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, L ANG L EY AIRFOI L -RESF.&RCH PROGRAM " Percy J. Bobbitt NASA Langley Research Center INTRODUCTION _ ; i The purpose of this paper is to give an overview of past, present, and future airfoil r e search activities at the Langley Research Center. The immedi- ate past and future occupy most of the discussion; however, past accomplish- ments and milestones going back to the early NACA years are dealt with in a grams. Indeed the seeds of the current surge in activity were sown a dozen • y e ars ago; th e p e digree of many of Langley's present-day facilities can be I broad-brush way to give a better perspective of current developments and pro- traced to the mid thirties. In addition to the historical perspective, a short description of the facilities which are now being used in the airfoil program is given. This is followed by a discussion of new airfoil developments, advances in airfoil design and analysis tools (mostly those that have taken place over the past 5 or 6 years), and tunnel-wall-interference predictive methods and measurements_ The last subject to be treated is future research r e q uirements.
HISTORICAL PERSPECTIVE Airfoil research at the Langley Memorial Aeronautical Laboratory began shortly after it was established and long before its first tunnel became opera- tional In 1920. As assessment of the state-of-the-art of airfoil technology in th e world was made and the airfoil data collected were put in a unified format and published for the benefit of the scientific community in the 1920, 1921, and 1923 NACA annuals (refs. I to 3). A few of these early airfoils are shown in figure I; they indicate in a graphic way the lack of understanding of flow physics that existed in those early days. The airfoil sketched at the to p is the USA I tested in an MIT tunnel at 13 m / sec (44 ft / sec) and is very similar to the Spad, Sopwith, Italian 2, and Eiffel 53 airfoils. The next two were tested at the Eiffel Laboratory in 1914 and were apparently designed to determine whether the performance of airfoils which are in fact two or three airfoils connected together would be superior to single-hump airfoils. Eiffel 44, the fourth from the top, has what appears to be a separation step on the top side; the philosophy behind its design is somewhat more obscure. It should be noted that the Eiffel Laboratory was probably the leading airfoil research center in the world prior to World War I and dozens of excellent airfoils were produced.
The first Langley airfoil, which appeared in the 1923 NACA annual, was the Langley Memorial Aeronautical Laboratory 54. It was tested in the first NACA wind tunnel, the WT-I 5-foot tunnel, which, as noted earlier, began operating in 1920.
Reynolds number scaling was alre a dy a serious concern in 1920 and was the mo tivatin g factor in th e d e si g n and construction of the variable d e nsity !
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}!:- : i ' tunnel (VDT). When it came on - line in 1923. it was the most advanced tunnel / ! in the world. It could operate at pressure_ up to 20 atmospheres and achieve i_ Reynolds numbers up to 3.3 x 106 for a 13-cm (5-in.) chord model Another ._ _i: i facility of note that was constructed in the late twenties was the 12-inch i high-speed tunnel which could produce velocities up to 350 m / sec (800 mph).
The latter half of the twenties saw the development of the NACA 4-digit _ and modified 4-d_git series of airfoils. A sketch of one of the most popular, _ the 4412, is given in figure 2. A calcuiative procedure for airfoils of arbi- trary shape was also formulated and provided a more rational basis for airfoil- family design.
Several more airfoil families were generated in the thirties including • the 5 - digit series, the l-series (also known as the 16-series), and the NACA laminar-flow airfoil family. A 5-digit and a laminar-flow airfoil section are depicted in figure 2 along with a GA(W)-2 for comparison. The laminar-flow series was preceded by a considerable amount of research on calculative m ethods for boundary layers and empirical transition criteria.
Wind-tunnel construction during the thirties was driven by a desire to test ,_ airfoils under conditions approaching the flight environment, especially those designed for extensive runs of laminar flow. The low turbulence tunnel (LTT) started running in the mid thirties and, in addition to providing useful data, served as a learning experience for the design of the Langley low-turbulence pressure tunnel (LTPT). The LTPT started operation in 1941 and is still in use.
By the mid forties, the characteristics of a large numbec of airfoils had been defined; design procedures were being relied on for definition of airfoil geometry and modifications to existing airfoils. A report summarizing most of these data and procedures was published in 1945 (ref. 4). This document later became the basis for a book by Ira H. Abbott and Albert E. von Doenhoff (ref. 5).
The late forties saw some shift in emphasis away from airfoil-section develop- ment to high-lift systems and boundary-layer transition and control.
A change in priorities in the early fifties necessitated a reduction in _ airfoil research, and by the mid fifties, it had completely disappeared. Air- _:_ foil research did not c ommen c e again until 1965 when R. T. Whitcomb conceived a : : _ new type of airfoil section for high subsonic speed applications (ref 6) By • .
¢, virt u e of a unique top side shaping, these airfoils were able t o delay the : i formation of shocks and hence, for a given thickness, increase the drag-rise b lach number. Since these airfoils are able to sustain large regions of super- ; ! : . critical flow without shock formation near their design condition, they have _. been termed "supercritical" or "shockless" airfoils.
The first Whitcomb supercritical airfoil was a two-element design; it was followed closely by a slngle-element concept. Its value was quickly grasped by the aircraft industry and dermnds for supercritical airfoils for a variety of flight conditions and applications soon foilowed. This demand and interest led to a number of actions. It was decided in 1968 to reactivate Langley's airfoil test facilities; a series of supercritical airfoils were designed; theoretical efforts to provide a design metllod were commenced; and flight demon- stration projects using the T2-C and F_V - ] aircraft were instituted. The first '_ d ividends fro m these actions came in the 1 9 70-71 time period whe n flight tests clearly validated the airfoil concept and the Langley 6- by 19-inch transonic . !
tunnel became operational The first design and analysis codes for super- critical airfoils were published in 1972. These codes, developed at the NYU " Courant Institute by a team of scientists led by P. R. Garabedian (ref. 7), are now in use all over the world.
The breakthrough in the design of airfoils for high subsonic applications precipitated a renewed effort to develop improved airfoils for low speeds. With the aid of a computer code developed at Lockheed under Langley contract by J.A. 4 : Braden, S. H. Goradia, and W. A. Stevens (ref. 8), R. T. W_itcomb designed the GA(W)-I airfoil. It was tested in 1972 and showed a potential for better climb characteristics than airfoils in common use. Requests for the design of, and data on, similar airfoils with different thickness ratios were numerous.
By 1973, the number of Langley researchers and organizations engaged in airfoil research to explore the new concepts had increased in response to indus- try pressures for more data. Informal communication and individual planning no longer provided the coordination required of such a large effort. Consequently, i in 1973, airfoil-research activities were programmized Since that time, pro- ; gross in the formulation of new airfoil designs and computer codes with improved capabilities has been remarkable. Some of the major milestones of the past 4 years are as follows: Langley 6- by 28-inch transonic tunnel and 0.3-meter transonic cryogenic tunnel became operational.
