Effects of nonlinear aerodynamics and static aeroelasticity on mission performance calculations for a fighter aircraft

EFFECTS OF NONLINEAR AERODYNAMICS AND STATIC AEROELASTICITY ON MISSION PERFORMANCE CALCULATIONS FOR A FIGXTER AIRCRAFT Gary L. G i l e s NASA Langley Research Center Hampton, VA Kenneth E. Tatum Planning Research Corporation Hampton, VA Willard E. FOSS, Jr.

NASA Langley Research Center Hampton, VA

JeREcu)HVG PAGE BLANK NOT Fll.ME0

INTRODUCTION During conceptual design studies of advanced aircraft, the usual practice is to use linear theory to calculate the aerodynamic characteristics of I candidate rigid (nonflexible) geometric external shapes. Recent developments and improvements in computational methods, especially computational fluid dynamics (CFD), provide significantly improved capability to generate detailed analysis data for the use of all disciplines involved in the evaluation of a proposed aircraft design.

This paper describes a multidisciplinary application of such analysis methods to calculate the effects of nonlinear aerodynamics and static aeroelasticity on the mission performance of a fighter aircraft concept.

The aircraft configuration selected for study was defined in a previous study using linear aerodynamics and rigid geometry. The.results from the previous study are used as a basis of comparison for the data generated herein. Aerodynamic characteristics are calculated using two different nonlinear theories, potential flow and rotational (Euler) flow. The aerodynamic calculations are performed in an iterative procedure with an equivalent plate structural analysis method to obtain lift and drag data for a flexible (nonrigid) aircraft. These s t a t i c aeroelastic data are then used in calculating the combat and mission performance characteristics of the aircraft. Comparisons are given between data obtained using conventional methods in the earlier study and the data obtained herein using more rigorous analytical methods.

Status

Aircraft conceptual design studies based on linear

aerodynamic theory and rigid geometric shape

Objective

To calculate the effects of nonlinear aerodynamics

and static aeroelasticity on the mission performance

of a fighter aircraft concept

Outline

Configuration definition

Analytical tools and procedures

Static aeroelastic results

Mission performance results

4 7 8 ARTIST'S CONCEPTION OF TVC AIRCRAFT This study needed a configuration which would demonstrate the applicability of the methods to realistic geometries, e.g., a complete fighter aircraft.

The aircraft chosen needed to provide some complexity without introducing difficulties which would detract from the research goals of the study.

A conceptual drawing of the aircraft selected is shown in the figure. The design incorporates many advanced technologies, including the concept of Thrust-Vector-Control (TVC). The TVC aircraft is a tailless, twin-engine vehicle utilizing multi-axis thrust vectoring for directional control and trim at supersonic speeds, both in cruise (Mach=2.0) and maneuver. The leading- a n d t r a i n i n g - e d g e devices are intended € o r subsonic maneuver, take- off and landing.

The configuration is the result of conceptual design studies, and only limited experimental data for the aircraft e x i s t , a l l f o r t h e rigid-body case. Experimental aerodynamic data for both the rigid and deformed shapes would be desirable for comparison with calculated data. The combination of a moderate-to-high wing loading for modern fighters and a relatively thin wing provided the potential for significant aeroelastic effects. Also, the use of thrust vectoring, instead of a horizontal tail, for trim and control eliminated the difficulties of analyzing multiple lifting surfaces, a problem inherent in many current production CFD codes. The simplicity of description coupled with potentially large physical effects made the TVC aircraft a desirable test-bed for the current study.

DISCRETIZED MODELS OF THE TVC AIRCRAFT defined by s e t s of p o i n t s which d e s c r i b e a i r f o i l c r o s s s e c t i o n s a t s p e c i f i e d span l o c a t i o n s . I n t h e region of t h e wing-body i n t e r s e c t i o n , t h e p o i n t s on t h e f u s e l a g e a r e l o c a t e d t o provide a smooth t r a n s i t i o n between t h e fuselage and wing.

The geometric i n p u t d a t a r e q u i r e d by t h e nonlinear aerodynamic a n a l y s i s proqrams are i l l u s t r a t e d a t the bottom of the figure. Geometry data are i n t e r p o l a t e d from t h e database geometry a t s e l e c t e d c r o s s s e c t i o n s from t h e ORIGINAL PAGE I S OF POOR QUALtTY AERODYNAMIC ANALYSIS METHODS The m i s s i o n a n a l y s e s i n t h i s s t u d y were based on f o r c e estimates f r o m t h r e e d i f f e r e n t a e r o d y n a m i c a n a l y s i s t o o l s . The b a s e l i n e m i s s i o n p r e d i c t i o n s u t i l i z e d l i n e a r a e r o d y n a m i c t h e o r i e s w i t h t h e a s s u m p t i o n t h a t t h e drag i s separable i n t o components, e . g . s k i n f r i c t i o n , wave, e t c . ( R e f s . 2 t o 7 ) .

