Higher Order Acoustic Modes Research Articles

Future challenges in computational aeroacoustics for fan broadband and combustor noise

Two critical areas for the design of quiet gas turbine engines, fan broadband and combustor noise, are briefly reviewed. Both of these noise sources are sensitive to local aerodynamic and geometric variations and thus are ideally suited for analysis by computational aeroacoustic methods. To demonstrate this point for combustor noise and show areas where improved understanding is needed, the scattering of an acoustic wave by a localized heat source is studied. The heat source produces gradients in the mean flow and the speed of sound that scatter the incident duct acoustic mode into vortical, entropic, and higher order acoustic modes. Solutions to the Euler equations are computed to (i) understand how variations in the amplitude and axial extent of a steady heat source and (ii) how unsteady heat release can modify the scattered solution. For an acoustic excitation interacting with a steady heat source, significant entropy waves are produced as the net heat addition increases at the expense of the transmitted acoustic energy. When the net heat addition is held constant, increasing the axial extent of the heat source results in a reduction of the entropy waves produced downstream and a corresponding increase in the downstream scattered acoustic energy. When unsteady heat release which is proportional to mass flow fluctuations in the duct is considered, a significant reduction in the entropy occurs and a corresponding increase in the transmitted and reflected acoustic waves occurs. These results suggest that the dominance of the indirect and direct combustor noise mechanisms are highly sensitive to the heat source lengthscale relative to the acoustic lengthscale and the character of the unsteady heat release.

Effect of ocean acidity on the mid-frequency ambient noise field in shallow water.

Due to increased acidification, Hester et al. [Geophys. Res. Lett. 35, L19601] estimate that by midcentury the sound absorption of seawater will decrease by almost 40%. In the present study, the expected relative increase in the mid-frequency ambient noise field is estimated. Emphasis is placed on shallow water scenarios with typical summertime sound speed profiles and frequencies from 1 to 5 kHz. A model is developed that assumes shallow water internal waves will redistribute energy from high-order acoustic modes excited by noise sources near the sea surface into ducted, low-order modes that propagate with low loss. Calculations are made as a function of pH level, the strength of the internal waves, and the bottom composition. The modeled noise field is beamformed and the effect on the so-called ambient noise notch is estimated.

Effects on acoustics caused by ocean solitons, Part B: Acoustics

Large amplitude internal solitary waves in the ocean can interfere with underwater acoustic signals. For certain acoustic parameters (source depth, receiver depth, and frequency) a redistribution of acoustical energy to higher-order acoustic modes can occur as the acoustic signal propagates through the solitary wave train. Depending on the ocean bottom composition, this can result in a significant loss in acoustical signal intensity. In order to simulate and understand this phenomena, it is necessary to generate a solitary wave train that is realistic and contains the spectral components that will interact with the acoustic signal. This requires a primitive equation nonhydrostatic ocean model. Part A [A.C. Warn-Varnas, S.A. Chin-Bing, D. King, J. Hawkins, K. Lamb, Effects on acoustics caused by ocean solitons: Part A. Oceanography, Nonlinear Anal., in press ( doi:10.1016/j.na.2009.02.104)] of this two-part article addressed that issue. In this work we use acoustic model simulations to demonstrate the mode linkage between the solitary wave train and the acoustic signal that can result in a large signal loss. Understanding the linkage allows for pre-examination of the solitary wave characteristics to determine if they could affect propagating acoustic signals. The procedure has the advantage that only a few computer runs are required from the ocean model and no lengthy computer runs are required from acoustic propagation models. Only a quick calculation of the acoustic mode eigenvalues is needed.

Full modal analysis of the Brillouin gain spectrum of an optical fiber

We present a numerical study of stimulated Brillouin scattering in optical fibers based on a full modal analysis of the acoustic and optical properties. The computation of each acoustic mode supported by the fiber structure allows us an accurate and detailed investigation of the characteristics of the Brillouin gain spectrum. We focus our attention on the contribution of the higher-order acoustic modes which are sometimes ignored because of computational issues in particular on optical fibers that act as acoustic antiwaveguides. Our analysis clearly highlights their role and their dependence on the physical and geometrical structure of the fiber.