Low-speed, medium-speed, and new supercritical airfoil families were defined.
i Low-drag general aviation airfoils were developed.
New airfoil design and analysis methods were formulated.
Theoretical and experimental research on massive separation began.
Theoretical and experimental studies on wall interference were initiated.
Q General aviation airfoil design and analysis service was created.
With the exception of the airfoil design service, these items are discussed in the subsequent sections. The airfoil design service, created in 1976 at Ohio State University, gives the general aviation industry access to the latest com- puter codes for airfoil design and analysis. Scientists, expert in the appli- cation of all NASA-developed codes, are available to render whatever level of service is required.
TEST FACILITIES i The NACA and its successor, the NASA, have always been in the forefront of wind-tunnel technology and test techniques. Tunnel facilities developed i_ , .., :_ .,:{ o v er th e past fe w y e ar s f o r airf o il t es ts and t h o se bei ng us e d in th e pr o gram that were construct e d many y e ar s ago continu e to provide a uniqu e capability f or two-dim e ns l onal test i ng. The four w i nd tunn el s whi c h are used p rimari l y f or a i rfo i l r e s e arch a r e : Lang le y l o w - turbulence pr e s su re tunn e l La n gle y 6- by 19-inch transon i c tunne l Lang l ey 6- by 28- i nch tran s on i c tunnel L ang l ey 0. 3-me t e r t r an s o n i c cr yo g en ic t u nn el (20 - b y 60 -cm te s t se ction ) Th e L a ng l ey 8-f oot tran s onic pres su re t u nne l ha s _i s o b e en used for airfoil te s ts but th is was d on e pr i or to the 6- by 28- 1n c h transon i c tunn e l and the 0. 3 -meter tran s oni c cr yog e n i c tunne l b e coming available.
Th e low - turbulence pre ssu r e tunn e l (LTPT ) , a s noted e arl ie r, b e gan op e ra- t i on i n 1941 a n d is still in r e gular u s e ( s ee fig. 3) . It is still s uper i or to m os t tunnel s in the worl d ov e r it s operatin g range, wh ic h is Ma t h number s from 0. I to 0.4 and Reynold s number s (bas e d o n a 0.6-m ( 2 -ft ) c hord ) from 1.0 x 106 to 3 0 x 106. New ge n e ral aviation air foi l s are developed with the aid o f this f aci l ity; l o w-s peed characteri s tics o f s upercritl c a l air f oi ls are al s o explored. In addition, the excellent flow quality of the LTPT make s it ideal to carry out research on airfoils de s igned for natural or contro l led l aminar flow. Planned improvement s f or thi s fac i lity will en a ble it t o obtain a c curate data for ve r y high -l lft systems and f or airfoils at higher angle s o f attack than is now possible.
T he 6 - by 1 9 -in c h t r an s oni c t unne l came o n- li n e in 1971 and has been u ti - liz ed fo r both routin e a i r foil t es ts a nd t ec hniqu e -d e v e lopm e nt r e s ea r c h. A cr oss - s ec tion drawing o f thi s faci lity i s giv e n in f ig u re 4. It is a blowdown- type tunne l with no independent c ontrol o f Ma c h numb e r and Reynolds numb e r , A 1 5 - c m (6-in.) c hord mod el c a n be tested to Reynolds numbers o f 4. 5 x 106 up to a Math number o f 1.0. Future utilization of the 6- by 19-in c h tunnel will be primarily in the area of technique developm e nt with speci a l emphasis cn wind- tunnel wall interferenc e .
Th e workh or se fa c ility of the air f oil r e sear c h is the 6- by 2 8- in c h tran s oni c tunnel, depicted in figure 5 . It s nor m al M a th number range is from 0.3 to 1.0 with Reynolds numbers up to 13. 5 x 106 for Math number s abov e 0. 5 .
Independent c ontrol-of M a t h n u m ber a nd Reynold s nu m ber is po ss ible. The 6- by 28-1nch tun n el is u s ed for re s ear c h on every type of airfoil, including high- s peed ge n eral avia t ion, sup e r c rlti c al, propeller, and rotorcraft. In the near fu t ure, the c apabilities of this fa c ility will be enhan c ed by =he inst a llation of a d yna m i c "rig" to c arry out un s teady o sc illatory and dynami c m otion tests.
Sidewall bound a ry-layer- c ontrol plate s will al s o be provided to in c rease the maxi m u m angle of attack at which useful data can be obtained.
Th e most v e rs a ti le a i r foi l f ac i l ity i s the 0. 3- meter transoni c c ryogeni c t u nn e l (T C T) eq u i p p ed wi th it s 20 - b y 60-cm te s t s e c tion. A p hoto g raph o f t his f a c ility i s g iv e n in f i g ur e 6 and sh ow s the u n usu al ge omet r y o f the tunne l with the test section at the top and the return leg at the bottom. The sketches given in fig u re 7 illu s trate thi s fact more clearly. The botto m sketch s hown i s the original three-di m ensional oct a gonal te st s ection, the one in the m iddle 1 4 i s t he tw o- d im e n s ion a l in ser t w i th sch li er en s ) s t e m i n pl a ce , and t he to p s ke t c h is a s e lf-str e a m l i nin g tw o - d i me ns io nal s e c ti on s o o n t o be c o ns t ructed.
T h e u s e oi! n i t r og e n at cry og en i c t empe ratures giv e s r i se t o R e y n o lds nu m - be rs u p t o a f a c to r 5 l a rge r than those o f a c o nv en t i on a l a i r t u nn e l. It als o a ll o ws o ne t o _o ntr o l Math num b er , R e y n o lds nu mb er , a nd d yn a m i c pr e ssure i nde- p e n de ntly , a c apa bi l i ty m o re impo r t a n t p e rhaps i n three-d im ens io nal t h an i n tw o - dim ensi o n _ l te stin g_ si n ce aer o e l ast i c a n d R eyn o lds n u mber e ffec t s ca n be i s ol at ed . R e ,mold s num b er s u p to 50 × 1 0 6 c a n b e ob t ai n e d f or a 1 5-c m ( 6 -in.)
ch o rd mo del. P r o duc tio n testin g in t h e TCT sh ou l d c omm enc e in t h e fa l l after c omp le tio n o f a n u m b er o f m in o r imp r o ve m e nts .
Fu rthe r d e t a il s o n t h e c a p a bili t i es a nd pl ans f o r L a n gl e y 's t w o -d i mens lo n a l r e search fac ili t ie s can b e f o un d in t h e p a p er by E . J . R a y i n these pr o ce e di n g s (ref . 9) .
Rese ar c h a ir c r af t ha v e b een used a s te s t fac ili t i es as w e ll as w i n d tunnels .