U s i n g a "Mach-box" r e p r e s e n t a t i o n o f t h e r i g i d wing, t h e i n d u c e d drag w a s o b t a i n e d f r o m l i n e a r i n t e g r a l e q u a t i o n s a n d a n estimate of a t t a i n a b l e l e a d i n g - e d g e s u c t i o n . F a r - f i e l d wave drag was computed b y t h e s u p e r s o n i c area r u l e .

I n a n e f f o r t t o improve t h e f o r c e p r e d i c t i o n s , two n o n l i n e a r a e r o d y n a m i c a n a l y s i s m e t h o d s were u s e d . The f i r s t , SIMP ( R e f . 8), s o l v e s t h e c o n s e r v a t i o n - l a w f o r m of t h e s t e a d y f u l l p o t e n t i a l e q u a t i o n b y a n i m p l i c i t s p a t i a l m a r c h i n g t e c h n i q u e . F i n i t e d i f f e r e n c e s are u s e d t o d i s c r e t i z e t h e d i f f e r e n t i a l e q u a t i o n . The s e c o n d c o d e , EMTAC ( R e f . 91, solves t h e u n s t e a d y E u l e r e q u a t i o n s b y a s i m i l a r s p a t i a l m a r c h i n g t e c h n i q u e . The d i s c r e t i z a t i o n i s b y f i n i t e volume f l u x b a l a n c i n g . Both c o d e s u s e t h e s a m e g e o m e t r y i n p u t a n d g r i d g e n e r a t i o n r o u t i n e s . The c o d e s are capable o f c o m p u t i n g s u p e r s o n i c f l o w f i e l d s f o r complex geometries, i n c l u d i n g mass f l o w i n t o i n l e t s .

The E u l e r e q u a t i o n s i n c l u d e f e w e r a s s u m p t i o n s t h a n t h e p o t e n t i a l e q u a t i o n s a n d , as s u c h , are presumed t o be more a c c u r a t e . However, t h e y a l s o r e q u i r e more c o m p u t e r r e s o u r c e s , as would be e x p e c t e d .

Linear theory

Wave drag: supersonic area rule

Drag-due-to-lift: integral equations

Nonlinear full potential theory (SIMP)

Finite difference spatial marching

3D steady inviscid conservation law

Euler theory (EMTAC)

Finite volume spatial marching

3D nonlinear inviscid equations

4 81 ORIGINAL PACE IS OF POOR QUALITY STRUCTURAL ANALYSIS METHOD The s t r u c t u r a l a n a l y s i s method, R e f . 1 0 , u s e d f o r t h i s s t u d y i s implemented i n a computer p r o g r a m r e f e r r e d t o a s ELAPS ( E q u i v a l e n t L a m i n a t e d Plate - S o l u t i o n ) . T h i s method r e q u i r e s o n l y a s m a l l f r a c t i o n o f t h e volume o f i n p u t d a t a compared t o a c o r r e s p o n d i n g f i n i t e - e l e m e n t s t r u c t u r a l model. The r ? s u l t i n g r e d u c t i o n i n n u m e r i c a l model p r e p a r a t i o n i s i m p o r t a n t d u r i n g e a r l y s:ages o f d e s i g n where many c a n d i d a t e c o n f i g u r a t i o n s a r e b e i n g assessed.

The wing s t r u c t u r e i s r e p r e s e n t e d as a n e q u i v a l e n t p l a t e i n t h i s f o r m u l a t i o n . The p l a n f o r m g e o m e t r y o f t h e s t r u c t u r a l box i s d e f i n e d by m u l t i p l e t r a p e z o i d a l s e g m e n t s as shown i n t h e f i g u r e . A c r o s s - s e c t i o n a l view o f a t y p i c a l segment i s a l s o shown. The wing d e p t h , h , camber d e f i n i t i o n , z c , a n d c o v e r s k i n t h i c k n e s s e s , t, are a l l d e f i n e d i n p o l y n o m i a l a s e g m e n t .

form o v e r t h e p l a n f o r m o f The R i t z method i s u s e d t o o b t a i n a n a p p r o x i m a t e l y s t a t i o n a r y s o l u t i o n t o t h e v a r i a t i o n a l c o n d i t i o n o f t h e e n e r g y o f t h e s t r u c t u r e a n d applied l o a d s .