Acoustic modal analysis and control in w-shaped triple-layer optical fibers with highly-germanium-doped core and F-doped inner cladding

The numerical study of acoustic modal properties in w-shaped optical fibers with high-delta germanium-doped core and F-doped inner cladding (F-HDF) is demonstrated. The cutoff conditions of acoustic modes in the F-HDF show opposite behaviors in contrast with those of optical ones because F-doped inner cladding contributes differently to acoustic and optical waveguides. The acoustic dispersion characteristics vary to a great extent with respect to the location of the acoustic modes in the fiber's core or in the fiber's inner cladding. The resonance frequency spacing between neighboring acoustic modes is theoretically and experimentally found to have a quadratic relation to the core's germanium concentration. We also investigate the critical conditions to move high-order acoustic modes into the F-doped inner cladding and validate the optimal feasibility of employing L(01) and L(03) acoustic modes to fiber-optic Brillouin-based discriminative sensing of strain and temperature.

A tunable microwave transistor oscillator with a resonator based on higher order bulk acoustic modes

The characteristics of a transistor oscillator of a set of frequencies stabilized with a frequency-tuned multifrequency resonator based on higher-order bulk acoustic modes are investigated. Variants of discrete electronic tuning of the oscillator frequency are presented.

Enhancement of stimulated Brillouin scattering of higher-order acoustic modes in single-mode optical fiber

Solving the elastic wave equation exactly for a GeO2-doped silica fiber with a steplike distribution of the longitudinal and shear velocities and density, we have obtained the dispersion, attenuation, and fields of the leaky acoustic modes supported by the fiber. We have developed a model for stimulated Brillouin scattering of these modes in a pump-probe configuration and provided their Brillouin gains and frequencies for an extended range of core sizes and GeO2 doping. Parameter ranges close to cutoff of the acoustic modes and pump depletion enhance the ratio of higher-order peaks to the main peak in the Brillouin spectrum and are suitable for simultaneous strain-temperature sensing.

Acoustic Fatigue of Impellers of Rotating Machinery

Impellers of air, gas, or steam moving rotating machinery are exposed to acoustic pressure loading (pressure pulsations) from acoustic waves generated in the gaseous medium from flow within the machine casing. The acoustic waves and the impeller structure contain a number of natural frequencies and corresponding mode shapes. The acoustic waves are expressed by pressure pulsations which typically consist of 1) fluctuating wall pressures, 2) plane waves, and 3) higher-order acoustic modes. Out of the three excitation phenomena, the higher-order acoustic modes are the most efficient excitation sources of impeller vibration. The reason for this is the interaction of these modes with impeller structural modes when they become coincident. Of importance is the coincidence of acoustic modes and structural modes with matching wave numbers. The most severe dynamic loading of the impeller occurs at complete coincidence in which in addition to a match in wave numbers (mode shapes) also matching of acoustic and structural frequencies occurs. The paper will provide the theoretical background of the physical phenomena governing the fluid-structure interaction which may lead to extreme loading of the impeller in an acoustically structurally coupled system. Such loading may result in vibration and structural fatigue (acoustic fatigue) and possibly in the destruction of the impeller.

Elastic properties of nanocrystalline zirconium–silicon–boron thin films

Thin amorphous films of ZrB3 grown on Si(111) substrates by chemical-vapor deposition are, upon annealing at 960 °C, transformed to films composed of nanocrystallites (6–10 nm extent) with a nominal composition of Zr0.9Si0.3B3. The independent elastic constants of the layers are determined from the dispersion of the surface and pseudo-Sezawa acoustic excitations and reveal large enhancements in the C11 and C44 constants accompanying the conversion of ZrB3 to the nanocrystalline phase. Since the transverse sound velocities of the binary and Zr0.9Si0.3B3 are in near resonance with the sound velocity of Si (VTSi=4.8 km/s), only the Rayleigh surface wave is localized to the film while all higher-order acoustic modes are evanescent. Despite the strong decay channels, high-lying excitations with velocities as large as 25 km/s (≫VTSi) are observed in Brillouin light scattering. Insight into these acoustic properties is provided by evaluating the elastodynamic Green’s functions and associated acoustic-mode densities.

