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NASA Te c hni c a l Me m orandum 7 8 7 50
(N A S A -TM-78750) WIN D - TU NNF L _R S TI_ G OF V _ C £ N78-30040 AND ST O L AIRCRA F _ (NASA ) _I F HC A O 5 / MF _0 1 C S CI. 0 1 A Unclas • G3 1 02 28584
WI N D -T UNNEL T ESTING OF V T OLANDSTOLAIRCRAFT
HARRY H , H E Y SO N
JUL Y 1 9 7 8
C _ _ C ' " r
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_ m nauIi cu and _"_ I . m pv I_mum h _ Hl m p l on , Virg i nia 23665 _, 11111' I II_ . I IIl l ILII I WIND-TUNNELTESTING OF VTOL AND STOL AIRCRAFT .
Harry H. Heyson Langley Research Center SUMMARY The basic concepts of wind-tunnel boundary interferenceare discussed and the developmentof the theory for VTOL-STOL aircraft is described. Features affecting the wall interference,such as wake roll-up, configuration differences, recirculationlimits, and interferencenonuniformity, are discussed. The effects of the level of correction on allowable model size are shown to be amenable to generalized presentation. Finally, experimental confirmation of wind-tunnel interferencetheory is presented for jet-flap, rotor, and fan-in-wing models.
INTRODUCTION Theoreticalaerodynamics is firmly based upon both implicit and explicit , assumptions of small perturbations. These assumptions are grossly violated by VTOL aircraft in low speed transition flight, and theory is often an unreliable guide to efficient desigr,. Under such circumstances,the wind tunnel generally stands as the sole source of reasonably good quantitativedata in transition flight. Although the fact is not generally recognized, wind tunnels also have problems in low-speed testing. Indeed, it has been observed that nobody believes a theory except the man who developed it, and nobody disbelieves a wind-tunnel test except the man who ran it.
; Many of the problems of wind-tunnel testing are purely mechanical. These ! , problems are intensifiedwith VTOL tests because the models invariably are i powered and they require large amounts of power. The power may be electrical, hydraulic,or pheumatic; however, irrespectiveof the type of power, there are severe problems in transmitting this power across balances without either foul- ing or large taces. It is also often a problem to contain the power source within the model without grossly altering the desired configuration lines.
Another class ef problem is aerodynamic imperfections in the flow. A wind • tunn e l does not p r o O u ce a flow which is "straight down the tube." Locally, the f l ow may differ b y several degrees from the main flow. It is really a necessity I to have detailed flow surveys over most of the usable test volume to provide not
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, only the basic v_locity calibration but also the variations in upwash, sidewash, and static-pressuregradient at any model location. All too often, such measure- ments do not existl The existerce of problems of this character often appears in upright-and-invertedtesting and in tare runs. Unfortunately, these funda- mental elements of a meaningful test program are also often omitted to obtain th e susp e c t "e co n o: r s " o f reduced tun;lel o ccupancy time. i q #' 1 • f , ) q ' The final problem in low-speed wind-tunnel testing is generally classed as ' "wall effects." This problem, in large degree, is accessible to theoretical treatment provided that the magnitude of the wall interference is kept within ,. reasonable bounds. The wall interferencetends to be proportional to lift coefficient and, therefore, becomes of great significance for VTOL configurations where the lift coefficient approaches infinity as the forward speed approaches zero.
: The present paper is largely concerned with wall-interferenceat low speed. " Numerous aspects of the theory are treated. Experimentallydetermined low-speed _ test results are discussed. Several examples of experimental measurements to !. i determine the adequacy of the theory are also presented.
i_ SYMBOLS A aspect ratio r AL V / STOL lifting element area AM momentum area of lifting system b distance of center of lifting system from right-hand sidewall of tunnel B semiwidth of wind tunnel CL lift coefficient CN,t normal-force coefficient of tail Cp momentum coefficient of jet, jet momentum / qS dB / dt pitching velocity ( D d rag ( so metimes used interchangeablywith Di) I Di ind u ced drag I h h eight o f m o del ab ov e wind-tunnel f loo r H semi-height o f wind t u nnel L lift m,n,N integers m* doublet in t ens it y pe r u n it a rea M u lo n g it ud i n al componen t o f m a ss f lo w fr om m odel Mw v er t lcal co m pon e n t o f mass f lo w fr om m od el l, . Ir ! 1 1 , t M T mass flow through wind tunnel n ratio of final to initial induced velocities (also used to denote , : perpendicular direction p static pressure • ° Po static pressure for upstream ! q dynamic pressure, _2pV 2 : , qc corrected dynamic pressure s semispan of wing !i S area SF fan area SW wing area !
Ts static thrust u,v,w velocities directed positive outward parallel to the X,Y,Z axes
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u momentum theory value of the longitudinal component of induced o ve l oc ity V forward (or tunnel)velocity Vj exhaust velocity of lifting fan or jet i w0 mom e ntum theory value of the v ertical component of induced velocity \ wh the value of w0 when hovering in free air x,y,z distances along X,Y,Z axes, positive outward from origin X,Y,Z Cartesian coordinates centered in model, X-axis runs directly aft (drag direction); Z axis directed upward (lift direction); and Y-axis directed to the side to form a right hand system m angle of attack . _c correcteO angle of attack a L=0 a n gle o f attack f o r z er o lift y width-height rati o of tunnel circulation o wind tunnel interferencefactor 6u,D wind tunnel interferencefactor for longitudinal velocity due to i induced drag 6u,L wind tunnel interference factor for longitudinal velocity due to ' induced lift I 6w,D wind tunnel interference factor for vertical velocity due to ; induced drag I_ _ wind tunnel interferencefactor for vertical velocity due to _; w,L induced lift i i ' ALi f an i n du c ed lift !
