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The measurement of wake and surface effects in the subcritical flow past a circular cylinder at rest… Ferguson, Nelson 1965

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THE MEASUREMENT OF WAKE AND SURFACE EFFECTS IN THE SUBCRITICAL FLOW PAST A CIRCULAR CYLINDER AT REST AND IN VORTEX-EXCITED OSCILLATION by NELSON FERGUSON B.Sc, University of Strathclyde, 1963 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF M.A.Sc. in the Department of Mechanical Engineering We accept this thesis as conforming to the required standard The University of British Columbia September, 1965 In presenting t h i s t h e s i s in p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I f u r t h e r agree that permission f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s re p r e s e n t a t i v e s . It i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission Department of Mechanical Engineering The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada Date March 11. 1966 ABSTRACT A pressure transducer, sensitive to acoustic level pressures, was designed and used to measure amplitude, frequency and phase of fluctuating pressure on the surface of a three inch diameter circular cylinder at rest and exhibiting large-amplitude vortex-excited oscillation i n a uniform incident wind flow. The phase of the fluctuating pressure relative to the cylinder motion and the cylinder amplitude and frequency were recorded. A disc probe connected to the pressure transducer was used in wake surveys for the stationary and oscillating cylinder. Measurements, made i n the Reynolds number range 1.5(10^) <H R< 4.1(10^), indicated the following: Fluctuating pressures on the surface of both a stationary and a vortex-excited circular cylinder experience amplitude modulation, being random for the stationary cylinder and c r i t i c a l l y dependent on wind speed for the vortex-excited cylinder. Fluctuating pressures for both a stationary and an oscillating cylinder are i n phase over one side of the cylinder and 180° out of phase with the opposite side. For a vortex-excited cylinder, the vortex frequency i s 'captured' by the cylinder frequency over a discrete range of wind speed. The amplitude of fluctuating pressure on the surface of a vortex-excited cylinder increases as the resonant wind speed (wind speed corresponding to maximum cylinder amplitude) i s approached, but before that actual wind speed i s reached, an abrupt decrease occurs, and the amplitude modulation nearly disappears. A sudden change of phase between cylinder motion and fluctuating pressure occurs near the resonant wind speed and the pressure wave form becomes asymmetrical. The longitudinal spacing of vortices i n the wake of a stationary and a vortex-excited cylinder i n i t i a l l y increases as the vortices are swept downstream from the f o r m a t i o n zone. V o r t e x - e x c i t e d o s c i l l a t i o n of a c y l i n d e r , as the resonant wind speed i s approached, produces an i n c r e a s e i n l o n g i t u d i n a l v o r t e x s p a c i n g and a c o r r e s p o n d i n g abrupt decrease i n l a t e r a l s p a c i n g . A t the resonant wind speed, the wake l o s e s i t s coherent p e r i o d i c i t y . i v CONTENTS Page No. I . ' I N T R O D U C T I O N 1 II. INSTRUMENTATION 7 2.1 Wind Tunnel 7 2.2 Models 7 2.3 Model Mounting System 9 2.4 Wake Traversing Gear 10 2.5 Pressure Transducer 11 2.6 Transducer Calibration Apparatus 15 2.7 Wake Probe 17 2.8 Displacement Transducer 17 2.9 Photography 18 I I I . EXPERIMENTAL P R O C E D U R E S 19 3.1 Calibration Procedures 19 3.1.1 Transducer Total Head, Steady Pressure Calibration 19 3.1.2 Cantilever Beam Calibration 20 3.1.3 Transducer Calibration 21 3.1.4 Model Tap Constriction Calibration 23 3.1.5 Wake Probe Calibration 24 3.2 Test Procedures 24 3.2.1 Tubing 24 3.2.2 Surface Pressures on Model, (a) Stationary Model, (b) Oscillating Model 25 3.2.3 Model Amplitude and Surface Pressure 25 3.2.4 Wake Survey 26 V Page No. IV. EXPERIMENTAL RESULTS 2 7 4.1 Fluctuating Pressures on the Surface of a Stationary Circular Cylinder 2 7 4.2 Wake Survey - Stationary Cylinder 2 8 4.3 Fluctuating Pressures on the Surface of an Oscillating Circular Cylinder 2 9 4.4 Wake Survey - Oscillating Cylinder 3 2 V. DISCUSSION OF RESULTS 3 4 VI. SUMMARY OF RESULTS 4 2 APPENDICES A Damping data for spring-model system. Spring Particulars.4 4 B Piezoelectric Crystal Response Data 4 5 C Pressure Transducer Components 4 6 D Wave Propagation i n a Tube 4 7 E Disc Static Probe 4 8 F Tunnel corrections to wind speed 4 9 BIBLIOGRAPHY 5 0 ILLUSTRATIONS 5 3 ILLUSTRATIONS Figure Number Page No, 1. Aerodynamic Outline of Wind Tunnel 53 2. Models, 3 inch diameter Circular Cylinder and 3 inch D-section 54 3. Plastic End Fitting for Circular Cylinder 55 4. Mid-span Bulkhead of D-section Model before Aluminum Skin was Attached 56 5» Pressure Tap Positions for D-section Model 57 6. Air Bearings, shaft and springs 58 7. Arrangement of Model Mounting System 59 8. Traversing Gear - Looking Downstream into Wind Tunnel Test Section 6 0 9. Traversing Gear in Test Section showing Working Area Side Panel 61 10. Diagrammatic Layout of Apparatus used in Crystal Response Investigation 62 11. Vibration Generator and Cantilever Beam Mounted in Frame 63 12. Typical Oscilloscope Traces of Crystal and Cantilever \ Beam Response 64-65 13. Pressure Transducer - Details 66 14. Pressure Transducer - Disassembly 67 15. Pressure Transducer 68 16. Pressure Transducer - Circuit Diagrams 69 17. Piston Arrangement at Upper End of Cantilever Beam showing Tube and Tube Clamp 70 18. Disc Probe 71 19. Diagrammatic Layout of Steady Pressure Calibration Apparatus 72 20. Pressure Transducer Signal vs. Total Head Steady Pressure 73 21. The Effect of a Static Pressure Rise in the Transducer Cavity on the Transducer Sensitivity to a Fluctuating Pressure 74 ,T . ILLUSTRATIONS (continued) Figure Number Page No. 22. Cantilever Beam Deflection vs. Strain Gauge Signal 75 23. Diagrammatic Layout of Pressure Transducer Calibration Apparatus 16 24. Pressure Transducer Calibration Apparatus 77 25. Transducer Calibration Data 78 26. Pressure Transducer Signal during Tube Oscillation with and without a Dummy Tube Connected 79 27. Amplitude Ratio and Phase vs. Frequency Model Tap Constriction Calibration 80 28. Phase and Amplitude Ratio vs. Frequency from Disc Probe Calibration 81 29. Typical Oscilloscope Traces of Pressure Signals from Disc Probe Calibration 82 30. Diagrammatic Layout of Wake Survey Apparatus 83 31. Typical Oscilloscope Traces of Fluctuating Pressure from the Surface of a 3 inch Diameter Stationary Circular Cylinder 84-91 32. Angular Distribution of Fluctuating Pressure Amplitude at the Fundamental Frequency on the Surface of a 3 inch Diameter, Stationary, Circular Cylinder 92 33. Fluctuating Pressure Coefficient C vs. N D 93 p K •*s 34. Coordinate Axes for Wake Survey 94 35« Phase and Amplitude of a Probe Signal in the Wake of a 3 inch Diameter, Stationary Circular Cylinder 95 36. Typical Oscilloscope Traces of Surface Pressure and Wake Probe Signal for a 3 inch Diameter, Stationary Circular Cylinder 96-97 37» Typical Oscilloscope Traces of Cylinder Oscillation and 90° Surface Pressure for 3 inch Diameter Circular Cylinder Exhibiting Vortex-excited Oscillation 98-IOI 38, Cylinder Oscillation Amplitude and Frequency, Fluctuating Pressure Frequency and Phase vs. Wind Speed 102 v i i i ILLUSTRATIONS (continued) Figuret Number Page No. 39« Typical Oscilloscope Traces of Fluctuating Pressure on the Surface of a 3 inch Diameter, Circular Cylinder Exhibiting Vortex-excited Oscillation 103-109 40. C and Angular Distribution of Fluctuating Pressure on the ^o Surface of a 3 inch Diameter Circular Cylinder Exhibiting Vortex-excited Oscillation 110 41. Oscilloscope Trace of Cylinder Oscillation