NASA Contractor Report 4066

Aerodynamic Analysis for Aircraft

With Nacelles, Pylons, and Winglets

at Transonic Speeds

Charles W. Boppe

CONTRACT NAS1-14732

APRIL 1987

G3/02
F

#

.... ± :-

.... x:__

z

_:T,-_/_-! '_7 _ ......
NASA Contractor Report 4066

Aerodynamic Analysis for Aircraft

With Nacelles, Pylons, and Winglets

at Transonic Speeds

Charles W. Boppe

Grumman Aerospace Corporation

Bethpage, New York

Prepared for

Langley Research Center

under Contract NAS1-14732

N/ A

National Aeronautics

and Space Administration

Scientific and Technical

Information Branch

1987

OONTENTS

Page

O0_ATIONAL METHOD .................................................... 9

Flow Equation ...................................................... 9

Computational Grid Approach ........................................ I0

Pod & Engine Nacelle Surfaces ...................................... ii

Pylon Surfaces ..................................................... 20

Winglet Surfaces ................................................... 25

Solution Process ................................................... 28

Pressure, Force &_nt Coefficients .............................. 30

Two-Dimensional Airfoil Analysis ................................... 33

OOMPARISONS &TYPICAL RESULTS ........................................... 37

Airfoil Correlations ............................................... 37

Nacelle Flow Simulations ........................................... 39

Pylon Interference Effects ......................................... 44

Winglet Flow Simulations ........................................... 46

Combined Interference Effects ...................................... 48

OONCLUDIN3 REKA_RKS...................................................... 55

APPENDIX A - COMPUTER 03DE DESCRIPTION .................................. 57

APPENDIX B - USAGE/MODIFICATIONS FOR _ CDC/VPS-32 VERSION ............ 131

APPENDIX C - GENERAL RECOMMENDATIONS FOR 09DE USAGE ..................... 137

REFERENCES .............................................................. 145

iii _ PAGE BLANK .NOT FiI.,M_D
Figure

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3

4

5

6

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8

9

10

11

12

13

14

15

16

17

ILLUSTRATIONS

Growth in Geometric Complexity for Transonic Flow

SL_ulations ...............................................

Multiple Grid Approach for Complex Aircraft Flow

Simulations ...............................................

Computational and Physical Nacelle Streamtube Surfaces ....

Crude/Fine Grid Arrangement for Pods and Nacelles .........

Nacelle and Pod Side Boundary Points ......................

Nacelle Inlet and Exhaust Boundary Points .................

Global Crude Grid Adjustment for Nacelle Positioning ......

Pylon Surface Boundary Points in Wing Fine Grid

System ....................................................

Physical and Computational Pylon Surfaces .................

Grid Points Required for Computing Pylon Inboard/Outboard

Boundary Conditions .......................................

Wing Tip Spanwise Grid System for Winglet and

Conventional Type Planforms ...............................

Crude/Medium/Fine Grid Arrangement for Wing-Tip-Mounted

Winglets ..................................................

Boundary Conditions at Infinity for Wing-Body

Analysis ..................................................

Boundary Conditions at Infinity for Airfoil Analysis ......

Two-Dimensional Airfoil Pressure Distribution

Correlation ...............................................

G-III with Pressure Tap Locations for Nacelle

Interference Study ........................................

G-III Nacelle On/Off Superimposed Computed Wing Upper

Surface Pressure Distributions, M_ = 0.85, a = 0 ° .........

Page

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10

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39

4O

iv
Figure

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19

2O

21

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25

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27

28

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31

32

ILLUSTRATIONS (cont 'd. )

G-III Nacelle On/Off Wing Pressure Distribution

Correlations, M_ = 0.85, a = 0 ° ...........................

C-5A Configuration ........................................

C-5A Inboard Nacelle Pressure Distribution

Correlation, M_ = 0.775, a = 2 °, NPR = 2.84 ...............

Comparison of C-5A Inboard Nacelle Port and Starboard

Pressure Distribution Correlations, M_ = 0.775, a = 2 ° ,

= 2.84 ................................................

C-5A Wing Stations for Pylon/Nacelle Interference

Study .....................................................

C-5A Inboard Engine Station Pressure Distribution

Correlation, M_ = 0.775, a = 2 °, NPR = 2.84 ...............

C-5A Outboard Engine Station Pressure Distribution

Correlation, M_ = 0.775, a = 2 °, NPR = 2.84 ...............

G-III Wing/Winglet Pressure Tap locations for

Evaluating Winglet Interference ...........................

C--III Wing Tip Pressure Distribution Correlation,

= 0.75, a = 4 ° .........................................

G-III Winglet Pressure Distribution Correlations,

M_ = 0.75, e = 4 ° .........................................

G-III Wing Pressure Distribution Correlation,

M_ = 0.78, a = 4 ° .........................................

Boeing KC-135 Wing and Winglet Pressure Distribution

Correlations, M_ = 0.78, _ = 2 ° ...........................

C-141 Configuration .......................................

C-141 Fuselage Geometry Model .............................

C-141 Wing Pressure Distribution Correlation,

M_ = 0.77, _ = 1.2 °, Re = 2x16 v ...........................

Page

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53

V
Figure

A-3

A-4

A-5

A-_

A-7

A-IO

A-II

A-12

ILLUSTRATIONS (cont 'd.)

Input Data Sequence .......................................

Sign Convention for Wing/Body and Wing/Nacelle

Position Variables ........................................

Body Boundary Point Limiters ..............................

Embedded Body Fine Grid Boundary Limiters .................

Sign Convection for Angular Argument of Fuselage/Nacelle

Pressure Output Stations ..................................

Sample Input Geometry Verification Plot with Error

in Z-Coordinate of Canopy Definition ......................

Sample Input Geometry Verification Plot with Error

in Y-Coordinate of Canopy Definition ......................

Sample Input Geometry Verification Plot for Fuselage ......

Sa_le Input Geometry Verification Plot for Wing

Sections ..................................................

Sample Input Geometry Verification Plot, Plan View ........

Sample Input Geometry Verification Plot, Head-on View .....

Sample Geometry Verification Plots for Configurations

with Nacelles, Pylons, and Winglets .......................

Page

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vi
SUMMARY

A computational method has been developed to provide an analysis for

complex realistic aircraft configurations at transonic speeds. Wing-fuselage

configurations with various combinations of pods, pylons, nacelles, and

winglets can be analyzed along with simpler shapes such as airfoils, isolated

wings, and isolated bodies. The flexibility required for the treatment of such

diverse geometries is obtained by using a multiple nested grid approach in the

finite difference relaxation scheme. Aircraft components (and their grid systems) can be added or removed as required. As a result, the computational

method can be used in the same manner as a wind tunnel to study high-speed

aerodynamic interference effects. The multiple grid approach also provides

high boundary point density/cost ratio. High resolution pressure distributions

can be obtained. Computed results are correlated with wind tunnel and flight

data using four different transport configurations. Experimental/computational

component interference effects are included for eases where data is available.

The computer code used for these comparisons is described in the appendixes of

this report.
2
INTRODUCTION

There has been a dramatic growth in the development of transonic computational methods during the past ten year period. This growth is stimulated

by the important role that high-speed non-linear methods now play in the detailed aircraft aerodynamic design process. Many advances have been related

to improvements in computing efficiency. In addition, the ability to treat complex geometric shapes has steadily improved. Murman and Cole (1), Bailey and

Steger (2), Keller and South (3), and Jameson and Caughey (4) have made important contributions to this evolutionary process. The primary goal of these efforts is the development of tools for solving practical aircraft design and analysis problems.

The first analysis schemes were applied to simple 2-D airfoil shapes and

axisymmetric bodies (see Fig. 1). Soon after this, isolated wing methods

evolved. Computations were performed on simple wing-body shapes during the

mid-1970's period. By 1980, aircraft configurations with various combinations

of nacelles, pylons, and winglets _5)'" could be analyzed.

Two different approaches have been implemented in the past. The first,

and simplest, employs a small disturbance-type flow equation coupled with

mean-surface boundary conditions. In time, it was noted that the classical

transonic small disturbance equation was not well suited to the analysis of

swept wing flows. The proper shock strength and the velocity at which the

flow equation changes type is not inherent in the equation when shock waves

have appreciable sweep. For this reason, today's small disturbance formulations typically incorporate a modified or extended small disturbance flow

equation. The second, and more sophisticated approach, employs the full potential equation (or Euler's equations) coupled with surface-conforming boundary conditions. This approach is complicated, not so much by the use of the

more complete flow equation, but rather by the difficulties associated with the

__ PAGE _LA_I_ HOT Ft_

3
application of exact boundary conditions. As configurations become more complex, it becomes difficult to construct a suitable coordinate system. As a result, the availability of full potential equation methods has" lagged that of the

small disturbance methods by several years.

Until recently, small disturbance and full potential equation methods were

constructed about a single continuous grid system. This approach provides a

smooth transition from the near to the far field regions when proper stretching

functions are used, but for a case as simple as a wing-body combination,

where axial grid point resolution must be high for the body and spanwise resolution must be high for the wing, problems arise. Problems are caused by

time and core storage restrictions of current computers and inefficiency of the

combined axial/spanwise grid system which stretches into the far field where it

is not required. Transonic wing-body analysis codes with single continuous

grid systems exhibit poor resolution on either the body or the wing because

these surfaces are not aligned. These difficulties can be overcome by not

implementing the traditional single grid approach.

SPE - SMALL PERTURBATION EQUATION

FPE - FULL POTENTIAL EQUATION

EE - EULER EQUATIONS

1971 - SPE 1976 - FPE 1972 - SPE

1972 - FPE _') 1974 -- FPE

1976- EE _ 1981 - EE

AIRFOIL AXISYMMETRIC BODY WING

1975 - SPE

1977 - FPE

WING-BODY

R84-I 137-0010

1978 - SPE

1979- FPE

WING-FUSELAGE

1980 - SPE

e2

WI NG-FUSELAGE-NACELLES-PYLONSWINGLETS-CANARDS

Figure 1 Growth in Geometric Complexity for Transonic Flow Simulations
Grid orthogonality presents another problem for "exact" boundary condition formulations. Boundary/grid orthogonality is easy to achieve for simple

2-D and 3-D shapes, but for complex shapes such as a wing-nacelle-pylon arrangement, it may be physically impossible to achieve an orthogonal grid for

all surfaces simultaneously. This often results in a lack of orthogonality at

the critical pylon-nacelle station. This could, depending on the severity of

the flow condition and the geometric shape, produce a jump in the metric

across the pylon-nacelle span line. The resulting "numerical" interference

effect might be interpreted as an "aerodynamic" interference effect during

applications. This also suggests, then, a re-evaluation the conventional single

grid approach.

When configurations are examined by wind tunnel testing, various components such as pods, pylons and winglets are removed and reattached to evaluate aerodynamic interference effects. If a three-dimensional computational

method is developed using the single grid approach, it will be necessary to

find a different coordinate mapping for each configuration modification. Perhaps a separate computer code would be required for each geometric shape involved. The configurations boundary points, mesh resolution, and ultimately,

the computed flow field would vary with each change to the coordinate system.

This problem is minimized if multiple grid systems are used. A single computer code can be used for the analysis of isolated bodies, isolated wings, and

wing-fuselage configurations with nacelles and additional lifting surfaces.

Boundary surfaces, along with their embedded mesh systems, can be added or

removed for analysis much in the same manner as wind tunnel model parts during experimentation.

A simple multiple nested grid approach was described in NASA CR-3243

(Reference 6). The simplicity of the grid embedding scheme is stressed because the probability of successfully simulating a transonic flow about a complex configuration will be increased if the methodology is simple. This report

describes the extension of the Reference 6 method to include the simultaneous

treatment of multiple wing and body surfaces. In particular, the provisions

that have been made for the analysis of pods, nacelles, pylons and winglets
are noted. The small disturbance character of the original wing-body method

is retained. The mean surface approximation permits the extensive use of rectangular coordinate arrays. This plays an important role in keeping the method simple.

The basic transonic Wing-Body COde (WIBCO) was described in Reference

6. As a result of this effort, a new computer code has evolved (WIBCO-PPW)

which in addition to the wing, body and wing-body capabilities of WIBCO, includes the new pod, pylon and winglet analysis capabilities. This report

should be used along with Reference 6 since certain elements of the two codes

which are common are not repeated herein (i.e., wing viscous effects, arbitrary fuselage modeling, wing, body, wing-body flow simulations).

The WIBCO-PPW Code has been developed for both IBM and CDC type

computers. _ Comments on usage and features of the NASA CDC version of the

code have been included as Appendix B.

* The author would like to thank Dr. Perry Newman for many valuable discussions during this code development effort. In addition, Mrs. Kara Haigler

made significant contributions by refining and verifying the NASA CDC version

of the code.
NOMENCLATURE

SYMBOLS

b

C,c

c0,%

CF , Cf

CL,C£

%,%

Cp

f

g

L

M.A.C.

M

N,n

P

R,r

R

T

ll,vjw

V

X,Y,Z

I"

¥

AX, AY, AZ

A¢

6*

rl

Wing or winglet span

Wing or winglet chord

Drag coefficient

Friction drag coefficient

Lift coefficient

Moment coefficient

Pressure coefficient

Surface shape function

Acceleration due to gravity

Pod or nacelle length

Mean aerodynamic chord of wing

Mach number

Nacelle inlet mass flow ratio

Nacelle nozzle pressure ratio

Surface normal

Pressure

Nacelle/pod radius

Gas constant

Absolute temperature

Velocity components

Ve locity

Cartesian coordinate axes

Angle-of-attack

Angle-of-yaw

Circulation

Specific heat ratio (Cp/Cv)

Mesh sp_cing in X, Y, and Z directions

Mesh spacing in _, q, and _ directions

Change in perturbation potential between iteration cycles

Boundary layer displacement thickness

Wing or winglet span position (2 y/b)

Wing skewed coordinate axes

Perturbation potential

7
Winglet toe-out angle, measuredfrom symmetryplane

Winglet cant angle, measuredfrom wing plane

Subscripts:

av ,AV

Body,B

C

cold

D

e

FIELD

FRICTION

g

hot

I

i

ib

i,j,k

J

loc, LOC

MAX

0

ob

pod,POD

pyl

REF

S

WAVE

WING,W

x,y,z

_,n,_

OD

Average

Body

Computational

Cold jet

Dummy value

Exhaust

Field

Friction

Geometric

Hot jet

Induced

Inlet

Inboard

Mesh indices

Jet

Local

Maximum

Total

Outboard

Pod

Pylon

Reference

Static

Wave

Wing

Partial derivatives with respect to x,y,z

Partial derivatives with respect to £,n,

Infinity

8
COMPUTATIONALMETHOD

Flow Equation

The classical transonic small-disturbance flow equation written in terms of

the disturbance velocity potential has been extended by retaining additional

terms found in the full potential equation. These terms make it possible to

resolve shock waves with appreciable sweep on wings in the X-Y (wing) plane.

The global flow equation is:

[1 - M2 - (y + 1) M2a "f + i M2 ,2 1¢ - 2M',_

-= ,_ x 2 x xx _'-,y xy

+ [1 - (y - 1)M2¢ }_ + _ = 0

'_,x yy zz

(I)

This equation is also used in each component embedded grid system. The only

exception is the winglet embedded fine mesh system. Wing-tip-mounted vertical winglets may, at certain conditions, exhibit shock waves, swept in the X-Z

(winglet) plane. To improve the ability to capture this type of shock wave,

¥ + 1 M2¢2]_ _ 2M2

" "_ X XX ,o g Xg

the following flow equation is used:

[_ _,_2 _ (_+ _)M2

_ cu X

(2)

+ [_ - (Y- 1)_2o i_ + _ : o

:' X ZZ yy

In Equation (2), the X-Y cross-flow terms have been replaced by equivalent

X-Z cross-flow terms.

Pylon-type surfaces, in general, are not highly loaded. Shock waves are

expected to propagate normally off neighboring components. Since swept pylon

shock waves are not expected in most applications, special provisions involving

the flow equation have not been made.
Computational Grid Approach

The feature which distinguishes this approach from that of other methods

is the use of multiple embedded grid systems. Conventional schemes employ a

single continuous computing grid system. The multiple grid approach provides

many advantages, if the analysis of complex shapes is the primary concern.

Figure 2 illustrates a transport configuration with the aircraft component grid

system boundaries included. The entire arrangement is positioned in the

center of a global Cartesian coordinate system. The global grid is stretched

so that boundaries represent infinity. This grid also serves a second purpose; it provides a means for interactions between the component embedded

grid systems. Crude and fine grid systems interact or communicate by using

an overlap region wherein the flow is computed twice for each iteration. This

procedure is described in Reference 6.

GLOBAL CRUDE

GRID

j_J_

/ __"_ EMBEDDED FINE

GRID SYSTEMS

RB4-1137-002D

Figure 2 Multiple Grid Approach for Complex Aircraft Flow Simulations

10
The embedded grid systems provide computational resolution that is much

more detailed than that of the surrounding global crude mesh. A detailed

analysis is performed only in a region close to the configuration where gradients are high. Ideally, three-dimensional methods should permit grid densities

that are higher than two-dimensional and axisymmetric counterparts. This

need is generated by the increased complexity of a flow field which has an additional dimension. The present method fulfills this requirement. There are

100 evenly spaced mesh points available in the streamwise direction along fuselage, nacelle and pod surfaces. In addition, wing, pylon and winglet chords

are modeled using 100 streamwise points.

Discretization errors at the crude/fine grid interface are a function of

both mesh spacing and flow gradient. Fine grid boundaries are positioned

sufficiently far from the boundary surface to insure that these errors are

small. Numerical experiments were used to "set" grid interface boundaries.

Pod and Engine Nacelle Surfaces

The conventional technique generally applied to body or fuselage shapes

was initially used for simulating pod and nacelle surfaces. This required that

a computational surface representing the nacelle extend from upstream to downstream infinity. Nacelle boundary conditions were applied along the length of

tube starting at the inlet face and ending at the exhaust exit. Computations

indicated that this approach would not be satisfactory. It is suspected that

the problem is related to the difference between the physical and computational

streamtube surfaces (Figure 3). The difficulty is compounded since these

streamtubes typically pass very close to wing or body surfaces. Physical

streamtubes are deflected by wing upwash/downwash fields. In addition, they

are contoured by inlet mass flow ratio and exhaust pressure ratio effects. The

computational streamtube is constrained to lie along existing grid lines. These

tubes may be contoured by appropriate slope-type boundary conditions, but

the physical position at which the boundary condition is applied is still constrained to lie on the computational grid surface. This erroneous streamtube

interference problem increases as wing-nacelle separation decreases. As might

11
be expected, the problem is more severe when streamtubes pass over a lifting

wing at transonic conditions than it is when streamtubes pass below the wing.

Exact position of inlet and exhaust streamtubes is difficult to determine.

If position was known, or if it could be calculated with confidence, it could

not be modeled easily. The best solution to this problem might be to eliminate

the streamtube completely. Appropriate flow field potentials can be assigned

to inlet and exhaust surfaces based on the inlet mass flow ratio and nozzle

pressure ratio. The flow will then develop naturally in front of and behind the

nacelle. This scheme should then also be suitable for modeling a pod or closed

store which does not generate inlet or exhaust streamtubes.

PHYSICAL STR EAMTUBE

COMPUTATIONAL STR EAMTUBE

(IF MODELED)

R84-I 137-003D

Figure3 Computational& PhysicalNacelleStreamtubeSurfaces

Figure 4 illustrates crude and embedded fine grid arrangement for a typical nacelle or pod surface. Two operational modes are available: if nacelle or

pod interference or nearby wing and fuselage surfaces is the primary concern,

the crude grid representation is sufficient; if details of pressures on the

nacelle surface are required, the fine grid solution can be obtained.

12
POD

BOUNDARY

POINT

O

O

POD FINE

GRID SYSTEM

R84-1137-004D

O,

I"--

CRUDE/FINE

GRID OVERLAP REGION

Figure 4 Crude/Fine Grid Arrangement for Pods & Nacelles

O

\

WING

PLANE

O

CRUDE

0 .,dl..,.,._. GRID POINT

O

Computations indicate that a four-point diamond pattern provides the best

approximation of the pod surface in the crude grid system. Grid points above

and below and to the left and right of the pod center point make up this pattern. Note that this "best" flow simulation pattern may not be the same for

other computational methods, because it depends on both the Y and Z mesh

spacing used and the typical size of aircraft nacelles. Approximately 10 to 20

mesh points fall along the nacelle in the axial direction. The actual number

depends on the length of the nacelle relative to other aircraft dimensions.

Approximately 28 mesh points represent the nacelle at each axial station if

the embedded grid system is used. One hundred evenly spaced points fall be

tween inlet and exhaust surfaces. The embedded fine grid interacts with the

global crude grid in the same manner as the wing and fuselage grid systems.

This requires a grid overlap region (Figure 4). Crude grid flow field potentials are interpolated (linearly) to determine fine grid boundary potentials

around the fine grid perimeter. Note that this perimeter also represents the

outer boundary of the overlap region. The fine grid system is then relaxed to

13
determine the detailed flow between the outer boundary and nacelle surface.

Resulting fine grid field potentials are interpolated to update crude grid points

which make up the inner boundary of the overlap region. The global crude

grid system is then relaxed and the cycle is repeated, The solution process

continues by alternately sweeping the fine and crude grid systems until both

are satisfactorily converged. Detailed pressure distributions are obtained by

differencing fine grid nacelle boundary potentials.

Figure 5 illustrates a typical nacelle boundary point along with field

points required for determining boundary potential values. For a nacelle

shape defined by:

f(×,z,z) = o (3)

the small disturbance boundary condition is:

f + f D + t : --I, (4)

x y v :_: '

Z

l

• POD BOUNDARY POINT

_0(j, k + 2) O FIELD POINTS

- Y _p(j, k + 1) _[-AZ

_{j + 2,k)

_j + 1,k)

R84-1137-005 D

=

V = V

g g

_OFIELD, N,a, fl, rig , AY, AZ)

r C

r = GEOMSURFACE RAD

g

r =COMPSURFACERAD

C

Figure 5 Nacelle & Pod Side Boundary Points

14
Three-point extrapolated differences are substituted for the velocities in

Equation (4). The boundary surface representing the nacelle is constrained to

lie along Cartesian grid lines. As a result, there are regions along the nacelle

where the computational nacelle surface and the geometric or physical nacelle

surface do not coincide. Slender body theory is used to provide a boundary

condition correction for both lifting and non-lifting displacement effects (Reference 6, page 28). The thickness correction is proportional to the ratio of

the geometric and computational nacelle radii. The correction due to flow incidence is proportional to the ratio of the two cross-sectional areas. The nacelle

boundary potential value is:

(j,k) = (5)

C

where

C C

[ -

+ N 4*(j,k + i) V(j,k + 2) + (a + a ) )2

z 2&Z pod

C

(5.i)

and

3

N N

__Z + _£

bY _Z (5.2)

When the solution process is complete, computational surface velocity distributions must be converted to provide velocity distributions on the true

nacelle surface. Once again, slender body theory provides the required cotrection:

V =V +(r -r

g c g c

(6)

15
Since inlet and exhaust streamtubes are not used in the present approach, it is necessary to develop boundary conditions for inlet and exhaust

surfaces. An effort has been made to minimize the number of variables required for specification of fore and aft flow conditions.

First, consider the exhaust surface. By using the energy equation, an

expression can be written for exit velocity (Reference 7):

J0

(7)

A similar expression can be written for the freestream velocity at infinity.

The following expression evolves for the jet to freestream velocity ratio:

Vj _ i) !T j)

_T ;

i)

YJ- lCPJs/PJol YJ

1 - (P'°s/P%) T

(8)

Note that if system entropy losses are assumed to be small, jet and freestream

static pressure are approximately equal; i.e.,

PJS P_:S (9)

and nozzle pressure ratio is defined by:

NPR = Pjo/P S (10)

In addition, Reference 8 provides an expression for freestream static to total

pressure ratio :

P ¥_o

S. = I + _ M _' - i (II)

P 2

_O

16
For a freestream velocity that is equal to unity, the expression for jet exit

velocity becomes :

(_j - i) T

Vj =

(¥ - l) o

yj - 1

- (1/NPR) YJ

1 - 1/(1 + 2

(12)

For simulating exhaust effects typically found in experimental data, the jet exhaust is cold and the following relations can be assumed:

yj = y = 1.4 (13.1)

Equation (12) reduces to:

T = T (13.2)

J _

VJcold = _I/ i -- (1/NPR) (l/ (i +0.2857 0.2M2)]

,it

(14)

For simulating flight test exhaust effects which typically involve hot jets, the

following assumptions are made:

Tj = 1500OF + 460_F (15.1)

T = 70°F + 460°F (15.2)

_j = 1.33 (15.3)

Equation (12) reduces to:

Vj = 2.0636 j_ - (I/NPR) 0.2481 hot (i/ (]. + 0.2M2)] (16)

17
Figure 6 illustrates an engine nacelle with grid points that are involved in

computing inlet and exhaust face boundary potentials. By using a three-point

extrapolated difference operator, an expression for exhaust velocity can be

written:

v : : + D = 1 + 1 (a_( - 3_ - D( ?

e x 25X I + 1) (I ) I + 2):

e e e (17)

Z

I

FREESTREAM VELOCITY, V

EXHAUST VELOCITY, V

e

X INLET VELOCITY, V i

AX

_i-2/i

_(i-1) i

_O(i)i

Vi= V i (MFR,_FIELD ,AX)

Me= Ve (NPR, Moo,_FIELD ,_X)

R84-1137-006D

_0(i) e

Figure6 NacelleInlet & ExhaustBoundaryPoints

Exit velocity is then set to be equal to jet velocity providing the following

expression for exhaust flow field potential:

2(i - Vj)&X + 4_(I + i) - _(: + 2)

e e

= 3 (is)

e

Values of Vj will depend on whether a cold or hot jet is being simulated.

