N A S A C O N T R A C T O R

R E P O R T -

A COMPUTER PROGRAM TO CALCULATE THE LONGITUDINAL AERODYNAMIC CHARACTERISTICS OF WING-FLAP CONFIGURATIONS WITH EXTERNALLY BLOWN FLAPS

Michuel R. Mendenhull, Frederick K . Goodwin? ,/ " , "" ; , :---.-.

and Selden B. SpungZer /' .

, ... .' ' _. 1 ,,'.

~ .\ . ,

Prepared by

NIELSEN ENGINEERING & RESEARCH, INC. Mountain View, Calif. 94043

for Langley Research Center

' . - ! . - .

. I

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON, 0. C. SEPTEMBER 1976

I

https://ntrs.nasa.gov/search.jsp?R=19760025043 2018-06-27T04:03:57+00:00Z

TECH LIBRARY KAFB, NY

- .. 00bL43L 1. Repott No. 3. Recipient's C a t a l o g No. 2. Government Accession No.

NASA CR-2706

)''le and "A ComDuter Proaram t o C a l c u l a t e t h e L o n a i t u d i n a l 5. Repor t Date

Aerodynamic Charac te r i s t i cs o f W ing -F lap Con f igu ra t i ons wit6 Ex te rna l l y B lown F laps "

I Peptember 1976 6. Performing Orqanization Code

I I- .- .

7. Author(s) .~

8. Performing Orqanlzation Report No. Michael R. Mendenhal l , Freder ick K. Goodwin and Selden B. Spangler

10. Work Unit No. 9. Performing Organization Name and Address

Nie lsen Eng ineer ing and Research , Inc . 510 Clyde Avenue Mountain View, C a l i f o r n i a 94043

11. Contract or Grant No.

NASl-13158 ~ I 13. Type of Report and Period Covered 12. Sponsoring Agency Name and Address

Washington, DC 20546 Na t iona l Ae ronau t i cs and Space A d m i n i s t r a t i o n 1 Cont rac to r Repor t

14. Sponsoring Agency Code

15. Supplementary Notes ~~ -

Langley Technical Moniter R. C. Goetz Final Report

- . ~ -~

16. Abstract T h i s document i s a u s e r ' s manual f o r t he compu te r p rog ram deve loped to ca l cu la te t he l ong i - t u d i n a l a e r o d y n a m i c c h a r a c t e r i s t i c s o f w i n g - f l a p c o m b i n a t i o n s w i t h e x t e r n a l l y b l o w n f l a p s . A vo r tex - l a t t i c e l i f t i n g - s u r f a c e method i s used t o model t h e w i n g a n d m u l t i p l e f l a p s . Each l i f t i n g s u r f a c e may be o f a r b i t r a r y p l a n f o r m h a v i n g camber and t w i s t , and t h e m u l t i p l e - s l o t t e d t r a i l i n g - e d g e f l a p system may c o n s i s t o f u p t o t e n f l a p s w i t h d i f f e r e n t spans and d e f l e c t i o n a n g l e s . The engine wake model c o n s i s t s o f a s e r i e s o f c l o s e l y spaced v o r t e x r i n g s w i t h c i r c u l a r o r e l l i p t i c c r o s s s e c t i o n s . The r i n g s a r e n o r m a l t o a wake c e n t e r l i n e w h i c h i s f r e e t o move v e r t i c a l l y and l a t e r a l l y t o accommodat t h e l o c a l f l o w f i e l d b e n e a t h t h e w i n g a n d f l a p s . The t w o p o t e n t i a l f l o w m o d e l s a r e u s e d i n an i t e r a - t i v e f a s h i o n t o c a l c u l a t e t h e w i n g - f l a p l o a d i n g d i s t r i b u t i o n i n c l u d i n g t h e i n f l u e n c e o f t h e wakes from up to two t u rbo fan enq ines on the semispan. The method i s l i m i t e d t o t h e c o n d i t i o n where the f low and geometry o f t h e c o n f i g u r a t i o n s a r e s y m m e t r i c a b o u t t h e v e r t i c a l p l a n e c o n t a i n i n g t h e w i n g r o o t c h o r d .

The c a l c u l a t i o n p r o c e d u r e s t a r t s w i t h a r b i t r a r i l y p o s i t i o n e d wake c e n t e r l i n e s a n d t h e i t e r a t i v e c a l c u l a t i o n c o n t i n u e s u n t i l t h e t o t a l c o n f i g u r a t i o n l o a d i n g c o n v e r g e s w i t h i n a p r e s c r i b e d t o l e r a n c e . The r e s u l t s a v a i l a b l e f r o m t h e p r o g r a m i n c l u d e t o t a l c o n f i g u r a t i o n f o r c e s a n d moments, i n d i v i d u a l l i f t i n g - s u r f a c e l o a d d i s t r i b u t i o n s , i n c l u d i n g p r e s s u r e d i s t r i b u t i o n s , i n d i v i d u a l f l a p h i n g e moments, and f l o w . f i e l d c a l c u l a t i o n a t a r b i t r a r y f i e l d p o i n t s .

This program manual con ta ins a d e s c r i p t i o n o f t h e use o f t h e p r o g r a m , i n s t r u c t i o n s f o r p r e p a r a - t i o n o f i n p u t , a d e s c r i p t i o n o f t h e o u t p u t , p r o g r a m l i s t i n g s , and sample cases.

17. Key-Words (Suggested by Authoris))

E x t e r n a l l y Blown Flaps STOL U n c l a s s i f i e d - U n l i m i t e d

~- ~ .~ I .. . ~~ ." ~ ~ ~ ~ _ _ _ _ _ _ _ _ _ _

Subject Category 02 19. Security Classif. (of this report) 1 20. Security Classif. (of this page) 21. No. of Pages .22. Price'

TABLE OF CONTENTS Page NO. Sect ion

SUMMARY 1

INTRODUCTION 2

DESCRIPTION OF PROGRAM 3

C a l c u l a t i o n Procedure Program O p e r a t i o n Program U s a g e

Limitat ions R u n t i m e

4 5 8

8 9

DESCRIPTION OF INPUT 10

V o r t e x - L a t t i c e A r r a n g e m e n t 10

Spanwise d i s t r i b u t i o n C h o r d w i s e d i s t r i b u t i o n

11 1 2

Je t Wake Specification I n p u t V a r i a b l e s Sample C a s e s

13 18 27

DESCRIPTION OF OUTPUT 29

Sample C a s e E r r o r Messages

29 32

PROGRAM L I S T I N G 33

REFERENCES 59

TABLE I 60

FIGURES 1 THROUGH 9 61

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A COMPUTER PROGRAM TO CALCULATE THE LONGITUDINAL

AERODYNAMIC CHARACTERISTICS OF WING-FLAP

CONFIGURATIONS W I T H EXTERNALLY BLOWN FLAPS

by Michael R. Mendenhall, Frederick K. Goodwin, and Selden B. Spangler

Nielsen Engineering & Research, Inc.

SUMMARY

This document i s a u s e r ' s manual f o r t h e computer program developed to ca l cu la t e t he l ong i tud ina l aerodynamic character is t ics of wing-f lap combinations w i t h ex te rna l ly blown f laps . A vo r t ex - l a t t i ce l i f t i ng - surface method i s used t o model t he wing and mult iple f laps . Each l i f t i n g s u r f a c e may be of arbitrary planform having camber and t w i s t , and the mult iple-s lot ted t ra i l ing-edge f lap system may cons is t of up t o t e n f laps wi th d i f fe ren t spans and def lect ion angles . The engine wake model consis ts of a series of c lose ly spaced vortex rings with circular o r e l l i p t i c c r o s s s e c t i o n s . The r ings a re normal t o a wake center l ine which is f r e e t o move v e r t i c a l l y and l a t e r a l l y t o accommodate the l oca l flow f ie ld benea th the wing and f laps . The two potent ia l f low models a re used i n a n i t e ra t ive fash ion to ca lcu la te the wing-f lap loading dis t r ibut ion including the inf luence of the wakes from up t o two turbofan engines on the semispan. The method is l i m i t e d t o the condition where the flow and geometry of the configurations are symmetric about the ver t ica l p lane conta in ing the wing root chord.

The calculation procedure starts wi th a rb i t ra r i ly pos i t ioned wake cen te r l ines and t h e i t e r a t i v e c a l c u l a t i o n c o n t i n u e s u n t i l t h e t o t a l configuration loading converges within a prescribed tolerance. The

r e su l t s ava i l ab le from the program include to ta l conf igura t ion forces and moments, ind iv idua l l i f t ing-sur face load d i s t r ibu t ions , inc luding pressure d i s t r ibu t ions , ind iv idua l f lap h inge moments, and flow f i e l d

ca lcu la t ion a t a r b i t r a r y f i e l d p o i n t s .

This program manual contains a descr ipt ion of the use. of the program, ins t ruc t ions for p repara t ion of input , a descr ipt ion of the output, program l i s t i n g s , and sample cases.

INTRODUCTION

A n engineering prediction method fo r ca l cu la t ing t he s t a t i c l ong i - tudinal aerodynamic cha rac t e r i s t i c s of wing-flap combinations with external ly blown f l aps (EBF) is presented in reference 1. An external ly blown f l a p is a STOL high l i f t device in which t h e j e t e f f l u x from turbofan engines mounted beneath the wing is allowed t o impinge d i r e c t l y on the t ra i l ing-edge s lot ted f lap system. A l a rge amount of additional lift is produced through engine wake def lec t ion and mutual interference e f fec ts . The purpose of the analysis i n reference 1 is to p rovide a potential f low method, r e q u i r i n g l i t t l e u s e of empirically determined information, to predict the detai led loading dis t r ibut ion on EBF

configurations. The method involves the combination of two poten t ia l flow models, a vor tex- la t t ice l i f t ing-sur face model of the wing and f l aps and a vortex r ing model of t h e j e t wakes. The t w o flow models a r e com- bined by direct superposi t ion such that a tangency boundary condition i s

s a t i s f i e d on the wing and f lap sur faces . A n i t e r a t i o n between t h e j e t wake posi t ion and the wing loading is carr ied out u n t i l the solut ion

converges.

The computer program described in this report is an improved and extended version of the program of reference 2. Modifications include the following. An improved vor tex- la t t ice l i f t ing-sur face method is

used i n which t h e t r a i l i n g l e g s of the horseshoe vortices are allowed t o bend around the f lap sur faces so t h a t a l l t h e t r a i l i n g v o r t i c i t y leaves the conf igura t ion tangent to the l as t f lap . The geometry speci- fication has been changed so that each f lap surface can be modeled as a separa te l i f t ing sur face wi th a maximum of ten f laps permit ted. The i teration procedure has been automated so t h a t t h e j e t c e n t e r l i n e s a r e posit ioned according to the local f low field direction beneath the wing and f l aps , and the i teration procedure can be carried out a specif ied number of times or until convergence to a specif ied tolerance is

achieved. The j e t cen te r l ine ca l cu la t ion has been automated so tha t , a f t e r s t a r t i ng w i th an a rb i t r a ry j e t l oca t ion , t he cen te r l ine is allowed t o move so t h a t it l i e s along local flow angles. The j e t model of re f - erence 2 was defined by a s e r i e s of c i rcular vortex r ings. The improved j e t model w i l l now hand le e l l i p t i c r i ngs ; t he re fo re , t he j e t may s t a r t a t the engine exi t wi th an axisymmetric cross section and change t o an e l l i p t i c c r o s s s e c t i o n a s it moves downstream and interacts with the

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l i f t i ng su r f ace . The je t c ross -sec t iona l a rea and shape must be specified by the user.

This document is a u s e r ' s manual for the computer program developed to car ry ou t the ca lcu la t ions in the EBF aerodynamic prediction method. Principal reliance is made herein to reference 1 f o r a description of t he de t a i l s of the method and the calculation procedure. Reference 1 also contains calculated resul ts and comparisons with data for a var ie ty of configurations. The following sections of t h i s r epor t w i l l provide a descr ipt ion of the program, a descr ipt ion of the input, a descr ipt ion of the output, a program l i s t i n g , and sample cases. The notation used is the same as tha t of reference 1.

DESCRIPTION OF PROGRAM

The purpose of t h i s s e c t i o n is to descr ibe the EBF aerodynamic prediction program i n s u f f i c i e n t d e t a i l t o p e r m i t a general understanding of the flow of the program and t o make the user aware of the analyt ical models used to represent the jets and the l i f t ing surfaces . Basical ly , the program models the l i f t ing surfaces with horseshoe vort ices whose circulation strengths are determined from a s e t of simultaneous equations provided by the flow tangency boundary condition applied a t a f i n i t e s e t of control points distributed over the wing and f laps . The boundary condi t ions include interference veloci t ies induced by some external source of disturbance such as the wake of a turbofan engine. The j e t wake is modeled by a s e r i e s of c losely spaced r ing vort ices , c i rcular o r e l l i p t i c a l i n shape, arranged on the boundary of t he j e t . The s t rength of the vort ices i s specified by t h e i n i t i a l v e l o c i t y i n t h e wake which is determined from the momentum i n t h e j e t . The j e t i s allowed to i n t e rac t w i th t he wing and f laps through the je t induced ve loc i ty f i e ld on the l i f t ing-sur face cont ro l po in ts . The wing and f laps are then a l lowed to interact wi th the j e t by forc ing the j e t c e n t e r l i n e t o be aligned with the f low direction beneath the l if t ing surfaces. This process is repeated i terat ively u n t i l convergence of both the l i f t ing-surface loading and je t cen ter l ine pos i t ion a re a t ta ined.

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Calculation Procedure

The general flow of the program, shown i n t h e f low char t in f ig- ure 1, proceeds as fol lows. After run ident i f icat ion information and cer ta in re fe rence quant i t ies are read in , the wing geometry is input and the wing l a t t i c e layout i s s e t up and output. This i s followed by similar ca lcu la t ions for the f lap sur faces . This conc ludes the l i f t ing- sur face geometry spec i f ica t ion ; therefore , the in f luence coef f ic ien t matrix, which is the left-hand side of the equation set and a function of geometry only, can be calculated. The matrix is t r iangular ized for use in the so lu t ion of the simultaneous equations. This concludes the f i r s t s e c t i o n o f t h e program which need be considered only once in each calculat ion.

The next section of the main program i s t h a t part i n which the so lu t ion is car r ied ou t and any i t e r a t i o n s are performed. The f i r s t s t e p is the i npu t o f t he i n i t i a l j e t parameters and the set up of the j e t cen ter l ines in p repara t ion for induced ve loc i ty ca lcu la t ions . The j e t induced veloci ty f ie ld a t each l i f t ing-surface control point is

computed a t t h i s t i m e . The right-hand side of the equation se t is now computed. Solution of the equation set produces the values for the c i r cu la t ion s t r eng ths o f each horseshoe vortex descr ibing the l i f t ing surfaces. Given the c i r cu la t ion s t r eng ths and t h e induced velocity f ie ld , the load d i s t r ibu t ions on t h e l i f t i n g s u r f a c e s a r e c a l c u l a t e d

and r e so lved i n to t o t a l fo rces and moments. A t t h i s p o i n t i n t h e so lu t ion , t he t o t a l fo rces and moments correspond t o t h o s e on a l i f t i n g surface in the presence of a j e t o r j e t s i n some specif ied posi t ion r e l a t i v e t o t h e wing and flaps. This may o r may not be a converged solut ion. Using t h e just-computed c i r cu la t ion s t r eng ths on the wing and f l aps , t he induced veloci ty f ie ld a t spec i f ied po in ts on the j e t center- l i n e s i s computed. The j e t induced veloci ty f ie ld a t these same poin ts i s a l s o computed assuming each j e t t o be i n i t s i n i t i a l l y p r e s c r i b e d posi t ion. The to t a l ve loc i ty f i e ld , i nc lud ing t he f r ee s t r eam, i s formed a t the spec i f ied po in ts on the cen te r l ine . The cen te r l ine a t each of these points i s assumed t o have the computed flow direction, and i ts pos i t i on is adjusted accordingly.

