This report contains a brief review of the unsteady aerodynamic and aeroelastic

phenomena of relevance to the operation of the Inco fan installation. The review

addresses issues associated with unsteady inlet flow phenomena due to an upstream

vortical wake and the aeroelastic flutter characteristics of the rotor assembly.

Based on the available information on inlet flow and blade structural dynamic

characteristics a number of conclusions are made. Firstly the vortical wake will be

three dimensional in nature, although the von Karman vortices generated from the

motor housing will predominate. These have the potential to induce vibration in the

fan blading, and should be investigated further. Secondly, it is recommended that the

potential for stall flutter and single mode bending-torsion flutter be further

investigated

Anderson, J.

Vezza, M.

English

Enlighten

nDEPARTMENT OFAEROSPACEENGINEERINGA Brief Review of Unsteady Aerodynamic and Aeroelastic Phenomena of a Fan Installation.byJ. Anderson and M. Vezza24 OCT 1997tISRARiEnginesringPERIODICALSU5000UNIVERSITYofGLASGOWA Brief Review of Unsteady Aerodynamic and Aeroelastic Phenomena of a Fan Installation.byJ. Anderson and M. VezzaDepartment of Aerospace Engineering University of Glasgow Glasgow G12 8QQ.on behalf ofJames Howden & Co. Ltd.I PERiOOiCALS\U30OOG. U. Aero Report No. 9719 October 1997.SummaryThis report contains a brief review of the unsteady aerodynamic and aeroelastic phenomena of relevance to the operation of the Inco fan installation. The review addresses issues associated with unsteady inlet flow phenomena due to an upstream vortical wake and the aeroelastic flutter characteristics of the rotor assembly.Based on the available information on inlet flow and blade structural dynamic characteristics a number of conclusions are made. Firstly the vortical wake will be three dimensional in nature, although the von Karman vortices generated from the motor housing will predominate. These have the potential to induce vibration in the fan blading, and should be investigated further. Secondly, it is recommended that the potential for stall flutter and single mode bending-torsion flutter be further investigated.1. Vortex Shedding from Bluff Bodies.The presence of a body in an air stream causes the air to divert around the body. Unless a sufficiently streamlined profile is presented to the oncoming stream the flow will detach, or separate, from the body surface. In general, for a stationary body in incompressible flow, the locations of the separation points on the surface are dependent on flow incidence and Reynolds number. However, if the body surface is characterised by sharp edges then the separation points are generally located at one or more of these edges and are essentially independent of Reynolds number. Fig. 1.1 illustrates these ideas in the case of two dimensional flow, that is where conditions pertaining to infinite aspect ratio are assumed.Subcrltical Reynolds number(a) bluff body - smooth surface, Re dependencySupercritical Reynolds number(b) bluff body - sharp edgesFig. 1.1. Flow conditions around bodies in 2-D flowThe wake of a bluff body results in velocity fluctuations which are much more coherent and of greater magnitude than natural flow turbulence. The fluctuations are caused by the alternate shedding of vortices of opposite sign from the sides of the body, as indicated in Fig. 1.2.Fig. 1.2. Vortex shedding from a body in 2-D flowThe so called von Karman vortices are defined by vortex filaments which extend (infinitely in theory) out of the flow plane. These are transported downstream in the wake, forming a vortex street. The frequency of vortex shedding is characterised bythe non-dimensional Strouhal number S = ^, where f b and V are the sheddingfrequency of complementary vortex pairs, the characteristic body dimension (usually cross-stream) and the flow speed respectively.Cyclic cross-stream forcing occurs on the generating body at frequency /, which generally varies linearly with V for sharp edged bodies, hi addition, along-stream forcing occurs at frequency 2/ , as this mechanism is related to the cyclic drag which is driven by the shedding of individual vortices. If the body is free to vibrate 3ien the response is maximised when f = N, the fundamental natural frequency of the body. In this case vortex "lock-in" tends to occur in which the frequency of shedding is tied into the oscillation frequency of the body over a limited speed range, as illustrated in Fig. 1.3.lock-in rangeV, V„Fig. 1.3. Vortex excitation of a bluff flexible cylinderA body which is immersed in the vortex wake of another will also experience cyclic forcing, with consequences similar to those described above should the forcing and natural frequencies coincide. Significant excitation can be induced on a body located as far as 8& downstream. Further downstream the structure of the vortices becomes more chaotic as momentum is transferred from the coherent vortex structures to lower strength, broader band turbulent eddies.The wake of a body in two dimensional flow does not remain two dimensional due to distortion and turbulent dissipation of the vortex filaments as they progress downstream. However the flow around a low aspect ratio body produces a highly three dimensional wake from the body itself. Fig. 1.4 illustrates the basic features of the flow about a rectangular block, from which the additional vortex structures can be identified.Mixing between recirculating and escaping wake flowsSeparation streamline' at surfaceFig. 