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CompEdu HPT / S5: Aeroelasticity / B1: Introduction / C5: Dynamic Aeroelasticity T. H. Fransson

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AEROELASTICITY IN AXIAL-FLOWTURBOMACHINES

Torsten H. Fransson

Book 1:INTRODUCTION

Chapter 5:

Dynamic Aeroelasticity

SUMMARY

The terminology found in the classical literature on aeroelasticity englobes a widevariety of terms. The underlying physical reasons for a specific phenomena may besimilar, although the terminology is diversified. This section gives an overview ofvarious terms appearing in the literature and specifies the main physical reasons whycertain types of fluid-structure interactions appear.

Fig. B1C5.1: Rotor blade row phenomena [Compressor figure originally fromMcNally, 1977, p. 458]


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The terminology "dynamic aeroelasticity" covers, as stated above, the interaction ofaerodynamic forces, inertial forces and elastic forces in Collar’s triangle of forces (Fig.1.3). Among the "dynamic aeroelastic" phenomena found in the literature, inconnection with aeronautics and turbomachines, the following can be mentioned:

Buffeting: "Repeated alteration of the aerodynamic forces acting on any part of anairplane in flight due to unsteady air flow that originates in a disturbance set upby some other part of the airplane". The term is often used as "irregularoscillation of the airplane or its parts resulting from such buffeting" (definitionaccording to Webster [1976, p. 291]). Försching [1974, p. 19], Platzer [1990a,p. 4] and Dowell et al [1980, p. 281] discuss the phenomena. The term"turbulent buffeting" is also sometimes used. The phenomena usually causeslow vibration amplitudes and thus fatigue failure.

Stargardter [1987, p. 20.4] indicates that buffeting in jet engines sometimesalso is called "separated flow vibration" or "bending flutter" and that it "is anirregular motion of the blades excited by turbulence in the flow field".

Other definitions are such that the structural component from which theseparated flow originates from can also be excited (i. e. not only downstreamstructures). As examples can be mentioned (I) Fung, 1969, p.10: “Buffetingis an irregular motion of a structure or parts of a structure in a flow, excited byturbulences in the flow”, (II) Bisplinghoff et al, 1955, page 2: “Buffetingcorresponds to transient vibrations of aircraft structural components due toaerodynamic impulses produced by the wake behind wings, nacelles,fuselage pods, or other components of the airplane”, (III) Mabey, 198???, p.22: “Separated flow provides an excitation, which at a given point may becharacterized by the rms level, the frequency spectrum, the degree ofcorrelation in space and time, and the length scale. The pressure fluctuationsexcite a response of the structural modes, called buffeting. Buffeting onset isdefined as the first appearance of a significant area of separated flow.”

Galloping: "Marked by a motion like that of one galloping; fast moving; rapidlydeveloping or increasing" (Definition according to Webster [1976, p. 931]). Thephenomena is discussed by Dowell et al [1980, pp. 285ff] who give as anexample the galloping of electrical power lines and street lamps. They also usethe terminology of "wake galloping" or "subspan galloping" to characterizethe galloping of cables in a bundle, where the downstream cable lies in thewake of the upstream one (Fig. B1C5.6). Dowell et al [1989, p. 314] indicatethat the mean and slowly fluctuating aerodynamic values seem to be thedriving force in this kind of aeroelastic interaction. To some extent gallopingcan thus be explained by "quasi-steady" theories, i. e. by considering that theaerodynamic forces reacts immediately to the vibration.


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Wind velocity

Frequency

Look-in region

Structure natural

frequency

Vortex shedding frequency

Fig. B1C5.2: Illustration to the wake galloping Fig. B1C5.3: Qualitative trend ofphenomena [Dowell et al, 1980, p. 292]. vortex shedding frequency with

wind velocity when lock-in occurs [Dowell et al, 1980, p. 295].

Vortex-shedding: Vorticities are shed from any body in an airstream. These areknown to take on discrete frequency values that depend on the geometry ofthe body, with the frequencies directly correlated with the velocity of theincident flow velocity. If the frequency of the vorticities are close to the naturalresonance frequency of the structure a phenomena of "lock-in" can appear inwhich the vortex shedding frequency locks at the structural vibration frequencyfor a certain domain of wind velocity (Fig. B1C5.3). This can lead to thedestruction of the structure. Dowell et al [1980, pp. 294ff] give as examplescertain vibrations of towers, suspension bridges (among others). Thephenomena is sometimes called "Strouhal excitation" (after Strouhal number)or "periodic wake shedding". It can be considered as a "self-excited"phenomena, as no upstream or downstream unsteadiness is introduced intothe system from outside.