A t t h i s p o i n t i n t h e s o l u t i o n , t h e f i r s t i t e r a t i o n is complete and the so lu t ion may o r may not be converged. The je t center l ines have been moved; t h e r e f o r e , t h e i r new posit ion does not correspond to the previously calculated induced velocity f ield on the wing and f laps ; thus , the

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interference loading on these l i f t i ng su r f aces does not correspond t o the cur ren t j e t pos i t ions un less the j e t s were moved only a small amount. The option i s ava i lab le in the program to s top he re o r t o con t inue on for addi t iona l i t e ra t ions .

If fu r the r i t e r a t ion is indicated, the program re turns to the beginning of the i terat ion sect ion and s t a r t s a second i t e r a t i o n by computing t h e j e t induced ve loc i ty f i e ld a t t he l i f t i ng - su r face con t ro l points. The solution continues as before. A t the end of the current i t e r a t ion , two checks are made. The f i rs t t e s t is on t h e l o c a l j e t centerline slopes. If these slopes have not changed an amount greater than a prescribed convergence tolerance, convergence is assumed t o be at ta ined, an appropriate message i s pr inted, and the solut ion is complete. I f the center l ine convergence tes t fa i ls , the same tolerance is appl ied to the current and previous values of t o t a l normal-force coef f ic ien t . I f t h i s t e s t i n d i c a t e s convergence, the program sk ips t o the f inal por t ion of the calculation procedure. I f the convergence t e s t f a i l s a f t e r t he p re sc r ibed maximum number of i t e ra t ions has been completed, an appropriate message is printed and the program sk ips to the f ina l sec t ion .

I n the f ina l sec t ion of the program, the j e t cen ter l ines cor re- sponding t o t h e l a s t i t e r a t i o n a r e o u t p u t . This jet configuration does not correspond t o t h e l a s t s e t of loadings on the wing and flaps unless convergence has been achieved, b u t it corresponds t o t h e j e t which should be used f o r the next i t e ra t ion . The purpose of pr int ing these center l ine parameters is two-fold. First, it allows the user to compare t h e l a s t used center l ines with the new versions; and second, it provides a centerline configuration w i t h which to cont inue the i t e ra t ions by r e s t a r t i ng t he program.

The f ina l ca lcu la t ion computation of the induced This option is provided so flow f i e l d i n t he v i c in i ty

t o be carried out, i f requested, is the ve loc i ty f ie ld a t spec i f ied f ie ld po in ts . tha t the user may invest igate the induced of a ho r i z ion ta l t a i l pos i t i on o r o the r

points of i n t e r e s t i n the f low f ie ld .

Program Operat ion

The EBF predict ion program is wri t ten in Fortran I V and has been run on CDC 6600 and 7600 computers. The version described i n t h i s

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document w a s designed t o be used under the FTN compiler with a l e v e l 2

optimization. Other compilers can be used with only minor modifications and lower optimization levels can be used with the only penalty being an increase in run time. N o tapes other than s tandard input and output u n i t s are required for a typical run, al though one option allows an ex terna l ly induced ve loc i ty f ie ld to be brought i n v i a t ape un i t 4.

The main program, WNGFLP, contains one i t e m which is not a standard feature of a l l FTN compilers. Between cards WNG162 and WNG174 t h e r e are two ca l l s to sub rou t ine REQFL. This is a request for an adjustment in the core memory t o make room for the inf luence coeff ic ient matr ix , FVN, which is s to red i n a one-dimensional array. The purpose of t h i s a d j u s t - ment i s t o minimize the core s torage used unt i l the large array is

required. FVN i s dimensioned f o r u n i t l e n g t h on card WNG043. I f sub- rout ine REQFL o r i t s equivalent is not available, the following changes are required. First, remove cards WNG162 through 174. Second, change the dimension of the FVN ar ray on card WNG043 t o a value which w i l l cover the maximum number of elements i n an inf luence coeff ic ient matr ix; t h a t is, the square o f the to ta l number of vortex-lat t ice panels on t h e conf igura t ion of in te res t . Thus, the dimension of FVN can be made la rge enough t o cover the l a rges t a r ray an t ic ipa ted , o r the minimum s i z e a r ray needed can be defined and the dimension changed as the nuniber of vortex panels is increased.

There i s an a l te rna t ive so lu t ion which minimizes storage requirements f o r t h e FVN a r ray when subroutine REQFL is not avai lable . Program WNGFLP can be turned into a subroutine with cards WNG162-174 removed and the FVN dimension s e t a t u n i t y . A shor t main program can be wr i t t en which con- s is ts of a blank common which sets the dimension of FVN to t he r equ i r ed s i z e and a c a l l t o sub rou t ine WNGFLP. I n t h i s way, a short f ive-card main program is a l l t h a t need be recompiled t o change the s ize o f the FVN ar ray . This a l te rna te se t up f o r a main program is i l l u s t r a t e d i n f igu re 2 t o accommodate a maximum vortex l a t t i ce of 165 elements. The changes t o t h e c u r r e n t main program, WNGFLP, t o make it a subroutine a re also shown i n t h i s f i g u r e .

The following is a l i s t of the components of the EBF program and 'a br ief descr ipt ion of the funct ion of each.

Main Program:

WNGFLP - controls the f low of the calculat ion and handles some input and output dut ies

6

" "" . _. . . . . .

Subroutines:

WNGLAT - reads in wing input data, lays out the vortex lattice on the wing, and outputs wing geometric information

FLPIAT - reads in flap input data, lays out vortex lattice on the flaps including wing trailing legs which lie on the flaps., and outputs flap geometric information

INFMAT - calculates influence coefficient matrix FLVF - calculates influence function for a finite length vortex

filament

SIVF - calculates influence function for a semi-infinite length vortex filament

RHSCLC - calculates the right-hand side of the simultaneous equations for the vortex strengths

LINEQS - triangularizes the square influence coefficient matrix SOLVE - solves for the circulation strengths LOAD - calculates the forces on the bound and trailing vorticity

associated with each area element

FORCES - calculates and outputs the spanwise loading distributions and total forces and moments and pressure distribution on the complete configuration

VELSUM - computes wing-flap induced velocity field at a specified point JET - reads in initial jet parameters, outputs total jet configurations,

and calculates jet wake induced velocities at specified points

JEWL - calculates the modified centerline position due to total velocity field induced on the centerline

CORECT - corrects field point locations relative to vortex rings to avoid singularities

VRING - computes velocity components induced by a single, circular vortex ring at an arbitrary field point relative to the ring

ERING - computes velocity components induced by a single, elliptic vortex ring at an arbitrary field point relative to the ring

JINTEG - solves for the J-integrals required in elliptic vortex ring equations

ELI1 - computes the generalized elliptic integral of the first kind 7

Subroutines (Cont 'd) :

EL12 - computes the generalized elliptic integral of the second kind ELLIPS - obtains complete elliptic integrals of the first and second

kinds from tables

QUART - solves a quartic equation CUBIC - solves a cubic equation QUAD - solves a quadratic equation

SIMSON - does a Simpson's Rule integration

Program Usage

Limitations.- It should be remembered that the prediction method is made up of potential flow models which presume the flow to be attached to the lifting surfaces at all times. When applying the program to configurations at very high angles of attack or to configurations with very large flap deflections, the results will generally be too high as separation may exist on portions of the real model.

The program is a model for the wing and flaps only; therefore, when comparing predicted results with measured characteristics on a complete configuration, the force and moment contributions due to such items as the fuselage, nacelles, and leading-edge slat must be included as additional items. This is illustrated in the data comparisons in reference 1.

There are certain limitations and requirements in laying out the vortex-lattice arrangement on the lifting surfaces. These are discussed in detail in the input section of this manual, but several of the more important items are noted as follows. Since the current version of the vortex-lattice method bends the trailing legs of the wing horseshoe vortices around the flaps, in laying out the geometry care must be taken that a flap surface not lie above the wing surface. For the same reason, flap surfaces may not overlap.

The program has the capability of computing the induced velocity field at any specified field point, but the modeling of the wing and flaps with horseshoe vortex singularities can cause numerical problems and unrealistic answers if a field point lies too near a singularity. A general rule to follow when computing induced velocities is that the

8

f ie ld po in t should no t be c loser to a l i f t i ng su r f ace t han one half the width of the nearest horseshoe vortex. This also has an effect on the layout of the points def ining the je t center l ines s ince wing and f l a p induced veloci t ies are important i n the center l ine i terat ions. This d e t a i l is described when the preparation of j e t i npu t is discussed.

Run time.- Both the vor tex- la t t ice l i f t ing-sur face and the vortex r ing je t models can be time consuming i n a typical calculation; conse- quently, their combination into the EBF program crea tes a calculat ion procedure which can be very costly in terms of computer time. When the program i s used i n t h e i t e r a t i v e mode, the required calculation t ime increases near ly l inear ly with the number of i terat ions. Est imat ing the computation time required for a calculat ion is d i f f i c u l t because of the -7ariables involved. Size of t he vo r t ex l a t t i ce , number of' f l aps , number of Jets , length of the je ts , shape of the je ts , spacing of the vortex rmgs , and i t e r a t ions a l l he lp de t e rmine t he t o t a l r u n time for a calculat ion. A l i s t of typical execution t imes for different combina- t i ons of the above parameters is presented i n Table I.

The long execut ion t imes for the e l l ip t ic j e t cases a re due en t i r e ly to the additional complexity involved i n computing the induced ve loc i t ies from e l l i p t i c vo r t ex r i ngs . The e l l i p t i c j e t c a s e s r e q u i r e so much execution t ime that multiple i terations have been avoided i n the use of the program to da t e . There are some approximations t o t r i m the r u n time f o r e l l i p t i c j e t s which have been used by the authors. A n equivalent c i r c u l a r j e t which has the same area d i s t r ibu t ion as the des i red e l l ip t ic J e t can be run through several i terations to get the approximate posit ions of the center l ine. The e l l i p t i c j e t s can then be put along these center- l i nes , and the calculation continued for one or two addi t iona l i t e ra t ions . I n t h i s way, t h e e l l i p t i c j e t e f f e c t on t h e l i f t i n g s u r f a c e s can be obtained a t some savings i n total execution t ime.

Another method used t o minimize execution t i m e is t o run t h e f i r s t severa l i t e ra t ions wi th a minimum s ize l a t t i ce to de te rmine the approxi - m.ate posi t ion of the j e t center l ines . Then, t h e f u l l l a t t i c e can be input with the je ts in their approximate posi t ions and ' the solution carr ied out several more i t e r a t i o n s t o convergence.

9

DESCRIPTION OF INPUT

This section describes the preparation of input for the EBF computer

program. In the fol lowing sect ions, some detailed information regarding the layout of t he vo r t ex l a t t i ce and the spec i f ica t ion of the je t wake are presented. This is followed by a l i s t i n g of a l l i npu t va r i ab le s and their format and posi t ions i n the input deck. The l a s t t o p i c i n t h i s s ec t ion is a sample input deck i l l u s t r a t i n g a typ ica l EBF calculation.

Vortex-Lattice Arrangement

The vor tex- la t t ice method used i n the EBF program is an extended and modified version of the wing-flap program presented i n reference 2. For that reason, the wing-flap configuration considered herein i s much more general than that previously handled, and the specif icat ion of the geometry for the input deck requires more de ta i l than the input of re f - erence 2. The cha rac t e r i s t i c s of the configuration parameters are 1 is ted below.

Winq

Mean camber surface may have camber and t w i s t .

Leading-edge sweep angle need not be constant across semispan.

Trailing-edge sweep angle need not be constant across semispan.

Taper need not be l inear and there may be d i scont inui t ies i n the

loca l wing chords.

Any dihedral angle i s allowed but it must be constant over the semispan.

Thickness effects are neglected.

Tip chord must be paral le l to root chord.

Flaps

0 A maximum of ten f laps may be considered, but no more than three

f l aps may be behind any one wing chordwise row of panels.

0 Each f l a p may have camber and t w i s t .

0 Leading and t r a i l i n g edges must be s t ra ight and unbroken on each f lap surface.

10

Flaps (cont Id)

0 Flap chord must have l inear taper .

0 Thickness effects are neglected.

0 There may be s l o t s between the f laps, but the leading edge of each f l a p l ies in the p lane of the adjacent upstream l if t ing surface.

The vortex-lattice arrangement describing the wing and f l aps i s

general enough to p rovide good f l e x i b i l i t y i n d e s c r i b i n g t h e l i f t i n g surfaces. A maximum of t h i r t y (30) spanwise rows of vort ices may be used, and each l if t ing-surface component can have a maximum of ten (10) chordwise vortices. The area elements on each l i f t i ng su r f ace have a uniform chordwise length a t each spanwise station. I n the spanwise direction, the widths of the area elements may be varied to f i t the loading s i tuat ions; that is, in regions of large spanwise loading gradi- ents, the element widths may be reduced t o allow closer spacing and more detai led load predict ions. The convergence of the predicted resul ts as a function of l a t t i c e arrangement i s described i n Appendix A of re fer - ence 2. These resu l t s apply to the cur ren t program with the following exception. In reference 2 , the spanwise distribution of t h e l a t t i c e elements on the f l aps was chosen independent of t h e l a t t i c e on the wing. I n the current program, the def lect ion of the wing t ra i l ing vor tex l egs requires that the spanwise lat t ice elements on the f laps be direct ly aligned with the lat t ice elements on the wing.

The maximum l a t t i c e s i z e on the complete configuration is f ixed a t 250 i n the program. The elements may be dis t r ibuted i n any proportion over the wing and f l aps , and for the sake of economy, considerably less t h a n t h i s t o t a l number should be used fo r most calculat ions as i l l u s - t r a t ed by the run t imes in the t ab le i n the previous section of t h i s document. The following comments, based on the recommendations of Appendix A of reference 2 and the authors experience, are offered as an aid to select ing the proper vortex-lat t ice arrangement for a wing-flap configuration.

Spanwise d is t r ibu t ion" Convergence of gross aerodynamic forces and moments to w i th in 1 percent is obtained by using not less than fourteen equally spaced spanwise rows of vortices. I f an unequal spanwise spacing is required to create a locally dense region of v o r t i c i t y , t h e i n i t i a l spacing should be laid out approximately equal, with additional rows

11

added in the regions of i n t e re s t . The spanwise spacing can be adjusted small amounts t o meet some additional requirements without changing the gross loading properties. For example, it i s desirable that engine wake centerlines be posit ioned directly beneath a row of l a t t i c e element control points; therefore, small adjustments i n t h e l a t t i c e can be made t o meet this requirement. I t is a l so des i r ab le t ha t t he re be some sym- metry i n the widths of the vortex elements about the engine centerline s t a t ion . This can cause some unusual distributions of l a t t i ce w id ths a s i l l u s t r a t ed i n f igure 3 where a t y p i c a l l a t t i c e arrangement on the four-engine EBF model of references 3 and 4 i s i l l u s t r a t e d . I n t h i s case the number of spanwise vortices was l i m i t e d t o f i f t e e n t o minimize t h e t o t a l number of elements i n t h e l a t t i c e . I n t h i s pa r t i cu la r ca se , the only suggested modification i n the spanwise layout would be t o add two addi t ional narrow rows of vort ices , one inboard of the inboard je t and one outboard of the outboard jet and redistribute the outboard vor t ices near the t ip in to s l igh t ly more narrow rows.