_u total longitudinalinterference velocity, AuL + AuD !
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AuD longitudinal interferencevelocity due to induced drag i AuL longitudinal interference v elocity due to lift J Aw total vertical interferencevelocity, AwL + AWD awD vertical interferencevelocity due to lift AWl. ve rtical interferencevelocity due to in d uced drag c downwash a ng le e w a ke d eflection d o wnward from , horizontal ef final rolled-up value of e ei i n itial val ue o f e at the lifting system \ A wing sweep angle rotor ti p - sp ee d ratio p mass den s ity of fluid m o ratio o f s pa n o f mo del to width of tunnel ¢ po t en ti al X w a ke d eflecti o n, a ft an d upward fr o m vertical I DISCUSSION
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I- I: BASIC CONCEPTS
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Closed Tunnel . _ Physically, the nature of boundary effects can be illustratedas in figure I. If the tunnel has closed walls, it is obvious that the general down- ward flow generated by producing lift will be stopped at the walls. This is • equivalent to adding to the flow an additional interference flow whose strength j at floor and ceiling is exactly opposite to the free air flow. Thus, in general, 1 for a closed tunnel _'
: + (I)
c where _ will be some positive quanitity; that is, the angle-of-attack set i n the t u nne l i s increased effective l y by the inteference.
Open Tunnel The opposite effect is generated by a completely open wind-tunnel. Here the wind-tunnel stream is smaller than the infinitely large stream upon which t h e aircraft acts i n free air. Since the aircraft is acting on less air, it must deflect the stream to a greater degree in the tunnel than in flight in or d er to m ai n tain the s ame lift. This is equivalent to adding some downward flow to the free-air flow; thus, in an open tunnel, the A_ of the preceeding e qu ation will generally be negative, reducing the effective angle-of-attack from that set in the tunnel.
BOUNDARY CONDITIONS Cl o s ed B ound ary E valuatingw a il effect s is a the o reticalboundary value pr o blem. The • a p p r o priate c o n d iti on s a t a c los ed b o undary are clear and unequiv o cable - the vel oc ity no rmal t o the wa l l must vani s h; that is, in terms o f the ve lo city po te nt i al ¢
0 (2)
Cn
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I i I Open Boundary lhe boundarycondition at a free surfaceis not as obvious. The pressure throughout the exteriorof the jet is constantand must be continuous across the i boundary. Thus,we may considerBernoulli's theoremon a streamline barely 1 withinthe jet, at a pointfar upstreamand at a point near the model,to yield
p+ [°2 +(v + w 2 =%+ v2 (3)
_ whereu, v, and w are the perturbations introduced by the model. Sincethe staticpressureis constantalong the edge of the jet p = Po' equation(3) becomes u2 + v2 + w2 + 2 Vv = 0 (4) J , If we now assumethat the disturbances of the model are small,the squares , . ) o f the p e rturbation velo c ities are negligible comparedto Vv , and the boundary cond i t ion s b e c o m es
v : o (s ) t
Thu s , f o r the op e n j e t th e lo n gitudinal ( ratherthan the normal ) component of velocityvani s he s at the boundary.
Two caution s must be ob s erved: fir s t,the open boundarie s will altertheir l ocations under the influence of the model; s econdly, for conditi o ns encountered by rotorsand VTOL' s at low speeds,the perturbation velocities may be much l argerthan the free s treamvelocitie s (fig.2). Both effectsviolatethe fore_ g o inganaly s i s and are not treatedanywherein the literature.Thus, great cau t ionmu s t be u s ed in interpreting the re s ultsof te s t s at low speedin open tunnel s .
CLASSICAL CORRECTIONS Prandtl(ref.2), Glauert(ref. 3 ), rheodorsen(ref.4), and many sub s equent author s developed theoretical treatment s of wall effectscomputing generalinteference factorsfor practical application in wind-tunnel te s ting.
The s e result s tyFically give the 6 in the equation G A_ • 6 S CL (6) T hi s f o rm ula ti on p r esen t ed p r oble m s a s soon as r o t o r s a nd VTOL m odels b egan t o be t es t ed. A t cons ta n t l ift, C L i nc r eased as V de cr eased so t ha t A_ bec amei n finitei n hove ri ng . Ac t u a l ly,this d lffi cul ty w a s m er el y a manifestati o n o f smallangleassumpti o ns, f o r the full equati o nwas tan As - Aw _ G S CL (7) V AT In this full form, infinite CL in hover merely said that Ac_ was 900; that ° is, the interferencewas a pure upwash in a closed tunnel. Unfortunately,the magnitude of the upwash was unavailable. An even greater problem was that the wake assumed for the calculation was totally incorrect, f_r t_e wake of a hoverin_ aircraft passes directly downward and not dl,ectly rearward.
VTOL-STOL CORRECTIONS Figure 3 shows the wake of classical theory, which under small perturbation assumptions,was assumed to progress directly downstream without deflection.
The main feature lacking was the large wake deflection characteristicof low- speed powered-lift aircraft. This feature was added by the anaiysis of reference 5. In that paper, the wake is assumed to be deflected from the verti- | e cal at some arbitrary angle X until it meets the floor, at which point it turns and runs off along the floor. The results are given in terms of inter- ference factors which yield the horizontal as well as the vertical interference velocities, and these, in turn, are separate_ into thos caused by the model lift forces and those caused by the drag forces. Characteristically,the wall effects : yield a change in effective velocity as well as in angle-of-attack.
