ISROMAC 2012 HawaiiISROMAC 2012, Hawaii
Turbomachinery Blade Vibrations Meeting the ChallengeMeeting the Challenge
Damian Vogt, KTH
2012 02 27
1
2012-02-27
2
12 B litres
3
1 M cycles
A Steam TurbineA Steam Turbine
The workhorse of power generation
Designed to operate for years
Part-load operation lead to failure of blades due to torsional vibrations in
7 seconds(Mazur et al., 2004)
4
An Aircraft EngineAn Aircraft Engine
The workhorse of air travel
Powerful, light, reliable
“… failure 3rd stage LP blade due t ib ti “to vibration “(Warwick, 2008)
5
Lessons LearntLessons Learnt
Turbomachinery blade vibrations can be
harmful
Failure is usually occurring within
short time
6
Let us define a ”turbomachinery ideal”?turbomachinery ideal ?
7
A Turbomachinery IdealA Turbomachinery Ideal
D bl
ReliableAvailable
Durable
Reliable
Fuel-flexibleLightweight
Silent
Eco-friendly Low-maintenance
Efficient Powerful
8
Affordable
Is there anything that Is there anything that prevents us from reaching
thi id l?this ideal?
9
Reaching or Not Reaching the IdealReaching or Not-Reaching the Ideal
D bl
ReliableAvailable
Durable
Reliable
Fuel-flexibleTurbomachinery blade vibrations are the
LightweightSilent
show-stopper No 1 that prevent us from reaching this ideal
Eco-friendly Low-maintenance
d expensive it iEfficient Powerful
… and expensive it is
10
Affordable
“90% f HCF bl d d i i “90% of HCF problems are covered during engine
development but the remaining part stands for 30% of [engine development] costs” [ g p ]
(El-Aini et al., 1997)
11
During the next 40 min…During the next 40 min…
• I want you to learnI want you to learn
What is the problem?What is the problem?
What is the challenge?
What can we do about it?What can we do about it?
12
Vibrations in Turbomachines
13
Vibrations in TurbomachinesVibrations in Turbomachines
• Induced by unsteady loadsInduced by unsteady loadsStructuralAerodynamical (fluid-structure interaction)
• Potentially leading to failure of components
• Types
Damped preferred
14
p p
Vibrations in TurbomachinesVibrations in Turbomachines
• Induced by unsteady loadsInduced by unsteady loadsStructuralAerodynamical (fluid-structure interaction)
• Potentially leading to failure of components
• Types
Damped preferredUnstable self-excited
15
p p
Failure due to overload
Vibrations in TurbomachinesVibrations in Turbomachines
• Induced by unsteady loadsInduced by unsteady loadsStructuralAerodynamical (fluid-structure interaction)
• Potentially leading to failure of components
• Types
~100Mio cycles
108 cycles
Failure due to High Cycle Fatigue (HCF)
cycles
Damped preferredUnstable self-excited
Limit Cycle Oscillations (LCO)
16
p p
Failure due to overloady ( )
HCF Haigh Diagram
Vibrations in TurbomachinesVibrations in Turbomachines
• Induced by unsteady loadsInduced by unsteady loadsStructuralAerodynamical (fluid-structure interaction)
• Potentially leading to failure of components
• Types
~100Mio cycles
108 cycles
Failure due to High Cycle Fatigue (HCF)
cycles
unsafe
Damped preferredUnstable self-excited
Limit Cycle Oscillations (LCO)safe
17
p p
Failure due to overloady ( )
HCF Haigh Diagram
Typical Flow-Induced VibrationTypical Flow Induced Vibration
A windy day
An open landscape
Structures exposed to flowStructures exposed to flow
18Nevada, US, May 2005
Cantilevered Beam VibrationCantilevered Beam Vibration
Flow-induced vibration
Unsteady load
Vibration mode
Vibration frequency
Why does it vibrate?
How does it vibrate?
