Interpolation of experimental data at hydro turbine draft ... · Interpolation of experimental data...
Transcript of Interpolation of experimental data at hydro turbine draft ... · Interpolation of experimental data...
Hakan Nilsson, Chalmers / Applied Mechanics / Fluid Dynamics
Interpolation of experimental data at
hydro turbine draft tube inlets
– a study of sensitivity to incomplete data
Hakan Nilsson and Olivier Petit
Chalmers University of Technology
Purpose:
Detailed experimental data at draft tube inlets are not detailed enough.
This work presents an approach for studying sensitivity to incomplete inlet data.
Hakan Nilsson, Chalmers / Applied Mechanics / Fluid Dynamics
LDA measurements at section Ia, Holleforsen Kaplan model
Z
R
Above the blade
Section Ia
Section Ib
2.5
3
3.5
4
0
0.5
1
1.5
2
2.5
3
0 0.2 0.4 0.6 0.8 10
0.5
1
1.5C
v
Hub (0) to shroud (1)Comparison of three velocity measurements at section Ia. Solid lines: Ia(1); dashed lines:
Ia(2); dotted lines: average of phase resolved measurements. Measurement markers: △:
tangential; �: meridional. The solid lines have error bars that correspond to the estimated
errors of the measurements. Contour plots: Left: axial, Right: tangential velocity.
Hakan Nilsson, Chalmers / Applied Mechanics / Fluid Dynamics
Validation of OpenFOAM in Holleforsen runner and draft tube
(velocity profiles at cross-sections Ia and Ib)
Z
R
Above the blade
Section Ia
Section Ib
0 0.2 0.4 0.6 0.8 10
0.5
1
1.5
2
Hub (0) to shroud (1), Ia
c v
0 0.2 0.4 0.6 0.8 10
0.5
1
1.5
2
Hub (0) to shroud (1), Ia
c v
0 0.2 0.4 0.6 0.8 1−0.5
0
0.5
1
1.5
Hub (0) to shroud (1), Ib
c v
Squares: measured axial velocity. Triangles: measured tangential velocity. In (a) the colors
correspond to two different measurements. In (b) and (c): Blue curve: quasi-steady draft tube,
Black curve: runner without hub clearance, Red curve: runner with hub clearance.
Hakan Nilsson, Chalmers / Applied Mechanics / Fluid Dynamics
Approach
• Perform an unsteady rotor-stator simulation of the full case
• Probe values along a radial line at the draft tube inlet, similar as LDA
• Compute the phase-average of all variables
• Apply the rotating phase-averaged variables at the draft tube inlet
• Study the influence of loss of different kind of data
This work is based on the Timisoara Swirl Generator, since results are already available.
Hakan Nilsson, Chalmers / Applied Mechanics / Fluid Dynamics
Full case, Draft Tube Inlet, Tangential Velocity
0 0.05 0.1 0.15 0.21.2
1.4
1.6
1.8
2
Time
Tan
gent
ial v
eloc
ity
Raw signal, probe 7
0 0.02 0.04 0.06 0.081.2
1.4
1.6
1.8
2
Time
Tan
gent
ial v
eloc
ity
Repeated over 360 degrees
0 2 4 6 8
x 10−3
1.2
1.4
1.6
1.8
2
Time
Tan
gent
ial v
eloc
ity
Repeated over 36 degrees
0 2 4 6 8
x 10−3
1.2
1.4
1.6
1.8
2
Time
Tan
gent
ial v
eloc
ity
Averaged over 36 degrees
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
3
3.2
Phase-averaged distribution
The low-frequency fluctuation, causing deviation in repetition, is due to the vortex rope.