1.4. 3-D vortex shedding from a rectangular block Inco Fan Motor HousingOf particular concern is the location of the motor housing upstream of the fan inlet. The basic geometry of the housing is illustrated in Fig. 1.5, which also indicates the onset flow direction.- -Th---- ^-----Ha' FlowI ^ b'r1 PLANFlowELEVATIONFig. 1.5. Geometry of motor housingThe dimensions h, d and b are 6.325m, 1.956m and 1.422m respectively, and the lee face of the box is located 5.283m from the fan inlet. The ratio h/b is 4.45, which should be doubled because of the ground plane, resulting in a value of aspect ratio of 8.9. At such values three dimensional shedding patterns should still be in evidence but the predominant shedding would be of the von Karman type in the plane of the cross-section illustrated in the plan of Fig. 1.5. The cross-sectional aspect ratio d/b is 1.38. Fig. 1.6 illustrates the Strouhal number variation with aspect ratio for rectangular sections. For the given aspect ratio the Strouhal number is 0.11.Fig. 1.6. Variation in Strouhal number with section aspect ratioThe predicted frequency of the von Karman shedding can be calculated from the Strouhal formula: ?svf^^=o.onvbwhere V is the onset flow speed at the housing. Note that the shedding of individual vortices is predicted to occur at'twice this value (0.154V).The distance of the fan inlet from the lee face of the box is 5-2SX.422 or 3.72 body dimensions, which can be considered as close proximity. This means that the shed vorticity, notwithstanding the three dimensional interactions referred to above, should possess a strongly coherent component at the fan inlet. The inlet contraction should aid the process of vortex dissipation into smaller eddies, although the duct length between fan inlet and rotor is very short for this process to advance significantly. The remainining coherent structures have the potential to induce vibration in the fan blading, which may be examined in the light of the above information.2. Flutter Phenomena in Axial-Flow Fans and CompressorsFlutter is a generic term used to describe a variety of self-excited dynamic aeroelastic instabilities. In general, axial-flow fans and compressors exhibit several distinct forms of flutter including stall flutter, choke flutter, and unstalled (or potential flow) flutter. For many years, stall flutter and choke flutter were considered the only possible types of flutter. However, current thinking is that unstalled flutter of cascades is also significant. This section describes the flutter phenomena appropriate to axial-flow fans and compressors operating in essentially subsonic flow regimes.2.1 Stall FlutterStall flutter in rotating blades is manifest by the appearance of coherent unsteady flow separation from the suction surface of the blades in which the blades vibrate sporadically at, or near, their natural frequency. There is no apparent correlation between the motions of adjacent blades, and the amplitudes of the vibrations change with time in an apparently random manner. This behaviour is distinct from vibration attributable to resonance with propagating stall which is essentially a flow instability phenomenon.Stall flutter is usually observed in the first torsional vibration mode. Empirical evidence suggests that the most important parameters governing stall flutter are the incidence and the reduced velocity V/bo) (the inverse of reduced frequency) at somecharacteristic radius of the blade such as 75%. Here, V is the flow speed, ^ is a characteristic dimension (usually the blade semi-chord), and o) is a reference blade frequency (usually the first torsional natural frequency).Figure 2.1 shows a typical stall flutter boundary in the reduced velocity parameter space.incidenceoQ0)>T3<UO3TJ(UStall flutterincidence (deg)Fig. 2.12.2 Unstalled FlutterThe unstalled flutter instability encountered in rotor blade assemblies of axial-flow fans and compressors typically takes the form of a cascade induced single mode blade-to-blade interaction flutter where both bending and torsion components in the blade vibration mode, and their relative size, play an important role. This is in contrast to the classical aeroelastic bending/torsion coalescence flutter of an isolated wing in which two or more vibration modes are involved.In general, the blade-to-blade flutter mode is characterized by a travelling wave pattern of the blade row in which all blades oscillate harmonically with the samemode shape and frequency but with a certain (constant) phase shift relative to each other. The origin of the interblade phase difference is the motion-induced unsteady aerodynamic forces which depend on individual blade motion history and the motion history of neighbouring blades. For N blades there are N possible interblade phase angles dn = iTtnfN, n = 0,l,N-1.While the assumption that the flutter mode shape coincides with a (single) vibration mode of the rotor is generally unreliable, particularly in the practical range of reduced frequencies, the error in this assumption decreases with increasing kinematic coupling in bending and torsion. Moreover, as the mass