Optimal Control of Part Load Vortex Rope in Francis Turbines

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
Simon Pasche ◽  
François Avellan ◽  
François Gallaire
Keyword(s):  
Optimal Control ◽  
Systematic Approach ◽  
Draft Tube ◽  
Vortical Flow ◽  
Vortex Rope ◽  
Part Load ◽  
Precessing Vortex Core ◽  
Hydraulic Machines ◽  
Optimal Force ◽  
Operation Flexibility

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.

Generation of Twin Vortex Rope in the Draft-Tube Elbow of a Francis Turbine During Deep Part-Load Operation

2021 ◽  
Author(s):  
Mohammad Hossein Khozaei ◽  
Arthur Favrel ◽  
Toshitake Masuko ◽  
Naoki Yamaguchi ◽  
Kazuyoshi Miyagawa
Keyword(s):  
Linear Correlation ◽  
Draft Tube ◽  
Pressure Fluctuations ◽  
Low Frequency ◽  
Model Tests ◽  
Francis Turbine ◽  
Deep Part ◽  
Swirl Number ◽  
Vortex Rope ◽  
Part Load

Abstract This paper focuses on the generation of twin vortex rope in the draft-tube elbow of a Francis turbine at deep part-load operation through analyzing the results of model tests along with numerical simulations. Model tests, including pressure fluctuations measurements, are conducted over 10 speed factors. By considering the frequency of the pressure fluctuations with respect to the swirl intensity at the runner outlet, the part-load operating range is divided into three regimes, with two clear transitions between each occurring at swirl numbers 0.4 and 1.7. For operating conditions with a swirl number S>0.4, a linear correlation between the frequency of the precessing vortex core and the swirl number is established. During deep part-load regime (S>1.7), low-frequency pressure fluctuations appear. Their frequency feature another linear correlation with the swirl number. Unsteady CFD simulation of the full domain is performed to elucidate the generation mechanisms of the low-frequency fluctuations. By tracking the center of the vortical structures along the draft-tube, generation of three vortices in the elbow responsible for the pressure fluctuations at the lowest frequency is highlighted: the main PVC hits the draft-tube wall in the elbow resulting in its break down into three vortices rotating with half the rotational speed of the PVC. Two of the vortices rotate with opposite angular position, constituting a structure of twin vortices. The periodic rotation of these three vortices in the elbow induces the low-frequency pressure fluctuations.

Unsteady vortical flow simulation in a Francis turbine with special emphasis on vortex rope behavior and pressure fluctuation alleviation

2017 ◽  
Vol 231 (3) ◽  
pp. 215-226 ◽  
Author(s):  
Xianwu Luo ◽  
An Yu ◽  
Bin Ji ◽  
Yulin Wu ◽  
Yoshinobu Tsujimoto
Keyword(s):  
Pressure Fluctuation ◽  
Swirling Flow ◽  
Draft Tube ◽  
Pressure Fluctuations ◽  
Flow Simulation ◽  
Vortical Flow ◽  
Francis Turbine ◽  
Vortex Rope ◽  
Spiral Vortex ◽  
Baroclinic Torque

Hydro turbines operating at partial flow conditions usually have vortex ropes in the draft tube that generate large pressure fluctuations. This unsteady flow phenomenon is harmful to the safe operation of hydropower stations. This paper presents numerical simulations of the internal flow in the draft tube of a Francis turbine with particular emphasis on understanding the unsteady characteristics of the vortex rope structure and the underlying mechanisms for the interactions between the air and the vortices. The pressure fluctuations induced by the vortex rope are alleviated by air admission from the main shaft center, with the water-air two phase flow in the entire flow passage of a model turbine simulated based on the homogeneous flow assumption. The results show that aeration with suitable air flow rate can alleviate the pressure fluctuations in the draft tube, and the mechanism improving the flow stability in the draft tube is due to the change of vortex rope structure and distribution by aeration, i.e. a helical vortex rope at a small aeration volume while a cylindrical vortex rope with a large amount of aeration. The preferable vortex rope distribution can suppress the swirl at the smaller flow rates, and is helpful to alleviate the pressure fluctuation in the draft tube. The analysis based on the vorticity transport equation indicates that the vortex has strong stretching and dilation in the vortex rope evolution. The baroclinic torque term does not play a major role in the vortex evolution most of the time, but will much increase for some specific aeration volumes. The present study also depicts that vortex rope is mainly associated with a pair of spiral vortex stretching and dilation sources, and its swirling flow is alleviated little by the baroclinic torque term, whose effect region is only near the draft tube inlet.

