MSC.Software 2013 Users Conference Paper No. AM-CONF13-34 1 A DLM-BASED MSC Nastran AERODYNAMIC FLUTTER SIMULATOR FOR AIRCRAFT LIFTING SURFACES Emil Suciu 1 , Nicholas Stathopoulos 2 , Martin Dickinson 3 and John Glaser 4 1 Formerly with Bombardier Aerospace; Currently Loads and Dynamics Analyst with L-3 Communications, 7500 Maehr Drive, Waco, Texas 76715, USA 2 Manager, Loads & Dynamics, Bombardier Aerospace 400 Cote-Vertu Road West Dorval, Quebec, H4S 1Y9, Canada 3 Principal Engineering Specialist, Loads & Dynamics, Bombardier Aerospace 4 Bombardier Aerospace (Retired) 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 Descr ambling 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. Keywords: Flutter Simulator, T-Tail, DLM, Modal Descrambling LIST OF SYMBOLSlm lm lm lm a a a a 4 3 2 1 , , , = lift correction factors for the modal descrambling factoring method for direct and interference forces and moments, n m l, 1 , c = reference chord; also denotes streamwise camber deformation; apparent from the context ChE h = elevator hinge moment due to horizontal stabilizer h (roll/bending) ChE = elevator hinge moment due to horizontal stabilizer α (torsion) ChE (h+) = elevator hinge moment due to horizontal stabilizer h (roll/bending) AND α (torsion) ChE β = elevator hinge moment due to vertical fin yaw β (torsion) ChE δE = elevator hinge moment due to elevator rotation ChE δR= elevator hinge moment due to rudder rotation ChRβ = rudder hinge moment due to yaw (β or V. Fin torsion)
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The current paper is a revision of the material contained in Reference [1]. The discussion
here applies to all T-Tails analyzed with linear unsteady aerodynamic methods such as the
Doublet Lattice Method (DLM, Reference [2]) with factoring.
Aerodynamic factoring is important; in Reference [3] it is shown that a flutter analysis of an
airplane under development without using factoring for the aileron and tab aerodynamic
hinge moments, when either 2-D strip theory or DLM aerodynamics is used, may not
predict flutter and in this particular case has led to an in-flight flutter incident. Intersecting(therefore interfering) lifting surfaces pose additional problems for the flutter analyst. FAA
Advisory Circular AC No. 25.629.1A recommends that interference effects be included in
flutter analyses. Parametric variations of calculated aerodynamic forces and moments are
recommended in order to cover uncertainties in calculated values. These parametric
variations are achieved through factoring.
It is known that the T-Tail flutter mechanism (generally referred to as the vertical fin
bending/ torsion mechanism) is strongly influenced by the unsteady aerodynamic forces and
moments present on the horizontal stabilizer. See Reference [4], where the effect of steady
upload on horizontal stabilizer on T-Tail flutter speed is appended to the MSC Nastran
flutter solution (Reference [5]) and an early attempt to separate and factor differently the
horizontal stabilizer direct lift due to horizontal stabilizer pitch/torsion from the interference
lift due to vertical fin torsion on the horizontal stabilizer of a T-Tail is described.
It is also known (Reference [6]) that the unsteady aerodynamic forces and moments present
on the horizontal stabilizer of a T-Tail consist of a superposition of direct forces and
moments resulting from the rigid and elastic motions of the horizontal stabilizer and its
control surfaces and tabs and of interference forces resulting from the oscillating vertical fin
and its control surfaces and tabs. The superimposed direct and interference aerodynamicforces and moments on the horizontal stabilizer are called stacked forces.
Thus, for general motion of a given arrangement of n lifting surfaces residing in the same
interference group, every lifting surface experiences 1 direct set of forces and moments and
n-1 sets of interference forces and moments. For n>2, each lifting surface experiences more
interference forces than direct forces!
