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DOI 10.1051/lhb/2009067

Analysis of the Rotor-Stator Interaction in a Radial Flow Pump
Analyse de l’interaction rotor-stator dans une pompe centrifuge
G. Cavazzini1, G. Pavesi, G. Ardizzon
Department of Mechanical Engineering, University of Padova, Via Venezia 1, 35131 Padova giovanna.cavazzini@unipd.it, giorgio.pavesi@unipd.it, guido.ardizzon@unipd.it

P. Dupont
Ecole Centrale de Lille, Laboratoire de Mécanique de Lille (UMR CNRS 8107), Lille, France

S. Coudert
Centre National de la Recherche Scientifique, Laboratoire de Mécanique de Lille (UMR CNRS 8107), Lille, France

G. Caignaert, G. Bois
Arts et métiers Paristech, Laboratoire de Mécanique de Lille (UMR CNRS 8107), Lille, France patrick.dupont@ec-lille.fr, sebastien.coudert@univ-lille1.fr, guy.caignaert@ensam.eu, gerard.bois@ensam.eu

et article présente une analyse des interactions entre la roue et le diffuseur aubé d’une pompe centrifuge. Les résultats expérimentaux ont été obtenus en utilisant la Vélocimétrie par Images de Particules (PIV 2D/2C) dans un canal inter aubes du diffuseur. Les écoulements dans ce canal de diffuseur sont analysés, dans divers plans de mesure entre le plafond et la ceinture, pour sept positions relatives de la roue par rapport au diffuseur et pour quatre conditions de fonctionnement. Une technique de post-traitement des résultats, fondée sur divers outils statistiques, a été appliquée à ces données expérimentales en vue d’accéder à une meilleure compréhension des phénomènes. Ces résultats expérimentaux sont comparés aux résultats obtenus par simulation numérique avec le code de calculs CFX.

C T

he paper presents the analysis of the interactions between the impeller and the vaned diffuser of a radial flow pump. Experimental data were obtained within one blade passage of a vaned diffuser using the 2D/2C PIV technique. The diffuser flow field was analyzed in various measuring planes in the hub to shroud direction, for seven relative impeller positions in the diffuser frame and in four different operating conditions. A post-processing procedure, based on statistical tools, was applied to the experimental results so as to validate their meaningfulness. The experimental results were compared to numerical data obtained with the help of CFX computer code.

I?n Introduction
In the turbomachinery field the control of the interaction effects between rotating and stationary parts is of major importance because of their influence on the flow field inside both components and on the performance of the machine in terms of stability, vibrations, noise and pressure pulsations, mainly at off-design conditions. This is of course more important as the gaps between stationary and rotating parts are becoming smaller in order to look for reduction of pumps. A lot of research work has been done for a long time in order to get a better knowledge of the phenom? ena developing in the interaction zone situated between the outlet
1. Corresponding author

of an impeller and the inlet of a diffuser. Many researchers have studied the flow field in the rotor-stator interaction zone with standard technique, like pressure transducers and hot wire anemometers, and with the laser techniques like Laser Doppler Velocimetry (L.D.V.) and more recently Particle Image Velocimetry (P.I.V.). Experiments were conducted to measure pressure fluctuations in diffuser radial pumps by Arndt et al. [1,2], Furukawa et al. [3], Guo and Maruta [4], Pavesi et al. [5,6] and the details of wake trans? port across the rotor were tracked in continuously running facilities thanks to LDV and PIV [7, 8, 9, 10, 11, 12, 13, 14]. Among the experimental techniques the PIV has spread because of the possibility of obtaining a global visualization of the fluid flow field with higher time resolution. In particular it received a great impulse by the informatics development that has also improved the numerical approach. The numerical

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analysis enriches the experimental results and at the same time it is validated by them. So a correlation between both approaches is an interesting method for understanding and studying in detail the complex interaction phenomena. Table?1 Impeller characteristics R1?=?141.1?mm R2?=?256.6?mm B2?=?38.5?mm β2?=?22.5? o (from the peripheral direction) Z1?=?7 S1?=?9?mm Nn?=?2500?rpm Qn?=?0.336?m3/s (at 1710?rpm)

