h[k\^^m NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS TECHNICAL MEMORANDUM No. 1181 INVESTIGATIONS ON REDUCTIONS OF FRICTION ON WINGS, IN PARTICULAR BY MEANS OF BOUNDARY LAYER SUCTION By Werner Pf erminger Translation "Untersuchungen iiber Reibungsverminderungen an Tragfliigeln, insbesondere mit Hilfe von Grenzschichtabsaugung" Mitteilungen aus dem Institut fiir Aerod3mamik an der Eid- genossischen Technischen Hochschule in Ziirich, Heraus- gegeben von Prof. Dr. J. Acker et, Nr. 13. UNIVERSITY OF FLORIDA DOCUMENTS DERARTMENT Washington '^^ BOX mOlf' ^""^^ ^^^ August 1947 GAINESVILLE. FL 32811-701 JSA I^'f I E ' UACA TM Wo. llBl TABL^ OF CONTENTS Preface Page Chapter 1: Introduction, Abstract 1 1. General reiaarfcs ■ 1 2. Earlier reports published on the reduction of frictional and profile drags and on related fields . 1 3. Influence of the transition-point position on the profile drag for larger Eoynolds numbers j statement of the purpose It- Chapter 2: Causes of Transition 6 1. Influence of the external pressure gradient on the • transition ■ 6 2-. Influence of the external tm:'"bulence on the transition; turbulence of the atmosphere ■ 10 Chapter 1'. Laminar P^rofiles with the Transition Taking Place Far To^mrd the Bear (without Boundai-y-Layer Suction) ... l6 1. GeneraJ. considerations l6 2. Preliminary tests on laminar profiles for smoobh ■ entrance ......... l6 3'. Laminar profiles for propellers • l8 'i-. Laminar profiles for w3.ngs 21 Chapter Ur Laminar Boundary -Layer Suction, General Eemarks . 26 l.:Aimo for fiirthsr development 26 2. Effect of suction of laminar boundary layer on the ' flow characteristics 26 3. Statement of the problem 2? \- History of developnent of the lamlnai-- boundary -layer suction 28 Chapter 5: Inve-stigation of- the- Lajminar Pressure Increase with Boundai:'y-Layer Suction for Smaller and Mcdiijim Eeynolds Numbers .-..•..■ ...«.- 36 1. Laminar suction tests with throe suction slots arran'::^ed one after the other 36' 2. Tests with laminar boundary-layer suction vrith a single suction slot 38 ^ NACA TM No. II8I Page Chapter 6: Investigation of the Slot Flow for Laminar Bouniaiy-Layer Suction with Single Slots h^ 1. Laminar suction tests with straight suction slot .... k^ 2. Investigation of the slot flow for laminar "boimdary- layer suction with si;ction slot (i) curved forward (definitions, see "beginning of chapter 5) ...... ^7 3. Investigation of the slot flow for laminar 'boundary- layer suction with the rearward curved suction slot (h) k8 Chapter J: Tests about Keeping a Bnundarj'" Layer for High Reynolds Uumbers Laminar with the Aid of Boundary -Layer Suction ... 50 1. Purpose of the tests 50 2. Test apparatus 50 3 . Measurements 5I' h. Symhols ejad evaluation of the section tests 52 5. Test results 59 6. Extension of Schlichting's theory on the laminar "boundary.- layer development with area suction in the case of the acceleration of the sucked air to the undisturhed free-stream velocity TJq ...... , 62 Chapter 8: Investigation of a Slightly Cam"bered Laminar Suction Profile of 10.5-Percent Thickness ... 65 1. Purpose of the investigation . 65 2. Profile, test arrangement 65 3. Meas'orements vrlth laminar "boundary-layer suction .... 66 h. Test results 69 5. Conclusions from the tests of chapters 7 and 8 for the design. of laminar suction profiles ^irfth the lowest possi"ble.drag for high Reynolds maa'bers 72 6, Prospects for application of laminar "boundary-layer suction in flight for high EejTiolds numbers 73 Appendix ...... 75 References ....... . . , . . • ■ , . • . , . 77 NACA TM No. II8I PREFACE The present report deals with the reduction of frictional drag "by maintaining a more extended laminar 'boundary layer, particularly vith the aid of 'boimdary- layer suction. The first chapters treat puhlications in this field, the causes of the houndary-layer transi- tion and a few laminar profiles without houndary- layer suction. Next, tests with laminar suction profiles are described. The "behavior of the suction slots for laminar boundary- layer suction was separately examined . The present report was begun in 19i+0 and financially supported by the Committee for Study of Aviation. I feel obliged and am glad to express here my sincere gratitude to this committee and particularly to its president, Prof. W. J. Ackeret for energetic support of my work. Digitized by tlie Internet Arcliive in 2011 witli funding from University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation http://www.archive.org/details/investigationson01unit NACA TM llo. 1181 llATIO^KL ADVISOHY COMfllTTEE FOR AEROMUTICS TECHNICAL MEM0SA1€)UM NO . II8I BIVESTTGATIONS ON REDUCTIONS OR FRICTION ON WINGS, IN PARTICULAR BY MEANS OF BOUNDARY-LAYER SUCTION* By WeiTier Pfennlnger CHAPTER 1 ■ INTRODUCTION, ABSTRACT 1 . General Remarks The drag of an airplane consists of the induced drag, the frictional and fo'tn dra'^ of wing, fuselage, tail unit, and, occasionallj'", radiator drag. Investigations have showii the frictional drag to "he the main portion of the dran^ Thus the reduction of sirrface friction has gained considerahle importance during the last years . Since the laminar friction is, in :"eneral, considera"bly lower than the turbulent friction, the frictional drag cou.ld "be reduced hy a laminar boundary layer as long as possible. The aim of the tests described here was to keep the boundary layer completely laminar up to the trailing edge of the wing. 2. Earlier Reports Published on the Reduction of Frictional and Profi].e Drags and on Related Fields (a) The possibility of reducinft friction by maintaining a laminar boundary layer for a longer time has been mentioned by B. M. Jones (reference l) . Bi M. Jones proved later (reference 2) that on finished wing profiles in flight there might appear laminar boundary layers of much greater extent and with the "Untersuchungen liber Reibimgsverminderungen an Tragfliigeln, insbesondere mitHllfevon Grenzschichtabsaugung" Mitteil^mgen aus dem Institut fur Aerodjniamik an der Eidgenosslschen Teclmlschen Hochschule in Zurich Herausgegeben von Prof. Dr. J. Ackeret Nr. I3. MCA TM No . 1181 transition point lying farther to the rear than was expected so far (compare Serby, Morf^an, and Cooper (reference 3))« B. M. Jones (reference 2), Squire-Young (reference U), Pretsch (reference 5), and Serby, Morgan, and Cooper (reference 3) investigated to vhat degree the transition-point position affects the frictional and profile drag. According to these investigations a farther rearward position of the transition point should make low profile drags possihle even for thicker profiles at higher Reynolds numhers, Ee . In fact, tests on "laminar profiles" of this type resulted in con- siderably smaller profile drac:s, particularly for weak external turhulence and larger Re (references 6, 7, and 8). During the second world war these laminar profiles were thoroughly investigated in various countries. (Td) The position of the transition point depends mainly on the external pressure distrihution, the external turlDulence, and the nature and cui-vature of the surface. The influence of the external pressure distribution on the transit! on -point position . was investigated "by S. M. Jones (reference 2), SerTjy, Morgan, and Cooper (reference 3), Hall and Hislop (reference 10), G. I. Taylor (reference 11), Faye and Preston (reference 12), Schutauer (reference, 13), Faye (reference it), etc. Flight tests hy Jones (reference 2), Serby, Morgan, and Cooper (reference 3), and the WACA (references 9 ^"^^ 15) showed that for "clean" surfaces transi- tion in fliijjit generally takes place in the region of the point of separation, even for higher Reynolds numbers. Wind-tunnel tests at moderate Re showed that the transition after a slight pressure increase, in general, takes place shortly after the separation point of the laminar layer as long as the external turbulence does not affect the transition (for instaiice, Hall and Hislop (refer- ence 10)) . A similar behavior in transition wa.s found on bodies of revolution (reference 16) . (c) Under the influence of an external turbulence the transition for higher Re occurs sometimes at a considerable distance before the point of laminar separation. The dependence of the transition on an external turbulence was studied by G. I. Taj'"lor (references 11, 17, and 18), von Karman (references I9 and 20), Dryden (references 21 to 2h) , L'. Prandtl (for instance (reference 25)), Schlichting (references 26 and 27), Tollmien (references 28 and 29)j Schubauer (reference 13), Faye and Preston (reference 12), Faye (reference 30), etc. For weaker external turbulence, in general, higher critical Reynolds numbers are obtained at the point of transition; compare, for instance, B. M. Jones (reference 2), Hall and Hislop (reference 10), Tani (reference 7), Lewis (reference 6), and also (reference I5) . MCA TM No . 1181 For accelerated flow, too, there result higher critical Ee, compare Dr.yd.en (reference 21) and Peters (reference 31) • (d) For application of laminar profiles in flight for higher Ee, knowledge of atmospheric tur'bulence and its influence on the transition ia important. The atmospheric turhulence was investigated in flight with hot wires, among others ty Stephens and .Hall (refer- ence 32) . These two authors reached the conclusion that in their tests the influence of the atmospheric tujrhulenc'e on the ■ transition was negligihle . American flight tests on a laminar profile of 15.9-percent thickness at Ee = 17 x 10° confinned this result (reference 15) • The influence of the wall curvature on the transition. was investigated experimentally, for instance, "by M. and F. Clauser (reference 33) and theoretically "by H. Gortler (reference 3^) • The mea,suremerits "by Clauser showed at the transition for convex (or concave) wall curvature higher (or lower) Re than for a straight wall (compare also L. Prandtl (reference 3?) and Bayleigh (reference 86)). (e) The influence of surface disturbances on the transition (ro uglinesses, tm-hulence \jlres, trip wires, rivets, unevenesses in the sheet-metal sMn, surface leaks, v;aves, etc.) was investigated, for instance, "by Yoiuig (reference 3'^), Hood (reference 37),- Tani (reference 3^), and Faj'-e a.nd Preston (reference 1?). Tests of the author showed that laminar profiles at higher Be are sensitive to waviness of the surface and that surface leaks must "be avoided in order to prevent the air from l)eing sucked from the wing interior and the boundary layer thus from 'becoming turbulent. (f) The pressu.re distribution of suitable profile shapes may be calculated with the aid of conformal mapping, for instance, according to Theodorsen (reference 39) (compare also references kO, kl, and k2)t The singularity methods which replace the profile by vortices, soiu^ces and sinks, take. less time for the detailed numerical calculation, but are less accurate. From the pressure distribution one may calculate the development of the boundary layer in the laminar and turbulent part of the profile . (g) The laminar boundary-layer development Taaj be determined, for instance, according to Pohlhausen (reference h^) , Falkner and Skan (reference hh) , Falkner (references ii5 and U6) , and Howarth (reference U8) . For moderately accelerated and slightly retarded flow the approximation method of Pohlhausen is well applicable as demonstrated by a comparison with Falkner 's method (references U5 and US) for an external velocity distribution U = loc^. According to Pohlhausen, the laminar-plate friction (pressure -gradient zero) MCA m No. 1181 is overestimated "by 3 "3 percent. (Comparison with Blasius (refer- ence ^7).) According to Hovarth (reference hQ) , the laminar separation starts in the case of the external velocity distribution U = Uq - hx at X = ^u' = -7.5 instead of X. = -12 according to Pohlhausen.-' For the case U = kx"'^ '^90^ the method of Falkner (references U5 and i|-6) results in "boundary-layer profiles with vertical, tangent already at \ = -5. Howarth (reference 51) gave a compilation of various methods for calculation of the laminar "boundary -layer development . L. Prandtl (reference kg) and H. Gortler (reference 50) investigated the laminar boundary- layer development by exact calculation and compared the different .imovn solutions with each other. Tomotika (reference 52) developed a method corresponding to that of P.ohlhausen for the three-dimensional case . (h) The turbulent boundary- layer development may be calculated according to A. Buri (reference 53), Gruschwitz (reference 5^), Kehl (reference 55), Squire-Young (reference k) , and Young (refer- ence 5^) • In most cases, the turbulent shear stress at the wall is the same as that for the flat plate with turbulent flow without pressure gradient for equal Eeg . The ratio S- = H was frequently 9 assumed constant (H = 1 .U for not too large pressure Increase). Otherwise, H could be determined from tut'bulent boundary- layer measurements as a function of the pressure increase (compare, for instance, Gruschwitz (reference 5^))' The turbulent boundary- layer development along the flat plate ^-rlthout pressure gradient was investigated, by Th. von Karman (references 57 and 58) and L. Prandtl (reference 59) • The boundary- layer development of the wake may be calculated, for instance, according to Squire-Young (reference h) , 3 . Influence of the Transition-Point Position on the Profile Drag for Larger Reynolds Kumbersj Statement of the Purpose For slightly cambered profiles of various thickness ratio d/t at Re = I5 x 10° the profile drag was calculated according to Squire-Young (refereflce h) for various positions of the transition point x/t (compare fig. 1). Furthermore,, the profile drag was MCA m No. 1181 calculated for a profile of l6-percent thickness for various Ee and different positions of the transition point. (See fig. 2.) For a rearT'Tard movement of the transition point at larger Re, Cy would drop to low values. In the ideal case (boundary -layer kept completely laminar up to the trailing edge), even thicker profiles would give very low drags for larger Ee's. Thicker profiles are structurally more favorable and permit larger spans, thereby reducin;^ the indticed drag which wou-ld re^sln significance due to: the decrease of the frictional drag. Moreover, thicker profiles permit a more favorable installation in the wing of fuel tanks, power plants, other loads, and finally, suction ducts. Fiirtheriaore, thicker profiles possess higher maximum lift with suitable high-lift devices. For faster airplajaes the maximum profj.le thiclmesR is probably dependent on the stipulation of siifficiently small superstre?.m velocities in order to reach high Mach numbers without compression shocks . According to these considerations, the following aim was set: Development of thicker profiles with small superstream velocities where the boundary layer remains, in flight, at high Beynolds 1 numbers, laminar as far toward the rear as possible, if possible as far as the trailing edge. The maximum lift for take-off and landing is to be a.s high as possible. The possibi.lities of keeping the boujidary layer laminar for a long tine are, for instance: (a) Use of profile forms where, by special design of the contoTir, the tr.ansition is shifted rearward (flat pressure distribution with small superstream velocities and. delayed pressure increase) . (b) Preventing the boimdary layer from becoming turbulent by means of boundary- layer suction, possibly in combination with profile forms with flat pressure distribution. In order to study the methods for keeping the boundary layer laminar for a longer time, one must know the presumable causes of transition. MCA TM-No. 1181 CHAPTER 2 - ■ CATBES OF TRANSITIOKr I 1 . Influence of the External Pressure Gradient , •• on the Transition Transition tests showed that, in general, the transition takes place after a slight pressure increase in the neinhtorhood of the point of laminar separation, as long as an external tur- hiLLenco does not affect the transition (references 2, 3, 10, 12, 13, 15;, lo^ and. 60) . These ohservations were confirmed "by tests of the author, for instance, en an NAOA 0010 profile (fig. 3), on laminar profiles of 10-percent and lU--percent thickness (figs, k and 5)> on a looij of revolution (fig. 6) and, later, hy D.amihar suction tests. With increasing Ee the transition point moves forward more slowly for laminar profiles than for so far conven- tional ones. These tests, as well as those of chapter 3 s-ud the later suction tests of chapter h, J+C, chapter 6, 3, chapters 7 and 8, ' were preformed in the large wind tunnel of the Institute d-escrihed in reference 6la, The wind-tunnel turhixLence was . i"2 "1 = ^^ = O.OOl+O to 0.00^^5 ^o "o The pressure gradient in the ad,justa,hle test section is very small. In figure 3 the pressure distrihution -2- is plotted on an WACA-0010 profile ( so far conventional profile form) for Cg, = Uot and various Ee = --— along the chord (U^ free- stream velocity, t = chord = .60 a). The static pressure p was measured through .5 millimeter cp "bore holes compai^ed to the static pressure Pq in the test section without wing. The free-- stream stagnation NACA TM No. II8I presaiore was tlo ~ ^o " "^o (So ~ ^^'iistur'bed total pressure^) . The positions of the transition point (arrows) were ascertained from the "break in the pressuxe-distrihution curves at the transi- tion (compare transition tests on MCA 0010-profile' with soot. '' coatinp-,' and stethoscope (reference 6lc))t For larger Be the determination of the position of the transition point from the break in the pressure distributions 'bec.ame unreliable. With increasing Ee the transition point shifts rapidly forward. Tn figures h and 5 the pressure distribution v/^o °^ '^■''^^ laminar profiles (fig. 12) is plotted versus the chord with d/t = 10 percent, t = O.T'imid/t = 1^*- percent, t = .70 m- The static pressixre p was measured with a static -pressure tube of d = 2.0-millimeter diameter, which was put tano-^'ential-ly to the test point in the flow direction versus p^ (static pressure in the test section for "turmel-emDtj" condition) . The four .h millimeter cp conn.ecting static -pressure holes of the static- pressure tube were located 10 millimeters behind the semicircu].a.r head and 100 millimeters ahead of the sting of 3.0 mJ.llimeters q). A comparison of pressure-distribution measurements on a laminar profile of lU.T~percent thickness and 2 .'4--percent camber of the . profile mean line showed that p/Qo on the upper and lower side, respectivel.y, was measured with the static-pressure tube on the average by 0.007 and O.OOU, respectively, too high, as compared with the measurement by means of connectin:55 static -pressure holes. The transition (arrow) was determined, by means of the, stethoscope (reference 6lc) and from the brea.k in the pressure- distribution curves (reference Ik). 3-By means of an annular equalizer opening at the end of the closed test section one succeeds in establishing there atmospheric pressure (for model present and tunnel empty condition) . The undisturbed static pressure for "model present" very far in front of the model is approximately equal to the static pressure p^ in the test section at the location of the model if the tunnel is empty (neglecting of the wake behind model and suspension) . It is self-evident that thereby the profile properties are given in such a manner as if the profile were working in a closed tunnel, not in the unlimited air sti-eam. Since the models investi- ga,ted here were small relative to the t\3nnel cross section (2.1 x 3% octagonal), the respective ^et correction was omitted (about a corresponding correction of q^, Uq, p^ for larger model dimensions for two-dimensional flow. (See chapter 8.) 