1、t! i _TIo_YoMMITI,E E_ FOR AERONAUTICSProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NATIONAL ADVISORY COMMITTEE FOR AERONAUTiC_TECHNICAL NOTE 3038LOW-
2、SPEED DRAG OF CYLINDERS OF VARIOUS SHAPESBy Noel K. Delany and Norman E. SorensenSUMMARYAn investigation has been conducted to find the approximate variationof the drag coefficient with Reynolds number of several cylinders havingdifferent cross-sectlonal shapes. Data were obtained for circular cylin
3、-ders, elliptical cylinders of two fineness ratios, rectangular and dia-mond cylinders of three fineness ratios, and two isosceles triangularcylinders (apex forward and base forward). Three different corner radiiwere tested on each of the shapes, except for the circular and ellipticalcylinders. Data
4、 were obtained for Reynolds numbers as low as ll, O00 andas high as 2,300,000. For some cylinders, frequencies of pressure fluc-tuations in the wake were measured for a limited range of Reynolds numbers.INTRODUCTIONA method of estimating the effects of viscosity on the forces andmoments for inclined
5、 bodies has recently been suggested (e.g., see refs.1 and 2). In the proposed method, the crossflow in planes perpendicularto the inclined axis of the body has been related to the flow around acylinder, and, hence, the resulting cross forces are related to the sec-tion drag coefficient. The use of t
6、he method requires a knowledge of thesection drag characteristics of cylinders. For bodies of revolution, thedrag coefficient of a circular cylinder may be used, for which data areplentiful. However, for bodies with cross-sectlonal shapes other thancircular, drag data are meager (e.g., see ref. 3).
7、It is the purpose ofthis report to present drag coefficients over a fairly wide range ofReynolds numbers (R = l04 to 2 l0s ) for a variety of cross sections.The measured drag coefficient for the circular cylinder in the sub-critical Reynolds number range was lower than the generally acceptedvalue. E
8、liminating the cause of this discrepancy, end leakage, wouldhave complicated unduly the testing technique, and, hence, the leakagewas allowed to remain.SYMBOLSbbofrontal width of cylinderfrontal width of basic cylinder without rounded cornersProvided by IHSNot for ResaleNo reproduction or networking
9、 permitted without license from IHS-,-,-2 NACA_N3038cCoCdfMqRrVbocorbofbVstreamwise dimension of cylinderstreamwise dimension of basic cylinder without rounded cornersdrag coefficient, dra_ per unit lengthqbfrequency of vortex discharge from one side of cylinderfree-streamMach numberfree-stream dyna
10、mic pressureReynolds number based on ccross-sectional corner radius of cylinderfree-stream velocitycross-sectional fineness ratio of basic cylindercross-sectional corner-radius ratio of cylinderStrouhal numberCORRECTIONSThe drag coefficients and Reynolds numbers have been corrected forthe effects of
11、 the wind-tunnel walls by the method of reference _. Thecorrections used were as follows:2_ (M,)2I + O.h(M,)2 _0_,. )aCd = Cd - i- (M)2 cdR = R + I- 0“7(M)2)II-(M+)20“h(M)2_-O_c d RThe primed values are the uncorrected values.Provided by IHSNot for ResaleNo reproduction or networking permitted witho
12、ut license from IHS-,-,-NACATN 3038 3No correction has been madefor the effect of spanwise flow due toleakage where the cylinders passed through the tunnel walls or due to theboundary layers on the walls of the wind tunnel.MODEL DESCRIPTION AND APPARATUSTo obtain data over the desired Reynolds numbe
13、r range it was neces-sary to construct cylinders of three different sizes for each cross-sectional shape. Sketches of the cross-sectional shapes and the charac-teristic dimensions are presented in table I. The size of each cylinderis designated by a nominal dimension (either l, 4, or 12 inches) whic
14、hcorresponds to a dimension of the basic cross-sectional shape. For thecircles and ellipses the nominal dimension is the diameter or major axis.For the cylinders with basic cross sections composed of straight lines,the nominal dimension is the length of the longest side, except for theisosceles tria
15、ngle for which the length of the base was taken as thenominal d_mension and the diamond for which the longest diagonal was takenas the nominal dimension.The corners of all the cylinders were rounded so that the cylindersof different sizes had comparable corner-radlus ratios (r_o). The threeradius ra
16、tios for the 12-inch cylinders were obtained by successivelyrounding the corners with radii from 1/4 inch to a maximum of 4 inches.The corners of the _-inch cylinders were rounded to correspond to onlythe smallest and largest radius ratios of the 12-inch cylinders. Only thesmallest radius ratio was
