Measurement of the Self-Oscillating Vortex Rope Dynamics for Hydroacoustic Stability Analysis

Flow instabilities in hydraulic machines often feature oscillating cavitation volumes, which locally introduce compliance and mass flow gain effects. These unsteady characteristics play a crucial role in one-dimensional stability models and can be determined through the definition of transfer functions for the state variables, where the cavitation volume is commonly estimated from the discharge difference between two points located upstream and downstream of the cavity. This approach is demonstrated on a test rig with a microturbine, featuring a self-oscillating vortex rope in its conical draft tube. The fluctuating discharges at the turbine inlet and the draft tube outlet are determined with the pressure-time method using differential pressure transducers. The cavitation volume is then calculated by integrating the corresponding discharge difference over time. In order to validate the results, an alternative volume approximation method is presented, based on the image processing of a high-speed flow visualization. In this procedure, the edges of the vortex rope are detected to calculate the local cross section areas of the cavity. It is shown that the cavitation volumes obtained by the two methods are in good agreement. Thus, the fluctuating part of the cavitation volume oscillation can be accurately estimated by integrating the difference between the volumetric upstream and downstream discharges. Finally, the volume and discharge fluctuations from the pressure-time method are averaged over one mean period of the pressure oscillation. This enables an analysis of the key physical flow parameters' behavior over one characteristic period of the instability and a discussion of its sustaining mechanisms.