Far-field Directivity Research Articles

Numerical Investigation into Effects of Viscous Flux Vectors on Hydrofoil Cavitation Flow and Its Radiated Flow Noise

In this study, cavitation flow around a hydrofoil and its radiated hydro-acoustic fields were numerically investigated, with an emphasis on the effects of viscous flux vectors. The full three-dimensional unsteady compressible Reynolds-averaged Navier–Stokes equations were numerically solved. The mass transfer model was adopted to model phase changes between liquid water and vapor. To resolve the numerical instability problem arising from the rapid changes in local density and speed of sound of the mixture, the preconditioning and dual-time stepping methods were employed. The filter-based turbulent model was applied to resolve the unstable cavitation flow field more accurately. In splitting the viscous terms, three approaches for dealing with viscous flux vectors were considered: the so-called viscous lagging, full viscous, and thin-layer models. Radiated hydro-acoustic waves were predicted by applying the Ffowcs Williams and Hawkings equations. The effects of the viscous flux vectors on the predicted flow fields and its radiated noise were then examined by comparing the hydro-dynamic forces, velocity distribution, volume fraction, far-field sound directivities, and sound spectrum of the three approaches. The results revealed that the thin-layer model can provide predictions as accurate as the full viscous model, but required less computational time.

Carbon nanotubes within polymer matrix can synergistically enhance mechanical energy dissipation

Safe operation and health of structures relies on their ability to effectively dissipate undesired vibrations, which could otherwise significantly reduce the life-time of a structure due to fatigue loads or large deformations. To address this issue, nanoscale fillers, such as carbon nanotubes (CNTs), have been utilized to dissipate mechanical energy in polymer-based nanocomposites through filler-matrix interfacial friction by benefitting from their large interface area with the matrix. In this manuscript, for the first time, we experimentally investigate the effect of CNT alignment with respect to reach other and their orientation with respect to the loading direction on vibrational damping in nanocomposites. The matrix was polystyrene (PS). A new technique was developed to fabricate PS-CNT nanocomposites which allows for controlling the angle of CNTs with respect to the far-field loading direction (misalignment angle). Samples were subjected to dynamic mechanical analysis, and the damping of the samples were measured as the ratio of the loss to storage moduli versus CNT misalignment angle. Our results defied a notion that randomly oriented CNT nanocomposites can be approximated as a combination of matrix-CNT representative volume elements with randomly aligned CNTs. Instead, our results points to major contributions of stress concentration induced by each CNT in the matrix in proximity of other CNTs on vibrational damping. The stress fields around CNTs in PS-CNT nanocomposites were studied via finite element analysis. Our findings provide significant new insights not only on vibrational damping nanocomposites, but also on their failure modes and toughness, in relation to interface phenomena.

A generalized sound extrapolation method for turbulent flows

Sound extrapolation methods are often used to compute acoustic far-field directivities using near-field flow data in aeroacoustics applications. The results may be erroneous if the volume integrals are neglected (to save computational cost), while non-acoustic fluctuations are collected on the integration surfaces. In this work, we develop a new sound extrapolation method based on an acoustic analogy using Taylor’s hypothesis (Taylor 1938 Proc. R. Soc. Lon. A 164 , 476–490. ( doi:10.1098/rspa.1938.0032 )). Typically, a convection operator is used to filter out the acoustically inefficient components in the turbulent flows, and an acoustics dominant indirect variable D c p ′ is solved. The sound pressure p ′ at the far field is computed from D c p ′ based on the asymptotic properties of the Green’s function. Validations results for benchmark problems with well-defined sources match well with the exact solutions. For aeroacoustics applications: the sound predictions by the aerofoil–gust interaction are close to those by an earlier method specially developed to remove the effect of vortical fluctuations (Zhong & Zhang 2017 J. Fluid Mech. 820 , 424–450. ( doi:10.1017/jfm.2017.219 )); for the case of vortex shedding noise from a cylinder, the off-body predictions by the proposed method match well with the on-body Ffowcs-Williams and Hawkings result; different integration surfaces yield close predictions (of both spectra and far-field directivities) for a co-flowing jet case using an established direct numerical simulation database. The results suggest that the method may be a potential candidate for sound projection in aeroacoustics applications.

