Research Papers

Flow in the Simplified Draft Tube of a Francis Turbine Operating at Partial Load—Part I: Simulation of the Vortex Rope

[+] Author and Article Information
Hosein Foroutan

Department of Mechanical
and Nuclear Engineering,
The Pennsylvania State University,
338C Reber Building,
University Park, PA 16802
e-mail: hosein@psu.edu

Savas Yavuzkurt

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

1Corresponding author.

Manuscript received October 6, 2013; final manuscript received February 7, 2014; accepted manuscript posted February 12, 2014; published online March 6, 2014. Assoc. Editor: Kenji Takizawa.

J. Appl. Mech 81(6), 061010 (Mar 06, 2014) (8 pages) Paper No: JAM-13-1423; doi: 10.1115/1.4026817 History: Received October 06, 2013; Revised February 07, 2014; Accepted February 12, 2014

Numerical simulations and analysis of the vortex rope formation in a simplified draft tube of a model Francis turbine are carried out in this paper, which is the first part of a two-paper series. The emphasis of this part is on the simulation and investigation of flow using different turbulence closure models. Two part-load operating conditions with same head and different flow rates (91% and 70% of the best efficiency point (BEP) flow rate) are considered. Steady and unsteady simulations are carried out for axisymmetric and three-dimensional grid in a simplified axisymmetric geometry, and results are compared with experimental data. It is seen that steady simulations with Reynolds-averaged Navier–Stokes (RANS) models cannot resolve the vortex rope and give identical symmetric results for both the axisymmetric and three-dimensional flow geometries. These RANS simulations underpredict the axial velocity (by at least 14%) and turbulent kinetic energy (by at least 40%) near the center of the draft tube, even quite close to the design condition. Moving farther from the design point, models fail in predicting the correct levels of the axial velocity in the draft tube. Unsteady simulations are performed using unsteady RANS (URANS) and detached eddy simulation (DES) turbulence closure approaches. URANS models cannot capture the self-induced unsteadiness of the vortex rope and give steady solutions while DES model gives sufficient unsteady results. Using the proper unsteady model, i.e., DES, the overall shape of the vortex rope is correctly predicted and the calculated vortex rope frequency differs only 6% from experimental data. It is confirmed that the vortex rope is formed due to the roll-up of the shear layer at the interface between the low-velocity inner region created by the wake of the crown cone and highly swirling outer flow.

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Fig. 1

(a) FLINDT project draft tube [12], (b) simplified draft tube and 2D axisymmetric computational grid, and (c) 3D computational grid

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Fig. 2

Velocity profiles at the inlet section of the computational domain

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Fig. 3

Streamline patterns for the steady axisymmetric simulation of flow in the draft tube, (a) case I (91% of BEP flow rate), and (b) case II (70% of BEP flow rate)

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Fig. 7

Isopressure surfaces in the draft tube for an instance in time, comparison of results using three different unsteady turbulence closure approaches

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Fig. 8

Vortex rope visualized by isopressure surfaces for (a) case I (91% of the BEP flow rate) and (b) case II (70% of the BEP flow rate) in comparison with experimental visualizations [29]

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Fig. 9

(a) Pressure fluctuations and (b) their normalized frequency spectra for case II

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Fig. 10

Isopressure surface (dark) representing vortex rope and isovelocity surface (light) representing the stagnant region for (a) case I and (b) case II for an instance in time

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Fig. 4

Profiles of (a) axial velocity, (b) circumferential velocity, and (c) turbulent kinetic energy in the draft tube for case I, comparison of results of various turbulence closure models

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Fig. 5

Profiles of (a) axial velocity, and (b) circumferential velocity in the draft tube for case II, comparison of results of various turbulence closure models

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Fig. 6

Profiles of axial velocity for (a) case I and (b) case II in the draft tube, comparison of axisymmetric and three-dimensional simulations



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