R. Srivastava, M.A. Bakhle, and T.G. Keith, Jr.

University of Toledo, Toledo, Ohio

G.L. Stefko

Glenn Research Center, Cleveland, Ohio

Flutter Analysis of a Transonic Fan

NASA/TM—2002-211818

September 2002
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R. Srivastava, M.A. Bakhle, and T.G. Keith, Jr.

University of Toledo, Toledo, Ohio

G.L. Stefko

Glenn Research Center, Cleveland, Ohio

Flutter Analysis of a Transonic Fan

NASA/TM—2002-211818

September 2002

National Aeronautics and

Space Administration

Glenn Research Center
Available from

NASA Center for Aerospace Information

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Available electronically at http://gltrs.grc.nasa.gov

This work was performed under funding from the Quiet Aircraft Technology Project of NASA

Glenn Research Center. Joseph E. Grady is the project manager. The authors also wish to gratefully

acknowledge the assistance and suggestions provided by Joseph Panovsky of Honeywell Engines,

Systems, & Services, Brian Fite of NASA Glenn and John A. Gazzaniga of QSS Group, Inc.

Acknowledgments
NASA/TM2002-211818 1 

FLUTTER ANALYSIS OF A TRANSONIC FAN 

R. Srivastava,* M.A. Bakhle,* and T.G. Keith, Jr.

University of Toledo 

Toledo, Ohio 43606 

G.L. Stefko

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

ABSTRACT 

This paper describes the calculation of flutter stability 

characteristics for a transonic forward swept fan configuration 

using a viscous aeroelastic analysis program. Unsteady NavierStokes equations are solved on a dynamically deforming, body 

fitted, grid to obtain the aeroelastic characteristics using the 

energy exchange method. The non-zero inter-blade phase 

angle is modeled using phase-lagged boundary conditions. 

Results obtained show good correlation with measurements. It 

is found that the location of shock and variation of shock 

strength strongly influenced stability. Also, outboard stations 

primarily contributed to stability characteristics. Results 

demonstrate that changes in blade shape impact the calculated 

aerodynamic damping, indicating importance of using accurate 

blade operating shape under centrifugal and steady 

aerodynamic loading for flutter prediction. It was found that 

the calculated aerodynamic damping was relatively insensitive 

to variation in natural frequency. 

INTRODUCTION 

Reducing noise has become a significant criterion in the 

design of modern turbomachinery fans. For fans with 

supersonic tip speeds, shock waves play a significant role in the 

generation of noise. Aggressive blade designs with forward 

sweep and lean are being used to improve the noise 

characteristics. These geometric features coupled with the 

presence of shock wave can lead to flutter instability. Flutter 

problems, usually detected during the design phase, result in 

program delays and cost overruns, adversely impacting the 

development and maintenance costs. Numerical flutter 

prediction methods will help in achieving the design objectives 

and developing a flutter free design. 

Several methods have been developed for the prediction of 

aeroelastic characteristics of turbomachines with various 

degrees of fidelity. Aeroelastic analyses based on energy 

exchange between vibrating blades and the surrounding fluid, 

have been reported for turbomachines using semi-analytical 

methods (Lane and Friedman [1], Smith [2]), linearized 

methods (Hall and Clark [3], Verdon [4]), Euler methods (He 

[5], Gerolymos and Vallet [6], Bakhle, et al. [7]) and viscous 

methods (Giles and Haimes [8], Siden [9], He and Denton 

[10]). A limited number of coupled aeroelastic analyses of 

turbomachine configurations have also been reported [11–13]. 

Williams, Cho, and Dalton [11] used a linear panel method to 

solve the eigenvalue problem. Gerolymos [12] and Srivastava 

and Reddy [13] solved the coupled aeroelastic equations based 

on an inviscid aerodynamic analysis. The majority of the 

methods are either analytical, applicable to two-dimensional 

geometry and/or ignore the viscous effects. 

The modern fans being designed to reduce noise are swept 

forward as well as leaned in the plane of rotation. These 

features coupled with transonic flow result in aeroelastic 

problems. For turbomachinery blade rows, flutter is observed 

primarily in single natural mode. Single mode flutter can be 

captured using the energy exchange method, which calculates 

the flow of energy between the vibrating blade and the 

surrounding fluid. A three-dimensional viscous aeroelastic 

analysis code TURBO-AE, based on energy exchange method 

has been developed and reported in [14]. The objective of the 

present study is to investigate the stability of a forward swept 

transonic fan geometry. The transonic fan analyzed, showed 

flutter at part speed. The TURBO-AE code is applied to 

calculate the flutter observed in the wind tunnel and to 

understand the flow features that caused the instability. 

