April 2009 

NASA/TM-2009-215708 

Flutter Sensitivity to Boundary Layer 

Thickness, Structural Damping, and Static 

Pressure Differential for a Shuttle Tile Overlay 

Repair Concept 

Robert C. Scott and Robert E. Bartels 

Langley Research Center, Hampton, Virginia 
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April 2009 

NASA/TM-2009-215708 

Flutter Sensitivity to Boundary Layer 

Thickness, Structural Damping, and Static 

Pressure Differential for a Shuttle Tile Overlay 

Repair Concept 

Robert C. Scott and Robert E. Bartels 

Langley Research Center, Hampton, Virginia 
Available from: 

NASA Center for AeroSpace Information 

7115 Standard Drive 

Hanover, MD 21076-1320 

443-757-5802 

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National Aeronautics and Space Administration. 
Abstract

This paper examines the aeroelastic stability of an on-orbit installable Space Shuttle patch

panel. CFD flutter solutions were obtained for thick and thin boundary layers at a free

stream Mach number of 2.0 and several Mach numbers near sonic speed. The effect of

structural damping on these flutter solutions was also examined, and the effect of structural

nonlinearities associated with in-plane forces in the panel was considered on the worst case

linear flutter solution. The results of the study indicated that adequate flutter margins exist

for the panel at the Mach numbers examined. The addition of structural damping improved

flutter margins as did the inclusion of nonlinear effects associated with a static pressure

difference across the panel.

1
Contents

1 Introduction 3

2 Structural Model and Analysis 3

3 Aeroelastic Analyses for a Linear Structure 4

3.1 Steady-State Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.2 Aeroelastic Analyses, Zero Structural Damping . . . . . . . . . . . . . . . . . 8

3.3 Aeroelastic Analyses, Nonzero Structural Damping . . . . . . . . . . . . . . . 13

4 Aeroelastic Analyses with Static Nonlinear Structural Effects 13

4.1 Nonlinear Structural Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4.2 Static Aeroelastic Analysis With Nonlinear Structure . . . . . . . . . . . . . . 15

4.3 Dynamic Aeroelastic Analysis with Nonlinear Structure . . . . . . . . . . . . 16

5 Concluding Remarks 21

2
1 Introduction

An on-orbit installable Space Shuttle patch panel was developed at the NASA Johnson Space

Center to be used in the event of damage to the thermal protection system tiles to enable

safe re-entry. It consists of a thin flexible carbon fiber reinforced silicon carbide (C/SiC)

plate backed with a layer of fibrous insulation that covers the area of damaged tile. The

plate and underlying gasket are secured to the tile with auger-like fasteners through holes

at discreet locations around the perimeter of the plate. As part of the development effort,

a series of panel flutter analyses were performed to determine whether the concept met the

required safety margins for the onset of flutter. These analyses indicated that at Mach

numbers of 2.0 and higher, adequate panel flutter margins existed within the shuttle flight

envelope. However, near Mach 1.0 empirical flutter analysis using the criteria described in

reference 1 yielded inadequate flutter margins.

To address the concerns regarding flutter margins, flutter analyses were performed using

CFL3D [2] where both inviscid (Euler) and viscous (Navier-Stokes) terms were used [3]. The

inviscid analyses indicated that panel flutter onset would occur at lower dynamic pressures

than had been predicted by the linear and empirical solutions; yet, the bottom line results

were the same with sufficient flutter margin still remaining at Mach 2 and inadequate flutter

margin when near Mach 1.0. The viscous flutter analysis for Mach 2.0 was consistent with

the inviscid solution. The viscous flutter analyses near Mach 1.0 indicated that the flutter

onset dynamic pressure when viscosity is included was, in fact, well outside the shuttle flight

envelope. For this study, the free stream Mach number and boundary layers for the two

Mach numbers examined were adjusted to roughly correspond to boundary layer profiles at

body point 1800 calculated with OVERFLOW [4]. Body point 1800 is located on the lower

surface at 80% of the vehicle length, on centerline.

The purpose of the present paper is to describe a follow-on study where the effects

of boundary layer thickness were examined in a more general sense. Specifically, flutter

solutions were obtained for thick and thin boundary layers at a free stream Mach number

of 2.0 and several Mach numbers near sonic speed. In addition, the effects of structural

damping were also considered as well as structural nonlinearities associated with in-plane

forces in the panel.

2 Structural Model and Analysis

The overlay panel is constructed of a C/SiC composite material and is 15 inches wide by 25

inches long with a thickness of 0.04 inches. A series of holes is placed along the perimeter of

the plate to accept the auger and washer fasteners that attach the overlay panel to Shuttle

tile. For the structural analysis, material corresponding to the holes was not removed from

the finite element model. The material properties used for the C/SiC material were taken

from experimental data obtained for a 0.13-inch thick plate of similar construction [5]. C/SiC

is a nonlinear material in the sense that the stress-strain curves for the material are linear

only for small strain. Additionally, the stress-strain behavior is different for compressive and

tensile loading. The linear structural analysis for vibration modes assumed an orthotropic

material with a modulus that is the average of the moduli obtained from compression and

tension tests at 2,000◦F given in reference 5.

