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24th Symposium on Hydraulic Machinery and Systems


                  J.M. Gagnon, M. Iliescu, G.D. Ciocan, C. Deschênes

              LAMH, 1065 avenue de la medicine, Québec, Canada, G1V 0A6, Canada
                      (418) 656-2131 -

     Laser and Optical measurement techniques have developed considerably in the past
few years within the hydraulic machinery field. Non-intrusive measurements such as
Particle Image Velocimetry (PIV) and Laser Doppler Velocimetry (LDV) are well suited
for the application but they are not implemented without any difficulties since refractive
indexes of air/glass/water interfaces play an important role in the optical arrangement.
Careful CAD design is therefore necessary to account for all the parameters affecting the
experiments and achieved precise measurements.

     This experimental work focuses on measurements of the flow at the outlet of a
model axial turbine runner. A stereoscopic digital PIV with Scheimpflug angular
displacement system is used and flow field results are compared against 2D-LDV
measurements. A 3D calibration method for PIV is marked out and uncertainty levels are
assessed. Statistical convergence is achieved on velocity and turbulent quantity for many
different phases of the runner giving information on flow phenomena, turbulent kinetic
energy and all three components of the velocity. The investigation is carried out for
design and off-design operating points of the hydraulic turbine.

      2D-LDV measurements are taken on three radial axis positions of the model cone,
i.e. at the entrance of the draft tube/runner outlet. Positions of the axis are orthogonal
with a 3D-PIV plane. Axial and circumferential velocity profiles are traced at the same
operating regimes as for 3D-PIV measurements and are used for comparison purposes as
well as for flow phenomena investigation. Emphasis is put through secondary flow
identification in the flow field. Turbulent kinetic energy results are also investigated and
aim to give better boundary conditions for the numerical simulation phases of the project.
      KEY WORD: PIV, LDV, conical diffuser, wake, blade-tip vortex, analytic solution
      Axial hydraulic turbines operated in low head power plants are increasingly popular
since high head reservoirs using turbines of the Francis type have been mostly exploited
in the past for economic purposes. For these new axial turbine plants, manufacturers and
utilities are searching for an extended range of operations with the highest attainable
efficiency possible. The optimal design needs therefore to consider the optimal condition
design, where most turbines have been built, and the other operating condition requested,
i.e. maximum and minimum head, overload and partial discharge. There are evident
needs for precise measurements on actual turbines to develop knowledge about the flow
and its behavior at off design conditions. This will lead to analytical and numerical
representations for operating points required in the conception process [1].

     The objective of the AXIAL T research project is to build a measurement database
on an axial turbine model for manufacturers and utilities. This database will help to
conceive new turbines that include off design operating conditions as conception
parameters. LDV, PIV and pressure measurements are planned for the inlet channel,
rotor-stator interface, runner and draft tube.

                              MEASUREMENT METHODS

    Figures below illustrate the LDV experimental installation at the LAMH laboratory.

                            Axis 5a
                            Axis 5b
                            Axis 5c

  Figure 1. 2D-LDV three optical accesses      Figure 2. LDV measurement setup at optical access
represented by Axis 5a, 5b and 5c at runner   5b.
    The 2D-LDV system used here is two-components, four-beams operated in
backward scatter on-axis-collection mode. There are two LDA (laser Doppler
anemometer) inside the probe head and each LDA uses two laser beams at the same
wavelength to measure one component of velocity. The probe diameter measures 60 mm
with the front lens having a focal length of about 400 mm.
    The measurement volume of the crossing beams is estimated to be ≈ 0.189 × 3.97
mm in size and there are 36 fringes with 5.27 µm separation. Bragg-cell shifting at 40
MHz is used to resolve directional ambiguity on a 5W Argon-ion laser. Fig. 2 shows a

24th Symposium on Hydraulic Machinery and Systems
picture of the measurement setup with a close-up view of the cone, linear guiding system
and LDV probe attached to it in black. Accuracy in the measurements is estimated to be ≈
2% of the measured velocity value [2].

