Stability boundaries for flow induced motions of tubes with an inclined terminal nozzle

A theoretical and experimental study is made of self-induced non-planar vibrations of a flexible tube conveying a fluid. The tube is fixed at one end and the fluid issues from a nozzle inclined to the axis of the tube at the free end. The effect of the inclined nozzle is to cause a pronounced sinusoidal static deformation of the tube. When a critical flow rate is exceeded the tube begins to flutter. The flutter oscillations occur either in the plane of the static deformation or perpendicular to this plane, depending upon the parameters of the system. An analysis of this phenomenon is carried out for small nozzle angles by a perturbation method. The results of the analysis are presented in terms of stability boundaries as a function of the system parameters. These results are confirmed qualitatively by means of simple experiments.