I n t h i s method, t h e wing d e f l e c t i o n i s assumed t o b e r e p r e s e n t e d i n p o l y n o m i a l f o r m as g i v e n f o r t h e b e n d i n g d e f l e c t i o n by

w = c o o + c l o x 1 +Czox 2 + c o l y l ' . . . +cmnx m n y

(1) The R i t z s o l u t i o n i s u s e d t o d e t e r m i n e t h e n u m e r i c a l v a l u e s of t h e set of unknown c o e f f i c i e n t s , Cmn, w h i c h m i n i m i z e t h e t o t a l e n e r g y . The s o l u t i o n , g i v e n i n t h e form of E q . ( l ) , p r o v i d e s a c o n t i n u o u s f u n c t i o n a l d e f i n i t i o n of t h e wing d e f l e c t i o n o v e r t h e p l a n f o r m . T h i s c o n t i n u o u s d e f i n i t i o n e x p e d i t e s t h e i n t e r f a c e o f t h e s t r u c t u r a l a n d a e r o d y n a m i c c a l c u l a t i o n s .

ELAPS - Equivalent Laminated Plate Solution

I Secondary structure

Main wing box

Reference *

Wing planform plane Wing cross section MISSION ANALYSIS METHOD A computer program which calculates the mission radius and maneuverability characteristics of combat aircraft, Ref. 11, is used in this study. This program has been used at the Langley Research Center to assess mission performance of proposed configurations and to indicate associated research programs which would be expected to yield the most beneficial improvements, Ref. 12. The program can be used (1) in an analysis mode to determine the performance characteristics of a given configuration or ( 2 ) in a sizing mode to determine the configuration size in terms of takeoff gross weight, wing loading, and thrust-to-weight ratio that best meets all the mission performance constraints. Only the analysis mode is used in this study.

A variety of military missions can be specified by using a desired combination of modules to calculate performance data for take-off, climb, cruise, loiter, dash, combat, descent, reserves, and landing segments of a mission profile. The definition of the.a'ircraftis given in terms of propulsion system characteristics, aerodynamic characteristics, along with size and weight of the vehicle. The propulsion characteristics are precomputed, usually from data supplied by an engine manufacturer. The aerodynamic characteristics are represented in terms of lift and drag coefficients as functions of aircraft angle of attack and flight Mach number. The size of the aircraft is defined in terms of the wing area, the size and number of engines, and the take-off gross weight.

Program used at Langley Research Center to calculate

mission radius and maneuverability characteristics

of mi I itary aircraft

Flight segments used

Takeoff Climb Cruise

Loiter Dash Combat

Descent Reserves Landing

Inputs to program

Propulsion

(engine decks)

Aerodynamics

(CLand CD vs. a and M)

Aircraft size

(wing area, takeoff gross weight)

COMPUTING ENVIRONMENT This study is typical of multidisciplinary analysis/design efforts in that several existing computer programs are used with each program being operated by a disciplinary specialist. The computer programs used in this study resided on several different computers as indicated on the figure. No attempt was made to convert all programs to reside on a single machine.

accommodate communication of data between Instead, procedures were set up to the various machines and programs, The required interfaces between the programs were written so as to minimize the volume of data that was transmitted between computers.

The size and location of the computers used included a MicroVAX I1 on an engineer's desktop, the CYBER 800 series computers at the NASA Langley central computer site, and the more powerful CYBER 205 and CRAY 2 required by the nonlinear aerodynamic programs. The CRAY 2 is part of the NAS computer complex located at NASA-Ames.

Operating

Computer

system

NOS

CYBER 800 series

GEOM

CYBER 800 series NOS

MiddletonCarlson

NOS

CYBER 800 series

Harris wave drag

vsos

CYBER 205

SIMP

UNICOS

CRAY 2

EMTAC

VMS

MicroVAX II

ELAPS

NOS

CYBER 800 series

Mission analysis

4 84 TVC MISSION DEFINITION The p r i m a r y m i s s i o n f o r t h e TVC i s one of h i q h - a l t i t u d e i n t e r d i c t i o n . The a i r c r a f t w a s d e s i g n e d t o c r u i s e a t Mach 2 w i t h a r a d i u s o f 5 0 0 n a u t i c a l m i l e s . A p a y l o a d o f 2 9 0 0 l b s . i s expended a t t h e r a d i u s s t a t i o n . Combat r e q u i r e m e n t s are f o r o n e a n d a h a l f s u s t a i n e d t u r n s a t Mach 2 a t an a l t i t u d e of 4 0 , 0 0 0 f t . w i t h a n u l t i m a t e maneuver c r i t e r i a of 8.1 g load f a c t o r . The m i s s i o n p e r f o r m a n c e c a l c u l a t i o n s u s e d t h e f o l l o w i n g f u e l a l l o w a n c e s . The t a k e o f f f u e l a l l o w a n c e i s t a k e n t o be t h e f u e l r e q u i r e d t o o p e r a t e t h e e n g i n e s f o r o n e - h a l f m i n u t e a t t h e maximum augmented t h r u s t l e v e l a n d t h e n f o r one m i n u t e a t t h e maximum non-augmented t h r u s t l e v e l . F u e l a l l o w a n c e f o r combat i s t h e amount r e q u i r e d t o meet t h e combat r e q u i r e m e n t s g i v e n a b o v e , The r e s e r v e f u e l a l l o w a n c e i s t h e f u e l r e q u i r e d t o l o i t e r f o r 2 0 m i n u t e s a t sea l e v e l .

