Interpolation of experimental data at hydro turbine draft ... · Interpolation of experimental data at hydro turbine draft tube inlets – a study of sensitivity to incomplete 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.


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.


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.


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.


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.


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)


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.


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.


Cross-sections that are examined

Section 1 at the draft tube inlet, section 2 just below, W0-2 are LDA sections.


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


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


1.4

1.6

1.8

2

2.2

2.4

2.6


1.4

1.6

1.8

2

2.2

2.4

2.6

Axi-symmetric inlet


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


1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

3.2


1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

3.2

Axi-symmetric inlet


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


0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18


0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

Axi-symmetric inlet


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


0

10

20

30

40

50

60

70


0

10

20

30

40

50

60

70

Axi-symmetric inlet


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


2

2.5

3

3.5

4

4.5

5

5.5


2

2.5

3

3.5

4

4.5

5

5.5

Axi-symmetric inlet


Cross-sections that are examined

Let’s continue with W0, W1 and W2, and compare with the LDA data...


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


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


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


Dim

ensi

onle

ss v

eloc

ity


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


Dim

ensi

onle

ss v

eloc

ity


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


Dim

ensi

onle

ss v

eloc

ity

Axi-symmetric inlet




0 0.5 1 1.5 2−1.5

−1

−0.5

0

0.5

1

1.5


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


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


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


Dim

ensi

onle

ss v

eloc

ity


0 0.5 1 1.5 2−1.5

−1

−0.5

0

0.5

1

1.5


Dim

ensi

onle

ss v

eloc

ity


0 0.5 1 1.5 2−1.5

−1

−0.5

0

0.5

1

1.5


Dim

ensi

onle

ss v

eloc

ity

Axi-symmetric inlet




0 0.5 1 1.5 2 2.5−1

−0.5

0

0.5

1


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


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


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


Dim

ensi

onle

ss v

eloc

ity


0 0.5 1 1.5 2 2.5−1

−0.5

0

0.5

1


Dim

ensi

onle

ss v

eloc

ity


0 0.5 1 1.5 2 2.5−1

−0.5

0

0.5

1


Dim

ensi

onle

ss v

eloc

ity

Axi-symmetric inlet


Pressure probe locations MG0, MG1, MG2, MG3


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


0 0.1 0.2 0.3 0.4−6

−5

−4

−3

−2

−1

0

Time

p/rh

o


0 0.1 0.2 0.3 0.4−6

−5

−4

−3

−2

−1

0

Time

p/rh

o

Axi-symmetric inlet



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


0 0.1 0.2 0.3 0.4−5

−4

−3

−2

−1

0

1

2

3

Time

p/rh

o


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



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


0 0.1 0.2 0.3 0.4−4

−3

−2

−1

0

1

2

Time

p/rh

o


0 0.1 0.2 0.3 0.4−4

−3

−2

−1

0

1

2

Time

p/rh

o

Axi-symmetric inlet



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


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


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


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

]


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

]


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


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

[%]


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


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

Documents

Interpolation of experimental data at hydro turbine draft ... · Interpolation of experimental data at hydro turbine draft tube inlets – a study of sensitivity to incomplete data