Figure 1 shows a general (or scrambled) mode of vibration of a T-tailed airplane at the
Figure 1. Scrambled Vertical Fin Bending/Torsion/HS Roll/Elevator Rotation/Rudder Rotation Mode at
the Aerodynamic Surface. A Few Direct and Interference Aerodynamic Forces and Moments are Shown
on the Empennage.
For every mode of vibration, rigid or elastic, the Modal Descrambling factoring method
(formerly known as the General Aerodynamic Derivatives Factoring Method, Reference [6])
performs the descrambling of the general modal motion at every aerodynamic strip and
replaces each scrambled mode with 5 simpler and always the same modes: heave (or
bending), pitch (or torsion), control surface rotation, tab rotation and elastic streamwisecamber deformation. Unsteady direct and interference aerodynamic forces and moments
distributions are then calculated for the descrambled modes and they are available for
factoring separately at every aerodynamic strip (Figure 2).
The MSC Nastran implementation of the DLM (Reference [5]) together with the MSC
Nastran SOL145 with the PKNL flutter solution method chosen and program LSP3G
(Lifting Surface Program 3 General) which implements the Modal Descrambling factoring
method (Reference [6]) and is in effect an aerodynamic flutter simulator are used for
calculating all the results presented here. MSC.PATRAN is used to display and animate
mode shapes.
2 MORE ON THE MODAL DESCRAMBLING FACTORING METHOD
Figure 2 illustrates the summary of the original Modal Descrambling factoring method
showing the descrambling of a general mode of vibration for a lifting surface strip into
simpler motions: heave h, pitch α, control surface rotation β and tab rotation δ and factoring
of the lift. Elastic streamwise camber deformation is not shown in this figure. Elastic
streamwise camber deformation and its effect on flutter calculations are discussed in detailin Reference [7].
The downwash vectors based on descrambled modal displacements (h, α, β, δ, c) for the
entire aircraft for any elastic or rigid mode look like:
(1)
with the scrambled downwash jw being the sum of the descrambled downwash vectors as
defined for the modal descrambling factoring scheme (Figure 2). The pressure coefficients
and integrated forces and moments can then be obtained for the scrambled or descrambledmodes:
(2)
with i,j=1,NBOX.
If Equation 2 operates on the scrambled modes, we have the typical aerodynamic analysis
which calculates stacked aerodynamic forces and moments and only the stacked forces will
be available for factoring; it will be later seen that this is incorrect. If Equation (2) operateson the descrambled modes of Equation (1), we have access to the descrambled aerodynamic
forces and moments, but not yet to the interference aerodynamic forces and moments.
In order to calculate the interference aerodynamic forces and moments, the entire aircraft
descrambled downwash vectors are then partitioned into n components. This number is
generally fairly small, such as 4 for the airplane analyzed: (1) wing with associated control
surfaces and tabs, (2) horizontal stabilizer with associated control surfaces and tabs, (3)
vertical fin with associated control surfaces and tabs and (4) engines, pylons, interference
Figure 8. Imaginary Parts of Total Unfactored and Factored Descrambled Direct and Interference
Stacked Cn on Horizontal Stabilizer of the T-Tail for General Mode of Vibration Shown in Figure 1.
k=0.700.
Flutter solutions for each stiffness model have been run using the common aerodynamic
model. First, the flutter solutions with no aerodynamic factoring have been performed.
Then, the flutter solutions with “nominal” aerodynamic factoring have been run. Then,
flutter solutions are run with parametric variations of various aerodynamic derivatives
factors from the nominal values. One derivative factor at a time is varied from nominal and
its effect on the flutter solution is noted.
Table 1 shows all the flutter solutions calculated with and without aerodynamic factoring
and all the variations of the aerodynamic derivatives factoring. The primed derivativesindicate nominal factored values. The magnitude of the up-or-down excursions from
nominal derivatives values is between 20% and 50% as indicated in Table I.