ratio of a solid metallic fan or compressor blade is generally large, both the flutter frequency and the corresponding flutter mode remain relatively unaffected by the aerodynamic loading. In practice, the flutter mode shape is usually (but not necessarily) associated with the lowest natural frequency blade vibration mode. However, within the practical range of design parameters and kinematic coupling, experimental evidence suggests that both torsional and bending branches can exhibit instability.Figure 2.2 illustrates the essentially single mode flutter characteristics of typical blade assembly. The schematic is derived from a two-mode flutter analysis based on the first bending and first torsional modes. The relative frequency is defined as to/£Or and the reduced velocity as VlbcoT. Here, the critical mode is associated with first torsional vibration mode.torsiondamping in bendingdamping in torsionbending-veQ.u33*(Q+vereduced velocity —►Fig. 2.2Assessment of the aeroelastic stability characteristics of a blade assembly is generally achieved through calculation of the neutral stability boundaries for a range of design and operating parameters (for example, mass ratio, structural damping, kinematic coupling, etc.). For preliminary design purposes, the blade assembly is assumed to be structurally tuned and the inlet flow velocity is assumed the same for all blades. For a tuned rotor subject to a single mode flutter, the concept of constant interblade phase angle implies that the travelling wave modes associated with Qn are the aeroelastic (flutter) eigenmodes.At the critical stability condition, the motion is sinusoidal and the interblade phase angle is constant. As a result, evaluation of the unsteady aerodynamic forces is feasible. In general, the unsteady aerodynamic forces depend on reduced frequencyand interblade phase angle. Flutter occurs at those values of reduced frequency and assigned phase angle dn satisfying the flutter eigenvalue problem. From these values, the critical inlet velocity VF can be determined. Among all solutions VF for the given discrete values 6n, the minimum value of VF is the physically correct critical flutter velocity.The qualitative effects of variation of the primary design and operating parameters on the flutter characteristics of a typical blade assembly can be ascertained from the resulting stability diagrams.Mass Ratio and Structural DampingIn the absence of structural damping, the stability boundary is independent of mass ratio. However, if structural damping is present a rotor blade with a large mass ratio (such as a solid metallic blade) will be more stable (that is, possess a higher critical flutter speed) than a blade with a small mass ratio. For non-zero structural damping, the mass ratio determines the magnitude of the destabilizing aerodynamic effect which can be tolerated before the system becomes unstable. In general, the stabilizing effect of structural damping is more pronounced in the case of bending flutter than in torsion flutter. Also, the range of interblade phase angle at which flutter occurs is constricted by the stabilizing effect of structural damping.Kinematic Coupling in Bending and TorsionKinematic coupling in bending and torsion plays a fundamental role in the aeroelastic coupling amongst oscillating blades. Important sources of kinematic coupling include blade pre-twist, centrifugal forces, and any offset between the blade inertial axis and elastic axis.Figure 2.3 illustrates the influence of kinematic bending/torsion coupling on the critical flutter reduced velocity, VF/bcoT, under variation of the bending/torsion vibration mode frequency ratio 7ffl = coBlcoT (in this example, the blade elastic axis is located at the mid-chord). In the vicinity of vibration mode frequency coincidence, 7^ = 1, the critical flutter velocity is dramatically reduced and is almost independent of kinematic coupling.The frequency ratio for first bending/first torsion modes of fan blades typically is in the range 0.3-0.7. However, current technology fan blades have second bending and first torsional natural frequencies close together with frequency ratios in the range 0.8-1.2. It is possible, therefore, that interactions between second bending and first torsional modes may be potentially hazardous. In addition, for blades with low mass ratio, aerodynamic mode coupling could lead to classical coalescence flutter.increasingkinematicccxiplingfrequency ratioFig. 2.3r3. ConclusionsBased on the brief assessment provided in sections 1 and 2, the following conclusionsare made:• The upstream flow into the fan will consist of a vortical wake generated from the motor housing. This wake will be three dimensional in nature but will consist predominantly of von Karman vortices in the plane of the cross-section. This unsteady flow has the potential to induce vibration in the fan blading and should be investigated further in association with the blading structural dynamic properties.• An assessment of the propensity of the blade assembly to encounter stall flutter is required. In addition, the possibility of a potentially hazardous single mode unstalled flutter involving the second flap vibration mode and first torsional vibration mode requires further clarification due to the close proximity of the natural frequencies of these modes.I