The m a j o r i t y o f t h e m i s s i o n i s p e r f o r m e d w i t h t h e a i r c r a f t a t Mach 2 c r u i s i n g c o n d i t i o n s (outbound and i n b o u n d ) . Combat c o n d i t i o n s o c c u r f o r a small p e r c e n t a g e of t i m e . The r e l a t i v e t i m e s p e n t i n e a c h o f t h e s e c o n d i t i o n s h a s a c o n s i d e r a b l e impact on t h e p e r f o r m a n c e r e s u l t s p r e s e n t e d l a t e r .

\

-

I

-

/ / i r

Cruise Y’

Altitude Combat

x 10-3 ft.

I I I I 1

0 100 200 300 400 500

Range, N. MI.

Cruise Mach number = 2.0

Payload = 2900 Ibs; expended at radius station

Combat is for 1 1/2 turns at max. sustained turn rate

at Mach number = 2 . 0 and altitude 40 000 ft

FLEXIBLE WING AERO/STRUCTURAL ANALYSIS PROCEDURE A flow chart of the iterative procedure to arrive at the aeroelastically deformed shape of a wing at a specified flight condition is shown in the figure. A detailed discussion of the original development of this procedure is given in reference 13. The process is initiated with the geometric shape determined during the conceptual design studies taken to be the shape of the flexible aircraft at cruise. This baseline shape is analyzed at cruise to yield the jig (fabrication) shape, and at maneuver for an initial estimate of the elastic maneuver loads. Application of these maneuver loads to the jig shape produces an initial approximation to to the elastic maneuver Iteration proceeds by computing loads on the current maneuver shape shape.

At each approximation and applying these loads to the jig shape.

aerodynamic load analysis the maneuver lift is maintained by adjusting the aircraft angle of attack. Convergence is achieved when the calculated air loads are consistent with the structural deflection from the jig shape.

The converged aerodynamic characteristics are then used in mission analysis calculations.

The continuous definition of the deformed wing shape used in ELAPS expedites An the interface between the aerodynamics and structures programs.

equivalent load vector corresponding to the number of unknown displacement function coefficients, Eq. 1, is required for analysis of the equivalent plate structure. This load vector is formed by integrating the product of the aerodynamic pressure and displacement function terms over each portion of the aerodynamic grid on the wing surface. In the structures-to- aero interface, these continuous, analytic definitions of displacements are evaluated at each point of the aerodynamic input geometry and used directly to generate a deformed configuration.

Procedure Assume shape

I Cruise loads Maneuver loads I . _

I I I I /

I Initial maneuver shape I

1 I No Are loads consistent

' - 1 with shape?

7 - 7 Mission analysis

CONVERGED STRUCTURAL DISPLACEMENTS D u r i n g t h i s d e s i g n s t u d y , t h e t h i c k n e s s d i s t r i b u t i o n of t h e wing c o v e r s k i n s w a s s i z e d i n i t i a l l y u s i n g loads o n t h e r i g i d c r u i s e s h a p e a t t h e 8 . l g l o a d f a c t o r , The d e f l e c t i o n , c a l c u l a t e d i n t h e aeroelastic a n a l y s i s , o f t h i s f i r s t s t r u c t u r a l model, h e r e i n referred t o as wing 1, c a u s e d a n i n b o a r d s h i f t o f t h e a e r o d y n a m i c p r e s s u r e s a n d a c o r r e s p o n d i n g r e d u c t i o n i n stress levels i n t h e c o v e r s k i n s . The t h i c k n e s s of t h e wing s k i n s w a s t h e n r e s i z e d u s i n g t h e 8 . l g aeroelastic loads. T h i s wing w i t h r e s i z e d ( r e d u c e d i s referred t o as wing 2 .

t h i c k n e s s ) s k i n s A r e d u c t i o n i n a i r c r a f t w e i g h t , as a r e s u l t of g o i n g f r o m wing 1 t o wing 2 , i s n o t i n c l u d e d i n s u b s e q u e n t p e r f o r m a n c e c a l c u l a t i o n s . The a i r c r a f t w e i g h t w a s estimated u s i n g w e i g h t e q u a t i o n s which i n h e r e n t l y i n c l u d e t h e e f f e c t o f r e d u c e d s t r u c t u r a l loads r e s u l t i n g f r o m aeroelastic d e f o r m a t i o n .

