rotor-stator interactions in a radial flow pump

ROTOR-STATOR INTERACTIONS IN A RADIAL FLOW PUMP

G. Pavesi*-G. Cavazzini*-P. Dupont**-S. Coudert**- G. Caignaert**-G. Bois**- G. Ardizzon*

*Department of Mechanical Engineering, University of Padua, Padua, Italy

giorgio.pavesi@unipd.it, giovanna.cavazzini@unipd.it, guido.ardizzon@unipd.it

** Laboratoire de Mécanique de Lille (UMR CNRS 8107), Lille, France patrick.dupont@ec-lille.fr, sebastien.coudert@univ-lille1.fr, guy.caignaert@lille.ensam.fr,

gerard.bois@lille.ensam.fr ABSTRACT

The paper refers to the analysis of interactions between the impeller and the vaned dif-fuser of a radial flow pump. It mainly focuses on the flow within one blade passage of a vaned diffuser in four operating conditions.

The 2D/2C PIV technique was used to analyze the diffuser flow field in various measuring planes in the hub to shroud direction, for one relative impeller position in the diffuser frame. These experimental results were compared to numerical data obtained with the help of CFX computer code.

NOMENCLATURE BB2 impeller outlet width R4 diffuser outlet radius BB3 diffuser constant width U2 peripheral velocity CX flow velocity component in x direction Z1 number of impeller blades CZ axial velocity component Z2 number of diffuser blades Cm2 meridional velocity component l section length N speed of rotation (rpm) s1 mean impeller blade thickness Q flow rate Δp0 total pressure rise Qn design flow rate β2 outlet impeller blade angle R1 impeller tip inlet radius ω speed of rotation (rad/s) R2 impeller outlet radius ϕ =Cm2/U2 flow coefficient R3 diffuser inlet radius ψ=Δp0/U2

2 total head coefficient

INTRODUCTION In the field of turbomachinery, one of the aims of research is to increase the machine perform-

ance. Therefore, a more in-depth knowledge of physical phenomena, which happen in turbomachi-nes, is indispensable. One of the main aspects is the control of the interaction effects between stationary and rotating parts because it influences the flow field inside both components and has ef-fects on machine stability, vibration, noise and pressure pulsations, maily at off-design conditions.

Many researchers have studied the flow field in the rotor-stator interaction zone with standard technique, like pressure transducers and hot wire anemometers [Arndt et al.,1990], and with the la-ser techniques like Laser Doppler Velocimetry (L.D.V.) and more recently Particle Image Veloci-metry (P.I.V.) [Akin, Rockwell, 1994; Eisele et al., 1997].

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 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.

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The present paper presents some new experimental data obtained using 2D/2C PIV within a blade passage of a vaned diffuser of a radial pump working with air. Five measuring planes were considered in the hub to shroud direction, with one relative position of the impeller in the diffuser frame, and several operating conditions. The experimental data were compared with the results ob-tained with the help of the CFX computer code. The discussion analyzes the diffuser performance in different operating conditions and the sources of discrepancies between experimental and numerical results.

EXPERIMENTAL FACILITIES The tests were carried out on the so-called SHF impeller, coupled with a vaned diffuser, and

working with air (fig. 1). To study only the interaction between impeller and diffuser, no volute was provided. Figure 2 presents the pump performance curve. The impeller was already used in previous studies, coupled with a short vaneless diffuser [Wuibaut et al. 2000, 2001a, 2001b, 2002a] and with two different vaned diffuser [Wuibaut et al 2002b, 2002c, Caignaert et al 2004, Dupont et al. 2005].

The test rig was the same as the one used for these studies. It was developed for the use of the Particle Image Velocimetry (PIV) technique. The description of the PIV technique, of the measure-ments device (fig. 3) and of the experimental set up is reported in the studies mentioned above.

