1、NATIONALADVISORYCOMMITTEEFOR AERONAUTICSTECHNICAL NOTE 4176ZFFECT OF FLOW INCIDENCE AND REYNOLDS ON LOW-SPEEEAERODYIWUVIIC CHARACTERJBTICS OF SEVERAL NONCIRCULARCYLINDERS WITH APPLICATIONS TO DIRECTIONALSTABILITY AND sPmGBy Edward C. PolhamusLangley Aeronautical LaboratoryLangleyWashingtonJanuary 19
2、58Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-TECH LIBRARY WE. NMA4NATIONAL ADVISORY COMMITTEEIillllllllllllllllllillllllilllFOR AERONAUTICS llnbb7ao .TECHNICU NOTE4176EFFECT OF FLOWAmoDYmMIcINCIDENCE AND REYNOLDS NUMBER ON IOW-SPEEDCHARACTERISTI
3、CSOF SEVERAL NONCIRCUIARCYLINDERSWITH APPLICATIONS TO DTIONALSTABILITY AND SPINNllJGBy Edward C. PohsmussumlARYThe aercdynsnic characteristicsof several noncircul.artwo-dimensionalcylinderswith axes normal to the stream at various flow incidence (anal-ogous to angles of attack of a two-dimensional a
4、irfoil and obtainedbyrotating the cylinders about their axes) for a range of Reynolds nmbershave been determined from low-speedwind-tunnel tests. The results indi-cate that these parameters have rather large effects on the hag end sideforce developed on these cy13nders. The side force is especially
5、criticalend very often undergoes a change in sign with a chenge in Reynolds num-ber. Since the flow incidence correspond to ccmbined sngles of attackand sideslip in the crossflow plane of three-dimensionalbodies, thesetwo-dimensionalresults appear to have strong implicationswith regard todirectional
6、 stability of fusekges at high angles of attack. These impli-cations, along with those associatedwithof aircraft, are briefly discussed.INTRODUCTIONthe spin-recovery characteristicsBecause of the current trend toward low-aspect-ratiowings and lerge-volume fuselages with long nose lengths, the relati
7、ve importance of thefuselage contribution to the aerodynamic characteristics of aircraft con-figurations is increasing rapidly. In addition, considerations such asinlet locations, engine installations, and wing-fuselage interferencehave led to a variety of fuselage cross sections. As indicated in re
8、fer-ence 1, for example, cross section can have considerable effect on boththe longitudinal end lateral aerodynsnThe cylinders were tested in the Lsmgley 300-MHI 7- by 10-foottunnel, and they spanned the tunnel from floor to ceiX.ng (fig. 2(b).In order to minimize any effects which might be caused b
9、y air leakagethrough the small clearance gaps where the cylinderspassed through thefloor and ceiling, each of the cylinderswas equippedwith an end plate(fig. 2(b). The forces and moments developed on the cylindersweremeasured by means of a mechanical balance system.In order to determine the degree t
10、o which the side-force character-istics of the two-dimensionalcylindersmight be indicative of thedirectional stability characteristicsof three-dimensionalbodies athigh angles of attack, three fuselageswere also testein the 300-MPH.- rProvided by IHSNot for ResaleNo reproduction or networking permitt
11、ed without license from IHS-,-,-NACATN 4176w7- by 10-foot tunnel. Detath ofsame longitudinal distribution ofd5the fuselages, all of which had thecross-sectionalarea, sre presentedin table I. The fuselages had ccmstaut sections from $ = 0.3200 tox= 0.7534, and for the rectsmgulsr fuselages the sectib
12、oth increase as the radius is decreased. This increase is, of course,associated with the more pronounced separation at the corners caused bythe increasing severity of the adverse pressure gradients as the radiusis reduced. The rather large effect of radius on the criticsl Reynoldsnunibermakes it som
13、ewhat difficult to predict, by interpolation, thedrag variation for radii other then those presented. In an attempt toalleviate this situation, the critical Reynolds numbers have been forcedto coincide by means of an empirical factor applied to the Reymlds num-ber, and the data have been replotted i
14、n the lower part of figure 9(a).It appesrs that, for the usual engineering accuracy required, only avertical interpolation need be made to obtain the drag variation for anyradius between = “om d 0“333”Figure 9(b) presents the results for the diamond cylinders - thatis, the ssme square cylinders rota
15、ted 45 to the stream. Although thesection drag coefficient is based on the maximum width normal to thestresm b, the corner radii are nondimensionalizedby b. for conveniencea71 in comparing the results with those from figure 9(a). For this,condition,it will be noted that, although the corner radius h
16、as a large effect on$ the critical Reynolds number, it has only a slight effect on the magni-tude of the section drag coefficient at subcritical Reynolds nuuibers,atleast for values of r/h. less then 0.333. The subcritical drag char-acteristics of the diamond cylinders are therefore considerably dif