Chordwise dis t r ibut ion.- Resul ts i n Appendix A of reference 2 i n d i -

ca te tha t four is the m i n i m u m number of chordwise vortices on the wing

f o r b e s t r e s u l t s and more than s ix vor t ices do not change the predicted loads appreciably. A l a rger number of chordwise vortices on the wing can be used i f a chordwise pressure distribution is the goal of the predictions.

The number of chordwise vortices on the f l aps i s somewhat a rb i t r a ry . A ru l e of thumb i s tha t the chord of the vortex element on t h e f l a p should not be greater than the chord of the wing elements. Generally, the chord of the flap elements w i l l be much smaller than the wing elements. If gross forces are the objective of the prediction, one or two chordwise vort ices per f lap are a l l that are needed. If pressure dis t r ibut ions are desired, there should be three to four chordwise vortices per f lap. The gross force w i l l change very l i t t l e w i t h addi t iona l f lap vor t ices .

A comment t h a t was made i n reference 2 i s also per t inent here . Care should be taken i n laying out vortices i n regions of wake impingement. Since interference of t h e j e t on t h e l i f t i n g s u r f a c e s i s " f e l t " o n l y a t the control points of the area elements, small vertical and/or l a t e r a l changes in t he wake centerline can cause unrealistic changes i n the wake induced loading i f the area e lements on the f lap are too large. This

1 2

is caused by the covering and uncovering of area elements whose cont ro l points f a l l near the boundary of t h e j e t . Resu l t s i nd ica t e t ha t i f a s u f f i c i e n t number of elements are used in the wake region of the wing and f l ap , t he element s i z e s w i l l be s u f f i c i e n t l y small so t h a t r e s u l t s w l l l not be unduly influenced by changes in wake locat ion.

The chordwise dis t r ibut ion of la t t ice e lements on t h e EBF model i n f igure 1 should be considered a m i n i m u m l a t t i c e . Flap 1 has b u t one row of vort ices , and f l a p s 2 and 3 have only two rows of vortices. This is adequate for force and moment ca l cu la t ions , bu t t he p re s su re d i s t r i - bu t ion resu l t s are not de ta i led enough f o r comparisons with data.

Jet Wake Spec i f ica t ion

The vortex r ing model used in the EBF program i s an extended version of t h e j e t wake program presented in reference 2. Whereas the o r ig ina l program considered only axisymmetric je ts with the center l ines posi t ioned a pr ior i , the p resent prograrri w i l l h and le e l l i p t i c c ros s - sec t ion j e t s and the cen ter l ines a re pos i t ioned by an i terat ive solut ion. This new method removes some of the tedious input preparation required by the previous program; however, t he new method requires careful layout of the Doints descr ibing the center l ine and of the r ings def in ing the j e t

boundary. The b e s t way t o i l l u s t r a t e t h e d e s c r i p t i o n o f a j e t model 1s t o go through a sample case f o r a t y p i c a l j e t . A vortex r ing model of the inboard j e t in re fe rences 3 and 4 i s developed as follows.

The f i r s t s t e p i s to locate the geometr ic posi t ion of the ac tua l enqine. From f igure 2 of reference 4 , the inlet of the inboard engine on t h e l e f t wing panel i s a t X = 1.43 m(4.68 f t ) , Y = -1.48 m(-4.85 f t ) , and Z = 0.42 m(1.38 f t ) i n t h e wing coordinate system with origin at the wing leading edge a t t he a i rp l ane cen te r l ine . The engine exi t i s a t X = -0.40m !-1.30 f t ) , Y = -1.48 m(-4.85 f t ) , and Z = 0.42 m(1.38 f t ) . As noted i n reference 2 , the j e t model should be extended upstream of the actual engine e x i t a distance of a minimum of two i n i t i a l r a d i i t o g i v e t h e model a chance t o deve lop the ex i t ve loc i ty p rof i le . Thus, t h e j e t model c o u l d s t a r t a t X = 1.43 m'(4.68 f t ) and go t o X t -0.40 m(-1.30 f t ) w i t h a constant radius. This i n i t i a l p o r t i o n o f t h e j e t i s longer khan necessary; therefore, i n t he interest of conserving computation t i m e , the j e t i s assumed t o s t a r t a t X = 0.14 m(0.45 f t ) , Y = -1.48 m(-4.85 f t) , 2 = 0.42 m(1.38 f t ) and have an i n i t i a l , cons tan t rad ius sec t ion wi th l ength o f 0.91 m(3.0 f t ) .

The in i t i a l c ros s - sec t iona l a r ea o f t he j e t i s assumed to equa l t he sum of t h e f a n e x i t area and the core engine exi t area. From f igure 4

13

I

of reference 4, the fan and core engine exit areas are 0.159 and 0.050 sqm (1.71 and 0.54 sq f t ) , r e s p e c t i v e l y . Thus, t h e i n i t i a l j e t a r e a i s 0.209sqa (2.25 sq ft) .which i s assume& to be modeled by an equivalent c i rcular cross section with radius of 0.258 meters (0.845 f t ) .

The next s tep is t o d e t d r m i n e t h e i n i t i a l e x i t v e l o c i t y i n t h e j e t model so t h a t we may specify the vortex cylinder strength. If the average velocity i n t h e e x i t is known from measurement, the vortex strength can be determined directly from equation (28) of reference 1;

t h a t is ,

V .

v v L 3 - 1 (1)

where Vj/V i t h e r a t i o of t he j e t ex i t ve loc i ty t o t he f r ee - s t r eam velocity and y/V i s the strength of a constant radius, semi-infinite length vortex cylinder which represents a j e t w i th t he co r rec t i n i t i a l momentum and velocity. Since the necessary velocity is not usually avai lable , an approximate value i s calculated using equation (29) from the same reference.

T o ge t V, from this equat ion, the engine thrust the densi ty ra t io , p/p,, i n the j e t a re requi red .

1 ( 2 )

coef f ic ien t , CT, and The dens i ty ra t io ,

def ined as the ra t io of the ambient a i r dens i ty t o t he j e t exhaus t density, can be estimated from the exhaust temperature. I n equation ( 2 ) ,

S i s the reference area used i n defining CT, and A, is t h e i n i t i a l j e t a r ea which i s calculated as the sum of the fan exi t area and the core engine exit area. Assuming a dens i ty ra t io o f 2 .6 , which i s reasonable for a tailpipe temperature of 538°C(10000F), and choosing an engine thrust coef f ic ien t of 1.0, equation ( 2 ) produces V. /V E 11.1. From e q u a t i o n ( l ) , the vortex cyl inder s t rength def ining the je t model vo r t i c i ty t o be i npu t

into the program i s y/V 10.1.

7

A t this point the expansion rate and the shape of t h e j e t must be chosen. If some empirical knowledge of t h e j e t t o b e modeled or of a t y p i c a l j e t i s avai lable , it should be included i n the specif icat ions

I n order to get the best physical model possible. Before a j e t i s chosen, a decision must be made as to the cross-sectional shape o f the

14

selected. Based on figure 10of reference 1, which was obtained from flaw field measurements, it is assumed that the jet cross section is a 2:l ellipse at a point just aft of the last flap. These same measure- ments are not used to determine the expansion rate because the measured jet velocity ratio is much lower than we are considering. If we assume that an elliptic jet expands at about the same rate as an axisymmetric jet, the rate of expansion can be obtained from figure 8 of reference 1. At approximately 12 radii downstream of the jet exit, the local radius is approximately 2.2 times the initial radius; therefore, the jet cross- sectkonal area has increased to approximately 4.8 times its initial area. Using this value and the assumed 2:l axis ratio, the jet is completely described at this one point aft of the flaps.

Assuming an axisymmetric jet with linear expansion between the engine exit and this point aft of the flap provides an area distribution for the jet. If we further assume that the jet remains axisymmetric until it reaches the flap surfaces and then, through linear variation of the length of the vortex ring axes, approaches the 2:l ellipse, we obtain the solid curve for x 12 ft. shown in figure 4. The circular jet with the same area distribution is shown'dashed in this figure. Both the circular and elliptic jets in figure 4 have nearly the same mass and momentum distributions along the jets. Beyond x, = 12 ft, the jet is downstream of the flaps, and its shape has less effect on the induced velocity field. Two options are open for this region of the jet. The elliptic shape can bemaintained and simply extrapolated to the end of the jet, or the shape can be changed back to circular and extraplated to the end. In the interest of saving computer time, the latter choice was made and the elliptic jet was returned to a circular shape in a short distance. This last region of the jet is assumed to have a lower rate Of expansion as shown in figure 4. The following table illustrates the parameters of the jet in the jet coordinate system.

j

15

xi m (ft)

0 ( 0 )

0.91 (3.0) 1.98 (6.5) 2.29 (7.5) 2.59 .(8.5) 2.74 (9.0) 2.90 (9.5) 3.05 (10.0) 3.35 (11.0) 3.66 (12.0) 3.96 (13.0) 4.57 (15.0)

6.10(20.0)

Equivalent Radius, R rn ( f t )

0.258 (0.845) 0.258 (0;845) 0.375 (1.23) 0.415 (1.36) 0 -448 (1 -47) 0.463 (1.52) 0.482 (1.58) 0.500 (1.64) 0.533 0.567 0.576 0.597 0.634

1.75) 1.86) 1.89) 1.96) 2.08)

k e a Ratic A h o

1.00

1.00 2.12

2.55

3.00 3.25 3.48 3.77 4.30 4.83 5.13 5.38 6.06

E l l i p t i

m - ( f t ) a

0.258 (0.845 0.258 (0.845 0.375(1.23) 0.451 (1.48) 0.531(1.74) 0.570 (1.87)

0.607 (1.99) 0.646 ( 2 . 1 2 ) 0.725 (2.38) 0.802 (2.63) 0.735 (2.41) 0.597(1.96) 0.634 (2.08)

I .c Axes

m - ( f t ) b

0.258 (0.845) 0.258 (0.845) 0.375 (1.23) 0.375(1.23) 0.375 (1.23) 0.378 (1.24) 0.381(1.25) 0.387(1.27) 0.393(1.29) 0.399(1.31) 0.463 (1.52) 0.597 (1.96) 0.634 (2.08)

T -

a/b

1.0 1.0

1.0 1.20 1.41 1.51 1.59

1.67 1.84 2.0

1.59

1.0 1.0

The above discussion includes the development of both an axisym- metric and an . e l l i p t i c j e t model. E i ther of t he je ts i n f i g u r e 4 or the above table could be used t o r e p r e s e n t t h e momentum i n the wake, and the only d i f fe rences in the predic ted in te r fe rence e f fec ts would be caused by the different port ions of the wing influenced by t w o jets. The e l l i p t i c j e t would tend t o spread the load out in a spanwise d i r ec t ion while the c i r c u l a r j e t would concentrate the in te r fe rence loading in to narrow regions on t h e l i f t i n g s u r f a c e s .

A new r u l e of thumb has been developed t o determine the t o t a l length of the j e t . In reference 2 , the length was spec i f ied on t h e basis of comparison with semi-infinite length vortex cylinder results. This method produced je ts with lengths the order of 150 %. The computer time required t o c .a lculate the induced veloci ty f ie ld from a j e t o f t h i s length i s excessive and not warranted on the basis of the small increase in accuracy achieved over shorter je ts . In us ing the cur ren t program, it is suggested that the j e t extend downstream a dis tance behind the l a s t flap equal t o the t o t a l chord of the wing and f l a p s combined. The user should investigate the e f f ec t o f j e t length on a particular configu- r a t ion by running one case with an extended j e t and comparing predicted results. Generally, je ts longer than suggested above are not required unless ve loc i ty f ie lds a long d i s t ance a f t of t he wing and flaps are required. I f this is the case , the j e t should be lengthened so tha t

16

it extends approximately one wing chord beyond t h e a x i a l s t a t i o n a t

which f i e l d points are desired.

The next item to be considered once the j e t l ength and shape are determined is the points on the cen ter l ine used to de f ine t he j e t . Linear interpolation between specified points i n t he t ab l e of j e t param-

e t e r s is used for intermediate points along the jet . Thus, tabular points on the cen ter l ine a re needed at the beginning, the end, and a t any p o i n t a t which there is a change i n the expansion rate of the boundary. For example, in f igure 4, the m i n i m u m required points i n t h e j e t t a b l e would be a t x, = 0, 3 , 6.5, 1 2 , 15, and 20. This small nurriber of points i s adequate for a descr ipt ion of t h e j e t i f it d i d not move during the calculat ion; but s ince the program i t e r a t e s on the centerline shape, additional points should be added to t he t ab l e . The procedure for laying out the appropriate number and location of points on the cen ter l ine should be carried out i n the following manner.

A sketch of the wing and f l ap su r f aces a t t he spanwise s t a t i o n corresponding to an engine location i s shown i n f igure 5. The j e t cen ter l ine , assumed s t r a i g h t , i s a l so shown i n i t s correct posit ion r e l a t ive t o t he wing and f laps . Keeping i n mind t h a t more points on the center l ine are required i n the region of grea tes t movement, the points chosen to descr ibe the cen ter l ine a re shown a s c i r c l e s i n the f igure. The points should be dense along the portion of the centerline near the flaps except i n the area immediately adjacent to the f lap (xj 2 10.7). Points are omitted from this area to avoid the numerical problems associ- ated with being too near a horseshoe vortex. Points can be spread f a r t h e r a p a r t a f t of the f laps s ince the induced ve loc i t i e s a r e reduced and the r e l a t ive motion of these center l ine points i s less than other points upstream. I n general , too many points are bet ter than too few except in troublesome regions near the lifting surfaces.

The l a s t c r i t i ca l pa rame te r t o be spec i f i ed is the spacing between the vortex r ings. Ideally, the closer the r ings, the more accurate the resul ts ; but the c loser the spacing, the more r ings requi red to make up t h e j e t model and the longer the computer time needed t o compute an induced velocity f ield. A compromise number for the r ing spacing i s a distance equal to approximately 0.1 Ro. This i s not a f i r m number, but it is generally a good estimate. The program has an opt ion bui l t in to it that al lows the spacing t o vary along the j e t through use of the var iable DSFACT. This is simply a multiplying factor used t o s c a l e up

.17

t h e r i n g spacing t o two or t h r e e times t h e i n i t i a l value. This option should never be used i n t h e v i c i n i t y o f the wing and f l a p s as t h e accuracy of the induced veloci ty f ie ld a t t he con t ro l po in t s w i l l be reduced. It is pe rmis s ib l e t o increase the spacing downstream of the las t flap. The use o f th i s sca l ing fac tor is i l l u s t r a t e d i n t h e sample input decks.

Input variables

The purpose of t h i s s e c t i o n is to descr ibe the var iab les requi red f o r i n p u t t o t h e EBF program. An input form i s presented in f igure 6; and for each i t e m of input data shown in the f igure , the fo l lowing information i s given. The format for each card and t h e program var iab le names are shown f i r s t . The card column f i e l d s i n t o which the da t a are t o be punched are a l s o shown. Within each block representing the card columns is the FORTRAN format type. D a t a punched i n I format are r i g h t j u s t i f i e d i n t h e f i e l d s , and da ta punched i n F format can be punched anywhere i n t h e f i e l d and must contain a decimal point.

