Understanding the coherent structures for different fluctuation frequencies at partial load condition of a Francis turbine

Abstract Computational fluid dynamics simulations are conducted to characterize the spatial and temporal characteristics of the flow field inside a Francis turbine operating in the excess load regime. A high-fidelity Large Eddy Simulation (LES) turbulence model is applied to investigate the flow-induced pressure fluctuations in the draft tube of a Francis Turbine. Probes placed alongside the wall and in the center of the draft tube measure the pressure signal in the draft tube, the pressure over the turbine blades, and the power generated to compare against previous studies featuring design point and partial load operating conditions. The excess load is seen during Francis turbines in order to satisfy a spike in the electrical demand. By characterizing the flow field during these conditions, we can find potential problems with running the turbine at excess load and inspire future studies regarding mitigation methods. Our studies found a robust low-pressure region on the edges of turbine blades, which could cause cavitation in the runner region, which would extend through the draft tube, and high magnitude of pressure fluctuations were observed in the center of the draft tube.

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Particle Image Velocimetry Test for the Inter-Blade Vortex in a Francis Turbine

Processes ◽

10.3390/pr9111968 ◽

2021 ◽

Vol 9 (11) ◽

pp. 1968

Author(s):

Lianchen Xu ◽

Xiaohui Jin ◽

Zhen Li ◽

Wanquan Deng ◽

Demin Liu ◽

...

Keyword(s):

Particle Image Velocimetry ◽

Particle Image ◽

Load Condition ◽

Specific Model ◽

Francis Turbine ◽

Stable Operation ◽

Suction Surface ◽

Partial Load ◽

Image Velocimetry ◽

Unit Speed

Hydropower units are usually operated in non-design conditions because of power grid requirements. In a partial-load condition, an inter-blade vortex phenomenon occurs between the runner blades of a Francis turbine, causing pressure pulsation and unit vibration, which hinder the safe and stable operation of power stations. However, the mechanism through which the inter-blade vortex generation occurs is not entirely clear. In this study, a specific model of the Francis turbine was used to investigate and visually observe the generation of the blade vortex in Francis turbines in both the initial inter-blade and vortex development zones. Particle image velocimetry was used for this purpose. In addition, we determined the variation law of the inter-blade vortex in the Francis turbine. We found that the size and strength of the inter-blade vortex depend on the unit speed of the turbine. The higher the unit speed is, the stronger the inter-blade vortex becomes. We concluded that the inter-blade vortex of such turbines originates from the pressure surface or secondary flow and stall of the blade at the inlet side of the runner at high unit speeds, and also from the backflow zone of the suction surface of the blade at low unit speeds.

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Investigation of Pressure Fluctuation and Pulsating Hydraulic Axial Thrust in Francis Turbines

Energies ◽

10.3390/en13071734 ◽

2020 ◽

Vol 13 (7) ◽

pp. 1734

Author(s):

Xing Zhou ◽

Changzheng Shi ◽

Kazuyoshi Miyagawa ◽

Hegao Wu ◽

Jinhong Yu ◽

...

Keyword(s):

Draft Tube ◽

Renewable Energy Sources ◽

Pressure Fluctuations ◽

Dominant Frequency ◽

Rotational Frequency ◽

Rapid Expansion ◽

Francis Turbine ◽

Axial Thrust ◽

Partial Load ◽

Hydropower Stations

Under the circumstances of rapid expansion of diverse forms of volatile and intermittent renewable energy sources, hydropower stations have become increasingly indispensable for improving the quality of energy conversion processes. As a consequence, Francis turbines, one of the most popular options, need to operate under off-design conditions, particularly for partial load operation. In this paper, a prototype Francis turbine was used to investigate the pressure fluctuations and hydraulic axial thrust pulsation under four partial load conditions. The analyses of pressure fluctuations in the vaneless space, runner, and draft tube are discussed in detail. The observed precession frequency of the vortex rope is 0.24 times that of the runner rotational frequency, which is able to travel upstream (from the draft tube to the vaneless space). Frequencies of both 24.0 and 15.0 times that of the runner rotational frequency are detected in the recording points of the runner surface, while the main dominant frequency recorded in the vaneless zone is 15.0 times that of the runner rotational frequency. Apart from unsteady pressure fluctuations, the pulsating property of hydraulic axial thrust is discussed in depth. In conclusion, the pulsation of hydraulic axial thrust is derived from the pressure fluctuations of the runner surface and is more complicated than the pressure fluctuations.

