Buffeting Excitation of Boiler Tube Vibration

Abstract

The origin of the vibration generated within an extensive bank of tubes that run transverse to the direction of gas flow through a boiler shell and whose movement is small enough in amplitude to have no perceptible effect on the motion of the gas, is examined on the supposition that, sufficiently deep inside the bank, the flow is essentially turbulent and, except for a general drift through the bank, exhibits no regular feature. Conditions of this kind are thought to be appropriate to certain types of heat exchanger used in nuclear power stations and operating at large Reynolds numbers. The source of vibration, either structural or gaseous, is associated with the randomly fluctuating forces imposed on the tubes by the turbulent eddies, and a simple argument is put forward to account approximately for the length scale of the most energetic of these eddies and consequently the frequency with which they encounter the tubes. It is further argued that the tubes are aerodynamically discriminating in their force response which is thereby narrowed spectrally and confined to the neighbourhood of the frequency corresponding to the energetic eddies. The subsequent structural or acoustic response is even more sharpened spectrally, owing to the small damping inherent in the system. A relation between the dominant frequency of the force fluctuations, the gas velocity and the geometrical arrangement of the tubes, that emerges from the argument, agrees in form with published observations of the sound emission from boilers under resonant conditions. A disposable constant appearing in the relation is also satisfactorily predicted in order of magnitude. The analysis applies to only one possible form of the vibration phenomenon; other forms, aero-elastic and vortex-excited, may appear under suitable conditions dependent upon Reynolds number, structural stiffness and damping.