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Research Papers: Flows in Complex Systems

Investigations of Compressible Turbulent Flow in a High-Head Francis Turbine

[+] Author and Article Information
Chirag Trivedi

Mem. ASME
Waterpower Laboratory,
Department of Energy and Process Engineering,
Norwegian University of Science and
Technology (NTNU),
Trondheim NO-7491, Norway
e-mail: chirag.trivedi@ntnu.no

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received January 15, 2017; final manuscript received July 18, 2017; published online September 20, 2017. Assoc. Editor: Bart van Esch.

J. Fluids Eng 140(1), 011101 (Sep 20, 2017) (17 pages) Paper No: FE-17-1035; doi: 10.1115/1.4037500 History: Received January 15, 2017; Revised July 18, 2017

Dynamic stability of the high-head Francis turbines is one of the challenging problems. Unsteady rotor–stator interaction (RSI) develops dynamic stresses and leads to crack in the blades. In a high-head turbine, vaneless space is small and the amplitudes of RSI frequencies are very high. Credible estimation of the amplitudes is vital for the runner design. The current study is aimed to investigate the amplitudes of RSI frequencies considering a compressible flow. The hydro-acoustic phenomenon is dominating the turbines, and the compressibility effect should be accounted for accurate estimation of the pressure amplitudes. Unsteady pressure measurements were performed in the turbine during the best efficiency point (BEP) and part load (PL) operations. The pressure data were used to validate the numerical model. The compressible flow simulations showed 0.5–3% improvement in the time-averaged pressure and the amplitudes over incompressible flow. The maximum numerical errors in the vaneless space and runner were 6% and 10%, respectively. Numerical errors in the instantaneous pressure amplitudes at the vaneless space, runner, and draft tube were ±1.6%, ±0.9%, and ±1.8%, respectively. In the draft tube, the incompressible flow study showed the pressure amplitudes up to eight times smaller than those of the compressible. Unexpectedly, the strong effect of RSI was seen in the upper and lower labyrinth seals, which was absent for the incompressible flow.

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Figures

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Fig. 1

An open loop hydraulic system in the Waterpower Laboratory, NTNU: (1) feed pump (2) overhead tank—primary, (3) overhead tank—secondary, (4) pressure tank, (5) magnetic flowmeter, (6) induction generator, (7) Francis turbine, (8) suction tank, and (9) basement

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Fig. 2

Locations of pressure sensors in the model Francis 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. 3

Constant efficiency hill diagram of the investigated model Francis turbine. QED and nED are the dimensionless quantities of discharge and speed, respectively. nED = 0.18 is the synchronous speed of the turbine.

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Fig. 4

Hexahedral mesh of the model Francis turbine with labyrinth seals: (1) blade leading edge, (2) upper (crown) labyrinth, and (3) lower (band) labyrinth

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Fig. 5

Maximum y+ value in the runner and guide passages at BEP. Mark with a circle indicates the maximum y+ value.

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Fig. 6

A systematic convergence of the hexahedral mesh in the computational domains of the model Francis turbine. Error bars show relative error with respect to the experimental values, and mext is the extrapolated value computed using GCI method.

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Fig. 7

Relative error (time-averaged pressure value) at the different locations in the turbine for BEP and PL. The negative error indicates overprediction of pressure as compared to the experimental value. VL: vaneless space and R: runner.

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Fig. 8

Velocity contours in the GV passages for BEP (top) and PL (bottom). VL1 and VL2 are the pressure sensor locations during the measurements; velocity contours are normalized with the maximum velocity of 11.8 m s−1. Contours correspond to the instantaneous time and runner position. The radial distance from the GV trailing edge to the blade leading edge is 17.6 mm and 20.1 mm for BEP and PL, respectively.

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Fig. 9

Velocity contours in the vaneless space during RSI at PL. SP indicated stagnation point at blade leading edge; 1, 2, and 3 are the regions of swirling flow. Velocity contours are normalized with the maximum velocity of 11.8 m s−1, and the scale is similar to that mentioned in Fig. 8. Contours correspond to the instantaneous time and runner position.