Wing-pylon-store interference problems: Platzer [1990a, p. 6] notes that thethis is a "aero-servo-elastic" instability encountered on the A-7A during flightflutter tests and that "the mode involved was anti-symmetric in nature andconsisted primarily of lateral motion of the center station stores and verticalmotion of the outboard station stores with small wing participation".

Snaking: "A persistant directional oscillation of an airplane" (Definition accordingto Webster [1976, p. 2154]). Platzer [1990a, p. 3] states that the phenomena isinfluenced by the fuselage and tail flexibilities.

Load Alleviation and Mode Stabilization Problems: Platzer [1990a, p. 6] indicatesthat such problems arise because of the demand of increasing size andstructural efficiency of modern airplanes.

Buzz: "A noisy vibration or very rapid flutter especially of a poorly functioningmechanical part (ex: a buzz developing in the ailerons of a plane at highspeed)" (Definition according to Webster [1976, p. 662]). Dowell et al [1980, p.


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110] defines the problem of "transonic buzz" as the one of a shock wave on awing that oscillates because of an oscillating control surface (Fig. B1C5.4).The same (or at least a very similar) phenomena is called "aileron buzz" byBisplinghoff and Ashley [1975, p. 108].

Oscillating shock wave

Oscillating control surface

Fig. B1C5.4: Illustration to the transonic buzz phenomena [Dowell et al, 1980, p.110].

Gust: "A rapid increase in wind speed relative to the mean strength at the time"(Definition according to AGARD [1980, p. 213]). In some terminology itcorresponds to a perturbation normal to the airfoil chord. The terminology isalso used in turbomachines to characterize periodic non-uniformities in theinlet flow to a blade row. The terms “vortical gust” and “potential gust” toidentify non-uniformities coming from velocity or static pressure perturbations,respectively, are also used.

Inlet distortion: Often used to characterize a disturbance approaching the firstblade row. It can be created by struts (see "forced vibrations" below) or, moreoften, by the fact that the engine does not fly at zero angle of attack. This lattercondition may mean that blades may run into a low flow region and becomestalled during part of the circumferential rotation, execute a few cycles ofvibrations, and then come into a region of good flow where the vibrations willdamp out. A case of modulated vibration due to periodic stall flutter excitationfollowed by positive aerodynamic damping in the "good flow" regime canappear [Sears et al, 1976, p. 323]. Partial admission in steam turbines mayeventually show similar behavior.

Forced vibration (also called wake interaction, resonance with a flow periodicityor rotor-stator interaction):Interaction of the wakes by an upstream blade row (or other obstacles) on adownstream one, and vice versa. In some contexts the interaction of theupstream blade row on the downstream one can be considered to be a gustinfluence. In this kind of vibration a clear coincidence in frequency can befound between the disturbancies in the airstream, or with the rotor passingfrequency, and the natural frequency of the blade. These vibrations are oftenanalyzed from high stresses represented in a Campbell diagram (Fig. B1C5.5),which represents the change in blade vibration frequency as the rotationalspeed of the machine increases, together with the corresponding engine orderfrequencies. Integral order vibrations correspond to vibrations when the bladevibration frequency lies close to one of the engine orders. From a practicalpoint of view, the strength of the excitation is often determined on non-vibrating


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blades. If this is the case, the investigation should then, strictly speaking, notbe classified under "aeroelasticity".

Fig. B1C5.5: To the left: Schematic example of Campbell diagram for a rotorblade. Crossings of an engine order and a vibration mode indicatepossible forced resonance, and crosses indicate either propagating stall,flutter or other non-synchronous excitation.To the right: Example of measured Campbell diagram with the strengthof the blade vibration amplitude superimposed

Low Engine Order Excitation: Similar as forced response, apart from the fact thatthe excitation is of the lower engine orders (first to about the 6th –10th). Thistype of excitation can appear because of a defect in the previous blade row(for example a guide vane which has been displaced, difference in coolingflow, ..), or from further upstream ( a strut, a combustor abnormality, …).

Potential interaction: Interaction between blade rows passing by each other. Onlythe change in the static pressure field is here considered, contrary to the wakeinteraction where only the wake is considered.

Non-integral engine order vibrations: This usually regroups all vibrations that arenot an integral of an engine order (see the Campbell diagram). As the exactcause of blade vibrations usually are difficult to establish, this terminology is aconvenient way to characterize problems of un-known nature.

