a dlm-based msc nastran aerodynamic flutter simulator for aircraft...
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MSC Software Confidential MSC Software Confidential
A DLM-BASED MSC Nastran AERODYNAMIC
FLUTTER SIMULATOR FOR AIRCRAFT LIFTING
SURFACES 2013 Regional User Conference
Paper No. AM-CONF13-34
Presented By: Emil Suciu
L-3 Communications Platform Integration Division, Waco, Texas
May 7, 2013
THE T-TAIL FLUTTER MECHANISM
REVISITED
Paper No. IFASD-2011-121
IFASD-2011, Paris, France, June 26-30, 2011
by Emil Suciu1, Nicholas Stathopoulos2,
Martin Dickinson2 and John Glaser3
1L-3 Communications, Platform Integration Division, Waco, Texas 2Bombardier Aerospace 400 Cote-Vertu Road West Dorval, Quebec, Canada H4S 1Y9 3Bombardier Aerospace (Retired)
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SUMMARY
A DLM-based aerodynamic simulator for flutter is used to
identify some of the most important aerodynamic drivers for
the T-Tail flutter mechanism of a complete aircraft. The
simulator is using the Modal Descrambling Factoring
Method, which permits individual variations of each direct
and each interference aerodynamic force, moment and
hinge moment independently of any other force or moment.
The sensitivity of the flutter solution to individual variations
of very large numbers of direct and interference
aerodynamic derivatives can be studied with ease.
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LINEAR FLUTTER ANALYSIS vs.
REALITY; SOME POSSIBLE OUTCOMES* 1. Analysis predicts flutter and it is there and at the right
speed; desired outcome
2. Analysis predicts flutter but it is not there; can cause headaches and unnecessary work
3. Analysis predicts flutter and it is there but at the wrong speed; can cause headaches and unnecessary work
4. ANALYSIS DOES NOT PREDICT FLUTTER AND IT IS THERE; A MOST UNDESIRABLE OUTCOME
*This assumes that we have some experimental or Navier-Stokes guidance
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WHY USE AERODYNAMIC FACTORING IN
FLUTTER ANALYSES?
• Theodorsen & Garrick, as far back as 1940 recognized that 2-D strip theory, especially when applied to full span wings, needs to be corrected for finite span effects, viscosity and compressibility
• The Doublet Lattice Method (DLM) is a 3-D linear theory (SUPERPOSITION APPLIES) which does not account for viscosity, shocks, vortices and lifting surfaces correct relative positions (interference), etc.
• FAA Advisory Circular AC No. 25.629.1A recognizes that intersecting surfaces pose special aerodynamic problems and recommends that intersecting lifting surfaces in-plane and interference effects be included in flutter analyses
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WHY USE AERODYNAMIC FACTORING?
continued
THERE ARE NUMEROUS OPPORTUNITIES TO
MESS UP FLUTTER ANALYSES; LACK OF
AERODYNAMIC FACTORING CAN BE ONE SUCH
OPPORTUNITY
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The T-46A Airplane Wing-Aileron-Tab Flutter Incident and
Post-Incident Analyses with Factoring (Ref. J. Aircraft Paper, May 1988,
by French, R.M., Noll, T.,Cooley, D.E., Moore, R. and Zapata, F.)
A Case When Analysis Did Not Predict Flutter And It Occurred in
Flight; Aerodynamic Factoring Was Not Used on Aileron and Tab
Bill Rodden used to hand out this paper at conferences
and recommend factoring to every flutter analyst
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Aerodynamic Factoring, continued
Direct quotation from the Giesing, Kalman and Rodden 1976 Report on Correction Factor Techniques for the DLM. On pressure factoring:
“One set of correction factors, determined from one mode, to other modes has not met with much success. Specifically, correction factors obtained using a pitch mode cannot be applied to pressures due to control surface deflections. The converse is also true.”*
*This conclusion is as valid today as it was in 1976.
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Aerodynamic Factoring, continued
HOWEVER, if we can apply the correction factors obtained from a k=0.0 pitch mode to a k≠0.0 pitch (or torsion) mode ONLY, from a k=0.0 control surface deflection mode to a k≠0.0 control surface deflection mode ONLY, from a tab k=0.0 deflection mode to a tab k≠0.0 deflection mode ONLY, etc., it would appear that we could meet with more success, as anticipated by Rodden in 1976.
It turns out that through MODAL DESCRAMBLING it is possible to replace any general mode of vibration with 5 simple and well ordered modes to which the approppriate factors can be applied.
