1、NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS TECHNICAL NOTE 2960 DRAG OF CIRCULAR CYLINDERS FOR A WIDE RANGE OF REYNOLDS NUMBERS AND MACH NUMBERS By Forrest E. Gowen .and Edward W. Perkins Ames Aeronautical Laboratory Moffett Field, Calif. Washington June 1953 Provided by IHSNot for ResaleNo reproduc
2、tion or networking permitted without license from IHS-,-,-1A NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS TECHNICAL NOTE 2960 DRAG OF CIRCULAR CYLINDERS FOR A WIDE RANGE OF REYNOLDS NUMBERS AND MACH NUMBERS By Forrest E. Gowen and Edward W. Perkins SUMMARY Pressure distributions around circular cylin
3、ders placed perpendicular to the stream for subsonic and supersonic flow conditions have been obtained. Drag coefficients calculated from these wind-tunnel tests and from transonic free-flight tests are presented. Drag data are presented for the Mach number range of 0.3 to 2.9. The Reynolds numbers
4、for the subsonic and supersonic Mach numbers were within the ranges of approximately 50,000 to 160,000 and 100,000 to 1,000,000, respectively. flow in the supersonic Mach number range of the tests. The drag coef- ficient increased with increasing Mach number to a maximum of apfiroxi- mately 2.1 at a
5、 Mach number of unity. range, the drag coefficient decreased with increasing Mach number to a value of about 1.34 at a Mach number of 2.9. tigations have been included for comparison. No effects of Reynolds number were found for In the supersonic Mach number Drag data from other inves- The effects o
6、f fineness ratio on drag at supersonic Mach numbers were also investigated and found to be small. INTRODUCTION Recent developments in the study of forces and moments on inclined bodies of revolution hzve led to a renewed interest in the drag characteristics of circular cylinders. R. T. Jones (refere
7、nce 1) has shown theoretically that the flow perpendicular to an inclined, infinitely long circular cylinder with a laminar boundary layer may be considered independent of the axial flow. and Perkins (reference 2) the local normal force on an inclined body of revolution was related to the drag of a
8、circular cylinder at a Mach number and Reynolds number based on the component of flow perpendicular In a recent paper by Allen . Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 NACA TN 2960 to the inclined axis of the body. The calculation of aerod
9、ynamic characteristics of inclined bodies of revolution by this method depends upon a knowledge of the drag characteristics of circular cylinders over a wide range of Reynolds numbers and Mach numbers. A survey of the data available on the drag of circular cylinders indicates that most of the data a
10、re restricted to Mach numbers less than about 0.3. At these low Mach numbers, many investigators have obtained circular- cylinder drag coefficients for a considerable range of Reynolds numbers. (See, for example, references 3 through 10, inclusive.) from most of these and from other investigations h
11、ave been conveniently summarized in reference 11. For Mach numbers above 0.5, there are little available data and within these data there is considerable scatter. The results The purposes of the present investigation were to extend the range of available datrz on circular cylinders to a Mach number
12、of about 3.0 and to investigate the effects of Reynolds number on circular-cylinder drag for supersonic Mach numbers. SYMBOLS CD d MO P P PO 90 R 0 II drag per unit Qod drag coefficient diameter of cylinder, inches free-strean Mzch number pressure coefficient - (“;Eo local static pressure on cylinde
13、r, pounds per square inch free-stream static pressure, pounds per square inch free-stream dynamic pressure, pounds per square inch Reynolds number based on free-stream conditions and cylinder diameter circumferential angle measured from the upstream stagnation point ratio of the drag coefficient of
14、a circular cylinder of finite length to that of a circular cylinder of infinite length . x L Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 2960 APPARATUS AND TESTS 3 I .-/ The investigation at high subsonic Mach numbers was performed in the
15、 Ames 1- by 3-1/2-foot high-speed wind tunnel, which is a single-return closed-throat tunnel vented to the atmosphere in the settling chamber. the window glass as shown in part (a) of figure 1. opposed orifices were located in each model at the tunnel center line. Circumferential pressure distributi
16、ons for the Mach numbers and Reynolds numbers shown in figure 2 were then obtained by rotating the whole window assembly through an angle of 90. The two cylinders tested were mounted directly in Two diametrically The experimental data presented for the transonic speed range were obtainedfrcm a curre