Amplitude and 90° Fluctuating Pressure During Transient build-up of Cylinder Displacement. Wind Speed 12.4 f.p.s. I l l 42. C 1 and C» vs. Wind Speed 112 P P *B o 43. Comparison of 'Capture' Data with Ref. (22) 113 44. Comparison of Phase Data with Ref. (23) 114 45• Phase and Amplitude of Probe Signal in the Wake of 3 inch Diameter Circular Cylinder Exhibiting Vortex-excited Oscillation (Longitudinal Traverse) 115 46. Amplitude of Probe Signal in the Wake of a 3 inch Diameter Circular Cylinder Exhibiting Vortex-excited Oscillation (Lateral Traverse) 116 47* Lateral and Longitudinal Spacing and Velocity of Vortices in the Wake of a 3 inch Diameter Circular Cylinder Exhibiting Vortex-excited Oscillation 117 i x ACKNOWLEDGEMENTS Sincere appreciation i s expressed for the guidance and encouragement given hy Dr. G. V. Parkinson during his supervision of this investigation. To the entire technical staff of the Department of Mechanical Engineering, the author expresses sincere thanks. Although the personal interest taken by the technicians i n the many problems which arose during the building of equipment i s , alone, reason enough for gratitude, such interest was merely representative of their cooperation throughout this programme. The processing of the seemingly endless number of oscilloscope photographs was performed by my wife and for the many hours she spent in the photographic darkroom and in subsequent identification of prints, I am sincerely grateful. The use of the f a c i l i t i e s of the Department of Mechanical Engineering i s gratefully acknowledged. Financial assistance was received from the National Research Council of Canada. X SYMBOLS V = air- velocity p = air density h = lateral dimension of cylinder section L = length of cylinder x = longitudinal coordinate for wake survey y = lateral displacement of oscillating cylinder or lateral coordinate for wake survey z = spanwise coordinate for wake survey Y = y/h = dimensionless amplitude k = spring constant of osci l l a t i n g system m ,= mass of oscillating system ton = (k/m)^^ = 2nfn = circular frequency of free undamped oscillation of system U = V/coh = dimensionless flow velocity ^ = kinematic viscosity Vh N R = = Reynolds number C' L = fluctuating l i f t coefficient f = frequency of vortex formation from one shear layer f = frequency of cylinder oscillation c S = fh/V = Strouhal number p = static pressure p' = mean amplitude of fluctuating pressure about a mean static pressure p ? = fluctuating pressure 2 C = p'/l/2pV = fluctuating pressure coefficient amplitude ^s (stationary cylinder) C = p'/l/2pV = fluctuating pressure coefficient amplitude ^o (cylinder exhibiting vortex-excited oscillation) a = l o n g i t u d i n a l spacing of v o r t i c e s i n the wake h = l a t e r a l spacing of v o r t i c e s i n the wake = f a = speed of v o r t i c e s i n the wake 9 = angular p o s i t i o n on c y l i n d e r surface a = speed of sound 6 = c a l i b r a t i o n p i s t o n amplitude -H. = c i r c u l a r frequency of p i s t o n t = time S u b s c r i p t s D = recorded from d i s c probe I . INTRODUCTION 1 Plow past a circular cylinder, for many years, has been a subject of discussion and investigation for theoreticians and practical engineers alike. The former accept the phenomena as a challenging problem for which, as yet, no satisfactory theory exists, while the latter are faced with the very real and insistent problems of the effects on structures such as smoke-stacks, aerial pipelines,, etc. It i s not the purpose of this section to give an his t o r i c a l background of the many investigations which have been undertaken since Leonardo da Vinci, in the fifteenth century, sketched vortex formation in the wake of bluff bodies ( l ) ; such an account i s given by Brooks (2), while a concise summary of available data up to 1962, including recent theoretical and experimental results (2), (3) for a variety of bluff body shapes i s given by Parkinson ( 4 ) , Although numerous investigators have turned their attention to the measurement and observation of flow around a stationary circular cylinder, i t must be pointed out that their work i s spread over a large range of Reynolds number (0,1<N R<10 ) and due to the dependence of flow character-i s t i c s on Ng, reliable date are s t i l l i n demand. Enough data are available, however, to enable the major flow regimes to be identified, A summary of these regimes with relevant references is given by Morkovin (5) and a more recent report by Kuchemann (6) summarizes past and present work in the more general f i e l d of concentrated vortex motion i n fluid s . For completeness, a brief description of each flow regime follows. a) N R < 1 No periodicity occurs i n the laminar wake and the flow pattern resembles that obtained by an ideal inviscid flow solution, b) "Twin-Vortex Stage", 3<-%<40 No periodicity occurs i n the laminar wake, but two large stationary 2 vortices form directly behind the cylinder, one on each side of the stream axis. c) "Incipient Karman Range", 40<N R<90 Immediate wake forms as in the "Twin-Vortex Stage", but downstream of the stationary vortices, the laminar wake is unstable. d) "Pure Karman Range", 90<N R < 300 A well defined, stable, vortex street forms i n the laminar wake and persists for a long distance downstream u n t i l the vortices are dissipated by viscosity. The vortices form an unsymmetrical double row, each vortex being opposite the mid-point of the longitudinal space between consecutive vortices in the other row, . e) "Subcritical Range", 300 < N R < 13(lO 4) Plow around the cylinder separates from the surface i n two laminar shear layers (the separation occurring near the transverse diameter). The two shear layers, whose transition to turbulence approaches the cylinder with increasing N R, r o l l up alternately into discrete vortices. A periodicity i s observed in the turbulent wake, but i t i s subsequently dissipated by viscous diffusion. The formation frequency occurs at a nearly constant Strouhal number, S = fh/V. This i s the N R range of the present investigation. f ) " C r i t i c a l and Post-Critical", 13(l0 4) < N R < 35(l0 5) Flow reattachment to the cylinder surface and subsequent turbulent reseparation occurs, resulting i n a narrowing of the wake. No discrete vortices are observed, the dominant periodicity of the wake being lost. g) "Transcritical", N R>35(l0 5) The point of flow separation moves towards the front of the cylinder resulting i n a wake which is wider than that of the preceding range. A dominant periodicity of the wake i s recovered. 3 Plow past a circular cylinder i s not s t r i c t l y two-dimensional, spanwise effects exist and have been observed by Humphreys (7) and Mattingly (8) i n the subcritical and c r i t i c a l range. Other investigators ( l ) , (9) have noted the three-dimensionality of the flow. The measurement of fluctuating effects on the surface and i n the wake of a stationary circular cylinder i n a uniform flow has been undertaken by several investigators; a brief account of their work follows. McGregor (10) investigated fluctuating pressures on a cylinder surface =Or 5(l04) and 12(10 V] by means of a condenser microphone. The microphone was mounted inside the cylinder and the fluctuating pressures were transmitted via a hole in the cylinder surface to the microphone cavity. An estimate of the osc i l l a t i n g l i f t and drag forces was obtained by integration of the surface pressure coefficients. A mathematical model of the flow was developed by assuming an alternating vortex to be positioned at the rear of the cylinder. A similar investigation was undertaken by Gerrard ( l l ) , 4(10^) < N R < (10^) , the pressure pick-up being essentially a condenser microphone type, but with the pressure sensitive area forming part of the cylinder surface. A different method of