19
Why Does it Vibrate?Why Does it Vibrate?
Exposed to flow
Flow creates an unsteady load
St tStructure
Structure (elastic)
Unsteady aerodynamic loadAero load
20
Structure (elastic)
How Does it Vibrate?How Does it Vibrate?
• Equation of motion
)(tFkxxm
Equation of motion
Structural part Excitation here aerodynamic forces
St tx: deformation coordinate
Structure modal coordinate
: natural frequency of kfrequencymode
Aero load
q ystructure m
N t l d ( d )frequency
21
Natural mode (eigenmode)f q y
How does Flow translate into Load?How does Flow translate into Load?
S
s dsnpF
SLoad
St t FlowStructurefrequencymode
p
Flow
Aero loadfrequency
ps
If p p (t) then F F(t)
22
f q ydirection
If ps=ps(t) then F=F(t)
Flow-Induced VibrationFlow Induced Vibration
Inertial forces Aerodynamic forces
)(tFkxxm Elastic forces
Resonance Resonance phenomenon
Same frequencySt t
Force in direction
q yStructurefrequencymode
Force in direction of mode
Aero loadfrequency
23
f q ydirection
Flow-Induced VibrationFlow Induced Vibration
Inertial forces Aerodynamic forces
)(tFkxxm Elastic forces
Resonance Resonance phenomenon
Same frequencySt t
Force in direction
q yStructurefrequencymode
Collar’s triangle of forces (1946)
Force in direction of mode
Aero loadfrequency
24
f q ydirection
Does this give the whole picture?
St t
picture?
Structurefrequencymode
Aero loadfrequency
25
f q ydirection
What about Damping?What about Damping?
)(tFkxxcxm
Structural damping
What are damping forces?
St t
Im
Damping forcesStructurefrequencymodedamping
p g
Aero loadfrequency
dampingRe
Inertial forces Elastic forces
26
f q ydirection
Damping forces are out-of-phase forces (wrt motion)
What about Damping?What about Damping?
)(tFkxxcxm
Structural damping
What are damping forces?
St t
Im
Damping forcesStructurefrequencymodedamping
p g
Aero loadfrequency
dampingRe
Inertial forces Elastic forces
27
f q ydirection
Damping forces are out-of-phase forces (wrt motion)
What about Aerodynamic Damping?
• The fluid around a structure that moves needs time
What about Aerodynamic Damping?
The fluid around a structure that moves needs time to reactThere is a phase lag between the fluid force and the
motion of the structuremotion of the structure
(Structural) damping forces
Imforces
Aerodynamic force
St t Aerodynamic damping force
Aerodynamic
Structurefrequencymodedamping
Re
Inertial forces Elastic forces
ystiffness force
Aero loadfrequency
damping
28
f q ydirectionphase
The aerodamping can get negative flutter
Bringing it TogetherBringing it Together
)(tFkxxcxm
)()()( tFtFtF edisturbancdampingae
As the aerodynamic damping depends on the motion of the structure (i.e. the modal coordinate), it can be included on the left-hand side
St t
)()()( tFxkkxccxm edisturbancaeae
Structurefrequencymodedamping
Aero loadfrequency
damping
)(tFXKKXCCXM
Multiple degrees of freedom: scalars vectors
29
f q ydirectionphase
)(tFXKKXCCXM edisturbancaeae
Important AspectsImportant Aspects
(Structural) damping
The ratio of structural to aero forces matters
Imforces
Aerodynamic force
St t
Aerodynamic damping force
Aerodynamic Structurefrequencymodedamping
Re
Inertial forces Elastic forces
Aerodynamic stiffness force
Aero loadfrequency
damping
The dynamics of the flow matters phase
30
f q ydirectionphase
Important Parameters
M i
Important Parameters
• Mass ratioRatio between airfoil mass
and mass of surrounding fluidfluid
20
4c
m
great influence of fluid on structure
• Reduced frequencySt t Reduced frequencyRelation between time-of-
