On the application of the Kirchhoff formula for moving surfaces

Myers, M. K.; Hausmann, J.

doi:10.1016/0022-460x(90)90784-w

Cited by 20 publications

(25 citation statements)

References 2 publications

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“…4 E% was presented in the simplified form shown here by Myers and Hausmann. 16 ES and EA represent a new formulation, and are shown here for the first time. A simplified form of (16) for a stationary, rigid surface was presented by the authors in reference 5.…”

Section: Tij = a 0 M K (Dtij/dy K ) +mentioning

confidence: 99%

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Integral methods for computational aeroacoustics

Pilon

Lyrintzis

1997

35th Aerospace Sciences Meeting and Exhibit

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New surface integral methods for use in computational aeroacoustics are developed and presented. The methods are derived for moving deformable surfaces. These surfaces may be real, solid surfaces, or computational control surfaces. These methods are derived as extensions to the popular Kirchhoff and Ffowcs Williams-Hawkings methods in use today. The equivalence of these two formulations is also presented. Test calculations are shown to validate the methods for use in jet aeroacoustics studies. However, the methods are presented in a manner that makes them easily applicable in cases where Kirchhoff and Ffowcs Williams-Hawkings methods have been used in the past. (Author) AbstractNew surface integral methods for use in computational aeroacoustics are developed and presented. The methods are derived for moving deformable surfaces. These surfaces may be real, solid surfaces, or computational control surfaces. These methods are derived as extensions to the popular Kirchhoff and Ffowcs Williams-Hawkings methods in use today. The equivalence of these two formulations is also presented. Test calculations are shown to validate the methods for use in jet aeroacoustics studies. However, the methods are presented in a manner to make them easily applicable in cases where Kirchhoff and Ffowcs Williams-Hawkings methods have been used in the past. Nomenclature c 0 = ambient sound speed gij = metric tensor components H(f) = Heaviside function Li = surface loading Lk, Rk = control surface dimensions M, M = surface & flow Mach numbers n -unit surface normal vector p, p = fluid pressure and density r,r = radiation & unit radiation vectors S, dS^ = control surface area Tij, Tij -Lighthill stress tensor (xi,t) = observer coordinates and time (yi,r) = source coordinates and time v.' = control surface local coordinates «i = fluid velocity Vi = control surface velocity 6(f) = Dirac delta function Kij = complex wave number ffij = viscous stress tensor 6 -emission angle u = angular frequency O = D'Alembertian wave operator Subscripts o = ambient conditions n = surface normal direction r = radiation direction

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Section: Tij = a 0 M K (Dtij/dy K ) +mentioning

confidence: 99%

“…The form of (16) and E\, E 2 were given by Farassat and Myers. 4 E% was presented in the simplified form shown here by Myers and Hausmann.…”

Section: Tij = a 0 M K (Dtij/dy K ) +mentioning

confidence: 99%

Integral methods for computational aeroacoustics

Pilon

Lyrintzis

1997

35th Aerospace Sciences Meeting and Exhibit

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“…The freestream speed of sound is assumed uniform at a^, and 0 is the angle between n and r. The simplified form for EI in Eq. (3) is taken from Myers and Hausmann [17]. Figure 1 shows a representative Kirchhoff surface in the nonrotating reference frame.…”

Section: Dsmentioning

confidence: 99%

New computational methods for the prediction and analysis of helicopter noise

Strawn

Oliker

Biswas

1996

Aeroacoustics Conference

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This paper describes several new methods to predict and analyze rotorcraft noise. These methods are: (1) a combined CFD and Kirchhoff scheme for far-field noise predictions, (2) parallel computer implementation of the Kirchhoff integrations, (3) audio and visual rendering of the computed acoustic predictions over large far-field regions, and (4) acoustic tracebacks to the Kirchhoff surface to pinpoint the sources of the rotor noise. The paper describes each method and presents sample results for three test cases. The first case consists of in-plane high-speed impulsive noise and the other two cases show idealized parallel and oblique blade-vortex interactions. The computed results show good agreement with available experimental data but convey much more information about the far-field noise propagation. When taken together, these new analysis methods exploit the power of new computer technologies and offer the potential to significantly improve our prediction and understanding of rotorcraft noise. (Author) ABSTRACTThis paper describes several new methods to predict and analyze rotorcraft noise. These methods are: 1) a combined computational fluid dynamics and Kirchhoff scheme for far-field noise predictions, 2) parallel computer implementation of the Kirchhoff integrations, 3) audio and visual rendering of the computed acoustic predictions over large far-field regions, and 4) acoustic tracebacks to the Kirchhoff surface to pinpoint the sources of the rotor noise. The paper describes each method and presents sample results for three test cases. The first case consists of in-plane high-speed impulsive noise and the other two cases show idealized parallel and oblique blade-vortex interactions. The computed results show good agreement with available experimental data but convey much more information about the far-field noise propagation. When taken together, these new analysis methods exploit the power of new computer technologies and offer the potential to significantly improve our prediction and understanding of rotorcraft noise.

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“…Using this convention the approximation for $' is written (10) in which N? are the shape functions written in terms of q1 and n2, the A .…”

Section: N$ =mentioning

confidence: 99%