investigation was employed by Heine (12) who mounted a pressure transducer remote from the cylinder. The fluctuating pressure was conveyed from the model surface to the transducer via a small bore tube. The pressure transducer relied upon the voltage response of a piezoelectric crystal to small displacements. Heine's investigation included, besides a circular cylinder, other body shapes of both bluff and streamline form. While the work described above produced estimates of the fluctuating forces on a cylinder by the indirect means of integration of the fluctuating pressures, direct measurement of forces has been made. Bishop and Hassan (13) 4 measured fluctuating l i f t and drag forces on a stationary circular cylinder placed in a water channel £3.6(10^)< NR< 11(10^)^ . Strain gauge trans-ducers, b u i l t into the cylinder supports, provided a means of fluctuating force measurement. The fluctuating forces on a short segment of a stationary circular cylinder were measured by Keefe (9). Measurements were made in a wind tunnel i n the range 5(lO^)<-N R 4 (10^). The effect of two circular discs mounted on the cylinder near the force transducer was examined. End effects were considered and experiments performed to establish the limits of their influence. In a higher range of Reynolds number, 4(l0 4)<N R< 6(l0^), Humphreys (7) investigated fluctuating l i f t and drag, the force transducers being incorporated i n the cylinder support. Further observations on span-wise effects are included i n his report. Measurements i n the wake of a stationary circular cylinder were f i r s t made by Fage and Johansen (14) who employed a hot-wire technique to determine the velocity and frequency of individual vortices passing down-stream, = 2.76(icft), Cylinder shapes other than circular were investigated in the above reference and, in an earlier paper by the same authors, measure-ments i n the wake of an inclined f l a t plate are reported. A photographic study of streamlines i n the wake of a stationary circular cylinder was made by Thorn (l5)» Dye techniques were used i n a water channel at low Reynolds numbers (20<NR< 80). A similar investigation i n air flow was carried out by Kovasznay (16). Hot wire measurements of velocity distribution and frequency were made i n the range 40 < U R <160. The effect of channel breadth on wake structure was investigated by Rosenhead (l7)» A water channel having a variable breadth was used, the cylinder being pushed through the water at various velocities (40 < N R <, 800). Wake structure was observed by means of the presence of aluminum powder on the water surface. In a more recent report by 5 Shair, et a l , (18), the effect of confining walls on the wake s t a b i l i t y i s discussed. Frequency and velocity measurements i n the wake of stationary circular cylinders made by Roshko ( l ) , (19) encompass the entire range of major flow regimes. Hot-wire measurements locating the position of the region of transition to turbulence and the manner i n which turbulence develops have been made by Bloor (20), in the range 100< N R<52(10^), The foregoing summary of investigations of surface and wake effects of flow past a stationary circular cylinder i s far from complete, yet i t s volume i s i n sharp contrast to that of published data for similar measurements on an oscillating cylinder. In particular, such data pertaining to vortex-excited cylinders are almost non-existent, a fact which might be related to the complications in instrumentation which arise from the cylinder motion. Vortex excitation of an elastically-mounted cylinder occurs when the frequency of the vortex formation (proportional to the wind speed i n the subcritical range, i„e,, S = constant), approaches a natural frequency of the elastic system. The periodic characteristic of the flow f i e l d causes a periodic pressure distribution on the cylinder surface and the resulting periodic forces excite cylinder oscillations over a discrete range of wind speeds. Typically, a graph of cylinder amplitude versus wind speed has a form not unlike that of a forced vibration with damping, while a graph of vortex frequency versus wind speed portrays a 'capture 1 phenomenon, i.e., when a particular wind speed in the cylinder oscillation range i s reached, the vortex frequency ceases to be proportional to wind speed, remaining at the natural frequency of the elastic system. At a wind speed greater than that for maximum cylinder amplitude, the vortex frequency reverts to the stationary cylinder value (S = constant). Measurements of vortex frequency, cylinder frequency and amplitude made by Brooks (2) verify the above 6 phenomenon. Reference (2) includes data obtained from a variety of cylinder shapes (circular cylinder, D-section and rectangles of various aspect ratios)} •capture' i s seen to occur both i n plunging and torsional modes of vibration for a D-section and a circular cylinder. Further evidence of 'capture' is reported by Eagleson, et a l . (2l) in a study of the torsional vibrations of f l a t plates when placed parallel to a uniform stream. When a cylinder i s forced to vibrate at a variable frequency in a uniform flow, frequency measurements in the wake show 'capture' behaviour. In investigations by Smirnov and Pavlihina (22) and Bishop and Hassan (23), the vortex frequency, over a range of cylinder frequencies, was found to be controlled. The adjustment of the vortex frequency to the cylinder o s c i l l a -tion frequency, as for the case of vortex excited cylinders, was found to be a sudden occurrence. With the exception of Bishop and Hassan's measurements of fluctuating l i f t and drag on a circular cylinder forced to vibrate at a variable frequency in a uniform flow, published technical literature i s devoid of surface effect measurements on oscillating cylinders. A similar exception for the case of wake effects for oscillating cylinders i s a report by Wehrmann (24) i n which the cylinder i s described to oscillate transversely to the flow at a frequency determined by a feedback c i r c u i t from a hot-wire in the wake. The following investigation i s an attempt to examine the amplitude, modulation, frequency, and phase of fluctuating pressures on the surface of both a stationary and vortex excited circular cylinder and to establish the geometry and behaviour of the wake. II. INSTBUMENTATION  2.1 Wind Tunnel The wind tunnel used in this programme is a low speed, low turbul-ence, return type. Velocities can be varied through the range 4 feet per second to 150 feet per second with turbulence level of less than 0.1$. The pressure differential across the contraction section of 7*1 ratio i s measured on a Betz micromanometer which can be read to 0.2 millimeter of water; the test section velocity i s calibrated against the above pressure di f f e r e n t i a l . The test section i s rectangular i n cross-section (36 inches by 27 inches) with 45° corner f i l l e t s . Variation of the corner f i l l e t s from 6 inches by 6 inches to 4 3/4 by 4 3/4 inches compensates for boundary layer growth. The spatial variation of velocity i s less than 0.25$. Tunnel power i s supplied by a 15 horsepower direct current motor driving a commercial axiflow fan with a Ward-Leonard system of speed control. An aerodynamic outline of the tunnel is shown in f i g . 1. 2.2 Models Two models were constructed, a 3 inch diameter circular cylinder and a 3 inch D-section ( f i g . 