Modern fan blades, by virtue of having a small thickness 

ratio coupled with forward sweep could be highly flexible in 

the tip region. High rotational speed and large aerodynamic 

loading result in significant changes in blade shape. It is 

important to accurately account for these changes in the 

analysis. To investigate the sensitivity of damping calculations 

to changes in steady blade deflection, calculations are also 

carried out by deforming the blade at the tip to change the blade 

twist by 0.5 deg such that the incidence angle at the section is 

increased. Also, results are obtained to investigate the impact of 

time step used in the analysis and sensitivity to natural 

frequency variation. These studies are carried out to gain an 

understanding of issues that need to be addressed in flutter 

analyses of similar fan configurations. 

THE TURBO-AE CODE

The aeroelastic solver TURBO-AE is briefly described in 

this section. The solver can model multiple blade rows 

undergoing harmonic oscillations with arbitrary inter-blade 

phase angles (IBPAs). It is based on a Navier-Stokes unsteady 

aerodynamic solver for internal flow calculations of axial flow 

*NASA Resident Research Associate at Glenn Research Center. 
NASA/TM2002-211818 2 

turbomachinery components, TURBO [15,16]. Viscous effects 

are modeled using the Reynolds-averaged Navier-Stokes 

equations. The two-equation k-ε turbulence model is used for 

closure. The aerodynamic equations are solved using a finite 

volume scheme. Flux vector splitting is used to evaluate the 

flux Jacobians on the left-hand side. The right-hand side fluxes 

are discretized using the high order Total Variation 

Diminishing (TVD) scheme based on Roe's flux difference 

splitting. Newton subiterations are used at each time-step to 

maintain accuracy. Symmetric Gauss-Seidel iterations are 

applied to the discretized equations for improved convergence. 

The aeroelastic characteristics of the rotor are obtained by 

calculating the energy exchange between the vibrating blade 

and its surrounding fluid. Positive work on blade indicates 

instability. The aeroelastic analysis is performed by first 

obtaining the “steady” aerodynamic solution for a given 

operating condition. The blades are then forced into a 

prescribed harmonic motion (specified mode, frequency, and 

IBPA) to calculate the unsteady aerodynamic response and 

thereby work-per-cycle W, Eq. 1. 

W = −p.d A

→

surface

∫ ∫ • (

∂ X

→

∂t

) dt (1) 

Where, p is the surface pressure, 

G

A is the area of the blade 

surface and G

X is the blade displacement associated with the 

forced harmonic vibration. The work W is then used to 

calculate the aerodynamic damping γ, using the average kinetic 

energy KE of the blade over one vibration cycle [17], Eq. 2. 

γ = − W

8πKE

 (2) 

The blade motion is simulated using a dynamic grid 

deformation technique. Phase-lagged boundary conditions are 

used to calculate the non-zero IBPA vibrations, which 

eliminates the need to model multiple blade passages. 

RESULTS AND DISCUSSION

A scale model of an experimental transonic fan with 22 

blades (Fig. 1) was tested in a rig. The design operating 

condition for the model tested was mass flow of 98.89 lbs/s 

with a relative tip Mach number of 1.4. The fan fluttered at part 

speed in the first natural mode [18], between the operating line 

and predicted stall line. The first natural mode is shown in 

Fig. 2, hotter colors signifying larger displacements. The mode 

shows a high degree of twist bend coupling, especially in the 

outboard section.. 

The results are presented here for 90 percent rotational 

speed. A grid with approximately 213,000 grid points per blade 

passage, 46 axial by 47 radial points on each surface, and a 

uniform tip-gap is used in the analysis. The blade shape and 

modal properties for 100 percent speed are used. 