     3D-PIV measurements are done at runner outlet on a vertical plane covering about
200 x 140 mm2. The plane is in a circumferential position located 90 degrees from LDV
Axes. The PIV system uses a Nd:YAG at 532 nm wavelength (green) laser and two CCD
cameras 1280 x 1024 pixels operated in dual-frame single exposure mode. The cameras
are positioned on both sides of the light sheet as shown in Fig. 3.
     Calibration is done with a special calibration target built from a waterproof polyester
sheet jet-ink printed with 2 mm diameters black dots spaced at 6 mm on a white
background. Polyester sheets were then glued carefully on both sides of a 6.35 mm thick
aluminum plate and placed under hub (Fig. 4, right). Dots from one side of the plate
match dots from the other side as mirror images for calibration purposes of both cameras.
     In Fig. 4 left, 28 mm lens are used on the CCD and located about 0.7m away from
the object. Laser pulses delay range from 60 to 130 µs depending of the operating point
of the turbine and correspond to particle displacement of about 5 pixels. The spatial
resolution is 3 degrees in the circumferential direction and 3 mm in the axial and radial
directions. Uncertainty in velocity measurements is estimated to be about 5% for high
accuracy sub pixel refinement in adaptive correlations [3].

Figure 3. 3D-PIV configuration under the semi-spiral casing (left) and angular displacement configuration
                             of cameras and laser under the runner (right).

  Figure 4. PIV camera and laser setup on lab (left) and calibration target under the runner temporarily
                               installed for cameras calibration (right).

24th Symposium on Hydraulic Machinery and Systems
     Both LDV and PIV experiments use hollow silver coated glass sphere particles of 10
µm as a reflective medium in the water. Their density matches with water density and
allow following the fluctuating flow up to the kilohertz [4].


      The choice of operating regimes is made to cover most of the efficiency hill and
account for principal operating conditions found in a low head power plant. Fig. 5
illustrates 8 operating points for LDV and PIV measurements. Regimes 1 to 9 are
investigated with a 2D-LDV probe at runner outlet and rotor-stator interface and regimes
1 to 6 with a 3D-PIV at runner outlet.

 Q11 [m3/s]

                                                                                                                                                                                                                                     96    38
                                                                                                                                                      9                                                                         0.
                                                                                                                                                                                     0 .9 8
                                                                                                                                        0 .9 7                                                                                       94

                                                                                                                     6                                                          9                                                          33
                                                                                                                                                                         0 .9
                                                                                                                                                       0 .9
                    0 .9
                                                                           0 .9
                                                                                  8                                                                                                  7                       .9 2
                                             6                                                   0 .9
                                                                                                        9                                                                   0 .9                         0
                                        0 .9                                                                                                                         8                                                                    31
                                                                                                                                                              0 .9
                                         0 .9                                                                            1                       3
                                                                          95                                         1                                               6
                                                                    0 .9                           2                                                          0 .9
                                                                             98                             0 .9 9                                                                                                                        29
                                                                      0   .9                                                                                 4
                                                                                                                                                      0 .9                          0 .9
                                                                       0 .9 9

                                                    0 .9 9 5                                                                                                                                                                              27
                                                                                      0 .9                                       0 .9

                                                     0 .9 8                                                 8                                                                                                                             25
                                                         0 .9
                                                    0 .9 4
                                                                       0 .9
                                                                                                   Hmax                  Hrated                      Hmin                                                           Point 7 : 17°, Hrated
                               0 .9 2

                                                  110                                              120                                               130                                           140                                150
                                                                                          n11 [rpm]
Figure 5. Normalized efficiency hill and selected operating points. Dashed lines -- : Opening angle. Solid
                                     lines - : Normalized efficiency.

     Definition of one phase and periods of the fluctuating flow are illustrated in Fig. 6.
A total of 60,000 acquisitions per position are made and referenced with an encoder
giving one pulse/rev. The velocity samples are sorted in 720 phase bins by the LDV
processor internal clock giving a circumferential resolution of 0.5 degree. The signal can
be decomposed following a Reynolds triple decomposition [5]:

                                                                              u (t ) = u + u ′ = u + u + u ′                                                                                                                 (Eq. 1)

24th Symposium on Hydraulic Machinery and Systems
    Where 〈u〉 is the phase averaged velocity, u’, the fluctuating velocity, u , the time
averaged velocity, and u , the phase velocity.
    One can see below the instantaneous LDV velocity signal marked with dots and the
phase-averaged velocity with solid line.
                                     A single
                                     acquisition over
                                     60 000

                                 Runner encoder to
                                 LDV proc.

