Quels défis pour la simulation des problèmes de vibrations dans les turbomachines ? | LIEGE CREATIVE, 30.11.2021

Mardi, 30 novembre 2021
Quels défis pour la simulation des problèmes de vibrations dans les
turbomachines ?
Elise Delhez (Département d'Aérospatiale et Mécanique, ULiège)
Caroline Raick (Siemens)

LIEGE CREATIVE, en partenariat avec :

Dr. Ir. Caroline Raick
Product Manager Simcenter 3D Rotor Dynamics
Siemens Digital Industries Software
Unrestricted | © Siemens 2021 | Siemens Digital Industries Software | Where today meets tomorrow.
Quels défis pour la simulation de
problèmes de vibrations dans les
turbomachines?

Rotor Dynamics
Industry applications
Page 2
Centrifugal compressor
Gas/steam turbines Centrifugal fans
Industrial fans
Centrifugal pumps Francis turbines
Turbo pumps
Turbo chargers Marine propulsion
ü Assemblies of rotating and non rotating parts and
connection devices (bearings)
ü Typical scenario of stability, critical speeds, unbalance, …
ü Survivability of the system under external excitations
(frequency, time) Thermal/pressure loads
Jet engines

Rotor Dynamics
Challenges in Industry applications
Page 3
Challenge #1
Large models
Realistic scenario
Challenge #2
Tools harmonization
Challenge #3
Digital Twin
Challenge #4
New designs & new applications
SIMULATION
ACQUISITION DATA

Rotor Dynamics
Challenge #1 – Large Models
• Axisymmetric models
• Assemblies of fixed and
rotating parts
• Dynamics analyses in various
conditions: rotation speed
range, pressure, temperature,
excitation frequencies, … to
compute the critical speeds
and stability, or dynamic
behavior
• Model reduction are welcome
(cyclic symmetry,
superelements)
Misalignment

Rotor Dynamics
Challenge #1 – Realistic scenario
Page 5
Rotor Dynamics Heat transfer
Blade loss Modal analysis
Unbalance and
Misalignment
Turbine blade
disk
Damping
Critical speeds
Axisymmetry
Nonlinear
Bearings
Multi-stage
cyclic symmetry
Thin blades

Models DOF Time
(s)
First forward
critical speed (Hz)
525552 528 18,906
45756 20 19,006
199254 75 18,943
18 1 19,006
Rotor Dynamics
Challenge #1 – Large Models
Page 6
Save time and keep accuracy !
Model representations
3D
Solids
2D
Multi Harmonics
Bearing
Cyclic symmetry
1D
Beams
Mixed
Super Element Thermal effect
Cyclic symmetry
Speed up
compared to 3D!
3D
2D
Superelement

Rotating Machines
Steam Turbine with Elastic Rotor and Fully Coupled Bladed Disks
Campbell diagram with the
combined 2D models
2D axi symmetric model
2D equivalent bladed disk
Challenges
§ Methodology to investigate coupling
between rotating shaft and bladed disks
under anisotropic supporting structures.
NAFEMS World Congress 2015
Different models tested and compared
• 2D axi-symmetric model, disk modelled by a lumped inertia, bearing modeled with lumped inertia and
local stiffness and damping , 2D equivalent bladed disk
• 2D combined models of the shaft and bladed disk.
• 3D model with cyclic symmetry conditions.
Analyses
• Static non linear computation under centrifugal loading in rotating frame for different rotational speeds
• Modal analysis for different rotational speeds in the rotational speed range [600-3000 rpm]
Combination of 2D models shows additional critical zones which highlights coupling.
Campbell diagram
Energy exchanged between modes
Veering phenomena
2D combined model
Analysis of rotating systems based on equivalent axi-symmetric models
2D model
2D bladed disk
Page 8

Rotating Machines
Turbopump Thermo-Elastic and Rotor Dynamics Study
A 2D axi-symmetrical approach
Modes and Campbell diagram
Axi-symmetrical Fourier harmonic model
Challenges
• A complex Thermo-elastic and rotor
dynamics problem: thermal
analysis, static analysis and rotor
dynamics analysis
• Developed multi-approach model
thanks to powerful and effective
capabilities of Samcef Rotors
• Super element representations for the rotating part and for the casing
• Duplex ball bearings
• Non linear harmonic and transient response
• Calculation of the effect of dispersion of data
Campbell
diagram
Loads in
bearings
Nodal displacements
Page 9

