[f^?ccive/h-/\W3h (^-> i^'kxj CONFIDENTIAL EM No. ATA31a AC A RESEARCH MEMORANDUM EXPERIMEETAL INVESTIGATION OF TBE EFFECTS OF ^/ISGOSITY ON TEE DEAG OF BODIES OF KE7/CLUTI0N AT A MACH MM3SB OF I.5 By Dean E . Chapman and Edward W . Perkins Ames Aeronautical Laboratory Moffett Field, Calif, UNIVERSITY OF FLORIDA DOCUMENTTS DEPARTMENT 1 20 MARSTON XIENCE UBRARY RO. BOX 117011 GAINESVILLE. FL 32611-7011 U^, CLASSIFIED DOCUMENT docTiment contains classified informatioii fectlng the National Defense of the United within the meaning of the Espionage Act, use 50:31 and 32. Its transmission or the revelation of its contents in any manner to an unauthorized person is prohibited by law. Information so classUled may be Imparted only to persons in the military and naval services of the United States, appropriate civilian officers and employees of the Federal Government who have a legitimate Interest therein, and to United States citizens of known loyalty and discretion who of necessity must be informed thereof. NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WASHINGTON' -April 3, 19^7 CONFIDEIOTIAL I 'Ji" >0f ' ' -^ '?t| 0^"^ M.Ck EM No. A7A31a COHFIDEWTIAL NATIOKAL /JDVISOHY COI-MITTieE FOB ^J]30KAUTIC3 pj:s5;j^ch i-^jeivIopaisum expepeierital dn^estigation of the effects of viscosity or: THE DRj'-iG OF BODIES OF RE^/^OLUTION AT A MICH KUl-IBER OF 1.5 By Dean E. Chapiiian end Edward V! . Perkins Tests were conducted to detc-nnine tho. effects of viscosity on tho dro.g and tase pressvire chai-actcrietics of various 'bodies cf rovolution at a Mach number cf 1.5. Eio aodols were tested lioth with saooth surfaeos and with, roughness added to ovalua.to the effects of Eoj'Tiolds number for Doth laminar and turbulent boundary la.yers . The principal geometric variables investigated were after— bodj- shape and length-diameter ratio. For moat models, force te^t^ and base pressure measurements wore made over a range of Soynolds numbers^ based on model length, from 0.6 million to ^.0 millions. Schlieron photographs vrorc used to analyzo the effects of viscosity on flow scpara^tion and shock— wave conf igiuration near the base and to verify the condition of the boundary layer as deduced from force tests. Tlie results are discussed and compared with theoretical calculations . Tho results show that viscosity effects are large and depend to a groat degree on tho body shape . The effects differ greatly for laminar and turbiilent flow in the boundary la.ycr, and within each regimo depend upon tho Eeynoldo number of the flow. Laminar flow was found up to a Eoynclds number of 6.5 millions and may possibly exist to higher values. Tlie flow over the aftorbod2/ and tho shock -wa,ve configuration near the baso are shown to be very much diff extent for laiiinar than for turbulent flow in the boundary layer. The base pressure is much higher with the tiir-bulent layer than with the laminar la.ycr, result- ing in a negative base drag in some ca.se s. TiiO total dra.g character- istics at a. given P.eynolds number are affected. ccnGidera.bly by the transition tc t-urbulent flow. The fore drag cf bodies without boat tailing or of boo.t-tailed bodies for which the effects of flow separation arc negligible can be calculated by adding the skin-- •friction drag based upon the assumption of the low— speed friction characteristics to the theoretical wave drag. COHPIDSIWIAL COlfiTDiiHTI^-L imCA B.M No . AYASla For laiainar flow in tho bounder;- I'l.yor tho offocts of virrvinj the Ro'TiGldG nurAer were foiind to be large, approxi^iatel^ doiil)lln<2 the base drag in man;' cases and increasing the total drag sbout 20 percent over the P.ejTiolds maaber i-enge investigated, foi- tiirbulent flow in the boundary layerj the effects of vaj^^ying the He^Tiolds number usually changed the base drag and total drag coeff: cients considerably. IK'IEODUGTION The effects of viscosity on the aer'^dyaa^aic characteristics of bodies moving at low subsonic speeds have been known for many years and have been evaluated "oy numerous investigstors. Tlae effects of viscosity at transonic speeds have been investigated only recently, and relatively large effects on the flow over air- foils are reported "oy Aclreret (reference 1) and Liepmann (reference 2) . Although the relative thoroiTghness of these two inveBtiga.tions has furnished a good start toward a satisfactory evaluation and under- standing of the effects of viscosity in transonic flow fields, still very little is Iniovm about the effects at pur'ely stipersonic speeds. The experiments reported in references 3^ ^j and 5 hava succeeded in evaluating the magnitude of the skin friction for supersonic flo'^rs in pipes and on ciirved surfaces. Soference 6 contains a small amount of data on the effects of Reynolds number on the drag of a sphere and a circular cylinder; however, those data are not appli- cable to aerodynamic shapes which are practical for supersonic flight. It has been generally assumed that the effects of viscosity are small and need be considered only whon determining tho magnitude cf skin friction. In reviewing past data for the effects of viscosity it was found that in many repoi'ts, such as references 7 and 8, tho model size was not statod, thereby rendering tho calculation of Reynolds number quite difficult. Preliminary tosts in the Ames 1- by 3-f not supersonic wind tunnel Ko. 1, which is a variable-preasuro tunnel, showed a relatively large effect of So^Tiolds number on tlio drag of bodies of revolution. The results of this cursory investigation were not reported because the magnitude of support interference was not Imown and because certain inaccuracies in the balance moasuremonts woro known to exist in the data taken at low tunnel prossuros . An investigation of v/ing— body intera.ction at supersonic speeds has boon conducted subsequently and tho results prosontod in roforonce 9. Because of tho support interference and tho balance ina.ccuracics noted at low pressures tho data presented therein of tho effect of Reynolds maibor on tho drag of smooth bodies are not sufficiently acc-oratc throughout the range of EojTiolds numbers for direct application to tho conditions of froo flight. CONFIDET'ITIAL NACA EM No. A7A31a CONFIDENTiAL 3 Since the effects of viscosity already were Icnovm to be relatively large at the outset of tliis invostigatiorij the p'orposs of the present research was made twofold. Tlie primary purpose was to develop an understanding of the Eiechanisn by which viscosity alters the theoretica.1 inviscid flow over bodies of revolution at supersonic speeds, and the secondary purpose to determine the magni- tude of these effects for the particular bodies investigated. i^JTAEATUS AHD TEST M3TH0D3 Vind Tunnel and Instrumentation A general description of the wind tunnel and the principal instrumentation used can be found in reference 9. Included therein is a description of the schlieren apparatus, which forms an integral part of the wind-tunnel equipment, and the strain-gage balance system employed for measuring aerodynamic forces . In order to obtain accurate data at low as well as high tunnel pressures, a more sensi- tive drag gage was used in the present investiga!tion than in the investigation of reference 9; however, all other details of the balance system are the same. For the purposes of ti.e present inves '■ligation, it is pertinent to add that the tunnel is equipped with three turbulence-reducing screens located in the settling chamber. The tunnel total pressure, the static roference pressure in the test section, and the pressure in the air chamber of the balance housing were observed on a mercury manometer. Because the differ- ence between the base pressure and the static reference pressure in the tost section is ordinarily too small (only 0.5 cm of m^rcur;' at low tunnel pressures) to be accurately road from a mercury, manometer, a supplementary manometer using a fluid of lower specific gravit;- was employed. Dibutyl phthalate, having a specific gravity of approximately I.05 at room temperatures, was used as an indicating fluid in this manometer instea.d of the conventional light manometer fluids, such as water and alcohol, because of its lower vapor pres- sure and its property of releasing little or no dissolved air when exposed to very low pressures. Models and Supports Photographs of the models, which were made of aluminum alloy, are shown in fig^jres 1 and 2, and their dimensions are given in figure 3. Models 1, 2, and 3 were each formed of a 10— caliber ogive nose followed by a short cylindrical section; they differ from one another only in the amount of boat tailing. The shape of the ogive was not varied in this investigation because the flow over it is not affected appreciably bj- viscosity. Models k, 5, and 6, vrhich differ COEFIDEWTIAL COHFIDEKTIAL . WACA EiM No, A7A31r from one another onlv j_n thiclmoss ra.tio, were formed oy parabolic arcs with the vortex at the position of maximiim thiclcncss. ?or convonionco, some of tho more important geometric properties of models 1 through 6 are listed in the f ollowina tahlc : Model 1 2 3 k 6 Frontal area. A(sq in) 1 .227 1 .227 1 .227 .866 1 ^758 •^ .k26 Nose Area- Longth- Base- half volume dinmotor area. angle ra.tio ::'atic ratio 0(dcg) A/(V)2/3 L/D i-.v-j'k 18.2 0.302 7.0 1.00 18.2 .309 7.0 .5:;8 18.2 .318 7.0 .3^8 11 3 .^05 8,8 .191 15.9 .33? 