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Fig. 10

Unsteady pressure fluctuations in the vaneless space (VL2) at BEP for two revolutions of the runner. Incompressible and compressible pressure data correspond to the numerical study.

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Fig. 11

Pressure variation in the vaneless space at BEP. The pressure variation corresponds to the blade passing frequency 167 Hz; t1: blade leading edge is facing the sensor/monitoring point, and t2: sensor/monitoring point is between two blades.

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Fig. 12

Spectral analysis of unsteady pressure fluctuations in the vaneless space (VL2) at PL; fb is the blade passing frequency 167 Hz normalized by the runner angular speed 5.54 Hz

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Fig. 13

Amplitudes of the blade passing frequency in a GV passage at BEP. GV1, GV2, GV3, GV4, and GV5 are the numerical monitoring points.

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Fig. 14

Interaction sequence of a blade with a GV in the vaneless space and the wave propagation; t1, t2, and t4 are the time of corresponding interaction. The time between t1 and t2 interaction is 4.29 × 10−4 s, which is equivalent to 0.857 deg angular rotation of the runner in this turbine.

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Fig. 15

Temporal variation of the RSI amplitude in the runner at BEP. Pressure variation corresponds to the GV passing frequency 156 Hz; t1: the GV trailing is facing the sensor/monitoring point; t2: sensor/monitoring point is between two GVs; and Δθ between t1 and t2 is 6.43 deg.

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Fig. 16

Interaction of a GV to the corresponding blade and development of pressure wave, which propagates to the blade passage. Figure (a) shows time (t1) of interaction, figure (b) shows time (t2) when the GV is exactly mid of the blade passage, and figure (c) shows time (t3) of succeeding interaction.

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Fig. 17

Unsteady pressure variation at runner locations R1, R2, R3, and R4 with respect to runner angular movement at BEP

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Fig. 18

Unsteady pressure variation at runner locations R1, R2, R3, and R4 with respect to runner angular movement at PL

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Fig. 19

Amplitudes of GV passing frequency 155 Hz on the blade pressure and suction sides at BEP and PL. Normalized chord length represents the numerical points from the blade leading edge to the trailing edge.

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Fig. 20

Amplitudes of unsteady pressure fluctuations in the runner (R1) during PL; fgv is the GV 155 Hz normalized by the runner angular speed 5.54 Hz

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Fig. 21

Comparison of experimental and numerical pressure fluctuations in the draft tube (DT1) at BEP load

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Fig. 22

Comparison of experimental and numerical pressure fluctuations in the draft tube (DT1) at PL load

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Fig. 23

Amplitudes of unsteady pressure fluctuations in the draft tube at PL

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Fig. 24

Axial velocity contours in draft tube cone at PL; left: simulations with SST turbulence model, and right: simulations with SAS modeling approach. Positive velocity indicates downward direction.

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Fig. 25

Velocity (magnitude) contours in draft tube cone at PL; left: simulations with SST turbulence model, and right: simulations with SAS modeling approach. The contours show the interaction between flow from the labyrinth seal and draft tube vortex rope.

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Fig. 26

Variation of flow velocity during an interaction between the vortex rope and flow from the labyrinth seal as the runner rotates. Points 1, 2, and 3 correspond to the location A in Fig. 25.

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Fig. 27

Velocity contours showing the interaction between the draft tube vortex rope and flow from the labyrinth seal as the runner rotates. A and B are the two opposite sides around vortex rope. The number at the corner of each figure represents runner angular position; 0 deg corresponds to the reference position of the runner. The velocity scale is same as observed in Fig. 25.

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Fig. 28

Two-dimensional view of the upper and lower labyrinth seals in the turbine

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Fig. 29

Velocity contours in the upper (left) and lower (right) labyrinth seals at BEP; Static: stationary wall of the seal, and Rotating: rotating wall of the seal (runner crown/band side)

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Fig. 30

Velocity along a line connected from static to the rotating wall of the upper and lower labyrinth seals. The normalized distance of “0” and 1 corresponds to static and rotating wall, respectively.

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Fig. 31

Amplitudes of RSI pressure fluctuations in the upper and lower labyrinth seals at BEP load

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