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Inter-blade flow analysis of a propeller turbine runner using stereoscopic PIV
Accepted Manuscript Inter-blade flow analysis of a propeller turbine runner using stereoscopic PIV Aeschlimann Vincent, Beaulieu S´ebastien, Houde S´ebastien, Ciocan Gabriel Dan, Deschˆenes Claire PII: DOI: Reference:
S0997-7546(13)00064-2 http://dx.doi.org/10.1016/j.euromechflu.2013.06.002 EJMFLU 2673
To appear in:
European Journal of Mechanics B/Fluids
Received date: 6 February 2013 Revised date: 7 June 2013 Accepted date: 7 June 2013 Please cite this article as: A. Vincent, B. S´ebastien, H. S´ebastien, C. Gabriel Dan, D. Claire, Inter-blade flow analysis of a propeller turbine runner using stereoscopic PIV, European Journal of Mechanics B/Fluids (2013), http://dx.doi.org/10.1016/j.euromechflu.2013.06.002 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Inter-blade flow analysis of a propeller turbine runner using stereoscopic PIV. AESCHLIMANN Vincent*, BEAULIEU Sébastien**, HOUDE Sébastien*, CIOCAN Gabriel Dan*, DESCHÊNES Claire*. * LAMH, Laval University, Quebec, Quebec G1V 0A6, Canada ** Alstom Power & Transport, Canada Corresponding author:
Aeschlimann Vincent [email protected] +1 418 656 2131 #2594
Abstract The paper presents the averaged velocity field inside the inter-blade channel of a propeller turbine runner measured using stereoscopic particle image velocimetry (SPIV) technique. In this manner measurements have been performed without any modification of the flow patterns, with the averaged three-dimensional velocity fields reconstructed from phase-averaged acquisition data based on the blade azimuth. Main and secondary flows were analysed for nine operating conditions, ranging from part to full load. The radial velocities and gradients play major roles in the inter-blade flow development. Using the λ2-definition for vortex detection, leading edge vortices were detected and identified under part load conditions.
Keywords Hydraulic Turbine; Particle Image Velocimetry (PIV); Phase-averaged; Vortex detection.
Highlights -
SPIV measurements performed inside a propeller hydraulic turbine runner.
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Three-dimensional velocity fields reconstructed from phase averaged measurements.
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Leading edge vortices detected under part load operating conditions.
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Both main relative and secondary flows analysed covering nine operating conditions.
1
Nomenclature second eigenvalues of S 2
λ2
2
efficiency (%)
ωc
vorticity, c-axis component (s-1)
C
velocity gradient tensor (s-1)
Ω
antisymmetric part of C
ΩR
runner rotation speed (rad/s)
Cref
reference velocity (m/s)
Cr,, Cθ, Cz
absolute velocity components (m/s)
D
shroud diameter at runner blade axis (m)
H
net head (m)
N
runner rotation speed (rpm)
N11
runner rotation speed, unit number (rpm)
Q
flow rate (m³/s)
Q11
flow rate unit number (m³/s)
Rref
runner radius (m)
S
symmetric part of C
Wr, Wθ, Wz
relative velocity components (m/s)
x, y, z
global reference frame, Cartesian
r, θ, z
global reference frame, cylindrical
XT,YT, ZT
calibration target reference frame
i, j, k
local reference frame
CFD
Computational Fluid Dynamics
LDV
Laser Doppler Velocimetry
OP
Operating Point
PIV
Particle Image Velocimetry
2
Introduction The present study is part of the AxialT project aimed at a better understanding of propeller turbines [1, 2]. Here, the focus is on the mean and secondary flows inside the turbine runner. The flow inside a turbine runner is complex and combines several features similar to those encountered around a finite length hydrofoil; also the rotation introduces additional phenomena such as the Coriolis acceleration and rotor-shroud interactions. For hydraulic turbine, the energy extraction occurs in the runner and an accurate prediction of the flow dynamics inside this component is the key to an efficient design. Nowadays, hydraulic turbine CFD calculations are an integral part of the design process. Improving the accuracy of flow simulations, either through modification of current strategies or by developing new ones, requires the use of accurate and relevant experimental data. In particular, accurate predictions of secondary flows and vortex development in the runner are important for runner optimization. The flow inside rotors has been characterized using theoretical approaches for both hydraulic and gas turbo-machines (cf. [3, 4]). One of the flow features presented by Raabe [3] and Vavra [4] is the relative steady rotor flow governed by the Coriolis acceleration, which induces a relative rotation in the opposite direction to the rotor rotation. Secondary flows and vortices have also been studied experimentally, Langston [5] provided a wide review of the various vortices detected around blades in plane and annular cascade flows, excluding blade tip clearance effects. Most of the vortices presented originate at the junction of the hub and the blade leading edge. At this location, a main vortex develops: a horseshoe vortex with one leg on the suction side, called the leading edge vortex, and the other leg on the pressure side known as the passage vortex. One common goal of inter-blade flow studies has been to detect and analyse the secondary flows. In gas turbines, such phenomena may significantly alter the heat transfer at the blades, whereas in hydraulic turbines vortices are of particularly interest regarding the inception of cavitation. In fact, due to the centrifugal acceleration, the vortex centers will be located where the pressure is the lowest, and hence where cavitation may start. Above all, losses and lift performance at the blade can be altered by such local phenomena. To perform experimental velocity measurements inside a rotating confined device is challenging and several attempts have already been conducted. Starting in the nineties, nonintrusive velocity measurements were performed inside rotors, with Particle Image Velocimetry (PIV) proving to be the most suitable technique [6].
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Rotor-stator interactions have been studied, using 2D-PIV in a centrifugal pump [7] and axial turbo-pump [8] with diffuser vanes. More recently, Yu and Lui [9] investigated the rotorstator interaction using a stereoscopic PIV system (SPIV) to acquire the three components of the velocity field inside the compressor stage. The development and impact of the rotor blade wakes on the stator were analysed. Rotating stall phenomena, with intermittent recirculation cells inside the inter-blade channels, were detected in a centrifugal pump under part load conditions using 2D-PIV [10]. Further analyses, using a time resolved system (TR-PIV), allowed the identification of the frequency and dynamics of this phenomenon [11]. The flow through the clearance between the runner blade tips and its casing is driven by the pressure gradient between the pressure and suction sides of the blades. Such flows roll up into the tip leakage vortices, whose development and breakdown have been observed using SPIV inside a compressor stage [9]. Later, the complete roll-up process was identified in a water-jet pump [12]. Refined measurements inside the blade tip gap and the inter-blade channel were obtained using a 2D-PIV system. The tip leakage vortex and the associated inner structures and interactions were then characterized. Multi-planar measurements have permitted the reconstitution of the averaged threedimensional velocity field. For example, a 2D-PIV system was used to acquire the axial and tangential velocities over six planes at different radial distances, inside a compressor rotor, ranging from the hub to mid span [13]. Also, an averaged three-dimensional velocity field has been obtained with multi-planar SPIV inside a compressor stage, for both the rotor and the stator, covering mid-span to the casing [9]. In these two particular studies, the lowest spatial resolution was in the out-of-plane direction, as the distances between consecutive planes were respectively 10 mm (equivalent to about 0.2 chord length or 0.1 span) and 18 mm (equivalent to about 0.1 chord length or 0.1 span). It seems from this review that only CFD data is capable of providing a high-resolution three-dimensional velocity field in the complete regions between two successive runner blades (i.e. the inter-blade channel) in hydraulic turbines. Nevertheless, experimental data are both useful and necessary to corroborate and confirm numerical simulations, even with partial information such as limited measurement areas and often the lack of some of the three velocity components.