The NASTRAN [6] finite element model of the installed overlay plate is shown in Figure 1. The locations of the fasteners are indicated by the nodes where all degrees of freedom are constrained. The model consists of 26,529 nodes with a combination of CQUAD4

elements and CTRIA3 elements. The tile and gasket are not modeled and the structural

damping is zero. An MSC.NASTRAN SOL 103, normal modes analysis was performed with

the first 25 modes having frequencies between 64 and 670 Hz as shown in Table 1. Modes

3
X

Y

 123456

 123456

 123456

 123456

 123456

 123456

 123456

 123456 123456 123456 123456 123456 123456 123456 123456 123456 123456

 123456 123456

 123456 123456

 123456 123456

 123456 123456

 123456 123456 123456 123456 123456 123456 123456 123456 123456

X

Y

Figure 1. Installed overlay panel finite element mesh consisting of 26,529 nodes. The

symbols and numbers on the mesh indicate the constrained degrees of freedom for the 34

nodes representing the fastener locations.

1 through 4 are shown in Figure 2. Additional details of the structural analysis including a

mesh convergence study and comparison of free-vibration analysis with experimental data

are described in reference [3].

3 Aeroelastic Analyses for a Linear Structure

The CFD code CFL3Dv6.4 [2, 7] was used for the flutter analysis. The CFL3D code solves

the time-dependent conservation law form of the Reynolds-averaged Navier-Stokes equations

using a finite-volume approach. Upwind-biasing is used for the convective and pressure terms

while central differencing is used for the shear stress and heat transfer terms. Implicit time

advancement is used with the ability to solve steady or unsteady flows. Sub-iteration and

multigrid capabilities are available for improved accuracy and convergence acceleration.

The typical procedure for CFL3D flutter analysis is to initially obtain a static aeroelastic

solution prior to running a solution to determine dynamic stability [7]. The static solution

is obtained by using artificially large values of damping ratio in the analysis, and CFL3D is

run until in it converges, establishing the static aeroelastic solution and associated flow field.

Next, the dynamic analysis is performed. The damping ratio is set to a realistic value and the

generalized coordinates are given small initial velocities. The analysis is run until dynamic

aeroelastic stability can be established: if the generalized coordinate values converge to a

finite value then the system is stable; but if they grow with time, then the system is unstable.

For each free-stream flow condition of interest, flutter onset is determined by varying the

dynamic pressure until the system becomes unstable.

Free stream temperature, velocity, and density (used in the dynamic pressure calculation)

were interpolated based on Mach number from the ISSHVFW Shuttle trajectory. Reynolds

numbers were estimated using standard atmosphere properties [8] for the interpolated altitude associated with the target Mach numbers. Note that for steady (non-aeroelastic)

4
Table 1. Modal frequencies from NASTRAN SOL 103, normal modes analysis.

Mode Frequency Frequency

rad/sec Hz

1 405.4 64.5

2 580.5 92.4

3 886.8 141.1

4 1044.6 166.2

5 1212.5 193.0

6 1318.8 209.9

7 1502.8 239.2

8 1871.0 297.8

9 1918.8 305.4

10 2023.1 322.0

11 2192.4 348.9

12 2457.7 391.2

13 2480.6 394.8

14 2539.8 404.2

15 2889.4 459.9

16 3117.0 496.1

17 3320.7 528.5

18 3333.2 530.5

19 3420.4 544.4

20 3505.6 557.9

21 3793.5 603.8

22 3890.9 619.3

23 4067.8 647.4

24 4201.6 668.7

25 4215.0 670.8

(a) Normal mode 1. (b) Normal mode 2.

(c) Normal mode 3. (d) Normal mode 4.

Figure 2. Vertical displacement of the first four normal modes of overlay panel obtained

using NASTRAN SOL 103. For each mode, red indicates maximum z values and blue

represents minimum z values.

5
Y X

Z

Figure 3. Computational grid used in viscous panel flutter analysis. Red lines denote block

boundaries.

analyses, only free stream Mach number, Reynolds number, and temperature are required.

Aeroelastic analyses require the selection of a velocity and dynamic pressure.

In the previous study [3] two separate computational grids were generated for the two

free stream Mach numbers considered. These meshes extended the upstream boundary of

the plate by 415 and 860 inches, respectively. The intent of that study was to match the

boundary layer profile from an OVERFLOW analysis of the shuttle at body point 1800.

For this study, a new, single computational grid was used, and the boundary conditions

were adjusted to control boundary layer thickness. For the thick boundary layer, the no-slip

boundary condition started 803.26 inches upstream of the panel, and for the thin boundary

layer, the no-slip boundary condition started 35.15 inches upstream of the panel.