Rotating stall: Flow instability in which stall cells rotate around the circumfery of themachine, often with a speed of about 45-55% of the circumferential speed ofthe machine (Fig. B1C5.6). This kind of flow instability can give large forces onthe blades, but its appearance is usually independent of any blade vibrations.In its origin it is thus not an aeroelastic phenomena.


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Fig. B1C5.6: Schematic illustration of rotating stall

Surge: Flow instability in which low-frequency high amplitude pressures traverse themachine. This kind of flow instability is associated with backward flow throughthe compressor, and can give large forces on the blades, but its apperance is,as for the rotating stall, usually independent of any blade vibrations. In itsorigin it is thus not an aeroelastic phenomena.

Stochastic excitation: Because of the relatively high turbulence in the flow in aturbomachine (turbulence in the incoming flow for a jet engine, turbulence fromseparations ,..), the blades will always be excited in a stochastic way, and willvibrate outside of their resonance region.

Acoustic resonance: Acoustic standing waves with very high noise levels(sometimes above 160dB in heat exchangers). In linear aerodynamic cascadeanalysis acoustic resonances appear in which the unsteady aerodynamicresponse of the blade shows a discontinuity. This phenomenon is discussed ina later section. Although he acoustic waves may resonate and propagate inannular ducts, significant amplitudes will only appear if there is an excitationsource which feeds energy into the perturbation. Vortex shedding can be onesuch mechanism, especially related to “vortex lock-in” as described above. Arecent study on this phenomena has been performed by Camp [1999].

Flutter: "A sustained oscillation due to the interaction between aerodynamicforces, elastic response and inertia forces" (Definition according to AGARD[1980, p. 189]). The terminology, according to this definition, corresponds inthis large sense to "dynamic aeroelasticity". The term "flutter" is howeverusually employed in the sense of "selfexcited vibrations", i. e. without anyunsteadiness coming from upstream or downstream. Thus the otherphenomena mentioned under "dynamic aeroelasticity" above are not includedin "flutter" (in a general sense "vortex shedding" could be included in theterminology of "self-excited vibrations", but this phenomena is usually treatedapart). Flutter usually appears above a critical flow velocity, gives largevibration amplitudes and a damage in a short period of time. Several sub-


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divisions of flutter are found in the literature, each with its own characteristicsand physical reasons. In the following several definitions will be given. Some ofthese are related only to the aeronautical field whereas some are used also inturbomachinery context. Some, on the other hand, are specific forturbomachine applications. The most important flutter domains in acompressor are illustrated in Fig. B1C5.7, which is an extension of thecompressor pressure ratio versus mass flow characteristic. This compressorflutter map has been established empirically throughout the years on blades ofconventional materials and shapes and it does not necessarily follow that itmust be identical in the future when more advanced airfoil shapes andmaterials are employed.

pressure ratio

massflow

surge line

operating line

100% speed 75%

50%

25%

choke line

increasing incidence

1

2

3

4

5

M 2 <1

M 1 <1

1

M 2 <1

M 1 >1

shock

2

M 2 <1

M 1 <1

shock

M=1

3

shock

M 1 >1

M 2 >1

4

M 2 <1

M 1 >1

shock

5

M 2 <1

M 1 <1

6

Fig. B1C5.7: Compressor flutter map (figure after Bölcs [1988]).

• Classical flutter: This is usually defined as flutter when the flow is attachedat all time and it involves directly the phase lag between the movement of astructure and the therefrom induced time-dependent aerodynamic forces.Depending on the time-lag (which may appear because of various physicalreasons) between the vibrating structure and the unsteady aerodynamic forcesacting on it the structure will either absorb energy from the flow, give energy to

1 Subsonic stall flutter2 Transonic stall flutter3 Choke flutter4 Supersonic started flutter at low back pressure5 Supersonic started flutter at high back pressure6 Classical (or potential flow) flutter


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the flow or remain neutral in this sense during a specific vibration cycle (Fig.B1C5.8). If the structure gives energy to the flow we speak about a dampedvibration from the aeroelastic point of view (Fig. B1C5.8b). If on the other handthe flow gives energy to the structure the vibration amplitude will increase(exited or unstable vibrating cycle) (Fig. B1C5.8a). Finally, if there is no energyexchange between the fluid and the structure during the oscillation cycle thevibration is neutral (during this specific vibration cycle). The way the structurebehaves over a certain period of time depends thus on the unsteadycharacteristics of the fluid and the structure over several vibration cycles. Fung[1969, p. 161] restricts the term flutter "to the oscillatory instability in a potentialflow, in which neither separation nor strong shocks are involved". This is adistinction which in the present context lies within "classical flutter".

