Theory relating to the noise of rotating machinery
1969; Elsevier BV; Volume: 10; Issue: 1 Linguagem: Inglês
10.1016/0022-460x(69)90125-4
ISSN1095-8568
AutoresJ. E. Ffowcs Williams, D. L. Hawkings,
Tópico(s)Heat Transfer Mechanisms
ResumoThis paper discusses and extends the theory of sound generation by multibladed single-stage fans operating in a free field. The results would also be applicable to shrouded fans provided that the shroud dimensions are small compared with the acoustic wavelength. The main point advanced is that it is inappropriate to regard the sound generation question as a boundary value problem governed by the homogeneous wave equation. Inhomogeneities of the equation caused by a finite velocity field in the vicinity of the fan induce a quadrupole distribution whose effect is studied. It is concluded that this effect is negligible only for low-speed, few-bladed fans in the first harmonics. For multibladed high-speed fans the quadrupole effects are important; both through the potential and turbulent velocity fields. In the absence of turbulence the inhomogeneous potential field may generate more sound than does the rotation of the steady blade loads, whereas the presence of turbulence provides a mechanism by which the potential field around the fan is scattered as sound. The theory of this mechanism is developed, and it becomes evident that it is vastly more important in generating the blade passage frequency sound heard near the axis of single-stage fans than any mechanism so far suggested. The paper then goes on to develop the theory of fan noise radiation at frequencies not necessarily related to the blade passage frequency, and is concluded by a formula relating the power spectral density of the fluctuating forces on a rotating blade to the spectral description of the radiation field.
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