International Journal of Fluid Machinery and Systems

Korean Society for Fluid machinery (한국유체기계학회)
권호 표지
DOI QR코드

DOI QR Code

Axisymmetric Swirling Flow Simulation of the Draft Tube Vortex in Francis Turbines at Partial Discharge

  • Susan-Resiga, Romeo (Department of Hydraulic Machinery, "Politehnica" University of Timisoara) ;
  • Muntean, Sebastian (Center for Advanced Research in Engineering Science, Romanian Academy - Timisoara Branch) ;
  • Stein, Peter (VA TECH HYDRO) ;
  • Avellan, Francois (Laboratory for Hydraulic Machines, Ecole Polytechnique Federale de Lausanne)
  • Accepted : 2009.09.20
  • Published : 2009.12.01
Download PDF
⟨ Previous Next ⟩

Abstract

The flow in the draft tube cone of Francis turbines operated at partial discharge is a complex hydrodynamic phenomenon where an incoming steady axisymmetric swirling flow evolves into a three-dimensional unsteady flow field with precessing helical vortex (also called vortex rope) and associated pressure fluctuations. The paper addresses the following fundamental question: is it possible to compute the circumferentially averaged flow field induced by the precessing vortex rope by using an axisymmetric turbulent swirling flow model? In other words, instead of averaging the measured or computed 3D velocity and pressure fields we would like to solve directly the circumferentially averaged governing equations. As a result, one could use a 2D axi-symmetric model instead of the full 3D flow simulation, with huge savings in both computing time and resources. In order to answer this question we first compute the axisymmetric turbulent swirling flow using available solvers by introducing a stagnant region model (SRM), essentially enforcing a unidirectional circumferentially averaged meridian flow as suggested by the experimental data. Numerical results obtained with both models are compared against measured axial and circumferential velocity profiles, as well as for the vortex rope location. Although the circumferentially averaged flow field cannot capture the unsteadiness of the 3D flow, it can be reliably used for further stability analysis, as well as for assessing and optimizing various techniques to stabilize the swirling flow. In particular, the methodology presented and validated in this paper is particularly useful in optimizing the blade design in order to reduce the stagnant region extent, thus mitigating the vortex rope and expending the operating range for Francis turbines.