Rotating Machines
Full Gas Turbine Thermo-Mechanical WEM
Full turbine analysis process
Rotor Dynamics analysis
Thermal analysis
Challenges
§ Deformation of rotor, stator,
flanges,…
§ Take into account the presence of
fluid without CFD
§ Identify clearances between rotor
and stator (thermal cycles of loads:
quasi-static and transient)
Different levels of fidelity models for phases of design:
• 2.5D multi-harmonics
• 3D Multi stage cyclic symmetry models
1. Thermal analysis
2. Static analysis
3. Rotor Dynamics analysis
Static analysis
Page 11

Rotating Machines
Multi-stages Bladed Drum Compressor
Multi-stage cyclic symmetry process of the bladed drum compressor
Challenges
• Predict the modal and dynamic
response analyses of a rotating
bladed drum compressor made of
several stages.
• Different meshes for the different
sub-sectors
• Solve the issue of missing
harmonics at interstage junctions
The multi-stage cyclic symmetry method
• relies on harmonic decomposition, with fundamentals added at interstage junctions.
The different cyclic fields are then coupled at the inter-stage junctions.
• Makes possible the study of multi-stages turbomachines dynamics behaviour,
achieving a reliable level of accuracy, taking benefit from the cyclic symmetry across
the different stages of the turbomachine
Harmonic computations and 3D
recombination
Rotating bladed drum
compressor
Decomposition in sector
accross different stages
Page 12
ICOGEN
project

Rotating Machines
Lateral rotor blade coupling in turbo-generator
Study vibrations at blade resonance – interactions does matter
Challenges
• Study the vibrations at blade
resonance and highlight the
interactions between the blades
and the shaft
• Large deformation in the bladed
disks, then use of tangent
superelement in the rotating frame
• New capability of parametric
superelement
• Combined model of 1D shaft and 3D bladed disk
• Blades are subjected to large deformation under centrifugal load, then a strong nonlinear
stiffening effect is taken into account. Bladed disks are represented by tangent
superelements in the rotating reference frame, at a given rotation speed.
• Parametric superelement is generated by interpolation.
• Combined calculation in the fixed and rotating frames to take nonsymmetry into account
• Study vibrations in the shaft and in the bladed disk, with observation of transfert of energy
between the shaft to the disk
Study vibrations in the shaft and in
the bladed disk, observation of
transfert of energy between the shaft
to the disk
Combined model of 1D
model (shaft) and 3D
bladed disks represented
by tangent superelements
Computations of the rotating
system under unbalance to
excite modes
Page 13

Rotor Dynamics
Page 14
SIMULATION
ACQUISITION DATA
Challenge #1
Large models
Realistic scenario
Challenge #2
Tools harmonization
Challenge #3
Digital Twin
Challenge #4

From Samcef Rotors to Simcenter 3D Rotor dynamics
Challenge #2 – Tools Harmonization
Page 15
1986
SAMCEF solvers
Developed, maintained, and commercialized
by SAMTECH since 1986
Technologies:
• Nonlinear statics and dynamics
• Rotor dynamics
• Laminates composites
• Heat transfer
1965
SAMCEF first
Development
SAMCEF
commercialized by
SAMTECH
SAMCEF Rotors evolution thanks to
industrial partners, and european
projects
2012
Now part of Siemens Digital
Industries Software
2019
Simcenter 3D Rotor Dynamics
New generation of rotor dynamics solutions
Based on SAMCEF Rotors technology, integrated
in the interdisciplinary CAE platform of Siemens :
Simcenter 3D.
Progressive integration of all SAMCEF Rotor
capabilities
Simcenter 3D
Rotor Dynamics
HOFIM
TURBOMACHINERY
MACFLY
VIVACE
ICOGEN

Page 16
Mechanical simulation
Simcenter 3D
Structural Dynamics
Rotor Dynamics

Page 17
Easily analyse dynamics
of rotating systems in a
fully integrated
environment
Ø Save time when the
model changes
Ø Ensure data consistency
Ø Fasten learning time
Ø Improve the collaboration
between teams
Benefits
Simcenter 3D, a fully integrated CAE environment
Geometry
Meshing
Optimization
Data Management