0.6

ψ

0.5 0.4 0.3 0.2 0.1 0 0.02

0.04

0.06

0.08

0.10

0.12 ? 0.14

0.16

Figure?2 : The pump performance curve. Table?2 Diffuser characteristics R3?=?273.6?mm (R3?-?R2)/R2?=?6.65?% R4?=?397.8?mm B3?=?40.0?mm B4?=?40.0?mm Z2?=?8 Diffuser design flow rate 0.80Qn To study only the interaction between impeller and diffuser, no volute was provided. Tables?1?and?2 report the main characteristics respectively of the impeller and of the vaned diffuser and (figure?2) presents the pump performance curve. The impeller was already used in previous studies, coupled with a short vaneless diffuser [13, 15, 16, 17] and with two different vaned diffusers [18, 19, 20, 21]. These previous studies highlighted that the absolute flow angle distribution at the impeller outlet was characterized by fluctuations of about in comparison with the mean flow direction for each blade passage, whatever the position of the impeller in the diffuser frame. These fluctuations resulted to increase as the flow rate increased. In this work the test rig was the same as the one used for these studies and was developed for the use of the Particle Image Velocimetry (PIV) technique. A detailed description of the PIV technique, of the measurements device and of the experimental set up is reported in the papers mentioned above. One blade passage of a vaned diffuser was analyzed by the 2D/2C PIV technique in order to obtain some new experimental results about the interaction phenomena developing in the diffuser. figures? 3 and 4 present respectively a scheme of the acquisition chain and the overall optical arrangement.

This paper presents an experimental analysis of the flow field inside one blade passage of a vane diffuser of a radial flow pump working with air. Five measuring planes were considered in the hub to shroud direction, with seven relative positions of the impeller in the diffuser frame and four different operating conditions. The experimental data, obtained using 2D/2C PIV, were validated by a statistical post-processing procedure and compared with the results of numerical analyses carried out with the help of the CFX code. The discussion analyzed the diffuser performance in different operating conditions and the sources of discrepancies between experimental and numerical results.

II?n Experimental facilities
The tests were carried out on the so-called SHF impeller, coupled with a vaned diffuser, and working with air (fig.?1).

Figure?1 : Shematic representation of the SHF impeller coupled with the vaned diffuser.

Figure?3 : The acquisition chain.

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Analysis of the Rotor-Stator Interaction in a Radial Flow Pump

Figure?6 : Seeding of the blade passage as seen by PIV cameras with an overlap? ping (black parts are the walls of the diffuser pas? sage).

Figure?4 : Optical assembly to create a laser sheet in one diffuser blade passage. The experimental database was made up with 400? instantaneous velocity fields for every measuring condition corresponding to?: ? Measurements in five planes between hub and shroud (B/ B3? =? 0.13, 0.26, 0.50, 0.74, 0.87 from the hub) labelled H1 to H5. ? Seven positions of the impeller in the vaned diffuser frame (figure? 5), corresponding to the following angular positions of one impeller blade in front of one diffuser vane? : ? =? -? 6.84o, 0.34o, 7.52o, 14.70o, 21.89o, 29.07o and 36.25o for positions 1?to?7 ? Four relative flow rates?: Q/Qn?=?0.43, 0.77, 1.00, 1.17?; ? impeller Reynolds number of 1.56*106. P.I.V. snapshots were simultaneously taken by two cameras positioned side by side and two single exposure frames were taken by each camera every two complete revolutions of the impeller at an impeller rotation speed of 1710? rpm (fig.?6). A software developed by the Laboratoire de Mécanique de Lille was used for the images treatment (crosscorrelation was used with a correlation window size of 32? x? 32? pixels2 and an overlapping of 50? %? ; correlation peaks were fitted with a three points Gaussian model). The obtained results, consisting in fields of 100?x?82?mm2, were then checked and cleared by the same software. Then the data, obtained with the two cameras, were elaborated with

a dedicated post processing technique to build a single domain and to calculate fluid-dynamic quantities in the analysis zone (velocity components, flow angles and turbulent rates). The velocities were measured with a relative accuracy of about 1.2?% for the larger flow rate (Q/Qn?=?1.17) and 2.2?% for the lower flow rate (Q/Qn?=?0.43). The results here presented refer to the relative impeller position of greater interaction with the diffuser blade (position P2 – fig.?5).

