystal Lithium Niobate Optical Fiber

Ordinary step-type fiber usually has only one obvious Brillouin scattering gain peak with a low gain coefficient, resulting in a poor sensing performance. As a promising material for nonlinear photonics, lithium niobate can significantly improve the Brillouin gain due to its higher refractive index when replaced with the core material. Furthermore, the higher-order acoustic modes make the Brillouin gain spectrum exhibit multiple scattering peaks, which could improve the performance of sensors. In this study, we simulated the Brillouin scattering properties of different modes of intramode in step-index lithium niobate core fibers. We analyzed the intramode-stimulated Brillouin scattering properties of different pump–Stokes pairs for nine LP modes (LP01, LP11, LP21, LP02, LP31, LP12, LP41, LP22, and LP03) guided in fiber. The results show that both the effective refractive index and Brillouin scattering frequency shift are decreased with the increase in the nine mode orders, and the values of which are 2.2413 to 2.1963, and 21.17 to 20.73 GHz, respectively. The typical back-stimulated Brillouin scattering gain is obtained at 1.7525 m−1·W−1. These simulation results prove that the Brillouin gain of the LiNbO3 optical fiber structure can be significantly improved, which will pave the way for better distributed Brillouin sensing and for improving the transmission capacity of communication systems.

Distributed multi-parameter sensing based on the Brillouin scattering effect in orbital angular momentum guiding fiber

The orbital angular momentum (OAM) guiding fiber is used as a sensing element to measure strain and ambient temperature, sensing information simultaneously in a classical BOTDR configuration, due to its higher-order acoustic modes and high stimulated Brillouin threshold. The Brillouin threshold, the Brillouin gain coefficient and the Brillouin gain spectrum (BGS) of OAM fiber at 1.5 µm are characterized and demonstrated theoretically and experimentally. Taking advantage of the special acoustic properties of the peaks caused by the hard cladding-core interface in the Brillouin scattering process, the distributed multi-parameter sensing (e.g., strain and/or ambient temperature) is verified over a 1-km OAM guiding fiber, with the respective errors of strain and temperature of 18.2 µɛ and 0.93 °C, respectively.

Designing a Facility for Measuring Higher-Order Acoustic Modes in Uniform Heated Flows

An experimental facility was recently developed at the Georgia Tech Research Institute to measure the acoustic scattering coefficients of a test article under mean flow, high-temperature, high-amplitude, and higher-order mode propagation conditions. The experimental facility acts like a two-sided impedance tube, in which the measurement section is a circular duct with 16 acoustic drivers and 16 microphones mounted on each side of the test article. Such a facility can be configured for grazing and bias flow measurements of acoustic liners with sound traveling in and against the direction of the flow. The new facility is designed to maximize the accuracy of acoustic measurements of higher-order modes in heated flows. The influence of experimental uncertainties on the acoustic measurements is analyzed using a Monte Carlo method. Measurements of half-wave resonators in quiescent air and heated flows demonstrate that the experimental uncertainty decreases as the absorption coefficient increases. High-sensitivity microphones produce extremely low uncertainty, and even lower-sensitivity pressure transducers are sufficiently accurate for many applications. This paper is intended to serve as a reference for designing and analyzing an experimental facility to measure the acoustic scattering coefficients in heated-flow and higher-order mode propagation conditions.

Acoustic, thermal, and viscous modes in MEMS perforated back plates

The back plates of MEMS microphones are commonly perforated with holes with radii on the order of a few micrometers. The plates themselves are only a few micrometers thick. Acoustic propagation in small pores is usually described in terms of the fundamental acoustic mode whose solution can be derived using the Low Reduced Frequency method of Tijdeman. Higher order acoustic modes and the viscous and thermal modes are assumed to be highly attenuated and negligible in pores of longer tubes. Since the holes in MEMS are relatively short, it is possible that additional modes may be necessary to accurately calculate the acoustic losses in the back plate. To investigate this possibility, Rayleigh’s determinant is solved numerically and the behavior of the additional modes beyond the fundamental as the pore size is reduced determined. For larger tubes, all modes behave as expected, but as the tube radius is reduced, the higher order acoustic modes become non-physical, leaving only the viscous and thermal modes as possible contributors to the attenuation.

Role of the modal composition of pump in the multi-peak Brillouin gain spectrum in a few-mode fiber

We study stimulated Brillouin scattering (SBS) in a few-mode graded-index fiber in both the intermodal and intramodal configurations. A multi-peak Brillouin gain spectrum (BGS) is observed in both types of SBS interactions owing to the presence of higher-order acoustic modes, whose contribution to the Brillouin gain is found to depend on the modal composition of the pump beam. The numerically simulated results match well with the experimentally observed multi-peak BGS in both the intramodal and intermodal cases. The linewidth of the individual BGS peaks are extracted from a multi-Lorentzian fit to the data and are found to be significantly different for different modal compositions of the pump beam.