8 > MCA 1M No. 1181 Tlie pressure distriliution -2- is plotted on figure 6 for a ■n *^o "body of revolution of i: = 0.212 at 0.U7 x L from the front UL for symmetrical flow at various "Re-^ = -rj-, (D = maximum diameter of the body of revolution, L = length of the "body of revolution = 0.85m). . The hody of revolution was held from "behind hy a cylindrical sting, suspension wires on the "body were avoided, p was measiured versus p^ (static pressure in the empty turoiel) "by means of a 2.0-millimeter cp static -pre ssture tube. The position of the transition point (arrow) was ascertained with the stethoscope and from the "break in the pressure -distribution curve . The sli^^t superstream velocities result in a pressure increase and transition far to the I'ear. Drag measurements : At the end of the "body of revolution at the jionctuTe to the sting the "boundary- laj'-er profiles were measured for symmetrical flow at various Kej^. The total pressure g in the "boundary layer was determined "by means of a flat total head tv.he of 0.2-millimeter x 2.5-millimeter inner cro3s section and 0.5 -millimeter eztemal height. The static pressure in the boundary layer was measvired. by means of a 2.0 -millimeter static pressure tube. From the boundary- layer measurement at the end of the body the moment^jm-loss area X^^ far to the rear was calculated for the undisturbed static pressure p„ according to Young (reference 56) . X„ = 2n / i- ( 1 - ^ ) r dr far toward rear K) wake The drag coefficient c^^^^ and c^^^ , referred to the "body surface area = 0.369m^ and the maximum cross- section area ■? X D = 0.025^1. itr, respectively, then becomes: Cwq - ' ""m - — -' ^^2/3 - 373' (V = Volme) - D^ ^ ■ , h . c„ (^®l) ^^ plotted on figure 6. c-,^ decreases with Ee^^ at first similarly to the friction of the laminar flat plate NACA m No. 1181 c-,^ = — 12 — see Blasius (reference' ^7) and increases again for ^' /Re higher r!ej__, due to more pronounced shifting forward, of the transition point (ohserv-ations Tsy stethoscope), caused "by the tunnel turhulence . The minimum drag coefficient referred to the maximim cross section resulted as c^„ = .OI96 . For smaller Re, ' stethoscope observations showed that the houndary layer at the end of the "body undergoes laminar separation and does not readliere with the properties of a turbulent houndary layer, therhy greatly increasing pressure and total drag. The position of the transition point can "be determined in different -ways'. (a) From hot-wire ohscj-^ations (compai-e, for instance, Dryden (reference 21)) (h) Ey measurement of the total surface pressure along the chord with a fine total head tube (references 2 and 10) (c) By boiAndary- layer measurements (compare, for instance, (reference I6)) (d) From the breai in the pressure-distribution curve at the transition, caused by ^ the sudden decrease of the displacement thickness 5^' at the transition (compare A. Fage (reference lU) and the pressure-distribution curves of figures 3, k, 5, 6, 39, Uo, U-Qo, etc., compare also calculations by A. Betz (reference 77) for discontinuous change of the curvature) (e) A-coustically by stethoscope observations (reference 6lc) (f) By soot coating (reference 6lc) (g) By measvirement of the total head of the f>oundary layer along the chord at a greater distance from the wall (reference 2) As long as the transition is caused by an external presaiu'e increase and not by an external turbulence, it takes place in a narrow comparatively well-defined zone . The methods indicated then yield, in general, the transition- point position reliably. Presumable cause for transition: According to Rayleigh (reference 62), Tietjens (reference 63b), and Tollmisn (reference 29) 10 ' NACA TM No. II8I laminar "boundary-layer profiles with inflection point, as they originate with rising pressure, are un.sta"ble. Transition tests showed that the transition occurs when laminar "boundary-layer profiles having a slight rearward flow in the neighTDorhood of the wall exist (compare, for instance (references 10, 13, and 78), this was confirmed "by transition ©"bservations of the author with soot coating for medium Ee . The originating of sufficiently strong vortices in the immediate neigh"borhood of the wall (as they form, for instance, for larger laminar pressure Increase, for discontinuities in the su.rface, "by an external tur"bulence, or for tu"be flows with sharp- edge inlet) seems to he required for the transition (compare L. Prandtl (reference 63a), J. Patry (refer- ence 6k), and L. Schiller (reference 79)). TJ v 1 The RejTiolds num"ber 'P.e-i = — - — referred to the distance 1 -^ V "between the laminar separation point and the start of transition resulted as He^ = ^0,000 to 70,000 as long as the external ti5r"bulence does not affect the transition (compare references 9 and 10 ,> confirmation "by measurements of the author) . U = mean velocity at the edge of the "boundary layer "between laminar separation point and start of transition. For very weak external turhulence and larger Be the tran- sition for laminar profiles is pro'ba'bly to "be expected in the region of the laminar separation point. 2. Influence of an External Tur"bulence on the Transition; TuT"bulence of the Atmosphere (a) Various drag measuxements and transition measurements on flat plates, profiles, and "bodies of revolution had shown that for larger Pxe^molds num'bers the transition, under the influence of the external tur"bulonce, takes place considerably farther in front and that the drag increases again. The same o"bservatlon was made in tests of the author on laminar profiles without boundary- layer suction (see, for instance, c^ (Pe) of a profile of 3«35"Percent thickness (chapter 7: fig. 88, curve a, and corresponding position of the transition point, fig. 89, also figs. J, 8, and 10) and on a body of revolution with flat pressure distribution and transition lying far back (fig. 6, chapter 2, l) . For larger Eejmolds numbers, individual turbulent bursts vrere determined in the boundary layer with a stethoscope which occur more and more frequently downstream with Increasing boundary -layer thickness until the boundary layer becomes fully turbulent. The transition takes place in a niore or NACA 1M No. 1181 11 less wide transition region; its poGitionls less readily ascertained according to the methods indicated in chapter 2, 1 than in the case of transition due to external pressure Increase. A renewed increase of the profile cijr-ag due to the external tur'bulence was also observed for laminar profiles with 'boundary- layer suction, for le.ri^er ■Re = -^- (figs. 18, 88, 9? or chapter h, kc, chapters 7 and 8), (b) Causes of transition for transition due to .an external turbulence: By the external turbulent velocity fluctuations considerable velocity fliictuations -Jn flow direction originate in a boundary layer (see Tollmien (reference 28b), G-. J. Taylor (refer- ences 11 and 18) and Drj'-den (reference 21)), thus causing temporarily unstable boundary-layer profiles with Inflection point and finally reverse flow in the neighborhood of the wall. The transition then occurs, as in the case of larger laminar pressure increase, due to the formation of vortices at the surface. There originate isolated turbulent discontinuities which become more and more frequent downstream with Increasing bounds,ry-layer thickness until the" bound3j:'y layer is fully turbulent. G. I. Taylor (reference I8), Hall and Hlslop (reference 10), Fage and Preston (reference 12), and Fage (reference 30) attempted to find a criterion for the transition due to an external turbulence. They assumed that the transition starts when there originate^ 'under the, influence of the external turbulent pressure fluctuations, momentarily boundary- layer profiles with vertical tangent, that is, X Pohlhausen = -12, or, respectively. Its mean square value U \dxy ^ci-itlcal According to G. I. Taylor (references 11 and 18) turbuJLent pressure fluctuations originate in the case of an external tur- bulence, their mean square value is, for isotrope turbulence. yW^(MP-^t 12 n with i2 2 u'^ - u^'^ 12 MCA TM No. 1181 X is a parameter connected- ^d-th the diffusion in a turbulent fxov (X.^ = length of the diffusion) . (X^ and A (mean magnitude of the smallest vortices significant for the dissipation) were, for instance, experimentally -determined "by Hall and Hi slop (reference 10 ) .from temperature distribution measurements "behind a heated vire and from measurements of correlation behind grids.) Taylor deduces by insertion of ' — i for isotrope turbu- \d.x/ lence behind a grid (mesh i/idth M) that the critical Ee^m-olds number I^e^.^i^ioal = (^jcritical ^^ ^ f^^ction of Cm) \^r^- 0" critical) - V-V-yc^itical VMJ VU7 \ A A r n./ wherein A = constant, :^ = A /A -, ■ . M ■ \/mu according to Taylor. This relation was exTDerimentallj' tested by Hall and Hislop (reference 10). Accordln-17 to it, Ke-^ ... , /r\0'2 ~A:'\ ^critical increases ^^^ith diminishing values [^j (— - ) somewhat more slowly than according to the theor.v, that is, X ,.. ^ decreases with . ' ' ' critical increasing Ee-jr , . This circumstance may perhaps be explained critical from the fact that a sufficiently strong reverse flow at the wall (X<-12) and not only X = -12 '(vertical tangent to the velocity profile) is decisive for the transition. For small Ee^ larger negative X-values are necessary for the transition if one assumes the reverse flow required for transition to be of equal strength (with equal circulation) . Turbulence criterion of Fage (reference' 30) : Under the assumption that the transition starts when momentarily a critical negative X-value is reached due to the turbulent-pressure fluctuations, Fage finds that the value ^ ^ 3-35(''=%lt-l=a^' N0.6(nVe\°-^ MCA TM No. 1181 13 ought to "be constant, with L turtvilence seal© (A ^) Ey correlation for velocitj'- fluctuations in 2 points at distance J perpendicular to flow Eofl = f — ) at the transition critical \v /critical Fage finda that |t decreases with increasing Pea L "critical ■» For accelerated or for retarded flow the transition occurs, due to external turbulence, at higher or at considei^aMy lower Ee^ -ralues, respectively, compai'e, for instance, figures 3 critical and k. Influence of the atmospheric turljulence on the transition: The turl)U.l(?nce measurements in flif?ht by vStephens ?ind Hall (reference 32) had given the result that, in their tests, the influence of the atmo-spheric turbulence on the transition was negligible. Jn most cases, the turbulence~de{pree of the atmosphere was very small: ^ "n f^.0003 for U = ^16 m/sec in calm air, U = velocity outside the bovmdary layer. Considerably larger turbulent fluctuations were formd for unstable stratification of the air (u'/U = 0.003 for U = h6 m/sec) ,' however; due to the turbulence scale which was so much larger than in the vdnd tunnel, their effect on the transition was, accordln'" to Stephens and Hall, of secondary importance. (Maf'nitude of the smallest vortices ~ 0.3 m). Stephens and Hall found the fluctuations in the boundary layer to be considerably smaller in fll'Tiht than in wind-tiinnel tests (refer- ence 21) . The same ojbservation was made in tests of laminar boundary layers in tunnels of low turbulence (reference 6) and in tests of the author with a tube flow at low tm'bulence. Ameiican measurements in flight on a laminar profile of 15 .9-percent thickness seem to confirm that the atmospheric turbulence affects the transition only slightly, even for larger Re (reference 15): For Be = ~~- = 19 x 1.0^ and a Mach number M = 0.52 the measured value was c^..^ = 0.0030, which from the viewpoint of calculation would correspond to a mean position of the transition point (mean of upper and lower side) of about .68t from the front in the region of the point of lami.nar separation. From boundary- layer calculaticns, shortly before the transition give a Reynolds number Reg = ^ = 260O, referred to the 11^ MCA TM No. 1181 momentum loss thickness B and the velocity U at the edge of the toimdary layer, that is, essentially more than was observed in conventional wind tunnels, 6 = momentum loss thickness = / ti i"*" " TT/ '^^ 6* = displacement thickness ^- ( 1 - ^] dy with S total TDOimdary- layer thickneea u velocity in the boundary layer at the (distance from the wall y Uq flight velocity Tests of the author with a laminar- tube flovr in the 'starting region showed that considerably hirher Ee can be reached for a free stream free of turbulence. Teigts \rx th a laminar-tube flow in the st artin": reP:ion . - The purpose of these tests was to obtain hi-h laminar Reynolds- numbers by means of a laminar- tube flow in the starting region. Te st arran gement . - A conical Inlet fimnel of .9 meter lenp;th (maximum diameter at the entrance .18 m) was fixed to one end of a cylindrical anticorrosion tube of 6 meter len^'th snd 0.025 "meter inner diameter. The transition to the tube was smooth. At the entrance of the inlet fimnel was a rectifier consisting: of circular tubules of 3 millimeters fp, about .1-m.illlmeter waJ.l thickne-ss and 0.2 meter len'th in stacks. A Laval nozzle was attached to the other end of the tube xvhich was connected with the evacuated supersonic tunnel of the Institute (reference 6la) . The air was sucked from the space . The air motion at the entrance of the inJ.et funnel was kept as small as possible. ' ^ Measurements .- Th© static pressure alon-^ the tu,be xra.s measured with 0.8 millimeter cp connecting static •- pressure holes inth the atmosphere as reference level. Further, the state of the boundary layer along the tube was tested with the stethoscope (reference 6lc) which was attached to the static-pressure holes. Constant air velocity was obtained thrc-ough tne Lnval n'jzzle afc the re;'ir end of NACA M No. 1181 15 the tube and distiirlDajices from upstream affecting the "boundary layer of the tute were avoided. With this test arrangement the tulDe flow could "be kept laminar up to considei'ahle Eesmold.s numbers, it Is true, accelerated flovr existed. The ma>:im.um. stagnation pressure at the end of the tube, in Its center, with laminar boundary layer' up to the end of the tube, araounted to 180 kilogratriS per meter^, corresponding to a velocity of 56.5 meters per second in the center of the tube. The' numerical evaluation, according to L. Schiller (reference 83), resulted in a total boundary- layer thiclmess 5 = 6 .2 jiiilliiaeters at the tube end and the following Beynolds numbers: Eef)3_ = 2UOO Beg * 6h'50 and W, = J?lEe=,') = 13.° xlO^ 'l=3(j'^s/)^" = 13.c with Re. = m, en = r -V^ (1 - lA £ d(E •■ r) U velocity at the edge of the boundary layer u velocity in boundary layer r variable radius E tube radius (0.012'5 ffi) So far, sphere or hot-wire measurements were performed frequently. for determination of the turbulence. The sphere test, in particular, becomes imrellable when the external turbulence is very weak. For many purposes,: for instance, the application of wind-tunnel tests on laminar profiles to flight conditions, the Eeg-values, which can be obtained with a laminar boundary layer and a flat pressure dlstribu.tlon, are the main object of interest, The manner in which these values are reached is often of little Importance. l6 NAG A TM No . 11 8l CHAPTER 3 LAM31IAB PPOFILES WITH THE TBAWSITION TAKING PLACE FAE TOWARD THE REAR (V/ITHOUT BOUNDARY-LAYER SUCTION) 1. General Considerations Since the transition occitrs mostly after a slight pressure increase, protatly those -profile forms will "be favorahle for keeping the "boiindary- layer laminar for a longer time in "which the pressure distrihution is flat and the press'-jire increase lies far toward the rear. The flat pressure distrilDution results in smaller superstream velocities an,d thvis higher Mach niauhers without compression shocks) of course, separations in the region of the pressure rise must he avoided. Profiles with such pressure disti'ihutions have the maximum thickness at (O.ii to 0.5)t from the front. 2. Preliminary Tests on Lam?.nar Profiles for Smooth i^ntrance A few slightly camhered laminar profiles of various thicknesses were designed according to these considerations (fig. 9) • The profile drag was detennined for smooth entrance for various Uot Re = —- — "bv means of the momentum method. (See, for instance, reference 6lc) (fig. 10).) The laminar profiles investigated here are, for larger Re, superior with respect to drag to profiles of equal thickness used so far. (Compare with the NACA profile 23012.) With increasing Re, c^ decreases more rapidly than for conventional profiles. The drag increase for larger Re (caused hy the faster forward travel of the transition point due to the external turhiilence) starts at higher Reynolds numbers than it did for profiles used so far. 2 Smooth entrance: No flow around the profile mean line at the nose of the wing. NACA TM No. II8I 17 For smaller Ps the laminar profiles "become more uxifavorable with respect to- drag since the "boimdexy layer remains laminar for too long, therefore undergoes laminar separation in the rear part of the profile and does not readhere a';5ain in a purely turbulent manner. (Ohservations hy stethoscope.) The pressure drag is there hy strongly increased . By artificially creating a tui^hulent houjndary layer in the region of the point of laminar separation it is possible, in many cases, to prevent a more extensive laminar separation and to obtain a turb'olent readhering of the boimdary layer connected with a corresponding drag decrease. Thus, the drag of the thin laminar profile number 7 for smaller Ee coitld be essentially reduced by blowing-off of air from fine blowing holes which rendered the boimdary layer in the region of , the point of laminar separation tiurbulent. The blowing holes of 0.8-mi.llimeter cp and S-millimeter length wero placed vertically to the wing surface, thay were on the upper side 133 millimeters, on the lower side ^1 millimeters ahead of the trailing edge. The wing chord, was t = O.60 meter. The spacing of the holes was 2.6 millimeters. The total energy of the air at the entrance of the blowing holes was practically equal -to the undisturbed total head in the tiinnel. Turbulent wed.ges originated behind the blowing holes ( obsej^vations by stethoscope and with soot coating) which rapidly fused, thus causing the boundary layer to become turbulent over the entire span. The mean profile drag c„ over the series of spaced holes °° U t was measured by the momentum method at various Ee = -2—, The V following drags resulted: ■ Be ir 1 .65- X 10^, 1 .13 X 10^, .76 X 10^^ .52 X 10'^ c„ = 0.0033,0.00365,0.00^+25^0.0053 "CO Cwoo ^s-s reduced mainly in the region Pe = (0,6 to 1*7) x 10 A further slight drag reduction for smaller Pe (0.3 x 10" to 0.6 X 106) vas obtained by placing the 0.8 millimeter 1/ blowing holes farther to the front of the wing (on the upper surface 155 millimeters, on the lower surface 110 millimeters ahead of the ; trailing edge) for equal spacing of the holes. Test results: l8 ^ WACA TN Mo. 1181 ■Re = 0.33 X 10^, 0.50 X 10^, 0.68 X 10-^, 1.10 X 10^ 0^ = 0.0063,0.0051,0.00^5,0.00395 ' For larger "Re, c is larger than for the case of the "blowing holes lying farther tovard the rear. The dashed c„ -curve of figure 10 of profile number 7 gives the optimum c,, -values for the most favorahle position of the "00 "blowing holes in the direction of the chord. Further tests showed that the spacing of the holes, the hole- diameter, and the total head at the entrance of the blowing holes may "be widely varied in order to make the "boundary layer for smaller Ee artificially turhulent . For smaller Ee, "boimdary- layer measurements at the trailing edge of the wing, with and without "blowing holes, resulted in considera"bly thinner and fuller "boundal-y layers (larger 6 /© values) when air was "blown into the "boundary layer. Similar tests showed that a laminar "boundary layer can "be made tur'bulent in a desired place "by other measures, too (steps in the surface, considera"ble roughnesses, etc.), compare, for instance, the tests with the profile num"be:'' 32 of 6-percent thicloiess with distur"bances. (See the appendix.) An increase of the ajigle of attack "beyond the angle of smooth inflow has the same effect in o"btaining for smaller Ee a tur"bulent readhering on the upper side and, hence, a smalle-r profile drag. (See profile-drag polars of the propeller profile num'ber 11 for smaller Re (fig. 11) .) 3. Laminar Profiles for Propellers On the "basis of the preliminary tests descri'bed above, propeller profiles with highest posBi"ble lift-drag i-atios were developed at moderate Cg. and with small superstream velocities. A few test results on a propeller profile of 9-percent thickness (num'ber 11) are shown as an example. (See fig. 11.) The corresponding profile coordinates may be seen^ from the table of coordinates. WACA TM Ko. 1.181 19 The investigated wing war?, a rectangular ^^ring of "b = 1 ,"30 meters span, t = 0.292 meter oliord and F = 0.37^ meter^ area of projection (= area of reference) . The wing ends, seen from the fi'ont, were rounded seraicirciilarly. (See, for instance, reference 6lc h'^/F = 5'98«) Measurements .- (a) Determination of: .^ c =^- c . ^^^A Q S -.-—.- Q . =: —- -— - C ^ q"^' '''%^' ^'V^"qoFt for various angles of attack "by means of three -component measurements (t) Momentum-measurements (total p-ressure and static pressure) O.IU6 meter "behind the wing in a ving section 0.22 meter laterally from the wing plans of symmetry outside of the suspension fittings U_t for various Ee = Hr ^^^ c^ (c) Transition measurements with the stethoscope 0.22 meter laterally'- from the wing plane of symmetrj' for various Ee .'md ca (start of transition and heginnlng of the fuJ.ly developed tur"bu].ent boundary layer) The chord of the camher line was chosen as line of reference . for a. The point of reference for c^j. /> {Cj,,, /,> 0,a- increasing} lies at a distance of t/U from the front on this line. The jet corrections for the dovmvrash and the induced drag for the closed tunnel were calculated according to de Haller (reference Qk) , The momentum measurements were evaluated in the customary manner. The local lift coefficient Cg_ at the moment^jm measuring station was put egiial to l.lOCg,' A few test results can he seen from figure 11: variation of Cg_ with c^;. at various Re (momentum measvu-ements), and the heginning of the developed turh^olent boundary layer on upper and surfaces for various Cg, and Ee;, Cp,(a) . ,^ ^ > for Ee = .76 x 10*^ cm,/,,(")j 20 , MCA TM No . 11 Bl In an optimum Cg -range, decreasing ■vd.th increaslftg Ee, the transition on "both i-ring svirfacea occixrs far toward the rear vhlch results in low profile drags. When this x-ango is exceeded the drag increases and the transition point on upper and. lower sides travels rapidly forward, the reason is the appearance of a suction peak at the wing nose due to the angle of attack. For larger Ca a, slight local turhulent separation occurs on the upper side (tufts and stethoscope observations) . c^, decreases "opt with increasing Ee somewhat more slowly than the laminar friction of the flat plate. For larger Be at moderate Cg^-values, more favoratle profile drag-lift ratios result. For smaller Re and smooth inflow c^^^ deteriorates since the "boundaTy layer of the upper wing surface undergoes lami.nar separation and does not readhere with the properitles of a turljijlont hoimdary layer (observation hy stethoscope) . Only for larger c^ the laminar "bovindary layer is disturbed so sti-ongly hy the incipient suction peak at the wing nose that the transition occurs in time to bring about a turbulent readhering of the boundary layer for smaller Ee (observation by stethoscope), c^ then decreases with CO increasing c^, and c„ lies at considorably larger Ca than "opt would correspond to the smooth inflow. A similar reduction of c^ t» with increasing Cg_ had resulted also in earlier measurements on ordinary profiles for smaller Re (Gottlnger Lieferungen I to IV (reference £o), F. Schjaitz (reference 8l), MCA measurements (reference 82) etc.) •' The lift and pitching-moment dlstribiition ^tcu. /u shows standard behavior in the optimum Ca-region. For lai'ger angles of attack, discontinuities appear in 0^(0.) the variations of Cg. with a and Cj_ ,, (a), due to the change of the effective profile camber by the thickening of the boundary layer on the upper wing surface which is caused by the forward shifting of the transition point after exceeding the optimum Ca,-region. The use of laminar profiles for propellers reduces their friction losses. Due to the smaller euperstream velocities, com- pression shocks start at higher Mach nismbers than for conventional profiles. The use of laminar profiler for propellers will probably rather lead to vrlder blades of smaJ.ler thickness ratio with relatively low ca~values under standard flirrht conditions. Hence, there results again higher admissible Mach numbers and a larger starting thrust . , NAPA m No . 