1、REPORT 1036EXPEIUMENTAL INVESTIGATION OF THE EFFECTS OF VISCOSITY ON THE DRAG AND _.BASE PRESSURE OF BODIES OF REVOLUTIONBy Dm- R. CH.4PAKS and E!DWKRD.SRMW4RYTats were conducted to determine the efecfg of supersonic speeds.The experiments reported in references 3, 4, and 5 havesucceeded in evaluati
2、ng the magnitude of the skin friction forsupersonic flows in pipes and on rotating surfaces, but not forflow over a sIender body or an airfoil? Reference 6 containsa small mqount of data on the effects of Reynolds number onthe drag of a sphere and a circukr cylinder; however, thesedata are not appli
3、cable to aeroc however, aII other detaik of the balance sjwterowere the same. The tunnel total pressure, the static reference pressure inthc test section, and the pressure in the air chamber of thebalance housing were observed on a mercury manometer,Because the difference between the base pressure a
4、nd thestatic reference pressurein the test sectim wa9ordinarily toosnd (only 0.5 cm. of mercury at low tunnel pressures) to beaccurateIy read from a mercury manometer, a supplementarymanometer using a fluid of lower specific gravity ww em-ployed. Because of its lower vapor pressuic“andits propertyof
5、 releasinglittle or no dissolved air when exposed to very lowpressures, dibuLtvIphthalate, having a specific gravity ofapproximateely 1.05 at room temperat.ures; was used as anindicating fluid in thismanometer instead of the conventionallight manometer fluids such as water and alcohol.MODELS AND SUP
6、PORTSPhotographs of the models, which were made of rduminurnalloy, are shown in figures 1 and 2, and their climcnsionaaregiven in figure 3. 310dels 1, 2, and 3 were each formed of a10-caliber ogke nose followed by a.short cylindrical scc.iou;they differ from one another only in the amount of l.xM-ti
7、. The shape of the ogive was not varied in thisinvestigation because the flow over it is not, aflectcd aplrcci-ably by viscosity. Models 4, 5, and 0, which differ fromfrom one another only in thickness ratio, were formed byparaboIic arcs with the vertex ab the position of maximumthickness. For conve
8、nience, some of the more importantgeometric properties of models 1 through 6 arc listed in thefollowing table:FrontafModelit (an.)1L 227kn:-:z- 1.2273.-_-.d-_- : ;2;4-_-_-.-5- 1.7586- 3.426.Nowhalfangle(deg)le conducted farther downstream in thetest section.Before and after each run precautions were
9、 taken to testthe pressurelinesfor leaks and the baancesystem for frictionor zero shift. Each run was made by starting the tunrd ata Iow pressure, usually 3 pounds per square inch absolute,and taking data at dif7erent leveIs of tunnel stagnationpressure up to a maxiumm of 25 pounds per square inchab
10、solute. Because of the lag in the manometer system,approximately 13 minutes at low pressures and 5 minutesat high pressures were allowed for conditions to come toequilibrium. The over-all variation in Reynolds numberbased on boclylength ranged from about O,IOX1.(Yto 9.4X 106.!Che specific humidity o
11、f the air usually was maintainedbelow 0.0001 pound of water per pound of dry air, and in allcases was beIow 0.0003,In general, each body was tested with a polished surfaceand then later with roughness added to fix transition. Asillustrated in figure 2 (a), several different methods of fixingtransiti
12、on on a body in a supersonic stream were tried. Theusunl c.arbomnclurnmethod employed in subsonic researchwas not used because of tlie danger of blowing Carborundumparticks into the tunnel-drive compressors. The mctlmltially adopted was to cement a WindowDistance abwn+ream from fhe ref%rencep-eesure
13、 orifice,inchesHGCEE 5.kfsI mxkfon of the tic premure in the teet ssetion of rhe M.1.f! nozzkIMode f 9.t6- - -I2 - - _r _1.f2 n r, u c :0i tIL-Thwretkal wam Qz (a)LQ1QQ .16 .x - -0 - _- ,$ .12 ,k , L-7%eorefiwffaredrag,(wave akagplusestimafed-Theorefiwlwove dmg /uminur fricffon).08 . f.04P)o / 2 3 4
14、 5Reynolds fiumber,Re, millions(8) Uncorrected data(b) Correfted rota.FIGURE6.-_-_-_-fi-_-_7-_-_Reynoldsnufnbero.6X1062.OXICP. 6X1OJL 5X1CF“calculatedprewlre co.efficient ofdead-airregionO.06.11. 10.1331ea,w;edbasepreseurecoefficientO. 06. 12. 11. 13. The preceding results indicate that under certsi
15、n con-ditions the bas pressure for kninar flow o-rer highlyboattailed bodies is directly related to the separationphenomenon which occurs forwwd of the base. This sug-gests that, if a means can be found to control the separa-tion, the base pressure aIao can be controlled.Ee-o.mxlot.VISCOSITY ON THE
16、DRAG AT A MACH NUMBER OF 1.5 815-The theoretical pressure distributions on models 4 and 5are similar to the pressure distribution on model 6, -whichisble and the flow closely follows the contour of the body;hence, the theoretical and experimental foredrags agree.The reason for the approximately cons
