turbomachinery blade vibrations

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


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




• Types

Damped preferredUnstable self-excited

15

p p

Failure due to overload




• Types

~100Mio cycles

108 cycles

Failure due to High Cycle Fatigue (HCF)

cycles


Limit Cycle Oscillations (LCO)

16

p p

Failure due to overloady ( )

HCF Haigh Diagram




• Types

~100Mio cycles

108 cycles

Failure due to High Cycle Fatigue (HCF)

cycles

unsafe


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


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


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


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


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


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


Blade rows

StationaryAero loadfrequency

damping

33

Rotating

f q ydirectionphase

Vibration of Bladed-Disk StructuresVibration of Bladed Disk Structures

Blades

St tTravelling Wave Modes


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

+


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


Aero loadfrequency

damping

36

f q ydirectionphase

TWM ND 6 FTTWM ND 6 FT

ND 6 FTND 6 FT=90deg ND nodal diameter




Aero loadfrequency

damping

37

f q ydirectionphase

TWM ND 12 FTTWM ND 12 FT

ND 12 FTND 12 FT=180deg ND nodal diameter




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


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


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


6000

Schematic Turbine Stage FlowSchematic Turbine Stage Flow


Aero loadfrequency

damping

41

f q ydirectionphase

Effect of Adjacent Blade RowsEffect of Adjacent Blade Rows

St t

n


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


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


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


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


6000

OP range

Turbomachinery AeroelasticityTurbomachinery Aeroelasticity


Aero loadfrequency

damping

48

(Giles, 1991)

f q ydirectionphase

Does this give the whole picture?picture?


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


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


Aero loadfrequency

damping

51

f q ydirectionphase

What can we do about this?


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


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


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


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 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


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

turbomachinery blade vibrations

Documents