The Level 16 flutter analysis capability was applied to an aspect-ratio-6.8 subsonic transport type wing, an aspect-ratio-1.7 arrow wing, and an aspect-ratio-1.3 all movable horizontal tail with a geared elevator. The transport wing and arrow wing results are compared with experimental results obtained in the Langley transonic dynamic tunnel and with other calculated results obtained using subsonic lifting surface (kernel function) unsteady aerodynamic theory

Cunningham, H. J.

Doggett, R. V., Jr.

English

NASA Technical Reports Server

SOMEAPPLICATIONSOFTHENASTRANLEVEL16
SUBSONICFLUTTERANALYSISCAPABILITY
Robert V. Doggett, Jr.; and Herbert J. Cunningham
NASALangley ResearchCenter
ABSTRACTANDSUMMARY
Results are presented that were obtained by applying the new Level 16
flutter analysis capability to an aspect-ratio-6.8 subsonic-transport-type wing,
an aspect-ratio-l.7 arrow wing, and an aspect-ratio-l.3 all-movable horizontal
tail with a geared elevator. The transport wing and arrow-wing results are
comparedwith experimental results obtained in the Langley transonic dynamic
tunnel and with other calculated results obtained using subsonic lifting surface
(kernel function) unsteady aerodynamic theory.
INTRODUCTION
Improvements in the NASAstructural analysis computer program (NASTRAN)
have been madecontinuously since the first public release of the program in
1970. These improvements have included bvth the upgrading of capability that
was included in the initial public version and the addition of new analysis
capabilities that were not included previously. Onenew capability that is
generally available in a standard level for the first time with the release of
Level 16 is subsonic flutter analysis. The flutter analysis is organized into
a new rigid format, APPAERO,SOLi0. The features and capabilities of the
Level 16 flutter analysis are the sameas those of the analysis originally
installed in a nonstandard Level 15.1 version (see refs. i and 2). As presently
implemented, the analysis is applicable to multiple, nonplanar, mutually inter-
fering lifting surfaces. The analysis is of the modal type. That is, the
flutter equations are formulated in terms of generalized modal coordinates using
a finite numberof the natural modesof the structure. These modesand frequen-
cies are determined using a conventional NASTRANfinite-element structural
model. The solution of the flutter equations is accomplished by the traditional
k-method. The generalized unsteady aerodynamic forces are determined using
doublet lattice unsteady aerodynamic theory which requires that the lifting
surface be divided into an array of trapezoidal boxes. As implemented in
NASTRAN,there is an aerodynamic grid point located at the center of each of
these boxes. The interconnection of the aerodynamic and structural models is
accomplished by using one-dimensional and surface spline functions to interpo-
late the modal displacements determined at the structural grid points to dis-
placements and slopes required at the aerodynamic grid points. The generality
of this structural-aerodynamic interface allows the user to select a structural
model that is best suited from structural considerations alone and an aerody-
namic model that is dictated by aerodynamic considerations alone. Capability
is provided for interpolating the generalized aerodynamic forces determined at
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https://ntrs.nasa.gov/search.jsp?R=19770013564 2020-03-20T07:36:04+00:00Z
specific values of the independent aerodynamic parameter, Machnumber, or
reduced frequency, to forces at intermediate values of these parameters.
The purpose of this paper is to present NASTRANflutter results for three
different configurations; namely, an aspect-ratio-6.8 subsonic-transport-type
wing, an aspect-ratio-l.7 arrow wing, and an aspect-ratio-l.3 all-movable
horizontal tail with a geared-elevator control surface. The NASTRANflutter
results for the transport wing and arrow wing are comparedwith wind-tunnel
model experimental results obtained in the Langley transonic dynamics tunnel
and with other calculated results obtained by using subsonic lifting surface
(kernel function) unsteady aerodynamic theory. The kernel function results were
obtained using NASTRANcalculated modesand frequencies and flutter analysis
methods similar to those contained in NASTRAN,such as surface spline interpo-
lation, generalized aerodynamic force interpolation, and the k-method of solu-
tion. All NASTRANflutter results presented were obtained using standard
Level 16 as installed on the CDC6000 series computers at the Langley Research
Center.
APPLICATIONS
Subsonic Transport Wing
The subsonic-transport wing for which NASTRANflutter results were obtained
was one of two wind-tunnel models tested in the Langley transonic dynamics tun-
nel to study possible supercritical-airfoil-section effects on flutter (see
ref. 3). A photograph of the swept, tapered, aspect-ratio-6.8 cantilever-
mountedwing installed on a fuselage half-body in the wind tunnel is presented
in figure i. The wing geometry, the structural model, and one of the aerody-
namic models used (doublet lattice box arrangement) are presented in figure 2.
Although the model construction was rather complex (fiberglass skins stabilized
by a full-depth honeycombcore with ballasting weights inserted in the core),
the wing was essentially a beamlike structure so NASTRANBARelements were used
in the structural model. The aerodynamic model shown in figure 2 contains
