Self-excited oscillations in collapsible tubes

Collapsible tubes are very important because they can be used to study a lot of biological structures, such as human blood vessels and trachea. They are usually simplified with the “Starling resistor model”, that consists of a collapsible tube clamped between two rigid supports and inserted in a room that can be pressurized. Internally there is a flow rate. Under certain circumstances, they can generate self-excited oscillations, where the shape of the tube and the fluid dynamics variables are changing cyclically. In the experimental setup there was a flow loop driven by a centrifugal pump. Two constant level reservoir, kept at different height, ensured to have flow rate inside the collapsible tube, that was located inside a pressurized chamber filled with fluid. The flow rate could be adjusted with two resistances located upstream and downstream of the tube. The flow rate was measured with a flow meter and the pressure of the chamber, the ones just upstream and the one just downstream of the tube were measured with pressure transducers. Two optical techniques were used: Stereo Motion Tracking allowed the reconstruction of the 3D shape of the tube, and Particle Image Velocimetry was implemented to study the flow field just downstream of the tube. The working fluid was a mixture of water, glycerin (used to increase the viscosity and to match the refractive index of the pipes) and rhodamine spheres (for the PIV). Two sets of experiments were carried out: while in the first one the upstream resistance was kept constant and the external pressure was increased, in the second one the difference between the pressure inside of the collapsible tube and the external one was constant, and the Reynolds number was increased. In the first case of the first set, the external pressure was too low to create a collapse of the tube. The tube was completely open and the flow inside of it was laminar. The results obtained from PIV were used to validate the experimental setup. In the second case considered, the external pressure was increased, and self-excited oscillations appeared. The downstream pressure oscillated as expected and the collapse of the tube was moving back and forth with a constant frequency. The flowfield shifted cyclically between laminar flow and high vorticity flow. In the last case considered, the tube was completely collapsed and the collapse was located in the downstream end of the tube. Even if the shape of the tube was steady, PIV results revealed that the flow filed was not steady but chaotic: there were not dominant frequencies. Considering the second set of experiments, when the Reynolds number was too low the tube was completely collapsed. The collapse was larger than in the first set of cases studied, the flow field was laminar and steady. When the Reynolds number was increased, self-excited oscillations occurred with a cycle that was similar to the oscillating one already studied. Also, the collapsed region of the tube was bigger than in the first set of experiments. The most important conclusions are that Reynolds number apparently is not the right non dimensional parameter to predict the onset of oscillations; moreover, oscillations of the flow field inside the collapsible tube can persist also when the tube in not oscillating any more. In addition, during the self-excited oscillations, the location of the collapse and the properties of the flow field inside of the tube are strictly related.