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Research Papers: Flows in Complex Systems

Unsteady Numerical Simulation of Flow in Draft Tube of a Hydroturbine Operating Under Various Conditions Using a Partially Averaged Navier–Stokes Model

[+] Author and Article Information
Hosein Foroutan

Department of Mechanical
and Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: hosein@psu.edu

Savas Yavuzkurt

Department of Mechanical
and Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: sqy@psu.edu

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received September 20, 2014; final manuscript received January 14, 2015; published online March 4, 2015. Assoc. Editor: Sharath S. Girimaji.

J. Fluids Eng 137(6), 061101 (Mar 04, 2015) (13 pages) Paper No: FE-14-1527; doi: 10.1115/1.4029632 History: Received September 20, 2014

The variable energy demand requires a great flexibility in operating a hydroturbine, which forces the machine to be operated far from its design point. One of the main components of a hydroturbine where undesirable flow phenomena occur under off-design conditions is the draft tube. Using computational fluid dynamics (CFD), the present paper studies the flow in the draft tube of a Francis turbine operating under various conditions. Specifically, four operating points with the same head and different flow rates corresponding to 70%, 91%, 99%, and 110% of the flow rate at the best efficiency point (BEP) are considered. Unsteady numerical simulations are performed using a recently developed partially averaged Navier–Stokes (PANS) turbulence model, and the results are compared to the available experimental data, as well as the numerical results of the traditionally used Reynolds-Averaged Navier–Stokes (RANS) models. Several parameters including the pressure recovery coefficient, mean velocity, and time-averaged and fluctuating wall pressure are investigated. It is shown that RANS and PANS both can predict the flow behavior close to the BEP operating condition. However, RANS results deviate considerably from the experimental data as the operating condition moves away from the BEP. The pressure recovery factor predicted by the RANS model shows more than 13% and 58% overprediction when the flow rate decreases to 91% and 70% of the flow rate at BEP, respectively. Predictions can be improved significantly using the present unsteady PANS simulations. Specifically, the pressure recovery factor is predicted by less than 4% and 6% deviation for these two operating conditions. A similar conclusion is reached from the analysis of the mean velocity and wall pressure data. Using unsteady PANS simulations, several transient features of the draft tube flow including the vortex rope and associated pressure fluctuations are successfully modeled. The formation of the vortex rope in partial load conditions results in severe pressure fluctuations exerting oscillatory forces on the draft tube. These pressure fluctuations are studied for several locations in the draft tube and the critical region with highest fluctuation amplitude is found to be the inner side of the elbow.

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Figures

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Fig. 1

Head losses of individual components of a hydropower plant normalized by the runner head loss at the BEP. Data source: Vu et al. [3].

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Fig. 2

Sketch of the scaled model Francis turbine and the FLINDT draft tube. Reproduced from Ref. [20]

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Fig. 3

Three-dimensional view of the regenerated FLINDT draft tube showing the components of a draft tube, and right and left channels

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Fig. 4

Side view of the regenerated FLINDT draft tube showing the investigated sections and points where unsteady pressure in monitored in this study

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Fig. 5

Velocity profiles at the inlet section of the computational domain (section S1 in Fig. 4 for cases A–C and section S0 in Fig. 4 for case D), (a) axial velocity profiles for cases A–C, (b) circumferential velocity profiles for cases A–C, (c) axial, radial, and circumferential velocity profiles for case D. Cases A–D correspond to 110%, 99%, 91%, and 70% of the flow rate at the BEP, respectively.

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Fig. 6

Radial distributions of time-averaged (a) axial and (b) circumferential velocity on section S2 for case A, comparison of (•) experimental data, (----) the present PANS model, (- - - -) the k-ε RANS model

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Fig. 7

Radial distributions of time-averaged (a) axial and (b) circumferential velocity on section S2 for case B, comparison of (•) experimental data, (----) the present PANS model, (- - - -) the k-ε RANS model

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Fig. 8

Radial distributions of time-averaged (a) axial and (b) circumferential velocity on section S2 for case C, comparison of (•) experimental data, (----) the present PANS model, (- - - -) the k-ε RANS model

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Fig. 9

Radial distributions of time-averaged (a) axial velocity on section S1, (b) circumferential velocity on section S1, (c) axial velocity on section S2, and (d) circumferential velocity on section S2 for case D, comparison of (•) experimental data, (----) the present PANS model, (- - - -) the k-ε RANS model

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Fig. 10

Locations of pressure transducers at four sections (see Fig. 4) in the draft tube where wall pressure is measured in experiments [7,23]

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Fig. 11

Distributions of wall pressure in the draft tube for four sections (see Figs. 4 and 10 for locations of these sections and the monitored points) for cases A–C, comparison of (•) experimental data, (----) the present PANS model, (- - - -) the k-ε RANS model [7]

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Fig. 12

Contours of instantaneous (top row) and time-averaged (bottom row) of axial velocity in the draft tube obtained by PANS simulations

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Fig. 13

Vortex rope in case D visualized by the isopressure surfaces at three instants of time

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Fig. 14

Wall pressure fluctuations monitored on eight points (four points on the inner side and four points on the outer side of the elbow) obtained by PANS unsteady simulations

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Fig. 15

Crack in concrete at the draft tube door for a hydroturbine operated for extended period of time at partial load operating conditions. Source: Ref. [2].

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Fig. 16

The RMS of wall pressure fluctuations in the draft tube for the eight monitored points in Fig. 14

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