Rotor Dynamics
Page 18
ü Dedicated solutions to rotor dynamics calculations
in a CAE integrated environment, for
• Critical rotation speeds, Campbell, damping diagrams
• Forced response (harmonic and transient)
• Unbalance, misalignment and blade-out event prediction
• Maneuvers
• Static / thermal preload
ü Pre-Post and Rotor modeling capabilities
• Assemblies of rotating and nonrotating parts, superelements
• Preparation of rotor models and simulation data
• Model reduction to account for rotor models specificities
• Bearings connections
• Results post-processing in Simcenter 3D
ü Tokenable solution

Simcenter Rotor Dynamics
Global Process
Page 19
CAD Mesh Rotating Parts Solution setup Post-processing
• Identify rotating part(s)
• Define global rotor speed or
individual speeds
• Post-process results
• Plot XY graphs
• Review energy distribution per
elements group
• Plot deformed shape on 2D
geometry
• Plot deformed shape with
recombined 3D results.
• Prepare geometry
• Create FEM (1D/2D/3D)
• Create rotor assembly
• Define connections (bearings,
bushings), concentrated masses
Choose a SOL 414 solution
• Complex modal analysis
• Frequency / Transient response
• Maneuvers
• Superelement reduction
Select dedicated data (e.g. modes,
Fourier harmonics, time steps,
damping)
Define Loads and boundary
conditions
Dual rotors and Casing
Recombined results on
the dual rotors

Pre / Post in an CAE integrated environment: Preparation of rotor models and assemblies, linked with CAD geometry.
Results postprocessing: Campbell diagrams, plots vs time or frequency, modes animation, energy distribution, displacements, 2D results
recombined for 3D post-processing, …
Highlights
Page 20
Efficient model reduction for large models
• Super element reduction technique
• 2D Fourier multi-harmonics
• Cyclic symmetry in case of periodic sectors
• Possibility to build the machine as an assembly of sub-models, using mixed representations
• Multiple rotors, with different rotational speeds and a free orientation in space.
Library of bearing and linking devices
Solvers
• Advanced technology applied to industrial cases
• Local non linearities taken into account
• Critical speed, modal, transient, harmonic analyses …
• Unbalance, misalignment, blade off event prediction
• Static or thermal preload
3D results
2D Multi-harmonics
Cyclic symmetry
MODELLING
SOLVER
SC3D

More information …
Page 21
Webinar
https://www.plm.automation.siemens.com/glob
al/en/webinar/rotor-dynamics/91115
Blog Post 1 : General
https://blogs.sw.siemens.com/simcenter/rotor-
dynamics-when-accuracy-is-a-matter-of-life-and-
death/
Webinar
Blog Posts
Blog Post 2 : Modeling
https://blogs.sw.siemens.com/simcenter/com
bine-solution-speed-and-accuracy-for-
axisymmetric-rotor-dynamics/
Presentation at the Turbo Expo 2021
Siemens Energy & Siemens DI.
R. Grein, U. Ehehalt, C. Siewert, N. Kill (2021).
Rotor-Blade Interaction During Blade Resonance
Drive-Through.
Turbo Expo ASME 2021.
Blog Post 3 : Bearings
https://blogs.sw.siemens.com/simcenter/bearing-
modeling-makes-or-breaks-rotor-dynamics-
simulations/

Rotor Dynamics
Page 22
SIMULATION
ACQUISITION DATA
Challenge #1
Large models
Realistic scenario
Challenge #2
Tools harmonization
Challenge #3
Digital Twin
Challenge #4

Unrestricted | © Siemens 2021 | 2021-01-20 | Rotor dynamics analysis | Siemens Digital Industries Software | Where today meets tomorrow.
Simcenter overview
Engineer innovation
CAE Simulation
Simcenter 3D, Simcenter STAR-CCM+, Simcenter Nastran,
Simcenter Femap, Simcenter FLOEFD, Simcenter Flotherm,
Simcenter MAGNET, Simcenter Madymo, Simcenter Tire,
Simcenter Motorsolve, Simcenter Multimech, ...
Physical Testing
Simcenter Testlab, Simcenter SCADAS,
Simcenter Testxpress, Simcenter Anovis,
Simcenter Soundbrush, Simcenter T3STER,
Simcenter POWERTESTER, ...
System Simulation
Simcenter Amesim, Simcenter Flomaster
Simcenter System Architect, Simcenter System Analyst
Simcenter Webapp Server, Simcenter Prescan, ...
Exploration
&
Analytics
-
HEEDS
Data
&
Process
Management
-
Teamcenter