6.2 .186 21.8 M9 k.k .187 In a.ddition to tho a.hovc-montionod models^ severcl other iDcdicB were tested for corta.in specific purposes. Thus^ models 7 '"^nd 8 wore made unLisua.ll.y long so that tho skin friction would he a. largo portion of the mea,sured drag, thereby enabling the condition of the boundary layer to be deduced from force tests. Various substitute ogives, shown in figure 2(a), were made interchangeable with the smooth ogive that is shown attached to the cylindrical afterbody of model 8. These ogives were p^'ovided with different types and amounts of roughness and could be tested either alone or with the long cylindrical afterbody attached. V/hen the ogives were tested alone, a. shroud of the same diameter as the ogive wa.3 used to replace the cylindrical afterbody. Model 9j a body vrith a, conical nose, and model 10, a. sphere, were tested in order to compare the results of the present investigation with existing theoretical calculations and with the results of other experimenta.l investiga- tions. Models 11, 12, 13, and Ik- were constructed to determine the effects of tho length-~dianeter ratio for a fixed shape of afterbody. In all cases when a smooth surface was desired, the models were polished before testing to obtain a. svu-face as free from scratches and machining marks as possible . Tho models were supported in two different ways : by a rear support a.nd by a, side support, as shown in figures k, 5j Qnd 6. The rear support used in the majority of the cases consists of a sting which supports the model and atta.ches to the balance beam. A thin steel shroud encloses the sting a.nd thereby eln.mina.tes tho aoro- djmamic ta.v'e foi-fos. Use of the rear support allov;-s force data, base pressixre data, a.nd schlioren photogra.ph3 to be taken simultaneously. The side support which attaches to the lowoi" side of the model ' consists of a 6— percent— thick airfoil of straight— side segments a.nd 'i'° semiwedge angle a.t the leading and tra.iling edges The COKFIDENT'IAL KACA RiM Ko. A7A31a COEFIDENTLyL aide support was used to dotormino the effects of the axial variatj.on in test-section static pressure on "base pressure, and, in conjunc- tion with a dummy rear support, to evaluato tho effects of support intorf crcnco . Base pressure data and schlieron photographs can bo ohtainod vrhon tho side support is used. Test Methods The tests wore conducted at zero angle of attacJc in a fixed nozzle dcsienod to provide a uniform Mach nuraher of approxiaatoly 1.5 in the test section. For the positions occupied hy the different models, the free— stream Mach numhor aotually varied from l.k<^ to 1.51. This is somewhat lower than the Mach nvimher of tho tests reported in reference 9j which vrore conducted farther dovmstream in the test section. Before and after each run precautions were taken to tost tho pressure lines for leaks and the balance system for friction or zero shift, Each rii.n was made hy starting the tunnel at a. low pressure, usually 3 pounds per square inch absolute, and taking dcta at different levels of tunnel stagnation pressure up to a maximum of 25 pounds per square inch absolute. Because of the lag in the manometer system, approximately 15 minutes at low pressures and 5 minutes at higli pressures were allowed for conditions to come to equilibrium. The over— all variation in Eeynolds number based on body length ranged from about 60, 000 to 9-^ millions. Tno specific humidity of the air usually was maintained below 0.0001 pound of water per pound of dry air, and in 0I.I cases wss below 0.0003. In general, each body was tested with 3. polished surface and then later with roughness added to fix transition. As illustrated in figuro 2(a), several different methods of fixing transition on a body in a. supersonic stroam were tried. Tho usual carborundum method employed in subsonic research was not used beca,UBo of the danger of blowing carborundum particles into the tunnel— drive compressors. The method finally adopted was to cement a, I/8— inch- wide band of particles of table salt around the body. Ti:is method proved successful at all but the very low Reynolds numbers. On models 1, 2, 3, and 12 roughness was located one-eighth inch down- stream of the beginning of tho cylindrical section. On models k, 5, and 6 tho roughness wa.s placed k.^ inches from tho nose ^nd on model 8 one-eighth inch upstream of tho beginning of tho cylindrical afterbody. Models 7, 9, io, 11, I3, and ik were tested in the smooth condition only. COHFIDEKTIiM 6 COnFrDEHTIAL NACA HI4 Uo ATA31a. KSSULTS Sediiction of Tata The force data. :'ncluded :in this report have ^oeen reduced to the usual ccofficient form through division hy the prodUvCt of the fres-stroara i-imcraic presstii'o and the frontal area of the body. If it is desired to refer these coefficients to (volume)'"' " the necessary conversion factors can "bo found in the table of the geoaotric properties of the models included in the section on models and supports In ep.ch casc^ conditions Just ahead of the nose of a, model are ta.kon as the free-stream conditions. The measurements of the pressure on the base of each model are referred to fro.; stream static pressure and made dimenaionless through division by the free— stream dyn&mic pressure. Thus, the base pressure coefficient is calcula,ted from the equation t^-D - Pi PB -^'- (i) wncre PS base pressure coefficient p-g prossur-e a.cting on the ba.se Pi frce--stroara static pressure qi fi^ee— stream dynamic pressure -The d;momiG pressiu-e is calculated from the isentroiiio relation snips. A small experimentally deter^mined correction is applied for the loss in tota.l pressure due to condensation of watur vapor in the nozzle. Tl'ie Reynolds numbe-r is based upon the body length a.nd is calcula.ted from the isentrorjic rcla.tienship3 using Sutherland's formula, for the variation of viscosity with the temperature of the air. It is convenient to consider the force due to the base pressure as a, sopara.te component of ohe total dra.g • Accordingly, the base drag is referred to the frontal area, and in coeffici^.'nt form is given by CB3 . PB^Si,, (2) CCriFIDSKTIAi MCA RM No. A7A31a. COTIFIDEriTTAL where A3 area of base A frontsl area of the liody The fore drag is defined as the sirni cf all drag foi'ces thet act on the "bod^ surfsce forward of the base. Hencej the coefficient is given by Cj>p = CD - Cd^ (3) wh-ro Cd is the total drag coefficient and .Ct,„ the fore drag coefficient. The concept of fore di^ag coefficient is useful for several reasons. It is the fore drag tha.t is of direct inportance to the practical designer when the pressure acting on the base of a body is altered by a, jet of gases from a power plant. Considering the fore drag as an independent component cf the total drag greatly simplifies the drag cnalj''sis of a given body. Finally, the fore dragj as will be explained later,, is not affected appreciably by interference of the rear supports used in the investigation. Since the nozzle calibration with no model present showed that the static pressixre along the axis of the test section is not constant (fig. 7)^ the meas^ored coefficients have been corrected for the increment of dra,g or pressure resulting froai the axial pressure gradient. A detailed discussion of this correction is presented in appendix A^ and the experimental j^istif icaticn shci-m in figiJires 8 and 9- Precision The table which follows lists the total uncertainty that would be Introduced into each coefficient in the majority cf the results if all of the possible errors tha,t are known to exist in the measurement of the forces and pressures and the determination of free-stream Mach number and gradient corrections were to accuiralate. Actually the errors may be expected to be partially compensating, so the probable ina.ccura,cy is about half that given in the tabic . The sources and esti-mated magnitudes of the probable errors involved are considered a.t greater length in appendix B. The values in the following table are for the lowest and highest tunnel pressures and vary linea^rly in between The table does not apply to data that are presented in figures 12(b), I6, 17 and for models 4, 5, and 6 in CGKFIDEKTIAL 8 COIIFIDSMTIAL ITACA I>M Kc. A7A31a figi/vros 26(a) and 32(a) whore the possi'Dlo variation in tho 'aalanco calibra.tion constant laay increjaso tho limits of error as disci'.sscd in appendix B Majxamim value of Maximum value of C oefficient error ct lovost pressure error at highest p rjssuro Total drag ± {2.¥^ plus O.CQJ^) ± (l.l.^> plus O.OOif) Fore drag ± (1.$'' plus O.GOh) ± (0.6:5 plus O.OCli-) Base prossuro ± (CS"^ plus O.OO5) ± P.?^- plus O.OO5) Base drag ± [0.&:" plus 0.005(Ae/A)] ± [0.5:1 plus 0.005(Ab/A)] Effects of Support Interforoncc Previous to the present investigation an extensive series ef tests wa.s conducted to detorsiino the "ood;^ shape and suppox't combina-- tions necessary to eliBinato or evaluate tho suj)pcrt interf o.i-'oncc . Based upon the results obtained, a, summary/' of which a.ppcars in appendix C, it is "believed that all the di^a.g data presented herein for the models tested in the smooth condition is free from support interference effects with the exception of the data sho-vm in figure 30. For the models tested with rouglmess, the fore drag data are free from interference effects, but an uncertainty in the base pressure coefficient exists which may vary from a minimum of -O.OO5 to a maximum of ±0.015 for the different bodies. As a result, the base drag coefficients and total drag coefficients for the same test conditions are subject to a corresponding small uncertainty. Schlieren Photographs Since m\;ch of the ba.sic information contained in this report is obtained from schlieren photographs, a somewhat detailed explana- tion of their interpretation is in order. A tj'pical schlieren photograph taken with the knife edge vertical is shc\m in figure 10, The various features of the flow are designated in this photograph which shows the entire field of view of the schlieren apparatus. Other items, such as the natural gradients inherent in the glass and the horizontal and vertical reference wires mounted outside of the tunnel are also apparent in this and other photographs presented in the report. The horizontal strealis that appear on seme of the schlieren photo.graphs are a, result of oil in the tunnel circuit due to temporarily faulty gasketing in one of the main drive compressors. Tee mottled appearance of the background is believed to result from the varying density gradients in the boundary layer flow on the glass windows . The schlieren photographs were taken with the knife edge both horizontal and vertical. Density gradients normal to tho stream C0NFID3KTIAL MCA SII Wo. A7A31a COKFJDEKTIAL direction are detected with the kn?".fe edge hcrizcntEl^ whereas th:5se parallel t:; the stream direction are detected with the knife edge vertical. For the horizontal orientation the loiife edge was placed 30 that increasing density gi'adients in a doT-m'^rard direction appear as white areas on the photographs. For the vertical orienta.ticn the knife edge was placed (except for the photograph in firg. 10 and the e-phere photographs in fig. 20) so tha.t increa,sing density gradients in the donTistreani direction appear as white Theoretical Calciilaticns Although at present no theoretical method is availa.blo for calculating the oaso pressure and hence the total drag of a "body, several methods are available which provide an excellent theoretical standard to which the experimental neasurements of fore drag can hs compared. In this report the thooroticol fore drag is considered to he the sum of the theoretical wa.ve drag for an inviscid flow and the skin— friction drag corresponding to the t^-pe of boundary layer that exists on the body. A tj-pical Mach net and the corresponding pressure distribution for the theoretical inviscid flow over one of the boat-tailed bodies tested in this investigation is shown in fig-are 11. For purposes of comparison the pressiure distribution as calcula,ted by the linear theor;^ of von Kaiman and Moore is included a.s is the press^ore coefficient at the nose of a cone, the included angle of which is equal to tho angle between the surfaae tangents at the nose of the ogive. Hiis latter is obtained