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To the authors’ knowledge, no velocity measurements have been carried out in the interblade channel of a hydraulic turbine. Furthermore, the leading edge vortex has only been detected from qualitative visualisations in previous experimental investigations. To fill this lack of experimental data, a velocity measurement campaign was undertaken, involving no modification of the flow patterns by instrumentation. The present paper presents the stereoscopic PIV techniques used to acquire the velocity field inside the inter-blade channel of the runner. From these high spatial resolution measurements (< 0.05 chord length), an averaged three-dimensional velocity field was reconstructed. The fine spatial resolution allows the evaluation of the nine components of the velocity gradient tensor and the streamline patterns. The mean and secondary flows were recorded and analysed for nine different operating conditions and the λ2-definition used to detect the position of vortices.
1. Experimental set-up 1.1 Propeller turbine model The 1950’s era propeller turbine used for the AxialT project is illustrated in Fig. 1. This turbine has a fronto-spiral casing with two intake channels. The draft tube consists of a conical diffuser followed by a diverging-converging elbow and a diverging duct separated by a pier leading to two unsymmetrical exit channels. The distributor is composed of 24 guide vanes and 24 stay vanes, paired with a 6-blade propeller runner. As indicated in Fig. 1, the reference frame is centered at the distributor mid-height, with the positive x-axis oriented towards the draft tube outlet, the positive y-axis following the right-hand rule convention, and the positive z-axis directed upwards. Extensive experimental investigations have been carried out using this scale model, for the intake, distributor, runner and draft tube (see [14-18]). The test rig consists of a closed-loop hydraulic facility with flow rates up to Q = 1 m3/s measured by an electromagnetic flow meter with an accuracy of 0.2%. Heads up to H = 50 m are measured according to IEC guidelines of 0.05%. Rotational speeds up to N = 2000 rpm can be achieved with an accuracy of 0.01% and net powers at the test section up to P = 170 kW. The rig is fully equipped with measurement systems for testing the performance of hydraulic turbine models according to the IEC 60193 standard and for monitoring internal flows and pressure fields. Following efficiency () hill chart measurements, nine (9) different operating points (OP) were chosen for the present investigation (Fig. 2). The chosen OPs include optimal (OP3), part load (OP8) and full-load (OP7) conditions, at three different rotational speeds. Dimensionless 5
operating conditions are summarized in table 1, using unit numbers Q11 and N11:
Q11
Q D H1/ 2
(1)
N11
ND H1/ 2
(2)
2
with N [rpm] the rotation speed, D [m] the shroud diameter at the runner blade axis and H [m] the net head. The runner rotation is counter-clockwise. OP3 is used as the reference operating point. Rref is the runner radius and the reference 2 velocity Cref is defined for each operating point as Cref Q / R ref .
1.2 Particle Image Velocimetry Stereoscopic particle image velocimetry (SPIV) is a non-intrusive measurement technique providing access to the three components of the instantaneous velocity field in a plane. A stereoscopic DANTEC PIV system was used to measure the phase-averaged velocity field over one blade passage. A vertical light sheet with a thickness of 5 mm, created by a Nd:Yag laser delivering 60 mJ per pulse, was projected to illuminate particles through the transparent Plexiglas wall of the conical diffuser. A 6 degree of freedom optical arm was used to position the light sheet and two HiSense cameras with a CCD resolution of 1024 x 1280 pixels² were installed in a stereoscopic configuration. The seeded particles used were silver-coated hollow glass spheres with an average diameter of ten microns (10 μm). Figure 3 illustrates the camera and laser sheet orientation. Two cameras set at different angles of view were required to obtain all three components of the velocity. The measurement plane was vertical, crossing the blade around mid span. The laser beam was aligned with the blade angle to minimize the size of the blade shadow on the measurement area. Also, the two cameras were positioned at 45° rather than the typical optimal value of 90°. This particular configuration was required to gain access to the measurement plane located between the blades. As can be seen in Fig.1, the spiral casing is hiding the major part of the runner blades so the cameras were positioned to get a view from underneath. Planar surfaces at the outer wall of the diffuser minimized optical distortion through the air-Plexiglas interface window. The Scheimpflug technique was used to provide the best focus on the measurement plane [19]. Because the cameras were positioned at 45° in the XT-ZT plane and get a view from 6
underneath the runner (about 30° in the YT-ZT plane), to correct the non-orthogonality of the camera to the measurement plane in both directions, two degree of freedom lens mounts were used. The time delay between two consecutive frame acquisitions was 70 µs; particle displacements generally satisfy the one-quarter rule (i.e. 8 pixels displacement). For the particle displacement and velocity calculations, an adaptive correlation was used starting from 64×64 pixels2 interrogation windows with two passes reduced to a final 32×32 pixels2 interrogation area with an overlap of 50%. Peak and local neighborhood validations, using the local median, were used to eliminate anomalous vectors [20]. A custom calibration target was designed to fit the inter-blade channel (Fig.4). Uncertainties in the positioning of the target with respect to the global reference frame (see Fig.1) were 1,1 mm; 0,4 mm and 0,3 mm respectively for the x, y and z-axes. A micrometer with an accuracy of 0,05 mm was used to displace the calibration target in the out-of-plane direction (ZTaxis in Fig.3 and 4). Eleven (11) images of the target were captured from -2,5 to 2,5 mm with 0,5 mm steps. The calibration was performed in water. The laser sheet was aligned with the target in the central position. Corrections were made for the distortion due to the different refractive indices of air, Plexiglas and water. The unwarping function used a 3rd order polynomial model in the XT and YT directions and a 2nd order one in the ZT direction. The accuracy of this unwarping method led to a maximum bias of 5% on the velocity components. The spatial sampling was about 3×3 mm over the 2D velocity field. The blade shadows reduced the valid measurement area, depending on the runner angular position. The velocity fields contained from 600 to 1900 vectors depending on the blade position inside the field of view. Additional details on the PIV set-up, calibration and validation can be found in Beaulieu et al. [15-16]. The runner position was monitored with a shaft mounted encoder generating one pulse per revolution, resetting a triangular ramp from which the azimuthal runner angular positions can be calculated. The measurements were performed at specific phase angles (i.e. runner positions). The shaft mounted encoder pulse signal is used to trigger the acquisition sequence. Different runner positions, corresponding to different phase angles, are obtained by adding a time delay to the trigger pulse. Recordings were made every 3 degrees of runner rotation, with 21 phases covering 60° of runner rotation, equivalent to one blade passage. At each phase angle, 1000 velocity fields were acquired ensuring a statistical convergence on the mean velocity norm with a bias of less than 1 %.
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Upstream of the runner, the flow comes from the spiral casing through 24 stay vanes and 24 guide vanes. Further downstream, the flow is not perfectly axisymmetric. The mass flow rate distribution through each guide vane passage is not necessarily the same, which can lead to a static flow unbalance at the runner inlet [17-18]. However, for this study the mass flow rate distribution is assumed to be uniformly distributed within each inter-blade channels. In addition, all the stay and guide vanes generate wakes leading to azimuthal variations and fluctuations. The magnitudes of those velocity non-uniformities are probably small and might dissipate rapidly. At first approximation, a quasi-axisymmetric flow conditions is assumed at the inlet of a given runner inter-blade channel. Based on this hypothesis, and for visualization purposes, the temporal evolution of the velocity in the measurement area can be transposed to the spatial evolution. A measurement volume was reconstructed from the 21 planar measurement areas corresponding to each phase. This reconstruction has been carried out by superposing the 21 measurement planes according to their relative position in the runner reference frame, as illustrated in figure 5. The resulting volume covers radial positions from 0.62×Rref to 0.77×Rref. The maximum distance between two consecutive planes (i.e. at the periphery of the measurement volume) was about 0.04×Rref, or roughly equivalent to 4% of the chord length. For postprocessing purposes, data has been interpolated to equidistant meshes using linear interpolation and Delaunay triangulation. This representation of the data was particularly interesting since it created a measurement volume providing the three-dimensional velocity vectors and the nine components of the velocity gradient tensor. The results were transposed into a cylindrical coordinate (r, θ, z) system centered on the global reference frame of the turbine with θ, the angular position in the x-y plane, defined as positive in the counter-clockwise direction. Velocities were represented in the rotating frame, moving at the runner rotation speed ΩR [rad/s] (ΩR = 2πN/60):
Wr Cr W W C r R W C z z
2.
