Optimal Control of Part Load Vortex Rope in Francis Turbines

The mitigation of the precessing vortex core developing in the draft tube of Francis turbines operating under part load conditions is crucial to increase the operation flexibility of these hydraulic machines to balance the massive power production of intermittent energy sources. A systematic approach following the optimal control theory is, therefore, presented to control this vortical flow structure. Modal analysis characterizes the part load vortex rope as a self-sustained instability associated with an unstable eigenmode. Based on this physical characteristic, an objective function targeting a zero value of the unstable eigenvalue growth rate is defined and subsequently minimized using an adjoint-based optimization algorithm. We determine an optimal force distribution that successfully quenches the part load vortex rope and sketches the design of a realistic control appendage.

[1]  Bhupendra K. Gandhi,et al.  Effect of transients on Francis turbine runner life: a review , 2013 .

[2]  Dwight Barkley,et al.  Prediction of frequencies in thermosolutal convection from mean flows. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  J. Meyers,et al.  Optimal control of energy extraction in wind-farm boundary layers , 2015, Journal of Fluid Mechanics.

[4]  Z. Qian,et al.  The effect of runner cone design on pressure oscillation characteristics in a Francis hydraulic turbine , 2012 .

[5]  François Avellan,et al.  Pressure Wall Measurements in the whole Draft Tube : Steady and Unsteady Analysis , 2002 .

[6]  Matthew P. Juniper,et al.  Structural sensitivity of spiral vortex breakdown , 2013, Journal of Fluid Mechanics.

[7]  F. Porté-Agel,et al.  Prediction of the hub vortex instability in a wind turbine wake: stability analysis with eddy-viscosity models calibrated on wind tunnel data , 2014, Journal of Fluid Mechanics.

[8]  O. Marquet,et al.  Sensitivity analysis and passive control of cylinder flow , 2008, Journal of Fluid Mechanics.

[9]  Denis Sipp,et al.  Global stability of base and mean flows: a general approach and its applications to cylinder and open cavity flows , 2007, Journal of Fluid Mechanics.

[10]  Hussaini M. Yousuff,et al.  A Self-Contained, Automated Methodology for Optimal Flow Control , 1997 .

[11]  Alin Bosioc,et al.  Flow-Feedback Method for Mitigating the Vortex Rope in Decelerated Swirling Flows , 2013 .

[12]  Sebastian Muntean,et al.  Numerical assessment of pulsating water jet in the conical diffusers , 2017 .

[13]  Yoshinobu Tsujimoto,et al.  Unsteady vortical flow simulation in a Francis turbine with special emphasis on vortex rope behavior and pressure fluctuation alleviation , 2017 .

[14]  François Avellan,et al.  Analysis of the Swirling Flow Downstream a Francis Turbine Runner , 2006 .

[15]  F. Avellan,et al.  Experimental Evidence of Hydroacoustic Pressure Waves in a Francis Turbine Elbow Draft Tube for Low Discharge Conditions , 2009 .

[16]  Shiyi Chen,et al.  Characteristics and Control of the Draft-Tube Flow in Part-Load Francis Turbine , 2009 .

[17]  P. Luchini,et al.  Structural sensitivity of the first instability of the cylinder wake , 2007, Journal of Fluid Mechanics.

[18]  O. Pironneau,et al.  SHAPE OPTIMIZATION IN FLUID MECHANICS , 2004 .

[19]  Timothy J. Barth,et al.  The design and application of upwind schemes on unstructured meshes , 1989 .

[20]  Frédéric Hecht,et al.  New development in freefem++ , 2012, J. Num. Math..

[21]  Uwe Ehrenstein,et al.  Adjoint based optimization and control of a separated boundary-layer flow , 2013 .

[22]  François Avellan,et al.  Part Load Vortex Rope as a Global Unstable Mode , 2017 .

[23]  Angelo Iollo,et al.  Feedback control of the vortex-shedding instability based on sensitivity analysis , 2010 .

[24]  H. Foroutan,et al.  Flow in the Simplified Draft Tube of a Francis Turbine Operating at Partial Load—Part I: Simulation of the Vortex Rope , 2014 .

[25]  Chirag Trivedi,et al.  Numerical Techniques Applied to Hydraulic Turbines: A Perspective Review , 2016 .

[26]  H. Imamura,et al.  Effect of J-Groove on the Suppression of Swirl Flow in a Conical Diffuser , 2010 .

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

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

[29]  Roger Temam,et al.  DNS-based predictive control of turbulence: an optimal benchmark for feedback algorithms , 2001, Journal of Fluid Mechanics.

[30]  Max Gunzburger,et al.  SENSITIVITIES, ADJOINTS AND FLOW OPTIMIZATION , 1999 .

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

[32]  Rahul Goyal,et al.  Experimental study of mitigation of a spiral vortex breakdown at high Reynolds number under an adverse pressure gradient , 2017 .

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

[34]  F. Avellan,et al.  Predictive control of spiral vortex breakdown , 2018, Journal of Fluid Mechanics.

[35]  Elijah Polak,et al.  Optimization: Algorithms and Consistent Approximations , 1997 .

[36]  François Gallaire,et al.  Self-consistent mean flow description of the nonlinear saturation of the vortex shedding in the cylinder wake. , 2014, Physical review letters.

[37]  Z. Qian,et al.  Numerical Simulation and Analysis of Pressure Pulsation in Francis Hydraulic Turbine with Air Admission , 2007 .

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

[39]  Thomas Bewley,et al.  A Linear Systems Approach to Flow Control , 2007 .

[40]  Alin Bosioc,et al.  Unsteady Pressure Analysis of a Swirling Flow With Vortex Rope and Axial Water Injection in a Discharge Cone , 2012 .

[41]  D. Barkley.  Linear analysis of the cylinder wake mean flow , 2006 .