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Experimental investigation of pressure fluctuations caused by a vortex rope in a draft tube

This content has been downloaded from IOPscience. Please scroll down to see the full text. 2012 IOP Conf. Ser.: Earth Environ. Sci. 15 062059 (http://iopscience.iop.org/1755-1315/15/6/062059) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 198.23.178.145 This content was downloaded on 07/02/2017 at 09:23 Please note that terms and conditions apply.

You may also be interested in: Experimental investigation of vortex control with an axial jet in the draft tube of a model pump-turbine O Kirschner, H Schmidt, A Ruprecht et al. Model and prototype investigations of upper partial load unsteady phenomena on the Francis turbine designed for head up to 120 m I Kuznetsov, A Zakharov, V Arm et al. Simulation of flow in a simplified draft tube: turbulence closure considerations H Foroutan and S Yavuzkurt Experimental investigation of the local wave speed in a draft tube with cavitation vortex rope C Landry, A Favrel, A Müller et al. CFD simulation of pressure and discharge surge in Francis turbine at off-design conditions D Chirkov, A Avdyushenko, L Panov et al. Experimental investigations of the swirling flow in the conical diffuser using flow-feedback control technique with additional energy source C Tnas, A I Bosioc, R F Susan-Resiga et al. Study on flow instability and countermeasure in a draft tube with swirling flow T Nakashima, R Matsuzaka, K Miyagawa et al. Numerical simulation of pressure fluctuation of a pump-turbine with MGV at no-load condition J T Liu, S H Liu, Y K Sun et al.

26th IAHR Symposium on Hydraulic Machinery and Systems IOP Conf. Series: Earth and Environmental Science 15 (2012) 062059

IOP Publishing doi:10.1088/1755-1315/15/6/062059

Experimental investigation of pressure fluctuations caused by a vortex rope in a draft tube O Kirschner, A Ruprecht, E Göde and S Riedelbauch Institute of Fluid Mechanics and Hydraulic Machinery, University of Stuttgart, Pfaffenwaldring 10, 70550 Stuttgart, Germany E-mail:[email protected] Abstract. In the last years hydro power plants have taken the task of power-frequency control for the electrical grid. Therefore turbines in storage hydro power plants often operate outside their optimum. If Francis-turbines and pump-turbines operate at off-design conditions, a vortex rope in the draft tube can develop. The vortex rope can cause pressure oscillations. In addition to low frequencies caused by the rotation of the vortex rope and the harmonics of these frequencies, pressure fluctuations with higher frequencies can be observed in some operating points too. In this experimental investigation the flow structure and behavior of the vortex rope movement in the draft tube of a model pump-turbine are analyzed. The investigation focuses on the correlation of the pressure fluctuation frequency measured at the draft tube wall with the movement of the vortex rope. The movement of the vortex rope is analyzed by the velocity field in the draft tube which was measured with particle image velocimetry. Additionally, the vortex rope movement has been analyzed with the captures of high-speed-movies from the cavitating vortex rope. Besides the rotation of the vortex rope due to pressure fluctuation with low frequencies the results of the measurement also show a correlation between the rotation of the elliptical or deformed rope cross-section and the higher frequency pressure pulsation. An approximation shows that the frequencies of the pressure fluctuation and the movement of the vortex rope are also connected with the velocity of the flow. Taking into account the size and position of the cavitating vortex core as well as the velocity at the position of the surface of the cavitating vortex core the time-period of the rotation of the vortex core can be approximated. The results show that both, the low frequency pressure fluctuation and the higher frequency pressure fluctuation are correlating with the vortex rope movement. With this estimation, the period of the higher frequency pressure pulsation is approximately a half rotation of the vortex core.

1. Introduction If Francis-turbines and pump-turbines operate at off-design conditions a vortex rope in the draft tube can appear. The appearance of the vortex rope corresponds to the strength of the swirl at the runner outlet [1]. The rotation of the vortex rope causes pressure oscillations. The frequencies of these pressure fluctuations are relatively low and can be in the range of an eigenfrequency of the power plant water passage. If the frequency of the pressure oscillation correlates with an eigenfrequency of the water passage, unacceptable amplitudes in the pressure oscillation may occur. As a consequence the operation range of the hydro power plant must be limited [2]. In addition to low frequencies caused by the rotation of the vortex rope and the harmonics of these frequencies also pressure fluctuations with higher frequencies can be observed. In figure 1 the pressure

