The program SUSSA ACTS, steady and unsteady subsonic and supersonic aerodynamics for aerospace complex transportation system, is presented. Fully unsteady aerodynamics is discussed first, followed by developments on normal wash, pressure distribution, generalized forces, supersonic formulation, numerical results, geometry preprocessor, the user manual, control surfaces, and first order formulation. The ILSWAR program was also discussed

Morino, L.

English

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https://ntrs.nasa.gov/search.jsp?R=19750017800 2020-03-22T21:42:31+00:00Z
(NASA-(:P-'42979)
	 COMPPESSIBLE UNS - F,AUY	 N75-2587
POTENTIAL. AEFonYNAMIC FLOW AkOUND LIFTING;
bOuIFS HAYING ARBITPAPY SHAPES AND MUTIONS
eaiennual Peport, 1 Jan. - Y) .Jun. 1975
	 Uacias
(Noston Un iv.)
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BOSTON UNIVERSITY
DEPARTMEN'P OF AEROSPACE ENGINEERING
	
.;	 BOSTON, MASSACHUSETTS 02215	 yyP
	
i	 M
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i
Seventh Semiannual Report for
NASA Grant for Research on	 {'
"Compressible Unsteady Potential 	 {
Aerodynamic Flow Around Lifting
Bodies Having Arbitrary Shapes
and Motions" (NGR-22- 009-030)
Covering the Period:	 Ali
January 1 thru June 30, 1975	 j
Principal Investigator:
Dr. Luigi Morino	 j
t
j
{
t
..; m:repared for	 iit
F
	NASA LANGLEY RESEARCH CENTER	 i
Hampton, Virginia
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1. Introduction
This is the Seventh Semiannual Report (covering the
period January ?. - June 30, 1975) for the NASA Grant NGR
22-00'+-030 for "Research on Compressible Unsteady Potential
Flow Around Lifting Bodies Laving Arbitrary Shapes and
Motions". Tt.e NASA Technical officer for this grant is
Dr. E. Carson Yates, Jr., of NASA Langley Research Center.
The objectives of the extension covering the period
January 1 - December 31, 1975 are:
1. Refinement of the program SUSSA ACTS to include:
fully unsteady aerodynamics, wing-body-tail
configurations, improved evaluation of the
pressure, evaluation of generalized aerodynamic
forces, special elements for control surfaces.
2. Assessment (and eventual full coxputer program)
for first-order solution, with varicus techniques
for improving the Kutta condition.
3. Additional items such as gust response and
nonlinear effects in supersonic and transonic
flaw (time permitting) .
2. Accomplished Results
The results accomplished duri
covered by this report (January 1
presented in this Section.
The results relative to SUSSA
followed by the ones for ILSA and
ng the six-month period
to June 30, 1975) are
ACTS are presented first,
by the flutter analysis
-3-
and the nonlinear analysis.
2.1 SUSf;A ACTS
The program SUSSA ACTS (Steady and Unsteady Subsonic and
Supersonic Aerodyr.am s for Aerospace Complex Transportation
System) is presented here. The new dc-velopment for fully
unste^4av findicial) aerodynamics is discussed first, followed
by new developments on normal wash, pressure distribution,
ge:laralized forces, supersonic formulation, numerical re-
sults, geometry preprocess_r, the user manual, control surfaces
and first-order formulation.
2.1.1 Indicial Aerod-namics
It is a well known issue in aeronautical engineering that
there exists a gap between the aerodynamic and control metho-
dology. Modern linear control. theories are based upon opera-
tional calculus (Laplace's transform, etc.), while aerody:iamic
theories around complex aircraft configurations are limited
to steady and oscillating flows. This limitation is not a
problem for flutter analysis (whereby the problem is circum-
vented by the introduction of the classical artificial- damping
concept). However this limitation becomes a problem, if
maneuverability and transient response are to be investigated.
On the other hand in this kind of analysis it may be assumed
that the motion consists of small per arbations around a
steady flow, and starts at time t=0 (this hypothesis is consis-
tent with the ones used for control analysis). Under these condi-
-4-
tions it is possible (wit!. the help of the finite-element
method for the space discretization) to obtain a very simple
and general formulation for unsteady potential compressible
aerodynamic flow for arbitrary (small-amplitude) motion. ThiF
formulation is presented in Ref. l where it is shown that the
relationship between the nodal-values of the velocity potential
and the ones of its normal derivative on the surface of the
aircraft is given by a system of differential-delay equations.
Taking the Laplace transform of this system one obtains an
algebraic matrix equa` i.on from which it is easy to obtain the
matrix transfer function. 	 During the past six months the
computer program SUSSA ACTS has been improved considerably.
The program has been simplified so that the coCe can Oe used
in the same way for steady oscillatory and unsteady, subsonic
and supersonic flows (no dia phragms are now required in
supersonic flow).
2.1.2 Normal Wash
A new formulation has been developed for the evaluation
of the normal wash from the boundary conditions. This formu-
lation allows for the eva l uation of the normal wash from
prescribed three-dimensional modes for completely arbitrary
configurations.
2.1.3 Evaluation of Aerody nanic Pressure
A new formulation has been developed for the evaluation
of the aerodynamic plassure. In SOSSA ACTS (Ref. la) a finite-
-5-
difference evaluation was being used. in RUSSA ACTS a finite-
,
	