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The problem is that the flutter analyst does not encounter the modes
of vibration of an aircraft in a predictable sequence (pure bending,
then pure torsion, then pure control surface rotation and torsion, then
pure tab rotation and torsion and finally pure elastic streamwise
camber deformation); the average mode of vibration is scrambled
and it looks forbidding, as below:
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USING MODAL DESCRAMBLING, FOR ANY LIFTING SURFACE
ARRANGEMENT, AT ANY AERODYNAMIC STRIP,
EVERY GENERAL MODE OF
VIBRATION LOOKS THE SAME! (1) pure bending +
(2) pure torsion +
(3) pure control surface rotation and torsion +
(4) pure tab rotation and torsion +
(5) pure elastic streamwise camber deformation
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WE CAN THEREFORE FACTOR EXACTLY
EACH OF THE DESCRAMBLED PURE MODES
EXCEPT FOR THE ELASTIC STREAMWISE
CAMBER DEFORMATION MODE, FOR WHICH
CORRECTION DATA IS GENERALLY NOT
AVAILABLE
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Schematic of Descrambling Process of General
Wing-Control Surface-Tab Mode Shape at the
Aerodynamic Surface
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There Is More to Aerodynamic Factoring Than
Only Modal Descrambling at the Aerodynamic
Surface; There Is Also Aerodynamic
Interference From Surface to Surface to
Consider
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Aerodynamic Forces on Lifting Surfaces: Direct,
Interference and Stacked Forces
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Aerodynamic Forces: Direct, Interference
and Stacked Forces (continued) For an arrangement of n lifting surfaces in the same
interference group, each surface or component
experiences 1 (one) direct set of forces and moments and
n-1 sets of interference forces and moments;
For n>2,there are more interference forces
than direct forces on any lifting surface!
Most (if not all) factoring schemes apply direct factors
ONLY TO THE STACKED FORCES
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α >0°
α >0° DLM model; only slopes for deflection
H.S. incidence can be controlled separately
Wing – Flap - Horizontal Stabilizer Interference Problem
at α >0°; Reality vs. DLM model (Capabilities & Limitations)
Reality: relative location of wing-flap-tail and their vortices
δF >0°
δF > 0°
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Wing – Flap –Horizontal Stabilizer Interference Problem
Calculated with Program ILSA (a MORINO METHOD)
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The Original Aerodynamic Derivatives (now
Modal Descrambling) Factoring Method Developed at De Havilland Aircraft of Canada (now
Bombardier) in 1987, then a division of the Boeing Company; method in use at DHC (Q300, Q200, Q400) and Boeing (on 777 aircraft)
This method accounts for surface-on-itself interference but does not treat lifting surface-to-lifting surface interference correctly, same as other factoring methods; no camber
Q300 Q400
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The Modal Descrambling Factoring Method
The modal descrambling factoring scheme descrambles all modal
motion and separates interference forces from direct forces and
permits separate factoring
Let’s say we divide the aircraft lifting surfaces into 4 components: (1)
wing, (2) H.S., (3) V. Fin, (4) engines + pylons + ventral fins
THEN: surface 1 moves only in bending; calculate all direct and
interference forces on all the components due to surface 1 bending;
THEN: surface 1 moves only in torsion; calculate all direct and
interference forces on all the components due to surface 1 torsion;
THEN: only the control surfaces of surface 1 rotate; etc.
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Factoring Direct and Interference
Aerodynamic Forces at any Aerodynamic
Strip of Any Component
Each aerodynamic strip has 64 factors if ncomp=4;
for 209 strips, for one Mach Number, we need a total
of 13376 factors
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Airplane Models Analyzed
Twin engine T-Tail airplane with H.S. anhedral
Manual control surfaces
3 stiffness levels of vertical fin are analyzed
Flutter analyses at one transonic Mach Number
The Modal Descrambling Aerodynamic Factoring Method is Used with the DLM to identify the important aerodynamic drivers of the T-Tail flutter mechanism
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Figure 1. Scrambled Vertical Fin Bending/Torsion/HS Roll/Elevator
Rotation/Rudder Rotation Mode at the DLM Aerodynamic Surface
with a Few DESCRAMBLED AND SEPARATED Direct and
Interference Aerodynamic Forces and Moments on the H.S.
