1、N 0 0 M w w c 4 m 4 z I AS A TECHNICA REPORT L AERODYNAMIC FORCES ON A STATIONARY AND OSCILLATING CIRCULAR CYLINDER AT HIGH REYNOLDS NUMBERS bY George W. Jones, Jr. Lungley Reseurch Center Joseph J. Cincotta The Martin Company and Robert W. Wu Zker George C. Mdrslbu ZZ Space FZight Center NATIONAL A
2、ERONAUTICS AND SPACE ADMINISTRATION WASHINGTON, D. C. FEBRUARY 1969 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-TECH LIBRARY KAFB, NW I II I llllll11111 lllll I 11111 llll11111lll Ill 0068432 AERODYNAMIC FORCES ON A STATIONARY AND OSCILLATING CIR
3、CULAR CYLINDER AT HIGH REYNOLDS NUMBERS By George W. Jones, Jr. Langley Research Center Langley Station, Hampton, Va. Joseph J. Cincotta The Martin Company Baltimore, Md. and Robert W. Walker George C. Marshall Space Flight Center Huntsville, Ala. NATIONAL AERONAUTICS AND SPACE ADMINISTRATION For sa
4、le by the Clearinghouse for Federal Scientific and Technical Information Springfield, Virginia 22151 - CFSTI price $3.00 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Provided by IHSNot for ResaleNo reproduction or networking permitted without lice
5、nse from IHS-,-,-CONTENTS Page SUMMARY . 1 INTRODUCTION 2 SYMBOLS . 3 APPARATUS AND TESTS . 7 Test Facility . 7 Model 7 Instrumentation and Dah-Reduction Procedures 10 Tests . 11 RESULTS AND DISCUSSION 12 Static Measurements 12 Static pressures 12 Dragdata . 17 Characteristics of Unsteady Lift Measu
6、red on Stationary Cylinder 26 Frequency content of unsteady lift 26 Magnitude of unsteady lift . 30 Measurement of Unsteady Lift Due to Cylinder Motion . 33 Power spectral density and root-mean-square values 33 Lift-force vector at frequency of cylinder oscillation 36 Aerodynamic derivatives of lift
7、 due to motion 36 CONCLUSIONS . 43 APPENDIX A . ESTIMATION OF SOLID-BLOCKAGE INTERFERENCE 45 APPENDIX B . DETAILS OF INSTRUMENTATION AND DATA-REDUCTION PROCEDURES 46 REFERENCES . 53 TABLES 55 iii Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-I AERO
8、DYNAMIC FORCES ON A STATIONARY AND OSCILLATING CIRCULAR CYLINDER AT HIGH REYNOLDS NUMBERS By George W. Jones, Jr., Joseph J. Cincotta, and Robert W. Walker SUMMARY A wind-tunnel investigation has been made of the steady drag and unsteady lift (lateral) forces on a stationary and oscillating circular
9、 cylinder in two-dimensional flow at Reynolds numbers from 0.36 X lo6 to 18.70 X lo6 and at Mach numbers M up to 0.6. The experimental data were obtained in the Langley transonic dynamics tunnel from tests of a 3-fOOt (0.914-meter) diameter cylinder instrumented to measure directly the unsteady lift
10、 and mean drag forces on the cylinder. The cylinder could be held fixed or oscillated laterally to the flow at frequencies from 3 to 20 hertz. tigation verified and considerably extended the range of previous knowledge in this area. The results of the inves- For the stationary cylinder, the most imp
11、ortant results may be summarized as fol- The static-pressure distributions, the mean drag coefficients at M 5 0.2, and the lows: Strouhal number of the unsteady lift forces follow the trends established by previous inves- tigators up to the limits of Reynolds number investigated. Reynolds numbers, e
12、ach of these parameters remains essentially constant; that is, the static-pressure distribution remains essentially the same above a Reynolds number of 8 x 106, the mean drag coefficient is approximately 0.54, and the Strouhal number is approximately 0.3. The unsteady lift force can be categorized i
13、nto three regimes depen- dent upon Reynolds number - wide-band random, narrow-band random, and quasi- periodic. The root-mean-square unsteady lift coefficient at Mach numbers less than 0.3 varies over a wide range at Reynolds numbers from 1.4 X lo6 to 8 X 106; then, at higher Reynolds numbers, it is
14、 a single-valued function which decreases with increasing Reynolds number. At higher (hitherto unexplored) For the oscillating cylinder, the most important results may be summarized as fol- Oscillation of the cylinder in the lift direction has no significant effect on the mean An unsteady lift due t
15、o cylinder motion, which increases with amplitude lows: drag coefficient. of motion, exists only when the cylinder is oscillated at or relatively near the aerody- namic Strouhal frequency for the stationary cylinder. This unsteady lift is a negative (destabilizing) aerodynamic damping force at cylin
16、der frequencies below the stationary- cylinder Strouhal frequency. As the cylinder frequency is increased through and above the Strouhal frequency, there is an abrupt change in the unsteady lift due to motion to a posi- tive (stabilizing) aerodynamic damping force. Aerodynamic derivatives with respe