Figure 3 shows the volume grid used in the analysis where the computational grid dimensions in the x, y and z directions are 249, 97, and 65, respectively. To run these jobs

on multiprocessor systems, the grid was split into 24 blocks whose boundaries are denoted

by the red lines, and the block index dimensions along with the boundary conditions were

selected to be multigridable to at least two coarser levels. Figure 4 shows the entire surface

grid, as well as a close-up of the surface grid in the vicinity of the overlay plate. The upstream boundary of the grid is x=-1,264.8 inches and the downstream boundary is x=256.81

inches. The lateral limits are y=-207.2 and y=220.2, and the vertical limit is z=1,036.21

6
X

Y

-1000 -500 0

-200

-100

0

100

200

(a) Surface grid, red lines denote block boundaries.

X

Y

-40 -30 -20 -100 10 20

-10

0

10

20

(b) Surface grid, overlay plate region.

Figure 4. Surface grid used in viscous panel flutter analysis.

7
inches. Note that in this computational space, the overlay panel occupies the space between

-2.44 inches and 25.56 inches in the x-direction and -0.97 and 14.03 inches in the y-direction.

3.1 Steady-State Analyses

The first step in an aeroelastic analysis is to obtain a converged steady-state solution where

the structure is treated as rigid. For these solutions, local time stepping was employed

with a CFL number of 2.0. In all cases multigrid was used with two coarser meshes and

the finest mesh, described above. The Spalart-Allmaras turbulence model was used in each

analysis. The steady-state solutions were deemed sufficiently converged for the purposes

of the subsequent aeroelastic analysis when the residual had been reduced by at least 4.5

orders of magnitude. Ten steady-state solutions were obtained using the Mach numbers,

Reynolds numbers, and temperatures interpolated from the ISSHVFW Shuttle trajectory

and the boundary conditions associated with the thick and thin boundary layer solutions.

For these ten steady-state solutions, the y+ values at the first grid point off the surface

ranged from between 0.54 and 1.34.

The local Mach numbers at the centerline, leading edge of the overlay plate are shown

in Figure 5 for the thin and thick boundary layer cases. The thin boundary layers are on

the order of 2 inches thick and should be representative of a point near the leading edge of

the vehicle. The thin boundary layers contain about 35 grid points. The thick boundary

layers are on the order of 10 to 15 inches thick and should be representative of a point well

downstream of a wing leading edge or nose of the orbiter. Finally, it is observed that the

Mach 0.98 and 1.02 solutions yield nearly identical flow in the vicinity of the panel. As such,

the Mach 1.02 solution was not considered in the aeroelastic analyses.

3.2 Aeroelastic Analyses, Zero Structural Damping

Static and dynamic aeroelastic analyses are performed using an appropriate steady-state

solution as the starting point. For aeroelastic analysis, additional input parameters are

required in the input deck. These parameters include the free stream velocity and dynamic

pressure, as well as, the modal frequencies noted in Table 1. In addition, a file containing

the mode shape displacements for the computational surface mesh must also reside in the

CFL3D working directory.

In the present study, the method described in reference 9 was employed for generating

the CFL3D modal input file (aesurf.dat). The codes based on this paper calculate a spline

interpolation of the NASTRAN mode shapes (.f06 file) to the surface mesh shown show in

Figure 2. Figure 6 shows the computational mesh displacements associated with normal

modes 1 and 2. Here, it is evident that the modal displacements in the computational

mesh were extrapolated to a rectangular shape defined by the maximum length and width

of the plate instead of having the rounded corners of the original NASTRAN model. This

approximation was necessary because of a limitation in the code of reference 9, but it should

have minimal effect on the solution. Due to limited resources available for this study, the

thickness of the plate (0.04 inches) was not modeled in the computational mesh. Finally,

it should be pointed out that when modal displacements are displayed they are greatly

exaggerated from the actual physical displacements. The edge displacements shown in the

figure are physically meaningful, but the actual displacements are quite small, generally

much less than 10% of the panel thickness.

The general procedure was to perform a sequence of two CFL3D runs. The first, a static

aeroelastic run, used a damping ratio for all modes of 0.999 and zero initial modal displacements and velocities. After 400 time steps, the static aeroelastic solution was sufficiently

converged, and a second, dynamic, CFLD3D run was performed using the restart file from

the first. For this dynamic run, structural damping is set to zero and and the initial modal

8
0 0.5 1.0 1.5 2.0 2.5

30

25

20

15

10

5

Z, inches

Local Mach Number

M∞ = 0.90

M∞ = 0.98

M∞ = 1.02

M∞ = 1.10

M∞ = 2.00

(a) Thin Boundary Layer

0 0.5 1.0 1.5 2.0 2.5

30

25

20

15

10

5

Z, inches

Local Mach Number

M∞ = 0.90

M∞ = 0.98

M∞ = 1.02

M∞ = 1.10

M∞ = 2.00

(b) Thick Boundary Layer

Figure 5. Boundary layers at overlay panel leading edge calculated using CFL3D.

9
velocities are given nonzero values. Dynamic aeroelastic stability is determined by observing whether the modal amplitudes grow or decay with time. Figure 7 shows the generalized

coordinate time histories of the first four modes for stable and unstable values of dynamic

pressure. The data shown to the left of the vertical line represents the static aeroelastic run

where a large damping value is used. The data to the right of the vertical bar is obtained

from a subsequent analysis where damping is set to zero and the generalized coordinates

are give a small initial velocity.

