Effect of friction and obstruction on the dynamics of a curved pipe conveying fluid with fixed ends

A dynamic model for a curved pipe conveying fluid with fixed ends is formulated using the extended Hamilton's principle. The external work done by the pump to overcome the frictional head loss and a semi-venturi model for the obstruction to the flow in the pipe are modelled. An eigenvalue analysis is conducted followed by a convergence study of the natural frequencies. The pipe vibration experiments are performed for a pulse velocity excitation to validate the computed natural frequencies. The influence of friction, curvature and obstruction on the eigenvalues of the system are studied using the developed model. In the absence of friction, the effect of small curvature on the dynamics of the pipe is found to be negligible and the higher curvature is observed to delay divergence instability. The presence of friction induces stiffness which delays divergence and flutter instability velocity, prominently at higher curvature. Similarly, the obstruction also delays flutter for higher curvature pipes. Both friction and obstruction have a stabilising effect at higher curvature at higher flow velocity. The presence of sharp bend or a sharp change in curvature is observed to initiate dynamic instability at very low flow velocity compared to the pipes without sharp bends. The influence of curvature and obstruction on the vibration of the pipe is studied from the experiments. The curvature and obstruction enhance energy redistribution and excitation in the experiments. The trends observed in the computed acceleration responses are in close comparison with the experimental responses. The effect of flutter instability is also observed at higher flow velocity in the experimental responses as predicted by the model.