                                 1 Period T=60°

                                                              1 Phase bin = 0.5°
                                                              720 phase bins total/360°

Figure 6. Illustration of instantaneous and phase averaged velocities provided by LDV measurements.

     In PIV measurements, images are acquired in phase with the runner position for 20
phases in between two blades using an encoder and a time delay adjusted depending on
the runner rotational speed corresponding to the turbine regime.
     PIV measurements are compared with LDV profile at Axis b and c in Fig. 7. There is
a good match in the tangential and axial profile of measuring methods.

  Axis 5b

  Axis 5c

   Figure 7. Comparison of normalized axial and tangential mean velocity profile for operating point 4.

     There are some disagreements with axial velocity for Axis 5b near the hub in Fig. 7,
top left. Differences can be explained by the third order polynomial calibration model and
magnification factor that increases the error near the PIV window border. Furthermore,
the fact that the PIV measurement plane is orthogonal to LDV axis combined with higher
swirl and asymmetric flow at off design condition might affect the results. One should
also consider errors in the tangential velocity profiles of PIV measurements, Cx, on top
right of Fig. 7, that may arise by the calibration model and the capability of estimating the
out of plane velocity component.

24th Symposium on Hydraulic Machinery and Systems
    Measurements with a 2D-LDV probe are taken in the conical diffuser on three axes:
Axis 5a, 5b and 5c.
        Operating point 6 – overload regime                      Operating point 1 – optimal regime

                                              Cx                                                      Cx

                       Hub                                                    Hub
                                   0.5 mm

                       R/R0                                                    R/R0

 Figure 8. Normalized axial and tangential velocity CZ, Cx for three optical accesses at operating point 6
                                                and 1.

      Normalized averaged velocity profiles are illustrated in Fig. 8 for overload and
optimal operating conditions. On the left, the swirl is clearly visible from the tangential
velocity, Cx, switching quickly from positive to negative values under the hub. The axial
velocity is decreasing at this location confirming the hub effect on the flow. These
phenomena are almost dissipated at Axis 5c where the axial velocity profile is flattened
and the swirl less expanded. On Fig. 8 right at optimal operating condition, there is
almost no swirl induced as expected for this regime.
      PIV mean velocity fields are plotted in Fig. 9. Contours at Cx,z = 0 are plotted to
illustrate a stagnation region under the hub on the axial velocity field (left) and swirl axis
on the tangential velocity field (right). Dashed lines indicate LDV axes.

                 Figure 9. Mean axial velocity (left) and mean tangential velocity (right).

     Phase-averaged contour of tangential velocity, total and turbulent kinetic energy is
plotted in Fig. 10 for Axis 5a, 5b and 5c.

24th Symposium on Hydraulic Machinery and Systems
Figure 10. Contour of phase-averaged tangential velocity, total kinetic energy and turbulent kinetic energy
                                         for operating point 4.

     The blade-tip vortices and wakes are clearly visible at Axis 5a and 5b of the figure
with 6 regions of high turbulent kinetic energy and velocity corresponding to 6 runner
blades. Blade wakes are less visible in the last two top right figures but still defined with
light lines from shroud to hub indicating higher total and turbulent kinetic energy at these
locations. At Axis 5c in the bottom three figures, vortices and wake are almost
completely dissipated and mixed.
                  Operating point 1 – optimal regime           Operating point 4 – partial discharge
                                                 Axe 5a                                         Axe 5a
                                                 Axe 5b                                         Axe 5b
                                                 Axe 5c                                         Axe 5c

Figure 11. Normalized deficit of relative velocity, (Wmax – Wmin)/W0 , for all axes and operating point 1 and
                 4. Solid ) Axis 5a. Dashed-dotted) Axis 5b. Solid-dashed ) Axis 5c.