The strategy for determining flutter onset that was employed in this study was to vary

free stream dynamic pressure while holding all other input parameters constant. Essentially,

this amounts to varying the free stream density. Strictly speaking, the flutter solutions obtained in this way aren’t matched point solutions. However, for the purposes of assessing

flutter margins, this approach was deemed adequate. By varying free stream dynamic pressure and examining the generalized coordinate time histories like those shown in Figure 7,

the stability characteristics for the thick and thin boundary layer cases were obtained. Exact values of flutter onset dynamic pressure were not obtained as this is relatively time

consuming and would provide little value added to the objectives of this study. Instead,

the flutter onset dynamic pressure was shown to reside in a relatively narrow range of free

stream dynamic pressure.

The zero damping ratio flutter results are shown in Table 2. Examination of these

data indicate that the effect of boundary layer thickness is most pronounced near sonic

speeds. Thicker boundary layers had a stabilizing effect on the plate at Mach numbers 1.10

and 0.98. At supersonic and subsonic Mach numbers, the thick and thin boundary layers

yielded similar flutter dynamic pressures. Significant flutter margins in dynamic pressures

were obtained for all conditions except the Mach 1.1, thin boundary layer case. Here the

flutter margin in dynamic pressure is a little over 2.0.

Table 2. Summary of flutter onset range of normalized dynamic pressure (q/qnominal

∞ ).

M∞ Thick BL Thin BL

Stable Unstable Stable Unstable

2.00 4.5 5.0 4.5 5.0

1.10 6.0 6.5 2.0 2.5

0.98 5.5 6.0 3.5 4.0

0.90 4.0 4.5 4.0 4.5

In Table 3 the results of the present study are compared with those from reference 3.

Here, dimensional dynamic pressure is shown for cases where comparable results were previously generated. In the previous study, the viscous flutter onset value was obtained with a

boundary layer that is similar, but not identical to the thick boundary layer used here. The

two studies are quite consistent with each other with regard to general trends and actual

flutter onset dynamic pressures. Both studies show an insensitivity to boundary layer thickness at supersonic Mach numbers. This is indicated by the fact that the Mach 2.0 flutter

dynamic pressure ranges are the same for the thick and thin boundary layers, and similarly

for the Mach 1.75 analyses from reference 3, the fluter onset values are nearly identical for

the viscous and inviscid cases. For Mach 1.1, the thick boundary layer result is very consistent with the previous viscous flutter onset value. For the Mach 1.1 thin boundary layer

analysis, a significant drop in flutter dynamic pressure is noted as compared with the thick

boundary layer case. This trend is consistent with the previous study where the inviscid

flutter onset value was much lower than its viscous counterpart.

Before proceeding with additional aeroelastic analysis, a few words about the actual

physical displacement of the overlay panel is warranted. When working with a modal rep10
(a) Mode 1.

(b) Mode 2.

Figure 6. Normal modes 1 and 2 interpolated to the CFD surface grid. For each mode, red

indicates maximum z values and blue represents minimum z values.

Table 3. Comparison of dynamic pressures (psf) with those from reference 3.

M∞ Present Study Previous Study (Flutter Onset)

Thick BL Thin BL CFL3D Piston Theory∗

Stable Unstable Stable Unstable Viscous Inviscid or Empirical∗∗

2.00 1,177 1,307 1,177 1,307 1,352∗

1.75 850 890

1.10 1,083 1,173 361 451 1,050 275 375∗∗

11
0

1

2

x 10−3

−5

0

5

x 10−4

−2

−1

0

x 10−4

0 200 400 600 800 1000 1200

−2

0

2

x 10−5

t, nondimensional

q

1

2

3

4

q

q

q

Static AE Solution

damping = 0.999

Dynamic AE Solution

damping = 0.0

(a) q∞ = 2.0q

nominal ∞ .

−0.01

0

0.01

−5

0

5

x 10−3

−2

0

2

x 10−3

0 200 400 600 800 1000 1200

−2

0

2

x 10−5

q

1

2

3

4

q

q

q

t, nondimensional

Static AE Solution

damping = 0.999

Dynamac AE Solution

damping = 0.0

(b) q∞ = 2.5q

nominal ∞ .

Figure 7. Generalized coordinate time histories for Mach 1.10, thin boundary layer, for

stable and unstable values of dynamic pressure. Flutter frequency = 68 Hz.

12
resentation of a structure, the net displacement of any point on that structure is a sum of

the generalized coordinates times their respective mode shape displacement at that point.