Cases Ran
(Derivatives factoring)
%(Vf -VfREF)/VfREF
Model 1
%(Vf -VfREF)/VfREF
Model 2
%(Vf -VfREF)/VfREF
Model 3
No Factoring 65.979 109.716 149.243
Nominal Factoring 0.000 11.313 126.452
Clβ factors=Clα factors 65.456 137.462 163.584
ChEh’*0.5 0.826 14.368 116.020
ChE(h+α)’*0.5 3.220 21.002 97.578
ChEδE’*1.2 1.899 14.588 92.678
ClδR Theoretical 7.570 23.066 139.994
ChR β’*0.5 -1.596 15.001 134.132
ChEδR ’*0.5 10.322 36.113 131.489
ChR δR ’*1.2 -1.817 10.542 135.701
ClhVF Theoretical 0.000 11.891 130.003
ChEβ’*1.2 2.119 16.598 128.269
Clα Theoretical 2.835 16.846 124.993
Nominal, camber discarded 2.009 15.029 125.048
CYVFβ’*1.2 -1.294 11.616 125.048
Table 1. Cases Ran; VfREF Is for the Nominal Factoring Case, Model #1; Primed Derivatives Are Factored
Nominal Values; Derivatives Factoring Variations Are from Nominal Values.
TOTAL UNFACTORED AND FACTORED DIRECT, INTERFERENCE AND
STACKED IMAGINARY Cn ON HORIZONTAL STABILIZER OF T-TAIL FOR
When a derivative is listed such as “ClδR Theoretical” in Table 1, it means that the
unfactored DLM-calculated value is used.
Figure 9 shows in graphical form the effect of both stiffness (and therefore mode shape)
variation and aerodynamic derivatives variation on the flutter mechanism of the T-Tail of all
three models analyzed. For clarity, not all the cases listed in Table 1 are plotted in Figure 9.
Figure 9. Effect of Vertical Fin Stiffness Variations and of Aerodynamic Factoring Variations, OneDerivative at a Time from Nominal on Flutter Speed of T-Tailed Aircraft. Primed Derivatives Are
Factored Nominal Values. Reference Speed Is for Nominal Factoring, Model 1.
It is immediately apparent that the change in the flutter solution due to changes in the Cl β
factors is dramatic; at the Mach Number analyzed, the T-Tail flutter speeds calculated with
the Clβ factors = Clα factors are decidedly optimistic (see Table 1 and Figures 6 and 9).
Figures 10 and 11 show the V-g and V-f plots for the complete aircraft for the nominal
factoring case (with the Clβ factors > Clα factors) and then for the nominal factors but with
the Clβ factors being equal to the Clα factors for Model No. 1. Again, the change in the T-
Tail flutter speed due to changes in the Clβ factors is dramatic.
Finally, in Figure 12, a graphical summary of the unsteady aerodynamic forces and their
phases on the horizontal stabilizer which affect T-Tail flutter are shown. Control surfaces
are not included. Positive yaw is assumed. The interference section lift Clβ is always
present. The geometric angle of attack at the horizontal stabilizer in yaw due to dihedral and
therefore the phase and magnitude of the top rolling moment can be modified by choosing
positive, negative or no dihedral. For steady state uplift on the horizontal stabilizer, theunsteady Queijo lift (References [8], [6]) is present and produces a top rolling moment in
phase with the interference lift and positive dihedral to produce the worst case for flutter.
Figure 12. A Summary of the Aerodynamic Forces and their Phases on the Horizontal Stabilizer Affecting
T-Tail Flutter; No Control Surfaces; Positive Yaw Is Assumed.
4 CONCLUSIONS
The scrambled vertical fin bending/torsion/horizontal stabilizer roll/elevator rotation/rudder
rotation mode at the aerodynamic surface (Figure 1) illustrates the complexity of the modal
motion participating in the T-Tail flutter mechanism.
The T-Tail flutter mechanism speed is strongly influenced by the bending and torsional
stiffness levels and motions of the vertical fin; this effect is known and is included here for
completeness. From the aerodynamic standpoint, the T-Tail flutter mechanism has been
shown to be dependent on a large number of aerodynamic forces, moments and control
surface hinge moments present on the horizontal stabilizer for the bending and torsional
modes of the vertical fin. Among these aerodynamic forces and moments, the Cl β
interference factor is the main aerodynamic driver of the T-Tail flutter mechanism.