(3)
Vortex identification 2.1 Vortex detection method The vortex identification methodology presented by Jeong and Hussain [21] was used in
the present study. The λ2-definition they proposed is an appropriate criterion for vortex 8
identification in the present case. For example, it allows vortex identification regardless of the reference frame chosen. Also, the λ2-definition does not require fore-knowledge of the convective velocity of the vortex cores or their axial directions. λ2 is the second eigenvalue of the symmetric tensor S , where S and Ω are the symmetric and anti-symmetric parts of the mean-velocity 2
2
gradient tensor C . The vortices are enclosed in the contours defined by λ2 < 0 [21] and their centers are defined where λ2 is a minimum, thus allowing one to estimate the vortex centerline. Figure 6 illustrates a few x-y planes of λ2 contours where a vortex has been detected next to the blade suction side, with its centerline plotted with a white line. High concentrations of vorticity and streamlines exhibiting concentric shapes, which are characteristic of vortex cores, were analysed. To obtain the vorticity, we viewed the vector fields in planes normal to the centerline (Fig.7, where i-j-k is an orthonormal coordinate system with k tangent to the vortex centerline and its origin O located at the vortex centerline). The velocity at the vortex centerline was assumed to be the convective velocity of the vortex. Subsequently, the latter was subtracted from the velocity fields of each normal plane, showing concentric streamlines around the vortex center (Fig.7b). The vorticity ωk normal to the plane was then calculated with respect to the local reference frame i-j-k. 2.2 Vortex identification and analysis Due to the vortex location and the restricted measurement area, it was difficult to determine accurately the extent of the vortex (Fig.7). The vortex indicates an elliptical shape that can be seen in the cross sectional view. A possible reason for this non-circular shape could be that the vortex is wandering in the radial direction. Since these results were obtained from averaged values of the velocity field, wandering of the vortex would have the effect of enlarging its calculated core dimensions [22]. These results may also indicate that a shearing stress field is deforming the core. However, when located inside the measurement area, an averaged vortex center can be specified and the corresponding centerline plotted. Figure 8 shows the centerlines identified for OP1, OP2 and OP9. At these three operating conditions, at part load and outside the optimal range of the turbine, the counter-clockwise vortices are parallel to the blade and close to the suction side at around mid-span. It is reasonable to assume that the vortex path is influenced by the inlet conditions. If vortices were also present at OP3 to OP8, then their respective center lines would have been located outside the measurement zone, so that they could not be identified. Furthermore, it was not possible to locate the starting point of the vortex from the PIV measurements. However, visualizations were performed using a high speed camera at OP9 [23]: As the pressure was 9
decreased in the test loop, cavitation occurred, providing visualisation of vortices in the low pressure areas (c.f. Fig.9). The higher the rotational velocity of the vortex, the lower the pressure at its center, making cavitating structures good candidates for vortex detection. A typical picture is presented in Fig.9. Cavitating structures were detected inside the inter-blade channels, starting at the leading edge and hub junction. These structures had an elongated shape parallel to the blade close to the suction side, reaching mid-span at the trailing edge. Their rotation was in the same counter-clockwise direction as the runner. All these qualitative features match the observations from the velocity field, validating the common assumption that similar vortices exist both with and without cavitation. This would indicate that the three vortex centre lines illustrated in Fig.8 correspond to leading edge vortices originating at the leading-edge hub junction.
3.
Relative flow The relative flow within the inter-blade channel presents a pattern similar to that occurring
in hydrofoil theory. In figure 10, using OP3, OP1 and OP8 as examples, the velocity field is extracted for a vertical slice at constant radius (θ-z). The velocity norm
W2 Wz2 is higher on
the suction side of the blade than on the pressure side. This non-uniform velocity distribution in the inter-blade channel was observed at the runner outlet and its convection and dissipation in the draft tube cone has been investigated in the case of the present propeller turbine model [18], as well as downstream of a Kaplan turbine [24-25]. Under part load conditions, the axial and tangential velocities are lower than at the optimal condition OP3, in accordance with the lower mass flow rate Q11. From optimal to full load conditions, OP3 to OP7, the main flow direction remains parallel to the blade, exhibiting good flow behavior with no flow separation detected based on observations of Wθ and Wz (Fig.10: OP3). However, at part loads, OP1, OP2, OP8 and OP9, a local deviation of the vector direction is discernible on the suction side of the blade, associated with the higher magnitude of the radial velocity Wr (Fig.10: OP1 and OP8). Concerning the radial component of the velocity, a gradient (∂Wr/∂θ) exists in the azimuthal direction indicating a lateral movement of the fluid in the inter-blade channel. Analyzing the Wθ and Wr velocity fields, the operating conditions became clearly distinguishable. In figure 11, the velocity field is extracted for x-y planes and represented as vectors, the color levels represent the vorticity ωz/ΩR. Figure 11 illustrates the three tendencies observed using OP3, OP1 and OP8 as examples. OP3 to OP7 are similar, showing no unusual local behavior for conditions varying from optimal to full load. For the part load operating points, OP1, OP2 and OP9, as mentioned earlier, a local counter-clockwise vortex is present on the blade suction side. 10
Finally, OP8 stands out with a similar counter-clockwise structure on the blade suction side, but now covering about a third of the measurement area. This structure was not detected using the λ2definition and its vorticity is much lower than that measured inside the leading edge vortices of OP1, OP2 or OP9. Furthermore the structure was much wider and thus might not actually be the leading edge vortex. The specific operating condition OP8 corresponds to the lowest measured Q11 and was farthest away from the best efficiency point, with a flow pattern that may be altering the lift on the blade. Inside the relative reference frame, rotating at the runner rotation speed ΩR, the Coriolis acceleration induces a relative rotational flow in the opposite direction to that of the runner (i.e. clockwise). If we consider a simplified case, consisting of an axial rotor with flat radial blades and irrotational flow at the inlet, steady and non-viscous, the relative flow would possess a rotational speed equal and opposite to that of the runner, leading to an axial vorticity ωz = -2×ΩR [3-4]. This simplified reference case, where the Coriolis effect prevails, is compared to the present experiment. First, inside the AxialT runner with inlet flow conditions varying from optimal to full load (OP3 to OP7), the vorticity ωz was found to be virtually constant over the entire measurement volume. The average vorticity of the relative flow was calculated and systematically found to be about -1.3×ΩR, where ΩR depends on the particular operating condition OP. The horizontal vorticity field at OP3 is presented in Fig.11 as an example, with similar uniform vorticity fields observed from OP3 to OP7. The vorticity magnitude in the experiment is lower than in the reference case, suggesting other flow behaviors are counterbalancing the Coriolis effect. Second, the relative flow induced by the Coriolis acceleration interacts with the local vortex pattern. For example, under part load operating conditions, counteracting to the Coriolis effect, the leading edge vortices induce a local counter-clockwise rotation on the blade suction side with a vorticity ωz ≈ 25×ΩR , with the OP2 and OP9 fields similar to that of OP1, illustrated in Fig.11. At OP8, the local flow structure induces a counter-clockwise rotation with a vorticity ωz ≈ 3×ΩR. Finaly, differences might also be induced by the passage vortex [5] acting in the opposite direction to that of the Coriolis acceleration, although the former was not identified from the present measurements.