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Optimal Control of a Wind Turbine for Tradeoff Analysis Between Energy Harvesting and Noise Emission

Volume 3: Nonlinear Estimation and Control; Optimization and Optimal Control; Piezoelectric Actuation and Nanoscale Control; Robotics and Manipulators; Sensing; System Identification (Estimation for Automotive Applications, Modeling, Therapeutic Control in Bio-Systems); Variable Structure/Sliding-Mode Control; Vehicles and Human Robotics; Vehicle Dynamics and Control; Vehicle Path Planning and Collision Avoidance; Vibrational and Mechanical Systems; Wind Energy Systems and Control ◽

10.1115/dscc2013-3826 ◽

2013 ◽

Cited By ~ 1

Author(s):

Mohamed L. Shaltout ◽

Dongmei Chen

Keyword(s):

Optimal Control ◽

Energy Harvesting ◽

Wind Turbine ◽

Load Condition ◽

Noise Emission ◽

Continuous Growth ◽

Control Approach ◽

The Public ◽

Partial Load ◽

Blade Pitch Angle

An optimal control approach for a wind turbine drivetrain with the objective of maximizing energy harvesting and minimizing noise emission is presented. One of the major challenges facing the public acceptance for continuous growth of wind turbine installation is its noise emission. However, reducing the noise emission could lead to decreased wind energy harvesting. As a result, a tradeoff arises between power generation and noise emission, especially when a wind turbine operates under the partial-load condition. This paper will show that through controlling the generator electromagnetic torque and/or the blade pitch angle, an optimal tradeoff between wind turbine energy harvesting and noise emission can be obtained. The dynamic model of a wind turbine drivetrain and a noise emission prediction model are also presented. Simulation results of using the proposed control design for different wind speed ranges are analyzed and compared.

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Flow-related mechanisms of draft tube surges observed at partial load of a francis turbine.

TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series B ◽

10.1299/kikaib.51.2406 ◽

1985 ◽

Vol 51 (467) ◽

pp. 2406-2413 ◽

Cited By ~ 1

Author(s):

Michihiro NISHI ◽

Shigenori MATSUNAGA ◽

Katsuhiko NISHITANI ◽

Takashi KUBOTA ◽

Yasutoshi SENOO

Keyword(s):

Draft Tube ◽

Francis Turbine ◽

Partial Load

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Flow in the Simplified Draft Tube of a Francis Turbine Operating at Partial Load—Part I: Simulation of the Vortex Rope

Journal of Applied Mechanics ◽

10.1115/1.4026817 ◽

2014 ◽

Vol 81 (6) ◽

Cited By ~ 17

Author(s):

Hosein Foroutan ◽

Savas Yavuzkurt

Keyword(s):

Experimental Data ◽

Axial Velocity ◽

Draft Tube ◽

Three Dimensional ◽

Operating Conditions ◽

Turbulence Closure ◽

Francis Turbine ◽

Outer Flow ◽

Vortex Rope ◽

Partial Load

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.

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Reduction of Voltage Harmonics in an Open-End Winding Induction Motor Driven by a Dual-Inverter with a Floating Capacitor in a Partial-Load Condition

IEEJ Journal of Industry Applications ◽

10.1541/ieejjia.21004866 ◽

2021 ◽

Author(s):

Akihito Mizukoshi ◽

Hitoshi Haga

Keyword(s):

Induction Motor ◽

Load Condition ◽

Partial Load ◽

Floating Capacitor ◽

Voltage Harmonics ◽

Open End Winding

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Stationary stall phenomenon and pressure fluctuation in a centrifugal pump at partial load condition

Heat and Mass Transfer ◽

10.1007/s00231-019-02579-0 ◽

2019 ◽

Vol 55 (8) ◽

pp. 2277-2288 ◽

Cited By ~ 5

Author(s):

Xuanming Ren ◽

Honggang Fan ◽

Zhifeng Xie ◽

Bing Liu

Keyword(s):

Centrifugal Pump ◽

Pressure Fluctuation ◽

Load Condition ◽

Partial Load

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Flow in the Simplified Draft Tube of a Francis Turbine Operating at Partial Load—Part II: Control of the Vortex Rope