	 element method is used. From the values of the potential
	 at
the centroids, the value of the potential at tie nodes is
evaluated (by average); from these, a hyperboloidal distribu-
tion of the potential within the elements and hence its de-
rivatives along T and	 are obtained. These yield the
perturbation velocity as
where ck* are the contravariant base vectcrs. From the ve-
lccity, the pressure can be easily evaluated through the
Bernoulli theorem. This formulation has been programmed
debugged and exercized. Several alternative methods have been
considered :or the extrapolation at the trailing edge. A
report describing the results is now being written. The
additional complexity introduced by other met' 	 does not
seem to be justified by the slight increase in 	 ;uracy.
?.1.4 Generalized Forces
A _general routine for the evaluation of the generalized
aerodynamic forces (from prescribed mode shapes) is now
available. These forces are given by
i	
MM dZ
where N is the prescribed mode shape (natural mode of
vibration). The integral can be evaluated by dividing it
-6-
into a sum of integrals over each element and evaluating
each integral by midpoint quadrature. The generalized
forces are evaluated as
1	 ^
= 4(4,N,02.,`1NI	 ^r`^ripL
where fa` 	 Lare the values of P at the nodes while [Q I is a
matrix which depends only upon the (geometry and the mode
shape (so that it can be evaluated once and for all and used
for various values of the Mach number and reduced frequency).
2.1.5 Supersonic Formulation
In SOSSA ACTS, 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 unsteady flow is treated exactly as in the
subsonic case, that is, both surfaces are considered simultan-
eouly 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
as well ,s in the supersonic range. The details of the new
formulation are presented in Ref. 3 where it is also shown
why in the formulation of Ref. 1 the use of the diaphragm was
necessary in order to avoid determinants equal to zero (in
the new formulation the time delay is evaluated from the
centro4d of the portion of the element inside the Mach fore-
cone, instead of the centroid of the element itself).
_7_
2.1.6 Numerical Results
The program SUSSA ACTS has been debugged and exercised.
The results obtained thus far are divided in two groups.
Ir. the first group the results are compared with existing ones
in order to assess the accurac , of the new formulation. The
second group deals with complex-frequency aerodynamics for
which no other (experimental or theoretical) results exist:
these are presented in Ref. 4 in order to give an idea of the
ca-abilities of the program SUSSA ACTS.
Tvpical results of the first group are presented in Ref. 4:
lift and moment for a rectangular wing oscillating in pitch
with reduced frequency k=1, as functions of the Mach number.
The analysis of convergence for the supersonic range is also
presented and indicates that the sr-All difference with existing
results might be due to convergence. A more thorough conver-
gence analysis is now under way.
In the second group of results, a wing-body configuration
oscillating in pitch with complex frequency s = .2 + it is
considered. Pressure distribution and generalized forces
are included.
2.1.7 Geometry Preprocessor
A new geometry preprocessor has been written. This includes
wing, body, vertical and horizontal tail. Matching of tail
and body is now underway.
q
I-8-
2.1.8 User Manual
The user manual has been written (Ref. 5) and will to
subm':ted shortly.
2.1.9 Control Surfaces
The control surfaces yield a logarithm singularity for
the pressure along the hinge line. This singularity can be
easily handled at present time by smoothing the slope d.iscon-
tnui*_y. However, small elements are then necessary in ucder
to handle the high curvature of the smoothed surface. There-
fore the ;ucstion of special elements is now being explored.
The analysis is now limited to simple wings in subsonic flow.
If a satisfactory approach is obtained (such as a square
root description for the potential) and if time permits the
formulation would be included in the program S's SSA ACTS.
2.1.10 First-order Formulation
The finite element formulation has been refined to allow
for linear variations in
	 and n directions of the intensity
