Numerical and experimental analysis of pressure fluctuations in the draft-tube of a Francis turbine using the swirl number

Pressure fluctuations in the draft-tubes of hydraulic turbines are the most dominant issues that may cause damages to a hydraulic power plant. When the frequency of the fluctuations coincides with one natural frequencies of the plant, resonance with high amplitude vibrations and pressure pulsations occurs, dramatically impacting the integrity of the plant. This research focuses on the part-load behaviour of a medium specific-speed Francis turbine (with specific speed 184 m.kW), designed by the authors in the framework of an industrial project. This paper combines the results of model tests with CFD simulation to investigate the part-load behaviour of the turbine. To do so, performance of the turbine is numerically simulated at one operating condition by solving the RANS equations via the commercial code ANSYS CFX 19.0. The k-ω SST turbulence model is used to predict the turbine performance. In addition, model tests are conducted in the range of 20% to 110% guide vane opening. To capture pressure fluctuations in the draft-tube, 12 static pressure sensors are installed in 4 different sections of the draft-tube. The no-swirl and other iso-swirl lines of the draft tube flow are first determined by using CFD results. Furthermore, pressure signals from model tests are analysed by performing cross spectral density analysis. Two transitions in the behaviour of the precessing vortex under part-load conditions occurring at given values of swirl number are observed. Finally, it is observed that linear correlations between the Strouhal number of the vortex rope frequency and the swirl number can be established within the 2nd and 3rd part-load regimes, independently of the values of the speed coefficient.