The interaction between a thin metallic panel and a Mach 2.25 turbulent boundary layer is investigated using a direct numerical simulation approach for coupled fluid-structure problems. The solid solution is found by integrating the finite-strain, finite-deformation equations of elasticity using a non-linear 3D finite element solver, while the direct numerical simulation of the boundary layer uses a finite-difference compressible Navier-Stokes solver. The initially laminar boundary layer contains low amplitude unstable eigenmodes that grow in time and excite traveling bending waves in the panel. As the boundary layer transitions to a fully turbulent state, with Reθ ≈ 1200, the panel's bending waves coalesce into a standing wave pattern exhibiting flutter with a final amplitude approximately 20 times the panel thickness. The corresponding panel deflection is roughly 25 wall units and reaches across the sonic line in the boundary layer profile. Once it reaches a limit cycle state, the panel/boundary layer system is examined in detail where it is found that turbulence statistics appear to be modified by the presence of the compliant panel, the effect of which is forgotten within one integral length downstream of the panel.

1.
C.
Glass
and
L.
Hunt
, “
Aerothermal tests of spherical dome protuberances on a flat plate at a Mach number of 6.5
,” NASA Technical Paper 2631,
1986
.
2.
C.
Glass
and
L.
Hunt
, “
Aerothermal tests of quilted dome models on a flat plate at a Mach number of 6.5
,” NASA Technical Paper 2804,
1988
.
3.
T.
Beberniss
,
M.
Spottswood
, and
T.
Eason
, “
High-speed digital image correlation measurements of random nonlinear dynamic response
,” in
Experimental and Applied Mechanics, Volume 6
,
Conference Proceedings of the Society for Experimental Mechanics Series
Vol.
9999
, edited by
T.
Proulx
(
Springer
,
New York
,
2011
), pp.
171
186
.
4.
I.
Jacobi
and
B. J.
McKeon
, “
New perspectives on the impulsive roughness-perturbation of a turbulent boundary layer
,”
J. Fluid Mech.
677
,
179
203
(
2011
).
5.
I.
Jacobi
and
B. J.
McKeon
, “
Dynamic roughness perturbation of a turbulent boundary layer
,”
J. Fluid Mech.
688
,
258
296
(
2011
).
6.
B. J.
McKeon
,
A. S.
Sharma
, and
I.
Jacobi
, “
Experimental manipulation of wall turbulence: A systems approach
,”
Phys. Fluids
25
,
031301
(
2013
).
7.
I. W.
Ekoto
,
R. D. W.
Bowersox
,
T.
Beutner
, and
L.
Goss
, “
Supersonic boundary layers with periodic surface roughness
,”
AIAA J.
46
,
486
497
(
2008
).
8.
I. W.
Ekoto
,
R. D. W.
Bowersox
,
T.
Beutner
, and
L.
Goss
, “
Response of supersonic turbulent boundary layers to local and global mechanical distortions
,”
J. Fluid Mech.
630
,
225
265
(
2009
).
9.
J.
Dugundji
, “
Theoretical considerations of panel flutter at high supersonic mach numbers
,” AFOSR Scientific Report 65-1907,
1965
.
10.
E.
Dowell
, “
Panel flutter: a review of the aeroelastic stability of plates and shells
,”
AIAA J.
8
,
385
399
(
1970
).
11.
E.
Dowell
, “
Aerodynamic boundary layer effects on flutter and damping of plates
,”
J. Aircr.
10
,
734
738
(
1973
).
12.
A.
Culler
, “
Coupled fluid-thermal-structural modeling and analysis of hypersonic flight vehicle structures
,” Ph.D. thesis,
Ohio State University
,
2012
.
13.
A.
Culler
and
J.
McNamara
, “
Impact of fluid-thermal-structural coupling on response prediction of hypersonic skin panels
,”
AIAA J.
49
,
2393
2406
(
2011
).
14.
M. J.
Lighthill
, “
Oscillating airfoils at high mach numbers
,”
J. Aeronaut. Sci.
20
,
402
406
(
1953
).
15.
E.
Eckert
, “
Engineering relations for heat transfer and friction in high-velocity laminar and turbulent boundary-layer flow over surfaces with constant pressure and temperature
,”
Trans. of the ASME
78
(
6
), p.