Experimental Investigation Of Double Precessing Vortex Rope Forming In Draft Tube Models

2015 ◽  
Vol 10 (2) ◽  
pp. 73-82
Author(s):  
Sergey Skripkin ◽  
Mikhail Tsoy ◽  
Sergey Shtork
Keyword(s):  
High Speed ◽  
Draft Tube ◽  
Hydraulic Turbine ◽  
Reynolds Numbers ◽  
Pressure Pulsations ◽  
Vortex Rope ◽  
Precessing Vortex Core ◽  
Turbine Equipment ◽  
Hydro Turbines ◽  
Design Pressure

This work is devoted to the experimental research of the flow structure in draft tube models of hydro turbines. Precessing vortex core was formed using fixed swirler in a flow such as observed in natural hydro turbines under off-design conditions. In laboratory conditions it has been able to find the effect of the transition between single- and double- vortex rope. Their frequency characteristics have been measured in the range of Reynolds numbers 5·104 –5·105 . Based on the analysis of data high-speed shooting the mechanism of complete transition between single and double vortex modes was investigated in detail. The investigation of this phenomenon is of particular interest for the design and operation of hydraulic turbine equipment due to off-design pressure pulsations with sudden changes in frequency and amplitude in a flow occurring.

Identification of Francis Turbine Helical Vortex Rope Excitation by CFD and Resonance Simulation With the Hydraulic System

2011 ◽  
Author(s):  
Se´bastien Alligne´ ◽  
Christophe Nicolet ◽  
Franc¸ois Avellan
Keyword(s):  
Hydraulic System ◽  
Draft Tube ◽  
Pressure Fluctuations ◽  
Resonance Phenomenon ◽  
Excitation Source ◽  
Francis Turbine ◽  
Scale Model ◽  
Vortex Rope ◽  
One Dimensional ◽  
Hydraulic Machines

Due to the growing development of new renewable energies, which production is difficult to foreseen, power grid is subjected to disturbances. Hydropower plants are one of the solution to restore the grid stability by allowing hydraulic machines, especially Francis turbines, to change quickly of operating points in a very large range of heads and power in order to cover the variation of the electrical demand. In part load conditions, the cavitating vortex rope is an excitation source for the whole hydraulic circuit. The frequency of the excitation may matches with one of the eigenfrequency of the system leading to resonance phenomena. The aim of this paper is to simulate this hydroacoustic resonance by identifying the excitation source with CFD numerical simulations of the cavitating vortex rope and simulating the response of the hydraulic system with a one dimensional compressible model. A one dimensional draft tube model including three key parameters is used: the excitation momentum source corresponding to the force induced by the vortex rope acting on the wall, the excitation mass source induced by the cavitation volume fluctuations and the thermodynamic damping modeling energy dissipation during the phase change between cavitation and liquid. These parameters are computed for the FLINDT reduced scale model with the help of unsteady CFD simulations considering both one phase and two phase simulations. Finally these parameters are injected in the one dimensional hydroacoustic model to simulate the resonance phenomenon. In out of resonance conditions, maximum of pressure fluctuations are found in the draft tube cone with an amplitude of 1% of the turbine head. However, when resonance occurs, maximum amplitude of pressure fluctuations reaches up to 6.8%.

Experimental and Numerical Analysis of the Cavitating Part Load Vortex Dynamics of Low-Head Hydraulic Turbines

2011 ◽  
Author(s):  
Se´bastien Houde ◽  
Monica S. Iliescu ◽  
Richard Fraser ◽  
Se´bastien Lemay ◽  
Gabriel D. Ciocan ◽  
...  
Keyword(s):  
Particle Image Velocimetry ◽  
Particle Image ◽  
Draft Tube ◽  
Experimental Methodology ◽  
Flow Measurements ◽  
Measured Velocity ◽  
Piv Measurements ◽  
Vortex Rope ◽  
Part Load ◽  
Image Velocimetry

The draft tube flow is a two-sided challenge for the operation of a hydraulic turbine. On one side, it is an important component for the performance of low to medium head turbines, where it can provide up to 40% of the extracted energy from the flow. On the other side, being a diffuser with a complex vorticity distribution at the inlet, vortex breakdown instability can occur at part load and generate a corkscrewed precessing vortex that can be associated with cavitation. The cavitating vortex rope, may generate undesired power output fluctuation and/or structural vibration. Therefore, draft tubes are much studied components but hard to tackle both numerically and experimentally. Within the framework of the AxialT project, the flow in the draft tube of a propeller turbine model operating at part load was studied using a combination of two-phase Particle Image Velocimetry (PIV) measurements and Unsteady Reynolds Averaged Navier-Stokes (URANS) simulations. The paper main focus is on the experimental methodology and results. It explains how Particle Image Velocimetry measurements were implemented, validated and post-treated to provide flow measurements in the draft tube cone at part load in the cavitating and non-cavitating regimes. It also describes various image processing techniques used to extract the velocity field around the cavitating vortex rope and to estimate the location of the water-vapour interface of the cavitating region. In the spirit of feeding experimental data to numerical simulations, an analysis of measured velocity profiles just under the runner is presented. Comparison between PIV measurements and preliminary URANS simulations is also illustrated.