The c o n v e r g e d s t r u c t u r a l d e f o r m a t i o n s a t 8 . l g load f a c t o r f o r wing 2 as computed by SIMP/ELAPS are shown i n the figure. The maximum d e f l e c t i o n ( m e a s u r e d f r o m t h e b a s e l i n e c r u i s e g e o m e t r y ) was 2 0 . 0 1 i n c h e s a t t h e wing , t i p t r a i l i n g edge. T h e l o a d i n g c a u s e d t h e wing t o t w i s t 6 . 0 8 degrees, edge down. S i m i l a r r e s u l t s were o b t a i n e d b y EMTAC/ELAPS w i t h t h e l e a d i n g maximum d e f l e c t i o n i n c r e a s i n g t o 2 1 . 3 7 i n c h e s . ~

300 Max displacement

= 20801 7 r

I Contour interval 085 in.

I

0 ' I I I I

100 200 300 400 500 600

X, in.

AERODYNAMIC CROSS-PLANE GRID The l e v e l o f d e t a i l o f t h e a n a l y t i c a l r e p r e s e n t a t i o n u s e d i n t h e s o l u t i o n of t h e aerodynamic f l o w e q u a t i o n s is i l l u s t r a t e d i n t h i s f i g u r e . A r e p r e s e n t a t i v e c r o s s - p l a n e g r i d a t a specific body s t a t i o n i s shown f o r one o f t h e deformed wing g e o m e t r i e s computed by SIMP. Both SIMP a n d EMTAC employ streamwise m a r c h i n g schemes t o i n t e g r a t e t h e f l o w e q u a t i o n s on s u c c e s s i v e p l a n e s , such as t h e one shown. A c o n i c a l f l o w s i m i l a r i t y s o l u t i o n i s g e n e r a t e d t o s t a r t t h e c a l c u l a t i o n on a p l a n e n e a r t h e nose of t h e a i r c r a f t , which i s assumed t o be sharp, t h e r e b y a l l o w i n g a n a t t a c h e d bow shock wave. T h i s s t a r t i n g s o l u t i o n d e f i n e s t h e incoming f l o w f o r t h e n e x t plane a small s t e p downstream. By r e p e t i t i v e l y s t e p p i n g ( m a r c h i n g ) from one p l a n e t o t h e n e x t , t h e e n t i r e l e n g t h of t h e body i s t r a v e r s e d . On e a c h plane a two-dimensional g r i d i s c o n s t r u c t e d a b o u t t h e body c r o s s - s e c t i o n , as shown, a n d a n u m e r i c a l d i f f e r e n c e a p p r o x i m a t i o n t o t h e f l o w e q u a t i o n s i s s o l v e d f o r t h e d e p e n d e n t v a r i a b l e s ( s ) , which f o r EMTAC are t h e d e n s i t y , v e l o c i t y components, a n d i n t e r n a l e n e r g y . P r e s s u r e c a n t h e n be d i r e c t l y computed from t h e s e q u a n t i t i e s u s i n g t h e ideal gas l a w . I n SIMP t h e v e l o c i t y components are computed by n u m e r i c a l l y d i f f e r e n t i a t i n g t h e v e l o c i t y P r e s s u r e a n d d e n s i t y are t h e n computed by t h e i d e a l gas l a w and p o t e n t i a l .

t h e B e r n o u l l i e q u a t i o n . Thus, a t e a c h l o n g i t u d i n a l s t a t i o n down t h e body surface, the flow variables, such as pressure, are computed at discrete l o c a t i o n s on t h e body s u r f a c e and o f f t h e s u r f a c e i n t h e f l o w f i e l d .

80 X 25 Points

2, in. 50

-50

0 50 100 150 200 250

Y, in.

DETAILS OF THE AERODYNAMIC FLOW FIELDS By using grids such as the one shown in the previous figure, the nonlinear aerodynamic codes provide a high degree of resolution of the flow fields about the aircraft. ! l ! h e contour plots of cross-plane pressure shown in this figure are representative of the detail attainable with SIMP and EMTAC. Such plots allow the calculated loads/pressures to be interpreted in light of the physics being modeled by the differential equations. For example, an upper-surface cross-flow shock wave is predicted by SIMP, evident in the concentration of isobars near Y-100. However, EMTAC does not indicate a shock impinging on the wing. Such localized differences in the flow field contribute to differences in the overall load distribution- and resulting deflections in the aeroelastic calculations. While each aerodynamic code gave substantially different computed flow features (i.e.

shocks, expansions, etc.), the overall character of each of these flow fields did not change significantly during the aeroelastic iterations with a given aerodynamics code. Even at the high maneuver conditions (8.lg's) where large structural deflections were computed, the overall character of the flow fields did not change, however the relative magnitudes or strengths of the aerodynamic pressures were affected by the deflections.