i00 doublet lattice boxes, five boxes along the chord at each of 20 span sta-
tions. The aerodynamic model in the figure was the basic one used in the
flutter analysis, but additional calculations were madeusing 50 boxes, five
per chord at i0 span stations, and also 200 boxes, five per chord at 40 span
stations. Note that the aerodynamic planform is slightly different from the
actual planform near the wing root and tip since curved planform edges are
approximated by the straight line segments of the doublet lattice boxes.
The first six calculated natural modesand frequencies of the wing were
used in the flutter analysis. Oblique projections of the calculated mode
shapes and the corresponding natural frequencies are shown in figure 3. Also
included in the figure are the measurednatural frequencies. The measuredand
calculated natural frequencies are in good agreement and, although not shownin
this figure, the calculated modeshapes are very similar to the measuredmode
shapes. One-dimensional spline functions were used to interpolate the modal
displacements in the flutter analysis.
496
The flutter results are presented in figure 4 as the variations of the
flutter frequency and dynamic pressure with Machnumber. The NASTRANresults
are indicated by the symbols in this figure. Also included are the experimental
flutter results (from ref. 3) and calculated results obtained using subsonic
lifting surface (kernel function) theory (ref. 4). A six-by-six collocation
point arrangement was used for the kernel function calculations. Both sets of
calculated results predict higher flutter frequencies and dynamic pressures
than were found experimentally. Although the kernel function results are in
better agreement with the experiment than the NASTRAN results, the differences
between the two calculations are not considered to be large and are not untypi-
cal of differences that occur in flutter analyses using different unsteady
aerodynamic theories. The NASTRAN results at Mach number 0.934 using 50, 100,
and 200 doublet lattice boxes show that the 100-box and 200-box results are
virtually the same, and that the 50-box results are only slightly higher.
Arrow Wing
The arrow-wing configuration was another wind-tunnel model and is shown
mounted in the wind tunnel in figure 5. The aspect-ratio-l.7, cantilever-
mounted model is a simplified 0.02-size version of the Supersonic Cruis_Air -
craft Research (SCAR) arrow-wing design. The experimental flutter data obtained
for this model will be used in validating flutter analysis methods applicable
to the arrow-wing configuration. The model geometry, structural model, and
aerodynamic model are presented in figure 6. The arrow-wing model was of simple
construction, being an aluminum-alloy plate covered with balsa wood to give the
desired airfoil shape. The structural model consisted of NASTRAN QUAD2 and
TRIA2 plate-bending elements. The basic aerodynamic model shown in figure 6
consisted of 108 doublet lattice boxes, nine along the chord at each of 12 span
stations. Some calculations were made using 60 boxes, 5 by 12, and 189 boxes,
9 by 21. Note that the aerodynamic model planform is slightly different from
the geometric planform.
The first five calculated natural modes were used in the flutter analysis.
Oblique projections of the calculated mode shapes along with the corresponding
natural frequencies are presented in figure 7. Also included in the figure are
the measured natural frequencies. The calculated and measured frequencies are
in reasonably good agreement. Surface-spline functions were used to interpolate
the modal displacements at the structural grid points to displacements and
slopes required for each doublet lattice box.
The flutter results are presented in figure 8 as the variations of the
flutter frequency and dynamic pressure with Mach number. Also included in the
figure are calculated results obtained using kernel function unsteady aerody-
namic theory (ref. 4) and some previously unpublished experimental flutter
results obtained in the Langley transonic dynamics tunnel by the first author
and Rodney H. Ricketts of the Vought Corporation, Hampton Technical Center.
A six-by-six collocation point arrangement was used in the kernel function
analysis. The NASTRAN results are in good agreement with the experiment. The
kernel function results indicate a flutter boundary lower than NASTRAN and the
experimental results. The NASTRAN results at 0.9 Mach number using 60, 108,
497
and 189 doublet lattice boxes show that the 108-box and 189-box results are
virtually the same, and that the 60-box results are slightly higher.
All-Movable Horizontal Tail
The third configuration which was studied is the aspect-ratio-l.3 all-
movable horizontal tail with geared elevator shown in the upper left sketch in
figure 9. This configuration is being used in a study to provide a better
understanding of the effects of elevator-gear ratio on flutter. Someinitial
results from this study are presented here. Elevator gear ratio as used herein
is defined by the sketch shownat the lower left in figure 9. Also included in
figure 9 is the basic aerodynamic model used. This model is a purely analytical
representation, that is, no physical model exists for which experimental flutter
data have been obtained.
The configuration consists of a stabilizer portion which can translate and
rotate about the stabilizer pitch axis which is located at 40 percent of the
root chord. A full-span elevator with unswept hinge line is hinged to the