l:)j the method of rafcronces IC and 11, The wa.vG drag for many of the bodies tested was calcijlatod by tho method of characteristics for rotationally s^.inmotric supersonic flow as given in roforcnccs 12 and 13. In accordance with tho theoretical results of roferencu 1^^ tho fluid rotation produced by the very small curvature of the head shock wave was neglected. This proccdujre is justified experimentally in reference 8, where the theoretical calculation using the method of characteristics as prosentod in reference 12 are sho-^m to be in excellent agreement with tho mea.sujred pressure distributions for ogives with cylindrical afterbodies. The calculation of the skin-friction drag in any given case requires a knowledge of the condition of tho boundary layer. In tho cases for which the schlicren photographs and tho force tests indi cated that the entire boundary layer was laminar^ the dorvo of theoretical fore drag used for comparison with tho experimental results was obtained oj adding to the wave drag a. theoretical skin-friction drag calculated by using tho low speed skin-friction coefficients for laminar boundary layer flow a.t the Reynolds n-jmbor COKFIDSNTIAL 10 COIFZDSIJTL'J. MCA SM I'Jo . A/A31a ■based on the full length of the model. This procediu^e, vhlch is in accordance with reference 3^ gives the oc-aatlon CDf = Cfia^j(AF/A) (1;) where €■■£)£ skin— friction drag: coefficient for the model at the F.e;'molds n-aciDerj Ee, "ba.sed on the full length of the nodel Cf- low-speed skin— friction coefficient for laminar "boundary- lajer flow at Ee Ay wetted area of the model forward cf the hsse A frontal area cf the model For the models witii rouglmess added it was assumed thr.t the distui'hance cf the boundary layer resulting from the so It hand v/as sufficient to ca.use transition to a. trn'oulont boundary layer to occur at the hand. Tlie "Uieoretical 3kin--friction drag was then obtained by means of the equation CL-f = Cf^am .-f + ^^turb r ; ~ "^^^^-"^^ V"T / ^''' where Cf'-i^ low— speed skin— friction coefficient for laminar boundary-- Isyer flew at the effective SejTiolds number. Re', based on the length of the model from the nose to the point where the salt band was added Aiam wetted area of that portion of the model for^rard of the salt band '-^fturb lov-speed skin-friction coefficient for turbulent boundary- layer flow at the EejTiolds nucber He, based on tije full length of the model Cf'-turb low-spoed skin-friction coefficient for turbulent boundai-y- layer flow at the effective Reynolds number Ee' COKFIDfillTI/i.L NACA RM No. A7A31a cnKFIDErTTL^i H Tliis method of calculation presuses thai, the fized roiiglineas was of such a nature as to cause the tur-b-iilent boundary- -layer flow downstreaia of tiie point where the roughness was added to be the sa2ie as would have existed had the boundary-layer flow been turbulent all the way frcn the nose of the body. DISCUSSIOIJ Flow Characteristics Before analyzing the effects of viscosity en the drag of the bodies of revolution, it is convenient to consider qualitatively the effects on the general characteristics of the observed flow. In so doing it is advantageous to consider first the condition of the boundary layor characterized by whether it is laminar or tur- bulent and then the effect of var-iation in Heynolds nuabsr on flow separation for each typo oft. boundary layer. Once the effects, on flow separation, of the Seynolds nvjnber and the condition of the , boundary layer are Iniovm, the observed effects on the shoclc— wave ccnf igui-ation at the base of the model are easilj"" explained. Likewise, once the effects on flew separation and shock-wave conf ig^oraticn are Icnown, the resulting effects of viscosity on the foro drag, base drag, and total drag are easily understood. Condition of the boimdary lajsr.— Since results observed at transonic speeds "(references 1 and 2) have shown that the general flow pattern about a. body depends to a narked dsgros on the tj^e of boundary la.yer present, it is possible that the boundary- layer flow at supersonic speeds also may be of primary importance in determining the over— all aorod;>Tianic chars-cteristics of a, body. Consequently, the determination of the extent of the laminar boundary layer under normal test conditions is of fundamental importance . In an attempt to determine the highest HejTiolds number at which laminar flow exists on models tested in this investigation, a relatively long polished body (model ") was tested from a low pressure up to the highest tunnel pressui'e obtainable. In this case, the diameter of the shroud -t'/iiich encloses the rear support sting was made the same as the diameter of the body. Tiie fore drag measurements on this model ai-'e shovm in figure 12(a) . Since the skin friction is a relativclj"- large portion of the measured fore drag, the condition of the boundary layer can bo deduced from those force tests. The data indicate that the boimdary la.yer on this body is still laminar up to the highest obtainable Be^Ticlds number of 6.5 millions. The computed fore drag data used for comparison arc obtained by adding a laminar or t'orbulcnt skin- friction coefficient based on low— speed characteristics to the COI'IFIDSKTIAL 12 COKF'TDEIWT-AL MCA SiM IIo . ATA^^la cjcperinental wave drag of the cgival nose. Tliis latter ia dotGmincd "by subtracting from tho fcrc- drs,.£ data of figv^-c l6 the lov-spojd laminar skin— friction ccofficionts for tho smooth cgivo at tho higher Reynolds mmhors where the error, resultinc from tho assisap- tion of the low-speod cooff iciontSj is a. small percent of the deduced wave dra£^. Schlieren photographs from which the condition of tho boundary layer may ho observed are sho-!-m in figure 13 . Tl';oy confirm tho previous finding by showing that transition docs no'O occur on the body, but bogins a, ehort distcnoj dowristricii froa tho base of tho model, as indicated by arTu\r 1 in the phot".Traph. A close examination of the photographs in figViro 13 reveals that the beginning of transition (arrow 1) is located at the same point on the support shroud as tho waves (arrows 2 and 3) which oi-iginate from a disturbance of the boundary layer. It wes found by moa,suiX'mcnt3 on tho schlieren photographs that tho point of origin of these waves on the shroud and tho intersection with the shroud of tho bow wave, which has been rcfloctod by tho test-section side walls, coincide. This suggests that transition on the shroud is being brougiit about prematurely by the reflected bow waves. Addi- tional ovidonco that this is not natural transition is obtained in noting from fi,gurc 13 that tho point where transition begins does not move with a chango in F.ejTiolds number. If the model were longer than a. critical length, which is about 11 inches for the conditions of the present tests, these reflected waves would strike the model somewhere on the afterbody and premature transition would bo expected to £'iffect tho rosLilts. Figure 12(b) shows the results of the measurements of fore drag on a l6. 7-inch body (model 3), which is considerably longer than the critical length. Tnesc force data confirm the above conjecture by clearly indicating a partially turbulent boundary layer en the body even at R.-jTiolds numbers os low a.s 2 millions. The schlieren photcgrophs of the flow over this body are presented in figure ih . It is seen that, in this case also, the transition to tiirbulent flow (arrcw l) is located at the snmo point as the waves (arrows 2 and 3) originating from the dist'orbance of the boundary layer bj?- the reflected bow wave. Similarly, an additional small wave (arrow k) con be traood ba.clr to a disturbance of the boundary layer caused by a. shock wave originating from a very sliglntly imperfect fit of the glass windows in the side walls. Although tho maxiiaum possible extent of laminar flow thot may bo o:q)octod on bodies of revolution cannot bo deteniiined on the basis of the present tests boca,use of this interference from the reflected shock waves, the foregoing results show that, under tlio conditions of those tests, a laminar boundary layer exists over the entire surface of a smooth model about 11 inches long up to at least 6.5 millions Reynolds number. In comparison to tho values normally encountered at subsonic speeds, a Ro;-nolds number of 6.5 millions at first appears to be COWWEmUL NACA RM No. A7A31a COriFIDSKTIPi I3 somewhat high for raaintcnanco of laminar flow over a/body, unless favorable pressure gradients exist over the ontiro longtii cf that body. The pressure distribution over model 'i , shoi'm in figure V^, has been determined by superimposing tlio pressure distribution which exists along the axis of the nozzle with no model present upon the theoretical pressure distribution calculated for model 7 by the method of characteristics. The resulting prcssuire distribution shews that the pressure gradient is favorable over the ogive, but is actually- adverse over the cylindrical afterbody. This suggests that the stability of the laminar boundary layer at a. Mach number of 1.5 may be considerably greater than at low Mach niirabors . An increase in the stability of the laminar boundary layer with an increase in Mach number ha,s been indicated previously by the theoretical work of references 15 and I6, and is confirmed experi- mentally for subsonic flows by the results of references 6 and 17 as well as by the exper?jnental data given for airfoils in reference 15. Some of the experimental research carried out in Germany are in disagreement with these results. In fact, part IV of reference 18 reports tha.t the schlieren observations made in the supersonic wind tunnels at Kochel indicated that the Eeynolds mmiber of transi- tion to turbulent flow on cones was even less than the value for an incompressible flow with no pressure gradient. On the ba,sis of the description of the Kochel wind tunnels given in part I of reference I8, it appears that because of several fa.ctors the condi- tions of flow therein are somewhat adverse to the formation of laminar boundary layers as extensive as those that would exist in free flight. One of the more important of these factors is believed to be the large number of shock waves which originate from imperfections in the nozzle walls and disturb the boundary layer over the body. These shock waves ordinarily number about 15 and are readily visible in various schlieren photographs. (See reference 21, for example.) In order to cause the laminar boundary layer to become tur- bulent in this investigation, an artifice such as adding roughness vras necessary. In a supersonic stream, however, the addition of roughness to a. body also will increase the wave drag of thax body. The magnitude of the wave drag due to roughness was determined by testing with full diameter shrouding and no afterbody