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Review Article

Numerical Techniques Applied to Hydraulic Turbines: A Perspective Review

[+] Author and Article Information
Chirag Trivedi

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

Michel J. Cervantes

Professor
Department of Engineering Sciences and Mathematics,
Luleå University of Technology,
Luleå SE-97187, Sweden;
Department of Energy and Process Engineering,
Norwegian University of
Science and Technology,
Trondheim NO-7491, Norway
e-mail: Michel.Cervantes@ltu.se

Ole Gunnar Dahlhaug

Professor
Department of Energy and Process Engineering,
Norwegian University of
Science and Technology,
Trondheim NO-7491, Norway
e-mail: ole.g.dahlhaug@ntnu.no

1Corresponding author.

Manuscript received April 30, 2015; final manuscript received January 22, 2016; published online February 23, 2016. Assoc. Editor: Gianluca Iaccarino.

Appl. Mech. Rev 68(1), 010802 (Feb 23, 2016) (18 pages) Paper No: AMR-15-1051; doi: 10.1115/1.4032681 History: Received April 30, 2015; Revised January 22, 2016

Applications of computational fluid dynamic (CFD) techniques to hydropower have increased rapidly in the last three decades. The majority of the experimental investigations of hydraulic turbines were supported by numerical studies and this has become a standard practice. In the paper, applied numerical techniques and flow modeling approaches to simulate the hydraulic turbines are discussed. Both steady-state and transient operating conditions of the turbines are considered for the review. The steady-state conditions include the best efficiency point (BEP), high load (HL), and part load (PL). The transient conditions include load variation, startup, shutdown, and total load rejection. The performance of the applied numerical models and turbulence modeling with respect to the operating conditions are discussed. The recently developed numerical technique (transient blade row modeling) using the Fourier transformation (FT) method is discussed. This technique allows guide vane and blade passages to be modeled with the pitch ratio other than unity. Numerical modeling and simulation of hydraulic turbines during the transient operating conditions is one of the most challenging tasks because guide vanes' angular movement is time-dependent and mesh should be dynamic/moving. Different approaches applied to simulate the transient conditions and their limitations are discussed. Overall, this review summarizes the role of numerical techniques, advantages, limitations, and upcoming challenges within hydropower.

Copyright © 2016 by ASME
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References

Figures

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Fig. 1

Modulation process between the runner blades and guide vanes of a hydraulic turbine. (Reproduced with permission from Zobeiri et al. [82]. Copyright 2006 by IAHR.)

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Fig. 2

Constant efficiency hill diagram of a high head model Francis turbine [68]. α is the guide vane angular position in degree, nED is the speed factor, and QED is the discharge factor.

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Fig. 3

Comparison of the experimental and numerical hydraulic efficiencies of a model Francis turbine [68]. ηh is the hydraulic efficiency and Q is the discharge in m3 s−1.

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Fig. 4

Comparison of experimental and numerical amplitude of pressure pulsations developed by the RSIs [85]. VL01 corresponds to the location of pressure measurement in the vaneless space (see Ref. [111]); EXP—experimental, ZLES—zonal LES, BG—medium mesh of 12 × 106 nodes, and NG—fine mesh of 14 × 106 nodes. (Reproduced with permission from Jošt et al. [85]. Copyright 2015 by IOP Science.)

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Fig. 5

Pressure variation at the runner downstream of a Kaplan turbine; the oscillations correspond to blade passing frequency; point 29 corresponds to the measurement location below the runner hub [56]

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Fig. 6

Three approaches of a turbine passage modeling. Left-hand side figure shows stay vane, guide vane, blade and splitter, and draft tube [43]. Middle figure shows a complete spiral casing, guide vanes, a blade passage with splitter, and a draft tube. Right-hand side figure shows a blade passage with split, extended runner outlet and a draft tube. (Reproduced with permission from Mössinger et al. [43]. Copyright 2015 by IOP Science.)