An F gv- I f lg ht er and a T2-C t r a in er a i rc r aft w e r e p _o v ide d w i t h n e w win g s t o de t e r mine _he p erf o r m ance o f s u p e rcr i t i ca l sect io ns i n f ligh t. In bo th a ppli ca- t lo ns , th e s u percr i t l c a l w i n g s pr o ved su p er io r to the o r igi n a l o nes.
S im i l a r p r oo f t e s t s o f th e new g e n e ral av iatio n a i rf oi l sect io ns h a v e b een c o n d u c t e d . The GA(W ) - I w a s test ed o n t he Advanced Techn ology L ig ht Twln- E n gi ne (A TL I T ) ai r c raft , o r i g i nally a Pip e r S e neca , a n d t h e GA (W) -2 o n the B ee ch Sund o wn er . The latt e r i s s ho wn in fli gh t n e ar C ol u mb u s, Ohi o , in fi g ur e 8.
NEW A IRF OIL D E V E LO PMENT S L a ng l e y ' s a i rfo i l research program invo l ve s a v a r i e t y of airfoi l t yp e s inc l u d i ng L o w- sp ee d ge ner al a vi a t io n* L o w - s p eed n a t u r a l la m i n a r fl o w M e di u m spe e d Tr a n s por t - type s upercr itl c a l* Lar g e c a rgo s up e rcr it lc a l La mi nar. - fl o w c o n t r o l ( LFC ) supercr it ical H e l ico p ter* Fighter Propeller By f ar, t he m os t effo rt h a s b ee n expen d e d on the thr e e ai r foil ty p es in d i c a ted by the a s t eri s k s , a n d mo s t of the subse q uen t di sc uss i on t reat s th e a cc ompl is h- m en t s a nd p l an s fo r th ese t y p es . N ew d esig n s f or t h e o t he r t y p es o f ai r f o ils (e xcep t LFC s upe r cr l tical ) have i n so me ca s e s Ju st b een te st ed a n 4, in o t her s , are awa i t in g t es t or fa b rica t i o n . Th e LFC ai r f o il i s b ein g de v elo ped unde r t he NASA Ener g y Effic i e n t Tr a nsp or t , La mi n a r Fl o w C o ntr o l P r o ject a nd i s l i s t e d a bo ve only f o r c o mpl et eness .
C om p a ris o ns o f e x p er i men t w i t h c a lcul at e d resul t s fr o m t he b_: s t l o w - s p e e d and su p e r cr l t i cal -a irf o il pr edi c tiv e me thod s hav e ge ne r a l l y sh o w n tha t th e '_ theories ar e a cc ur a te. Th e or e ti ca lly d e t e rmin e d pressure distributions and lift and moment coefficients c orr e late well w i th experiment; absolute-drag levels are sometim e s in poor agreement. How e ver, predictions of relatlve-drag level and drag-rise Ma t h numb e r can usually be relied on. A result of these observations is that a philosophy has been adopted to test only a few repr e - s_ntatlve s ampl es o f e a c h typ e of air f oi l to e sta bl ish th e validity of t h e th e ory. This phi l osophy has been applied in th e c ase of the n e w Langley low- speed a i rfoil family. Figure 9 show s th e range of thicknesses and l l ft coeffi - cients of th e new design_ a s w ell as the i r status. Fiv e airfoils have already been t e st e d, and four oth e rs have be e n des i gned for future test i ng. These test • result s c oupl e d with availab le computer codes wil l enable other a i rfo i ls of this type to be de si gned w i th c ol a pl e t e conf i d e nc e . Add i tional i nformation on NASA's l ow - and medium-sp e ed airfo il s can be obtained from the M c Gh ee -B e asley paper in these proceedings (ref. I0).
The matrix of shapes wh ic h c onst i tute the NASA super c r l tical airfo i l family is shown in fi gure I0. Design l l ft co e fficients vary from 0 to 1.0, and thick - n e ss ratios from 0.0 2 to 0.21. This fam i ly is based on improv ed design proc e - dures d e veloped by R. T. Whitcomb and were defin e d by us i ng th e transon ic Bauer-Garabedlan-Korn analysis code (ref. 7 ) . Only two designs have been tested to dat e ; four others ar e in the p l ann i ng s tag e s. M a ny other des i gns are ava i lable for test, a s i ndicated by th e so l id dots, but it is likely that on l y about hal_ w i ll b e s c honor e d.
f Rotor-a i rfoll research has the same ob je ctiv e s as those for c onventional airfoils, that is, the evaluation of new a l rf o il-des l gn methodology by w i nd- tunne l and f li ght test s and de ve l opm e nt of improved s e ctions. Unfortunat e ly, their ach i evem e nt is cons i derably more d i fficult with current m e thods. Analysis tools which apply for two-d i mens l onal steady f l ow must, in som e rat i onal way, be applied to the rapidly changing, thre e -dlmens l onal environment of a rotor blade where re l at i v e velocities may c hange from h ig h subsonic . o low subson i c, or reverse direction in one revolut i on. Re s ults contained in the pr o ceeding papers by G. J. Bingham, K. W. Noonan, and H. E. Jones and C. E. Morr i s, Jr.
would seem to i nd ic ate that progr e ss is be i n g made in this area (r e fs. 11 and 12 ) .
Three new rotor airfo i ls designed for tests on th e A H -IC h e licopter as well as in Langley' s two-d l m e ns l onal wind tunn e ls are shown in figure I ] . Each has been desi g n e d by a d i fferent m e thod: th e f i rst using a transon i c hodograph equation solution t e chn i qu e , the se con d us i ng a lln e ar-potential - equation method with compress i bi l ity c orrect i ons (parametr ic crest l ine ) , and the third using th e transon ic f ull-pot e ntial- e quat l on me thod (supercr l tlcal technology) o f F. Bau e r, p. Garab e dlan, and D. Korn (re f . 7). All thre e have b e en tested in both the Lan gle y 6- by 19- 1 n c h and 6 - b y 2 8-inch transonic tunn e ls as w e ll as in fli g ht.
The tota l rotor-airfoil-d e v e lopm e nt eff ort c an best b e ju dg ed by the facL that a t o ta l o f 2 9 airfo ils have been t e st e d, 2 1 in the 6- by 28 -1nch tunnel and 8 i n the 6- by 1 9-in c h tunn el . Some of the parti c ipating organizat i ons involved are 1 6 ,4 ..................................................... _ .................. ¢,_ / .......... ...... ..... _ 6- by 19-inch transonic tunnel NASA U.S. Army R&T Laboratories (AVRADCOM) Bell Helicopter Textron National Aerospace Laboratory (NLR), Netherlands 6- by 2B-inch transonic tunnel Bell Helicopter Textron Boeing Co.
Hughes Aircraft Co.