III?n Numerical procedure
Computations were performed by using the commercial software package CFX 10.0. A fully-turbulent boundary layer was assumed on both blades and wall surfaces. The turbulence was modelled by the Detached Eddy Simulation Model (DES), which combines features of classical RANS formulations with elements of Large Edge Simulation (LES) methods. It is based on the idea of covering the boundary layer by a Shear Stress Transport k-w model and switching the model to the Smagorinsky-Lilly model in detached regions. The LES model was utilized in order to take advantage of its ability to provide information on turbulent flow structures and spectral distribution, which might be important to predict noise or vibrations due to stator-rotor interaction. An unsteady model was used for all the computations. For the interface between stator/rotor blocks the standard transient sliding interface approach was chosen. For the discretisation in time a second order dual time stepping scheme was adopted. The time step for the explicit scheme was chosen according to a rotation of the runner, of about one degree resulting a Courant Number of about CFL? =? 3. The maximum number of iterations for each time step is set to 5, in order to give mass residues of 10-6, momentum residues of 10-4, turbulence kinetic energy and energy dissipation of 10-4. An H-type grid was used for the impeller, whereas a O-type grid was adopted for the diffuser. The leakage from the labyrinth seal was also considered (fig.? 7) and several H-blocks were built to describe the cavities. The grid was globally of 3.9? ?? 106 points, with y+ values below 50 in the whole computational region.

Figure?5 : Impeller blade positions in the dif? fuser frame.

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Figure?8 : Analysis Sections Definition. The comparison of the experimental results with the data of the DES model in the first 10? positions at mid-span for the four analysed flow rates is shown in fig.?9. The velocity profiles are in good agreement with the experimental data except near the blade pressure side (y/l? =? 1). The reasons of these discrepancies could be both numerical and experimental. As regards the possible numerical error sources, the stream-wise grid resolution and the choice of the turbulent model were considered. Moreover the blade roughness prescribed in the computations was presumed not to be in perfect agreement with the experimental one. The numerical simulations were carried out considering the walls as hydraulically smooth. As a matter of fact, the diffuser blade surfaces were painted with a special mixture in order to eliminate the laser reflection problems. This mixture was characterized by a minor granulation that increased the surface roughness. Among the experimental limits, the reflections problems and the difficult seeding near the blade pressure side were considered. To verify the influence of these factors on the highlighted discrepancy, the experimental results were compared with those of a previous measurement campaign on the same pump configuration aimed at studying the rotorstator interaction zone at the impeller discharge. In the campaign here presented the lighting is obtained with a single laser sheet coming in from the outlet part of the analyzed diffuser vane passage, whereas in this previous one two laser sheets, coming from different directions, illuminated the rotor-stator interaction zone passing through blades made of glass (fig.? 10). The double-laser sheets configuration is characterized by a better agreement between numerical and experimental results, as proof of the influence of the reflection problems on the quality of the experimental results near the blade pressure side (fig.?11). Finally, the presence of secondary flows and/or the boundary layer development near the blade pressure side were also assumed to influence the experimental results accuracy. Some other differences among the four analyzed flow rates can be highlighted. For Q/Qn? =? 1.00 the numerical velocity estimation agrees quite well with the experimental data except near the diffuser blade leading edge (fig.? 9). The reason for this discrepancy could be the reflection problems, combined with an insufficient illumination in that zone due to the single laser sheet coming in from the outlet part of the analyzed diffuser vane