A Brief Review of Unsteady Aerodynamic and Aeroelastic Phenomena of a Fan Installation. G. U. Aero Report no. 9719

Enlighten: Publications

nDEPARTMENT OF
AEROSPACE
ENGINEERING
A Brief Review of Unsteady Aerodynamic and 
Aeroelastic Phenomena of a Fan Installation.
by
J. Anderson and M. Vezza
24 OCT 1997
tISRARi
Enginesring
PERIODICALS
U5000

UNIVERSITY
of
GLASGOW
A Brief Review of Unsteady Aerodynamic and 
Aeroelastic Phenomena of a Fan Installation.
by
J. Anderson and M. Vezza
Department of Aerospace Engineering 
University of Glasgow 
Glasgow G12 8QQ.
on behalf of
James Howden & Co. Ltd.
I PERiOOiCALS
\U30OO
G. U. Aero Report No. 9719 
October 1997.

Summary
This report contains a brief review of the unsteady aerodynamic and aeroelastic 
phenomena of relevance to the operation of the Inco fan installation. The review 
addresses issues associated with unsteady inlet flow phenomena due to an upstream 
vortical wake and the aeroelastic flutter characteristics of the rotor assembly.
Based on the available information on inlet flow and blade structural dynamic 
characteristics a number of conclusions are made. Firstly the vortical wake will be 
three dimensional in nature, although the von Karman vortices generated from the 
motor housing will predominate. These have the potential to induce vibration in the 
fan blading, and should be investigated further. Secondly, it is recommended that the 
potential for stall flutter and single mode bending-torsion flutter be further 
investigated.

1. Vortex Shedding from Bluff Bodies.
The presence of a body in an air stream causes the air to divert around the body. 
Unless a sufficiently streamlined profile is presented to the oncoming stream the flow 
will detach, or separate, from the body surface. In general, for a stationary body in 
incompressible flow, the locations of the separation points on the surface are 
dependent on flow incidence and Reynolds number. However, if the body surface is 
characterised by sharp edges then the separation points are generally located at one or 
more of these edges and are essentially independent of Reynolds number. Fig. 1.1 
illustrates these ideas in the case of two dimensional flow, that is where conditions 
pertaining to infinite aspect ratio are assumed.
Subcrltical Reynolds number
(a) bluff body - smooth surface, Re dependency
Supercritical Reynolds number
(b) bluff body - sharp edges
Fig. 1.1. Flow conditions around bodies in 2-D flow
The wake of a bluff body results in velocity fluctuations which are much more 
coherent and of greater magnitude than natural flow turbulence. The fluctuations are 
caused by the alternate shedding of vortices of opposite sign from the sides of the 
body, as indicated in Fig. 1.2.
Fig. 1.2. Vortex shedding from a body in 2-D flow
The so called von Karman vortices are defined by vortex filaments which extend 
(infinitely in theory) out of the flow plane. These are transported downstream in the 
wake, forming a vortex street. The frequency of vortex shedding is characterised by
the non-dimensional Strouhal number S = ^, where f b and V are the shedding
frequency of complementary vortex pairs, the characteristic body dimension (usually 
cross-stream) and the flow speed respectively.

