Identification of a non-linear model for fluidelastic instability in a normal triangular tube array

Fluidelastic instability of a single flexible cylinder subject to fluid cross flow has been investigated in arrays of rigid tubes arranged in a normal triangular configuration with pitch ratios of and . The test facility designed and built for this purpose has two novel features: (i) the flexible tube is supported by a linear structure which allows only pure translation of the tube in a direction perpendicular to the flow; (ii) the linear damping of the structure can be modified passively using a specially designed electromagnetic shaker (EMS) without affecting the modal stiffness or mass. This device can also be used to provide a measurable excitation force, either random or deterministic. For the two tube bundles considered, the parameters of a linearized model of the fluid force acting on the tube have been identified using both a time domain and frequency domain technique. The linear fluid damping and stiffness appear to vary with dynamic head for a pitch ratio of , but this was not observed for the other array. The parameters from the linearized models have been used to produce estimates of the stability boundaries. For pitch ratio the predictions agree reasonably well with experimentally determined thresholds. However, for the pitch ratio of , the linearized model is inadequate as the predicted critical velocities overestimate the experimental values by as much as 100%. Using a force state mapping technique, a non-linear model of the fluid force has been identified for this array. The fluid stiffness is modelled as the sum of a linear and a cubic spring and two models for the fluid damping are considered. The predictions for stability thresholds from the non-linear model are in much better agreement with experiment. The limit cycle amplitudes are overestimated, but they agree qualitatively with the trends found experimentally. The results suggest that none of the available theoretical models for single degree of freedom fluidelastic instability are universally applicable.