Figure?7 : Seal system at the impeller inlet (left) and outlet (right). As regards the boundary conditions, mass flow rates obtained from the experimental data were prescribed at the inlet boundary and at the labyrinth close to the impeller inlet with stochastic fluctuations of the velocities with 5?% free-stream turbulence intensity. At the impeller outlet the leakage mass flow rate was controlled by the known pressure in the large plenums upstream the labyrinth. The surfaces were supposed as adiabatic walls with a noslip condition. An automatic near-wall treatment smoothly switched from a low-Reynolds number formulation to a wall function formulation. As regards the exit boundary conditions, the experimental pressure level was prescribed as average pressure at the diffuser outlet. In the post-processing phase the numerical results were elaborated both to be compared with the experimental data and to enrich the experimental results with information useful for the turbulent phenomena interpretation. Since coherent vortices are thin convex low pressure tubes, the Q-criterion is strictly connected with their existence and reflects the amount of strain and vortical motions in the vector fields, and hence it is an interesting way of turbulence visualization. It was presented for three-dimensional flows by Hunt [22] and it is defined as?: where S is the rate of strain tensor?: is the vorticity tensor. (3.2) (3.1)

IV?n Comparison between numerical and experimental results
The velocity profiles were evaluated in 50? equal spaced positions normal to the mean line of the overlapping part of one diffuser passage (fig.? 8) in the 5? analysed planes (H1.. H5).

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Analysis of the Rotor-Stator Interaction in a Radial Flow Pump

Figure?9 : Comparison between the P.I.V. results (dashed lines with circle and triangles) and the nu? meri? cal results (continuous lines) in the blade-to-blade surfaces (position P2, H3).

Figure?10 : Lighting methods.

passage (figs.? 5-10). The laser light could not be adequate, close to the blade leading edge, for obtaining the appropriate illumination. This hypothesis is strengthened by the better agreement between numerical and experimental results obtained in the previous measurement campaign, where the double-laser configuration, besides reducing the reflection problems, also guaranteed a better lighting near the blade leading edge (fig.?11).

For Q/Qn? =? 0.77 and Q/Qn? =? 1.17 the agreement remains quite good, whereas for Q/Qn? =? 0.43 the velocity seems to be over-predicted. The experimental errors on the evaluation of the mass flow rate and of the velocity components do not seem to justify this over-prediction. This discrepancy could be explained by the experimental data dispersion depicted by the probability density distribution in the analyzed sections (fig.? 12). The probability density gives the probability that

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Figure?11 : Comparison of lighting methods.

a variable is in a particular interval and it is a “smoothed” version of the histogram. The dispersion of the experimental data is characterized by a decreasing of the probability density function and hence of the meaningfulness of the mean velocity value. In this case, the experimental data inconsistency could determine a discrepancy between the numerical and the experimental results. Vice versa, where the probability density is characterized by great values with a narrow bell-shaped distribution, the experimental data can be considered as meaningful and the discrepancy between experimental and numerical results could be due to other error sources. For Q/Qn? =? 0.43 the probability density is very small in the first 20?sections and then increased a little in the second part of the passage (figs.?9-12-13). An attempt to increase the accuracy of the experimental data using the velocity values having the maximum probability density (dashed lines with

Figure?12 : Probability density in the blade-to-blade surface H3, position P2 (Q/Qn?=?0.43?; Q/Qn?=?1.00).

