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NASA NTRS2017

A New Formulation of Time Domain Boundary Integral Equation for Acoustic Wave Scattering in the Presence of a Uniform Mean Flow

It has been well-known that under the assumption of a constant uniform mean flow, the acoustic wave propagation equation can be formulated as a boundary integral equation, in both the time domain and the frequency domain. Compared with solving partial differential equations, numerical methods based on the boundary integral equation have the advantage of a reduced spatial dimension and, hence, requiring only a surface mesh. However, the constant uniform mean flow assumption, while convenient for formulating the integral equation, does not satisfy the solid wall boundary condition wherever the body surface is not aligned with the uniform mean flow. In this paper, we argue that the proper boundary condition for the acoustic wave should not have its normal velocity be zero everywhere on the solid surfaces, as has been applied in the literature. A careful study of the acoustic energy conservation equation is presented that shows such a boundary condition in fact leads to erroneous source or sink points on solid surfaces not aligned with the mean flow. A new solid wall boundary condition is proposed that conserves the acoustic energy and a new time domain boundary integral equation is derived. In addition to conserving the acoustic energy, another significant advantage of the new equation is that it is considerably simpler than previous formulations. In particular, tangential derivatives of the solution on the solid surfaces are no longer needed in the new formulation, which greatly simplifies numerical implementation. Furthermore, stabilization of the new integral equation by Burton-Miller type reformulation is presented. The stability of the new formulation is studied theoretically as well as numerically by an eigenvalue analysis. Numerical solutions are also presented that demonstrate the stability of the new formulation.

Hu, Fang↗

NASA NTRS1995

Scattering Of Nonplanar Acoustic Waves

Report presents theoretical study of scattering of nonplanar acoustic waves by rigid bodies. Study performed as part of effort to develop means of predicting scattering, from aircraft fuselages, of noise made by rotating blades. Basic approach was to model acoustic scattering by use of boundary integral equation to solve equation by the Galerkin method.

Gillman, Judith M.↗

NASA NTRS1985

Scattering of acoustic waves into Tollmien-Schlichting waves by small streamwise variations in surface geometry

By using the triple-deck scaling of Stewartson (1969) and Messiter (1970) it is shown that small but relatively sudden surface geometry variations that produce only very weak static pressure variations can nevertheless produce strong, i.e. O(1), coupling between an externally imposed acoustic disturbance and a spatially growing Tollmien-Schlichting wave. The analysis provides a qualitative explanation of the Leehey and Shapiro (1979) boundary-layer receptivity measurements and is in good quantitative agreement with the Aizin and Poliakov (1979) experiment. It may also explain why small 'trip wires' can promote early transition.

Goldstein, M. E.↗

NASA NTRS1978

Measurements and analysis of farfield scattering from a prolate spheroid

The farfield acoustic scattering by a prolate spheroid with axial point sources near the tip of the body was measured. Data were taken for ka between 10 and 160, where a is the semimajor axis of the spheroid. Comparisons were made with numerical results obtained by an integral equation based on the simple-source method, with appropriate coordinate stretching introduced to permit high-frequency solutions with a minimal number of grid points. Theory and experiment agree within experimental error except for the highest frequencies in the shadow region, where very rapid changes in pressure make precise measurements difficult. The results show that for frequencies of aeroacoustic interest, the scattered field is very large and cannot be ignored.

Bayliss, A.↗

NASA NTRS1993

Modal ring method for the scattering of sound

The modal element method for acoustic scattering can be simplified when the scattering body is rigid. In this simplified method, called the modal ring method, the scattering body is represented by a ring of triangular finite elements forming the outer surface. The acoustic pressure is calculated at the element nodes. The pressure in the infinite computational region surrounding the body is represented analytically by an eigenfunction expansion. The two solution forms are coupled by the continuity of pressure and velocity on the body surface. The modal ring method effectively reduces the two-dimensional scattering problem to a one-dimensional problem capable of handling very high frequency scattering. In contrast to the boundary element method or the method of moments, which perform a similar reduction in problem dimension, the model line method has the added advantage of having a highly banded solution matrix requiring considerably less computer storage. The method shows excellent agreement with analytic results for scattering from rigid circular cylinders over a wide frequency range (1 is equal to or less than ka is less than or equal to 100) in the near and far fields.