Sikorsky Aircraft Wortmann THEORETICAL DEVELOPMENTS The ability to design airfoils and to analyze flows about them has grown by leaps and hounds over the past 10 years. Aid=d and abetted by a new genera- tlon of computers and improved solution techniques, designers can now quickly analyze supercrltical airfoils with and without shocks and multlelement air- foils, taking into account viscous effects. Significant progress has also been made in the treatment of airfoils with regions of separated flow. Many of the advancements cited have come out of the Langley airfoil-research program and ma n y m o r e ar e in st o r e .
Cpeclflc area s wh e r e significant progress has b e en made and / or effort is b e in g a p plied are D e si g n and an a lysis codes Sho c k / boun d ary-layer interac tion Trailing-edge interaction Leadlng- ed g e bubbl e interaction S e parate d flow Multl e l e ment airfoil anal y sis Unsteady flow A sh o rt d is c us s ion of e a c h of these topics follows.
Perhaps th e most si g nificant d e velopment in airfoil theory in the past dec ade w a s th e formulation of the hodograph design and "circl e- plan e " analysis c ode s fo r _up e rcritical airfoils by the Garabedian-Korn-Bauer team at th e NYU C o urant Institut e (ref. 7 ) . The o r iginal and improv e d versions of these two p ro g rams a r e in use a round the world and constitute on e of th e k e y technology a d van ce s b e ing utilized by th e air c raft industry in th e d e sign of the next gen- eration of c ommercial transports. Fi g ure 12 shows an airfoil whi c h w as d e sign e d using both t he design and a nalysis cod e s. The top side geometry depicted was arriv e d at through rep e ated runs of th e design c od e ; the bottom side r e sulting from these same c al c ulations was furth e r modifi e d by using th e an a lysis code to m a ke su cce ssive chan ge s in th e bottom c ontour until the desired pr e ssure dis- tri b ution was o b taine d . The pressure distribution de pict ed in fi g ur e 13 was o b tain e d from th e analysis cod e for a Mach nu m ber of 0.73 and a lift coeffi- c i ent o f 0.60.
I?
A second set of programs capable of solving both the analysis and design problems was put together by L. Carlson of texas A & M about 2 years ago (ref. 13). Carlson solves the full potential equations in the physical plane on a C a rtesian coordinate system. His method has one advantage over the hodo- graph approach of Garabedian in that it can design airfoils for input pressure distributions with shocks. An example of this feature is glven in f i gure 13.
The design program was given the pressure distribution defined Lv the dashed line with a shock at approximately the 75-percent-ahord station. The computer program produced the airfoil shown at the bottom and the slightly modified pressure distribution given by the solid line. Inserting the derived airfoil shape into the analysis program produced the circles and triangles which are in nearly perfect agreement with actual design input (the solid line).
On e of the most v ex ing problems in airfoil analysis is the d e t e rmination of drag, particularly at high subsonic speeds when imbedded shocks occur and under separated flow conditions. Mo_t of the boundary-layer routines in use today for calculation of boundary-layer displacement tPickness and skin-friction drag do not apply in regions where strong interactions occ u r with the invlscld flow. Three of these interaction regions are being studied in the Langley alrfoil-research program; these are shock / boundary-layer, traillng-edge, and leadlng-edge bubble interaction.
The shock / boundary-layer interaction problem has been studied under NASA grant at the University of Michigan for the past 3 or 4 years. The investiga- tion started with an idealized laminar-boundary-layer / oblique-shock case and proceeded through a series of steps to the normal-_hock / turbulent-boundary-layer problem discussed in these proceedings in a paper by A. F. Messiter and T. C.
Adamson (ref. 14). The next step will be to take this ]ocalized analysis and patch it into one of the full-potential airfoil-analysis programs such as the one developed by F. Bauer, P. Garabedian, and D. Korn described earlier (ref. 7) .
The traillng- e dge interacti o n may be even more important from a drag stand- p o int since th e • last 5 to I0 percent of the airfoil is responsibl e for most of the error in drag predictions. Empirical fixes currently employed in the b o undazy-lay e r routines near the trailing edge are generally reliable in terms of pr e ssure-di_trlbutlon predictions but are not consistent for drag estimates.
R. E. M e lnlk o f Grumman Aerospace Corporation has carried out a detailed analyt- ical tr e atment of the trail_ g-edge interaction which holds promise of improved d rag predicti o n. He has found that accounting for the effect of wake curvature is c rucial, a_d an airfoil analysis comput e r code, due to A. Jameson:. has been modified to in cl ud e th i s e ffect. A pr e s s ur e distribution m ad e using this c od e is shown in fi g ur e 14. I= i s for the Korn 0.75 airfoil at a Mach number of 0.7 and a se c tion lift co e ffl c l e nt of 0.669. Th e oretical and exp e rimental pres- sur e s are c l e arl y in excell e nt a g reem e nt; the drags are not. The theoreti c al drag was 0.0082 as compared to an experim e .ntal value of 0.0107. There is some opinion that the experimental valu e is too hi g h by abou t 20 counts, but this cannot b e verified, (There is a g en e ral c onc e rn about most experim e ntal dra g d at a .) Dra g corr e lations made using data on a GA(W)-2 airfoil at super c rltlcal sp ee ds obtained in an Oh i o Sta_e Univ e rsity wind tunnel wlth a divided plenum are quit e g ood. Mor e research is requir e d to oh_aln or identify "interf e rence t fr ee " experimental d a ta , F u rth e r d e: : _ils of the trail : _ --ed g e - interacti o n m e tho d ol og y can b e found in the p a pe r by R . E. M e __ :hese p ro ce e d ings (ref. 15 ) .
Theoretical tr e atment of the leading-edge bubble interaction has been attempted by W. R. Briley and H. McDonald (ref. 16_ using a n iterative tech- nique where b y th e pressur e is pr e scribed and boundary - !ay_r profiles a nd dis- placem e nt thickness e s ar e det e rmined. The pzessure is recalculated for th e eff e ctiv e shap e , and a new pr e ssur e input is f o rmulated based on differences betw ee n th e old and new pressures. In a low-l_vel effort, the same type of probl e m is b e ing attempted at Langley using a different procedure whereby the displacement thickness is pr e scrib e d. This procedure, which has been developed by J. E. Carter and S. F. W o rn o m o f Langley (ref. 17 ) , is thought to have cer- tain advantages over the pressure-prescribed method. It has b e en successful in calculating separated-flow bubbles in a depression and at the juncture of an afterbody-sting combination.
Airfoil flows with large am o unts of separation have been c a lculated for a numb e r of y e ars using lin e ar methods and empirical assumptions related to the print o f separation and the separated region itself. More recently, these flow probl e ms have be e n attacked using both numerical time-asymptotic methods for the Navi e r-Stokes equation and finite-differ e nce relaxation methods for various f o r m s o f the nonlinear - potential - flow equation. The latter are used with a b o undary-layer routine which is applied up to the point of separation.