A similar expression can be derived for the value of the flow field potential at the inlet face. In this case, inlet mass flow ratio provides the required

velocity relation :

18
v[

- MFR

V

V = MFR = I +

[ x

(19.1)

(19.2)

or

1

MFR = 1 +-

2AX 3.(_.) _ i - 1) "([. - 2)'

l 1 L

(2O)

The inlet flow field potential becomes:

2(MFR - 1)AX + &:P(I. - I) - _([. - 2) (21)

1 t

_ =

I. 3

1

For pods and stores, or other bodies which do not have inlet and exhaust flow

fields associated with them, both inlet and exhaust velocities are set to 0

(MFR = 0), to simulate stagnation conditions. Tail and nose flow field potentials are then computed according to Equations (i8) and (21), respectively.

Positioning of the computational nacelle surface in the global crude grid

structure is an important aspect of obtaining a good flow simulation. The vertical or Z grid system is constructed using a tangent function for stretching

and the wing average chord length as a characteristic length (see Reference 6,

page 12). If existing mesh points are interrogated to find the closest point to

the nacelle centerline, more often than not, a poor flow simulation results.

Calculations indicate that computed interference effects between the nacelle and

wing are very sensitive to small changes in nacelle position. For this reason,

it becomes very important to assure that computational and physical nacelle

heights are identical. For configurations with nacelles or pods, the basic vertical grid system is adjusted (compressed) until the grid point just beyond the

nacelle centerline position (as measured from the wing plane) fails on that position. This grid adjustment procedure has been illustrated in Figure 7.

19
f

!

\

\

\

_WING PLANE

COMPUTATIONAL

NACELLE SURFACE

BOUNDARY POINTS

PHYSICAL NACELLE

SURFACE

t

CONVENTIONAL Z-GRID

PHYSICALCOMPUTATIONAL NACELLE HEIGHT

MISMATCHED

COMPRESSED Z-GRID

TO YIELD CORRECT NACELLE

HEIGHT

R 84-1137-007 D

Figure 7 Global Crude Grid Adjustment for Nacelle Positioning

Spanwise positioning of the nacelle surface is not as critical as vertical

positioning in most applications. The existing spanwise grid system places 18

mesh lines between the centerline and wing tip. Positioning the wing tip between two mesh lines to simulate proper aspect ratio is still the most critical

requirement. As a result, the computational nacelle center may be positioned

as much as 3°_ half-span away from the physical nacelle center position. This

type of discrepancy will, as a rule, not lead to simulation problems. But in

certain applications (i.e., fuselage mounted nacelle), the spanwise nacelle position may be as critical as the vertical position. Special grid provisions or

compromises might be required to successfully simulate this type of flow.

Pylon Surfaces

Wing surfaces are modeled in an embedded grid system that is skewed and

tapered to "fit" the wing planform (Figure 2). The spanwise lines (_) of this

grid system are aligned with wing constant percent chord lines. As a result,

a smooth simulation of wing leading edge flow is obtained and chordwise resolution is uniform between the root and tip of the wing.

2O
Modeling of a surface which is not aligned with this grid system presents

a problem. A symmetry plane and fuselage side are good examples of nonaligned surfaces (see Reference 6, page 24). Numerical stability is impaired in a

region near the nonaligned surfaces and, in some cases, the relaxation solution

diverges. Some investigators have unswept grid lines in these critical

regions; however, the resulting local Cartesian grid typically produces erroneous oscillating pressure distributions. Pylon surfaces, like fuselage sides

and symmetry planes, are not aligned with existing wing grid structure.

Thus, the primary problem that must be overcome if pylon surfaces are to be

modeled, is due to tile inherent numerical instability of the pylon boundary

condition.

Existing grid lines which cross the wing planform in the spanwise direction are generated by a hyperbolic tangent function and the requirement that

the wing tip be centered between two grid lines. Eighteen lines are constrained to lie between the symmetry plane and wing tip. The computational

pylon surface is positioned at one of these existing spanwise grid lines. A

discrepancy which may be as large as 390of wing semi-span can exist between

the physical and computational pylon span position. Note that this is also true

for nacelle positioning. No attempt has been made to correct for this displacement effect.

Figure 8 illustrates arrays of mesh points which are embedded along the

wing. At any particular span station, the X-Z system is Cartesian in character. This wing grid system is also used to represent the pylon boundary surface. A separate grid system specifically for the pylon surface is not used.

In addition, special provisions for swept leading edge simulation in the rectangular grid have not been made. As a result, current pylon modeling permits

camber, twist and thickness variations; but the pylon planform is constrained

to have no sweep or taper. This limitation has been sketched in Figure 9.

21
EMBEDDED WING

GRID S_

t ! \"-. _

PYLON SURFACE

BOUNDARY POINTS

R84-1137-008D

Figure 8 Pylon Surface Boundary Points in Wing Fine Grid System

I

PHYSICAL PYLON SURFACE

/

COMPUTATIONAL

PYLON SURFACE

R84-1137-OO9D

Figure 9 Physical & Computational Pylon Surfaces

22
The standard wing fine grid system vertical boundaries are positioned

based on a percentage of wing root chord length. When pylons are modeled,

however, the fine wing grid lower boundary must be adjusted to insure that

the pylon lower surface does not project below the grid limit. This is accomplished by positioning the lower grid boundary at the pylon base level and altering the vertical grid spacing so that the total number of vertical grid points

remains within original limits.

There are several approaches that can be used to enforce pylon boundary

conditions. In this effort, an attempt has been made to find the best compromise between providing a good flow simulation and providing a stable numerical

solution that will converge for a variety of different flow/geometry cases.

Calculations made to date indicate that if extrapolated differences are used to

"set" the inboard and outboard pylon surface potential values, instabilities in

the pylon leading edge region will result. Similarly, if pylon boundary conditions are used as a constraint on the cross-flow velocity, the solution will

diverge. By using dummy potential arrays, however, a scheme can be developed which actually enhances the numerical stability of the solution. Calculations indicate that a satisfactory flow simulation is also obtained.

Figure 10 illustrates which grid points are involved in generating dummy

potential values for inboard and outboard pylon surfaces. In the skewed grid

system, the velocity component, v, can be written:

y n y _ y (22)

This can be set equal to the pylon boundary slope:

y pyl py[ (23)

where the sign convection is due to tile inboard surfaces of both winglets axld

pylons being specified as the input airfoil section "upper" surface. A

special tw>-point (first order accurate) difference operator can be used to

provide an approximation of the _ and _ derivatives. The expression for

the inboard surface dt_Tmy potential point becomes:

23
= Y ' ,SX ' _[b

(24)

A similar expression can be written for the outboard surface dummy potential

point:

_Do b =

_ __Z :_ -i_' -

-_X _(i-1, ..i-l) k¥ (i,.j) PY_-ob PY[ i

q

_ X

(25)

For each side, note that the coefficient of the dummy potential point is greater

than the coefficient of other points involved. This enhances the effective diagonal dominance of the system.

• DUMMY POINTS / / INBOARD SURFACE

O F,ELO PO,NTS / /,i BAO_N_ARYEN T

/ _.

/ s / ' I VERTICAL WAKE

( O, SURFACE J

/ / / " BOUNDARY

/ L_,

NOTE: FOR SWEPT-BACK WINGS, _y <0

R84-I 137-0 i0 [D

Figure 10 Grid Points Required for Computing Pylon

Inboard/Outboard Boundary Conditions

24
The computational method operates with three planes of grid point potentials in core at one time. When a pylon station is reached, the outboard plane

is modified in the region which is directly aligned with the pylon surface.

Equation 24 provides the temporary dummy flow field potential values. The

inboard pylon surface is then relaxed in a manner similar to that used for

normal field points. When the wing/pylon trailing edge is reached, the original outboard potential values are replaced, and inboard plane dummy values

are established. The outboard side of the pylon surface is then relaxed and

the pylon surface simulation is complete. Vertical pylon circulation is computed by:

:(z) = *J - _a

PY[ ib ob (26)

This value of circulation provides the jump condition required for differencing

across the pylon wake surface:

_(j-i k) - 2_(j,k) + (_(j+l,k) + F(Z))

¢ = ' (27)

nnib _n2

(_(j-l,k) - r(Z)) - 2¢(j,k ) + ¢(j+l k) (28)

nnob _n2

Winglet Surfaces

For wing-tip-mounted winglets, the small size of the lifting surface alone

presents a formidable obstacle. Winglet planform areas are typically between

1/40 and 1/70 the area of the main wing. Sufficient resolution must be provided for both wing and winglet surfaces simultaneously. The stability problems which occurred when pylon development was in progress are not incurred

since rectangular ffrid systems are set up specifically for winglet surface simulation to overcome the resolution problem.

25
Spanwise grid arrangement for a conventional wing tip is shown in Figure

11. The wing tip is positioned midway between two grid lines. This provides

the best approximation of wing tip aerodynamics. If a winglet is modeled, the

grid system must be adjusted to provide grid lines at the wing tip. These

wing tip points are used for both the winglet boundary surface and the vertical winglet wake which extends to downstream infinity.

CONVENTIONAL WING TIP WINGLET WING TIP

R84-1137-011 D

Figure 11 Wing Tip Spanwise Grid System for Winglet

& Conventional Type Planforms

If a fine grid system were embedded along the winglet surface in the

same manner currently used for wing surfaces, a diverging solution would

probably result. This would be caused by the large disparity in resolution

between the existing global crude grid structure and the embedded fine grid

system. To overcome this problem, an intermediate mesh system is placed

around the wing tip region. Figure 12 illustrates the resulting three-level

grid arrangement required for resolving details of winglet flow fields. Both

the global crude grid and intermediate grid are rectangular in character. The

winglet embedded (fine) grid system is skewed and tapered to fit the winglet

planform.

During the first phase of the solution process, only crude and intermediate grid systems are active. Winglet boundary conditions are imposed in the

26
higher resolution intermediate grid system. Since vertical line relaxation is

used, the boundary condition is enforced by specifying" the cross-flow velocity

component in Equation (i). (Note that this will involve both the ¢y and Cxy

terms.) Winglet circulation and wake jump computations are identical to those

specified for pylon surfaces (Equations 26, 27 and 28). Crude grid winglet

points form a fixed potential surface and flow field potentials are generated by

the interpolating values found in the intermediate grid. Most important, however, the crude grid system provides a means for carrying vertical wake circulation downstream.

_/ GLOBAL

WINGLETFINE CRUDE GRID

GRID SYSTEM

INTERMEDIATE GRID _/["-_.

FOR AUGMENTING . /\ I _

WING _FINE / -J _" GRID SYSTEM

RB4-1137-012 D

Figure 12 Crude/Medium/Fine Grid Arrangement for

Wing-Tip-Mounted Winglets

The winglet flow field computed during the first phase of the solution

process is used to provide a starting point for the second phase which requires crude-medium-fine grid interactions. Fine winglet grid boundary con27
ditions and fine wing grid boundary conditions are identical. Only the coordinate direction is changed. For the winglet inboard surface, the boundary condition is:

2 $( - _(

_yy(X,Yib,Z ) =A-Y ( j-l,k) j,k) _ (f, - Swtt)] (29) AY wltib

The outboard surface condition is:

q_y (X,Yob,Z) = _2_AyI¢(J'k)-AY_ (j+l,k) - (f'wlto b Bwlt )] (30)

During the second phase of the solution process, flow field potentials are fixed

on both crude and intermediate grid winglet surfaces. The global crude grid

solution provides outer boundary potentials for the intermediate grid. The intermediate or medium grid solution provides outer boundary potentials for the

embedded fine grid system.

Solution Process

This section describes the procedure which is used to solve for the multiple wing and body surface flow field. The procedure includes steps that are

executed when nacelles, pylons and winglets are attached to the basic wingbody configuration. For simpler configurations, individual component steps are

simply bypassed. Figures 2, 4 and 12 may prove to be useful in visualizing

operations which are to be described. The solution process can be broken

down into two separate phases.

Phase 1 : INITIAL CRUDE GRID FLOW FIELD SOLUTION

An initial solution is obtained with the wing-body represented in

the etude mesh. Typically, 100 iterations are sufficient. After 60%

of the crude cycles are completed, flow field potentials from the

global crude grid are used to establish a starting flow in the wing

tip augmented grid (TAG). Note that TAG was referred to as an

intermediate grid in the winglet surface section. For the remaining

28
40%of the crude grid cycles, winglet boundary conditions are enforced in TAG and the global grid serves also to carry wing and

winglet wake systems downstream.

Phase 2: CRUDE/FINE GRID INTERACTION

Step 1: Using global crude grid flow field potentials obtained in Phase 1,

a starting flow field for the embedded wing grid is established. A

similar initialization procedure is performed for the embedded pod or

body grid system. Flow field potentials from TAG provide a starting flow field for the winglet embedded grid system. Pylon outboard potential arrays are set equal to inboard potential values

which make up the basic wing flow field. Pylon circulation distributions are set to zero.

Step 2 :

Step 3 :

The wing fine grid system is relaxed with outer perimeter potential values fixed and conventional Neumann boundary conditions at

fine grid section boundary points. Crude grid wing boundary point

potentials are updated based on results from this step.

The winglet fine grid system is relaxed in a manner similar to

that in Step 2. Both the crude grid and TAG winglet surface

boundary potentials are updated.

Step 4 : Wing boundary layer 5" is computed. Embedded body fine grid

perimeter points are updated, based on global crude grid field potentials. Body fine grid boundary potentials are computed.

Step 5 : The body fine grid system is relaxed subject to fixed potential

values on the grid perimeter, body surface, and wing plane surface

(see Figure 15, Reference 6).

Step 6 : The crude grid body surface is updated based on fine grid field

potentials determined in Step 5.

29
Step 7: The nacelle fine grid system is relaxed in a manner similar to

that of the body (Steps 5 and 6). In addition, however, flow field

potentials at inlet and exhaust faces must be determined before each

relaxation sweep.

Step 8: The global crude grid is relaxed using Dirichlet boundary potentials generated by Steps 1-7. Field potentials from the crude grid

now provide outer boundary potentials for embedded grid arrays.

Step 9: The TAG is relaxed with fixed perimeter and winglet surface

boundary points.

Steps 1 through 9 are repeated until the grid systems are satisfactorily

converged. Typically, 80 cycles are sufficient. When the boundary layer option is selected, a boundary layer displacement thickness (5*) will be computed every 20th iteration starting with the fifth iteration in phase two. The

5" gradient is added to the wing surface slope for the wing boundary condition required in step 2. If the fine body or pod grid option is selected, grid

perimeter potentials are updated every 10th iteration and the grid systems are

relaxed every second iteration to conserve computing resources.

Pressure, Force and Moment Coefficients

Pressure, force and moment coefficient calculations for wing and body

components are described in Reference 6. All pressure coefficients on pod,

pylon, and wingiet components are computed in the same manner as those described in Reference 5. Pylon surfaces, which are perpendicular to the wing

plane, do not contribute to the total configuration forces and moments. For

this reason, only nacelle and winglet force and moment calculations wiil be described.

3O
Winglet section coefficients are obtained by integrating pressure coefficients on both inboard and outboard surfaces.

c

C - I f (CPi b - CPo b) dx (31)

_t Ctoc o

c

C (Io¢) _ 2 l 7 (¢Pib

mw_t C[o c o

- CPo b) (X£o c - Xc/4

dx

(32)

c dYib dYob

_ 1 f [cp _) - CPobL dx Cd C[ ib ( dx w_t oc o

(33)

In addition, a sectional moment about the axial reference position is computed.

c

= i r (Cp - C )(XIo c dx C M.A.C. J - XREF) (34) m_t C[oc o £b Pob

Winglet lift, moment and drag coefficients are obtained by integrating section coefficients across the winglet span and multiplying by winglet cant angle.

b/2

CLwLT = cos _ -b2 Jg

o

CI C_

oc _it

dy

C (35)

a v

b/2

2

CMwLT = cos a _ f

o

Clo c C

mwl t

C

av

dy (36)

2

CDp (WLT) =

b/2

o

Clo c Cd

C c wit ) dy

av

(37)

31
Winglet skin friction drag is computed by using the Prandtl-Schlichting formula

corrected for compressibility effects (see Equation 64, Reference 6).

Pod or nacelle force and moment coefficients are obtained by integrating

surface pressure distributions and adding a skin friction component based on

wetted area. A pod cross-sectional force coefficient distribution is computed

first.

Rl Rl OC OC

- , dy (38) --i f [C • N ] dy I [Cp, Nz]LOWE R

C_ 2R[ P z UPPER 2R[oc -R_ pod oc -Rto c oc

and

R1 OC R LOC

Cd _ 1 f [Cp. Nx]UPPE R dy + i

pod 2R[oc -R[oc 2Rloc -RIJoc [Cp, Nx ]LOWER dy (39)

The longitudinal coefficients are then integrated along the length of the body.

Similarly,

L C% • RIo c

1 I pod ] d__

CLpoD =_ L R

o max (4O)

CMpoD -

L Cl .

i r [ pod Rl°C

L2 Jo Rmax ] (xl°c -

XRE F) d£

(41)

and

cd • R1

L pod oc

i r [ R

CDpoD = _

L

o max

(42)

As was the case for winglets, the pod skin friction coefficient is computed

using the Prandtl-Schlichting formula (see Equation 64, Reference 6).

32
The total configuration force and moment coefficients are obtained by adding the various component coefficients.

C L + +

= CLwIN C + CLBoD Y CLwL T CLpoDs (43)

÷ +

C M = CMwIN C + CMBoD Y CMwL T CMpoDs (44)

C D + +

= CDwIN C + CDBoD Y CDwL T CDpoDs

(45)

Two-Dimensional Airfoil Analysis

The modified small disturbance equation/planar boundary condition approach, the basis for the present method, may in some cases produce results

which are inferior to those that would be obtained if a full potential

equation/exact boundary condition method were available. These discrepancies

might become significant when surface shapes have extraordinarily high gradients or when flow conditions are extreme. Unfortunately, it would be difficult

to evaluate potential problem areas when complex configurations are of

interest. Flow interference can be complex and many different components of

the computational method are contributing to the final result. For these

reasons, special provisions have been made to permit analysis of twodimensional airfoil shapes. Abundant experimental data and easy-to-use full

potential equation/exact boundary condition computer analyses can then be

used to assess problem areas in two dimensions before complex threedimensional analyses are performed.

Figure 2 illustrated the position of the wing embedded fine grid system.

This mesh array is made up of a series of two-dimensional arrays (see Figure

8). If a single planar array is used at the symmetry plane, a tv_3-dJmensional

airfoil can be treated. Unlike the wing-body case (see Figure 13), however,

far field boundaries which represent infinity are non-zero since the airfoil appears as a concentrated point vortex. This has been illustrated in Figure 14.

33
/

FRONT PLANE

9=0

BACK PLANE

9y y+gzz = 0

i/

J

SIDE PLANE

9=0

RB4/1137-013D

Figure 13 Boundary Conditions at Infinity for Wing-Body Analysis

F

_p= --J

2

F

9 = -

4

A

Z

3r

--" X 9 = -

4

__J

9=0

I

I

i

9=-F

R84-1137-014D

Figure 14 Boundary Conditions at Infinity for Airfoil Analysis

34
The global flow equation (Equation 1) which is used for all threedimensional computations is simplified by eliminating all cross-flow terms when

airfoil analysis is required.

11 _ M2m_ (r + l)M2® m Xy +2i M2®2j%×, m X

+

Z Z

o (46)

Airfoil pressure coefficients are computed using the following equation.

Cp = + (1 - M2)¢ 2] (47) -[2¢x ' x

35
36
tn.ANKNOT aJW}

COMPARISONS & TYPICAL RESULTS

Correlations with experimental data for isolated bodies, isolated wings,

and wing'-body combinations were presented in Reference @ using tile basic

wing-body code. These examples will not be included in this report, but it

should be noted that the present method will reproduce those results in addition to providing the more complex configuration flow simulations contained

herein. Thus, the present method can be used to analyze I) two-dimensional

airfoils, 2) isolated wings, 3) isolated bodies, 4) wing-body combinations, and

5) aircraft configurations with as many as four pods/nacelles, four pylons, and

wing-tip-mounted winglets. This provides flexibility for studying component

interference effects.

The computations which follow illustrate the new airfoil and nacelle,

pylon, winglet simulation capabilities. Component interference effects are

shown for cases where component on/off wind tunnel data is available. For

some components (nacelles and winglets), detailed pressure comparisons are

included. For one case (G-III), flight data is used to augment wind tunnel

results.

Airfoil Correlations

Two airfoils have been selected for correlation studies. The NACA 0012

airfoil is somewhat conventional in shape. It is also a section which is often

used in theoretical or analytical test samples. The second airfoil selected is

the new type NASA LS(1) airfoilwhich features considerable aft-loading. Experimental data for these sections can be found in Reference 9 along with

Korn-Garabedian and Carlson 2-D code analysis results. Correlations with experimental data using the present method can be seen in Figure 15.

37
D

Z

Lu

_J

www W

_0

_J_J

ZZZZ

I111

ZZ

ww

XXll

Wm_

00 ×+

. 2

I i r | I ]

0 0 0 0 0 0

0 0 0 0 0 0

C_ CO _ O. _

"7 0 q) 0 0 0

Q0

0 _

0

_ _ O_ [ii _'L--} 0 'C]

x

I _ I I I I l

0 0 0 0 0 0 0

0 0 0 0 0 0 0

o o, c_ d o

/'/

0

0

o.

0

II

.J

-IZ

CP_

c5

II

0

I

,<

T

n

_Jr',-

J

U-O

c2-__

p_

z_

_,I

o_.

u-O)

C?

o

e0

C

0

3

o

0

i5

0

,<

e-.

o

.i

E

0

I--

.I

IJ.

38
Nacelle Flow Simulations

Two different transport configurations have been selected for comparisons

to experimental data. Together, they illustrate both nacelle operational modes.

The first, a crude grid nacelle simulation, provides flow disturbances on the

wing. The second involves a fine embedded grid computation which is used to

predict detailed pressures on the engine nacelle surface.

Figure 16 illustrates the G-III configuration. This transport has a low

wing and two fuselage-mounted nacelles. The wing has an aspect ratio of 6,

and a taper ratio of 0.279. Wing" leading edge sweep is 31.7 degrees.

Nacelles are canted 2.75 degrees nose up, and 0.5 degrees nose inboard.

T

77=0.

E

_ • L

R84-1137-016D

Figure 16 G-Ill with Pressure Tap Locations for Nacelle Interference Study

G-III cruise conditions occur near Mach 0.75 and an angle-of-attack of 4

degrees. The wing root pressure distribution at this flow condition is relatively shock free and not very challenging for the transonic computational

method. For this reason, a higher Mach number case has been selected for

comparisons. The Mach 0.85 flow condition exhibits a strong shock wave.

The selected incidence must be lower than cruise levels to avoid flow separation.

39
Wing upper surface, superimposed, computed pressure distributions for

the basic wing-fuselage and the wing-fuselage-nacelle cases can be seen in

Figure 17 at Mach 0.85 and 0 degree angle-of-attack. A single shock wave

spans the wing between the fuselage side and wing tip. With the nacelle

mounted, the shock wave disappears in the wing-fuselage-nacelle juncture region. Resulting flow on the wing under the nacelle exhibits a deceleration in

front of the inlet face, and an acceleration just behind the inlet lip. The inlet

MFR for this case is 0.66.

0.6

R84-1137-017D

//

WING-FUSELAGE

WING-FUSELAGE-NACELLE

MFR = 0.66

Figure 17 G-Ill Nacelle On/Off Superimposed Computed Wing Upper Surface

Pressure Distributions M_ 0.85, (_ = 0 °

Correlations with experimental data at three span stations along the wing

can be seen in Figure 18. Note that the character of this complex

three-dimensional flow field is predicted quite well. The lower surface pressures are essentially unaffected by the presence of the engine, and the

interference effect can be observed to decay properly as distance from the

nacelle increases. Experimental data is taken from Reference 10.

4O
mOmO

D_D_

ZZZZ

o \j

IP

I i I r • ,"

ZZ

LIJ UJ

_ _ >- >-

wwO0

a. a_ w w i,,

XX!I

<!

0

Z

0 D × +

L9

w

J

/ '

c_) i__.'