2). Since i t was intended to oscillate both models under vortex excitation, weight was the dominant consideration i n the design. Pressure taps on the surface of the models with internal tube connections leading to the ends of the models complicated the effort to minimize weight. Combined with surface f i n i s h and strength considerations, the above complica-tion suggested that a thin aluminum skin with plastic f i t t i n g s be adopted as a construction technique. Polyethylene tubing used to convey the pressure from the surface taps was 0.066 inch inside diameter, 0.095 inch outside diameter, and 4 feet i n length. The above choice resulted from an 8 investigation of various tube diameters (see par. 3.2„l)o Circular Cylinder A 3 inch outside diameter, 0.022 inch wall thickness aluminum tube provided the body of the model. Plastic end f i t t i n g s which allowed the model to be rotated about i t s own axis, yet remain attached to the air bearing shaft brackets, were secured by an epoxy adhesive to the aluminum tube. A typical end f i t t i n g i s shown in f i g . 3* Sue to the advantages of the symmetry of the section and the a b i l i t y to rotate the model, the distribution of pressure taps on the model surface was kept to a minimum. Four taps were equally spaced (30°) over one quadrant of the model surface at mid-span. Two spanwise taps, 3 inches and 6 inches above mid-span, were positioned i n line with one extremity of the above quadrant. Pressure tap holes in the model surface were 0.025 inch i n diameter. To maintain the unmarred surface f i n i s h which resulted from lathe-polishing of the aluminum tube, i t was decided to insert pressure tube connections from the ends without resorting to sp l i t t i n g the aluminum tube longitudinally and partially spreading to allow access. Plastic blocks, which were radiused to f i t the model inside diameter, were d r i l l e d to effect a 90° bend. An epoxy adhesive served to bond the plastic block to the aluminum and to the polyethlene tubing. The polyethylene tubing was f i r s t bonded to the plastic block; the block was then f i t t e d on an insertion device which allowed alignment with the .025 inch tap in the aluminum skin and contact pressure to be applied to the model interior. For the four equally spaced taps at mid-span, a quadrant-shaped plastic block was made to accommodate the four tube connections and was inserted as a unit. 9 D-Section Construction of the D-section model (fig , 2) was similar to that of the circular cylinder. The radiused surface was cut from a length of 3 inch outside diameter, 0.022 inch wall thickness aluminum tube while the f l a t face was of 3/32 inch thick clear plastic. Plastic end f i t t i n g s were similar to those of the circular cylinder and allowed rotation of the model about a longitudinal axis. Plastic stiffening bulkheads were f i t t e d at the quarter span positions. Due to the asymmetry of the section at non-zero angles of attack i t was necessary to distribute 32 pressure taps around the model surface at mid-span. Two pressure taps were located at one extremity of the radiused surface, 3 inches and 6. inches from mid-span. Tube connections to the 0.025 inch holes i n the model surface were made by the same method used with"the circular cylinder. A mid-span bulkhead was d r i l l e d to accommodate the tube connections, but where space did not allow such a connection, a \ small plastic block was f i t t e d as close as possible to the mid-span^position. Pig. 4 shows the mid-span bulkhead and individual plastic blocks before the radiused aluminum skin was attached. The distribution of the pressure taps on the model surface i s given in f i g . 5. 2.3 Model Mounting System An air bearing system designed by Smith (3), had been found satis-factory during his tests and during subsequent experiments (12). This arrangement of model mounting was adopted. The models were constrained to one degree of freedom (plunging) with a minimum of damping from the mounting system. Slots i n the top and bottom panels of the test section allowed the model to be attached to the a i r bearing shafts. Pig. 6 shows typical bearings, shaft and model bracket: In the photograph, the model i s not mounted and the 10 tunnel access panel has been removed. Air supply for the bearings was produced by an Ingersoll-Rand 2-stage compressor, model 11 3/4 x 7 x 8 VHB-2, via a 250 cubic foot storage tank. A flexible hose conducted the air to a throttling valve at the tunnel test section. To provide the elastic system for the model four he l i c a l , tension springs were attached to the shaft brackets and to the air bearing frame. An arrangement of the model, bearings, shafts, and springs i s shown in f i g . 7. The springs were designed so that the natural frequency of the spring-mass system allowed the aerodynamic investigations to be carried out at wind speeds greater than 10 feet per second. A streamline model (25) was used to determine the damping due to the spring-bearing system. These data are given in Appendix A along with spring dimensions. 2.4 Wake Traversing Gear To enable a wake probe to be positioned with control of movement in a later a l , vertical and longitudinal sense, a traversing gear was designed. While accuracy of probe placement was the basic requirement, tunnel blockage and convenience of control had to be considered. Tunnel blockage was kept to a minimum as can be seen in f i g . 8 . To provide accurate placement in the lateral direction, a 5/8 inch 10 acme, double start lead screw spanned the test section. Two followers mounted on the lateral lead screw carried vertical, l/4 inch - 20 NC lead screws enclosed i n guide tubes. The probe mounting brackets were carried by follower nuts on the vertical lead screws. The entire assembly was mounted on a horizontal, r i g i d frame which, having grooved wheels to match r a i l s on the exterior of the tunnel side panels, could be positioned longitudinally. To allow the longitudinal motion of the frame, new side panels ( f i g . 9) having 3/4 inch longitudinal slots were designed and f i t t e d to the test section. The upstream end of the slots could be extended 11 to the removeable window section, thus the entire traversing gear could be removed from the tunnel with a minimum of dismantling* Hand wheels con-t r o l l i n g both lateral and vertical motion of the probe were conveniently-mounted on the working area side of the frame (fig* 9)° Rotation of the vertical lead screws was achieved by flexible shafts* A scale attached to the r a i l on the tunnel side panel gave a direct reading of longitudinal position. The error i n positioning the probe was estimated to be approximately l/32 inch, or about 1$ of cylinder diameter. This accounted for clearance play i n the lead screws and guides. 2.5 Pressure Transducer The type of measurements, i.e., fluctuating acoustic level pressures, which were to be made in this programme suggested that use be made of a transducer developed by Heine (12). Heine's design incorporates a rubber diaphragm and a standard ceramic crystal commonly used i n phonographs. Diaphragm deflections due to the fluctuating pressures are transmitted by means of a link to the crystal which, i n turn, produces a voltage output. During i n i t i a l work with the above transducer, however, doubts arose as to the nature of i t s response, and the following investigation was carried out. To examine the response of the crystal independent of tubing, cavity and diaphragm, a link connection was made from the crystal direct to a cantilever steel beam, (section 2.6). Amplitude and frequency of the beam deflection were controlled by a Goodmans Model V47 Vibration Generator attached to the free end of the beam. Strain gauges mounted on the beam gave a signal proportional to beam deflection, thus crystal displacement. A diagrammatic layout of apparatus is shown in f i g . 10 and the cantilever beam, vibration generator and frame are shown in f i g . 11. Observation of signal 12 amplitudes and phase relation over a frequency range of 10 cycles/sec. to 80 cycles/sec. for both sinusoidal and non-sinusoidal displacement wave forms showed that the crystal output depended upon the rate of displacement rather than pure displacement only. Typical oscilloscope traces of strain gauge and crystal output are shown in f i g . 