_ R . W. Barnw e ll of Langley was the first to extend the ideas developed
i
i using linear pot e ntial equations to the finite difference approach (ref. 18).
In Barnwell's calculation the separation point was not solved for; it was pre- scribed. An extension of his approach, whereby the separation point is deter- min e d in the calculation, has been undertaken by L. Carlson of Texas A & M under NASA grant (ref. 19). Some preliminary results have been obta±_ed and an e xample is shown in figures 1 5 and 16. These figures show the pressure distri- bution at an a ngle of attack o f 18° and lift vs. angle of attack for the GA(W)-2 ai rf o i l a t a free - stream M at h numbe r o f 0.1 5 . Note i n figure 15 that the flo_ . : : separates at about 6Q per c en t of the chord. Also, it should be recognized that at an angle of at t a c k of 18°, the a lzfoil is beyond its maximum lift. Further explora t ion of this technique is underway.
So far the dis c ussion of theorpt4 c al developmer t s has been constrained to s lngle-eleme n t airfoils. Progress has also Seen made in the analysis of - iti- el e ment sys t e m s. Several analytical methods have been developed around t he country over the past 6 years, and t heir cap a b1_ities and limitat_ons are fairly !
well known. The fea t ures of the multi,_le m ez_tprogr am developed by Lockheed foc Langley (ref. 8), and later m odified by Boeing to make it more efficient ' (ref. 20), are listed in figure 17. This is the same program described earlier in the "His t orical Perspec t ive" section as h a ving been used by Whltcomb to design the GA(W) - I low-speed airfoil. As can be see n in figure 17 , the program computes all the quantities of interest for a s many as 7 elements. Correlations of theory wi t h experi m ent show that this co m puter code yields results of good accuracy u p to the point of flow separation. Fur t her improvement_ are contem- plated t o improve the accuracy of the drag pred i c tion, _ncluding an improved
i 19
sl o t -- flow analysis and a trailing -e dg e -i n t e ractl on patc h . T he f o r m er w o uld be attempt e d by applying operator splitting m e t h ods t o t he N avler-Sto k es e q ua ti on s.
A companion study using the tlme-av e raged N a vi e r-Stok e s e quations is being carried ou t under NA S A grant at Mlssissippi S tate Univ e rsity (r e f. 2 1 ). It h as reach e d the point where a two-el e ment, c ompressible, t u rbulent flow code is now being debugged. A mapping proc e dure is us e d to transf o rm t he airf o il el e m e nts and the external flow field onto th e int e rior of a r e ctan g l e wh e r e t he equa- tions are solved. The coc din a t e system in t he p h ysical plan e is s ho wn i_ figur e 1 8 . N o t e that th e coor d in a te grid seems to compr e ss in regions w h ere th e most r e s o lution is req u ired. It is expe ct e d that t h is comput e r program wh e n fully developed will provid e an e xc ellent b en c h mark by which mor e a ppr ox i - mate and faster tec h niques can be ju d g ed , including t h os e treating separat e d flows.
The ability to analyze two-dim e nsi o nal u n steady transonic fl o ws is v e ry much inferior to what o ne can do wi t h ste a dy flows. T his is natural sinc e t h e unsteady nonlinear potential equation is much more difficult to solve. A num- b er of procedur e s have b ee n tri e d; t h e two develop e d under the Lan g l e y progr a m which have had the mest success are th e nonli n ear, s m all-distur b ance solution of Weatherill, Ehlers, and Sebastian (Bo e ing) (ref. 22) and the full-pote n tial- equation solution of Isogai at Langley. An example calculation from t h e Is o gai code is giv e n in figure 19. It is for a steady, hiBh Math num be r flow wh e re data are available. Theoretical results from a purely inviscid calculation and on e in which the boundary-layer displ a c e ment eff e ct is iuclud e d ar e plotted. The lack of a proper accounting of the sh o ck / boundary-layer interaction is the probaol e caus e for much of the disagr e em e nt.
An e xtension of the Isogai code to include the effect of an oscillating flap is discussed in a paper by R. M. Bennett and S. R. Bland in these pro- ceedings (ref. 2 3).
TUNNEL-WALL INTERFERENCE The discussion of wind-tunnel-w a ll int e rfer e nce research has been is o lated in a separate section, apar t from theor e tical developm e nts and facilitles, because of its special charact e r and importance. Langl e y research in this area involves both theoretical and exp e rimental studies for the assess m ent and elimi - nation of wall interference. A llst of many o f thes e activiti e s follows: Slotted walls Barnwell correction of slot p a ramet e r Parametric slott e d wall study in 6- by 19 - inch transonic tunn e l S l ot flow diag n o stic surv e y s in 8- f oo t tr a n son i c p ress u re tunn e l Adaptive walls Flexible wall experiment in 6- by 19-inch transonic tunnel F l exible wall theoretical pr e diction l wo-dimensional adaptive w a] Is for 0.3-meter transonic cryog e nic tunnel 2 0 " !
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C omput a t i on al m et h o do l ogy ! Tr a nson i c a ssess m e n t u s i ng exper im enta l bound a ry cond i t io ns T S o me o f th e s e are d i sc us sed i n t he f ol l o wi ng pa r a gr a ph s.
! R. W_ Barn we l l has d o ne a n e xh aus tive st ud y of s lotte d -wall bo u n d ar y con - ditions and has provid e d new in s i g ht s into t h e deficien c ies of old e r methods.
With th e aid o f existing data, he has d e riv e d a s emi e mpirical d e sign me t h od for s lotted-wa l l tunn el s. $ o_ e of th e data utiliz e d c ame out of a parametric experimental study con d ucted in the 6- by 19-inch transon i c tun n el b y Ever h art and _rnwell and reporte d elsew h ere in thes e procee d in g s (re f . 24 ) .
Very l ittle da t a are availa b l e on the details of the flow in , and _d j a c e n t to, tunn el wa ll slot s . More is need ed to ena b l e a better asse ss m e nt of viscous e ffect_ a n d h o mogeneous boun da ry - condi t ion assumptio n s. An exp e rimental inve s - tigation is being carri e d out in the 8- foot transonic pr e ssure tunnel to pro- vi de s o m e o f t he needed d a ta .
Langl e y has h ad a cooperative effort in a d aptive wall res e arch wit h t h e Universit y of S outham p ton, England, for several y ears (ref. 25 ) . In-house the 6- by 19 - inch transonic tunn e l has b e en us e d to explore this te ch nique. Calcu- lations carri e d out by Newman (LaRC ) and And e rson (DCW Ino u stri e s ) for c ompari- son with the 6 - by 1 9-inch tunnel tests are discussed in their paper in c luded in these conferenc e proceedings (r e f. 26 ) . All of these a ctivitie_ have con- tributed to tPe design of an adaptiv e -wall two-dimensional section for the 0.3-m e ter transonic cryogenic tunnel.