17、ferentfrom those of the square cylinders. AMo, the drag characteristics ofthe circular cylinder are more similsr to those of the diamond cylinders(fig. 9(b) than those of the square cylinders (fig. 9(a). For example,both the circular and dimnond cross sections etibit a gradual transi-tion from subcr
18、itical to supercriticalfluw conditions,whereas the squarecyllnders exhibit a rapid transition for the range of radii investigated.Some of these observationsmaybe explained, to some extent at least, bythe theoretical.pressure distributions presented in figure 10. Thesedistributions were calculatedby
19、the method of reference 12. The pres-sure distributions indicate, as might be expected, that the generalcharacter of the flow about the diamond cross section with round cornersis considerablymore similsr to the flow about the circular cross sectionthan about the square cross sectim with round corner
20、s. In view of thissimilarity, it is not surprising that the general drag characteristicsof the circular cylinder are similar to those of the diamond series. Theextreme adverse pressure gradients encountered on the dismond cross sec-tion, despite large corner radii, would lead one to belleve that the
21、breakaway point is very near the position of maximwn width and probablyaccounts for the fact that the subcritical drag is relatively independenta71 of corner radius and is considerablyhigher thsn that for the circularcylinder (fig. 9(b). The transition in subcritical drag characteristics*Provided by
22、 IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-8 NIICATN 4176between the square cylinders,which are extremely sensitive ti cornerradius, and the diamond cylinders,which are relatively insensitive tocorner radius, is shown in figure I-1. In this figure the sect
23、ion dragcoefficient,which is based on the respective maximum projectedwidthsnormal to the flow b, is plotted as a function of the incidence offlow for various corner radii; the sqwre cylinders correspond to= 0 andthedimnond cylinders correspond to #=45. In addition tothe results of the present inves
24、tigation,the variation of cd with _(.=O),for shap corners therefore,the separated flow persists to a mch higher Reolds number (fig. 12(a). 0nuriberof about 1,500,000,and, at the highest Reynolds nuniberattained,the section side-forcecoefficienthas decreased to almost zero. It isinteresting to note t
25、hat the critical Reynolds number, if based on corrier “ -radius, would be approximatelythe same for the two cylinders.The results presented in the lower part of figureJ2(a) indicatethat the section side-force characteristicsfor the trhngular cylinderare considerablydifferent from those of the squsre
26、 cylinders. At 10WReynolds numbers a small negative side-forcecoefficient occurs, whereasat the higher Reynolds numbers a fairly hrge positive side-force coef-ficient occurs. This general trend is opposite to that observed for thesqusre cylinders and might be explainedby the foil.owirigsketcheswhich
27、are based on tuft studies:Subcritical ReynoldsSketch (c)nuniber SupercriticalReynolds numberSketch (d) -.At subcriticalReynolds numbers (sketch (c), the flow separates at bothleading corners, and only a,smal.1negative side-force coefficient isdeveloped. However, at supercriticalReynolds numbers, the
28、 flow attaches “#on the right-hand corner (sketch (d),which has the least adverse pres-sure gradient, and is deflected in a direction that pr-educesa positive -w”-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 4176 11side force. Note that th
29、e flow is deflected in the same directionbythe triangular cylinder at supercriticalReynolds numbers (sketch (d).as by the square cylinder at subcritical Reynolds numbers (sketch (a)and this fact apparently accounts for the opposite trends with Reynoldsnuniberbetween the two cross sections.Figure 12(
30、b) presents the variation of section side-force coefficientwith Reynolds number for the cylinders having dismond and rectangularcross sections at a flow incidence of 10. The results obtainedwiththe dismond cross sections (see upper plot of fig. 12(b) show relativelylittle effect of Reynolds number,
31、and, as t be eqected the side-forcecharacteristicsare somewhat similar to those of the triangular cylinder(see lower plot of fig. 12(a). The lower plot of figure X2(b) presentsa comparison of the results obtained for the two rectangular cylindersand for the square cylinder; the trendswith Reynolds n
32、uniberare essen-tiall.y.thesame for all.three cylinders. The flow studies previouslypresented for the squsre cylinder apparently also apply for the rectsm-ti cynders; therefore, no further discussionwill be given exceptto point out again that the changes in critical Reynolds nuuibersareassociatedwit
33、h the fact that the Reynolds numbers in the present inves-. tigation are based on co rather than corner radius. In order to illus-trate this fact, the results for the square and rectangular cylinders arepresented as a function of Reyuolds number based on corner radius inifigure E!(c).”In figure 12,