-<.

i I

T r " r --

o o o

_Y

/y

/

/

+,

/

o

LL

LL

0

.-I

I11

C'

Z

I

i, iI

'< /

/

/

I

iI

,}

ri

f

/

×xX_X  ̧ _+

\

Z

0

w

Z

I_x_ + _ •

<>

{

i

I

I

o _ c_ q_ d d d

0

(D

.o

c_

c

a_ li

Z •

_m

.__

Cl

,-4

41
The C-5A configuration is illustrated in Figure 19. For flow conditions

near the cruise point (Moo-- 0.775 and a = 2.0 degrees), an embedded fine grid

has been positioned around the inboard engine nacelle. Experimental data can

be found in Reference 11. The actual engine consists of a fan cowl, turbine

cowl and plug. Engine surface discontinuities and expected flow separation aft

of the fan cowl cannot be properly modeled using the present attached flow

methodology. For this reason, the long duet flow-through nacelle (Configuration 10, Reference 11) is modeled for analysis. Computed results are compared

to experimental pressures which were measured on the basic nacelle (Configuration 1).

f

R84-]137-019 D

Figure 19 C-5A Configuration

Correlations with experimental data at three stations around the nacelle

can be seen in Figure 20. Note that both basic and flow-through nacelle

shapes have been sketched. Computed results on the turbine portion of the

nacelle can only be considered as approximate. They are included because the

character of this flow which is influenced by the wing leading edge is properly

predicted.

Figure 21 shows inboard nacelle port and starboard comparisons superimposed. The variation in flow character is probably caused by a combination

of interference effects that include fuselage effects inboard, second nacelle

effects outboard, and the swept back wing leading edge.

42
DF. Poor qUALrr{

°

•o-_J_ o

r,,

z

w

o

w

J

z

w

rrrr

w©

_. w

x'r

w_-- r

"T

0 +

0 0,-

/0

o

o)'

_=:: ._o

•7, Q o', o d 6

/-

oh

• ,'$

00

o,

r r _ • - ,

_r o _r m.

o o o o

a.

o

rr

0

ILl

"1"

F-

_J

0

Z

ZI

n,-

-r

I-.-

0

._1

u..

/

i :i

i 'i

i

i

w

J

J

\

,i

S

o

0

¢-

o

i5,=

_ tr

_Z

113c

g_

Of',,

,_ iJ

.__

u..

o

o.

43
-0.8

-0.4

o- 0.0 L)

0.4

0.8

R84-1137-021D

LEGEND

C) PORT SIDE EXPERIMENT

[] S]ARBOARD SIDE EXPERIMENT

PORT SIDE THEORY

--- STARBOARD SIDE IHEORY

0 o

FLOW THRU

NACELLE

(THEORY)

NN_ _ BASIC - . NACELLE

Figure 21 Comparison of C-5A Inboard Nacelle

Port and Starboard Pressure Distribution

Correlations

Mo_0.775 _=2 ° NPR=2.84

Pylon Interference Effects

The C-5A configuration (Figure 19) has been selected to demonstrate the

pylon computational capability. Reference 11 provides experimental data for

the basic C-5A wing-fuselage configuration and various configurations with different pylon and nacelle combinations. Wing pressure data which illustrate

pylon interference effects are available at both pylon span stations (Figure

22). For the wing lower surface, pressure taps are positioned on both sides

of the wing pylon juncture. A double shock wave system exists inboard of the

mid-semi-span region; outboard, only a single shock wave exists. Correlations

with experimental data at the inboard station for the pylon/nacelle on and off

can be seen in Figure 23. Outboard station comparisons can be found in

44
,Tw = 0.39 '£/w = 0.60

R84-1137-022D

• WING UPPER/LOWER SURFACE

PRESSURE TAP LOCATIONS

Figure 22 C-5A Wing Stations for Pylon/Nacelle Interference Study

LEGEND

c,

_J

A

x

+

y

UPPER SURFACE EXPERIMENT

LOWER INBOARD SURFACE EXPERIMENT

LOWER OUTBOARD SURFACE EXPERIMENT

UPPER SURFACE THEORY

LOWER INBOARD SURFACE THEORY

LOWER OUTBOARD SURFACE THEORY

-1.2

-0.8

,,z_,_%_,<>. -1.2-

9 j'

J >' -0.8-

-0.4

0.0

Cp

0.4

+

0.8

1.2 J + /

R84-1137-023D

x

e'_'_ -0.4

:c:°

_, 0.4-

÷

NACELLE/PYLON OFF

0.8"

:__,,_ J : j, _.

×

×+

+

_" NACELLE/PYLON ON

÷

1.2 /

Figure 23 C-5A Inboard Engine Station Pressure Distribution Correlation

M=0.775 _=2 ° NPR=2.84

45
Figure 24. Note that pylon/nacelle interference pressures are properly predicted and the multiple shock wave character is accurately reproduced. These

comparisons were made for Configuration 1 in Reference 11. The Pj/P value

of 1.5 converts to an NPR of 2.84.

-1.2

-0.8

-0.4

0.0

Cp

+

0,4 -4

+

]

+

0.8

1.2

R84-1137-024D

-1.2

NACELLE/PYLON OFF

-0.8

-0,4 1

0.0

Cp

0.4

0.8

1.2-

/ +

NACELLE/PYLON ON

Figure 24 C-5A Outboard Engine Station Pressure Distribution Correlation

IVI= 0.775 _ = 2° NPR = 2.84

Wing let Flow Simulations

P_eference 10 provides experimental data suitable for verifying the

winglet computational capability. The G-III configuration with labeled experimental pressure tap stations can be seen in Figure 25. Figure 26 illustrates

the wing tip comparison for both winglet on and off. It is interesting to note

that the more complex winglet/wing tip arrangement shows better agreement.

This is probably caused by differences in wing tip rake for the two planforms.

The analysis method cannot resolve details of the highly swept tip-leading-edge

contour, thus, it predicts higher loadings in the leading edge region than

those given by experiment. The winglet-on wing tip is trapezoidal in character and, therefore, in better agreement with the wing tip region computational

model.

46
Wwlt = 030

0.50 ._

R84-1137-025 D

Figure 25 G-Ill Wing/Winglet Pressure Tap Locations

for Evaluating Winglet Interference

LEGEND

© UPPER SURFACE EXPERIMENT

[] LOWER SURFACE EXPERIMENT

x UPPER SURFACE THEORY

+ LOWER SURFACE THEORY

Cp

-1.2

-0.8

-0.4

0.0

0.4

0.8

'3, _- -1.2

/ /

-O.B

-0.4

Cp

0.0

WINGLETS OFF

SECTION CL = 0.438, CM = 0.016, CD = -0.0054

R84-1137-026D

0.4

0.8

/

f

WINGLETS ON

SECTION CL = 0.505, CM = -0.017, CD = 0,0057

Figure 26 G-Ill Wing Tip Pressure Distribution Correlation

M_ 0.75 _ = 4°

4?
Winglet pressure distribution correlations at three stations along the

winglet span can be seen in Figure 27. Viscous effects are not modeled in

these computations. A mild shock wave can be identified as it follows the

leading edge of the winglet on the inboard side.

-1,2

-0.8

-0.4

Cp

o.o ,_

0.4

0.8

\

\

LEGEND

O INBOARD SURFACE EXPERIMENT

[] OUTBOARD SURFACE EXPERIME-NT

x INBOARD SURFACE THEORY

+ OUTBOARD SURFACE THEORY

Cp

-1.2

-0.8

-0.4

0.0

0.4

0.8

,©0

0

:: Cp

-1.2

-0.8

-0.4

0.0

0.4

0.8

%

rtwl t = 0.15 nwlt = 0.50 'lwl t = 0.80

SECTION CL = 0.560, SECTION CL = 0.652, SECTION CL = 0.580,

CM = -0.043, CD = -0.0281 CM = -0.014, CD = -0.0216 CM = -0.091, CD = -0.0114

R64-1137-027 O

Figure 27 G-Ill Winglet PressureDistribution Correlations ME 0.75 _ = 4°

Combined Interference Effects

Pressure distributions across the G-III span show the good results that

can be obtained after modeling all configuration components (see Figure 28).

This comparison includes both wind tunnel and flight data.

The KC-135 provides an additional case that can be used for code validation (Reference 12). This configuration has four pylons, four engine nacelles,

and wing-tip-mounted winglets. Pressure data is available at several wing

stations and several winglet stations. Strong shock waves are not present at

cruise conditions. If flow conditions are pushed beyond the cruise point, wing

tip flow separation is apparent. Comparisons with experimental data at the

48
J 1 • r 1 t

0 0 0

0 0 0 00 0 0

• . o. "K.

....

_) I T I I 1

0 0 0 0 0

0 0 0 0 0 0

o0. ,_. 0 _- co

0

0o

c_

II

1

0

0

t'4

,<

c} ,<

._j n

uJ IZ

Z Lu

>. _ II- I0

x • o

x • o

× • o

d

II

0 i T r r

0 0 _ 0 0

0 0 0

'-; 9 9 o d

Q.

0

F

0 0

0 8 0 0

0 0

_" 0 _ O0

0

m.

o

i

0

i i i i

0 0 0

_. o. _. co.

C_ 0 0 0

C)

0

m

9

0

r_

c_

rl

,1

49
cruise point can be seen in Figure 29. It should be pointed out that the

winglet is positioned at a 90 degree angle to the wing surface when modeled in

the computational method. In reality, both the KC-135 and G-III winglets are

canted outboard 15 degrees.

The C-141 transport configuration can be seen in Figure 30. This case is

interesting because it illustrates interference effects caused by nacelles,

pylons, and fuselage fairings. The fuselage geometry model, made up of body

and cross-section lines, can be seen Figure 31. Wing-body juncture and landing gear fairings can be identified.

Figure 32 compares unpublished wind tunnel pressure data taken at

four wing stations. The flow condition is M : 0.77, a = 1.5 degrees, and R =

oo e

2 X 106 . Note the analysis method angle-of-attack is 1/2 degree higher than

that of the experiment. The experimental variations in flow field character

which result from the addition of nacelle/pylon combinations are predicted quite

well.

*Wind tunnel data obtained from M. Lores, Lockheed-Georgia Cxm_any.

5O
-1.2

-0.8

-0,4

Cp

0.0

0.4

0.8

-1,2

-0.8

-0.4

Cp

0.0

0.4

0,8

-1.2

-0.8

-0.4

Cp

0.0

0.4

0.8

000

:_ [3 [3

× × x

+++

"%,..

17w = 0,93

l?w = 0.79

' f',

'r'tw = 0,33

EXPERIMENT --UPPER SURFACE

EXPERIMENT-- LOWER SURFACE

ANALYSIS - UPPER SURFACE

ANALYSIS - LOWER SURFACE

-1.2

-0.8

-0.4

Cp

0.0

0.4

\

\

/

/

/

/

/

1

0.8

/

/

\ /.,._,

\ / _

\ / -°.84

-0.4

/ %0.0

0.4

0.8

\

-1.2 ,

_.8 l

-0.4 1

CP0.0 i

o, i

L

0,8-'

t?wl t = 0.80

/'/wit = 0.50

..... %,.,.,

17wlt = 0.15

:z.--_.....

R84-1137-029 O

Figure 29 Boeing KC-135 Wing & Winglet PressureDistribution Correlations M = 0.78

oo

_=2 _

51
R84-1137-030D

Figure 30 C-141 Configuration

RB4-1137-031D Figure 31 C-141 Fuselage Geometry Model

52
1.200

0.800

0.400

Cp 0.000

-0.400

-0.800

-1.200

1.200

0.800

0.400

Cp 0.000

0.400

0.800

STATION 1,17 = 0.19

,,.

,j

_f

%1

NACELLES & PYLONS OFF

STATION 2, 'r/:0.42

ol .200

-0.800

-0.400

4

L

Cp 0,000

!

0.400

0.800

1.200 J

-1.200

.0.800

-0.400

Cp 0.000

0.400

0.800

000

[3[3[3

x x x

+++

EXPERIMENT--UPPER SURFACE

EXPERIMENT-- LOWER SURFACE

ANALYSIS - UPPER SURFACE

ANALYSIS - LOWER SURFACE

G_<!

r-f _ "{';L;;?. -

7

NACELLES & PYLONS ON

i  ̧ ̧ ̧, i

_I+..,_... " ) :

)

t

• \

-1.200 I

NACELLES & PYLONS OFF

1.200 J

f- - ._ -_

NACELLES & PYLONS ON

R84-1137-032E)(1)

Figure 32 C-141 Wing Pressure Distribution Correlation Moo= 0.77 e = 1.2 ° R e = 2 x 106 (Sheet 1 of 2)

53
- 1.200 •

49.800

49.400 _

Cp 0.000

0.400

i

J

0.800

1.200 i

STATION 3, 1 = 0.64

I

I -1.2oo

I

49.800 i

I

1

: 4 -0.400

[_+ +%+•

+

Cp 0.000

0.400

0.800

NACELLES & PYLONS OFF

1.200

STATION 4, 1_= 0.79

000

x × x

+++

EXPERIMENT - UPPER SURFACE

EXPERIMENT - LOWER SURFACE

ANALYSIS - UPPER SURFACE

ANALYSIS - LOWER SURFACE

;_-_'_=_:, 7 _ _.

r

+-

NACELLES &PYLONS ON

-1.200 ,

-0.800

49.400 J

Cp 0.000 7

f

I

0.400 '

I

1T

-1.200 •

49.800

-0.400

Cp 0o000

0.400

O3OO _ O.8O0 i

"" o_,_ __'i 1 7

>, ,

\%

%

1.200 _ 1.200

NACELLES & PYLONS OFF NACELLES & PYLONS ON

R84-1137-032D(2)

Figure 32 C-141 Wing Pressure Distribution Correlation M= 0.77 _ = 1.2 ° R e = 2 x 10 6 (Sheet 2 of 2)

54
CONCLUDING REMARKS

The computational method described has been specifically developed to

provide an engineering analysis for realistic aircraft configurations at transonic

speeds. It is unique in its ability to treat a variety of shapes. This feature

should prove to be useful in the study of aerodynamic interference effects.

Compared to existing methodology, the approach provides very high computational resolution. Resolution varies between 200 boundary points for a simple

airfoil to over 9000 points for a complex wing-fuselage combination with

nacelles, pylons and winglets.

Method flexibility, which is required for treating a variety of complex

shapes, is balanced by the simplicity of its components. Coordinate systems

are essentially rectangular in character, a simple two-dimensional strip boundary layer analysis provides viscous corrections, and finally, a fast, easy to

use fuselage modeling system yields arbitrary body shape surface normals.

While more sophisticated components could be used, the simplicity and cost

effective character of the present arrangement should enhance the probability

of obtaining accurate flow simulations.

55
56
APPENDIX A

CODE DESCRIPTION

OONTENTS

GENERAL (X)MPUT}_ CODE DESCRIPTION ...................................

INPUT DATA FORMAT ...................................................

SAMPLE I_ DATA SETS ..............................................

OUTPUT DATA (PRINT AND PLOT) _T .................................

INPUT GEOMETRY VERIFICATION .........................................

SUBROUTINE CALL SEQUENCE ............................................

SUBROUTINE DESCRIPTION ..............................................

KEY VARIABLE DESCRIPTIONS ...........................................

Page

59

64

73

86

92

97

102

ii0

I:__ PAGE BLANK NOT FILkt_D

57
58
GENERAL COMPUTER CODE DESCRIPTION

The computer code is operational on both IBM and CDC type cx:zputers.

Overlay structures are not used although this approach (for reducing core requirements) may be advantageous depending on facility charging algorithms.

The IBM version using the extended H compiler (opt = 2) requires approximately 970K10 for storage and execution. There is considerable use of temporary disk storage units. Since interpolation and searching is required, a result of the mesh embedding approach, it is useful to have planar potential (¢)

arrays separate and addressable. As a result, 15 different units are currently

employed. The disk unit number and a description of contents are listed below.

DISK NUMBER

1

8

12

13

14

15

80

81

82

83

84

85

86

87

88

DESCRIPTION

Input data transferred to Unit 1 (formatted data)

Quick-geometry problem diagnosis printed-output

Global crude grid potential array

Fine wing grid potential array

Fine body/nacelle grid potential array

Fine winglet grid potential array

Crude grid wing upper/lower surface boundary conditions

Fine wing grid upper/lower surface boundary conditions

Fine wing grid x-coordinate array

Fine wing grid section surface ordinates

Crude grid body surface normal (direction cosines)

Fine grid body surface normal (direction cosines)

Fine wing grid shearing angles

Wing and body pressure coefficient arrays

Boundary layer displacement thickness slope

2his appendix describes the IBM code version whereas Appendix B gives only

the modifications for the CDC code version.

PR.E_ pAGE I_L.ANK NOT FILM_ 59
Computer running time will of course va,'y depending" on the facility and

the mode of operation or operating system. The absolute levels specified may

be out dated shortly after they are specified. IBM 370/3081 running times are

specified below, however, since the relative increment for various options will

remain essentially steady, these increments will be useful for estimating the

time and cost of using different options.

CASE

Isolated body

Isolated wing

Airfoil

Isolated wing w/viscous interaction

Wing-body (body modeled in

crude grid)

Wing body w/pod-pylon-wink'let

Wing-body (body modeled in

fine grid)

Geometry/Grid verification

TIME_ (CPU Minutes)_

5 (50 crude/50 fine iterations)

14 (100 crude/80 fine iterations)

7 (150 crude/150 fine iterations)

15 (I00 crude/80 fine iterations)

15 (100 crude/80 fine iterations)

15 (i00 crude/80 fine iterations)

20 (100 crude/80 fine iterations)

1 (No iterations)

An effort has been made to minimize the amount of data required to define

the configuration geometry and flow condition. This should simplify matters

for most applications involving configuration analysis and reduce the chances

for input errors. For example, the computational grid systems (extent and

density) have been set in the FORTRAN coding to provide good results under

most conditions. Occasionally, it will be advantageous to manipulate the preset

values and limiters. FORTRAN coding changes will be necessary if this is the

case. The following values and limiters may be modified in certain special applications:

1) Gas constant (_ = 1.4)

2) Fine wing/body embedded grid limits or extent

3) Fine wing/body embedded grid density

4) Subsonic relaxation factor (w = 1.5)

5) Boundary layer transition (X/Ctran = 0.05)

6) The number of inviscid cycles between each viscous calculation (currently set to 20)

6O
All sample cases were computed using the basic code without modification. If

code modifications of type (2) or (3) are made care must be taken to insure

that common and dimensioned arrays are sufficient and consistent.

Input data format description can be found on the following pages. Descriptions are thought to be relatively straightforward except in the case of

wing section definition. It is important to extend wing planform/section definition to the symmetry plane even for wing-body configurations. This serves

several purposes. First, the code will compute a wing-body juncture which

will be a function of both configuration geometry and the computational grid

system. If the computational juncture is slightly inboard of the geometric

juncture, section definition in this region becomes important. Second, the input planform shape provides both aspect ratio for the lift-induced drag computation and reference lengths and areas used to reduce integrated pressures

to give force and moment coefficients. Finally, data input for defining a

wing-body configuration can be used directly for the isolated wing ease. This

feature can be used to study wing-body interference effects.

It is important to note that provisions have been made for inputting a

wing reference area. This number is used to reduce integrated pressure coefficients to provide wing or wing-fuselage total lift, drag, and moment coefficients. All other reference areas and lengths are computed from input geometry and printed at the end of the output stream. If reference values used

to reduce experimental data are different than those computed by the code,

then C_T_uted force and moment coefficients must be rescaled.

The computer code has been structured to permit the analyses of common

aircraft configurations. There are a number of restrictions, however, that

should be identified before modeling is started:

1) No boundary layer 5' computed for winglet surfaces.

2) No differencing approximations for seeondary lower surface winglet.

3) No provisions made for pylon surface attached to top of wing.

4) The fine embedded nacelle/pod grid option cannot be used along with

the pylon option; crude pod and fine pylon representation only.

61
5) The wing.let cant ang.le is used only to resolve force and moment coefficients. Computational wing'let surfaces are always perpendicular to

the wing" surface.

6) The fine body grid and fine nacelle/pod grid potential arrays use the

same dimensioned space. The two options cannot be implemented simultaneously.

7) In addition to the current rectang.ular pylon planform restriction, the

computational pylon lower surface is fixed at the wing fine grid lower

boundary.

8) Fuselage shoulder mountednacelles must be positioned to allow at

least one meshcell between the nacelle and the fuselage.

An overall view of the input data sequence can be seen in Figure A-1.

Figure A-2 illustrates relationships between tile wing" to body distance (ZWING)

and the wing. to pod distance (ZBODY1).

NACELLE/PODGEOMETRY A

FUSELAGE GEOMETRY

NOTE: COMPONENT CARD

ONLY REQUIRED FOR

WING-BODY CASE

(CASE = 3)

WINGLET GEOMETRY

PYLON GEOMETRY

WING GEOMETRY

COMPONENT CARD

CASE CARD

I/

TITLE CARD

R84-I 137-033C)

Fig. A-1 Input Data Sequence

62
NOTE : ZWlNG IS WING DISPLACEMENT MEASURED FROM FUSELAGE c_f..

(ZMAPAXlS FOR ARB. BODY DEFINITION).

-- _ . ZBODYI(-)

MEASURED FROM WING PLANE.

ZWING(-I ZBODY1 (+)

RB4-1137-034D

Fig. A-2 Sign Convention for Wing/Body & Wing/Nacelle Position Variables

63
INPUT DATA FORMAT

Excluding literal cards, all input data cards are punched in seven field

ten digit format (7F10.0). A decimal point is required in each field.

CARD CARD VARIABLE

NUMBER COLUMN NAME

Card I-A 1-80 TITLE

DESCRIPTION

Configuration or run title to identify graphic

and printed output.

Card 2-A 1-10 CASE

11-20 AMACH

21-30 AOA

31-40 RE

41-50 AXIT

51-60 AXITF

61- 70 VISMOD

CASE = i. Isolated Body (omit cards -W)

CASE = 2. Isolated Wing (omit cards -B)

CASE = 3. Wing-Body

Mach Number (AMACH < 1.0)

Angle-of-Attack (degrees)

Reynolds Number (X106)

Number of initial crude grid iterations.

(AXIT = 0. for geometry verification only)

Number of crude/fine grid iteration cycles.

VISMOD = 1. No viscous effects.

VISMOD = 2. Viscous effects computed at

end of inviscid analysis.

VISMOD = 3. Inviseid/viscous interaction.

NOTE: Omit card 3-A for CASE = I or CASE = 2.

Card 3-A 1-10 PY

11-20 VER

21-30 POD

Number of pylons(0 <_PY <_2.)

Winglet code VER = 0. No winglet.

VER = 1. Winglet definition to

follow on cards WLT.

Number of Ix)ds or nacelles(0 <_POD <-2.)

!

NOTE: Two-dimensional airfoils can be analyzed by setting ASECT = I I

for the isolated wing CASE = 2. }

Formatted input data files are created as card images.

64
CARD

NUMBER

NOTE:

CARD VARIABLE

COLUMN NAME DESCRIPTION

Omit card set W for CASE = 1 (card 2-A).

Card 1-W I-I0 ASECT

11-20 ANIN

21-30 ANOSW

3i-40 XMOM

41-50 ZWING

51-60 REFAR

61-70 WS

Number of streamwise sections defining wing

planform (i <-ASECT <_20).

Number of ordinates defining each wing section (ANIN <-60).

ANOSW = 0. Sharp nose wing sections.

ANOSW = 1. Blunt nose wing sections.

X-position about which moment is to be computed.

Z-position of wing" (waterline), see Fig. A-2.

Wing reference area.

Wing Cp distribution plot sealing per inch

(typically 0.4 or 0.8).

NOTE: Card set 2-W through 5-W is repeated ASECT times.

Card 2-W 1-10 XPL

11-20 YP

21-30 XPT

31-40 TWIST

41-50 AKODE

51-60

Wing section leading edge (X-value).

Wing section span position (Y-value). First

Y-value must be 0.0 (symmetry plane), even

for wing-body case.

Wing section trailing edge (X-value).

Wing section local incidence (twist angle in

degrees).

AKODE = 0. Section ordinates identical to

preceding section (omit cards

3-W through 5-W).

AKODE = 1. New section definition expected

on cards 4-W and 5-W.

Number of fine X-grid points at wing tip

station (default = i00). Read only on

first Card 2-W.

65
CARD

NUMBER

CARD VARIABLE

COLUMN NAME

Card 3-W 1-70 XINW

DESCRIPTION

Wing section X-coordinates

fined only for first wing

values expected).

(cards 3-W desection, ANIN

Card 4-W 1-70 YINU Wing section upper surface Y-coordinates

(ANIN values).

Card 5-W 1-70 YINL Wing section lower surface Y-coordinates

(ANIN values).

I_IE: Read Card set PY, PY times (Card 3-A).

Card 1-PY 1-80 TITLPY Pylon title to identify printed output.

Card 2-PY i-i0 PSEC

11-20 PIN

21-30 PNOS

31-40 PSTA

Number of streamwise sections defining pylon

planform (2 < PSEC < 10).

Number of ordinates defining each pylon section (PIN < 60).

PNOS = 0. Sharp nose pylon sections.

PNOS = 1. Blunt nose pylon sections.

Y - position of pylon on wing.

NOTE: Card set 3-PY through 6-PY is repeated PSEC times.

Card 3-PY i-I0 XPYL*

11-20 ZPYL*

21-30 XPYT*

31-40 TPIST

Pylon section leading edge (X-value).