Figure 3 shows the steady aerodynamic loading on the 

blade surfaces for 90 percent speed at a condition near the 

operating line. Shock wave structures are clearly evident from 

these figures. An oblique shock appears near the leading edge 

on the suction surface over the entire span. A normal shock 

extends across the blade passage in the aft section of the blade 

 

Figure 1. Transonic fan 

Figure 2. First natural mode 

on the suction surface. For the in-board sections, this shock is 

outside the blade passage (in front of blade leading edge) on the 

pressure surface side. However, the shock is completely 

ingested within the passage in the outboard sections of the 

blade. This shock pattern is typical for a flow condition 

referred to as moderate to high loading for blades with a 

supersonic leading edge operating in subsonic axial flow. As 

the back pressure is increased, moving the operation point 

towards the stall line, the shock moves forward and becomes 

stronger. This results in flow separation on the suction surface 

in the middle section of the blade. The separation is large 

enough to stall the blade resulting in a break down of the 

numerical analysis. The observed breakdown of the analysis 

due to flow separation could not be verified, as velocity profiles 

were not measured during the experiment. 
NASA/TM2002-211818 3 

Figure 3. Steady blade surface pressure near operating line for 

90 percent speed 

Dynamic Analysis

Experiments showed blade flutter in the first natural mode, 

Fig. 2, (natural frequency 351 Hz) for 32.73 deg IBPA (2 Nodal 

Diameter forward traveling wave) [18]. To establish the least 

stable mode the analysis was carried out for several pressure 

ratios and IBPAs. 

Flow separation for higher back pressures was observed in 

the hub region of the blade resulting in unsteadiness of the 

mean flow. Because of the mean flow unsteadiness, one needs 

to ensure that the blade vibration amplitude is large enough so 

as to minimize the impact of mean flow unsteadiness on the 

unsteadiness due to blade vibrations, yet should be small 

enough to maintain linearity. The calculated time history of 

mass flow is shown in Fig. 4 for flow with and without blade 

vibration for a back pressure of 16.2 pounds per square inch 

(psi). The blade is forced into vibration at 180 deg IBPA and 

351 Hz. It can be seen from Fig. 4 that for the vibration 

amplitude chosen for the analysis, the unsteadiness due to blade 

vibration is at least an order of magnitude larger than the mean 

flow unsteadiness. It can also be seen that the flow converges to 

periodicity in roughly 10 oscillations. 

Figure 4. Variation of mass flow for the transonic fan, with and 

without blade vibration 

Figure 5 shows the aerodynamic damping calculated for 

several different back pressures and IBPAs. For lower back 

pressures, the least stable IBPA was found to be 0 deg. 

However, as the back pressure was raised moving the fan 

operating condition towards the stall line, the 32.73 deg IBPA 

(2 nodal diameter forward traveling wave) became the least 

stable. Flutter was observed in the wind tunnel for 32.73 deg 

IBPA. 

Figure 5. Variation of aerodynamic damping with back 

pressure and IBPA for the transonic fan 

The calculated variation of aerodynamic damping with 

back pressure is shown in Fig. 6 at 32.73 deg IBPA. As may be 

seen in the figure, as the back pressure is increased, the 

aerodynamic damping decreases rapidly, dropping to 

approximately 0.2 percent of critical damping at a back 

pressure of 16.4 psi. Increasing the back pressure above 16.4 

psi for 90 percent speed resulted in stalled flow with large 

separation on the suction surface in the mid section of the 

blade. This separation was found to be shock induced and 

prevented a steady mean flow from which the blade vibration 

analysis could be carried out. These results indicate that the 

32.73 deg IBPA is the least stable IBPA for first natural mode, 

as observed in experiments, and that the aerodynamic damping 

rapidly decreases with increasing back pressure. 

From Fig. 6 it is evident that the characteristics of variation 

of aerodynamic damping changes significantly as the back 

pressure is varied. Initially the damping is not affected much 

by an increase in back pressure, at least up to the operating line, 

which falls close to a back pressure of 15.7 psi. Further 

increase of the back pressure results in a dramatic change in 

damping variation, becoming inversely proportional to 

variation in back pressure. To understand the reason for such a 

change, flow details were investigated for back pressure values 

of 15.2, 15.9 and 16.4 psi. Figure 7 shows the distribution of 

work on the blade surface. Majority of the blade shows little 
NASA/TM2002-211818 4 

Figure 6. Variation of aerodynamic damping for 16.4 PSI back 

pressure. Forced vibration in the first natural mode at 351 Hz 

and 32 deg IBPA 

contribution towards establishing the flutter characteristics of 

the blade. Outboard sections of the blade contribute most 

significantly. This has a side benefit from an analysis 

perspective. Resolving the flowfield on the inboard sections is 

probably not significant and hence coarse grid may be used in 

this region, concentrating more grids in the outboard sections of 

the blade. These figures also show that over certain areas on the 

Figure 7. Work distribution on blade surface for various back 

pressures 

blade positive work is being done on the blade indicating a 

destabilizing contribution. These plots, when superimposed 

with relative Mach number plots, indicate that the positive 

work regions are centered around the shock location. 