flight of fluid particle across airfoil during one
Structurefrequencymodedamping
ufc
Ttk 2
oscillation periodAero loadfrequency
damping
31
uTk aero damping reduced ( negative)
f q ydirectionphase
Application to Turbomachines
St tStructurefrequencymodedamping
Aero loadfrequency
damping
32
f q ydirectionphase
Turbomachine EnvironmentTurbomachine Environment
St tStructurefrequencymodedamping
Blade rows
StationaryAero loadfrequency
damping
33
Rotating
f q ydirectionphase
Vibration of Bladed-Disk StructuresVibration of Bladed Disk Structures
Blades
St tTravelling Wave Modes
Structurefrequencymodedamping
Aero loadfrequency
damping
34
Disk Bladed diskf q ydirectionphase Vibration characterized by disk and blade behavior
Vibration of Bladed-Disk StructuresVibration of Bladed Disk Structures
Blades2ND 3ND
+ ++--
++
+
+--
-
St tTravelling Wave Modes
1E
+
Structurefrequencymodedamping
1F
1E
Aero loadfrequency
damping1T
35
Disk Bladed diskf q ydirectionphase Vibration characterized by disk and blade behavior
TWM ND 0TWM ND 0
ND 0ND 0=0deg ND nodal diameter
FT forward traveling
BT backwards travelingBT backwards traveling
St tStructurefrequencymodedamping
Aero loadfrequency
damping
36
f q ydirectionphase
TWM ND 6 FTTWM ND 6 FT
ND 6 FTND 6 FT=90deg ND nodal diameter
FT forward traveling
BT backwards travelingBT backwards traveling
St tStructurefrequencymodedamping
Aero loadfrequency
damping
37
f q ydirectionphase
TWM ND 12 FTTWM ND 12 FT
ND 12 FTND 12 FT=180deg ND nodal diameter
FT forward traveling
BT backwards travelingBT backwards traveling
St tStructurefrequencymodedamping
Aero loadfrequency
damping
38
f q ydirectionphase
Depicting Natural FrequenciesDepicting Natural Frequencies
]f [H
z]Modes can approach each other
2F1T
3.1kHz
4.2kHz
1F
St t 1 5kHz
N/2 ND1F +-4 ND
Structurefrequencymodedamping
1.5kHz
1F 0 ND1F +-1 ND
Frequencies vary with engine speed
F i i h d l di800Hz
[rpm]
Aero loadfrequency
damping
6000
Frequencies can vary with nodal diameter800Hz
39
[rpm]f q ydirectionphase
6000
Depicting Natural FrequenciesDepicting Natural Frequencies
]f [H
z]Modes can approach each other
2F1T
3.1kHz
4.2kHz
1F
St t 1 5kHz
N/2 ND1F +-4 ND
Structurefrequencymodedamping
1.5kHz
1F 0 ND1F +-1 ND
Frequencies vary with engine speed
F i i h d l di800Hz
[rpm]
Aero loadfrequency
damping
6000
Frequencies can vary with nodal diameter800Hz
40
[rpm]f q ydirectionphase
6000
Schematic Turbine Stage FlowSchematic Turbine Stage Flow
St tStructurefrequencymodedamping
Aero loadfrequency
damping
41
f q ydirectionphase
Effect of Adjacent Blade RowsEffect of Adjacent Blade Rows
St t
n
Structurefrequencymodedamping
u
span
Aero loadfrequency
damping
42
f q ydirectionphase
Effect of Adjacent Blade RowsEffect of Adjacent Blade Rows
St t
t=60/[rpm]/N f=1/t
n
Structurefrequencymodedamping
Spatially varying flow quantity
u
span
Aero loadfrequency
damping
Fdisturbance(t)
43
f q ydirectionphase Translates into time in rotor frame of reference
An Excitation DiagramAn Excitation Diagram
] EO : Engine OrderEO 60
f [H
z]EO 20
EO : Engine Order
f=[rpm]/60*60
f=[rpm]/60*20
f
EO 11
f2
St t
2kHz
f=[rpm]/60*N1 (=11)
EO 11
f1
Structurefrequencymodedamping 1 1kHz
[rpm]
Aero loadfrequency
damping
6000
1.1kHz
44
[rpm]f q ydirectionphase
6000
Effect of Neighbour BladesEffect of Neighbour Blades
The flow around one blade is affected The flow around one blade is affected
by the motion of itself AND the motion of the neighbour blades
St tAerodynamic coupling
Structurefrequencymodedamping