Pylon section height (Z-value).

Pylon section trailing edge.

Pylon section local incidence in degrees (for

positive TPIST - pylon nose rotation toward

centerline).

*Note: Pylon planform description used for pylon wetted area calculation

(pylon skin friction) only. Planform shape is now restricted to

the boundaries of the wing fine grid system below the wing.

66
CARD

NUMBER

Card 3-PY

(contd)

CARD VARIABLE

COLUMN NAME

41-50 PKOD

DESCRIPTION

PKOD = 0. Section ordinates identical to

preceding section (omit cards

5-PY and 6-PY).

PKOD = 1. New section definition to follow.

Card 4-PY 1-70 XINP

Card 5-PY 1-70 YINUP

Card 6-PY 1-70 YINLP

NOTE:

Pylon section X-ordinates (cards 4-PY defined only for first pylon section, PIN values

expected),

Pylon section inboard surface coordinates

(PIN values).

Pylon section outboard surface coordinates

(PIN values).

Omit card set WLT for WLT = 0 (Card 3-A).

Card I-WLT 1-80

Card 2-WLT i-i0

TITLW Winglet title

VSEC Number of streamwise sections defining winglet planform (2 <_VSEC <_I0).

11-20 VIN Number of ordinates defining each winglet

section (VIN < 60).

21-30 VNOS

31-40 VANGL

VNOS = 0. Sharp nose winglet sections.

VNOS = 1. Blunt nose winglet sections.

Winglet cant angle in degrees (for positive

VANGL - winglet rotation upward from wing

plane).

67
CARD CARD VARIABLE

NUMBER COLUMN NAME DESCRIPTION

NOTE: Card set 3-WLT through 6-WLT is repeated VSEC times.

Card 3-WLT I-I0 XVL

11-20 YV

21-30 XVT

31-40 TVIST

41-50 VKOD

Winglet section leading edge.

Winglet section span position (Note: Winglet

is defined in plane of wing).

Winglet section trailing edge.

Winglet section local incidence in degrees

(for positive TVIST, winglet nose rotated

toward centerline).

VKOD = 0. Section ordinates identical to

preceding section (omit cards

5-WLT to 6-WLT).

VKOD = 1. New section definition to follow.

Card 4-WLT 1-70 XINV Winglet section X-ordinates (cards 4-WLT defined for first winglet section only, VIN

values expected).

Card 5-WLT 1-70 YINUV Winglet section inboard surface ordinates

(VIN values).

Card 6-WLT 1-70 YINLV Winglet section outboard surface ordinates

(VIN values).

NOTE: Ctnit Card set B for CASE = 2 (Card 2-A).

Card i-B 1-10 BKOD = 1. Infinite cylinder (only RADIUS need be

input).

BKOD =-1.Same as BKOD = 1. No embedded body

grid. Crude grid body representation only.

BKOD = 2. Simple axisymmetric body definition requested (input XINB, RIN on card(s) 2-B

and 3-B).

68
CARD

NUMBER

Card I-B

(contd)

CARD

COLUMN

11-20

21-30

31-40

41-50

51-60

61-70

VARIABLE

NAME DESCRIPTION

BKOD =-2.Same as BKOD = 2. No embedded body

grid. Crude grid body representation only.

Complex body definition requested (input

model on card(s) 4-B

BKOD = 3.

Quick-Geometry

through 13-B).

BKOD =-3.Same as BKOD = 3. No embedded body

grid. Crude grid body representation only.

BNOSE Body (X-value)_For BKOD = -+2. or -+3. nose

BTAIL Body tail (X-value) j

BNIN Number of axisymmetric body coordinates to

be input for BKOD = -+2 only (BNIN < 60).

RADIUS Cylinder radius for BKOD = -+I only.

ANOSB ANOSB = 0. Sharp nose body'_BKO D +2 only.

ANOSB I. Blunt nose body .J

BS Body Cp plot scaling per inch (typically

0.08).

NOTE: Omit card sets 2-B and 3-B for BKOD = ±1 or BKOD = 23.

Card(s) 2-B 1-70 XINB Axisymmetric body X-coordinates (BNIN

values).

Card(s) 3-B 1-70 RIN A'xisymmetrie body radii (BNIN values).

NOTE: Omit card sets 4-B through 13-B for BKOD = -+1 or BK(X) = +2.

Card 4-B 1-70 VTITLE Quick-Geometry model title.

Card 5-B 1-10 ACSM Number of distinct cross-section models

(i _ ACSM_ i0). (ACSMcard sets 6-B

and 7-Bwill follow).

69
CARD

NUMBER

CARD VARIABLE

COLUMN NAME

Card 6- B 1-10 ADUM

11-20 AARC

21-60 CTITLE

DESCRIPTION

Running count of current cross-section

model (I-ACSM).

Number of arcs in current cross-section

model (I < AARC < 10). (A__RC Card(s) 7-B

will follow).

Title or descriptor of current cross-section

model.

Card 7- B

Card 8- B

1-8 ARCNAM Arc or component name.

11-14 ASHAPE Arc or component shape.

21-28 PNTNAM(1) Control point name for beginning of this arc.

31-38 PNTNAM(2) Control point name for termination of this

arc.

41-48 PNTMAN(3) Slope control point name for this arc, if

required.

I-I0 ANTCSM

Card 9-B 1-10 ADUM

Card 10- B

7O

11-20 AMODEL

21-30 XCSMS1

31-40 XCSMS2

I-I0 BLINE

11-20 ALIAS

Number of cross-section models to define

entire body (1 _ P27IX:2_ < 10). (_

card(s) 9-B will follow).

Running count of current cross-section model

( 1 - AN T C SM)

Index corresponding to already defined

cross-section models (between 1 and ACSM).

Starting X-station for current cross-section

model.

Ending X-station for current cross-section

model.

Number of body line models to be defined by

se_nents (i <-BLINE < 25). (BLINE card

sets II-B and 12-B follow).

Number of body line models to be aliased

(i _ ALIAS < 25). (ALIAS card(s) 13-B

follow).
CARD CARD VARIABLE

NUMBER COLUMN NAME DESCRIPTION

Note: Card set ll-B and 12-B is repeated BLINE times.

Card I1-B 1-10 BLSEG

11 BYORZ

12-19 BNAME

Number of segment(s) defining body line

model (1 -<BLSEG -<10).

The letter Y or Z indicates which data

definition is to follow.

Body line name to be defined.

Card 12-B I-4 SSHAPE

11-20 D(1)

21-30 D(2)

31-40 D(3)

41-50 D(4)

51-60 D(5)

61-70 D(6)

Segment shape.

X-station for beginning of segment.

Y or Z value corresponding to D(1).

X-station for termination of segment.

Y or Z value corresponding to D(3).

X-station for segment slope control point.

Y or Z value corresponding to D(5)

Note:

Card 13-B

Card set 13-B is repeated ALIAS times.

11 BYORZ The letter Y or Z indicates which data

definition is to follow.

12-19 BNAME Body line name to be defined.

21 AYORZ The letter Y or Z indicates which definition

is to be used for aliasing.

22-29 ANAME Body line name to which BNAME is aliased.

NOTE: Read Card set PCD, PCD times (Card 3-A).

Card 1-POD 1-70 TITLEP Pod/nacelle title to identify graphic and

printed output.

71
CARD

NUMBER

Card 2-POD

Card 3-POD

CARD VARIABLE

COLUMN NAME

i-i0 PTYPE

11-20 BNOSE1

21-30 BTAIL1

31-40 YBODY1

41-50 ZBODY1

51-60 BNIN1

61-70 ANOSB1

I-I0 BODALF

11-20 BODBET

21-30 FIFP

31-40 FMFR

41-50 FNPR

DESCRIPTION

PTYPE = 0. Closed body (pod, tank, etc.).

PTYPE = I. Engine nacelle - cold jet. I

PTYPE =-1. Engine nacelle - hot jet. I I_I_R

and FNPR expected on Card 3-POD.

Pod nose (X-position).

Pod tail (X-position).

Pod span position (Y-position).

Pod height (Z-position).

Number of coordinates defining pod

geometry (BNIITI _ 30).

ANOSB1 = 0. Sharp nose pod.

ANOSB1 = 1. Blunt nose pod.

Pod angle- of-attack.

Pod yaw angle (positive-nose of pod away

from centerline).

Pod embedded grid code FIFP = 0. Pod

FIFP = O. crude grid only.

FIFP = 1. Fine pod grid used.

Engine inlet mass flow ratio, MFR.

Engine nozzle pressure ratio, NPR.

Card 4-POD 1-70

Card 5-POD 1-70

XINBP

RINP

Axisymmetric pod non-dimensional

X-ordinates (BNIN1 values).

Axisymmetric pod non-dimensional radii

(BNI1TI_ values).

72
SAMPLE INPUT DATA SETS

NACA 0012 AIRFOIL

2. 0.80_

I. 56.

O. O.

0.0 0

0.05000 0

0.18000 0

0.32000 0

0.46000 0

0.60000 0

0.74000 0

0.88000 0

o.0 0

0.035_0 0

0.05610 0

0.06000 0

0.055q0 0

0.04570 0

0.03270 0

0.01700 0

0.0 -0

-0.035_0 -0

-0.05600 -0

-0.05990 -0

-0.05530 -0

-0.04560 -0

-0.03260 -0

-0.01680 -0

I00.0 O.

.00200 0.00500

.06000 0.08000

.20000 0.22000

.34000 0.36000

._8000 0.50000

.62000 0.64000

.76000 0.78000

.90000 0.92000

.00780 0.01210

.03830 0.04300

.05740 0.05840

.05980 0.05940

.05420 0.05300

.0_410 0.04230

.03070 0.02850

.01450 0.01200

.00780 -0.01210

.03830 -0.0_300

.05730 -0.05830

.05970 -0.05920

.05420 -0.05280

.04400 -0.0_220

.03060 -0.02840

.01440 -0.01190

1.94 3. O0 J50

1.0 0.25 O.

- O.

0.01000

0.10000

0.24000

0.38000

0 52000

0 66000

0 80000

0 94000

0 01690

0 04670

0 05910

0 05880

0 05170

0 04050

0 02630

0 00950

-0.01690

-0.04670

-0.05900

-0.05860

-0.05160

-0.04040

-0.02620

-0.00930

150.

1.

0.02000

0.12000

0.26000

0.q0000

0.54000

0.68000

0.82000

0.96000 0

0.02350 0

0.049&0 0

0.05960 0

0.05810 0

0.05030 0

0.03370 0

0.02_10 0

0.00680 0

-0.02350 -0

-0.04980 -0

-0.05950 -0

-0.05_00 -0

-O.050kO -o

-0.03_60 -0

-0.02400 -0

-0.00670 -0

3.0

0 03000 0.04000

0 14000 0.16u00

0 28060 0.36000

0 42000 D.q4000

0 56000 0.5_C0_

0 70006 0.72060

0 8q000 0.85006

9&O00 1.000_0

02330 0.03220

05230 0.05640

06003 0.06010

05730 0.656_0

04690 0.04720

03670 G.03480

02180 0.03940

00420 O.O015U

62_30 -0.03220

05236 -0.05_30

05990 -0.06000

.05720 -0.35630

.04_70 -0.04720

•03660 -0.03470

.02160 -O.019EG

.00400 -0.00130

73
NASA AIRFOIL

2.

I.

O.

0

7

50

60

77

94

0

LSI

0.722 -1.50 4.96 l_ . I_.

38. 1.0 0.25 O. I

O. I00.0 0. O.

0 0.20000 0 50000 1.25000 2.50300

50000 I0.00000 12 50000 15.03000 I?.50005

00000 35.00000 39 99998 4q.9999S 50.00000

00000 62.50000 64 99998 67.50000 69.99998

q9998 80.00000 82 49998 85.00000 87.50000

99998 97.50000 I00 00000

0 1.03000 1 65000 2.46000 3.56000

3.0

0._

3.75000 5.0G000

19.9999_ 25._0000

55.00000 57.Ggg98

72.50000 75.00000

89.99998 _2.50000

4.00000 4.51000

5.28000 5.88000

8.20000 8.40000

7.67000 7.39000

_.97000 4.47000

I.I0000 0.49000

0.0 -0.66000

-2.94000 -3.28000

-_._9000 -4.52000

-3.37000 -5.07000

-1.10000 -0.78000

-0.07000 -0.28000

6 57000

8 49000

7 08000

3 95000

-0 15000

-0 97000

-3 57000

-_ 49000

-2 76000

-0 51000

-0 71000

6.77000 7.12000 7.q2000 7.88000

8._6000 8.33000 8.07000 7.89000

6.72000 6.33000 5.91000 5.q5000

3.qlO00 2.85000 2.28000 1.70000

-l._qO00 -1.8_000 -2.23000 -2.50000

-3.80000 -3.9_000 -4.150J0 -_.30000

-_.57000 -_.17000 -3.86G00 -3.62000

-2._3000 -2.10000 -1.75000 -I.q3C_0

-0.28000 -0.12000 0.0 0.01000

74
KC-135

3. 0.78

2. i.

6. 26.

28.66 0.0

O. 0.5

I0. 15.

45. 50.

80. 85.

0.740 1.750 6 .572 7.661

8.766 8.258

3.445 2.584

0.000 -0.872

-3.665 -4,510

-6.044 -5.678

-2.309 -1.732

32.02 4.37

36.38 10.36

0.536 1.399

5.511 6.436

7.7257 .382

3.188 2.391

0.000 -0.733

-2.646 -3.318

-5.007 -4.793

-1.998 -1.498

41.41 16.73

0.374 1.123

4.699 5.530

6.736 6.509

2.929 2.197

0.000 -0.570

-1.787 -2.265

-3.782 -3.696

-1.593 -1.194

50.81 29.30

0.306 0.997

4.423 5.210

6.370 6.178

2.904 2.178

0.000 -0.465

-1.187 -1.479

-2.568 -2.501

-1.039 -0.775

69.27 53.96

TRANSPORT WITH PODS,

2.0

2.

O.

70.27

0.75

20.

55.

90.

2.055

8.380

7.620

1.723

-i 076

-5 228

-5 185

-i 155

62 89

57 86

1.654

7.070

6.895 i .594

-0.895

-3.925

-4.448

-0,999

59.20 1 .340

6.047

6.136

1.465

-0.684

-2.731

-3.487

-0,796

64.90

1.198

5.704

5.850

1.452

-0.558

-1.770

-2. 330

-0.520

77.27

INBOARD PYLON

2. 26. 1.0

O. -19.0 1.0

O. 0.5 0.75

i0.0 15.0 20,0

45.0 50.0 55.0

80.0 85.0 90.0

O. 0.50 0.90

3.24 3.86 4.34

4.90 4.64 4.30 i .76 I .22 0.7

O. -0.50 -0.90

-3,24 -3.86 -4.34

-4.90 -4.64 -4.30

-1.76 -1.22 -0.7

O. O. 1.0

OUTBOARD PYLON

2. 26. 1.0

O. -25.0 1.0

O. 0.5 0.75

I0.0 15.0 20.0

45.0 50.0 55.0

80.0 85.0 90.0

O. 0.50 0.90

3,24 3.86 4.34

4.90 4.64 4.30

1.76I .22 0.7

O. -0.50 -0.90

-3.24 -3.86 -4.34

-4.90 -4.64 -4.30

-1.76 -I .22 -0.7

O. O. 1.0

PYLONS,

5.25

52.90

2.22

1.25

25.

60.

95.

2.539

8.860

6.870

0.861

-1.390

-5.757

-4.618

-0.577

2.02

1.75

2.060

7.500

6.284

0.797

-1.123

-4.401

-3.995

-0.499

1.46

1.687

6.422

5.643

0.732

-0.837

-3.118

-3.174

-0.398

0.70

1.519

6,050

5.412

0.726

-0,657

-2.059

-2.078

-0.260

-I.0

22.12

O.

1.25

25,0

60.0

95.0

1.15

4.66

3.88

0.26

-1.15

-4.66

-3.88

-0.26

O.

38.00

0.

1.25

25.0

60.0

95.0

1.15

4.66

3.88

0.26

-1.15

-4.66

-3.88

-0.26

O,

AND WINGLET8

i00.

-4.25

1.0

2.50

30.

65.

i00.

3.470

9.137

6.029

O.

-1.915

-6. 104

-4.041

O.

O.

1.

2.840

7.760

5.570

O.

-1.475

-4.746

-3.496

O,

1.0

2.350

6.666

5.049

O.

-1.053

-3.425

-2,787 0i 0 2 160 6 280 4 880 0

-0.750

-2.275

-I .818

O.

O.

1.0

2.50

30.0

65.0

I00.0 i .70

4.90

3.40

O.

-1.70

-4.90

-3.40

O.

O.

1.0

2.50

30.0

65.0

i00.0

1.70

4.90

3.40

O.

-1.70

-4.90

-3.40

O.

O.

80.

1440.0

5.0

35.

70.

4.830

9.218

5.168

-2.613

-6.275

-3.464

3.998

7.920

4.782

-1.915

-4.980

-2.996

3.360

6.805

4.380

-1.307

-3.642

-2,389

3.130

6.430

4.267

-0.895

-2.445

-1.558

5.0

35.0

70.0

2.36

5.02

2.88

-2.36

-5,02

-2.88

5.0

35.0

70.0

2.36

5.02

2.88

-2.36

-5.02

-2.88

I,

0.8

7.5

40.

75.

5.813

9.105

4.300

-3.178

-6.250

-2.886

.850

7.910

3. 985

-2.290

-5.070

-2.497

4.114

6.829

3.687

-1.544

-3.763

-1,991

3.857

6.449

3.605

-1.041

-2.543

-1.299

7.5

40.0

75.0

2.82

5.02

2.34

-2.82

-5.02

-2.34

7.5

40.0

75.0

2.82

5.02

2.34

-2.82

-5.02

-2.34

75
KC-135 WINGLET

2. 38. 1.0 75.0

72.07 53.96 77.27 -4.0 i . 0

0. 0 .2 0.5 1,25 2,50

7.50 10.0 12.5 15.0 17.5

30.0 35.0 qO.O :*5.0 50.0

60.0 62.5 65.0 67.5 70.0

77 .5 SO.O _2.5 85.0 87.5

95.0 97.5 i00.0

0. 0.77 1.19 1.79 2.:.9

3.89 q.33 4,69 4.99 5.25

6.05 6.21 6.28 6.27 6.18

5.72 5.5q 5.33 5.08 :*.$i

3.8q 5.:.9 3.11 2.70 2.2_8

0.89 0 .5S -0 .20

O. -0. 51 -0.:*I -0,60 -0.77

-1.18 -1.32 -i.:*q -I,5:* -!,$I

-i .76 - i . 7_* -1.68 -1.55 -i .:.4

-0. 90 -0.71 -0.52 -0.53 -0. 15

0.36 0.49 0 .60 0.65 0.6q

0.21 -0.15 -0.67

78.32 61.96 80.00 -:*.0 O. C

-2. 0.00 108. 30 22. 5.04

O. 2.0 :*.0 6.0 8.0

lq.O 16.0 20.0 30.0 40.0

70.0 78.0 80.0 85.0 90.0

108.3

0. 2.50 3.35 3,90 :*.30

4. 95 5. Oq 5.04 5.04 5. Oq

5.0:* 5.0:* 4.92 4.65 q.20

2.60

KCI35A INBOARD ENGI_'E NACELLE

O, 33.464 :.5.610 22.05 -3.816

2. O. O. O. O.

O. 0.58 1.81 4.61 7.57

21.90 27,66 39.19 q3.31 50.72

91 . 06 96 .82 100 . 0

9.72 10.21 10.87 11.69 12.35

13.83 !q.16 14.00 14.16 lq.O0

10.0:* S.40 7.41

KCI35A OUTBO#RD ENGINE NACELLE

O. :.5.8_0 57.986 38.15

2. 0, O. O.

O. 0.58 I.SI q.61

21.90 27.66 39.19 q3,31

91.06 96.82 100,0

9.72 10.21 10.87 11.69

13.83 14.16 14.00 14.16

10.04 8.40 7.:*i

-3.816

O.

7.57

50,72

12.35

I:*.00

3.75

200

55.0

72.5

90.0

2.96

5.:*7

5.99

4.51

I .84

-0.90

-1.67

-!.22

0 04

0 59

!

!0.0

50.0

95,0

q .60

5.04

3.55

17

10 37

62 2:*

12 8:*

13 67

17

10.37

62.2:*

12.8:*

13.67

5.00

25.0

57.5

75.0

92.5

3.33

5.81

5.87

:*.19

1.38

-1.00

-i .75

-1.06

0.20

0.:.5

12.0

60.0

i00.0

4 30

5 04

2 65

0

16.1G

79.53

13.58

ll.gq

O.

16.14

79.53

13,50

11.94

76
GULFSTREAM III

3.

O.

14.

275.0 0.

0.0

0.10000

0.45000

0.80000

-0.05467

-0.01245

-0.02274

-0.07309 -0

-0. 05467 -0

-0.09489 -0

-0,13145 .-0

-0.12940 -0

302.7 45.0

-0.06251 -0

-0. 02281 -0

-0. 02643 -0

-0.07555 -0

-0.06251 -0

-0.09900 -0

-0.12963 -0

-0.12603 -0

321.2 75.0

-0. 06846 -0

-0.03067 -0

-0.02970 -0

-0.07764 -0

-0.06846 -0

-0.10172 -0

-0. 12822 -0

-0.12339 -0

328.0 86.0

CONFIGURATION NITH NINGLET AND NACELLE

0.780 4.00 3.10 80.

1. 1.

26. 1.0 451.3

508.72 0.0

0.00500 0.00750 0 01250

0:15000 0.20000 0 25000

0 50000 0.55000 0 60000

0 85000 0.90000 0 95000

-0 04646 -0.04435 -0 04088

-0 00905 -0.00845 -0 00902

-0 02857 -0.03483 -0 04147

08260 -0.09212 -0 10163

06342 -0.06548 -0 06876

10287 -0.10912 -0 11465

13344 -0.13438 -0 13447

12634 -0.12234 -0 11750

519.7 0.0

05440 -0.05240 -0 04908

01835 -0.01672 -0 01651

05161 -0.03744 -0 04390

08430 -0.09277 -0 10112

07061 -0.07249 -0 07551

10588 -0.11137 -0 11608

13143 -0.13217 -0 13214

12275 -0°11895 -0 11473

526.9 0.0

06048 -0.05856 -0 05540

02556 -0.02323 -0 02245

03434 -0.03976 -0 04588

08605 -0.09375 -0 10098

07600 -0.07775 -0 08055

10771 -0.11242 -0 11640

12984 -0.13047 -0 13033

12015 -0.11659 -0 11277

529.6 0.0

100.