attached, first the smooth ogive, and then the ogives with various amounts and kinds of roughness added (fig. 2(a.)) . The corresponding fore drag measurements are shown in fig-ure 16. These data illustrate that little additional drag is attributable to roughness at the low Beynolds numbers v;here the boundary layer is relatively thick, but that an appreciable amount of wave drag is attributable to it at the higher Eeynolds numbers . For all subsequent resixlts presented, the amount of drag caused 'by the artifical roughness is subtracted from the measured da,ta taken for the bodies CCI>rFlDElWi;>i li^ CO^TFIT'aJTIAI. tested vith transition fixed. In order to calculate the amount cf drag caused Idj the rov-shneas for aiodsls of diajneters different frosi the ogives tested, it v;as assumed that for any model the increaient in dxag coefficient a.ttr it) vi table to the drag of the artificial roughness wa,3 inversely proportional to the diameter of the uodel, at the sta,tion at which the roughness was applied. The fore drag meesi^rsments of model 8, which consists of a cylindrical afterbody with any one of the interchan.jeaole ogives, directly attached, are presented in figure 17. These data, from which the drag increment due to tlie added roughness ha,s heen s^1'o— tracted as noted previously, show that the degree of roughness produced by sand- blasting the surface of the ogive is insufficient to cause transition at low F.eynolds number^.,; whereas, the roughness produced by the 3/l6-inch- or the 3/S-inch--wide salt band ca.used transition at all EejTiolds numbers. A vivid illusti-ation of the turbulent character of the boundary layer on those bodies with roughness added is given oy the schlisren photographs in figuore l3. The bound8.ry layer is beat seen in the photograph taken with the knife edge horizontal. A comparison of these photographs with those of laminai- bcundorj' layers (fig. 13.) for example) illustrates how the condition cf the boundary layer is apparent from schlieren photographs. Tl:8 results at transonic speeds reported in references 1 and 2 have shc'.vn tiiat the same changes in pressure distribution and shock- wave conf igioraticn brought about bj' transition due to inherent boundary-layer instability at high RejTiolds numbers can also be brought about at those speeds by any cf several means. The artifices v'sed in references 1 and 2 included fine-grain roughness, free- stream tv^'bulence, and a single large distm-bance; the resultln.g aerod^.Tiamic effects were the same, provided in each case the boundary layer was changed from laminar to turbulent. Consequently, no matter what causes the boundary layer to become tvc.-'bulen'u in free fligl-jt, it seems likely that, excluding possible small differences in skin friction, the resulting effects on the aerodynamic character- istics cf the body will be very nearly the same as if the boundary layer vro re made turbulent by roughness alone j a.s is the case in the- experijnents conducted in this investigation. Flow Sepa ration.— Changes in fiov,' sepai-ation brought about by changing the boundar^r-layer flow from laminar to tux'bulent alter the effective shape of the body, the shock— wave configuration, and also the drag. It is therefore essential to consider the effects on flow separation of both the condition of the boundary layer and the Eeynolds number. Tlie location and degree of separation of the la;iiinar boundary layer for the boat tailed bodies tested in the smooth condition COrJFIDEl^TLU, NACA mi Wo A7A3ia coKii'iDErrfniL 15 varied noticealDly witli the Keynolds niraber of flow. -Ths schlieren photographs of Model 6 in figure 19 are tj-pical of tl^is effect. Additional photogi-Ephc, presented in figuro 20, illiistrate the same phenomena in the flew over models 2, Z, and IC, each at two. different Heynclds numhsrs . In each case, as the Ee^'-nolds nimiber of the flow is increased, the separation decreases, the convergence of the wak:e increases, and the trailing shock wave moves forward. Separation of an apparently laminar boundary layer has "oQQn pointed out previously by Ferri in reference 19 for the tvro- dimensional supersonic flow over the surface of curved airfoils. The schlieren photographs therein indicate that a shock wave forms at the point of laminar separation. On the other hand, the schlieren pictures of the flow fields for the bodies of revolution testod in the present investigation, show no definite shock wave accompanying separation except for the sphere (fig. 20) in which case the shock wave is very weak indeed. It may be concluded, therefore, that a separation of the laminar boundary layer is not necessar-ily a.ccompanied by a, shock wave at supersonic speeds. The same con elusion for transonic flows has been drawn in reference 2 . It might be surmised tha.t the trailing shock wa.ve situated some distance downstream of the separation point is interacting with or, perhaps, even causing the flow separation b;;' virti;e of pressure disturbances propagated upstream through the subsonic portion of the wake and boundary la.yer. Some indication that this is not the case is given by the schlieren photogra,phs in figures I9 and 20 It can be seen from these photographs that the trailing shock wave moves upstream and the point of separation moves downstream as the Eeynclds number is increa,sed. It would logically be expected tha.x. this decrease in the distance between the shock wave and the separa- tion point would intensify any possible interaction between these two elements. The photographs show, however, that the degree of separa- tion actually decreases a.s the tra.iling shock wcve moves upstream. Tl;is suggests that the trailing shock wave does not have much influence on the laminar separation. Additional evidence which corroborates this conjectore was noted in the cour-se of the investiga,- tion of support interference, wherein it was found that if the diameter of the support behind models 2 and 3 was increased, the trailing shock wa.ve moved forward, but the base pressure and laminar separation did not change , On this basis it appears likolj'' that the cause of the laminar separation is not associated with a shock wave, btit with other phenomena,. In order to analyze more closely the details of the flow s-3pa,ra,tion, tiae pressure distribution along tho streamline just outside of the separated boundary la.ver was calculated for sevora.l flow conditions over models 3 and 6. The calcii.lations were made using the method of characteristics, and obtaining the contora" of the streamline just outside the separated boundary layer from enlargements of the schlieren photographs. Typical results from COIIF'IDErJTIAL 16 COKFIDEWTIAL NACA RM No, ATA^la these ca.lciilation3 for modsl 3 s-o presented in figure 21. It is seen tha.t the pressure on the outside of the boundary" layer is approxinatel;' constant, downstream of the point of separation, a,s is characteristic along the houndery of a ''dead-water region. The pressure along the line of separation can be expected to be approxi ina.tely equal to that in the dead water region, and hence, equal to the base pressui'e. A comparison of the calculated values cf the avorage pressure in the dead-water region with the measured values of the ba,se prsssui^e for several conditions cf flow ever models 3 and 6 is given in the following table: Calculated pressu^Tu coeffi- cient of dea,d Model Reynolds number water region Measured base pressure cosff; Icient -0 .06 — .12 — .11 — .13 3 0.6 X 10® -0.06 3 2.0 X 10® -.11 6 .6 X 10^ -.10 6 1.5 X 10° - 13 Tlio preceding results indicate that for laminar flow the ba,se preasur-e, at lea.st for bott- tailed bodies, is detormined 'by the degree of separation which occurs forward of the base. This suggests that, if a means can be f o\md to control the soparacion, the base pressure also can be controlled. The theoretical pressixre distributions on models k and 5 ^'^^ similar to the pressure distribution on model 6, which is shown in figure 22. In ea.ch case, the laminar separation observed in the Bclilioren photographs is located at a. point upstream of which tho pressure docroasos continually along the diroction of flow. For subsonic flow this condition ordinarily woiild be termed favorable and separation would not be expected. It thus appeal's tliat the separation phenomena, observed ar'e of a different nature from those which commonly result from a retardation of the fluid particles in the boundary layer. Fi:irthor research on this 3ubj--ct is necessary in order to gain a satisfactory^ understanding of che observed results. The findings of previous investigations in low-speed flows indicate that if a boundary layer which is normally laminar over the afterbody is made turbulent by either natural or artificial means, the resistance to separation is increased greatly. The tests on models 2, 3j ^} 5j and 6 with rougl-.ness addod show clearly that this is also the ca.SG in supersonic flows The two schliei^en photographs presented in figure 23 wore taken of model 6 with and without roughness added and arc typical of this effect. A compari- son of the two photographs shows that, without rouglmoss added, separation occurs near the pcint of maxim-am thickness, but if transition is fixed ahead of this point such separation no longer occurs . COKFIDEJITIAL MCA BM no. A7A31a COKFIDEKTIAL Shod:— we. vo conf igurat lor It is t.D "bo expected that the changes in flov scp'.retion due to changes in the condition of the 'boundary layer and in the Soynclds nujmoor of the flow will oring ah out changes in the shoclc- wave conf igiiration at the baso of a body. The schlieron photographs of figures 19 and 20, which shew hovr the losinar separa- tion doci-casos and the ccnvorgence of the valzo increases as the Ee^Tiolds number is increased, also shew that those phoncmona are acccinpaniod by a forward motion of the trailing shock wave . In genera,]., as long as the boundary layer is laiiiinar., the trailing shock wave moves forward as the BejTiolds nujnber increases^, but no major change in the shock— wave conf igui'-ation takes place. The shock— wave conf igia-ation with a. turbulent bcundary layer, however, is vury much different from the configuration with a laminar layer, as is illustrated ''oy the schlicren photographs of model 6, sho-vHi in figure 23- Such configuration changes due to the transition to turbulent boundary— layer flew correls.tc quite well with the angle 3 that the tangent to the surface Just ahead cf the ba.se malces with the axis of 3;>'a32etry. Figure 2k shows the changes in shock— wa.ve configuration for models 1 througlj t arranged in order of increasing angle p. It is seen tha.t, on the boat- tailed bodies vrith a, small angle P, the ti-ansition to a, turbulent boundary layer is accompa.nied by the a.ppearance of a weak