Cyclic cross-stream forcing occurs on the generating body at frequency /, which 
generally varies linearly with V for sharp edged bodies, hi addition, along-stream 
forcing occurs at frequency 2/ , as this mechanism is related to the cyclic drag which 
is driven by the shedding of individual vortices. If the body is free to vibrate 3ien the 
response is maximised when f = N, the fundamental natural frequency of the body. 
In this case vortex "lock-in" tends to occur in which the frequency of shedding is tied 
into the oscillation frequency of the body over a limited speed range, as illustrated in 
Fig. 1.3.
lock-in range
V, V„
Fig. 1.3. Vortex excitation of a bluff flexible cylinder
A body which is immersed in the vortex wake of another will also experience cyclic 
forcing, with consequences similar to those described above should the forcing and 
natural frequencies coincide. Significant excitation can be induced on a body located 
as far as 8& downstream. Further downstream the structure of the vortices becomes 
more chaotic as momentum is transferred from the coherent vortex structures to lower 
strength, broader band turbulent eddies.
The wake of a body in two dimensional flow does not remain two dimensional due to 
distortion and turbulent dissipation of the vortex filaments as they progress 
downstream. However the flow around a low aspect ratio body produces a highly 
three dimensional wake from the body itself. Fig. 1.4 illustrates the basic features of 
the flow about a rectangular block, from which the additional vortex structures can be 
identified.
Mixing between recirculating 
and escaping wake flows
Separation 
streamline' 
at surface
Fig. 1.4. 3-D vortex shedding from a rectangular block 
Inco Fan Motor Housing
Of particular concern is the location of the motor housing upstream of the fan inlet. 
The basic geometry of the housing is illustrated in Fig. 1.5, which also indicates the 
onset flow direction.

- -
T
h---- ^-----H
a
' Flow
I ^ b'r1 PLAN
Flow
ELEVATION
Fig. 1.5. Geometry of motor housing
The dimensions h, d and b are 6.325m, 1.956m and 1.422m respectively, and the lee 
face of the box is located 5.283m from the fan inlet. The ratio h/b is 4.45, which 
should be doubled because of the ground plane, resulting in a value of aspect ratio of 
8.9. At such values three dimensional shedding patterns should still be in evidence 
but the predominant shedding would be of the von Karman type in the plane of the 
cross-section illustrated in the plan of Fig. 1.5. The cross-sectional aspect ratio d/b is 
1.38. Fig. 1.6 illustrates the Strouhal number variation with aspect ratio for 
rectangular sections. For the given aspect ratio the Strouhal number is 0.11.
Fig. 1.6. Variation in Strouhal number with section aspect ratio
The predicted frequency of the von Karman shedding can be calculated from the 
Strouhal formula: ?
svf^^=o.onv
b
where V is the onset flow speed at the housing. Note that the shedding of individual 
vortices is predicted to occur at'twice this value (0.154V).
The distance of the fan inlet from the lee face of the box is 5-2SX.422 or 3.72 body 
dimensions, which can be considered as close proximity. This means that the shed 
vorticity, notwithstanding the three dimensional interactions referred to above, should 
possess a strongly coherent component at the fan inlet. The inlet contraction should 
aid the process of vortex dissipation into smaller eddies, although the duct length 
between fan inlet and rotor is very short for this process to advance significantly. The 
remainining coherent structures have the potential to induce vibration in the fan 
blading, which may be examined in the light of the above information.