24th Symposium on Hydraulic Machinery and Systems
     Dissipation of the wake is further investigated in Fig. 11, where the deficit of relative
phase averaged velocity reaches a maximum for Axis 5a and decreases at Axis 5b and 5c
located downstream in the cone. There is a faster mixing of the shear flow at partial
discharge in Fig. 11 right since the velocity deficit and magnitude is lower. In both cases,
peaks of deficit velocity are not axially symmetric and reach higher values at position
R/R0 ≈ 0.8, indicating stronger wakes at this location of the cone for axes b and c. The
phenomenon may be attributed to azimuthal non-uniformities of the flow in the cone
induced by the semi-spiral casing for this operating point.
     In Figure 12, the progression of the blade-tip vortex is clearly visible from the
contour and indicated with an arrow. Region of high tangential velocity are convected
and dissipated downstream the cone as the phase increases.

         Hub                                            Hub

                  Phase 4                                               Phase 8

         Hub                                             Hub

                 Phase 12                                               Phase 16
                             Figure 12. Blade-tip vortex progression.

                                 ANALYTIC SOLUTION
     Analytic solutions of axial and tangential experimental velocity profile at runner
outlet are found with least-squared solver and compared with analytic profiles found in
the literature. Velocity functions are defined from the superposition of Batchelor vortices
and solid body rotation [6,7]:

24th Symposium on Hydraulic Machinery and Systems
                                                              r2             r2 
                                          C z = U 0 + U 1 exp − 2  + U 2 exp − 2 
                                                              R              R                                                                                          (Eq. 2)
                                                                1              2 

                                     r 2 
                                           R        R2 
                                                        2   2
                                                                   r 2 
                             1 − exp − 2  + Ω 2
                           C x = Ω 0 r + Ω1 1
                                      R                 1 − exp 2 
                                                                  R               (Eq. 3)
                                          r
                                          1 
                                                    r           2  
     Coefficients of Eq. 2 and Eq. 3 are given in table 1 below for different location and
turbine types. C Analytic 1 coefficients come from the Helice runner outlet velocity
profiles of the current study while Muntean [8] and Resiga [6] profiles are respectively
from a Kaplan runner inlet and a Francis runner outlet.

                   Table 1. Swirl parameters from Eq. 2 and 3 for different turbine and operating points
                 Analytic profile                          Ω0                Ω1             Ω2                      U0                 U1             U2            R1                R2

     C Analytic 1 - Helice                                0.6284          -0.5649       2.9232               1.0801             -0.6064          -0.3530           0.3800          0.1857

     Muntean - Kaplan [8]                                 0.2938          4.1594        -0.3949              0.3223             -0.8120             0.4358         0.3351          0.7614

       Resiga – Francis [6]                               0.3177          -0.6288       2.2545               0.3070              0.0106          -0.3189           0.4664          0.1305

     Analytic profiles corresponding to coefficients of Table 1 are plotted in Fig. 13 and
14. In the first case on the left, there is an intense swirl at runner inlet for Muntean profile
characterized by a high value of Ω1 and Cx decreasing quickly as it gets closer to the
shroud, at R/R0 ≈ 1. In all other cases for Cx, the velocity follows a different pattern and
increases close to shroud. The difference is attributed to the presence of blade-tip
vortices at runner outlet not present in runner inlet and increasing the mean tangential
velocity close to shroud such as seen in Fig. 9 and 12. Influence of the hub is clearly
visible in the right figure where all axial velocity profiles follow the same shape but the
absolute magnitude differs.
       1                                                                                         1.4





       0                                                                                         0.6



                                                                    Cx Exp.                      0.2
                                                                                                                                                                   Cz Exp.
     -0.6                                                           Cx Analytic 1
                                                                                                                                                                   Cz Analytic 1
                                                                    Muntean - Kaplan                                                                               Muntean - Kaplan
     -0.8                                                           Resiga - Francis                                                                               Resiga - Francis
                                                                    Cx Analytic 2                                                                                  Cz Analytic 2
      -1                                                                                         -0.2
            -1      -0.8    -0.6   -0.4     -0.2    0       0.2    0.4     0.6    0.8   1               -1   -0.8        -0.6   -0.4    -0.2    0      0.2   0.4      0.6    0.8      1

                                                   R/R0                                                                                        R/R0
Figure    13.     Analytic      and                                      experimental            Figure 14. Analytic and experimental axial velocity
circumferential velocity profile.                                                                profile.