THE WAKE SKEW ANGLE
t
Momentum Considerations I It i s already obvious that the wall effects will depend upon the skew angle I R X It will evolve that they also depend upon u0 and w0 , the mean l induced velocities at the lifting system. Simple V / STOL momentum theory (ref. 6) shows that
W o 14. 1 (8)
v__+
1 + W o
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w h er e Wh = " = V n_A
" v ( 9)
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Th e soluti on o f e qua ti o n (8) i s s h o wn graphically i n figure 5 . V a lu e s of
W o / Wh m a y be re a d directly fr o m figure 5 f o r de s ired v a l u e s o f V / wh and _" t J J t * % j The solution of e_u_tion (8) is shown graphically in figure 5. Values of Wo / W h may be read directly from figure 5 for desired values of V / wh and Di / L . The corresponding value of Uo / Wh is simply (Di / L)(Wo / Wh) and the wake skew angle is folmd as W_ _ W 0 cos x -_ (I0) p The momentum analysis of reference 6 is relatively crude; however, it has been found to provide good agreement with experiments for a wide variety of diverse configurations. Figure 6, from reference 7, illustrates the agreement obtained for jet flaps and for a ducted fan combined with external flaps.
Other investigationshave obtained comparable agreement for lifting propellers, helicopter rotors, and fan-in-wing configurations.
Wake Rollup The angle obtained from momentum theory is the angle at which the main flow leaves the lifting device. The wind tunnel analysis is based on the deflection of the vorticity in the wake, which is not necessarily the same angle. Con- sider the wake of a uniformly loaded wing, a simple horseshoe vortex, as shown in figure 7. At the center of lift on the bound vortex, the bound vortex con- t r ib u te s n o thing to the in d u c ed v e lo c ity; howev e r, each trailing leg contributes Wo / 2, so that the tota l induced velocity at the center of lift is wo . In the center of the wake far behind the _ing, the bound vortex is too far away t o have any effect; however, each trai : ing l eg is now effectively doubly infinite in l e ngth and contributes wo to the induced velocity, for a total , .
induced velocity of 2 wo . This is a typical n = 2 system, where the ind u ce d v e l o cities double at infinity. In contrast, consider the induced t velocity in the far wake on one of the trailing legs. Because it is straight, this leg induces no veloclt'_-y on itself. The other vortex, being twice as far from this vortex as it is from the center of the wake, contributes only Wo / 2 .
Thu s , the vortex wake itself is grogressing downward only half as rapidly as would be indicted by the induced velocity at the lifting system. A more elaborate analy s is for an el_iptically loaded wing based on reference 8 indi- cates a similar factor of 7 {/ 4 .
Even though a simple wing may seem vastly different from a rotor of a VTOL aircraft, the effect of rollup i s similar. Figure 8 shows contours of vorti- clty mea s ured behind a lifting rot o r (ref. g). If undi s torted, the wake would be a skewed cylinder, and one would expect to find the vorticity within the elliptic inter s ectionof the wake and the survey plane. In reality, most of the wake roll s up immediately into rather concentrated vortices centered only ha l d as f a r b e l o w t he r o tor as in d icated by mome n tum the o ry. Even the co mple x fl o ws fr o m multiple jet s r o ll up (fig. g fr o m ref. I0) and o bey a s imilar t re nd .
,4 • Figure I0 illustrates some plausible relationships be t ween the final and initial wak e deflections. A simple factor between initial and final valu e s will yield an obviously incorrect vlaue in hover. This may be corrected by noting , that tangents should be used for the large defl e ctions near hov e ring as indica- ted on the figure. In any event, most wind-tunnel tests will involve deflection angles of 600 or less, and the use of any of these relationshipswill make little . difference, provided that one of them is us e d.
G e neral Wake Model i Next, a simp l e inclusive wake model is required. Consider two such diverse lifting systems as a rotor and a wing (fig. ll). The r otor wake may be con- sidered as an assemblage of vortex rings of strength , while the wind wake is a simple horseshoe vortex. Prandtl has shown the identity between a area surrounded by vortices and the same area covered by a uniform doublet distribu- tion. Thus, the rotor wake in this concept becomes a stack of circular doublet sheets, and the wing wake becomes a single continuous doublet sheet. If these i wakes are examined from greater and greater distances, they appear progressively | more narrow until the point is reached where either system appears to be a i uniform distribution of point doublets along a line. This is an admirable economy, for this singlet wake concept may be used to represent almost any lift- ing system. This is the wake model used in reference 5.
Calculating Correction Factors The conditions at the edge of the tes t se c tion may be me t by setting up a dou bly i n finite image system as in figure 12. The varying conditions for open boundaries and c l osed wal l s are obtained by a suitable choice of sign effect pair. This pair i s obtained by the superpositionsshown schematica ll y in fi g u re 1 3 . Wall effe c t s are the difference between the wind tunnel and free air.
Ra t her than actua ll y perf o rm the subtraction, the central free-air wake is
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mere l y o mitted fr o m the superposition s . The entire procedure i s executed within the computer. Whi l e table s of correction factors have been published, many facili t ies have t he s ame, or imi l ar, programs operationa l on their computers.