17、nt investigation performed by the Langley Pilotless Aircraft Research Division, and the details of this investigation are given in reference 12. The supersonic tests were conducted in the Ames 1- by 3-foot supersonic wind tunnels Nos. 1 and 2. The nozzles of these tunnels are similar and both are eq
18、uipped with flexible top and bottom plates. Tunnel No. 1 is a single-return, continuous-operation, variable-pressure wind tunnel with a maximum Mach number of 2.2. Tunnel No. 2 is an intermittent-operation, nonreturn, variable-pressure wind tunnel with a maximum Mach number of 3.8. The model install
19、ation shown in figure l(b) was used in both tunnels. distributions were obtained at nine longitudinal stations on the model. Circumferential pressure To investigate the end effects on the circular cylinder, tests vere performed with and without the end plate shown in figure l(b) for the Mach numbers
20、 and Reynolds numbers given in the following table. Data were taken at only one Reynolds number for a Mach number of 2.9. Reynolds number (millions) 0.16 * 38 -58 - 13 Mach number I 1.98 I .20 .42 I 34 .74 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-
21、,-,-4 NACA TN 2960 RESULTS AND DISCUSSION General Characteristics of Flow About a Circular Cylinder Subsonic Mach numbers.- Characteristics of the flow around circular cylinders at speeds below the critical Mach number (Mo 0.4 reference 11. In general, for Reynolds numbers below the critical Reynold
22、s number range,l the flow is characterized by a laminar boundary layer on the cylinder accompanied by a periodic discharge of vortices in the wake. critical range, the boundary-layer flow on the cylinder becomes turbulent, the separation point moves downstream, and the pressure recovery in the separ
23、ated-flow region increases. For these latter conditions there is apparently no periodic discharge of vortices from the cylinder although measurements of the wake fluctuations have indicated some predominate frequencies. (Page 421 of reference 11.) At velocities above the critical Mach number compres
24、sion waves form on the cylinder. This shock formation, which occurs alternately first on one side of the cylinder and then on the other, is accompanied by a forward movement of the boundary-layer separation point and violent oscillatiocs of the wake. (See fig. 3.) These oscillations may be periodic
25、although this has not been confirmed since no measurements in the wake at supercritical Mach numbers are available. Schlieren pictures taken during the present investigation and the data of reference 13 indicate that for certain test conditions a periodic dis- charge of vortices occurs. However, eve
26、n though a number of schlieren pictures taken at one tunnel setting (i.e., one Mach number and Reynolds number) in the Ames 1- by 3-1/2-foot wind tunnel indicated a periodic flow in the wake, others for apparently the same test conditions indicated completely turbulent wake flow. are well known and
27、have been discussed in considerable detail by Golds L ein in As the Reynolds number is increased through the In the supercritical Mach number range no effect of Reynolds number on the flow about the models was found for the limited Reynolds number range of the present investigation. f Supersonic Mac
28、h numbers.- At supersonic speeds, for the cylinder tested in the Ames 1- by 3-foot supersonic wind tunnels, no significant changes in the flow field occurred with increasing Mach number or Reynolds number. A typical shadowgraph picture of the supersonic flow The range of Reynolds numbers through whi
29、ch the drag coefficient decreases from 1.2 to about 0.3 is usually defined as the critical Reynolds number range. a Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 2960 5 . field about the test cylinder is shown in figure 4. appear on the bou
30、ndary-layer plate ahead of the bow shock wave are oil streaks left by a minute amount of oil on the plate. The detached bow wave shows a double shadow on the boundary-layer plate. that the second shadow resulted fromthe intersection of the bow shock wave with the tunnel-wall boundary layer at the wi
31、ndow near the free end of the cylinder. The bow wave curved around the free end of the cylinder so that the intersection with the tunnel-wall boundary layer was displaced slightly downstream from the position of the wave ahead of the cylinder. This picture and those taken for Mach numbers of 1.98 an
32、d 2.9 indicated a small disturbance in the flow which appears to originate at cide with the line of boundary-layer separation. wake between the cylinder and the trailing shock wave, shown for a Mach number of 1.49, is typical for all the test Mach numbers. ing Mach number the width of the minimum se
33、ction of the wake decreased. The streaks that It was found 6 = 100 to 120. The origin of this disturbance appears to coin- The sharply converging With increas- Pressure Distribution Subsonic Mach numbers.- Typical pressure distributions for subsonic Mach numbers are presented in figures 5(a) and 5(b