Hakan Nilsson, Chalmers / Applied Mechanics / Fluid Dynamics
Full case, Draft Tube Inlet, Phase-Averaged Variables
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
Radial velocity
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
3
3.2
Tangential velocity
1
1.5
2
2.5
3
3.5
Axial velocity
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
Turbulent kinetic energy
0
10
20
30
40
50
60
70
Dissipation
2
2.5
3
3.5
4
4.5
5
5.5
Pressure (p/ρ)
Hakan Nilsson, Chalmers / Applied Mechanics / Fluid Dynamics
A new boundary condition for 2D cylindrical interpolation
Velocity:
inlet{
type angResolvedT99FixedValue;varNameR UrIn; //Rad. component namevarNameT UtIn; //Tang. component namevarNameA UyIn; //Axial component nameccsAngleCorr 0; //Current angleQ 0.522; //Volume flow
}
Scalar fields:
inlet{
type angResolvedT99FixedValue;varName teIn; //Variable nameccsAngleCorr 0; //Current angle
}
Dictionary boundaryProperties:
ccsCenterPoint (0 0 0); //\ccsAxis (0 0 1); // >Cyl.coord.systemccsBaseDir (1 0 0); ///interpDir rIn; //Non-tangential directioninterpCoordName rIn; //Non-tangential nametangCoordName tIn; //Tangential nameomega -96.34217469; //Rot.speedrotatingInletFileName rotatingInletProperties.dat;
The values are read from dictionary lists,ordered as an orthogonal mesh in θ-r/a.The rotatingInletProperties.dat file:
rIn 18(4.4999999999999998e-024.5499999999999999e-02...);
tIn 361(1.7453292519943295e-023.4906585039886591e-02...);
UrIn 6498(4.0968094339622625e-022.6610867924528304e-02...);
Values first loop in increasing θ direction, and
then in increasing non-θ direction (r/a).
Accepts periodic sector in θ-direction.
Hakan Nilsson, Chalmers / Applied Mechanics / Fluid Dynamics
Studied cases
• Full case (rotor-stator interaction)
• Draft tube only, (same mesh as in full case)
Additional variants of ”draft tube only”:
- Without flow correction
- Zero radial velocity
- Zero radial velocity and
reduced tangential inlet resolution
- Axi-symmetric inlet
The following slides show that although the tangential resolution of the runner blade wakes
differ, the velocity profiles and pressure fluctuations do not depend much on the different inlet
conditions. However, the head loss does.
Hakan Nilsson, Chalmers / Applied Mechanics / Fluid Dynamics
Cross-sections that are examined
Section 1 at the draft tube inlet, section 2 just below, W0-2 are LDA sections.
Hakan Nilsson, Chalmers / Applied Mechanics / Fluid Dynamics
Section 2, Phase-average, radial velocity
−0.9
−0.8
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
Full case
−0.9
−0.8
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
Draft tube only
−0.9
−0.8
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
No flow correction
−0.9
−0.8
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
Zero Radial velocity
−0.9
−0.8
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
Zero rad.vel Red.tang.res.
−0.9
−0.8
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
Axi-symmetric inlet
Hakan Nilsson, Chalmers / Applied Mechanics / Fluid Dynamics
Section 2, Phase-average, tangential velocity
1.4
1.6
1.8
2
2.2
2.4
2.6
Full case
1.4
1.6
1.8
2
2.2
2.4
2.6
Draft tube only
1.4
1.6
1.8
2
2.2
2.4
2.6
No flow correction
1.4
1.6
1.8
2
2.2
2.4
2.6
Zero Radial velocity
1.4
1.6
1.8
2
2.2
2.4
2.6
Zero rad.vel Red.tang.res.
1.4
1.6
1.8
2
2.2
2.4
2.6
Axi-symmetric inlet
Hakan Nilsson, Chalmers / Applied Mechanics / Fluid Dynamics
Section 2, Phase-average, axial velocity
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
3
3.2
Full case
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
3
3.2
Draft tube only
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
3
3.2
No flow correction
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
3
3.2
Zero Radial velocity
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
3
3.2
Zero rad.vel Red.tang.res.
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
3
3.2
Axi-symmetric inlet
Hakan Nilsson, Chalmers / Applied Mechanics / Fluid Dynamics
Section 2, Phase-average, k
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
Full case
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
Draft tube only
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
No flow correction
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
Zero Radial velocity
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
Zero rad.vel Red.tang.res.