of tl-e source and the doublet integrals within each element.
It should be noted that in view of the high priority given to
the nonlinear analysis (high subsonic and low supersonic, section
2.3) it was agreeed, with Dr. E. Carson Yates, Jr., technical
monitor of the grant, that the first order formulation be given
lower priorities. The present preliminary analysis is limited
to steady subsonic flow. Parallelipipedal elements are now
available. Various ways to implement the Yutta condition are
f
_g_
now being explored. Add±.iional work on first order formulation
is given in Section 2.2.3.
2.2. ILSAWR
The program ILSAWI(incompressibl.e lifting surface aerody-
namics with wake roll-up) is described here. The computer
program SUSSA ACTS, analyzes steady and oscillatory subsonic
and supersonic flows around complex configurations. For
applications to wing-body combinations the hypothesis of
straight-vortex wake seems to be acceptable. However, an
accurate analysis of the wing-tail interaction might require
the correct geometry of the wake. The aim of this portion
of the project was to assess a numerical procedure for the
evaluation of the effects of the wake geometry to several
configurations. Lifting-surface theory has been used for
the purpose of performing the feasibility analysis, in order
to avoid unnecessary complications in this preliminary analysis.
Once the method is proven, it is a straight-forward matter to
extend the formulation to SUSSA ACTS.
2.2.1 Formulation
The method considered here makes use of a theoretical
formulation developed by Morino and Suciu (Ref. 6). The wake-
roll-up implementation is g4.ven in Ref. 7. As the thickness
of the wing goes to zero, one obtains a lift:.,-ig surface
formulation
a no	 X 4 7 na no` r
	 (2.1)
^I
_lp_
For the purpose of solving (2.1), the lifting surface is divided
into small qudrilateral elements (hyperboloidal elements) with
the geometry given by the four corner points. For the approach
considered here, it is assumed that the value of the doublet
intensity is constant over the surface of an element, say at
the centroid. The wake contributes only to the row of boxes in
contact with the trailing edge. A system of linear algebraic
equations, in the unknowns, .''t is obtained by imposing the
boundary condition at the centroids of the elements. The doublet
distribution is then easily obtained.
For obtaining a rolled-up geometry for the wake, the
following scheme is used: the wake is initially assumed to
consist of staight vortex lines. The wake strips are then
divided into boxes. By taking the gradient of the velocity
potential, one can easily obtain the velocity induced by the
wing and the wake at any point: in the flow field, in particular
at the corner points of the wake elements. Then, the vortex
lines of the wake are realigned to be parallel to the velocities
at prescribed points. This gives a better approximation to
the problem. An improvement is obtained by a process of
iteration. The convergence of the iteration scheme has also
been considered here.
2.2.2 Results
The lifting surface formulation described above has been
4.mplemented in a computer program ILSAWR (acronym for Incompressible
1
i
_T
e^..i -__ I
-11-
Lifting Surface Aerodynamics with Wake Roll -Up). Typical
results are described here.
Converged wake patterns for a rectangular wing of AR - 8,
at 5° angle of attack are given in detail in Refs. 7 and 8.
Comparisons with existing results as well as the influence of
the rolled - uF wake on the pressure distribution on the wing
are also presented, ( the nonlinear Bernoulli Equation has been
used in evaluating the pressure coefficient).
The analysis of the convergence of the solution is pre-
sented in Appendix A of Ref. 7. The convergence of the
iteration scheme is considered in Appendix B. of Ref. 7.
2.2.3 First-Order Analysis
A first-order formulation for incompres3ible lifting
surface aerodynamics has been developed. A computer program
for implerTenting of such formulation has been written and is
now being debugged.
2.3 Flutter Analysis
A preliminary work for flutter analysis was completed
and is presented in Ref. la. Additional work in this direction
is not necessary in view of the development of the program
FCAP being developed by Aerospace Systems Incorporated (see
Ref. 9 . )
i
71-	 __ i - 
__
	
