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Article

Investigation of the Time Resolution Set Up Used to Compute the Full Load Vortex Rope in a Francis Turbine

1
Institute of Sustainable Energy, School of Engineering, HES-SO Valais-Wallis, Rawil 47, 1950 Sion, Switzerland
2
Laboratory for Hydraulic Machines Ecole Polytechnique Fédérale de Lausanne, Avenue de Cour 33 bis, 1007 Lausanne, Switzerland
3
Waseda Research Institute for Science and Engineering, Waseda University, Tokyo 169-8555, Japan
4
Institute of Sustainable Energy and Institute of Systems Engineering, School of Engineering, HES-SO Valais-Wallis, Rawil 47, 1950 Sion, Switzerland
*
Author to whom correspondence should be addressed.
Academic Editor: Florent Ravelet
Appl. Sci. 2021, 11(3), 1168; https://doi.org/10.3390/app11031168
Received: 2 December 2020 / Revised: 20 January 2021 / Accepted: 20 January 2021 / Published: 27 January 2021
(This article belongs to the Special Issue New Advances of Cavitation Instabilities)
The flow in a Francis turbine at full load is characterised by the development of an axial vortex rope in the draft tube. The vortex rope often promotes cavitation if the turbine is operated at a sufficiently low Thoma number. Furthermore, the vortex rope can evolve from a stable to an unstable behaviour. For CFD, such a flow is a challenge since it requires solving an unsteady cavitating flow including rotor/stator interfaces. Usually, the numerical investigations focus on the cavitation model or the turbulence model. In the present works, attention is paid to the strategy used for the time integration. The vortex rope considered is an unstable cavitating one that develops downstream the runner. The vortex rope shows a periodic behaviour characterized by the development of the vortex rope followed by a strong collapse leading to the shedding of bubbles from the runner area. Three unsteady RANS simulations are performed using the ANSYS CFX 17.2 software. The turbulence and cavitation models are, respectively, the SST and Zwart models. Regarding the time integration, a second order backward scheme is used excepted for the transport equation for the liquid volume fraction, for which a first order backward scheme is used. The simulations differ by the time step and the number of internal loops per time step. One simulation is carried out with a time step equal to one degree of revolution per time step and five internal loops. A second simulation used the same time step but 15 internal loops. The third simulations used three internal loops and an adaptive time step computed based on a maximum CFL lower than 2. The results show an influence of the time integration strategy on the cavitation volume time history both in the runner and in the draft tube with a risk of divergence of the solution if a standard set up is used. View Full-Text
Keywords: vortex rope; Francis turbine; cavitation; CFD; RANS vortex rope; Francis turbine; cavitation; CFD; RANS
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MDPI and ACS Style

Decaix, J.; Müller, A.; Favrel, A.; Avellan, F.; Münch-Alligné, C. Investigation of the Time Resolution Set Up Used to Compute the Full Load Vortex Rope in a Francis Turbine. Appl. Sci. 2021, 11, 1168. https://doi.org/10.3390/app11031168

AMA Style

Decaix J, Müller A, Favrel A, Avellan F, Münch-Alligné C. Investigation of the Time Resolution Set Up Used to Compute the Full Load Vortex Rope in a Francis Turbine. Applied Sciences. 2021; 11(3):1168. https://doi.org/10.3390/app11031168

Chicago/Turabian Style

Decaix, Jean, Andres Müller, Arthur Favrel, François Avellan, and Cécile Münch-Alligné. 2021. "Investigation of the Time Resolution Set Up Used to Compute the Full Load Vortex Rope in a Francis Turbine" Applied Sciences 11, no. 3: 1168. https://doi.org/10.3390/app11031168

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