A p plying Co rrecti o ns The app l ica t i o n o f c o rrec t i o n s to data can bec o me very invo l ved; h o wever, . i n th e s imp l e s t ca s e, the e q uati on are s h o wn in figure 14. The in t erference fac t or s are o b t aine d fr o m the d igital computer. The increment s in the h o r i - z o nt a l an d vertica l in du ced ve l ocities are defined in term s of the i_terference . fac t or s , t he m o men t um area o f the l ifting sy s tem ggenera l l AM = _ b_ / 4), the cro ss s ec t iona l area o f the tunnel AT , an d t he induced ve lo citie s uo and wo a t t he l lf t ing sys t em. The s e in t erferenceve lo citie s combi , e as s h o wn to o b t ain a c o rrecti o n A_ to a n gle o f at t ack an d a rati o qc / q by which t o c o rrec t t he d y na mi c p r essu r e .
J III II . U L. . -- _ o The typical behavior of the interference factors in a closed tunnel is illustrated in figure 15. The vertical interference due to lift w,L corre- sFonds to the of classical theory. When the wake trails directly rearward ( : 90°), the value of w , L is identical to the classical (with a factor of -4 because of an altered definition) _nd the other three interference factors I are zero. Thus, the V / STOL theory includes classical theory as a special case.
As the wake is depressed downward toward 0o, the magnitude of the vertical interference increases and u,L takes on a positive value resulting in a i decrease of effective forward velocity. The factors and are such w,D u,D as to r _agnify these effects for positive drag and to decrease them for negatiw drag.
It is tempting to think that wall effects depend upon the ratio of the momentums in the wake and througK the tunnel. Such, however, is not the case, for the derivation shown in figure 16 indicates that the interference depends upon the mass-flow ratios rather than the momentum ratios. Thus, for equal interference factors, an efficient system obta;ning lift by giving a small impetus to a large mass of air will have larger wall effects than an inefficient s ystem which l ifts by giving a large impetus to a small mass of air .
Large Models Up to this point, the wake of the model has been represented by only a single string of doublets. Although this procedure is useful, such a wake is a s a t i s factory representationonly of models which are "vanishingly small" with respect to the wi n d-tunnel dimensions. Glauert pointed out decades ago (ref. 3).
: that s uch an a ss umption was inadequate for classical corrections if the span of m the m od e l excee d ed I 0 p e r c ent o f t h e tunnel width. Th e s ame c o n cl u s i on is true -_ f o r V / STOL co rrections. _ / Simple s uperposition o f the "vanishinglysma11: wakes may be used to _ i p r o vide rea so nably a de quate representationsof the wakes of large models. A few ru d imentary examples of this technique were presented in reference 5; _ howe v er, the s y s tematic elaboration of the method was first published in
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reference 12 for V / STOL aircraft. That paper presents a set of proce d ures for _ the d igital computer which result directly in the average interference and its _' distributi o n f o r r o tors, swept wings, jet-lift VTOL's and a number o f combined sys te ms.
F ig u re 17 i llus tratesthe procedure of reference 12 for a swept wing. The wi n g i s re p re s ente d by ten d o ublet s trings. The result is the summation of fig u re 18 which i s eva l uated within the computer. A simi l ar s ummati o n and c o m.
pu ter p rnce du re i s pr o vide d f o r a r o tor by u s ing a wake c o n s i s ting o f an a ss emb l age o f 20 do ub l et s tring s a s in figure 19. The s et o f c o mputer pr o gram s f o r the s e ca l c ul ati o n s i s available in the literature, and the program s are o perati o na l at many wind-tun n e l faci l itie s .
$ A c e rtai n am o u n t o f th ou ght pri o r t o ch o o s ing the m o de l may be neces s ary fo r r a ti o na l a p plic a tion o f c o rrection s . Certain typ e s o f con fi g uration such a s I0 I k.. _ _ i I J I I ?
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those illustrated in the upper portion of figure 20 result in a more or less blended wake. in most cases, these can be treated as if they were simple wings, j!
In other cases, two very distinct wakes may be generated (lower portion of I figure 20). In such cases, the wall effects must consider, in addition, the contributionon each piece engendered by the presence of the other piece within the tunnel walls. Successful application of corrections to such models probably
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requires the provision of internal balances to separate the forces arising from " each portion of the aircraft.
Increasinglymore complicated configurationsmay be built L ' #from thei_ separate elements as indicated in figure 21. However, the suc ce ssful applica- tion of corrections depends o n the ability to measure the actual performance of each of the elements while they are operating in the presence of each other.
This may not be a great penalty. Such information is highly desirable as basic information for such configurationsand the instrumentJ_ionshould be provided in any event.
LIMITS OF CORRECTION Nonuniformity of Interference There are limits to the magnitude of the corrections that can be tolerated without distorting the wind-tunnel flow so badly that the resulting data loses m eaning. On e obviou s limitation is the crude nature of the theoretical treat- I merititself. Refinement is not truly necess3ry provided that the overall magni- tude of the corrections is modest; after all, even a I0 percent error in a lO to 20 percent effect i s only 1 to 2 percent of the total. Generally, the combined I eff ec t o f th e mea s ureme n t-systema cc uracies is that great, i T h e n o nunif o rm nat u re o f t he in te rf e rence c an be illustrated by computing the flow field in the central plane of a helicopter rotor (fig. 22), and adding to that field the interferencevelocities caused by the tunnel walls. The
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re su lti n _ fl o w is s h o w n in figure 23. For the conditio . ,chose, the correction angle a_ i s 8.3 degrees. Thu s , the flow angle s in free air are t h ose mea s ured with re s pect to a new axis s ystem cocked by this angle with re s pect to t un n el axi s . Thi s may improve things at the rotor, but it obvi o usly make s the c o m p ari so n w o r s e far in front o f, and far behind the rotor. In short, the am oun t o f wall effect varie s with tunnel locati o n; the fl o w i s highly di s t o rted.