1181 21 h. Laminar Profiles for Wings A "baelc requirement for i-pod win2 x 10^') the drag la increased comin "by the influence of the tunnel turhiilence vrhich is caused hy the more rapid forward moving of the transition point d-ae to an external turbulence ffig. 3) . Verifying calculations of the profile drag for Be = 2 X 10° on laminar profiles of various thicknesses for the positions of the transition point, which had heen experimentally determined, gave the following result: The drag increase vrlth the profile thickness is primarily due to earlier transition for a larger profile thickness, only secondarily to higher form drag and increased skin friction "becauBe of the higher superstream velocities for thicker profiles. In order to test sultahle landing aids and ailerons for laminar profiles, three -component measurements were perfoimed for a laminar profile of lU-percent thickness (fi,'^. 12) on a rectangv-lar wing of "b = 1.50 meters span and t = 0.2^0 meter chord. (The wing ends seen from the front were rounded off semicirculariy .) Figure 13 shows the landing aids investigated, in retracted condition. A Fowler flap C of a chord of 0.3^^-8 t which extended over the entire span was used as landing aid. It extends soraewhat heyond the main wing toward the rear and. hence makes possible the attach- ment of a trailing-edge aileron D of 0.125 t chord which aJ.so extends over the entire span. For strmdard fli;..;ht conditions, this aileron serves as twist with resiolting small flap control moments whereas for low- speed fli.g}i.t the extended Fowler flaps could assume the lateral control, perlaaps in combination with the trailing-edge aileron. In this manner the Fowler flap may be constructed so as to extend over the entire span.. A further Cq -increase for extended Fowler flaps coiold be obtained by additional use of the trailing-edge aileron D, by extending of slats B and A at the Fowler flap C and at the main profile. The retracted front slat A would cause, under standard flight conditions, an e.arly turbulence of the boundary layer on the upper wing surface, in order to avoid this, the slat A was built partly into the upper s'orface of the main wing and thus a smooth surface obtained. Momentimi measurements showed that the profile drag was not measurably increased by the installation of landing aids at I?e = 1.07 X 10° when the slot between Fowler flap and trailing-edge aileron was sealed. In the fiill-.scale model, probably the -Grooves between main wing and the two slats also ouglit to be sealed. MCA TM No. 1181 23 The receding corner on the upper wing Burfa.co "between main wing and trailinf<-edge aileron also does not meas-ura"bly increase the drag in high- speed flight (according to moment\im measiirementa) . COMPILATION OF THE HIGH-LIFT ME.ASnEET-ffiWTS (Pe ^- (0.70 to 0.75) X 10^): 3p = lOl'TLM FLAP DEFLFCTION, 3q = TRAn.ING-EDGE AILERON r)EM.£CTION State max Fowler flap C extended, hoth slats A and B retracted (1) (3f = 52^.. PQ = 0°, trailing-edge aileron slot open 2.82 Pp = 52°, pQ ■ = 0^, trailing-edge aileron slot closed 2.79 Pf = ^-8^ Pq = 31*^, trailin,q-edge aileron slot open 3.12 Pf = -80> Pq • = 30^, trailing-edge aileron slot closed 2.885 Fowler flaT) C and Fowler flap -slat B extended, slat A at the ma:?n viiiR 1- stracted Sj, = 69°, ^ Pp = = 0°, 15°, trailing-edge aileron slot closed 3.U2 Pf = 69"", Po, = = iS*^, trailing-edge aileron slot open 3.605 Fowler flap C and hoth slats A and B extended Pf = ^'9", Bq = 0°, "5°, trailing-edge aileron slot closed 3.93 Pf = ^9°, Pq = l^''^ trailing-edge aileron slot open ii.05 Fowler flap G and frontal slat A extended, slat B ret racted Pf = ^7^, Pq - C^, trailing-edge aileron slot closed 3. 1+0 Pf = ^7^ Pg = 0°, trailing-edge aileron slot open 3.^3 Pf = ^^"> Pq = 18°, trailing-edge aileron slot closed 3. '19 Pf = '^^°. Pq. = 27^, trailing-edge ai.leron slot open 3.68 c„ is referred to the wing chord for retracted landing flaps. 2k WACA TM Wo, ll8l The effect of the trailin^-edge aileron of 12.5-percent t chord was investigated separately for retracted landing aids ( three -coEiponent and momentiTm measurements for vaorious control surface deflections Pq) . c and Cjn /, (>0^ a- increasing) were measured for various a "by means of three- component measiurements, c^_^ "by momentum measurements 0.I9 meter "behind the v/ing at 0.11 meter ].ateral distance from the wing plane of symmetry. The camter line was chossn as l3.ne of reference for a, the point of reference for Cm ,, lies in t/k from the front on this line. The local lift coefficient at the momentum test point was put equal to l.lOcj^. The P.eynolds number in the three-component and momentum measure- mentc! was Pe = --^ = O.80 x 10-^ and l.C^ x 10", res-aectively . The test results can "be seen fr-om figures lU to Jo. Owing to deflection of the trailing- edge aileron extending over the entire span, a favorahle envelope polar with low profile drags results for stendo.rd flight conditions in a considerable Cg-range. (See fig. Ih ,) The transition-point position in the optimum Cg^-range is only sllf:htly shifted forward hy moderate deflections of this narrow control surface (observations hy stethoscope) . At the recedin.^ comer on the upper wing surface hetween main wing and control surface, a local separation on the upper control surface is avoided in the optimum Cg^-range up to Pq = 20° according to ohservations "by stethoscope and tufts, hence, a low profile drag for lar^^er positive control surface deflections is attained. For 3q = -5° and -10'^ the "boumdai-y layer at the nose of the control surface on the lower wing surface was made artificially turbulent hy providing a receding step (fig. 13) in order to avoid a more extensive laminar separation on the bottom of the control surface and to obtain a turbulent readherinc. Observatjons by stethoscope showed that the boundary layer of the lower \ring surface for Pq < -5^ underr^^ent laminar separation unless the boundary layer was artificially controlled, and would not readhere completely turbulently. Correspondingly, there resulted (according to momentum measurements) relatively large profile drags. By providing the receding stop F on the lower surface 23 millimeters ahead of the flap nose, the boundary MCA TM No. 1181 25 layer 'became turbulent at Re = 1 .07 x 10 to 5 millimeters "behind the la,tter (according to stethoscope observations) and the profile drag decreased (momenttim measurements fig. Ih) . The variation of Cg and Cj^ ,, versus a f 01- various control- surface deflections Pg can "be seen from figures I5 and 16 . 3y deflection of the trailing- edge aileron Cg^ undergoes a relatively considerable change which will prohably cause rolling mojnents sufficient for normal-flight conditions. For 3q = 0*^ the maximum lift without landing aids is c^, = I.06. The angle of attack at the stall is rather larger than for con- ventional profiles of equal thickness. The lift increase is normal for the optimum c^-range and decreases sharply for larger a, hence, one can attain rather sm^J-ler positive gust loads than for earlier conventional profiles of equal thickness and cambor. The zsi-o moment for 3q = 0° is Cjj^o = -0 .027 and may be kept arbitrarily small by small negative control sui'-face deflections. The pltchlng-moment dlstrlbu.tion for moderate Pq probably will be siofflciently uniform. 26 V MCA OM No. II8I CE4FTER h immPS BOUIMDAPY- LAYER SUCTION, GENERAT. REMARKS 1 . Aims for Fujrther Development The tests of chapter 3 showed that the profile dra^n; can "be considerahly lowered "by a suitahle profile shape. With increasing profile thickness the drag will increase relatively strongly, the main reason teing the earlier transition for gi'eater profile thickness, ConsideraToly lover drags wo'old "be possible "by main- taining the "boundai'y layer tip to the trailing edge completely laminar. For larger Reynolds m:im'ber3 rery low drags would then result even for thicker prox'iles. (See figs. 1 and 2.) Thus the following tests were undertaken which aimed at the development of thicker profiles where, for la;^ge Reynolds numhers and in flight, the boundary laj-er remains laminar u.p to the trailing edge for a sufficient Ca-range. In order to obtain high Mach numbers without compression shocks, slight maximum superstream velocities are desirable, that is, the pressure dis- tribution is supposed to be uniform far toward the rear. Bcundar;';-layer suction made it possible to maintain in the present tests the boi;mdary layer completely laminar up to the trailing edge . 2. Effect of Suction of Laminar Boundary Layer on the Flow Characteristics The suction of a laminar boundary layer has various effects: (a) Augmentation of the laminar pressure increase: According to chapter 2, 1, the transition occurs for a weak laminar pressure increase caused by l.amj.nar separation of the boundary layer. By elimination of the greatly retarded portion of the boundary layer in the neighborhood of the wall with rising pressure, by means of suction ( through separate slots or by area suction) the laminar separation and hence the transition could be avoided even for considerable pressiire increases. A favorable effect is created in many cases by the so-called sink effect: The location of siiction acting as sink produces in its neighbojr-hood an additional pressiire field with accelerated flow. Its superposition on the KACA TW Wo. 1181 27 external flow at the location of suction results In a steeper pressure increase from the flow conditions iimiediately ahead of the suction point to the stagnation point "behind the suction slot. Hence, the remaining precsrire incx-ease aJ.ong the vail is correspondingly reduced. (h) Attainment of higher Reynclds nimbers Be - -ii- with V laminsr "boundary layers: According to chapter 2, 2 (influence of an external turhulence on the transition) one o"btains for a given external tu:.-;"balence with a lainlnar "boundary layer, a maximum critical Reynolds nuiia"ber Eoq = ( 2k ) ^ (IJ = velocity ■^critical V^ / critical ^ at the ef'i.ge of the "boundary layer.) Since the increasing of 9 and Esg, respectively, along the chord can "be reduced "by "bo'pdary- la^yer suction, it should "be possiblo to o^btain hitiher Ee -• -~2—, for eoual admissihle maximum Reynclds numbers Reo . "critical (c) Ey "boundary- layer suction and reaccelera±ion of the suction air to free™ stream velocity, a part of the relatively la_rge kinetic wake energy of the laminar "boundai^/' layer can "be recovered and the power required for propulsion can thus "be reduced. Professor Ackeret (reference 65) was the first to point out the possi"blllty of reducing the power required for propulsion of airplanes "by utiliza- tion of the kinetic wake energy. (d) With the aid of "boundary- layer suction the "boundary layer could "be iaaintr:,ined completely 1-arainar for a larger ran^e of angle of attack in spite of the occurring greater pressure increases which would extend the c^-rantie with low drag. 3 • Statement of the Pro"blem A boundary layer on thicker profiles for larger Reynolds m.Tmhor kept completely laminar with the aid of "bo ijndary- layer "^ suction is equivale?it to the maintenance of laminar "boundary layer for high Re with simioltaneous strong pressui'e increase . In order to ©"btain lowest possi"ble drags the losses in the suction- slots miist "be reduced. The "boundar;'- layer continuing "behind the suction slots is not to "be additionally distur"bed "by the suction itself . Besides, the customary stipiilations for wings must "be- o"bserved , (See chapter 3 and k.) 28 NACA TM No. II8I A wing with laminar "boimdary-layer suction of equal strength and rigidity should not become much heavier than customary wings without suction. In carrying out the tests the problems connected with laminar houndajry- layer suction were at first investigated separately, step "by step, and then gradually combined. The test sequence was as follows: 1. Test with laminar boundary- laj'-er suction on a slightly cambered profile of 6.75-percent thickness with a single suction slot in 77 percent t from the leading edge on the upper surface to investigate the basic aptitude of boiindary- layer suction for maintaining a boundary- layer laminar (chapter k, k) , 2. Study of the laminar pressure increase •vri.th boundary- layer suction in separate slots for smaller to medium Reynolds numbei-s Be (chapter 5) • 3 . More detailed investigation of the flow in the suction slots for laminar boxmdary- layer suction (slot losses, sink effect, slot flow, etc.) (See chapters 5 and 6.) k. Test for obtaining higher Reynolds numbers ■vri.th laminar boundary layers with the aid of boundary-layer suction for intentionally small external pressiire increase and normal wind- tunnel tiurbulence (chapter 7, Tests on a Thin Symmetrical Profile with Suction) . 5 . Investigations of the laminar boundary- layer suction for larger pressure increase and higher Reynolds numbers on a slightly cambered profile of 10.5-percent thickness with con- ventional thickness distribution (without extended flat pressujre distribution ahead of the pressure rise) . (See chapter 8.) k. History of Development of the Laminar Boundary-Layer Suction (a) In 1928 the assumption was expressed for the first time, by B. M. Jones, that a boundary layer miglit pei-'haps be maintained laminar for a longer time with the aid of boundary-layer suction which would reduce the frictlonal drag. (b) L. Prandtl calculated the laminar boundary-layer development with suction for pressure increase, under the supposition ^ohlhausen " "-"-^ (reference 72, pp. 117 and II8) . MCA m Wo. 1181 29 (c) Laminar sirct^on tests on a plifjhtly cambered profile of 6.75-percent thicimess. The first test, made for the purpose of orientation^ on a sliioiitly camtered profile of 6.75-re2'cent thick- ness Trf.th a sinfsle suction slot in 77 percent t from the leading ed^e on the upper surface (autumn 19^0 and winter 19''0-Ul) showed that it is possible , hy ho-ondary- layer suction, to maintain the houndary layer completely laminar and to olstain low profile drags. The investigated profile (2) with the suction slot can he seen from figure 17- The wing \ra.s mounted between end disks in the wind tunnel of the Institute. Data ; Chord t = 0.14-51 meter Profile thickness d/t = .0675 in O.39U t from the leading edge Nose curvatiire radius R /t = 0.0035 ' Slot in 0.77 t fr-om the leadin:^ edge on the upper surface, minimum slot width g = I.3 millimeters and s = 0.9 millimetei} slot directed toward the rear at s.n angle of ^5^ to the surface . T0.3 suction slot was developed as a diffuser \rith an 8° opening angle in order to convert part of the kinetic eneray of the sucked air into pressure ard hence obtain smaller negative pressures in the suction chamber and smaller pressures and power req^uire- ments for the suction blower. The development of the suction slot as a diffuser for the puxpose of a partial conversion' of the ' velocit" energy of the sucked air into pressujre was f 01- the first tim.e successfully applied in turbulent suction tests by A. Gerber (reference 69) on a suggestion by Professor Ackeret. The slot inlet was desi-^ied on the basis of a thesis by H. Bleixl.er, invsLiti^Aatid 'cj Professor Acker.^t. The slot flow was ti-eated by H. Bleuler as a free jet with constant pressure along the jjet edge, under the assumption of frictionless flow. SYMBOLS Drag measiarements : t wing chord (0.'+51 m) 30 - NACA m Wo. 1181 I slot length (0.32k m) F area of referenco • (tZ) (0 .lk6 rrP) 3 minimimi slot width gQ -undlstiirhed total pressure outside of "boimdary layer or wake, measured with atmosphere as reference level p static preseui'e in center of side wall of wind tunnel at ■beginning of test section, measured with atmosphere as reference level qg free-stream dynamic pressure, kilograms per meter^ (g^ - p^) Uq free-stream velocity meters per second ( j/%0 ) Pg^ static pressure in center of suction chamber, measiured compared with p^, kilogj.-'ams per meter^ Ap„ suction "blowei- pressvire, kilograms per meter^ u-j^ mean velocity of sucked air perpendicular to wing in suction cham.'ber at location of static pressure measurement (Suction Quantity , ... ^ , . . \ ^ - ._ _=_ s2__ _ — _ — Q^i this location) ^^ Cross section of the su.ction ch??2nDer J u^ -exit velocity of sucked air rearward in free-stream direction, meters per second Q ■ suction quantity (m^/s) measured by calibrated venturi nozzle of 17.^ millimeters ^ at narrowest cross section and 2B.0 millimeters ^ ahead of nozzle ■if 6 displacement thickness ahead of suction slot Qg U5*Z where U = velocity at edge of ■boimdary layei' ahead of slot U^t\ Ee Eeynolds nvim'ber l -^~- ' Drags : W„ total profile drag decisive for propulsion W ' drag contribution of wake NACA TM Wo. 1181 31 V drag contrl.'bution of suction "blower Dlmenslonless coefficients: On suction- quantity coefficient Cp suction-Mover pres3ia:e coefficient ( — =J Pa (; ' UoV c„ coefficient of total t»roflle draf^ c ' coefficient of drag contribution of valce (determined by momentum measurements in vrake) I -^— j /w j^r coefficient of drar^; contribution of suction blower 8 Measurements: The static pressure p^^ was measured, for U_t various Ee = ~-^^ and suction quantities Qi in the center of y - a' the si.icticn chamber (%vith .5 millimeter Jhen u^ j- Uq, the sucked air far behind the -vrlng has another momentuin than far toward the front) the charge of momentum is (for u^ < Uq, at signifies drag, for u^^ > U^ thrust. The propulsive power requirement for overcoming the drag contrihution of the wake W«, ' and pQf,(UQ - U;^), will he, if a propeller in flight or installed in a tijnnel with the efficiency Tjr, is provided: ^^- hi,' + pQ^(Uo - u^) U ^P The entire power requirement for overcoming of the profile drag "becomes: Qa(i^A^ - Pa-^O k' + PQe.(Uo - ua)] U^ L = Lg + Lp = ^— ^ + J= = Depending on the exit velocity u. of the sucked air, L is distrihuted unequally "between L^ and L_,. The minimum total power requirement Iv,-ir. results for t: — = 0^ ti„ and n^ may, Lu.il (jy -e 'p in the general case, also "be functions of u/^. It is now assumed that T\„ and t) are independent of u^. Then there "becomes for ^ = 0: ^ = Is MCA TM Wo. 1181 33 Let furthermore an eqnal efficiency of propeller and suction "blower "be assroned: t)^, = t^ =: t). ^°^ ^n *^^^- ^A = ^o ^-^ •'^in 00 o that is, where Ap, = -U.^"^ - Po - -U.T = Suction-blower pressure for acceleration of the sucked air to Uq Under the assumptions given a.l)ove (equal efficiency of suction ■blower and propeller, acceleration of the sucked air to 11^ toward the rear) one may calculate for the drag evaluation precisely as if the suction "blower had a 100-percent efficiency. The total drag coefficient decisive for the propulsion "beconies: Vr.co Q„Ap, ^w., ~ TTv ■■ ~| + cv^' =.<='Q<'^P3 "*■ ^Vco' = ^Wg + Cv„' 00 s = .9 Trm and 3=1.3 mm Fig. 21 2 hot-wire photographs v^ith and withoixt suction (figs. 22 and 23) . 2 photographs with soot coating (laminar and turbulent) (figs, 2U and 25) . By "boundary- layer suction it was poSsitle to maintain, for Eeynolds numl-ers up to Re = -2- = 800,000 on upper and lower surface a completely laminar Tooundary layer (hot-wire photographs, figs. 22 and 23, and photographs, figs. 2k and 25 with soot coating, confirmation "by stethoscope ohservations) . Generally, only weak and slow laminar velocity fluctuations were ascertainable ■behind the suction slot. The laminar pressure increase on the upper surface from the pressure minimum to the trailing edge amounted to 35 percent of the pressure difference "between stagnation point and pressure minimum . The lowest total drag was, with s = 0.9-millimeter slot "i"* c-5^ = 0.0035 (power required for ■^^min width for Re = .9 x 10^ suction included) . For smaller Re, c„ increased somewhat more slowly than the laminar friction of the flat plate. For larger Re, c^^. increases again since, ovring to the Influence of the tunnel turhulence, the transitions on the upper side occur already ahead of the suction slot (as was shoT-m "by stethoscope and soot-coating otsei'vations) . Hence, the boundary layer remains MCA m No. 1181 35 tvLi-tulent 'behind the slot in spite of increased stiction. The drag is definitely larger without suction than with it. The suction quantities cq required for keeping the "boundary layer laminar were very small particularly for a slot vddth 8 = 0,9 millimeter* in general only a fraction of the displaceiuent thickness & had to he sucked off the laminar "boimdary layer ahead of the slot (I5 percent to 50 percent for Ee = 0.2 X 10^ to 0.9 X 10^). (See fig. 21 CQopt(Ee) for s = .9 ran and s = 1.3 mm.) The required minimiim suction quantity for a suction slot of the width s = 1,3 millimeters was larger than the one for s =0.9 millimeter (fis. 21). If the suction is too weak, a local laminar separation occurs at the suction point and the "boundary layer "behind the slot "becomes rapidly tur"bulent (according to ohservations "by stethoscope, soot coating, and hot wire) . Correspondingly, for very weak suction c^.