In the case of panel flutter, the static and dynamic displacement is governed largely by

the first few modes especially modes 1 and 2. For the panel examined here, the maximum, normalized modal displacement is approximately 48 and 46, respectively for modes 1

and 2. Thus, the maximum panel displacement can be approximated by the summation the

generalized coordinates for modes 1 and 2 times these modal displacements. Examination

of the static aeroelastic solutions associated with the nominal dynamic pressures yields a

maximum static panel displacement of approximately 0.05 inches. For the elevated values

of dynamic pressure where flutter was obtained, maximum static panel deflections of up to

0.5 inches were obtained. The dynamic component for aeroelastically stable analyses was

generally on the order of 0.05 inches or less. For the unstable cases where the amplitudes

were diverging, the dynamic component was a function of the length of the simulation. In

all dynamic analyses, any nonlinearities in the aerodynamics were fully captured, but structural nonlinearities were not. Panel flutter tends to result in a limit cycle due to structural

nonlinearities, but this feature can not be captured in the analyses contained herein.

3.3 Aeroelastic Analyses, Nonzero Structural Damping

The procedure for this analysis is exactly the same as previously described except that the

CFL3D analysis where stability is determined is run with nonzero values for damping ratio.

The strategy employed here was to take the unstable dynamic pressure for each case in

Table 2 and examine what value of damping is necessary to yield a stable or neutrally stable

result. The results shown in Table 4 indicate a general trend where lower Mach number

cases are more sensitive to damping than higher Mach number cases. The low Mach number

cases were stabilized by a relatively modest, 2% damping. The supersonic cases in three

out of four cases, were not stabilized by the addition of 10% damping. It should be pointed

out that since the exact flutter onset values are not known, it is unclear how far from

neutral stability these unstable cases were. Thus, the trend noted above remains tentative.

Nonetheless, these analyses have shown that structural damping does have a stabilizing

effect on flutter and provides some guidance on the level of damping required to have an

effect.

Table 4. Structural damping effects on panel stability.

M∞ Thick BL Thin BL

q/qnominal

∞ damping Stability q/qnominal∞ damping Stability

2.00 5.0 0.10 unstable 5.0 0.10 unstable

1.10 6.5 0.05 stable 2.5 0.10 unstable

0.98 6.0 0.02 neutral/stable 4.0 0.02 neutral/stable

0.90 4.5 0.02 stable 4.5 0.02 stable

4 Aeroelastic Analyses with Static Nonlinear Structural

Effects

For panel structures, in-plane tension forces are stiffening terms, and if the tension forces are

constant, a linear problem results. However, when out-of-plane forces are applied to a panel

that is restrained at its edges, the tension and, as a result, the stiffness are both functions

of the out-of-plane deformation. This results in a nonlinear problem. In this section of the

13
Figure 8. Overlay panel deflection due to a static pressure difference across the panel of 0.1

psi obtained using NASTRAN SOL 106.

paper, the static effects of the out-of-plane pressure forces and deformations on the Shuttle

overlay panel will be considered for the previously examined Mach 1.10, thin boundary layer

case. This was the case that showed the lowest flutter margin and was thus selected for

this assessment. It should also be pointed out that only positive pressure differences were

considered where the panel was deformed outward. Negative values would tend to suck the

panel against the shuttles tiles and hole filler material making the panel unlikely to flutter,

or at the very least, require a fully nonlinear flutter analysis that is far beyond the scope of

the present study.

The following subsections will describe and demonstrate the various elements of the

aeroelastic analysis with static nonlinear effects. First, NASTRAN will be used to show the

effects of static pressure difference on the natural frequencies of the overlay panel. Next, a

procedure that loosely couples NASTRAN and CFL3D to obtain a static aeroelastic solution

will be shown. Finally, a method for utilizing the preceding analysis procedures for dynamic

aeroelastic analysis will be shown and demonstrated for the Mach 1.10, thin boundary layer

case.

4.1 Nonlinear Structural Analysis

This type of static nonlinear problem can be solved using NASTRAN SOL 106. This solution

procedure essentially performs a series of linear analyses where the load is incrementally

increased to the desired level. As these iterations proceed, the stiffness matrix is updated to

include the stiffening effects of in-plane tension. This process is repeated within NASTRAN

until the solution converges. Figure 8 shows the results of a static nonlinear analysis where

the static pressure difference across the panel is 0.1 psi.

14
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Static Pressure Difference Across Panel, psi

Modal Frequency, Hz.

600

500

400

300

200

100

Mode 1

Mode 2

Mode 3

Mode 4

Mode 5

Mode 6

Mode 7

Mode 8

Mode 9

Mode 10

Figure 9. Natural frequency variation with static pressure difference across panel.

Using the method described in reference 10, a linear normal modes analysis (NASTRAN

SOL 103) can be performed using the stiffness matrices from the converged NASTRAN

SOL 106 analysis. Figure 9 shows how the frequencies of the first 10 normal modes vary

as a result of performing sequential NASTRAN SOL 106 and 103 analyses for each static

pressure difference. For the overlay panel, the modal frequencies are strong functions of the

static pressure difference across the panel.

For the purposes of this study, a static pressure difference of 0.1 psi was arbitrarily

assumed for the subsequent static and dynamic aeroelastic analysis. While this specific

value was arbitrary, the decision was guided by the fact that a negative value would tend

to suck the panel in against the tiles surrounding the hole or hole filler material both of

which should be stabilizing effects. Also, the positive value of 0.1 psi was deemed large

enough to provide a meaningful increase in modal frequencies as indicated in Figure 9. For

this pressure, the frequency of the first mode doubles, and the frequency of the tenth mode

increases by 15%.

