Research Papers: Gas Turbines: Turbomachinery

Compressible Large Eddy Simulation of a Francis Turbine During Speed-No-Load: Rotor Stator Interaction and Inception of a Vortical Flow

[+] Author and Article Information
Chirag Trivedi

Waterpower Laboratory,
Faculty of Engineering,
Department of Energy and Process Engineering,
NTNU—Norwegian University of
Science and Technology,
Trondheim 7491, Norway
e-mail: chirag.trivedi@ntnu.no

Contributed by the Turbomachinery Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received July 17, 2017; final manuscript received January 18, 2018; published online June 27, 2018. Assoc. Editor: Riccardo Da Soghe.

J. Eng. Gas Turbines Power 140(11), 112601 (Jun 27, 2018) (18 pages) Paper No: GTP-17-1369; doi: 10.1115/1.4039423 History: Received July 17, 2017; Revised January 18, 2018

This work investigates the unsteady pressure fluctuations and inception of vortical flow in a hydraulic turbine during speed-no-load conditions. At speed-no-load (SNL), the available hydraulic energy dissipates to the blades without producing an effective torque. This results in high-amplitude pressure loading and fatigue development, which take a toll on a machine's operating life. The focus of the present study is to experimentally measure and numerically characterize time-dependent pressure amplitudes in the vaneless space, runner and draft tube of a model Francis turbine. To this end, ten pressure sensors, including four miniature sensors mounted in the runner, were integrated into a turbine. The numerical model consists of the entire turbine including Labyrinth seals. Compressible flow was considered for the numerical study to account for the effect of flow compressibility and the reflection of pressure waves. The results clearly showed that the vortical flow in the blade passages induces high-amplitude stochastic fluctuations. A distinct flow pattern in the turbine runner was found. The flow near the blade suction side close to the crown was more chaotic and reversible (pumping), whereas the flow on the blade pressure side close to the band was accelerating (turbine) and directed toward the outlet. Flow separation from the blade leading edge created a vortical flow, which broke up into four parts as it traveled further downstream and created high-energy turbulent eddies. The source of reversible flow was found at the draft tube elbow, where the flow in the center core region moves toward the runner cone. The vortical region located at the inner radius of the elbow gives momentum to the wall-attached flow and is pushed toward the outlet, whereas the flow at the outer radius is pushed toward the runner. The cycle repeats at a frequency of 22.3 Hz, which is four times the runner rotational speed.

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Fig. 2

Locations of pressure sensors in the turbine. Sensors R1, R2, R3, and R4 are in the runner; DT1, DT2, DT3, and DT4 are in the draft tube cone; and VL1 and VL2 are in the vaneless space.

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Fig. 1

Open-loop hydraulic system of the model Francis turbine at the Waterpower Laboratory, NTNU: 1—feed pump, 2—overhead tank-primary, 3—overhead tank-secondary, 4—pressure tank, 5—magnetic flowmeter, 6—generator, 7—Francis turbine, 8—downstream tank, and 9—basement

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Fig. 3

Hexahedral mesh (medium type) in the model Francis turbine with Labyrinth seals: 1—blade leading edge, 2—crown Labyrinth seal, and 3—band Labyrinth seal

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Fig. 4

Computational domain of a Francis turbine considered for the numerical simulations. The Labyrinth seals are not shown.

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Fig. 11

Pressure and velocity in the vaneless space for an instantaneos position of the runner. The contours correspond to midspan. Radii r1 and r2 indicate at the runner inlet and guide vane trailing edge locations, respectively.

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Fig. 12

Unsteady pressure fluctuations with respect to runner angular movement (left) and frequency spectra (right) at R1, R2, R3, and R4 locations and comparison with LES

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Fig. 13

Velocity (magnitude) contours of unsteady flow in the runner at an instantaneous time. Contours are at midspan of the runner. Velocity contours are in rotating frame of reference and the velocity unit is m s−1.

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Fig. 14

Inception of vortical flow in the blade passage and blockade near the blade trailing edge. Contours are at midspan of the runner and are in rotating frame of reference. (a) 0 deg, (b) 6 deg, (c) 12 deg, (d) 18 deg, (e) 24 deg, and (e) 30 deg.

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Fig. 15

Velocity contour near the blade pressure and suction sides. Contours are created at a normal distance of 2 mm from the no-slip wall of the blade.

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Fig. 16

Unsteady pressure fluctuations and frequency spectrum at DT1 location in the draft tube cone. The frequencies are normalized by runner rotational speed 5.5 Hz.

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Fig. 17

Pressure contour in the draft tube cone at NLS. The right side of figure shows pressure variation along a line S1 passing from DT1 to DT2 and a line S2 passing from DT3 to DT4.

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Fig. 18

Velocity contour in the draft tube cone at NLS. The right side figure shows circumferential, axial, and radial velocity along the lines S1 and S2. Contours of circumferential, axial, and radial velocity correspond to section plane at S1.

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Fig. 19

Factor of pressure fluctuations in the crown and band Labyrinth seal at NLS. L1 are the numerical monitoring points located in the narrow gap near the vaneelss space and in the comb section, respectively.

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Fig. 20

Velocity contour in the crown Labyrinth seal at NLS. L1 and L2 are numerical monitoring points.

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Fig. 5

A systematic convergence of the pressure data in the Francis turbine. Meshes m1, m2, m3, and m4 correspond to 4.85, 9.32, 18.5, and 36.88 ×106 nodes, respectively.

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Fig. 6

Validation error (êv) at the pressure sensor locations for the SST, SAS, and LES modeling approaches

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Fig. 7

Turbulent structures in the runner (iso-surface of Q = Cq(Ω2-S2)), where Q = 1.46 × 104 s−2. The scale indicates the eddy viscosity ratio (R = μt).

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Fig. 8

Comparison of experimental and numerical pressure variation in the vaneless space (VL1) during NLS. The pressure and amplitudes are normalized using Eq. (16). The frequency is normalized with the runner rotational speed and fb is the blade passing frequency.

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Fig. 9

Blade and guide vane interaction sequence in the Francis turbine and the propagation of the pressure waves from the interaction point

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Fig. 10

Guide vane trailing edge wake and vortex shedding for different angular position of the runner. The left figure shows normalized velocity along a radial line (showed in red color) from the guide vane wall (radii = 0) to the runner inlet (radii = 1). Velocity (v*) is computed using Eq. (19). The right figure shows velocity contours at the guide vane trailing edge for 0 deg, 4 deg, 8 deg, and 12 deg angular position the blade; where 0 deg indicates that the reference blade is aligned with the guide vane trailing edge.

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Fig. 21

Wall shear stress in the crown Labyrinth seal at NLS. Wall shear stress is in Pa.

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Fig. 22

Velocity contour in the band Labyrinth seal at NLS. L2 is the numerical monitoring point.




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