12. Data for this particular investigation are given in Appendix B. It w i l l be noted that although the strain gauge signal amplitude was kept constant, the crystal output increased when a non-sinusoidal displacement wave form was introduced. Above 50 cycles/ sec. the beam displacement signal tends to a sinusoidal wave form and the crystal output returns to that of the sinusoidal displacement case. Non-sinusoidal displacement of the cantilever beam was achieved by emitting a triangular wave form from the low frequency function generator and accepting the response of the vibration generator-beam system. The apparent sensitivity of the crystal to wave shape, rather than wave amplitude, the necessity to rely upon a sinusoidal wave shape calibration (12), and the inadequate sensitivity at the low wind speeds used i n this programme suggested that a different means of determining fluctuating pressure be found. Due to the fact that part of this investigation was to measure fluctuating pressures on the surface of oscillating models, i t was necessary to design a transducer which was either both light and small, (this would enable i t to be incorporated inside the model), and insensitive to acceleration or, alternatively, the pressure could be conveyed via a tube to an externally mounted transducer. The latter method, employed by Heine (12),was chosen to avoid the practical problems of miniaturization and inertia. The effect of the tubing on the signal amplitude and phase was subsequently investigated (section 3 .2 .1) . Following the work of Heine, i.e., u t i l i z i n g the response of a rubber diaphragm to the fluctuating pressures, a means of converting this deflection 13 into an electrical signal was sought. A crude, f i r s t attempt to employ an electrical resistance which varied with light intensity (Phillips type no. B 8 731 03) showed that a shutter placed i n a light heam from an ordinary flashlight bulb required a minute displacement to give a substantial resis-tance change, the relationship between resistance change and shutter displacement being a function of the light intensity. By mounting the shutter on the rubber diaphragm and subjecting the latter to fluctuating pressures of the order of magnitude of those expected on the models, a suitable resistance change was observed. In order to convert this change in resistance to a voltage signal, the light dependent resistance was included in one arm of a two arm bridge c i r c u i t and connected to a bridge amplifier and meter ( E l l i s Associates BAM-l). The output from the above instrument was displayed on a cathode ray oscilloscope. Since the upper limit of arm resistance which could be used with the bridge amplifier and meter was 2000 ohm and since the light dependent resistance at a light intensity available from a simple 6 volt bulb-battery ci r c u i t was of the order of 30,000 ohm, i t was necessary to connect a shunt resistance across the arm. I n i t i a l l y , a 0-2000 ohm potentio-meter was used as a shunt, thus the arm resistance could be varied. The second 0-2000 ohm potentiometer was used as the dummy arm of the bridge c i r c u i t . The above arrangement, although producing a clean signal, proved to be extremely susceptible to temperature changes thus making i t impossible to maintain a bridge balance. The dummy arm was modified to include a light dependent resistance and shunt similar to that in the active arm, but in this case, the light beam was interrupted by a stationary shutter which could be adjusted to bring the light dependent resistance value equal to that i n the active arm. This proved to eliminate, to a large extent, the thermal d r i f t problem, Once optimum shunt resistance values were chosen, the 14 potentiometers were replaced by f i r s t , standard carbon resistances (10$ tolerance) and secondly, deposited carbon film precision resistances (l$ tolerance). Thermal d r i f t continued to cause a small, but awkward unbalancing effect on the c i r c u i t . The source of this thermal d r i f t was found to be the thermal in s t a b i l i t y of shunt resistances: i t was eliminated by the use of strain gauges as shunt resistances. The gauges were steel compensated and mounted on a mild steel f l a t bar in a temperature compensating c i r c u i t . A secondary problem arose with the vibration of light bulb filaments. Various commercially available bulbs were tested, but even with the most suitable, i t was found necessary to insert ground glass between the light source and the light dependent resistance. This diffusion of the light beam reduced the filament vibration effect, and made the bulb alignment relative to the light dependent resistance less c r i t i c a l . The latter problem arose only when i t was necessary to replace bulbs. Other parameters of the design were investigated. Diaphragm stiffness and shutter widths were varied. It was found that a more flexible diaphragm than that used by Heine was necessary to give the required sensitivity. Pig. 13 and f i g , 14 show details of the f i n a l design. The entire transducer casing and shunt resistances were enclosed in a cabinet ( f i g . 1 5 ) . Meters on the cabinet face were included to serve as a rough guide when setting light intensity. During tests, f i n a l adjustment to light intensity was made as described in section 3.1.3. A schematic wiring diagram for the transducer is given in f i g . 16. A detailed l i s t of transducer components is given i n Appendix C. Later work with oscillating tubing (section 3.1.3) led to the following modification of the transducer casing. In order to admit a pressure fluctuation to the side of the diaphragm opposite.to that inside the cavity, a hole was d r i l l e d through the casing side to intercept the central hole 15 above the shutter. The ground glass effected a pressure seal at the light dependent resistance; a similar translucent seal was inserted i n the bulb holder socket. A set screw isolated the volume surrounding the shutter and diaphragm from the dummy arm components. Correlation of two pressure signals on the model surface, or a model surface pressure with a wake signal, .required that two pressure transducers be used. The transducers were bu i l t identical in a l l respects and the c a l -ibration data (section 3.1.3) given i n f i g . 25 applies to both. 2.6 Transducer Calibration Apparatus In previous work (12) a calibration technique included the use of a horn driver, cavity and a sound level meter (sections 3.1.4 and 3.1.5). Due to distortions arising from the amplifier and the response of the horn driver, the lower frequency limit for such an arrangement proved to be 15 to 20 cycles/sec. Heine (12) extended the calibration below this limit by u t i l i z i n g the linear nature of the signal amplitude versus frequency curves. Due to the fact that the frequency of pressure fluctuations anticipated in this experimental programme f e l l almost entirely within the range 7-20 cycles/ s e c , it'was f e l t that a more positive means of calibration should be adopted. Since i t had been decided to mount the transducer outside the tunnel test section, thus employing tubing to convey the pressures from the model surface (or from a wake probe) to the transducer, an investigation of the effects of the tubing on .the. signal., phase relation was necessary (section 3.2.1). This aspect. ,pf the programme further pointed out the need for a calibration procedure which would give a reference signal which was in a known phase relation with the generated pressure at the pressure source. A piston-cylinder type calibration had been attempted by Heine (12), 16 employing a piston of a much smaller diameter than that of the cylinder: a refinement of this technique was adopted, A piston was introduced directly into the polyethylene