Body station 503 in.

Flexible SIMP 100r ,- in. Flexible z, EMTAC n 50 100 150 200 250 Spanwise location 4 89 COMPARISON OF SPANWISE PRESSURE DISTRIBUTIONS The aerodynamics and structural analysis codes were coupled through the aerodynamic loads as represented by pressure coefficient distributions over the wing surface. Representative spanwise pressure variations are shown in this figure as computed by SIMP and EMTAC at specific axial (body) stations.

Two of these distributions are for the baseline rigid geometry while the third is for the aeroelastically deformed solution as computed by EMTAC/ELAPS. Each plot is part of the overall solution at a vehicle lift coefficient of approximately 0.361, however the section lift coefficient at each body station changes due to axial shifts of the load distribution produced by different aerodynamic theories and from the aeroelastic deformations.

A significant feature of these distributions is the unloading of the outboard wing region due to the static aeroelastic deformation. Also significant is the more physically realistic loading computed by EMTAC as opposed to SIMP in the region of the wing tip. At the high lift conditions required for maneuver, the assumption of potential theory is questionable, and, while this study has shown usable results from a potential flow code, the Euler indications are that the more complete theory, represented by ~ equations, provides more reliable results.

Body station 503

-.4 r

-.2

Pressure

coefficient ,

CP

.2

FORCE PREDICTIONS FOR THE TVC AIRCRAFT A s t h e p r e s s u r e d i s t r i b u t i o n s are key q u a n t i t i e s i n t h e s t a t i c a e r o e l a s t i c c o m p u t a t i o n s , t h e i n t e g r a t e d p r e s s u r e s i n t h e f o r m s o f drag a n d l i f t are key q u a n t i t i e s i n p e r f o r m a n c e c a l c u l a t i o n s . The s o l i d c u r v e shown i n t h e f i g u r e i s t h e drag p o l a r computed by t h e b a s e l i n e l i n e a r a e r o d y n a m i c t h e o r y , i n c l u d i n g t h e i n d u c e d drag ( o f t e n r e f e r r e d t o as d r a g - d u e - t o - l i f t ) a n d t h e wave drag, assumed t o be a c o n s t a n t a t a g i v e n Mach number. S e l e c t e d n o n l i n e a r a e r o d y n a m i c c a l c u l a t i o n s are shown by t h e s y m b o l s f o r b o t h r i g i d a n d f l e x i b l e g e o m e t r i e s . A t low l i f t c o e f f i c i e n t s , t h e d i f f e r e n c e i n r e s u l t s b e t w e e n n o n l i n e a r a e r o d y n a m i c t h e o r i e s , i n c l u d i n g t h e effects o f s t a t i c a e r o e l a s t i c i t y , i s n e g l i g i b l e a n d s i n g l e s y m b o l s are shown t o i n d i c a t e t h e drag i n c r e m e n t predicted b y n o n l i n e a r t h e o r y . A t h i g h e r l i f t s , however, t h e d i f f e r e n c e s are n o t i c e a b l e w i t h p r o g r e s s i v e l y h i g h e r drag predicted b y SIMP a n d EMTAC, w i t h r i g i d a n d f l e x i b l e g e o m e t r i e s . I n p a r t i c u l a r , f o r t h e case o f a f l e x i b l e wing, t h e drag c o e f f i c i e n t f r o m a e r o e l a s t i c c a l c u l a t i o n s u s i n g EMTAC ( E u l e r t h e o r y ) i s a b o u t 0 . 0 0 2 5 greater t h a n t h a t c a l c u l a t e d u s i n g SIMP ( F u l l p o t e n t i a l t h e o r y ) .

N o t e t h a t w h i l e t h e l i n e a r t h e o r y a s s u m e s separable wave a n d i n d u c e d d r a g , t h e n o n l i n e a r t h e o r i e s i n c l u d e b o t h of t h e s e components i n t h e c a l c u l a t i o n o f a s i n g l e drag v a l u e .

