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.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Dörfler, P., Sick, M., and Coutu, A., 2013, Flow-Induced Pulsation and Vibration in Hydroelectric Machinery, Springer, London, Chap. 2.
Sick, M., Dörfler, P., Michler, W., Salllaberger, M., and Lohmberg, A., 2004, “Investigation of the Draft Tube Vortex in a Pump-Turbine,” 22nd IAHR Symposium on Hydraulic Machinery and Systems, Stockholm, Sweden, June 22–July 2.
Ciocan, G. D., Iliescu, M. S., Vu, T. C., Nennemann, B., and Avellan, F., 2007, “Experimental Study and Numerical Simulation of the FLINDT Draft Tube Rotating Vortex,” ASME J. Fluids Eng., 129(2), pp. 146–158. [CrossRef]
Zhang, R. K., Mao, F., Wu, J. Z., Chen, S. Y., Wu, Y. L., and Liu, S. H., 2009, “Characteristics and Control of the Draft-Tube Flow in Part-Load Francis Turbine,” ASME J. Fluids Eng., 131(2), p. 021101. [CrossRef]
Vu, T. C., Devals, C., Zhang, Y., Nennemann, B., and Guibault, F., 2011, “Steady and Unsteady Flow Computation in an Elbow Draft Tube With Experimental Validation,” Int. J. Fluid Mach. Syst., 4(1), pp. 85–96. [CrossRef]
Sick, M., Michler, W., Weiss, T., and Keck, H., 2009, “Recent Developments in the Dynamic Analysis of Water Turbines,” Proc. Inst. Mech. Eng. Part A: J. Power Energy, 223(4), pp. 415–427. [CrossRef]
Yaras, M. I., and Grosvernor, A. D., 2003, “Evaluation of One- and Two-Equation Low-Re Turbulence Models. Part I—Axisymmetric Separating and Swirling Flow,” Int. J. Numer. Methods Fluids, 42(12), pp. 1293–1319. [CrossRef]
Dhiman, S., Foroutan, H., and Yavuzkurt, S., 2011, “Simulation of Flow Through Conical Diffusers With and Without Inlet Swirl Using CFD,” ASME-JSME-KSME Joint Fluids Engineering Conference, Hamamatsu, Japan, July 24–29, ASME Paper No. AJK2011-03005. [CrossRef]
Ruprecht, A., Helmrich, T., Aschenbrenner, T., and Scherer, T., 2002, “Simulation of Vortex Rope in a Turbine Draft Tube,” 21st IAHR Symposium on Hydraulic Machinery and Systems, Lausanne, Switzerland, September 9–12.
Guo, Y., Kato, C., and Miyagawa, K., 2006, “Large-Eddy Simulation of Non-Cavitating and Cavitating Flows in an Elbow Draft Tube,” 23rd IAHR Symposium on Hydraulic Machinery and Systems, Yokohama, Japan, October 17–21, Paper No. 95.
Paik, J., Sotiropoulos, F., and Sale, M., 2005, “Numerical Simulation of Swirling Flow in Complex Hydroturbine Draft Tube Using Unsteady Statistical Turbulence Models,” J. Hydraulic Eng., 131(6), pp. 441–456. [CrossRef]
Avellan, F., 2000, “Flow Investigation in a Francis Draft Tube: The FLINDT Project,” 20th IAHR Symposium on Hydraulic Machinery and Systems, Charlotte, NC, August 6–9.
Iliescu, M., Ciocan, G. D., and Avellan, F., 2008, “Analysis of the Cavitating Draft Tube Vortex in a Francis Turbine Using Particle Image Velocimetry Measurements in Two-Phase Flow,” ASME J. Fluids Eng., 130(2), p. 021105. [CrossRef]
Susan-Resiga, R., Muntean, S., Hasmatsuchi, V., Anton, I., and Avellan, F., 2010, “Analysis and Prevention of Vortex Breakdown in the Simplified Discharge Cone of a Francis Turbine,” ASME J. Fluids Eng., 132(5), p. 051102. [CrossRef]
Rudolf, P., 2009, “Connection Between Inlet Velocity Field and Diffuser Flow Instability,” Appl. Comput. Mech., 3, pp. 177–184.
Mauri, S., 2002, “Numerical Simulation and Flow Analysis of an Elbow Diffuser,” Ph.D. thesis, EPFL, Lausanne, Switzerland.
Wilcox, D. C., 2006, Turbulence Modeling for CFD, DCW Industries, La Canada, CA.
Hanjalic, K., 2004, “Closure Models for Incompressible Turbulent Flows” (VKI Lecture Series 2004/2005), von Kármán Institute, Rhode-St-Genese, Belgium.
Launder, B. E., and Spalding, D. B., 1972, Lectures in Mathematical Models of Turbulence, Academic, London.
Shih, T. H., Liou, W. W., Shabbir, A., Yang, Z., and Zhu, J., 1995, “A New k-ε Eddy Viscosity Model for High Reynolds Number Turbulent Flows,” Comput. Fluids, 24(3), pp. 227–238. [CrossRef]
Menter, F. R., 1994, “Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications,” AIAA J., 32(8), pp. 1598–1605. [CrossRef]
Menter, F. R., Kuntz, M., and Langtry, R., 2003, “Ten Years of Industrial Experience With the SST Turbulence Model,” Turbulence, Heat and Mass Transfer, Vol. 4, K.Hanjalic, Y.Nagano, and M. Tummers, eds., Begell House, Redding, CT.
Kalitzin, G., Medic, G., Iaccarino, G., and Durbin, P., 2005, “Near-Wall Behavior of RANS Turbulence Models and Implications for Wall Functions,” J. Comput. Phys., 204, pp. 265–291. [CrossRef]
Nishi, M., Matsunaga, S., Kubota, T., and Senoo, Y., 1982, “Flow Regimes in an Elbow-Type Draft Tube,” 11th IAHR Symposium on Hydraulic Machinery and Systems, Amsterdam, Netherlands, September 13–17.
Cervantes, M. J., Engström, T. F., and Gustavsson, L. H., 2005, “Turbine-99 III: Proceedings of the 3rd IAHR/ERCOFTAC Workshop on Draft Tube Flows,” Porjus, Sweden, December 8–9.
Vu, T. C., Koller, M., Gauthier, M., and Deschenes, C., 2010, “Flow Simulation and Efficiency Hill Chart Prediction for a Propeller Turbine,” 25th IAHR Symposium on Hydraulic Machinery and Systems, Timisoara, Romania, September 20–24.
“OpenFOAM: The Open Source Computational Fluid Dynamics (CFD) Toolbox,” 2004, Silicon Graphics International Corp., http://www.openfoam.com
ANSYS, 2010, ANSYS FLUENT 13.0 User's Guide, Ansys Inc., Canonsburg, PA.
Jacob, T., 1993, “Evaluation sur Modèle Réduit et Prédiction de la Stabilité de Fonctionnement des Turbines Francis,” Ph.D. thesis, EPFL, Lausanne, Switzerland.
Nishi, M., and Liu, S. H., 2012, “An Outlook on the Draft-Tube-Surge Study,” 26th IAHR Symposium on Hydraulic Machinery and Systems, Beijing, China, August 19–23.


Grahic Jump Location
Fig. 1

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

Grahic Jump Location
Fig. 2

Velocity profiles at the inlet section of the computational domain

Grahic Jump Location
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)

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
Fig. 7

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

Grahic Jump Location
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]

Grahic Jump Location
Fig. 9

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

Grahic Jump Location
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




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In