^. increases again (fig. 19). For en optimum suction quantity cn results ■opt the lowest drag c„ , co , increases with increasing Eeynolds ^'■^in ■'opt numher (fig. 21). For cq > cq ^ the skin friction increases "behind the slot (thinner "boundary layer), hence, c^ increases with Cq. 00 In general, the corresponding negative suction pressuxes c- in the suction cham"ber were small (fig. 21) although, for "opt laminar suction, the conversion of the velocity energy of the Slicked air into pressure in the slot difftiser was not particularly good (compare plater tests). (d) In connection with these laminar suction tests with a single slot, M, Eas performed, on the suggestion of Professor Ackeret, in the Institute for Aerodynamics, Zurich, tests with laminar "boundary suction hy means of a sort of area suction consisting of 35 narrow slots arranged one after the other. VJith this area suction one o"btained laminar pressure increases of a"bout 53 percent to 55 percent of the pressiire difference "between stagnation point and pressure minimum for smaller Eeynolds numbers (references 66, 67, and 68) . (e) H. Schlichting calcul.ated the laminar "boundary-layer development on a flat pD.ate with area suction for constant suction intensir.y (reference 70) . Furthermore, Schlichting calculated recently the lejninar "boundary-layer development with- area suction on a Joukowsky profile (reference 71) • 36 ■ NACA TM No. 11 8l CHAPTER 5 BPTESTIGATION OF THE LMHIM PRESSURE IWCBEASE WITH BOUiro-ffiY-LAYER SUCTION FOE SMALIE? AND MEDIUM EEYWOLDS NUMBERS 1. Laminar Suction Tests with Three Suction Slots Arranged One After the Other The suction tests with the laminar profile of 6.75"Percent thickness for Pe = 0.8 x 10^, showed a laminar pressure increase of 35 percent with a single suction slot. With area suction a laminar pressure increase of 53 percent to 55 percent was attained. More laminar suction tests were performeci with three suction slots lying one after the other in the suction tunnel used "by M. Pas with the aim to o'btain larger laminar pressure increases with relatively few slots. Definitions for the suction tests with single slots in the suction tunnel (chapter 5, 1, chapter 5^ Sh, 2c, and 2d, chapter 6, 1 and 6, 2) . q . dynamic pressure at edf-e of "boundary layer qj3j maximum dynamic pressure at edge of houndary layer at narrowest section of tunnel 1- = 1 - ^2 cim % Ap static pressure at test plate or at walls of slot diffuser, rLeaf-;T,r3d wi th .5 ?aillii)ieter (j> Taoro holes with static I-^-es:i.ire at test plate ao narrowest p].ace of tmmcl as reference level p^ static pressure in suction chamber, measured with O.5 millimeter 9' '£'-■' i^o holes with static pressvire at test plate at narrcwfi.st place of tunnel as reference level slot length (O.Uo m) NACA TM No . 11 8l 37 s minimum slot width 6* displacement thiclaiess ahead of ^lot (S* was calci^lated every time from measvired pressure distribution for mean suction quantity according to Pohlhausen (reference ^3))* Qg = lib' I, with U = velocity at edge of "boundary layer ahead of suction slot h displacement of slot trailing odge with respect to slot inlet, h > for inward displacement Qg^ suction quantity measured with callhrated measuring nozzles .Vg_ velocity of sucked air at end of slot diffuser, determined' from difference of total g at slot exit (measured with 1.0 mm (/i total, head tube) and static pressure p;^ in suction chamlDer in neigh'borhood of test point for velocitj'' distribution. (The test arrangement can he seen from fig. 26.) The flat test plate was provided with thi'ee suction slots the shape of which can he seen from figure 27. The slots were perpendicitLar to the surface and were developed as diff users ■^■ri.th small opening angle ( slot shape a) By adjust- ment of the opposite vail Nr. V the Internal T'idth of the tunnel and the press'jre distribution at the test plate could he changed. The boundary layer of the opposite wall also was kept laminar by suction. The width of the test plate and the slot length were UOO mlllimstsrs . The pressure distribution along the test plate was determined for various siiction quantities Q and tunnel widths . The state of the boundary layer behind the slot was verified by hot vire and stethoscope. The test results can be seen from figures 28 and 29. At the arrow behind the third slot the boundary layer was still laminar. Considerably larf^er laminar pressvire Increases .. resulted with boimdary- layer. suction than without it (maximum - 63 percent with kO mm tunnel width) . The sink effect makes an. essential, contribution to the .laminar pressiare increase, particularly for stronger external pressiire increase . .The significance of the sink effect for turbulent boundary- layer- suction was .pointed out repeatedly (Ackeret, Prandtl, 0. Schrenk, Gerber (references 69, 72, 73, 7h, and 75)). 38 • NACA TM No . llQl . 2. Testa with Laminar Boundary -Layer Suction with a Single Suction Slot The piirposo of these tests was a more detailed study of the flow phenomena in the neighborhood of a suction slot for laminar "boundary-layer suction (sink effect, laminar pressure increase down to the transition; flow in the suction slot and pressure losses in the slot) . ■ (a) Tests with laminar "boundary- layer suction in the water tank .- (g) Tests on a sinfjle slot: A few laminar suction tests for the purpose of orientation were performed with various slot shapes. The suction slot was placed on a symmetrical profile of 10-percent thickness (at 0.^3 t from the leading edge) and t = 1.21 m chord at a distance of 0.71 m from the leading edge. The slot was developed as diffuser with small opening ang3.e. ■ The model ^^ras toved through the water with a velocity of 0.1 to 0.2 meter per second. The flow in the region of the suction slot was made visi"ble "by sprinkled-on aluminum poxNrder and photographed. (Compare the flow pictures figs. 30 to 3^-) In general, the laminar "boundary- layer suction operated faultlessly even for very different slot shapes and suction of variou.s strength. The laminar "boundary layer, continuing "behind the slot to which no suction was applied, was mostly undistur'bed by the suction. The flow in the suction slot separated on one side of the slot. With increasing suction quantity the slot must "be made wider in order to avoid high velocities at the slot exit and corre- spondingly large slot losses. For smaller suction quantities the slot width must "be reduced since otherwise a local laminar separation occurs at the slot inlet (fig. 31(g))* The tests with the suction wing of 6.75-percent thickness (chapter U, h) and later laminar suction tests showed that in such cases the "boundary layer "behind the slot "became rapidly tur"bu2ent (o"bservatlon "by stethoscope). Due to outward curvature of the profile surface ahead of the suction . slot (fig. 31) and a stronger local pressure increase ahead of the slot, a laminar separation may occur for weak suction; there"by the "boundary layer "behind the slot also "becomes rapidly tur'bulent. Forward-curved suction slots (figs. 30(e), 30(f), 31(a), 31(h), and 31(c)) are especially sensitive in this respect. NACA m Wo. 1181 39 In a few cases the slot trailing edge was shifted various defjrees toward the outside and the Inside, respectively. (See flGS. 30(c), 31(d), and 31(e).) A too great inward shifting may eventually also lead to a local laminar separation at the slot inlet (fig. 38) Qiid thus render the laminar suction ineffective. (See later tests chapter 5, 2 test F with slot (h) with h = I.3 mm Im^rard shifting.) (3) A test with several narrow suction slots placed one after another (a sort of area suction) shows how the laminar houndary layer oozes into the wing interior (fig. 32). (7) On a thin symmetrical profile, suction was. applied to the laminar TDOujidary layer at the trailing edge of the wing. The first suction tests wei'e performed without a partition wall in the suction slot and gave a negative resi.ilt: for starting conditions a stagnation point originated in the free stream behind the suction point which traveled at the slightest dlsturhance toward one or the other wing side. (See fig. 33('b) .) By means of a partition wall in the slot, the rear stagnation point was fixed on that wall. (See figs. 33(a) and 33(c).) The boundary laj'er "behind the slot was mostly very thin. By rotation of the partitioning metal sheet and. "by suction of different magnitude on upper and lower surface one may shift the rear stagnation point and thus (as remarked "by Professor Ackeret) change the circiolation around the wing. The laminar suction of the trailing edge is very sensitive to the shape of the wjng surface shortly ah,ead of the slot. For a slot inlet .which is too round the "boundary layer ahead of the slot undergoes a laminar separation; if the inlet Is too pointed there result large negative pressures at the slot, inlet, hlgli velocities in the suction slot, and large slot losses. (5) Another test with laminar "boiindary- layer suction was performed in the water tank with a slotted flap wing of chord t = 0.61 m (d/t - 0.158). The "boisndary layer could "be maintained completely laminar hy means of siiction on main wj.ng and flap for various flap deflections (fig. 3^). The Eeynolds number was Ret ^ 100,000 to 120,000. !+0 , NACA TM No . II8I ("b) Laminar suction tests vlth the slot (a) (see fig. 2? and for definit ions Tee "beginning of chapter ^) .- With the test apparatiis used for the laminar suction tests with three slots (chapter 3, l) , laminar suction tests with only the suction slot farthest to the front were performed (slot 8hape(a)). The test plate was plane . Suction was applied over the width of the ttinnel of UOO millimeters. The pressure distrltution on the test plate was measured, with the minimum slot width s, suction quantity Q , tunnel width and free- stream velocity "being varied. The trailing edge of the slot coTAld "be adjusted at different heights with respect to the slot Inlet (displacements h > for Inward shifted trailing edge of the slot) . The influence of the suction quantities Qa and Q„/5 , ,* respectively, (5 = displacement thlclcness ahead of the slot) of the slot width and of the shifting of the slot trailing edge on the sink effect were Investigated. Figuxes 35 and 36 show a few p^^essure distri"butlons on the test plate in the region of the suction slot. In the investigated cases, the "boundary layer remained laminar "behind the slot (according to stethoscope o"bservations) . The laminar pressure increase due to sink effect Increases with growing suction quantity Qg^ and Increasing inward shifting of the slot trailing edge and vice versa, whereas a change in the slot width produces practically no effect. With increasing slot width, stronger suction must "be applied in order to avoid a local laminar separation at the suction point and a rapidly "becoming tur"bulence of the "boundary layer "behind the slot (according to stethoscope o"bservations) . The measured laminar pressure Increase due to slnlc effect is considera"bly larger than it would "be under the assumption of frlctionless flow; "by the "boundary-layer suction the displace- ment thickness b* "becomes suddenly smaller "behind the suction slot, and, correspondingly, the effective surface (at the distance 6 from the wall) is shifted nearer toward the wall. With an effective surface of such wavy development a stronger local pressure increase would result as shown in respective calculations "by A. Betz (reference 77) and pressure-distrl"butlon measurements at transition due to external pressure increase, where the displacement thickness also decreases suddenly. (See figs. 3, ^, 5, etc'.) By superposition of a sink at the suction point, there originates a considera"bly larger pressure increase due to sink effect than for frlctionless flow. By inward or outward shifting * MCA m No. 1181 li-l of the trailing edge of the slot this effect may he still increaaed or decreased. In further measurements (c) the attempt was made to increase the laminar pressure increase, due to sinlc effect, still further by wavy development of the veil in the neighhorhood of the suction point, particularly for larger auction quantities Qq^/Qs*. It is true that the required minimum suction quantities, for which the "boundary layer hehind the suction slot still remains completely- laminar, •'.Till prohahly increase: the slowest 'bounda.ry layer parts to which no suction was applied can he retarded at the most to the velocity zero at the stagnation point "behind the slot. For larger " external pressure increase (for instance, due to stronger sink effect "because of waviness of the surface at the suction slot) and for smaller suction quan.tities sometimes a strong local pressure increase and a rapid transition of the 'boimdfi.ry layer occurs "behind the slot. (See later measurements: fig. 39, test 8a, fig. J+0, test IOq^q.) jLsi- In'^''esti^vation o f the suctio n slot ("h) wit h the t es t p late ("b) for la minar bound a ry- layer sr ;ction.- The form of the test plate ("bT and the suction s3.ot (b) can "be seen from figures 37 and 38. (See "beginning of chapter 5 for definitions.) The slot ("b) was perpendicular to the surface and was also designed as dif f user with small opening angle . The external pressure distri"bution could he varied "by adjustment of the opposite wall Y, the hoimdary laj-er of which was maintained laminar "by suction. To the test plate, suction was applied over the tunnel width of ii-00 millimetei-s . The pressure distri"bution at the test plate and the transition- point position were determined for various suction quantities Q and Qg^/Q g.)!.^ respectively, for various free-stream velocities and timnel widths . The transition-point position evidenced "by the "break in the pressure-distri"bution cur've which in turn was caused "by the sudden reduction in displacement thickness due to the transition, was also determined from observations by stethoscope. At the transition, considerable fluctuations in static pressure could be ascertained by means of a sensitive manometer. The results of the pressure distribution and transition measure- ments can be seen from, the figures 39 to ^l-^!-. k2 NACA m No.. 1181 The experiences described In the last section with regard to sink effect were confirmed: increase of the laminar pressiire Increase, due to sink effect, with grooving suction quantity Qg, and Qg^/Q5-;<-, respectively, and with increasing inward shifting of the trailing edge of the slot, and vice versa. An excessive inward shifting (h = I.3 urn) did not av.gment the sink effect any f ui^ther . Higher laminar pressure increases due to sink effect result for larger external press^ore increase (^-mm tunnel width) than for 80 -millimeter tunne]. w'.dth^ however, the minimum suction quantities Qa/Q&"- were increased. With increasing RejTiolde numher, the pressure increase due to sink effect decreases slightly and vice versa, for equal suction quantity Qa/Qs* (cojnpare figs. Uo and Ul) . q^ = 32.6 kg/m^ ^^S. 39, % - |i6,28 k^m2 The sink effect is Increased "by the waviness of the surface in the region of the suction slot. Of course, as was to he expected, larger minimum suction quantities Qa/*^'6* ^^^ required to maintain a laminar "boundary layer "behind the slot. The total laminar pressiu^e increase up to the transition point is, generally, considerably larger than without suction. It increases with gro'vring suction q^^antity as well as with rising external pressure increase (comparison of the tests with Uo-miu and 80 -mm tunnel width) . For equal Qg^/Qg^ the transition occurs earlier with growing Reynolds niim"ber, similar to the case without boundary -layer suction (compare fig. kO and kl) q_ = 16.3 kg/m2 and 32.6 kg/m^ also figure 39 ^m = J 8-15 kg/m2 [16. 3 kg/m" MCA TM Ko. 1181 k^ By inward shifting of the trailing edge of the slot (stronger sink effect), the laminar pressure increase before the transition is sliglitly augmented and vice versa, under the assumption of equal suction power. Tests- lU with h = ,9 to h = -0.3 see fig. '+2 Tests 17 with h = O.9 and h = -0.3 see figs hC , 14-3 Tests 18 with h = O.9 and h = -0.3 see figs.UO, k3 An excessive inward shifting of the trailing edge of the slot (h = 1.3) deteriorates the laminar pressure increase again (figs. k2 and i^U) . Increasing of the sink effect and the Laminar press^are Increase lay a slightly wavy formation of the surface in the region of the suction slot, sinilar to the form of the test plate (b), is usefiil probably only for larger s^iction quantities Qa/Q^^J it is less so for smaller ones. (d) Laminar suction t ests with slot (b) and test plate (d) (See fi'jc 37 ») .- By increasing the waviness in the region of the suction slot (b) (see form of the test plate (d)) the sink effect and the laminar pressure increase before the transition was augmented still further for stronger suction; see the pressure distribution at the test plate (fig. ^5)« Of course, still larger minlmijm siiction quantities than for slot (b) with test plate (b) are required in order to keep the boundary layer behind the slot completely laminar. Further laminar suction tests with the single slot (g) (fig. k6) gave similar results (fig. ^7) • The suction tests with the plate (d) showed that a boundary layer for a flow around a slightly protruding comer may be maintained laminar by means of the boundary-layer suction, if a suction slot is placed in the corner. kk MCA 1M Wo . 1181 Stannary Eegarding Laminar Pressure Increase with Boimdary Layer Suction for Small up to Medium Eejmolds Numters For small up to medium Re (N = I/3 Rg*^ ahead of the slot varied between O.U and 0.8 x 10") laminar 'boundary-layer suctioii makes high laminar presstire increases with relatively few suction slots possihle; generally, only a fraction of the respective displacement thickness b* ahead of the slots must "be sucked off. In most cases the sink effect makes a considerable contribution toward the laminar pressure increase. For larger suction quantities Q^/Qg*, an augmenting of the pressure increase due to sink effect by suitable shaping of the surface is usef^Jil; it is less so for small ones. KACA TM No. II8I 1^5 CHAPTER 6 niVESTIGATION OF THE SLOT 510W FOE LAMDTAR BOUNDARY- " LAYER SIJCTIOW WITH SINGLE SLOTS 1, Laminar Suction Tests with Straight Suction Slot The teat apparatus for the tests of chapter 6 was the same as for the tests of chapter 5« (a) Tests with slot ( a) (see fl'-;. 27 gnd f or de finitions see tiep;innln;q of chapter ^) .- The test plate was plane. Suction was applied over the tunnel width of i<-00 millimeters . Measurements: The static pressure in the suction tank was measured for various Ruction quantities Q^ and Qa/Qg*? rasp^ctlvely, (6* = displacement thickness ahead of the slot), slot widths s and stagnation pressures or ReynoMs numbers, respectively. Further- more, the trailing edge of the slot was made to shift to various extents outward or inward with respect to the slot inlet. 'The distrihution of the sta.tic pressure in the stiction chsm'ber with the varjT-ing suction quantity can he seen 'from figures U3 to 53 • TJith growing eviction quantity, the negative pressure in the suction tank Increase. For larger Re, the suction quantity Qa/Q-S* "being equal, they are smaller; the same holds true for wider suction slots . . If the trailing edge of the slot is shifted Inward, larger negative pressures result at the slot inlet and in the suction tank due to the stronger sink effect . Inward or outward shifting of the trailing edge of the slot causes, conditions otherwise "being equal, only unessential changes In the pressure difference "between suction ch.amher and the place directly ahead of the suction slot. In order to o"btain a uniform suction along the span, the slot . width and the' extent of the inward or outward shift of the trailing • edge of the vslot along the span must, as far as possi"ble, remain constant. If the trailing edge of the slot is somewhere shifted fiurther inward, less air is sucked there', sometimes this fact may cause a local laminar separation shortly ahead of the slot; also, the "boundary layer "behind the slot may "become, rapidly tur"buJ.ent at that location, as was shown in o"bservations "by stethoscope hS . > NACA m No. 1.181 (confirmed in the laminar suction tests of chapters 7 snd 8). From the point of transition a tur"bulent wedge spreads toward the rear in the usual maimer. If the slot is slightly narrower in some place, less 'boimdary-layer air is sucked there. The laminar boundary layer "behind the slot then thickens; sometimes an earlier turhulence" may occur, imless the preceding or the following slot is widened accordingly. (b) Tests with slots (b), test plate (h) (fin:s. 37 and 38 ) . - The static pressures in the suction tank and alonp; the slot diffuser were measiured, together with the velocity distribution at the slot exit for various suction quantities, slot widths, and stagnation pressures. Other conditions being equal, practically the same pressure differences between suction chamber and the place directly ahead of the slot resulted as for the slot (a) . By lengthening the slot diffuser from I6 milljineters to 2^ milli- meters, the negative pressure in the suction tanJc t/as slight reduced and the pressure increase in the slot diffuser slightly augmented (fig. ^k'f see also later tests with suction slot curve rearward, chapter 6, 3) , For a slot width of s = 0.8 mm and qj^ = 16.3 kg/m^, a weak uniform pressure increase occiurs in the slot diffuser which increases with growing suction quantity (fig. 'ih) . The velocity distribu.tions at the slot exit for slot width s = 0.83 mm, q^ - 8,15 'ksfsP-, 16.3 kg/m^, 32.6 Ygl^s^ , and various suction quantities can be seen from figures 55 "to 57. For weak suction the velocity distribution at the slot exit is laminar with a weak reverse flow on the front side of the slot. For stronger suction the slot flow separates on the rear side of the slot and the suction air flows, at a relatively'" high velocity, into the suction tank near the front side of the slot. Accordingly, the conversion of the kinetic energy of the suction air into pressure is not particularly favorable in the slot diffuser (see figiu^e: Distribution of the static pressure in the slot diffuser) . The minimum slot losses result for small suction quantities O^/Qq*; suction is applied only to the innermost slowest parts of the boundary layer. ■ ■ The conversion of the velocity energy of the suction air into pressure in the slot diffuser would Improve if the slot flow would 'This fact was, in cases of inaccurately adjusted suction slots, established by observation by stethoscope repeatedly. MCA TM IIo. 1181 J^T readhere txirTDnlently "before 'the end oT the slot end the velocity distribution at the Blot oxit voiili teccme unifurm- Further laminai- auction tests vith the slot (h) nhowed tha.t this aim was attained by increased slot •width, larger suction quantities, and s^tagnation pressurea, 'that is, for larger ^RejTiolds maahers, referred to the slot flow (tests K, L, s = Li-tmi slot width, q,-^ =32.5 Icg/m"^) . The velocity distribution at the slot exit vas for s = I.3 ram and Cjji = 32.5 kg/m^' relatively unifo.rra. (See fig. 53.) The transition- point position behind the slot shows that the "boundary layer ahead of and behind the slot vas laminar . The pressure distributions alon '; the slot diffuser (fig. 59) shew s,t the presumable transition p'^int of the slot flow a rapid press-ore increase and strong fluctuatlciis in t>ie st^.tic pressure, similarly to tlie conditional found at the trsnsiticn of a laminar boundary layer for increasing pressure. For s = 1.3"mm slot width and q.