4.2 Static Aeroelastic Analysis With Nonlinear Structure

Reference 11 describes a procedure to loosely couple CFL3D with NASTRAN for the purpose

of obtaining a static aeroelastic solution that includes membrane type structural nonlinearities. This procedure was developed for a 2-D problem and was enhanced for the present

3-D problem. The goal of this procedures is to take the output of one code and make it

available to the other. In this case, MATLAB [12] scripts (m-files) were written to do the

following: 1) Read and pass the pressure coefficient data from the CFL3D output to the

input of the NASTRAN SOL 106 analysis; and 2) Process and pass the NASTRAN struc15
tural analysis results (nodal displacements) to CFL3D. The details of these two procedures

will be described next.

To transfer pressures from CFL3D to NASTRAN, the pressure coefficients were read from

a CFL3D output file (cfl3d.prout). These coefficients were converted to pressures using the

dynamic pressure appropriate for the Mach number and altitude being examined, and the

resulting pressures were then interpolated to the structural mesh using linear interpolation.

Finally, a bulk data file (.bdf) containing PLOAD2 cards is generated. This pressure data

file is used in the NASTRAN SOL 106 analysis by way of an include statement in the main

input deck.

To transfer the structural displacements from NASTRAN to CFL3D, the displacements

are read from the NASTRAN output file (.f06). The structural displacements are then

interpolated to the CFD grid points and written to the file newsurf.p3d. Within the CFL3D

input file, the keyword idef ss is set to unity which forces CFL3D to read the newsurf.p3d

file and deform the grid accordingly. Due to an apparent bug in CFL3D where the surface

deformation defined in newsurf.p3d is added at each time step, two CFL3D runs are required

here. First, CFL3D is run for a single time step with key word idef ss=1 so that volume grid

is deformed in to the static aeroelastic shape defined by the file newsurf.p3d. Then CFL3D

is restarted and run with idef ss=0 for multiple time steps sufficient for the generalized

forces to converge. To improve convergence, CFL3D is run in steady mode (iunst=0) for

this analysis.

To conduct a static aeroelastic analysis, these two procedures are repeated until convergence. For the case of 0.1 psi pressure difference, a converged static aeroelastic solution is

shown in Figure 10. As the problem is dominated by the static pressure difference, only three

cycles were necessary for convergence with a cycle defined as a converged CFL3D analysis

followed by a converged SOL 106 structural analysis. For this panel, the SOL106 analysis

required about twice the CPU time as a SOL 103 analysis. This deflection can be compared

with the non static aeroelastic analysis shown in Figure 8. Unlike the displacements in

Figure 8, the displacements in Figure 10 are not symmetric from left to right.

4.3 Dynamic Aeroelastic Analysis with Nonlinear Structure

Several previously described analysis procedures will now be combined to perform the overlay

panel flutter analysis that includes static nonlinear structural effects. These procedures

include the nonlinear static aeroelastic analysis where NASTRAN SOL 106 is coupled with

CFL3D followed by a NASTRAN normal modes analysis using the stiffness matrix from a

prior nonlinear analysis. The previously described normal mode interpolation to the CFL3D

surface grid along with the conventional modal flutter analysis within CFL3D will also be

used. The modal flutter analysis procedure has many steps that can most easily be described

in the following list.

1. Obtain a converged, nonlinear static aeroelastic solution using the loosely coupled

NASTRAN SOL 106 and CFL3D static solution procedure.

2. Perform a NASTRAN SOL 103 analysis (normal modes analysis), using the final

stiffness matrix from the preceding step.

3. Extract the frequencies and mode shapes from the NASTRAN SOL 103 output file.

Put modal frequencies in CFL3D input file.

4. From the converged static aeroelastic solution in step 1, restart CFL3D (irestart=1)

from previous steady run in unsteady mode (iunst=2) with modal deflection turned

off (moddfl=-1).

16
Figure 10. Overlay panel deflection from nonlinear static aeroelastic solution with pressure

differential across the panel of 0.1 psi, the thin boundary layer, and Mach 1.10.

5. Extract converged generalized forces from the CFL3D output, put these values in

the CFL3D input file as input parameter gf0. This step ensures that the pressure

forces and internal stresses initially sum to zero so that no additional static aeroelastic

deformation is obtained within CFL3D.

6. Restart CFL3D (irestart=1) with modal deformation turned off (moddfl=-1). After

this run, net generalized forces should be near zero. Without this step, a transient in

the generalized force will be introduced.

7. Restart CFL3D (irestart=1) with modal deformation turned on (moddfl=0) and a

large value of modal damping (damp=0.999). This will remove any generalized coordinate transient associated with the net generalized force not being identically zero.

8. Restart CFL3D (irestart=1) with modal deformation turned on (moddfl=0) , modal

damping set to zero (damp=0.0), and a perturbation value for the modal velocities

(x0(2*n)=0.05). This step in the procedure is where stability is determined.