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fluctuation is shown. The frequencies of these fluctuations are no multiple of the vortex rope rotation frequencies and differ from frequencies of externally forced fluctuations like e.g. rotor-statorinteraction. Koutnik et al presented the rotation of a cavitating elliptical rope cross-section as the cause of these fluctuations in higher part load operation [3, 4]. In figure 2 a scheme of this rotation in addition to the rotation of the vortex rope is depicted.    g  n u k n  a w h  c s k c  ru D e tr e i m r o n

0.010

rotation of the vortex rope

0.005

elliptical cross section

0.000

of the vortex core

-0.005 -0.010 -0.015 -0.020 0.00

rotation of the elliptical 0.10

0.20

0.30

cross section of the vortex core

0.40

rotation of the vortex time Zeit[s][s] higher frequency fluctuation (approx. 2.7.fn) rope (approx. 0,3.fn)

Figure 1. Fluctuation of the wall pressure.

Figure 2. Scheme of the rotation of the elliptical vortex cross section. Experimental investigations of the flow structure in a draft tube were done at a model pump-turbine in the laboratory of the Institute of Fluid Mechanics and Hydraulic Machinery (IHS). To reduce the complexity of the problem, measurements with a simplified straight cone draft tube, instead of the usually used elbow draft tube, are accomplished. The experimental investigations with the focus on the global flow structures [5] and on higher frequency pressure fluctuations measured at the draft tube wall [6] was presented by the authors. In this paper the correlation between the pressure fluctuation and the movement of the surface of the cavitating vortex rope with two different approaches are shown. In the first approach the correlation between the frequencies of the pressure fluctuation and the movement of the vortex rope core was analyzed. Therefore the vortex rope in the straight draft tube has been visualized by cavitation in the core of the rope and the shape of the cavitating vortex rope was captured by high-speed videos. Additional frequencies of the fluctuation were compared to the movement of the vortex rope which was approximated by the velocities in a longitudinal cross section of the draft tube. 2. Test rig and selected operating point The measurements were carried out at the closed-loop test rig of the IHS. The relevant part of this test rig is illustrated in figure 3. A speed-regulated direct current motor drives two pumps. In this experiment the two pumps operate serially. The pumps deliver the water to the headwater vessel. The water flows from the vessel to the pump-turbine model. The pump-turbine is also connected to a speed-regulated direct current motor-generator. A straight acrylic glass cone is built into the pumpturbine representing the draft tube; see figure 3 on the right. The cone has a diameter of 182 mm at the inlet and a diameter of 400 mm at the outlet. The cone angle is 2 x 10°. Downstream the acrylic glass cone a straight pipe with a nominal diameter of 400 mm and a length of approx. 2.4 m is installed. Afterwards the water flows via pipes into the tailwater vessel, which is built with an air-subjected dome, in order to vary the pressure level of the test rig. The water flows from the vessel back to the pumps passing an electromagnetic flow meter. For this investigation a part load operating point was selected. This operating point is according to specific speed n11 at best efficiency and at reduced specific discharge to 0.72· Q11 at best efficiency. The velocity was measured at high-pressure level i.e. at non-cavitating conditions. The visualization of the vortex rope with cavitation and the capturing with the high-speed-camera was accomplished at conditions corresponding to σ-value of 0.137. There are no differences in the amplitude and frequency of the low frequency pressure fluctuation between the two operating conditions.

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Figure 3. Scheme of the test rig and sectional drawing of the pump-turbine. 3. Experimental setup The static pressure fluctuations in the draft tube were measured with piezo-resistive transducers at the wall of the draft tube. The piezo-resistive transducers are of the type 4043A10 of the manufacturer Kistler and were used in combination with the amplifier of the type 4601. The pressure fluctuations presented in this paper were measured at a position 99 mm downstream of the draft tube inlet (figure 3). The results of this measurement are presented as normalized values in the time domain and in the frequency domain. The fluctuation of the measured pressure is normalized by the head with equation (1). For the presentation in the frequency domain the frequency is normalized by the runner speed. The maximum error of the measured pressure fluctuation is 0.15% of the pressure caused by the head.