Baumeister, Kenneth J.↗

NASA NTRS1992

Modal element method for scattering of sound by absorbing bodies

The modal element method for acoustic scattering from 2-D body is presented. The body may be acoustically soft (absorbing) or hard (reflecting). The infinite computational region is divided into two subdomains - the bounded finite element domain, which is characterized by complicated geometry and/or variable material properties, and the surrounding unbounded homogeneous domain. The acoustic pressure field is represented approximately in the finite element domain by a finite element solution, and is represented analytically by an eigenfunction expansion in the homogeneous domain. The two solutions are coupled by the continuity of pressure and velocity across the interface between the two subdomains. Also, for hard bodies, a compact modal ring grid system is introduced for which computing requirements are drastically reduced. Analysis for 2-D scattering from solid and coated (acoustically treated) bodies is presented, and several simple numerical examples are discussed. In addition, criteria are presented for determining the number of modes to accurately resolve the scattered pressure field from a solid cylinder as a function of the frequency of the incoming wave and the radius of the cylinder.

Baumeister, Kenneth J.↗

NASA NTRS2013

Acoustic Suppression Systems and Related Methods

An acoustic suppression system for absorbing and/or scattering acoustic energy comprising a plurality of acoustic targets in a containment is described, the acoustic targets configured to have resonance frequencies allowing the targets to be excited by incoming acoustic waves, the resonance frequencies being adjustable to suppress acoustic energy in a set frequency range. Methods for fabricating and implementing the acoustic suppression system are also provided.

Kolaini, Ali R.↗

NASA NTRS1977

Measurements and analysis of far-field scattering from a prolate spheroid

The far-field acoustic scattering by a prolate spheroid with axial point sources near the tip of the body was measured. Data were taken for ka between 10 - 160 where (a) is the semi-major axis of the spheroidal. Comparisons were made with numerical results obtained by an integral equation based on the simple source method, with appropriate coordinate stretching introduced to permit high frequency solutions with a minimal number of grid points. Theory and experiment agree within experimental error except for the highest frequencies in the shadow region, where very rapid changes in pressure make precise measurements difficult. The results show that for frequencies of aeroacoustic interest, the scattered field is very large and cannot be ignored.

Bayliss, A.↗

NASA NTRS1992

Scattering of p-modes by a sunspot

The acoustic scattering properties of a large sunspot are determined from a Fourier-Hankel decomposition of p-mode amplitudes as measured from a 68-hr subset of a larger set of observations made at the South Pole in 1988. It is shown that significant improvement in the measurement of p-mode scattering amplitudes results from the increased temporal frequency resolution provided by these data. Scattering phase shifts are unambiguously determined for the first time, and the dependence of the p-mode phase shift and absorption with wavenumber and frequency is presented.

Braun, D. C.↗

NASA NTRS1991

Effect of centerbody scattering on propeller noise

This paper describes how the effect of acoustic scattering from the hub or centerbody of a propeller will affect the far-field noise levels. A simple correction to Gutin's formula for steady loading noise is given. This is a maximum for the lower harmonics but has a negligible effect on the higher frequency components that are important subjectively. The case of a blade vortex interaction is also considered, and centerbody scattering is shown to have a significant effect on the acoustic far field.

Glegg, Stewart A. L.↗

NASA NTRS1993

Modal element method for scattering and absorbing of sound by two-dimensional bodies

The modal element method for acoustic scattering from a 2-D body is presented. The body may be acoustically soft (absorbing) or hard (reflecting). The infinite computational region is divided into two subdomains - the bounded finite element domain, which is characterized by complicated geometry and/or variable material properties, and the surrounding unbounded homogeneous domain. The acoustic pressure field is represented approximately in the finite element domain by a finite element solution, and is represented analytically by an eigenfunction expansion in the homogeneous domain. The two solutions are coupled by the continuity of pressure and velocity across the interface between the two subdomains. Also, for hard bodies, a compact modal ring grid system is introduced for which computing requirements are drastically reduced. Analysis for 2-D scattering from solid and coated (acoustically treated) bodies is presented, and several simple numerical examples are discussed. In addition, criteria are presented for determining the number of modes to accurately resolve the scattered pressure field from a solid cylinder as a function of the frequency of the incoming wave and the radius of the cylinder.

Baumeister, K. J.↗

NASA NTRSDate not supplied

Aeroacoustic Optimization of Installed Propeller Configurations with Scattering and Shielding Effects

An optimization capability is developed for acoustic scattering and shielding of installed propellers and rotors, based on a spacetime Galerkin time domain boundary element method (TDBEM). The time domain approach is particularly suitable for efficient simulation of transient, rotating, and broadband noise sources such as propellers. The use of algorithmic differentiation allows efficient evaluation of design sensitivities required for gradient-based design optimization with a large number of design variables. We present a validation exercise for the coherent broadband scattering capability against an analytical solution, showing excellent agreement. We then demonstrate the optimization tool on a series of inverse design cases with broadband and rotating sources, as well as an optimization problem for a propeller-wing configuration. The results show good performance for optimization problems with the characteristics of realistic installed propeller configurations.