tube; the piston diameter was matched to the tube inside diameter and the necessary clearance was sealed by vaselines Fluctuat-ing pressures were obtained from the piston oscillations. Quantitative pressure fluctuations were calculated following the theory given i n Appendix D. Since the pressure produced by the piston was a function of both piston amplitude and frequency, a control of both these parameters was necessary. The cantilever beam and calibration frame already used to investigate the response of Heine's transducer crystal (12) provided a ready means by which to achieve this control. The mild steel beam had a cross section of 1.032 inches by 0,108 inches. From the top of the clamp to the centre of the vibration generator attachment was 6 3/4 inches. Four Budd Metalfilm strain gauges (type C6—121, 120 ohms) were mounted i n a four arm bridge c i r c u i t on the beam just above the clamp. The calibration frame was r i g i d l y constructed of 3/8" thick mild, steel plate. A clamp on the base provided a means of holding the beam i n a vertical position and slotted holes allowed adjustment of both the clamp horizontal position and the vibration generator vertical position. Calibra-tion frame and beam are shown i n f i g . 11. By mounting the piston opposite the vibration generator at the upper end of the cantilever beam the required control was achieved. A simple bracket and clamp which was r i g i d l y attached to the frame held the polyethylene tube. The upper end of the cantilever beam with piston attached and tube clamp i s shown in f i g , 17, The strain gauges on the beam provided a means of determining piston displacement as well as a signal which was in phase with piston dis-placement and thus 90° out of phase with the pressure generated hy the piston. The frequency of the piston oscillations depended upon the chosen setting of the function generator. To accommodate the various inside diameters of tubing which were investigated, i t was necessary only to sub-stitute the corresponding diameter piston. A diagramatic layout of the calibration apparatus i s shown in f i g . 23. 2.7 Wake Probe On the assumption that the air flow i n the wake was mainly in the plane of the model cross-section, i.e., spanwise components were of a lower order of magnitude, a disc probe was constructed ( f i g . 18). A similar probe had been investigated (27) as a means of static-pressure determination and for that particular purpose was found to be insensitive to changes of flow direction i n the plane of the disc and not subject to scale effect. Appendix B includes data taken from ref. (27). It w i l l be noted from the data that a yaw of + 3° out of the plane of the disc produced only a slight effect on the C value. P The use of such a probe for the determination of fluctuating pressures raised a question as to the interpretation of the transducer signal and to that end, a calibration test was performed (section 3.1.5). 2.8 Displacement Transducer A signal corresponding to model amplitude was obtained from an air core transformer designed and used by Smith (3) and i n subsequent experiments (12). The coaxial cylindrical construction allowed the air bearing shaft to be inserted between the primary and secondary windings, thus varying the magnetic coupling. A 10 kc frequency signal supplied "by a Hewlett-Packard 200 CD oscillator was modulated by the shaft oscillations and this signal was r e c t i f i e d by means of a f u l l wave r e c t i f i e r ( 3 ) . The resulting signal was displayed on one channel of a Tektronix Type 5^4 Storage Oscilloscope. The linear nature of the displacement transducer response was established and a calibration was performed during each series of tests. 2.9 Photography The storage capabilities of a Tektronix Type 564 Storage Oscillo-scope enabled the experimental data to be displayed for qualitative observation and to be recorded on film for later detailed analysis. Satis-factory results were obtained by the use of an Asahi Pentax 6HI4, single lens reflex, 35 nun camera with a no. 3 , 49 inm close up lens attachment. The camera was mounted on the oscilloscope by means of a specially designed mounting bracket. Film used was Kodak Plus-X Panchromatic and best exposure values were found to be f 2 . 8 at l / 3 0 sec. Enlargements (4 inches by 5 inches) were printed. Over two thousand data shots were taken and the majority of the processing was performed i n the dark-room of the Department of Mechanical Engineering. 19 III. EXPERIMENTAL PROCEDURES  3.1 Calibration Procedures 3.1.1 Transducer total head, steady pressure calibration Calibration of the transducer for fluctuating pressures was performed" at a mean tube-cavity pressure close to atmospheric pressure. During tunnel tests, however, the mean pressure level depended upon the distribution of the static pressure around the model surface. It was necessary, therefore, to ensure that the response of the transducer to steady pressures was sufficiently linear to allow the calibration data to be used for model tests, A total head tube placed in the wind tunnel test section was connected to fi r s t , a Lambrecht micromanometer and second, the pressure transducer, A diagrammatic outline of the apparatus is given in f i g , 19, The oscilloscope amplifier was set to give a read-out of the d.c. signal and the transducer output was recorded at increasing increments of total head. The results, plotted in fig. 20, show that the linear portion of the curve extends to approximately 20 mmwg, well above the required range of investigation. A further check on the effect of the static pressure level in the transducer cavity was made, A fluctuating pressure at a frequency of 30 cps was subjected to various increasing cavity static pressures. The amplitude of the fluctuating pressure signal remained constant over the established linear response range of static pressure levels (fig. 21). If desired, the transducer calibration data could be applied at cavity static pressure_s above the linear range by applying correction obtainable from fi g . 20, i,e, the ratio, slope of curve at required cavity pressures slope of curve in linear range. This procedure was investigated and found to give reasonable results. 3.1.2 Cantilever Beam Calibration The mild steel cantilever beam used to indicate piston amplitude and phase relation i n the transducer calibration and subsequent tube investigations i s described i n section 2.6. Beam deflection was interpreted from a voltage signal given by a bridge amplifier and meter ( E l l i s Associates, BAM-l). The entire transducer calibration was dependent upon a consistent method of determining piston amplitude and since the gain control on the bridge amplifier meter varied the amplitude of the beam deflection signal, a means of calibrating the BAM-1 gain control was established. Two strain gauges (Budd Metalfilm, 120 ohm) were mounted on a short section of aluminum, in a temperature compensating two arm bridge c i r c u i t . After connections had been made to the bridge amplifier and meter, and bridge balance obtained, an internal resistance ( l M ohm) in the above instrument was shunted across one arm of the strain gauge c i r c u i t . The unbalance caused a current to flow i n the bridge and a meter reading was registered. Adjustment of the gain control varied this reading and for convenience, i t was set at 100 on the upper scale of the meter face. Thus, as long as the same bridge amplifier and meter was used, the gain control setting, determining the signal proportional to a given deflection could be duplicated. The gain calibration c i r c u i t was incorporated i n the pressure transducer cabinet. A depth micrometer r i g i d l y mounted i n a manner such that i t s shaft was opposite the piston at the upper end of the beam, applied the deflecting force and gave a measure of deflection. Since the required piston displacements were small, the change of slope at the beam end could be neglected and caused no problems in regard to piston misalignment or pressure sealing. Calibration results are plotted i n f i g . 