34、side-force results were presented for only one angleof flow incidence. Figure 13 summarizes the variation of section side-force coefficientwith flow incidence for all the cylinders of the presentinvestigation and for those of references 7, 8, and 14. Results, whereavailable, are shown for Reynolds n
35、umbers of 1,000,000 and 200,000. Alsoshown is the theoretical value for a flat plate(w)” e opplots of figure 13 show the changes in the variation of side-force coef-ficient with flow incidence as the cross section gradualdy changes froma rectangle with major axis normal (when # = 0) to the flow to a
36、nNACA 001 airfoil section alined (when = 0) with the flow. At thelower Reynolds number the curve for the initial rectangular cross sectiondiffers greatly from the theoretical curve for the flat plate, but thisdifference diminishes as the airfoil section is approached. The resultsalso indicate that a
37、t the higher Reynolds number the vmiatim of with approaches that for the flat plate.regardless of cross-sectionalshape. Although interesting observations csn also be made with regsrdto the results presented in the bottom of figure 13, they sre not dis-cussed here since they will be considered in con
38、nectionwith application. to directional stabili.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-12 M(M TN 4176 wDirectional Stability and Spinning Characteristics Lof Three-DimensionalBodiesIn order.to illuwbrate the degree to which the side-force ch
39、aracter-istics of the two-dimensionalcylindersmight be indicative of the direc-tional stability characteristicsof three-dimensionalbodies at higham.glesof attack, tests have been made on one circular-cross-sectionfuselage and on two rectangular-cross-sectionfuselages. The fuselages(see table I) were
40、 tested at an angle of sideklip of 5 through sm angle-of-attack rsnge from O.0 to 24, end the side-forcecoefficient (basedonmaximum cross-sectionalarea) developed is presented in the upper plotof figure 14. The side-forcecoefficient,rather than-the yawing-moment .=coefficient,was selectedbecause the
41、 yawing moment is dependent upon theparticular moment reference point selected and because existing methods of applying two-dimensionaldata to three-dimensionalbodies appear tobe more successfulwith regard to the overall force than with regard tothe distribution of the force (fig. 9 of ref. 15). The
42、 results indicatethat the side force developedby the fuselage having a-circulsr cross .sectionwas relatively Independent of angle uf attack. However, the side .force developedby the fuselages having rectangular cross sectionswasgreatly dependent upon angle of attack, especiallyfor the rectangularfus
43、elage with the major axis vertical md this result is in general Dagreementwith the trends indicated in reference 1. It shouldbe men-tioned that for current aircraft,with their long fuselage noses andshort tail lengths, the side-force ch=acteristics indicated for therectangul fuselageswould tend to i
44、ncrease-thefusebge directionalinstability at high angles of attack and supercriticalcrossflow Reynoldsnumbera.The side-forcevsriation for the three fuselages, as estimatedwiththe aid of the two-dimensional-cylinderdata, is presented in the lowerpart of figure 14. It shouldbe pointed out that, for th
45、e subcriticalcrossflow Reynolds rnmiberswhich existed in the three-dimensionaltests,the side forces developed on the two-dimensionalcylinderswould resultin a trend with angle of attack opposite to that encountered on the three- dimensionalbodies end that it was necessary to use supercritical valuest
46、o obtain a reasonable correlation. Tnis fact, however, is not surprising”in view of the rather large degree of interdependence%etween the cross-flow and the axial flow observed in references4 and 5 for angles ofattack up to 30 or 40. Although considerablevariation exists betweenthe measured and esti
47、mated side forces for each of the rectangular fuse-,:.:-=.lages, the general trend, with regard to the effect of fuselage cross ”+section, appears to be sufficientlywell defined to allow the use of two-.dimensional cylinder data in the selection of fuselage cross sections. .a71Also, a more rigorous
48、method of applying the two-dimensionaldata might” .be expected to result in better agreement. In view of the shortcomings wProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 4176 13.of the methods currently available, the use of the simplified m
49、ethod.was believed to be justified. In this method it was assumed that thesmall potential force on the boattailed afterbody, as predicted.bytheory, was not attained because of afterbody separation. The potential-flow contributionto the side force was therefore restricted to theexpanding section of the nose, and the potential side-force coefficientis-givm-by t