In this work one blade passage of a vaned diffuser was ana-lyzed by the 2D/2C PIV technique in order to obtain some new experimental results. Flow fields were determined for various op-erating conditions of the pump in five measuring planes at dif-ferent heights in the hub to shroud direction. A previous work analyzed the diffuser performance in one operating condition for seven relative impeller positions in the diffuser frame [Pavesi et al. 2006]. The present paper extends the analysis to four different operating conditions for one relative impeller position.

The main characteristics of the so called “SHF” impeller, used for tests in air, and of the vaned diffuser, are respectively reported

in tab. 1 and 2. The impeller Reynolds number was 1.56*106.

Figure 1 Schematic representa-

tion of the SHF impeller coupled with the vaned dif-fuser.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16ϕ

As regards the absolute flow angle distribution at the impeller outlet, fluctuations of about ±5° in comparison with the mean flow direction were measured for each blade passage, whatever the position of the impeller in the diffuser frame [Caignaert et al, 2004]. These fluctuations increased as the flow rate increased.

ψ

Figure 4 presents the overall optical arrangement.

Figure 2 The pump performance curve PIV measurements were made for

Tab. 1 Impeller characteristics Tab. 2 Diffuser characteristics R1 = 141.1 mm Z1 = 7 Z2 = 8 R2 = 256.6 mm S1 = 9 mm

R3 = 273.6 mm (relative radial gap with impeller = 6.65%)

BB2 = 38.5 mm Nn = 2500 rpm R4 = 397.8 mm BB3 = 40.0 mm Qn = 0.336 m3/s

(at 1710 rpm ) BB4 = 40.0 mm

Design flow rate = 0.80Qn β2 = 22.5° (measured from

the peripheral direction)

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the impeller speed of rotation 1710 rpm. So, two single exposure frames were taken each two complete revolutions.

The experimental database with that vaned diffuser was made up with 400 in-stantaneous velocity fields for every measuring condition corresponding to:

• Four relative flow rates for the pre-sent paper: Q/Qn = 0.43, 0.77, 1.00, 1.17;

• Two simultaneous views with fields of 100 mm X 82 mm (fig. 6)

• One position of the impeller blade in the vaned diffuser frame (la-belled P2 in fig. 5), corresponding

to 0.34° of angular position of one impeller blade in front of one diffuser vane • 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.

Figure 3 The acquisition chain

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).

P.I.V. snapshots were simultaneously taken by two cameras positioned side by side. A home made software, developed by the Laboratoire de Mécanique de Lille, was used for the images treat-ment. With the same software, the obtained results, were checked and cleared with a cleaning procedure that removed aberrant vectors due to reflection problems during the PIV measurements. Then the data, obtained with the two cameras (fig. 6), 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).

NUMERICAL PROCEDURE The commercial software package CFX 10.0 was used for performing the numerical simulations

on the entire machine. On both blades and wall surfaces the boundary layer was assumed fully-turbulent. The Detached Eddy Simulation Model (DES) was chosen as turbulence model. It has the characteristic of classical RANS formulations combined with elements of Large Eddy Simulation (LES) methods. The Shear Stress Transport k-ω model covers the boundary layer while the Smagorinsky-Lilly model is applied in detached regions.

Since one of the interesting analysis aspects is the possible prediction of noise and vibrations due to stator-rotor interaction, the LES peculiarity of providing information on turbulent flow structures and spectral distribution is useful.

An unsteady model was used for all the computa-

Figure 4 Optical assembly to create a laser

sheet in one diffuser blade passage. Figure 5 Impeller blade positions in the diffuser

frame.

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tions. For the interface between stator/rotor blocks the standard transient sliding interface ap-proach was chosen.

The scheme adopted for the discretisation time was a second order dual time stepping. For the explicit scheme the time step definition was based on the impeller rotation and it was of about one degree. The numerical data were acquired between 2.5 and 2.625 impeller revolutions. The overall CPU computation time was 19 days in a cluster of 2.19 GHz processors. So the final Courant Number was about CFL=3. A maximum number of five iterations was fixed for each time step, resulting in a mass residues of 10-6, mo-mentum residues of 10-4, turbulence kinetic en-ergy and energy dissipation of 10-4.