To investigate this in more detail, the pressure coefficient 

at 90 percent span, around the shock location on the suction 

surface, is plotted in Fig. 8 for the three back pressures. 

Instantaneous pressure coefficient at five instants of time over 

one period of oscillation is shown. The steady pressure 

coefficient is also shown to highlight the variation of shock 

strength from the mean position. It is clear that as the back 

pressure is increased the shock moves upstream. Also, the 

variation in the pressure change associated with the shock, 

changes significantly. It is these changes that contribute to 

positive work on the blade. These figures indicate that the 

location of shock and associated changes in strength are 

responsible for the change in characteristics of the variation of 

damping and are responsible for flutter. 

(a) back pressure 15.2 psi 

(b) back pressure 15.9 psi 

Work 
NASA/TM2002-211818 5 

(c) back pressure 16.4 psi 

Figure 8. Pressure coefficient variation over one period of 

oscillation cycle for back pressures of 15.2, 15.9, 16.4 psi 

The blade natural vibration frequency for a rotor is 

proportional to the rotational speed. Hence, for 90 percent 

speed the blade natural frequency would be lower than that at 

100 percent speed. To investigate the impact of change in 

frequency, a sensitivity study was carried out by varying the 

natural frequency. Calculations were performed for 20 percent 

higher as well as 20 percent lower natural frequency for 100 

percent speed at 32.73 deg IBPA. These changes in frequency 

resulted in changes of less than 0.1 percent of critical damping 

ratio, indicating a low sensitivity to natural frequency. It 

should be noted here that changes in rotational speed will also 

impact the mode shape, however, in the present study no 

attempt was made to alter the mode shape. 

Analysis was also performed at the second natural 

vibration mode, which was stable in the experiment. The 

aerodynamic damping calculated was much higher than those 

for the first mode, indicating the second mode to be more stable 

than the first mode. These results show that the analysis 

successfully calculates the natural mode and IBPA of instability 

identifying the flutter characteristics of the transonic fan. 

For the back pressure of 16.4 psi, the experiment showed 

flutter, whereas the analysis predicted the fan to be marginally 

stable. The analysis correctly predicted the least stable mode, 

however, it did not predict a negative aerodynamic damping. A 

possible reason for that was thought to be the use of an 

inaccurate operating blade shape. The analysis at the 90 percent 

speed was performed using the design speed geometry and 

characteristics. To investigate the influence of changes in blade 

shape on the aerodynamic damping, the analysis was carried 

out by altering the twist distribution, such that the blade twist 

changed from mid-span to tip varying linearly from zero 

change at mid span to 0.5 deg change at the tip. The change in 

twist distribution is such that it increases the incidence of the 

blade. Structural analysis showed the blade twist change at the 

tip to be of this order for the 90 percent speed. The variation in 

aerodynamic damping with oscillation cycles is shown in 

Fig. 9. The changes in twist reduce the damping moving it 

closer to instability. Earlier studies have shown smaller time 

steps to have moderate impact on the damping calculation, see 

Fig. 6. As the calculated damping is close to zero, the impact of 

smaller time steps was also investigated. Most of the analysis 

was carried out using 100 steps per oscillation cycle in order to 

minimize the computational cost. The computational cost 

varies linearly with the number of steps per cycle used in the 

analysis. Three different time steps were used, 100, 200 and 

300 steps per oscillation cycle. The impact of time step size is 

also shown in Fig. 9. From 100 steps per cycle to 200 steps per 

cycle there is a measurable change in damping. Whereas using 

300 steps per cycle the change is small and does not justify the 

additional computational cost. From this study it was decided 

that the 100 steps per cycle is good for investigating the trends 

of the behavior. For cases where a more accurate damping 

value is required, 200 steps per cycle should be used. Since the 

difference is approximately 0.2 percent of critical damping, use 

of smaller time steps will be significant only in the 

neighborhood of zero damping or flutter boundary. 