Fi gu re 24 illu s trate s the effect o f s o me o f the type s o f d i s t o rti o n which may be enc oun tere d . If the in t erference increa s es laterally fr o m the center o f t he mo d e l , t he wi n g tip s s e s a greater l o cal angle- o f-attack. The s ame effect cou l d be genera t e d in a u nif o rm flow by twi s ting the tiop s upward (wa s h-i n ).
Effect ive l y,with r es pec t to the air, the mode l i s di s t o rte d in the t u nne l and may be su bject t o premat u re tip s ta ll .
Interferencegeneral l increa s e s f o r so me di s tance d o wn s tream fr o m the m od el. Thl s g enerate s a c u rved fl o w. With re s pect t o a unif o rm fl o w, the m od el wo u l d s ee the s ame l o cal angle s o nly if it had an increa s ed camber.
1 1 Similarly, this curvature effectively results in an altered tail height and tail setting. All of these effects may be considered as disto r tions of tne _:odel.
Figure 25 presents an alternate viewpoint. Here the model is subjected to a linearly varying wall-interference. As shown on the right-hand siue of the figure, this nonuniformity is equivalent to operating in free air at a different angle-of-attackand also with an imposed rate of pltch.
Removing the effects of nonunifon_ flow "_om the model data is exceedingly difficult, and it imposes a limit on the allowable magnitude of the wall effects.
The old rule-of-thumbwas that '_ should be less than 2°. Such small limits insure that nonuniformity will be small; however, 20 also partially accounts for i the even more approximate nature of classical wall corrections . A larger limit may be allowable when using the more elaborate correctiuns of references 5 and I?.
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Recirculation .f -I i.i The complete flow in the tunnel has been explored in de_ . , in reference 13.
"i Figures 26-29 show isometrics of the flow in the central plane of a rotor and in _ the plane of the floor for wake skew angles of 700 to lO°. In each case, the ,_ flow in free air is shown on the left, and the flow in a closed wind-tunnel is within a diameter or so of the rotor. For > , = 500 (fig. 27), the flows are I shown on the right. For X = 700 (fig. 26), the two flows are very similar ", fairly similar except for a stagnant region immediately in front of the inter- t section of the wake and floow. In this region, the wind tunnel flow becomes , stagnant, and the velocity around the _ides of the intersectionis greater in the tunnel. When the skew angle is 30u (fig. ?8), the flow ahead of the inter- f section is strongly reversed and there is a notable outward f_ow from the inLer- section. At X = lOU (fig. 29), these effects ere greatly magnified, a large vortex-likemotion involves the forward portion of the rotor, and the flow is reversed, and will separate from, the ceiling aft of the rotor.
It is clear that the rotor wake will be grossly altered by flows such as shown in the preceeding figures. Figure 30 illustratesthe deformations. The flow squirts forward ahead of the rotor, in a manner sure woll up into a vortex, and is drawn aft and upward behind the rotor. Examination of the deformed wake , f (fig. 30) i nd i c ates t hat the deformation will magnify the theoretical effects.
The overall flow to be expected is sketched in figure 31. A large cylindrical sheet of vorticity forms ahead of the rotor and passes off to the sides. As it approaches the walls, it sees the effect of its own image in the wall and c limbs u pward. T he initial portion of the vortex sheet is clearly shown in the i tuft-grid photcgraph of figure 32.
Obviously the flow in the tunnel can be so unlike _,-ee-air flow that tests nw1ypr o duce invalid results. The theory, which does n)" _ntlude wake deforma- _ tlon is inadequate to predict the limits of testing. Instead, controlled test- i Ing i_ ne c e ss ary to d etermi n e li m its; indeed thi_ "recircula c ion"limit was 1 i - His results are functi o n o f wind-tunnel width-he'ght ratio, and can be rer-_st in the f o rm sh o wn in figure 33. The criterion is a function of the distance iiii i n itia ll _ f ound i n suc h tes ts by Rae at the Uni v ersity of Wa s hington (ref. 14 ).
behind the model at which the theoreticalwake strikes the floor. Additional values placed on figure 33 indicate that grossly different models follow the same rule.
Wind-Tunnel Boundary Layer " The limits of figure 3_ may be far more generous when testing to obtain data for ground effect since a somewhat similar recirculationoccurs in ground effect as well. Here a different problem arises because of the wind-tunnel boundary layer. Figure 34 illustrates the effect schematically. When there is no boundary layer as in the upper part of the figure, the initial flow reversal is relatively small; however, ti_is disturbance can propagate forward in the low energy tunnel boundary-layer,locally causing increased angles in the flow near the nose until the model stalls at the nose. These effects can be eliminated by eliminating the boundary layer on the floor; the most direct way is to pro- vide a belt moving with free stream velocity as the floor. Figure 35 (from ref. 15j shows one experimentaldeterminationof the conditions ,whichrequire such treatment.
CHOOSING MODEL SIZE The complexity of the corrections at low speed makes it rather difficult _o predict the allowable size of a model for a given test. Reference 16 attempts to provide a set of generalizedcorrec;ion charts to provide some guidance in selecting sizes. As the starting point, reference 16 uses momentum theory to fo.-mthe results upon CL rather than the momentum skew angle × . The definition of CL is first divided by (Wh / Wh)2, to obtain J L CL = - (ll) ½pV2S (Wh / Wh)2 !'