4. Streamline pattern 11
The streamlines, calculated from the average relative velocity field, provide informative description of the shear stresses inside the relative velocity field. A qualitative observation stems from the streamline patterns shown in figure 12 (OP3). As an example, four of the streamlines (AA’, BB’, CC’ and DD’) have been plotted at heights Z1 to Z2 for OP3 (The dashed lines represent the radial and circumferential directions). Using the example given by Munson et al. [26], if a pair of small sticks forming a right angle cross pattern were located at Z1, according to the streamlines, they would rotate as they move to location Z2. The stick AB would rotate counter-clockwise from Z1 to A’B’ at Z2 whereas the stick CD would rotate clockwise to C’D’. The fact that the right angle between AB and CD is not maintained constant downstream, indicates the existence of shear stresses in the flow. The length changes of AB and CD can be due to both shear and strain. These observations differ from the purely theoretical cases of irrotational free vortices and rotational forced vortices illustrated in [26]. The vorticity thus represents both the rotation of the fluid and also a part of the shear stresses. In fact, the fluid motion can be decomposed into three elementary components: pure shear, rigid body rotation and irrotational strain [27]. A second insight is provided by figure 13, for OP3, where the averaged velocity of the horizontal plan under consideration has been subtracted from the velocity field. This reveals the secondary flow pattern, highlighting a saddle point at the center of the velocity field. This streamline pattern can be modeled by superimposing pure shear and irrotational strain [27]. Because of the strong influence of local three-dimensional structures on the main flow, further work such as numerical simulation is required to identify all the flow features composing the inter-blade flow.
5. Conclusion The three dimensional averaged velocity field inside the inter-blade channel of a propeller hydraulic turbine was measured using stereoscopic particle image velocimetry (PIV). Measurement volumes were reconstructed artificially from planar measurements at different runner positions. The three components of the averaged velocity vector were then measured inside a portion of the inter-blade channel, providing light on the inner flow structures. The turbine model was tested at nine operating conditions ranging from part to full load, with the flows unaffected by the non-intrusive instrumentation. Measurements were made inside the runner channel, revealing complex flow patterns similar to those encountered in full scale hydraulic turbines. 12
Using the λ2-definition, vortex cores were identified, together with their centrelines, crossing the measurement zone for three part-load operating conditions. Visualisation studies under cavitating conditions, identified these structures as leading edge vortices. These significantly altered the relative flow inside the inter-blade channels. The radial velocities and gradients play a major role in the development of the inter-blade flow showing that twodimensional simplifications should be avoided. The Coriolis acceleration induces a relative flow in the opposite direction to that of the runner. This secondary induced flow was shown to be counterbalanced by local phenomena, showing complex interactions. An important limitation regarding the present investigation was the restricted measurement area. The covered span extended only from 0.62×Rref to 0.77×Rref. Further work is planned, including numerical simulations, to extend the present analysis over the complete runner. The data gathered during the present study should prove useful in the validation of numerical simulations.
Acknowledgments The authors would like to thank the participants of the Consortium on Hydraulic Machines for their support and contribution to this research project: Alstom Power & Transport, Andritz Hydro LTD, Edelca, Hydro-Quebec, Laval University, NRCan, Voith Hydro Inc. Our gratitude also goes to the Canadian Natural Sciences and Engineering Research Council, who provided funding for this research.
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Turbines, in: Proceedings of ASME-JSME-KSME Joint Fluids Engineering Conference, AJK2011-FED, Hamamatsu, Shizuoka, Japan, 2011. [15] S. Beaulieu, C. Deschênes, M. Iliescu, R. Fraser, Flow Field Measurement Through the Runner of a Propeller Turbine Using Stereoscopic PIV, in: Proceedings of the 8th Int. Symp. On Particle Image Velocimetry – PIV’09, Melbourne, Victoria, Australia, 2009a. [16] S. Beaulieu, C. Deschênes, M. Iliescu, G.D. Ciocan, Study of the flow field through the runner of a propeller turbine using stereoscopic PIV, in: Proceedings of the 3rd IAHR Int. Meeting of the Workgroup on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems, Brno, Czech Republic, 2009b. [17] J.M. Gagnon, G.D. Ciocan, C. Deschênes, M.S. Iliescu, Numerical and Experimental Investigation of Rotor-Stator Interactions in an Axial Turbine: Numerical Interface Assessment, in: Proceedings of the ASME 2008 Fluids Engineering Division Summer Meeting, FEDSM2008-55183, Jacksonville, Florida, 2008. [18] J.M. Gagnon, V. Aeschlimann, S. Houde, F. Flemming, S. Coulson, C. Deschênes, Experimental Investigation of Draft Tube Inlet Velocity Field of a Propeller Turbine, J. Fluids Eng. 134 (10) (2012) 101102. [19] C. Willert, Stereoscopic digital particle image velocimetry for application in wind tunnel flows, Measurement Science and Technology 8 (12) (1997) 1465-1479. [20] J. Westerweel, F. Scarano, Universal outlier detection for PIV data, Exp. Fluids 39 (6) (2005) 1096–1100. [21] J. Jeong, F. Hussain, On the identification of a vortex, J. Fluid Mech. 285 (1995) 69-94. [22] A.L. Heyes, R.F. Jones, D.A.R. Smith, Wandering of wing-tip vortex, in: Proceedings of the 12th Int. Symp. On Application of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 2004. [23] S. Cupillard, A.M. Giroux, R. Fraser, C. Deschênes, Cavitation Modeling in a Propeller Turbine, in: Proceedings of the 4th Int. Meeting on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems, Belgrade, Serbia, 2011.
15
[24] B.G. Mulu, P.P. Jonsson, M.J. Cervantes, Experimental investigation of a Kaplan draft tube – Part I: Best efficiency point, Appl. Energy 93 (2012) 695-706. [25] P.P. Jonsson, B.G. Mulu, M.J. Cervantes, Experimental investigation of a Kaplan draft tube – Part II: Off-design conditions, Appl. Energy 94 (2012) 71-83. [26] B.R. Munson, D.F. Young, T.H. Okiishi, Fundamentals of Fluid Mechanics, New-York: 5th Edition, John Wiley, 2006, p.302. [27] V. Kolar, Vortex identification: New requirements and limitations, Int. J. Heat and Fluid Flow 28 (2007) 638-652.