For the Mach 1.10, thin boundary layer case with static pressure difference of 0.1 psi,

Figure 11 compares the first two normal modes obtained from step 2, above, with those

obtained from the linear procedure used previously in this paper. The nonlinear static

procedure has a significant effect on both mode shapes as shown here, as well as, the modal

frequencies as previously shown in Figure 9. Both of these effects can be expected to alter

the flutter behavior of the panel.

For the Mach 1.10, thin boundary layer case with static pressure difference of 0.1 psi and

q∞ = 5.5q

nominal

∞ , the generalized force and generalized coordinate time histories associated

with steps 4, 6, 7, and 8 are shown in Figure 12. The vertical lines separate the steps which

17
(a) Mode 1, Nominal Procedure. (b) Mode 1, Nonlinear Static Procedure.

(c) Mode 2, Nominal Procedure. (d) Mode 2, Nonlinear Static Procedure.

Figure 11. Comparison of the first two mode shapes obtained using only NASTRAN SOL

103 with mode shapes obtained using the modified procedure where NASTRAN SOL 103 is

proceeded by the nonlinear, static aeroelastic solution (NASTRAN SOL 106 coupled with

CFL3D). For each mode, red indicates maximum z values and blue represents minimum z

values.

18
−20

0

20

40

0

50

0

20

40

0 200 400 600 800 1000 1200 1400 1600 1800 2000

−4

−2

0

2

t, nondimensional

gf

1

2

3

4

Modal Deection On:

Aeroelastic Solutions, Static & Dynamic

ζ=0.0

Modal Deection O!:

Acquire & Verify 

Generalized Forces

ζ=0.999

gf

gf

gf

Step: 4 6 7 8

(a) Generalized force time histories.

−2

0

2

x 10−4

−2

0

2

x 10−4

−5

0

5

x 10−5

0 200 400 600 800 1000 1200 1400 1600 1800 2000

−1

0

1

x 10−5

t, nondimensional

q

1

2

3

4

q

q

q

Modal De!ection On:

Aeroelastic Solutions, Static & Dynamic

ζ=0.0

Modal De!ection O":

Acquire & Verify 

Generalized Forces

ζ=0.999

Step: 4 6 7 8

(b) Generalized coordinate time histories.

Figure 12. Generalized force and coordinate time histories for Mach 1.10, thin boundary

layer, for a stable value of dynamic pressure, q∞ = 5.5q

nominal

∞ . The dynamic analysis was

preceded by a converged nonlinear static aeroelastic solution.

19
−20

0

20

40

−100

0

100

−200

0

200

0 200 400 600 800 1000 1200 1400 1600 1800 2000

−5

0

5

t, nondimensional

gf

1

2

3

4

Modal Deection On:

Aeroelastic Solutions, Static & Dynamic

Modal Deection O!:

Acquire & Verify 

Generalized Forces

ζ=0.999

gf

gf

gf

ζ=0.0

Step: 4 6 7 8

(a) Generalized force time histories.

−5

0

5

x 10−4

−5

0

5

x 10−4

0

2

x 10−4

0 200 400 600 800 1000 1200 1400 1600 1800 2000

−1

0

1

x 10−5

−5

t, nondimensional

q

1

2

3

4

q

q

q

ζ=0.0

Modal De!ection O":

Acquire & Verify 

Generalized Forces

ζ=0.999

Modal De!ection On:

Aeroelastic Solutions, Static & Dynamic

Step: 4 6 7 8

(b) Generalized coordinate time histories.

Figure 13. Generalized force and coordinate time histories for Mach 1.10, thin boundary

layer, for an unstable value of dynamic pressure, q∞ = 6.5q

nominal

∞ . This dynamic analysis

was preceded by a converged nonlinear static aeroelastic solution. Flutter frequency = 143

Hz.

20
are also labeled above. Step 4 is where the generalized forces are allowed to converge to

nonzero values as shown in Figure 12(a). After the converged values of generalized force are

added to the CFL3D input deck, the generalized forces all have a value of zero for steps 6

and 7. Finally, in step 8 modal deflection is turned on and the generalized forces change

dynamically with the generalized coordinates shown in Figure 12(b). For this analysis, the

panel is aeroelastically stable.

This analysis was repeated for q∞ = 6.5q

nominal

∞ with the time histories shown in Figure 13. Here, the panel is clearly unstable with a flutter frequency of 143 Hz which is

consistent with the normal mode frequencies for modes 1 and 2 shown in Figure 9 for 0.1 psi

pressure difference. In this instance, the inclusion of static nonlinear effects was a stabilizing

effect.

5 Concluding Remarks

An on-orbit installable Space Shuttle overlay panel was developed at the NASA Johnson

Space Center to be used in the event of damage to the thermal protection system tiles to

enable safe re-entry. Previous flutter analyses indicated that at Mach numbers of 2.0 and

higher, adequate panel flutter margins existed within the shuttle flight envelope. However,

near Mach 1.0 empirical flutter analysis yielded inadequate flutter margins. As a result,

CFD flutter analyses were conducted indicating that when viscous effects were considered,

adequate flutter margins existed.