A third appro a ch to the wall interference pro b lem h as b een proposed in the proceedings paper by W. B. Kemp, Jr. (ref. 27 ) . Through the use of pressures m easured near the tunneJ _ - alls as b o undary conditions in a tunnel flow analysis program, he is able to determine whether a flow is correctable and, if so, what the corrections should be. The m e thod, in effect, eli m inates the need for detailed knowledge of slot flows, porous wall flows, and so forth.
FU T URE RESEARCH REQUIREMENTS A recurring theme in much of the researc h discussed was the need to improve the accuracy of drag predictions. Existing codes must be modified or new codes created to include the effects of strong interactions and flow separation.
Although not discussed previously, turbulence models are also a source of drag error and a _trong effort is needed to impLuve them.
J Good progress in the prediction of flows with large separation was indi- cated, but many of the techniques are new anJ require further exploration. In '? o_d e r to obtain accurate data to validate th e se theories, it is mandatory that _ sidewall treatments in two - dim e nsional facilities be implemented and r e fined.
" j : There is a dearth of unsteady pressure data at supercrltical speeds. In addition to classical oscillatory data, dynamic-stall and buffet-type flows must be simulated. Wall interference corrections for unsteady motions is an area that has hardly b ee n scratched. '_ 2 1 I _; .
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Im pr ove d wall c o rrec tion proced u res fo r s t eady flow a re st il l a req ui re- m ent; t he use o f m e a sured wall pressures s ho u l d b e pushed . S t rea m l i ne-w a ll t es t sec ti ons sh o uld be " h a rd w i red " t o c o m puters s o t ha t the wa l l adjus t men t s can be a u to m a t ed.
As kno wled g e o f f lo w s t a b i llt y i m pr o ves , mo re research w i ll be carr i ed o u t o n z m tu r al lamin a r flow _n d lami na r f l o w wlth suct io n. Th i s will require , i n ma ny c a s e s, imp rov e men t s i n t u nne l fl o w q ua l lt y a nd r e d u c e d t u nn e l n oi s e . C o n- ti n n ed im pr o ve me n t i n analysis tool s to acc o un t f o r n e w s t ab ilit y t he o T _ es and - d a t a w i l l a l s o be necess a ry.
F u ll -sca l e R eyn o l d s n um b e r data a r e alw a ys d e s i r e d. O n l y a f e w fac iliti e s aro und t he w o rld can o b t a i n t h e leve l s req u ired f o r la rg e- t ransp o r t a i rf oi l sectio n s . D e t a il ed c o mparis o ns o f t he da t a fr o m t hese fac iliti es are r eq u i r e d to ferre t o u t err o r s o urc e s; eff o r t s to o b t a i n b o u ndary-layer d i agn o s ti c da t a i should be i ncre a sed. F i n al ly , it should be r ecogn i zed th a t ai rfo i ls a re used i n a t hree- i di m ens io n a l env ir on m e nt . C o ns i der a bl y mo re eff o rt to I nc l ude t he effects o f ! _, e e p and ta per i_ t he desi gn of air f oi l sec t i o ns i s nee d ed . I n a dd itio n, t he diff e r e n t e nvi r onm ents o f t h e _ rln g r oot, m idspa n re g i o n , and tip sh o u ld be better defin e d so th a t ai r f o il secti o ns can be des ign ed t aking i n to acc o un t tbese diff e rences.
Clearly, there are m_ n y research o p po rtuni ti es and chal l en g es in a i rf oi l aerod y n a mi cs . I f t he y a r e u n der t a k e n w i t h t h e sa m e e n thus i as m as that appl i e d d u rin g t he pa s t d e cad e , then a noth e r quantu m l e ap in alrfoil - aer o d y naml c s c apa b ilitie s c an b e e xpect e d.
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\ : APP EN DI X S YMB OLS I n t h i s ap pend i x, s ym bo l s w h ich a re used on t he f i gures a re de fi ned .
p - p_ _. C p p res su re c oe fficien t , q_ p* - p_ C* soni c pr e ssure co e ffi c ient, P q_ c ai r foil ch o rd cd sec tio n d r a g co e ffi c i en t , Dza_ force q _ c L ift cz s ect io n lift c oeffi c ient , q-_- Pitchin g moment cm s ection pitchin g -mome n t co e fficient , 2 q_c M f ree -str e am M ach numb er p local static pr e ssur e p_ fr ee -str e am static pressur e , p static pressur e at sonic velocity q, free-str e am dynami_ pr e ssure R unit Reynolds number Rc R e ynolds numb e r based on airfoil c hord t ma x imum air f oi l thi c kne s s V_ fr ee -str e am v e locity a ngle of attack 6* boundar y -layer displacement t h ickness p_ fr ee -stream d e nsity J l m _ R E F E R E NC E S i. Sixth A nnual R e por t of the National A dv is ory Co mm i ttee for Aer o nautics - 1 92 0 . U. S . G o vernment Pr i nt i n g O ffice, 1 92 1 .
2. Seventh An nual P epor t of the Nationa l Ad v i sory Co m mittee for Aeronautics - 1 92 1 . U.S. Go vernment Printing O ffice, 1923.
% 3. Ninth A nnual Rep o rt o f the N at io nal Ad v i sory Co mmi ttee f o r Aer o na u tics - 1923. U.S. Gov e rnment Printing Office, 1924 .
4 . Abb ot t, Ira H .; V o n D o enh o ff, A l ber t D.; and S tl vers, L o ui s S., J r.: < Su mma ry o f A i rf oil Data. NACA Re p. 82 4, 1 945. (Super s edes NACA i _ L- 56 0. ) L i 5. Abbo tt , Ira H.; an d Von Doenhoff, Albert E.: Theory of Wing Sect l on s .
Dover Publ., Inc., c.1959.
6 . Wh lt c o mb , Richard T.; and C l a r k, Larry R.: An A ir f oi l Shape f o r E ff i c i e n t Fl i gh t a t Supercr lt lca l Math Nu m bers. NASA TM X- 110 9, 1 9 6 5.
7 . Bauer, F.; Garabed l an , P.; and K o rn , D.: A The o ry o f Supe r cr ltl cal Wing i Sec tio n s, W it h C ompu t er Progr a ms and Ex a mples. Volu m e 66 of Le ct ure No t e s i n E c o n o m i cs a nd M a th e matica l Sys te ms, Sprlnger-Ver l a g , 1 9 7 2.
8 . Braden , J . A . ; G o rad l a , S . H. ; and S t evens , W . A . : Ma t he m a ti cal M o del f o r Tw o -D im ens lo na l Mu ltl c om p o nen t A irfoils i n V i s co us F lo w. N AS A C R - 1 8 4 3, 1 9 71 .