ChEδE
ChEh
ChE
ChEβ
ChEδR
Clh
Cl
ClhVF
Clβ
ClδR
CYVFβ
CYVFδR
ChRβ
ChRδR
Blue= DIRECT FORCE
Red = INTERFERENCE FORCE
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Horizontal Stabilizer DLM Symmetric Derivatives
Calculation
Three Elementary Unit Rigid Mode Shapes for Calculating
Horizontal Stabilizer - Elevator Symmetric Aerodynamic Derivatives with the DLM
(1) Rigid Heave (2) Rigid Pitch
(3) Rigid Elevator Rotation
The Direct Clα Factor Is Derived from Here; Most
Factoring Schemes Only Factor the Direct Clα on the
H.S.
(3) Rigid Elevator Rotation
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Empennage DLM Antisymmetric Derivatives Calculation
1. Rigid Side-to-Side Motion 2. Rigid Yaw
Four Elementary Unit Rigid Mode Shapes for Calculating Fin Aerodynamic Derivatives with the
DLM; Interference to Horizontal Stabilizer is Automatic
3. Rigid Rudder Rotation 4. Rigid Tab Rotation
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Figure 5. Typical DLM vs. CFD Horizontal
Stabilizer Spanwise Clβ Distribution. k=0.000.
Figure 6. Typical CLα and CLβ Total Factors vs.
Mach Number for the Horizontal Stabilizer;
k=0.000
Rigid Unit Vertical Fin Yaw
Typical Horizontal Stabilizer CLα and CLβ Factors vs.
Mach Number; k=0.000
Mach Number M
Aer
od
ynam
ic F
acto
rs
CLα Factor vs. M
CLβ Factor vs. M
Analysis CLβ Factor
Analysis CLα Factor
1.000
CLα Factor<1.000
CLβ Factor>1.000
CLβ Factor<1.000
DLM vs. CFD Clβ Distribution on Horizontal Stabilizer; k=0.000
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
semispan, η
Cn*c
/cav
e
CFD
DLM
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Figure 3. Real Parts of Unfactored Descrambled
Direct and Interference Cn on Horizontal Stabilizer
of the T-Tail for General Mode of Vibration Shown
in Figure 1; k=0.700.
Figure 4. Imaginary Parts of Unfactored
Descrambled Direct and Interference Cn on
Horizontal Stabilizer of the T-Tail for General Mode
of Vibration Shown in Figure 1; k=0.700.
DESCRAMBLED UNFACTORED DIRECT AND INTERFERENCE REAL Cn ON
HORIZONTAL STABILIZER OF T-TAIL FOR GENERAL (SCRAMBLED) MODE OF
VIBRATION; k=0.700
-0.010
-0.008
-0.006
-0.004
-0.002
0.000
0.002
0.004
0.006
0.008
0 0.2 0.4 0.6 0.8 1
semispan η
Rea
l Cn
CN DUE TO HS ROLL/BENDING
CN DUE TO HS TORSION
CN DUE TO ELEVATOR ROTATION
CN DUE TO HS CAMBER
CN DUE TO V. FIN LAT BENDING
CN DUE TO V. FIN TORSION
CN DUE TO RUDDER ROTATION
CN DUE TO RUDDER TAB
ROTATION
CN DUE TO V. FIN CAMBER
DESCRAMBLED UNFACTORED DIRECT AND INTERFERENCE IMAGINARY Cn ON
HORIZONTAL STABILIZER OF T-TAIL FOR GENERAL (SCRAMBLED) MODE OF
VIBRATION; k=0.700
-0.005
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0 0.2 0.4 0.6 0.8 1
semispan η
Imag
inar
y C
n
CN DUE TO HS ROLL/BENDING
CN DUE TO HS TORSION
CN DUE TO ELEVATOR ROTATION
CN DUE TO HS CAMBER
CN DUE TO V. FIN LAT BENDING
CN DUE TO V. FIN TORSION
CN DUE TO RUDDER ROTATION
CN DUE TO RUDDER TAB
ROTATION
CN DUE TO V. FIN CAMBER
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Effect of Aerodynamic Factoring on T-Tail Flutter Speed.
%(Vf-VfRef)/VfRef vs. Vertical Fin Stiffnesses; All Speeds in KEAS
0
20
40
60
80
100
120
140
160
180
1.000 1.125 1.250 1.375 1.500
Vertical Fin EI & GJ Stiffness Ratios
%(V
f-VfR
ef)/
VfR
ef
No Factoring
Nominal Factoring
Clβ factor=Clα factor
ChEh'*0.500
ChE(h+α)'*0.500
ChEδE'*1.2
ClδR Theoretical
ChEδR'*0.500
ChEβ'*1.2
Figure 9. Effect of Vertical Fin Stiffness Variations and of Aerodynamic Factoring
Variations, One Derivative at a Time from Nominal on Flutter Speed of T-Tailed
Aircraft. Reference Speed Is for Nominal Factoring, Model 1.