Note t h a t a l l length parameters in the input l i s t have dimensions; therefore , special care must be taken tha t a l l lengths and areas are inpu t i n a cons is ten t se t of units.

I t e m number 1 is an index NHEAD which ind ica tes how many cards of information are t o f o l l o w i n i t e m nuniber 2. The value of NHEAD must be

one or g rea te r .

Item number 2 is a s e t of NHEAD cards conta in ing ho l le r i th in for - mation identifying the run and may start and end anywhere on the card. The cards are reproduced in the output just as they are read in.

I t e m number 3 cons is t s o f one card and contains the fol lowing information:

SREF

REFL

reference area used i n forming aerodynamic coe f f i c i en t s

reference length used in forming aerodynamic moment coe f f i c i en t s

XM, ZM x and Z coordinates of point about which p i tch ing moment is calculated; wing coordinate system and pos i t i ve d i r ec t ions a r e shown i n f i g u r e 3 and the following sketch

TOL to le ranceon CN used for convergence cri terion; a typical value i s 0.05

18

DTH l i m i t , in degrees, on t h e maximum def lec t ion angle of the j e t cen te r l ine ; t h i s va lue is general ly 70-85 percent of the maximum f l a p def lect ion angle and is always input as a negative nurriber

I t e m number 4 spec i f ies the va lue o f NWREG, the number of wing regions. The value of NWREG must be one o r g rea t e r . The purpose of d iv id ing the wing into regions i s to hand le d i scon t inu i t i e s i n l oca l chord length. Region 1 must always extend from Y = 0 t o the t i p . The sequence and posit ion cf other regions is a rb i t r a ry . A wing with three regions is shown in the fol lowing sketch.

t " * Y

CRW

"-.- - " - " #3 C IN - #2 " C IN

I P H I D

z -Y p" SSPAN -+

7 Moment center

Z

19

Item nuniber 5 conta ins th ree quant i t ies which a r e a l s o shown i n the previous sketch. They are:

CRW root chord of region 1, posi t ive quant i ty

SS PAN wing semispan, positive quantity

PH I D wing dihedral angle, degrees; posit ive dihedral i s shown i n the sketch

Items 6, 7 , and 8 are data descr ibing wing region number 1. Data input for this region determine the spanwise dis t r ibut ion of vor t ices f o r a l l wing regions and a l l f l a p s . The present program requires that. the same spanwise d i s t r i b u t i o n e x i s t on a l l s u r f a c e s .

Item number 6 contains f ive indices . They are:

NCW number of chordwise vortices on wing region 1, 1 <_ NCW < 10

MSW number of spanwise vortices on l e f t wing panel, 1 2 MSW < 30

NTCW

N U N 1

t w i s t and/or camber? NTCW = 0, no NTCW = 1, yes

i f wing has no t w i s t and the camber d i s t r ibu t ion is s i m i l a r a t a l l spanwise s t a t ions , NUN1 = 1; f o r a l l other cases NUN1 = 0 (omit i f NTCW = 0)

NPRESW is the wing pressure d i s t r ibu t ion to be ca lcu la ted and pr inted? NPRESW = 0 , no

NPRESW = 1, yes

The m i n i m u m number of spanwise horseshoe vortices is determined by the wing-flap combination geometry. The program requires that vor tex t r a i l i ng l egs l i e a t t he fo l lowing l oca t ions :

(a) the root chord and t i p chord (b) the side edges of a l l wing regions (c ) the s ide edges o f a l l f l aps (d) points where there are breaks i n leading-edge or trailing-edge

sweep

Item number 7 i s a s e t of MSW+l cards which specify the following:

Y coordinate of the Ith t r a i l i n g l e g on t h e l e f t wing panel; Y is a negative number on t h e l e f t wing panel, but posit ive values may be input and program w i l l correct the s ign [ ~ ( l ) = O.O,y(~sw+ 1) = -SSPAN]

PSIWLE ( I) leading-edge sweep of wing sec t ion t o t he r i gh t of the Ith t ra i l ing l eg , degrees ; pos i t ive swept back (measured i n wing planform plane)

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PS IWTE ( I) t r a i l i n -edge sweep of wing sec t ion to the r igh t of the Izh t ra i l ing leg, degrees; posi t ive swept back (measured i n wing planform plane)

NFSEG ( I ) number of flaps behind wing sec t ion t o t he r i gh t of the Ith t r a i l i n g l e g

When I = 1 , Y (I) = 0 and the other three quantit ies are omitted.

I f NTCW = 1 in i tem number 6, item number 8 i s included i n the input data deck. These data specify the t w i s t and/or camber d i s t r ibu t ion of wing region number 1 i n terms of the tangent of the local angle of a t tack of the camberline for a root chord angle of a t tack of zero degrees. The input data are:

ALPHAL (J) tan ad of the region 1 camberline a t the vor tex- l a t t i ce con t ro l po in t s . I f N U N 1 = 1, only data for the chordwise row adjacent to the root chord are input. The f i r s t v a l u e is for the control point nearest the leading edge. If NUN1 = 0, d a t a f o r a l l chordwise rows must be input s tar t ing nearest the root chord and working outboard. Data f o r each row s t a r t on a new card (omit i f NTCW = 0) .

The vor t ex - l a t t i ce con t ro l po in t s a r e a t t he midspan of the three-quarter chordline of each elemental panel laid out by NCW, MSW, and t h e Y ( 1 ) ' s of items 6 and 7.

-~ Item - numbers 9 , 10 , and 11 are input data for the other wing regions. If NWREG, item number 4, is one, items 9, 10, and 11 are omitted. If

NWREG > 1, these items are repeated i n sequence for regions 2 through NWREG .

Item number 9 contains two indices which loca te t h i s wing region spanwise r e l a t i v e t o r e g i o n 1. They specify the subscripts of the elements i n the Y ( I ) array, input i n item 7 , associated with inboard and outboard side edges of this region.

I I N inboard side edge is a t Y ( I I N )

IOUT outboard side edge is a t Y (IOTJT)

Item number 10 contains f ive quantit ies. They are:

NCW

NTCW

number of chordwise vortices in this region, 1 5 NCW 2 10

t w i s t and/or camber f o r t h i s wing region? NTCW = 0, no NTCW = 1, yes

2 1

NUNI

C I N

i f t h i s wing region has no t w i s t and the camber d i s t r ibu t ion is s i m i l a r a t a l l spanwise s t a t ions , NUNI = 1; f o r a l l o t h e r c a s e s N U N I = 0 (omit i f NTCW = 0 for th i s reg ion)

inboard side-edge chord (see sketch), positive quantity

TESWP sweep angle of the t ra i l ing edge of th i s reg ion , degrees

The vor t ices a re l a id ou t using the value of NCW for th i s reg ion and the portion of the Y (I) array beginning w i t h Y ( I I N ) and ending w i t h

Y ( IOUT) . Item nuniber 11 is included i n the input data deck if NTCW = 1 i n item

10. These data specify the t w i s t and/or camber d i s t r ibu t ion fo r t h i s

wing region. These data are prepared i n the same manner as described under item number 8, the similar information for wing region 1.

Item number 1 2 specif ies the number of f lap regions, NFREG. For a

wing alone, NFREG = 0 and items 13 through 16 are not included i n the input data deck. A f lap region i s a p a r t i c u l a r f l a p arrangement behind some spanwise region of the wing. The program w i l l handle a total of ten f laps .

Item number 13 contains four items of input which are repeated i n sequence NFREG times.

N I N R E G number of f laps i n this region, 1 < N I N ~ G < 3

I I N inboard side edge l i e s a t Y ( I 1 N ) of item 7

IOUT outboard side edge l i e s a t Y ( IOUT) of item 7

The next three items of input data are repeated i n sequence N I N R E G

times beginning with the flap nearest the wing t r a i l i n g edge and moving rearward.

Item number 14 contains four indices. They are:

NCF number of chordwise vortices on t h i s f lap, 1 NCF < 10

NTCF

N U N I

t w i s t and/or camber for t h i s f l a p ? NTCF = 0, no NTCF = 1, yes

if t h i s f lap has no t w i s t and the camber d i s t r ibu t ion i s s i m i l a r a t a l l spanwise s t a t ions , N U N I = 1; for a l l o ther cases NUNI = 0 (omit i f NTCF = 0 f o r t h i s f l ap )

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NPRESF i s a pressure dis t r ibut ion to be calculated and p r in t ed fo r t h i s f l ap? NPRESF = 0 , no NPFUSF = 1, yes

The vort ices are la id out using the value Of NCF f o r t h i s f l a p and the portion of the Y ( I ) array input as i tem 7 beginning with Y ( I I N ) and

ending with Y(I0UT). I I N and IOUT were input in item 13.

I t e m number 1 5 contains data which loca te th i s f lap wi th respec t to the sur face ahead of it, specify the inboard and outboard edge chords, and give the streamwise deflection angle.

GAP I N the dis tance between the leading edge of t h i s f l a p and t h e t r a i l i n g edge of the preceding surface, measured i n the plane of the preceding surface at the inboard side of t he f l ap

CFU? I N inboard side-edge chord of this f l a p

GAPOUT the gap distance at the outboard edge of t he f l ap

CRFOUT outboard side edge of t h i s f l a p

DELXZ the streamwise deflection angle measured r e l a t i v e t o t h e wing root chord direction, degrees

A streamwise plane containing the inboard edge of a double-slotted f lap configuration i s shown i n the following sketch. The leading edge of each f l a p l i e s i n the plane of the preceding surface. A l l quan t i t i e s i n item 1 5 are input as posit ive values.

WING -1

- It :em number 16 i s included i n the input data deck i f NTCF = 1 i n item 14. These data specify the t w i s t and/or camber d i s t r ibu t ion of t h i s f l a p . They are prepared in the same manner as described under item number 8 fo r t he wing except that the t w i s t and/or camber angles

23

are measured relat ive to the angle of the f lap inboard s ide-edge chord. These angles are a l l measured i n a streamwise plane.

I t e m number 17 contains one index.

NRHS t h e number of successive cases t o be t r e a t e d f o r this wing-flap combination, NRHS 2 1

The successive cases permitted by NRHS are those which a f fec t on ly the r ight-hand side of the equation set fo r t he c i r cu la t ion s t r eng ths

(eqs. (14) and (15) i n r e f . 1). Thus, the wing-flap geometry must remain unchanged in successive cases . Changes are permi t ted in items 18 through 23; therefore , the successive cases may involve different angles of at tack and/or d i f f e r e n t j e t wakes.

The l a s t s i x items of input data are repeated in sequence NRHS times.

Item number 18 contains seven quantit ies which are:

ALFA

K E I

NFPTS

KJET

MJETCL

N J E T V

wing root chord angle of a t t a c k r e l a t i v e t o t h e free stream, degrees

index indicating whether or not an externally induced ve loc i ty da ta se t is t o be inpu t v i a t ape 4 K E I = 0, no K E I = 1, yes; data set is read from TAPE4 i n a

3E13.6 format

number o f po in t s i n v i c in i ty of wing-flap combination a t which wing-flap induced velocit ies are t o be ca lcu la ted , NFPTS 2 0

index indicating type of in te r fe rence ca lcu la t ion K J E T = 0 , no j e t calculation, externally induced

v e l o c i t i e s may be r e a d i n i f K E I = 1

t i m e , no i t e r a t i o n

u n t i l convergence is a t ta ined , which ever o c c u r s f i r s t

K J E T = 1, j e t interference calculat , ion made one

KJET >_ 2, i t e r a t i o n on j e t cen te r l ine KJET times o r

index used t o r e s t r i c t v e r t i c a l motion of j e t center- l i n e d u r i n g i t e r a t i o n MJETCL = 0, no r e s t r i c t ion o f cen te r l ine motion MJETCL = 1, center l ine res t ra ined from moving

v e r t i c a l l y upwards toward wing o r f l a p s

index indicat ing 'whether or not j e t induced v e l o c i t i e s are t o be included in external f low f ie ld calculat ion when NFPTS > 0 NJEW = 0 , j e t induced velocit ies not included NJETV = 1, j e t induced velocit ies included in f low

f i e l d c a l c u l a t i o n

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NJETCL index used t o r e s t r i c t h o r i z o n t a l motion of j e t cen te r l ines du r ing i t e r a t ion NJETCL = 0, j e t cen te r l ine is r e s t r i c t e d from moving

NJETCL = 1, j e t f r e e t o move l a t e r a l l y under influence l a t e r a l l y o u t of o r ig ina l X-z plane

of wing-flap induced velocity field

The indices K E I and MJETCL are included for diagnostic purposes; and for typical usage of t h e program, both indices should be zero. K E I

i s used t o i n p u t an in t e r f e rence ve loc i ty f i e ld induced by some source of dis turbance other than a j e t wake. It cannot be used along with a j e t wake; thus, i f KEI = 1, KJET = 0. The index MJETCL = 1 i s ava i lab le t o restrict t h e v e r t i c a l motion of t he je t c e n t e r l i n e s i n c e r t a i n special cases. On occasion, large induced upwash veloci t ies beneath the wing have forced the je ts upward and caused unusually large j e t i n t e r f e r e n c e e f f e c t s on t h e wing. The index MJETCL is provided so t h a t the e f f e c t of t h i s upward j e t motion can be invest igated by the user .

The l a s t index, NJETCL, i s provided t o r e s t r i c t t h e l a t e r a l motion o f t he j e t c en te r l ines . Under a swept wing-flap configuration, large induced spanwise velocities can move t h e j e t cen ter l ines ou t of the i r

or ig ina l p lanes . This can cause d i f f icu l t ies in the in te r fe rence ca lcu- l a t i o n i f t he spanwise d i s t r i b u t i o n of vo r t i ce s is spec i f ied in a symmetric pa t te rn about the in i t ia l cen ter l ine pos i t ions . Typica l EBF measured span-load distributions ( ref . 4) indicate very little l a t e r a l motion of

t h e wake c e n t e r l i n e s ; t h e r e f o r e , t h e o p t i o n t o r e s t r i c t t h i s movement is provided. It is suggested that NJETCL = 0 be used f o r b e s t r e s u l t s .

Items 19 through 22 i d e n t i f y t h e i n i t i a l j e t wakes, and they are

omitted i f KJET = 0.

I t e m number 19 is a s ing le card conta in ing s ix ind ices per ta in ing t o t h e j e t ca lcu la t ion . They are:

NHEAD number of heading cards t o i d e n t i f y t h e j e t model, NHEAD 2 1

NJET number of j e t wakes ; N J E T = 1 fo r one j e t w a k e , etc.

NCYL

NNUM

number o f en t r i e s i n t ab l e de f in ing j e t parameters, 2 < NCYL < 25

index control l ing calculat ion of J- integrals required by e l l i p t i c v o r t e x r i n g s NNUM = 0 , i n t eg ra l s ca l cu la t ed ana ly t i ca l ly NNUM = 1, integrals calculated numerical ly

25

NPRINT index .indicating whether or not optional output from t h e j e t program i s required

NPRINT = 0, induced Velocities a t wing control points output from subroutine JET

NPRINT = 1, i n d i v i d u a l j e t v e l o c i t i e s a t each control point output from subroutine JET

NPRINT = -1, minimuin Output

NCRCT index indicating whether or not f ield point locations are corrected with respect to vortex r ing locat ions NCRCT = 0, correct ions made NCRCT = 1, corrections not made ( t o be used for

diagnostic purposes only) The l a s t t h ree i nd ices i n item 19 are provided for diagnostic

purposes only. For general program usage, these indices should be NNUM = 0, NPRINT = -1, and NCRCT = 0. NNUM should be nonzero only if

d i f f i c u l t i e s a r i s e i n t h e c a l c u l a t i o n of e l l i p t i c j e t s . T h i s is discussed i n a la te r sec t ion descr ib ing e r ror messages. When the index NPRINT is equal t o z e r o , j e t induced ve loc i t ies a t the cont ro l po in ts are output as they are computed. This is a duplication of output. If the user requires information regarding the contribution of each indivi- d u a l j e t t o t h e t o t a l induced v e l o c i t y a t a control point , NPRINT = 1

w i l l cause this output to be pr inted. NCRCT i s an index used during program development to i nves t iga t e a s i t u a t i o n i n which a control point was located very near the edge of a vortex r ing. Unreal is t ical ly large ve loc i t i e s were induced u n t i l the re la t ive pos i t ions between the control point and the vortex zings were corrected. This correction places the vortex r ings on e i the r s ide of the control point equidis tant from the point.