^ = 3P«5 kg/m^, the slot losses and negative pressures in the suction tanlc are sli;-Tht. (See fig. 60.) Summary Eef^^arding the Losses in the Straight Suction Slot for Laminar Boundary Layer Suction Design of the suction slots as diffusers will make it possible to convert part of the kinetic energ;^ of the suction air in them into pressure. For weak suction or smal.l Beynol-ds manbers, the slot flow separates and the pres^ur-e increase in the slot . diffuser is oorrespondln(;?3-y email. ' For atrongei- suction, wider slots and higher Btegnt.ti ••■n prer^svu'es, that is, for larger Reynolds numbern of the slct flew, it becomoe turbulent mid adheres, thereby causing a considerable riressufo incroaae in the slot diffuser- The slot Icbbcs tht;n boccme low. 2 . Investigation of the Slot Flow for Laminar Boimdary- Layer Suction with the Suction Slot' ( i) Cixrved Forward (SDefinitions,See Be.Pilnniiig of Chapter 5) V/ith the suction slot (i) curved forward (see fig. 3^), laminar suction teats were performed in the same manner as with slot (a) lf.8 NACA TM No. 11 8l and (Is). The static pressure in the suction tank and the velocity distrihution at the slot exit were determined. The velocity distributions at the slot exit for s = l.Jj:5-inm slot xrtdth and q_y^ = 32 .7 kp/m^ and the corresponding static pressures in the suction tank for varioiis suction quantities can "be seen from the figures 62 and 63. For weak suction, that is, smaller Re of the slot flow, the slot (i) "behaved like the straight slot (a) or (h) . For stronger suction, that is, lar;?:er Re of the slot flow, the flow continued in the investigated cases on the front side of ^,the slot flow under laminar separation; accordingly, the resulting •■ slot losses and negative pressures in the auction tank were larger than for the straight slot (a) or ("b) . The transition of the slot flow is prohahly retarded "by the stalDilizing effect of the outward curved front side of the slot. ■ 3» Investigation of the Slot Flow for Laminar Boundary-Layer Suction ^Tith the Rean^ard Curved Suction Slot (h) On the hasis of the laminar suction tests with straight and forward curved suction slots, one may assume that the slot flow for a rearward curved suction slot (h) (fig. 6h) "becomes sooner tuj"hulent than for the straight slot, due to the concave cujr^ature of the front side of the slot . A laminar boundary layer for concave or convex ciirvature becomes turbijilent sooner or later, respectively, than on a plane s^orface; measijrements by F. and M. Clauser (refer- ence 33) and M. Fauconnet at the Institute for Aerodynamics, ■E. T. H. Zurich (not yet published) demonstrated this fact. In order to examine the assumption above, laminar suction tests were performed with a single rearward curved suction slot (h) (fig. 6h) which, was located on the bottom of a slightly cambered profile of 10.5-percent thickness (chapter 8). The suction slot was placed at a distance of 0.73 meter from the wing nose. Provisions were made for auxiliary suctions on both sides of the test suction, which had a length of .18 meter. Measurements: The static pressure Pg. in the suction tank and p on the front side of the suction slot were measured for WACA TM Wo. 11 Si .. h9 varlovis stannation pressures and suction quantities for s = l.O-mm and s = 1.25 -mm slot width, with the wing angle of attack remaining constant. Pa_ and p were ascertained hj means of .5-raillimeter (ji pressure holes with the static pressure Pq as reference level ( see chapter 3, determination of H^) . The distrihution of the static pressure ahead of the slot and in the slot diffuser for various slot widths, stagnation pressures, and suction quantities Qg^/05* can he seen from figures 66 to 72. S* = "boundary layer displacement thickness alaead of the suction slot calcuJ.ated according to Pohlhai.isen from the measured pressu3."e distrj.tution (fig. 65). The static pressure increased sharply at the presumable transition, point in 'the strai;?ht rear part of the slot diffuser_; adjoinin*^, a further wealr pressurr increase took place. Lengthening of the slot diffuser proved generally favorable . The pressiure increase in the slot diffuser and hence the con- version of the kinetic energy of the suction air into pressure are for the slot (h) su.perior to those for the straiivht slot (a) or (h), particularly for smaller Re of the slot flow. Cor;;-ospondingly, the resulting negative pressures in the suction tank are smaller. (See figs. 73 and 7lj-.) 50 - NACA TM No. 11 8l CHAPTER 7 TESTS ABOUT KEEPING A BOllWDASY LAYER FOR HIGH REYNOLDS MMBERS LAMIWAR WTH TEE AID OF BOUNDARY-LAYER SUCTION 1. Pvirpose of the Tests The purpose cf the tests is study of the laminar toundary- layer development with suction for larger Reynolds numbers, normal wind-tunnel turhidence and - at first - slight external pressure increase on a symmetrical profile of 3.35-P^J^cent thickness for zero angle of attack (profile shape see fig. 75(a)). The laminar "boundai\Y layer was sitcked off tlirough ei-ght consecutive slots . Furthermore, the problem had to be investigated, whether one could attain, for similar external pressure distribution, equal maximum RejTiolds numbers for la:ninar flow Reg or Re§* referred to the momentum loss or displacement thickness •^fith or without boimdary- layer suction. 2. Test Apparatus The TTing, constructed of wood of t = 2.032 m chord, was erected vertically in the closed wind-timnel test section. The span was equal to the height of the test section (2.12 m) . For reasons of measuring technique, suction was applied to one wing surface only) the comparison for conditions without suction was gained from the measurements on the opposite side without suction. The suction slots I - VTII may be seen from the slot drawing l6. They are straight and have a rearward inclination of 60'-' . As before, they were designed as diffusers with small opening angle. In order to intensify the sink effect, the surface was made slightly wavy in the slot region, accordin;'^ to the tests of chapter 5 (fig* 7^) . In the first tests the wavinese was exaggerated; consequently, the boundary layer remained laminar only with very strong suction. Slot width and relative position of slot inlet and slot trailing edge were asjustod along the span as constant as possible. The laminar boundary- layer development with suction was investigated at the wing center, the location of the suction slots MCA TM Ko. 1181 51 with the pertinent suction chsmlDers (fig. 75(t>))' Auxiliary suctions laterallj'-. to the test suction made it posPihle to kee;n the ■boundary- layer in the entire test section l«Eiinnr. Suction was applied aep'^.ratelj'' throw
  • f -!5 ApJ + W..' i^ \Uo Fi (2) where APs = ^ U,2 - P .. 2 g 2 o ^a 2 Ut (3) The factor 2 in the first term stems from the fact that Q,^ was measured for- one wing side only, '■ Dimensioni-ess: • ■ ■ • W„ where (k) ... ,. 20., Cw = 2 -X- = dra^; contri"bution of the wa]ce iX> t (0^ for one wing side) (5) 56 \ NACA TM No. 11 8l With the suction- quantity coefficient =Qi = UqF and the suction 'blower- pressure coefficient C- = ~^ (6) ^Si ^o (7) there iDecomes ; VTTI CV^ = Z— ^Oi^'P, + ^Veo' = Cv^, + Cw.^' (8) i=l Si where VIII XT- 1=1 3,, = > Co .c-r, = drag contrihution cf the suction "blowers (9) In order to determine c^^^ the dra.g contrihutions c-^^ of CO ^ the suction "blowers and c^^ ' °^ ''^^® wake were ascertained. CO c,. : For the various tests, the va].ues c^ and c„ of ^g ' '''i Pgl the slots I to VIII were determined according to (6), (7), (3) and hence c-j^^ according to (9)' p/2uj^2 was in most cases negli'Dihly small compared to p/2Uq •• Pa* he In order to determine c,, = —^, G ^^ was ascertained as follows; The "boundary -layer profile iras measured at station G9 millimeters "behind the slot VIII at a distance of 1.790 meters from the front. MCA TM No. 1181 " 57 From G- on, the laminar "boundary-layer development ( moment im -loss TTfl thickness 9 and Ee^ = -^ was calculated -t/ith the measured ^ V ■ pressure distribution up to the expei Inentelljr deteirmined transition point according to Fallaier and Howarth (references if-5, ^6 and kd)). At the trensition point 6 was assumed constant. .From the transition to the trailing edge 6 was determi-ned "bj means of a method of differences according to Souire-Yoijng (reference ^-l-); a wall shearinf^ stress Tq equal to the one of the turbiaj-ent flat plate Td.thou.t pressure gradient for eaual 'Rbq = W- (U = velocity at the "boijndary- " S* layer edge) and with H = -r- = 1.^0 = constant was presupposed; 9 — = — 2_ -n_3(H + 2) (houndary-layer momentum equation) where H + 2 = 3.U: U' = — , s along suv-face, ds The wall shearing stress is "^o = -^ = meg) where t, = 2.557 X In (Ji.075Reg) according to Squire-Young ( reference h) . 58 NAG A TM No. 11 8l TABLE FOE t, (Reg) ACCORDHirG TO SQUIRE-YOIMG i+OO 18.91 600 19.9^ 800 20.68 ]000 21.26 1500 22.29 2000 23.02 3000 2h .06 UOOO 2U.80 5000 25.36 .7000 26.23 ■ 10000 27 .1^ 15000 28.18 Reg 20000 28.91 30000 29.99 Uoooo 30.70 50000 31.27 2 X 105 3? .05 i X 10." 31^.83 10^ 38.9 i^ The variation of 9 in the vake from the trailing edge to very far toward the rear was determined also according to Squire -Young (reference k) , with the assi:mption that in the %ralce In §)-.f (see also reference 6lc). The momentum loss thickness 9r„ far toward the rear 'becomes; %+5 with the index h referring to the trailing edge. With H^^ = l.*;, 000 "becomes 9o3 — 9 W hence follow c „ ' and c w«> w« WACA TM No. 1181 59 5 . Test Results The test results can be seen from the figures 77 to 90 and the test talales which contain the fcll.owin-:' data, (see at the end of the report) . Test-Nos. Cq and Gp , for the eight suction slots, the momentimi-loss thickness 9 and the static pressure at tlie "boundary- layer test point G. The pressure distributions along the chord, the static pressures in the suction chamhers and the transitlon~po5.nt positions (arrows) for various Ee and suction quantities are plotted in fiisnires 77 to 80 . The- pressure distributions are flat and show a slirht pressure increase only in the rear part of the profile. The laminar pressure increase before the transition amounts to 17 to 21.5 percent of the pressiure difference between stagnation point and pressure minimimi. At the suction points appears the typical pressure increase due to sink effect which increases ^^rith growing suction quantity. Generally, the boundary layer is accelerated between the slots. Only behind slot Till occurs a stronger , Itmiinar pressuore increase which finally leads to the transition in general shortly ahead of the trailing edge. In most cases the pressure distribution cuj^ves show the typical break during tran,sition. . ■ The negative pressures in the suction cheanbers increase with growing siiction quantity. .They are smaller for larger Ee, also for wider suction slots. , , . In the cases of larger Ee or of smaller sixction quantities the transition point travels. forward. The suction quantities Cq. required to keep the boundary layer laminar up to a place shortly ahead of the trailing edge are generally small. With increasing suction quantity more '.suction has to be applied, see optimum curve CQ^ (Re) for the minimum total drag. (See fig. 81.) For suction quantities smaller than cqj. one may ascertain * '"opt by stethoscope, isolated tirrbulent bursts in the rear part of the 60 \ KACA TM Ko. 11 8l profile, which, with decreasing suction quantity rapidly iDecome more frequent and start f ajr'ther toward, the front . The transition starts earlier and takes place in a mere or leps wide trannition region which is no longer sharply defined. In these cases the "boimdary layer "becomes tui-lnxLent tj the effect of the wind-tuiinel turbulence. The critical Reynolds numbers Pe^^ = -— durln,:^ transition, where the houxidary layer under the effect of the external turbulence barely remained l.giiiinar, were for Re = 2 to U X 10^, Refl = ^30 to 880 Icr ■ with the narrower suction slots as well as with the wider ones. For larger Be resulted somewhat lower Eea . cr The critical Eeg,-values are sliohtly larger on the suction side than on the opposite wall to which no suction had been applied ajid are practically of the same magnitude as for the laminar profile lU-percent thickness in figu.re 12. It may be concluded that a laminar boundra-y la;j'-er with suction reaches the transition point, due to an exterrnal turbul.ence, for equal Peg-values, as without suction for identical flat exteraal pressure distribution if the slots are correctly adjusted. Smaller Reo restJ-ted only for very weak svictlon. The "^cr suction slots probably were too wide for very small suction quantities (as was sho^m by a verifying calculation of the laminar boundary- layer development with suction); hence, a local laminar separation occurs at the slot inlet thus causing the boundary layer continuing behind the slots to be distixrbed (observation by stethoscope). The boundary- layer profiles at the station G 9 millimeters behind the slot VTII for various . sviction qiirmtitios and dynaraic pressures can be seen from figures 32 to 87. For weak suction, the boundary-layer profiles are similar as on a flat plate without pressure .firadient (Blasius (reference k2)) ■and become fuller with increasing suction quantity. (See also measurements by M. Ras (references 66 to 68) with laminar area suction and calculations by H. Schlichting (reference 70 ) about laminar area suction on a flat plate.) •. ■ ■ . : MCA TM No- 1181 ■ 61 In figure 88 the optimvm total divag c^^ with suction (curve b) Uot is plotted versus "Re = -^^— and oomt)ared vith the opposite side , V (curve a) to which no suction had "been applied. For larger Re the drag is considerably reduced by the laminar boundary- layer suction. The increase of the drag due to tunnel turbulence starts with sixction for considerab].y larger 'Se, Without suction cvk, decreases with Be similarly to the l-Miinar plate friction to Re = 10" and increases again for larger P.e, owing to the forward travel of the transition due to the wind- tunnel turbulence (fig. 89) . Up to Ke = h- X 10° the drag vrith boundary- layer suction was only slightly larger than the laxainar plate friction: the Reyiiolds numbers Reg were relativelj'" low. For "Re = ^- X 10^ resu],ted Cwoo = 0.00107, For laxgev Re (>ij- x 10°) c^.^ increased again due to the effect of the tunnel turbulence: The "suction in the suction slots must be made stronger and stronger, in order to avoid - at larger Re - turbulent discontiniaities which increase the' skin friction and start at Reg ^. Hence, larger slot losses and very thin laminar boundary layers result directly behind the suction slots, causing an incx-ease of the surface friction. Thereby the drag c^j , for larger Re, again increases, although it was by means of suction possible to maintain the boimdary layer laminar up to Re = 5, if- X 10°. For larger Re the lowest drags resulted precisely with the start of a few isolated turbulent bursts which did not yet cause a large increase in skin friction. The plot of the ^farlation of c^j._ .and cv^,- versus the suction quantity c^,, for Re -- 3 .0 x 10^ can be seen from figure 90. H-o ■ Cxj. varies with Co- similar I:'" as for the first laminar •* CD W,-^ suction wing of 6.75-percent thickness (chapter k, h) : c„ is smallest for the optimum suction quantity cq+ , • For Wco ■. -^ - ^^opt smaller Cq -values turbulent discontinuities appear in the rear part of the profile, increasing c^__^^. For larger cq , the laminar ■boundary layer becomes thinner (see boundary- layer measurements figs. 82 to 87) causing an increase in skin friction and c^,_. Widening of the slots resulted in smaller negative pressui'eB In the suction tank and thus in somewhat lower Cy and Cy (test 38, lU*, 5^). 6? > NACA TM Wo. 1181 The drag could Tse decreased still farther Uy placing;; more suction slots behind slot VIII, thus 1 . Maintaining the boun.dacy Is.yer laminar up to the trailing edge 2. Recovering a conaiderahle part of the kinetic -wal?:e energj' of the "boundary "".ayer at the trailinri edge (presupposition'; acceleration of the suction air to Uq) The dashed cui've c (fig. 3^) shovs the drags which may he attained hy placing two more slots near the trailing edge. The curve c was calculated from the test values with the aid of a theory of the laminar "boundary -layer developm.ent ^d-th siiction. The fact that the drag siianificant for the propulsion can he lower than the laminar pla,te friction can he e::plained hy :the partial recovery of relatively large kinetic ^mke energy of the laminar houndary layer. By wake utilization t,h.e drag of the laminar flat plate could he decreased, on principle, hy 21,3. percent (fig. 88, curve d) . 6. Extension of Schlichting's Theory on the Laminar Boundary-Laj'^er Development with Area Suction in the Case of Acceleration of the Sucked Aii^ to the Undi stiorhed Free-Stream Velocity IT^ H. Schlichting c^alculated the laminar hoiuidary -layer development on a flat plate with area suction at constant suction velocity - '^q perpendicularly to the plate (reference 70) . Schlichting made the following formulation for the velocity distrlhuticn in the ho^indary laj'er; . J^ = 1 - e"^ + Kr,e-n. r, = -~I~- . ■ ^l(^) thus,' he ohtained the distrlhution of the skin friction c,, shown ■ ■ • , , V in. figure 9I for various Re and suction intensities - ~ (Uq = undisturhed f re e ■ stream velocity). *^ KACA TM No. 1181 63 The condition on the plate infinitely far toward tho i-ear is given with strict accuracy whereas for smaller Re, c^p is ov©restima.ted. Without suction the result is, according to Schlichting, , . c = ■ . : ? instead of —'-—— according to Blasius If the suction air is accelerated to U^ without loss, the drag c.^Tp which is significant for the propulsion hecomes con- siderahly lower then the skin fi-iction c-^^ , the reason is the recovery of the kinetic wake energj'- of the sucked air which otherwise moves forward with the plate ^ (See fig. 9-«) '^'^^ 3^ infinitely long plate c^^p hecomes c^ - -c,^^ . The drag c^p for acceleration of the suction air to U^ decreases with P.e considerahly more sti-ongly thsj) the surface friction c„ ( under the assumption of unifoiin suction intensity - v-p )• Hence, low drags c^p hecome possihle at larger Be for relatively thin laminar "boundary layers which are, with respect to stability, better controllable . Conversely, it is probably possible to obtain, for higlaer admissible laminar Ee-values (with weak external tuj^bulence) with the aid of the laminar boundary-layer suction very large P.e ■under lamin.ar conditions; the drag Ctjj would become only slightly larger than the laminar-plate friction. A further drag reduction vrould j^esv-lt if one wou3.d, moreoveir, accelerate the boundary layer at the end of the plate without loss to Uq, thus possibly recovering its wake energy. (See fig. 93 •) The utilization of the wake energy of the boimdary layer on a laminar suction profile could be attained with relatively small losses by gradual suction of the bouni^ary layer in the rear pai't of the profile through several sviction s.lots placed one behind the other for a static pressure increasing toward the rear, and by reacceleration of the sucked air to IIo. In each slot, suction need be applied only to a fraction of the respective boundary Ifjyer, so that small slot losses reaul.t. In this manner a thin la.mln£;r boundary layer would result at the trailing edge of the wingj its 6h NACA TM No. 11 8l wake energy- woiild now "be only sliglat; moreover, it is parti.all7 recovered dvtrlng the following acceleration in the wake. An arrangGDient of pj.-'essure propellers also would make it possiWe to recoA'"er a small part of the ■boundary- layer wake energj^ (as in the similar case of wake propellers of ships) . mCA TM Ko. 1181 65 CHAPTER 8 BTVI'STIG-ATTON OF A SLTGifTLY CAMBERED LAMBL'YR SUCTIOIJ PSOFILE OF 10.5-PSRCENT THICKlffiSS 1, Purpose of the Investigation The laminar pressure increase with ho^jndarj'-- layer sviction vas studied for higher 'Re, at normal wind-tunnel turhulence and for T-arious Cg^, on a slightly canx'bered profile of lO.'5-percent thickness and conventional thickness distrihution. Furthe?Taore, the drag reduction "by the laminar boundary- layer auction \7as investigated. 2. Profile, Test Arrangement The investigated profile with the suction slots can he seen from figure 9k, Profile thickness d/t = O.IO5 Curvature of the mean line f/t = 0,019 Nose curvatiwe radius Bq A = .0097 With the selected, thickness distribution, the pressure increase on the upper surface starts relatively far to the front . The wing which was made of wood vas erected vertica].ly "between floor and ceiling of the closed ^dlnd-tunnel test section. In the central wing section were the test suction slots of »l8 meter length with auxiliary suction slots on "both sides. Suction was applied to the "boundary layer on the upper surface through lU slots and on the lower sixrface through 10 slots. For most tests the foremost slots of the upper surface were sealed TcLth putty and no suction was applied to them (see test tahles) . A separate suction chamber, in which the static pressure vra.s measured, was connected to each suction slot. The suction quantity of each test suction slot was determined "by cali"brated measuring noz?,les attached to the lower end of the suction chamber. The suction chamhers were conlcally developed in suction direction and had a cross section with ample dimensions. The aiuciliary suctions were adjusted as similarly as possible to the test suction. ^e ' WACA TM No. 1181 Form and position of the suction slots can be seen from figure Sh. The narrow slots which are developed as diff users have a rearward inclination of 60'-^ . The forward or rearward curvature of the Blots served only for deflection of the suction air, not for an artificial production of turliulence of the slot flow. In order to intensify the laminar pressm^e increase hy sink effect, the surface in the slot region was made slightly vxavy on the hasis of earlier tests, for te.'