24th Symposium on Hydraulic Machinery and Systems
     One should note the difference between the experimental and the analytic profile in
both tangential and axial velocity figure. At the left, the difference between Cx Exp. and
Cx Analytic 1 is minimal but in the right figure, the experimental axial velocity increase
close to shroud and this phenomenon is not captured by the Cz Analytic 1 curve. The
introduction of two symmetrical counter-rotational Batchelor vortices in Eq. 2 and 3 at
location R/R0 ≈ 0.75 have helped to match axial velocity profile. This is shown by Cz
Analytic 2 curves characterized by small radius and velocity coefficients vortex.
Coefficients of added vortices are given in Table 2 below.

         Table 2. Swirl parameters of two counter-rotational vortices added to Eq. 2 and 3
            Analytic profile         Ω3        Ω4        U3        U4        R3       R4

            Cx,z Analytic 2        -0.0147   0.0147    0.2592   -0.2937    0.1625   0.1625

     Finally, it is interesting to compare the radius of main vortices R1 and R2 found in
Table 1 with the hub radius: Rhub/R0 = 0.375. In our case, the first coefficient R1 = 0.3800,
is closest to the hub radius and its associated vortex show the hub influence.

     This paper presents conical diffuser measurement methodology to build a database in
an axial hydraulic machine model. 3D-PIV and 2-D LDV measurements are presented
and compared. It is found that main flow phenomena are visible in both methods.
Emphasis on swirl, blade-tip vortices, wakes and flow non-uniformities was included in
the analysis.
     Experimental axial and tangential velocity profiles are matched with analytic profiles
in the last part of the paper. It is found that experimental and analytic curve shapes match
but additional vortex functions should be included to represent the blade-tip vortex in the
axial velocity profile.
     Knowledge gained from the database will help to design and optimize axial
hydraulic turbines with CFD and optimization tools in future research.

     The authors would like to thank all the partners of the Consortium on Hydraulic
Machines. Special thanks to Hydro-Quebec, Alstom Hydro Canada, Voith Siemens, Va
Tech Hydro, CVG Edelca, NRCan and NSERC for their support and contribution to this
research project.

[1]    KUENY, J.-L., LESTRIEZ, R., HELALI, A. and HIRSCH, C. (2004), Optimal
design of a small hydraulic turbine, 22nd IAHR Symposium on Hydraulic Machinery and
Systems, Stockholm, Sweden.

[2]   CIOCAN, G.D., AVELLAN F. and KUENY J.L. (2000), Optical Measurement
Techniques for Experimental Analysis of Hydraulic Turbines Rotor-Stator Interaction,

24th Symposium on Hydraulic Machinery and Systems
Proceeding of the ASME 2000 Fluids Engineering Division Summer Meeting, Boston,

[3]    RAFFEL, M., WILLERT, C. and KOMPENHANS, J. (1998), Particle Image
Velocimetry, Sprigner, Berlin, 253 p.

[4]    CIOCAN, G.D. (1998), Contribution à l’analyse des Ecoulements 3D Complexes
en Turbomachines, Ph.D. thesis, Institut National Polytechnique de Grenoble, Grenoble,

[5]    LYN, D.A., EINAV, S., RODI, W. and PARK, J.-H. (1995), A laser-Doppler
velocimetry study of ensemble-averaged characteristics of the turbulent near wake of a
square cylinder, J. Fluid Mech., vol 304, pp. 285-319.

[6]    Susan-Resiga, R., Ciocan, G.D., Anton, I. and Avellan, F. (2006), Analysis of the
Swirling Flow Downstream a Francis Turbine Runner, J. Fluid Eng., vol. 128, pp. 177-

[7]     BATCHELOR G.K. (1964), Axial Flow in Trailing Line Vorticies, J. Fluid Mech.,
20, pp. 645-658.

C. (2004), 3D Flow analysis in the spiral case and distributor of a Kaplan turbine, 22nd
IAHR Symposium on Hydraulic Machinery and Systems, Stockholm, Sweden.

24th Symposium on Hydraulic Machinery and Systems

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