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
Axi-symmetric inlet
Hakan Nilsson, Chalmers / Applied Mechanics / Fluid Dynamics
Section 2, Phase-average, epsilon
0
10
20
30
40
50
60
70
Full case
0
10
20
30
40
50
60
70
Draft tube only
0
10
20
30
40
50
60
70
No flow correction
0
10
20
30
40
50
60
70
Zero Radial velocity
0
10
20
30
40
50
60
70
Zero rad.vel Red.tang.res.
0
10
20
30
40
50
60
70
Axi-symmetric inlet
Hakan Nilsson, Chalmers / Applied Mechanics / Fluid Dynamics
Section 2, Phase-average, p/rho
2
2.5
3
3.5
4
4.5
5
5.5
Full case
2
2.5
3
3.5
4
4.5
5
5.5
Draft tube only
2
2.5
3
3.5
4
4.5
5
5.5
No flow correction
2
2.5
3
3.5
4
4.5
5
5.5
Zero Radial velocity
2
2.5
3
3.5
4
4.5
5
5.5
Zero rad.vel Red.tang.res.
2
2.5
3
3.5
4
4.5
5
5.5
Axi-symmetric inlet
Hakan Nilsson, Chalmers / Applied Mechanics / Fluid Dynamics
Cross-sections that are examined
Let’s continue with W0, W1 and W2, and compare with the LDA data...
Hakan Nilsson, Chalmers / Applied Mechanics / Fluid Dynamics
Velocity profiles at W0, compared with measurements
Measurement markers: +: Meridional, x: Tangential
0 0.1 0.2 0.3 0.4 0.5 0.6−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
Dimensionless survey axis
Dim
ensi
onle
ss v
eloc
ity
Full case
0 0.1 0.2 0.3 0.4 0.5 0.6−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
Dimensionless survey axis
Dim
ensi
onle
ss v
eloc
ityDraft tube only
0 0.1 0.2 0.3 0.4 0.5 0.6−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
Dimensionless survey axis
Dim
ensi
onle
ss v
eloc
ity
No flow correction
0 0.1 0.2 0.3 0.4 0.5 0.6−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
Dimensionless survey axis
Dim
ensi
onle
ss v
eloc
ity
Zero Radial velocity
0 0.1 0.2 0.3 0.4 0.5 0.6−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
Dimensionless survey axis
Dim
ensi
onle
ss v
eloc
ity
Zero rad.vel Red.tang.res.
0 0.1 0.2 0.3 0.4 0.5 0.6−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
Dimensionless survey axis
Dim
ensi
onle
ss v
eloc
ity
Axi-symmetric inlet
Hakan Nilsson, Chalmers / Applied Mechanics / Fluid Dynamics
Velocity profiles at W1, compared with measurements
Measurement markers: +: Meridional, x: Tangential
0 0.5 1 1.5 2−1.5
−1
−0.5
0
0.5
1
1.5
Dimensionless survey axis
Dim
ensi
onle
ss v
eloc
ity
Full case
0 0.5 1 1.5 2−1.5
−1
−0.5
0
0.5
1
1.5
Dimensionless survey axis
Dim
ensi
onle
ss v
eloc
ityDraft tube only
0 0.5 1 1.5 2−1.5
−1
−0.5
0
0.5
1
1.5
Dimensionless survey axis
Dim
ensi
onle
ss v
eloc
ity
No flow correction
0 0.5 1 1.5 2−1.5
−1
−0.5
0
0.5
1
1.5
Dimensionless survey axis
Dim
ensi
onle
ss v
eloc
ity
Zero Radial velocity
0 0.5 1 1.5 2−1.5
−1
−0.5
0
0.5
1
1.5
Dimensionless survey axis
Dim
ensi
onle
ss v
eloc
ity
Zero rad.vel Red.tang.res.
