Acoustic Impedance Boundary Research Articles

On the application of acoustic liners for the reduction of jet-flap installation noise

In this work, an experimental and numerical analysis of the feasibility of using acoustic liners to reduce the acoustic far-field radiation of a subsonic jet near a flat plate is presented. The Boundary Element Method (BEM) with a wavepacket model of the jet noise and considering an acoustic impedance boundary condition was used to calculate the far-field noise for different conditions. A parametric optimization was performed in order to find an optimum impedance in terms of the Overall Sound Pressure Level reduction. Semi-empirical models of acoustic liners were then used to design a liner with an impedance as close as possible to the optimum impedance. The liners were built using additive manufacturing and tested in terms of their acoustic impedance and the resulting noise reduction when applied to a region of the flat plate. The BEM simulations, considering the impedance, showed good agreement with experimental data. Overall, by means of the BEM model, optimization and liner semi-empirical models, it was possible to design an acoustic liner which significantly reduced the installation noise at the far-field, with the overall noise reduction between 2 dB to 4 dB depending on observation angle.

Extending material distribution topology optimization to boundary-effect-dominated problems with applications in viscothermal acoustics

A new formulation is presented that extends the material distribution topology optimization method to address boundary-effect-dominated problems, where specific boundary conditions need to be imposed at solid–fluid interfaces. As an example of such a problem, we focus on the design of acoustic structures with significant viscous and thermal boundary losses. In various acoustic applications, especially for acoustically small devices, the main portion of viscothermal dissipation occurs in the so-called acoustic boundary layer. One way of accounting for these losses is through a generalized acoustic impedance boundary condition. This boundary condition has previously been proven to provide accurate results with significantly less computational effort compared to Navier–Stokes simulations. To incorporate this boundary condition into the optimization process at the solid–fluid interface, we introduce a mapping of jumps in densities between neighboring elements to an edge-based boundary indicator function. Two axisymmetric case studies demonstrate the effectiveness of the proposed design optimization method. In the first case, we enhance the absorption performance of a Helmholtz resonator in a narrow range of frequencies. In the second case, we consider an acoustically larger problem and achieve an almost-perfect broadband absorption. Our findings underscore the potential of our approach for the design optimization of boundary-effect-dominated problems.

Measurements of the normal incidence sound absorption coefficient for Non-standard sized absorbers in impedance tubes

A measurement method is proposed for the normal incidence sound absorption coefficient of absorbers whose sizes are non-standard and distinctly smaller than inner dimensions of the impedance tube cross section, and the accuracy of the method is also evaluated. In this method, a type of parallel-arranged acoustic material (PAM) is to fill the non-standard sized absorber to be a flat inhomogeneous acoustic impedance boundary (IAIB) with the standard size. Then acoustic impedance of IAIB is measured in impedance tubes according to ISO 10534–2, and the acoustic impedance and absorption coefficient of the non-standard absorber is evaluated with the proposed method. Numerical simulations and experimental measurements were conducted to compare absorption coefficients of non-standard absorbers evaluated by the proposed method with those of the standard sized absorbers of same materials, where the influence from the IAIB parameters on accuracy of the proposed method are investigated as well. Numerical results show that, absorption coefficients measured by the proposed method for non-standard absorbers differ within 10% from the actual values if the area ratio of the absorber to the impedance tube cross section is larger than 43%, and acoustic impedance of PAM and the area ratio of the absorber mainly influence the evaluated results. Experimental results provided further validations on the proposed method.