17、tested on the 1-inch cylinders.The 12- and _-inch cylinders were constructed of pine and were lac-quered to produce highly polished surfaces. All the 12- and _-inch cylin-ders were mounted vertically in the test section of the wind tunnel(fig. 1). The clearances or gaps between the ends of the cylin
18、ders andthe wind-tunnel walls were of the order of 1/16 inch. Force measurementswere made by means of the wind-tunnel balance system with these gapsunsealed.The 1-inch cylinders were constructed of metal with smooth groundsurfaces. These models were mounted between end plates (fig. 2) with gapsbetwe
19、en the end plates and the model of about 1/32 inch. The forces weremeasured by means of a strain-gage balance (fig. 3).The accuracy of each cylinder was checked at several spanwise loca-tions by means of templates. A visual check showed that both the contouraccuracy and straightness of the cylinders
20、 were satisfactory.Measurements of the frequency of the pressure fluctuations were madein the wake for a number of the 12-inch cylinders by means of a pressure-sensitive cell mounted in the tip of a probe. The cell was brought towithin 12 to 18 inches of the downstream surfaces of these cylinders an
21、dProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACATN 5038then located so that the pressure fluctuations produced by the vorticesshed from one side of the cylinders could be measured. In a few cases,simultaneous measurements were made on both sides
22、 of the wake with a pairof cells.The tests were made in the Ames 7-by 10-foot wind tunnel. The vari-ation of the average free-stream velocity and Mach number with Reynoldsnumber is shown in figure 4.RESULTSThe variations of drag coefficient with Reynolds number for thevarious cylinders tested are pr
23、esented in figures 5 to 14. The data forthe circular cylinder are presented in figure 9; the fineness ratio 1:2and 2:1 ellipses in figure 6; the fineness ratio 1:2, i:I, and 2:1 rec-tangular cylinders in figures 7, 8j and 9; the fineness ratio 1:2, i:I,and 2:1 diamond cylinders in figures i0, ii, an
24、d 12; the isosceles tri-angular cylinders with the apex forward and with the base forward infigures 13 and 14. Also shown in these figures is the variation ofStrouhal number with Reynolds number for those cases where measurementsof the pressure fluctuations in the wake were made.Comparison of the va
25、lues of the drag coefficients for a circularcylinder from references 5 and 6 with the data of the present investiga-tion (fig. 9) indicates sizable differences for subcritical Reynoldsnumbers (R = 1.3 X 104 to 2.9 105). The values of the drag coefficientobtained for the _- and 12-inch circular cylin
26、ders are approximately 1.0,as compared to 1.2 obtained in the previously cited investigations. Thisdifference in the drag coefficient was due to the flow of air throu6h thegaps in the tunnel walls at the ends of the model. Pressure distributions(not presented) measured at the midspan of the cylinder
27、s with the gapsbetween the wind-tunnel walls and the cylinder sealed and unsealed indl-cated this to be true. The effect of sealing the gaps was to decreasethe pressure on the lee side of the cylinder. This effect is assumed tobe the result of preventing the flow of air of approximately free-streams
28、tatic pressure into the separated region on the lee side of the cylinder.It was not possible to evaluate the effects of the end leakage on thedrag coefficient of the circular cylinder at supercritical Reynolds num-bers because the drag coefficients could not be calculated from the pres-sure distribu
29、tions with sufficient accuracy. However, comparison with thedata of references _ and 6 indicates that the critical Reynolds numberranges are in good agreement, and at supercritical Reynolds numbers of l0s and 6 x 105, the agreement of the drag coefficients is reasonable.Some influence of end leakage
30、 on the drag measurements for all theother cylinders may have been present also. It is felt that the data aresufficiently accurate to indicate, at least qualitatively, the changes in t =Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 3038 5dr
31、ag of the various shapes (ellipses, rectangles, diamonds, and triangles)with corner radius ratio and fineness ratio.Table I presents values of the drag coefficient at Reynolds numbersof l0s (except where the lowest test Reynolds number was about 2 l05 )for the various shapes tested. Examination of t