Figure 6 Seeding of the blade passage as seen by PIV cameras with an overlapping (black parts are the walls of the diffuser passage).

An H-type grid was used for the impeller, whereas a O-type grid was adopted for the dif-fuser. 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 60 in the whole computational region.

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.

Figure 7 Seal system at the impeller inlet (left) and outlet (right).

The previous analysis, with the relative flow rate Q/Qn = 0.77 [Pavesi at al. 2006], has pointed out an over-prediction of the leakage flow rate entering at the impeller outlet, due to the numerical imprecise loss estimation in the gaps. In this work the loss coefficient in the gaps was increased to minimize the mass flow error.

The surfaces were supposed as adiabatic walls with a no-slip condition. As regards the exit boundary conditions, the experimental pressure level was prescribed as average pressure at the dif-fuser 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-crite-rion 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 [Hunt, 1987] and it is defined as:

[ ] 0S5.0Q 22 >−Ω= (1)

where

( )[ ]Tuu5.0S ∇+∇= (2)

is the rate of strain tensor and

( )[ ]Tuu5.0 ∇−∇=Ω (3)

is the vorticity tensor.

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COMPARISON BETWEEN EXPERIMENTAL AND NUMERICAL 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 mid-height plane (H3). The comparison of the experimental results with the data of the DES model in the first 10 positions is shown in fig. 9. The velocity profiles are quite in good agreement with the experimental data except near the pressure side. The reasons of this discrepancy were partly discussed in the previous work for

Q/Qn=0.77 [Pavesi et al. 2006]. The stream-wise grid resolution and the choice of the turbulent model were considered like possible numerical error sources. Moreover the blade roughness pre-scribed in the computations (smooth surface) was presumed to be not in perfect agreement with the experimental one. On the other side the experimental 2D PIV limits were investigated. The presence of three-dimensional vortexes due to the leakage flow rate and the velocity fluctuations due to the rotor-stator interaction were assumed to influence the experimental results accuracy. Moreover among the experimental limits the reflection problems and the difficult seeding near the blade pres-sure side have to be considered.

Figure 8 Analysis Sections Definition

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. The reason for this discrepancy could be an insufficient illumination in that zone. For the tests one single light sheet was used, with light coming from the outlet part of the analyzed diffuser vane passage (fig. 6). Therefore, the laser light could be not ade-quate, close to the blade leading edge, for obtaining the appropriate illumination.

Q/Qn=0.43 Q/Qn=0.77

Q/Qn=1.00 Q/Qn=1.17 Figure 9 Comparison between the P.I.V. results (dashed lines with circle and triangles) and the nu-

merical results (continuous lines) in the blade-to-blade surfaces (position P2, H3).

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For Q/Qn=0.77 and for 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 mass flow rate and of velocities components do not seem to justify this over-prediction. The discrepancy could be explained by the experimental data dispersion depicted by the probability density distribution in the analyzed sections (fig. 10).

Figure 10 Probability density in the blade-to-blade surface H3 (Q/Qn=0.43; Q/Qn=1.00).

The probability density gives the probability that a variable is in any particular interval and it is a "smoothed out" version of a histogram. Where the dispersion of the experimental data increases, the probability density diminishes and a discrepancy between the numerical and experimental re-sults due to the experimental data inconsistency appears. Vice versa, where the probability density is great, there is a good agreement between the data. For Q/Qn=0.43 the probability density was very small in the first 20 sections and then increased a little in the second part of the passage. The agreement with the numerical data is acceptable in the second part of the diffuser but it is not so good overall (figs 9-10-11). For Q/Qn=1.00 the probability density is high everywhere except in the pressure side boundary layer development zone (figs 9-10-11). The experimental data inconsistency could be explained with 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 for Q/Qn=0.77 (fig. 13). Their presence 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 blades wakes (fig. 12 – R=256.6 mm). Afterwards, the leakage flow rate entered in the gaps between impeller and diffuser (fig. 12-R=258.1 mm), and interacted with the impeller blades wakes (R=270-273 mm). The interaction amplified the leakage effects and created two large vortices that involve all the diffuser passage (fig. 13).