Optimum Design for Inlet and Outlet Locations of Circular Expansion Chamber for Improving Acoustic Performance

The acoustic characteristics of expansion chamber will be changed with the variation of inlet/outlet location due to the higher order acoustic mode in a high frequency in which the plane wave theory is not available. In this paper, the acoustic performance of reactive type expansion chamber with circular cross-section is analyzed by using the modified mode matching theory. The sensitivity analysis of four-pole parameters with respect to the location of inlet and outlet is also suggested to increase the acoustic performance. The acoustic power transmission coefficient is used as cost function, and the location of inlet and outlet is used as design variables. The steepest descent method and SUMT algorithm are used for optimization technique. Several results showed that the expansion chamber with optimally located inlet/outlet had better acoustic performance than concentric expansion chamber.

Solar p and g modes in a model with a convection layer above a sub-adiabatic interior

We study high-order acoustic modes which reside in the outer layers of the solar interior. Magnetic field effects are not taken into account in this paper as we wish first to filter out how the modal frequencies depend on physical characteristics of a particular model structure of the Sun. In particular, we are interested in how the modal frequencies of solar global oscillations depend on the thickness of the convection layer and on the temperature gradient of the solar interior below. The model we use consists of three planar layers: an isothermal atmosphere, while the convection layer and the interior have temperature gradients that are adiabatic and sub-adiabatic, respectively. The presence of a convection layer with a finite thickness brings in additional modes while the variations in temperature gradient of the interior cause shifts in eigenfrequencies that are more pronounced for the p modes than for the g modes. These shifts can easily be of the order of several hundreds of μHz, which is much larger than the observational accuracy.

A modeling study of acoustic propagation through moving shallow-water solitary wave packets

Propagation of 400-Hz sound through continental-shelf internal solitary wave packets is shown by numerical simulation to be strongly influenced by coupling of normal modes. Coupling in a packet is controlled by the mode coefficients at the point where sound enters the packet, the dimensions of the waves and packet, and the ambient depth structures of temperature and salinity. In the case of a moving packet, changes of phases of the incident modes with respect to each other dominate over the other factors, altering the coupling over time and thus inducing signal fluctuations. The phasing within a moving packet varies with time scales of minutes, causing coupling and signal fluctuations with comparable time scales. The directionality of energy flux between high-order acoustic modes and (less attenuated) low-order modes determines a gain factor for long-range propagation. A significant finding is that energy flux toward low-order modes through the effect of a packet near a source favoring high-order modes will give net amplification at distant ranges. Conversely, a packet far from a source sends energy into otherwise quiet higher modes. The intermittency of the coupling and of high-mode attenuation via bottom interaction means that signal energy fluctuations and modal diversity fluctuations at a distant receiver are complementary, with energy fluctuations suggesting a source-region packet and mode fluctuations suggesting a receiver-region packet. Simulations entailing 33-km propagation are used in the analyses, imitating the SWARM experiment geometry, allowing comparison with observations.

How to drive roAp stars

Rapidly oscillating Ap stars constitute a unique class of pulsators with which to study non-radial oscillations under some — even for stars — unusual physical conditions. These stars are chemically peculiar, they have strong magnetic fields and they often pulsate in several high-order acoustic modes simultaneously. We discuss here an excitation mechanism for short-period oscillation modes based on the classical κ mechanism. We particularly stress the conditions that must be fulfilled for successful driving. Specifically, we discuss the roles of the chemical peculiarity and strong magnetic field on the oscillation modes and what separates these pulsators from δ Scuti and Am-type stars.