Rotor Dynamics with Simcenter Testlab
Measurement and analysis of shaft motion in bearings
Unrestricted | © Siemens 2021| Siemens Digital Industries Software | Where today meets tomorrow.
Page 24
10
-10 -8 -6 -4 -2 0 2 4 6 8
Hz
578
120
175
225
275
325
375
425
475
525
rpm
0.50 (X)
-0.50 (X)
2.5
-2.5 µm
2.5
-2.5
µm
2.5
-2.5
µm
X
Y
1:1
Measure dynamic motion of shafts
in hydro bearing using key-phasor
and proximity probe
Dedicated tool for In depth
analysis combining orbit,
centerline, polar, full spectrum plot
and operational deflection shape
SIMULATION
ACQUISITION DATA
Webinar
https://www.plm.automation.siemens.com/glo
bal/en/webinar/rotor-dynamics/88950

Rotor Dynamics
Page 25
SIMULATION
ACQUISITION DATA
Challenge #1
Large models
Realistic scenario
Challenge #2
Tools harmonization
Challenge #3
Digital Twin
Challenge #4

Rotor Dynamics
Challenges #4 – New challenges!
Page 26
Challenge #4
New challenges driven by new designs and new applications
Ø Electric motors
Rotating system in an electromagnetic field …
Ø Bladed rotors
Propellers, helicopter blades, drones, air taxis, …
Ø Bearings models with increasing accuracy
Ø Nonlinearities
Thin flexible blades, contact rotor-casing …

Rotor Dynamics
Conclusion
Page 27
SIMULATION
ACQUISITION DATA
Challenge #1
Large models
Realistic scenario
Challenge #2
Tools harmonization
Challenge #3
Digital Twin
Challenge #4
Challenge #1
Large models &
Realistic scenario
Efficient model reduction
Dedicated rotor analyses
and scenarios
Challenge #2
Tools harmonization
Capitalization of
all simulation tools
in a unique CAE environment
Challenge #3
Digital Twin
Simulations studying a large variety of situations
avoiding large costs of real prototypes,
&
Tests acquisition of rotor dynamics data
monitoring and postprocessing
Challenge #4
Towards new challenges in studying
the vibrations in rotating systems

Thank you !
Contact
Caroline Raick
Simcenter 3D Rotor Dynamics Product Manager
Simulation and Test Solutions
Siemens Digital Industries Software
caroline.raick@siemens.com

Rotor/stator interactions in turbomachines
Towards new modeling tools
Élise Delhez
Liège Créative
November 2021

2
▶ Context
▶ Numerical simulations
▶ Going forward
Content

3
▶ Context
▶ Going forward
Content

4
Contact in turbomachines
shaft/bearing
blade/blade
blade/casing
blade/disk

5
▶ High relative speeds
▶ Strong influence of operating
clearance
▶ Contact stiffening
Contact in turbomachines
blade/casing

6
Multifaceted challenges
Power generation
Aerospace industry
Automotive industry
Naval industry
▶ Safety
▶ Weight
▶ Cost
▶ Maintenance
▶ Performance

7
Contact, but not only!
Fan stage
▶ Large slender blades
▶ Geometric
nonlinearities
Compressor stages
▶ Reduced operating
clearance
▶ Abradable coating
Turbine stages
▶ Extreme temperatures
▶ Use of new materials

8
▶ Multiphysics
Aerodynamic loading, blade vibration, abradable wear, thermomechanics, …
▶ Nonlinear
Contact, large displacement, materials
Complex dynamics

9
▶ Context
▶ Going forward
Content

10
▶ Cost and complexity of
experimental tests
▶ No existing facility for multi-stage
full-scale experimental setups
Numerical simulations: why?

11
Numerical simulations: how?
Time integration & frequency methods
Ω

12
Time integration
Ω

13
Time integration
Ω↗
Ω

14
Time integration
Ω↘
Ω

15
Time integration
Frequency
method
Ω

16
Time integration & frequency methods
Time integration Frequency methods
Wide compatibility with contact algorithm 
Easy extension to multiphysics 
Transient & chaotic response 
Qualitative understanding 
Assessment of stability 
Both strategies are required

17
Model order reduction
ROM with contact interface
3D FE model
+ inertial effects
+ geometric nonlinearities
1 blade
#
DOFs

18
Model order reduction
ROM with contact interface
3D FE model
+ inertial effects
+ geometric nonlinearities
1 blade bladed disk
#
DOFs