The acoustic impedance of three-dimensional turbines

Thermoacoustic stability assessment of gas turbine combustors requires an acoustic impedance boundary condition for the downstream turbomachinery. Actuator disk type analytical methods offer rapid predictions of acoustic impedance in an iterative design process; previous studies show that this class of models works well for cascades consistent with a two-dimensional assumption. Real turbines, however, are three-dimensional with multiple stages, coolant flows, and leakage flows. The first part of this paper validates a cambered semi-actuator disk model for the acoustic impedance of a realistic multi-stage turbine using non-linear time-marching computations: the two methods agree to within 9% for incident pressure waves and 14% for incident entropy waves. Simulations of the multi-stage turbine with different inlet conditions confirm that, to a close approximation, inlet corrected flow and hence Mach numbers and acoustic impedance are constant during off-design operation. The second part of the paper then applies both analytical and computational approaches to families of parametrically generated turbine stages to quantify three-dimensional design effects. The results show that the influence of hub-to-tip ratio on acoustic impedance is weak, and the two-dimensional analytical model is accurate even for high aspect ratio stages. Front-loaded camber lines increase axial Mach number within blade passages, raising acoustic impedance by up to 51% compared to a datum quadratic camber line. Varying the stator–rotor axial gap changes the relative phase of reflections from vanes and blades, causing the total impedance to either increase or decrease, at different frequencies, by up to 11%. The cambered semi-actuator disk method consistently captures the correct trends, showing that the physical basis of the model is sufficient to produce a broadly applicable design tool for rapid assessment of turbine impedance boundary conditions.

Distribution of Methane Plumes on Cascadia Margin and Implications for the Landward Limit of Methane Hydrate Stability

Nearly 3,500 methane bubble streams, clustered into more than 1,300 methane emission sites, have been identified along the US Cascadia margin, derived both from archived published data and 2011, 2016–2018 dedicated multibeam surveys using co-registered seafloor and water column data. In this study, new multibeam sonar surveys systematically mapped nearly 40% of the US Cascadia margin, extending from the Strait of Juan de Fuca in the north to the Mendocino fracture zone in the south, and bounded East–West by the coast and the base of the accretionary prism. The frequency-depth histogram of the bubble emission sites has a dominant peak at the 500 m isobar, which extends laterally along much of the Cascadia margin off Oregon and Washington. Comparisons with published seismic data on the distribution of bottom simulating reflectors (BSR), which is the acoustic impedance boundary between methane hydrate (solid phase) and free gas phase below, correlates the bottom simulating reflectors upward termination of the feather edge of methane hydrate stability (FEMHS) zone and the newly identified bubble emission sites off Oregon and Washington. The Cascadia margin off northern California, where the BSR ends seaward of the FEMHS, has fewer sites centered on the 500 m isobaths, although data are more limited there. We propose that the peak in bubble emission sites observed near the 500 m isobath results from migration of free gas from beneath the solid phase of the BSR upslope to the FEMHS termination zone, and suggest that this boundary will be useful to monitor for a change in methane release rate potentially related to a warming ocean.

Numerical Investigation of Combustion Instabilities in a Single-Element Lean Direct Inject Combustor Using Flamelet Based Approaches

Abstract In this paper, high-fidelity large eddy simulations (LES) along with flamelet-based combustion models are assessed to predict combustion dynamics in low-emission gas turbine combustor. A model configuration of a single-element lean direct injection (LDI) combustor from Purdue University (Huang et al., 2014, “Combustion Dynamics Behavior in a Single-Element Lean Direct Injection (LDI) Gas Turbine Combustor,” 50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Cleveland, OH, July 28–30.) is used for the validation of simulation results. Two combustion models based on the flamelet concept, i.e., steady diffusion flamelet (SDF) model and flamelet generated manifold (FGM) model are employed to predict combustion instabilities. Simulations are carried out for two equivalence ratios of φ = 0.6, and 0.4. The results in the form of mode shapes, peak to peak pressure amplitude and power spectrum density (PSD) are compared with the experimental data of Huang et al. (2014, “Combustion Dynamics Behavior in a Single-Element Lean Direct Injection (LDI) Gas Turbine Combustor,” 50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Cleveland, OH, July 28–30.). The effect of variation in the time-step size hence acoustic courant number is studied. Further, two numerical solver options, i.e., pressure-based segregated solver and pressure-based coupled solver, are used to understand their effect on the solution convergence regarding the number of time-steps required to reach the limit cycle of the pressure oscillations. A truncated (half) domain simulation is performed by applying an appropriate acoustic impedance boundary condition at the truncated location. Overall, the simulation results compare well with the experimental data and trends are captured accurately in all simulations. It builds confidence in flamelet-based combustion models for the use in combustion instability modeling which is traditionally done using finite rate chemistry models based on reduced kinetics.