Sound radiation from finite cylindrical shell excited by inner finite-size sources

The study of the characteristics of noise sources in cylindrical shells is the foundation of sound field prediction. Although noise sources are usually regarded as point sources to simplify the calculation model in noise source localization and waveguide sound propagation, the approximation is limited to far-field problems. For the near-field acoustics problems in engine room and ship cabin, the radiated noise possesses the spatial directivity because of the complex vibration distribution of the noise source surface. Moreover, the sound scattering on the surface of finite-size sources makes the noise source itself act not only as the energy input of sound field, but also as the scatterer to change the structure of sound field in the environment. These factors lead to large errors when the finite-size source is simplified into a point source. In order to explore the influence of finite-size source on the acoustic field inside and outside the underwater vehicle structure, the shell coupled equation is constructed by combining thin shell theory, equivalent source and Green function. The effects of source surface scattering and directivity on the acoustic field inside and outside the cylindrical shell are studied. The results show that the accuracy of finite-size source construction is related to the equivalent source location. It proves that equivalent source allocation should be arranged in the middle of the geometric center of sources and its structural surface. Sound scattering from the surface of the finite-size source will change the sound field inside the shell, and then the resonant peaks of the cavity are shifted to the high frequencies as the source volume increases, which causes a strong sound transmission phenomenon in some frequency bands. In addition, the directivity of the finite-size source has little effect on the intensity of the sound field inside and outside the shell, which is evident in changing the far-field directivity of the radiated sound field. The research results are valuable for noise prediction and noise control.

Numerical Simulation of Hydraulic Fracturing in Low-/High-Permeability, Quasi-Brittle and Heterogeneous Rocks

In this study, an elastic-brittle-damage constitutive model was incorporated into the coupled fluid/solid analysis of ABAQUS to iteratively calculate the equilibrium effective stress of Biot’s theory of consolidation. The Young’s modulus, strength and permeability parameter of the material were randomly assigned to the representative volume elements of finite element models following the Weibull distribution function. The hydraulic conductivity of elements was associated with their hydrostatic effective stress and damage level. The steady-state permeability test results for sandstone specimens under different triaxial loading conditions were reproduced by employing the same set of material parameters in coupled transient flow/stress analyses of plane-strain models, thereby indicating the reliability of the numerical model. The influence of heterogeneity on the failure response and the absolute permeability was investigated, and the post-peak permeability was found to decrease with the heterogeneity level in the coupled analysis with transient flow. The proposed model was applied to the plane-strain simulation of the fluid pressurization of a cavity within a large-scale block under different conditions. Regardless of the heterogeneity level, the hydraulically driven fractures propagated perpendicular to the minimum principal far-field stress direction for high-permeability models under anisotropic far-field stress conditions. Scattered damage elements appeared in the models with higher degrees of heterogeneity. The partially saturated areas around propagating fractures were simulated by relating the saturation degree to the negative pore pressure in low-permeability blocks under high pressure. By replicating previously reported trends in the fracture initiation and breakdown pressure for different pressurization rates and hydraulic conductivities, the results showed that the proposed model for hydraulic fracture problems is reliable for a wide range of pressurization rates and permeability conditions.

A quadratic model for the far-field direction of arrival estimation

In this paper, we address the problem of estimating the directions of arrival of far-field source signals. For that, we propose a new nonuniform linear array that allows the analyst to model the array data snapshot as a second-order polynomial phase signal. This permits the use of polynomial phase parameter estimation and time-frequency based estimation techniques, in addition to existing direction of arrival estimation methods. Furthermore, for the purpose of simplifying the analysis, we propose here an estimation technique based on the Wigner–Ville distribution kernel. Examples and Monte-Carlo simulations are presented to show the validity, effectiveness, and statistical efficiency of this technique.

Analytical and experimental investigation into the effects of leading-edge radius on gust–aerofoil interaction noise

This paper investigates the effects of local leading-edge geometry on unsteady aerofoil interaction noise. Analytical results are obtained by extending previous work for parabolic leading edges to leading edges of the form $x^{m}$ for $0<m<1$. Rapid distortion theory governs the interaction of an unsteady vortical perturbation with a rigid aerofoil in compressible steady mean flow that is uniform far upstream. For high-frequency gusts interacting with aerofoils of small total thickness this allows a matched asymptotic solution to be obtained. This paper mainly focusses on obtaining the analytic solution in the leading-edge inner region, which is the dominant term in determining the total far-field acoustic directivity, and contains the effects of the local leading-edge geometry. Experimental measurements for the noise generated by aerofoils with different leading-edge nose radii in uniform flow with approximate homogeneous, isotropic turbulence are also presented. Both experimental and analytic results predict that a larger nose radius generates less overall noise in low-Mach-number flow. By considering individual terms in the analytic solution, this paper is able to propose reasons behind this result.

