The present paper focuses on the vortex rope that arises when operating a model Francis turbine at a part load condition: 65% of the Best Efficiency Point (BEP). The investigation is performed numerically using the Large Eddy Simulation (LES) approach with the Dynamic Smagorinsky Model (DSM). Such approach and turbulence model are implemented in the overset finite element open source code, FrontFlow/blue (FFB). Furthermore, a cavitation model is implemented allowing computations for non-cavitating and cavitating conditions. Thanks to the use of the K supercomputer, located at Kobe in Japan, and to the use of large computational mesh (123 million elements), it is shown that the frequency of the precession of the vortex rope as well as the head can be accurately computed. However, the predicted amplitude of the fluctuation did not fully agree with the experiment. Differences in a particular region near the back side of the elbow are about 35%. A comparison between the variation of the size of the vortex rope and the swirl number has been investigated and showed a clear relation. The location of the vortex rope and the minimum of the pressure were also investigated and showed that they do not fully share the same location. Furthermore, in a preliminary study to the computation of the cavitating vortex rope, computations of the flow around a Clark-11.7% hydrofoil under cavitation condition and for angles of attack of 2° and 8° are carried out. The results showed the common issue for this computation, i.e. the sharp change of the lift and drag coefficients could not be accurately predicted. Currently underway are the computation of the cavitating vortex rope. The effect of the cavitation on the vortex rope will be studied and reported at a later stage.
Numerical investigation of the upper part load vortex rope behaviour in a Francis turbine
