Analysis of the Swirling Flow Downstream a Francis Turbine Runner

An experimental and theoretical investigation of the flow at the outlet of a Francis turbine runner is carried out in order to elucidate the causes of a sudden drop in the draft tube pressure recovery coefficient at a discharge near the best efficiency operating point. Laser Doppler anemometry velocity measurements were performed for both axial and circumferential velocity components at the runner outlet. A suitable analytical representation of the swirling flow has been developed taking the discharge coefficient as independent variable. It is found that the investigated mean swirling flow can be accurately represented as a superposition of three distinct vortices. An eigenvalue analysis of the linearized equation for steady, axisymmetric, and inviscid swirling flow reveals that the swirl reaches a critical state precisely (within 1.3%) at the discharge where the sudden variation in draft tube pressure recovery is observed. This is very useful for turbine design and optimization, where a suitable runner geometry should avoid such critical swirl configuration within the normal operating range.

[1]  François Avellan,et al.  Active control of Francis turbine operation stability , 1999 .

[2]  Yih-huei Wan,et al.  Short-Term Power Fluctuations of Large Wind Power Plants , 2002 .

[3]  S. V. Alekseenko,et al.  Helical vortices in swirl flow , 1999, Journal of Fluid Mechanics.

[4]  François Avellan,et al.  Werle´-Legendre Separation in a Hydraulic Machine Draft Tube , 2002 .

[5]  Sebastiano Mauri,et al.  Numerical Simulation and Flow Analysis of an Elbow Diffuser , 2002 .

[6]  François Avellan,et al.  Performance Analysis of Draft Tube for Gamm Francis Turbine , 1996 .

[7]  W. Hawthorne,et al.  Some Exact Solutions of the Flow Through Annular Cascade Actuator Discs , 1950 .

[8]  Fazle Hussain,et al.  Analysis of inviscid vortex breakdown in a semi-infinite pipe , 1998 .

[9]  R. J. Moffat,et al.  Contributions to the Theory of Single-Sample Uncertainty Analysis , 1982 .

[10]  B. Saravanos,et al.  Statistical Analysis of Experimental Data , 2008 .

[11]  Gino Blommaert.  Etude du comportement dynamique des turbines Francis , 2000 .

[12]  Qian Zhongdong,et al.  Numerical simulation and analysis of pressure pulsation in Francis hydraulic turbine with air admission , 2008 .

[13]  C. J. Knight,et al.  A Variational Formulation of the Compressible Throughflow Problem , 1974 .

[14]  C. Whiting,et al.  The evolution of a perturbed vortex in a pipe to axisymmetric vortex breakdown , 1998, Journal of Fluid Mechanics.

[15]  Lingjiu Zhou,et al.  Simulations and Measurements of Pressure Oscillations Caused by Vortex Ropes , 2006 .

[16]  George S. Dulikravich,et al.  Stream function and stream-function-coordinate (SFC) formulation for inviscid flow field calculations , 1986 .

[17]  B. Fornberg,et al.  Steady axisymmetric vortex flows with swirl and shear , 2008, Journal of Fluid Mechanics.

[18]  Viriato Semiao,et al.  A new second‐moment closure approach for turbulent swirling confined flows , 2003 .

[19]  S. Leibovich.  Vortex stability and breakdown - Survey and extension , 1984 .

[20]  R. W. Fox,et al.  Effects of swirling inlet flow on pressure recovery in conical diffusers , 1971 .

[21]  E. K. Spiridonov.  Designing an ejector pump for a hydraulic system for discharging water and emptying tanks , 2005 .

[22]  Romeo SUSAN-RESIGA,et al.  Axisymmetric Swirling Flow Simulation of the Draft Tube Vortex in Francis Turbines at Partial Discharge , 2009 .

[23]  Inviscid evolution of incompressible swirling flows in pipes : The dependence of the flow structure upon the inlet velocity field , 1999 .

[24]  New features of swirling jets , 2000 .

[25]  P. Saffman,et al.  Inviscid swirling flows and vortex breakdown , 1995, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[26]  T. Fredrik Engström.  Simulations and experiments of turbulent diffuser flow with hydropower applications , 2003 .

[28]  Y. Shmyglevskii,et al.  On “vortex breakdown” , 1995 .

[29]  Gabriel Dan Ciocan.  Contribution à l'analyse des écoulements 3D complexes en turbomachines , 1998 .

[30]  Design and Manufacturing of a Convergent-Divergent Test Section for Swirling Flow Apparatus , 2008 .

