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Modelling and Analysisof MultiphysicalInteractions inHydropower RotorSystems
Martin Karlssonkarmar@ltu.se
Polhem LaboratoryDivision of Computer Aided DesignLulea University of Technology971 87 LuleaSweden
OutlineBackground and Introduction
Electromechanical Models
Fluid-Rotor Interactions
Identification of Excitations and Eigenfrequencies
Conclusions
Outlook
The Research ProblemHow should multiphysical interactions in a hydropower
rotor system be modelled, simulated and evaluated, in
order to predict the dynamical behaviour?
M−→x + (C + ΩG)−→x + K−→x =−→
F (1)
Appended Papers
Paper A
Paper B
Paper C
Paper E
Paper D
Paper F
Identification
Fluid-rotor
Electromechanical
Whirling Dependent Forces
−0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3−0.25
−0.2
−0.15
−0.1
−0.05
0
0.05
0.1
0.15
0.2
Relative eccenticity in x−direction [−]
Rel
ativ
e ec
cent
icity
in y
−di
rect
ion
[−]
20% 1*Ω and 10% 3*Ω
Fr = kM,re + cM,re, Ft = kM,te + cM,te (6)
M−→x + (ΩG + C − CM,r − CM,t)−→x + (K − KM,r − KM,t)
−→x =−→
F , (7)
Results
−2 −1 0 1 2 3−100
−50
0
50
100
150
200
250
Relative Whirling [−]
Fo
rce
[kN
]Electromagnetic Forces
Results
−2 −1 0 1 2
3.7
3.75
3.8
3.85
3.9
3.95
4
4.05
4.1
4.15
Relative Whirling [−]
Re
lativve
Eig
en
Fre
qu
en
cy [−
]
First Forward Mode
−2 −1 0 1 2 3−0.01
0
0.01
0.02
0.03
0.04
0.05
Relative Whirling [−]
Da
mp
ing
Ra
tio
[−
]
First Forward Mode
Results
−2 −1 0 1 2
−3.75
−3.7
−3.65
−3.6
−3.55
−3.5
−3.45
−3.4
Relative Whirling [−]
Re
lativve
Eig
en
Fre
qu
en
cy [−
]
First Backward Mode
−2 −1 0 1 2 3−0.01
−0.005
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
Relative Whirling [−]
Da
mp
ing
Ra
tio
[−
]
First Backward Mode
Effect of Boundary Conditions
YX,Z
Section Ia
Section Ib
θ [rad]
y’ [m
]
0 1 2 3 4 5 60.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
0.26
−2.2
−2
−1.8
−1.6
−1.4
−1.2
−1
−0.8
−0.6
−0.4
−0.2
θ [rad]
y’ [m
]
0 1 2 3 4 5 60.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
0.26
−2.2
−2
−1.8
−1.6
−1.4
−1.2
−1
−0.8
−0.6
−0.4
−0.2
θ [rad]
y’ [m
]
0 1 2 3 4 5 60.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
0.26
−2.2
−2
−1.8
−1.6
−1.4
−1.2
−1
−0.8
−0.6
−0.4
−0.2
Results
−0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2−0.5
−0.4
−0.3
−0.2
−0.1
0
0.1
0.2
Relative Force in x−direction [−]
Rela
tive F
orc
e i
n z
−dir
ecti
on
[−
]
Axi-symmetric inlet
Wicket gate inlet
Spiral casing inlet
Added Coefficients
K
θ(t)
Jp
YX,Z
Section Ia
Section Ib
Jpθ + Cθ + Kθ = M(t), (8)
(JP + JP,F luid)θ + (C + CFluid)θ + (K + KFluid)θ = M(t), (9)
Identification
500 1000 1500 2000 25000
0.05
0.1
0.15
0.2
Perturbation Frequency [rad/s]
Pol
ar In
ertia
[Nm
s2 ]
52 rad/s62 rad/s72 rad/s
500 1000 1500 2000 25000
50
100
150
200
250
300
350
400
450
Perturbation Frequency [rad/s]
Dam
ping
[Nm
s]
52 rad/s62 rad/s72 rad/s
Results
500 1000 1500 2000 2500
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
Perturbation Frequency [rad/s]
Red
uctio
n of
Eig
enfr
eque
ncy
[−]
52 rad/s (undamped)62 rad/s (undamped)72 rad/s (undamped)52 rad/s62 rad/s72 rad/s
500 1000 1500 2000 25000.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Perturbation Frequency [rad/s]
Dam
ping
Rat
io [−
]
52 rad/s62 rad/s72 rad/s
Results
5 10 15 20 25 300
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Relative Frequency [−]
Re
lative
Fo
rce
[−
]
Hydraulic Forces at 30% Load
ConclusionsThe electrical and hydraulic system shows large influence on systemcharacteristics and excitations
Damper windings seems to damp the excitation of an unstable mode
Electric forces has the same characteristics as earlier presented forasynchronous machines
Boundary conditions for a CFD-model has a large influence oncorresponding forces and moments
Operational analysis of a hydropower rotor system requires goodunderstanding of the physics in the different components
Outlook
Paper A
Paper B
Paper C
Paper E
Paper D
Paper F
Shape deviations
and pole configurations
Characteristics due to
different inlet and operating
conditions
Parallel stator windings
Transient operations of components and whole system
Modelling and simulationExperimental characterisation Optimization
AcknowledgementElektra (Elforsk AB and Swedish Energy Agency)
Kempe Foundations, Knut and Alice Wallenberg Foundation,Swedish Hydropower Center
The Swedish Research Council (SNIC)
Urban Lundin, Håkan Nilsson, Richard Perers
Rolf Gustavsson and Mattias Nässelqvist
Jan-Olov Aidanpää and Thommy Karlsson
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