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Analysis of the Rotor-Stator Interaction in a Radial Flow Pump

Figure?13 : Comparison between the P.I.V. results (dashed lines with circles and triangles) and the nu? meri? cal results (continuous lines) in the blade-to-blade surfaces (position P2, H3?=?0.5).

circles-figs.? 9-13) was taken, but no notable effects on the overall flow field were obtained. For Q/Qn?=?1.00 the probability density is high everywhere except in the pressure side boundary layer development zone (figs.?9-12-13). The experimental data inconsistency could be explained by the presence of two vortexes numerically identified at the diffuser entrance on the blade pressure side near the end-walls for Q/Qn? =? 0.43 and Q/Qn? =? 0.77 and of small vortexes near the blade pressure side in second part of the diffuser passage for Q/Qn? =? 1.00 and Q/Qn? =? 1.17 (fig.14). The great unsteadiness of the velocity values in the zone of vortex development is highlighted by the comparison of the FFTs of the velocity components determined in a point near the suction side at the entrance of the diffuser pas-

sage (fig.15 – section? 01) and in a point near the pressure side in the zone of maximum error (fig.? 15 – section? 14) with the FFT of the velocity components determined in the second half of the diffuser passage far from the blade profiles (fig.?15 – section 30). The results are reported as a function of the ratio between the frequency f and the sampling frequency fs of the data. Concerning the velocity component in the mean flow direction Cx, for Q/Qn? =? 0.43 the two points localized near the blade profiles presents several peaks having amplitudes greater and more significant than those of the peaks in the FFT of the point placed in the mean flow, whereas the velocity component in the direction normal to the mean flow presents the same FFT peaks amplitude for all the three

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Figure?14 : Secondary flows in the diffuser (position P2).

Figure?15 : FFT of the velocity components determined in three points of the diffuser passage?: near the suction side (dotted line-Section 01)?; near the pressure side in the zone of greater errors (grey line-Section 14)?; in the second half of the passage far from the blade profiles (black line-Section?30).

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Analysis of the Rotor-Stator Interaction in a Radial Flow Pump

points. This highlights the presence of intense secondary flows near both the blade profiles, proceeding in the mean flow direction. On the other side, for Q/Qn? =? 1.00 only the point near the blade pressure sides has a FFT characterized by several peaks of greater amplitude, confirming the presence of perturbing vortexes mainly near the blade pressure side of the diffuser passage. The development of the vortexes inside the diffuser passage was strictly connected with the leakage flow rate and the impeller blade passage. For Q/Qn? =? 0.43 at the impeller outlet, before the gaps, the Q-criterion points out the impeller blade wakes (fig.16 – R? =? 256.6? mm). Afterwards, the leakage flow rate entered in the gaps between impeller and diffuser (fig.? 16 – R?=?258.1?mm) and interacted with the impeller blade wakes (fig.? 16, R? =? 270 – 273? mm). The interaction amplified the leakage effects and created two large vortexes involving all the diffuser passage (fig.?14). Their intensity decreased along the passage, but at the diffuser outlet throat they were still present. For Q/Qn?=?0.77 the phenomenon was quite similar, but the leakage flow rate effects were a little less important and at the diffuser inlet throat the vortexes did not extend along the whole diffuser width. At the impeller design flow rate (Q/Qn?=?1.00) the blade wakes, coming from the impeller increased their perturbing

influence on the diffuser flow field, involving the whole diffuser width even though with greater intensity near the shroud (fig.?16). The leakage flow rate, entering in the gaps between impeller and diffuser, had not enough strength to create the two vortexes described above (fig.? 14). However, a small vortex, probably due to the cores of turbulence associated with the blade wakes (fig.? 17), appeared near the suction side at mid-span (fig.? 14). It proceeded along the diffuser passage, moving towards the passage centre. In the second part of the diffuser passage, it interacted with the turbulence due both to the leakage flow rate effects and to the wake transport (fig.? 17) and generated a second small vortex near the pressure side still at mid-span (fig.? 14). Then this second vortex moved in the axial direction and at the diffuser outlet throat was positioned near the hub. The development of these secondary flows is in good agreement with the inconsistency of the experimental results highlighted by the validation procedure (figs.?9-12-13). The diffuser flow field at Q/Qn? =? 1.17 is characterized by the development of secondary flows similar to that described above for Q/Qn? =? 1.00 with a further reduction of the leakage flow rate effects and an increased of the perturbation of the blade wakes. The intensity of the turbulence near the pressure side increased (fig.?17), further perturbing the experimental results quality (fig.?9).

