https://www.cs.odu.edu/~mln/ltrs-pdfs/NASA-2003-pas-ksb.pdf

Modeling aerodynamically generated sound of helicopter rotors

A unified approach is used to derive many of the current formulas for calculation of discrete frequency noise of helicopter rotors and propellers. Both compact and noncompact results are derived. The noncompact results are based on the solution of Ffowcs Williams-Hawkings (FW-H) equation. The compact formulations are obtained as the limit of noncompact source results. In particular, the linearized acoustic theories of Hawkings and Lowson, Farassat, Hanson, Woan and Gregorek, Succi, and Jou are discussed in this paper. An interesting thickness noise formula by Isom and its extension by Ffowcs Williams are also presented.

Linear Acoustic Formulas for Calculation of Rotating Blade Noise

Formulations 1 and 1A are the solutions of the Ffowcs Williams-Hawkings (FW-H) equation with surface sources only when the surface moves at subsonic speed. Both formulations have been successfully used for helicopter rotor and propeller noise prediction for many years although we now recommend using Formulation 1A for this purpose. Formulation 1 has an observer time derivative that is taken numerically, and thus, increasing execution time on a computer and reducing the accuracy of the results. After some discussion of the Green's function of the wave equation, we derive Formulation 1 which is the basis of deriving Formulation 1A. We will then show how to take this observer time derivative analytically to get Formulation 1A. We give here the most detailed derivation of these formulations. Once you see the whole derivation, you will ask yourself why you did not do it yourself!

/pdf/derivation-of-formulations-1-and-1a-of-farassat-3kje2aynn2.pdf

Derivation of Formulations 1 and 1A of Farassat

An advanced time approach for acoustic analogy predictions

A review of recent advances in the use of surface integral methods in Computational AeroAcoustics (CAA) for the extension of near-field CFD results to the acoustic far-field is given. These integral formulations (i.e. Kirchhoff's method, permeable (porous) surface FfowcsWilliams Hawkings (FW-H) equation) allow the radiating sound to be evaluated based on quantities on an arbitrary control surface if the wave equation is assumed outside. Thus only surface integrals are needed for the calculation of the far-field sound, instead of the volume integrals required by the traditional acoustic analogy method (i.e. Lighthill, rigid body FW-H equation). A numerical CFD method is used for the evaluation of the flow-field solution in the near field and thus on the control surface. Diffusion and dispersion errors associated with wave propagation in the far-field are avoided. The surface integrals and the first derivatives needed can be easily evaluated from the near-field CFD data. Both methods can be extended in orde...

https://engineering.purdue.edu/~lyrintzi/JAAfinal.pdf

Surface integral methods in computational aeroacoustics—From the (CFD) near-field to the (Acoustic) far-field

An accurate prediction of the noise produced by helicopters requires a good understanding of the noise generating mechanisms involved Such an understanding can lead to controlling the noise of existing helicopters by avoiding noisy regimes of flight or by redesigning the main and tail rotors The present investigation is concerned with approaches which are suitable for the calculation of discrete frequency noise of helicopter rotors The governing differential equation of acoustics used in a consideration of acoustic formulations is the Ffowcs Williams-Hawkings (FW-H) equation Attention is given to a method reported by Farassat (1981), a method developed by Succi (1979), and a procedure discussed by Woan and Gregorek (1978)

The prediction of helicopter rotor discrete frequency noise

A review of propeller discrete frequency noise prediction technology with emphasis on two current methods for time domain calculations

On the Effect of Strand Damage on the Operating Margin of a Nb3Sn Rutherford cable

An accurate prediction of the noise produced by helicopters requires a good understanding of the noise generating mechanisms involved. Such an understanding can lead to controlling the noise of existing helicopters by avoiding noisy regimes of flight or by redesigning the main and tail rotors. The present investigation is concerned with approaches which are suitable for the calculation of discrete frequency noise of helicopter rotors. The governing differential equation of acoustics used in a consideration of acoustic formulations is the Ffowcs Williams-Hawkings (FW-H) equation. Attention is given to a method reported by Farassat (1981), a method developed by Succi (1979), and a procedure discussed by Woan and Gregorek (1978).

G. P. Succi

Papers

The prediction of helicopter rotor discrete frequency noise

A review of propeller discrete frequency noise prediction technology with emphasis on two current methods for time domain calculations

On the Effect of Strand Damage on the Operating Margin of a Nb3Sn Rutherford cable

The prediction of helicopter rotor discrete frequency noise