Journal of Applied Mechanics ◽

10.1115/1.4026818 ◽

2014 ◽

Vol 81 (6) ◽

Cited By ~ 15

Author(s):

Hosein Foroutan ◽

Savas Yavuzkurt

Keyword(s):

Flow Rate ◽

Draft Tube ◽

Pressure Fluctuations ◽

Companion Paper ◽

Francis Turbine ◽

Control Technique ◽

Outer Flow ◽

Vortex Rope ◽

Stagnant Region ◽

Partial Load

Numerical simulations and investigation of a method for controlling the vortex rope formation in draft tubes are carried out in this paper, which is the second part of a two-paper series. As shown in the companion paper, formation of the vortex rope is associated with a large stagnant region at the center of the draft tube. Therefore, it is concluded that a successful control technique should focus on the elimination of this region. In practice, this can be performed by axially injecting a small fraction (a few percent of the total flow rate) of water into the draft tube. Water jet is supplied from the high-pressure flow upstream of the turbine spiral case by a bypass line; thus, no extra pump is needed in this method. It is shown that this method is very effective in elimination of the stagnant region in a simplified draft tube operating at two part-load conditions, i.e., at 91% and 70% of the best efficiency point (BEP) flow rate. This results in improvement of the draft tube performance and reduction of hydraulic losses. The loss coefficient is reduced by as much as 50% for the case with 91% of BEP flow rate and 14% for the case with 70% of BEP flow rate. Unsteady, three-dimensional simulations show that the jet increases the axial momentum of flow at the center of the draft tube and decreases the wake of the crown cone and thereby decreases the shear at the interface of the stagnant region and high velocity outer flow, which ultimately results in elimination of the vortex rope. Furthermore, reduction (by about 1/3 in the case with 70% of BEP flow rate) of strong pressure fluctuations leads to reliable operation of the turbine.

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Characteristics and Control of the Draft-Tube Flow in Part-Load Francis Turbine

Journal of Fluids Engineering ◽

10.1115/1.3002318 ◽

2009 ◽

Vol 131 (2) ◽

Cited By ~ 50

Author(s):

Ri-kui Zhang ◽

Feng Mao ◽

Jie-Zhi Wu ◽

Shi-Yi Chen ◽

Yu-Lin Wu ◽

...

Keyword(s):

Swirling Flow ◽

Draft Tube ◽

Flow Behavior ◽

Load Condition ◽

Francis Turbine ◽

Tube Flow ◽

Reversed Flow ◽

Part Load ◽

Axial Pressure Gradient ◽

Flow Phenomena

Under part-load conditions, a Francis turbine often suffers from very severe low-frequency and large-amplitude pressure fluctuation, which is caused by the unsteady motion of vortices (known as “vortex ropes”) in the draft tube. This paper first reports our numerical investigation of relevant complex flow phenomena in the entire draft tube, based on the Reynolds-averaged Navier–Stokes (RANS) equations. We then focus on the physical mechanisms underlying these complex and somewhat chaotic flow phenomena of the draft-tube flow under a part-load condition. The flow stability and robustness are our special concern, since they determine what kind of control methodology will be effective for eliminating or alleviating those adverse phenomena. Our main findings about the flow behavior in the three segments of the draft tube, i.e., the cone inlet, the elbow segment, and the outlet segment with three exits, are as follows. (1) In the cone segment, we reconfirmed a previous finding of our research group based on the turbine’s whole-flow RANS computation that the harmful vortex rope is an inevitable consequence of the global instability of the swirling flow. We further identified that this instability is caused crucially by the reversed axial flow at the inlet of the draft tube. (2) In the elbow segment, we found a reversed flow continued from the inlet cone, which evolves to slow and chaotic motion. There is also a fast forward stream driven by a localized favorable axial pressure gradient, which carries the whole mass flux downstream. The forward stream and reversed flow coexist side-by-side in the elbow, with a complex and unstable shear layer in between. (3) In the outlet segment with three exits, the forward stream always goes through a fixed exit, leaving the other two exits with a chaotic and low-speed fluid motion. Based on these findings, we propose a few control principles to suppress the reversed flow and to eliminate the harmful helical vortex ropes. Of the methods we tested numerically, a simple jet injection in the inlet is proven successful.

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