Part Load Vortex Rope as a Global Unstable Mode

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Simon Pasche ◽  
François Avellan ◽  
François Gallaire
Keyword(s):  
Flow Field ◽  
Large Scale ◽  
Vortex Breakdown ◽  
Control Strategies ◽  
Renewable Energy Sources ◽  
Vortex Rope ◽  
Part Load ◽  
Spiral Vortex ◽  
Electrical Generation ◽  
Operation Flexibility

Renewable energy sources (RES) have reached 23.7% of the worldwide electrical generation production in 2015. The hydraulic energy contribution amounts to 16.6% and comes mainly form large-scale hydropower plants, where Francis turbines represents 60% of the generating units. However, the future massive development of RES will require more advanced grid regulation strategies that may be achieved by increasing the operation flexibility of the Francis generating units. Part load operating condition of these turbines is hindered by pressure fluctuations in the draft tube of the machine. A precessing helical vortex rope develops in this condition, which imperils the mechanical structure and limits the operation flexibility of these turbines. A thorough description of the physical mechanism leading to the vortex rope is a prerequisite to develop relevant flow control strategies. This work, based on a linear global stability analysis of the time-averaged flow field, including a turbulent eddy viscosity, interprets the vortex rope as a global unstable eigenmode. In close resemblance to spiral vortex breakdown, a single-helix disturbance develops around the time-averaged flow field and growths in time to finally form the vortex rope. The frequency and the structure of this unstable linear disturbance are found in good agreement with respect to the three-dimensional (3D) numerical flow simulations.

Numerical Simulation of Pressure Vibrations in a Francis Turbine Draft Tube With Air Admission

2014 ◽  
Author(s):  
Renfang Huang ◽  
An Yu ◽  
Xianwu Luo ◽  
Bin Ji ◽  
Hongyuan Xu
Keyword(s):  
Draft Tube ◽  
Load Condition ◽  
Flow Simulation ◽  
Rotation Frequency ◽  
Francis Turbine ◽  
Stable Operation ◽  
Hydraulic Efficiency ◽  
Operation Condition ◽  
Vortex Rope ◽  
Part Load

The pressure vibrations in a draft tube are harmful for the stable operation for a Francis turbine at part load conditions. In this paper, air admission is proposed to depress those pressure vibrations. The unsteady flow in a Francis turbine, whose hydraulic performance has been tested experimentally, is simulated at a part load operation condition. The flow simulation is conducted using RANS methods coupling with SST k-ω turbulence model. The results indicate the pressure vibrations in the turbine are reasonably predicted by the present numerical method. Based on the calculations, the dominant pressure vibration component for a hydro turbine operated at part-load condition is caused by the vortex rope in draft tube, and its frequency is near 0.2 times of the runner rotation frequency. The frequencies of pressure vibration do not change by air admission, and the pressure vibration amplitude decreases with the air admission. Further, the depression effect for pressure vibration would be improved if air admission is from the crown holes instead of the spindle hole. The results also indicate that the turbine hydraulic efficiency changes periodically with the pressure vibration induced by vortex rope in turbine draft tube, would be degraded with air admission from the spindle hole, and improved with air admission from the crown holes. With the increase of air admission, the turbine hydraulic efficiency would improve. The present research will be helpful for the safe operation of Francis turbines.

Analysis and Control of Part-Load Unsteady Flow in Francis Turbine’s Draft Tube

2007 ◽  
Author(s):  
Ri-Kui Zhang ◽  
Feng Mao ◽  
Jie-Zhi Wu ◽  
Shi-Yi Chen ◽  
Yu-Lin Wu ◽  
...  
Keyword(s):  
Mass Flux ◽  
Pressure Fluctuation ◽  
Draft Tube ◽  
Load Condition ◽  
Vortical Flow ◽  
Francis Turbine ◽  
Effective Control ◽  
Complex Flow ◽  
Part Load ◽  
Axial Pressure Gradient

By using the Reynolds-averaged Navier-Stokes (RANS) equations, the complex unsteady vortical flow in the entire draft tube of a Francis turbine under a part-load condition, with severe low-frequency pressure fluctuation, is investigated numerically to gain an in-depth understanding of the physical characters of the flow including its stability and robustness, and thereby to seek effective control means to alleviate or even eliminate the strong pressure fluctuation. Our main findings are as follows: In the cone segment of the draft tube, the vortex rope is due to the global instability of the flow caused crucially by the reversed axial flow at the inlet. In the elbow segment of the draft tube, the reversed flow coexists side by side with a fluid channel that carries the mass flux downstream due to favorable axial pressure gradient. In the outlet segment of the draft tube, the mass-flux channel always goes through a fixed outlet, leaving the other two with nearly zero flux. The entire draft-tube flow, although undesired under part-load condition, forms a globally robust system. The principles for effectively controlling this complex flow are proposed. A simple water jet injection at the inlet is numerically proven successful.

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