-47.0

1.0

0.02500

0.30000

0.65000

1.00000

-0.03409

-0.01059

-0.04846

-0. 11114

-0.07480

-0. 11965

-0.13398

-0.11150

1.0

-0. 04276

-0.01725

-0.05090

-0. 10947

-0. 08106

-0.12020

-0.13149

-0.10984

1.0

-0.04943

-0. 02275

-0.05279

-0.10821

-0.08568

-0.I1986

-0.12952

-0. 10858

1.0

-0.05208

-0. 02497

-0.05350

-0.10771

-0.087{)6

-0.11957

-0. 12874

-0.10808

1.0

-0. 06282

-0.03425

-0.05626

-0.10572

-0.09433

-0.11789

-0. 12551

-0. 10608

1.0

-0.06866

-0.03942

-0.05778

-0.10465

-0.09766

-0. 11679

-0. 12369

-0. 10502

1.0

-0.06830

-0.03883

-0.05690

-0.10333

-0. 09783

-0. 11687

-0.12281

-0.10369

1.0

-0. 06756

-0. 03759

-0. 05508

-0.10055

-0. 09825

-0.11691

-0.12099

-0.10091

-0.07081 -0.06289 -0.06099 -0

-0.03377 -0.02847 -0.02586 -0

-0.03113 -0.03550 -0.04072 -0

-0.07817 -0.08637 -0.09368 -0

-0.07080 -0.07812 -0.07981 -0

-0.10266 -0.10825 -0.11263 -0

-0.12767 -0,12922 -0.12980 -0

-0.12235 -0.11915 -0.11571 -0

352.7 126.0 539.4 0.0

-0.08021 -0.07258 -0.07083 -0

-0 04618 -0.04025 -0.03671 -0

-0 03751 -0.04070 -0.04509 -0

-0 07824 -0.08511 -0.09198 -0

-0 08021 -0.08648 -0.08793 -0

-0 10532 -0.10913 -0.11228 -0

-0 12539 -0.12671 -0.12711 -0

-0 11827 -0.11531 -0.11229 -0

364.4 145.0 544.0 0.0

•-0 08522 -0.07780 -0.07614 -0

-0 05281 -0.04666 -0.04270 -0

-0 04145 -0.04397 -0.04775 -0

-0 07739 -0.08420 -0.09102 -0

-0 08522 -0.09085 -0.09215 -0

-0 10566 -0.10872 -0.11153 -0

-0 12415 -0.12533 -0.12563 -0

-0 11620 -0.11340 -0.11061 -0

378.0 167.0 549.3 0.0

-0 08537 -0.07765 -0 07592 -0

-0 05232 -0.04615 -0 04216 -0

-0 04089 -0.04336 -0 04701 -0

-0 07624 -0.08301 -0 08978 -0

-0 08537 -0.09119 -0 09249 -0

-0 10575 -0.10888 -0 11169 -0

-0 12382 -0.12480 -0 12496 -0

-0 11511 -0.11226 -0 10940 -0

402.7 207.0 559.0 0.0

-0 08567 -0.07738 -0.07555 -0

-0 05130 -0.04508 -0.04104 -0

-0 03970 -0.04208 -0.04556 -0

-0 07387 -0.08054 -0.08721 -0

-0 08567 -0.09187 -0.09319 -0

-0 10592 -0.10919 -0.11198 -0

-0 12294 -0.12361 -0,12349 -0

-0 11283 -0.10985 -0.10687 -0

05790

02487

04669

10070

08250

11633

12961

11204

.06805

.03486

.05026

.09885

.09022

.I1516

.12666

.10922

.07350

.04042

.05246

.09784

.09418

.11420

.12505

,10781

.07324

.03986

.05165

.09655

.09450

.11433

.12426

.I0654

.07270

.03868

.05004

.09388

.09518

.11453

.12263

.i0389

134582.4

0.05000

0.35000

0.70000

-0.02419

-0.01369

-0.05585

-0.08334

-0.12419

-0.13299

-0.03373

-0.01905

-0.05848

-0.08880

-0.12382

-0.13026

-0.04099

-0.02382

-0.06044

-0.09275

-0.12294

-0.12813

-0.04391

-0.02590

-0.06110

-0.09424

-0.12250

-0.12727

-0.05561

-0.03455

-0.06320

-0.09957

-0.12051

-0.12366

-0.06191

-0.03938

-0.06389

-0.10159

-0.11938

-0.12162

-0.06147

-0.03878

-0.06290

-0.10149

-0.11959

-0.12070

-0.06057

-0.03753

-0.06086

-0.10147

-0.11928

-0.11872

1.0

0.6

0.07500

0.40000

0.75000

-0.01713

-0.01760

-0. 06385

-0.08974

-0.12819

-0. 13151

-0.02726

-0.02224

-0.06670

-0.09450

-0.12697

-0.12848

-0.03498

-0. 02618

-0.06884

-0.09783

-0.12573

-0. 12612

-0.03804

-0. 02787

-0. 06947

-0.09900

-0.12519

-0.12515

-0.05032

-0. 03554

-0.07088

-0. 10288

-0.12308

-0 . 12116

-0.05687

-0.04008

-0,07057

-0. 10387

-0.12194

-0.11899

-0.05641

-0. 03948

-0.06947

-0.10387

-0. 12186

-0.11797

-0.05544

-0.0382 <*

-0.06721

-0.10391

-0.12150

-0.11582

77
452.7 288.0 578.7 0.0 1.0

-0.08651 -0 07666 -0.07457 -0.07130 -0 06566 -0.05815 -0.05279

-0.04849 -0 04213 -0.03799 -0.03548 -0

-0.03643 -0 03865 -0.04176 -0.04568 -0

-0.06751 -0 07386 -0.08021 -0.08656 -0

-0.08651 -0 09375 -0.09513 -0.09705 -0

-0.10635 -0 10954 -0.11212 -0.11434 -0

-011993 -011992 -0.11917 -011784 -0 -010653 -010321 -0.09990 -oo9659 -o

479.9 -0.08717 332.0 -0.07612 589-40738 °'°-0_ -0.07037 10-0

-0.04631 -0.03987 -0.03561 -0.03299 -0

-0.03389 -0.03608 -0.03890 -0.04252 -0

-0.06280 -0.06885 -0.07489 -0.08094 -0

-0.08717 -0.09518 -0.09664 -0.09860 -0

-0.10676 -0.10946 -0.11164 -0.11345 -0

-0.11714 -0.i1670 -0.11564 -0.11393 -0

-0.10160 -0.09803 -0.09447 -0.09091 -0

502.8 369.0 598.4 0.0 1.0

03425 -0.03q09 -0.03478

05039 -0.05555 -0.06134

09291

09957 -0.10218 -0.104_2

11631 -0.11809 -0.11931

11582 -0.11319 -0.10984

09327

06425 -0.05630 -0.05073

03162 -0.03139 -0.03213

04690 -0.05181 -0.05713

08698

10081 -0.10315 -0.10510

11508 -0.11625 -0.11699

11167 -0.10869 -0.10516

08734

-0.08789 -0 07569 -0.07323 -0.06953 -0 06280 -0.05435 -0.0_854

-0.04396 -0 03737 -0.03300 -0.05022 -0 02875 -0.02840 -0.02925

-0.03101 -0 03316 -0.03587 -0.03923 -0 04321 -0.04787 -0.05279

-0.05799 -0 06352 -0.06915 -0.07479 -0 08042

-0.08789 -0 09680 -0.09832 -0.10030 -0 10231 -0.10410 -0.10551

-0.10674 -0 10877 -0.iI040 -0.11186 -0 11299 -0.11374 -0.11403

-0.11375 -0 11291 -0.11147 -0.10950 -0 10693 -0.1036¢ -0.09992

-0.09609 -0.09227 -0.08844 -0.08461 -0 08078

513.9 387.0 602.8 0.0 1.0

-0.08833 -0.07543 -0.07286 -0 06881 -0.06191 -0.05316 -0.0_718

-0.04257 -0.03587 -0.03146 -0 02861 -0.02701 -0.02658 -0.02753

-0 02929 -0.03145 -0.03408 -0 03728 -0.04109 -0.04556 -0.05032

-0 05533 -0.06049 -0.06582 -0 07115 -0.07648

-0 08833 -0.09769 -0.09931 -0 10130 -0.10324 -0.10445 -0.10545

-0 10638 -0.10792 -0,I0937 -0 11060 -0.11153 -0.11204 -0.11203

-0 11154 -0.11053 -0.10894 -0 10678 -0.10396 -0.10061 -0.09676

-0 09278 -0.08879 -0.08481 -0 08083 -0.0768_

540.5 _30.0 613.2 0.0 1.0

-0 08969 -0,07_83 -0,07178 -0 06722 -0,05948 -0,04968 -0,04313

-0 03819 -0.03115 -0.02667 -0 02347 -0.02156 -0.02091 -0.02191

-0 02369 -0.02596 -0.02852 -0 03143 -0.03481 -0.03863 -0.04505

-0 04757 -0.05200 -0.05614 -0 06014 -0.06414

-0 08969 -0.10053 -0.10233 -0 10458 -0.10632 -0.10538 -0.10458

-0 10425 -0.10443 -0.10528 -0 10594 -0.10620 -0.10601 -0.10540

-0 10432 -0.10266 -0.10052 -0 09781 -0.09462 -0.09110 -0.08673

-0 08229 -0.07784 -0.07339 -0 0689_ -0.06_50

552.8 450.0 618.1 0.0 1.0

-0.09055 -0.07451 -0.07127 -0 06635 -0.05796 -0.04758 -0.04061

-0.03544 -0.02824 -0.02363 -0

-0.02010 -0.02231 -0.02490 -0

-0.04511 -0.04732 -0.05111 -0

-0.09055 -0.10234 -0.10428 -0

-0.10236 -0.10161 -0.10218 -0

-0.09939 -0.09748 -0,09503 -0

-0.07558 -0.07085 -0.06613 -0

G-III WINGLET

3. 24.

576.0 _50.0

0 0.005

0 20 0.25

0 55 0.60

0 90 0.95

0 0 0,0088

0 04762 0.05049

0 04212 0.03850

0 01060 0.00605

02027 -0.01803 -0.01754 -0.01840

02782 -0.03104 -0.03459 -0.03870

05571 -0.05632

10664 -0.10846 -0.10626 -0.10401

10245 -0.10231 -0.10179 -0.10087

09190 -0.08859 -0.08503 -0.08030

06140 -0.05668

1.0 75.0

618.1 0.0 1.0

0.01 0.02 0.05 0.10 0.15

0.30 0.35 0.40 0.45 0.50

0.65 0.70 0.75 0.80 0.85

1.0

0.01198 0.01650 0.02580 0.03615 0.04311

0.05175 0.05150 0.05020 O. 0_.805 0.04534

O. 03425 O. 02990 O. 02515 O. 02034 O. 01535

0.00170

0 0 -0.00780 -0.01007 -0.01290 -0.01740 -0.02163 -0.02424

-0.02577 -0.02650 -0.02670 -0.02640 -0.02555 -0.02440 -0.02295

-0.02100 -0.01845 -0.01500 -0,01070 -0.00620 -0.00250 0.00010

0.00155 0.00100 -0.00220

602.5 483.5 631.0 O. 1.0

0.0 0.01166 0.01608 0.02183 0.03160 0,04160 0.04790

0.05270 0.05625 0,05855 0.05995 0.06060 0.06060 0.05967

0.05790 0.05540 0.05200 0.04755 0.04230 0.03665 0.03030

0,02300 0.01385 0,00300

0.0 -0.00757 -0.01012 -0.01300 -0.01709 -0.02045 -0.02202

-0.02265 -0.02265 -0.02220 -0.02115 -0.01975 -0.01793 -0.01555

-0.01280 -0.00975 -0.00630 -0.00270 0.00070 0.00360 0.00480

0.00430 0.00200 -0.00220

629.0 517.0 644.0 0.0 0.0

-3. 8.0 864.5 O. O. O. 0.4

78
GULFSTREAM FUSELAGE QUICK-GEOMETRY MODEL

3.

I.

BODYLO

BODYHI

2.

CANLO

CANSI

NINDF

3.

CAHOPLO

CANOPSI

WIHDSI

CANOPUP

5

i

2

3

4

5

i0.

3.

ELLX

LINE

CUBI

5.

ELLX

LINE

CUBI

LINE

CUBI

1.

LINE

3.

CUBI

LINE

CUBI

3.

EILX

LINE

CUBI

I.

LINE

1.

LINE

2.

LINE

LINE

2.

LINE

LINE

1.

LINE

G-Ill

I.

2.75

O.

46.67

93.33

9.82

14.04

8.42

2. NOSE TO WINDSHIELD BASE

ELLI BDYBCL BDYHHB BDYLSCP

ELLI BDYHHB BDYTCL BDYUSCP

3. WINDSHIELD

ELLI BDYBCL BDYMH8 BDYLSCP

ELLI BDYMHB CANLOW CANLSCP

LINE CANLON BDYICL

4. CANOPY

ELLI BDYBCL BDYMHB BDYLSCP

ELLI BDYHHB CAHLOW CANLSCP

LINE CAHLOW CANHIE

ELLI CANHIE BDYTCL CAHTSCP

I. 8.0 64.0

2, 64.0 83.5

3. 83.5 133.0

i. 133.0 575.5

i. 575.5 864.5

II.

ZBDYBCL

8.0 78.5 133.0 53.0 8.0

133.0 53.0 575.5 53.0

575.5 53.0 864.5 114.5 625.0

ZBDYTCL

8.0 78.5 64.0 113.5 8.0

64.0 11.3.5 83.5 132.5

83.5 132.5 133.0 147.0 98.0

133.0 147.0 575.5 147.0

575.5 147.0 864.5 114.5 653.0

YCENTER

8.0 O.O 864.5 0.0

ZBDYMHB

8.0 78.5 181.0 100.0 135.5

181.0 lO0.O 502.0 I00.0

502.0 lOB. 0 864.5 114.5 616.5

YBDYMHB

8.0 O. 206.0 47.0 8.0

206.0 47.0 502.0 47.0

502.0 47.0 864.5 0. 636.0

ZCAHLOW

64.0 113.5 133.0 113.5

ZCAHHIE

83.5 132.5 133.0 132.5

YCANLOW

64.0 O. 79.5 28.0

79.5 28.0 133.0 42.0

YCANHIE

83.5 0. 96.0 24.5

_6.0 24.5 133.0 34.0

YCANTSCP

83.5 0. 133.0 22.0

ZMAPAXIS ZBDYHHB

YMAPAXIS YCENTER

ZCANTSCP ZBDYTCL

ZCANLSCP ZCANLOW

YCANLSCP YBDYMHB

YBDYTCL YCENTER

YBDYBCL YCENTER

YBDYLSCP YBDYrlliB

ZBDYLSCP ZBDYBCL

YBDYUSCP YBDYMHB

ZBDYUSCP ZBDYTCL

NACELLE

481.25 668.75 78.95 73.3 16.0

-0.5 O. 0.66 2.0

6.67 13.33 20.00 26.67 33.33

53.33 60.00 6,_ .67 73.33 80. O0

100.0

12.0 13.05 13.69 13,89 14.04

13.96 13.62 13.13 12.21 ii. 16

6.81

53.0

53.0

94.5

147.0

147.0

I00.0

I00.0

47.0

47.0

0.0

40.00

86.67

14.04

9.89

79
C-5A TRANSPORT WITH ENGINE PODS AND PYLONS

3. 0.775 2.50 2.5 I00, 80. 3.0

2. O, 2,

5. 31. 1.0 165.3 20.0 18720.0 1.0

109.96 O. 189.17 4.18 O.

0.0 0 25000 0 50000 0.75000 1.00000 2.00000 4.00000

6.00000 8

20.00000 25

55.00000 60

90.00000 95

0.56298 i

3.94282 4

6.00648 6

6.55966 6

2.56929 I

0.56336 -0

-2.92237 -3

-5.24884 -5

-5.57466 -5

-1.16210 -0

167.37 69.5

00000 i0

00000 30

00000 65

00000 I00

16181 1

39117 6

39246 6

26794 5

66900 0

41909 -0

00000 12.00000 14.00000 16.00000 18.00000

00000 35.00000 40,00000 45.00000 50.00000

00000 70.00000 75.00000 80.00000 85.00000

ooooQ

49063 1.74381 1.95621 2.59646 3.35606

76414 5.05056 5.33436 5.58457 5.79552

67631 6.85000 6.91954 6.91625 6,76694

90856 5.45495 4.90702 4.25141 3.48790

12887

70382 -0.89820 -1.06155 -1.56102 -2.31165

0.58099

3.98024 4

6.09324 6

6.78242 6

2.58115 I

0.58099 -0

-2.57321 -2

-4.04572 -4

-4.01791 -3

-0.98114 -0

154.10 82.0

41914 -3.83526 -4.15688 -4.47850 -4.76203 -5.00587

68123 -5.98528 -6.16150 -6.20322 -6.11709 -5.90316

13833 -4,58723 -3.96548 -3.29717 -2.57890 -1.84615

57491 -0.12896

201.06 2.90 1.0

1 16726 1.69248 1.75712 1.96323 2.60530 3.38237

44052 4.80000 5.11966 5.41050 5.66225 5.87825

49263 6 78225 6.97204 7.06200 7.06200 6.97212

50284 6 14336 5,68417 5.11525 4,41675 3.58518

44331 0 II019

39277 -0 70676 -0.90126 -1.06083 -1.51522 -2.11367

92607 -3 20495 -3.40705 -3.60305 -3.77372 -3.90973

23388 -4 42525 -6.69639 -6.68732 -4.40760 -4.24770

71824 -3 34869 -2.90013 -2.429_7 -i.94043 -1.46043

53175 -0 11019

203.17 2.68 1.0

0.53031

5.98975 q

6.12201 6

6.84322 6

2.59158 I

0.58031 -0

-2.47998 -2

-3.70284 -3

-3.56939 -3

-0.94637 -0

i 15696 1.49673 1.75361 1.96380 2.60772 3.38790

63000 4.79000 5.14097 5.43662 5.69037 5.90815

53237 6.82620 7.00831 7.10610 7.11697 7.02803

57149 6 20261 5.75806 5.18479 4.47149 3.59955

37545 0 10949

39956 -0 70439 -0.89548 -1.05719 -1.49729 -2.06062

79766 -3 03450 -3.20384 -3.36684 -3.50283 -3.60234

88321 -3 98274 -4.01792 -3.99696 -3.92039 -3.77952

31939 -2 98628 -2.60584 -2.19457 -1.77261 -1.35957

52253 -0 10949

167.59

0.60323

4.06878 4

6.17917 6

6.76147 6

2.47901 I

0.60323 -0

-2.45674 -2

-3.57137 -3

-3.53591 -3

-0.86666 -0

108.0 211.27 2.18 1.0

I 24885 1.57273 1.82851 2.04443 2.69783 3.47276

51000 4.89000 5.21000 5.51035 5.74338 5.96338

57927" 6.85882 7,04174 7.11491 7.10258 6.98062

45772 6.05988 5.58484 5.00134 4.28537 3.44006

35890 O.IIOZO

38175 -0.72092 -0.91419 -1.07370 -1.52129 -2.06233

74150 -2.95825 -3.10856 -3.25177 -3.37625 -3.47381

73756 -3.86369 -3.93764 -3.93943 -3.87902 -3.76297

26171 -2.94664 -2.54515 -2.13052 -1.70554 -1.28083

47665 -0.11080

204.32 178.80 233.32 0.9 1.0

0 74507 1.58808 1.96509 2.27170 2.4?666 3.17314 3.94205

4 51033 4.91000 5.27655 5.54855 5.82055 6.05628 6.26366

6 66873 6.83983 7,10184 7,1_633 7.15015 6.99679 6.70912

6 31043 5 83194 5.25652 4.59713 3.89070 3.19065 2.46205

i 74123 0 96068 0.10068

0 76507 -0 23683 -0.68123 -0.92621 -I.13260 -1.62776 -2.07020

-2 32072 -2 46180 -2.54245 -2.59064 -2.63146 -2,67519 -2.72437

-2 77355 -2 95676 -3.20575 -3.67032 -3.63361 -3.64473 -3.53790

-3 31576 -2 99489 -2.61661 -2.19781 -1.77575 -1.29685 -0,85767

-0 45959 -0 20068 -0.10068

C-5A INBOARD PYLON

2. 31. 1.0

O. -13.0 1.0

O. 0.12048 0.25301

1.0 1.25301 1.87952

15.0 20.0 25.0

55.0 60.0 65.0

90.0 95.0 i00.0

O. 0.48193 0.68675

1.42169 1.57831 1.90361

3.91566 4.08434 4.22892

4.02410 3.83133 3,59036

1.43373 0.79518 0.08436

69.48

O. 1.0

0.37349 0.69398 0 .62651 0.74799

2.49398 5.0 7.61446 i0.0

30.0 60.0 65.0 50.0

70.0 75.0 80.0 85.0

0.85542 1.02410 1.12048 1.24096

2.18072 2.81928 3.22892 3.53012

4.25301 4.25301 4.22892 4.14458

3.28916 2.92771 2.49398 2.00000

O. -0.48193 -0.68675 -0.85542 -1.02410 -1.12048 -1.24096

-1.42169 -1.57831 -1.90361 -2.18072 -2.81928 -3.22892 -3.53012

-3.91566 -4.08434 -4.22892 -6.25301 -4.25301 -4.22892 -4.14658

-4.02610 -3.83133 -3.59036 -3.28916 -2.92771 -2.49398 -2.00000

-1.43373 -0.79518 -0.08434

O. O. I. O. O.

8O
C-5A OUTBOARD PYLON

2. 31. 1.0 108.14

O. -13.0 1.0 O. 1.0

O. 0.12048 0,25301 0.37349 0.49398 0.62651 0.74799

1.0 1.25301 1.87952 2.49398 5.0 7.61446 10.0

15,0 20.0 25.0 30.0 40.0 45.0 50.0

55.0 60.0 65.0 70,0 75.0 80.0 85.0

90.0 95.0 100.0

O. 0.48193 0.68675 0.85542 1.02410 1.12048 1.24096

1.42169 1.57831 1.90361 2.18072 2.81928 3.22892 3.53012

5.91566 4.08436 4.22892 4.25501 4.25301 4.22592 4.14458

4.02410 3.83133 3.59036 3.28916 2.92771 2.49398 2.00000

1.43373 0.79518 0.08434

O. -0,48193 -0.68675 -0.85542 -1.02410 -1.12048 -1.24096

-1.42169 -1.57831 -1.90361 -2.18072 -2.81928 -3.22392 -3.53012

-3.91566 -4.08434 -4.22892 -4.25301 -4.25301 -4.22_92 -4.14458

-4.02410 -3.83133 -3,59036 -3.28916 -2.92771 -2.493_ -2.00000

-1.43373 -0.79518 -0.08434

O. O, i. O. 0.

-3. -30.0 380.04 O. 0.0 O. 0.4

LOCKHEED C-5A FUSELAGE

4.

1.

BODYLO

BODYHI

2.

BODYLO

BODYSI

BODYUP

3.

BODYLO

BULSID

BODYSI

BODYUP

4.

BODYLO

BULSID

BDDYSI

BODYHI

5.

i.

2.

3,

4.

5.

10.

4.

ELLX

ELLY

LINE

ELLY

3.

ELLX

LINE

ELLY

3.

ELLY

LINE

ELLY

I.

LINE

3.

ELLX

LINE

ELLY

3.

ELLX

LINE

ELLX

3.

ELLX

LINE

ELLX

1.

LINE

I.

LINE

1.

LINE

2,

ELLI

ELLI

3.

ELLI

LINE

ELLI

4.

ELLI

ELLI

LINE

EILI

4.

ELLI

ELLI

LINE

ELLI

1.

2.

3.

4.

i.

13.

ZBDYTCL

-30.0

-5.0

10.0

290.0

ZBDYBCL

-30 0

I0.0

215 0

ZBDYMHB

-30 0

I0.0

215 0

YCENTER

-30 0

YBDYMHB

-30 0

I0.0

300 0

ZFAIRT

92.0

112.0

140.0

YBULSI

141,0

160.0

204.0

ZBULSI

141.0

ZBULTOP

141.0

YBULTOP

141.0

YBDYBCL

YBDYTCL

QUICK-GEOMETRY MODEL

NOSE/TAIL

BDYBCL BDYMHB BDYLSCP

BDYHHB BDYTCL BDYUSCP

_ING-BODY FAIRING

BDYBCL BDYIIHB BDYLSCP

BDYrIHB FAIRT

FAIRT BDYTCL BDYUSCP

W-B FAIRING N/ I._IIEEL FAIRING

BDYBCL BULSI BULLSCP

BULSI BULTOP BULUSCP

BULTOP FAIRT

FAIRT BDYTCL BDYUSCP

AFT FUSELAGE N/ WHEEL FAIRING

BDYBCt BULSI BULLSCP

BULSI BULTOP BULUSCP

BULTOP BDYMHB

BDYMHB BDYTCL BDYUSCP

-30.0 92.0

92.0 141.0

141,0 185.0

185.0 224.0

224.0 380.04

-4.0 -5.0 18.0 -30.0 5,5

18.0 I0.0 23.38 i .0 23.38

23 . 38 290 . 0 23 • 38

23.38 380.04 13.0 335.0 23.38

-4.0 I0.0 -23.38 -30.0 -23.38

-23.38 215.0 -23.38

-23.38 380.04 13.0 265.0 -23.38

-4.0 I0.0 0.0 -20.0 0.0

O. 215.0 O.

O. 380.04 13.0 300.0 0.0

0. 380.04 0.0

0.0 I0.0 21.0 -30.0 21.0

21.0 300.0 21.0

21.0 380.04 0.0 320.0 21.0

0.0 112.0 20.0 92.0 20.0

20.0 140.0 20.0

20.0 185.0 0.0 185.0 0.0

19.0 160.0 27 •54 141 .0 27 •54

27.54 204.0 27.54

27 •54 224 •0 I 9.0 224.0 27.54

-16.0 224.0 -16.0

-6.0 224.0 -6.0

20 •0 224 . 0 20 • 0

YCENTER

YCENTER

81
YHAPAXIS YCENTER

ZT'IAPAXI5 ZBDYI'IHB

ZBDYUSCP ZBDYTCL

YSDYUSCP YRD :'LHB

YBDfLSCP YBD ,'UHB

Z['DYLSCP Z3DYBCL

YFAIRT YBD',tlHB

YBtJL LSgP ':BULSI

ZSULLSCP ZBDYPCL

YBULUSCP YB[;LSI

Z_ULUSCP ZEULTf_P

C5A ZHBOARD EilGIME NACELLE (CONFICURATION !,

i. 115.41

O. --i.

O. 0.3G

30.17 34.91

62.0_ 67.17

_8.79 92.02

13,99 14.Z9

15.gq 15.Q9

13.70 13.35

11.02 IC.50

CSA OUTBOARD ENGINE

i, !36.2C

O. -i.

O. 0.38

30.17 34._i

62.0g 67.17

88.79 92.02

13.99 14.39

15.8_ 15.49

13.70 13.35

11.02 10.50

161.90

O.

1.58

37.$9

71.35

94.91

lq.£O

15.1%

12.95

i0.00

flACSLLE

182.69

C,

1.58

37 59

71 33

94 91

lq 80

15 16

12 95

I0 O0

69.(8 -13.1

I, 1.93

3,55 6.34

39.65 A%.7_

75.49 79.77

9S.50 ICO.O

15.20 15.61

iq.97 iQ.gO

!2.G9 12.10

9.30 8.93

108.14

I.