Maks J Groom↗

NASA NTRSDate not supplied

Aeroacoustic Optimization of Installed Propeller Configurations with Scattering and Shielding Effects

Maks J Groom↗

NASA NTRSDate not supplied

On the Implementation and Further Validation of a Time Domain Boundary Element Method Broadband Impedance Boundary Condition

A time domain boundary integral equation with Burton-Miller reformulation is presented for acoustic scattering by surfaces with liners in a uniform mean flow. The Ingard-Myers impedance boundary condition is implemented using a broadband multipole impedance model and converted into time domain differential equations to augment the boundary integral equation. The coupled integral-differential equations are solved numerically by a March-On-in-Time (MOT) scheme. While the Ingard-Myers condition is known to support Kelvin-Helmholtz instability due to its use of a vortex sheet interface between the flow and the liner surface, it is found that by neglecting a second derivative term in the current time domain impedance boundary condition formulation, the instability an be effectively suppressed in computation. The proposed formulation and implementation are validated using a NASA Langley Research Center Grazing Flow Impedance Tube (GFIT) experimental dataset with satisfactory results. Moreover, a minimization procedure for finding the poles and coefficients of the broadband multiple impedance model is formulated in this paper by which, unlike the commonly used vector-fitting method, passivity of the model is ensured. Numerical tests show the proposed minimization approach is effective for modeling liners that are commonly used in aeroacoustic applications.

Time Domain Impedance Boundary Condition↗

NASA NTRS2015

Noise Characteristics of a Four-Jet Impingement Device Inside a Broadband Engine Noise Simulator

The noise generation mechanisms for four directly impinging supersonic jets are investigated employing implicit large eddy simulations with a higher-order accurate weighted essentially non-oscillatory shock-capturing scheme. Impinging jet devices are often used as an experimental apparatus to emulate a broadband noise source. Although such devices have been used in many experiments, a detailed investigation of the noise generation mechanisms has not been conducted before. Thus, the underlying physical mechanisms that are responsible for the generation of sound waves are not well understood. The flow field is highly complex and contains a wide range of temporal and spatial scales relevant for noise generation. Proper orthogonal decomposition of the flow field is utilized to characterize the unsteady nature of the flow field involving unsteady shock oscillations, large coherent turbulent flow structures, and the sporadic appearance of vortex tubes in the center of the impingement region. The causality method based on Lighthill's acoustic analogy is applied to link fluctuations of flow quantities inside the source region to the acoustic pressure in the far field. It will be demonstrated that the entropy fluctuation term in the Lighthill's stress tensor plays a vital role in the noise generation process. Consequently, the understanding of the noise generation mechanisms is employed to develop a reduced-order linear acoustic model of the four-jet impingement device. Finally, three linear acoustic FJID models are used as broadband noise sources inside an engine nacelle and the acoustic scattering results are validated against far-field acoustic experimental data.

Broadband↗

NASA NTRS1997

An Investigation of High-Order Shock-Capturing Methods for Computational Aeroacoustics

Topics covered include: Low-dispersion scheme for nonlinear acoustic waves in nonuniform flow; Computation of acoustic scattering by a low-dispersion scheme; Algorithmic extension of low-dispersion scheme and modeling effects for acoustic wave simulation; The accuracy of shock capturing in two spatial dimensions; Using high-order methods on lower-order geometries; and Computational considerations for the simulation of discontinuous flows.

Casper, Jay↗

NASA NTRS1983

Low frequency acoustic and electromagnetic scattering

This paper deals with two classes of problems arising from acoustics and electromagnetics scattering in the low frequency stations. The first class of problem is solving Helmholtz equation with Dirichlet boundary conditions on an arbitrary two dimensional body while the second one is an interior-exterior interface problem with Helmholtz equation in the exterior. Low frequency analysis show that there are two intermediate problems which solve the above problems accurate to 0(k(2) log k) where k is the frequency. These solutions greatly differ from the zero frequency approximations. For the Dirichlet problem numerical examples are shown to verify the theoretical estimates.

Hariharan, S. I.↗

NASA NTRS1986

Low frequency acoustic and electromagnetic scattering

This paper deals with two classes of problems arising from acoustics and electromagnetics scattering in the low frequency stations. The first class of problem is solving Helmholtz equation with Dirichlet boundary conditions on an arbitrary two dimensional body while the second one is an interior-exterior interface problem with Helmholtz equation in the exterior. Low frequency analysis show that there are two intermediate problems which solve the above problems accurate to 0(k/2/ log k) where k is the frequency. These solutions greatly differ from the zero frequency approximations. For the Dirichlet problem numerical examples are shown to verify the theoretical estimates.

Hariharan, S. I.↗