Quantification of acoustic and hydrodynamic fields in flow duct systems

Internal wall pressure fluctuations downstream of a flow disturbance in a cylindrical duct consist of a propagating acoustic field of both plane wave and higher-order acoustic modes superimposed onto hydrodynamic turbulence. Various methods exist in both the time and the frequency domain to separate the hydrodynamic from the acoustic components. Coherence functions and cross-spectra may be used to separate the correlated parts from the uncorrelated parts of the internal wall pressure fluctuations for frequencies less than the (1,0) mode. Data collected for air flow through a 40 mm diameter pipe downstream of a flow disturbance has been examined. Changes to the degree of spatial coherence of the turbulent field at different axial locations were evident. In addition, a comparison of the acoustic spectrum between the separation, flow recovery and fully developed regions reveals the presence of standing waves and a change in spectral peak density of the propagating waves.

Separation of dispersed phases from liquids in acoustically driven chambers

A separation process for the collection and processing of fine secondary phases in liquids has been developed, in which a stationary acoustic field at ultrasonic frequencies is superimposed on suspensions flowing through filled chambers. The acoustic radiation force acts to drive second-phase inclusions to either the nodes or antinodes of the stationary field, and acts to hold the secondary-phase material in position relative to the bulk liquid flow. Separation devices consisting of broadband lead-zirconate—lead-titanate transducers, bonded to the ends of glass and aluminium tubes (up to 4 cm in diameter and 25 cm in length, and ranging from 0.9 to 2 mm in wall thickness), were constructed. These were driven with continuous a.c. voltages at specific frequencies in the range of 0.35–1.4 MHz to obtain a forced coincidence response in which the flexural vibrations of the tube wall are matched in phase and geometry with higher-order acoustic duct modes in the liquid. This excitation produced stationary fields with peak acoustic pressures of the order of 1 MPa in water. Particles ranging in size from 0.1 to 100 μm have been concentrated in aqueous media into nodal zones with characteristic times of less than 1 s. Chambers with 0.11 volume, driven at frequencies near 625 kHz, use approximately 25 W of electrical power. Collection efficiencies of up to 97.5% have been measured. The trapped particles can be moved to either end of the cell and removed through an exit port by repeatedly sweepping the driving frequency over a known range and period. Applications of these principles include separations from fluid mixtures of fine solids, immiscible liquids, or biological cells.

Active control of higher-order acoustic modes in ducts

The active control of higher-order acoustic modes within a semi-infinite hard-walled rectangular duct is examined analytically for harmonic constant volume velocity sound sources. The effect of source location, size, strength, and relative phase upon the total mean acoustic power flow is investigated for both single and dual control source configurations, at a number of excitation frequencies. For the analysis, the primary source is mounted in the plane of the duct cross section, which may be a uniform surface of arbitrary finite impedance. It was found that the reduction in total acoustic power is dependent upon the relative location of the primary and control sources, both laterally across the wall of the duct and axially along the duct. The reduction in total acoustic power was found to be a maximum at axial source separation distances corresponding to multiples of half-wavelengths of the propagating modes, and at relative lateral locations such that the primary and control source mode shape function values were equivalent.

The effect of toroidal magnetic fields in the overshoot layer on the eigenfrequencies of stellar oscillations

The overshoot layer in stellar convection zones is slightly subadiabatic and can be considered as a stable region for storage of magnetic flux. Belvedere, Pidatella and Stix (1986) estimated the size of the overshoot layer and computed the magnetic field strength, beyond which toroidal flux tubes become unstable to buoyancy, for a number of main sequence spectral types ranging from F5 to K0. Here we estimate the relative frequency perturbation of high order acoustic modes due to the presence of a non-oblique axisymmetric magnetic field in the overshoot layer. We find that increases with the advancing spectral type, the predicted frequency splitting being large enough to be detected by observations, at least for the Sun.We conclude that magnetic field induced frequency splitting of high order acoustic modes may well be due to a toroidal field of relatively moderate strength just beneath the bottom of the convection zone.