Aero loadfrequency
damping
45
f q ydirectionphase
Aero Damping vs Nodal DiameterAero Damping vs Nodal Diameter=15deg
ND 1 FTND 1 FT
=180deg
ND 12 FT
ND nodal diameter
St t FT forward traveling
BT backwards traveling
Structurefrequencymodedamping Least stable mode
Aero loadfrequency
damping Least stable mode
46
=-90deg
ND 6 BT
f q ydirectionphase
Bringing it TogetherBringing it Together
]
EO 60
Forced response
f [H
z]EO 20
Forced response
2F1T
1F
St t EO 11Structurefrequencymodedamping
EO 11
Fl tt
[rpm]
Aero loadfrequency
damping
6000
Flutter
47
[rpm]f q ydirectionphase
6000
OP range
Turbomachinery AeroelasticityTurbomachinery Aeroelasticity
St tStructurefrequencymodedamping
Aero loadfrequency
damping
48
(Giles, 1991)
f q ydirectionphase
Does this give the whole picture?picture?
St tStructurefrequencymodedamping
Aero loadfrequency
damping
49
f q ydirectionphase
The Complete PictureThe Complete Picture
]
EO 60Flow instability
f [H
z]EO 20
Non-Synchronous Vibrationse.g. vortex shedding
2F1T
1F
St t EO 11Structurefrequencymodedamping
EO 11
Fl tt
[rpm]
Aero loadfrequency
damping
6000 Forced response
Flutter
50
[rpm]f q ydirectionphase
6000
OP range
The RealityThe RealityExperimental Campbell DiagramKielb et al. ASME Turbo Expo,
2003
Experimental Campbell DiagramKielb et al. ASME Turbo Expo,
20032003Acceleration to 95% Speed
2003Acceleration to 95% Speed
St tStructurefrequencymodedamping
Aero loadfrequency
damping
51
f q ydirectionphase
What can we do about this?
St tStructurefrequencymodedamping
Aero loadfrequency
damping
52
f q ydirectionphase
Facing Vibration ProblemsFacing Vibration Problems
• Anticipate problemsAnticipate problemsEnsure during engine design that vibration problems do
not occur
A id ib i d flAvoid resonant vibrations and flutter
If occurrence cannot be avoided, ensure that the problems are not harmful
St t
Low forcing levels
Low negative damping
p
Structurefrequencymodedamping
Low negative damping
• Remedy problemsEnsure that certain operating points are avoided
Aero loadfrequency
damping
High positive damping
Ensure that certain operating points are avoidedEnsure that the problems are made harmless
53
f q ydirectionphase
g p p g
HCF tolerant materials
Designing for Vibration SafetyDesigning for Vibration Safety
St tHavig in place a design process that
Structurefrequency
d
involves aeromechanical analyses
Structural analysesmodedamping
Static loads, mode shapes, frequencies, damping
St tAero loadf Aerodynamical analyses
Mutual interaction
Structurefrequencymodedamping
frequencydirectionh
Aerodynamical analysesUnsteady aerodynamic forcing
Aerodynamic damping
Aero loadfrequency
dampingphase
Aerodynamic damping
HCF fatigue analyses
54
f q ydirectionphase
Stresses and fatigue behaviour of materials
An Example Aeromech Design ProcessAn Example Aeromech Design Process
55
Mayorca, 2011
An Example Aeromech Design ProcessAn Example Aeromech Design Process
56
Mayorca, 2011
An Example Aeromech Design ProcessAn Example Aeromech Design ProcessAn Example Aeromech Design ProcessBack to Aero design
An Example Aeromech Design Process
Designed for vibrational safety
57
Mayorca, 2011
Aeromech and our Turbomachinery IdealAeromech and our Turbomachinery Ideal
D bl
ReliableAvailable
Durable
Reliable
Fuel-flexibleEfficiency is king
LightweightSilent
Eco-friendly Low-maintenance
But never at the cost of safetyEfficient Powerful
y
58
Affordable
Which are state-of-the-art aeromechanical analyses?aeromechanical analyses?
