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Efficient Simulation of Acoustic
Fluid-Structure Interaction
Models by Means of Model
Reduction
E. B. Rudnyi, M. Moosrainer, CADFEM GmbH
H. Landes, SIMetris GmbH
9th International Conference on Theoretical and Computational Acoustics, Dresden, 2009
Outline
Introduction to model reduction
Model reduction for acoustics
Case study: loudspeaker sound field
1
9th International Conference on Theoretical and Computational Acoustics, Dresden, 20092
Model Order Reduction
Relatively new technology
Solid mathematical background:
Approximation of large scale
dynamic systems
Dynamic simulation:
Harmonic or transient simulation
Industry application level:
Linear dynamic systems only
9th International Conference on Theoretical and Computational Acoustics, Dresden, 20093
From Finite Elements to System Simulation
Electrothermal Simulation with IGBTs.
Physics &
Geometry
System of
n ODEs
Reduced
System of
r << n ODEs
FEM MOR
OMEGA
M3 ~B
A
C
I1CI1BI1A N
H
EQU
RTH_ChipK := 1.5
CTH_JC_TH := 1m
H1
CTH_ChipC_TH := 10m
RTH_CaseK := 0.2
CTH_CaseC_TH := 0.1
RTH_Sink_Conv
K := 1.02
THM1 THM2 THM3
RTH_Sink_Rad
K := 4.2
Tambient
VALUE := 300
Celsius
PEL
9th International Conference on Theoretical and Computational Acoustics, Dresden, 20094
Model Reduction as Projection
Projection onto low-
dimensional subspace
How to find subspace?
Mode superposition is not the best way to do it.
zx V
x V
z
=
uxx BKE
uzz BVKVVEVV TTT
E
Er
9th International Conference on Theoretical and Computational Acoustics, Dresden, 20095
Implicit Moment Matching
Padé approximation
Matching first moments for the
transfer function
Implicit Moment Matching:
via Krylov Subspace
0
0 )( i
i ssmH
mi mi,red, i 0, ,r
BKsEsH1
)(
0
0, )( i
redired ssmH
s0 0
V span{ (K 1E,K 1b)}
uxx BKE
9th International Conference on Theoretical and Computational Acoustics, Dresden, 20096
MOR for ANSYS: http://ModelReduction.com
FULL files
Linear Dynamic
System, ODEsCxy
BuKxxExM MOR Algorithm
Small dimensional
matrices
Current version 2.5
ANSYS Model
Simulink,
Simplorer,
VHDL-AMS
9th International Conference on Theoretical and Computational Acoustics, Dresden, 20097
HDD actuator and suspension system
Prof J. S. Han.
Transactions of the
KSME, A, Vol. 31,
No. 5, pp. 541-549,
2007.
9th International Conference on Theoretical and Computational Acoustics, Dresden, 20098
Model Reduction as Fast Solver
Simulation of the reduced
model is a few seconds.
Arnoldi Process is fast:
Transient and harmonic
response analysis for the cost
comparable with that of a
static solution.
It is advantageous to use
MOR even the reduced model
is used only once:
Design,
Geometry optimization.
9th International Conference on Theoretical and Computational Acoustics, Dresden, 20099
Finite Element Discretization for Acoustic with FSI
FLUID29/FLUID30 in ANSYS
The element size should be smaller than wavelength
High dimensional models
Unsymmetric matrices
Not proportional damping:
Second Order Arnoldi
(SOAR)
a
s
a
fss
a
s
afs
s
F
F
p
u
K
KK
C
Cj
MM
M
00
002
9th International Conference on Theoretical and Computational Acoustics, Dresden, 200910
Thesis
9th International Conference on Theoretical and Computational Acoustics, Dresden, 200911
Adhesive Bonded Joint Benchmark
Mechanical Structure - SHELL181
Adhesive – SOLID45
Fluid – FLUID30
Single excitation point
Global and local damping
9th International Conference on Theoretical and Computational Acoustics, Dresden, 200912
Comparison
9th International Conference on Theoretical and Computational Acoustics, Dresden, 200913
Timing
Problem in ANSYS
37988 elements, 38712 nodes, 62581 free DoFs
Full solution in ANSYS for 200 frequencies
16695 s – 4.6 hours – 83 s per frequency
Proportional to the number of frequencies
MOR for ANSYS
Reading ANSYS files – 3 s
Model reduction – 170 s
Proportional to the number of vectors
Simulation of the reduced model
4 s
9th International Conference on Theoretical and Computational Acoustics, Dresden, 200914
Fluid Structure Interaction at Acoustic Level
By courtesy of Voith Siemens Hydro Power Generation
GmbH & Co. KG
9th International Conference on Theoretical and Computational Acoustics, Dresden, 2009
Loudspeaker – Calculation Scheme
9th International Conference on Theoretical and Computational Acoustics, Dresden, 2009
Tymphany Speaker - Modeling
Import of geometry data into ANSYS Workbench
Geometry repair and export to ANSYS classic for further
processing with NACS interface
Tymphany Speaker
Quartermodel
Typ.: nonlinear, < 200.000 el.
Cross-section model
Typ.: linear, > 1 Mio. el.
acoustics
mechanic
magmech
magnetic
ABCs
1 m dist.
Assumption: baffled setup
9th International Conference on Theoretical and Computational Acoustics, Dresden, 2009
Some pictures from ANSYS
18
9th International Conference on Theoretical and Computational Acoustics, Dresden, 2009
Procedure
Two cases:
Undamped: Damping only due to the adsorbing BC.
Damped: Materials damping in the loudspeaker.
ANSYS and MOR:
Linux, 4 processors, 16 Gb RAM
ANSYS: 60 frequencies in the range 0-12000 Hz
The mechanical force does not depend on frequency (only FSI)
Electrical properties of the loud speaker were neglected
Expansion point is 60000 rad (omega = 2 Pi f)
Dimension of the reduced model is 1000
Postprocessing in Python on Windows
600 frequencies in the range 0-12000 Hz
19
9th International Conference on Theoretical and Computational Acoustics, Dresden, 2009
SPL
20
Damped and
undamped
results are
shifted in
respect to
each other
9th International Conference on Theoretical and Computational Acoustics, Dresden, 2009
Phase Angle
21
9th International Conference on Theoretical and Computational Acoustics, Dresden, 2009
Undamped: Phase Angle
22
9th International Conference on Theoretical and Computational Acoustics, Dresden, 2009
Relative Difference for Pressure
23
9th International Conference on Theoretical and Computational Acoustics, Dresden, 2009
Undamped: Convergence (relative error for pressure)
24
9th International Conference on Theoretical and Computational Acoustics, Dresden, 2009
Damped: Convergence (relative error for pressure)
25
9th International Conference on Theoretical and Computational Acoustics, Dresden, 200926
Timing
Problem in ANSYS
1170389 nodes, 1176817 DoFs
Full solution in ANSYS for 60 frequencies
13498 s – 3.8 hours – 224 s per frequency
Proportional to the number of frequencies:
600 frequencies is about 38 hours
MOR for ANSYS
Reading ANSYS files – 10 s
Model reduction – 11927 s – 3.3 hours
Simulation of the reduced model (Python, SciPy, 1 processor)
300 s
9th International Conference on Theoretical and Computational Acoustics, Dresden, 200927
Conclusion
Model reduction is working for the case study, but the convergence is
rather slow.
It is still faster than the full solution in ANSYS though.
Further would-be research:
Multiple-expansion points?
Imaginary expansion point?