Now substitute equation (9) into equation (ll) to yield L
s k i
Simplifying eq u ation (12) and noting that A = 4S2 / S yields I _nA C L : (13) F r o m mo m e n tum the o ry (ref. 6)
= - ta n X + (14)
Substitute equations (I 0 ) and (]4) (n o ting that V / wh = (V / Wo)(Wo / Wh)) into equation (14) to obtain (for n = 2) CL
. 2 (15)
Figure 36 has been prepared by calculating CL / A for a range of X and Di / L. In the simple case of an unpowered , ,, ing, exafnination of the "shaft" power by mom e ntum theory shows that Di / L = cot X. In that case, equation (15) reduces to , CL _ --- sin2x cos X (15) ! Equatio, - (15) is also shown in figure 36. Observe that one of the most I fundamental and far-reaching consequences of powered lift is that the conven- tional relationship between induced drag and lift is destroyed. A V / STOL air- ,!I craft can operate anywhere in the plane of figure 36. Any lift coefficient can i be obtained by the V / STOL aircraft. This is in distinct contrast to the con- -1 ventional wing where the relationship between induc e d drag and lift restricts the maximum lift coefficient to I CL + 1.209 A (16) , I I The parameters displayed on figure 36 are sufficient to calculate the wall interference for a given span-width ratio _ in any given wind tunnel. This ! interference can be plotted in terms of As and qc / q on the same plane as in i figure 37. Similar charts are also presented for the difference in corrections i at the wing and at the tail, as well as for the distortions across the span of th e wing.
Maximum plausible values for these various quantities can be assigned according to how much detail is to be incorporatedinto the data reduction for a given wind-tunnel test. Then a simple chart such as figure 38, shows the maximum CL / A for which acceptable data can be obtained. It is interesting that A_ seldom limits testing, and that Rae's recirculation limit largely is applicable to small models only. In most cases, various nonuniformitiesof interferenceset the limits.
The degree of effort expended in correcting data can have a large effect on the usable testing range. Reference 16 sets three levels ranging from no correction s at all to a maximum effort where the details of span loading are involved. As shown in figure 39, the level of corrections applied to the data can affect the allowable range of lift coefficient by an e,,_ire order of magnitu d e.
EXPERIMLNIAI VFRIFICATION I Over a period of y_ars, a substantial effort has been made to verify the i , wall effects predicted by the theory of reference 5. Fiqure 40 provides a list- I ing of a number of these test programs, and many of the test models are shown I in figures 41 to 43. In general, the experimental results were quite encouY- E aging, with the preciseness of correlation being largely a function of the _ rlgor with which the corrections w e re applled. T i megeneral results are _ illustrated by the following samples: Jet Flap The first test presented her e in was conducted on the jet flap model shown ii in figure 44. This model had a full-span t r ailing-edge jert flap with a fixed 90o deflection angl_. The model was mounted on a strain-gage sting balance.
A separate balance was provided for the simple rectangula_ tail. Tests were conducted in Langley's 300-mph 7xlO-foot tunnel and in a smaller 2.70xi.88-foot test section. These results were originally presented in reference 17.
The test results for lift are presented in figures 45 and 46. At C_ = 1.5, where the model has a distinct stall, correcting the data has brought the stall angle into complete agreement with a correction angle _ of about 5°. At C_ : I0, corrections fail at angles of attack in excess of about I0 °, Thi s angle of attack corresponds to Rae's recirculation limit as presented earlier in figure 33. A comparison based on the tail normal-forces is pre- s ented in figure 47. The corrected data is a9ain coincident within the accuracy of the data. i _ i Lifting Rotor !_ The second example concerns a tail behind a lifting rotor (ref. 18). This ii i' system, shown earlier in figure 41, was tested in the University of Washington i!
8xl2-foot tunnel, as well as within a 4x6-foot insert in that tunnel. The data I_ is presented directly as a wall effect, in that the difference in tail zero-lift !I angle is shown as a function of tip-speed ratio. The line marked recirculation limit was determined from earlier tests (ref. 14) and not from this test. Above this limit line, the theoreticalcorrections eliminate the effect of the walls to a point within the order of accuracy of the tests.
Fan-in-Wing The final example is an extensive study (ref. 19) on the fan-in-wi h gmodel shown in figure 49. The model was equipped with two tip-turbine-drivenfans and tail was equipped with a separate strain-gage balance. Overall forces were obtained from the wind-tunnel balances. This model was tested in a number of i" J i different test sections. Figure 50 illustratesthe comparative model and test-sectionsizes. In addition to those shown, the model was also tested in the 30x60-footand 40x80-foot tunnels.
One early criteria for testing without corrections was developed !
empirically in reference 20. The appropriate ratios given by that reference i for this test are shown in figure 51. These values indicate that in many cases there should be no wall effects. In contrast, the uncorrected data (fig. 52a) !
indicaterather large wall effects in all of the smaller tunnels. These differences collapse into a single data set when corrections are applied !
(fig. 52b).
