The computer program SUSSA ACTS (Steady and Unsteady, Subsonic and Supersonic Aerodynamics for Complex Transportation Systems) are presented in the final version. The numerical formulation and the description of the program and numerical results are included. In particular, generalized forces for fully unsteady (complex frequency) aerodynamics for a wing-body configuration, in both subsonic and supersonic flows, are discussed. The mathematical analysis includes completely arbitrary motion. The numerical implementation was limited to steady and oscillatory flows. A more general aerodynamic formulation in the form of a fully transient response for time-domain analysis and the aerodynamic transfer function (Laplace transform of the fully unsteady operator) for frequency-domain analysis is outlined

Morino, L.

Tseng, K.

English

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https://ntrs.nasa.gov/search.jsp?R=19750018233 2020-03-22T21:38:11+00:00Z
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(NASA -CR-1429TH) SUSSA ACTS: A COMPUTER
PROGRAM FUR STEADY AND Uk5'tEADY, SUBSUNIC
AND SUPERSONIC AFPODYNAMICS FOR AEROSPACE
COMPLEX TPANSPORTATION SYSTEMS (Hostan
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SUSSA ACTS'
A Computer Program for Steady
and Unsteady, Subsonic and
Supersonic Aerodynamics for
Aerospace Complex Transportation
Systems+
by
Ka Din Tseng* and Luigi Morino**
Boston University
+ This work was supported by a NASA Grant NGR-22-004-030.
Technical Monitor Dr. E. Carson Yates.
Graduate student, research assistant, student member AIAA.
** Associ-ate professor, member AIAA.
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SUSSA ACTS: A Computer Program for Steady and
Unsteady, Subsonic and Supersonic
Aerodynamics for Aerospace Complex
Transportation Systems
by
Ka Din Tseng and Luigi Morino
Boston University
Presented here is the final version of the computer pro-
gram SUSSA ACTS ( Steady and Unsteady, Subsonic and Supersonic
Aerodynamics for Complex Transportation §ystems). The paper
includes the numerical formulation, the description of the
program and numerical results. In particular, generalized
forces for fully unsteady (complex frequency) aerodynamics for
a wing-bod y configuration, in both subsonic and supersonic
flows, are included.
The mathematical analysis, based upon an integral formula-
tion presented in Refs. 1 and 2, includes completely arbitrary
motion. The numerical implementation of Refs. 3 and 4 was
limited to steady and oscillatory flows. On the other hand,
in order to perform a linear-system analysis of the aircraft,
it is convenient to use more general aerodynamic formulation,
i.e., fully transient response for time-domain analysis, and
the aerodynamic transfer function (Laplace transform of the
fully unsteady operator) for frequency-domain analysis (Ref .
5). Such formulation is outlined (at least in preliminary
form) in Ref. 6, where some numerical results (for pressure
on thin rectangular wings) are also presented*
*The formulation is presented in details in Ref. 7, enclosed
-here.
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The formulation has now been completed and implemented in
the computer program SUSSA ACTSB Numerical results are also
available. The formulation, the program and the results are
also presented in this paper. Since the present paper is an
extension of Ref. 6, only the items not considered in Ref. 6 are
presented here (detailed description of some of these items is
given in Ref. 7, attached here). These include:
1. Evaluation of the downwash for complex configurations
from prescribed three dimensional mode shapes (Ref. 6
was limited to thin wings with vertical displacements).
2. Improved evaluation of the potential from the downwash:
the analysis in the supersonic regime is now as simple
as its subsonic counter part (Ref. 6 had to introduce
diaphragm for supersonic partially subsonic wing plan£orm)
3. Finite-element evaluation of pressure (Ref. 6 used
finite-difference and was limited to thin wings).
4. Evaluation of fully-unsteady generalized forces for
arbitrary configurations (Ref. 6 was limited to lifts
and moments for thin wings). "To the author's knowledge
this is the only computer program which can handle
fully unsteady (complex-frequency) aerodynamics for
complex configuration(wing-body-tail preprocessor is
already available). For such configurations other
programs can handle only steady state in the supersonic
range, and only wing-body configurations in oscillatory
motion for the subsonic range.
METHOD OF SOLUTION
The method presented here is based upon a formulation
developed by Morinol,2 . The formulation, by making use of the
Green function method applied to the equation of the velocity
potential, yields an integral equation relating the unknown
potential on the surface of the body to its known downwash.
By maki.ng use of . the finite-element method, and by the
assuming	 that the potential is constant within each quadri-
-17
- 4 -
are presented in Ref. 9 where it is also shown why in the for-
mulation of Ref. 6 the use of the diaphragm was necessary in
order to avoid determinants equal to zero•(. in the new formulation
the time delay,e±, is evaluated from the centroid of the portion
of the element inside the Mach forecone, instead of the centroid
of the element itself ).
NUMERICAL RESULTS
Because of space limitation, only a few basic results are
presitiEed in this meeting abstract: additional results will be
included in the final paper.
The results presented here are divided in two groups.-In
the first group the results are compared with existing ones
in order to assess the accuracy of the new formulation. The second
group deals with complex-frequency aerodyn!mics for which no
other ( experimental or theoretical) results exist: these are
presented in order to give an idea of the capabilities of the
program SUSSA ACTS.
Tipical results of the first group are p):-asented in Fig. 1:
lift and moment for a rectangular wing oscillating in pitch 	 ia
with reduced frequency k=1, as functions of '-he Mach number.
The analysis of convergence for the supersonic range is presented 	 1
in Fig. 2 and indicates that the small difference with exis-
ting results might be due to convergence. A more thorough
x
convergence analysis is now under way. It should be emphasized
again that the results of Morino and Chen are obtained using
a diaphragm, while the present results are obtained without
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In the second group of results, a wing - body configuration
oscillating in pitch with complex frequency s = .2 + it is
considered. The wing is rectangular with chord c = 1, span s = 6,
thickness h = .09. The body is composed of three parts. The cen-
tral portion is cylindrical with radius r c= .5 and length l c = 1.
The forward portion has rf = 1/2 - 1/8(x - xLE)2 and length
if
 = 2. The aftward portion simulates the body wake and is
cylindrical with length 1  = 9 and radius rA = .5. The configura-
tion is symmetric. Therefore the results are antisymmetric.
The pressure distribution is presented in rig. 3 and 4 for
M = . 24 and 1.42 respectively. The lift (per unit dynamic
pressure is L = 1.39 + il.51, for M = .24, L = 1.85 + il.78 for
M= .5, L = 2.77 + i2.39 for M = .75 and L = 1.35 + i0.36 for M = 1.42.
CONCLUSIONS
The formulation, the computer program SUSSA ACTS and numerical
results have been presented. The program is the only existing
program for steady, oscillatory and fully unsteady, subsonic and
supersonic aerodynamics around completely arbitrary aircraft
configurations. Other existing programs for complex configurations
can handle only wing-body configurations in oscillatory subsonic
flow, and arbitrary configurations in steady subsonic and super-
sonic flows.
1
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Improvements with respect to the formulation of Ref. 6 in-
c^
	 clude (see Introduction) the arbitrary-configuration complex
frequency evaluation of the downwash, of the pressure coefficient
and the generalized forces, as well as a new technique which
allows for the same treatment for both subsonic and supersonic
range (no diaphragm required).
The results are in good agreement with existing ones. Also,
the results for complex-frequency subsonic and supersonic genera-
lized forces for wing-body configuration are the first ones
ever obtained.
1REFERENCES
1. Morino, L., "A General Theory of Unsteady Compressible
Potential Aerodynamics', NASA-CR-2464, 1974 (supercedes
Boston University ENG-'.R-72-01, 1972).
2. Morino, L., "Unsteady Compressible Potential Flow Around
Lifting Bodies : General Theory", AIP.A Paper No. 73-196, 1973
3. Morino, L.,and Kuo, C.C.,"Subsonic Potential Aerodynamics
for Complex Configurations : A General Theory", AIAA J.,
Vo1.12,No.2, Feb. 1974,pp. 191-197.
4. Morino, L.,Chen, L.T.,and Suciu., E.O.,"Steady and oscilla-
tory Subsonic and Supersonic Aerodynamics Around Complex
Configurations", AIAA J.,Vo1.13,No.3, March 1975, pp. 368-
374.
5. Lomax, H.,"Indicial Aerodynamics", AGARD Manual on Aero-
elasticity,Part II,Chapter 6, Nov. 1960.
6. Morino, L.,and Chen, L.T.,"Indicial Compressible P'.)tential
Aerodynamics'Around Complex Aircraft Configurations",Present-
ed at the NASA Conference on Aerodynamic Analysis Requiring
Advanced Computers. (Hampton, Va.),March 4-6, 1975.
7. Noll, R.B.,I4orino, L.,"Flight Control Analysis Program(FCA'P)
for Arbitrary Configuration Flexible Aircraft with Active
Control",Vol. I,ASI-TR-75-23, May, 1975:(pertinent sections
enclosed here)
8. Tseng, K.D.,Chen, L.T.,and Morino, L.,"SUSSA ACTS : Steady
and Unsteady, Subsonic and Supersonic,Aerodynamics for Aero-
space Complex Transportation Systems",Vol. II : A User's
Manual. In preparation.
9. Tseng, K.D. and Morino, L.,"Unsteady Supersonic Formulations
for SUSSA ACTS",B.U.C.E.-TR-75-01,in preparation.
10. LF.schka, B.,"Zur Theorie der Harmonisch Schwingenden Tragenden.
Flache bei Unterschallenstromung",Zeitschrift fur Flugwis-
senschaften, 11 (1963),Heft 7, pp. 265-292.
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lateral element, the integral equation is approximated by a linear
system of N equations relating N (unknown) values of the poten-
tial to N (known) values of downwash at the centroids of N elements.
For the sake of generality and flexibility, in particular,
for structural analysis, the downwash is expressed in terms of
the generalized coordinates and generalized velocities (see 	 V :i
section 3-3 of Ref. 7).
From the potentials at centroids of elements, by an averagi,ig
scheme (by which the potential at a corner is approximated by
the average value of potentials at the centroids of the elements
in its immediate surroundings, see section 3-4 of Ref. 7)
	 the
potentials at the nodal points are obtained and consequentially
the potential at any point on the surface can be expressed by
a finite-element interpolating formulation with bi-linear global
shape functions. Finally, the pressure coefficients and gener-
alized forces can :,a evaluated by eqs. 3-51 and 3-54 of Ref. 7.
COMMENTS ON SUPERSONIC FORMULATION
In Refs. 4 and 6, the equations for the upper and lower
surfaces were solved independently for supersonic leading edge
wings while diaphragms were used for wings with partially or
totally subsonic leading edge. In the final version-of SUSSA
ACTS, supersonic unstc_,dy flow is treated exactly as in the sub-
sonic case, that is, both surfaces are considered simultaneously
and diaphragms can be removed without any loss of accuracy or
efficiency. This is a considerable improvement. For, the use
of the program is now very simple in the subsonic regime as well
as in the supersonic range. The details of the new formulation
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SUSSA ACTS: A computer program for steady and unsteady, subsonic and supersonic aerodynamics for aerospace complex transportation systems

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