Typical Horizontal Stabilizer CLα and CLβ Factors vs.
Mach Number; k=0.000
Mach Number M
Aer
od
ynam
ic F
acto
rs
CLα Factor vs. M
CLβ Factor vs. M
Analysis CLβ Factor
Analysis CLα Factor
1.000
CLα Factor<1.000
CLβ Factor>1.000
CLβ Factor<1.000
MOST ANALYSES ARE HERE
ALL SHOULD BE HERE
SOME ARE HERE
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Figure 10. V-g and V-f Plots of Model No. 1 T-Tail Flutter Solution for
Nominal Aerodynamic Factoring; Clβ factors > Clα factors
Figure 11. V-g and V-f Plots of Model No. 1 T-Tail Flutter Solution for
Nominal Aerodynamic Factoring; Clβ factors = Clα factors.
Modal Damping; T-Tail Aircraft Model #1; Nominal Aerodynamics Factoring;
Clβ factors > Clα factors
-0.30
-0.25
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
V (KEAS)/Vmax
da
mp
ing
, gVertical Fin Bending
Vertical Fin Torsion
Rudder Rotation
Modal Frequency; T-Tail Aircraft Model #1; Nominal Aerodynamics Factoring;
Clβ factors > Clα factors
0
5
10
15
20
25
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
V (KEAS)/Vmax
Fre
qu
en
cy
(H
z)
Vertical Fin Bending Vertical Fin Torsion
Rudder Rotation
Modal Damping; T-Tail Aircraft Model #1; Nominal Aerodynamics Factoring;
Clβ factors = Clα factors
-0.30
-0.25
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
V (KEAS)/Vmax
da
mp
ing
, g
Vertical Fin Bending
Vertical Fin TorsionRudder Rotation
Modal Frequency; T-Tail Aircraft Model #1; Nominal Aerodynamics Factoring;
Clβ factors = Clα factors
0
5
10
15
20
25
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
V (KEAS)/Vmax
Fre
qu
en
cy
(H
z)
Vertical Fin Bending Vertical Fin Torsion
Rudder Rotation
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A Summary of the Aerodynamic Forces and their Phases on the Horizontal
Stabilizer Affecting T-Tail Flutter; No Control Surfaces; Positive Yaw Is Assumed.
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For an airplane having 2600 aerodynamic boxes, for
109 modes, the MSC Nastran DLM complete flutter
solution with 8 k-values takes approximately 30 minutes
on a desktop PC with 8GB RAM.
For the same configuration divided into 4 groups, the
general aerodynamic factoring program labors for
approximately 9 minutes; it uses the stored AICs
calculated by the DLM, but it processes 20 downwash
vectors/mode (4X5) vs. 1/mode for the DLM; LSP3G
mode processing is much more extensive than DLM; no
attempt so far to optimize LSP3G.
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CONCLUSIONS
The unsteady aerodynamic forces on the horizontal
stabilizer drive the T-Tail flutter mechanism
The interference Clβ factor is the most important
aerodynamic driver for the antisymmetric T-Tail flutter
mechanism
The direct ChEδE, ChEα, ChEh and interference ChEδR and
ClδR also are important derivatives drivers
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CONCLUSIONS, continued
Variations of the symmetric direct Clα factor have no
measurable effect on the antisymmetric T-Tail flutter
mechanism;
The antisymmetric T-Tail flutter mechanism exhibits a lot of
sensitivity with the EI & GJ values of the vertical fin (well
known)
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CONCLUSIONS, continued The use of the modal descrambling factoring method will
also benefit the flutter and gust analyses of:
Wing-low mounted horizontal stabilizer flutter with
differently factored direct and interference
aerodynamics
Wing-engine nacelle flutter with differently factored
direct and interference aerodynamics
Gust Loads analyses with differently factored direct
and interference aerodynamics
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• The Modal Descrambling Factoring Method allows the
user unprecedented access to and individual control
of all direct and all interference aerodynamic forces,
moments, control surface and tab hinge moments at
any lifting surface of an aircraft; in effect a flutter
simulator
CONCLUSIONS, the end
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Part of 1995 effort to calculate T-Tail flutter speed
reduction with horizontal stabilizer upload; first
proposal to separate and factor differently Clα and
Clβ
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G-II T-Tail Wind Tunnel-
Measured Flutter Boundary
MD=0.90 (20% Margin)
GV T-Tail DLM-Calculated Flutter Boundary
MD=0.97 (15% Margin); factors on Clβ = Clα
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