shock wave originating at the base of the body (models k and 2) . For bodies with larger boat tail angles (model 5; "the strength of this W3.ve, hereafter termed the "base shock W£,ve," increases until it is approximately a.s strong as the original trailinvg shock wave. For even larger boat— tail angles, the base shock W3.ve becomes more distinct, a.nd eventually is the only a.ppreciable shock wave exist-- ing near the base of the body (models 3 a.nd 6) . In sLich a case, the compression through the base shock wave occurs forward of the base. Tliis, as will be shown later, greatly increases the base pressure and decreases the base drag. Since the change in shock- wave configuration caiised by the addition cf roughness is due to the greater resistance to flow separation cf the turbulent boundary layer, it may be expected that the above shock— wave conf igu.rations for "Ghe turbulent boundary layer vjill be obta.ined regardless of the cause cf transition. Compared to the phenomena observed with a laminar boundary la.yer (fig. 19), changes in the Reynolds number for a body with a turbulent boundary layer do not alter the shock wave corif iguration to any significant extent, because the turbulent layer, even at low Seynolds numbers, ordinarily does not separate. Tliis fact is evident in figure 25, which shows the schlieren photographs of model 3 a,t different Peynolds numbers with roughness added. Ko apparent change in the flow characteristics takes place as the Reynolds n'omber is increased. With a turbulent boundary la.yer, therefore, the effect on base drag of varying the Eeynolds number may be expected to be much less than with a laminar layer. COI\!FirE>JTIAL 18 COinriDEKTIAL KACA El-i Ho. A7A31a Analysis of the Drsg D'ita The qualitative effects of viscosity on flow sepai-ction and on shock-wave conf igxiration, which ha.ve "been discussed in the preceding secticns. provide the physical hasis for understanding the effects of varying the P.e^Tiolds niAiahor and changing the condition of the boundary layer on the drag coefficients of the various hodies tested. Fore drag.— The fore dra,!5 coefficients of models 1 through 6 with laminar flow in the 'boundary layer are shcvm in figure 26(a,) as a. function of the Reynolds numher. These data, show tha,tj ovei' the Eeynclds n^'Jinber range covered in the tests^ the fore di-ag of model 1 decreases ahout 20 percent, while that of model 6 increases aoout 15 percent. The fore drag of the other bodies does not change a.];ipreci&bly. The reason the effects of Seynolds number vary considerably with different bodj' shapes is clearl;'' illustrated b;' a. comparison of the measiired fore drags with the theoretical fore drags. In figure 27(a) the theoretical and mea,sured values of fore drag are compared for model 1, which has no beat tailing, and for model 3> whdch is typical of the boat-tailed models. From this comparison, it is seen that, as previovisly noted for other models without boat tailing, the thooretical and experimental fore drags for model 1 are in good agreement. The decrease in fere drag with increasing Beynolds number for the bodies without boat taaling is duo entirely to the decrease in skin— friction coefficient. For model 3^ which has considerable boat tailing, the curves of fig-ure 27(a) shew that the theoretical and experimental fore di'ags agree only a.t high Beynolds numbers. At the low EejTiolds numbers the measured fore drags are lower than the theoretical values because of the separation of the laminar boundary layer a.s previously illustrated b;^ the schlieren photographs in figures 19 snd 20. V/'ith separation, the flow over the boat tail does not follow the contour of the body, and the pressure in the accompanjring dead- water region is higher than it would be if the separation did not occur (fig. 21) . This makes the actual fore di-'ag lower than the theoretical value for a flow without separa- tion. At the higher Ec^'Tiolds numbers, tho sopai'"a.tion is negligible and the flow closely follows the contour of the body; henco, the theoretical and experimental fore drags agree. Tlio roa,son for the approximately constant fore drag of models 2, 3, ^, and 5> therefore, is tha.t tho changes duo to skin friction and flow separation arc compensating. For model 6 with a smooth surface, the fore drag shown in figure 26(a) rises rather rapidly at low Reynolds numbers because the separctlon effects for this relatively thick body (fig. 19) more than compensate for the changes in skin friction due to the variation of tho Ro;i-nold3 nixmbor. Figure 26(b), which shows tho fore drag coefficients of models 1 through 6 with roughness added, indicates that the fore drag for all tho bodies docroasos a.3 tho Reynolds number increases above a COI!FIDENTIAL NACA EM ITo. A7A31a CdtETDETITBi 19 Koynolds nvaaber of 1.75 nillions. Tnis is to oo expected, since with the change to turbulent "boundai^y layer and consequent elimination of separation, the onlj'^ factor remrininc; to influence the foi'e drac ■ coefficients is the decrease of skin-friction coefficients with increase in Bo:,T::olds numhor. Below a Reynolds niimher of 1.75 millions, howevur, the fore drac ^- ^H "thf^ models except model 1 increases with increasing He2."nolds numhor. The cause of this somewhat puzzling tehavicr is apparent upon closer examination of the data. Figure 27(1)) shows a comparison of the theoretical fore drags with the experimental values for models 1 and 3 with roughness added. The theoretical value for skin— friction drag was calculated assuming laminar flow up to the location of the roughness, and turbulent flow behind it. Tliis value of di^ag was added to the theoretical wave drag to obtain the theoretical fore drag. It is seen from f '.gvire 27(b) that for model 1 the cvirves of theoretical and experimental fore di-a.g ha,ve the previously indicated trend of decreasing drag with increasing EejTiolds number ove.r the entire range . However, for model 3^ which is typical of the boat-tailed bodies, the measured fore drag at low Reynolds nujnbei-s falls considerably below the theoretical value in the manner previously noted. The reason for this is evident from an examination of the achlieren photographs shown in f igui-e 28, which were t&ken of the flow over models 3 and 6 with roughness added. Tliey show that at the low SejTLolds numbers a flow separation siiailar to that observed for an undisturbed laminsjr boundary layer (fig. 19) is evident, and the resulting shoclc— wave configuration is characteristic of the config- uration foi" a laminar boundary layer rather than that for a turbu- lent boundarj^ layer. It appears tha.t, at the low Seynolds numbers, the amount of roughness added does not cause transition far enough upstream of the point for laminar separation so tha.t the free stream can provide the boundarj'" layer with the necessary additional momentum!! to prevent separation. The portions of the drag curves in which the desired transition was not realized ore shown dotted over the region in which separation was apparent from the schlieren pictures. For model 1, the schlieren photographs showed that at the low Seynolds numbers the amount of rouglmess added was suffi- cient to effect transition some distance ahead of the base, although not irmediately aft of the roughness. The agreement between the experimental and the theoretical results obtained by the use of equations (h) and (5) indicates that, at a Mach number of 1.5 and in the range of Re^/nolds numbers covered by this investigation, the familiar low— speed skin-friction coefficients can be used to estimate drag due to skin friction at supersonic speeds. This confirms the results of references 3j ^j and 5 and extends their application to the evaluation of skin— friction drag for supersonic flow on bodies of revolution. C0]VIFIDEIITI.'5iL :ITIAL NACA EiM TTo . A7A31a A comparison of the curves of fic-ures ■26(a) and 26i"o) shows that for- a given iDody at a, given vsliis of the Heynolds numher the fore drag with roughness added is consistently higher than the correspcinding fore drag of the SBiooth--sv.rfaced tody. In the general case, this over— all increase in fore dra,g is attrihuta-hls Doth to the increase in the slrin-friction drag of the tody and to the elimination of separation with consequent increase in the pressure drag of the 'boat tail. For model 1, which has no heat tailingj the increase in skin friction is the solo factor contribut- ing to the increase in fore drag. Ba se pressur e and base drag.— Figure 29(a.) shows the base pressure coefficients plotted as a ft^nction of the Reynolds minfocsr for Bodels 1 through 6, each with a smooth surface. It is evident from the data, in this figure that the effects of Reynolds nimlier on base pressure for a body with a. laminar boundary layer are quite large, In the range of Eeynolds numbers covered, the base pressiire coeffi- cient of model 1 increases about 60 percent, and the coefficients of models 2, 3^ STii. k more than double. The tbiclcor bodies, modeio 5 and &, do not exhibit such large changes in base 'pressure coefficient, for the coefficients apparently reach a maxiiaum at a. x-elatively low EejTiolds number, and then decrea.se with further increase in the SejTLolds number. Tho ba,se pressux-e coefficients for models 1 through 6 with roughness added are vshcwn in figure 29(b). Here again, the portions of the curves which correspond to the low Reynolds number region \rherein transition did not occur far enough upstream to prevent 3epara.tion are shown as dotted lines. Model 1 exhibits the lowest base pressure and model 6 the highest; in this latter case the base pi-essure is even higher than the free-stream sta.tic pressure. The physical reason for this is evident from the schlieren photograph at the bottom of figure 23, which shows that a compression through the shock wave occuj?s .just ahead of the base of model 6. Except for the laJrge changes in pressure coefficient a,t low Eeynolds niJinbers where the desired transition was not effected, the variation of base pressiu'e coefficient with P.e.