3.53

39 65

75 49

£8 50

15 20

lq 97

12 _9

9.30

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1.93

6.3¢

64.7Q

79.77

100.0

15.61

14.80

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8.93

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0

T>_ X-2539)

26.0

19.25 19._S

51.10 56.99

!;1.85 gq.97

16.01 16.01

I_.45 I_.I0

11.79 11.54

36.0

12.25 19.88

51.10 56.99

Si._5 8q.97

16.01 16.01

!¢._5 14.10

11,79 11.54

82
C-141 TRANSPORT WITH PODS AND PYLONS

3. 0.82 -0.3 36.0 100. 80. 3.

2. O. 2.

6. 33. 1.0 747.99 85.0 463007.0 0.8

648.76 O. 1045.54 4.89 1.0

O. 0.002408 0.009607 0.021530 0.038060 0.059040 0.084266

0,113495 0.146447 0.182804 0.222216 0.264303 0.308660 0.354859

0.402456 0.450993 0.5 0.549011 0.597547 0.645144 0.691344

0.735700 0.777787 0.817199 0.853555 0.886507 0.915736 0.940962

0.961941 0.978471 0,990393 0.997593 1.0

O. 0.010839 0.019266 0.027140 0.034418 0.041114 0.047226

0.052771 0.057762 0.062198 0.066040 0.069274 0.071815 0.073591

0.074499 0.074464 0.073450 0.071465 0.068551 0.064789 0.060277

0.055175 0.049126 0.042299 0.035174 0.028283 0.021681 0.015644

0.010439 0.006214 0.003099 0.001191 0.000548

O. -0.007695 -0.015563 -0.022735 -0.028997 -0.034457 -0.039186

-0.043259 -0.046734 -0.049646 -0.052012 -0.053822 -0.055037 -0.055602

-0.055437 -0.054479 -0.052711 -0.050132 -0,046857 -0.042895 -0.038417

-0.033620 -0.029048 -0.024745 -0.020469 -0.016421 -0.012715 -0.009258

-0.006250 -0,003781 -0.001972 -0.000902 -0.000548

709.51 113.60 1062.45 4.44 1.0

0 0.010402 0.018683 0.026436 0.033623 0.040246 0.046301

0 051798 0.056733 0.061120 0.064922 0.068117 0.070612 0.072354

0 073246 0.073197 0.072173 0.070185 0.067274 0,063510 0.059035

0 053955 0.048009 0.041336 0.034369 0.027628 0.021199 0.015324

0 010255 0.006139 0.003104 0.001244 0.000617

0 -0.007613 -0.015273 -0.022194 -0.028211 -0.033438 -0.037952

-0.041829 -0.045123 -0.047867 -0.050087 -0.051776 -0.052897 -0.053399

-0.053203 -0.052245 -0.050524 -0.048042 -0.044870 -0.041056 -0,036852

-0.032331 -0.028064 -0.023881 -0,019742 -0.015872 -0.012279 -0.008938

-0.006034 -0.003690 -0.001971 -0.000954 -0.000617

875.95 426.57 1108.76 2.68 1.0

0 0.008481 0.015968 0.023056 0.029734 0.035960 0.041691

0 046925 0,051651 0,055865 0.059550 0.062643 0.065006 0.066662

0 067546 0.067507 0.066524 0.064600 0.061798 0.058169 0.053788

0 048790 0.043247 0.037220 0.030960 0.024872 0.019225 0.013866

0 009265 0.005640 0.003025 0.001452 0.000927

0 -0.007009 -0.013598 -0.019253 -0.024035 -0.028082 -0.031496

-0.034367 -0.036773 -0.038743 -0.040312 -0.041492 -0.042249 -0.042551

-0.042335 -0.041530 -0.040198 -0.038345 -0.035862 -0.032981 -0.029791

-0.026339 -0.022870 -0.019502 -0.016308 -0.013138 -0.010145 -0.007451

-0.005158 -0.003299 -0.001973 -0.001188 -0.000927

970.00 610.61 1168.16 2.0 1.0

O. 0.009672 0.017676 0.025221 0.032209 0.038329 0.043795

0.048929 0.053559 0,057574 0.061091 0.064058 0.066351 0.067961

0.068811 0.068739 0.067726 0.065764 0.062924 0.059250 0.054829

0.049790 0.044213 0.038187 0,032121 0.026136 0.020200 0.014781

0.009914 0.006080 0.003314 0.001649 0.001094

O. -0.008537 -0.014707 -0.020053 -0.024283 -0.027654 -0.03010

-0.032494 -0.034330 -0.035952 -0.037221 -0.038194 -0.038813 -0.039056

-0.038847 -0.038094 -0.036832 -0.035076 -0.032742 -0.030065 -0.027074

-0_023953 -0.020878 -0.017915 -0.014951 -0.012050 -0.009334 -0.006916

-0.004857 -0.003190 -0,002020 -0.001324 -0.001094

1046.90 761.11 1216.72 I.I0 1.0

O. 0.010861 0.019412 0.026801 0.033809 0,040077 0.045764

0.051155 0.055703 0.059494 0.062821 0.065645 0.067854 0.069416

0.070227 0.070119 0.069069 0.067069 0.064185 0.060466 0.055998

0.050912 0.045301 0.039291 0,033280 0,027176 0.021081 0.015406

0.010456 0.006450 0.003576 0.001849 0.001273

O. -0.007864 -0.015035 -0.020423 -0.024372 -0.027112 -0.028905

-0.030311 -0.051517 -0.032754 -0.033689 -0.034434 -0.034903 -0.035080

-0.034886 -0.034193 -0.033012 -0.031370 -0.029209 -0.026693 -0.023989

-0.021234 -0.018547 -0.015925 -0.013294 -0.010747 -0.008389 -0.006294

-0.004527 -0.003120 -0.002099 -0.001480 -0.001273

i147.81 958,89 1280,_5 -0,36 1.0

O. 0.011822 0.020558 0.029023 0.037201 0.043904 0.049966

0.055534 0.059913 0.063263 0.066214 0.068748 0.070790 0.072251

0.072985 0.072806 0.071682 0.069612 0.066645 0.062835 0.058284

0.053105 0.047429 0.041455 0.035483 0.029030 0.022233 0.016142

0.011014 0.006945 0.004003 0.002223 0.001626

O. -0.010134 -0.017776 -0.022607 -0.024847 -0.025861 -0.025927

-0.025799 -0.025793 -0.026292 -0.026582 -0.026890 -0.027076 -0.027139

-0.026981 -0.026417 -0.025407 -0.023997 -0.022188 -0.020096 -0.018016

-0.015950 -0.013922 -0.011912 -0.009968 -0.008134 -0,006497 -0.005069

-0.003860 -0.002889 -0.002189 -0.001765 -0.001625

83
84

C-141

2.

O.

O.

I .75

15.00

32.50

50.0

67.50

85.00

O.

2.95773

7.12800

7.98394

7.05800

5.20471

2.73725

O.

-2.95773

-7.12800

-7.9839G

-7.05800

-5.20q71

-2.73723

O.

C-141

2.

0.

O.

1.75

15.00

32.50

50.0

67 .50

85.00

O.

2.95773

7.12800

7.98394

7.05800

5.20471

2.73723

O.

-2.95773

-7.12800

-7.98394

-7.05800

-5.20471

-2.73723

O.

--3.

LOCKHEED

4.

I.

BDDYLO

BODYHI

2.

FAIRLO

FAIRSI

FAIRTP

3.

NHEELO

WHEELSI

WHEELUP

FAIRS

FAIRT

4.

WItELO

NHELS

WHELU

UPPER

5.

i.

2.

3.

4.

5.

11.

3.

ELLX

LINE

CUBI

INBOARD PYLON

49.

-15.0

0.25

2.00

17.578

35.00

52.50

70.00

87.50

1.16140

3.14664

7.43384

7.93194

6.83912

4.88600

2.33959

-i.16140

-3.14664

-7.4338(*

-7.93194

-6.83912

-4.88600

-2.33959

O.

1.0

1.0

0.50

2.50

20.0

37.50

55.00

72.50

90.00

I .62826

3.48600

7.65000

7.84905

6.60357

4.55577

1.93000

-1

-3

-7

-7

-6

-4

-1

1.

OUTBOARD PYLON

62826

48600

65000

84905

60357

55577

93000

49. 1.0

-18.0 1.0

0.25 0.50

2.00 2.50

17.578 20.0

35.00 37.50

52.50 55.00

70.00 72.50

87.50 90.00

1.16140 1.62826

3.14664 3.48600

7.43384 7.65000

7.93194 7.84905

6.83912 6.60357

4.88600 4.55577

2.33959 1.93000

-1.161(.0 -1.62826

-3.14664 -3.48600

-7.43384 -7.65000

-7.93194 -7.84905

-6.83912 -6.60357

-4.88600 -(*,55577

-2.33959 -1.93000

O. i.

230.4 1818.0

C-141 QUICK-GEOMETRY

278.91

O.

0.75

5.00

22.50

40.00

57.50

75.102

92.50

,1.98016

4.73800

7.81298

7.73800

6.35225

4.20014

1.50820

-1.98016

-4.73800

-7.81298

-7.73800

-6.35225

-4.20014

-1.50820

O.

1.0

7.50

25.00

42.50

60.00

77.50

95. O0

2 27227

5 60000

7 92200

7 60107

6 08600

3 86170

1 07400

-2.27227

-5.60000

-7.92200

-7.60107

-6. 08600

-3.86170

-1.07400

O.

(*56.89

O. 1.0

0.75 1.0

5.00 7.50

22.50 25.00

40.00 42.50

57.50 60.00

75.102 77.50

92.50 95.00

1.98016 2.27227

4.73800 5.60000

7.81298 7.92200

7.73800 7.60107

6.35225 6.08600

4.20014 3.86170

1.50820 1.07400

-i 98016 -2.27227

-4 73800 -5.60000

-7 81298 -7.92200

-7 73800 -7.60107

-6 35225 -6.08600

-4 20014 -3.86170

-i 50820 -1.07400

O, O.

O. O.

FUSELAGE MODEL

1.25

I0 0

27 50

45 O0

62 50

80 O0

97 50

2.52600

6.24200

7.98298

7.44066

5.80545

3.49800

0.62728

-2 52600

-6 2(*200

-7 98298

-7 44066

-5 80545

-3 49800

-0 62728

1.25

i0.0

27.50

45.00

62.50

80.00

97.50

2 52600

6 24200

7 98298

7 4(*066

5 80545

3 49800

0 62728

-2.52600

-6.24200

-7.98298

-7.4(*066

-5.80545

-3.49800

-0.62728

O.

2.

ELLl

ELLI

3.

ELLI

LINE

LINE

5.

LINE

LIHE

LINE

LINE

LINE

4.

LINE

LINE

LINE

ELLI

NOSE TO TAIL

BDYBCL BDYMHB BDYLSCP

BDYMIIB BDYTCL BDYUSCP

FUSELAGE WITH WING MOUNT FAIRING

BDYBCL BDYMHB BDYLSCP

BDYr'IIlB BS

BS BDYTCL

FUSELAGE WITH WHEEL AND WING FAIRING

BDYBCL WL

WL WT

WT BDYMHB

BDYRHB BS

BS BDYTCL

FUSELAGE WITH WHEEL FAIRING

BDYBCL WL

WL WT

WT BDYr4HB

BDYMHB BDYTCL BDYUSCP

I. Z30.4 650.0

2. 650.0 794.0

3. 794.0 1050.0

(*. 1050.0 1198.0

1. 1198.0 1822.0

8.

ZBDYBCL

230.4 -15.0 445.0

445.0 -85.0 II00.0

II00.0 -85.0 1822.0

0.4

1.50

12.50

30.00

47.50

65.00

82.50

100.0

2.75230

6.73996

8.00200

7.25903

5.51140

3.12325

0.16800

-2.75230

-6.73996

-8.00200

-7.25903

-5.51140

-3.12325

-0.16800

1.50

12.50

30.00

47.50

65.00

82.50

100.0

2,75230

6.73996

8.00200

7.25903

5.51140

3.12325

0.16800

-2 75250

-6 73996

-8 00200

-7 25903

-5 51140

-3 12325

-0 16800

-85.0 230.4 -85.0

-85.0

70.0 1485.0 -85.0
3.

ELLX

LINE

CUBI

1.

LINE

10.

ELLX

LINE

CUBI

LINE

CUBI

CUBI

LINE

LINE

LINE

CUBI

3.

CUBI

LINE

CUBI

2.

CUBI

CUBI

3.

LINE

LINE

LINE

3.

LINE

LINE

LINE

3.

LINE

LINE

LINE

i.

LINE

3.

LINE

LINE

LINE

C-141

O.

O.

O.

4.52

12 55

68 79

98 99

12 53

14 40

15 26

14 72

9.61

C-141

O.

O.

O.

4.52

12.55

68.79

98.99

12.53

14.40

15.26

14.72

9.61

YBDYMHB

230.4

445.0

1475.0

YCENTER

230.4

ZBDYTCL

230.4

270,0

310.0

400.0

650.0

785.0

1050.0

1250.0

1350.0

1450.0

ZBDYMHB

230.4

445.0

1150.0

ZB5

650.0

785.0

YBS

650.0

690.0

1000.0

ZWL

794.0

900.0

ii00.0

YWL

794.0

900.0

1100.0

ZWT

794.0

YWT

794.0

900.0

1100.0

ZMAPAXIS

YMAPAXI5

YBDYTCL

YBDYBCL

YBDYUSCP

ZBDYUSCP

YBDYLSCP

ZBDYLSCP

O.

85.0

85.0

O.

-15.0

qO.O

70.0

85.0

85.0

110.0

85.0

94.0

107.0

Iii.0

-15.0

O.

O.

60.0

111.0

60.0

85.0

85.0

-85.0

-75.0

-75.0

O.

136.5

136.5

-24.0

73.0

136.5

136.5

ZBDYHHB

YCENTER

YCENTER

YCENTER

YBDYMHB

ZBDYTCL

YBDYHHB

ZBDYBCL

INBOARD NACELLE

667.91

2.

0.25

5.52

14.56

72.81

100.0

12.92

14.59

15.31

14.35

9.34

883.32

O.

0.50

6.53

16.26

77.82

13.10

14.76

15.32

13.75

OUTBOARD NACELLE

755.02

1.0

0.25

5.52

14.56

72.81

100.0

12.92

14.59

15.31

14.35

9.34

970.43

O.

0.50

6.53

16.26

77.82

13.10

14.76

15.32

13.75

445.0

1475.0

1822.0

1822.0

270.0

310.0

400.0

650.0

785.0

1050.0

1250.0

1350.0

1450.0

1822.0

445.0

1150.0

1822.0

785.0

1050.0

690.0

I0O0.0

1050.0

900.0

Ii00.0

1198.0

900.0

ii00.0

1198.0

1198.0

900.0

1100.0

1198.0

278.91

I.

1.0

7.53

54.18

81.84

13.37

14.90

15.32

13.17

456.89

I.

1.0

7.53

54.18

81.84

13.37

14.90

15.32

13.17

85.0

85.0

0.0

O.

40.0

70.0

85.0

85.0

110.0

85.0

94.0

107.0

111.0

70.0

O.

O.

70,0

111,0

60.0

85.0

85.0

60.0

-75.0

-75.0

-85.0

136.5

136.5

O.

-24.0

136.5

136.5

73.0

-95.00

2.

1.5

8.54

55.23

85.86

13.58

15.01

15.32

12.49

-95. O0

2.

1.5

8.54

55.23

85.86

13.58

15.01

15.32

12.49

230.4

1685.0

230.4

330.0

700.0

850.0

1645.0

330.0

1440.0

700.0

850.0

30.0

2.5

9.54

58.75

89.88

13.92

15,11

15.26

11.72

30.0

2.5

9.54

58.75

89.88

13.92

15.11

15.26

ii .72

85.0

85.0

22.0

85.0

II0.0

110.0

111.0

O.

O.

111.0

111.0

O.

3.51

10.54

63.77

93.89

14.18

15.18

15.06

10.85

O.

3.51

10.54

63.77

93.89

14.18

15.18

15.06

10.85

85
OUTPUT DATA (PRINT ,_ PLOT) FORMAT

Printed and plotted output data is provided. Since a typical print or plot

sequence is lengthy, only a brief description of each type of output will be

provided here. Note that samples of plotted output can be found in the results and geometry verification section of this report.

Printed Output

The printed output can be divided into three distinct sections.

Section I Input Data Listing/Geometry and Grid System

Verification

Section II Relaxation Solution Convergence History

Section III Computed Velocities, Pressures, Forces, Moments,

Reference Lengths and Areas

Within each section, the output data will be printed in the following sequence.

Section I

• Input Data Listing

• Case Flow Condition

• Nominal Extent of Fine Embedded Grid Systems

• Quick-Geometry Model Error Diagnostic Information (BKOD = +3 only)

• Configuration Position in Global Crude Grid System*

• Body Crude/Fine Grid Limiters (See Note #1, following page)

• Global Crude Grid Coordinates

• Fine Embedded Wing Grid Coordinates

• Pylon Limiters (PY >0)

• Pod/Nacelle Limiters and Boundary Conditions (Pod > 0)

• TAG Grid System Coordinates (VER # 0)

• Winglet Grid System Coordinates (VER> 0)

• Fine Embedded Body Grid Coordinates

* The configuration is positioned to prevent crude cartesian grid points from

falling near the wing leading edge.

86
Section II

Phase 1 (Global Crude Grid Solution)

A

The following information is printed for each crude grid iteration.

t Iteration Count

• MaximumCorrection to the Flow Field Potential (A¢ MAX)

• Grid Position of 5¢ MAX

• Wing Spanwise Circulation (F) Distribution

NOTE #1

The body crude and fine grid limiters are the J and K values which

define special grid points. These limiter values represent the first grid point

relaxed beyond a fixed potential body boundary point. By using the J and K

limiters listed, a sketch of the body boundary surface can be composed. A

typical limiter listing can be found in the table below:

FINE GRID BODY BOUNDARY POINT LIMITERS

J KUP KLO JSD

1 20 6 10

2 20 6 10

3 20 6 10

4 20 7 10

5 19 7 10

6 19 7 10

7 18 7 10

8 17 7 10

9 16 7 10

10 15 8 10

CRUDE GRID BODY BOUNDARY POINT LIMITERS

J KUP KLO JSD

1 22 15 4

2 21 15 4

3 20 15 4

4 19 16 4

87
The body boundary surface points have been sketched below in Fig. A-3.

CRUDE GRID FINE GRID

24 _-

23

22

21 F ]

2o !

19 II

4

18

17 d

16 IH _i_- --

15

14

J=12345

R84-1137-035D

21

20

19 i '_

17

16

15

14

13 _

12

11

10

9

8

7

4

4

Ii

IIb

Ih

Ib

Ilill 41 4bil J_

ILd AL

i

I

!

j=l 2 34 5 6 7 8 910

Figure A-3 Body Boundary Point Limiter$

Following the body boundary point limiters, additional limiters will be

listed if the embedded fine body grid option has been selected. The following

figure indicates that IBGI, IBGL, JBG, KBGU and KBGL grid points represent

the first crude point relaxed beyond the embedded fine grid boundary.

EMBEDDED/

FiNE

GRID

R84-1137-036D

_1

% KBGU m

i

• KBGL

FigureAm, EmbeddedBody Fine Grid BoundaryLimiter$

GLOBAL

.-----CRUDE

GRID

88
The following information is printed at the end of

Solution.

ro

B

the Global Crude Grid

Section Mach Chart (0 indicates subsonic flow)

(1 indicates supersonic flow)

(8 indicates wing section surface)

(7 indicates wake surface)

Span row number/n-position/local chord length, chord position,

pressure coefficient, disturbance velocity, section circulation (r).

Phase 2 (Crude/Fine Grid Interactions)

The following information is printed for each crude/fine

cycle.

grid iteration

Phase 1 (A) Output for Fine Embedded Wing Grid System

Pylon Vertical Circulation Distribution (PY > 0)

Phase I (A) Output For Fine Embedded Winglet Grid System (VER > 0)

Phase I (A) Output For Fine Embedded Pod Grid System (FIFP>0

Only)

Phase I (A) Output For TAG (VER # 0)

TAG Circulation Distribution For Wing and Winglet

Phase 1 (A) Output for Fine Embedded Body Grid System

(for BKOD > 0 only)

Phase 1 (A) Output for Global Crude Grid System

Wing Spanwise Circulation (I')Distribution

For viscous interaction cases, the following information is printed every

20th cycle.

• Wing Upper/Lower Surface Boundary Layer Separation Point (x/c)

• Boundary Layer 5* Slope Added to Wing Boundary Conditions.

Section III

The following information is printed at the end of the solution process.

• Phase 1 (B) Output for Wing Embedded Fine Grid System

• For (VISMOD = 2,3) Wing Upper/Lower Surface Boundary Layer

Separation Point (x/c)

89
• Wing Section C_W, %, Cdw, Cf w

Note: CmW is section moment about local quarter chord position

• Spanwise Load, Moment, Drag Distributions

• Wing Exposed Area, Total Area, Aspect Ratio, Taper Ratio, Mean

Aerodynamic Chord, Average Chord, X-position about which Moments

are computed

•

Total Wing C LWING, CMwING, CDwING

• Pylon Surface Pressures

• Phase I (B) Output For Winglet Embedded Fine Grid System

• Winglet Spanwise Load, Moment and Drag Distributions

• Winglet Area, Average Chord

• Winglet C L, C M, CD, CDFRICTION

• Pod/Nacelle Pressure Coefficients (see Figure A-5 for

argument sign conventions)

angular

90 °

45 °

0 °

_90 °

R84-1137-037D

\\

_45 °

0 °

-90°

-135 °

-180 °

180 °

45 °

135 °

90 °

Figure A-5 Sign Convention for Angular

Argument of Fuselage/Nacelle

Pressure Output Stations

9O
• Pod/Nacelle Surface and Projected Areas

• Pod CL, CM, CD, CDFRICTION

• Pylon Surface Area and Friction Drag

• Wing Pressure Drag CDp(w)

• Wing Friction Drag" CFwING

• Body Grid Mach Chart

• Body Angular Cut Pressure/Velocity Distribution

• Body Longitudinal Load and Drag Distribution

• Body Length, Wetted Area, Projected Area, Max.

Reynolds Number based on body length

• Total Body CLBoDY , CMBoDY , CDp(b)

• Body Pressure Drag CDp(b)

• Body Friction Drag CF B

• Total Configuration CL, CM, C D

• Wing-Body Wave Drag CDwAvE

• Wing-Body Friction Drag C F

• Wing-Body Lift-Induced Drag CD I

• Wing-Body Spanload Efficiency Factor E

Cross-sectional Area,

Plotted Output

The plot output can be divided into two separate sections.

Section I (Input Geometry Verification)

• Title/Case/Flow condition Label

• Body Cross- Sections

• Input Wing Sections

• Configuration Planview

• Configuration Head-On View

Section II (Computed Results)

• Superimposed wing pressure distributions (upper/lower surface)

total wing C L, CM, C D label.

• Wing planform with section shapes at computed span stations.

with

91
• Detailed wing section pressure distributions with Section C_, C m, C d

label.

• Detailed Winglet Pressure Distributions with Section C_, C m, C d label

• Detailed Pod/Nacelle Pressure Distributions

• Detailed body angular cut pressure distributions.

• Body longitudinal load plot with body CL B, CM B, CD B and wing-body

CL, CM, C D label.

• Wing-body spanload plot with span efficiency, lift-induced drag, wave

drag, friction drag label.

INPUT GEOMETRY VERIFICATION

Coding for graphical inspection of input wing and body geometry has

been included. Since the program requires considerable computer time and

core storage to operate and some facility budgets may not provide for a

number of error-filled submittals, it is recommended that the geometry

verification mode of operation be used before submitting a complete and

expensive relaxation solution. The graphic output coupled with printed output

for geometry and grid systems should be sufficient to diagnose user input

errors. In particular, it has been found advantageous to make the geometry

cheek and perform a single crude and a single fine grid iteration (very cheap)

to check code flow before a complete analysis is performed.

The body cross-section array is first to be plotted after case title and

flow conditions are listed (see Figure A-6). In this case, an error in specifying a Z-coordinate of the canopy top centerline is apparent. In Figure A-7,

an error in specifying a Y-coordinate of the windshield base is illustrated.

Finally, Figure A-8 illustrates the corrected and final shape of the fuselage to

be analyzed.

The defining wing chord sections are displayed after the body geometry

(see Figure A-9). Each is plotted to a ten inch chord so errors in coordinates

will become visible. It is important to note that there is no mapping involved

in the present method; thus, no coordinate smoothing or manipulation is employed. Irregularities in input coordinates will cause oscillations in computed

pressure distributions.

