Draft tube modelling for prediction of pressure

fluctuations on prototype

S. Alligné, C. Landry, C. Nicolet, F. Avellan

SHF – Machines hydrauliques et cavitation

Cetim Nantes

74 route de la Jonelière

France

3-4 juin 2015

Contents

• Problematic

• Methodology

• 1D modelling�System

�Cavitation flow in draft tube

• Experimental investigations at reduced scale model� Identification of DT parameters

�Dimensionless numbers

• Prediction on prototype�Eigenmodes

�Forced response2

Problematic

3

Reduced scale model Prototype

Direct transposition of

pressure fluctuations

1D simulation model

Methodology

4

Methodology

5

6

SIMSEN� SIMSEN software:

�Hydraulic circuit

� Electrica installations

�Rotating inertias

�Control system

� SIMSEN software:

�Hydraulic circuit

� Electrica installations

�Rotating inertias

�Control system

Modeling

from

water

to wire

1D Modelling• Piping system modelling:

�Mass and momentum equation:

�Electrical analogy:• (Bergeron, 1950; Paynter, 1953 )

7

R/2Lh/2 Lh/2

C

Rh

R/2

Hi

HciQi Qi

Hi+1

2

0H a Q

t gA x

∂ ∂+ =∂ ∂

02

12

=+∂∂+

∂∂

QgDA

Q

t

Q

gAx

H λ

0

01

=+∂∂+

∂∂

=∂∂+

∂∂

IRt

IL

x

U

x

I

Ct

U

ee

e

Storage

Losses

Inertia

Datum.

Q1 Q2

D, a, λdx

H1 H2

1D Modelling

• Turbine characteristic:

8

Dimensionless factors:

Unit speed factor:

Unit discharge factor:

Unit torque factor:

1D Modelling• Cavitation draft tube flow

9

Divergent geometry(Tsujimoto et al.)

2 20

2 3 2

1 ''0x h

DQ Q Q Q h QK S

gA t gA x gA x gA gA x

τ π µρ ρ

∂ ∂ ∂ ∂+ − + + − + =∂ ∂ ∂ ∂

x

AK

x

∂=∂

Convective terms(New)

Dilatation viscosity(Pezzinga et al.)

11 2 1 c

dQ dhQ Q C

dt dtχ− = +

11

cV

Qχ ∂= −

∂

2c

c

V gAdxC

h a

∂= − =∂( )1 2, ,cV f Q h Q=

S.Alligné, C. Nicolet, Y. Tsujimoto, F. Avellan, Cavitation SurgeModelling in Francis Turbine Draft Tube, In Publication

process for Journal of Hydraulic Research, 2014

1D Modelling

• Cavitation draft tube flow:

�Lumped model

�Distributed model

10

Nb=1

Nb=32

1D Modelling

• Draft tube model parameters:

�Wave speed

�Second viscosity : dissipation induced by the phase change during cavitation volume fluctuations

�Excitation source : induced by the vortex rope

�Mass flow gain factor : not considered

• Effect of parameters:

� and influence damping and frequency of eigenmodes

� The excitation source is external to the system

11

a

''µ

hS

( ), ''aα µ

1χ

a ''µ( ), ''f a µ

hS

Methodology

12

Identification of &

13

inQɶ

physicalΣ( ),s sA fpf sf

Resonance identificationEigenfrequency & amplitude response

SimsenΣ( ),s s pA f f=

( )ph fɶ

SimsenΣ pf

( ), ''a µ

( )p

p

h f

f

ɶ

Forced Response

Eigenmodes

Comparison

New

set

of p

aram

eter

s

( ), ''a µ( ), ''pf a µ

hɶ

inQɶ

a ''µC.Landry, A. Favrel, A. Müller, C. Nicolet, F. Avellan, Experimental identification of the local wave speed and the second viscosity in cavitatingdraft tube flow, In Publication process for Journal of Hydraulic Research, 2015

Identification of

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physicalΣ ( )ropeh fɶ

ropef

hS

e

sx

( ), ,h sS e x

hS

SimsenΣForced Response

Comparison

ropef( )ropeh fɶ

( ), ,h sS e x

New

set

of p

aram

eter

s

C.Landry, EPFL Thesis N°6547, 2015

Methodology

15

Dimensionless Numbers

• Wave speed and second viscosity

16

( )2

w

out v

ag

p p

ρ βΠ = =−

a ''µ

C.Landry, A. Favrel, A. Müller, C. Nicolet, F. Avellan, Experimental identification of the local

wave speed and the second viscosity in cavitatingdraft tube flow, In Publication process for Journal

of Hydraulic Research, 2015

( )'' 2 2''1natural c

out v w

fM

p p

µ ρβρ

= = Π −−

Cavitation Mapping

17

( ) , ,ED EDn Q Frβ σ

P Mβ β=Transposition Law

Froude similitude

respected !

C. Landry, EPFL Doctoral Thesis N°6547, 2015

Excitation Source Mapping

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( ) , ,ED EDh n Q Fr

S σ

PrefP M

h h Mref

HS S

H

=

PrefP MMref

De e

D

=

PrefP M

h h Mref

Dx x

D

=

Transposition Laws

Froude similitude

fulfilled!

C.Landry, EPFL Thesis N°6547, 2015

Methodology

19

Prototype - 1D Modelling

• SIMSEN System model

20

( )2

w

out v

ag

p p

ρ βΠ = =−

( )'' 2 2''1natural c

out v w

fM

p p

µ ρβρ

= = Π −−

β

,ED EDn Q

Fr

σ

( )a t

( )'' tµ

Prediction of eigenmodes

• DT parameters and predicted eigenmodes

�Unstable eigenmodes with lumped model

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Prediction of eigenmodes

• Shape of pressure and discharge 1st eigenmode

�Small changes on eigenmodes shapes

22

Distributed

Constant Parameters

Distributed

Variable Parameters

Prediction of pressure fluctuations

• 2 investigated OP

�Eigenmodes

�Excitation source

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Prediction of pressure fluctuations

• System response

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8.2% Hturb

1.2% Hturb

Conclusions

• Methodology applied for transposition of pressure

fluctuations on reduced scale model to prototype:

�Prediction of different amplitudes as function of the OP

�Froude similitude should be respected

�Mass flow gain factor neglected

• Second campaign planned

• Could change predicted amplitudes

• Measurements on prototype scheduled for

validation

25

P Mβ β=

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HYPERBOLEHYdropower plants PERformance and flexiBle Operation towards Lean integration of

new renewable Energies

LMH Laboratory for Hydraulic Machines

Merci pour votre attention!

Power Vision Engineering Sàrl1, ch. Des Champs-CourbesCH-1024 EcublensSwitzerlandwww.powervision-eng.chinfo@powervision-eng.ch

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