Noise breakout from flat-oval ducts

Two theoretical treatments concerning the transmission of internally propagated sound at low frequencies through the walls of “flat-oval” ducts are described. One of these is based on a numerical solution to the equations of motion for the duct walls, and the other on a forced wave duct wall response to the internal sound field. Only the plane internal acoustic mode is considered. Both theories are in reasonable agreement with experimental data at low frequencies, though discrepancies are noted in the region where higher order acoustic modes can propagate within the duct. The chief feature of interest in the wall transmission loss mechanism of flat-oval ducts is that the flat walls radiate most sound energy at low frequencies, and a mass law behaviour predominates, but at high frequencies a ring resonance effect, connected with the curved walls, is noted; this lowers the transmission loss near the ring frequency, where the curved walls radiate the greater part of the acoustic power.

Analysis of higher-order mode effects in the circular expansion chamber with mean flow

The effects of higher-order acoustic modes produced by the areal discontinuities of the simple expansion chamber with mean flow on the acoustic performance are studied. The chamber is modeled as a piston-driven circular rigid tube with no losses and, by using the Fourier–Bessel expansion, a general expression of the output pressure to the given input uniform volume velocity is obtained for a whole chamber. Quantitative estimation for the transmission loss can be performed using the derived four-pole parameters, whereas the characteristics of the chamber, as a result of the interactions between the plane wave and the transverse waves, can be easily investigated with respect to the relative locations of the inlet/outlet, the chamber length, and the mean flow. The expression as a form of C in four-pole parameters is adopted to describe the chamber characteristics for computational convenience. All the parameters involved in the experimental works by Eriksson [L. J. Eriksson, J. Acoust. Soc. Am. 72, 1208–1211 (1982)] are taken in the examples. Using the derived four-pole parameters, the transmission losses for both the concentric and offset inlet/outlet configurations are predicted and compared with the experimental results. The theoretical results of the present study are in good agreement with the experiments of the authors and the previous works.

Mechanisms of the generation of external acoustic radiation from pipes due to internal flow disturbances

Extensive spectral measurements of the internal wall pressure fluctuations, pipe wall acceleration, and external acoustic radiation due to the disturbance of a fully developed turbulent air flow in a pipe by 90° radiused bends, 45° and 90° mitred bends, and butterfly and gate valves are presented. The measurements were made at sufficient distances downstream of the disturbance for an undisturbed hydrodynamic regime to be re-established, and for the only remaining disturbance to be a superimposed internal acoustic field radiated from the disturbance. This internal acoustic field, which can be responsible for extending the influence of the disturbance throughout a piping system, comprises, in general, both plane wave and higher order acoustic modes, although its detailed character depends on the particular characteristics of the individual fittings. It gives rise to increases in pipe wall vibration and external radiation, by large amounts in the cases of the more severe disturbances, over those due to undisturbed turbulent pipe flow. The background theory of pipe wall response and radiation which provides the framework for interpretation of the experimental results and identification of sound generation mechanisms is also presented. At frequencies at which only plane acoustic waves can propagate in the pipe, both forced peristaltic motion and resonant modes of the pipe wall contribute to the acceleration response of the wall. For a circular pipe with uniform wall thickness, theory predicts no coupling between plane waves and resonant wall modes of circumferential order m>0; but departures from the ideal state result in excitation of apparently all pipe modes with resonance frequencies in this range. High subsonic and supersonic structural modes and the peristaltic motion (which, because of augmentation of acoustic velocity by the flow, is supersonic with respect to the external fluid) all have high radiation ratios and make the dominant contributions to the external sound radiation. Increases in pipe wall response and external radiation are largest at frequencies at which higher order acoustic modes can propagate, in which case coincidence effects lead to strong excitation of supersonic pipe modes. A previous conclusion that coincidence occurs at a frequency close to the cut-off frequency of the acoustic mode involved is confirmed. The results show the effect of the combination of the set of discrete resonance frequencies of the pipe wall and the influence of the flow on the wavenumber-frequency relation for the acoustic modes in producing four different principal wavenumber coincidences for each acoustic mode, in agreement with theoretical predictions.