^/nolds number is relatively small for the bodies with roughness added. From a comparison of the curves for the bodies with roughness added to the corresponding curves for the smooth-surfa.ced bodies, it is evident that a large change in the base pressure coefficient is attributable to the change in the condition of the boundary layer. In genera.l, the base pressures for bodies with roughness added are considerably higher than the corresponding base pressures for tho smooth-s-arfaced bodies. In the case of the. .boat-tailed bodies the' physical reason for this increase in the base pressure is the appearance of the base shock wa,ve, as shown in figure 2U, For model 1, which has no boat tailing, the mixing action and greater thickness of the t\i.rbulent boundary layer are proba,bly T-IACA EM ITo. ATA31e COriFIDIJJTIAL 21 responsitlo for the oboerved increase. The foregoing data shovf that tl;e effects of P.sjTiolds nruahsr and condition of the hcundary layer on the "oase preosiire of a hody moving at supersonic speeds depend considera-oly upon the shape of tbe ef cer- "body. In order to ascertain whether the effects of viscosity also depend u.pcn the length-diaiaeter ratio for a fixed shape of af tei-hody, soEe models of different length diameter ratios were tested and the data presented in fibres 3C'(a) and 3''3(h) which show the variation nf hass pressure coefficient with EejTiolds muaher. The data presented in this figure are not free of support interference. From these data it is apparent that the effects of viscosity on the haso pressure increase with the length-diameter ratio of the "body. It is to be noted that the "base pressure increases as the len^ith diameter ratio increases. This is somewhat at variance with the results of reference 20 (also reported in reference 18)^ which shewed an effect^ hut not a, systematic one, of length-diemotor ratio on the base pressiu'o of bodies without boat tailing. The ba.se drag coefficient can bo obtained from the base pressure coefficient of the models by using equation (2) . The base drag coefficients for the smooth- surfaced bodies are presented in figure 31(a) and for the bodies with roughness added in figure 31(b). These curves are, of course, similar to the corresponding curves of base pressure coefficient given in figures 29(a) and 29(b; . In this form the ordinates can be added directly to the fore drag coeffi- cients of figure 26 to obtain tl-^o total dra.g coefficient of a. given body. It is seen that the contribution of the base pressure to the total drag is ver.y small for models with large amounts of boa.t tailing, siich as models 3j ^j 5j and 6. Total drag.- The total drag coefficients for models 1 through 5 with smooth surfaces are shown in figi-i-e 32(a) as a function of Se^'nolds number- Eiose data, show that the drag coefficients of both models 1 and 2 v.'ith a laminar boundary layer increase a little over 20 percent from the lowest to the highest value of Bcj'nolds numb'-;r obtained in the tests. The other models exhibit somewhat smaller changes. The data presented in figures 26 and 3I indicate that the principal effect controlling the vajriation of total drag with HejTiolds number for laminar flow in the boundar;" layer is the effect of Reynolds number on the base drag of the bodies. For the special case of highly boat-tailed bodies, however, this effect is of little relative importance because the ba.se drag is a small part of the total drag. In such ca.ses, the over all variation of drag coefficient is due almost entirely to the variation of fore drag with SejTiolds number. Figure 32(b) shows the total drag coefficients plotted as a function of the ?.e;mclda number for models 1 tiirough 6 with rough- ness added. Again, the portions of the curves that are oho-^m dotted COKFIDSlTTI/^i 22 COJIFIDENTIAL IIACA EI.^ No. A7A31a represent the Se^/nolds nvziher region in vhlch tlie amount of roughness added is insufficient to csuse transition far enougii upstream so that separation is prevented. All the curves have approximately the sane trend, the ever— all effect on the drag coeff icients oeing a.hout I5 percent or less fcr the various "ocdies. A comparison of the curves of total drag for bodies with rough- ness added to the corresponding curves for "bodies with smooth surfaces shows a.n interesting phenomenon. At the higher SejTiolds numhers the drag of models 1 and 6 is actually decreased slightly hy the addition of roughness, in spite of the corresponding inci-ease in skin— friction drag. The rea,son is, of courrse, that the "base drags are very much lower for the turbulent boundary layer than fcr the laminar. The drag coefficients of the other "bodies (models 2, 3, k, and 5) are somewhat higher with rouglmess added, "because the increase in friction drag of "the tur"bulent "boimdary layer is greater than the decrease in "base dreg. The importance of alwa;'/s considering "both the F.ejTiolds nurfoer of the flow and condition of the boundary layer is ilJ-ustrated by the total drag characteristics of model 2. For example, if model 2 were tested with a turbulent boundary layer at a Sejniolds number of 2 millions, the drag would be about 35 percent higher than if tested with a laminar boundary'' layer at a. Eeynclds number of one-half million. Although discrepancies as large as these have not been reported as yot in the drag data from different supersonic wind tunnels, certain consistent differences, varying from alsout 5 to 25 percent, have been reported (reference 21) in the drag data of similar projectiles tested in the Gottingen and the Kochcl tunnels. Although in reference 21 the discrepancies between the two tunnols wore attributed only to the variation in skin friction with Eo;molds ntanbor, it appears from the results of the pres-jnt investigation that such discrepancies are attributable primarily to diff3rences in flow separation and base pressiu-o. A comparison of the effects of viscosity for pointed bodies with the effects fcr a blunt body shows clearly that body shape must be considered, and- that conclusions about viscosity effects based upon tests of blunt bodies may be completely inapplicable to the aerodynamic shapes which are suitable for supersonic flight. For oxamplo, in tho case of a sphere at I.5 Mach num-ber with an over- all Eeynclds nvimbor variation of from 7-5 x IC" "to 9.0 x 10^, the agroomcnt between the drag data from Gottingen (reference 7), Pocnom^mdo (rofercnco- 21), and the present wind tunnel is within 1 percent of tho values measured for free-flight (references 7 and 22) . It is evident that the effects of viscosity on the drag of a sphere arc quite different from the effects on tho pointed bodies tested in this investigation. COMTDEJITIAL NACA H-I No. A7A31a COJJFIDSTJTIAL 23 C0NCI.U3I0KS The conclvtsions which I'oirLcnv apiDly for a I-!ach nuiaber of 1.5 and at RejT^olds nuribers cased u;rion model length up to alDout J) idillions for bodies of revolu^.ion similtir to the ones tested. 1. The effects of viscosity differ greti.:ly for laminar and tui'bulen- flow in the boundary layer, and within each regime depend u'oon the Se^TiClda nunber of the flow and the shape of the body, 2. laminar flow was found on the smooth bodies up to a EejTiolds nrjiber of 6.5 millions exxd i!B,y possibly exist to considerably higher values . 3. A comparison boween the teat results for laminar and for turbulent flow in the boundary layer at a fixed value cT the EejiTiolds number shows th8,t: (a) The resistance to separation with tvjrbulent i'lo\T in the boundary layer is much greater. (b) The shook— wave coni'i£'uration near the base depends upon the tj-pe of the boundary— layer flow and the relative degree of boat tailing. (o) The fore drag coefficients with tuxbulent boun.dary layer ordinarily are higher. (d) The base pressure is much higher with -he ti.-jrbulent boundax-y layer. (e) The total drag is usually higher w:" th the tiorbulent botmdary layer. h. For laminar flow in the boundary layer the following effects were fouiad: (a) The laminar bouxidary layer sepai-atss forv:ard of the base on all boat-tailed bodies tes ..ed^ and the position of separation varies noticeably wi ch Beynolds number. Laminar seriaration is not necessarily accom'oanied "oy a shock wave originating from ohe point of separation. On many of the models the separation is located in a region \ipstream of which the -nresjsure continually decreases in che direction of the flcAT. (b) The trailing shock vrave moves forward slightly as the Eej/nolds nurr.ber is increased, bu". no significant change takes place in the shock— wave configuration near the base. COKFIDErTTIAL 2l| COrlFIDSUTIAL KACA SJ-i Ho. A7A?la (c) With increasing ?.o^•nold3 n-aiilsors, tho fare dra,g cooffl- cionts incroasG for highly Dcat— tailod hc-dlcs rnd dGcroasG foi* todies without hoat tailing. For aodGr- atolj"- "boat— teiiod "bodios the variation of the fore drag coofficijnt with ";G."nold3 nurihor is rolativjl;r small. (d) Tiio haso pross'oro of tho "boat— tailed hodios -s controlled hy the laainar 3opara.ticn snd changes inorkodly with Sej-nolds nvinbor. Foi-- hodios with the same aftorhcdj' sha.pc, the base pressure also doponds upon the length -disnc tor ratio of tho hody. (e) Total dr".g varies considerably with Sc^Tiolds nviaber. changing more than 20 percent for several of tho models . 5. Fox" tu^.-bulvnt flow in tho boundory layer the following effects Were found: (n) Separction does not crdinrrily occur. (b) Tho shock— wave conf igura,tion no?.r tho hose does not change noticcablj'" a^s tho Hoynolds niraber changes. (c) Tho fore drag coefficients decroaso slightly as the Ecynolds number is increased. (d) The base pressure changes very little- with changing Eoynolds n-omber. (e) The totr^l drag decreases as tho Hcj^^iolds number is increased . Amos Aeronautical Laboratory, national Advisory CoEinittce for Aeronautics, Moffott Field, Crlif. C0I3FIDEUTIAL NACA HiM No. A7A31a CCRFIDSvTIAL 25 APPSroiX A VASIATIGII 07 TSST-3SCTI0IJ STATIC PKESSURE Since the static pressure with no model present veried along the axis of the test section as shcvn in figure 7, it was necessary to apply a correction to the mcasiu'ed .coefficients to account for the increment in drag or presstire resulting from this axial pressure gradient. Although the axial variation of test -section static pressiure is not monotonic, the pressiu-as at the do'-mstreain end of tha test section are uniformly lower than the pressures of the vip— stream end where the nose of the models are ordinarily placed. This means that the actual pressure exerted at e. given point on a "body is lower than it would he if the ambient pressure gre.dient were zero as it is in free fligiit. Tlse gradient corrections are calculated on tlie assumption tha,t the magnitude of the pressure exerted at an arbitrary point on the body in the timnel is lower than it would be if no gradient were present by an increment equal to the amount which the static pressure decreases (with no model present) from the position of the model nose to the position of the arbitrary point. It is not necessary to include the corresponding axial variation of djniamic pressure in the corrections since it varies only -0.2 percent from the moan test-section value used in all calculations. The corrections to the measured coefficients of model 1 located 2.5 inches downstream from the reference pressure orificoj for example _, amount to +0.012 in fore drag coefficient and -0,026 in base drag coefficient; the corresponding percentages of the umcorrected coefficients of fore drag and base