Item number 20 is a s e t of NHEAD cards (from item 19) containing hol le r i th in format ion ident i fy ing the j e t . The information may s t a r t and end anywhere on the card and the information is reproduced i n the output j u s t as it i s read i n .

The following two items are repeated in sequence NJET times.

Item number 2 1 cons is t s of one card which contains the following j e t spec i f i ca t i ons :

GAMVJ (J) the s t rength of the vortex cylinder representing the ex i t ve loc i ty of t h e J ' t h j e t under the l e f t wing panel

DS (J) the r ing spacing of the vortex r ings i n t h e J ' t h j e t ; a typical value i s 0 .1 F+, where Ro i s the i n i t i a l r a d i u s of a c i r c u l a r j e t ; i f an e l l i p t i c j e t i s t o be used, the appropriate spacing i s 0.1 bo

26

I

XQ ,YQ, ZQ the coordinates , in the wing system, of the o r ig in of t h e j e t model (YQ < 0)

Item number 22 cons is t s of NCYL cards containing the following information.

XCLR ( J, N) YCLR ( J,N) ZCLR ( J,N)

t he N ' th s e t of coordinates specifying the centerline of t h e J ' t h j e t i n t h e je t coordinate system(fig.8(b))

AJET ( J , N ) t he semi-major axis of ' the vor tex r ing a t the N ' th point on the cen ter l ine of t h e J ' t h j e t

BJET ( J , N ) t he semi-minor a x i s a t t h e sartie point

THETA(J,N) the s lope of t he cen te r l ine i n deg rees a t t he po in t being considered; THETA is negative when the center- l i n e is bent down to pass beneath the f lap

DSFACT(J,N) scale factor for the spacing between the vortex r ings downstream of, the N'th point; i n region of wing and flaps, the values should be 1.0; a f t of t h e l a s t f lap, the values can be greater than 1.0

When a c i r c u l a r j e t CLOSS section i s being described, AJET = BJET; and when e l l ip t ic c ross sec t ions a re be ing descr ibed , AJET > BJET.

Item number 23 i s a s e t of NFPTS cards containing the X , Y , Z coordi- nates i n the wing system, a t which the wing-flap induced velocit ies are to be calculated. This term i s omitted i f NFPTS = 0.

Upon completion of the calculat ions specif ied by the above input deck, the program returns to the beginning. Additional input decks, s tar t ing with i tem 1, may be stacked one af ter another .

Sample Cases

I n t h i s s ec t ion , two sample cases are described t o i l l u s t r a t e t h e input preparation and the use of the program. The f i rs t sample case i s a complete calculative example involving a four-engine EBF configu- ra t ion wi th e l l ip t ic c ross -sec t ion je t s . The second sample case i s an l l l u s t r a t i v e example of a wing with multiple regions and multiple f laps and a single engine. Its purpose is to p rovide a check run for the program.

The EBF configuration chosen for the first sample case is the four- engine model from references 3 and 4. The vortex-lat t ice layout on the wing and f laps is discussed i n the Vortex Lattice Arrangement sect ion and the ac tua l l a t t i ce arrangement i s shown i n f igure 3. The f l a p

27

deflect ions chosen for this case correspond to the landing configurat ion, dfl/bf,/6f, = 15O/35O/55'. This par t icular configurat ion and l a t t i c e arrangement are used extensively for the comparisons with data i n reference 1

The j e t wake model chosen f o r t h i s sample case i s t h e e l l i p t i c c r o s s - sect ion example discussed i n t h e J e t Wake Specif icat ion sect ion and shown i n f igure 4. The i n i t i a l j e t c e n t e r l i n e i s one which resu l ted from three i te ra t ions us ing the c i rcu lar c ross -sec t ion je t a l so shown i n f igure 4. The calculat ion is s e t up t o run two i t e r a t i o n s (KJET = 2) because of the large execution time required by e l l i p t i c j e t s . The to ta l t ime required for two i terat ions, wi th the input deck s e t up as shown i n f igure 7 ( a ) , is approximately 600 seconds on the CDC 6600. I f the c i r cu la r j e t r ad ius d i s t r ibu t ion shown in f i gu re 4 is subs t i tu ted for t h e e l l i p t i c j e t a x e s , t h e same run requires approximately 200 seconds.

A second sample input deck is i l l u s t r a t ed i n f i gu re 7 (b ) . Th i s input deck, t o b e used a s a check r u n fo r t he program, descr ibes the hypothetical EBF configuration shown i n f igure 8. The wing shown i n f i g u r e 8 ( a ) , i s modeled as two reg ions for i l lus t ra t ive purposes , bu t wing region 2 could j u s t as eas i ly be modeled as a f lap surface with zero gap and zero deflection. Double-slotted f laps deflected 20° and 40° and a s ingle , unslot ted f lap def lected l o o make up the two regions of the trail ing-edge f lap system. A m i n i m u m l a t t i c e i s specif ied on the l i f t ing sur faces to keep the ca lcu la t ion shor t . Wing region 1 is modeled by a 7 x 2 l a t t i c e and region 2 is modeledby a 2 x 1 l a t t i c e . Flaps 1 and 2 have three spanwise rows of vort ices due t o t h e i r p o s i t i o n behind the wing. One chordwise row of vor t ices i s placed on f l a p 1 and two chordwise rows on f l a p 2. Flap 3 i s represented by a s ingle vortex-lattice element.

A s ing le c i r cu la r j e t wake 'wi th i n i t i a l j e t ve loc i ty f i ve t imes f r ee stream (C 0.5) i s p l aced a t Y = -11. Since this case is only a check r u n for the program, t h e j e t is not extended downstream of t h e l a s t f l a p a s f a r a s is normally recommended. The expansion rate i s l inear as the rad ius increases to two and one-half times i ts i n i t i a l v a l u e between xj = 3 and 18. A sketch of the jet and i t s pos i t i on r e l a t ive t o t he wing and f l a p i s presented i n f igure 8 (b) . The ring spacing is s e t a t 0.1 and it is cons tan t un t i l xj = 1 5 where it is doubled fo r t he remainder of the je t l ength . Assuming a turning eff ic iency of 75 percent, the l i m i t on the turning angle of t h e j e t c e n t e r l i n e is s e t a t -30'.

FL

28

Some incidental features of t h i s sample ca lcu la t ion a re the following. Two i te ra t ions a re spec i f ied ( K J E T = 2 ) , and a f t e r t h e l a s t i t e ra t ion , the induced ve loc i ty f ie ld , inc luding the j e t induced veloci- t i e s (NJETV = 1) , i s ca lcu la ted a t four f ie ld po in ts (NFPTS = 4) . The j e t is f r e e t o move v e r t i c a l l y (MJETCL = 0) and l a t e r a l l y (NJETCL = 1) under the influence of the veloci ty f ie ld beneath the wing and f laps . Pressure dis t r ibut ions are computed on t h e l e f t wing panel, f lap 2 i n region 1, and f l a p 1 i n region 2. The output corresponding to this input deck is presented i n the next section.

DESCRIPTION OF OUTPUT

This section describes the output from the EBF- program. The contents of a t yp ica l s e t of output from one of the previously described sample cases is discussed. This i s followed by a descr ipt ion of some of the e r ro r messages which may be output during execution of the program.

Sample Case

The output generated during the execution of the sample case shown i n f igure 8 (b) i s presented i n f igure 9. Each page of output i s described as follows.

The f i rs t page of output, shown as f i gu re 9 (a ) , i s headed by the program t i t l e "EBF AERODYNAMIC PREDICTION PROGRAM, I' followed by the ident i f icat ion information on the several cards a t the f ront of the input deck. This is followed by the reference quantit ies consisting of the reference area and length and the center of moment location. Next on t h e f i r s t page i s the wing input data. A l l of the input describing the wing geometry and l a t t i c e arrangement i s included i n th i s sec t ion .

Output page 2 i n f igure 9(b) contains a l l the input data descr ibing the f laps including the geometry and the la t t ice arrangement . A l s o

printed on t h i s page are the coordinates of the four corners of each f l a p i n a coordinate system fixed i n t he f l ap w i th t he o r ig in a t t he leading edge of the inboard chord of the f lap . The purpose of these coordinates is two-fold. First, t h e y i l l u s t r a t e t h e s l i g h t l y d i s t o r t e d shape of the f laps that occurs because the f laps are at tached to swept t r a i l i n g edges of the upstream surface. The f laps are required to span a cer ta in length which is defined in planform; therefore, the actual

29

surface must be longer when it is def lected around a swept hinge l ine.

Second, the coord ina tes a re usefu l in loca t ing the f lap loading cen ter of pressure defined in the flap coordinate system and printed on a l a t e r

Page

Output page 3 i n f igure 9 (c) is headed with the t i t l e "HORSESHOE

VORTEX PROPERTIES." This table l ists a l l t h e p r o p e r t i e s o f t h e l a t t i c e elements on each l i f t i ng su r f ace . The quan t i t i e s i n t h e l a s t column on t h i s page labeled "ALPHAL(J) I' are the input values of conibined t w i s t a d camber. This table completes the configuration dependent information. The f i r s t i tem following the table is a l i s t of the var iables per ta ining to the run to fo l low. The angle of a t tack, ALPHA, i n degrees, the indices from item 18 of the input deck, and the convergence tolerance ( 5 percent) are printed here. The l a s t l i n e of output on t h i s page is a statement regarding the l i m i t appl ied to the j e t cen ter l ine def lec t ion . I f a l i m i t is not specified, no statement i s printed.

The fourth page of output is a l i s t i n g of t he j e t i npu t a s shown i n f igure 9 (d) . The var iables pr inted are the same values input via the card deck with the addition of two columns of numbers. The var iable SCL i s the curvi l inear dis tance measured along the cen te r l ine i n the Same

units as the other center l ine dis tance var iables . For a s t r a i g h t j e t Centerline with no inc l ina t ion (THETA = 0) , SCL i s the Same as XCL. The l a s t C O l U m n , iden t i f ied as P, i s the perimeter of t h e j e t a t t h e p a r t i - cu la r s ta t ion .

The next page of output shown i n f igure 9 (e) i s t h e f i r s t o u t p u t from the program af te r the c i rcu la t ion s t rengths a re computed. This page, labeled "HORSESHOE VORTEX STRENGTHS FOR ALPHA = xx.x DEGREES," contains the computed c i rcu la t ion s t rength on each la t t ice e lement . The circula- t ion s t rengths ( G A " A / V ) a r e p r i n t e d i n t h e l a s t column on the page. Also shown on t h i s page are the external ly induced je t veloci t ies a t each control point. These ve loc i t i e s , U E I , V E I , and WE1 are made dimension- less by the free-stream velocity and the i r pos i t ive d i rec t ions a re def ined according t o t h e wing coordinate system; that i s , U E I i s positive forward and WE1 is posi t ive downward. I f external ly induced veloci t ies are read i n via tape 4 (KEI # 0 ) , these ve loc i t ies a re p r in ted on t h i s page. Also noted a t t he t op of the page, directly beneath the angle of a t tack , i s the i t e r a t i o n n u d e r "NTIME" tha t cor responds to the p r in ted resu l t s .

30

I

The output shown i n f i g u r e 9 ( f ) i s headed a t t h e t o p "AERODYNAMIC

LOADING RESULTS FOR ALPHA = xx.xx DEG." This is followed by a r e i t e r a t i o n

of the reference quant i t ies which are followed by the spanwise load d is t r ibu t ions . On e a c h l i f t i n g s u r f a c e a t each spanwise l a t t i c e s t a t i o n the span-load coefficient, the section normal-force coefficient, and the sect ion axial-force coeff ic ient are presented. These r e s u l t s a r e normal and ax ia l to the p lane of the ' par t icular l i f t ing surface. Fol lowing the section coefficients are the wing-alone force and moment coeff ic ients . These resu l t s a re for bo th r igh t and l e f t wing panels. The axial force, C A W , and the drag force, CDW, a re bo th def ined as pos i t ive a f t . The pitching moment i s pos i t ive in the d i rec t ion tha t t ends to increase the angle of a t tack of the wing.

The next section of output on t h i s page is the individual f lap force and moment coef f ic ien ts . These coef f ic ien ts a re for the f laps ,on t h e l e f t s i d e of the configuration only. CNF i s normal to the ind iv idua l f lap sur face and the center of pressure of the normal force on t h i s f l a p i s a t XF (CNF) and Y F ( C N F ) where these coordinates are i n the f lap coordi- nate system defined i n f i gu re 9 (b ) . The axial-force coeff ic ient , CAF,

and i t s spanwise center of pressure, Y F ( C A F ) , follow. The spanwise force, CYF, and i ts center of pressure, X F ( C Y F ) , are the next items; and f ina l ly , the hinge-moment coef f ic ien t , CHF, is the l as t i t em. The sign convention of the f lap hinge moments i s such t h a t a posit ive hinge moment would tend to increase the f lap def lect ion angle . The hinge moments are taken about the flap leading edge. The l a s t items on this

page are the complete configuration force and moment Coefficients. These are resolved into the wing coordinate system and the sign convention i s consis tent w i t h that descr ibed for the wing alone.

I f pressure dis t r ibut ions are requested, they are output on the next page shown i n f igure 9 (9) . The chordwise location, X/C, a t which the pressure coeff ic ients are calculated corresponds to the locat ion of the bound l e g i n each l a t t i c e element. It should be remembered t h a t the pressure i s constant over the ent i re la t t ice e lement . The l a s t l i n e on the page is the number of the i t e ra t ion j u s t completed.

The ve loc i ty f i e ld induced by the wing-flap loading and t h e j e t models a t s p e c i f i c p o i n t s on the j e t c en te r l ines i s pr in ted a t the top of f igure 9 ( h ) . The coordinates, in the wing system, correspond t o t h e points def ining each je t center l ine with the except ion of the f irst two points on each centerline. These points represent the physical engine

31

I

locat ion and a re assumed s ta t ionary and not al lowed. to move with the remainder of the wake; therefore, induced velocit ies are not needed. The perturbed j e t posi t ion i s shown on the lower portion of t h i s page of output. Notice that the j e t deflection angle, THETA, is set equal to the prescr ibed l i m i t of -30° a t two points on the center l ine. Thus, the new center l ine has not been allowed t o move as far as the induced veloci ty f ie ld wanted

t o move it. I f a second i t e r a t i o n were not prescribed, the last page of output

containing the induced veloci ty f ie ld a t specif ied f ie ld points would be pr inted i f requested (NFPTS > 0 ) . I f not requested, th is would complete the output.