2. Flutter Phenomena in Axial-Flow Fans and Compressors
Flutter is a generic term used to describe a variety of self-excited dynamic aeroelastic 
instabilities. In general, axial-flow fans and compressors exhibit several distinct forms 
of flutter including stall flutter, choke flutter, and unstalled (or potential flow) flutter. 
For many years, stall flutter and choke flutter were considered the only possible types 
of flutter. However, current thinking is that unstalled flutter of cascades is also 
significant. This section describes the flutter phenomena appropriate to axial-flow 
fans and compressors operating in essentially subsonic flow regimes.
2.1 Stall Flutter
Stall flutter in rotating blades is manifest by the appearance of coherent unsteady flow 
separation from the suction surface of the blades in which the blades vibrate 
sporadically at, or near, their natural frequency. There is no apparent correlation 
between the motions of adjacent blades, and the amplitudes of the vibrations change 
with time in an apparently random manner. This behaviour is distinct from vibration 
attributable to resonance with propagating stall which is essentially a flow instability 
phenomenon.
Stall flutter is usually observed in the first torsional vibration mode. Empirical 
evidence suggests that the most important parameters governing stall flutter are the 
incidence and the reduced velocity V/bo) (the inverse of reduced frequency) at some
characteristic radius of the blade such as 75%. Here, V is the flow speed, ^ is a 
characteristic dimension (usually the blade semi-chord), and o) is a reference blade 
frequency (usually the first torsional natural frequency).
Figure 2.1 shows a typical stall flutter boundary in the reduced velocity 
parameter space.
incidence
o
Q
0)>
T3
<U
O
3
TJ
(U
Stall flutter
incidence (deg)
Fig. 2.1
2.2 Unstalled Flutter
The unstalled flutter instability encountered in rotor blade assemblies of axial-flow 
fans and compressors typically takes the form of a cascade induced single mode 
blade-to-blade interaction flutter where both bending and torsion components in the 
blade vibration mode, and their relative size, play an important role. This is in 
contrast to the classical aeroelastic bending/torsion coalescence flutter of an isolated 
wing in which two or more vibration modes are involved.
In general, the blade-to-blade flutter mode is characterized by a travelling wave 
pattern of the blade row in which all blades oscillate harmonically with the same

mode shape and frequency but with a certain (constant) phase shift relative to each 
other. The origin of the interblade phase difference is the motion-induced unsteady 
aerodynamic forces which depend on individual blade motion history and the motion 
history of neighbouring blades. For N blades there are N possible interblade phase 
angles dn = iTtnfN, n = 0,l,N-1.
While the assumption that the flutter mode shape coincides with a (single) vibration 
mode of the rotor is generally unreliable, particularly in the practical range of reduced 
frequencies, the error in this assumption decreases with increasing kinematic coupling 
in bending and torsion. Moreover, as the mass ratio of a solid metallic fan or 
compressor blade is generally large, both the flutter frequency and the corresponding 
flutter mode remain relatively unaffected by the aerodynamic loading. In practice, the 
flutter mode shape is usually (but not necessarily) associated with the lowest natural 
frequency blade vibration mode. However, within the practical range of design 
parameters and kinematic coupling, experimental evidence suggests that both 
torsional and bending branches can exhibit instability.
Figure 2.2 illustrates the essentially single mode flutter characteristics of typical blade 
assembly. The schematic is derived from a two-mode flutter analysis based on the 
first bending and first torsional modes. The relative frequency is defined as to/£Or 
and the reduced velocity as VlbcoT. Here, the critical mode is associated with first 
torsional vibration mode.
torsion
damping in bending
damping in torsion
bending
-ve
Q.
u
3
3*
(Q
+ve
reduced velocity —►
Fig. 2.2
Assessment of the aeroelastic stability characteristics of a blade assembly is generally 
achieved through calculation of the neutral stability boundaries for a range of design 
and operating parameters (for example, mass ratio, structural damping, kinematic 
coupling, etc.). For preliminary design purposes, the blade assembly is assumed to be 
structurally tuned and the inlet flow velocity is assumed the same for all blades. For a 
tuned rotor subject to a single mode flutter, the concept of constant interblade phase 
angle implies that the travelling wave modes associated with Qn are the aeroelastic 
(flutter) eigenmodes.
At the critical stability condition, the motion is sinusoidal and the interblade phase 
angle is constant. As a result, evaluation of the unsteady aerodynamic forces is 
feasible. In general, the unsteady aerodynamic forces depend on reduced frequency