Figure?16 : Influence of the leakage flow rate on the Q-criterion.

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Figure?17 : Leakage flow effects and impeller blade influence on the Q-Criterion near the shroud (H4).

V?n Conclusions
A vaned diffuser coupled with a SHF impeller was studied. A 2D/2C PIV technique was used to analyze in detail the flow field in one blade diffuser passage in four different operating conditions for one relative position of the impeller in the diffuser frame. The experimental results were compared with those of numerical computations performed by compressible Detached Eddy Simulation model. The comparisons between numerical and experimental results highlighted some differences. The local inconsistency of the results was discussed and the influence of possible numerical error sources (accuracy of discretisation, time step, turbulence model) and experimental 2D PIV limits (reflection and seeding problems, illumination problem, perturbing turbulent phenomena) was discussed. Two phenomena resulted to greatly affect the flow field inside the diffuser? : the leakage flow rate effects and the impeller-diffuser interaction effects. At low flow rates, the leakage flow rate entered in the gaps and interacted with the impeller blade wakes creating two large vortexes on the pressure side of the diffuser blade that probably affect the velocity PIV measurements. Moreover turbulence cores probably due to the rotor-stator interaction, coming from the impeller outlet, proceed in the diffuser passage and decreased the probability density in the centre of the diffuser passage and on the blade suction side. At higher flow rates, as the pressure difference between the impeller outlet and the atmosphere becomes lower, the leakage effects diminished and the two vortexes disappeared. The impeller blade wakes were instead greater and a secon-

dary flow developed in the passage, creating small vortexes moving in the hub-to-shroud direction. The experimental results were in good agreement with the numerical data with the exception of the boundary layer development on the blade pressure side.

VI?n Nomenclature
B2 B3 CX CZ impeller outlet width diffuser constant width flow velocity component in x direction axial velocity component R4 U2 Z1 Z2 l s1 Δp0 β2 ω φ ψ diffuser outlet radius peripheral velocity number of impeller blades number of diffuser blades section length mean impeller blade thickness total pressure rise outlet impeller blade angle speed of rotation (rad/s) flow coefficient total head coefficient

Cm2 meridional velocity component N Q Qn R1 R2 R3 speed of rotation (rpm) flow rate design flow rate impeller tip inlet radius impeller outlet radiusM diffuser inlet radius

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Analysis of the Rotor-Stator Interaction in a Radial Flow Pump

VII?n References
[1] Arndt N., Acosta A. J., Brennen C. E., Caughey T. K. (1989) — Rotor-stator interaction in a diffuser pump. J. Turbomach. 111(3) 213-221 [2] Arndt N., Acosta A.J., Brennen C.E., Caughey T.K. (1990) — Experimental investigation of rotor-stator interaction in a centrifugal pump with several diffusers. ASME J. Fluids Eng. 112 98-108 [3] Furukawa A., Takahara H., Nakagawa T., Ono Y. (2003) — Pressure fluctuation in a vaned diffuser downstream from a centrifugal pump impeller. Int. J. Rotating Mach. 9(4) 285-292 [4] Guo S., Maruta Y. (2005) — Experimental investigations on pressure fluctuations and vibration of the impeller in a centrifugal pump with vaned diffusers. JSME Int. J., Ser. B. 48(1) 136-143 [5] P avesi G. , C avazzini G. , A rdizzon G. (2008) — Timefrequency Characterization of the Unsteady Phenomena in a Centrifugal Pump. Int. J. Heat and Fluid Flow. 29 1527-1540 [6] P avesi G. , C avazzini G. , A rdizzon G. (2008) — TimeFrequency Characterization of Rotating Instability in a Centrifugal Pump with a Vaned Diffuser. Int. J. Rotating Mach. ID 202179 [7] Akin O., Rockwell D.O. (1994) — Interaction of zones of flow separation in a centrifugal impeller-stationary vane system. Exp. Fluids. 17 427-433 [8] Eisele K., Zhang Z., Casey M.V., Gülich J., Schachenmann A. (1997) — Flow analysis in a pump diffuser Part I? : LDA and PTV measurements of the unsteady flow. ASME J. Fluids Eng. 119 968-977 [9] El Hajem M., Akhras A., Morel R., Champagne J.-Y. (2001) — Rotor stator interaction in a centrifugal pump equipped with a vaned diffuser. Proc. 4th Eur. Conf. on Turbomach., Fluid Dynamics and Thermodynamics, Firenze, Italy, March?2001. [10] Akhras A., El Hajem M., Champagne J.-Y., Morel R. (2004) — The flow rate influence on the interaction of a radial pump impeller and the diffuser. Int. J. Rotating Mach. 10(4) 309-317 [11] Sinha M., Katz J. (2000) — Quantitative visualization of the flow in a centrifugal pump with diffuser vanes-I? : on flow structures and turbulence. ASME J. Fluids Eng. 122(1) 97-107 [12] S inha M., K atz J. , M eneveau C. (2000) — Quantitative visualization of the flow in a centrifugal pump with diffuser vanes-II? : addressing passage-averaged and large-eddy simula-