0 0.5 1 1.5 2−1.5
−1
−0.5
0
0.5
1
1.5
Dimensionless survey axis
Dim
ensi
onle
ss v
eloc
ity
Axi-symmetric inlet
Hakan Nilsson, Chalmers / Applied Mechanics / Fluid Dynamics
Velocity profiles at W2, compared with measurements
Measurement markers: +: Meridional, x: Tangential
0 0.5 1 1.5 2 2.5−1
−0.5
0
0.5
1
Dimensionless survey axis
Dim
ensi
onle
ss v
eloc
ity
Full case
0 0.5 1 1.5 2 2.5−1
−0.5
0
0.5
1
Dimensionless survey axis
Dim
ensi
onle
ss v
eloc
ityDraft tube only
0 0.5 1 1.5 2 2.5−1
−0.5
0
0.5
1
Dimensionless survey axis
Dim
ensi
onle
ss v
eloc
ity
No flow correction
0 0.5 1 1.5 2 2.5−1
−0.5
0
0.5
1
Dimensionless survey axis
Dim
ensi
onle
ss v
eloc
ity
Zero Radial velocity
0 0.5 1 1.5 2 2.5−1
−0.5
0
0.5
1
Dimensionless survey axis
Dim
ensi
onle
ss v
eloc
ity
Zero rad.vel Red.tang.res.
0 0.5 1 1.5 2 2.5−1
−0.5
0
0.5
1
Dimensionless survey axis
Dim
ensi
onle
ss v
eloc
ity
Axi-symmetric inlet
Hakan Nilsson, Chalmers / Applied Mechanics / Fluid Dynamics
Pressure probe locations MG0, MG1, MG2, MG3
Hakan Nilsson, Chalmers / Applied Mechanics / Fluid Dynamics
MG0, pressure signal (phase determined by flow)
0 0.1 0.2 0.3 0.4−6
−5
−4
−3
−2
−1
0
Time
p/rh
o
Full case
0 0.1 0.2 0.3 0.4−6
−5
−4
−3
−2
−1
0
Time
p/rh
oDraft tube only
0 0.1 0.2 0.3 0.4−6
−5
−4
−3
−2
−1
0
Time
p/rh
o
No flow correction
0 0.1 0.2 0.3 0.4−6
−5
−4
−3
−2
−1
0
Time
p/rh
o
Zero Radial velocity
0 0.1 0.2 0.3 0.4−6
−5
−4
−3
−2
−1
0
Time
p/rh
o
Zero rad.vel Red.tang.res.
0 0.1 0.2 0.3 0.4−6
−5
−4
−3
−2
−1
0
Time
p/rh
o
Axi-symmetric inlet
Hakan Nilsson, Chalmers / Applied Mechanics / Fluid Dynamics
MG1, pressure signal (phase determined by flow)
0 0.1 0.2 0.3 0.4−5
−4
−3
−2
−1
0
1
2
3
Time
p/rh
o
Full case
0 0.1 0.2 0.3 0.4−5
−4
−3
−2
−1
0
1
2
3
Time
p/rh
oDraft tube only
0 0.1 0.2 0.3 0.4−5
−4
−3
−2
−1
0
1
2
3
Time
p/rh
o
No flow correction
0 0.1 0.2 0.3 0.4−5
−4
−3
−2
−1
0
1
2
3
Time
p/rh
o
Zero Radial velocity
0 0.1 0.2 0.3 0.4−5
−4
−3
−2
−1
0
1
2
3
Time
p/rh
o
Zero rad.vel Red.tang.res.
0 0.1 0.2 0.3 0.4−5
−4
−3
−2
−1
0
1
2
3
Time
p/rh
o
Axi-symmetric inlet
Hakan Nilsson, Chalmers / Applied Mechanics / Fluid Dynamics
MG2, pressure signal (phase determined by flow)
0 0.1 0.2 0.3 0.4−4
−3
−2
−1
0
1
2
Time
p/rh
o
Full case
0 0.1 0.2 0.3 0.4−4
−3
−2
−1
0
1
2
Time
p/rh
oDraft tube only
0 0.1 0.2 0.3 0.4−4
−3
−2
−1
0
1
2
Time
p/rh
o
No flow correction
0 0.1 0.2 0.3 0.4−4
−3
−2
−1
0
1
2
Time
p/rh
o
Zero Radial velocity
0 0.1 0.2 0.3 0.4−4
−3
−2
−1
0
1
2
Time
p/rh
o
Zero rad.vel Red.tang.res.