22. Although beam design calculations showed that the vibration mode 21 change occurred outside the frequency range of interest, experimental evidence was obtained which confirmed the calculations. Two strain gauges in a two arm bridge circuit were mounted approximately at the mid-span of the beam. The phase relationship between signals from these gauges and those mounted near the clamped end showed that the change of mode occurred between 125 cycles per second and 140 cycles per second. 3.1.3 Transducer Calibration A diagrammatic outline of the transducer apparatus is shown in fig. 23 and the actual apparatus is shown in fig, 24. Prom the theory given in Appendix D, piston amplitudes were calculated for several pressure amplitudes (0.0005 psi to 0.050 psi) through a frequency range of 5 cycles/ second to 100 cycles/second. The low frequency function generator provided control over the frequency and amplitude of the piston; the amplitude was interpreted from the beam strain gauge signal. Beam deflection and bridge amplifier gain calibration were established as described in section 3,1,2, The dual input to a Tektronix Type 502A Oscilloscope enabled the phase relation between the piston motion and the transducer response to be investigated. For a constant value of fluctuating pressure amplitude at a given frequency and a tube of given length and diameter, the amplitude and phase of the transducer signal was governed by two factors: bridge amplifier gain setting and light intensity. Calibration of the amplifier gain was achieved by means of the calibration circuit described in section 3,1,2. A 0,5 H ohm internal shunt resistance was used and the meter set to read 70 on the top scale. The 0-10 ohm potentiometer in the transducer light circuit (fig, 16) allowed the power input to the bulbs to be varied. The extreme sensitivity of the transducer output to light intensity suggested 22 that for calibration, no reliance be put on the light circuit meter readings. The following calibration procedure was adopted and used throughout the test programme. Bridge amplifier gains for both the strain gauge and transducer circuits were calibrated as previously discussed. A known pressure, generated at 10 cycle/second, was introduced to the transducer cavity by means of a 4 foot, 0 .066 inside diameter, polyethylene tube. Adjustment of the light circuit potentiometer controlled the transducer output and allowed a standard signal to be established. The above procedure was repeated at the beginning of each series of tests and proved to be satisfactory in producing consistent results. Calibration curves (fig. 25) based on the above 10 cycles/second standard signal were then applicable to a l l model surface pressure data. The effect of the model tap constriction on the above calibration is discussed in section 3 . 1 . 4 . Tube connection to the transducer was a simple press f i t of the tube outside diameter into the transducer casing. Since, when connected the tube, cavity and piston formed a closed volume, the static pressure level was dependent upon the depth of the tube insertion. To ensure that calibra-tion was performed at, or near, atmospheric pressure, a plastic connection block was fitted at the transducer casing. A 0 .030 inch diameter hole drilled from the surface of the block to intercept the pressure tube bore at 90° , allowed the tube to be inserted with no increase of the static pressure level. After insertion, adhesive tape on the block surface effected a pressure seal. Since it was required to record surface pressure data from an oscillating model, it was unavoidable that the tube connection to the transducer be subjected to oscillations of the model frequency. Initial bench testing showed that the fluctuating pressures arising from tube 23 flexure were of the same order of magnitude as those on the model surface. In order to eliminate this signal, the transducer was modified (see section 2.5), and a dummy tube, similar to that leading from the model surface pressure connection, was f i t t e d . Both tubes led from the transducer casing to the lower end of the model and, since they were bound together, experienced similar oscillations. At the model, the dummy tube was led along the under-side of the test section and the open end located i n an area free of induced air flow. The length of the dummy tube was approximately 4 feet. Since the tube motion was common to both and the tubes reported to opposite sides of the transducer diaphragm, the signal resulting from the tube motion was cancelled. Before using this arrangement in the actual tunnel tests, a bench investigation was carried out. Fig. 26 shows typical CRO traces with and without the dummy tube attached: tubes were oscillated by hand to amplitudes far exceeding those experienced during model tests, 3.1,4 Model Tap Constriction Calibration The transducer calibration procedure described in section 3,1,3 was performed on tubing which did not duplicate the geometrical end conditions of the model tap. In order to determine the effect of the model surface tap constriction, the following investigation was undertaken. Using the calibra-tion apparatus employed by Heine (l2), i.e. a horn driven cavity pressure source, fluctuating pressures were produced. Calibration apparatus i s shown in f i g . 24. Comparison of signals from an open-end tube and an identical tube with a simulated model tap connected showed that the model tap had a negligible effect on the signal amplitude and phase. Due to amplifier distortion and horn driver response at low frequencies, quantitative pressures could not be measured. Signal amplitude ratios and relative phase angles for 24 a range of frequencies 0 -80 cycles/second were recorded and are shown i n f i g . 27» To ensure t h a t no e f f e c t s due to the c a v i t y geometry or tube p o s i t i o n i n the c a v i t y were i n c l u d e d , two i d e n t i c a l open-ended tubes were i n v e s t i g a t e d ; the s i g n a l s from the tubes remained i n phase and equal i n amplitude throughout the frequency range. 3.1.5 Wake Probe C a l i b r a t i o n C a l i b r a t i o n of the wake probe ( f i g . 18) was c a r r i e d out by means of the horn d r i v e r and c a v i t y shown i n f i g . 24. As discussed i n s e c t i o n 3,1.4, q u a n t i t a t i v e pressure measurements could not be made. P i g . 28 shows the e f f e c t of the probe on s i g n a l amplitude and phase angle r e l a t i v e to a tube connected t o a simulated model tap. During i n v e s t i g a t i o n s , i n t o the e f f e c t of tube lengths and diameters on s i g n a l a t t e n u a t i o n and phase l a g ( s e c t i o n 3 , 2 ,l), i t was noted t h a t the phase r e l a t i o n was independent of pressure lamplitude. Thus, the phase r e l a t i o n g i v e n i n f i g . 28 c o u l d be accepted w i t h some degree . of confidence. T y p i c a l o s c i l l o s c o p e t r a c e s of a f l u c t u a t i n g pressure s i g n a l from the wake probe and a simulated model tap are shown i n f i g . 29. 