tion modelling issues in turbomachinery flows. ASME J. Fluids Eng. 122 (1) 108-116 [13] Wuibaut G., Bois G., Dupont P., Caignaert G., Stanislas M. (2002) — PIV measurements in the impeller and the vaneless diffuser of a radial flow pump in design and off-design operating conditions. ASME J. Fluids Eng. 124(3) 791-797 [14] Benra F. K., Feng J., Dohmen J. (2008) — PIV Measurements of Unsteady Flow in a Diffuser Pump at Different Flow Rates. 12th ISROMAC, Hawaii, USA, February. 17-22 [15] Wuibaut G., Dupont P., Caignaert G., Stanislas M. (2000) — Experimental analysis of velocities in the outlet part of a radial flow pump impeller and the vaneless diffuser using Particle Image Velocimetry. XX IAHR Symp., Charlotte, USA, 6-9?August?2000. [16] Wuibaut G., Dupont P., Bois G.., Caignaert G., Stanislas M. (2001) — Analysis of flow velocities within the impeller and the vaneless diffuser of a radial flow pump. Proc. Inst. Mech. Eng. Part A J. Power Eng. 215 801-808 [17] Wuibaut G., Dupont P., Bois G., Caignaert G., Stanislas M. (2001) — Application de la vélocimétrie par images de particules à la mesure simultanée de champs d’écoulements dans la roue et le diffuseur d’une pompe centrifuge. La Houille Blanche. 2 75-80 [18] W uibaut G. , B ois G. , D upont P. , C aignaert G. (2002) — Rotor stator interactions in a vaned dif-fuser of a radial flow pump for different flow rates using PIV measurement technique. paper FD-ABS018. 9th ISROMAC, Hawaii, USA, February?10-14,. 018 [19] Wuibaut G., Bois G., Caignaert G., Dupont P., Stanislas M. (2002) — Experimental analysis of interactions between the impeller and the vaned diffuser of a radial flow pump, paper GU03. XXI IAHR Symp., Ecole Polytechnique Fédérale de Lausanne, Switzerland, September?9-12. [20] Caignaert G., Wuibaut G., Dupont P., Bois G. (2004) — Rotor-stator Interactions in a Vaned Diffuser Radial Flow Pump. paper B5-2. XXII IAHR Symp., Stockholm, Sweden, June?29 – July?2,. [21] Dupont P., Schneider T., Caignaert G., Bois G. (2005) — Rotor-stator interactions in a vaned diffuser radial flow pump, paper FEDSM2005-69038. ASME 5th Int. Symp. on pumping machinery, Houston, USA, June?19-23. [22] Hunt J.C.R. ((1987)) — Vorticity and vortex dynamics in complex turbulent flows. Proc. CANCAM, Trans Can Society for Mech Eng. 11(1) 21-35

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