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
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
• 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
Identification of &
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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
14
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
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
18
( ) , ,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
Prototype - 1D Modelling
• SIMSEN System model
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( )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
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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