____ __
T
I - L
-12-
2.4 Nonlinear Analysis
The nonlinear formulation for low supersonic flow has been
improved with respect to the one presented as an appendix in
the grant proposal. The new formulation is given in Ref. 10.
for high subsonic flow. A preliminary computer program for nun-
linear analysis of rectangular wings in subsonic flows is now
being written. It is hoped that the numerical results might
give a new insight about the supercritical subsonic range.
3. References
Morino, L., and Chen, L.T., "Indicial Compressible Potential
Aerodynamics Around Complex Aircraft Configurations",
Presented at the NASA Conferencte on Aerodynamic Analysis
Requiring Advanced Computers.
	
(Hampton, Va.), March 4-6, 1975.
Ia. Chen, L.'P., Master Thesis, Boston University, College
of Engineering, 1975.
2. Morino, L., Chen, L.T., and Suciu, E.O., "Steady and
Oscillatory Subsonic and Supersonic Aerodynamics Around
Complex Configurations", AIAA J., Vol. 13, No. 3, March
1975, pp. 368-374.
3. Tsenq , K.D. and Morino, L., "Unsteady Supersonic Formu-
lations for SUSSA ACTS", Boston University, College of
Engineering, TR-75-01, in preparation.
4. Tseng, K.D., and Morino, L., "SUSSA ACTS: A Computer
Program for Steady and Unsteady, Subsonic and Supersonic_
Aerodynamics for Aerospace Complex Transportation Systems"
submitted for presentation at the AIAA XIV Aerospace
Sciences Meeting.
5. Tseng, K.D., Chen, L.T., and Morino, L., "SUSSA ACTS:
Steady and Unsteady, Subsonic and Supersonic Aerodynamics
for Aerospace Complex Transportation Systems", Vol. II:
A User's Manual., in preparation.
6. Morino, L. and Suciu, E.O., "A Finite-Element Method for
Lifting Surfaces in Steady IncDmpressible Subsonic Flow",
Boston University, College of Engineering, TR-74-05,
December, 1974.
-13-
7. Suciu, E.O., Master Thesis, Bosto.i University, College
of Engineering, 1975.
•	 8. Suciu, F. O., and Morino, L., "A Nonlinear Finite Element
Analysis of Lifting Surfaces in Steady IncompresEible
Flows with Wake Roll-up", submitted for presentation at
the AIAA XIV Aerospace Sciences Meeting.
9. Noll, R.B., Morino, L., "Fight Control Analysis Program
(FLAP) for Arbitrary Configuration Flexible Aircraft with
Active Control", Vol. I, ASI-TR-75-23, May, 1975.
10. Morino, L., "Nonlinear Analysis of Low Suspersonic Aero-
dynamics for Complex Aircraft Configurations", Boston
University, Colleqe of Eng ineering, TN-75-01, 1975.
R


Compressible unsteady potential aerodynamic flow around lifting bodies having arbitrary shapes and motions

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