Linear theory,

rigid

A

SIMP, rigid

0 SIMP, flex.

/

.4 V

Lift 1

coefficient, -3

CL I

0 .01 .02 .03 .04 .05 .06 .07 .08

Drag coefficient, CD

(wave + induced)

AERODYNAUIC DATA FOR PERFORMANCE ANALYSIS The required aerodynamic input t o the mission analysis program consists of the l i f t , drag, and angle of attack variations f o r the specified mission.

These three variables a r e r e l a t e d a s shown i n the figure f o r t h e baseline l i n e a r theory prediction and t h e SIMP and EMTAC predictions f o r t h e r i g i d and f l e x i b l e geometries. The angle of attack i s an input t o SIMP and EMTAC and t h e CL i s computed f r o m the integrated pressures. The CD shown includes the estimated s k i n f r i c t i o n and roughness drag. These l a t t e r two components i n t h e o r i g i n a l l i n e a r theory calculations. A n were i d e n t i c a l t o those used analysis code solving t h e Wavier-Stokes (viscous) equations would couple these e f f e c t s w i t h t h e wave and induced drag components and eliminate t h i s approximation.

The curves shown f o r t h e nonlinear r i g i d / f l e x i b l e cases were derived by x r v e f i t t i n g t h e values obtained from a limited s e t of computations since t h i s was a research project, not an a i r c r a f t development p r o j e c t . Basic assumptions f o r t h e curve-fits were: 1.) the nonlinear predictions convergec t o t h e same values a t low l i f t , and 2 . ) both t h e CL/alpha and CL/CD curves were of second order. A s might be expected, t h e l i n e a r predictions a r e the most optimistic and include nonlinear theory and/or static a e r o e l a s t i c i t y r e s u l t s i n degradation of the available l i f t and increase i n predicted drag.

/ e

.5

.4

/ i f I

Lift .3

coefficient, a - Lineartheory

b - SIMP, rigid

CL .2

c - SIMP,flex.

d - EMTAC, rigid

.I

e - EMTAC,flex.

I

L

I

0 .05 . 10 . 15

0 5 10 15 20

Angle of attack, a Drag coefficient, C D

(degrees)

49 2 CObdBAT PERFORMANCE OF TEE TVC AIRCRAFT The effect of nonlinear aerodynamics and static aeroelasticity on the combat performance of the TVC aircraft is indicated on the figure. The specific power, P , , is a measure of the energy maneuverability of an aircraft for combat. This parameter is a direct function of the difference between the thrust and the drag. The load factor for maximum sustained turning occurs where the specific power is equal to zero. At a greater load factor, the specific power is negative and the aircraft is not able to sustain the flight condition. The increased drag levels of the nonlinear aerodynamic and the non-rigid structural considerations result in lower sustained load factors and associated turn rates. The decrease in load factor is from a value of 8.19,s to about 7.19's. In addition to the loss in maneuvering capability, the amount of fuel used during combat is increased from 1000 lbs. to 1143 lbs. Consequently, the fuel available to cruise is reduced and as a result the mission radius capability is reduced.

As indicated, using the different nonlinear aerodynamic theories result in the largest reduction in calculated combat performance, with aeroelasticity contributing a somewhat smaller increment. Consideration of aeroelasticity often has a significant effect on maximum roll rate characteristics of a fighter aircraft, Refs. 14 and 15. However, the roll rate characteristics of the TVC aircraft were not calculated in this study.

Mach 2.0, altitude = 40 000 ft

Ps = (thrust - drag) x velocity/weight

Y O

2000 - Procedure gmaX reduction

Linear, rigid 8.09 I

----- SIMP, rigid 7.60 6.0

--- SIMP, flex. 7.40 8.5 EMTAC, rigid 7.16 11.5 EMTAC, flex. 7.09 12.4 P S Specific power, gmax at Ps 0 ftlsec 1 3 5 7 9 Load factor, g MISSION PERFORMANCE OF THE TVC AIRCRAFT The increased drag levels estimated f o r the nonlinear aerodynamics and for the f l e x i b l e s t r u c t u r a l considerations r e s u l t i n m i s s i o n radius losses of up - I d 68 N . M i . Approximately 75 percent of each of t h e losses is due t o t h e 7' reduced cruise efficiency as a d i r e c t r e s u l t t o t h e increased drag estimates given b y t h e nonlinear codes. The remaining 25 percent of each of t h e losses i s due t o the reduction i n available c r u i s e f u e l associated w i t h the increased combat f u e l allowance.

As would be expected f o r t h i s p a r t i c u l a r mission, t h e e f f e c t of a e r o e l a s t i c i t y on a i r c r a f t range i s minimal. However, f o r a mission i n which a large percentage of t o t a l time i s spent i n combat conditions, including t h e e f f e c t s of a e r o e l a s t i c i t y i n design and analysis could become important.