Acoustic topology optimization of sound absorbing materials directly from subdivision surfaces with isogeometric boundary element methods

This paper presents an acoustic topology optimization approach using isogeometric boundary element methods based on subdivision surfaces to optimize the distribution of sound adsorption materials adhering to structural surfaces. The geometries are constructed from triangular control meshes through Loop subdivision scheme, and the associated Box-spline functions that generate limit smooth subdivision surfaces are employed to discretize the acoustic boundary integral equations. The effect of sound-absorbing materials on the acoustic response is characterized by acoustic impedance boundary conditions. The optimization problem is formulated in the framework of Solid Isotropic Material with Penalization methods and the sound absorption coefficients on elements are selected as design variables. The potential of the proposed topology optimization approach for engineering prototyping is illustrated by numerical examples.

Numerical simulation of a turbulent channel flow with an acoustic liner

Numerical simulations of a compressible turbulent channel flow with an acoustic impedance boundary condition are performed to assess how the flow is modified compared with a channel flow with rigid walls. When the liner resonance frequency is not too large and the resistance sufficiently small, turbulent statistics deviate from those obtained with rigid walls and surface waves are found traveling along the liner surface. For small resonance frequencies these waves are two-dimensional, they have a large wavelength compared to the turbulent structures and modulate these structures. As a result, they transport momentum toward the impedance wall, causing a drag increase. When the resonance frequency increases, the waves along the liner surface progressively lose their spanwise coherence while their streamwise wavelength decreases to get close to the flow typical length scales, which may also result in a drag increase when the resistance is sufficiently small. In the cases in which the surface waves are two-dimensional, a connection is established between them and the unstable modes computed by using a linear stability analysis. Given the streamwise periodicity of the channel, a temporal stability analysis is performed rather than a spatial analysis, the latter being more frequently encountered in acoustic mode computations. This temporal analysis shows that the unstable mode in the vicinity of an acoustic liner arises from the A-branch of wall modes.

Discrete singular convolution method for one-dimensional vibration and acoustics problems with impedance boundaries

Discrete Singular Convolution (DSC) method has proved its accuracy in free and forced vibration analyses of structures with several simple boundary conditions. However, classical boundary implementation procedure of the DSC fails for the structures having more complex boundaries. This study improves the DSC to make it applicable for more complex boundaries such as structures having mechanical and acoustic impedance boundaries. The impedance boundary condition implementation is carried out by employing Taylor series expansion rather than using classical procedure. In this study, for vibration analyses, mechanical impedance is modelled via mass-damper-spring elements attached to the end of a bar. Natural frequencies and vibration frequency response to a harmonic excitation of the bar are obtained for mechanical impedance boundary condition. For acoustic analyses, several acoustic impedances are firstly applied to the end of a duct. In this analysis, sound pressure level distribution along the tube for two different frequencies is obtained. Then the frequency response of sound pressure to a monopole source of a duct with a glasswool material attached to both ends is also computed. Frequency dependent surface acoustic impedance of this glasswool material is experimentally determined by using impedance tube method. All results are verified by analytical (if available) and finite element computations. It is clearly shown that the introduced procedure is an accurate way in handling impedance boundaries for vibration and acoustic analysis via the DSC.

Analysis of Acoustic Characteristics of Arbitrary Triangular Prism and Quadrangular Prism Acoustic Cavities

This paper proposes a method for the analysis of acoustic modals and steady‐state responses of arbitrary triangular prism and quadrangular prism acoustic cavities based on the three‐dimensional improved Fourier series. First, the geometric models of arbitrary triangular prism and quadrangular prism acoustic cavities are established. To facilitate the calculation, the bottom and top surfaces of the irregular cavity are converted into the unit square domain by a coordinate transformation. Internal sound pressure‐admissible functions are constructed, and energy expressions are derived after coordinate transformation based on the three‐dimensional improved Fourier series. The acoustic modals of arbitrary triangular prism and quadrangular prism acoustic cavities are obtained by the Rayleigh–Ritz technique. At the same time, a point sound source excitation is introduced into the cavity to further study the steady‐state responses of prismatic acoustic cavities with different acoustic impedance boundary conditions. The reliability and universality of the method are verified by comparing with the finite element results. The method and results can provide some references and benchmarks for future research and application.