p = h + 20° p = h + 200°

+ +

- - 0

0 π /2 3 π /2π 2 π ω t

+ +

- -

0

0 π /2 3 π /2π 2 π ω t

h . h

0

0 π /2 3 π /2π 2 π ω t

f ~

h

. h

0

0 π /2 3 π /2π 2 π ω t

f ~

Power Power

a: 20o phase lead of force b: 200o phase lead of forcetowards motion => towards motion =>Structure absorbs energy Structure gives energyfrom the flow to the flow

Fig. B1C5.8: Schematic illustration of unsteady flow interacting with a vibratingstructure during a typical vibration cycle

• Coalescense flutter, also called merging frequency flutter, coupled mode flutteror bending-torsion flutter: The distinguishing feature of this flutter type is thattwo frequencies are on their way to merging when flutter appears. The flow isas for the classical flutter considered to be attached during the whole vibrationcycle. At the critical flutter speed the frequencies have often not yet mergedbut are close together (Fig. B1C5.9) (see for example Dowell et al [1980, p.


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103]). For wings this type of flutter is sometimes called "classical flutter" or"classical coalescense flutter".

Fig. B1C5.9:Dimensionless frequencies ω/ωα and damping ratios ξ of the aeroelasticmodes of the typical section, plotted versus airspeed parameter1/kα=2U/cωα for incompressible flow with xα=0.024, rα=0.62,ωh/ωα=0.227, m/(ρ−_cS)=38, a=-0.36 [Bisplinghoff and Ashley, 1975, p.237]. (Note that 2UF/(cω) corresponds to the inverse of the criticalreduced frequency.)

• Singe degree of freedom flutter: This flutter type is different from coupledmode flutter in as far as only one vibration mode is present. The flutterfrequency is often virtually the same as the frequency of one of the systemmodes with no flow around it (see for example Dowell et al [1980, p. 104]).

• Stall flutter: "Flutter in one or more degrees of freedom near stall" (Definitionaccording to AGARD [1980, p. 411]). The positions of this type of flutter in anaxial-flow compressor is schematically represented in Fig. B1C5.7 (regions "1"and "2"). As the name indicates, this type of flutter is situated close to the stallline of the compressor map, and it is thus usually believed that the flow isstalled, or at least largely separated, but this is not necessarily so in all cases.An introduction to the problem is given by Dowell et al [1980, pp. 267ff] and bySisto [1987b, pp. 7.1ff]. This is a type of flutter frequently found inturbomachines, but also one for which no theory exists today. The prediction ofthis flutter type relies thus almost exclusively on empirical relationships. Thephenomena is characterized by an abrupt decrease in the flutter speed as theflow becomes stalled. Dowell et al [1989, p. 270] points out that themechanism for energy transfer between the airfoil and the flow is usually not ofthe coalescence type and that it does not rely on a phase lag between thedisplacement of the structure and the aerodynamic responce. Stall flutter isthus an essentially non-linear phenomena. Coupling between modes and anaerodynamic phase lag may however still be present and may to some extentalter the result, but the basic physical phenomena does not change because ofthese influences.


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• Dynamic stall flutter:Vibration such that the flow is attached on part of theairfoil during part of the cycle and stalled (in principle fully) during part of thecycle.

• Choke flutter:This type of flutter appears near the choke line of axial-flowcompressors (at negative incidences and parts speed conditions) and isprobably characterized by choked flow, separations and shock waves ("3" inFig. B1C5.7).

• Shock-induced flutter: Terminology usually employed when strong shocksoscillate on the surface (Fig. B1C5.7). Can be closely related to "transonicbuzz" on isolated airfoils.

• Supersonic unstalled flutter: A type of classical flutter that appears in thesupersonic flow region. In the compressor map this kind of flutter ischaracterized by low back pressure ("4" in Fig. B1C5.7). This kind of flutter incompressors usually appears as a torsional mode and is sometimes called"supersonic torsional flutter" [Sears et al, 1976, p. 295].

• Supersonic flutter at high back pressure: As the back pressure is increased,the shock waves will move up the blade. This type of flutter is probablyaccompanied by a strong in-passage shock wave, together with a boundarylayer separation ("5" in Fig. B1C5.7). This kind of flutter in compressorsusually appears as a bending mode and is sometimes called "supersonicbending flutter" [Sears et al, 1976, p. 295].