stabilizer. The elevator hinge line is at 75 percent of the root chord. Since
the stabilizer and elevator were analyzed as rigid surfaces, there are no
camber or bending deformations. The horizontal tail wasmodeled structurally
using spring (CELAS2)elements to represent the translational, pitch, and
elevator-rotational stiffnesses. The mass and inertia of the stabilizer and
elevator were modeled using concentrated masses (CONM2). The elevator gearing
was effected by using multipoint constraints (MPC's). Oblique projections of
the calculated modeshapes for the 2 to 1 gear-ratio configuration are shownin
figure i0. It should be pointed out that since the elevator rotational stiff-
ness spring was in series with the gearing mechanism, the elevator rotational
angles in the modeshapes are not simply the stabilizer pitch angle times the
gear ratio. The calculated natural frequencies for all gear ratios studied are
tabulated on this figure. Note that the modeshapes are composedof varying
combinations of vertical translation, stabilizer pitch, and elevator rotation.
The modeshapes for the other gear ratios studied are similar to those shownin
the figure, the primary differences being in relative angular rotation between
the stabilizer and elevator. Also note that increasing the elevator gear ratio
had little effect on the first-mode frequency while the second-modefrequency
systematically decreased and the third-mode frequency systematically increased
as the gear ratio was increased.
To meet the purposes of the present study, it was not only necessary to
have a simple structural model to facilitate the changing of structural param-
eters, but it was also desired to have a simple aerodynamic model (minimum
numberof doublet lattice boxes) in order to keep computational costs low since
the CPUtime required for the unsteady aerodynamic forces is approximately pro-
portional to the square of the numberof boxes. Since the 25-box arrangement
shown in figure 9 gave results essentially the sameas a large 100-box arrange-
ment, this admittedly coarse model was used as the basic aerodynamic model.
Surface spline functions were used to interpolate the modal displacements. A
separate spline function was used for the stabilizer and elevator in order to
account properly for the geometric discontinuity in the downwashthat occurs at
the elevator hinge line.
498
The calculated flutter results are presented in figure ii as the variation
of flutter frequency and dynamic pressure with elevator gear ratio. Allcalcu-
lations were madefor a density of 0.515 kg/m3 (42 percent of sea-level stand-
ard air density) at a Machnumberof 0.80. Both the flutter dynamic pressure
and frequency increase as the gear ratio is increased indicating that gearing
the elevator is mildly favorable from a flutter point of view. The trend of
these data is consistent with that presented in reference 5 where wind-tunnel
flutter results are presented for a relatively complex geared-elevator model
having a planform similar to the one used here.
CONCLUDINGREMARKS
Results from applying the NASTRANLevel 16 subsonic flutter analysis (which
uses doublet lattice unsteady aerodynamic theory) to three configurations have
been presented. The three configurations studied were (i) a swept, tapered,
aspect-ratio-6.8 subsonic-transport-type wing, (2) an aspect-ratio-l.7 arrow
wing which is representative of supersonic cruise aircraft configurations of
current interest, and (3) an aspect-ratio-l.3 all-movable horizontal tail with
a geared-elevator control surface. The NASTRANresults for the subsonic-
transport wing and the arrow wing were in good agreement with wind-tunnel model
experimental flutter results and were consistent with other calculated flutter
results obtained using subsonic lifting surface (kernel function) unsteady aero-
dynamic theory. The NASTRANresults for the horizontal-tail configuration with
geared elevator indicated a gradual increase in flutter frequency and dynamic
pressure with increasing gear ratio. Although no experimental and other calcu-
lated results are available for the specific horizontal tail studied here, the
trends of the NASTRANresults are the sameas those determined in reference 5
for a similar, but more complex, configuration.
REFERENCES
.
.
.
.
Doggett, Robert V., Jr.; and Harder, Robert L.: Subsonic Flutter Analysis
Addition to NASTRAN. NASTRAN: User's Experiences. NASA TM X-2893,
September 1973, pp. 507-529.
Jew, Howard: Delta Wing Flutter Based on Doublet Lattice Method in NASTRAN.
NASTRAN: User's Experiences. NASA TM X-3278, September 1975, pp. 603-613.
Farmer, Moses G.; and Hanson, Perry W.: Comparison of Supercritical and
Conventional Wing Flutter Characteristics. Proceedings AIAA/ASME/SAE
17th Structures, Structural Dynamics, and Materials Conference (King of
Prussia, PA), May 5-7, 1976, pp. 308-614. (Also available as NASA
TM X-72837.)
Watkins, Charles E.; Woolston, Donald S0; and Cunningham, Herbert J.:
A Systematic Kernel Function Procedure for Determining Aerodynamic Forces
on Oscillating or Steady Finite Wings at Subsonic Speeds. NASA TR R-48,
1959.
499
o Ruhlin, Charles L.; Doggett, Robert V., Jr.; and Gregory, Richard A.:
Geared-Elevator Flutter Study. Proceedings AIAA/ASME/SAE 17th Structures,
Structural Dynamics, and Materials Conference (King of Prussia, PA),
May 5-7, 1976, pp. 598-607.
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Some applications of the NASTRAN level 16 subsonic flutter analysis capability

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