17、ct to displacement of the components of unsteady lift due to motion decrease nonlinearly with increasing amplitude of motion. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-INTRODUCTION The aerodynamic forces produced by flow about circular cylinder
18、s with the longi- tudinal axis perpendicular to the flow have been of interest since the ancient invention of the Aeolian harp. For some time it has been generally known that the behavior of a cylinder in a laminar flow at low Reynolds numbers is characterized by the formation of a K however, the ac
19、tual loads did not exceed 30g. The cylinder model and torque-bar suspension assembly formed a resonant system in the cylinder translatory mode. The natural frequencies of the system could be varied by moving the clamping mechanisms along the torque bar and reclamping; the effective length of the tor
20、que bars was changed in this manner. The system could be tuned between 3 and 20 hertz so that the force required to drive the model in the translatory mode at any desired frequency in this range was minimized. This force was supplied by the hydraulic shaker system, which had one shaker attached to e
21、ach end of the inner cylinder. Each of these two shakers was capable of providing a force up to 1400 pounds (6227 newtons) at 3 inches (7.62 cm) maximum amplitude, and the system could control the amplitude throughout a frequency range from 3 to 20 hertz. single console to obtain synchronized amplit
22、ude at each shaker head, The shakers were controlled from a Vibration tests were conducted to determine the elastic resonant frequencies of the These tests showed that the natural frequencies of the model were well model assembly. above the range of interest of the test data, with the lowest value b
23、eing 70 hertz. Instrumentation and Data-Reduction Procedures A Martin-developed instrumentation system called the Inertia Compensated Balance (ICB) was used to measure directly on the stationary or oscillated cylinder the unsteady aerodynamic lift force on the 2.33D-length instrumented outer-cylinde
24、r section. ICB system electrically combined the signals from the lift strain-gage force transducers with the signals from a strategically located accelerometer in such a manner as to cancel This 10 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-out
25、the forces due to inertia and give a direct measure of the unsteady aerodynamic lift force. manner, a failure of the drag ICB system (unrepairable in the time available) during model checkout prevented such measurements. However, measurements of the mean drag on the large instrumented outer-cylinder
26、 section were obtained from the drag transducers. A single row of static-pressure orifices measured the static-pressure distribution around the cylinder at one longitudinal station, 1.14 diameters from the lower end of the outer cylinder. An oil-film technique described in reference 12 was used to o
27、btain photographic and eye-witness visualization of the mean flow on the cylinder surface. Although.it was initially planned to measure the unsteady drag force in a similar A number of data-reduction procedures, both “on-line“ and “after-the-fact, I were used to analyze the data, particularly the un
28、steady lift-force data on the stationary and oscillating cylinder. The mean square value, the power spectral density, the autocorrela- tion function, and the probability density were obtained in addition to time-history samples of the lift force. by means of an analog computer into its components in
29、 phase and 90 out of phase with displacement. Also, for the oscillating cylinder, the unsteady lift force was resolved A more detailed description of the instrumentation and the data-reduction procedures used to analyze the signals from the instrumentation is presented in appendix B. appendix gives
30、instrumentation block diagrams and presents a discussion of the equipment techniques, the analysis parameters, and the relative accuracies for the data-reduction procedures. This Tests During the test program, the mean drag and unsteady lift forces were measured at Reynolds numbers from 0.36 x 106 t
31、o 18.70 X lo6 at Mach numbers up to 0.6 with the cylinder held stationary and with the cylinder oscillated at model reduced frequencies fhD/V from 0.06 to 0.50. Static pressures were measured only with the cylinder held stationary. of Reynolds number and allowed a separate investigation of Mach numb
32、er and Reynolds number effects on the aerodynamic force measurements. The test program was accomplished in two phases. In the first phase, measure- The use of air and freon test mediums at various densities gave a broad range ments were made of the static pressures, unsteady lift, and mean drag with
33、 the cylinder held stationary in the flow. 0.03-inch (0.762-mm) gaps between the fixed and instrumented cylinder sections was seriously disturbed, even though the gaps were equipped with a labyrinth seal. After a period of experimentation, an additional sealing of the gaps with a silicone rubber com