59
An Example Aeromech Design ProcessComputational StructuralAn Example Aeromech Design ProcessComputational StructuralDynamics (CSD)
Cyclic symmetric models(0) 100k DOF per sector
Model size not extremely criticalfor modal analysis (other thanstress analysis)y )
Updated system matrices (e.g. stiffening effects)
Modeling of material damping, friction damping, dampingcoatings
60
An Example Aeromech Design ProcessComputational StructuralComputational Fluid An Example Aeromech Design ProcessComputational StructuralDynamics (CSD)Computational Fluid Dynamics (CFD)
Cyclic symmetric models(0) 100k DOF per sectorForced responseFull-size 3D time-marching RANS Details (tip clearance, inter-rowModel size not extremely criticalfor modal analysis (other thanstress analysis)
( p ,gaps, cavities) modeled (but not always)(0) 100k-1M nodes per passagey )
Updated system matrices (e.g. stiffening effects)
( ) p p gUsually single or few passages
Aerodynamic damping
Modeling of material damping, friction damping, damping
Aerodynamic damping3D time-marching or linearizedviscous approachesMode shapes from FEM (loosecoatingsMode shapes from FEM (loosecoupling) or time-marchingCFD/CSD (strong coupling)
61
Example: Aero Damping CFDp p g
62
How well are we doing in these analyses?these analyses?
63
When are we doing well?When are we doing well?
• If we can give a state-of-the-art analysis tool to an If we can give a state of the art analysis tool to an average (trained) engineer and expect that we get an accurate and reliable result
Proficiency in use
Accuracy with respect to test data
Reliability with respect to repetitivity
Clarity about objectives
64
Example Steady CFDExample Steady CFD
• Highly detailed 3D RANS simulations are state-of-Highly detailed 3D RANS simulations are state ofthe-art and are (if employed correctly) very reliable
L t d t t
65
Let us do a test
Test: Prediction Steady LoadingTest: Prediction Steady Loading
• Test case (high-subsonic LPT) given to 6 groups of Test case (high subsonic LPT) given to 6 groups of students (3-4 students per group) trained in using ANSYS CFX
• InputGeometryBoundary conditions (inlet profiles outlet pressure)Boundary conditions (inlet profiles, outlet pressure)
• TaskTo predict the steady aerodynamic loadingTo predict the steady aerodynamic loading
• Students performedMeshingMeshingSimulation setupSolvingExtraction of loading
66
Extraction of loading
Centralized post-processing
Let us now do a similar test on Let us now do a similar test on a typical aeromechanical
l ianalysis
67
Test: Prediction of Aero DampingTest: Prediction of Aero Damping
• Test case (transonic compressor) given to specialistsTest case (transonic compressor) given to specialistsin 5 European turbomachinery industriesHighly renown industrial partners that build state-of-the-
art gas turbinesart gas turbines
Design intent: low ( negative) aero damping as stall is approacheddamping as stall is approached
68
FUTURE - Flutter-Free Turbomachinery Blades
Test: Prediction of Aero DampingTest: Prediction of Aero Damping
• Test case (transonic compressor) given to specialistsTest case (transonic compressor) given to specialistsin 5 European turbomachinery industriesHighly renown industrial partners that build state-of-the-
art gas turbinesart gas turbines
Design intent: low ( negative) aero damping as stall is approached
• InputGeometrydamping as stall is approachedBoundary conditions (inlet profiles, outlet pressure, speed)
• TaskTo predict the minimum aerodynamic damping vs pressure ratio
• Industries performedCSD analyses ( modes)Steady CFD ( speedline)Unsteady CFD ( damping at various OPs)
69
FUTURE - Flutter-Free Turbomachinery Blades
y ( p g )
Centralized post-processing
Test: Prediction of Aero DampingTest: Prediction of Aero Damping
0.8%
0.2%
-0.3%
Prediction error in the order of predicted damping
70
Two different viewpoints
71
Manager’s vs Engineer’s ViewsManager s vs Engineer s Views
“What is the probability that this component will fail?”