Figure 10 compares the steady pressure coefficient and 

work contributions from the suction and pressure surfaces at 

the 95 percent span location. The results for the original grid 

are (Fig. 10(a)) obtained using 100 steps per cycle, where as for 

the deformed grid the results (Fig. 10(b)) are for 200 steps per 

cycle. These comparisons are to understand the differences in 

calculated damping for the deformed shape. Primarily the 

Figure 9. Effect of time steps and change in twist distribution 

for a 0.5 deg change in twist at tip of the blade 
NASA/TM2002-211818 6 

suction surface contributes to the positive work whereas the 

pressure surface contributes to negative work providing a 

stabilizing influence. The area of positive work is centered 

around the normal shock on the suction surface. However, there 

are two main differences that are observed from these figures. 

First, we find that the shock on the suction surface has moved 

upstream by roughly 5 percent. In addition, the work 

(a) Original Geometry 

(b) Deformed geometry 

Figure 10. Pressure coefficient and work distribution at 

95 percent span 

contribution associated with this shock has also moved. Only 

minor changes in the level of work are observed. A second 

change, which is more significant from the work perspective, is 

seen on the pressure surface. The area of negative work in the 

leading edge region is reduced, and the peak is higher but 

narrower for the deformed shape. This change contributes 

mainly to a reduction in the damping for the deformed shape. 

The primary reason for this difference is the motion of the 

shock on the pressure surface. Figure 11 shows the steady 

pressure contours and Fig. 12 show the instantaneous pressure 

contours at five instants of time over the vibration cycle for 

steady and deformed geometry at 95 percent span. The steady 

contours show that a normal shock wave extends from the 

suction surface across the blade passage. For the original grid, 

the shock intersects the pressure surface at the leading edge, 

whereas for the deformed geometry the shock is just ahead of 

the leading edge. Figure 12 shows the shock movement over 

the oscillation cycle for the two geometries considered here. 

Instantaneous pressure contours near the pressure surface 

leading edge are shown for five time instants over one cycle of 

vibration. For ease of comparison, these contours are plotted 

next to each other going from left to right with increasing time. 

The pressure surface, leading edge, and time instants 

corresponding to the contour are marked on the figures. From 

Fig. 12 a it can be seen that the shock stays on the blade surface 

for the original geometry, whereas for the deformed geometry 

(Fig. 12 b), the shock intersects the blade for part of the 

vibration cycle, moving on and off the blade surface over the 

oscillation cycle. This shock motion on and off the blade 

 Original geometry Deformed geometry 

Figure 11. Pressure contours for 16.4 psi at 95 percent span 
NASA/TM2002-211818 7 

surface is the reason for differences in work contribution on the 

pressure surface between the two geometries. The effect of this 

motion is to reduce the overall stabilizing effect from the

pressure surface, reducing the aerodynamic damping for the 

deformed geometry. 

(a) Original geometry 

(b) Deformed geometry 

Figure 12. Instantaneous pressure contours over one vibration 

cycle with time period T, near pressure surface leading edge at 

95 percent span for back pressure of 16.4 psi 

Approximately 95 Mega Words of computer memory and 

one hour of computational time per 100 steps was required on 

the Cray C-90 computer located at the NAS facility of NASA. 

CONCLUDING REMARKS

An aeroelastic analysis program based on the NavierStokes equation has been used to calculate the flutter 

characteristics and to investigate the behavior of aerodynamic 

damping variation for a forward swept transonic fan geometry. 

Calculated variations of aerodynamic damping with back 

pressure and IBPA is presented for a condition where flutter 

occurred during testing. Although a negative aerodynamic 

damping was not calculated, the analysis yielded some good 

results and trends. The analysis correctly predicted the mode 

and IBPA of flutter. Also, the trend for calculated aerodynamic 

damping clearly indicated a negative aerodynamic damping 

would result with further increasing the back pressure. 

Unfortunately, the analysis showed that a stalled flow field 

would emerge for any further increase of the back pressure. 

Although flow separation was captured along with vortex 

shedding, deep blade stall posed a numerical problem. Results 

also showed that a majority of the blade surface does not 

contribute towards the stability characteristics. But the 

stabilizing and destabilizing effects were concentrated near the 

shock location and were restricted to outboard stations of the 

blade. 

Detailed examination of the flow features indicated that 

normal shock on suction surface has a destabilizing effect and 

results in a large area of positive work centered around the 

normal shock. The area of the destabilizing effects depended 

on the location of the shock. Higher back pressure moved the 

normal shock forward increasing the area of positive work. 

This coupled with the mode shape resulted in an increased 

variation of the blade surface pressure over one oscillation 

cycle causing the destabilizing influence to increase. 