34、- pound was found to essentially eliminate the disturbance. except for sufficient drag data to illustrate the problem, only the static-pressure data During this phase, the flow in the vicinity of the three Because of this gap effect, 11 Provided by IHSNot for ResaleNo reproduction or networking perm
35、itted without license from IHS-,-,-are presented from this phase of the program. In the second phase of the tests, with the gaps sealed with silicone rubber, measurements were made of the unsteady lift and mean drag forces, both with the cylinder held fixed and with the cylinder oscillating laterall
36、y over a range of frequencies and amplitudes. Before starting this phase of the tests, the flexible tubing between the static-pressure orifices and the manometer board was removed in order to permit the cylinder to be oscillated. Consequently, no static-pressure mea- surements were taken with the ga
37、ps sealed with silicone rubber. The procedures used in measuring the static pressures and the unsteady lift and mean drag forces were as follows: For static-pressure measurements, a desired wind- tunnel test condition was established and held constant until the manometer board stabil- ized and a pho
38、tograph was taken of the manometer board. unsteady lift and steady drag aerodynamic forces, a desired test condition was established and held constant while a 1- to 2-minute data sample was recorded and an “on-line“ analy- sis was made. For measurement of the RESULTS AND DISCUSSION The results and d
39、iscussion are organized so that static data such as pressure dis- tributions and mean drag are presented first. These data are accompanied by remarks about flow conditions observed during the tests. After these data have been discussed, the unsteady lift on the stationary cylinder and the unsteady l
40、ift due to cylinder motion are presented. Static Measurements Static pressures. - Static-pressure distributions were measured at one longitudinal station, 1.14 diameters above the floor of the test section, by using 48 static-pressure orifices spaced around the periphery of the cylinder. The pressur
41、e distributions were measured on the stationary cylinder at Reynolds numbers from 0.36 X lo6 to 18.70 x lo6 at Mach numbers from 0.05 to 0.46. Figure 5 presents, in order of increasing Reynolds number, nine selected pressure distributions. Reynolds numbers less than about 0.75 X lo6, difficulty was
42、experienced in holding a steady tunnel velocity; therefore, measurements of the tunnel flow parameters and the static-pressure distributions are subject to inaccuracies not found at Reynolds numbers above about 0.75 x 106. For static-pressure distributions at The pressure distributions at Reynolds n
43、umbers from 0.52 X lo6 to 1.31 X lo6 (figs. 5(a) and 5(b) show bulges at r$ =: 100 and r$ =: 260O. These bulges are believed to be evidence of the occurrence of laminar separation bubbles. As discussed in refer- ence 13, at very low Reynolds numbers, the flow on a cylinder is laminar with a laminar
44、12 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-A 1 .o 0 - 1 .a c P -2.c -3 .( 1 .o a - 1 .c -2s - -3. 0 1 .o C -1.( -2. -3. 0 0 d M RN 0.52 X lo6 0.294 0.623 .66 X lo6 .066 .563 .73 X lo6 .177 .688 40 80 120 2 -c 160 c1 0.064 .003 .062 240 (a) Pr
45、essure distributions at Reynolds numbers from 0.52 x 106 to 0.73 X 106. 280 3 20 360 Figure 5.- Selected pressure distributions measured around circumference of cylinder at one longitudinal station and at several Reynolds numbers. 13 Provided by IHSNot for ResaleNo reproduction or networking permitt
46、ed without license from IHS-,-,-A 17 1.0- -1.0 -2.0 -3.0- 1 -1. C P -2.1 -3 .( 0 1 .o 0- 0 - -1.0 - -2.0 -3.0 4, deg (b) Pressure distributions at Reynolds numbers from 0.81 X lo6 to 3.49 X IO6. Figure 5.- Continued. 14 Provided by IHSNot for ResaleNo reproduction or networking permitted without lic
47、ense from IHS-,-,-A 1 .o 0 - 1 .o C P -2.0 -3 .O IC 1 ! -0.004 .ooo d 0.583 0 1 .o 0 -1.0 -2.0 -3 .O 0.177 .310 14.08 x 10 lo6 3 -82 a. u - .O 0 1.0, 0 -1.0 -2.0 -3 .O 0 40 80 120 160 200 240 280 320 360 (c) Pressure distributions at Reynolds numbers from 8.27 x 106 to 17.82 x 106. Figure 5.- Conclu
48、ded. 15 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-separation. At higher Reynolds number, the separated laminar boundary layer undergoes transition and reattaches to form a laminar separation bubble after which the turbulent flow separates at some point downstream. Figure 6 shows a visualization of a typical laminar separation bubble on the cylinder obtained by the oil-film technique described in reference 12. The laminar bubble and the downstream turbulent separation lines are clearly discernible (the white vert