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Their intensity decreased along the passage, but at the diffuser outlet throat they were still pre-sent.

For Q/Qn=0.77 the phenomenon was similar, but the leakage flow rate effects were a little less important and at the diffuser inlet throat the vortex did not involve the whole passage. Flow fluctua-tions coming from the impeller outlet create turbulence cores that proceed in the diffuser passage on the blade suction side (fig.14). These flow fluctuations, having no-coherent correlation in space and in time [Pavesi, Ardizzon, 2006], help in affecting the probability density in the diffuser passage centre and had effects on the velocity PIV measurements.

At the impeller design flow rate (Q/Qn=1.0) the blades wakes involved the entire hub-to-shroud zone, but were more intense near the shroud (fig. 12). In the gap between impeller and diffuser the leakage flow rate did not affect the flow so much to create the two vortex described above (fig. 13).

Q/Qn=0.43 Q/Qn=1.00

Figure 11 Comparison between the P.I.V. results (dashed lines with circles and triangles) and the nu-

merical results (continuous lines) in the blade-to-blade surfaces (position P2, H3 =0.5)

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At mid span a small vortex, probably due to the pressure gradient, appeared near the blade suc-tion side with its axis normal to the PIV plane. It proceeded along the diffuser passage, shifting to-wards the passage centre. Its development gave rise to a secondary flow that involved the blade

Figure 12 Influence of the leakage flow rate on the Q-criterion

Q/Qn=0.43 Q/Qn=0.77

Q/Qn=1.00 Q/Qn=1.17

Figure 13 Secondary flows in the diffuser

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Q/Qn=0.43 Q/Qn=0.77

Q/Qn=1.00 Q/Qn=1.17

pressure side creating a second small vortex still at mid span. Then this second vortex moved in the shroud-to-hub direction and at the outlet diffuser throat it was positioned near the hub. Since this secondary flow developed in a plane normal to that analyzed with the PIV, the velocity PIV measurements were negatively affected (fig. 9). For Q/Qn=1.17 the behaviour was similar to that of Q/Qn=1.00 with small leakage flow rate effects and with quite the same secondary flow effects de-scribed above. The flow fluctuations were a bit more important and seem to affect the velocity PIV measurements in the passage centre (fig. 9).

Figure 14 Leakage flow effects and impeller blade influence on the Q-Criterion near the shroud (H4 =0.74)

CONCLUSION A vaned diffuser coupled with a SHF impeller was studied. One diffuser passage was analyzed

in detail with a 2D/2C PIV technique in four different operating conditions for one relative position of the impeller in the diffuser frame. The experimental results were compared with that of numerical computations performed by compressible Detached Eddy Simulation model.

The comparisons highlighted some differences due to the importance of two phenomena: 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 af-fect the velocity PIV measurements. Moreover flow fluctuations due to the rotor-stator interaction, coming from the impeller outlet, proceed in the diffuser passage and decreased the probability den-sity 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 secondary flow developed in the passage, creating small vortexes. The experimental results were in good agreement with the numerical data with the exception of the boundary layer development on the blade pressure side.

The analysis was also performed for each position of the impeller in the diffuser frame allowing the analysis of unsteady rotor-stator interaction. Complementary work has to be done to get an

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experimental evaluation of the leakage flow rates. Further experimental works will also be carried out in a next future, using time resolved PIV and, or 2D/3C PIV.

ACKNOWLEDGEMENTS The authors thank CNRS and Région Nord Pas de Calais for their financial support in PIV

equipment. This work was, also, partly supported by Fondazione Ing. Gini.

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