1273
(
1956
).
16.
C. M.
Ostoich
,
D. J.
Bodony
, and
P. H.
Geubelle
, “
Fluid-thermal response of spherical dome under a mach 6.59 laminar boundary layer
,”
AIAA J.
50
,
2791
2808
(
2012
).
17.
R.
Gordnier
and
M.
Visbal
, “
Computation of three-dimensional nonlinear panel flutter
,”
J. Aerosp. Eng.
16
,
155
(
2003
).
18.
M. R.
Visbal
and
R. E.
Gordnier
, “
Numerical simulation of the interaction of a transitional boundary layer with a 2-d flexible panel in the subsonic region
,”
J. Fluids Struct.
19
,
881
903
(
2004
).
19.
M.
Visbal
, “
On the interaction of an oblique shock with a flexible panel
,”
J. Fluids Struct.
30
,
219
225
(
2012
).
20.
M.
Visbal
, “
Shock/boundary layer interaction over a flexible panel
,” AIAA Paper 2012-1092, Presented at the 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition,
2012
.
21.
A.
Crowell
,
B.
Miller
, and
J.
McNamara
, “
Computational modeling for conjugate heat transfer of shock-surface interactions on compliant skin panels
,” 52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Denver, CO, 4–7 April
2011
).
22.
S.
Pirozzoli
,
F.
Grasso
, and
T.
Gatski
, “
Direct numerical simulation and analysis of a spatially evolving supersonic turbulent boundary layer at M = 2.25
,”
Phys. Fluids
16
,
530
(
2004
).
23.
A.
Eggers
,
One-Dimensional Flows of an Imperfect Diatomic Gas
(
National Advisory Committee for Aeronautics
,
1949
).
24.
M.
Vinokur
, “
Conservation equations of gasdynamics in curvilinear coordinate systems
,”
J. Comput. Phys.
14
,
105
125
(
1974
).
25.
B.
Strand
, “
Summation by parts for finite difference approximations for d/dx
,”
J. Comput. Phys.
110
,
47
67
(
1994
).
26.
K.
Mattsson
,
M.
Svärd
, and
J.
Nordström
, “
Stable and accurate artificial dissipation
,”
J. Sci. Comput.
21
,
57
79
(
2004
).
27.
M. H.
Carpenter
,
D.
Gottlieb
, and
S.
Abarbenel
, “
Time-stable boundary conditions for finite difference schemes involving hyperbolic systems: Methodology and application for high-order compact schemes
,”
J. Comput. Phys.
111
,
220
236
(
1994
).
28.
M.
Svärd
,
M. H.
Carpenter
, and
J.
Nordström
, “
A stable high-order finite difference scheme for the compressible Navier-Stokes equations, far-field boundary conditions
,”
J. Comput. Phys.
225
,
1020
1038
(
2007
).
29.
M.
Svärd
and
J.
Nordström
, “
A stable high-order finite difference scheme for the compressible Navier-Stokes equations: No-slip wall boundary conditions
,”
J. Comput. Phys.
227
,
4805
4824
(
2008
).
30.
J.
Nordström
,
J.
Gong
,
E. V.
der Weide
, and
M.
Svärd
, “
A stable and conservative high order multi-block method for the compressible navier-stokes equations
,”
J. Comput. Phys.
228
,
9020
9035
(
2009
).
31.
D. J.
Bodony
, “
Accuracy of the simultaneous-approximation-term boundary condition for time-dependent problems
,”
J. Sci. Comput.
43
,
118
133
(
2010
).
32.
T. H.
Pulliam
and
D. S.
Chaussee
, “
A diagonal form of an implicit approximate-factorization algorithm
,”
J. Comput. Phys.
39
(
2
),
347
363
(
1981
).
33.
J.
Kim
,
D. J.
Bodony
, and
J. B.
Freund
, “
LES investigation of a Mach 1.3 jet with and without plasma actuators
,” AIAA Paper 2009-0290, Presented at the 47th Aerospace Sciences Meeting & Exhibit,
2009
.
34.