32、hese data indicate thatthe drag coefficient either remained essentially constant or decreasedwith an increase of the corner radius ratio and that, in general, thedrag coefficient decreased with increasing fineness ratio.Although the Strouhal number data were meager, comparison of thedata of figures
33、5 to 14 indicates that at subcritical Reynolds numbersthe Strouhal numbers for all the shapes were close to 0.2.At supercritlcal Reynolds numbers the Strouhal number data presentedare for the predominant frequencies encountered, with the exception ofthe fineness ratio 2:1 rectangle where the disturb
34、ances in the wake wereperiodic and had a value of about 0.4.Ames Aeronautical LaboratoryNational Advisory Committee for AeronauticsMoffett Field, Calif., Aug. 25, 1953REFERENCESl.1e.Allen, H. Julian, and Perkins, Edward W.: A Study of Effects of Vis-cosity on Flow Over Slender Inclined Bodies of Rev
35、olution. NACARep. 1048, 1991.Van Dyke, Milton D.: First-Order and Second-Order Theory of Super-sonic Flow Past Bodies of Revolution. Jour. Aero. Scl., vol. 18,no. 3, Mar. 19_l, pp. 161-179.Lindsey, Walter Frank: Drag of Cylinders of Simple Shapes. NACARep. 619, 1938.Allen, H. Julian, and Vincentl, W
36、alter G.: Wall Interference in aTwo-Dimenslonal-Flow Wind Tunnel, with Consideration of the Effectof Compressibility. NACA Rep. 782, 19_.Stack, John: Compressibility Effects in Aeronautical Engineering.NACA ACR, 1941.Provided by IHSNot for ResaleNo reproduction or networking permitted without licens
37、e from IHS-,-,-6 NACATN 3038BeBursnall, William J., and Loftin, Laurence K., Jr.: ExperimentalInvestigation of the Pressure Distribution About a Yawed CircularCylinder in the Critical Reynolds Number Ramge. NACA TN 2463, 1951.Relf, E. F., and Simmons, L. F. G.: The Frequency of the EddiesGenerated b
38、y the Motion of Circular Cylinders Through a Fluid.R. & M. 917, British A.R.C., 192_.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACATN 3038 7OOIxeJProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
39、8 NACA TN 3038Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 3038f-409gJr400IProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-i0 NACA TN 3038Figure 2.- Method of mounting 1-1nch cylinders betw
40、een end plates in thewind tunnel.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACATN 3038 ii.Figure 3.-The straln-gage balance for the 1-inch cylinders.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,
41、-,-NACA TN 3038Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 3038/13Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-14 NACATN 3o3832I.8.6.4.3fb/V I04 2 3 4 6 810 s 2 3 4 6 810 e 2 3Reynolds
42、number, Rb) 2:i fineness rofioFigure 6.-Voriotion of drog coefficient ond Strouhol number with Reynoldsnumber for the elliptic cylinders.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-&NACA TN 3038432I.854“_._I.8.6.4.30A.iI0 _ I(o) r/b= 0021(b) ribo
43、-0.083IVom/nalsize,inches/24I12me 4_- fb/Vfb/V- ,Iv_L F-iI2 3 4 6 810 e 2 3 4 6 8/0 c 2 3Reynolds number, R(C) r/b o=0.2.50Figure 7 .-Voriotion of drog coefficient ond Strouhol number with Reynoldsnumber for the h2 fineness rotio rectongulor cylinders.Provided by IHSNot for ResaleNo reproduction or
44、networking permitted without license from IHS-,-,-16 NACA TN 3038432I.82_ .6“_._(o) r/bo=O.021I.8.6.4.,3.2.IIVominolsize, incheso /24 I- Ref 3- fb/V(b) rib o= O.167“ fb/VI0 “_ 2 3 4 6 8 lO s 2 3 4 6 8106Reynolds number, R(c) r/bo- O.3332 3Figure 8.-Voriotion of drog coefficient and Strouho/ number w
45、ith Reynoldsnumber for the h fineness ratio rectongu/or cylinders.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.VNACA TN 303832I.8.6(o) r/bo=O.042_v_F-7172 .8I.8.6.4.30.2JI0“_(b) r/bo= O.167Nosize, inches/2 -fb/V Ill2 3 4 6 8 I08Reynolds number,(c
46、J r/4,-0.5002 3 4 6 8106 2 3RFigure 9 .-Variahbn of drag coefficient and Strouhal number with Reynoldsr_mber for the 2:1 fineness ra#b rectangular cylinders.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-18 NACA TN 303842.8 - -5(b)r/bo=0.083I.8.6.4.
47、30.2 o0.IiOlNominolsize, inches124I12im_ fb/Vfb/V.2 34 6810 s 2 34 6Reynolds number, RJ._P8 I0 e 2 3(c) rib o- 0.167Figure IO.-Voriotion of frog coefficient ond Strouhol number with Reynoldsnumber for the L.2 fineness rotio diomond cylinders.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 3038 1932I.832I.8.6.4.3.2(eJ rib o- 0.015.INominolsize, incheso 12o 4= I- Ref 3= /2 -C-Q(b) r/bo- QII8fb/VIJ I/k- fb/VI0 4 2 3 4 6 8 IO s 2 3 4 6 8 I0 6 2 3Reynolds number, R(c) r/bo= 0235