However, addi t iona l i t e ra t ions a re reques ted ; therefore , the j e t defined i n f igure 9 (h) is allowed t o i n t e r f e r e on the wing and f l aps . The r e s u l t s of the second i t e r a t i o n a r e shown i n f igures 9 (i) , ( j ) , ( k ) , and ( a ) and these results are analogous to those j u s t described i n f igures 9 (e) , ( f ) , (9) , and (h) , respectively. If convergence has not been achieved or the maximum number of i terat ions completed, s imilar groups of four pages w i l l be printed u n t i l convergence o r maximum number of i t e r a t i o n is reached. A t t h i s po in t , a statement regarding the convergence s i tua t ion , number of i t e r a t i o n s , and current level of con- vergence ( D E L ) i s p r i n t e d a s i l l u s t r a t e d a t t h e bottom of f igure 9 ( J ) . I f convergence within the specified tolerance (TOL) is achieved, the message !I**** CONVERGENCE ATTAINED I N x ITERATIONS, DEL = x.xx****" i s printed.

The l a s t page of output containing the induced veloci ty f ie ld a t spec i f ied f ie ld po in ts is shown in f i gu re 9 (m) . Note that both wing-flap per turbat ion veloci t ies and to t a l ve loc i t i e s a r e p r in t ed on t h i s page. This concludes the discussion of the output from the EBF predict ion

program.

Error Messages

The fol lowing error messages may be printed during program execution.

"ERROR I N JET , B .GT.A"

is pr inted when an e l l i p t i c j e t is input with the semi-minor axis longer than the semi-major axis. This is a f a t a l e r r o r .

"EXECUTION TERMINATED, ERROR I N DS I'

32

i s printed when the vortex spacing is input as zero or less than zero. This is a f a t a l e r r o r .

"ANALYTICAL J ( N ) ERROR, XX POINTS"

is a warning message p r in t ed t o a l e r t t he u se r t ha t t he ana ly t i ca l ca l cu - l a t i o n of the J-integrals had numerical d i f f icul t ies a t the noted number of points. The program automatically switches to a numerical calculation technique for these points; therefore, the answers are correct. I f the number of points is a la rge f rac t ion of t h e t o t a l number of control points , there may be some er ror in the spec i f ica t ions of t h e j e t s o r i n t he l oca t ion o f t he j e t s w i th r e spec t t o t he l i f t i ng su r f aces . For example, t h i s e r r o r message would be pr inted i f one of t h e j e t s was located outboard of the wing t i p by mis take o r i f the j e t cen ter l ine was located i n the plane of the wing. I f the e r ror message p e r s i s t s , consider switching to the numerical technique via the index NNUM i n the input data. The penalty for using the numerical procedure is increased computer time and a s l ight decrease i n the accuracy of t h e j e t induced veloci ty calculat ions.

I f the je t center l ine def lect ion angle becomes -90° or less during i terat ion, the fol lowing message is printed.

"ERROR I N JETCL j k -90.00''

where j i s the number of t h e j e t and k is the number of the point on the center l ine causing diff icul ty . This i s a f a t a l e r r o r . The e r ror is caused by th i s par t icu lar po in t be ing too near one of the vort ices on the wing o r f l ap . To correct the s i tuat ion, adjust the posi t ion of the point i n question upstream or downstream a small amount and rerun or res tar t the calculat ion with the previous i terat ion.

PROGRAM L I S T I N G

The EBF aerodynamic prediction program consis ts of a main program, WNGFLP, and twenty-four subroutines. Each deck is ident i f ied by a three- l e t t e r code i n columns 74-76 and each deck is sequence'd with a three-digi t number i n columns 78-80. The t ab le below w i l l a c t a s a tab le of contents for the program l i s t i n g on the following pages.

33

PROGRAM

WNGFL P

WNGLAT

FLPLAT

INFMAT

FLVF

S I V F

RHSCLC

LINEQS

SOLVE

LOAD

FORCES

VELSUM

J E T

J E T C L

CORECT

VRING

ERING

J I N T E G

E L I 1

E L I 2

ELL IPS

QUART

CUBIC

QUAD

S IMS ON

I D E N T I F I C A T I O N

WNG

WLT

FLT

I N F

FLV

SIV

RHS

L I N

SOL

LOD

FOR

VEL

JET

J C L

C RT

VRG

ERG

J I N

EL1

EL 2

ELL

QRT

CBC

QAD

SIM

PAGE NO.

35

37

39

41

43

43

44

44

45

45

46

49

51

53

53

54

54

55

56

56

57

58

58

58

58

34

C C C c C C c C

c c C

C C C

C C C

C c

OUT 018 01) 050 051 OSR 011 011 os5 OSb 051 os1 819 Ob0 Ob1 Ob2 Ob1 ObU ObS O b b O b 7 Ob8 ObV 010 0 1 1 0?2 A05 U T 1 OTU 0 1 1 OTb 0 7 T

C c C

C c t

1 0 0 0

C t c

C C C

C C C

C C C

C C C C

C C C

C C C

C ADD C O R t A R E A C O R I N C L U L N C E C O L C F I L I t N l M A T R I X C I F R € O F L I1 kOT A V b I L A 8 L E t REMOVt T H I E S E C T I O N AND I k C R t A S L C THC D I M C N S I O N E OC F V N I N OLANM COPMON, ABOVE, T O M T O T * H T O T

C C WERL WTOT V TOTAL hUM0ER Of V O R T E X P A N E L 8 ON HIh5 AND C L A P

C C C

C C C

C C C C

C C C C C C C C C E C C c e C C C C

C

C C C

C E C

C A L C U L A T E I H I L U E N C L C O E l C l C I l i k l L L C T H I N D I I D C I F V N

C A L L I N ? M A T

T R I A N O L I J L A I I I L L C C T H A N D I I D t

C A L L L ~ N C O ~ I M T D T I ? V N I

R E I D H U M B E I O f R I G M T ) I D E O , AND COS CACN C I N D V O R T C X I T R E N G T Y I AND LOAD D I I l l I l U l l O N

R€AOlIrTOl) NRW8 DO TI K R 8 l , N R H 8 R E A D l ¶ , T 1 ~ I A L ? A , K E I , N f P T S I K J L l r v J I I e L l N J E l V ~ N J L T C L IC ( U J C T o L E I O I N J L T V V O

I F K J E T l O NO J F T C A L C U L A T I O N l I N D U C E D V C L O C l T I C 8 * A I OE I N P U T r l J E T C A L C U L A T I O N w YO I T L R A T I U N ON C E N T E R L l N C D Z J E T C A L C U L A T I O N . I T E R A T I @ N ON C E N l E R L I N C U N T I L

CONVCROLNCLI OR K J E T T I M E 6

N J E T C L 8 0 NO L A T L L I A L M O T I O N OF JET CL ALLOWED N J E T C L B I J E T C L PRLE TO MOVE I N Y = D I R L C T I O N

I GAMMA GO TO e5

02 CONTINUE

C A L L L O f l D l I M V E L I C A L L F O R C I I

C

Y

5 C CALCULI~C vELOClTI l1 AT ICtcIClCO l l E L D COIUTS C

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M L I Ob9 .Ll Ob@

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rLT O T I rL1 01b

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nLT 011 n L l 0 1 0

nLT 011

* L l u 9 J *LT 0 9 1 hLT 0 9 5 r L 1 01b hLT 0‘47 “ L l oes .Ll 0 9 9

WLl $06 MLT 101 *LT IOb hL t 107 UL l 1 0 s *LT 100 hLT 110 nLT 111 nLT 112 nLT 1 1 1

WLT 1b9

C C C

C c C

C C C

C C C

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50

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F L l o o v FLT 010 FLT 011 FLT 012 P C 1 013 F L l D I U FLT 015 1 0 1 I,

L 0

f L 1 111 FLT I18 C L l I 1 9 FLT I20 FLT 1 2 ) F L I 122 F L I I 2 1 t L 1 I ? & F L I 125 F L l IZb F L l 127 FLT I11 f L I 129 f L 1 110 FLT 131 FL1 132 FL I 133 FLT 134 t L 1 113 FL1 ISb FLT 131 CLT I 3 U F L I I39 FLT 140 F L l 1 4 1 fLT IY2 CL1 I41 F L I I U Y f L 1 IUS FLT LYb F L I 1 0 1 FLT l U 8 F L I 1119 C L I 150 P L I 1 5 1 FLT IS2 FLT 153 C L I I l U F L l 155 FL1 1Sb F L I IS7 FLT l I 8 FLT IS9 CL1 I b O F L I 1 6 1 FL1 162 F L l 163 FL1 I b U I L 1 l b 5 FLT I 6 b FLT LbI f L T IbO FL1 169 F L l I 1 0 F L l 1 7 1 + L l 112 CLT I73 C L l I 7 4 FL I 175 F L 1 I 7 b FL1 171 F L I 118 FL1 17s FL1 180

230 220

C

h

2UO + L I 25c f L I 259

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FLI IbP F L Y 2h9 F L T 2 1 0 F L I 211

F L T 2 7 1 F L l 218 F L T 2 7 9 F L 1 280

F L T 282 F L I 281

F L 1 2 8 1 F L T 284 ILT 285 t L T 88b t L 1 287 f L 1 288 t L 1 289 F L T 260 FLI 291 F L T 2P2 F L I I 9 3 F L T 294

00; 001 004 005 O O b 0 0 1 008 009 010 O l l 012 013 019 0 1 5 O l b 0 1 1 018 O I P 0 2 0

022 0 2 1

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C A L L I L V ? lJTOT.UlOT.1U

C C L

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AI..CDX 12.IDI CALL S I V C ulolIu1ol*Cu V1OlWVTOl*~V n T O 1 # ~ T O l * F u I IIXl VlrnVl 21.18 CALL 8IVP UTOlIUT0l .CU VlOlwVTO1=CV clOllwfOl.C* 00 10 1bT

I l N I l E T l A I L I N G LEE1 I N 1 TWII PLAI I H C a I ARC CLAP8 BEHIND lMI1 ONi!. COMCUTL THE lNPLULNCI OF

F L V on1 FLV 002 FLV 0 0 3 FLV 906 CLV 005 bLV 00, FLV 001 bLV O O t I L V 0 0 1

FLY 0 1 1 FLV 010

FLV 012 CLV 011 PLV 014 TLV 0 1 1 FLV OIL I L V 017 FLV 018 bLV 91r FLV 020 CLV 021 FLV 022 FLV 0 2 1 FLV OZY FLV 025 PLV 02b FLV 021 I L V OLI PLV 011 FLV 010 FLV os1 FLV OIL FLV 053 FLV 0 3 8 PLV u s TLV 01. FLU 017 FLV 018 PLV 019 CLV O Y O PLY 011 F L Y n u FLV o u 3 ILV O Y Y FLV 015 FLV O M 1 FLV OUT FLV O Y 8 FLV 0.w

PLV os1 PLV os0

PLV 052 CLV 051 CLV 058

1 1 v 001 1 1 1 002 S I V 0 0 3 S l V 0 0 1 S1V 005 SIV OOb SIV on7 S l V 008 IlV 0 0 1 IIV 010 IIV 011 81V 012 IIV 011 S I 1 OII

P P lY.V(D.V~

CU.O,O t v.o.0 f l . O . 0

, C C C C C F C C C

c F. c C C C

C C

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C C C C C

COMMON I A T A H / I I N A L F , C O I L L ?

R IOH7 HAND I I D C FOR WING CONlROL COIN11 I C ( C M V L L I 00 TO #I

LOOP OVlR MINE CONTROL POINT) fOR C L I l WITH NO EXTLRNALLV INDUCED V E L O C I T I L I

B I U a 1 1

31V @ I T S I V 0 1 b

Y I V 0 1 8 SI* 0 1 9 S I Y 0 2 0 S I V 021 S l V 0 2 2 S I V 0 2 s S I V 024 S I V 025

S1V 0 2 1 31V OZb

S l V O t 8 IIV 029 S I V 0 1 0 S I V 031 5 1 v 0 1 2 S I V 0 3 1 S I V U I Y IIV 0 3 1

L I h UOb L 1 * 0 0 1 L l h 008 L I h 0 0 1 LlOd 0 1 0 L I N 0 1 1

L l N Y 1 1 L I h 0 1 2

L l h 0 1 4 L I * 015 L I N 01b L I N 01) L 1 N Oii L l N 019 L I N 020 L I k 0 2 1 L I N 022 L I N 0 2 1 L I N U I U L I N 025 L I * 0 2 6 L I ~ o n L l h U Z B L I N O l S L I N 0 3 0

R

SllL 001 SOL 0 0 2 SL'L 0 0 1 SUL OUU SUL 0 0 5 SOL O O r SOL 0 0 1 SUL 008 I U L 000 IOL 0 1 0 IOL 011 IOL Ole! IOL 013 IOL 014 SOL 0 1 1 SOL Olb a u 017 IOL o t a SOL 019 80L 0 2 0 I U L 021 SOL 022 SOL 025 SOL 024

LOD 001 LOO 0 0 1

LOO oas LOD 01b LOO 017 LOO 0 2 1 LUD 0 1 1 LOD 010 LOD 011 COD OS2

- ~ . ",

LOO 013 LOO O S Y LOD OIS Lun Oib - ~ ." LOD oa7 LOO 018

coo oao LOO 0 8 1

LOD 041 LOU 042 LOD OPJ

LOO 045 LOD 064

1 1 0

100 i O i 201

LUD DYb LOD Ob7 LOO o u n LGD O b 1

LOU us1 LUU 050

LOD 052 LUD OS3 LUD 05lr LUG 015

LOU 057 LUU OSb

LOO Ob0 LOD 0 5 1

LO9 DL1 LOD O b 2 LUD Ob3 LOU Ob4 LOO 065 LUD Obb LOU 067 LGU OLD LUD Oh0

LUU 05C

LOD 070 LUD 0 7 1 LOO 072 LOO 013 LUD 074 LOD 075 LOO 07b -~~ . - LUU 071 LOO 014 LUD 071 LOU O D 0 LOU U D l LUU OD2 LUD Ob3 LOO O I Y

LOU 0 1 0 LUD 001 LOD 0 1 2 LUD 0 1 3 LOU 0 1 1 LUD 01s LOU 0 1 1

LUD 0 1 1 LUD 017

LUD 0 1 1 LOD 1 0 0 LUL, 101 LOD 102 LOO 10) LUO I 0 6 LOD 10s LOO 1 0 1 LOO 107 LOU LOO LOD I09 Lull I10 LUD I l l LOD 112 LOO 1 1 1 LUD 114 LUU I 1 1 Ll'D ll* LUD I 1 7 LUD I I b

LUD 110 L O D 110

LOD 111 LUD I22 LOD 111

C 8S

I100

1210 C

1nAILIN6 LlG LOAD1 ON FLAP1 0- LOOP OVER CLAP1

E COMPUlC T U I TRAILING LC1 LOA01 ON Y M I I FLAP C

LOO 1 Z I LUD 11Y LOD

LOD I21 LUC 111

LOD 121 LOD 110 COD I11 LOD 112 LOD 111 LOO 131 LOD 111 COD 116 LOO 111 LOO 116 LOD 118 LOO 1YO LOO 181 COD l I 2 LOO I U S LUD lum LUD 11s LOO l b b LOO 1 I l LOD 141 LOO 11) LOO IS0 LUD 1 I l LOO 112

LOD 154 LOD l S 3

LOD 151 LOO i s * LOO 11T LOO 111

LOD 160 LOD IS*

LOO 1b1 LUD L IZ LOD l b 1 LO0 1b1 LOO l b 1 LUD 166 LUD l b l LOO l b 8 LOO I * * LOD 110 LOO 111 LO9 112 LOD ITS LOD 11r