16
Table 1 Operating conditions
Fig.1
Propeller turbine model
Fig.2
Efficiency hill chart and operating points (
Fig.3
Measurement area, camera and laser sheet positions
Fig.4
Calibration target
Fig. 5
Measurement volume reconstruction from 21 measurement planes
Fig. 6
Vortex center line identification using λ2 contours at OP1
Fig. 7
Plane normal to the vortex centerline, OP1; a) local reference frame, b) velocity field and vorticity
η/ηref;
guide vane opening)
ωk Fig. 8
Vortex center lines
Fig. 9
Visualization of the cavitating leading edge vortex (OP9)
Fig. 10 Relative average velocity field; vectors: (Wθ, Wz) and contours: Wr /Cref ; r/Rref = 0.68 Fig. 11 Relative velocity field; z/Rref = -0.8; velocity vectors: (Wr , Wθ); vorticity contours: ωz/ΩR Fig. 12 Streamline deviation, OP3 Fig. 13 Secondary flow; OP3; z/Rref = -0.8; velocity vectors and streamline structure
17
Table 1 Operating conditions
OP
Guide vane opening [°]
N11/N11 ref
Q11/Q11 ref
η/ηref
1
25
1
0.828
0.86
2
31
1
0.963
0.974
3
33
1
1
1
4
38
1
1.071
0.992
5
33
0.976
0.99
1.002
6
33
1.05
1.016
0.976
7
44
1.05
1.168
0.969
8
17
1
0.612
0.673
9
27
0.976
0.875
0.906
Fig. 1
Propeller turbine model
18
η/ηref;
Fig. 2
Efficiency hill chart and operating points (
Fig. 3
Measurement area, camera and laser sheet positions
19
guide vane opening)
Fig. 4
Calibration target
Fig. 5
Measurement volume reconstruction from 21 measurement planes
Fig. 6
Vortex center line identification using λ2 contours at OP1
20
a)
b) Fig. 7
Plane normal to the vortex centerline, OP1; a) local reference frame, b) velocity field and vorticity
ωk
Fig. 8
Vortex center lines
21
Fig. 9
Visualization of the cavitating leading edge vortex (OP9)
Fig. 10 Relative average velocity field; vectors: (Wθ, Wz) and contours: Wr /Cref ; r/Rref = 0.68
22
Fig. 11 Relative velocity field; z/Rref = -0.8; velocity vectors: (Wr , Wθ); vorticity contours: ωz/ΩR
Fig. 12 Streamline deviation, OP3
23
Fig. 13 Secondary flow; OP3; z/Rref = -0.8; velocity vectors and streamline structure
24
S0997-7546(13)00064-2 http://dx.doi.org/10.1016/j.euromechflu.2013.06.002 EJMFLU 2673
To appear in:
European Journal of Mechanics B/Fluids
Received date: 6 February 2013 Revised date: 7 June 2013 Accepted date: 7 June 2013 Please cite this article as: A. Vincent, B. S´ebastien, H. S´ebastien, C. Gabriel Dan, D. Claire, Inter-blade flow analysis of a propeller turbine runner using stereoscopic PIV, European Journal of Mechanics B/Fluids (2013), http://dx.doi.org/10.1016/j.euromechflu.2013.06.002 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Inter-blade flow analysis of a propeller turbine runner using stereoscopic PIV. AESCHLIMANN Vincent*, BEAULIEU Sébastien**, HOUDE Sébastien*, CIOCAN Gabriel Dan*, DESCHÊNES Claire*. * LAMH, Laval University, Quebec, Quebec G1V 0A6, Canada ** Alstom Power & Transport, Canada Corresponding author:
Aeschlimann Vincent [email protected] +1 418 656 2131 #2594
Abstract The paper presents the averaged velocity field inside the inter-blade channel of a propeller turbine runner measured using stereoscopic particle image velocimetry (SPIV) technique. In this manner measurements have been performed without any modification of the flow patterns, with the averaged three-dimensional velocity fields reconstructed from phase-averaged acquisition data based on the blade azimuth. Main and secondary flows were analysed for nine operating conditions, ranging from part to full load. The radial velocities and gradients play major roles in the inter-blade flow development. Using the λ2-definition for vortex detection, leading edge vortices were detected and identified under part load conditions.
Keywords Hydraulic Turbine; Particle Image Velocimetry (PIV); Phase-averaged; Vortex detection.
Highlights -
SPIV measurements performed inside a propeller hydraulic turbine runner.
-
Three-dimensional velocity fields reconstructed from phase averaged measurements.
-
Leading edge vortices detected under part load operating conditions.
-
Both main relative and secondary flows analysed covering nine operating conditions.
1
Nomenclature second eigenvalues of S 2
λ2
2
efficiency (%)
ωc
vorticity, c-axis component (s-1)
C
velocity gradient tensor (s-1)
Ω
antisymmetric part of C
ΩR
runner rotation speed (rad/s)
Cref
reference velocity (m/s)
Cr,, Cθ, Cz
absolute velocity components (m/s)
D
shroud diameter at runner blade axis (m)
H
net head (m)
N
runner rotation speed (rpm)
N11
runner rotation speed, unit number (rpm)
Q
flow rate (m³/s)
Q11
flow rate unit number (m³/s)
Rref
runner radius (m)
S
symmetric part of C
Wr, Wθ, Wz
relative velocity components (m/s)
x, y, z
global reference frame, Cartesian
r, θ, z
global reference frame, cylindrical
XT,YT, ZT
calibration target reference frame
i, j, k
local reference frame
CFD
Computational Fluid Dynamics
LDV
Laser Doppler Velocimetry
OP
Operating Point
PIV
Particle Image Velocimetry
2
Introduction The present study is part of the AxialT project aimed at a better understanding of propeller turbines [1, 2]. Here, the focus is on the mean and secondary flows inside the turbine runner. The flow inside a turbine runner is complex and combines several features similar to those encountered around a finite length hydrofoil; also the rotation introduces additional phenomena such as the Coriolis acceleration and rotor-shroud interactions. For hydraulic turbine, the energy extraction occurs in the runner and an accurate prediction of the flow dynamics inside this component is the key to an efficient design. Nowadays, hydraulic turbine CFD calculations are an integral part of the design process. Improving the accuracy of flow simulations, either through modification of current strategies or by developing new ones, requires the use of accurate and relevant experimental data. In particular, accurate predictions of secondary flows and vortex development in the runner are important for runner optimization. The flow inside rotors has been characterized using theoretical approaches for both hydraulic and gas turbo-machines (cf. [3, 4]). One of the flow features presented by Raabe [3] and Vavra [4] is the relative steady rotor flow governed by the Coriolis acceleration, which induces a relative rotation in the opposite direction to the rotor rotation. Secondary flows and vortices have also been studied experimentally, Langston [5] provided a wide review of the various vortices detected around blades in plane and annular cascade flows, excluding blade tip clearance effects. Most of the vortices presented originate at the junction of the hub and the blade leading edge. At this location, a main vortex develops: a horseshoe vortex with one leg on the suction side, called the leading edge vortex, and the other leg on the pressure side known as the passage vortex. One common goal of inter-blade flow studies has been to detect and analyse the secondary flows. In gas turbines, such phenomena may significantly alter the heat transfer at the blades, whereas in hydraulic turbines vortices are of particularly interest regarding the inception of cavitation. In fact, due to the centrifugal acceleration, the vortex centers will be located where the pressure is the lowest, and hence where cavitation may start. Above all, losses and lift performance at the blade can be altered by such local phenomena. To perform experimental velocity measurements inside a rotating confined device is challenging and several attempts have already been conducted. Starting in the nineties, nonintrusive velocity measurements were performed inside rotors, with Particle Image Velocimetry (PIV) proving to be the most suitable technique [6].