Features of the Interaction of a Magnon Bose—Einstein Condensate with Acoustic Modes in Yttrium Iron Garnet Films

The interaction of a magnon Bose—Einstein condensate (mBEC) in a perpendicularly magnetized yttrium iron garnet film with high-order acoustic modes appearing at the sizes of an yttrium iron garnet substrate has been studied experimentally. Narrow energy absorption lines of the mBEC have been observed at the coincidence of frequencies. The minimum relaxation of the mBEC has been detected under acoustic antiresonance conditions when the precession frequency is exactly in the middle between acoustic resonance modes. This discovery will allow the optimization of coherence times when fabricating quantum magnonic devices.

Methodology for Measuring Higher-Order Acoustic Modes in Uniform Heated Flows

In this paper, the complete methodology for measuring the acoustic properties of a test article under uniform heated flow and higher-order mode propagation conditions is developed from the theory of higher-order mode propagation in circular ducts. The major steps in the methodology include modal decomposition based on multiple acoustic pressure measurements; determination of the acoustic scattering matrix using a multiple-source method; and calculation of the sound power reflection, transmission, dissipation, and absorption coefficients from the scattering matrix. These steps are based on contributions by a number of authors spanning several decades, but the purpose of this paper is to unify the various techniques and nomenclature used by these authors into a single, cohesive methodology. Thus, this paper is intended to provide a comprehensive reference on the methodology for measuring the acoustic scattering coefficients under the conditions of uniform heated flows and higher-order mode propagation.

Analysis of throwing power for megasonic assisted electrodeposition of copper inside THVs

The deposition of increased volumes of Cu down an interconnect through-hole via (THV) of a Printed Circuit Board (PCB) is highly desirable for the fabrication of increasing component density and PCB stacks. A quality metric, called micro-throwing power, characterises the volume of Cu that can be deposited within a THV. In this paper, we analyse the influence of 1 ± 0.05 MHz megasonic (MS) assisted agitation applied to copper (Cu) electroplating baths on the micro-throwing ability of a standard, non-filling Cu electroplating solution. Our results indicate that megasonic agitation is shown to increase the Cu deposition volume within a THV by 45% for an increase of MS pressure from 225 W to 450 W, highlighting the significance of acoustic pressure as a key parameter to control MS THV plating volume. Bulk fluid flow rate within a 500 L plating tank is shown to increase by 150% due to Eckhart acoustic streaming mechanisms, compared to existing bath agitation techniques and panel movement. From MS plating experiments and COMSOLTM finite element acoustic scattering simulations, transducer orientation is shown to influence plating performance, with higher-order acoustic resonant modes forming within THVs identified as the cause. Simulations indicate that higher potential acoustic energy was coupled into a 0.200 mm diameter THV cavity, width-to-length aspect ratio (ar): 8:1, than a larger cavity of diameter 0.475 mm, ar 3.4:1. The maximum acoustic energy coupled into THV cavity is observed for a wavefront propagating along the axis of the cavity entrance, indicating an ideal alignment for the MS plating setup.

Coupled Fan–Stator Aerodynamic and Acoustic Response to Inflow Distortion

Abstract Turbofan rotor–stator aeromechanic and aeroacoustics modeling has been traditionally developed by considering separately the aerodynamic and acoustic response of the fan and the stator to inflow nonuniformities. The present paper develops a model for the coupled fan–stator response for a realistic 3D geometry. The coupling mechanism is assumed to be mainly carried by scattered waves bouncing back and forth between the fan and the stator. The relationship between sources and state elements at three regions (inlet (1), in-between fan and stator (2), and exit (3)) is derived in terms of a scattering matrix S. The model is applied to two fan configurations: (1) a fully subsonic fan and (2) a transonic tip speed fan. The scattering matrix terms, up to the 5th blade passing frequency (BPF), are calculated by using CAAT, an Euler-based code. Results show coupling adds about 6 dB to the sound power level (PWL) of the transonic fan configuration but has a small effect for the subsonic fan configuration. The analysis of the propagating modes shows that, for the transonic configuration, the inlet mode at 1BPF propagates in regions 2 and 3 but is cut off in region 1. This reinforces the coupling process by trapping the acoustic mode 1BPF in region 2. Although this trapped energy is mainly due to the 1BPF of the fan wake, the fan scatters this energy into higher order acoustic modes and thus produces redistribution toward higher frequency of the acoustic spectra. Finally, adding a liner in region 2 reduces the energy of 1BPF mode propagating upstream and impinging on the fan. This mitigates the effect of the fan–stator coupling.