“What is the benefit of doing a certain analysis in a specific way?”
72
p y
Where are the big challenges?
73
Key ChallengesKey Challenges
• Aerodynamic forcingAerodynamic forcingCorrect prediction of forcing levelsTaking into account details (tip clearances, cavities, etc)
• Aerodynamic dampingCorrect prediction of damping levelsStrongly dependent on steady flow phenomenaStrongly dependent on steady flow phenomenaTransition usually not modeled at all
• Non-synchronous vibrations• Non-synchronous vibrationsExtremely difficult to delineate where to search forPost-diction possible, pre-diction extremely challengingU ll i l i 360d d l lti Usually involving 360deg models, multi row
• DampingC t di ti f f i ti d d l d i
74
Correct prediction of friction dampers and novel damping concepts (coatings, air film, piezo, eddy current)
Key ChallengesKey Challenges
• Aerodynamic forcingAerodynamic forcingCorrect prediction of forcing levelsTaking into account details (tip clearances, cavities, etc)
• Aerodynamic dampingCorrect prediction of damping levelsStrongly dependent on steady flow phenomenai Strongly dependent on steady flow phenomenaTransition usually not modeled at all
• Non-synchronous vibrations
Having engineers that are trained in
interdisciplinary analyses and problem solving• Non-synchronous vibrations
Extremely difficult to delineate where to search forPost-diction possible, pre-diction extremely challengingU ll i l i 360d d l lti Usually involving 360deg models, multi row
• DampingC t di ti f f i ti d d l d i
THRUST – Turbomachinery Aeromechanical University Training
75
Correct prediction of friction dampers and novel damping concepts (coatings, air film, piezo, eddy current)
y gwww.explorethrust.eu
Does this give the whole picture?picture?
76
Realistic ComponentsRealistic Components
115115m
+64%
70m
64%
70m
A single value tells us only half of the story
Mistuned forced response
77
Analyzing Realistic ComponentsAnalyzing Realistic Components
• Realistic components are mistunedRealistic components are mistuned
• We usually simplify analyses (such as to keep computational costs low)computational costs low)
• As a consequence, the such analyses are not good enough to make relevant decisionse oug to a e e e a t dec s o s
• Even if full-scale full 360deg aeromechanical analyses were possible, direct analyses of a specific y p , y pmistuned setup were only of little valueLevel and type of mistuning change a lot over time
Mistuned Analyses paired with Probabilistic Aspects are the answer
78
p
Let us bring this to the point
79
SummarySummary
• An overview over turbomachinery blade vibrations, An overview over turbomachinery blade vibrations, analyses techniques and challenges has been given
• Despite the fact that we nowadays have very • Despite the fact that we nowadays have very sophisticated analysis tools, we are not in a position to predict turbomachinery blade vibrations down to single digit accuraciessingle digit accuracies
• Still, turbomachines have and will be designed with h h d h l kthese methods while taking into account
conservative safety margins
The future calls for top-of-the-line analyses taking into account variability of engines and yielding failure probabilities
80
failure probabilities
h lmahalomahalo
81