Research Papers: Flows in Complex Systems

Part Load Vortex Rope as a Global Unstable Mode

[+] Author and Article Information
Simon Pasche

Department of Mechanical Engineering,
Laboratory for Hydraulic Machines,
Swiss Federal Institute of Technology (EPFL),
Avenue de Cour 33bis,
Lausanne CH-1007, Switzerland
e-mail: simon.pasche@alumni.epfl.ch

François Avellan

Department of Mechanical Engineering,
Laboratory for Hydraulic Machines,
Swiss Federal Institute of Technology (EPFL),
Avenue de Cour 33bis,
Lausanne CH-1007, Switzerland
e-mail: francois.avellan@epfl.ch

François Gallaire

Department of Mechanical Engineering,
Laboratory of Fluid Mechanics and Instabilities,
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 March 11, 2016; final manuscript received December 22, 2016; published online March 16, 2017. Assoc. Editor: Kwang-Yong Kim.

J. Fluids Eng 139(5), 051102 (Mar 16, 2017) (11 pages) Paper No: FE-16-1160; doi: 10.1115/1.4035640 History: Received March 11, 2016; Revised December 22, 2016

Renewable energy sources (RES) have reached 23.7% of the worldwide electrical generation production in 2015. The hydraulic energy contribution amounts to 16.6% and comes mainly form large-scale hydropower plants, where Francis turbines represents 60% of the generating units. However, the future massive development of RES will require more advanced grid regulation strategies that may be achieved by increasing the operation flexibility of the Francis generating units. Part load operating condition of these turbines is hindered by pressure fluctuations in the draft tube of the machine. A precessing helical vortex rope develops in this condition, which imperils the mechanical structure and limits the operation flexibility of these turbines. A thorough description of the physical mechanism leading to the vortex rope is a prerequisite to develop relevant flow control strategies. This work, based on a linear global stability analysis of the time-averaged flow field, including a turbulent eddy viscosity, interprets the vortex rope as a global unstable eigenmode. In close resemblance to spiral vortex breakdown, a single-helix disturbance develops around the time-averaged flow field and growths in time to finally form the vortex rope. The frequency and the structure of this unstable linear disturbance are found in good agreement with respect to the three-dimensional (3D) numerical flow simulations.

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Grahic Jump Location
Fig. 1

Cross section of the FLINDT geometry with the location of the sections 1.3 and 1.75 and their cross planes where pressure sensors are located

Grahic Jump Location
Fig. 6

Velocity profiles of the time-averaged flow field of the Moody draft tube for different location along the cone, (a) just after the runner, (b) at section 1.3, and (c) between sections 1.3 and 1.75

Grahic Jump Location
Fig. 5

Time-averaged axial velocity field of the vortex rope (a), where the solid black curve is the isocontour CZ¯=0. Zoom on the recirculation region at the tip of the runner cone (b)

Grahic Jump Location
Fig. 4

Vortex rope appearing in the original draft tube (a) and in the Moody draft tube (b) highlighted by the same isopressure, and the corresponding instantaneous axial velocity field on the ZX-cross section

Grahic Jump Location
Fig. 3

Time-averaged velocity profile for the axial and tangential component at the centerline of sections 1.3 (a), (c) and 1.75 (b), (d) for the original and Moody draft tube of the present 3D numerical flow simulations and the LDV measurements [7]

Grahic Jump Location
Fig. 2

Phase-average of the wall pressure signals at sections 1.3 (a) and 1.75 (b) at the sensor 1,2,3, and 4 of the experimental data [6] and the present 3D numerical flow simulation of the original elbow

Grahic Jump Location
Fig. 8

Eigenvalue spectra of the vortex rope for azimuthal wave number (a) m = 0, (b) m = 2, and (c) m = 1 with standard deviation of the eigenvalues with respect to the mean flow resolution, highlighted by error bars

Grahic Jump Location
Fig. 7

Time-averaged turbulent Reynolds number used for the stability analysis

Grahic Jump Location
Fig. 9

Single unstable eigenvalue computed with the spatially varying eddy viscosity (dash line) and variation of the unstable eigenvalue (circle) with respect to the turbulent Reynolds number Ret=140−30,000 when frozen approach is used, the pulsation (a) and the growth rate (b)

Grahic Jump Location
Fig. 10

Three-dimensional reconstruction of the axial velocity field for the unstable eigenmode ω = 0.20 + 1.43i, m = 1 (a) and the 3D axial velocity disturbance from the 3D numerical flow simulation (b)



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