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MOR for ANSYS in turbine dynamics
Felix Lippold / Dr. Björn Hübner
Voith Hydro Holding
MOR for ANSYS in turbine dynamics | CADFEM2009 | Felix Lippold | 2009-11-19 | 2
Outline
1. Introduction and motivation
2. Modelling acoustic-structure coupling
3. Model order reduction
4. Applications
5. Summary
MOR for ANSYS in turbine dynamics | CADFEM2009 | Felix Lippold | 2009-11-19 | 3
IntroductionRotor-Stator Interaction (RSI)
RSI generation in vaneless space
Pressure pulsation Vibration unsteady forces fatigue
MOR for ANSYS in turbine dynamics | CADFEM2009 | Felix Lippold | 2009-11-19 | 4
Pressure distribution (unsteady CFD)
Rotating blades pass wake
of steady parts
Interacting pressure fields
Pressure pulsations
Harmonic analysis
MotivationRSI background
MOR for ANSYS in turbine dynamics | CADFEM2009 | Felix Lippold | 2009-11-19 | 5
MotivationSimulation methods
Surrounding water influences structural dynamics (added-mass)
Acoustic-Structure coupling required
Harmonic response analysis with turbine in water
Highly resolved ( f = 1.0 Hz) frequency response analysis
High computational effort for large systems
Not applicable for product development or parameter studies
Reduce number of unknowns
MOR for ANSYS in turbine dynamics | CADFEM2009 | Felix Lippold | 2009-11-19 | 6
Finite-Element model used in harmonic analysis
Linear-elastic SOLID elements for runner structure.
Acoustic FLUID elements for surrounding water.
Complex load vectors for rotating pressure fields.
ModellingAcoustic-structure coupling
MOR for ANSYS in turbine dynamics | CADFEM2009 | Felix Lippold | 2009-11-19 | 7
runner structure water as acoustic fluid
RSI pressure mode
shapes imposed at
vaneless space
impedance boundary at the outled
to eliminate outgoing waves
fixed support at the
shaft connection
modeling of
gaps and seals
Harmonic response analysis of turbine runner in water
MOR for ANSYS in turbine dynamics | CADFEM2009 | Felix Lippold | 2009-11-19 | 8
ModellingCoupled acoustic-structure equations
Equations of motion
)(A
S
A
SAS
A
S
ASA
Stq
b
b
p
u
K
KK
p
u
E
E
p
u
MM
M
Formally equivalent to
)(tqbxKxExM
But:
non-symmetric matrices
non-proportional damping matrix
fluid damping EA only for impedance boundaries
MOR for ANSYS in turbine dynamics | CADFEM2009 | Felix Lippold | 2009-11-19 | 9
MOR TheoryStructural dynamics without damping
0)(δ T tqbxKxMx
εzVx
)(tqbxM xK
z
Vx
)(tqrbzrM z
rK
TTTVzx
0)(δ TTTT tqbVzKVVzMVVz
Original system
Approximated DOF vector
Reduced system
MOR for ANSYS in turbine dynamics | CADFEM2009 | Felix Lippold | 2009-11-19 | 10
MOR TheoryFind subspace V
Natural mode shapes: Possible but computational costly and
often not the best choice for unsymmetric matrices or arbitrary load
shapes.
Krylov subspace via Arnoldi process: Easier to compute
(especially for unsymmetric matrices) and good approximation for
arbitrary load shapes.
Arnoldi process for calculating reduction vectors vi:
bKv1
1 i1
1i MvKv i1i yKv LUK
,...,,, 13
12
11 vAvAAvvspanV MKA1
MOR for ANSYS in turbine dynamics | CADFEM2009 | Felix Lippold | 2009-11-19 | 11
MOR theory
Harmonic response analysis of the reduced system (with damping)
Solution in frequency domain:
Proportional damping definition at the reduced system level
Rayleigh damping:
Constant global damping ratio :
titi eei rrrr2 )(ˆ bzKEM
tiet )(ˆ)( zz
rrr KME
rr
2KE
tiettt ω)()()( rrrr bzKzEzM
Proportional damping
may be defined and varied
at the reduced system level
without loss of accuracy
since it does not influence
reduction vectors!
MOR for ANSYS in turbine dynamics | CADFEM2009 | Felix Lippold | 2009-11-19 | 12
MOR for ANSYS(1)
Application and methodology
Linear PDEs,1st or 2nd order in time, discretized with ANSYS.
Linear structural dynamics, structure-acoustic coupling, heat
conduction, ...
Not applicable for non-linear systems (e.g. turbulent flow)
MORforANSYS reads ANSYS full-files and reduces large
scale systems (106 DOFs) to low order systems (100 DOFs).