Acoustic performance of a resonating perforated liner with incident axial and circumferential acoustic modes

Perforated liners are a common form of passive damping device used in engineering applications to damp acoustic pressure fluctuations. The liner has many orifices arranged over the surface with a rear cavity, where the liner can be designed to resonate akin to an array of Helmholtz resonators in parallel. However, whilst a Helmholtz resonator is insensitive to the incident mode, the large surface area and rear cavity of a perforated liner can generate internal mode shapes that affect the acoustic performance. This paper presents a quasi-one-dimensional analytical model capable of capturing the variation in acoustic performance as the internal cavity segmentation is altered with incident higher-order acoustic modes in a narrow annular duct. Thus, the model can allow the generation of circumferential mode shapes. The model shows, when the liner is highly segmented circumferentially, the liner behaviour is akin to that with an incident axial wave. The segmentation causes the internal cavity pressure to fluctuate uniformly at a similar frequency to a Helmholtz resonator with the same effective cavity dimensions. When the cavity length is significant relative to the wavelength, circumferential mode shapes are generated within the cavity and the frequency of resonance increases based on the circumferential frequency component. The model is then compared to an example experimental data set obtained from a facility designed to allow circumferential modes to cut-on simultaneously with an axial mode. A description of the facility and the multi-microphone decomposition method applied to decompose simultaneous modes of unknown orders and relative magnitudes is presented. The model has good agreement with the experimental results for a small cavity segmentation, although there is deviation observed at high frequencies when the cavity length becomes significant relative to the circumferential wavelength.

Acoustic Supercoupling in a Zero-Compressibility Waveguide

Funneling acoustic waves through largely mismatched channels is of fundamental importance to tailor and transmit sound for a variety of applications. In electromagnetics, zero-permittivity metamaterials have been used to enhance the coupling of energy in and out of ultranarrow channels, based on a phenomenon known as supercoupling. These metamaterial channels can support total transmission and complete phase uniformity, independent of the channel length, despite being geometrically mismatched with their input and output ports. In the field of acoustics, this phenomenon is challenging to achieve, since it requires zero-density metamaterials, typically realized with waveguides periodically loaded with membranes or resonators. Compared to electromagnetics, the additional challenge is due to the fact that conventional acoustic waveguides do not support a cut-off for the dominant mode of propagation, and therefore zero-index can be achieved only based on a collective resonance of the loading elements. Here we propose and experimentally realize acoustic supercoupling in a dual regime, using a compressibility-near-zero acoustic channel. Rather than engineering the channel with subwavelength inclusions, we operate at the cut-off of a higher-order acoustic mode, demonstrating the realization and efficient excitation of a zero-compressibility waveguide with effective soft boundaries. We experimentally verify strong transmission through a largely mismatched channel and uniform phase distribution, independent of the channel length. Our results open interesting pathways towards the realization of extreme acoustic parameters and their implementation in relevant applications, such as ultrasound imaging, acoustic transduction and sensing, nondestructive evaluation, and sound communications.

Acoustic Supercoupling in a Zero-Compressibility Waveguide.

Funneling acoustic waves through largely mismatched channels is of fundamental importance to tailor and transmit sound for a variety of applications. In electromagnetics, zero-permittivity metamaterials have been used to enhance the coupling of energy in and out of ultranarrow channels, based on a phenomenon known as supercoupling. These metamaterial channels can support total transmission and complete phase uniformity, independent of the channel length, despite being geometrically mismatched with their input and output ports. In the field of acoustics, this phenomenon is challenging to achieve, since it requires zero-density metamaterials, typically realized with waveguides periodically loaded with membranes or resonators. Compared to electromagnetics, the additional challenge is due to the fact that conventional acoustic waveguides do not support a cut-off for the dominant mode of propagation, and therefore zero-index can be achieved only based on a collective resonance of the loading elements. Here we propose and experimentally realize acoustic supercoupling in a dual regime, using a compressibility-near-zero acoustic channel. Rather than engineering the channel with subwavelength inclusions, we operate at the cut-off of a higher-order acoustic mode, demonstrating the realization and efficient excitation of a zero-compressibility waveguide with effective soft boundaries. We experimentally verify strong transmission through a largely mismatched channel and uniform phase distribution, independent of the channel length. Our results open interesting pathways towards the realization of extreme acoustic parameters and their implementation in relevant applications, such as ultrasound imaging, acoustic transduction and sensing, nondestructive evaluation, and sound communications.