^t 21 consideralDly less than for the test 2? to 55 (see profile sketch). The suction slots along the span were as far as possible identically adjusted (constant slot width and shifting of the trailing edge of the slot relative to the slot inlet al.cng the slot) . 3. Measurement with Laminar Boundary-Layer Suction (a) Pressure distribution along the chord, measured with 0.5-millimeter (/• pressure holes and vrith 1.0 iiiUlimeter ^ static-pressure tube; (b), (c) suction qufmtity and static pressure in the different test-suction chaiabers (with calibrated measuring nozzles and with 0.5 mm ^ bore holes) ^ (d) momentum measurements in the wake . The boimdary -layer condition In the suction regj on was verified by stethoscope. The boujidar^' -laj^er suction was regulated to the Icwect possiblu total drag. The tests were preformed for various Cg, (from pressure u,.t distribution) and Pie = ~~; in a few cases the suction quantity was varied. For the tests 2? to 55 the slot widths were enlarged as compared to test 21. For comparison, c^^ without suction in the part of the . "^Dii-n wings to which no suction had been applied was determined for various P.e by means of the momentum method. (8ee fig. 95.) WACA TM No. 1181 67 Symbols and Evaluation of the Suction Tests Wing chord t = I.O35 m Span of the test suction "b = O.18 m Eeference area F = "bt = O.186 m^ The investigated ving was relatively large, compared to the cross- sectional area of the test section (3 x 2.12 m, octagonal). The profile then operates "between side walls or in a wing cascade (mirrored wings) . In order to obtain from the test values the properties of the investigated wing as individual profile in the unlimited air stream, the undisturbed free- stream dsmamic pressure c^ and the free-stream velocity Uq, respectively, and the static pressures at the profile evaluated as follows: The tunnel side walls and the wings mirrored on them, respectively, cause the test irtng in the center of the tunnel to he subjected to a stream of air with a velocity which is by AU larger than the free-stream velocity U,^ far toward the front: Uq = "Ucq + AU. (The index G refers to the cascade.) AU is the incremental velocity due to the mirrored mngs at the location of the test wing. The undisturbed static pressvire Po at the location of the test wing is by p/2 (Uq^ - Uq^^) lower than the static pressure p far ahead of the wing. The incremental velocity AU at the location of the test wing tmder the influence of the mirrored wings was calculated by replacing each of them by a source and sink at 0.8-meter distance in free- stream direction and a vortex. The strength was chosen so that the maximum thickness of the mirrored wings equalled the one of the test wing. The mirrored vortices do not cause an incremental velocity in free- stream direction in the tunnel center at the test wing location, on the other hand, with growing Ca the effective profile camber is increased by Af (see Prandtl-Betz (reference 85): Af/t = 0.0023c^. There resulted ^ = O.OO6, thus U^ = 1 .006U . The following quantities were measured: the static pressures p^ and p^^ on both tunnel side walls at the location of the maximum prof ile"^ thickness for installed test wing, fujrthermore, the total head gg and the static pressxire p^^' at the location of the test wing (for "empty -tunnel" condition) (p^ , p^p', and g^ were were measured with the atmosphere as reference level) . In general, p^ and p^.j are different due to the circulation around the wing. Because of the displacement effect of the wake behind the wing p^ ' is slightly different from Pop* 68 NACA m No. 1181 The static pressures p at the profile surface and p^^ in the suction chamhers were determined with p^ as^ reference level. Evaluation of Pq, qg, U^ from p^ , P^.^g*" The incremental velocity AU^ at the tunnel side walls at the location of the maximum profile thickness under the influence of the test wing and the mirrored wings together was calc^olated^, all wings wei^e replaced "by a source and a sink at 0.8 meter distance each. From PvT + Pvo AU^^ AU, and p^j. = — ■^'-^ ^^ follows the undisturted static pressure Pq at the location of the test wing (squared term? of AU and AU^ neglected) : Pq - P.^ ^ 2(AIV - A U) with y- = .015 'lo = So - Po The further symtoJ-S end the drag evaluation are the same as in chapter h, h. Acceleration of the sucked air to U^ and eq^^al efficiency of propeller and suction blower were presupposed. The kinetic energy S^l^ of the sucked air in the suction chamber was included in the "blower pressure Ap^. Q,g_. suction quantity of slot {i), measured with calibrated measuriniv nozzles of same shape as in tests of chapter 7 Ap^_ suction blower pressui'e for slot (i) f q^o ~ Pg,i " ^'^hj Vg_. static pressure in the suction chamber (i), measured with *i .5 -millimeter ^ holes MCA TM No. 1181 69 p static pressure at the surface Ee = ^v~ Suet ion -quantity coefficient cq. = rr-^ of the slot (i). Total suction-quantity coefficient O" = x: for upper side, ^Q = Z_.-, "Qi i=l-l4 I'-IO' for the lower side. ° i=l JLO-' Drag contribution of the suction tlovrer: I'-IO' DraR contribution of the wake c„ ' = — -, determined by momentum ^'Vo t measurements. Total profile drag significant for the lift °Wco " °Wco ■*■ °Wn Cg. vas evaluated from the pressure -distribution measurements. The test results can be seen from the test tables and the figures 95 to IO3 . h. Test Results The minimum drar with laminar boundary -layer suction (power required for suction included) is plotted versus Ee for various c^ in figure 95 and is compared •'.■ri. th the measurement without suction. 70 WACA TM No. 11 8l In spite of the thiclmess distri"bution which is not particularly favorahle in'.th respect to 6.raff,, the resulting total drag for Re = 2,2 X 10*3 is c^^, = 0.0023 with suction, compared to °wco = 0. 00^535 withovit suction for Re = 1 A x 10 . With suction opt ^ C, decreases with Re up to 2 x 10"^ similarly to the laminar friction of the flat plate and is only slightly larger than the latter. For Re> 2.2 x 10°, c„ increases again due to the wind- tunnel turhulence ( atartin£^ of isolated turhulent 'bursts similarly as in the suction tests of chapter 7) • By widening of the suction slots (tests 27 to 55) the slot losses and c^ were reduced (comparison of the tests 27 and 21). Fimare 96 shows the optimum profile drag polars wj.th laminar "boundary- layer suction for various Ee. Since the "boundary layer was kept completely laminar up to the traillnpj edge on "both winr'? surfaces, c, remains low in a considerable Ca,-ran Cq . •) the laminar / "opt V^^^ > '^Qoptj skin friction and the total drag c^,^ increase. For weaker suction f cq < CQ j isolated turbulent bursts start in the boundary layer, in the region of the pi-essure increase, xjhich become rapidly more frequent -s/ith decreasing suction quantity and increase the skin friction and c„ . NACA TM No. 11 8l 71 The percent-drag contriTDution of the suction hlowers to the total drag is considei-able, particularly for larger P.e . Figui'e 98 shows a comparison of the wakes with and without suction. The drag contribution of the wake with suction is very- much smaller than the drag without suction. The pressure distrlhutions along the chord can he seen from figures 99 to IO3 . The test points ohtained hy pressure holes and the static pressures in the suction chambers are plotted. The pressure-distribution curves were supplemented by measurements with a 1.0 (f) static -pressure tube; the corresponding test points do not appear in the plot . For larger Ee considerable laminar pressure increases were obtained with the aid of boundary -layer suction, for instance, in test No. Ca Re Laminar pressure increase (percent) 27.1 hk 55.3 0.232 .587 2.16 X 10^ 2.22 1.1^5 U9 56 63.3 The sink effect makes an essential contribution to the laminar pressure increase. For a few cases the laminar boundary-layer development was determined a].ong the chord down to the trailing edge . The bovindary- layer development along the wall between the slots was calculated according to Pohlhausen (reference U3) . The boundary -layer momentum- loss thickness 9 directly behind the locations of suction was determined according to Bemovilli from the momentum-loss thickness of the boundary -layer part ahead of the suction point to which no suction had been applied (mixing within the boundary layer with pressure increase as a z'esult of sink effect neglected) . There- from resulted Q along the choi'd and Reg = -^, respectively (U = velocity at the edge of the boundary layer at the particular station) . Those critical Reynolds numbers Reg were designated by Reg , where the boijtndary layer Ju-st remained laminar on both CI surfaces d.own to the trailing edge. Influence of the external pressure distribution on For not too small Ca"values (cg^ ^ 0.27) similar Reg cr Reg : ''cr resulted 72 NACA TM Ko. 11 8l on the lower vlng siorface (flat pressure distribution) as for the symmetrical suction profile of 3.35-percent thiclmess of ch&pter 7 {Reg ^^ - 800 to 850) . On the other hand Eeg on the upper surface in the pressure-increase region was eRScntlally lower, particularly for larger Cg (Eeg = 550 (at start of pressure increase) to UOO to '+50 at the end of the pressure increase in the neiighhorhood =)• of the trailing edge). Thus, similarly to the case without suction, higher (or essentially lower) Ken than for pressure gradient •^cr zero resixLt for accelerated (or retarded) external flow for laminar boundary -layer suction. Infl usance of the sirJc effect on Rep„^.- The tests 21 and 27 ■vrith sinlr effect of different strength resuJ-ted in practically equal Reo -values, with Cn . remalninp; the same. Thus it seems that ^ ■ "opt primarily the total external pressure increase is decisive for the stability of a laiainar boundary layer with suction with Increasing pressure. Whether this total external preesuxe increase is to a larger or sraall.er extent created by sink effect or by the flow along the wall seems, within certain limits, of lesser Importance. If one calculates from the velocitj'' gradient u' of the external pressure distribution as it would result without sink effect a quantity X = 5^/vu' (which corresponds to the Pohlhausen method), the following values result in the region of increasing pressure on upper and lower side: X = -2 (start of the pressure increase) to -8 (at the end of the pressure increase). Therefore, similar negative X-values are obtained for laminar pressure increase with bonndai'y-layer suction as without suction, under the assump- tion of equal external tvirbulence and equal Reg . 5. Conclusions from the Tests of Chapters 7 and 8 for the Design of Laminar Suction Profiles with the Lowest Possible Drag for High Reynolds Numbers In order to obtain for laminar suction profiles highest possible Re@ over a large range of the wing chord, and thus a low surface friction and small drag for lai^ger P,e, one should use profile shapes with uniform pressure distribution and a pressure increase occurring far toward the rear, as they were developed for laminar profiles without suction (chapter 3) . This corresponds to the combination of the test of chapters 7 and 8. MCA TM No. 1181 73 Weak suction onlj'' would have to "be applied in the region of flat pressure dlstrihu-tion. Boundarj'-layer. thiclcneas and Ee^^^ would have to "be reduced "bj suction aJiead of the pressure increase. So much suction would have to he applied in the region of pressra'e u' increase that, for the present turhulence — - = 0.00^1, Bbq remains Esn ^ 500 and \ = ~u' does not hecome excessively- negative X^ ^ -6). (u' = velocity gradient of the external, pressure dlstrihution without sink effect) . 6 , Prospects for Application of Laminar Boiandary-Layer Suction in Flight for High Eeynolds Numbers The calculation for flight measurements on a laminar profile of 15 .9 -percent thickness (I5) resulted, ahead of the transition, in a Eeynolds numher Eeg = ™ = 260O in the region of the point of laminar separation (chapter 2, 2), that is, about three times more than for the present wind-tunnel tests. Hence, presumably, for laminar. suction profiles in flight, with a boundary layer kept completely laminar, about three times smaller drags for nine times U„t , higher Ee = --ii- are Tsossible than had been measured in the wind 1 V ; tunnel. For higher flight velocities the percent atmospheric turbulence — - decreases; thus one could then expect higher ^o laminar flow Ee and lower drags, at least as long as no com- pressibility disturbances appear. \ The drags of ftiselage and tail unit also could be considerably reduced by maintaining the boimdary layer laminar with the aid of suction. The fairings from wing to fuselage, etc., also could, I In principle, be kept laminar by boundary-layer suction. The induced drag which now gains renewed importance may be reduced by enlarging of the span and Increasing of the flight velocity, possibly by staggered flight arrangement (as used by migratory birds). The optimum drag/lift ratio wou3.d result for small Ca, that is, for high flight speed at not extreme altitudes. Large spans require wings with sufficiently thick profiles ar).d -Jk NACA TM Wo. 1181 adroit design of the wing structure. In order to obtain high Mach . numbei-B without compression shocks, the superstream velocities ought to remain as small as possible. For laminar suction profiles in flight exists the possibility to adapt the boimdary -layer thickness and Ee^, respectively, by means of boundary -layer suction to the respective state of tur-bulence of the atmosphere, i'or higher atmospheric turbulence .stronger suction would have to be applied farther toward the front in oi-dei" to keep Eeg sufficiently low and to obtain a lower sensitivity with respect to variations in angle of attack due to gusts, etc Conversely, weaker suction could be applied in case of the air being very calm, resulting in larger Eeg and correspondingly lowei- drags. Translated by Maiy L. Mahler National Advisory Committee for Aeronautics MCA TM No. 1181 75 APPEiroiX REDUCTION OF THE PROFUSE DRAG FOR SMALL Re BY ARTIFICIALLY PRODUCED TURBULENCE OF THE BOUNDARY LAYER IN THE REGION OF THE POINT OF LAMINAR SEPARATION It had. teen shoxm on the propeller profile number 11 of 9-percent thickness (fig. 11, chapter 3, 3) that the liouQdary layer of the upper wing sui'face rmdergoes, for small Re and smooth inflow, laminar separation and does not turhulently readhere (stethoscope) 5 hence, the profile drag is sometimes considerably increased. Only for larger Cg^ the "boundary layer of the upper wing surface is disturhed so much that the transition occurs in time to ohtain here a turbulent readhering of the boxandary layer for smaller Re . A report on tests on a medium-cambered profile of 6-percent thickness (fig. 10^) follows. The profile-drag polars on this profile were, for smaller Re, improved by artificially produced tiirbulence of the boundary layer on the upper wing sui'face in the region of the point of laminar separation with the aid of surface disttirbances (steps in the svirface, see fig. lO^i-: disturbances 1 and 2) . For various Re and c^ momentum measurements were performed on the smooth wing and T-dth the disturbances 1 and 2. (See profile- drag polars figs. lOU to 107.) For low Re the profile-drag polars are definitely improved by use of the disturbances, the boundary layer after the disturbance generally ttirbulently readhering and undergoing laminar separation only for very small Re (observation by stethoscope) . The disturbance then would have to extend farther to the front. The weaker or stronger disturbance 1 or 2, respectively, improves the drag polar mainly in the Re-region of 250,000 to 300,000 (or 200,000, respectively). For larger Re the boundary layer becomes unnecessarily ear.ly tiArbulent due to the disturbance (observations by stethoscope), thereby correspondingly Increasing the profile drag. The Rejniolds number Re^ = — referred to the distance I from the start of the disturbance to the start of transition resulted for the present case as Re^ = i)-8,000 76 MCA TM No. 1181 (l - distance from start of dlstnr'bance to start of transition; U = mean velocity at the "boundary- layer edge iDetween start of disturbance and start of transition) . The method of producing an artificial tiirbulence of a laminar ■botmdary layer in the region of the point of laminar separation is, in general, succesBfully appllcahle if otherwise a stronp:er laminar separation occiirs and the boundary layer does not turbulently rea'ihere . MCA TM No. 1181 77 EEFEKENCES 1. Jonesj B. M. : Skin Friction and the Drag of Streamline Bodies. E.M. 1199, 1928, 1929. . . 2. Jones, B. M. : FXight Experiments on the Bounda);y Layer. J. A. Sciences 1938, Jan. , vol. ^, no. 3; P- 8I. 3. Ser"by, J., Morgan, M. , and Cooper, E* = Flight Tests on the Profile Drag of 14 Percent and 25 Percent Thick Wings. E.M. 1626, 1937- k. Squire, H- B. , and Yo'iong, A- D. : The Calculation of the Profile Drag of Aerofoils. E.M. -I838, 193 8. 5. Pretsch, J-: Zux- theoretischen Berechnxmg des Profilwiderstandes. Jahrhuch 193^ "iei" Deutschen Luftfaiirtforschung, pp. I-60. 6. Lewis, G. W. : Some Modern Methods of Eesearch in the Problems of Flight, Low Turbulence Wind Tunnel. The Journal of the Eoyal Aeronautical Society 1939, p- 779- 7» Tani, I., and Mituisi, S. : Contributions to the Design of Aerofoils Suitable for High Speeds Eep. of the Aeronautical Eesearch Institute. Tokio, No. I98, Sept. 19^0. 8. Pfenninger, W. : liber die aerodynamische Durchbildung von Flugelstrebenanschlussen. Flug^/ehi' und-Teclmik, Sept. 19^2. 9. Jacobs, Eastman; and von Doenhoff , A. E. : Transition as it Occurs .".ssociafced with aixd Following Laminar Separation- 5th Intern. Congr. f or, appl. Mech. , Cambr. , Mass- 1938, P- 311- 10. Hall, A., and Hislop, G. : Experiments on the Transition of the Laminar Boundary Layer on a Flat Plate. R-M. 18^3, 1938- 11. Taylor, G.. I.: •, Some Recent Developments in the Study of Turbulence. Proc 5th Intern. Congr. for appl. Mech., Cambr., Mass- 1938- 12. Fage, A., and Preston, H. : Experiments on Transition from Laminar , to Turbulent Flow in the Boundary Layer. Proc Roy. Soc A, vol. 178, 19'a. 13. Schubauer, G. : Airflow in the Boundai'-y Layer of an Elliptic Cylinder. NACA Eep. No. 652, 1939- 78 WACA TM No. 1181 ik. Fafi-e, A.: The Airflow Around a Circular Cylinder in the Begion where the Boundary Layer Separates from the Surface. P.M. 1179, 1928 . Fage, A.: On Reynolds Efumhers of Transition. E.M. I765, 1937 • Fage, A,: Experiments on a Sphere at Critical Reynolds Numhers. E.M. I766, 1937. 15. Amerlkanische ?rofilwiderstandsmessun:'^;en im Flu^^e an einem 15 .9 percent dicken Laminarprof il lait einer "King Cohra" (nach Eeiseherichten) . 16. Lyon, H. M.: Flow in the Boundary Layer of Streamline Bodies. R.M. 1622, 193 '^. 17. 18. Taylor, G. I.: Statistical Theory of Turbulence, Parts I - 17, Proc . Boy, Soc . A, vol. I5I, no. 873, Sept. 1935, Part 7, Proc. Poy. Soc. A, vol . I56, no. 888, Au{t. I936. 19. Von Kannan, Th.: Tu.rhiilence and Skin Friction. Joixmal of the Aeron. Sciences Jan. 193^' 20. Von Karman, Th.; Turlnulenoe. Joixrnal of the Poyal Aeron. Soc, vol. hi, no. 32ii-, p. 1109, Dec. 1937. Von Karman, Th.: Some remarks on the Statistical Theory of Turhulence. Proc. of the 5th. Int. Congr, for Appl . Mech. Camhr., Mass. 193 8. 21. Dryden, H. L.: Airflow in, the Boijndary Layer near a Plate. N.A.C.A. Pep. 562, 1936. 22. Dryden, H. L.: Turrhulence and the Boundary Layer. Journal of the Aeron. Sciences Jan, 1939' 23. Dryden, H. L.; Turhulence, Companion of Peynolds numher. Journal of the Aeron. Sciences, April 193*1. 2U. Dryden, H. L.: Turbulence Investif.;ations at the National Bureau of Standards. Proc. of the 5th Intern. Conrr. for Appl. Mech. Camhr., Mass. I938. 25. Prandtl, L,: Beitra^nie zum Turhulenzsymposium. Proc. of the 5th Intern. Confer, for Appl. Mech. Camhr., Mass. I938. Prandtl, L.: ijber die' Entstehunei: der Tiu-hulenz . ZAMM 1931, p. U07. NACA TM No. llSl T9 26. Schlichting, Ht : Bereclmwig der Anfaciiimg kleiner Stor'unp'en l5ei der Plattenstrom-ung. Z.A.M.M. 1933, Bd. I3, Heft 3- 27. Schlichtirig, H. : Zur Entstehimg der Tiirbiilenz "bei der Plattenstromung . Nachr, Gos. Wiast Gbttingen, Math.-Phys. Klasse 1933, p. I81. 28a. TollmJ.en, W,: ITber die Entstehung der TurlDtilenz Nachr. Ges. Wiss. . Gottingen, Math,-Pliys. Elasse I929, p. 21. 28b . Tollraien, W . : Tiber die Korrelation der Geschwindigkeits- komponenten in periodisch schwankenden l-firlDelverteilungen. Z.A.M.M. 1935, p. 96. 29. Tollmlen, ¥.: Ein allgeneines Kriterium der Instatilltat larninarer Geschwlndlgkei 'GYerteilungen. Kachr. Ges. Wlss. Gottingen, Math.-Phye. Klasse 1935, Fachgruppe 1, p. 79* 30. Fage, A.: Transition in the Boundary Layer Caused "by Txirtulence . P.M. 1896, 1942.' 31. Peters, H.: A Study in Ecundary Layers. 5th Intern. Congr. for Appl. Mech. Canibr., Mass. 1938, p. 393. 32. Stephens, A. V. and Hall, A.: Hot-Wlres in Flight. Proc . 5th Intern.. Congr. for Appl. Mech. CaiaTDr., Mass. 1938, p. 336. 33 • Clauser, M. and F.: The Effect of Curvature on the Transition from Laminar to Turbulent Boundary Layer. N.A.C.A. T.Er. 613, 1937. 3^. Gortler, H.: Instabilit'dt laminarer Grenzschichten an konkaven ¥&iden gegenuber gewissen 3- ^-linens ionalen Storungen. Z.A.M.M. 19^1-1, p. 250. riachr. Ges. Wiss.Gottingen, Math.