34、) .2 At Mach numbers less than the critical, the experimental pressure distri- butions are in fair agreement with the theory over most of the upstream half of the cylinder. considerable divergence between experimental and theoretical pressure distributions with the experimental curves showing the ty
35、pical large region of separated flow over the downstream half of the cylinder. The effects of Reynolds number are shown by the curves for Reynolds numbers of 314,000 and 426,000. distributions of pressure coefficient for Reynolds numbers below and above the critical range of Reynolds numbers, and in
36、dicate the increase in pressure recovery in the separated-flow region which occurs as the critical Reynolds number is exceeded. Over the remainder of the cylinder there is Thesewrves are typical of the At subsonic Mach numbers above the critical Mach number (fig.5( b) , the effects of compressibilit
37、y are evidenced in the increase of the pressure coefficients on the windward side of the cylinder with increasing Mach number. The pressures over the downstream surface of the cylinder are, in general, less than those measured at subcritical Mach numbers. The adverse pressure gradient, which is usua
38、lly 2The data of figure 5( a) were obtained from unpublished -results of recent tests made in the Ames 7- by 10-foot wind tunnel. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-6 NACA TN 2960 associated with boundary-layer separation, is evident in
39、the data for Mach numbers of 0.3, 0.5, and 0.6. Mach number of 0.7, which is similar to those obtained in the range of Mach numbers above 0.623, shows little, if any, adverse pressure gradient. Since the flow in the wake of the cylinder at subsonic Mach numbers above the critical was of an oscillato
40、ry character (see fig. 3), it would be expected that the pressures in the region of separation and over the aft part of the cylinder would not be steady; hence, the pressures recorded by the manometer system in this region would be only the average static pressures. The effects of Reynolds number on
41、 the pressure distribution were found to be neglibible at Mach numbers above the critical for the limited Reynolds numbers of this investigation. The pressure distribution for a Supersonic Mach numbers.- Typical pressure distributions about a circular cylinder at supersonic Mach numbers are shown in
42、 figures 5(c) - _. . and 5(d). The distributions for all three supersonic Mach numbers are somewhat similar to the pressure distributions at subsonic supercritical Mach numbers. However, the variation with Mach number is different in that there is a general increase in pressure coefficient over the
43、entire body with increasing Mach number (fig. 5(c). For the supersonic Mach numbers investigated, the separation point was located in the 100 to 120 region and the pressures on the cylinder in the separated-flow region were more uniform than for subsonic flow. Although the shadowgraph of figure 4 in
44、dicated a small disturbance in the external flow field near the position of separation and the flow in this vicinity appeared to be steady, detailed pressure distributions failed to reveal the expected pressure rise (or local adverse pressure gradient) at the position of the disturbance. separated-f
45、low region approach a vacuum as the Mach number is increased. The pressure coefficient at the forward stagnation point (e = 0) was, for all supersonic Mach numbers, in close agreement with the pitot- pressure coefficient calculated with the aid of Rayleighs equation. As shown in figure 5(c), the pre
46、ssures in the The pressure distributions of figure 5(d) are typical of the data for Mach numbers of 1.49 and 1.98. Reynolds number range of this investigation, which included the critical Reynolds number range for subsonic flow, there is no effect of Reynolds number on the pressure distribution at s
47、upersonic Mach numbers. These data show that for the Figure 5(e) shows experimental distributions of pressure coefficient for various Mach numbers. Included in the figure are the theoretical distributions for the limiting ewes of Mach numbers near zero (incompressible potential theory) and a Mach nu
48、mber of infinity (Newtonian theory, reference 14). Over most of the cylinder the pres- sures calculated from the theory for infinite Mach number were higher than those measured for the highest Mach number of the present investi- gation. Nevertheless, the experimental distribution of pressure Provide
49、d by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 2960 7 . C f coefficient approached the theoretical distribution as the Mach number was increased. The theoretical curve shown does not take into con- sideration the effects of centrifugal forces which would be expected to result in a reduction of the local pressure coefficient on th
