Analytic Formulation and Numerical Implementation of an Acoustic Pressure Gradient Prediction

Lee, Seongkyu; Brentner, Kenneth S.; Farassat, F.

doi:10.2514/6.2007-3710

Cited by 14 publications

(29 citation statements)

References 7 publications

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“…Equation 7 is the starting point for the compact forms of Farassat's formulations derived in this paper. The derivations are simplified by using a shorthand notation introduced by Lee 26 and include deformation of the source surface and compact line, 27 outlined in Eq. 8.…”

Section: Derivationmentioning

confidence: 99%

“…Pressure gradient formulations provide the incident field on the scattering body and at the observer while the scattering codes provide the scattered field. 26 The sum of the incident and scattered fields is then the total noise at the observer. There are currently three pressure gradient formulations implemented in ANOPP2: Formulation G0, G1, and G1A.…”

Section: B Pressure Gradient Formulationsmentioning

confidence: 99%

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Compact Assumption Applied to Monopole Term of Farassat’s Formulations

Lopes

2017

Journal of Aircraft

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Farassat's formulations provide an acoustic prediction at an observer location provided a source surface, including motion and flow conditions. This paper presents compact forms for the monopole term of several of Farassat's formulations. When the physical surface is elongated, such as the case of a high aspect ratio rotorcraft blade, compact forms can be derived which are shown to be a function of the blade cross sectional area by reducing the computation from a surface integral to a line integral. The compact forms of all formulations are applied to two example cases: a short span wing with constant airfoil cross section moving at three forward flight Mach numbers and a rotor at two advance ratios. Acoustic pressure time histories and power spectral densities of monopole noise predicted from the compact forms of all the formulations at several observer positions are shown to compare very closely to the predictions from their non-compact counterparts. A study on the influence of rotorcraft blade shape on the high frequency portion of the power spectral density shows that there is a direct correlation between the aspect ratio of the airfoil and the error incurred by using the compact form. Finally, a prediction of pressure gradient from the non-compact and compact forms of the thickness term of Formulation G1A shows that using the compact forms results in a 99.6% improvement in computation time, which will be critical when noise is incorporated into a design environment.

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Section: Derivationmentioning

confidence: 99%

Section: B Pressure Gradient Formulationsmentioning

confidence: 99%

Compact Assumption Applied to Monopole Term of Farassat’s Formulations

Lopes

2017

Journal of Aircraft

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“…This time-domain ESM did not receive much attention and was not been used for practical engineering problems until Lee et al [77][78][79] presented significant improvements of the method and revived it. Lee et al [77][78][79] used analytical formulations of the pressure gradient 80 for the boundary condition to derive a new formulation to include the effect of a uniform motion of the surface and equivalent sources and to consider the incident field generated by arbitrary moving sources such as rotor blades. They introduced a first-order shape function to discretize the source strength in time and used the SVD to improve the numerical instability issue.…”

Section: Equivalent Source Methodsmentioning

confidence: 99%

“…(18) is the incident field, which is known and can be determined by using the analytical formulation for the pressure gradient for arbitrary moving sources. 80 The left-hand side involves the strength of equivalent sources, which is a main unknown. The final matrix form is given as follows:…”

Section: Equivalent Source Methodsmentioning

confidence: 99%

Review: The Use of Equivalent Source Method in Computational Acoustics

Lee

2017

J. Comp. Acous.

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This paper reviews the equivalent source method (ESM), an attractive alternative to the standard boundary element method (BEM). The ESM has been developed under different names: method of fundamental solutions, wave superposition method, equivalent source method, etc. However, regardless of the method name, the basic concept is very similar; that is to use auxiliary points called equivalent sources to reconstruct the acoustic pressure for radiation or scattering problems. The strength of the equivalent sources are then determined via various approaches such that the boundary conditions on the boundary surface are satisfied. This paper reviews several frequencydomain and time-domain ESMs. There are several distinct advantages in these types of methods: (1) the method is a meshless approach so that it is easy and simple to implement; (2) it does not have a numerical singularity problem that occurs in the BEM; (3) the number of equivalent sources can be fewer than the number of surface collocation points so that the matrix size is reduced and a fast computation is achieved for large problems. The main issue of the ESM is that there is no rule to find out the optimal number and position of equivalent sources. In addition, the ESM suffers from the numerical instability that is associated with the ill-conditioned matrix. Some guidelines have been suggested in terms of finding the number and position of the sources, and several numerical techniques have been developed to resolve the numerical instability. This paper reviews the common theories, numerical issues and challenges of the ESM, and it summarizes recent developments and applications of the ESM to aircraft noise.

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“…They claimed that their formulations have an advantage over pressure gradient formulations [3] in that their formulations are simpler and provide faster computations. This comparison is based on the assumption that the pressure gradient formulations were developed and used to obtain the acoustic velocity components indirectly.…”

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confidence: 99%