[31]  J. Ortega-Casanova,et al.  Inviscid vortex breakdown models in pipes , 1999 .

[32]  Fazle Hussain,et al.  The nature of inviscid vortex breakdown , 1997 .

[33]  Thierry Jacob,et al.  Francis Turbine Surge: Discussion and Data Base , 1996 .

[34]  K. F. Riley,et al.  Mathematical Methods for Physics and Engineering , 1998 .

[35]  R. P. Benedict,et al.  ASME Measurement Uncertainty , 1985 .

[36]  W. Egli,et al.  Force- and loss-free transitions between flow states , 1985 .

[37]  François Avellan,et al.  Flow Investigation in a Francis Draft Tube : the Flindt Project , 2000 .

[38]  François Avellan,et al.  Optical Measurement Techniques for Experimental Analysis of Hydraulic Turbines Rotor - Stator Interaction , 2000 .

[39]  Marcel Escudier,et al.  Confined Vortices in Flow Machinery , 1987 .

[40]  S. Leibovich.  THE STRUCTURE OF VORTEX BREAKDOWN , 1978 .

[41]  D. Snyder,et al.  Numerical simulation of bubble-type vortex breakdown within a tube-and-vane apparatus , 2000 .

[42]  S. Widnall,et al.  Examination of group-velocity criterion for breakdown of vortex flow in a divergent duct , 1980 .

[43]  E. GOLDWAG.  Hydraulic Turbines , 1966, Nature.

[44]  John K. Harvey,et al.  Some observations of the vortex breakdown phenomenon , 1962, Journal of Fluid Mechanics.

[45]  R. R. Long.  STEADY MOTION AROUND A SYMMETRICAL OBSTACLE MOVING ALONG THE AXIS OF A ROTATING LIQUID , 1953 .

[46]  X. M. Wang,et al.  An Experimental Study on Fins, Their Role in Control of the Draft Tube Surging , 1996 .

[47]  W. Egli,et al.  Vortex breakdown as a fundamental element of vortex dynamics , 1988 .

[48]  Peter N. Joubert,et al.  Vortical flow. Part 1. Flow through a constant-diameter pipe , 2002, Journal of Fluid Mechanics.

[49]  M. Oberlack,et al.  Symmetry investigations on the incompressible stationary axisymmetric Euler equations with swirl , 2007 .

[50]  D. E. Muller.  A method for solving algebraic equations using an automatic computer , 1956 .

[51]  T. Brooke Benjamin,et al.  Theory of the vortex breakdown phenomenon , 1962, Journal of Fluid Mechanics.

[52]  J. Keller,et al.  ON THE INTERPRETATION OF VORTEX BREAKDOWN , 1995 .

[53]  F. Hussain,et al.  Effect of deceleration on jet instability , 2003, Journal of Fluid Mechanics.

[54]  S. Leibovich,et al.  Disrupted states of vortex flow and vortex breakdown , 1977 .

[55]  Bhimsen K. Shivamoggi,et al.  Axial flow in trailing line vortices , 1979 .

[56]  Shixiao Wang,et al.  The dynamics of a swirling flow in a pipe and transition to axisymmetric vortex breakdown , 1997, Journal of Fluid Mechanics.

[57]  F. Avellan,et al.  Experimental Study and Numerical Simulation of the Flindt Draft Tube Rotating Vortex , 2007 .

[58]  Sebastiano Mauri,et al.  Numerical Prediction of the Flow in a Turbine Draft Tube : Influence of the Boundary Conditions , 2000 .

[59]  M. Zangeneh,et al.  A compressible three‐dimensional design method for radial and mixed flow turbomachinery blades , 1991 .

[60]  Jun Matsui,et al.  Suppression of Swirl in a Conical Diffuser by Use of J-Groove , 2000 .

[61]  Michel Cervantes,et al.  Effects of boundary conditions and unsteadiness on draft tube flow , 2003 .

[62]  Klaus Schittkowski,et al.  NLPQL: A fortran subroutine solving constrained nonlinear programming problems , 1986 .

[63]  G. Batchelor,et al.  An Introduction to Fluid Dynamics , 1968 .

[64]  Dorota Kral,et al.  Active Flow Control Technology , 1999 .

[65]  F. B..  Introduction to Bessel Functions , 1939, Nature.

[66]  Thomas Vekve,et al.  An experimental investigation of draft tube flow , 2004 .

[67]  M. Cervantes,et al.  On the Use of the Squire-Long Equation to Estimate Radial Velocities in Swirling Flows , 2007 .