• Panel flutter: This is a flutter of surface skin panels, which appears entirely asa supersonic phenomena [Bisplinghoff and Ashley, 1975, pp. 419ff]. Includedherein is the flutter of flat panels, cylindrical panels and cylindrical shells.Flutter of heat shields in afterburners is an example. In modern cases of panelflutter thermal stresses may be important (see Garrick [1963, p. 134]).

• Whirl flutter: Dowell et al [1980, p.378] states that "the source of this flutterinstability is primarily associated with the fact that an angle-of-attack changeon a propeller produces a yawing moment and a sideslip angle produces apitching moment" (see also Platzer [1990a, p. 5] and xx [1961a, b]).

• Whirling: Andjelic et al [1987] uses this terminology for self-excitedvibrations of heat exchanger tubes where the aerodynamic coupling betweenthe tubes is of importance.

• Wing-tail interference flutter: Platzer [1990a, p. 6] states that "the problemstems from an apparent aerodynamic and structural interaction between thewing and horizontal tail of variable sweep wing configurations when the wingapproaches the tail".

• Space shuttle flutter problems: Platzer [1990a, p. 6] states that "if the tail ofthe orbiter vehicle is placed above the wing of the booster in biplane fashion


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detrimental interference effects could result and a new type of interferenceflutter could occur. Furthermore, shock reflections between orbiter and boostercould induce a new type of panel flutter".

• Valve Flutter: Flutter of valves in turbomachines during their opening or closingperiods.

• Ovalling: "Wind-induced shell-mode oscillation of thin metal stacks,involving deformation of the cross-section (strictly in the second circumferentialmode - hence the name - but by common usage, in higher circumferentialmodes also)" according to Paidoussis et al [1987].

• Propellor flutter: Flutter of propeller blades

• Buffeting flutter: Fung [1969, p.328] discusses this as a combination ofbuffeting of a tail that lies in the turbulent wake of a wing that flutters. He statesthat buffeting flutter causes wing and aileron damages. See also "buffeting"above.

• Elevator flutter: Collar [1946, p. 67] mentions that aeroelastic science hasits beginning in antisymmetric elevator flutter [Barstow and Fage, 1916]. Thiskind of flutter involves several degrees of freedom, such as pitching of theaircraft, vertical translation of the aircraft and wing bending.

• Flutter of wings carrying engines: This expression is employed by Collar[1946, p. 68].

• Antisymmetrical wing flexure-torsion flutter: Also this expression isemployed by Collar [1946, p. 68]. He states that the phenomenaantisymmetrical normal vibration modes, as well as a freedom to roll.

• Chordwise bending flutter: Sears et al [1976, pp. 292, 320, 330] discuss thisas a problem on highly loaded high-speed fan blades. Some indications thatthis kind of vibration is a camber distortion or camber bending is discussed.

Self-excited vibration: Another terminology for flutter. Here a small controversyexist in the literature. From the point of view of the aerodynamicist concernedwith the unsteady flow self-excited vibrations (or flutter) appear as soon as theaerodynamic work changes from damping to excitation. For the engineerevaluating experiments with vibrating blades, the term flutter-limit insteadmeans the point where large amplitudes of the blades are noticed. Obviously,the two definitions do correspond if the mechanical damping in the system iszero (see fig. B1C5.10).


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0

Mechanical damping

Unsteady excitation

0

"self-started"

"self-excited" blade vibrations

Aerodynamically damped cascade

Fig. B1C5.10:Schematic illustration of relationship between unsteady aerodynamicexcitation and structural damping of a blade. Note that the "self-startedlimits are the ones of interest for the turbomachine designer, whereas theunsteady aeroelastician usually is more interested in the "self-excitedlimit".

CONCLUSIONS

From the above discussions it is noted that it is difficult to make a clear distinctionbetween the various definitions (or rather descriptions) of different aeroelasticphenomena. Not seldom do several phenomena act together simultaneously tocreate even more complicated flow and vibration structures. In practice the designerhas to occupy himself with the decision of which type of vibrations that arepermissible (and at which strength), and which ones that have to be avoided in thewhole operating range of the machine.

The main overall factors related to aeroelasticity are the external excitations (up-and/or down-stream) as well as the phase angle between blade oscillation and theresulting unsteady force acting on the vibrating blade. Other factors of specificimportance to turbomachinery applications will be discussed in the following chapters.

aeroelasticity in axial-flow turbomachineslecture_n… · as examples can be mentioned (i) fung,...

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