LOO 1 I b LOO 171

LOO 111 LOD 111 LOO 118 LOO 110 LOO 111 LOD 112 LOD 183 LO0 18I LOD 115 LOO 18b LOD 111 LOD 181 LOO lI* boD 180 LOD 191 LOO l e 2 LOO l S 1 LOD 194 COD lI5 LOD 1 I b LOO 111 LUD 198 LUD 189 LOD ZOO

195

b

450

so0 I 0 0

LOU 201 LUD 2@2 LUD LO1

LOU 110 LOO 111

LOO ZlI LOO 211

LUD LtI LUD 215 LOO 2 l b LOO 211 LUD 211 LUD 219 LUD ZZO LOU 211

LUD 2 Z b LOO 211 LOD 221

Coo i i i LOD 211 LOU Z3* LUD ZMO LUD ZUl LDD LIZ LOU zrs LUD 214 LOO / I 5 LOO 2Ib

LUO a18 LUD 211

LOD ZII LUD 250 LUO 251 LUD 111 LOO 253 LOD ZSY EUD is5 LOD 25b LOU a51

LUU 258 LUD d50

LClD ZbO

FUR O B I

2

I

40

30 ZP

5 0

t

C C

E C C

C C C

VEL 0 0 1 I L L 002 VLL 0 0 3

VtL 005 VEL O O Y

VEL 007 VEL onb

C

C C c

F C C

130 C C C

131

v t L o i l I L L 0 1 1 VtL 018 VtL 020 VtL U Z I VtL 022 VEL 0 1 3

VtL 025 I L L OZU

VtL u l b VLL l l ? l VLL u z t WLL 0 2 9

VtL 0 3 1 r t L 0 3 d v t L 0 1 3 VLL 034 VfL 035 VLL 03b VLL 0 3 1 VEL 0 3 8 VLL 019 VtL 0 4 0 VEL O Y I VtL au2 I L L uu1

VEL O Y S Vll O Y U

VLL 046 VCL U U I VtL O U I VtL OYP

V t L 051 VlL 05G

VtL us2 VEL 0 5 1

VLL 055 VLL P5U

VtL OSb

VLL 0311

v t L 0 5 1

VLL 05P VtL U58

VLL Ob0 VLL Ob1 ULL UbZ VEL Ob1 I L L ObU VLL Oh5 VLL O b b VtL Oh1 VtL O b H

V t L O T O UlL Ob8

V t L 012 VEL 011

VEL 0 1 4 "EL U T 4

VEL 015 VtL 0 1 b d t L V I 1 VLL OTe V L L OTP VLL OR0 VEL 0 8 1 V l L O W *LL 0 1 1 VtL U8Y

UI 0

L C C

C c C

C C C C

c c c

v t L on5

VEL 087 4 t ~ one L t L ouv v t L no0 V t L 0 9 1 kLL 092 VtL o o , 4 t L 094 VtL 0 9 5

VLL 0 9 7 VtL 09b

VLL 0 9 0 VtL 099 VtL 100 VLL 101 YtL 102 VtL 103 VtL 1 0 4 VEL 1@5 VLL 100 VtL 1 0 1 VtL 106 VtL 1 0 9 VtL 110 VEL Ill VLL I 1 2 VtL 113 VEL 11Y VEL 115 VEL l l b V t L 1 1 1 VEL 118 VtL 119 VtL 120 VEL 121 VLL 122 VEL 12s VEL 124 VEL 125 VLL 126 VEL 127 VtL 128 VtL 119 VEL 110 VEL 131

VfL 133 VEL 112

VLL 13U VLL 135 V t L 13b VEL 137

VLL 11q VEL 130

VLL 1 4 0 VEL 141 VLL 1 4 2 VEL 1 ~ 3 VtL 144 VEL l U 5 VLL I46 VEL I U 7 VEL 140 VCL l e e

VtL IS1 VEL IS0

V t L 152 4 L L 153 VtL 1SU VEL I55 VEL I5b VEL 151 4LL I50 VLL 15.

VtL I b l VFL 1 b O

VtL O O b c C

C c C

C C C

E C

d t L I O U

WLL 10b v t L 105

v t L 1 1 7 WEL 180 I L L 189 I t L 1qn V t L 191 VEL 192 VEL 1 9 1 VEL I P M VLL I95 r t L 19b VEL 191 VtL 190

VtL z o o " t L I99

VtL 2117

U t L 209 $EL 2 0 1

VtL 210 VtL 1 1 1 . VCL 112 VEL 213 *LL 2 l U d t L 215

VtL z 1 r VfL 218 WtL 214 VtL 220 VtL 221

VtL 121 b t L 222

VEL Z Z Y VtL 2 2 1 VtL 2z* VEL d 2 7 VtL 220 VCL 229 V C L r s n

I L L d l b

.. -. VtL 2 3 1 V t L 212 VtL 233

C C C c C C C C C C C C C C C C C C C C C C

C

J t I 010

J L l 012 J t I 011

J L l J t l J t T J L I J t 1 J t l J L I J t I

". ". JEI Om2 J L l O Y J JL I U Y Y JL I O Y 5

". ". J t l UbO J t I Ob8

J € l UT0 JL1 0 7 1 J t l 072

J t I tJ7u JL1 0 1 1

J k I 075 J L l 01s J L I 0 1 7 J L I 078 J L l Ole

J t l J t I JET

0 1 7 01.8 088 0 9 0 091 092 001 o v u 0 9 5 0 9 6 0 9 1 UP0 099 L O O I D 1 1 0 2 I 0 3

I05 I O U

I O b I 0 7 1011 1 0 9 110 1 1 1

J t l 1bY J L I ibS J t l I b o J L I l b 7 J t l l o 6 J t l l b 9 J t l 170 J t l , 1 7 1 JE I 1 7 2 J t l 1 7 3 J t l 1711 J t l 1 7 5 J L I l l b J tT 1 7 1 J E l I18 J L l 119 JEl IO0 J t l 1 8 1 J t l 182 J t l l e1 J L I l e u J t l In5 J t l ! A b

J t l JC 1 J t 1 J t l J t 1 J t I J t 1 JET JET j t l J t l JET

J t l J f I

JET C C C

J t 1 J t l j E 1 Jk I JE 1 J t l JL1

I

r lHLTA(N

j t r i c i J t l LOR J L l 189 J L I IPO

;G80;0 " .

J t l JLT

I 1 2 I 1 3 1 1 1 115 I I b 1 1 7

J t l 191 J t l 192 J t l IPS J t l I Y U JL1 I P S J t l 190 J t l I 9 7 JL1 198 J t l 109 J t l 200 JE l 201

J t l ? 0 1 JL f Z O U JEI 2 0 5 J t 1 1 0 b JEI 2 0 7 JEI 208 J t l 209 J E l ZIP J t l 211 J t l 212 J t l 111 J L I 219. J t l 215 Jfl ZIb J t I 2 1 7 J I I 216 J t l 219

J ~ I rnz

r J11

1 1 8 L I P JL1

J L I J L l it T JE 1 JET

J L I J t 1

J t l J t I JEl

JEl J tT

JET J t l J E l

JEI 1 4 1 J t l l U Z C C O R R t C l CIELD POINT LOCAlIOUI I F D L S I l l E D

c

JET l U 8 JET l u 9 JET 150 JET 151 J t l 152 JEl 1 5 1 JET l S u J t l 155 JtT 156 JtT 151 JET 1 5 0 JET 119

50 uo 9 1

C C C

JLT Iio JET l b l J L I LIZ J t l I b 1

SUBr)OU11NE J t l t L ( N l l H E 1 1 0 L l JCL n o 1

CALCULATE T h t CUAhGE I h J t l CIhlfRLINE COSIllUh DUE IO THE

JCL 0 0 2 JLL 0 0 3 JCL oou JCL 0 0 5

I k D U C t D VtLrCl lV FIELD OF I M t * lkG/FLIP AhD J E l

JCL U I I JCL 0 1 2 JCL 0 1 3

""" cu TO so

JCL J l b JCL 0 1 1 JCL 018

JCL 020 JCL 0 1 1 JCL 021 JCL 021 JCL 024 JCL 025 JCL O Z b JCL 027 JCL 028 JCL 021 JCL 0 3 0 JCL 031 JCL 0 3 1 JCL 0 3 3 JCL 03Y JCL 4 1 4 JCL 035 JCL 03b JCL 037 JCL 018 JCL 019

JCL a l p

JCL O Y O JCL 0 9 1 JCL OUZ

JCL OYb JCL O Y 7 JCL 0 4 0 JCL O Y 9 JCL 0 5 0 JCL 051 JCL 052 JCL OS3

E

C C C

C c C

$LIBROUTIN€ C l I h C ~ G A * ~ A ~ I A ~ I ~ ~ l 2 r V l ~ L Z ~ V ? K ~ V ~ V ~ V P 2 1 E R G 0 0 1

CUM?UTL THE I N D U C t l , V L L O C l l Y c U * C O N L Y T I D U E T O AN E L L I P T I C A L ERG 0 0 3 LRG 0 0 1

VOllLl R I N G E R G O O Y L U G 0 0 1

v ? x m o , o vPvmo.0

ERG 017 ERG 0 3 8 E R G 05s E U G OUO E R G O Y l E R G i U 2 LUG ou3 ERG OPU L U G O P 5 ERG O Y I E Q G O M 1

1 ,OE-OTI T O b0

Jlh 001

JIM 0 0 3 JIN OD2

JIM 0 0 1 Jlu 005 JIM 0 0 1 JIM 0 0 1 JIM 008 JlW OOq JIU 010 JIM O l l

J1* 0 1 1 J1M 012

JIh O I U JlN 015 JlN 010 Jlu O l T JIM 018 JIM 0 1 s

Jlh 021 JIN 022 JIM 021 JIh 028

JIM OZb Jlh 0 2 1 JIM 028 J l h O I V JIN 010 JIk 011 JIM 012 J IM 033 Jlk 014 JIh 035 JIM 03b J l N OIT JIM 0 3 8 Jlh 0 3 1