19
My work: geometric & contact nonlinearities
Development of a methodology to study in a numerically efficient way
the contact interactions of bladed disks
while accounting for their geometrically nonlinear behavior
Reduced order modeling
(ROM) techniques

20
Reduced order model
෩
𝐌 ሷ
𝐪 + ෨
𝐂 Ω ሶ
𝐪 + ෩
𝐊 Ω 𝐪 + ෤
𝐠𝑛𝑙 𝐪 = ሚ
𝐟𝒆 + ሚ
𝐟𝑐 𝐪, ሶ
𝐪
Projection-based reduction
Full order model
𝐌 ሷ
𝐮 + 𝐂 Ω ሶ
𝐮 + 𝐊 Ω 𝐮 + 𝐠𝑛𝑙 𝐮 = 𝐟𝑒 + 𝐟𝑐 𝐮, ሶ
𝐮
𝐮 = 𝚽𝐪
Projection basis? – Projection of the nonlinear terms?

21
Craig-Bampton basis augmented with modal derivatives[★]
𝚽 = [𝚿 𝚯 Ξ]
Reduction basis 𝚽
[★] L. WU et al., A modal derivatives enhanced Craig-Bampton method for geometrically nonlinear
structural dynamics, in Proceedings of the ISMA Conference 2016.

22
Craig-Bampton basis augmented with modal derivatives
𝚽 = [𝚿 𝚯 Ξ]
▶ 𝚿 = 𝑟𝑏 constraint modes
▶ 𝚯 = 𝑟𝑐 fixed interface modes
▶ Ξ = 𝑟MD modal derivatives
1

23
𝚽 = [𝚿 𝚯 Ξ]

24
𝚽 = [𝚿 𝚯 Ξ]

25
▶ STiffness Evaluation Procedure (STEP)[★]
- ෤
𝐠𝑛𝑙 𝐪 = ෩
𝐀𝐪⊗𝟐 + ෩
𝐁𝐪⊗𝟑
- ෩
𝐀 and ෩
𝐁 from nonlinear static analyses with imposed displacement
Reduced nonlinear forces ෤
𝐠𝑛𝑙 𝐪
[★] A. MURAVYOV et al., Determination of nonlinear stiffness with application to random
vibration of geometrically nonlinear structures, Computers and Structures, 2003.
Nonlinear
static analyses
𝐠𝑛𝑙 𝐮
Projection
Identification
of ෩
𝐀 and ෩
𝐁
෤
𝐠𝑛𝑙 𝐪
𝚽

26
Projection-based reduction
conserves the general form
of the equation of motion
Reduced contact forces ሚ
𝐟𝑐 𝐪, ሶ
𝐪
Craig-Bampton reduction
allows to retain the physical
contact interface
Usual contact algorithms can be used in the reduced space
▶ Lagrange multipliers

27
Contact scenario
▶ Blade rotating at a constant speed Ω about 𝐞𝐳
▶ Contact initiated by ovalization of the casing
Ω

28
Interaction maps
Contact + geometric nonlinearities
Contact nonlinearities
0 mm·s 0.09 mm·s
1B
1T
2B
𝑬𝑶 = 𝟒
1B
1T
2B
𝑬𝑶 = 𝟔
𝑬𝑶 = 𝟖
𝑬𝑶 = 𝟒
𝑬𝑶 = 𝟔
𝑬𝑶 = 𝟖

29
Contact stiffening
Contact + geometric nonlinearities
Contact nonlinearities
0 mm·s 0.09 mm·s
1B
1T
2B
𝑬𝑶 = 𝟒
1B
1T
2B
𝑬𝑶 = 𝟔
𝑬𝑶 = 𝟖
𝑬𝑶 = 𝟒
𝑬𝑶 = 𝟔
𝑬𝑶 = 𝟖
𝚫𝟏𝐁/𝑬𝑶𝟔
𝚫𝟏𝐁/𝑬𝑶𝟒
𝚫𝟏𝐁/𝑬𝑶𝟔
𝚫𝟏𝐁/𝑬𝑶𝟒

30
▶ Context
▶ Going forward
Content

31
▶ Better understand the physics of the phenomena
▶ Development of more efficient numerical strategies
Challenges
Guidelines for aircraft
engine design
Accounting for contact
in blade design

Quels défis pour la simulation des problèmes de vibrations dans les turbomachines ? | LIEGE CREATIVE, 30.11.2021

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Quels défis pour la simulation des problèmes de vibrations dans les turbomachines ? | LIEGE CREATIVE, 30.11.2021