Efficient combination of acceleration techniques applied to high frequency methods for solving radiation and scattering problems

An improved ray-tracing method applied to high-frequency techniques such as the Uniform Theory of Diffraction (UTD) is presented. The main goal is to increase the speed of the analysis of complex structures while considering a vast number of observation directions and taking into account multiple bounces. The method is based on a combination of the Angular Z-Buffer (AZB), the Space Volumetric Partitioning (SVP) algorithm and the A∗ heuristic search method to treat multiple bounces. In addition, a Master Point strategy was developed to analyze efficiently a large number of Near-Field points or Far-Field directions. This technique can be applied to electromagnetic radiation problems, scattering analysis, propagation at urban or indoor environments and to the mutual coupling between antennas.Due to its efficiency, its application is suitable to study large antennas radiation patterns and even its interactions with complex environments, including satellites, ships, aircrafts, cities or another complex electrically large bodies. The new technique appears to be extremely efficient at these applications even when considering multiple bounces.

Effect of compressibility and non-uniformity in flow on the scattering pattern of acoustic cloak

During the last decade, most of acoustic cloak research has been done within a theoretical framework in which the medium is at rest. However, such an acoustic cloak cannot preserve its unique properties or functions to make an object acoustically invisible in the presence of flow. In this study, we propose a theoretical framework to accurately investigate the effect of compressibility and non-uniformity in flow on the scattering pattern of acoustic cloak. In the formulation, the wave operator is coupled with the non-uniform velocity vector, and the equivalent source terms due to mean flow are divided into the compressibility effect and the non-uniformity effect with their own physical meanings. Numerical simulation shows the difference in far-field directivity between previous and present formulations. The polarity of the equivalent sources in the present formulation shows hexapole and skewed quadrupole patterns for non-uniformity and compressibility effects, respectively, and their magnitudes increase with power laws of Mach number as the Mach number increases. As an application, we make use of the present formulation for predicting the acoustic scattering from newly designed convective cloaks. The simulation results show better performance compared to the existing convective cloak.

A sound extrapolation method for aeroacoustics far-field prediction in presence of vortical waves

Off-surface integral solutions to an inhomogeneous wave equation based on acoustic analogy could suffer from spurious wave contamination when volume integrals are ignored for computation efficiency and vortical/turbulent gusts are convected across the integration surfaces, leading to erroneous far-field directivity predictions. Vortical gusts often exist in aerodynamic flows and it is inevitable their effects are present on the integration surface. In this work, we propose a new sound extrapolation method for acoustic far-field directivity prediction in the presence of vortical gusts, which overcomes the deficiencies in the existing methods. The Euler equations are rearranged to an alternative form in terms of fluctuation variables that contains the possible acoustical and vortical waves. Then the equations are manipulated to an inhomogeneous wave equation with source terms corresponding to surface and volume integrals. With the new formulation, spurious monopole and dipole noise produced by vortical gusts can be suppressed on account of the solenoidal property of the vortical waves and a simple convection process. It is therefore valid to ignore the volume integrals and preserve the sound properties. The resulting new acoustic inhomogeneous convected wave equations could be solved by means of the Green’s function method. Validation and verification cases are investigated, and the proposed method shows a capacity of accurate sound prediction for these cases. The new method is also applied to the challenging airfoil leading edge noise problems by injecting vortical waves into the computational domain and performing aeroacoustic studies at both subsonic and transonic speeds. In the case of a transonic airfoil leading edge noise problem, shocks are present on the airfoil surface. Good agreements of the directivity patterns are obtained compared with direct computation results.