3
Rotor-stator interactions have been studied, using 2D-PIV in a centrifugal pump [7] and axial turbo-pump [8] with diffuser vanes. More recently, Yu and Lui [9] investigated the rotorstator interaction using a stereoscopic PIV system (SPIV) to acquire the three components of the velocity field inside the compressor stage. The development and impact of the rotor blade wakes on the stator were analysed. Rotating stall phenomena, with intermittent recirculation cells inside the inter-blade channels, were detected in a centrifugal pump under part load conditions using 2D-PIV [10]. Further analyses, using a time resolved system (TR-PIV), allowed the identification of the frequency and dynamics of this phenomenon [11]. The flow through the clearance between the runner blade tips and its casing is driven by the pressure gradient between the pressure and suction sides of the blades. Such flows roll up into the tip leakage vortices, whose development and breakdown have been observed using SPIV inside a compressor stage [9]. Later, the complete roll-up process was identified in a water-jet pump [12]. Refined measurements inside the blade tip gap and the inter-blade channel were obtained using a 2D-PIV system. The tip leakage vortex and the associated inner structures and interactions were then characterized. Multi-planar measurements have permitted the reconstitution of the averaged threedimensional velocity field. For example, a 2D-PIV system was used to acquire the axial and tangential velocities over six planes at different radial distances, inside a compressor rotor, ranging from the hub to mid span [13]. Also, an averaged three-dimensional velocity field has been obtained with multi-planar SPIV inside a compressor stage, for both the rotor and the stator, covering mid-span to the casing [9]. In these two particular studies, the lowest spatial resolution was in the out-of-plane direction, as the distances between consecutive planes were respectively 10 mm (equivalent to about 0.2 chord length or 0.1 span) and 18 mm (equivalent to about 0.1 chord length or 0.1 span). It seems from this review that only CFD data is capable of providing a high-resolution three-dimensional velocity field in the complete regions between two successive runner blades (i.e. the inter-blade channel) in hydraulic turbines. Nevertheless, experimental data are both useful and necessary to corroborate and confirm numerical simulations, even with partial information such as limited measurement areas and often the lack of some of the three velocity components.
4
To the authors’ knowledge, no velocity measurements have been carried out in the interblade channel of a hydraulic turbine. Furthermore, the leading edge vortex has only been detected from qualitative visualisations in previous experimental investigations. To fill this lack of experimental data, a velocity measurement campaign was undertaken, involving no modification of the flow patterns by instrumentation. The present paper presents the stereoscopic PIV techniques used to acquire the velocity field inside the inter-blade channel of the runner. From these high spatial resolution measurements (< 0.05 chord length), an averaged three-dimensional velocity field was reconstructed. The fine spatial resolution allows the evaluation of the nine components of the velocity gradient tensor and the streamline patterns. The mean and secondary flows were recorded and analysed for nine different operating conditions and the λ2-definition used to detect the position of vortices.
1. Experimental set-up 1.1 Propeller turbine model The 1950’s era propeller turbine used for the AxialT project is illustrated in Fig. 1. This turbine has a fronto-spiral casing with two intake channels. The draft tube consists of a conical diffuser followed by a diverging-converging elbow and a diverging duct separated by a pier leading to two unsymmetrical exit channels. The distributor is composed of 24 guide vanes and 24 stay vanes, paired with a 6-blade propeller runner. As indicated in Fig. 1, the reference frame is centered at the distributor mid-height, with the positive x-axis oriented towards the draft tube outlet, the positive y-axis following the right-hand rule convention, and the positive z-axis directed upwards. Extensive experimental investigations have been carried out using this scale model, for the intake, distributor, runner and draft tube (see [14-18]). The test rig consists of a closed-loop hydraulic facility with flow rates up to Q = 1 m3/s measured by an electromagnetic flow meter with an accuracy of 0.2%. Heads up to H = 50 m are measured according to IEC guidelines of 0.05%. Rotational speeds up to N = 2000 rpm can be achieved with an accuracy of 0.01% and net powers at the test section up to P = 170 kW. The rig is fully equipped with measurement systems for testing the performance of hydraulic turbine models according to the IEC 60193 standard and for monitoring internal flows and pressure fields. Following efficiency () hill chart measurements, nine (9) different operating points (OP) were chosen for the present investigation (Fig. 2). The chosen OPs include optimal (OP3), part load (OP8) and full-load (OP7) conditions, at three different rotational speeds. Dimensionless 5
operating conditions are summarized in table 1, using unit numbers Q11 and N11:
Q11
Q D H1/ 2
(1)
N11
ND H1/ 2
(2)
2
with N [rpm] the rotation speed, D [m] the shroud diameter at the runner blade axis and H [m] the net head. The runner rotation is counter-clockwise. OP3 is used as the reference operating point. Rref is the runner radius and the reference 2 velocity Cref is defined for each operating point as Cref Q / R ref .
1.2 Particle Image Velocimetry Stereoscopic particle image velocimetry (SPIV) is a non-intrusive measurement technique providing access to the three components of the instantaneous velocity field in a plane. A stereoscopic DANTEC PIV system was used to measure the phase-averaged velocity field over one blade passage. A vertical light sheet with a thickness of 5 mm, created by a Nd:Yag laser delivering 60 mJ per pulse, was projected to illuminate particles through the transparent Plexiglas wall of the conical diffuser. A 6 degree of freedom optical arm was used to position the light sheet and two HiSense cameras with a CCD resolution of 1024 x 1280 pixels² were installed in a stereoscopic configuration. The seeded particles used were silver-coated hollow glass spheres with an average diameter of ten microns (10 μm). Figure 3 illustrates the camera and laser sheet orientation. Two cameras set at different angles of view were required to obtain all three components of the velocity. The measurement plane was vertical, crossing the blade around mid span. The laser beam was aligned with the blade angle to minimize the size of the blade shadow on the measurement area. Also, the two cameras were positioned at 45° rather than the typical optimal value of 90°. This particular configuration was required to gain access to the measurement plane located between the blades. As can be seen in Fig.1, the spiral casing is hiding the major part of the runner blades so the cameras were positioned to get a view from underneath. Planar surfaces at the outer wall of the diffuser minimized optical distortion through the air-Plexiglas interface window. The Scheimpflug technique was used to provide the best focus on the measurement plane [19]. Because the cameras were positioned at 45° in the XT-ZT plane and get a view from 6
underneath the runner (about 30° in the YT-ZT plane), to correct the non-orthogonality of the camera to the measurement plane in both directions, two degree of freedom lens mounts were used. The time delay between two consecutive frame acquisitions was 70 µs; particle displacements generally satisfy the one-quarter rule (i.e. 8 pixels displacement). For the particle displacement and velocity calculations, an adaptive correlation was used starting from 64×64 pixels2 interrogation windows with two passes reduced to a final 32×32 pixels2 interrogation area with an overlap of 50%. Peak and local neighborhood validations, using the local median, were used to eliminate anomalous vectors [20]. A custom calibration target was designed to fit the inter-blade channel (Fig.4). Uncertainties in the positioning of the target with respect to the global reference frame (see Fig.1) were 1,1 mm; 0,4 mm and 0,3 mm respectively for the x, y and z-axes. A micrometer with an accuracy of 0,05 mm was used to displace the calibration target in the out-of-plane direction (ZTaxis in Fig.3 and 4). Eleven (11) images of the target were captured from -2,5 to 2,5 mm with 0,5 mm steps. The calibration was performed in water. The laser sheet was aligned with the target in the central position. Corrections were made for the distortion due to the different refractive indices of air, Plexiglas and water. The unwarping function used a 3rd order polynomial model in the XT and YT directions and a 2nd order one in the ZT direction. The accuracy of this unwarping method led to a maximum bias of 5% on the velocity components. The spatial sampling was about 3×3 mm over the 2D velocity field. The blade shadows reduced the valid measurement area, depending on the runner angular position. The velocity fields contained from 600 to 1900 vectors depending on the blade position inside the field of view. Additional details on the PIV set-up, calibration and validation can be found in Beaulieu et al. [15-16]. The runner position was monitored with a shaft mounted encoder generating one pulse per revolution, resetting a triangular ramp from which the azimuthal runner angular positions can be calculated. The measurements were performed at specific phase angles (i.e. runner positions). The shaft mounted encoder pulse signal is used to trigger the acquisition sequence. Different runner positions, corresponding to different phase angles, are obtained by adding a time delay to the trigger pulse. Recordings were made every 3 degrees of runner rotation, with 21 phases covering 60° of runner rotation, equivalent to one blade passage. At each phase angle, 1000 velocity fields were acquired ensuring a statistical convergence on the mean velocity norm with a bias of less than 1 %.