Seismo-Stratigraphic and Structural Interpretation of Seismic Data of Titas Gas Field, Bengal Basin, Bangladesh

ABSTRACT In the present study, seismic interpretation has been carried out over Titas structure of Bengal basin, Bangladesh to figure out its seismo-stratigraphic and structural behavior. Seven well marked reflecting horizons (R-01 to R-07) have been identified within the Neogene sedimentary sequences using 18 seismic sections and well log data. A new seismic stratigraphy of Neogene sequences has been proposed for the Titas structure ruling out the traditional lithostratigraphy. The studied structure has been divided into 3 megasequences (MS1, MS2 and MS3). Reflector R-01 and R-03 represent the tops of the megasequence 2 (MS2) and megasequence 1 (MS1) respectively. These well marked reflectors are correlated with the top of the traditional litho-groups called Tipam and Surma. Reflectors R-02 and R-04 represent acoustic impedance boundaries within MS2 and MS1 due to lithological gradation. However, R-02 and R-04 are not considered as sequence/ formation boundaries because geologically these are not well defined. Reflectors R-05, R-06 and R-07 represent top of the gas-bearing zones A, B and C that belongs to MS1. All these interfaces or reflectors are anti-form with a central long crestal zone. It forms a north-south trending semi-domal sub-surface anticlinal structure having a semi-dome shaped closure. The structure is asymmetric with steeper eastern flank and gentler western flank. The crestal region is essentially plain with discontinuous reflection. The semi-domal nature of the anticline is in contrast to the neighboring narrow anticlines. Structural pattern suggests its development in relation to the NE-SW trending stress field due to convergence of Indian plate with Burmese plate. Structures of the shallower and deeper reflectors are formed at different phases of structural development.

Compressible turbulent channel flow with impedance boundary conditions

We have performed large-eddy simulations of isothermal-wall compressible turbulent channel flow with linear acoustic impedance boundary conditions (IBCs) for the wall-normal velocity component and no-slip conditions for the tangential velocity components. Three bulk Mach numbers, Mb = 0.05, 0.2, 0.5, with a fixed bulk Reynolds number, Reb = 6900, have been investigated. For each Mb, nine different combinations of IBC settings were tested, in addition to a reference case with impermeable walls, resulting in a total of 30 simulations. The adopted numerical coupling strategy allows for a spatially and temporally consistent imposition of physically realizable IBCs in a fully explicit compressible Navier-Stokes solver. The IBCs are formulated in the time domain according to Fung and Ju [“Time-domain impedance boundary conditions for computational acoustics and aeroacoustics,” Int. J. Comput. Fluid Dyn. 18(6), 503–511 (2004)]. The impedance adopted is a three-parameter damped Helmholtz oscillator with resonant angular frequency, ωr, tuned to the characteristic time scale of the large energy-containing eddies. The tuning condition, which reads ωr = 2πMb (normalized with the speed of sound and channel half-width), reduces the IBCs’ free parameters to two: the damping ratio, ζ, and the resistance, R, which have been varied independently with values, ζ = 0.5, 0.7, 0.9, and R = 0.01, 0.10, 1.00, for each Mb. The application of the tuned IBCs results in a drag increase up to 300% for Mb = 0.5 and R = 0.01. It is shown that for tuned IBCs, the resistance, R, acts as the inverse of the wall-permeability and that varying the damping ratio, ζ, has a secondary effect on the flow response. Typical buffer-layer turbulent structures are completely suppressed by the application of tuned IBCs. A new resonance buffer layer is established characterized by large spanwise-coherent Kelvin-Helmholtz rollers, with a well-defined streamwise wavelength λx, traveling downstream with advection velocity cx = λx Mb. They are the effect of intense hydro-acoustic instabilities resulting from the interaction of high-amplitude wall-normal wave propagation (at the tuned frequency fr = ωr/2π = Mb) with the background mean velocity gradient. The resonance buffer layer is confined near the wall by structurally unaltered outer-layer turbulence. Results suggest that the application of hydrodynamically tuned resonant porous surfaces can be effectively employed in achieving flow control.