Far field directivity of an omnidirectional parametric loudspeaker consisting of piezoelectric ultrasonic transducers set on a sphere

In this work, it is proposed to extend the convolution model for the far-field directivity of a parametric loudspeaker array (PLA) in [C. Shi and Y. Kajikawa, J. Acoust. Soc. Am. 137 (2) (2015)] to predict the far-field sound field generated by an omnidirectional parametric loudspeaker (OPL). The original two-dimensional model, intended for flat PLAs, relies on convolving the directivity of the primary waves with the Westervelt one, rather than on performing their product. This allows one to deal with piezoelectric ultrasonic transducers (PZTs) having large beam widths, typical of PLA applications. The model is herein enhanced to three dimensions, to predict the far-field pressure level of the difference wave at any observation point in space, for a PZT located and pointing anywhere. This makes the model amenable to compute the far-field directivity of PLAs on curved surfaces. In particular, it is shown how it can be applied to compute the far-field pressure of an OPL consisting of a spherical surface wit...

Numerical simulation and experimental research of spectral noise characteristics for the four-wheel landing gear

Numerical simulation and wind tunnel experiment were conducted for flow field and flow noise characteristics of four-wheel landing gear. Under the landing speed, large eddy simulation method was applied to simulate the unsteady turbulent flow field around the landing gear. In addition, vortex-acoustic theory was also employed to compute the intensity and position of sound source, and integral method of FW-H equation was used to solve the sound field generated from different components and their combinations, analyze the noise generation mechanism, spectral characteristics and far-field directivity. Meanwhile, the contribution of each component to the total noise was assessed. The aerodynamic acoustic experiment was conducted for landing gear in the wind tunnel, and a microphone was applied to measure and obtain the spectral characteristics of noise, which was compared with the numerical computation result. As shown from the result, a good agreement was found between the experimental and numerical results. Besides, it was shown from the simulation result that small parts ignored in the computational sound field played a greater impact on prediction result of noise, especially high-frequency noise. As shown from landing gear vorticity and sound pressure distribution, sound source was mainly distributed in the solid surface of various components for the landing gear. Additionally, sound source was also occurred in the vortex shedding positions behind each component. Greater energy and density of the sound source were found in the gap formed between tire and bogie and in the pillar stairs. The tire noise showed maximum contribution to the total noise, followed by the bogie noise, while the pillar noise was minimal. The total noise spectrum was closest to the tire noise spectrum.

Far-Field Performances Prediction of High Frequency Projectors Using Secondary Source Array Method

This paper investigates the prediction of the far-field performances of high frequency projectors using the second source array method (SSAM). The far-field parameters can be calculated accurately using the complex acoustic pressure data of two very close parallel planes which lie in the near-field region of the projector. The paper simulates the feasibility of predicting the far-field parameters such as transmitting voltage response and the far-field directivity pattern. The predicting results are compared with that calculated using boundary element method (BEM). It shows very good agreement between the two methods. A planar high frequency projector is measured using the near-field method. In order to verify the predicting results, the far-field measurement is performed for the same projector. The comparison of the results shows that the near-field method is capable to precisely predict the far-field parameters of the projector.

Numerical investigation on radiation characteristics of aero-intake noise with ground effects

A hybrid method for the prediction of far-field Aero-intake noise from gas turbine engine with ground effects has been developed. The near-field predictions were obtained by solving the linearized Euler equations with computational aeroacoustic techniques composed of high-order finite difference scheme, non-reflecting boundary condition, overset grids, and parallel computational methods. Kirchhoff integral method was used for the prediction of far-field directivity patterns. In order to predict the noise propagation, ray theory is applied with Geographical Information System (GIS) terrain profile data. Then, the noise level on the ground has been predicted and analyzed, including the effects of air absorption, ground reflection, and diffraction.

Synthesis of Scan- and Frequency-Invariant Low-Sidelobe Tapers for Planar Array Antennas

The impact of the array factor (AF) on the synthesis of a low-sidelobe taper for planar array antennas with a periodic element grid is investigated. A low-sidelobe taper that is synthesized for those far-field directions of the AF belonging to only visible direction, cosine $u$ - $v$ space, can seriously deteriorate with respect to peak sidelobe level (PSLL) when the main beam is scanned or the operating frequency is raised. In order to get a scan- and frequency-invariant taper, its synthesis must comprise all far-field directions of the AF including those of invisible $u$ - $v$ space. This communication describes the Fourier properties responsible for the degradation of taper sidelobe level performance when the taper synthesis excludes the invisible space region of the AF. Examples are presented for a circular array antenna to illustrate the impact of the invisible region of the AF on sidelobe performance. The presented results refer to phase-only and amplitude-only sidelobe tapers. The requirements to realize for aperiodic planar array antennas’ scan and frequency proof patterns with invariant PSLL are shortly addressed.