92
GULFSTREAM II ISOLATED FUSELAGE .'_)'

ISOLATED BODY CASE 1 __.*_,J

MACH = 0.800 ALPHA = 3.10 ..._'_ _'_

RE = 1o00 M ____'__

BODY CROSS-SECTIONS

R84-1137-038D

Figure A-6 Sample Input Geometry Verification Plot with Error in Z-Coordinate

of Canopy Definition

GULFSTREAM II ISOLATED FUSELAGE

ISOLATED BODY CASE 1

MACH = 0,800 ALPHA = 3.10

RE = 1.00 M

BODY CROSS-SECTIONS

R84-1137°039D

Figure A-7 Sample Input Geometry Verification Plot with Error in Y-Coordinate

of Canopy Definition

93
GULFSTREAM II ISOLATED FUSELAGE

ISOLATED BODY CASE 1 _-_ b) )

MACH =0.800 ALPHA=3.10 . _,_,!J

RE=,oo M -<_'_ )Y

BODY CROSS_SECTIONS

R84-1137-040D

Figure A-8 Sample Input Geometry Verification Plot for Fuselage

INPUT WING SECTION 1 2Y/B = 0.00

INPUT WING SECTION 2 2Y/B = 0.12

f

INPUT WING SECTION 3 2Y/B = 0.35

R84-1137-041D

Figure A-9 Sample Input Geometry Verification Plot for Wing Sections

94
A configuration plan-view will follow the wing section figures. This

should be used to insure that the wing planform is properly defined and its

placement on the fuselage is correct (see Figure A-10). Finally, a head-on

view is plotted (see Figure A-11). Once again, check to see that the wing

and body are indeed attached. Geometry verification plots which illustrate

typical nacelle, pylon and winglet positioning checkouts can be seen in Figure

A-12.

ff84-I 137-042D

PLAN VIEW

Fig. A-10 Sample Input Geometry Verification Plot, Plan View

WING PLANE

HEAD-ON VIEW

J

R84-I 137-043D

Fig.A-11 SampleInput GeometryVerification Plot, Head-OnView

95
-5A

PLAN VIEW

R84-1137-044D

PLAN VIEW

PLAN VIEW

R84-1137-045D

Fig. A-12 Sample Geometry Verification Plots for Configuration with

Nacelles, Pylons and Winglets

96
SUBROUTINE CALL SEQUENCE

MAIN

SLOPE

SPLINE

"-'----" BGLIM

BODLIM

GEVER

=---,----- PYSET

PODSET

TAGSET

•--.------- VERSET

"'--"--" SPLINE

_Q

_-- SAREA

- SLOPP

SLOPE

TAGSL

SLOPV

SPLINE

SPLINE

SPLINE

SPLINE

NOTE :

Q

®

©

FUSELAGE GEOMETRY DEFINITION

FUSELAGE GEOMETRY INTERROGATION

RELAXATION/BOUNDARY LAYER ROUTINES

- c_ 97
SUBROUTINE CALL SEQUENCE Q

QWIKDE

CSMDEF

_CSMCHK

_BLMDEF

_BLMCHK

L---GEMOUT

DSETUP

DLOKUP

DSETUP

DLOKUP

CURVES

L,,_-KRVDEF

98
SUBROUTINE CALL SEQUENCE

QWIKLO _ CSGEOM

- SMOTH

BLMSET - CURVES

_BLGEOM

CSMSET

.__ BBLGEOM

n CSMCOE

AORDER

_THELIM i CSMFLT

-- CSMINT

CSCALC

SINCOS

• VDOTV

_MDOTV

SINCOS

CSCALC

BLGEOM

_CSMCOE

LINLIN

LINELL

_ELLELL

SINCOS

_IDOT v

_MDOTV

CROSS

ELLCAL

_ELLCAL

CROSS

ESTNXT

_SETNXT

99
SUBROUTINE CALL SEQUENCE

r-- TRID

mGLOBAL ..,_ POD _ TRID

/

--BODYC _ TRID

t._- WINGLET_ TRID

mBODVAL

_ PODVAL

-INTURP _ FILL

--INTERB

--POCRUD

i-.--,.TRID

-- WINGF -...-.,_ TAGFIL - TFILL

I

_-,,,I NTU RP _FILL

-- BODYF _TRID

_PLOTER

--BODFIX _INTEGW

_INTEG

_INTURP

_POFINE = _INTURV

_LIDRAG

CONTRL"

PODCP

SPLINE

_SMOTH

_BODFM'_,.

SPLINE

FILL

FILLV

MAST --

_PODFM

VINTER Q

- BLAR _S_MOT H

-TAGFIL _TFILL

-TAGREL_TRID

INTURV _FILLV

PODF _ TRID

INTURV

- VINGF _1_

/

=----"- TRID

- INTERP

©

_FIT2

_DELTA1

_'-'-'INTRP

_--SERIES _ RFAST _FAST

_PDAREA

FILLV

IO0
SUBROUTINE CALL SEQUENCE Q

SLOPY

STRIPK

BLLAM

VBRAD

SPLN1

SPLNlX

ORDIN

VNUSUB

_SLOPBL

_TANCAL

SPRINT

FINT

SOLVEB

ORDIN

_REDUCX

_RLORD

GORD

SIMPSN

GRAD

GORD

I01
SUBROUTINE DESCRIPTION

AORDER

BGLIM

BLAR

BLGEOM

BLLAM

BLMCHK

BLMDEF

BLMSET

BODFIX

BODFM

BODLIM

BODVAL

Orders a set of numbers by permutation index

Computes wing fixed potential surface limiters in fine embedded

body grid

Main control routine for laminar and turbulent modified

chordwise boundary layer calculation. Computes boundary layer

displacement thickness (5") slope for viscous/inviscid interaction

mode of operation

Assigns body line model values and derivatives to

control point coordinates

Computes Thwaites laminar boundary layer with Rott and Crabtree

compressibility modification

Correlates and checks the input data deck and the

indices for the generated body line math models

Defines body line models from the input data

Controls the determination values and first and second derivatives

for all body line models at a given x-station

Computes potentials on fixed wing/wake surface in body fine grid

given solution in fine wing grid and global crude grid

Computes integrated body force and moment coefficients

Computes J and K limiters for body boundary in both crude and

fine grid system_

Computes body boundary point potential values

102
BODYC Finite difference approximations and relaxation solution for body

boundary in crude grid

BODYF Finite difference approximations and relaxation solution for fine

body grid

CONTRL Main control routine for relaxation solution of governing

equation, interpolation, boundary layer analysis and

printed/plotted output

CROSS Solves for the intersection of two lines in a plane

CSCALC Computes radial position and derivatives for specified

cross-section model, arc, and O'

CSGEOM

CSMCHK

Is the main subroutine in the look-up portion of the

QUICK System. It is called to establish r'= f(O',x). It calls

appropriate subroutines to evaluate body line values and construct cross-section geometry at a given x-station. It is used for

all geometry model interrogation

Correlates and checks the input data deck and the

indices for the cross-sectional math model

CSMCOE Composes the equations which are to define the

cross-section geometry at a given station

CSMDEF Logically defines the cross-section models from the input data

CSMFLT Creates control point definitions to permit the insertion of a

smooth fillet between cross-sectional arcs

CSMINT Locates user specified intersections between cross-sectional arcs

and adjusts their use-theta limits

103
CSMSET Sets up the control point coordinate arrays used to define the

cross-section geometry at a specified x-station

CURVES Calculates values and first and second derivatives for

individual curve fits

DELTA1 Interpolation routine for wing spanload

DLOKUP Is a simple look-up routine. It assigns an index to

match an input name to a codeword list, but is not

adding new items to that list

capable of

DSETUP Is an adapting dictionary look-up routine. New items are added

to a codeword list, an index (counter) is returned for the

codeword, and an indicator (INEW) is set equal to 1 when a new

item is encountered

ELLCAL Set up for ellipse

ELLELL Calculates intersection of two ellipses

ESTNXT Estimates non-linear root by modified inverse quadratic

FAST Fast Fourier transform of complex data

FILL Performs interpolation controlled by INTURP

FILLV Assists INTURV interpolation process

FINT Simultaneous triple interpolation

FIT2 Determines cubic spline fit coefficients for input spanload

distribution

104
GEMOUT Ensures that all body lines required by a cross-sectional

model are defined for the range of that model

GEVER Controls geometry verification plotting

GLOBAL Finite difference approximations and relaxation solution

for global crude grid

GORD Bradshaw's G function

GRAD Slope of a function at its tabulated points

INTEG Integrates wing load distributions for lift, moment and drag

coefficients

INTEGW Intergrates winglet section coefficients to obtain total lift, moment

and drag

INTERB Interpolation routine for body fine/global crude grid

communication

INTERP Interpolation for pod crude/fine grid interaction

INTRP Converts input spanload distribution to a fine over spaced

distribution

INTURP Controls interpolation for filling fine mesh points using crude grid

potential values. Updates crude mesh given fine solution.

Updates fine mesh given crude solution

INTURV Interpolation for winglet fine/TAG/crude interaction

KRVDEF Calculates coefficients for the various curve fits

associated with body line math models

105
LIDRAG Main control routine for computing lift induced drag efficiency "E"

using a Fourier analysis

LINELL Solves for the intersection of a line and an ellipse

LINLIN Solves for intersection of two lines

MAIN Controls reading of input data and sets boundary and initial

conditions. Sets up arrays and storage areas. Sets up crude

and wing and body fine coordinate systems

MAST Controls cubic spline fit for interpolation of input

spanload distribution

MDOTV Performs matrix multiplication of a vector

ORDIN Linear interpolation

PDAREA Computes pod surface and projected areas

PLOTER Controls all graphic output (except input geometry verification)

POCRUD Prints results in global crude grid; roach chart, wing

upper/lower surface pressure coefficients

POD Pod crude grid relaxation process

PODCP Compute pod/nacelle pressure coefficients

PODF Pod/nacelle fine grid relaxation process

PODFM Computes pod/nacelle forces and moments

PODSET Set up for pod/nacelle simulation. Pod geometry input

106
PODVAL Computes pod/nacelle boundary condition for crude and

fine grid

POFINE Prints output results for fLne grid arrays

PYSET Set up for pylon surface simulation. Pylon geometry input

QWIKDE Main control routine for Quick-Geometry definition and check out

QWIKLO Main control routine for interrogation of Quick-Geometry math

model

REDUCX Performs interpolation to new grid

RFAST Fast Fourier transforms of real data

RLORD Bradshaw's L function

SAREA Computes body surface area given an array of cross-sections

SERIES Determines Fourier series coefficients

SETNXT Reorders points for non-linear root finder

SIMPSN Simpson's rule integration

SINCOS Adjusts input interrogation angles for top and bottom dead center

SLOPP Computes pylon boundary conditions

SLOPV Computes winglet boundary conditions

SLOPBL Slope of a tabulated function at an arbitrary point

107
SLOPE Computes boundary conditions for wing surface and axisymmetric

bodies

SLOPY Computes wing surface slopes

SMOTH Function for smoothing an array of values

SOLVEB Solution of two simultaneous linear algebraic equations

SPLINE Computes a cubic spline through a set of points

SPLNI Computes continuous derivatives interpolation by means of a cubic

fit

SPLNIX Entry for special cases requiring extrapolation beyond ends of X

and Y tables

SPRINT Prints output of profile results

STRIPK Starting condition setup and flow control for laminar/turbulent

boundary layer prediction

TAGFIL Interpolation for TAG/crude grid interaction

TAGSET Set up for wing tip augmentation grid TAG

TAGSL Computes wing boundary conditions for TAG

TAGREL Relaxation process for TAG

TANCAL Computes characteristic angles for use in B.L. solution

(equation 21 of Bradshaw and Ferriss)

TFILL Assists TAGFIL interpolation process

108
THELIM Creates and controls use-theta arrays to establish continuity in

the cross-section model

TRID Solves tri-diagonal matrix

VBRAD Computes Bradshaw compressible 2-D turbulent boundary layer

simulating 3-D boundary layer on infinite yawed wing by

Nash-Tseng modified chord technique

VDOTV Computes a vector dot product

VERSET Set up for winglet fine embedded grid system. Winglet geometry

input

VINGF Winglet fine embedded grid relaxation process

VINTER Performs cubic 5' fit for separated boundary layer in wing

section cove regions

VNUSUB Computes the Nash effective viscosity

WINGF Finite difference approximations and relaxation solution for wing

fine grid

WINGLET Crude grid relaxation process for winglet in crude grid

system

109
KEY VARIABLE DESCRIPTIONS

This description of key program variables and constants which are located

in several common blocks will be useful in understanding flow logic.

VARIABLE DESCRIPTION

AK The value 1-M 2

ALAM Wing taper ratio (X)

ALPHA Angle- of- attack (radians)

AMAC Wing mean aerodynamic chord (MAC)

AMACH Mach number

AM2 The value M2

AOA Angle-of-attack (degrees)

AR Wing aspect ratio (AR)

BAREA

BCF

Body wetted area

Body skin friction coefficient

BCL Wing crude grid lower boundary slopes

BCLF Wing fine grid lower boundary slopes

BCLP Pylon outboard boundary condition

BCLT Wing lower surface boundary condition in TAG

BCLV Winglet outboard boundary condition

II0
VARIABLE DESCRIPTION

BCU Wing crude grid upper boundary slopes

BCUF Wing fine grid upper boundary slopes

BCUP Pylon inboard boundary condition

BCUT Wing upper surface boundary condition in TAG

BCUV Winglet inboard boundary condition

BNOSE X coordinate of body nose

BNOSEP X coordinate of pod/nacelle nose (input as _ I)

BODCD Body (integrated) drag coefficient

BODCL

BODCM

Body (integrated) liftcoefficient

Body (integrated) moment coefficient

BPAREA Body projected area

BS Body plot scaling coefficient

BTAIL X coordinate of body tail

BTAILP X coordinate of pod/nacelle tail (input as BTAIL I)

CA Global crude grid stretching coefficient (_x)

CAV Wing average chord (CAv)

CAVW Winglet average chord

IIi
VARIABLE

CB

DESCRIPTION

Global crude grid stretching coefficient (_xx)

CC

CCT

CD

CDI

Global crude grid stretching coefficient (my)

TAG stretching coefficient (my)

Global crude grid stretching coefficient (nyy)

Lift induced drag coefficient

CDINT Wing section integrated drag

CDINW Winglet section drag coefficients

CDT

CE

TAG stretching coefficient (_yy)

Global crude grid stretching coefficient (¢z)

CET TAG stretching coefficient (¢z)

CF Global crude grid stretching coefficient (¢zz)

CFINT Integrated wing section friction coefficient

CFT TAG stretching coefficient (_zz)

CIR Wing circulation (r)

CIRPC Pylon circulation at crude grid vertical cuts

CIRPY Pylon circulation at fine grid vertical cuts

CIRV Winglet circulation at vertical span cuts

112
VARIABLE

CIRVC

DESCRIPTION

Winglet circulation at crude grid vertical cuts

CLINT Wing section integrated lift

CLINW Winglet section liftcoefficients

CMINT Wing section integrated moment

CMINW Winglet section moment coefficients

CMLOC Wing section integrated moment about local quarter chord

CMLOW Winglet section local moment coefficients

CPL Wing lower surface pressure coefficient

CPU Wing upper surface pressure coefficient

CPUPOD Pod pressure coefficients

CSCUT Body x station for cross-sectional cut

DELSL Wing boundary layer slopes for section lower surface

DELSU Wing boundary layer slopes for section upper surface

DETA Global crude grid mesh spacing in n direction

DIM Configuration length for non-dimensionalizing maximum potential

updates

DRDXC Axisymmetric body slope distribution in crude grid

113
VARIABLE

DRDXCP

DESCRIPTION

Pod/nacelle boundary condition

DRDXF Axisymmetric body slope distribution in fine grid

DRDXFP Pod fine grid boundary condition

DXB Fine body grid mesh spacing in X direction

DXBP Fine pod grid mesh spacing in X direction

DXI Global crude grid mesh spacing in _ direction

DXV Winglet fine grid mesh spacing in X direction

DXW Fine wing grid mesh spacing in X direction

DYB Fine body grid mesh spacing in Y direction

DYBP Fine pod grid mesh spacing in Y direction

DYV Winglet fine grid mesh spacing in Y direction

DYW Fine wing grid mesh spacing in Y direction

DZB Fine body grid mesh spacing in Z direction

DZBP Fine pod grid mesh spacing in Z direction

DZETA Global crude grid mesh spacing in _ direction

DZW Fine wing grid mesh spacing in Z direction

114
VARIABLE

E

DESCRIPTION

Wing spanload efficiency

ETA coordinates for global crude grid (transformed space)

ETAT TAG n coordinates

FMFR Nacelle inlet mass flow ratio

FNPR

G

H

IBGI

Nacelle exhaust nozzle pressure ratio

The value (_+I)M 2

The value ( _- 1) M2

Crude grid I value of body grid inner overlap region forward boundary

IBGIP Crude grid I value at pod fine grid forward boundary

IBGL Crude grid I value of body grid inner overlap region aft boundary

IBGLP Crude grid I value at pod fine grid aft boundary

IL Crude grid wing leading edge I value

ILEF Wing fine grid leading edge I value

ILEV Fine grid winglet leading edge I value

ILT TAG wing leading edge I value

ILV TAG winglet leading edge I value

ILVC Crude grid winglet leading edge I value

115
VARIABLE

IMACH

DESCRIPTION

Code for subsonic (0) or supersonic (1) flow at a grid point

IMAX Maximum number of crude grid points in X direction

IMAXB Maximum number of fine body grid points in X direction

IMAXBP Maximum number of fine pod grid points in X direction

IMAXV

IMAXW

INOSE

_ximum number of winglet fine grid points in X direction

Maximum number of fine wing grid points in X direction

Fine body grid I value at body nose

INOSEC Crude grid I value at body nose

INOSEP Crude grid I value at pod nose

INOSPF Fine grid I value at pod nose

IPTYPE Nacelle type - closed body/hot jet/cold jet

IT Crude grid wing trailing edge I values

ITAGI Crude grid I limiter for forward TAG boundary

ITAGIT On/off code for wing tip augmentation grid (TAG)

ITAGL Crude grid I limiter for aft TAG boundary

ITAIL Fine body grid I value at body tail

ITAILC Crude grid I value at body tail

116
VARIABLE DESCRIPTION

ITAILP Crude grid I value at pod tail

ITALPF Fine grid I value at pod tail

ITEF Wing fine grid trailing edge I value

ITER Iteration count

ITEV

ITMAX

Fine grid wi_4_let trailing edge I value

_ximum ntm_er of TAG grid points in X direction

ITT TAG I value of wing trailing edge

ITV TAG I value of winglet trailing edge

ITVC Crude grid I value of winglet trailing edge

JBG Crude grid J value of body grid inner overlap region side boundary

JBGIP Crude grid J value at pod fine grid inboard boundary

JBGLP Crude grid J value at pod fine grid outboard boundary

JBY Fine grid J value of winglet section plane

JMAX Maximum number of crude grid points in Y direction

JMAXB Maximum number of fine body grid points in Y direction

JMAXBP Maximum ntrnber of fine pod grid points in Y direction

JMAXV Maximum number of winglet fine grid Y-stations

117
VARIABLE

JNOSEP

DESCRIPTION

Crude grid J value at pod position

JROOT Crude grid J value at wing root

JSD Fine body grid J value at first influence of body boundary points

JSDC

JSDPL

Crude grid J value first influenced by body boundary

point

Fine pod grid J limiter at pod side-left

JSDPR Fine pod grid J limiter at pod side-right

JTAGI Crude grid J limiter for inboard TAG boundary

JTAGO Crude grid J limiter for outboard TAG boundary

JTIP Crude grid J value at _dalg tip

JTIPT TAG J value at wing tip

JTMAX Maxim_ number of TAG grid points in Y direction

KBB Fine body grid K value at wing plane

KBC Crude grid K value at wing plane

KBGL Crude grid K value of body grid inner overlap region (lower)

KBGLP Crude grid K value at pod fine grid lower boundary

KBGU Crude grid K value of body grid inner overlap region (upper)

KBGUP Crude grid K value at pod fine grid upper boundary

118
VARIABLE

KBOD

DESCRIPTION

Code for body in crude grid (0) or fine embedded grid (1)

KBW Fine wing grid K value at wing plane

KLOC

KLOF

Crude grid K limiters for body surface (lower)

Fine grid K limiters for body surface (lower)

KLOPF Nacelle fine grid lower surface K limiters

KMAX Maximum number of crude grid points in Z direction

KMAXB Maximum number of fine body grid points in Z direction

KMAXBP _ximum ntm%ber of fine pod grid points in Z direction

KMAXW Maximum number of fine wing grid points in Z direction

KNOSEP Crude grid K value at pod position

KODB Body option code...cylinder, axisymmetric, arbitrary

body (input as BKOD)

KOPOD Number of pods/nacelles (input as tKD)

KOPY Number of pylon surfaces (input as PY)

KOVER Number of winglets (input as VER)

KPLO Crude grid lower K limit of pylon surface

KT TAG K value of wing plane

119
VARIABLE

KTAGL

DESCRIPTION

Crude grid K limiter for lower TAG boundary

KTAGU Crude grid K limiter for upper TAG boundary

KTC

KTIPV

Crude grid K value at winglet tip

TAG win4glet tip K value

KTMAX Maxim_n number of vertical (Z) points in TAG

KUPC Crude grid K limiters for body surface (upper)

KUPF Fine grid K limiters for body surface (upper)

KUPPF Nacelle fine grid upper surface K limiters

MAXIT Maximum number of initial crude grid iterations (input as AXIT)

MAXITF Maximum number of crude/fine grid cycles (input as AXITF)

MODV Mode of operation for viscous effects (input as VISMOD)

NCASE Case description...wing, body or wing-body case (input as

CASE)

NINB Number of ordinates defining axisymmetric body shape

(input as BNIN)

NINBP _r of pod ordinates defined (input as _rIN l)

NINP IA_ber of ordiD_tes defining each pylon section (input as PIN)

NINV Number of ordinates defining each input winglet section

(input as VIN)

120
VARIABLE

NINW

DESCRIPTION

Number of ordinates defining each wing section (input as ANIN)

NOSEB

NOSEBP

Blunt/sharp nose body code (for spline fit)

Sharp/blunt nose shape code for pods

NOSEW Blunt/sharp nose wing code (for spline fit)

NOSP Pylon sharp/blunt nose code

NOSW Sharp/blunt winglet section nose shape code

NPOA Number of fine X-grid points between lead_g and trailing

edge of each wing section

NPOB Number of fine body X-grid points between nose and tail of

body

NPSEC Number of defining pylon sections (input as PSEC)

NSECT Number of defining wing sections (input as ASECT)

NTC Number of points representing body cross-sections in crude grid

NTF Number of points representing body cross-sections in fine body

grid

NTOTAL Total number of crude grid points in single X-Z plane

NTOTB Total number of fine body grid points in single X-Z plane

NTOTV Total number of fine winglet grid points in single X-Y plane

121
VARIABLE

NTOTW

DESCRIPTION

Total number of fine wing grid points in single X-Z plane

NVSEC

NWPO

Number of winglet sections defined (input as VSEC)

Code for print out of crude grid results for diagnostic purposes

_AREA Pod surface area

PBL Fine body grid wing/wake lower surface potentials

PC1 Global crude grid potential (q_) arrays

(Note: Only three planes are in core at one time)

PC2 Global crude grid potential (¢) arrays

(Note: Only three planes are in core at one time)

PC3 Global crude grid potential (,) arrays

(Note: Only three planes are in core at one time)

PCF Pod/nacelle skin friction coefficient

PCL Crude grid wing/wake lower surface potentials

PFI Fine embedded wing and body potential arrays.

(Note: Only three planes are in core at one time)

PF2 Fine embedded wing and body potential arrays.

(Note: Only three planes are in core at one time)

PF3 Fine embedded wing and body potential arrays.