17、tant foredmg ofmodels 2,3,4, and 5, therefore, is that the changes due to skinfriction and flow separation are compensating. For model6 with a smooth smface, the foredrag shown in figure 23 (a)rises rather rapidly at low Reynolds numbers because theseparation effects for this relatively thick body (
18、fig. 16)more than compensate for the changes in skin friction due”to the variation of the Reynolds number.Figure 23 (b), which shows the fomlrag coefficients ofmodel 1 through 6 with roughness added, indicates that theforedrag for all the bodies decremes as the Reynolds num-ber increases above a Rey
19、nolds number of 1,75X 10.This is to be expected, since with the change to turbulentboundary layer and consequent ehnination of separation,the only factor remaining to idluence the fredrag coefi-”cients is the decrease of skin-frict.iou coefficients with in-crease in Recynolds number. Below_ a Reynol
20、ds numberof 1.75X 10“, however, the.foredrag of all the models exceptmodel 1 increases with increasing Reynolds number. Thecause of this somewhat puzzling behavior is apparent uponcloser examination of the data.Figure 24 (b) shows a comparison of the theoretical fcwe-drags h the experimental values
21、for models 1 and 3 withroughness added. The theoretical value for skin-frictiondrag was calculated assuming Iaminar flow up to the loca-tion of the roughness, and turbulent flow. behind it. lllisvalue of drag was adcled to the theoretical wnvb drag toobtain the theoretical foredrag. It is seen from
22、the corresponding per-centages of the uncorrected CmfEc.ientsof foredrag and basepressure are 12 and 15, respectively.Because the gradient correction is relatively Iarge in thepresent tests an experimental justification of such theoreticalcorrections is in order, The validity of the corrections asap
23、plied to foredrag is confirmed by tests on model 9, whichconsists of a conical nose with a 20 included anglo and ashort cylindrical afterbody. The theoretical foredrag of thisbody, which is equal to the sum of the wave and friction dragscan be eily determined as a function of RcynoMs number.The wave
24、 drag of the conical nose is given by the calcultitionsof Taylor and Maccoll (references 10 and 11). The frictions.1drag can be estimated using the low-spmd la.minar skin-h-iction coefficients, since the boundary layer was complctdykunimu. over this model. A comparison of the. corrcctccland uncorrec
25、ted foredrag with the theoretical forekag isshown in figure 6. The corrected foredrag coefficients aroseen to be in good agreement with the theoretical vrdtl.;whereas the uncorrected data fall below the wave drag athigh tunnel pressures. This latter condition, of courac, rcp-reeentsan impossible sit
26、uation for a body without bonttailing.In order to check experimentally the validity of the colTcc-tions as.applied to the measured base pressmw,model 1 wastested on the side support at five different positions along theaxis of the test section. Because the support system re-mained fixed relative to
27、the body, the int.erfcrenc.eof thesupport “isthe same in each case, hence, any discrepancies inthe measured base pressures at the various positions amattributable only to the pressure gradient along t.hc tunnelaxis. F3gure 7 shows that the uncorrected l.msc pressuredata taken at the five different p
28、ositions differ by about25 percent, but the corresponding five sets of corrcckd datafalI within about +1.5 percent of their mean, thus confirmingthe validity of the correctiori.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-EXPE7TAL INKESTIGATTON OF
29、 TEE EFFECTS OF VISCOSITYAPPENDIX BPRECISION OF DATAThe accuracy of the results presented can be estimated byconsidering the possible errors hence, errorsresulting from the variation of hee-streti.m Mach numberfrom 1.49 to 1.51 are negligible.On the basis of the data presented in figures 6 and 7, it
30、 isestimated that for alI tunnel pressures the uncertainty in t-hegradient corrections to tohd drag, foredrag, and base pres-sure coefhcients can cause at the most an error in thesecoefllcients of +0.004, +0.004, and +0.005, respectively.It should be noted that in the table on precision; presentedin
31、 the section on results, this source of error, which is indpendent of tunnel pressure, is aqressed as an incrementand not as a percentage of the measured coefficient.Previous investigations have shown that an uncertaintymay be introduced in supersonic wind-tunnel data if thehumidity of the tunnel ai
32、r is wry high. To determine theeffects of this variable in the present investigation, thespectic humidity was varied bmm t-he lowest vtdues (appro-ximately 0.0001 ) to values approximately 20 times thosenormally encountered in the tests. g and be pressuremeasurements wwe taken on a body with a cotiw
