Study on Criterion of Acoustic Resonant Vibration with Unsteady Fluid Dynamic Force

Ducts containing a tube bundle undergo acoustic resonant vibration. It is considered that the acoustic vibration is a kind of forced vibration by means of Karman vortex. However, it will be more reasonable to think that the vibration is a kind of mutual excited vibration, because fluid dynamic force excites a sound pressure and the sound pressure also generates the new fluid dynamic force. Equation of motion of sound pressure was derived from the mutual excited mechanism with the unsteady fluid dynamic forces. It was revealed from the equation that the imaginary part of the fluid dynamic force acting on the tube bundle supplies the energy of sound and on the other hand, radiation of sound consumes the energy. By comparing the supplying and consuming energies, it became possible to calculate a boundary where the acoustic resonant vibration will occur. The mechanism of supplying and consuming energies is discussed in this paper.