- Phys. Klasse 19^0, p. 1. 35. Prandtl, L.: Elnflugs stabllisierender Krafte auf die Ttirbulenz. Vortrage aus dem Gebiet der AerodjTiamik land verwandter .Gebiete. Aachen I929, p. 1. ,36. Young, A. D.: Sui-face Finish and Performance. Aircraft Eng. Sept. 1939. ... 37. Hood, M. J.: Surface Roughness and Wing Drag. N.A.C.A. T.N. 695. Aircraft Eng. Sept. 1939. 80 NACA TM Wo. 11 8l 38, Tanl, I., Hama, E, and Mltuisi, S.: On the Pemissll»le Eoushness in the Lamjnar Boundary Layer. Eep. of the Aeron. Research Institute Tokio, No. I99, Oct. 19^0. 39. Theodorsen, T. and Garrick, I.: General Potential Theory of ArMtrai'y ^^ing Sections. K.A.C .A. Eep. U52, 1933. UO. Kochanovsliy, W.: Z\ir Berechnun^ der Bruckvertellung u"ber den TJinfang "beliehig geformter Flngelschnitte . Jahrb. 1937 der Deutschen Luftfahrtforschung, pp. l-:;8. D.7.L.- Jahrbuch 1937, p. 139. Ul. Kochanowsl?7, W.: Weitere Ergehnisse von Druckverteilungs- reclinwigen an "beliebigen Flugelsclinitten. Jahrtuch 193^ der Deutschen Luftfahrtforschung, pp. 1- 62. h2, Pinkerton, 5. M.: Calculated and Measured Pressure Dlstrihution over the Mid span Section of N.A.C.A. ij-lj-12 Airfoil. N.A.C.A. P,ep. 563, 1936. h3' Pohlhausen, K.: Zur naherungsveisen Inter-ration der Differentialgleichung der laninaren Grenzschicht . Z.A.M.M. 1921, p. 252. kk, Falbier, Y. M. and Skan, S. v;.; Some Approximate Solutions of the Boundary Layer Equations. R.M. ISl't-, 1930. U5. Falkner, 7. M.: A Further Investigation of Solutions of the Boundary Layer Equations. R.M. 188^, 1939 . U6. Falkner, Y, M.: Simplified Calc\ilation of the Laminar Boundary Layer. R.M. I895, igi+l. kj . Blasius, H.: Gren?,schlchten in FlUssigkeiten mlt klelner Peihung. Zeitschr. f . Math. u. Phys. Bd. 56, p. 1, I908. Diss. G5ttingen I907. ^8. Hovrarth, L.: On the Solution of the Laminar Boundary Layer Equations. Proc . Roy. Soc . A, Ko. 9I9, vol, l6k, I938. if 9. Prandtl, L.: Zur Berechnung der Grenzschichten. Z.A.M.M. 1938, p. 77. 50. Gortler, H.: Weiterentiidcklung eines Grenzschlchtprofils "bei gegehenem Druckverla^jf . Z .A .M .M . 1939 , p . 129 . NACA TM No. 11 SL 81 51. Howarth, L.: Steady Flow in the Boimdary Layer near the Surface of a Cylinder in a Stream. E.M. 1632, JvJ.j 193^. 52. Tomotika, S.: The Laminar Boimdary Layer on the S-urface of a Sphere in a Uniform Stream. E.M. 1678^ 1935. 53. Buri, A.: Sine Berechnvingsgrundlage fur die turhulente Grenzschicht hei beschleunigter vnd. verzogerter Gncid- stromung. Diss. Ziirioh 1931 • 5^. GruschwitZ;, E.: Die. turhiilente, Eei'bim.'-isschicht in eTsener Stromuno hei DruckalDfall vind Druckanstieg. Ing. Archiv, 1931, p. 321. 55' Kehl, A,: Untersuchijngen uher konvergente Vind. divergente turlivilente Eei "bungs schichten. Ing.. Archir, 19^3, P« 293* 56. Young, A. D.: The Calculation of the., Total and Skin Friction Drags of Bodies of Revolution at 0° Incidence. E.M. l&jk, 1939. 57' "Von Karman, Th.: ijber larainare ttnd tujf'bulente ReilDung. Zeitschr. f. angew. Math. u. Mech. 1, 1921, p. 233. 58. Gottinger Nachrichten 1930, p. 58, Vortrag auf dem 3f Int. Kongr, f . techn. Mech. in Stockholm .1930 (Verhandlungen dieses Kongr. Bd 1, p. 85). Von Karman, Th.: Theorie des Eeihungswiderstandes. In Hydromech. ProMeme des Schiffsantriehs 1932. 39- Prandtl, L.: Ergehnisse der A.V.A. Gottingen No. 3 (I927), p. 1. 60. Von Dcenhoff, A.: A Preliminary Investigation of Boundary Layer Transition Along a Flat Plats with Adverse Pressujre Gradient. N.A.C.A, T.N. 639,- 1938. ■ • 6la. Ackeret, J.: Das Institut fiir Aerodynamik an der Eidg. Techn. Hochschule. 6113. DatT'jyler, G.: Eine Apparatiir zur Messimg turbid.enter Schwankungen in StrBmungen. 6lc . Pfenninger, W: Verglelch der Impulsmethode mit der Wagung "bei Profilvri-derstandsmessttngen. Mitteilung No. 8 des Inst. f. Aerodyn. E.T.H. Z'urich, I9U3. 62 NACA TM Wo. 11 8l 62. Lord Eayleigh: On the Instability of Certain Fluid Motions. Proc London Math. Soc 11, p. 57, lB8o und 19, P- 67, I887. (Scientific Papers vol. I, p. h-'Jk unc. vol. Ill, p- 170 63a. Prandtl, L. : Bemerkungen uber die Entstehung der Tm-hulenz. Z.A.M'.M. 1921, p. U3I. , ., . 63"b. Tietjens, 0.: Beitrage uber die Entstehung der Turhulenz. Diss. Gottin^^en, 1922. Z.A.M.M. 192^, p.' 200. - -■ 6^\-' Patry, J.: Instabilite- d'une raiige'e de toU-rhillons de long d'une paroi. Helvetica Physica Acta 19^+3, P- ^3* 65. Ackeret-, J.:,, Probleme des B'lugzeugantriebs in Gegenwart und : ■■ .Zukuaift. Schweiz. Bauzeitung, Bd. 112, No. 1/1938. ' ■ ■ 66- Ackeret, J., Eas, M. , and Pfenninger, W. : Verhinderimg des ; ■ ■ ' . Tj;irbul.ent'.';erlens einer Grenzschicht diu ch Absaugving. D-ie Nat-arwiseenschaften 19'a, £9- Jahrg., Heft 'a, p. 622. 61 ■ Ra,s,. M. , and Ackeret, J.: Uber Verhinderung der Grenzschicht- .turbulenz durch Absauguxig. Helvetica Physica Acta 19'+i' 68.. Baa,, M; :. Diss. Paris: Contributions al'etuiede la cpuche limte aspire'e, 19•-^5• ■'.■' • 69' Gerber, A. : Untersuchungen 'liber Gienzschichtabsauguiig. Mitteilung ...Wo, 6. des Inst, fiir Aerodynauiik E. T. H- Zurich, 1936. 70. Schlichting, H. : Die Grenzschicht an der ebenen Platte mit .: Absaugung und Ausblasen, Luftfahi-tforschimg 1942, p. 179, p. 293. • ■• ' • 71. Sclalichting, E. : Berochnung der lamlnaren Grenzschichtentwlcklung mit Absaugunfj an einem Jo\ikowskyprof il. Caliiers d'Aei'odynamlq.ue, Wo. 3, Oct.-Wov. 19-+5. 72. Prandtl, L. : The Mechanics of Viscous Fluids. Aerodynamic Theory, Duj-and, '/ol. Ill, Div. G- ' ' ■ 73- Prandtl, L. : Stromiongslehre, .1942. . ' , . ' Jk' Schrenk',- 0. : ,. Grenzschichtsbsaugung ;ir.d Seiakereirirkujig. Z.A.M.M., . Bd.. 13, 1933, p- 180.. , ;;■ : , , ■ 75- Schrenk, 0.: Versuche mit Absaugeflugeln. Z-'f-M- 1931; Heft 9- Luftfatu-tforschung 1935, V- 10- WAG A TM Wo. 11 31 83 76. Ackeret, J.: Grenzschichtatsaugung. Zeitschrift des V.D.I., Wo. 35, p- 1153. Sept. 1926. 77- Betz, A. : Verlauf der Str'cinimgsgeschwindigkeit in der Wahe einer Tfand toei unsbetiger Snderimg der Krilmraung • Liiftfahrtforschiing 19h2, Liefg. k, p. 129. 78. Jordan, P.: Auftriebsberechnung und BtrbmungsvorgSnge beim ttberschreiten des Maximalauftriebs- Diss. GOttin.r^^en 1939 (Luftfahrtforschung; Bd. I6, 1939, p- l8'+) . 79- Schiller, L-: Verh. des 3. Intern, Kongr. fUr techn. Mechanik I, p. 226, 1931- Z.A.M.m" Ik, p. 36, 1934. Froc of the 5th Intern. Congr. for Applied Mechanics, p. 315, 1938. 60. Ergehnisse der Aerodyn. Yei-siTchsariStalt zu Gbttingen, Lieferungen I, III, IV. 81. Sclimitz, F. W.: Aerodynamik des Flu^modells (TragflUgel- messungen l) . 82. Jacobs, E. N. , and SherTaan., A.: AJrfoil Section Chajr-acteristics as Affected by "variations of the Reynolds Number. WACA Eep. Wo. 586, 1937- 83. Schiller, L. : Untersiichungen uber laminare und turbnlente Stromx'xig, Forschungsarbeiten anf dem Gebiet des Ing. -Wesens Wo. 21|8, 1922. &k- Ealler, P. de: L' influence des limites de la vexne fluide sur les caracterisbiques aerodynamiq.ues d'une nurface portante- Mittellmig des Inst. f. Aerodynamik E-T.H. Ziii-ich, Wo. 3> 193^ • <,85. Prasidtl and Betz: . h Abhandlungen zur Hydrodytiamlk tad Aerodynamik, Gottingen 1927- 86. Eayleigh: Proc Roy. Soc. A, l9l6, p. 1^+8. NACA TM No. 1181 84 TABIi OF COORDINATES Laminar profil e Laminar profile « Propeller profile No. 11 d/t = 0.10 in 0.49 t from the front d/t = 0.140 in 0.44 t from the front R^/t = 0.008 f/t = 0.00525 in 0.60 t from the front f/t = 0.0245 in 0.41 t from the front i/t yoA -yuA x/t yo/t -yu/t »/t yoA -yuA 0.00107 -0.00107 0.0030 -0.0030 .025 .0190 .0115 .025 .019 .014 .025 .0324 .0180 .OB .0285 .0142 .05 .02567 .01954 .05 .0443 .0224 .1 .0419 .0174 .1 .03435 .0272 .1 .0600 .0284 .2 .0581 .0190 .15 .0404 . 03235 .3 .0788 .0380 .3 .0680 .0182 .2 • 0446 .0364 .3 .0892 .0420 .4 .0723 .0166 .3 .0511 .0411 .4 .0940 .0436 .5 .0723 .0142 .4 .0547 .0431 .5 .0936 .0436 .6 .0692 .0126 .5 .0556 .0443 .6 .0868 .0416 .7 .0617 .0095 .6 .0550 .04275 .7 .0736 .0360 .8 .0486 .0071 .7 .0502 .0394 .8 .0492 >|^84 T0148 .9 .0288 .0032 .8 .0393 .0329 .9 .0140 .95 .0154 .0012 .85 .0309 .0267 .95 .0040 .0068 .975 .0087 .0000 .9 .0194 .01926 1 .925 .95 .975 1 .01334 .0078 .00405 .0144 .0088 .0031 % /t = 0.009 Rg/t = 0.019 *To the laminar profile d/t = 0.14 (fig. 12). According to measurements of F. Feldmann in the high-speed tumel of the InsUtute (description, 61 a.) compression shocks for this profile start, for shoclcless entrance, at a Mach number M = 0.71. For M = 0.76 - 0.77 and shockless entrance the lift decreases and disturbances in longitudinal stability appear. (Re = 570,000) 85 NACA TM No. 1181 No. 14* 53 12 38 13 % 32 .3 32 .3 32, .2 32 .4 32 .2 u. 23 ,68 23 .60 23, .76 23 .84 23, .73 V 16 .00 X 10" -6 15 .85 X 10" ■6 16, .lOx 10"^ 16. .25X 10"^ Re 3 .004X 106 3 .015 xlO^ 2, .998x 10^ 2 .981 X 10^ 2 .982 X 10^ e nun .487 .532 0, .557 .584 .524 for W% .033 .026 .020 .013 .028 Slot C q/2Voo' % Cq/2%o \ Cqx10"^/2 Cp Cq/2%o Cp Cq/2%0 \ 1 0.0752 1.102 0.0643 1.098 0.0552 1,106 0.0466 1.092 0.0637 1.111 2 .0376 1.143 .0318 1.127 .0267 1,142 .0233 1.110 ,0308 1.153 3 .0342 1.105 .0293 1.096 .0243 1,117 .0216 1.083 .0286 1.125 4 .0342 1.078 .0294 1.074 .0254 1,074 .0220 1.063 .0292 1.079 5 .0352 1.165 .0303 1.149 .0258 1,150 .0220 1.119 .0298 1.166 6 .0453 1.118 .0395 1.107 .0336 1.102 .0290 1.089 .0389 1.115 7 .0344 1,120 .0283 1.105 .0237 1.097 .0207 1.085 .0288 1.109 8 .0288 1.123 .0242 1.106 .0198 1.092 .0173 1.059 .0226 1 .117 Cq,%o 0.618 0,556 0.4690 0.4C4 0.514 Cwg%o .725 ,613 .522 .441 .612 No. 14 16 17 jg 15 % 32. .2 32 .0 32 .0 32 .0 32 .2 "o 23, .73 23 ,63 23 .66 23 .63 23 .73 V 16 .20 X 10" 6 16, ,30 X 10"^ 16 .15 X 10' ° 16 .10 X 10"^ Re 2, .982 X 10 |6 2. .960X10 6 2, .942X 10^ 2, ,964X 10^ 2 .998 X 10^ nun 0. .494 0, .416 0. .372 .308 ,456 for p/qo ,036 .049 050 .056 .043 Slot Cq/20/oo CQ/2V00 ^g Cq/2%0 '^Pg ' Cq/2 /oo % Cq/2%0 Cp *^g 1 0.0750 1.118 0.1084 1.145 0.1282 1.165 0,1703 1.225 0.0912 1,128 2 .0351 1.182 .0534 1.243 .0651 1.276 ,0843 1.386 .0449 1.207 3 .0335 1.146 .0491 1.190 .0591 1.207 .0773 1.276 .0412 1.167 4 .0338 1.083 .0498 1.094 .0598 1.101 .0770 1.116 .0419 1.088 5 .0353 1.191 .0521 1.259 .0628 1.299 .0817 1.393 .0429 1.222 6 .0462 1.125 .0672 1.160 .0809 1.194 .1042 1.263 .0560 1.140 7 .0341 1.125 .0481 1.175 .0581 1.211 .0740 1.369 .0399 1.149 8 .0286 1.140 .0393 1.229 .0497 1.297 .0602 1.444 .0352 1.179 Cq^Voo 0.644 0.936 1.130 1.458 0.786 CwgO/„„ .732 1.104 1.370 1.885 .908 Translator's note: A value o f Cq/2 ' 00 Cp 10" 3/2 of 0.0752 denotes a value of Cg of 0.0000752" NACA TM No. 1181 86 No. 20 19 33 34 36 % 45 .07 45 .6 45 .0 45 .1 45 .3 Uo 28 .22 28 .32 28 .19 28 .22 28 .17 V 16 .43 A 10"^ 16 .30 X 10' ■6 16 .41 X 10' -6 16 .41 X 10' ■6 16 .OlX 10"^ Re 3 .488 X 10 3 .530 X lO*' 3 .49 X lo' B 3 .496 X lo'' 3 .575 X 10^ mm for v/\ .422 .472 .456 .376 .276 .035 .028 .032 .037 .049 Slot Cq/s^/oo Sg '^q/S^/oo \ Cq/2°/oo \ CQ/2V00 \ CQ/2V00 \ 1 0.0807 1.107 0.0645 1.094 0.0713 1.097 0.1032 1.113 0.1554 1.152 2 .0402 1.155 .0317 1.127 .0358 1.134 .0506 1.174 .0764 1.232 3 .0366 1.122 .0292 1.098 .0327 1.101 .0470 1.121 .0696 1.146 4 .0369 1.077 .0292 1.070 .0330 1.073 .0467 1.080 .0691 1.089 5 .0388 1.174 .0303 1.144 .0344 1.152 .0495 1.195 .0736 1.258 6 .0495 1.122 .0393 1.100 .0434 1.109 .0633 1.141 .0942 1.208 7 .0360 1.119 .0286 1.097 .0316 1.104 .0470 1.139 .0691 1.212 8 .0290 1.139 .0238 1.094 .0260 1.115 .0394 1.188 .0575 1.320 Cq^o/oo 0.696 0.552 0.616 0.894 1.328 .785 .611 .684 1.018 1.585 No. 37 39 41 43 40 ^ 45 .4 11. .15 10. .96 11. .29 11. .40 «o 28. ,20 13. ,93 13. .81 14. ,01 14, •^2 V 16. .01 X lO"'' 16. ,00 X 10"^ 16. ,00 X 10"^ 16. .00 XIO"^ 16. ,15 X 10"° Re 3. .580 X 10^ 1. .768 X 10^ 1. .753 X 10^ 1. .779 X 10^ 1. ,775 X 10^ ^mm 0. .230 0. .870 0. 830 0. .760 0. ,842 for v/% 051 001 • 009 019 ,004 Slots Cq/2°/oc • \ CQ/2V00 CQ/2V00 ' ^Ps CQ/2V00 ' \ Cq/2V„c ■ \ 1 0.1958 1.202 0.0268 1.094 0.0428 1.111 0.0623 1.126 0.0314 1.099 Z .0963 1.297 .0144 1.115 .0213 1.140 .0306 1.177 .0164 1.121 3 .0876 1.176 .0137 1.089 .0200 1.104 .0286 1.129 .0160 1.091 4 .0867 1.100 .0137 1.073 .0200 1.082 .0286 1.093 .0151 1.075 5 .0929 1.321 .0137 1.116 .0200 1.146 .0293 1.190 .0151 1.125 6 .1172 1.283 .0175 1.099 .0261 1.118 .0385 1.135 .0203 1.105 7 .0862 1.289 .0138 1.083 .0200 1.105 .0274 1.136 .0163 1.089 8 .0752 1.463 .0113 1.071 .0157 1.099 .0226 1.136 .0124 1.081 CQt°/oo 1.676 0.250 0.372 0.536 0.286 C,gO/oo 2.104 .273 .414 .610 .315 87 NACA TM No. 1181 No. 44 46 45 42 32 % 11, .31 11.49 11 .30 11, .37 45. .3 "o 14, .03 14.13 14, .03 14, .04 28. .22 V 16. .00 X 10-6 16.00 "lO"^ 16. .00 X 10-6 16, .00 X 10"^ 16, .30 xlO"^ Re 1. .780 X 10^ 1.793 ■* 10^ 1. .780 xlO^ 1. .783 xlO^ 3. .515 XIO^ e mm 0. ,700 0.598 0. .668 0. ,780 0. ,486 for p/q^ 027 .048 ,035 ,015 ,024 Slot Cq/2%0 ' \ Cq/2°/oo Cp Cq/2°/o, ' \ Cq/2%0 ' \ Cq/2%0 ' \ 1 0.0812 1.143 0.1258 1.184 0.1010 1.162 0.0514 1.117 0.0571 1.094 2 .0399 1.217 .0618 1.316 .0500 1.260 .0257 1.160 .0282 1.122 3 .0374 1.153 .0573 1.209 .0464 1.177 .0245 1.117 .0258 1.097 4 .0377 1.104 .0579 1.129 .0461 1.115 .0238 1.086 .0263 1.066 5 .0393 1.239 .0601 1.347 .0484 1.285 .0245 1.164 .0271 1.133 6 .0508 1.157 .0772 1.216 .0629 1.181 .0316 1.123 ,0352 1.088 7 .0363 1.174 .0584 1.265 .0457 1.212 .0232 1.119 .0256 1.089 8 .0292 1.186 .0466 1.326 .0373 1.248 .0183 1.112 .0220 1.070 Cq o/^^ 0.702 1.088 0.872 0.444 0.494 C^Voo .822 1.352 1.048 .501 .543 g No. 55 54 35 56 57 % 45.4 32.5 45.5 45.1 57.8 "o V 27.97 23.64 28.23 27.87 31.73 15.85 X 10"^ 15.85 X 10-** 16.01 XIO"" 15.85 X10"° 16.03 X10"° 4.02X10^ He 3-582 xlO^ 3.030 xlO^ 3.580X10^ 3.570 XIO^ ^mm 0.420 0.440 0,316 0.328 0.442 for v/lo .034 .038 .046 .045 .031 Slot Cq/2°/oo \ Cq/2Voo \ C(/2Voo \ Cq/2°/oo \ C,/2°/oo \ 1 0.0792 1.095 0.0931 1.110 0.1284 1.126 0.1228 1.118 0.0678 1.087 Z .0400 1.133 .0463 1.166 .0638 1.193 .0610 1.187 .0336 1.112 3 .0364 1.097 .0426 1.117 .0587 1.128 .0559 1.123 .0308 1.084 4 .0366 1.073 .0430 1.081 .0581 1.084 .0559 1.082 .0310 1.064 5 .0384 1.157 .0447 1.193 .0618 1.219 ,0590 1.215 .0326 1.128 6 .0487 1.115 .0573 1.133 .0775 1.169 ,0748 1.154 .0423 1.090 7 .0344 1.112 .0407 1.141 .0573 1.172 .0536 1.164 .0305 1.086 8 .0298 1.123 .0353 1.166 .0469 1.238 ,0456 1.224 .0268 1,072 Cq^o/oo 0.686 0.806 1.104 1,056 0.592 C 0/ .763 .916 1.284 1.217 .645 NACA TM No. 1181 88 No. 58 60 61 59 62' 1o 57.9 ,58.3 58.1 57.9 78.9 "o 31.75 31.71 31.68 31.76 37.02 V 16.03 * 10-6 15.90 X 10-6 15.90 X 10-6 16.03 X 10-6 16.06 X 10-6 Re 4.02 " 10^ 4.05 « 10 6 4.045 X106 4.02 X 106 4.68 X 106 ^om. 0.385 0.276 0.218 0.327 0.219 for p/qo ■ 0.036 .047 .053 .043 .047 Slot Cq/2 /oo \ Cq/2 /oo % Cq/2°/oo ^Pg Cq/2°/oo Cq/2%0 \ 1 0.0786 1.090 0.1338 1.127 0.1708 1.163 . 1025 1.100 0.1452 1.132 2 .0390 1.122 .0662 1.207 .0818 1.258 .0515 1.147 .0649 1.186 3 .0360 1.091 .0606 1.129 .0760 1.157 .0468 1.100 .0645 1.121 4 .0363 1.069 .0604 1.079 .0753 1.087 .0464 1.072 .0637 1.076 5 .0373 1.144 .0634 1.232 .0863 1.308 .0490 1.171 .0728 1.237 6 .0483 1.105 .0822 1.152 .1091 1.204 .0628 1.127 .0922 1.166 7 .0348 1.098 .0601 1.161 .0775 1.225 .0437 1.126 .0653 1.165 8 .0305 1.099 .0511 1.224 .0647 1.336 .0385 1.163 .0542 1.226 Cq^o/oo C,^o/„„ 0.682 1.154 1.480 0.882 1.246 .749 1.338 1.791 .989 1.443 No. 64 70' 65' 66 71" % 79.3 109.1 79.5 79.6 109.9 Do 37.27 44.07 37.32 37.34 43.97 V 16.32x10-6 16.80 X 10-6 16.32 X 10"6 16.32X10"" 16.38 X 10"'' Re 4.63 X 106 5.33x106 4.64X10 6 4.645 X 106 5.45x106 ^» 0.259 0.231 0.294 0.328 0.186 for p/% .044 .038 .041 .036 .039 Slot V2V00 •^Ps CQ/2V00 Cq/sVoo \ CQ/2V00 \ Cq/sVoo % 1 . 1216 1.111 0.1356 1.114 0.1017 1.099 0.0895 1.093 0.1903 1.151 2 .0544 1.152 .0611 1.126 .0464 1.132 .0411 1.120 .0833 1.166 3 .0644 1.106 .0626 1.090 .0462 1.095 .0406 1.088 .0864 1.103 4 .0537 1.074 .0632 1.069 .0460 1.071 .0409 1.068 .0868 1.079 5 .0610 1.199 .0678 1.161 .0512 1.175 .0458 1.157 .0938 1.211 6 .0772 1.143 .0857 1.126 .0651 1.123 .0575 1.110 .1204 1.177 7 .0542 1.133 .0609 1.110 .0453 1.109 .0403 1.102 .0860 1.167 8 .0444 1.173 .0496 1.166 .0383 1.130 .0334 1.101 .0690 1.262 Cq °/oo 1.076 1.172 0.880 0.778 1.632 C,//oo 1.178 1.310 .982 .858 1.894 Transition 10 millimeters ahead of trailing edge, Individual turbulent bursts earlier. ^Individual turbulent bursts further forward. Frequent turbulent bursts further forward. Transition 5 millimeters ahead of trailing edge, individual turbulent bursts earlier. 89 NACA TM No. 1181 No. 21 87 30. 1 32 34 % 69.8 69.5 85.0 54.8 103.8 V_ 35.15 36.3 39.0 31.2 42.8 V 16.60 X 10-^ 16.88 » 10-6 16.93 < 10-6 16.55 X 10-6 16.45 « 10-6 Re 2.188 » 10^ 2.160 « 106 2.382 » 106 1.946 X 106 2.690 « 106 c. 0.232 0.232 0.232 0.232 0.232 Slot Qj X 10-3 % Qj X 10-3 \ Qi X 10-3 \ Qa X 10-3 \ Q.x 10-3 \ 1 2 0.070 1.258 3 0.287 1.483 0.332 1.477 0.403 1.477 0.260 1.472 0.496 1.488 4 0.254 1.553 0.260 1.550 0.313 1.545 0.202 1.627 0.383 1.551 5 0.279 1.521 0.323 1.503 0.391 1.510 0.260 1.500 0.474 1.508 6 0.480 1.483 0.548 1.454 0.667 1.460 0.445 1.449 0.807 1.463 7 0.647 1.443 0.661 1.457 0.800 1.457 0.538 1.447 0.966 1.456 8 0.377 1.389 0.471 1.358 0.581 1.361 0.391 1.357 0.701 1.356 9 0.654 1.317 0.680 1.292 0.828 1.301 0.560 1.292 0.988 1.300 10 0.335 1.230 0.346 1.227 0.410 1.228 0.279 1.223 0.497 1.224 11 0.522 1.151 0.510 1.139 0.781 1.148 0.531 1.144 0.930 1.149 12 0.315 1.121 0.312 1.113 0.393 1.117 0.261 1.116 0.460 1.113 13 0.387 1.024 0.374 1.020 0.544 1.038 0.374 1.032 0.635 1.036 14 0.506 0.972 0.390 0.950 0.457 0.954 0.321 0.944 0.544 0.955 l' 0.083 1-189 0.043 1.167 0.084 1.176 0.055 1.181 0.116 1.186 2' 0.288 1.209 0.295 1.189 0.390 1.198 0.260 1.195 0.471 1.194 3] 0.166 1.175 0.149 1.123 0.192 1.133 0.136 1.136 0.236 1.134 4 0.191 1.160 0.133 1.120 0.169 1.134 0.118 1.133 0.204 1.131 5. 0.225 1.158 0.234 1.108 0.312 1.115 0.218 1.114 0.374 1.112 6" 0.368 1.127 0.331 1.107 0.430 1.119 0.297 1.117 0.516 1.119 7' 0.315 1.100 0.382 1.075 0.520 1.082 0.363 1.079 0.621 1.079 8' 0.503 1.021 0.534 1.015 0.682 1.018 0.473 1.016 0.810 1.012 9* 0.359 1.007 0.375 1.006 0.502 1.018 0.350 1.017 0.301 1.016 10' 0.809 0.989 0.824 0.971 0.906 0.984 0.725 0.980 1.210 0.983 Cq °/oo 0.784 No. 0.792 0.907 0.762 0.990 '''"u" 0.506 21.1 21.2 21.3 0.503 0.576 No. 30.2 0.516 No. 32.3 0.610 No. 34.2 f: 1.290 1.340 1.470 1.572 1.295 1.483 1.574 1.278 1.253 1.600 1.690 \ 1.557 1.622 1.790 1.928 1.560 1.790 1.905 1.626 1.490 1.936 2.048 •=-. 0.838 0.755 0.678 0.657 0.720 0.590 0.520 0.880 0.930 0.590 0.680 '=.." 2.395 2.377 2.468 2.685 2.280 2.380 2.426 2.406 2.420 2.626 2.690 On both sides laminar up to the trailing edge NACA TM No. 1181 90 No. 35 36. 2 38.1 39 40 % 39.1 25.0 65.4 70.4 39.7 "o V 26.4 21.1 31.32 35.3 26.6 16.60 < 10-6 16.62 t 10-6 16.45 X 10-6 16.62 « 10 -6 16.56 X 10-6 Re 1.639 X iqB 1.309 f 10 6 1.966 » 106 2.206 » 106 1.656 X 106 Ca 0.232 0.232 0.372 0.372 0.372 Slot Qg X 10-3 \ la X 10- «a X 10"' \ Q^ X 10-3 \ QaX 10-3 % 1 2 3 0.192 1.487 0.168 1.480 0.395 1.624 0.488 1.630 0.302 1.615 4 0.147 1.527 0.131 1.562 0.278 1.635 0.343 1.651 0.216 1.635 5 0.193 1.501 0.170 1.534 0.359 1.676 0.440 1.680 0.286 1.574 6 0.335 1.448 0.296 1.467 0.568 1.611 0.694 1.511 0.449 1.606 7 0.398 1.454 0.366 1.480 0.691 1.487 0.840 1.490 0.542 1.487 8 0.297 1.360 0.260 1.378 0.472 1.385 0.674 1.385 0.374 1.385 9 0.428 1.290 0.376 1.304 0.683 1.311 0.822 1.318 0.543 1.307 10 0.254 1.229 0.218 1.246 0.393 1.236 0.472 1.236 0.323 1.236 11 0.403 1.145 0.323 1.164 0.616 1.154 0.754 1.155 0.496 1.156 12 0.253 1.126 0.210 1.146 0.288 1.115 0.350 1.118 0.267 1.124^ 13 0.300 1.036 0.270 1.063 0.403 1.019 0.484 1.027 0.361 1.027 14 0.400 0.981 0.424 1.019 0.335 0.939 0.400 0.941 0.386 0.966 1' 0.048 1.189 0.038 1.212 0.026 1.025 0.032 1.028 0.022 1.023 2' 0.146 1.172 0.124 1.203 0.121 1.049 0.292 1.048 0.095 1.048 3' 0.104 1.138 0.090 1.156 0.064 1.050 0.076 1.061 0.055 1.053 4' 0.093 1.138 0.081 1.162 0.060 1.052 0.072 1.053 0.063 1.053 6' 0.170 1.113 0.148 1.135 0.099 1.058 0.119 1.049 0.080 1.066 6' 0.228 1.119 0.198 1.143 0.149 1.043 0.180 1.043 0.119 1.042 7' 0.281 1.078 0.242 1.095 0.217 1.028 0.262 1.028 0.176 1.027 8* 0.366 1.018 0.316 1.035 0.356 0.981 0.410 0.979 0.310 0.982 9' 0.256 1.019 0.220 1.043 0.262 0.979 0.314 0.978 0.239 0.989 10' 0.726 1.006 0.642 1.030 0.756 0.960 0.868 0.954 0.708 0.976 Cq "/oo 0.733 0.816 0.940 1.062 1.009 1.014 0.922 Cg • 0.492 No. 35.2 0.534 0.362 0.396 0.331 0.398 No. 39.2 39.3 0.377 1.225 1.300 1.350 1.302 1.468 1.390 1.340 1.412 1.376 1.486 1.299 1.464 1.556 1.632 1.618 1.828 1.737 1.681 1.761 1.710 1.857 1.594 c/,. 1.020 0.910 1.110 0.748 0.668 0.693 0.707 0.657 0.692 0.635 0.90 2.472 2.466 2.742 2.366 2.496 2.430 2.388 2.418 2.402 2.492 2.494 On toth sJ Ldes lajnlnar up to the trailing edge No. 38.2 38.3 38.4 91 NACA TM No. 1181 No. 41 43.1 44 46 47 1o 25.5 55.8 71.80 39.9 25.8 Vo 21.2 31.4 35.70 26.46 21.24 V 16.36 X 10-6 16.47X 10' 6 16.60 > 10-6 16.25 Xlo-6 16.25 V 10-6 Re 1.337 xlO^ 1.968 X lO'' 2.220 X106 1.682 XIO^ 1.352 X 106 Ca 0.372 0.480 0.480 0.480 0.480 Slot Qa» 10~3 % <3a " 10" 3 \ Q^K 10-3 \ Qa X 10-3 \ Q^x 10-3 \ 1 2 3 0.218 1.617 0.461 1.736 0.530 1.718 0.354 1.736 0.257 1.726 4 .157 1.657 .324 1.769 .372 1.736 .251 1.749 .184 1.745 5 .208 1.593 .43 9 1.668 .500 1.645 .345 1.665 .258 1.664 6 .338 1.510 .662 1.577 .754 1.563 .518 1.568 .392 1.564 7 .406 1.505 .805 1.558 .920 1.536 .610 1.549 .471 1.552 8 .283 1.397 .548 1.431 .628 1.413 .430 1.429 .325 1.427 9 .411 1.315 .786 1.353 .894 1.342 .622 1.348 .470 1.347 10 .245 1.246 .465 1.268 .526 1.255 .367 1.266 .281 1.268 11 .374 1.163 .630 1.166 .718 1.159 .494 1.165 .370 1.171 12 .215 1.140 .310 1.134 .345 1.122 .263 1.136 .220 1.144 13 .280 1.047 .426 1.045 .454 1.033 .370 1.046 .300 1.053 14 .392 1.008 .322 0.940 .330 0.934 .404 0.964 .400 1.004 1' .015 1.036 .017 .953 .020 .940 .012 .945 .009 0.950 2' .069 1.058 .082 .993 .092 .988 .063 .990 .048 .994 3' .020 1.061 .050 .993 .057 .987 .036 .996 .027 .999 4* .018 1.062 .031 1.011 .036 1.005 .017 1.010 .011 1.010 5' .060 1.056 .063 1.007 .074 1.004 .053 1.013 .043 1.018 6' .090 1.047 .103 1.015 .115 1.010 .078 1.013 .061 1.013 7> .133 1.033 .125 1.007 .141 1.004 .120 1.005 .093 1.005 8' .256 0.991 .227 0.967 .257 0.963 .280 0.967 .249 0.976 9' .195 1.005 .219 .975 .248 .960 .232 .976 .193 .988 10- .580 0.988 .794 .948 .887 .943 .660 .953 .535 .964 '=Qo°/o 0.896 1.057 1.050 1.020 No. 45 0.979 0.993 •^Qu " .364 No . 