Calculation of aerodynamic characteristics of airplane configurations at high angles of attack

119 Pages·2005·5.33 MB·English

https://ntrs.nasa.gov/search.jsp?R=19880019507 2019-02-28T23:58:55+00:00Z
NASA Contractor Report 4182
Calculation of Aerodynamic
Characteristics of Airplane
Configurations at
High Angles of Attack
J. B. Tseng and C. Edward Lan
FZight Research Laboratory
University of Kansas Center for Research, Inc.
Lawrence, Kansas
Prepared for
Langley Research Center
under Grant NAG1-635
National Aeronautics
and Space Administration
Scientific and Technical
Information Division
1988

SUMMARY
In this study, calculation of longitudinal and lateral-
directional aerodynamic characteristics of airplanes by the VORSTAB
code is examined. The numerical predictions are based on the
potential flow theory with the corrections of high angle-of -attack
phenomena; namely, vortex flow and boundary layer separation
effects. To account for the vortex flow effect, vortex lift, vortex
action point, augmented vortex l i f t and vortex breakdown effect
through the method of suction analogy are included. The effect of
boundary layer separation is obtained by matching the nonlinear
s e c t i on da t a with the t hre e -dime ns iona 1 1i f t chara c t e r i s t i c s
.
iteratively
Through correlation with results for nine fighter
configurations, it is concluded that reasonably accurate prediction
of longitudinal and static lateral-directional aerodynamics can be
obtained with the VORSTAB code up to an angle of attack at which
wake interference and forebody vortex effect are not important.
Possible reasons for discrepancy at higher angles of attack are
discussed.
. .
iii

LIST OF SYMBOLS
Fourier coefficients
an
b Span
C Local chord
-
C Mean aerodynamic chord
.CN A characteristic length in the calculation of
augmented vortex lift. See Equation (47).
c, C’ Sectional leading-edge singularity parameter
Sectional drag coefficient
‘d
Drag coefficient
CD
Induced drag coefficient
CDi
Sectional lift coefficient
CR
Total lift coefficient
CL
Rolling moment coefficient
CR
ac,/ a B
a‘;
ac,/
C ac ,/ aF
Rr
Sectional pitching moment coefficient
‘m
Total pitching moment coefficient
Cm
Yawing moment coefficient
Cn
acn/ a B
Body normal force coefficient based on maximum cross-
sectional area
Sectional normal force coefficient due to body vortex
‘N ,V
lift
c ~VA, Total augmented-vortex normal force coefficient on a
body
r 1
Pressure coefficient
cP
Lifting pressure coefficient
ACP
Sectional leading-edge suction coefficient
cS
-
2
C cc IC sin a
S s
Sectional leading-edge thrust coefficient
Total leading-edge suction coefficient
cs
Sectional side-force coefficient of a body
csf
Total suction force coefficient produced by a body
‘sf ,N
nose section
Sectional leading-edge thrust coefficient
Side force coefficient
Augmented vortex lift
Ratio of vortex-induced vertical velocity to the free
stream (Equation 65) or ratio of sectional lift
coefficients from 2-D and 3-D calculations (Equation
81)
h Vortex action point location on a body. See Equation
(73)
R Leading-edge length
Body nose length
RN
G Local tip suction singularity parameter
k Residual vortex l i f t factor
+
n Unit normal vector
N Number of chordwise vortex elements in a strip
P Roll rate
-
P pbf 2V,
Pitch rate
r Radial coordinate or yaw rate
r rbf 2V,
vi
-+
r Position vector
Average vortex action radius in producing force
'av
through momentum transfer. See Equation (46).
Leading-edge radius
rO
Vortex action point location measured from the
r V
leading-edge
R Body radius
S Reference area
Total tip suction coefficient
Induced velocity components along x, y, z
coordinates, respectively
Total velocity vector
Induced normal velocity
Freestream velocity
Cartesian coordinates with x being positive pointing
downstream, a positive y pointing to the right, and a
positive z pointing upwards
Body axial station downstrem of which the potential
xP
flow does not exist
Body axial station at which the vortex separation
XS
starts
Nondimensional x-distance from the trailing edge to
the vortex breakdown point
Leading-edge x-coordinate
Spanwise location of vortex breakdown point
nondimensionalized with respect to half span
- cs-
Nondimensional centroid location of the
YC
distribution from inboard to II of cs(max)
Distance from apex toc centroid of cs-distribution
from inboard to n of , measured along the
leading edge and refergd8at& half span
vii
4
=e Camber surface ordinate
z-coordinate of the leading edge
2%
Greek
a Angle of at tack
a Sectional angle of zero lift
0
a for vortex breakdown at the trailing edge in
symmetrical loading
a Angle of attack of initial vortex separation
S
a Difference in angles of attack at tip and root
tw
sections, negative for washout
B Sideslip angle, or 4 3
Aileron deflection angle
6A
6 Angle of chordwise camber slope
C
6r Rudder deflection angle
11 y/b/2
r
Sectional circulation
Nondimensional streamwise vortex density
yX
Y or Y Nondimensional spanwise vortex density
Y
A Sweep angle
Geometric dihedral
Velocity potential
P Dens ity
8 Angular coordinate of a body cross section
Angular location of the augmented-vortex action point
on a body cross section
Angular location of the vortex action point on a body
cross section
viii
Subscript
a Ant isymmetr ical loading
aug Augmented
a Due to a in symmetrical loading
B Sideslip
BR Vortex breakdown on the right wing
BL Vortex breakdown on the left wing
f Fuselage
R Leading edge
maX Maximum
n Normal direction
P Roll rate
r Yaw rate
t Tip
tw Twist
v, le Leading-edge vortex
W Wing
Normal to a planform
Z
W Freestream
Abbrevi at io n
PAN AIR Panel Aerodynamics
QVLM Quasi-Vortex-Lattice Method
SAAP Stalled Airfoil Analysis Program
VSmRO Vortex Separation Aerodynamics