7
Upstream of the runner, the flow comes from the spiral casing through 24 stay vanes and 24 guide vanes. Further downstream, the flow is not perfectly axisymmetric. The mass flow rate distribution through each guide vane passage is not necessarily the same, which can lead to a static flow unbalance at the runner inlet [17-18]. However, for this study the mass flow rate distribution is assumed to be uniformly distributed within each inter-blade channels. In addition, all the stay and guide vanes generate wakes leading to azimuthal variations and fluctuations. The magnitudes of those velocity non-uniformities are probably small and might dissipate rapidly. At first approximation, a quasi-axisymmetric flow conditions is assumed at the inlet of a given runner inter-blade channel. Based on this hypothesis, and for visualization purposes, the temporal evolution of the velocity in the measurement area can be transposed to the spatial evolution. A measurement volume was reconstructed from the 21 planar measurement areas corresponding to each phase. This reconstruction has been carried out by superposing the 21 measurement planes according to their relative position in the runner reference frame, as illustrated in figure 5. The resulting volume covers radial positions from 0.62×Rref to 0.77×Rref. The maximum distance between two consecutive planes (i.e. at the periphery of the measurement volume) was about 0.04×Rref, or roughly equivalent to 4% of the chord length. For postprocessing purposes, data has been interpolated to equidistant meshes using linear interpolation and Delaunay triangulation. This representation of the data was particularly interesting since it created a measurement volume providing the three-dimensional velocity vectors and the nine components of the velocity gradient tensor. The results were transposed into a cylindrical coordinate (r, θ, z) system centered on the global reference frame of the turbine with θ, the angular position in the x-y plane, defined as positive in the counter-clockwise direction. Velocities were represented in the rotating frame, moving at the runner rotation speed ΩR [rad/s] (ΩR = 2πN/60):
Wr Cr W W C r R W C z z
2.
(3)
Vortex identification 2.1 Vortex detection method The vortex identification methodology presented by Jeong and Hussain [21] was used in
the present study. The λ2-definition they proposed is an appropriate criterion for vortex 8
identification in the present case. For example, it allows vortex identification regardless of the reference frame chosen. Also, the λ2-definition does not require fore-knowledge of the convective velocity of the vortex cores or their axial directions. λ2 is the second eigenvalue of the symmetric tensor S , where S and Ω are the symmetric and anti-symmetric parts of the mean-velocity 2
2
gradient tensor C . The vortices are enclosed in the contours defined by λ2 < 0 [21] and their centers are defined where λ2 is a minimum, thus allowing one to estimate the vortex centerline. Figure 6 illustrates a few x-y planes of λ2 contours where a vortex has been detected next to the blade suction side, with its centerline plotted with a white line. High concentrations of vorticity and streamlines exhibiting concentric shapes, which are characteristic of vortex cores, were analysed. To obtain the vorticity, we viewed the vector fields in planes normal to the centerline (Fig.7, where i-j-k is an orthonormal coordinate system with k tangent to the vortex centerline and its origin O located at the vortex centerline). The velocity at the vortex centerline was assumed to be the convective velocity of the vortex. Subsequently, the latter was subtracted from the velocity fields of each normal plane, showing concentric streamlines around the vortex center (Fig.7b). The vorticity ωk normal to the plane was then calculated with respect to the local reference frame i-j-k. 2.2 Vortex identification and analysis Due to the vortex location and the restricted measurement area, it was difficult to determine accurately the extent of the vortex (Fig.7). The vortex indicates an elliptical shape that can be seen in the cross sectional view. A possible reason for this non-circular shape could be that the vortex is wandering in the radial direction. Since these results were obtained from averaged values of the velocity field, wandering of the vortex would have the effect of enlarging its calculated core dimensions [22]. These results may also indicate that a shearing stress field is deforming the core. However, when located inside the measurement area, an averaged vortex center can be specified and the corresponding centerline plotted. Figure 8 shows the centerlines identified for OP1, OP2 and OP9. At these three operating conditions, at part load and outside the optimal range of the turbine, the counter-clockwise vortices are parallel to the blade and close to the suction side at around mid-span. It is reasonable to assume that the vortex path is influenced by the inlet conditions. If vortices were also present at OP3 to OP8, then their respective center lines would have been located outside the measurement zone, so that they could not be identified. Furthermore, it was not possible to locate the starting point of the vortex from the PIV measurements. However, visualizations were performed using a high speed camera at OP9 [23]: As the pressure was 9
decreased in the test loop, cavitation occurred, providing visualisation of vortices in the low pressure areas (c.f. Fig.9). The higher the rotational velocity of the vortex, the lower the pressure at its center, making cavitating structures good candidates for vortex detection. A typical picture is presented in Fig.9. Cavitating structures were detected inside the inter-blade channels, starting at the leading edge and hub junction. These structures had an elongated shape parallel to the blade close to the suction side, reaching mid-span at the trailing edge. Their rotation was in the same counter-clockwise direction as the runner. All these qualitative features match the observations from the velocity field, validating the common assumption that similar vortices exist both with and without cavitation. This would indicate that the three vortex centre lines illustrated in Fig.8 correspond to leading edge vortices originating at the leading-edge hub junction.
3.
Relative flow The relative flow within the inter-blade channel presents a pattern similar to that occurring
in hydrofoil theory. In figure 10, using OP3, OP1 and OP8 as examples, the velocity field is extracted for a vertical slice at constant radius (θ-z). The velocity norm
W2 Wz2 is higher on
the suction side of the blade than on the pressure side. This non-uniform velocity distribution in the inter-blade channel was observed at the runner outlet and its convection and dissipation in the draft tube cone has been investigated in the case of the present propeller turbine model [18], as well as downstream of a Kaplan turbine [24-25]. Under part load conditions, the axial and tangential velocities are lower than at the optimal condition OP3, in accordance with the lower mass flow rate Q11. From optimal to full load conditions, OP3 to OP7, the main flow direction remains parallel to the blade, exhibiting good flow behavior with no flow separation detected based on observations of Wθ and Wz (Fig.10: OP3). However, at part loads, OP1, OP2, OP8 and OP9, a local deviation of the vector direction is discernible on the suction side of the blade, associated with the higher magnitude of the radial velocity Wr (Fig.10: OP1 and OP8). Concerning the radial component of the velocity, a gradient (∂Wr/∂θ) exists in the azimuthal direction indicating a lateral movement of the fluid in the inter-blade channel. Analyzing the Wθ and Wr velocity fields, the operating conditions became clearly distinguishable. In figure 11, the velocity field is extracted for x-y planes and represented as vectors, the color levels represent the vorticity ωz/ΩR. Figure 11 illustrates the three tendencies observed using OP3, OP1 and OP8 as examples. OP3 to OP7 are similar, showing no unusual local behavior for conditions varying from optimal to full load. For the part load operating points, OP1, OP2 and OP9, as mentioned earlier, a local counter-clockwise vortex is present on the blade suction side. 10
Finally, OP8 stands out with a similar counter-clockwise structure on the blade suction side, but now covering about a third of the measurement area. This structure was not detected using the λ2definition and its vorticity is much lower than that measured inside the leading edge vortices of OP1, OP2 or OP9. Furthermore the structure was much wider and thus might not actually be the leading edge vortex. The specific operating condition OP8 corresponds to the lowest measured Q11 and was farthest away from the best efficiency point, with a flow pattern that may be altering the lift on the blade. Inside the relative reference frame, rotating at the runner rotation speed ΩR, the Coriolis acceleration induces a relative rotational flow in the opposite direction to that of the runner (i.e. clockwise). If we consider a simplified case, consisting of an axial rotor with flat radial blades and irrotational flow at the inlet, steady and non-viscous, the relative flow would possess a rotational speed equal and opposite to that of the runner, leading to an axial vorticity ωz = -2×ΩR [3-4]. This simplified reference case, where the Coriolis effect prevails, is compared to the present experiment. First, inside the AxialT runner with inlet flow conditions varying from optimal to full load (OP3 to OP7), the vorticity ωz was found to be virtually constant over the entire measurement volume. The average vorticity of the relative flow was calculated and systematically found to be about -1.3×ΩR, where ΩR depends on the particular operating condition OP. The horizontal vorticity field at OP3 is presented in Fig.11 as an example, with similar uniform vorticity fields observed from OP3 to OP7. The vorticity magnitude in the experiment is lower than in the reference case, suggesting other flow behaviors are counterbalancing the Coriolis effect. Second, the relative flow induced by the Coriolis acceleration interacts with the local vortex pattern. For example, under part load operating conditions, counteracting to the Coriolis effect, the leading edge vortices induce a local counter-clockwise rotation on the blade suction side with a vorticity ωz ≈ 25×ΩR , with the OP2 and OP9 fields similar to that of OP1, illustrated in Fig.11. At OP8, the local flow structure induces a counter-clockwise rotation with a vorticity ωz ≈ 3×ΩR. Finaly, differences might also be induced by the passage vortex [5] acting in the opposite direction to that of the Coriolis acceleration, although the former was not identified from the present measurements.