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Fig. 7

Axial (left) and radial (right) velocity distribution at the runner outlet during BEP operating condition of a model Francis turbine [43]. G1 corresponds to numerical simulation of a complete Francis turbine. G2 corresponds to numerical simulation with a guide vane passage and a blade passage. G3 correspond to numerical simulation with spiral casing, distributor, a blade passage, and a draft tube. G4 corresponds to numerical simulation with spiral casing, distributor, a blade passage with extended outlet, and a draft tube. c0, cax, and cu are the mean, axial, and tangential velocity, respectively. (Reproduced with permission from Mössinger et al. [43]. Copyright 2015 by IOP Science.)

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Fig. 8

Comparison of k–ω-based SST and SAS-SST turbulence models used to simulate the draft tube flow during PL operation [104]. Runner revolution from 0 to 60 corresponds to k–ω-based SST model and from 61 to 180 corresponds to SAS-SST model; DT11 and DT21 are the numerical monitoring points under PL operating conditions locations. (Reproduced with permission from Nicolle and Cupillard [104]. Copyright 2015 by IOP Science.)

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Fig. 9

Decomposition of the energy spectrum in the solution associated with RANS and LES. (Reproduced with permission from Buntic et al. [70]. Copyright 2005 by Politehnica University of Timisoara, Romania.)

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Fig. 10

Comparison of hydraulic efficiency, head, and torque at the BEP, PL, and HL operating conditions; CC—commercial code, OF—open foam, Exp—experimental, and Exp. corr—experimental data with correction factor [102]. (Reproduced with permission from Amstutz et al. [102]. Copyright 2015 by IOP Science.)

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Fig. 11

Head oscillations over the operating range of a Francis turbine; Δγ corresponds to guide vane opening, H is the head. (Reproduced with permission from Magnoli [116]. Copyright 2014 by Marcelo Vinicius Magnoli.)

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Fig. 12

Amplitude of pressure pulsations in a model Francis turbine [68]. Left-hand side figure indicates the amplitude observed at BEP. Right-hand side figure indicates the amplitude observed at HL (full-load instability region). VL01, P42, S51, and P71 are the locations of pressure sensors at vaneless space, blade pressure side, suction side, and trailing edge, respectively. DT11 and DT21 are the sensors located on the wall of the draft tube cone. The frequency is normalized by the runner angular speed.

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Fig. 13

Comparisons of head, discharge, torque, and hydraulic efficiency of a model Francis turbine at PL operating condition [85]. Dark color bar indicates the difference with flow leakage losses based on labyrinth seal modeling. (Reproduced with permission from Jošt et al. [85]. Copyright 2015 by IOP Science.)

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Fig. 14

Unsteady pressure variation in the vaneless space (VL01) during PL conditions of a model Francis turbine [68]; t is the time in seconds, n is the runner angular speed in revolution per second, and p̃E is the ratio of absolute amplitude in kPa and density times specific hydraulic energy at the BEP

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Fig. 15

Comparison of flow modeling approaches applied to a Francis turbine. Left-hand side configuration used for Fourier transform, middle configuration used for PT, and right side configuration shows complete turbine [104]. (Reproduced with permission from Nicolle and Cupillard [104]. Copyright 2015 by IOP Science.)

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Fig. 16

Variation of the blade and splitter torque in a model Francis turbine at BEP operating condition. PT—profile transform, FT—Fourier transform, and 360—complete turbine modeling [104]. (Reproduced with permission from Nicolle and Cupillard [104]. Copyright 2015 by IOP Science.)

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Fig. 17

Closing of the radial flow turbine distributor vanes during load variation and the corresponding change of mesh. Mesh at 88%, 70%, and 30% opening represents the vane position at HL, BEP, and PL during turbine shutdown, respectively.

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Fig. 18

Comparison of blade loading during Francis turbine startup [146]. (Reproduced with permission from Nicolle et al. [146]. Copyright 2014 by IOP Science.)

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