41.2 0.293 No. 43.2 43.3 0.290 0.315 .287 .320 Cg " 1.260 1.315 1.350 1.390 1.430 1.340 1.362 1.335 1.266 1.313 1.551 1.624 1.770 1.828 1.882 1.740 1.772 1.717 1.650 1.678 1.13 1.10 0.735 0.695 0.660 0.710 0.680 0.850 0.935 1.075 •=w." 2.681 2.724 2.505 2.523 2.542 2.450 2.452 2.567 2.585 2.753 On both sides lamd jiar up to the traJ ling edge NACA TM No. 1181 92 No. 54 55.3 56 .1 57 .3 1o 22.2 29 .3 40.4 18.05 V„ 19.63 22 .58 26.56 17.75 V 16.07 X 10"^ 16 .07 X 10"^ 16.17 X 10"^ 16.17X10"^ Re 1.260 xio^ 1 .450 X 10^ 1.696 xio^ 1.134 xlO° Cft 0.163 .587 0.587 0.587 Slot Qa ^ 10-^ \ Q^ X lO""' \ Q^ y 10"^ '^. Qa y 10-^ 1 0.328 1.748 0.424 1.761 0.220 1.732 2 .187 1.792 .243 1.804 .125 1.792 3 0.121 1.399 .404 1.820 .522 1.819 .276 1.823 4 .116 1.489 .169 1.796 .218 1.795 .116 1.797 5 .166 1.466 .273 1.750 .349 1.749 .187 1.769 6 .247 1.420 .492 1.661 .624 1.664 .344 1.661 7 .301 1.424 .543 1.624 .697 1.619 .379 1.636 8 .209 1.339 .390 1.487 .496 1.484 .275 1.504 9 .305 1.271 .580 1.401 .736 1.404 .407 1.412 10 .123 1.196 .333 1.307 .426 1.299 .236 1.320 11 .266 1.146 .436 1.182 .560 1.178 .296 1.200 12 .245 1.131 .213 1.170 .272 1.165 .146 1.190 13 .287 1.057 .298 1.074 .378 1.075 .286 1.135 14 .476 1.044 .351 0.979 .43 9 0.983 .558 1.157 1' .087 1.255 .021 .042 .073 .116 .096 .555 2' .144 1.268 3' .075 1.205 4' 5' 6' 7' 8' 9' 10' .116 .276 .210 .261 .2 95 .252 .518 1.156 1.213 1.155 1.096 1.018 1.042 0.972 .028 .059 .072 .158 .146 .548 .971 .988 .987 .950 .956 .928 .036 .070 .086 .197 .185 .681 .970 .988 .988 .949 .960 ,931 0.980 .995 1.001 0.959 .970 .977 *g C-' " 0.784 1.286 1.167 .611 No. 55.2 55.4 0.264 No. 56.2 0.273 1.395 1.430 1.405 1.480 1.550 1.597 1.440 1.644 1.985 1.936 2.045 2.154 2.221 1.975 1.360 0.95 0.97 0.92 0.730 0.710 1.145 3.004 2.935 2.906 2.965 2.884 2.931 3.120 On b oth sides laminar up to th e trailing edge Figs. 1,2 NACA TM No. 1181 Of V (V3 CV4 C(5 (* 0,7 0.« 0^ 1 -J- Figure 1.- Influence of the transition -point position on the profile drag for various profile thicknesses; Re = 15 x 10 . LaKlnar flat plate ?•'*" C^.'-i. Position of transition point completely laalnar Figure 2,- Influence of the transition-point position on the profile drag for various Re; d/t = 0,16. NACA TM No. 1181 Figs. 3,4 NACA 0010 iTurb it'C^OOA-^ ,\ \ , I .c,.o _fo opo*^ PnJ x_N ' f\\ \ Figure 3.- Pressure distributions along the chord on the profile NACA 0010 for various Re; c^= 0. (The pressure distributions for the different Re are every time shifted vertically downward by Ap/Sq " ^•-'■•) "^^^ start of transition is denoted by arrows, t = 0.60 m. Figure 4.- Laminar profile d/t = 0.140 (fig. 12), t = 0.70 m. Pres- sure distributions along the chord and transition start (vertical arrows) for smooth inflow. The lower figure shows the pressure distributions in the rear part of the profile for various Re on an enlarged scale. Fig. 5 NACA TM No. 1181 NACA TM No. 1181 Fig. 6 Pressure distribution ^ without shifting I c>- o cj- a 0) w B +-> CD B o B S o CD 1 — I •r-l ^-^ O 0) CD g) •iH NACA TM No. 1181 Fig. 11 Ca - 0.4 for saootta Inflow Propeller profile d/t = 0.09 - fn n5 r^ CU CO O ( \ 4 aid (r B = 1 ailer Vi\ 1 T-j qn (D 1\ s ^ a.S \ ° :S S '^w \ i/) ••-' 'i^ CO \ "^ hD .. II bO -- * -i \ ^g^ O \ O -M C \ 'n "tJ 00 \ 1* \ :^ w^. o \ VH ^_> O A \ P f=! i \ ^ O " J \ ^ii ^ \. 1/ ' \ mnar A = lap (t -^ a ^ -I. ' Si co-c^.g \ / -"I o A J a; „ " V 7 ^ -M o P ^ M NACA TM No. 1181 Fig. 14 Hoaentui aeasureaents for He = 1.07 x 10^ and various Aileron slot closed and sealed Oj0O6 act 0012 COM 0.016 Figure 14.- Laminar profile for wing, d/t = 0.14, t = 0.250 m (fig. 13). Profile -drag polars (momentum measurements) for various trailing -edge aileron deflections p . Aileron slot between upper and lower surface sealed. Re = 1.07 x 10 6 Figs. 15,16 NACA TM No. 1181 T3 '^ o II ao CO T— ( bL •r-H o II ct5 O O W d ^ I. ^ +-> T3 O id I— I O CD Cj CD TO ^v, I CD S LO w O LO o I— I w o u 0) 1—1 •1-1 < O' o 0) n o (D I— I •rH 03 CD I :=i •r-l Cti ^1 +-> w o •1-1 ^H OJ > O 73 (D ■—I oi CD w d) o cd 'M ^< m u o 1 — I u a o CD NACA TM No. 1181 Fig. 17 ® d/t = 90% In 36^ t from the front Figure 17,- Laminar suction profile 2 with a single suction slot on the upper surface, d/t = 0.0675 in 0.394 1 from the front. Profile 1, d/t = 0.09, without suction. Fig. 18 NACA TM No. 1181 o ^ 0) Oi o NACA TM No. 1181 Figs. 19-21 ooos O0O4 aooos qooio Q0015 Figures 19,20.- Laminar suction profile 2. Total drag c^ (Cq) and drag contribution of the wake c^ '(^^q) for various Re, s = 1.3 millimeters. 00006 00004 'Ooe 0,2 B Re 1010 Figure 21,- Laminar suction profile 2, Optimum suction quantity Cq^ and pertaining static pressure cpg^ in the suction chamber for optimum total drag, s = 0,9 millimeter and 1.3 millimeters. Figs. 22,23 NACA TM No. 1181 a) b) I Wi ...J^LJi c) Figure 22,- Hot-wire photograph, 30 millimeters ahead of the trailing . edge on upper side 0,2 millimeter over the surface, (a) Without suction, slot closed: turbulent; (b) time trace (f = 400/sec); (c) with suction: laminar, Cq = 0.0009 Re = 275,000, u»/Uq = 0.0044. 'M'ff^lff^^'- rmmmmmmff. a) c) Figure 23.- Hot-wire photograph, 30 millimeters ahead of the trailing edge on upper side 0.2 millimeter over the surface, (a) Without suction, slot closed: turbulent; (b) with suction (c^ = 0.0016): laminar; (c) time trace (500/sec), Re = 790,000,Si'AJo = 0.0040. NACA TM No. 1181 Figs. 24,25 Figure 24.- Boundary -layer observation with soot coating for laminar suction (everything laminar with the exception of the edge of the boundary layer). Figure 25,- Boimdary -layer observation with soot coating with horizontal turbulence wire (greatest part turbulent). NACA TM No. 1181 Figs. 26,27 Opposite wall Test plate I" - ; ; f ' ^^ ;/ ■ -1'"^ • ■ / >//> / ■ \ ' __ ■" 1 Suction ehaatier Figure 26.- Laminar suction tests with three single suction slots arranged one after another. Test arrangement. Figure 27.- Shape of the suction slot (a). Fig. 28 NACA TM No. 1181 %_%^fO 20 JO 40S06070e090nOnO 120cm ® 1 1 1— I T 1 1 1 1 1 Pressure distribution without laalnar suction Laalnar pressure Increase = 11){ up to transition » 20J04O5O6070da90l00n0 120cm Here still laalnar pressure distribution for laalnar suction with 3 suction slots Laalnar pressure Increase = 63)1 up to transition Figure 28.- Laminar suction tests with three suction slots. Static pressure at the test plate for various suction quantities and tunnel widths. NACA TM No. 1181 Fig. 29 100 * cm Transition start Figure 29.- Laminar suction tests with three suction slots. Static pressure at the test plate for various suction quantities and tunnel widths. q/qjn = 1 "f^' b = 0.40 m. T ab 1 e to figure 29. Na Tunnel width mm N L- m \ \ ^_ 1 ,/ ~^ — - 'r>m \ .^ 2 ..^ 'P — VO- — 3 ^.^ S >lot a 0,2 0,4 06 08 'P \0 10 "Mm 'P Vim 20 40 cm 61 K Test 29 S X^ X \1 ^^ — \ \2 -^ ^ ^\ \J r-^ N 1 \4 =^ . s slot a Vo. slot 40 cm 60 « Test 25 s nA 08 N \1 v.._ ID \^ U \3 L ip — \4 5^ ^ :^ -*■ slot a Table to figure 35. Test 5 TTITn A mm Qa 10-' Co/Q*. 1m Test i m-m h mm Qa I0-' m'/s «a/<3<« 9m kg/m' 23. 1 0.85 0.35 1.97 0.268 8,14 29. 1 0.85 0,35 0.77 0.106 8.14 2 1.24 0.170 2 062 0.085 8.14 3 0.77 0.IO6 3 0.55 0,063 4.07 4 0.60 0.082 4 1.14 0,187 16.2S 25. 1 0,80 0.6O 0.80 0,109 8,16 30, 1 0,85 0,7 0.82 0.113 8.14 2 1.25 0.171 2 0.64 0.087 8.14 3 1.95 270 3 56 0.092 4.07 4 0,62 0.085 4 1.17 0, 1 34 16.28 5 5 081 o.in 8.14 2B. 1 0.85 1.25 0.171 8.15 2 0.79. 0,108 3 0.61 0.084 Figure 35,- Laminar suction tests with the single suction slot (a). Opposite wall V, tunnel width 80 millimeters. Tests 23, 25, 28, 29, 30: Influence of the suction quantity Qg^ and the shifting of the slot trailing edge on the pressure distribution (sink effect). Figs. 36,37 NACA TM No 1181 n " ' 40 cm 60 I (^2 - V, 80 mm ! T« St V 1 08 \ s in !^ 1 " V V \.^ in ^ V ^? ""h. V --3 — '/<« slot a 40 cm 1 60 . Testur *? s T i of ^ 10 \ \ ■— ^ \ \ ^2 '^' a/q„ ip 1 ' 3 ^» ^^- "'^ Slot a 4^ 40 cm 60 . 0? 0,1- t V, 80'T>n< J 1 Test V,V °\ \ s 10 N \. ^ --' \ \ ^ 2 .' ,0 V \ ^. \ \^ ^ 4 ...-" ^ ' \ ■t-^5 ^ 10 X \ ^6 . ^^ Vn„ Slot a Figure 36.- Laminar suction tests with the slot (a). Tunnel width 80 milli- meters. Tests in, IV, V, VI: Influence of the suction quantity and slot 9 width on the pressure distribution (sink effect), (i-^ = 8.15 kg/m . Table to fl gure 3 6. Test 5 mm h mrn Q^ lO-Jm'/s QaQi* Test 5 TTITTI A mm Ca lO-'mVs Cam'/s 5,67 0,674 4,07 0,483 2,76 0,323 1,19 0,141 1,59 0,189 2,01 0,239 0,2 20 40 60 80 X cm h = 1,0 " N •-25 \ N, i ^•< '^' \ s S Tr< ins It Ion 1,0 \ ^ ^ n 1rr> .3...I "%?, °':S 00761 7704- f"yi Figure 41.- Laminar suction test with slot (b) (L 25), test plate (b) 40-millimeter tunnel width, s = 1.3 millimeters, h = 1.0 millimeter, q^ = 32.6 kg/m^, Q^ = 0.00767 m^/s = 0.77 x Q6*. ^m NACA TM No. 1181 Fig. 42 Figure 42.- Laminar suction tests with slot (b), test plate (b), 40-millimeter tunnel width, s = 0.8 millimeter, q^^ = 16.3 kg/m^, Q^ = 0.00201 m^/s = 0.239 X Q8*. Influence of the shifting h of the slot trailing edge (fig. 38) on the laminar -pressure increase up to the transition (arrow) and the sink effect. Test h mm 141.3 1,3 I40,Q o.y 14o,G 0,6 Ho ,2 0,2 14-0,3 -0,3 Figs. 43,44 NACA TM No. 1181 02 04 06 08 J.-, '0 "op ■ 20 40 60 X cm 80 OjB '•-03 ^P 1 1 V^ 40 mm 1 \ v^ s / \ N, ^'7 n- N \, \ N -0 4- i N ^^. -•llfl \ \ "m %, slot b, plate b Slot b Figures 43,44.- Laminar suction tests with slot (b), test plate (b), 40- miUimeter tunnel width, s = 0.8 millimeter, q_^ = 16.3 kg/m^. Pressure distribution up to the transition (arrow) for- considerable outward shifting (h = -0.3 mm) or inward shifting, respectively, (h = 1.3 mm) of the slot trailing edge. Test // mm Qa ■ 10-> m'/s Q..Qi. / 17-0.3 0,3 2,73 0,325 / 18-0,3 0,3 4,12 0,488 f 201.3 1,3 12,2 1,45 /^18l,3 1.3 4,05 0,48 NAGA TM No. 1181 Figs. 45,46 15 25 04 061-02 08 _ 04 . 1C % IS "0 50 60 70 _)! cm 4* Slot b, plate d 06 0,8 1.0 "A .44 -06- i^^ 10 20 30 ;^ ee- N? Q;,1d'!!L* '^"' °<^ 46 1,79 45 2,77 44 4,00 4 7 5,62 48 7,25 49 990 10 2SL. 0& 30 40 5^ 60 70 80 X cm 47 ^ 40 in. V, 40 mm 5 = 08 mm ^,4. -0, 0,8 1,0- 50 4Q_ "l 70 80 « C" 4« "•--M 50 60 ,^^0 aO»cm 49 --1 ^48 u<^^- ■^ 46 6C_X cm 46 t /cm 45 -45 46 I Figure 45.- Laminar suction tests with slot (b), test plate (d) (fig. 37), 40-millimeter tunnel width, s = 0.8 millimeter, q^ = 16.3 kg/m"^. Influence of the suction quantity Qg^ on the laminar -pressure increase up to the transition (arrow) and the sink effect. Figure 46.- Suction slot (g). Figs. 47,48 NACA TM No. 1181 80 cm 7,80 0,94 4,69 0,5b Figure 47.- Laminar suction tests with the slot (g), 40-millimeter tunnel width, s = 0.8 millimeter, q^ = 16,3 kg/m^. Pressure distribution at the test plate. Transition marked by arrow. Figure 48.- Laminar suction tests with the suction slot (a) (fig. 27). 80-millimeter tunnel width, slot diffuser length 16 millimeters. Static pressure 1 - P^/q^^^ in the suction chamber for various suction quantities Qa/Q5*, stagnation pressures q widths s. m and slot NACA TM No. 1181 Figs. 49-53 «./««* 5£ .2 7 Slot a «. J / S = 0.3 «■ / 7/ h = 0.2 SI / / p / / / 4 / / r A /^ / y / y A ^ ^ y' A ^ 1 Slot diff user "■ length 16 1 1 1 ■ ■ , 1 ig 0.1 O.i 0l3 Figure 52. "a/**' 0.1 0.3 ««/««' Figures 49-53.- Laminar suction tests with the suction slot (a) (fig. 27). 80-millimeter tunnel widtii, slot diffuser length 16 millimeters. Static pressure 1 - P/^^/q^^ in the suction chamber for various suction quanti- ties Qa^/Q5*, stagnation pressures q^ and slot widths s. Fig. 54 NACA TM No. 1181 No. 1 2 3 4 5 6 QaQt' 5.67 0,674 4.07 0,433 2.76 0.326 2.76 0,326 1,98 0,234 1,59 0.187 Figure 54.- Laminar suction tests with slot (b), test plate (b), (figs, 37 and 38), 40-millimeter tunnel width, q = 16.3 kg/m^. Static pressure ^m 1 - Ap/q in the suction slot for various suction quantities Q3/Q6*. ■•m NACA TM No. 1181 Figs. 55-57 ■s s 0, N° 0«10JJ 13? 1 292 0392 2 220 q306 3 VS 0243 4 110 0153 5 080 0111 ^ H Slot b NS 0,1 ^irf 9^' 1 3^63 0,360 2 2,79 0,276 Figure 55-57,- Laminar suction tests with slot (b), test plate (b), 40-millinieter tunnel width, s = 0.83 millimeter, slot diffuser length 24 millimeters. Velocity distribution at the slot exit for various suction quanti'ies Qg^ and stagnation pressures q^^^. Figs. 58,59 NACA TM No. 1181 Figure 58.- Velocity distribution at the slot exit for various suction quantities, q = 32.5 kg/m^. 4 •Front side of slot O Rear side of slot 'm-SSS^ Figure 59.- Static pressure along the slot diffuser for various suction quantities, q^ = 32.5 kg/m2. NACA TM No. 1181 Figs. 55-57 Figure 55-57,- Laminar suction tests with slot (b), test plate (b), 40 -millimeter tunnel width, s = 0,83 millimeter, slot diffuser length 24 millimeters , Velocity distribution at the slot exit for various suction quantises Qg^ and stagnation pressures q^^^. Figs. 58,59 NACA TM No. 1181 .Figure 58.- Velocity distribution at the slot exit for various suction quantities, q = 32.5 kg/m^. • Front side of slot ORear side of slot Q„.32 6S Figure 59,- Static pressure along the slot diffuser for various suction quantities, qj„ = 32.5 kg/m2. NACA TM No. 1181 Figs 60,61 1-p, «/qm 012 CV€ Ck6 '.0 V2 Qo/QtT Figure 60. - Static pressure in the suction chamber for various suction quantities Q^^/QS* and stagnation pressures q^^. 1-Pp./q Q«/Q(^' Figure 61,- Laminar suction tests with slot (b), test plate (b), 40-millimeter tunnel width, s = 2.0 millimeters, h = 1.0 millimeter. Slot diffuser length 24 millimeters. Static pressure in the suction chamber for various suction quantities Qa_/Q5 * and stagnation pressures q^^^. Figs. 62,63 NACA TM No. 1181 0.2 0,4 06 OS 1.0 1 J 'Vof Figure 62,- Laminar suction tests with suction slot (i) curved forward (fig, 38), test plate (b), s = 1.45 millimeters, 40-millimeter tunnel width. Static pressure in the suction chamber for various suction quantities and stagnation pressures. 1 Qoioes 1.08S 2 cvxisis qsi8 3 qOOS43 OlS43 « 0flO34O Q340 Figure 63,- Laminar suction tests with forward curved suction slot (i) (fig. 38), test plate (b), S = 1,45 millimeters, 40-millimeter tunnel width. Velocity distribution at the slot exit for various suction quantities, q^ = 32,7 kg/m2. The slot flow undergoes laminar separation on the front side of the slot. NACA TM No. 1181 Figs, 64,65 ////////A D \-.1«"' Suction tank Front wall y/////////////////////////// yy//y^y///)^/////////////////////////////////y ItTlOiwfn ^j Figure 64,- Rearward curved suction slot h. Suction slot X un Figure 65,- Laminar suction tests with slot h. Static -pressure distri- bution p/Qq along ttie chord. Figs. 66-72 NACA TM No. 1181 6f) TOO 710 ' 7«0 I ■"*7«0 08 r^ -V 1 ipmm -V % 7,."»(,« r\ 0130 f \ -oa r ^QITJ III \ A '/ 0.173 ^ x~"-\ 01136 1 0- * ■ L— 1 L ( m 71 o\ "0 740 I mm 7«0 ?iO '«o IrranTM \ St. s V /^ •^ // •A ^ S ^^ -1 72 ^ 1 1 c " 71 M 7. K) ' ^ M V (0 1 "M» Figures 66-72.- Laminar suction tests with slot h. Distribution of the static pressure p/q^ ahead of the slot and along the slot diffuser for various suction quantities Q^/Q5* and stagnation pressures qQ. Minimum slot width s = 1.0 millimeter and 1.25 millimeters. 8 * = displacement thickness ahead of the slot. Table for Figures 66-72. Qa kg/in* 32,1 44,0 7,1 21,2 13.0 (3i,.l(r^ni=/s (* = 0,18 in 5,10 5,52 3,48 4,60 4,05 NACA TM No. 1181 Figs. 73 -75a CD B a o o -4-> o w CD 5 II I OJ bo m O C/3 rj cu CO o w •l-l ^ • o^ in d (11 u -t-> T) (U o S ^ •g o 'T-i U.J U C\1 (T( • > 1—1 ;h V, o ^1 1=1 15! ^ CO o m -4-> o r— I CO o •1-1 -u O 1^ Ui ■*-> si hD •l-t CD CD sa rt CO o o •rH JU II c^ CD CD Fig. 75b NACA TM No. 1181 ^ ^A» -Pd Pa TO the suction r Tentlltttor Figure 75(b).- Side view for covered opposite wall. •NACA TM No. 1181 Fig. 75c Figure 75(c).- Test nozzles for measurement of suction quantities. Fig. 76 NACA TM No. 1181 Slot _ Figure 76.- Suction slots I - VTH. NACA TM No. 1181 Figs. 77,78 Re = 3.00 X 10 • Suction tank _P J Transition — Test llo» TV" Test 16 Oil Test 19(19 ) Re = 3.58 X 10 Test 20(65} ^^— i— flf^'r^^fl Test 35(56) Vl^h^ki-t4^i^ Figures 77,78.- Pressure distribution along tb.e chord, static pressure in the suction chambers (solid circles) and transition start (verti- cal arrows) for various Re and suction quantities. G = boundary - layer test point. Figs. 79,80 NACA TM No. 1181 1 01 C Test 42 P ■To p ^0 Slot ' ^ HI IV V ,, ^,1 villi +4 Test 44 TRANSITION , SUCTION TANk 1o iVI Vll VIII Test 66 Re = 4. 62 X 10 6 o.'Z Test 65 Re = 4.62 « 10 62 66 X 10 a Re = 4.03 X 10 01 P q„ Test 37 Figures 79,80.- Pressure distribution along the chord, static pressure in the suction chambers (solid circles) and transition start (verti- cal arrows) for various Re and suction quantities. G = boundary - layer test point. NACA TM No. 1181 Figs. 81-85 opt 10" Re Figure 81.- Optimum total suction quantity c total drag (calculated for both wing sides). Qt, opt (Re) for optimum 1.0 OB 06 0.4 02 . ^ s W^ w^* ^ J? ^ >» J ^ ^ J6 q,= 32.1 kg/ff^ ^i' si* — — Test Re^ ■ 300 10^ ^ ^ 1 ^ 1.0 03 06 0,4 0.1 1 44^^^^^ 43 '4' ^39 -Test w ^40 q-1l3kglm-^ i m Re^ . miO* / 4 y'"M 12 3 4-56 7/-%, Wu OJB 0.6 0.4 02 Jl 1 ^ ^^ A #^ ^ / ^^ ^0- 78.5 t^^ / ^ — Test R\. 465 to' 1 J y^. 3^%. Figures 82-85.- Velocity distribution u/\J (y) in the boundary layer at the point G 9 millimeters behind the slot Vm for various Re and suction quantities. Figs. 86-88 NACA TM No. 1181 1.0 OB 06 0.4 02 36 'k ^ 3^ w ^^ " % ^^ *7?1 ^Test ^ M q^ --iS.ii«^' \0 " X ""•, -454»0* f jy> J XT'" Figures 86,87.- Velocity distribution uAJ (y) in the boundary layer at the point G 9 millimeters behind the slot VIII for various Re and suction quantities. 07 08 09 1 Figure 88.- Drag variation c (Re) without suction (curve a) and with laminar suction (curve b), suction blower power included. Presuppo- sitions: ^p- = 1 aJ^d acceleration of the sucked air to Uq, The kinectic energy of the sucked air in the suction chambers was taken into consideration, c^ is calculated for both wing sides. The drag increase for higher Re is caused by the wind-tunnel turbulence. 1 = laminar friction of the flat plate (Blasius (47)), t = turbulent friction of the flat plate (Schlichting), (a) = c^ without suction, 00 (b) = c„. with suction, (c) = c^ with suction, if there were two more suction slots arranged behind slot Vni (mathematically), (d) = 0.787c^j^j, NACA TM No. 1181 Figs. 89,90 5 ip V 'f * V 2? 30 4p sp\tf Figure 89.- Transition-point position for various Re on the not-sucked opposite wall (observations by stethoscope), a = transition start, X = start of the developed turbulent boundary layer (measured from the front). Figure 90.- Influence of the total suction quantity Cq^ on the total drag c^ and the drag contribution c^g. of the suction blowers, c^ , c^g., Cq^. are calculated for both wing sides. Re = 3.00 x 10°. In the tests 54, 14*, 38 (solid circles) one somewhat widened the suction slots, thus reducing the negative pressure in the suction chambers and therewith c^g. and ^w„ • Figs. 91,92 NACA TM No. 1181 W' !I0^ 4 ■ro' 710' 10' 2J0' 410' 7tO' K)' 2)0 4 Figure 91.- Frictional drag c^j^ of a laminar flat plate with area suction for various Re Schlichting (70). for various Re and suction velocities - 'OqAJ^ according to W' 210' 4-10^ ?-to' W' 2-10' 4-10'- 7-10'n' 2-10' 4I0' 7V' lO' Figure 92.- Drag c 9 of a laminar flat plate with area suction for various Re and suction velocities -^qA^o for lossless acceleration of the sucked air to Uq (suction blower power included). NACA TM No. 1181 Fig. 93 OflOOZ 0WO1 21(f 4Kf licfio' 210* 410* 710' 10' 210' 4I0' 7t(f lO" Re Figure 93.- Drag 0^3 of a laminar flat plate with area suction for various Re and suction velocities -X)q/\]^ for lossless acceleration of the sucked air and the boundary layer at the plate end to Uq (suction blower power included). Fig. 94 NACA TM No. 1181 Q) O U ft Gi O O II LO d^ II " o CD W I— ( m! CD o •r-l O -4-> •.-( C/3 O CD CO [x. NACA TM No. 1181 Figs. 95,96 0.007 with suction 0.00J5 0.5 0.6 0.70.8 1-10'' 1.2 1.5 2 2.5 J Re 4-10^ Figure 95.- Laminar -suction profile, d/t = 0.105. Optimum total drag c^ with suction (suction-blower power included) for various Re and c„, furthermore, c w. without suction. 'mm .07 4 06 05 04 0.3 01 0.1 For various Re i t^- 1 Re 1^ nl 210' 1 1 ■ -I.IIO' ^ Ss^ ^ Turbulence 77- 1 1 ""' 0.004 0.001 0.002 0003 0004 Cw^ Figure 96.- Laminar suction profile, d/t = 0.105. c^(c^^) with suction for various Re (suction-blower power included). Figs. 97,98 NACA TM No. 1181 1 12 14 15 Ca^, Figure 97,- Laminar -suction profile, d/t = 0.105. Influence of the suction quantity Cq on c ~ 00 ° Figure 98.- Laminar -suction profile, d/t = 0.105. Total-pressure distri- bution in the wake with and without boundary -layer suction. NACA TM No. 1181 Figs. 99-102 « static pressure In the suction tank Suction tank c.-q23J Bt. 2.188 10 °?\ On both sides laalnar up to the trailing edge gjo^ jq .^-^] Ha r-'X^-^^i-^-^^S^- "0 Static pressure In the suction tank 7^ 8 9 I4A I' 0,2 03 04 qs qe Q7 Cp72 1— i^ Hi Slot Test 38' l>e= VI65W 10 ::^ Vt Upper and lower side eoapletely laalnar Re-2.16'10 On both sides laalnar up to the trailing edge %, -0.7 q. Slot l3 i" -0,6 -0,5 -04 -0,3 -0,2 -0.1 ' v^ :^ -J- ^-' JQ -tt 0,1 q2 Q3 0,4j 0.5 , 0,6 o ), 08 gfr l Vt Upper and lower side coapletely laalnar JX Static pressure In the suction tank Figures 99-102.- Laminar -suction profile, d/t = 0,105. Pressure distri- butions along the chord for various Cg.. In test 21 the sink effect is weaker than in the corresponding test 27. Figs. 103,104 NACA TM No. 1181 C,. 0.587 Test 55.J »i.i4510' Upper and lower side eoapletely laminar w Static pressure '-' In the suction tank Figure 103.- Laminar -suction profile, d/t = 0.105, Pressure distri- butions along the chord for Cq^ = 0,587. Profile32 4-^106, -J-C1027 . 5?-0,003 „. . ^ I ^ ' r ^ r Disturbance r- 0,360 m without disturbance 2. Disturbance i. Figure 104.- Profile 32, d/t = 0,060, smooth wing, and with disturb- ances (1) and (2). NACA TM No. 1181 Figs. 105-107 QD04 OPM qoi2 DPI* qp04 <*x» qnt Figure 105.- Profile -drag polars of the profile 32 without disturb- ances (smooth wing). Figure 106.- Profile -drag polars of the profile 32 with disturb- ance 1. Disturbance s. QpM OlOM qoi2 Figure 107.- Profile-drag polars of the profile 32 with disturbance 2. -ilfl 3 1262 08106^647