JIM 0 4 1 Jlh DUO

J1* 0 4 2 JlN O M 3

JIM OU5 JIM OMb JIM O Y 1 J I N O Y 8 JIM 0 1 1 JIM OS0 JIM OS1 JIM 012

JIM o m

J W a m

J I M a u

Jlk J l N

C C C C C c C c C C C C C

C C

c C C C C c c C

C C C C C F c c E c C C

t L 1 0 0 1 ELL 002 E L I 0 0 5

C L I 005 E L I 004

t L 1 0 0 1 L L I 001

E L I 0 0 8 E L I 0 0 9 EL1 0 1 0 E L I O I L EL1 0 1 2 ELL 015 E L I 0 1 4 E L I 015

EL1 0 1 1 E L I 0 1 6

E L I 018

t L 1 020 E L I 0 1 9

L L l 0 2 1 E L I 0 1 1

~~~ ..

E L I 021 t L 1 o t r E L I 0 2 1 E L I 0 2 6 t L I 0 2 1 E L I 028 E L I 029

L c c C C C C C C C C C c c c C C C c C C C C C c C c C c C C C C c C C C C C C C

L L I ou5 t L I OYU t L I P P S t L I 0 4 b t L I O U T E L I QUR. t L 1 0119 L L I u 5 0 t L I o s 1 t L I 052 CLI 0 5 1 t L I u5u CL1 055 L L I U58 E L I 057 t L I 05n L L I 05P L L l ObU f L 1 O b 1 E L I Ob2 t L 1 Ob5 t L I O 8 U t L 1 Ob5 t L 1 Ob8 t L I O b 7 k L I Ob8

t L z on1 EL2 0 0 2 t L Z 0 0 3 EL) o n u LLZ 0 0 5

€ 1 2 0 0 1 kLd OQb

cLz on0 t L L 009 t L z o l n t L 2 O l l t L 2 Q I ? LL2 U I 3 t L 2 0111 kLZ 0 1 5 kL2 O l h LLZ 0 1 7 E L I 0 1 8 t L 2 010 EL2 0 2 0 t L 2 0 2 ) ELL 022 EL2 0 2 3 t L 2 ozu t L 2 025 EL) UZb t L 2 021 ELZ 011) t L 2 029

t L 2 0 1 1 EL2 03u

I

C 2

3

C U

5 b

t

C

C

C

9 10

11

IZ I3

I U 15

lb C

C 11

t L L uu3 EL2 o u u EL2 0 4 5 EL2 O U b t L 2 0117 t L Z OUD t L Z ;UP t L I 050 t L 2 o s 1

t L 1 u s 1 t L 2 052

t L L Oll L L L 018 ELL O I V L L L 020 t L L 021 ELL 022

t L L uzu t L L 0 2 3

L L L 0?5 ELL O Z b t L L U 2 7 t L L O?b

L L L 030 k.LL Q Z P

t L L u3.2 t L L 031

L L L 03) L L L 0 3 U t L L 015 ELL Q 3 b L L L 037

ELL 019 tLL QUO t L L U U I t L L o u 2 L L L O U ) t L L nuu ELL O M 5 ELL OUb t L L O U T ELL Dum t L L OUP t L L osu t L L 0 5 1 L L L 052 L L L OS3

L L L 055 t L L o s u

L L L 056 ELL 0 5 1 ELL ozn

CLL Ob0 L L L 0 5 9

L L L OIL t L L O b 1

L L L O b 3 L L L O b U t L L Ub5

L L L Ob7 ELL D b b

ELL 068 L L L O b 9

t u u3n

t u oln

E L L 0 1 1 L L L 011

CLL 013 ELL O l U

ELL 01. L L L 0 1 s

L L L 011 LLL O l b t LL nrq

c c

D l t L 1 05u L L Z 055 EL2 O 5 b

I I 3 U 5 b 1 8 9 A n L D E I

i L 2 o s 7 t L 2 OS8 EL2 OS9 t L 2 O b 0

G C C C

t L Z 011 E L I 0 7 1 EL2 0 7 9 CLZ 01s

L L Z 0 7 1 LLZ 07b

L L Z 018 EL2 019 E L I 080 E L I 081 L L I 082 EL2 085 EL2 OOU EL2 085

/ I I I 1

b 1 8 9 A

c D E F

n L L d O O b EL2 0 8 1 E L 2 0 0 8 L L Z on*

EL2 011 EL2 0 1 0

EL2 0*2 t L 1 0 1 )

I1,lb c

E L I OVb t L 2 u11 t L Z 098

E L 2 I O 0 L L Z 099

ELZ 1 0 1

t L L 0 0 1 ELL 0 0 2 t LL 00s I L L O O Y t L L 00s ELL OOb L L L 007 L L L OD8 L L L 009

L C C

1 0 I I I2 I 3 20

22

2 1

25 I O

20

30

cnc 0 0 1 cuc 0 0 2 C

CBC O O Y C cnc O O J

CEC 005 C I C O O b C e C 007 I CBC 0 0 8 CBC 0 0 9 CBC 010 z CBC 0 1 1 cuc 0 1 2 CbC 013 CBC 0 1 4 CBC 015 CBC O l b C U C 017 t B t 018 cnc 019 CdC 0 2 0 cnc 021 LUC 022 C l C 023 CUC O Z Y CLlC 0 1 5 CbC 0 2 1 CBC 027 cnc 028

1

REFERENCES

1. Mendenhall, M. R., Spangler, S. B., Nielsen, J. N., and Goodwin, F. K.: calculation of the Longitudinal Aerodynamic Characteristics of Wing-Flap Configuration6 with Externally Blown Flaps. NASA CR-2705, 1976.

2. Dillenius, M. F. E., Mendenhall, M. R., and Spangler, S. B.: Calculation of the Longitudinal Aerodynamic Characteristics of STOL Aircraft with Externally-Blown Jet-Augmented Flaps. NASA CR-2358, Feb. 1974.

3. Aoyagi, K., Falarski, M. D., and Koenig, D. G.: Wind-Tunnel Investi- gation of a Large-Scale 25O Swept-Wing Jet Transport Model with an External Blowing Triple-Slotted Flap. NASA TM X-62,197, Nov. 1973.

4. Perry, B., I11 and Greene, G. C.: Wind-Tunnel Investigation of Aerodynamic Loads on a Large-Scale Externally Blown Flap Model and Comparison with Theory. NASA TN D-7863, Mar. 1975.

NIELSEN ENGINEERING & RESEARCH, INC. Mountain View, California

November 1975

59

Wing-Flaps Vortex L a t t i c e Elements

26

104 120 135

156

126 126 126

135 135 135 135

135 135

149

No.

1

O f f

O f f

O f f

O f f

2

2 2

2 2

2 2

2 2

2

Jets

Shape

C i rcu la r

""""

""""

""""

""""

Circular C i rcu la r C i rcu la r

C i rcu la r C i rcu la r C i rcu la r C i rcu la r

E l l i p t i c a l E l l i p t i c a l

C i rcu la r

Length

18

"

"

"

"

20 20 20

20 20 20 20

20 20

20

- AS

0.1

"- "- "- "- 0.1 0.1 0.1

0.1 0.1 0.1 0.1

0.1 0.1

0.1

Cterations

2

1 1 1 1

3 4

5

1

2 3 4

1

2

1

Angles of

Attack

1

2 1 2

2

1 1

1

1 1 1

1

1 1

1

Execution Time (Sec . CDC-6600

FTN,OPT=2

8

40

48 90

120

1 7 0

215 27 0

85 140

200 2 60

330 590

100

CDC-7600 FTN,OPTt2

35

45

T a b l e I.- Typical execution times f o r EBF pred ic t ion program.

PROGRAM WNGFLP I

I

Inpu t da t a fo r a l l f l aps and layout vortices

Add core area for influence I coef f ic ien t mat r ix

Calculate influence coefficient l e f t hand s ide, FVN I FLVF

s IVF U

Triangular ize l e f t hand s ide

""""""""""_ (Begin i t e r a t ion s ec t ion )

I n p u t i n i t i a l jet parameters

I I CORECT and calculate induced

ve loc i ty d i s t r ibu t ion IWNG 222 JET VRING ~ & ELLIPS CUBIC QUAD

QUAD

JINTEG E L I 1

ELI2

- ERING QUART

SIMSON

Figure 1.- General flow chart of program WNGFLP.

m N

Calculate right hand side of equations I

I WNG 238

Solve for vorticity distributions I for this right hand side I WNG 242

Calculate loads, forces I and moments 1 h’NG 278 ‘ WNG 279

I Calculate wing-flap-jet induced ve loc i ty f ie ld on jet centerline I WNG 311

I I

I I WNG 312

(Calculate new j e t I centerline position) IWNG 319

[End iteration section]

Figure 1.- Continued.

P Compute f i n a l jet

centerl ine parameters

Calculate velocit ies at spec i f i ed f i e ld po in t s

END

1 WNG 320

I I I I I

I I I I I" 352

I I I I I

' W G 350

i

"

Figure 1.- Concluded.

m W

I

Figure 2.- Al ternate card decks def ining program MAIN and Subroutine WNGFLP.

Wing

F lap 1

F l a p 2

F l a p 3

Figure 3 . - Vortex-latt ice arrangement for EBF configuration of references 3 and 4.

‘f Top V i e w E l l i p t i c cross s e c t i o n ”” C i r c u l a r cross s e c t i o n

a 2-

0 I”-~--~--IT-”

0 2 4 6 8 10 1 2 14 16 18 20

X j

Region Wing -4- F l a p s -+

b 2 -

” _” - ”

0 I r ” - r - - r - ~ ~ - - r “ ~ r - ” r I- O 2 4 6 8 10 1 2 1 4 1 6 18 20

X j

Figure 4.- J e t wake model boundary spec i f i ca t ion .

Bound v o r t i c i t y

C o n t r o l p o i n t &

Y \r - Y

1

J e t c e n t e r l i n e

0" - ." (3

0 P o i n t s i n c e n t e r l i n e table

I I I I I I I I I J 3 4 5 6 7 8 9 10 11 12

F i g u r e 5.- Je t c e n t e r l i n e s p e c i f i c a t i o n i n region n e a r l i f t i n g s u r f a c e s .

ITEM 1

ITEM 2

ITEM 3

ITEM 4

ITEM 5

ITEM 6

FORMAT (20A4), NHEAD cards 1

TITLE - A

t

FORMAT (6F10 .0 ) , 1 card

FORMAT (15) , 1 card

pyG[ FORMAT (3F10 .0 ) , 1 card 1 ll 21 ~

I CRW I SSPAN I PHID J! F F

(a ) Page 1.

F i g u r e 6.- I n p u t forms for EBF pred ic t ion program.

ITEM 7

ITEM 8

ITEM 9

FORMAT (3F10 .0 ,15 ) , M S W + 1 cards rNPSEG(I) Y ( 1 ) 1 3 I PSIWLE(I) l 2 l PSIWTE(I)I j 31 30

F F 1 F I 1

I I I 1

Omit item 8 i f NTCW = 0 MSW sets of cards if NTCW = 1 and NUN1 1 FORMAT (8F10.0) , NCW values, eight per card. One set of cards if NTCW 1 and NUN1 1

I 1 ALPHAL(’1) l”ALPHAL(2) I 21 P~ALPHAUNCW)I 51 8 1 , 7 1 - . . . I

I I I I I I I I

Omit itenie 9,10, and 11 i f NWREG - 1. If NWREG > 1, repeat items 9,10, and 11 i n sequence. NWREG - 1 times

FORMAT (215)

ITEM 10 FORMAT (315, 2F10.0)

(b) Page 2 .

Figure 6 . - Continued.

ITEM 12

ITEM 13

ITEM 14

FORMAT (I5), 1 card

1 6 11 EGI I I N I IOU”

-it items 13,14,15, and 16 if NFREG = 0. I f NFREG > 0 , item 1 3 , 1 4 , 1 5 , and 16 are repeated in sequence NFREG times.

FORMAT ( 4 1 5 ) , 1 card 1 0 1 1 10 21

NCF INTCF I NUN1 PPRESF I I I I I I I

NOTE: More than one s e t of items 14,15, and 16 may be required by NINREG on item 13.

ITEM 15 FORMAT ( 5 F 1 0 . 0 ) , 1 card 1 1 1 21

GAP I N 3 1

I CRF I N I GAPOUT CRFOUT I F F I F I F I F

4 1 DE-

5 1

Omit item 16 i f NTCF = 0 IOUT - I I N sets of cards i f NTCF = 1 and N U N I = O ITEM 16 FORMAT ( 8 F 1 0 . 0 ) , NCF va lues , e igh t to a card. /One set of cards i f NTCF = 1 and N U N 1 3 1

I 1 ALPHAL (1) f ALPHAL (2) 1 Z l . . . 31 4 1 5 1 6 1 7 1 ALPHAL (NCF)

F 1

I

ITEM 1 7 FORMAT (151, 1 card

[ N F S [ Items 18,19,20,21,22 and 23 are repeated i n sequence NRHS time.

ITEM 18 FORMAT ( F 1 0 . 0 , 6 1 5 ) , 1 card 1 11 10 21 20 31 38 4 1

( c ) Page 3.

Figure 6.- Continued.

Omit items 1 9 , 2 0 , 2 1 and 22 i f WET = 0

ITEM 19 FORMAT (6151, 1 card

1 e 11 10 21 28 3 1

Items 2 1 and 22 are repeated i n sequence NJET times. ITEM 2 1 FORMAT (5F10.5), 1 card

GAMVJ(J) I 11 DS (J) XQ (J) 2 1 3 1 4 1

W ( J ) I ZQ (J) F 1 F I F 1 F I F

ITEM 22 FORMAT (7F10 .5 ) , NCYL cards 1 1 1 2 1 3 1 4 1 5 1 71

Omit item 23 i f NFPTS = 0

I T P i 2 3 FORMAT (3F10.0) , NFPTS cards

1 11 ?1 XFP I YFP

3 1 ZFP

F F I F I

(d) Page 4.

F i g u r e 6. - Conc luded .

3 3 1 1 3

72

6 0

0 1 .s

1l.a 0 1 1 . 3 0 11.5 0 1 1 1 3 L 1 1 . 5 8 1 1 . 3 8 1 1 1 3 0 11,s 1

2.0 11.3

0

1 0. 1 1 I S 20 .0

0 .1 2.0 00 .0

1 0 0 1 0.0 1 . 2 0 . 0 1 . 0 1

1 0 . 0

VJIV.5

1.0 1 . 0 1 1 0 1 .o 1 . 0 1 . 0 1 . 0 1 . 0 1 . 0 1 . 0 1.0 1.0 2 . 0 2.0 2.0

(b) Sample case 2 .

Figure 7 . - Concluded.

73

X

-20 -1 5 -10 -5

winq Region 1 I - I

-0

Region

L

Flap Flap Region 1 2

Region 2 6 = 100 f,

2

(a) Planform view.

Figure 8.- EBF conf igu ra t ion fo r Sample Case 2.

74

V

(b) Jet c e n t e r l i n e d e t a i l .

Figure 8.- Concluded.

75

I

S P A N k I S E L@CAfIOh

0,00000 2,500013 5 . 0 0 0 0 0 9 , 0 0 0 0 0

13 .00000 15,50000 1 8 ~ @ 0 0 0 0 2 0 , 0 0 0 0 0

L V , i ? O O O O a u , 2 0 0 0 0 24,00000 zo,Zoooa E u , a 0 0 0 0 2 0 , 2 0 0 0 0 a4,20@00

11,300OO 1 1 e 3 0 0 0 0 1 1 , 5 0 0 0 6 1 1 a 3000O 1 1 a 3 0 0 0 6 11,~OOOO 1 1 e 3 0 0 0 0

(a) Page 1.

Figure 9.- Sample ou tpu t from EBF prediction program.

76

0,00000 0.00000 - 1 . 1 0 0 0 0 0 . 0 0 0 0 0

- 1 , 1 1 3 Y T -2.00120 -,3IJ5T -a.OOlPO

(b) Page 2 .

Figure 9.- Continued.

77

W R S E S H D t V O R T E l PROPERTIES

V O R T E X hU"!R

J

1 z 5 Y 5 b 1 0 9

10 11 1 1 15 10 1 s l b

VORTLX NUM8CR

J

-1,25000

=1,25000 -lm.?IOOO

-3,lJOOO -3,13000 - s m r 5 0 n o -7m00000 -1,00000

-1 1 ,00000 -11,00000 -1u.asooo .14~2J000 -11~15000

~ l P m 0 0 0 0 0 -16,lSOOO

-19.00000

o;ooooo 0 .00060 0 , 0 0 0 0 0 0 , 0 0 0 0 0 o.oooon o,onoon 0 .00000 0 .00000 0 .00000 0 ,00000 0 .00000 0 .00000 0,00000

0 .00000 0 .00000

o.ooooe

-1,05000 -1.25000 -1.25000 -3.75030 -3,75000 -5.15000 -7,00000 -1,00000

-1 1 m O O O O O -11,00000

.1C*1500Q -16,75000 -19.00000 r19.00000

-1u.aYooo -14,asooo

O a O O O O O 0 ,00000 0 ,00000 0 ,00000 0 , 0 0 0 0 0 0 ,00000 0 ,00000 O m O O O O O O m O O O O O 0,00000 0.00000 0,00000 0,00000 0 ,00000 0.00000 0,00000

1,25000

1 ,Z5000 lm250O0

1 ,z5000 1,25000 1 ,zsooo 2.00009 2,00000 2.00000 2,00000 l ,a5000 1,2s000

1,asooo 1,00000 1,00000

1 BPS000

A L r w r KEI 0 10,000

NFPTS R J f T TOL MJETCL NJETV NJLTCL Y I ,01000 0 1 1

8URf ACE 810pc

A L P H A L t J )

0.00000 0.00000 0,00000 O m O O O O O Om00000 Om00000 0,00000 0,00000 0,00000 0,00000 0,00000 0.00000 0,00000 0,00000

0,00000 0,00000

SURFACE 810ct

ALPHAL(J)

0.00000

O m O O O O O 0,00000

UURFACC SLOPE

ALPHAL(J )

0,00000. 0,00000 0,00000 0.60000 0,00000 0,00000

s G - M a ID-

XCL 0 , 0 6 0 3.1 000 5 , 0 0 0 7 , 0 0 0

1 0 , 0 0 0 1 1 , 0 0 0 i l e S O O lZ,OOO 12,500 1 3 , 0 0 0 I 9 ,so0 lS,OOO 16,000 18,000

w o o

VCL 0,000 0 , 000 0 , 0 0 0 0,000 0,000 0 , 0 0 0 o,(ioo 0,000 0 , 000 0 , oflo 0,000 0 , 0 0 0

0 , 0 0 0

0 ~ 0 0 0

0,000

G A ” b / V 9 , 0 0 0 0

ZCL 0 , 0 0 0 0,000 0.000 0 , 0 0 0 0,000 0,000 0 , 0 0 0 0 , 0 0 0 0,000 0,006 0 , 0 0 0 0.000 0,000 0,000 0 , 0 0 0

YP - L , 0 0 0 0

8CL Q ,000 3 , 0 0 0 I , 0 0 0 7 , 0 0 0 9,OQr)

1 0 , 0 0 0 I l . 0 0 0 1 1 , 5 0 0 1 ~ , 0 0 0 10 ,SQO 1 3 , 0 6 0 14,SQO 15,000 16,000 18 ,000

Y O - 1 1 , 0 0 0 0

THETA 0 , 0 0 0 0,000 0 , 0 0 0 0 , 0 0 0 0 , 0 0 0 0 , 0 0 0 0 , 0 0 0 0,000 0,000 0,000 0 , 0 0 0 0 , 000 0 , 0 0 0 0 , 0 0 0 0,000

ZQ 2 , 0 0 0 0

A 1 ,000 1 ,000 1,206 1 , 4 0 0 1,600 1 , 7 0 0 1,800 1,890 1,900 1,950 2 ,000 2 , 1 4 0 2,200 iI .300 2 ,500

1 o o o 0

1 , 0 0 0 1 ,040 1,200 1,900 1,600 1,700 1,800 1 ,8JO 1,900 1 ,950 2,000 2, IS0 2,200 2,300 2 ,500

DZJC A t 1 1.000 1,000 1.000 1,004 1 ,000 1,000 l~m000 1,000 1,000 1.000 1 ,000 1 , 0 0 0 2.000 2,000 2 ,000

VOATCX NUMBER

J

1 2 3 U 5 b 7 e P

10

12 1 1

13 14 IS l b

VORTEX NUMBER

J

17

19 le

VORTEX NUMBER

J

20

E2 21

23 2 0 2 s

VORThk YUMBER

J

Zb

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(e) Page 5.

Figure 9.- Continued.

80

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(f) Page 6 .

Figure 9.- continued.

I T E R A T I O N 1

(9) page 7-

F i g u r e 9. - Cont inued .

82

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(i) Page 9.

Figure 9. - Continued.

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(j) Page 10.

Figure 9.- Continued.

85

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