0 0.1 0.2 0.3 0.4−4
−3
−2
−1
0
1
2
Time
p/rh
o
Axi-symmetric inlet
Hakan Nilsson, Chalmers / Applied Mechanics / Fluid Dynamics
MG3, pressure signal (phase determined by flow)
0 0.1 0.2 0.3 0.4−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
Time
p/rh
o
Full case
0 0.1 0.2 0.3 0.4−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
Time
p/rh
oDraft tube only
0 0.1 0.2 0.3 0.4−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
Time
p/rh
o
No flow correction
0 0.1 0.2 0.3 0.4−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
Time
p/rh
o
Zero Radial velocity
0 0.1 0.2 0.3 0.4−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
Time
p/rh
o
Zero rad.vel Red.tang.res.
0 0.1 0.2 0.3 0.4−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
Time
p/rh
o
Axi-symmetric inlet
Hakan Nilsson, Chalmers / Applied Mechanics / Fluid Dynamics
Head (phase determined by flow)
0 0.1 0.2 0.3 0.4−0.606
−0.604
−0.602
−0.6
−0.598
−0.596
−0.594
−0.592
−0.59
Time [s]
Hea
d [m
]
Full case (different range)
0 0.1 0.2 0.3 0.4−0.606
−0.604
−0.602
−0.6
−0.598
−0.596
−0.594
−0.592
−0.59
Time [s]
Hea
d [m
]Draft tube only
0 0.1 0.2 0.3 0.4−0.606
−0.604
−0.602
−0.6
−0.598
−0.596
−0.594
−0.592
−0.59
Time [s]
Hea
d [m
]
No flow correction
0 0.1 0.2 0.3 0.4−0.606
−0.604
−0.602
−0.6
−0.598
−0.596
−0.594
−0.592
−0.59
Time [s]
Hea
d [m
]
Zero Radial velocity
0 0.1 0.2 0.3 0.4−0.606
−0.604
−0.602
−0.6
−0.598
−0.596
−0.594
−0.592
−0.59
Time [s]
Hea
d [m
]
Zero rad.vel Red.tang.res.
0 0.1 0.2 0.3 0.4−0.606
−0.604
−0.602
−0.6
−0.598
−0.596
−0.594
−0.592
−0.59
Time [s]
Hea
d [m
]
Axi-symmetric inlet
Hakan Nilsson, Chalmers / Applied Mechanics / Fluid Dynamics
Inlet interpolated flow variation before correction
– the reason for the disturbances in head
Fluctuations in the order of 0.001%!!!
0 100 200 300 4000.0905
0.091
0.0915
0.092
0.0925
0.093
0.0935
Time step (360 per lap)
Inle
t flo
w e
rror
[%]
Hakan Nilsson, Chalmers / Applied Mechanics / Fluid Dynamics
Conclusions
• Phase-resolved measurements in T-99 draft tube:
– No radial component
– Lack of boundary layer data
– Differences in repeated measurements
– 7% flow error in integrated velocity
Lack of radial component has been accused to be the main problem
Runner simulations show that hub boundary layer is very important
• TSG results in the present work:
– No major problem with lack of radial component
– Velocity profiles not sensitive to inlet variations
– Pressure frequency not sensitive to inlet variations
– Head loss sensitive to inlet variations:
Flow fluctuations cause disturbances
Mean head loss differs
Hakan Nilsson, Chalmers / Applied Mechanics / Fluid Dynamics
Thank you for your attention!
Acknowledgements
• Prof. Romeo Susan Resiga and Dr. Sebastian Muntean for providing the
Timisoara Swirl Generator geometry, and the experimental data.
• SNIC (Swedish National Infrastructure for Computing) for providing com-
putational resources.
• SVC (Swedish Hydro Power Center, www.svc.nu)1 for financial support.
1Swedish Energy Agency, ELFORSK, Svenska Kraftnat, CarlBro, E.ON Vattenkraft Sverige, Fortum Generation, Jamtkraft, Jonkoping Energi, Malarenergi,
Skelleftea Kraft, Sollefteaforsens, Statoil Lubricants, Sweco VBB, Sweco Energuide, SweMin, Tekniska Verken i Linkoping, Vattenfall Research and Development,
Vattenfall Vattenkraft, VG Power, Oresundskraft, Andritz Hydro, Chalmers, LTU, KTH, UU