Stability analysis and design of time-domain acoustic impedance boundary conditions for lined duct with mean flow.

This work develops the so-called compensated impedance boundary conditions that enable stable time domain simulations of sound propagation in a lined duct with uniform mean flow, which has important practical interest for noise emission by aero-engines. The proposed method is developed analytically from an unusual perspective of control that shows impedance boundary conditions act as closed-loop feedbacks to an overall duct acoustic system. It turns out that those numerical instabilities of time domain simulations are caused by deficient phase margins of the corresponding control-oriented model. A particular instability of very low frequencies in the presence of steady uniform background mean flow, in addition to the well known high frequency numerical instabilities at the grid size, can be identified using this analysis approach. Stable time domain impedance boundary conditions can be formulated by including appropriate phaselead compensators to achieve desired phase margins. The compensated impedance boundary conditions can be simply designed with no empirical parameter, straightforwardly integrated with ordinary linear acoustic models, and efficiently calculated with no need of resolving sheared boundary layers. The proposed boundary conditions are validated by comparing against asymptotic solutions of spinning modal sound propagation in a duct with a hard-soft interface and reasonable agreement is achieved.

Energy based Markov Chain Monte Carlo algorithms for Bayesian model selection

Markov Chain Monte Carlo (MCMC) algorithms for Bayesian model selection have been increasingly applied to acoustics applications. One of challenging tasks required in Bayesian model selection is the exploration of high-dimensional multi-variate spaces such that a key quantity, termed the Bayesian evidence, can be estimated in order to rank a set of competing models. This work presents a class of energy-based MCMC algorithms specifically designed to estimate the Bayesian evidence. As illustrative examples, the energy-based MCMC algorithms are applied to the problem of filter design as used in human head-related transfer functions and in acoustic impedance boundaries within the finite-difference time-domain framework for room-acoustics simulations.

Calculation on Acoustic Scattering of Viscoelastic Layer Coupling with Elastic Shell

This paper is devoted to numerical research on coupling between elastic spherical shell and the coated viscoelastic layer as well as the scattering of incident plane wave by the double-layer spherical shell. The scattering sound field is solved based on impedance boundary condition by boundary element method (BEM). Dynamic finite element method (FEM) is used to numerically simulate the acoustic impedance boundary condition which involved in the coupled spherical shell. Impedance distribution for elastic spherical shell and elastic spherical shell coated viscoelastic layer is calculated and its effect on the target strength (TS) is discussed finally.

Efficient spectral domain formulation of loading effects in acoustic sensors

The liquid loading effect on microacoustic sensors can be modeled using an acoustic impedance boundary condition. A rigorous expression for the acoustic impedance matrix in the spectral domain is derived for isotropic linear elastic layers backed by a defined impedance, which allows to model the loading effect resulting from non-uniform excitation. A wavenumber dependent matrix (3×3) is obtained, rather than the scalar shear and pressure impedances obtained by one-dimensional models (plane wave). This formulation is generalized to enclose linear viscous fluids. Furthermore, the impedance matrix is also calculated for problems with different boundary conditions such as half-space, free surface, rigid backing, and defined impedance boundary conditions. The latter enables the formulation to be applied to systems of layers of any number and composition. The results are compared to the 1D expressions of bulk impedance for the half-space and the transmission line equations for layers of finite thickness. In contrast to these 1D expressions, the coupling of pressure- and shear-wave propagation is considered which yields modified results. Furthermore, from the acoustic impedance matrices, Green's function matrices can be derived, which allow to model complex layered structure problems as will be outlined.

A Refined Modeling for the Liquid Loading Effect in Microacoustic Sensors

The liquid loading effect on microacoustic sensors can be modeled using an acoustic impedance boundary con- dition. A rigorous expression for the acoustic impedance tensor is derived for isotropic linear elastic layers backed by a defined impedance. This formulation is generalized to enclose viscous liquids. Furthermore, the impedance tensor is also applied to the half-space, free surface and rigid backing boundary conditions and is compared to the one dimensional expressions of bulk impedance for the half-space and the transmission line equations for layers of finite thickness. In contrast to these 1D expressions, the coupling of pressure- and shear-wave propagation is considered which results in interesting phenomena for viscous liquid layers. For example, it is found that also for liquid layers much thicker than the decay length of the shear waves (e.g., hundreds of nanometers for a QCR in the lower MHz range), the boundary affects the shear impedance, due to pressure and shear wave coupling.