Harmonic (or transient) analyses of the reduced order system
performed by functions written in Python.
DOF results back transferred to ANSYS for stress calculation
and post-processing (graphics, animations).
Limitations: changing load shapes, non-proportional damping.
(1) E.B. Rudnyi, J.G. Korvink: Model order reduction for large scale engineering
models developed in ANSYS, PARA 2004, LNCS 3732, pp. 349-356, 2006.
MOR for ANSYS in turbine dynamics | CADFEM2009 | Felix Lippold | 2009-11-19 | 13
ApplicationFrancis turbine runner in water
Structure of the Francis turbine runner and monitoring points on trailing edge
MOR for ANSYS in turbine dynamics | CADFEM2009 | Felix Lippold | 2009-11-19 | 14
Axial displacement@centre trailing edge – no damping
Amplitude spectrum (Dim=100) Deviation related to ANSYS results
ResultsNo damping
MOR for ANSYS in turbine dynamics | CADFEM2009 | Felix Lippold | 2009-11-19 | 15
Pressure distribution on runner for f = 40 Hz
Ansys (90 000 DOFs) Reduced (Dim=100)
REAL part of pressure
solution
Deviation < 0.2%
IMAG part of pressure
solution
Deviation < 0.2%
ResultsVerification of reduced order method
MOR for ANSYS in turbine dynamics | CADFEM2009 | Felix Lippold | 2009-11-19 | 16
Axial displacement for f = 40 Hz
Ansys (90 000 DOFs) Reduced (Dim=100)
REAL part of pressure
solution
Deviation < 0.2%
IMAG part of pressure
solution
Deviation < 0.2%
ResultsVerification of reduced order method
MOR for ANSYS in turbine dynamics | CADFEM2009 | Felix Lippold | 2009-11-19 | 17
Parameter studyDamping variation
Global damping in
reduced model:
no damping, 1%, 2%
MOR for ANSYS in turbine dynamics | CADFEM2009 | Felix Lippold | 2009-11-19 | 18
Summary
Introduction to RSI in hydraulic machinery
Excitation of turbine structure
Modelling acoustic-structure coupling for
water-filled turbine runner
Model order reduction to reduce
computational effort
Successful application and verification
with Francis turbine runner
)(tqbxM xK
MOR for ANSYS in turbine dynamics | CADFEM2009 | Felix Lippold | 2009-11-19 | 19
MOR for ANSYS in turbine dynamics | CADFEM2009 | Felix Lippold | 2009-11-19 | 20
Non-Proportional Damping (local variation including acoustic FSI) with MORforANSYS
Local damping multiplier j or FSI with structural Rayleigh
damping and/or impedance boundary conditions
Non-proportional but constant damping matrix.
Reduction vectors depend on the damping properties.
Possible solution procedures on the next slide.
Local damping ratios j or FSI with structural DMPRAT
Non-proportional and frequency dependent damping matrix or
complex stiffness matrix.
Both not supported by MORforANSYS
Approximately use global damping ratio for reduced system.
MOR for ANSYS in turbine dynamics | CADFEM2009 | Felix Lippold | 2009-11-19 | 21
Non-Proportional but Constant Damping Matrix E
Reduction vectors are
calculated without damping,
but original damping matrix
will be reduced, too.
Bad approximation!
Always working, but add.
damping of reduced syst.
and back transformation
to ANSYS not possible.
Not appropriate!
Works well for impedance
boundary conditions. At
the reduced system level,
a global damping ratio
may be defined in addition.
qbKxxExM
MOR for ANSYS in turbine dynamics | CADFEM2009 | Felix Lippold | 2009-11-19 | 22
ResultsIncluding damping effects
2% global damping for reduced model
2% structural damping in ANSYS w/ and w/o Impedance bc
Amplitude spectrum (Dim=100) Deviation related to ANSYS results
MOR for ANSYS in turbine dynamics | CADFEM2009 | Felix Lippold | 2009-11-19 | 23
Pressure distribution on runner for f = 40 Hz
Ansys (DMPR=1.0%) Reduced (Damping 1%)
REAL part of pressure
solution
Deviation < 2.0%
IMAG part of pressure
solution
Deviation < 2.0%
ResultsIncluding damping effects
MOR for ANSYS in turbine dynamics | CADFEM2009 | Felix Lippold | 2009-11-19 | 24
Axial displacement for f = 40 Hz
Ansys (DMPR=1.0%) Reduced (Damping 1%)
REAL part of pressure
solution
Deviation < 2.2%
IMAG part of pressure
solution
Deviation < 2.2%
ResultsVerification of reduced order method