The second most important driver is the elevator hinge moment due to elevator rotation,
then it is the elevator hinge moment due to horizontal stabilizer roll/bending and torsion,
broken down into about 1/3rd due to horizontal stabilizer roll/bending and 2/3rd due to
pitch/torsion. The factors on the ClδR and ChEδR also have a strong effect on the calculated
speed of the T-Tail flutter mechanism. The flutter speed sensitivity due to variations of the
horizontal stabilizer lift due to vertical fin lateral bending is relatively small (see Table 1).
Vertical fin direct derivatives variations have small but measurable effects on calculated T-
Tail flutter speeds for all three airplane models. The elastic streamwise camber deformation
on the entire aircraft also has a small effect on the T-Tail flutter speeds for all three airplane
models (Table 1); the camber effect is more pronounced on other aircraft lifting surfaces
calculated flutter speeds (see also Reference [7]).
The presence of the wing aerodynamic surface with or without factoring also influences the
T-Tail flutter mechanism. Whether the wing is or is not in the same interference group withthe T-Tail lifting surfaces has little effect on the calculated T-Tail flutter speed; the effect is
mostly dynamic, transmitted through the fuselage.
The effects on the calculated T-Tail flutter mechanism speed of individual variations of all
these aerodynamic forces, moments and hinge moments have been explored (Figure 9)
through the use of the flutter simulator program implementing the Modal Descrambling
factoring method.
A good knowledge of measured or CFD-calculated direct and interference aerodynamic
derivatives is therefore essential for the accurate calculation of the T-Tail flutter mechanismspeed using the DLM or similar methods and the Modal Descrambling Factoring Method.
Other applications of the Flutter Simulator program implementing the Modal Descrambling
Factoring Method are for the flutter analysis of the wing-horizontal stabilizer in close
vertical proximity and for the wing-engine nacelle flutter analysis; aerodynamic interference
is important for these cases. Gust loads analyses could also benefit from the use of the
Modal Descrambling Factoring Method. Last but not least, the more accurate set of
generalized aerodynamic forces matrices QHHL generated by the Modal Descrambling
Factoring method can be used in nonlinear calculations of limit cycle oscillations caused by
control surface free play (Reference [9]).
The flutter simulator program gives the user unprecedented control over all direct and all
interference aerodynamic forces, moments and control surfaces and tabs hinge moments for
factoring on any lifting surface of the aircraft.
5 ACKNOWLEDGEMENTS
Messrs. Frederic Bradley and Jason Bensimhon of the Bombardier Dynamics Group have
contributed with the preparation of the structural dynamic model and with the voluminousaerodynamic data compilation required for this project.
[1] Suciu, E., Stathopoulos, N., Dickinson, M. and Glaser, J.,”The T-Tail Flutter Mechanism
Revisited”, Paper No. IFASD-2011-121, Presented at the International Forum for
Aeroelasticity and Structural Dynamics, Paris, France, June 26-30, 2011.
[2] Giesing, J.P., Kalman, T.P., and Rodden, W.P., “Subsonic Unsteady Aerodynamics for
General Configurations, Part I, Vol. I – Direct Application of the Nonplanar Doublet
Lattice Method”. Air Force Flight Dynamics Laboratory Report No. AFFDL-TR-71-5
Part I, Vol. I, 1971.
[3] French, R.M., Noll, T.,Cooley, D.E., Moore, R. and Zapata, F.; "Flutter Prediction
Involving Trailing Edge Control Surfaces"; Journal of Aircraft, May 1988, Vol 25, No 6.
[4] Suciu, E., “MSC/NASTRAN Flutter Analyses of T-Tails Including Horizontal StabilizerStatic Lift Effects and T-Tail Transonic Dip”, Presented at the 1996 MSC/NASTRAN
World Users’ Conference, Newport Beach, CA, June 3-7, 1996.