The mitigation of the precessing vortex core developing in the draft tube of Francis turbines operating under part load conditions is crucial to increase the operation flexibility of these hydraulic machines to balance the massive power production of intermittent energy sources. A systematic approach following the optimal control theory is, therefore, presented to control this vortical flow structure. Modal analysis characterizes the part load vortex rope as a self-sustained instability associated with an unstable eigenmode. Based on this physical characteristic, an objective function targeting a zero value of the unstable eigenvalue growth rate is defined and subsequently minimized using an adjoint-based optimization algorithm. We determine an optimal force distribution that successfully quenches the part load vortex rope and sketches the design of a realistic control appendage.
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August 2019
Research-Article
Optimal Control of Part Load Vortex Rope in Francis Turbines
Simon Pasche,
Simon Pasche
Laboratory for Hydraulic Machines,
Department of Mechanical Engineering,
Swiss Federal Institute of Technology (EPFL),
Avenue de Cour 33bis,
Lausanne CH-1007, Switzerland
e-mail: simon.pasche@alumni.epfl.ch
Department of Mechanical Engineering,
Swiss Federal Institute of Technology (EPFL),
Avenue de Cour 33bis,
Lausanne CH-1007, Switzerland
e-mail: simon.pasche@alumni.epfl.ch
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François Avellan,
François Avellan
Professor
Laboratory for Hydraulic Machines,
Department of Mechanical Engineering,
Swiss Federal Institute of Technology (EPFL),
Avenue de Cour 33bis,
Lausanne CH-1007, Switzerland
e-mail: francois.avellan@epfl.ch
Laboratory for Hydraulic Machines,
Department of Mechanical Engineering,
Swiss Federal Institute of Technology (EPFL),
Avenue de Cour 33bis,
Lausanne CH-1007, Switzerland
e-mail: francois.avellan@epfl.ch
Search for other works by this author on:
François Gallaire
François Gallaire
Professor
Laboratory of Fluid Mechanics and Instabilities,
Department of Mechanical Engineering,
Swiss Federal Institute of Technology (EPFL),
Lausanne CH-1015, Switzerland
e-mail: francois.gallaire@epfl.ch
Laboratory of Fluid Mechanics and Instabilities,
Department of Mechanical Engineering,
Swiss Federal Institute of Technology (EPFL),
Lausanne CH-1015, Switzerland
e-mail: francois.gallaire@epfl.ch
Search for other works by this author on:
Simon Pasche
Laboratory for Hydraulic Machines,
Department of Mechanical Engineering,
Swiss Federal Institute of Technology (EPFL),
Avenue de Cour 33bis,
Lausanne CH-1007, Switzerland
e-mail: simon.pasche@alumni.epfl.ch
Department of Mechanical Engineering,
Swiss Federal Institute of Technology (EPFL),
Avenue de Cour 33bis,
Lausanne CH-1007, Switzerland
e-mail: simon.pasche@alumni.epfl.ch
François Avellan
Professor
Laboratory for Hydraulic Machines,
Department of Mechanical Engineering,
Swiss Federal Institute of Technology (EPFL),
Avenue de Cour 33bis,
Lausanne CH-1007, Switzerland
e-mail: francois.avellan@epfl.ch
Laboratory for Hydraulic Machines,
Department of Mechanical Engineering,
Swiss Federal Institute of Technology (EPFL),
Avenue de Cour 33bis,
Lausanne CH-1007, Switzerland
e-mail: francois.avellan@epfl.ch
François Gallaire
Professor
Laboratory of Fluid Mechanics and Instabilities,
Department of Mechanical Engineering,
Swiss Federal Institute of Technology (EPFL),
Lausanne CH-1015, Switzerland
e-mail: francois.gallaire@epfl.ch
Laboratory of Fluid Mechanics and Instabilities,
Department of Mechanical Engineering,
Swiss Federal Institute of Technology (EPFL),
Lausanne CH-1015, Switzerland
e-mail: francois.gallaire@epfl.ch
Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received June 20, 2018; final manuscript received January 9, 2019; published online February 13, 2019. Assoc. Editor: Matevz Dular.
J. Fluids Eng. Aug 2019, 141(8): 081203 (12 pages)
Published Online: February 13, 2019
Article history
Received:
June 20, 2018
Revised:
January 9, 2019
Citation
Pasche, S., Avellan, F., and Gallaire, F. (February 13, 2019). "Optimal Control of Part Load Vortex Rope in Francis Turbines." ASME. J. Fluids Eng. August 2019; 141(8): 081203. https://doi.org/10.1115/1.4042560
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