4. Streamline pattern 11
The streamlines, calculated from the average relative velocity field, provide informative description of the shear stresses inside the relative velocity field. A qualitative observation stems from the streamline patterns shown in figure 12 (OP3). As an example, four of the streamlines (AA’, BB’, CC’ and DD’) have been plotted at heights Z1 to Z2 for OP3 (The dashed lines represent the radial and circumferential directions). Using the example given by Munson et al. [26], if a pair of small sticks forming a right angle cross pattern were located at Z1, according to the streamlines, they would rotate as they move to location Z2. The stick AB would rotate counter-clockwise from Z1 to A’B’ at Z2 whereas the stick CD would rotate clockwise to C’D’. The fact that the right angle between AB and CD is not maintained constant downstream, indicates the existence of shear stresses in the flow. The length changes of AB and CD can be due to both shear and strain. These observations differ from the purely theoretical cases of irrotational free vortices and rotational forced vortices illustrated in [26]. The vorticity thus represents both the rotation of the fluid and also a part of the shear stresses. In fact, the fluid motion can be decomposed into three elementary components: pure shear, rigid body rotation and irrotational strain [27]. A second insight is provided by figure 13, for OP3, where the averaged velocity of the horizontal plan under consideration has been subtracted from the velocity field. This reveals the secondary flow pattern, highlighting a saddle point at the center of the velocity field. This streamline pattern can be modeled by superimposing pure shear and irrotational strain [27]. Because of the strong influence of local three-dimensional structures on the main flow, further work such as numerical simulation is required to identify all the flow features composing the inter-blade flow.
5. Conclusion The three dimensional averaged velocity field inside the inter-blade channel of a propeller hydraulic turbine was measured using stereoscopic particle image velocimetry (PIV). Measurement volumes were reconstructed artificially from planar measurements at different runner positions. The three components of the averaged velocity vector were then measured inside a portion of the inter-blade channel, providing light on the inner flow structures. The turbine model was tested at nine operating conditions ranging from part to full load, with the flows unaffected by the non-intrusive instrumentation. Measurements were made inside the runner channel, revealing complex flow patterns similar to those encountered in full scale hydraulic turbines. 12
Using the λ2-definition, vortex cores were identified, together with their centrelines, crossing the measurement zone for three part-load operating conditions. Visualisation studies under cavitating conditions, identified these structures as leading edge vortices. These significantly altered the relative flow inside the inter-blade channels. The radial velocities and gradients play a major role in the development of the inter-blade flow showing that twodimensional simplifications should be avoided. The Coriolis acceleration induces a relative flow in the opposite direction to that of the runner. This secondary induced flow was shown to be counterbalanced by local phenomena, showing complex interactions. An important limitation regarding the present investigation was the restricted measurement area. The covered span extended only from 0.62×Rref to 0.77×Rref. Further work is planned, including numerical simulations, to extend the present analysis over the complete runner. The data gathered during the present study should prove useful in the validation of numerical simulations.
Acknowledgments The authors would like to thank the participants of the Consortium on Hydraulic Machines for their support and contribution to this research project: Alstom Power & Transport, Andritz Hydro LTD, Edelca, Hydro-Quebec, Laval University, NRCan, Voith Hydro Inc. Our gratitude also goes to the Canadian Natural Sciences and Engineering Research Council, who provided funding for this research.
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Table 1 Operating conditions
Fig.1
Propeller turbine model
Fig.2
Efficiency hill chart and operating points (
Fig.3
Measurement area, camera and laser sheet positions
Fig.4
Calibration target
Fig. 5
Measurement volume reconstruction from 21 measurement planes
Fig. 6
Vortex center line identification using λ2 contours at OP1
Fig. 7
Plane normal to the vortex centerline, OP1; a) local reference frame, b) velocity field and vorticity
η/ηref;
guide vane opening)
ωk Fig. 8
Vortex center lines
Fig. 9
Visualization of the cavitating leading edge vortex (OP9)
Fig. 10 Relative average velocity field; vectors: (Wθ, Wz) and contours: Wr /Cref ; r/Rref = 0.68 Fig. 11 Relative velocity field; z/Rref = -0.8; velocity vectors: (Wr , Wθ); vorticity contours: ωz/ΩR Fig. 12 Streamline deviation, OP3 Fig. 13 Secondary flow; OP3; z/Rref = -0.8; velocity vectors and streamline structure
17
Table 1 Operating conditions
OP
Guide vane opening [°]
N11/N11 ref
Q11/Q11 ref
η/ηref
1
25
1
0.828
0.86
2
31
1
0.963
0.974
3
33
1
1
1
4
38
1
1.071
0.992
5
33
0.976
0.99
1.002
6
33
1.05
1.016
0.976
7
44
1.05
1.168
0.969
8
17
1
0.612
0.673
9
27
0.976
0.875
0.906
Fig. 1
Propeller turbine model
18
η/ηref;
Fig. 2
Efficiency hill chart and operating points (
Fig. 3
Measurement area, camera and laser sheet positions
19
guide vane opening)
Fig. 4
Calibration target
Fig. 5
Measurement volume reconstruction from 21 measurement planes
Fig. 6
Vortex center line identification using λ2 contours at OP1
20
a)
b) Fig. 7
Plane normal to the vortex centerline, OP1; a) local reference frame, b) velocity field and vorticity
ωk
Fig. 8
Vortex center lines
21
Fig. 9
Visualization of the cavitating leading edge vortex (OP9)
Fig. 10 Relative average velocity field; vectors: (Wθ, Wz) and contours: Wr /Cref ; r/Rref = 0.68
22
Fig. 11 Relative velocity field; z/Rref = -0.8; velocity vectors: (Wr , Wθ); vorticity contours: ωz/ΩR
Fig. 12 Streamline deviation, OP3
23
Fig. 13 Secondary flow; OP3; z/Rref = -0.8; velocity vectors and streamline structure
24