and interblade phase angle. Flutter occurs at those values of reduced frequency and 
assigned phase angle dn satisfying the flutter eigenvalue problem. From these values, 
the critical inlet velocity VF can be determined. Among all solutions VF for the given 
discrete values 6n, the minimum value of VF is the physically correct critical flutter 
velocity.
The qualitative effects of variation of the primary design and operating parameters on 
the flutter characteristics of a typical blade assembly can be ascertained from the 
resulting stability diagrams.
Mass Ratio and Structural Damping
In the absence of structural damping, the stability boundary is independent of mass 
ratio. However, if structural damping is present a rotor blade with a large mass ratio 
(such as a solid metallic blade) will be more stable (that is, possess a higher critical 
flutter speed) than a blade with a small mass ratio. For non-zero structural damping, 
the mass ratio determines the magnitude of the destabilizing aerodynamic effect 
which can be tolerated before the system becomes unstable. In general, the stabilizing 
effect of structural damping is more pronounced in the case of bending flutter than in 
torsion flutter. Also, the range of interblade phase angle at which flutter occurs is 
constricted by the stabilizing effect of structural damping.
Kinematic Coupling in Bending and Torsion
Kinematic coupling in bending and torsion plays a fundamental role in the aeroelastic 
coupling amongst oscillating blades. Important sources of kinematic coupling include 
blade pre-twist, centrifugal forces, and any offset between the blade inertial axis and 
elastic axis.
Figure 2.3 illustrates the influence of kinematic bending/torsion coupling on the 
critical flutter reduced velocity, VF/bcoT, under variation of the bending/torsion 
vibration mode frequency ratio 7ffl = coBlcoT (in this example, the blade elastic axis is 
located at the mid-chord). In the vicinity of vibration mode frequency coincidence, 
7^ = 1, the critical flutter velocity is dramatically reduced and is almost independent 
of kinematic coupling.
The frequency ratio for first bending/first torsion modes of fan blades typically is in 
the range 0.3-0.7. However, current technology fan blades have second bending and 
first torsional natural frequencies close together with frequency ratios in the range 
0.8-1.2. It is possible, therefore, that interactions between second bending and first 
torsional modes may be potentially hazardous. In addition, for blades with low mass 
ratio, aerodynamic mode coupling could lead to classical coalescence flutter.
increasing
kinematic
ccxipling
frequency ratio
Fig. 2.3
r
3. Conclusions
Based on the brief assessment provided in sections 1 and 2, the following conclusions
are made:
• The upstream flow into the fan will consist of a vortical wake generated from the 
motor housing. This wake will be three dimensional in nature but will consist 
predominantly of von Karman vortices in the plane of the cross-section. This 
unsteady flow has the potential to induce vibration in the fan blading and should 
be investigated further in association with the blading structural dynamic 
properties.
• An assessment of the propensity of the blade assembly to encounter stall flutter is 
required. In addition, the possibility of a potentially hazardous single mode 
unstalled flutter involving the second flap vibration mode and first torsional 
vibration mode requires further clarification due to the close proximity of the 
natural frequencies of these modes.
I





http://eprints.gla.ac.uk/185140/1/185140.pdf

A Brief Review of Unsteady Aerodynamic and Aeroelastic Phenomena of a Fan Installation. G. U. Aero Report no. 9719

Abstract

Similar works

Full text

Available Versions

Enlighten

Enlighten: Publications