Layout optimization of thin sound-hard material to improve the far-field directivity properties of an acoustic horn

To improve the far-field directivity properties of a given mid-range acoustic horn, previously designed by shape optimization to exhibit almost ideal transmission properties in the frequency range 1.6---9.05 kHz, we apply layout optimization of thin sound-hard material in the interior of the horn. The purpose of the optimization is to place scattering material to prevent the sound intensity to increasingly be concentrated, with increasing frequency, along the horn axis. Absence or presence of thin sound-hard material is modeled by an equivalent surface transmission impedance, and the optimization algorithm determines the distribution of air or sound-hard material along a "ground structure" in the form of a grid inside the horn. The surface impedance is numerically handled using a newly developed finite-element formulation that allows exact enforcement of a vanishing impedance, corresponding to air, which would not be possible using a standard formulation. Horns provided with the optimized scatterers show a much improved angular coverage, compared to the initial configuration, with beam widths that exceed 60 ? uniformly over the operational frequency range, without destroying the good transmission properties of the initial horn.

Printed monopole antennas on uniaxial substrate: theory and simulation

The performance of printed monopole antennas (PMAs) on uniaxial substrate is studied and the same is theoretically analysed using spectral domain immittance approach. Using immittance approach, field components of unit current source is evaluated first and then directivity is also calculated. The theoretical values of the far-field radiation pattern and directivity of uniaxial substrate based rectangular PMAs are validated by high frequency structure simulator (HFSS), whereas return loss is calculated using HFSS.

Resonant mode characteristics of a cajón drum and its effect on sound directivity

The cajon is a hand percussion instrument originally from Peru. Spanish for “large box” or “crate,” the cajon is typically a box enclosure with a thin wooden plate at the front that serves as the playing surface. Many resonance modes are excited when a player strikes the front plate, as recently studied by Pehmoeller and Ludwidgsen [J. Acoust. Soc. Am. 138, 1935 (2015)]. In this study, scanning laser Doppler vibrometry is coupled with high-resolution far-field directivity measurements to examine source vibration and the resultant sound field. Ties between the plate modal vibration and far-field sound radiation spatial patterns are shown. In particular, the non-uniform front plate normal velocities at higher-order resonances result in distinct nulls in the far-field directivity. Avoidance of these nulls yields recommended microphone locations for cajon sound amplification.

Analytical prediction of radiation from a multi-element variable-directivity spherical loudspeaker array and construction and measurement of a prototype

An analysis of radiation from a spherical surface with twelve radiating spherical caps oriented in a dodecahedral arrangement is performed. The approach generalizes the classical single cap solution by utilizing spherical trigonometry transformations to create many spherical caps in different orientations. The calculations include far-field directivity, surface impedances, and net radiated power for a variety of cap motions within the spherical array. Simulations show how well the discrete caps can produce monopole, dipole, and higher mode directivity patterns. Relative motions of the caps are calculated that best simulate these individual radiation modes. The frequency ranges for accurate reproduction of these radiation modes using discrete caps are quantified, and the role of large cap sizes to extend the range is shown. At higher frequencies, the phase interference between discrete cap radiators cause the intended radiation patterns to break down in complicated ways. A prototype 12-element spherical speaker enclosure has been constructed, with the help of a 3-D printer, and tested in an anechoic chamber. The configuration of typical cone loudspeakers creates constraints on the practical design of spherical speakers, limiting the radiating area fraction. Driver design changes to allow more compact spherical speakers with extended frequency range are suggested.

Unidirectional Lasing from Template-Stripped Two-Dimensional Plasmonic Crystals.

Plasmon lasers support cavity structures with sizes below that of the diffraction limit. However, most plasmon-based lasers show bidirectional lasing emission or emission with limited far-field directionality and large radiative losses. Here, we report unidirectional lasing from ultrasmooth, template-stripped two-dimensional (2D) plasmonic crystals. Optically pumped 2D plasmonic crystals (Au or Ag) surrounded by dye molecules exhibited lasing in a single emission direction and their lasing wavelength could be tuned by modulating the dielectric environment. We found that 2D plasmonic crystals were an ideal architecture to screen how nanocavity unit-cell structure, metal material, and gain media affected the lasing response. We discovered that template-stripped strong plasmonic materials with cylindrical posts were an optimal cavity design for a unidirectional laser operating at room temperature.