Percent loss

0 Rigid

U Flexible A in radius

400 t

300 1

Radius

N. MI. *oat

loot

Linear Full potential, Euler,

SIMP EMTAC

CONCLUDING REMARKS A multidisciplinary analysis procedure has been developed that includes aerodynamic, structural and performance calculations. Use of this procedure is demonstrated by analyzing the effects of nonlinear aerodynamics and static aeroelasticity on the performance of a TVC fighter aircraft.

Representation of the wing structure as an equivalent plate allows aeroelasticity considerations to be included early in the design process before a finite element model is available. In addition, the continuous definition of the wing deformation permits the interface to the aerodynamics Two programs, one programs to be written in a simple but general manner.

based on full potential theory and the other based on Euler theory, were incorporated to provide a comparison of the effect on the calculated aerodynamic characteristics. There were significant differences in the pressure fields and the Euler theory predicted higher overall drag than full potential theory.

The aircraft performance was affected primarily by aerodynamic theory rather than aeroelastic effects. The combined effect gave a maximum loss in sustained load factor of 12% and a mission radius loss of 14% compared with linear aerodynamic calculations on a rigid aircraft. The cost-effectiveness of using these more rigorous analytical procedures for preliminary design must be determined by individual design organizations. As is demonstrated, this procedure provides the capability to provide refined design data.

However, the potential for these data to provide improvements in the final aircraft design must be assessed in view of the practical limitations imposed by budget and calendar time for a particular project

e

Multidisciplinary analysis procedure developed

that includes aerodynamic, structural, and

performance calculations

Equivalent plate structural representation expedites

aeroelastic calculations

e

Significant differences in pressure fields with

improvements in aerodynamic modeling

(linear, full potential, Euler)

e

Performance affected primarily by aerodynamic theory;

maximum sustained load factor loss 12%

mission radius loss = 14%

e

Cost-effectiveness of procedure decided by user

REFERENCES 1. Hall, J. F.; Neuhart, D. H.; and Walkley, K . B. : An Interactive Graphics Program for Manipulation and Display of Panel Method Geometry. NASA CR 166098, March 1983.

2. Sommer, S. C.; and Short, B. J.: Free-Flight Measurements of Turbulent- Boundary-Layer Skin Friction in the Presence of Severe Aerodynamic Heating at Mach Numbers from 2.8 to 7.0. NACA TN 3391, 1955.

3. Harris, R. V., Jr.: An Analysis and Correlation of Aircraft Wave Drag.

NASA TM X-947, 1964.

4. Carlson, H. W.; and Middleton, W. D.: A Numerical Method for the Design of Camber Surfaces of Supersonic Wings With Arbitrary Planforms.

NASA TN D-2341, 1964.

5. Sorrells, R. B.; and Miller, D. S.: Numerical Method for Design of Minimum-Drag Supersonic Wing Camber With Constraints on Pitching Moment and Surface Deformation. NASA TN D-7097, 1972.

6 . Carlson, H. W.; and Miller, D. S.: Numerical Methods for the Design and Analysis of Wings at Supersonic Speeds. NASA TN D-7713, 1974.

7. Middleton, W. D.; and Lundry, J. L.: A System for Aerodynamic Design and Analysis of Supersonic Aircraft. NASA CR 3351-3354, 1980.

8. Shankar, V.; Szema, K-Y; and Bonner, E.: Full Potential Methods for NASA CR 3982, Analysis/Design of Complex Aerospace Configurations.

May 1986.

9. Szema, K-Y; Chakravarthy, S.; and Shankar, V.: Supersonic Flow Computations Over Aerospace Configurations Using an Euler Marching Solver. NASA CR 4085, July 1987.

10. Giles, G. L.: Further Generalization of an Equivalent Plate Representation for Aircraft Structural Analysis. NASA TM 89105, February 1987.

11. FOSS, W. E., Jr.: A Computer Technique for Detailed Analysis of Mission Radius and Maneuverability Characteristics of Fighter Aircraft. NASA TP 1837, March 1981.

12. Coen, P. G.; and FOSS, W. E., Jr.: Computer Sizing of Fighter Aircraft. NASA TM 86351, January 1985.

13. Tatum, K. E.; and Giles, G. L.: Integrating Nonlinear Aerodynamic and Structural Analysis for a Fighter Configuration. AIAA Paper No. 87-2863. Presented at the 1987 AIAA/AHS/ASEE Aircraft Design, Systems and Operations Meeting, St. Louis, Missouri, Sept. 14-16, 1987.

14. Static Aeroelasticity in Combat Aircraft. AGARD Report No. 725, January 1986.

15. Static Aeroelastic Effects on High Performance Aircraft. AGARD Conference Proceedings No. 403, July 1987.