The present study has expanded on the previous work by looking in more detail at the

effects of boundary layer thickness for additional Mach numbers near sonic speeds. In addition, the effects of structural damping were considered, as well as, structural nonlinearities

associated with in-plane forces in the panel. These analyses described in this report indicated that the Space Shuttle overlay panel has adequate flutter margins for Mach numbers

of 2.0 and below. The analysis showing the lowest, yet still adequate, flutter margin was

the Mach 1.1, thin boundary case. More detailed conclusions are listed below.

• The results of the present study are consistent with those of reference 3.

• Flutter onset is relatively insensitive to boundary layer thickness near Mach 2.0, but

thicker boundary layers have a stabilizing effect near sonic speeds.

• As expected, the addition of structural damping tended to increase the flutter onset

dynamic pressure for the overlay panel. In addition, the results suggest that damping

is more effective at stabilizing the panel at near sonic Mach numbers than at supersonic

Mach numbers. A more detailed analysis would be required to confirm and quantify

this trend.

• The nonlinear structural effects of a static pressure difference across the panel was

examined. It was shown that a pressure differential results in increased stiffness and

modal frequencies.

• A procedure for performing a static aeroelastic analysis with nonlinear structural

effects followed by a dynamic aeroelastic analysis within CFL3D was described and

demonstrated. For the case examined, the static pressure difference and the inclusion

of static nonlinear structural effects resulted in a significant increase in flutter margin.

References

1. Lemley, C. E.: Design Criteria for the Prediction and Prevention of Panel Flutter,

Volume I: Criteria Presentation. AFFDL-TR 67-140, 1967.

21
2. Krist, S. L.; Biedron, R. T.; and Rumsey, C. L.: CFL3D User’s Manual (Version 5.0).

NASA/TM-1998-208444, June 1998.

3. Bey, K. S.; Scott, R. C.; Bartels, R. E.; Waters, W. A.; and Chen, R.: Flutter Analysis

of the Shuttle Tile Overlay Repair Concept. NASA/TM-2007-214857, Mar. 2007.

4. Buning, P. G.; Jespersen, D. C.; Pulliam, T. H.; Klopfer, G. H.; W. M. Chan, J. P. S.;

Krist, S. E.; and Renze, K. J.: OVERFLOW User’s Manual, Version 1.8m. , Jan. 2000.

5. Cuneo, J.: A-Basis Mechanical Thermal Properties of GE 2D C/CSiC for RCC Plug

Program. ITAR Test Report SRI-ENG-06-15-11502.01, Huntsville, AL, 2006.

6. MSC.Nastran 2005. Installation and operations guide, 815 Colorado Blvd., Los Angeles,

CA 90041, 2005.

7. Bartels, R. E.: CFL3D Version 6.4 General Usage and Aeroelastic Analysis. NASA/TM2006-214301, 2006.

8. Bertin, J. J.: Engineering Fluid Mechanics. Prentice-Hall, Inc., 1984.

9. Samareh, J. A.; and Bhatia, K. G.: A Unified Approach to Modeling Multidisciplinary

Interactions. AIAA/NASA/USAF/ISSMO Multidisciplinary Analysis and Optimization

Symposium, no. 2000-4704, Long Beach, California, Sept. 2000.

10. Smalley, K. B.; Tinker, M. L.; and Fischer, R. T.: Investigation of Nonlinear Pressurization and Modal Restart in MSC/NASTRAN for Modeling Thin Film Inflatable Structures. 42nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit, no. 2001-1409, Apr. 2001.

11. Scott, R. C.; E.Bartels, R.; and Kandil, O. A.: An Aeroelastic Analysis of a Thin Flexible Membrane. 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics,

and Materials Conference, no. 2007-2316, Honolulu, Hawaii, Apr. 2007.

12. MATLAB. Users guide, 3 Apple Hill Drive, Natick, MA 01760, 2008.

22

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 4. TITLE AND SUBTITLE

Flutter Sensitivity to Boundary Layer Thickness, Structural Damping, and 

Static Pressure Differential for a Shuttle Tile Overlay Repair Concept

5a. CONTRACT NUMBER

 6. AUTHOR(S)

Scott, Robert C.; Bartels, Robert E.

 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

NASA Langley Research Center

Hampton, VA 23681-2199

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National Aeronautics and Space Administration

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14. ABSTRACT

This paper examines the aeroelastic stability of an on-orbit installable Space Shuttle patch panel. CFD flutter solutions were 

obtained for thick and thin boundary layers at a free stream Mach number of 2.0 and several Mach numbers near sonic speed. 

The effect of structural damping on these flutter solutions was also examined, and the effect of structural nonlinearities 

associated with in-plane forces in the panel was considered on the worst case linear flutter solution. The results of the study

indicated that adequate flutter margins exist for the panel at the Mach numbers examined. The addition of structural damping 

improved flutter margins as did the inclusion of nonlinear effects associated with a static pressure difference across the panel.

15. SUBJECT TERMS

Aerodynamics; Boundary layer; Flutter; Flutter sensitivity; Shuttle tile

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