Keywords

References

  1. Escudier, M., 1987, “Confined Vortices in Flow Machinery,” Annual Review of Fluid Mechanics, Vol. 19, pp. 27-52. https://doi.org/10.1146/annurev.fl.19.010187.000331
  2. 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,” Journal of Fluids Engineering, Vol. 131, 021101-1-13. https://doi.org/10.1115/1.3002318
  3. Susan-Resiga, R., Ciocan, G. D., Anton, I., and Avellan, F., 2006, “Analysis of the Swirling Flow Downstream a Francis Turbine Runner,” Journal of Fluids Engineering, Vol. 128, pp. 177-189. https://doi.org/10.1115/1.2137341
  4. Ruprecht, A., Helmrich, T., Aschenbrenner, T., and Scherer, T., 2002, “Simulation of Vortex Rope in a Turbine Draft Tube”, Proceedings of the 21st IAHR Symposium on Hydraulic Machinery and Systems, Lausanne, Switzerland, Vol. 1, pp. 259-276.
  5. Sick, M., Stein, P., Doerfler, P., White, P., and Braune, A., 2005, “CFD Prediction of the Part-Load Vortex in Francis Turbines and Pump-Turbines,” International Journal of Hydropower and Dams, Vol. 12, No. 85.
  6. Stein, P., Sick, M., Doerfler, P., White, P., and Braune, A., 2006, “Numerical Simulation of the Cavitating Draft Tube Vortex in a Francis Turbine,” Proceedings of the 23rd IAHR Symposium on Hydraulic Machinery and Systems, Yokohama, Japan, paper F228 (on CD-ROM, ISBN 4-8190-1809-4).
  7. 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,” Journal of Fluids Engineering, Vol. 129, pp. 146-158. https://doi.org/10.1115/1.2409332
  8. Susan-Resiga, R., Vu, T. C., Muntean, S., Ciocan, G. D., and Nennemann, B., 2006, “Jet Control of the Draft Tube Vortex Rope in Francis Turbines at Partial Discharge,” Proceedings of the 23rd IAHR Symposium on Hydraulic Machinery and Systems, Yokohama, Japan, paper F192 (on CD-ROM, ISBN 4-8190-1809-4).
  9. Olendraru, C., and Sellier, A., 2002, “Viscous effects in the absolute-convective instability of the Batchelor vortex”, Journal of Fluid Mechanics, Vol. 459, pp. 371-396. https://doi.org/10.1017/S0022112002008029
  10. Szeri, A., and Holmes, P., 1988, “Nonlinear Stability of Axisymmetric Swirling Flows”, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 326, No. 1590, pp. 327-354. https://doi.org/10.1098/rsta.1988.0091
  11. Blackburn, H. M., and Sherwin, S. J., 2004, “Formulation of a Galerkin spectral element - Fourier method for three-dimensional incompressible flows in cylindrical geometries,” Journal of Computational Physics, Vol. 197, pp. 759-778. https://doi.org/10.1016/j.jcp.2004.02.013
  12. Alekseenko, S. V., Kuibin, P. A., Okulov, V. L., and Shtork, S. I., 1999, “Helical vortices in swirl flow,” Journal of Fluid Mechanics, Vol. 382, pp. 195-243. https://doi.org/10.1017/S0022112098003772
  13. Kuibin, P. A., Okulov, V. L., and Pylev, I. M., 2006, “Simulation of Flow Structure in the Suction Pipe of a Hydroturbine by Integral Characteristics,” Heat Transfer Research, Vol. 37, No. 8, pp. 675-684. https://doi.org/10.1615/HeatTransRes.v37.i8.30
  14. Iliescu, M. S., 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,” Journal of Fluids Engineering, Vol. 130, 021105-1-10. https://doi.org/10.1115/1.2813052
  15. Avellan, F., 2000, “Flow Investigation in a Francis Draft Tube: The FLINDT Project,” Proceedings of the 20th IAHR Symposium on Hydraulic Machinery and Systems, Charlotte, North-Carolina, U.S.A., Paper DES-11.
  16. Avellan, F., 2004, “Introduction to Cavitation in Hydraulic Machinery,” 6th International Conference on Hydraulic Machinery and Hydrodynamics, Timisoara, Romania, Scientific Bulletin of the Politehnica University of Timisoara, Transactions on Mechanics, Tom 49(63), Special Issue, pp.11-22.
  17. Shih, T.-H., Liou, W. W., Shabbir, A., Yang, Z., and Zhu, J., 1995, “A New $k-{\epsilon}$ Eddy Viscosity Model for High Reynolds Number Turbulent Flows - Model Development and Validation,” Computer & Fluids, Vol. 24, No. 3, pp. 227-238. https://doi.org/10.1016/0045-7930(94)00032-T
  18. Nishi, M., Matsunaga, S., Okamoto, S,. Uno, M., and Nishitani, K., 1988, “Measurement of Three-dimensional Periodic Flow in a Conical Draft Tube at Surging Condition,” in Rohatgi, U. S., at al., (eds.), Flow in Non-Rotating Turbomachinery Components, FED, Vol. 69, pp. 173-184.
  19. Kirschner, O., and Ruprecht, A., 2007, “Vortex Rope Measurement in a Simplified Draft Tube,” 2nd IAHR International Meeting of the Workgroup on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems, Timisoara, Romania, Scientific Bulletin of the Politehnica University of Timisoara, Transactions on Mechanics, Tom 52(66), Fasc. 6, pp. 173-184.
  20. Keller, J. J., Egli, W., and Althaus, R., 1988, “Vortex Breakdown as a Fundamental Element of Vortex Dynamcis,” Journal of Applied Mathematics and Physics (ZAMP), Vol. 39, pp. 404-440. https://doi.org/10.1007/BF00945061

Cited by

  1. Analysis and Prevention of Vortex Breakdown in the Simplified Discharge Cone of a Francis Turbine vol.132, pp.5, 2010, https://doi.org/10.1115/1.4001486
  2. Unsteady Pressure Analysis of a Swirling Flow With Vortex Rope and Axial Water Injection in a Discharge Cone vol.134, pp.8, 2012, https://doi.org/10.1115/1.4007074
  3. An Outlook on the Draft-Tube-Surge Study vol.6, pp.1, 2013, https://doi.org/10.5293/IJFMS.2013.6.1.033
  4. Swirling and cavitating flow suppression in a cryogenic liquid turbine expander through geometric optimization vol.229, pp.6, 2015, https://doi.org/10.1177/0957650915589062
  5. Modelling and optimization of the velocity profiles at the draft tube inlet of a Francis turbine within an operating range vol.54, pp.1, 2016, https://doi.org/10.1080/00221686.2015.1119763
  6. Computational and Theoretical Analyses of the Precessing Vortex Rope in a Simplified Draft Tube of a Scaled Model of a Francis Turbine vol.139, pp.2, 2017, https://doi.org/10.1115/1.4034693