pressure are 12 and 15j respective!;"-. Because the gradient correction is rela.tivoly large in the present tests and apparently has not been applied in the past to svipersonic wind— tunnel data., an experimental justification of such thooretical corrections is in order. The validity of the corrections as e.pplied to f ci-e drag is confirmed by tests on model 9j which consists of a, conical nose with a 20° included angle and a short cylindrical afterbody. The theoretical fore drag of this bed;-, vmich is equal to tho sum of the wave and friction drags, can be easilj' calculated as a function of Reynolds miaber. The wave drag of tho conical nose is given accurately by the experimentally confirmed calculations of Taylor and Maccoll (references 10 and ll) . Tlie fricticnal drag can be calculated using the low— spoed laminar skin- friction coefficients In accordance with references 3 snd 11, since the boundar;- layer was completely laminar over this model. A com- parison of the corrected and uncorrected fore drags with the theo- retical fore di^ag is shovm in figiu-e 8. The corrected fore drag coefficients are seen to bo in gcjd agreement with tho theoretical values; whorcas tho uncorrected data, fall below tho wave drag at high tunnel pressures. Tiiis latter condition, of course, represents an impossible situation for a. body without boat tailing, COIIFIDEHTIAL 26 CCiaTOSITTLAL NAGA PJVi Ko . A^A31a In oi'der to check experiaentally the valld:lt.y of the correctioris as applied to the nes.s'ie-ed Lase pressi^^rej acdsl 1 was tested on the side support a.t five different positions along the axis of the test section. Because the support system remained fixed relative to the ■faod^^j the interference of the support is the sane in each case^ hence , any discrepancies in the measured ha.se pressures at the various positions are atticutable only to the pressure gradient along the tannel axis. Figure 9 shows that the uncorrected hase pressure data taiien at xhe five different positions differ oj at out 25 percent^ hut the corresponding five sets of corrected data fall within about ±1.5 percent of their mean, thuG cor_fir2iing the validity of the ccrrecxion. COICTIDSI^ITIAL riACA EM No. A7A31a CCI3FIDEKTIAL • 2? AP?EI©IX B Ills accuracy of the results Dresented ca.n oe estinatod b J considering the possible errors that are kno-i'm to be involved in the aeasui'enent of the forces and pressijuresj and in the determina- tion of the free--stream Mach ni^ber and gradient corrections. The force measurements are subject to errors from shifts in tho balance zero due to teraperature effects, and also from a shift in the ccJ-ibration constant. The zero shift, which is less than -1 percent of the force data at low pressures and less than ±0.2 poi-cent at high pressures, was chocked periodic?!!/ dj running the tunnel througl:; the complate temporature range with no force a.pplijd to the balance. In the majority of cases the variation of the balance calibration constant, which was checl:ed before and after ea.ch series of tests, permitted a possible deviation of ±0.3 percent in the force data. All data presented in figures 12(b), l6, ITj and the data for models ^, ■ ?, and 6 in figr-ires 26(a) and 32(a) were obtained during a. pei-iod between two consecutive balance calibrations for which the constant differed by 6.4 percent. A comparison of the data obtained during this period with theoretical results and with the results of subsequent reruns of some of the srme models indicates that the change in balance calibration occured before the data in question were obtained. Tlie results in the aforementioned figures were therefore computed on the basis of the later calibration. It is estimated that the maximvmi error in the balance calibration constant for these results is at worst no greater than +0.3 "to —3 .0 percent. The pressure data, including the dynami-^ pressure^ are subject to small erroi-s resulting from possible inexact readings of the mercu:ry manometers. The base pressiore data, are also subject to an "additional error resulting from the small variation in the specific gravity of the dibutyl phthalate indicating fluid. At the most, these sources can cause an error in tlis total and fore drag coeffi- cients of about ±0.3 percent, and in the base drag coefficient of about ±C.c percent. Tlie error in d3T:iamic pressure due to the uncertainty in the free— stream Mach number is negligible, since the isentropic relation for the dynamic pressure as a function of I-'ach number is near a maximian at a Mach number of 1.5. For slender bodies of revolution the variation of the force coefficients \/-ith Mach number is quite small; hence, erroi-s resulting from the variation of free-stream Mach number from 1.49 to 1.51 ^'-^^ negligible. On the basis of the data, presented in figures 8 and 9, it is estimated that for all tunnel pressures the uncertainty in the gradient corrections to total drag, fore drag, and base pressure coefficients can cause at the most an error in these coefficients CC3MFIDEI^TL\L 28 CO?lFIDErTi;^-L KACA Wi IJo. ATA^Ie of ±0.00k, ±C..OCk,p.nd. ±0.005, rGspectively. It should 136 noted that in the talile on precision, presented in the section on results, this Gcurce of error, which is independent of t^mnel pressure, is expressed as an increment and not as a percentage of the measured coefficient. Previous investigations have shown that an uncertainty may be introduced in supersonic wind— tu.nnel data if the humidity of the tunnel air is very high. To determine the effects of this variable in the present investigation, the specific hiunidity was varied from the lowest values (approxiaatel;'' O.OOOl) to values approximately 20 tines those normally encountered in the tests. T^rag and base pressure measurements were taken en a body with a conical head and also on a sphere, T-ze res'ults showed no appreciable effect of humidity over a range much greater than that encountered in the prosont tests, provided the variation in test— section dj/namic pressure with the change in humidity was taten into account in the reduction of the data. It is believed, therefore, that the precision of the results presented in this report is unaffected by humidity. COriFID^ITIAL KACA EM No. A7A31a COrFIDEIWIAL 29 APPEIIDIX C EFFECT OF SUPPOET HVTTEPi'EHEITCS A rmowledge of the effects of support interference upon the data in cuasticn is essential to an understanding of its e>T)plica.— "bility to frcG flight conditions. Previous to the present invoati-- gation an extensive series of tests were conducted to detorTnino the body shape and support combinations necessary to evaluate the support interference . In genoralj it -vra,s found that for the models tested in the sraooth condition (laminar boundary layer) the effect of the rear supports used in the present investigation was negligible in all respects for the boat-tailed models 2 and 3 and was appreciable only in the be.so prossi;re measurements for model 1. On the basis of these results it is believed that the roar supports used for the other highly boat- tailed bodies (models k, ^, and 6) have a negligible eifoct on the drag of the model. For" model 1 combinations of rear support and side support were used to evaluate the effect of the rear support on the base px'essure . The evaluation was made on the assumption of no mutual interference botv/eon the rear support and side support, and was checked by the use of two different combinations of side support and rear support. The data, indicate that the assumption is j^istified within the limits of the experimental accuracy and that the corrected, intorf c-rence— free base pressures deduced by this method differ only slightly from those measured with the side support alone. For the bodies with roughness added (producing a. turbulent boundary layer) a complete investigation of the support interference was not made; consequently, a definite quantitative evaluation of the intorferonce effects for each body in this condition ca,nnct be given. From the data that were obtained it has boon found that the fore drag is unaffected by the presence of the supports used in the present investigation, but that a snail amount of interference is evident in the baso prossuro coefficient which may vajcj from a. miniraum of ±0.005 to a maximum of ±0,015 foj^ "the different bodies. This imcertainty in the base pressure coefficient results in a cor- respondingly small uncertainty in the baso drag coefficient and in the total drag coefflciont. COKFKEIvIIAL RESEARCH UBRARY COI-jFIDEITTI^i ITACA Hi-I No. A7A3I0 1. Ackoret^ J., Feldnann, ¥., and Eott, IT.: Investigations of Ccsipros.^icn Shocks and Bcundarj- Le,yor3 in Geses Ilovin-s at High Spood KACA TM No. III3, 19^7- 2. LicTJiaann, E.V.'.: Further Investigationc- cf the Interaction of 3oy-nd5r;' Lajor and Shock Wavos in Transonic Flow. Jour. Aoro . Sci., vol. 13, no. 12, Dec. 19^6. 3. Thoodorson, Thoodorc, and Rogiorj Ai-'th-or: Exporiinontg on Drag of Eovolving Disks, Cylinders and Streamlino Sods at High Syocds. HACA ACE No. L4Fl6, 19^4. k . Kocnan, Joseph H., and IToumnnn, Ernost P.: Friction in Pipes at Supersonic and Subsonic Velocities. WACA IN Nc . 963, 19^5. 5. Frosoll, W.: Flow in Smooth Straigl:t Pipes at YolO'-itios Abovo and Below Sound Velocity, MCA TM No.. 84l|-, 193'3 . 6. Ferri, Antonio: Influenza del K-ijanerc di Seynclds ai Grsndi Kumori di i4ach , Atti di Guidonia No. 67-69, 19^2. 7 l-Jalchner, 0.: Systoina.tischo Geschossiaesseingon im Windlcanal Lllienthcil-Gosellschaft fur Liiftfahrtf ors::hung, Borich I38, Toil 1, Oct. 19^1 6. Bach, F.: Druckvorteilungsmossungen an Goschossmodollon. Deutsche Luf tfahrtf erschun3, mi 6057, Mar. 19^5 9. Van Dyko, Milton D,: Ajrod.^Tiainic Characteristics Including Scale Effect of Several Wings r.nd Bodies Alone and in Combina- ticn at a Mach Fjmhor of I.53. IIACA RM IIo . a6K22, 19^6. 10. Maccoll, J.W.: The Conical Shock Wave Formed by a Cone Moving at a High Speed. Proc . of the Eoyal Sec. of London, s^jr. A, vol. 159, Apr. 1, 1937. 11. Taylor, G.I , and Maecoll, J.W.: The Air Pressure en a Cone Moving at H:^ Speeds, Proc. of the Koyal Goc . of London, sor. A, vol 139. Fob. 1, 1933 12. Sauer, P.: Method of Characteristics for Three-Dimensicnal Axially Syimetrical Supersonic Flows. KACA TM No. 1133, I9U7. COKFIDEMTIAL UAGA mi IIo. A7-A31a COWFIDE?JTL^ 31 13, Savior, i<.: ThGorotlfcho Einfiilii-vng in dij Gasdynf^Tijk. Bcrl""n, Springer J 1?U3 (RcQrintjd "by Edwards Eros., Ann Arbor, Mich., 19^5.) Ik. TDlLracin, \-J., and Sob£i"cr, M.: Botationssj-raractrischo Uborschallstroraimgon. Lillcntljal-Gcsellscliaft fur Livftfahrtforschuns, Bc-richt I39, Toil 2, Oct., 19i;l. 15. Allen, E Julian, and Ifits:>erg, Gerald E.: 'Tl^e Effect of Ccnpressi'bilitj on the Gro-srtii of tho Laninar 3oundai-y Ijayer on Low-Drac3 Wines and BodioE. NA.CA ACS, Jan. 19^13. 