Iterative solution of high-order boundary element method for acoustic impedance boundary value problems

A high-order boundary element method for time-harmonic acoustic impedance boundary value problems is presented. The method is based on the Galerkin-type formulation of the Burton–Miller integral equation (BMIE) with high-order polynomial basis and testing functions. This formulation has several important advantages: It is free of the interior resonance problem, the hypersingular integral operator of the traditional BMIE formulation can be avoided, it leads to faster convergence in terms of the number of unknowns than the low-order methods and it shows a good performance with iterative solvers. To avoid the numerical difficulties associated to the implementation of the singular surface integral equations, the singularity extraction technique is applied to evaluate the integrals in the singular and near-singular cases. The resulting matrix equation is solved iteratively with the generalized minimal residual method (GMRES) and a simple preconditioner based on the incomplete LU factorization is applied to expedite the convergence. Numerical results indicate that the BMIE formulation with Galerkin method and high-order basis functions has good convergence properties for various geometries and boundary conditions on a wide frequency range when the GMRES method is applied to solve the matrix equation iteratively. This, in turn, indicates that the formulation is well suited for an efficient application of fast solution procedures, such as the fast multipole method.

Magnetotelluric evidence for a deep-crustal mineralizing system beneath the Olympic Dam iron oxide copper-gold deposit, southern Australia

The iron oxide copper-gold Olympic Dam deposit, situated along the margin of the Proterozoic Gawler craton, South Australia, is the world's largest uranium deposit and sixth-largest copper deposit; it also contains significant reserves of gold, silver, and rare earth elements. Gaining a better understanding of the mechanisms for genesis of the economic liberalization is fundamental for defining exploration models in similar crustal settings. To delineate crustal structures that may constrain mineral system fluid pathways, coincident deep crustal seismic and magnetotelluric (MT) transects were obtained along a 220 km section that crosses Olympic Dam and the major crustal boundaries. In this paper we present results from 58 long-period (10–104 s) MT sites, with site spacing of 5– 10 km. A two-dimensional inversion of MT data from 33 sites to a depth of 100 km shows four notable features: (1) sedimentary cover sequences with low resistivity ( 1000 Ω·m) Archean crustal core from a more conductive crust and mantle to the north (typically <500 Ω·m); (3) to the north of Olympic Dam, the upper-middle crust to ∼20 km is quite resistive (∼1000 Ω·m), but the lower crust is much more conductive (<100 Ω·m); and (4) beneath Olympic Dam, we image a low-resistivity region (<100 Ω·m) throughout the crust, coincident with a seismically transparent region. We argue that the cause of the low-resistivity and low-reflectivity region beneath Olympic Dam may be due to the upward movement of CO2-bearing volatiles near the time of deposit formation that precipitated conductive graphite liberalization along grain boundaries, simultaneously annihilating acoustic impedance boundaries. The source of the volatiles may be from the mantle degassing or retrograde metamorphism of the lower crust associated with Proterozoic crustal deformation.

Formulation of a numerical process for acoustic impedance sensitivity analysis based on the indirect boundary element method

The objective of the work presented in this paper is the formulation, implementation and validation of an algorithm for computing the acoustic sensitivity with respect to the unequal impedance boundary conditions in an indirect boundary element method (IBEM). The IBEM integral equations are considered for all possible acoustic boundary conditions including velocity, pressure, unequal impedance, and simultaneous velocity and unequal impedance boundary conditions. The numerical system of equations is developed using a variational approach. The sensitivity formulation is based on analytically differentiating the system of equations formed by the variational approach with respect to the unequal acoustic impedance boundary conditions. Numerical sensitivity results obtained using the formulation developed in this paper are compared to analytical solutions in order to validate the new formulation.