33、d head andalso on a sphere. The results showed no appreciable effectof humidity over a rmge much greater than that encounteredin the present tests, provided the variation in test-sectiondynamic pressure with the change in humidity -was takeninto account in the reduction of the data. It is believed,t
34、herefore, that the precision of the remdta presented in thisreport is unaffected by humidi.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-828 RllPORT 1036-NATIONAL ADVI”RY COMMIti%1313FOR AERONAUTICSAPPENDIX cEFFECT OF SUPPORT INTERFERENCEA knowledg
35、e of the effects of support interference uponthe data in question is easential to an understanding of itsapphability to free-flight conditions. Previous to the pres-ent investigation an extensive serk of tests were conductedto detmmine the body shape and support combinationsnecessary to evaluate the
36、 support interference.In generaI, it was found that for the models tested in thesmooth condition (laminar boundary layer) the effect ofthe rear supports used in the present investigation wasnegligible for the boattailed models 2 and 3 and was appre-ciable only in the base pressure measurements for m
37、odel 1.For model 1, combinations of rear support and side supportwere used to evaluate the effect of the rear support on thebase pressure. The evaluation was made on the assumptionof no mutual intmference between the rear. support andside support and was checked by the use of two differentcombinatio
38、ns of side support and rear support. The dataindicate that the assumption is justified within the hitsof the experimental accuracy and that the corrected, inter-ferencdree base pressures deduced by this method difFeronly slightly from those measuredwith the side support aIone.For the bodies with rou
39、ghness added (producing a turbu-lent boundary layer) a complete investigation of the supportinterference was not made; consequently, a definiti quan-titative evaluation of the interference effects for each bodyin this condition cannot be given. From the data that wereobtained it has been found that
40、the foredrag is not affectedappreciably by the presence of the supports used in thepresent investigation, but that a small amount of interferenceis evident in the base pressure cm%iient which may varyfrom a minimum of +0.005 to a maximum of. +0.015 forthe different bodies. This uncertainty in the ba
41、se pressurecoefficient results in a correspondingly small uncertaintyin the base drag coefficient and in the total drag coefficient.REFERENCES1. Ackeret,., Feldmann,F., and Rott, N.: Investigationsof Com-pression Shocks and Boundary Layers in Gases Moving atHigh Speed. NACATM 1113,1947.2, Liepmann,H
42、. W.: Furthernvwtkwtio.mof the lntemctionofBoundaryLayerand ShockWavesin TraneonioFlow. Jour.Aero.Sci.,vol. 13,no. 12,Dee. 1946,pp. 623-687.a. Theodorsen,Theodore,andRegier,Arthur:Experimentsoh Dragof RevolvingDisks,Cylindemand StreamlineRods at HighSpeeds. NACA Rep. 793; 1944. (Formerly NACA ACRL4F
43、16)4. Keenan,Joseph H., and Neumann, Ernest P.: Friction in I?ipm atSupersonic and Subeonia Velocities. NACA TN 963, 1946.6. Fr6sml, W.: Flow in Smooth Straight les at Velocities Aboveand Below Sound Velocity. NACA TM 844, 1038.6. Fer ”R.: Charakt eristikenverfahren ftir Riiu-mliche Acheensym-metris
44、che UberschalLetromungen. Zentrale ftir Wissenschaft-liohes Berichtswssen, Ikrlin, F. B. No. 1269, Aug. 14, 1940.(Available as NACA TM 1133)13. Sauer, R.: Theoretische Einfiihrung in die Gasdynamik. Berlin,Springer, 194%, (Reprinted by Edwards Brns., Ann Arbur,Mioh., 1945.)14. Tolimein, W., and ScMi
45、fer, M.: Rotationseymmetrieclm ber-schallstromungen. Lllienthal-Gesellechaft f Gr Luftfahrtfm-schung, Bericht 139, Teil 2, Oct. 1941, pp. 6-15.15. Allen, H. Julian, and Nitzberg, Gerald E.: The Effect of Compres-sibility on the Growth of the Laminar Boundary Layer on Low-Dra Wings and Bodies. NACA T
46、N 1255, 1947.16. Matt, H.: Hochgesohwindfgkcitsmeesungen an Rund-und Pm-fflstangen versohiedener Durchmeeser. , Lilienthal-Geeellschaf tftlr Luftfahrtforsohung, Bericht 156, Oct. 1942, pp. 100-113.17. Lees,- Lester: The Stability of the Laminar Boundary Layer in aCompressible Fkdd. NACA Rep. 876,194
47、7, (Formerly NACATN 1860)18. Lehnert, R.: Systematfsche Messungen an neun einfachcnGchoasformen im Vergleich zu M=ungen der AVA-G Ferri, Antonio: Experimental Fsulti with Airfoils Tested in theHigh-Speed TunneI at Guidonia. NACA TM 946, 1940.20. Erdmann, S.: Wideretandebeatirnmung Von Kegeln und Kug
48、elnaus der Druckverteihmg bei Ubereohallg-chwindigkeit. Lilien-thal-GeaelLschaft fiir Luf tfahrtforeohung, Bericht 139, TeiI 2,oct.-l94l.21. Charters, A. C., and Thomas, R. N.: The Aerodynamic Perform-ance of Small Sphena from Subeonia ta High Supersonic Veloc-ities. Jour. Aero. Sci., vol. 12, No. 4, Oct. 1945, pp. 468-47&Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
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