16. Lcc:), Lester, and Lin, Chia Chiao: Investigation of the Stability of the Laminar Boundary Layer in a Coapresaiblo Fluid. miCk TE No. III5, 19i^6. 17. Mctt, li.: Hochgo3cbwlndlgkoix3incs3"angcn an 5und— und Prof ilstangon ycrschoidencr DiJi'clULcssor. Lilientlial- Gosollschaft fur Lva"tfalu-tf or.?.chungen, Boricht 156, Oct. 19^2, 18. Gvcn, P.E.: Note on tho Apparatus and Work of tho W.V.A. Supersonic Institute at Kochel, 3. Germany. Part I, (LR.vs TII IX' . 1711) Oct. 19^15, &nd Part TI , (Pu^E IT: IIO. 17^2) Jan. 19^-6. (British/u.S. Restricted) . 19. Forri, Antonio: Expoririontal Results with Airfoils Tested in tho High-Speed Tunnel at Guidonia. I6\CA IM No. Qk6, 19^0. 20. Erdmann, S.: Widerstandsbostininuaig Von Kogcln und Kugcln aus d^.r Druckverteilung bci Uborschallgoschwindiglioit. Lilionthal-Gcscllschaft fiir L^^f tfaiirtf orschungon, Boricht 139j Toil 2, Oct. 1941. 21. Lehnort, ?,.: Systeraatischo i'oGstingen an neun einfachon Goscliossf orsien im Vergleich zu Mossungen der AVA-Gottingcn . Lili'jnthal -Gosellschaf t fur Lujftfahrtf orschungen, Boricht 139.> Toil 2, 19kl. 22. Charters, A.C., snd Tl-^omas, P.K.: Tho Aerodynamic Porfomance of Small Spheres from Subsonic to High Supersonic Volocitics, Jour. Aero. Sci., vol. 12, no. h, Oct. 19^5- COI!FIDEITTIi\L 1 FACA RM No. A7A31 a CONFIDENTIAL Figure 1 > 0) ft O Si .2* 'o a CONFIDENTIAL NACA RM No. A7A31 a CONFIDENTIAL Figure 2 a (o) Models used for boundary-layer tests and for comparison tests with other investigations. Figure 2. — Special-purpose models. CONFIDENTIAL 1 NACA RM \o. A7A31 a CONFIDENTIAL Figure 2 b (/') Models used to evaluate effect of length-diameter ratio on base pressure. Figure 2. — Concluded. CONFIDENTIAL HAOA Rlt Ho. A7A31a rig. 3 CONriOENTIAL I o z z o o z H t-l oo (DO 9 o n u z z o o z OOHFIDKlfTIAL Q o •a \9 Q O 5 Id X(3 o Q O 5 o ^ACA RM No. A7A31 a CONFIDENTIAL Figure 4 /^.MASr//v NACA A-10584 10-1-46 Figure 4.— Schematic diagram of model installation with rear support and drag gage. CONFIDENTIAL NACA RM No. A7A31 a CONFIDENTIAL Figure 5 >Q;a:gjw«57.;<,\wtwi» .~iewrn»-^3c 'Wf'f^^TS'-' NACA A-10585 IO-t-4e Figure 5. — Schematic diagram of model installed with side support. CONFIDENTIAL I NACARM No. A7A31a CONFIDENTIAL Figure 6 (a) Rear support. (/)) Side support. Figure 6. — Typical model installations. CONFIDENTIAL NACA A-10567 9-20--< \0 Ol 1* «a rH bOP -H ol -H rH n u m Vl .H O j:j O » h o O IH 3 do> a> -H T1 H T) -< -p a) O rH d rH O da (i-K a a P-a >. o VI d (D HO -p o O U (S H (D 1 3 (H +> U> h IS tH o ♦» -H » O a a 0. 9 \ / _ 5 51 \ / a \ / ■ o . V no. r • - o o d o » w M h Vl O-H VI h o o a: -^ \ ' O ■'H.Q 09 OrH o-e XI rH O i« f< Vl o o \ i 5- • K E B B \ c i r 3 r 1 ) CO o>c» lo CO I* rH rH rH CM ) ! ' i ) K C K CBS > 2. 4 IBS* X K K !) i > 1 □ O < t> + X r> pi I / y J. > > < Uj D O a 1 1 "^ i'o \ T^io-i a y O fel °°\ \ N c "" ^ 3 Nrt ;- t ^ o CO o o 1* o CM O o I a -rl o ''/"d-d 'exnssGjd eouejajei oq. pojiejei smesGid ofaBaB jo ^usfOTJjeoo CONFIDENTIAL +> a> 0) i IS ■H Vl ^^ > d +• o a r^ -rl d OJ-P » ■H O o K w^-^ V X \\ - v-^ PRESSURE DISTRIBUTION M = 1.5 FIGURE II. -TYPICAL MACH NET AND PRESSURE DISTRIBUTION FOR THE FLOW OVER A BOAT TAILED BODY. NACA A-10 6 83 10-21-46 CONFIDENTIAL I lAOA RM lo. A7A31ft Fig. 12 OOHriOENTIAL to t •J S 3 r-l o •3- s s Srj a- H 1 o SPg It* 43 H ti ii t-i 3a> oo OSS 2g ^! as o HI 1 1 O^ 1 o ■33 A, La3 i r \ &9 / o / ^ / o / r-l 00 / o / St) i-l o o / o f -lAS-2 / t^H* •*3 o C3 >v a a: "3 c o o I oj t-t « 3. hi to o ca CO o s 'do 'q.n8TOTj:jsoo Sbjp gjoj a O 3 i-l fi.1 3 1. 3-^ oa o ■rt 1 1 ' 5 . a p a » rH It += c O T-l u l3 1 *3 r-l a ^ i o a H too SPg 1 ^■3 S-2 1 a ' P 3 a ps^ / / ^ p. 3 I Lid r-l rH O / / 'o / n Ti / / / i X' O^ 1 ■^ o Vi o « B O o u O bp e-ri Vi T) V( O <-< 4 O O Crj ^ O >. « C ^ e o ■u PS-h ■ d M ■o -rt ja T) r-l 4 +> fl o a -H •«-4 CD -I a OS > »r-l I o 2 a* o Si 4> to oo C9 O ra CD o o CONFIDENTIAL NACA RM No. A7A31 a CONFIDENTIAL Figure 13 I Re=3.7 X 10". b Re=6.5 X IQs. iFlGURE 13. — Schlieren photographs showing laminar flow over the cyhndrical afterbody of model 7 at two values of the Reynolds number. Knife edge horizontal. CONFIDENTIAL XACA RM No. A7Am a CONFIDENTIAL Figure 14 («) Knife edge vertical. (b) Knife edge horizontal. Figure 14. — Schlieren photograph showing premature transition on the cylinder afterbody of model 8. Reynolds number 9.35 million. CONFIDENTIAL [ HAOA Bit lo. A7A31a riga. 15,16 C0N7IDK1ITIAL 1 i 1 j> D M ^ W M / 3<» oo Ol-l 1 / +> TJ "HtJ n 5= \ 1 / Id O c M rt a j3 3 ODO §1 \ >v \ / ■ 4^ iH +3 O ri IS g) . o CO o ■* C9 O iH iH M 4> ■ a o > o CO v< o *•« h h B e e d f4 3 bO o c 3 tM o CB U V. t3 Oi-<«-< o o o &e -r-l O -1 J3 bO ■HT) > I 1 1 ■H h » bO (5 (D 3 ID j3 a>. T\ h n p. +> O O- 1 1 a bO \ \ r-l \ 1 s VI 1 1 c o \ 1 1 4^ X) in \ \ \ r-4 «> O IS 5« IS r-l r-l I \ \^ \ ID C K ^1 c p.3 f< ) ) 1-1 o o o o H ■►< / / 13 3 / // / OS o C ■H /-■ \ \ o > \ J3 jrf^ ^ \ \ ^ ^ ^-^ \ / s O a o o -H r-l -P bO h o u m o 13 +» o 4 F4 U TJ P.O a r-l o o «> a a> o u t* la a CI ID tb/ld d . o o o i-l r-l I CONflDEKTlAL o I ■ j^r ,\ ■. .-, ._^£ARCH LIBRARY "A NACA BM No. A7A31a Fig. 17 CONFIDENTIAL ^-Roughneee added 16,7 'Shroud ^28 .24 0) -I .16 «M «H n o .12 .08 .04 ::^^ NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS Jixperimental wave drag plus turbulent frict 'Experimental wave drag ■plus laminar friction" ■^Experimental wave drag o Smooth surface— D 1/4 inch knurled band O Ogive completely sandblasted A 3/8 inch salt, band V 3/16 inch salt band ) 2 4 6 8 10 Reynolds number, Re, millions Figure 17.- Variation of fore drag coefficient with Reynolds number for model 8 with various amounts of roughness. CONFIDENTIAL 12 I NACA RM No. A7A31 a CONFIDENTIAL Figure 18 (a) Knife edge vertical. (6) Knife edge horizontal. Figure 18.- — Schlieren photographs of model 8 with transition fixed. Reynolds number 7.2 million. CONFIDENTIAL NACA RM No. A7A31 a CONFIDENTIAL Figure 19 Re=0.58 X 10^. Re=0.87 X lU". Re = l.l X lOe. Re = 1.4 X lO'-' pIGURE 19. — Schlieren photographs showing the effect of Reynolds number on laminar separation for I model 6. Knife edge vertical. I CONFIDENTIAL XACA RM Xo. A7A31 a CONFIDENTIAL Figure 20 Re=0.79 X lO'i. Model 2 ^^HMlKdi^^S.' 'jT-^crac^ Ee=1.2 X 10«. Re=3.8 X 10« Ee=3.8 X 10». Model 3 Ee=U.lU X lU". Re=0.45 X lO". Model 10 Figure 20. — Schlieren photographs showing the effect of Reynolds number on laminar separation for models 2, 3, and 10. Knife edge vertical. CONFIDENTIAL NACA RM No. A7A31a riga. 21,22 » CONi'IDEJJTIAL 1 3 > » C 3 '?, u i C CD O -H IB II a: 3 r-I J3 O CD j4 O-CD o d o a! --( o m M C ►JO c o a o ^1 O tH O ^-* 3 3 O Id m P ■i o '/ '''^ a o / ^ ^' •^ * o e a ^ ^ ^ Y \ ^ ^ y \ / ^ ,--' \^ >-" \ / o o to o OJ o I o CM Tb/td - d 'juefOfjjsoo ejnsaajj e Ti ID .X1 Oj 1 -H -(J t. O h ^ d d a bo a h TJ o a ol g a 4J « p 3 o o ^1 (S o h J3 l-H ■a c o / ; , 1 oo ^9« / ^ li OD £5 o a u P h •p >. o 3 \ a \ u> o It \ Br-t ■o M O 3 ■ K-H- B > O S U -ri p. " H r-J O o ■H a> to 3 JO 3 o rH \ T3 o o o at XI / / a ■< 3 / / y X ^ u o . 3 o IS a: to «> c; M O iH e^ ^^ r-ICO 3 • OO rH o * o to o CM o CM Tb/Td - d 'iU9TOfjj8oo sinsseij COHFIDENTIAL NACA RM No. A7A31 a CONFIDENTIAL Figure 23 (o) Laminar boundary layer, Re = 0.87 x 10'' (b) Turbulent boundary layer, Re = 0.87 x lO". IGURE 23. — Schlieren photograjDhs of model 6 illustrating the effect on flow separation of the condition of the boundary layer. CONFIDENTIAL NACA RM No. A7A31 a CONFIDENTIAL Figure 21 Model 1 Re = 3.8x lO". ^ = 0". Model 4 Re=4.0 X 10". ;3=8.55°. Model 2 Re=3.8 X 10°. (3=9.08°. Re= Blodel 5 ^2.7 X 10". ^2.13°. Model 3 Re = 3.8 X 10'\ ^=15.25°. Model 6 Re = l.l X 10". /3=16.75°. Turbulent. Figure 24. — Schlieren photographs showing the effect of turbulent boundary layer on shock-wave con- figuration at base of models 1, 2, 3, 4, 5, and 6. Knife edge vertical. CONFIDENTIAL NACA RM No. A7A31 a CONFIDENTIAL Figure 25 Re = 1.2 X lU''. Ee=2.6 X 10''. Re=3.9 X 10^ Re=5.1 X 10". Figure 25. — Schlieren photographs showing the absence of any effect of Reynolds number on the flow over the afterbody of model 3 with roughness added. Knife edge vertical. CONFIDENTIAL NACA I I Qq *q.u9T0f JJ900 3i3jp ejoj CONFIDENTIAL BACA Rli No. A7Aola rig. 27 CONriOEMTIAI, I 1 (3 O ■« V ID c m o -H r-t rH •H S o: ID to 9 la CD ■d r-i o o ♦> T3 O n to i-i o o -H — H- •a 3 rH ID 3 a CD O ^1 tv 0) r-l 3 If •a a a 1 1i 3 f "^ /I / 1 1 E- IH So rH > TS a) o d c o o 0) u o ui ^ K Q / ' I \ \ (S 3 D / 1 1 oo on Eh a o o 1/ d d — h" // (DO r- / / c a •o rH o • rH CrH c M iD-d P-o n h 1 a a- o w — d c — § i-i — o « TJ o a c O o ■a ^^ d c 1 C -H s M & to t o rH S H (S rH 4J o 3 3 rH p. 1 1 rH d C o • •H -H *> O a I y ' 1 SP ■a 1 1 ,''' i O VI e a +1 ■a a 1 s? > d r' iSP V J3 O 1 15 1 . (H d 15 1. o -H 4J _H T) a o o d o _ d o c ■rt o. +> .H • +J h O . O -H « h i w O C H O P .H M o O -H q imJ li a o •H M h O d — <; -6 6 — ^^ 711 1 b; Rougbneee added 4 1 -^ ■*^ n r 1 Hodel 1 \ /^ • D 2 3 (a) Smooth cond Ltio ■\ \ k / 4 5 S 1 J 1 1 12 3 4 5 Reynolds number. Re, mllllonB 12 3 4 5 Reynolds number, Re, mllliona Figure 29. Vajiation of base preeeure coefficient with Reynolds number for models 1, 2, 3, 4, 5, and 6 in the smooth condition and with roughness added. o o o s e 24 ^^ ^ / 0^ ^ C=^ — ^ _^^_ 20 ^ 7 r Uo in! n i./n m 4 .■^4 D L lartn IR L /O - fiO 08 c ] " 12 " 5.00 > • 13 • 6.00- ^ ■ 1 "7.00 7 * 14 • 9.00 A • 1 1 • ?.o i. 04 , 1 1 1 1 1 (a} Smootn condition 1 1 1 1 1 (b) Rou Shne IS a Idsd 12 3 4 5 Reynolds number. Re, millions 12 3 4 5 Reynolds number, Re, alllious figure 30.- Variation of base pressure coefficient with Reynolds number for bodies without boat-tailing but with different length-diameter ratios. CONFIDENTIAL NACA RU No. A7A^la .24 .20 Flge. 31,32 CONFIDSNTIAL m a o 16 .12 08 .04 .04 ^ >^ Not 1 1 1 1 ): Flagged Bymbole denot 1 1 1 1 e xerune > h 3 i V ^ 0^ t ' O _ A a .<> V N Uodel 1 " 2 " 3 " 4 « 5 " 6 —6 ^ ^^ ^y- A & y [^ -o— JT- ■ I /s^" _A- /L ^9— 9- F^ p^_ -0 D— 0- -o- > F^ t*-^ - ^ <> -0 (a) 8mo 0th 1 conditio 1 n (b) Roughn eee 1 added i 12 3 4 5 ReynoldB number, Rs, millions 12 3 4 5 Reynolds number, Re, mllllone Figure 31.- Variation of base drag coefficient with Reynolds number for models 1, 2, 3, 4, 5 and 6 in smooth condition and with roughnase added. ^:zz n o o o D^ / z '-' .16 ilATION&L A0VI80RY OOlOlITTES _rOR AERONAUTICS. _ .08 (^ .0 Model 1 .D o , V (aj Smooth condition (b), Roughness added 12 3 4 5 Reynolds number. Re, millions _L aug. _L 12 3 4 5 Reynolds number, Re, millions Figure 32.- Variation of total-drag coefficient with Reynolds number for modsls 1, S, 3, 4, 5 and 6 in ths smooth condition and with roughness added. OONriOENTIAI. UNIVERSITY OF FLORIDA 3 1262 08106 580 6 UNIVERSITY OF FLORIDA DOCUMENTS DERARTMENT T20 MARSTON SCIENCE UBRARY PO. BOX 117011 GAtNESVILLE.FL 32611-7011 USA ,1