9. R ay, E dward J. _ Langl e y's Tw o -D im e ns lo nal Rese a r c h Fa ci l iti es - Capab ilitl es and P l ans. Advan c ed A i rf oll Te c hn olog y Re sea rc h , Vol u me I , NASA C P -2 04 5, Pt . I, 1 9 7 9. (Paper 1 5 o f t h is com pi l a tio n.)
1 0. M a Ghee , R o ber t v .; B easley , W illi a m D.; and Whl tco mb , R i chard T.: NASA L o w- and M ed i um-Speed A ir f oll Devel _ pmen t . Advan c ed A i rf oll Te c hn olo gy Resear c h , V ol ume II , NASA CP-20 46 , 1 9 7 9.
ii . Bingha m, Gene J.; N oo nan, K ev l n W.; and J o nes , Henry E .: Resul t s o f an I nves ti ga tio n o f Several New R ot orcraf t A i rf oi ls as Rela t ed t o A i rf o il Require me n t s . Advanced A i rf oi l Techn o l og y Research V o lu m e If, NASA C P -20 4 6, 1 9 7 9.
12 . Mo rr i s , Charles E . K. , Jr . : A Fli g h t I nves ti ga tio n _f A oto r A i rf oi ls .
Advanced A i rf oll Techn o l o gy Rese a r c h , Vo lum s If, NASA CP-20 46 , 1 9 7 9.
1 3. Ca rl s o n, L. A .:. Trans o ni c A i rf oi l Design Us i ng C v r t e slan C oo rd i n at e s .
NASA CR-25 7 8 , 19 7 6.
1 4. Mess it er , A . F . ; and Ada m s o n , T . C ., Jr . : A S t udy o f t he I n t erac tio n o f a Normal Sh o c k W a ve Wit h a Turbulen t B o undary L a yer a t Trans o n i c Speeds .
A dv an c ed Ai r fo i l T e c h no l o g y R e searc h, Vol u m_ I, NASA CP -20 45, Pc . i, 1979.
(P a per 21 of th is co mpil a t i on.) ' i 2 4 L
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13 . Melnl k , Ro b e r t E.: Wak e Cur v a tur e a n d T r a ili ng Edg e Int erac t i on Ef f ects in Visco us Fl o w _ ,e r Ai r f oi ls. A dv an c e d A irf oi l Tech no l ogy R esea r c h, V o lu me I, NASA CP-20 4 5 , Pt . 1, 1 9 7 9. ( P ape r 20 of t h i s compi l ation . ) 1 6. B ri l e y, W. Roge r ; a nd M c D on al d, Henry: Nu me r i ca l P redic t i o n o f I nc omp res- s ible Se p ara t i o n B u bb l e s. J . F l u id Mech. , v ol . 6 9 , p t . 4, J u n e 2 4, 1 9 7 5 , pp . 63 1 -65 6 .
1 7 . Ca rt er , J a m es E. ; an d W or n om, S tep hen F.: S ol u tlo ns f or I n compre ss ib l e S e para te d B o undary Layers I nclu d in g Vi sc o us- l nviscid I n t erac t i o n. A ero - dyna m ic Analys e s Requirin g Adv a nced C om pu te rs , Part I, NASA S P -3 4 7 , 19 7 5 , pp. 1 2 5 - 1 50.
i 18 . Barn well , Ri c h a rd W.; S ewell , Wi llia m G .; and E v er h ar t, Jo el L. : Des ign a n d C a llb ra tion o f S lot ted W alls f o r Trans o n i c A irfoil Wi n d T u nne l s.
_ i 1 979. (P a p e r 1 8 o f t h i s c ompila t io n.) !
i Advan ced A irf o il Techn o l og y R es e a rc h , V o lume I, N ASA CP-2 04 5 , P t. i , 19. Car l so n, Le l and A. ; an d Ro c h oll, B ru c e M.: A pp li c a tion o f D i r e c t - I n v e rs e T e ch niq u e s to Ai rf oi l Anal y s i s an d Des i gn. Adv a nce d Ai rf oll T e ch nology R esea r ch , V ol u m e I, N ASA CP-20 4 5 , P t. 1, 1 9 7 9. (Pa p er 5 o f this comp i l a tl on. ) 20. B run e, Gue nte r W . ; an d Man k e, J o se p h W.: U pgr a ded Visc o us F lo w A nal y sis o f M ult l elemen t A i rf oi ls . Advanced A i rf oi l Techn o l o gy Research , Volume I , NASA C P -20 4 5 , Pt . 1, 1 9 7 9. ( P a p e r 1 0 o f this c omp i l a t i o n.)
21 . Th o mps o n , Jo e F .; Turn e r , L o u i s ; L o n g, W. S e rr i l l a nd B e a rd e n , 3 o hn H.: Numeric a l Solu t ion o f t he N avier-S t okes Eq u a t i o ns f o r Ar b i t rary Tw o - Di m ens i ona l M u lt i - El ement Air f o ils . Advanced Ai rf oi l T echno l ogy, Volume I, NA S A CP -2 045, Pt . i , 1979. (Paper ii of this co m pilation.)
22. Weatherill, Warren H.; Ehlers, F. Edwa rd ; and Sebastian, Jame s D.: A Procedure for Analyzing Tran s onic Flow Over Harmonically Oscilla t ing Airfoils. Advanced Airfoil Technology Re s ear c h, Volume I, NASA CP-204 5 , Pt. 2 , 1 9 7 9 . ( Pa per 4 3 o f thi s co m pi l a tion.)
23. Bennett, Rober t M.; an d Bland, Samuel R .: So m e Tran s o n ic P o t en t ia l Flow Cal c ulat i ons for the NA C A 64A006 A i rfoil Wi t h an Os c illating Flap.
A d van c e d A i rfo i l Te c hnology Resear c h, Volume I, NASA C P-204 5 , Pt. 2, 197 9. (Paper 45 o f tb_s c ompi l ati o n.)
24. Everhart, Joel L.; sa d Barnwell, R i c ha rd W.: A Para m et ric Experimental S t u d y of the Sl ott e d -Wall Bo u n d a r y C o ndi t ion. A d v a nce d Airf o il Te c hnol o gy R esear c h, V olu m e I, NASA C P-204 5 , Pt. 2, 19 7 9. ( P aper 30 of t hi s c o m pi la t i on.)
25. G oo d yez, Mi chae l J .: De v e lo p m en t s in Airf o i l T e s t in g T e chni q ues a t Universi t y o f Sou t hamp t o n . Advanced A i rf oi l Techn o l og y Research , Vo lu m e I, NAS A C P -20 4 5 , Pt . 1, 1 9 7 9. (P a pe r 1 6 o f t his c ompi l atio n .)