A study was also performed to understand the effect of 

various parameters on the calculation of aerodynamic damping. 

The study showed that the aerodynamic damping was 

insensitive to the variations in vibration frequency. However, it 

should be noted that only the frequency was altered without 

altering the mode shape. It was also found that the blade shape 

under operating conditions is important. A small change of 0.5 

deg in twist at the blade tip led to a better correlation of 

damping with measurements, where the original shape had 

predicted marginal positive damping. Changes in blade shape, 

although moved the suction surface shock further upstream in 

the outboard sections, do not measurably change the level of 

positive work. On the other hand, the negative work on 

pressure surface was reduced in the front section of the blade 

reducing the overall blade stability, resulting in better 

correlation with measurements. Thus it is important to use the 

correct shape in the analysis for more accurate calculation of 

damping, especially near the flutter boundary. 

Changes in time step for unsteady analysis were found to 

have a moderate impact. Although the trends did not change, 

the smaller time step reduced the aerodynamic damping. 

However, these differences would be of significance for 

damping calculations only in the vicinity of neutral stability. 

T/5 

2T/5 

3T/5 

4T/5 

T 

T/5 

2T/5 

3T/5 

4T/5 

T 

Pressure 

surface 

Blade 

leading edge 

Blade 

leading edge Pressure 

surface 
NASA/TM2002-211818 8 

From these studies the following conclusions can be drawn 

that could be useful in similar analyses: 

(a) Shock location and its strength have a strong influence 

on blade stability 

(b) In-board sections of the blade do not contribute 

towards establishing the stability characteristics, thus a 

coarser grid in this region can be used to reduce 

computational cost. 

(c) Accurate blade operating shape is important for 

accurate damping prediction as it establishes the shock 

structure on the blade, which in turn affects the 

stability. Variations in vibration frequency were found 

to be less significant. 

(d) Larger time steps can be used away from the neutral 

stability region for determining the trends, however, 

close to neutral stability; smaller time steps need to be 

used for accurate stability predictions. 

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Subsonic Oscillating Blade-row Aerodynamics,” NACA 

TN 4136, 1958. 

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[3] Hall, K.C., Clark, W.S., “Linearized Euler Predictions 

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[5] He, L., “An Euler Solution for Unsteady Flows Around 

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[13] Srivastava, R., and Reddy, T.S.R., “Comparative Study 

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University, Mississippi, 1989. 

[17] Carta, F.O., “Coupled Blade-Disk-Shroud Flutter 

Instabilities in Turbojet Engine Rotors,” Journal of 

Engineering for Power, July 1967, pp. 419–426. 

[18] Fite, B.E., Private Communications, NASA Glenn 

Research Center, January, 2001. 
This publication is available from the NASA Center for AeroSpace Information, 301–621–0390.

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14

Flutter Analysis of a Transonic Fan

R. Srivastava, M.A. Bakhle, T.G. Keith, Jr., and G.L. Stefko

Aeroelasticity; Turbomachine; Fan; Viscous; Numerical

Unclassified -Unlimited

Subject Category: 07 Distribution: Nonstandard

Prepared for the Turbo Expo 2002 cosponsored by the American Society of Mechanical Engineers and the International

Gas Turbine Institute, Amsterdam, The Netherlands, June 3–6, 2002. Portions of this material were presented at the

meeting. R. Srivastava, M.A. Bakhle, and T.G. Keith, Jr., University of Toledo, Toledo, Ohio; and G.L. Stefko, NASA

Glenn Research Center. R. Srivastava and M.A. Bakhle, NASA Resident Research Associates at Glenn Research Center.

Responsible person, R. Srivastava, organization code 5930, 216–433–6045.

This paper describes the calculation of flutter stability characteristics for a transonic forward swept fan configuration

using a viscous aeroelastic analysis program. Unsteady Navier-Stokes equations are solved on a dynamically deforming,

body fitted, grid to obtain the aeroelastic characteristics using the energy exchange method. The non-zero inter-blade

phase angle is modeled using phase-lagged boundary conditions. Results obtained show good correlation with measurements. It is found that the location of shock and variation of shock strength strongly influenced stability. Also, outboard

stations primarily contributed to stability characteristics. Results demonstrate that changes in blade shape impact the

calculated aerodynamic damping, indicating importance of using accurate blade operating shape under centrifugal and

steady aerodynamic loading for flutter prediction. It was found that the calculated aerodynamic damping was relatively

insensitive to variation in natural frequency.