(Note: Only three planes are in core at one time)

122
VARIABLE

PFL

DESCRIPTION

Fine wing grid lower surface potentials

PI

PLTAG

II

TAG wing lower surface potential array

PODALF Pod/nacelle incidence relative to fuselage

PODBET Pod/nacelle yaw angle

PODCD Pod/nacelle drag coefficient

PODCL Pod/nacelle lift coefficient

PODCM Pod/nacelle moment coefficient

PPAREA Pod projected area

PTAG TAG field potential (¢) array

PVCL Winglet outboard surface potential (¢) array for crude grid

PVL Winglet fine embedded grid outboard surface potential (¢) array

PVTL Winglet TAG outboard surface potential (¢) array

PYAREA Pylon surface areas

PYLO Pylon fine grid outboard surface potential (¢) array

PYLOC Pylon crude grid outboard surface potential (¢) array

RADIUS Radius of body cylinder (input option)

123
VARIABLE

RAVC

RAVF

DESCRIPTION

Crude grid average body radius for boundary condition

calculation

Fine grid average body radius for boundary condition

calculation

RC Axisymmetric body radius distribution in crude grid

RCP Radii for pod surface after positioning

RE Freestream Reynolds number

RF Axisymmetric body radius distribution in fine grid

RFP Pod radii in fine grid

RIN Radial coordinates defining axisynvaetric body (input option)

RINP Radial coordinates defining axisymnetric pod

RMAX Body maximum radius for computational body surface

RMAXP Pod maximum radius

SDD Wing spanwise drag coefficient CC d

CAV

SDW Winglet spanwise drag coefficient CC d

C AV

SEXP Wing exposed area

124
VARIABLE

SFD

SGRAD

DESCRIPTION

Wing spanwise friction coefficient CCf

CA V

Body side slope at wing-body juncture

SLD

SLW

SMD

SMW

TCIR

Wing span load coefficient CC_

CAV

Winglet spanwise load coefficient CC_

CAr

Wing spanwise moment coefficient CC

m

CA V

Winglet spanwise moment coefficient CC

m

C

AV

Wing circulation at TAG wing span cuts

TDX TAG A X spacing

TDY TAG A Y spacing

TDZ TAG A Z spacing

THETC Body crude grid angular cuts

THETF Body fine grid angular cuts

THETFP Angular cuts for pod boundary points

TITLE Case title for identifying graphic and printed output

TLE Wing leading edge X value at TAG span cuts

TPIST Pylon yaw incidence or twist

125
VARIABLE

TSLOC

DESCRIPTION

Wing local sweep angle at wing fine grid boundary points

TTE Wing trailing edge X value at TAG span cuts

TVIST Winglet section incidence angle or twist

TWIST Wing twist (incidence) distribution

VANGL Winglet cant angle, measured from wing plane

VAREA Winglet area

VCD Winglet drag coefficient

VCL Winglet lift coefficient

VCLE Crude grid X value of winglet leading edge

VCM Winglet moment coefficient

VCTE Crude grid X value of winglet trailing edge

VLE Winglet leading edge X value after positioning

VTE Winglet trailing edge X value after positioning

W Relaxation factor

WAREA Wing area S W

WCD Wing drag coefficient

126
VARIABLE

WCF

WCL

DESCRIPTION

Wing friction drag coefficient

Wing liftcoefficient

WCM Wing moment coefficient

WCORD Wing section local chord length

WS Wing plot scaling coefficient

X X coordinate for global crude grid (physical space)

XBF X coordinate for body fine grid

XBFP Fine pod grid X array

XI coordinate for global crude grid (transformed space)

XILE coordinate of local wing section leading edge

XINB X coordinates defining axisymmetric body (input option)

XINRP X coordinates defining axisymmetric pod

XINP X ordinates defining pylon

XINV X ordinates defining winglet section

XINW X ordinates defining wing section

XITE coordinate of local wing section trailing edge

XLE X coordinate of local wing section leading edge

XLET X coordinate of wing tip leading edge

127
VARIABLE DESCRIPTION

XMOM Position about which configuration moments are computed

XNC Body normal vector X direction at crude grid body points

XNCP Pod normal vector X direction at crude grid points

XNF Body normal vector X direction at fine grid body points

XNOSE X coordinate of body nose repositioned in crude grid

XOL Non-dimensional distance along body length and wing chord

XOLP X stations for pod surface after positioning

XPL X coordinate of input wing section leading edge

XPT X coordinate of input wing section trailing edge

XSF X coordinate defining wing section at each fine grid plane

points

XTAG TAG grid X array

XTAIL X coordinate of body tail repositioned in crude grid

XTE X coordinate of local wing section trailing edge

XTET X coordinate of wing tip trailing edge

XVF

XVL

Winglet fine grid X array

X value of winglet leading edge at input stations

128
VARIABLE

XVT

DESCRIPTION

X value of winglet trailing edge at input stations

XWF Fine embedded wing grid X coordinate

Y Y coordinate for global crude grid (physical space)

YBF Y coordinate for body fine grid

YBFP Fine pod grid Y array

YBODYP Y coordinate of pod/nacelle axis (input as YBGDY l)

YINL Y ordinates defining lower wing section

YINLP Y ordinatesdefining pylon outboard surfaces

YINLV Y ordinates defining winglet outboard surface

YINU Y ordinates defining upper wing section

YINUP Y ordinates defining pylon inboard surfaces

YINUV Y ordinates defining winglet inboard surface

YNC Body normal vector Y direction at crude grid body points

YNCP Pod normal vector Y direction at crude grid points

YNF Body normal vector Y direction at fine grid body points

YOB Wing span station (2Y/b)

YP Y coordinate of input wing section trailing edge

129
VARIABLE

YSF

DESCRIPTION

Y coordinate defining wing section at each fine grid plane

YTAG TAG grid Y array

YTIP Y coordinate of wing tip

YV Y value of winglet input stations

YVF Winglet fine grid Y array

Z Z coordinate for global crude grid (physical space)

ZBF Z coordinates for body fine grid

ZBFP Fine pod grid Z array

ZBODYP Z coordinate of pod/nac_lle axis (input as ZBC[)YI)

ZETA C coordinate for global crude grid (transformed space)

ZETAT TAG 4 coordinates

ZNC

ZNCP

Body normal vector Z direction at crude grid body points

Pod normal vector Z direction at crude grid points

ZNF Body normal vector Z direction at fine grid body points

ZOB

ZTAG

Winglet span station (y/b)

TAG grid Z array

ZWF Fine embedded wing grid Z coordinate

ZWING Wing height relative to center of body

130
APPENDIX B

USAGE/MODIFICATIONS FOR LaRC CDC/VPS-32 VERSION

The LaRC VPS-32 version of the WIB(X)-PPW code, using VSOS 2.1.5 (opt = E)

requires less than 1 millionlo storage for load and execution. Differences

are noted as follow:

i. FILES USAGE

Thirteen (13) disk units are used, including one for a solution

save/restart. The planar potential arrays are set up and accessed as

table lookup in a large labeled common block, eliminating disk units 2,

3, 4, and 5 (units 12, 13, 14, and 15 of IBM code) by dummy READMS,

WRITMS referencing. Several options are available for the solution

save/restart capability, using unit 7 (unformatted data). Data needed by

a separate plot program are saved on units 80, 82, 83, 87, 88 (all

unformatted) and unit 9 (formatted).

2. UNIT 1 DATA INPUT

Through use of unit 1 data input the user can redefine certain key

parameters that have been code-defined (hard coded). These code-defined

values should be used initially to enhance the probability of proper

execution for input geometry. Parameter values revert to default

settings if keys for changes are not activated. Unit i data referenced

in the infora_tion which follows use 8-field lO-digit format (SFIO.O)

with decimal point required. Default values for variables are included

in the description for variables. The changes allowed are:

a) Number of fine x-grid points at wing tip is specified on Card I-W

rather than Card 2-W.

b) Save/restart of solution in the crude/fine grid only.

c) Redefinition of wing fine grid boundaries.

d) Redefinition of transition location at all span stations for viscous

flow.

e) Redefinition of relaxation factors and interaction frequency in the

general solution process.

The notation of appendix A for configuration indentification is used to

indicate the card image modifications and additions for these allowed

changes. Note that only the variables redefined from appendix A are included

here.

131
CARD

NUMBER

Card 2-A

CARD

COLUMN

i-i0

VARIABLE

NAME

CASE

SGN (CASE)

DESCRIPTION

ICASEI Key describing the type of

configuration.

CASE = i. Isolated Body (omit cards -W).

CASE = 2. Isolated Wing (omit cards -B).

CASE = 3. Wing-Body.

Trigger to control relaxation

factors and interaction

frequencies in general solution

process.

CASE > O. Same as original input, no

additional input required on

Card 2-A-2.

CASE < O. Read additional input,

Card 2-A-2.

61-70 V ISMOD IVISMOD Key describing extent of viscous

effects.

VISMOD = i. No viscous effects.

VISMOD = 2. Viscous effects computed at

end of inviscid analysis.

VISMOD = 3. Inviscid/viscous interaction.

SGN (VlS_OD) Trigger to redefine transition

location, x/c, for viscous

fl,_.

VISMOD > 0. Same as original code--

no additional input

required on Card 6-W.

VISMOD < 0. Read additional input,

Card 6-W.

132
CARD CARD VARIABLE

NUMBER OOLUMN NAME

Card 2-A

(contd)

NOTE:

Card 2-A-I

NOTE:

Card 2-A-2

(Note:

DESCRIPTION

71-80 START START = 0. Conventional independent run

(default).

START = i. Save final solution at end

of current AXITF iteration

cycles.

START = 2. Restart solution at previous

AXITF+I iterations; do not save

final solution.

START = 3. Restart solution at previ_Is

AXITF+I iterations; save final

solution at end of current AXITF

iteration cycles.

START = 4. Save solution at end of a

specified crude/fine iteration

cycle during a conventional

independent run. This option

requires additional data,

Card 2-A-I.

Card 2-A-I required only for START = 4.

i-i0 AXITF2 Crude/fine iteration cycle at which

solution is saved during a conventional run.

(AXIT+I < AXITF2 < AXITF)

Card 2-A-2 required only for CASE < O.

i-i0 RFSUB Subsonic relaxation factor (default = 1.5).

11-20 P_BL Relaxation factor for boundary layer

(default = 0.6).

21-30 XITBLI Crude/fine iteration cycle at which boundary

layer is initially relaxed (default = 5.0).

31-40 XITBLF Frequency of boundary-layer relaxation in

crude/fine solution (default = 20.0).

41-50 XITFBB Frequency of fine body (pod) boundary value

potential update in crude/fine solution

(default = 10.0).

Any variable set = 0.0 is assigned default value.)

133
CARD

NUMBER

Card I-W

CARD

(X)L_

I-i0

VARIABLE

NAME

ASECT

DESCRIPTION

IASECT] Number of streamwise sections

I !

defining wing planfom

(i _ ASECT _ 20).

SGN (&SECT) Trigger to redefine wing fine

grid boundaries

AsEcr > 0. Same as original code, no

additional input required

on Card I-W-I.

ASEC_ < O. Read additional data,

Card I-W-I.

NOTE:

Card I-W-I

(Note:

71-80 AQXFG AQXFG = -I. Code sets i00 fine x-grid points

at wing tip station (default).

AQXFG = 0. Code determines the number of

fine x-grid points at wing tip

station.

AQXPG = other. Number of fine x-grid

points at wing tip

station.

(I0. < AQXFG < 99.)

Card I-W-I required only for ASEC_ < 0.

i-i0 AWLE Percent of wing fine grid in front of leading

edge (default = 20.).

I 1-20 AWTE Percent of wing fine grid behind trailing

edge (default = i0.).

21-30 AWLS percent of wing fine grid below wing

(default = I0.).

31-40 AWUS Percent of wing fine grid above wing

(default = 30.).

Any variable set = 0.0 is assigned default value.)

134
CARD

NUMBER

CARD VARIABLE

COLUMN NAME DESCRIPTION

Card 2-W

NOTECard 6-W

51-83 Field unused.

Card 6-W required only for VIS_K_) < O.

1-80 ATRIP Transition location, x/c, at every wing

span station for viscous flow. Specify

from inboard to outboard for 18 upper

surface values, 18 lower surface values,

respectively. (Default values assigned,

.05, at all wing span stations. )

135
136
APPENDIX C

GENERAL RECOMMENDATIONS FOR CODE USAGE

The computer program described herein has been implemented by a number of investigators. To date, over 75 different configurations (see Table

C-I) have been modeled and analyzed. Because of problem three-dimensionality and inherent code flexibility, however, it is impossible to verify the

computer program for all of the possible option combinations, shape variations

or flow conditions that might be of interest. Despite this, good results should

be obtained if the user is aware of the following recommendations.

I. PRACTICE

There are several factors that combine to foil initial attempts by new

users performing transonic aircraft analysis. These factors are listed below.

• Complex geometry input/definition

• Complexity/sensitivity of transonic flow fields

• Character of finite-difference relaxation process.

Experience indicates that input and checkout of a complex geometric shape

such as a fuselage can be a difficult task when setting up for a subsonic panel

code analysis. For transonic analyses, the problem is aggravated further by

the complexity of the flow field and sensitivity to what may appear as minor

surface irregularities. Experience with subsonic "panel" methodology does not

prepare the user for transonic code applications.

The problem is compounded by the nature of finite-difference relaxation

processes which require a computational grid system. A surface definition

discrepancy may, in addition to causing erroneous computed pressures, result

in generation of an improper grid system.

As a result, it is recommended that the user become familiar with the

computer code by first analyzing simple shapes such as isolated wings and
AIRFOILS (2-D)

NACA 0012

NASA LS(1 )

NASA TRANSPORT AIRFOIL

WINGS

ONERA M-6

RAE 101

NACA WING (RM A9K01)

LOCKHEED/AFOSR (3 CONFIGS)

LTV SKEWED CAMBER WING

ISOLATED BODIES

NACA SHARP NOSE BODY (RM L53H04, 2 CONFIGSt

NASA BLUNT NOSE BODY (TN D-7331)

GRUMMAN GULFSTREAM II FUSELAGE

STORE CALIBRATION BODY

DOUGLAS A-4 FUSELAGE

NIELSEN STORE

EA-6B TAIL POD

NTF 5 ° CALIBRATION CONE

PATHFINDER I FUSELAGE

NACABODYOF REVOLUTION (RM A9126)

WING-BODY/WING-FUSELAGE

GRUMMAN F-14 (3 CONFIGS}

NACA RESEARCH MODEL (RM L51F07}

NASA RESEARCH MODEL (TM X-3431)

GENERAL DYNAMICS F-16

GENERAL DYNAMICS F-Ill/TACT

LAVI FIGHTER

LTV A-7 SUPERCRITICAL WING CON F IG

DOUGLAS TRANSPORT MODEL

GRUMMAN X-29A FORWARD SWEPT WING DEMONSTRATOR"

BOEING 747-200

BOEING 747-SP

NASA F-8 RESEARCH CONFIG

ROCKWELL HiMAT CANARD DESIGN

NASA USB TRANSPORT

GRUMMAN/AIR FORCE STAC/CDAFCONFIGS

BOEING B-52

NASA TAILOR-MATE (2 CONFIGS)

NASA ENERGY EFFICIENT TRANSPORT

ROCKWELL CANARDED RESEARCH FIGHTER CONFIG.

GRUMMAN ATF-RESEARCH FIGHTER CONFIG

BEECH TRANSPORT

NACA SKEWED WING RESEARCH MODEL (RM A58C03)

NTF-PATHFINDER II FIGHTER

COMPLEX CONFIGURATIONS (NACELLES/PODS t PYLONS, WINGLETS}

SPACE SHUTTLE (LAUNCH CONFIG)

LOCKHEED L-101t

GULFSTREAM AEROSPACE G-Ill

BOEING KC-135

DOUGLAS WING-BODY-NACELLE-PROP SLIPSTREAM

LOCKHEED C-141

BOEING 767 WINGLET STUDY

DOUGLAS DC-10 WINGLET STUDY (2 CONFtGS)

LOCKHEED C-SA

BOEING 747 WINGLET STUDY

GRUMMAN A43F PYLON STUDY

GRUMMAN DESIGN 698 TILT-NACELLE V/STOL

FUJI TRAINER (3CONFIGS)

GRUMMAN VTX WINGIWINGLET DESIGN

GRUMMAN E-2 WINGLET STUDY

ARA MODEL Mfo4 RESEARCH CONFIGURATION

NASA LET NACELLE/PYLON STUDY (2 CONFIGS)

ROCKWELL HIMAT

NTF-PATRFINDER I TRANSPORT

GULFSTREAM AEROSPACE G-IV WING

GRUMMAN DESIGN 623 V/STOL AERO-PROPULSION INTEG STUDY

NASA POD-IN-WING CONFIG

NASA PROP-FAN SIMULATOR

R84-1137-046D

Table C-1 Configurations Analyzed Using Transonic Wing-Body Code

138
isolated bodies at transonic conditions. Complex aircraft shapes should be

attacked after a basic knowledge of i) the computer code, and 2) the character of transonic flow fields is in hand. Then, when a problem surfaces, the

user can determine whether the computer code is at fault, the input data is in

error, or the flow condition is unreasonable.

2. NON-POTENTIAL PHENOMENA

In general, most aircraft operate in a low-gradient or "small disturbance"

world. Flight efficiency degrades rapidly if disturbances are large. As a

result, the present small-disturbance formulation has been found to be applicable to many different configurations over an extraordinary range of flow

conditions. The user should be aware, however, that there are many cases

for which the code can not be expected to provide a good flow simulation. If

geometry and flow conditions combine to produce severe flow gradients, flow

separation will occur. If the separation region is large (i.e., ~10% chord on

the wing) the computational and physical flows will not agree. In addition, if

vortices generated at the wing leading edge or by configuration components

interact with surfaces that are of interest, flow predictions will be compromised.

3. DRAG PREDICTION

Consistent prediction of absolute and incremental drag values is not

possible with today's 3-D computational methods. This program is not the

exception. Some useful incremental drag predictions have been obtained

during project applications, but good results have not been obtained with

sufficient regularity to recommend usage. In general, the simpler the shape,

the higher the probability that drag predictions will be useful.

4. LIFT CONVERGENCE

All of the 3-D c(x_utations included in this report were generated using I00

crude grid iterations and 80 cycles in the fine/crude system. Experience

indicates that the resulting convergence level is sufficient for most engineering

applications. In other words, the accuracy vs cost ratio is high. For some

high aspect ratio transport wings, however, this level of convergence may

139
cause a portion of the wing lift to be lost. One way to compensate for this

effect is to analyze the configuration at 1/2 degree greater incidence than that

of the experiment. This was done for the C-141 and C-5 comparisons shown

in the results section.

For some specialty applications or for eases where computing costs are not

a concern, excellent results have been obtained by using 150 crude iterations

followed by 150 cycles in the crude/fine system. Other investigators have

improved flow simulations by increasing the relaxation factor from _ = 1.5 to

w = 1.75. The new user should begin by using" standard cycle/factor values

and experiment upward if convergence or comparisons are not satisfactory.

5. WING TIP DIVERGENCE

Analyses performed on highly loaded wings with severe taper and high

sweep indicate that occasionally a diverging numerical condition can develop at

the wing tip. It occurs only when very strong shock waves form at the wing

tip and experience indicates that occurrences are close to conditions for which

the flow separates. The numerical condition is caused by improper zones of

dependence and/or unfavorable wing tip mesh cell aspect ratios. A rotated

difference scheme is now under development. The new scheme eliminates this

problem but requires additional refinements and an extensive check-out effort.

A simpler "fix" has been achieved by automatically reducing wing tip mesh

resolution. This resolution reduction scheme has been automated by computing

a "probability of divergence" factor which is based on Maeh number, incidence, wing thickness, and planform taper. Occasionally, an application might

surface for which the automatic system fails. For these cases, the user can

specify the number of fine mesh points at the wing tip (the input variable

AQXFG). Tne highest resolution possible without divergence indicators

(pressure "wiggles", increasing ACMAx ) should be sought.

6. COMPARISONS IN HIGH SPANWISE GRADIENT REGIONS

At transonic speeds, flow gradients might be high in the wing spanwise

direction. This is particularly noticeable near wing-fuselage junctures,

wing-winglet junctures, or mid-wing regions where multiple shock wave sys140
tems coalesce. The computational method predicts chordwise pressure distributions at a number of spanwise locations. These "output" stations may not

be aligned with experimental data stations or locations where output is

required. Since small span position discrepancies might result in significant

pressure differences, some applications may require that output data be interpolated or extrapolated.

On a related matter, it should be noted that the fuselage side is modeled

by mesh points positioned along a wing span cut. Depending on the wing/

fuselage spatial relationship, the "physical" body side might be as much as 1/2

mesh cell away from the "computational" body side. This presents no problem

for most applications, but for some cases where exact juncture pressures are

required, and the I/2 mesh cell shift occurs, the flow simulations may be

compromised.

7. GRID GENERATION

The computational method has been developed with the philosophy that

engineering users should not have to modify grid systems for most applications. Instead, the systems should be constructed in the same consistent

manner for each ease. It can be seen by studying the input data format that

only the configuration geometry and flow conditions are input. Grid generation has been automated. A knowledgeable user might modify the coordinate

systems for special applications, but this requires sufficient familiarity with

the coding to make changes to the FORTRAN.

This automated grid philosophy does not guarantee that an "optimum"

system will always be generated, particularly for complex configurations with

many components. For example, a transport might feature two nacelles positioned below each wing at different heights. The code in its present form is

capable of representing only a single height or position for both nacelles.

Thus it may be necessary to perform two different analyses to obtain results

for each component at its proper position.

An attempt has been made to insure that a nacelle or pod is modeled at

its proper distance from the wing by adjusting the grid so that grid points

141
representing the nacelle centerline are positioned at the requested nacelle

location. This does not insure, however, that the computational nacelle wing

gap will equal the physical gap. This is an important aspect of many flow

simulations. The user should observe what the computational gap is between

the points which represent the side of the nacelle facing the wing and the

points which represent the wing plane. If this gap is not equal to the physical space between the components, the nacelle height variable should be

adjusted until a match is obtained.

8. SUPERCRITICAL AIRFOIL/WING COVE SEPARATION

The boundary layer method incorporated is of the finite difference type

which terminates once separation is encountered. The viscous analysis is

initiated after an initial inviscid pressure field is generated. For super

critical-type sections the initial severe unfavorable pressure gradient found in

the cove or lower surface trailing edge region tends to induce a premature

separation. A temporary displacement thickness (5*) must be "fit" for the

cove region to allow the solution process to continue. This fitting process is

quite crude and often a true, computed, attached flow boundary layer is never

achieved despite the fact that experimental data indicates the flow is attached.

It has also been noted that the code tends to predict supercritical section

cove pressures that are higher than experimental values. Predicted wing

section lift levels might be several percent too high with an attendant nose

down pitching moment increment.

9. SURFACE SHAPE IRREGULARITIES

The present method does not employ conformal mappings for wing sections

and no smoothing operation is performed on wing section ordinates which are

input. No attempt should be made to "smooth" surface breaks caused by

control surface deflections or irregularities resulting from poor manufacturing

processes. Experience indicates that the code will simulate the resulting

pressure disturbances quite well. For some applications, these predictions will

be useful.

142
I0. WINGS WITH STRONG VISCOUS INTERACTIONS

Some applications might feature wing contours for which viscous effects

are quite severe. Good agreement can be obtained for these cases, but the

total number of iterations may have to be increased by a factor of 3 or 4.

143

REFERENCES

I. Murman, E. M., and Cole, J. D. : "Calculation of Plane Steady Transonic

Flow," AIAA J., vol. 9, Jan. 1971, pp. 114-121.

2. Bailey, F. R., and Steger, J. L.: "Relaxation Techniques for ThreeDimensional Flow about Wings," AIAA J., vol. 11, Mar. 1973, pp. 318-325.

3. Keller, J. D.; and South, J. C., Jr.: "RAXBOD: A Fortran Program for

Inviscid Transonic Flow over Axisymmetric Bodies," NASA TM X-72831,

Feb. 1976.

4. Jameson, Antony; and Caughey, D. A.: "A Finite Volume Method for

Transonic Potential Flow Calculations." A Collection of Technical

Papers - AIAA 3rd Computational Fluid Dynamics Conference, June 1977,

pp. 35-54. (Available as AIAA Paper 77-635.)

5. Boppe, C. W.; and Stern, M. A.: "Simulated Transonic Flows for Aircraft

with Nacelles, Pylons, and Winglets," AIAA Paper 80-0130, Jan. 1980.

6. Boppe, C. W.: "Transonic Flow Field Analysis for Wing-Fuselage

Configurations," NASA CR-3243, May 1980.

7. Hesse, W. J.; and Mumford, N. V. S.: Jet Propulsion for Aerospace

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TN D-8474, July 1977.

146

1. Rep(xt No. 2. Government Accession No.

NASA CR-4066

4. Title and Subtitle

Aerodynamic Analysis for Aircraft With

Nacelles, Pylons, and Winglets at

Transonic Speeds

7. Author(s)

Charles W. Boppe

9. Performing Or_nization Name and Addre_

Grun_an Aerospace Corporation

Bethpage, NY 11714

"_" S_nsoring Agency Name and Addr_s

National Aeronautics and Space Administration

Washington, DC 20546-0001

3. Recipient's Catalog No.

5. Repo_ Date

April 1987

6. Performing Organization Code

8. Performing Organ;zation Report No.

10. Wock Unit No.

11. Contract or Grant No.

NASI-14732

13. Type of Report and Period Covered

Contractor Report

14. Sponsoring Agency Code

534-02-13-13

15, _pplementary Notes

Langley Technical Monitor"

Final Report, Part I

Perry A. Newman

16. Abstract

A computational method has been developed to provide an analysis

for complex realistic aircraft configurations at transonic speeds.

Wing-fuselage configurations with various combinations of pods,

pylons, nacelles, and winglets can be analyzed along with simpler

shapes such as airfoils, isolated wings, and isolated bodies. The

flexibility required for the treatment of such diverse geometries

is obtained by using a multiple nested grid approach in the finitedifference relaxation scheme. Aircraft components (and their

grid systems) can be added or removed as required. As a result,

the computational method can be used in the same manner as a wind

tunnel to study high-speed aerodynamic interference effects.

The multiple grid approach also provides high boundary point

density/cost ratio. High resolution pressure distributions can

be obtained. Computed results are correlated with wind tunnel

and flight data using four different transport configurations.

Experimental/computational component interference effects are

included for cases where data are available. The computer code

used for these comparisons is described in the appendices.

17. Key Words (Sug_t_ by Author(sl)

Transonic Flow

Computational Aerodynamics

Flow Simulations

Finite Difference Relaxation

Interference Effects

19. _urity Oauif. (of this reportl T 20. _urity Cla_if. (of this _ge)

Unclassified I Unclassified

18. Oistribution Statement

Unclassi fied_Unlimited

Subject Category 02

21. No. of Pages ] 22. Price

154 J A08

For sale by the National Technical InformationService, Springfield, Virglma 22]61

I/'"

NASA-Langley, 198)