On the Underlying Fluid Mechanics Responsible for Damping Controlled Fluidelastic Instability in Tube Arrays

Granger and Paidoussis hypothesized that damping controlled fluidelastic instability is in fact due to the generation and convection of vorticity. In this paper a simple wake model consisting of a convecting vortex sheet is proposed to represent the transient nature of fluidelastic forces present in a tube array. Using this model, the memory function proposed by Granger and Paidoussis has been obtained by numerical integration without the need to calibrate the model with experimental data. The resulting function is found to compare well with the first and second order approximations which were determined empirically. However, the current model does not exhibit the physically unrealistic features of the approximations. Furthermore, the memory function has been combined with experimental data for the static fluid force to produce a prediction of the critical velocity for a range of mass damping parameter. This stability threshold is in reasonable agreement with experimental data. Therefore it is concluded that vorticity transport is in fact the mechanism responsible for damping controlled fluidelastic instability.