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,j 2 6. Ne wm a n, Pe r ry A. ; and And e r so n, E . C.: Analyt ic a l D e si gn o f a Co nt ou r e d Win d- Tunnel Liner f or S u p e rcritical T_sting. Advan c ed Airfoil Technology _ Rese a rch , Vo lu me I , NASA C P - P 0 4 5 , Pt . 2, 1 97 9. ( Pap e r 33 o f t h i s c ompilation.)
2 7. K e mp, William B . _ Jr.: Transonic ._ssessment of Two-Dimensional Wind Tunnel Wa l l Int e r fe r e n ce U sin_ M e asured Wal l Pre s sur e s. Advan c e d Airfoil T e ch- no l ogy Re sea rch, Volume I, NASA CP-2045, Pt. 2, 1979. (Paper 31 of this compi la tion.)
E I F FE L 47 ( 1914 ) EIFFEL _ (1914 ) EIFFEL 44 _ _ ( 19 14) (1921 ) L / VIAL 5 4 Figure I. - Early airfoil shap e s.
NACA 4412 ---__ _ / _ NACA 23012 > NACA 6 5 1-412 __ NASAGA( W ) - 2 ; t i c = 0. 1 3 Figure 2 .- Comparison of older NACA airfoils with the NASA GA(W)-2 airfoil.
I Figure 3. - The Langley low-turbulence pressure tunnel.
o..: :;: . :: :: : . ' .: "'"""_ - : ' ===: ' : : : _ :: : _ . , ii, : :l i! i : : - ENC L OSURE , : DI FF US ER ; ! r T E S T S EC T IO N ., , ! . . .! . .. , ,, . , !:: ..........".... :*S E T TLI NG CHAMBER : I i : AI R IN L E T :: ".' :::' .' . " . ' . ' . ' . ............. i . ' : " :: ' / .; ;MA N IF OL D L I NE S Figure 4. - Cross - s e ctlon drawing of Langley 6 - by 19 - 1nch transonic tunnel.
• o _ .G '_ . ,_ . _
Figure 5.- Phot o graph of the Langl e y 6- by 2 8-inch tran s onic tunnel.
Fi g ur e 6.- Photo g r ap h of th e Lan g l e y 0.3 -me t e r transoni c c ryogeni c tunnel w ith 2 0- by 60 -c m two-dlm e nston a l test s ec tion.
2 g J .!
SELF-STREAM L INING WA LL / ... ,._ 2-D INSERT 3 " D O C T _ .GONAL INSE R T t Figur e 7. - Interch a ngeable test s e ct i o n capab i l i ty of 0.3-m e ter transon i c cryogenic tunnel.
Figu r e 8 .- GA(W)-2 ai r foil on B e ech Sun d own e r. . __'v _-- I
.0 o+ 25 _ +
•24 F t i c
• _-'__ o . _ _
y /
• SHAPE DEFI N ED [-I TESTS PLANNED [' .04 - m T ESTS COMP L ETED I ra ]NEW LS(2)AIRFOI L S O .2 .8 l.O 1 ! 2 cl , des i gn Figur e 9. - L a n g l e y l o w -s p eed a irf o il f a mily.
0 DESIGN I N ITIATED [] TESTS P LANN ED •20 • TESTS COMPLETED • 24 I 7// • SHAPE DEFI N ED • 16 / / ' / // / t i c t / c . l? __, / _ // _ O.i4 .08 _ // _ , _t _ 0 . 1 0 .(Nt _ 0 . 06
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c l . d e sign Fi gu r e I 0. - NAS A su p ercrl ti ca l a i r f o il fa m ily.
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; ' I NAME; DES IGNMETHOD _ _ _ _ .__ _ NLR-I; DUTCH HODOGRAPH COMPUTER PROGR A M __ _ _ RC - SC2 ; UPPr. : R - SURFA C E SUPERCRITICAL TECHNOLOGY Figu re I I. - Air f o i ls for AH -IG Zllgh t t e st.
- 1 .5 - L Figur e 12 . - Pr ess u re d i s t r ibuti o n ov e r an LF C a i rf oil ca l c ul ated by th e K o rn - C arab e dlan a nalysis pr og ram .
H = 0.7 3; c Z = 0.60.
-l. 2 - --- INVERSE INPUT A C TUAL INVERSE 0 Z_ DIRE C T SOLUTION ' ", 8 - C _' P - . 4--- C p ,
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F ig ure 13. - Compar i son of d i re ct and i nverse Cp di s t r i bu ti ons calcula t ed by Car l son comp ute r codes. Hoo = 0.80; a - -0.5 °.
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Cp "' : .4 ,:: F i gure 1 4 .- T h e o ret i ca l p ressure d i s t r ib u tion o n K orn 0. 7 5 a i rfo i l i n c lu di n g t ra i l i n g -ed g e int era cti on. _ m 0 .7; C l m 0.669. ' l L . _ I ' " -6 CASE S Y MBO L c[ cd cm
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J' _ THEORY - _ 1 1.9 4 O. 03 6 0 -0 . 041 - 4 1.95 O. 0315 -0.0 65 Cp -2 0 . 5 1.0 x / c Fig u r e 1 5 .- Th eo r e ti c al an d expe rim en t a l p r essu r e d i s t r i b uti o n co m p aris ons f o r G A( W )-2 airfoil with lerg e s ep a r at ed fl o w r e gi o n . MQ o = 0 .1 5; a = 18°.
2 . 4- 2 . O- r 1.6- c_ 1. 2- ER I MENT . 4 - / [ 3 THEORY
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0 t / I I 1 I I I J -8 0 8 1 6 24 a , dec j Figur e 16,- E x p e rim e nt a l and th e o re ti ca l vari a tions of cI with a for GA(W ) - 2 a irfoll.
3 4 # TRANS ITION- _ i LAM I _''_ N AR_ _ TURBUL E N T _ _ CAPABILITIES PROGRAM FEATURES • I TO I CO M PONENTS • POTENT I AL-FLO W SOLUT I ON • VAR I ABLE a. Moo AND R • BAS I C BOUNDARY L A YER • F I XEDAND / OR FRE E TRANS I T I ON • SLOT-FLO W ANALYS I S • CONFLUENT BOUNDARY LAYERS • CO M PUTE5 c[. c d . Cm. AND • CO M B I NED SOLUT I ON BOUNDARY LAYERS. C P Figur e 1 7 .- Tw o -dim e nsion a l visc o us-fl o w multiel e ment airfoil program features.
i 3s 36 'I - . 6 -- THEO RY _ INVIS C ID . , / _ O " " . .,,_ \ .... WITH 6" -.4- '_ " ""!i O E X PE R I M ENT - .2 Ol / ,
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0 .2 .4 .6 .8 1.0 X / C Figur e 1 9 . - Stea dy f l ow c a lculation for the NACA 64A006 a irfo i l using Isog a i un s teady p o tential flow cod e . M oo = 0.8 7 5 ; _ = 0.
3 7