Considerableeffort has been expended in the past measuring and correlating the "fan-induced"lift of fan configurations. One such correlation (ref. 21) is shown in figure 53. The chosen conditions are = 0° and V / Vj = 0.4. There are, of course, significant differences between forward and aft locations; however, those configurationswhich are reasonable balanced in moments appear to be along the shaded region. The uncorrected values from the present test in the 44x88-inch section for the complete configuration,both with and without the tail load, bracket the same shaded area. Unfortunately, the "fan-induced"lift vanishes (fig. 52a) when the data is corrected. Indeed, the corrected data closely follows a theoretical analysis (ref. 22) in which the interferencebetween the fans and the wing is totally neglected.
Figure 54 and 56 demonstrate the effectivenessof corrections at higher angles of attack and at the tail. In almost all cases, the correlation degeneratesat very low values of V / Vj. This effect is caused by recircula- tion, which is more suitably predicted in the present case by the results of Tyler and Williamson (refs. 23 and 24).
i f I i . . ' - ' -- - " IIIII I III _LL , L_t . I _._l '1__ / | _ - -1 _ l°'_- . -I , - i- ,--.-, _ ..... . , , _ f \ v I i l I _ [ J _ _ _ _ _ REFERENCES ' I _ L. P O PE, AL AN; AN D HAR PER , J OH N J.: LOW - S PEED W I N D TUN N El.
,_iI I T ES T ING., JOHN WILEY AND SONS, NEW YOR K , 1952. - / _ 2 . PR A NDTL , L. ; A ND T EI TJ ENS, O . O . I J, P, DE N hA RTO G t TR A NS. I : APP LI ED HYDR O- AND A ER OM E CHANICS. D O VER _ PUBot INC.p L95 7 . PP 222-225.
3. G L A U ERT, H .: THE ELE M E NTS (I F A E ROFOIL A ND AIRSCREW T HEOR Y , , 2 NO ED. , CAMBRIDGE UNIV. P R ESS , L 94B . PP | B 9 - I98. . _ 4 . T H__O DO RSEN , T H E O DORE: T _E T HEORY O F WI N D-TUNNEL WALL IN T ERFERENCE . NACA PEP. 4tO , tQ3t.
i 5 . HEYSON,HARRY H .: LINEARIZED THEORY OF WIND-TUNNEL JET-
BOUNDARY CORRECTIONS AND GROUND EFFEC T FOR VTOL / STOL A IRCRAFT . N A SA TR R-IZ4 , 1962 .
b . HEYSONtHARRY H . : NOMOGRAPHIC SOLUTION OF THE MOMEN T UM EQUATION FOR V T OL-S T OL AIRCRAFT. NAS A TN D-8IA , L 9 6 1 ( ALSO AVAILABLE AS : V / STOL MOMENTUM EQUATION , SPACE / AERDN .
VOL.3B,NO . 2t JULY t 1962 , PP B- I B TO B-20. ) 7. NEt ¢ SOM , WIL L IAM A., JR .: WIND-TUNNEL INVESTIGATION OF A DEFLEC T ED-SLIPSTRE A M CRUISE-F A N V / STOL AIRCRAF T WING . NASA TN D-4262 , L 9 6 7.
8 . CO N E , _ARENCE 0.: A THEORETICAL INVESTIGATION OF VOR T EA-SHEET DEFORMATICN BEHIND A HIGHLY LOADED WI N G AND ITS EFFECT ON LIFT. NAS A TN D-657, Lg6 L.
9 . PEYSON, HARRY H.; AND KATZOFF, S. : INDUCED VELOCITIES NEaR A LIFTING ROTOR WITH NONUNIFORM DIS K L OADING. NASA R F P. L3 L 9, L 95 7. ( SU P ER S EDE S NACA T N 3 6 90 BY HE Y S3N AND KATZOFF AN D NACA T N 3 6 g[ BY HEYSON.)
L O . F_ARGA S O[, , RICHARD J.: JET-INDUC ED EFFEC T S IN T RANSI T ION CONF , ON V / STOL AN D S T OL A I R CR AF T . NASA S P -ll 6 , [966.
• P P " 70 - 1 . 90.
llL . F 'R & NDTL t L.; AND T E I TJENS , O . G . (L. R O SENHEAD _ T R ANS.): FUNDA ME N T A L S O F HYDR O- A ND AEROMECHANICS .
DOVER P UB . , INC., 1 9 5 7 . P P 2 0 0-20 7 .
L 2. H EY S O N , HARRY H.: USE O F S U PE R P( ] SITI O N I N DIG I TAL C O M P U T E R S T O O B T A IN WIND-TUNN E L IN TERFE RENCE FAC T O R S F O_ ARBI T R AR Y C O N F IG U R AT ION S , WITH PA R T IC ULA R R EFER - F N . E TO V I S T OL M O D EL S. N ASA T R R- 3 02 , I969.
ORIGIZ_ AL PAGE BS ] 7 OF PO O R Q UALITY I I
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J 1 3 . H F YSON, HARRY H.: THEO R E TI CA L STUDY CF C OND I T I ONS LI; 4ITING V I STO L T ESTING I N WIND TUNNE L S W IT H SOL I D F I . OOR . N ASA T N D-S B].9 , 1 9 70.
1 4 . RA E t WI L L IAM H. , JR.: L IM I T S O N M IN I M UM-S PEE D V / ST OL WIN J-TUNN E L T E S T S . JO U R .OF AIRCRA F T _ Vr JL. 4, NO. 3 , ! MA Y-JU NEt 1967 t PP 240 - 2 5 4.
{ " = 15 T URNERt T H O MA S R.; A MOVING-B ELT G ROUN D PLAN E FOR ' WIND- T UNN EL GR O UND S IMU L ATION AND R E SULT S FOR TWO JE T- i FLAP C ONF I GURAT IONS. N ASA TN D - AZ28 , t967 .