 

2 p H   g

(1)

The axial and radial components of the velocity in a longitudinal section are measured with PIV. For the velocity measurement a two-dimensional PIV-system is used. The PIV-system consists of a double-pulsed Nd:YAG-laser with 25 mJ per pulse and a maximum repetition rate of 20 Hz. The laser light is coupled via a light arm to the optics. The photos were taken by a CCD-camera with a resolution in space of 1280 x 1024 pixels and a 12 bit brightness resolution by a repetition rate of 8 Hz. An interrogation area with a size of 64 x 64 pixels was used in the measurement. For seeding polyamide particles with nearly round shape and an average size of 90 μm are used. Due to the conical shape of the draft tube and the coupled different angle of refraction a correction of the optical distortion is done by geometrical calibration. A program corrects the positions and the size of the velocity vectors by means of a transfer matrix. To enlarge the investigated area in the draft tube to a length of 400 mm downstream the inlet, eight subareas are measured and connected together. Additionally the velocity fields at each measured subarea are measured with two different camera positions to correct the movement of the seeding particles perpendicular to the measurement plane. To resolve the movement of the vortex rope phase-locked measurements were accomplished. To trigger the velocity measurement to the rotation of the vortex rope the pressure signal is used. Therefore the pressure signal is filtered with a band pass filter (filter frequencies 0.043 x fn and 4.3 x fn) and amplified. The stability of the periodic time of the trigger signal is depicted in figure 4. The deviation

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based on 800 measured values lead to an average value of 2.2% and the maximum deviation of the frequency is clearly below 10%. For each camera position in every subarea 1000 velocity vector-fields are measured and averaged for the respectively delay time. The accuracy of the velocities measured by PIV is approximated with 8% related to the average velocity at the draft tube inlet. The velocity is normalized by the head with equation (2).

cv 

v 2 H g

(2)

Figure 4. Deviation of the measured frequency in the trigger signal. 4. Pressure fluctuation and visualization Figure 5 displays the pressure fluctuation in the time and frequency domain. A very strong peak at a frequency of 0.295 times the runner speed and its harmonics can be seen. The nearly constant frequency in the low pressure fluctuation is caused by a closely constant rotation of the vortex rope. Beside the dominant frequency of the vortex rope rotation and its harmonics an increase in the amplitude in a range between 1.7 and 3.5 times of the frequency of the runner speed can be seen. The maximum value in that range is at a frequency of approx. 2.7 times of the frequency of the runner speed.

Figure 5. Pressure fluctuation time domain (left), frequency domain (right). In figure 6 a sequence of images from the high-speed video is depicted. This sequence shows a frame rate of 0.85 captures per runner rotation. The five pictures show a complete rotation of the vortex rope. In the last picture the position of the vortex rope is nearly the same position of the vortex rope like in the first picture. The calculated frequency of the vortex rotation is about 0.294 times of the frequency of the runner speed. This fits very well to the frequency of the low pressure fluctuation. In figure 7 a sequence of images from the high-speed video is shown. The frame rate of the sequence is 39.8 captures per runner rotation. The images show in detail the rotation of the cavitating

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vortex core shape. The structure of the surface on the last picture looks like the structure of the surface in the first picture, so the second period starting after fourteen pictures. The calculated frequency of the period from the video images is about 2.8 times of the frequency of the runner speed. This frequency fits very well to the frequency of the measured increased amplitude in the pressure fluctuation.

Figure 6. Low frame rate sequence of pictures from high-speed-video (left to right).

Figure 7. Sequence of pictures from the high-speed video (top left to bottom right). 5. Estimation of the vortex core movement by the PIV results In figure 8 a sequence of 12 phase locked velocity-fields is shown. The movement of the vortex core can be seen very clearly. As mentioned before the velocity measurement is triggered with the low frequency pressure fluctuation. For all phase locked velocity fields the same difference in the delay time was used during the measurement. There is a phase shift of 30°in the velocity fields, which are shown in figure 8. Each phase locked velocity field is like a time averaged velocity field to all fluctuations which are not connected to the rotation of the vortex rope. For the estimation of the higher frequency pressure fluctuation a phase locked velocity vector field with the vortex core close to the location of the pressure tap is selected. The selected velocity field is shown in figure 9. From the

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pictures of the surface of the cavitating vortex core a diameter of approx. 20 mm was identified. The phase averaged dimensionless circumferential velocity is approximately 0.064 at the distance of 10 mm to the center of the vortex core. That leads to a frequency for one rotation of the vortex core of about 1.2 times of the frequency of the runner speed. It is assumed, that the cross section has a flattened shape that looks like an elliptical cross section (figure 7). So a new period starts after a half rotation of the vortex core. This leads to the doubling of the frequency (2.4 times of the runner frequency) which is in the range of the higher frequency pressure fluctuation.