D. J.
Bodony
, “
Heating effects on the structure of noise sources of high-speed jets
,” AIAA Paper 2009-0291, Presented at the 47th Aerospace Sciences Meeting & Exhibit, Orlando, FL, 5–8 January
2009
.
35.
M.
Sucheendran
,
D. J.
Bodony
, and
P. H.
Geubelle
, “
Coupled structural-acoustic response of a duct-mounted elastic plate with grazing flow
,”
AIAA Journal
(to appear).
36.
G.
Zagaris
,
D. J.
Bodony
,
M.
Brandyberry
,
M. T.
Campbell
,
E. G.
Shaffer
, and
J. B.
Freund
, “
A collision detection approach to chimera grid assembly for high fidelity simulations of turbofan noise
,” AIAA Paper 2010-836, Presented at the 48th AIAA Aerospace Sciences Meeting and Exhibit, Orlando, FL,
2010
.
37.
J.
Kim
,
M.
Natarajan
,
D. J.
Bodony
, and
J. B.
Freund
, “
A high-order, overset mesh algorithm for adjoint-based optimization for aeroacoustics control
,” AIAA Paper 2010-3818, Presented at the 16th AIAA/CEAS Aeroacoustics Conference, Stockholm, Sweden,
2010
.
38.
D. J.
Bodony
,
G.
Zagaris
,
A.
Reichert
, and
Q.
Zhang
, “
Aeroacoustic predictions in complex geometries
,” in
IUTAM Symposium on Computational Aero-Acoustics for Aircraft Noise Prediction
, edited by
R. J.
Astley
and
G.
Gabard
(
Procedia Engineering
,
2010
), Vol.
6
, pp.
234
243
.
39.
M.
Crisfield
,
Non-linear Finite Element Analysis of Solids and Structures, Volume 2: Advanced Topics
(
John Wiley & Sons Ltd.
,
Chichester, England
,
1997
).
40.
C. M.
Ostoich
, “
Aerothermal and aeroelastic response prediction of aerospace structures in high-speed flows using direct numerical simulation
,” Ph.D. thesis,
University of Illinois at Urbana-Champaign
,
2013
.
41.
S.
Pirozzoli
and
F.
Grasso
, “
Direct numerical simulation of impinging shock wave/turbulent boundary layer interaction at M = 2.25
,”
Phys. Fluids
18
,
065113
(
2006
).
42.
N. D.
Sandham
,
Y. F.
Yao
, and
A. A.
Lawal
, “
Large-eddy simulation of transonic turbulent flow over a bump
,”
Int. J. Heat Fluid Flow
24
,
584
595
(
2003
).
43.
M. R.
Malik
, “
Numerical methods for hypersonic boundary-layer stability
,”
J. Comput. Phys.
86
,
376
413
(
1990
).
44.
S. B.
Pope
,
Turbulent Flows
(
Cambridge University Press
,
Cambridge, UK
,
2000
).
45.
D.
De Graaff
and
J.
Eaton
, “
Reynolds-number scaling of the flat-plate turbulent boundary layer
,”
J. Fluid Mech.
422
,
319
346
(
2000
).
46.
W.
Soedel
,
Vibrations of Shells and Plates
(
CRC
,
2004
), Vol.
177
.
47.
W.
Xie
,
H.
Lee
, and
S.
Lim
, “
Normal modes of a non-linear clamped-clamped beam
,”
J. Sound Vib.
250
,
339
349
(
2002
).
48.
P. P.
Friedmann
,
J. J.
McNamara
,
B. J.
Thuruthiamatta
, and
I.
Nydick
, “
Aeroelastic analysis of hypersonic vehicles
,”
J. Fluids Struct.
19
,
681
712
(
2004
).
49.
J.
McNamara
, “
Aeroelastic and aerothermoelastic behavior of two and three dimensional lifting surfaces in hypersonic flow
,” Ph.D. thesis,
University of Michigan
,
2005
.
50.
P. J.
Schmid
, “
Dynamic mode decomposition of numerical and experimental data
,”
J. Fluid Mech.
656
,
5
28
(
2010
).
51.
I.
Doghri
,
Mechanics of Deformable Solids: Linear, Nonlinear, Analytical, and Computational Aspects
(
Springer Verlag
,
2000
).
You do not currently have access to this content.