' 1 6 , H E Y S ON, HARRY H.: R A PI D E S T IMA T ION OF WIND T U NNEL C ( IRR E C T ION S WITH APPLIC A TIONS TO WIND TU NNEL AND MOg E L DE S IGN. N ASA TN D - 6 4 16 , t91t.
IT. HEY S O N , HARRY h. ; AND GRUNW A LD, KA LMAN J.: WIND TUNNEL BO U NDARY INTERFER E NCE FOR V I S T O L TESTING. CCN F E RE NCE O N V / ST C } L AND STOL A IRCR A FT_ N AS A S P - I[6 , I00 6. PP 40 ? -434 .
I B, R A =, WIL L I A M H., J R.; AND S HINDOt SHO J IRO : CCMMEN TS ON V I S TOL WIN D T U NN EL D A TA AT LO W ' FC RWA RD S PEED S . PROC EE D.
T HIRD CAL I AVLABS SYMPO S IUM ON AERODYNA H ICS O F RO T ARY WI N G A N D V / STOL A IR CRAFT . VOL . _._ B UFFA L O , N .Y. t J U NE @ i B - ZO _ 1 9 69.
f
19 , HE Y SO N t H A RR Y H.: THE E FF EC T OF WIND- T UNNE L WA L L - IN T ER- k F E RENC E O N THE P ER FO R MAN C E OF A F AN-IN-WING V T OL MO DE L.
NASA TN D-751 8 , 197 4.
ZO . CO O K , W OOOR OW L .; A N D H IC KE Y, DAVID H .: COM P ARISON OF -\ WIN D - TU NN EL AN D F L I GH T - TEST A ERO DYNAM I C D A T A IN THE T R A N S I T ION- F LIGH T S P EE D RANGE FOR F IVE V I S T O L A IR C R AFT.
CON F , O N V / STOL A ND ST O L A I RCRA F T . N ASA S P - l l6 _ 1966 , PP 66 T - 66 7 . (AL S O AVA I L A BLE AS A GA R D R EP T 520 t 1 965.1 _I , H ICKEY t DAV I D H .; AND COO K t W OO _ R OW L.; AER O DYNA MIC S O F V I ST O L AIR C RAFT PO W ERED BY LIF T FANS. AGARD CP ZZt PA PE R NO 1 5 _ S _ : P T 1967.
ZZ , HE Y SONt HARRY H. : T HE OR E T I CAL AND E X P E R I M E NTAL I NV E ST I - GA T I ON O F THE PER F OR M AN CE OF A FAN- I N- WI N G V T OL CONF I G- " URAT I ON. NASA TN D-TAO Bt 1 9 73 .
Z3, TYL E R t R. A.; AND WI LL I AMS O N _ R. G .: EXP E R I ENC E W I T H TH E NR C 1 0 F T.XZ O FT. V /S TO L PROPULSION T UNNEL - S O ME PRAC TIC AL ASP E CTS O F V / S T OL E NG I NE M ODEL T E ST I NG.
CA N, AER O. A N D SPACE JOUR , tVOL | 0_ NO 9 _ S E PT 1 972 .
PP ]Lg [ - 199, i LP L _ , k k JI ,.,, • - _ " j 24. T Y L ER, R . A . ; AN D WI LL IAM S ON, R. G .: WIN D TUNNEL TES T ING OF V / S TO L E NG I N E MO D E LS - S OME OB S E R VE D F L OW INT E R- AC T ION AND TUNNEL EFFECTS. A G ARD- C P- 9 1-?It PAPER NO 8, D E C. LgTL .
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1 0 . Wo rk Un,l N O • _ _. , f_ . ,,. g _ g ._,_. t ,_. N . _. a.d Ad m ._ 516-50-23-01 NASA Langley Research Center _ , _. , , ._, o , G , _ , . : .r Hampton, Virginia 23665 13 T ype of _ e p (Jr| _ r, ! f' , 'f_ ,, I '" _v,.r * _!
1_( S l_ m _ o t,n g Agcq_ Cy Ndrr , e @ r i l l Addl'ess Techni caI Men!grandL,n_ .
N ational Ae r o nautic s an d Spa ce Adm inistration _ 4 Sp on m , ,.g a_, . _,_ v , : _, Washington,DC 20546 15_J pple, ,_t ary NolI$ C o llateral r e l ease o f no te s f o r lecture pre s ented in Seminar on A e r od y nam i cs of V I S T nL Aircraft a n d Helic op ters dt the Pennsylvania State University.
U n i ve r s ity Pa r k. PA , Ju l y 3 1 -A ugu s t 4 . 19 7 8. , _ 16 A l_,| t I N _I The b a s i c concep t s o f w i nd- t unnel bound ary i n terfere nc e are discussed a n d t h e developm e n t o f t he t heo ry f o r VTOL-STO Lair c raft is de s c ribed . Feat u r e s affecting t he wall in t e rf e r ence , such as w ake r oll-up, con fi gu rati on d iffer enc e s, re c ir cul a - tl on 1 iml ts . a nd i n terferencen onun if o rmity,are discussed. The effects of the leve l o f c o rrecti o n o n al lo wab l e m o de l si z e are shown to be amenable to genera l ized presentation. F inally, experimental confirmation of wind-tunnel interferencetheory , , i s pre s e n te_ f o r jet-flap, r o t o r, and fan-in-wing models.
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