Figure 8. Phase locked velocity in a longitudinal section [7]. 6



Note, this rough estimation has neglected the influence of the cavitation on the velocity field. The low frequency pressure fluctuation for this operation point is independent for the cavitating and noncavitating condition (not shown here). The higher frequency is depending on the pressure level that is caused by the different positions of the surface of the cavitating vortex core. In addition there is an influence in the local velocity field at the surface of the cavitating vortex core by cavitation, too. An additional check for the correct phase lock of the velocity fields to the vortex movement is done with the positions of the vortex core within the velocity fields. The distance between two vortex cores in a phase locked velocity field is in average 255 mm. Based on the frequency of the low pressure fluctuation, a normalized velocity of cv = 0.066 is determined. The estimated value fits well with the time averaged velocity at the position of the vortex cores. In figure 10 the time averaged velocity field in a longitudinal section is depicted. The red rhombi in the picture mark the different positions of the vortex cores. The positions of the vortex cores are located in the region with the calculated velocity. Thus, a correct trigger signal for the vortex rope movement was selected.

Figure 9. One phase locked velocity field at the vortex core.

Figure 10. Time averaged velocity in a longitudinal section with marked vortex cores [7].

6. Results of the comparison Figure 11 shows a sketch of the vortex rope movement in a longitudinal section. The rotation of the vortex rope leads to a movement of the vortex core downstream in the shear layer between the main flow and the stagnation region in the center of the draft tube. Additionally the vortex rope core rotates around its axis. Flow Flow vortex rope stagnant region

One rotation of the vortex rope

Figure 11. Sketch of the vortex rope movement [7]. A correlation between the pressure fluctuation and the movement of the vortex rope can be identified. The pressure fluctuation is a superposition of the low frequency pressure fluctuation caused

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by the rotation of the vortex core and the higher frequency pressure fluctuation caused by the rotation of the vortex rope. 7. Conclusions Besides the pressure fluctuation with the frequency of the vortex rope rotation, also higher frequency pressure fluctuations can be observed in the investigated operating point. Based on a high-speed video a correlation between the rotation of a deformed shape of the vortex rope cross-section and the pressure pulsation is shown. In an additional comparison of the pressure fluctuation frequency with the measured velocity at the position on the surface of the cavitating vortex core approximately 180° rotation of the vortex core is calculated for one period of the higher frequency pressure fluctuation. Thus, the measured pressure fluctuation seems to be a superposition of the pressure fluctuation caused by the rotation of the vortex core and the pressure fluctuation caused by the rotation of the vortex rope. Acknowledgments We want to acknowledge Mr. Giese and Mr. Neumann (Voith Hydro) for making the first high-speedvideos of our experiment, so that we were able to do this investigation. Nomenclature BEP Best efficiency point cv Normalized velocity [-] D Diameter or the runner [m] f Frequency of the fluctuation [Hz] fn Frequency of the runner speed [Hz] g Gravity constant [m/s2] H Head of the turbine [m] n Runner speed [rpm], samples[-]

Specific runner speed [rpm](=n.D/H0.5) ~ p Pressure fluctuation [Pa] Q Turbine discharge [m3/s] Q11 Specific discharge [m3/s] (=Q/(D2.H0.5))  Normalized pressure fluctuation [-]  Thoma Number [-]  Density of water [kg/m3] n11



References [1] Goede E, Ruprecht A and Lippold F 2004 On the influence of runner design on the draft tube vortex Proc. 13th Int. Seminar Wasserkraftanlagen (Wien, Austria, 2004) [2] Ruprecht A and Helmrich T 2003 Simulation of the water hammer in a hydro power plant caused by draft tube surge Proc. of ASME FEDSM 4th ASME_JSME Joint Fluids Engineering Conf. (Honolulu, USA, 6-10 July 2003) [3] Koutnik J, Krüger K, Pochyly F, Rudolf P and Haban V 2006 On cavitating vortex rope from stability during francis turbine part load operation Proc. of IAHR Int. Meeting of WG on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems (Barcelona, Spain, 28-30 June 2006) [4] Koutnik J, Faigle P and Moser W 2008 Pressure fluctuations in francis turbines-theoretical prediction and impact on turbine Proc. of 24th IAHR Symp. on Hydraulic Machinery and Systems (FOZ DO IGUASSU, Brasil, 27-31 October 2008) [5] Kirschner O and Ruprecht A 2007 Vortex rope measurement in a simplified draft tube Proc. 2nd IAHR Int. Meeting of the Workgroup on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems (Timisoara, Romania, 24-26 October 2007) [6] Kirschner O, Ruprecht A and Göde E 2009 Experimental investigation of pressure pulsation in a simplified draft tube Proc. of 3rd IAHR Int. Meeting of the Workgroup on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems (Brno, Czech Republic, 14-16 October 2009) [7] Kirschner O 2011 Experimentelle Untersuchung des Wirbelzopfes im geraden Saugrohr einer Modell-Pumpturbine Ph.D Thesis (Stuttgart: Universität Stuttgart)

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