Fluid Elastic Whirling of a Tube Row

An analytical model for flow-induced vibration of a tube row in a cross flow is formulated. A criterion for the onset of instability is developed. The tubes are modeled with different stiffnesses and damping normal and parallel to the free stream to simulate effects which arise in heat exchangers. The critical reduced velocity required for the onset of instability is shown to increase sharply with the separation of natural frequency between tubes. The effect of an adjacent wall and rows composed of a small number of tubes is explored. The model reduces to an experimentally validated criterion for symmetrically supported tubes.