3.2 Test Procedures 3.2.1 Tubing The pressure transducer c a l i b r a t i o n apparatus discussed i n s e c t i o n 2.6 and s e c t i o n 3.1.3 was used to i n v e s t i g a t e the e f f e c t of tube le n g t h and diameter on the a t t e n u a t i o n and phase s h i f t of the pressure s i g n a l . Tube diameters of 0.070, 0.066, 0.055 and 0.045 inches were used and each tube was t e s t e d f o r lengths of 5*0, 4.0, 3.0, 2.0, 1,0 f e e t . F l u c t u a t i n g pressure amplitudes of 0.0005, 0.00075, 0.001, 0.002, 0.003, 0.004 and 0.005 p s i 25 were generated by the piston at frequencies ranging from 5 cycles/second to 100 cycles/second. Amplifier distortion occurred at low frequencies and proved to be a problem when determining phase angle relationships from the oscilloscope traces, 3.2.2 Surface Pressures on Model (a) Stationary Model Two pressure transducers (section 2,5) were connected to the pressure taps on the model surface, A reference pressure signal (90°) was displayed simultaneously with a signal from the other tap positions. Signal amplitude modulations were recorded by utilizing the storage capabilities of the Tektronix Type 564 Storage Oscilloscope on slow sweep speeds. Faster sweep speeds, portraying fewer cycles, provided data on frequency and phase relation. Pressure readings were taken at several wind speeds in the range 10 feet/second to 30 feet/second. (b) Oscillating Model Pressure data were obtained as described above, but due to tube oscillations, a dummy tube (section13.1.3) connection to each pressure transducer was necessary. 3.2.3 Model Amplitude and Surface Pressure A signal from the model displacement transducer (section 2.8) and a pressure signal from the model surface were displayed simultaneously on the oscilloscope screen. As in the surface pressure investigation, a slow sweep speed provided a record of amplitude modulation, while faster sweep speeds enabled the frequency and phase relation to be observed. Data were taken at several wind speeds through the model oscillating range. Correlation 26 of surface pressure and model amplitude was obtained for both the transient model amplitude build-up region and at steady state amplitude. The build-up region was investigated by triggering the CRO sweep while the model was stationary, i.e., no air being supplied to the air bearings} on opening the air bearing throttling valve, model oscillations were allowed to build-up. 3.2.4 Wake Survey In order to correlate pressure signals from the model surface with those in the wake, one pressure transducer was connected to the 90° tap on the model and the other connected to the disc wake probe (section 2.7). Tube connections to the transducers were identical (5.0 feet long by 0.066 inch inside diameter). Calibration of the probe is discussed in section 3.1.5* The control offered by the traversing gear (section 2.4) enabled the probe to be positioned in the model wake. Lateral traversing determined the position of probe signal maximum amplitude. Longitudinal traversing at the above lateral position provided a phase relation of the probe signal relative to the surface pressure signal. A diagrammatic outline of the apparatus is given in fig. 30. The signals from both transducers were allowed to build up on the screen of the Tektronix Type 564 Storage Oscilloscope until a coherent relation of the fundamental was detectable. In order to obtain a coherent build up, i t was necessary to trigger the CRO externally from the model surface pressure signal. Since stable triggering required approximately a 3 volt signal (peak to peak), the model signal was fed into a voltage amplifier before entering the trigger circuit of the oscilloscope. A Bogen 60 watt/ amplifier provided a power supply for the voltage amplifier. Adjustment of the triggering level of the oscilloscope selected a signal amplitude which led to a coherent build-up. The procedure for wake survey was identical for both stationary and oscillating models. 27 IV. EXPERIMENTAL RESULTS 4 . 1 Fluctuating Pressures on the Surface of a-Stationary Circular Cylinder A three inch diameter c i r c u l a r cylinder, mounted as described i n section 2 . 3 , spanned the test section of the wind tunnel. A i r was not admitted to the a i r bearings, thus cylinder o s c i l l a t i o n was prevented. Measurements of f l u c t u a t i n g pressures on the cylinder were made as described i n section 3 . 2 . 4 , [ l . 5 (lO 4) < N R < 4 . 1 (lO 4)] . Typical oscilloscope traces of a f l u c t u a t i n g pressure signal are shown i n f i g . 31. I t i s seen that the signal experiences a random amplitude modulation which i s i n phase around the cylinder. The fast sweep traces i n f i g . 31 show that the f l u c t u a t i n g pressures at the fundamental frequency are i n phase over one side of the model and 180° out of phase with the opposite side. F ig. 31 ( f ) shows the appearance of the second harmonic at the 180° tap position. Pressure fluctuations were not detectable at the 0° tap posi t i o n . The observation that the pressure amplitude modulation was i n phase at a l l points on the cylinder enabled the pressure d i s t r i b u t i o n to be plotted i n terms of a r a t i o , the amplitude of the f l u c t u a t i n g pressure at 90° being the common reference. A planimeter was used to determine the area of the envelope on the slow sweep traces and from t h i s , both a mean signal amplitude and the r a t i o of mean signal amplitudes were obtained. The d i s t r i b u t i o n of fluctu a t i n g pressures on the model surface at several Reynolds numbers i s shown i n f i g . 32 together with e a r l i e r measurements by Gerrard ( l l ) and McGregor (lO). Fig. 33 shows the v a r i a t i o n of C with N_ at the 30°, 60°, p a. 90°, 120 and 150° pressure tap locations. Since each data photograph included a signal from the 90° tap, several C' values were available for ^s that p a r t i c u l a r position. Strouhal numbers calculated from frequencies measured on the cylinder surface and i n the wake (section 4.2) agree with published data (0.191 < S< 0.202). 28 4.2 Wake Survey-Stationary Cylinder The survey was performed at a wind speed of 13.80 feet per second, approximately the resonant wind speed for the oscillating cylinder (section 4.4)« The coordinate axes referred to in the following text and figures are defined i n f i g . 34« Wake survey procedure i s outlined i n section 3.2,4. Phase and amplitude of the probe signal (fundamental frequency signal only) for longitudinal and lateral traverses made i n the wake are shown in f i g . 35? the phase shown i s corrected for the relative probe signal lag discussed i n section 3,1.5* A second harmonic signal, arising from the interaction of vortices being shed from opposite sides of the cylinder, was observed when the probe was positioned close to the stream axis (y = 0). Fig. 36 shows typical oscilloscope traces of the model surface pressure (90°) and probe signals. Signal amplitude date were taken from the oscilloscope traces after a coherent build up of signal had been attained, and phase data were taken from single sweep traces. The cylinder surface pressure reference signal was taken from the same side of the stream axis as the probe signal. For x/h> 5 (f i g , 35) the decrease i n signal amplitude and the lack of a clearly defined fundamental, prevented further collection of phase data. The down-stream position of the f i r s t 'in phase1 signal (x/h^l.O) correlates with the position of the maximum amplitude of the probe signal. Phase data from both sides of the stream axis (y = 0) are i n agreement and plot as a line having a slope which, close to the cylinder, decreases downstream and farther down-stream reaches a constant value. Thus in the region x/h<3.0, the long-itudinal spacing of the vortices increases as they are carried downstream. From the lateral traverse at x/h = 1,33 and x/h = 2.67 i t is seen that the 29 lateral vortex spacing, assumed to correspond to maximum amplitude of the probe signal i s quite clearly defined. Lateral traversing at x/h = 1.33 was taken as a standard procedure; this gave the more clearly defined lateral spacing of the vortices, particularly i n the case of an oscillating cylinder (section 4*4). 4.3 Fluctuating Pressures on the Surface of an Oscillating Circular Cylinder When free to oscillate i n the air bearing system (section 2.3), the cylinder was found to develop appreciable amplitudes from rest over a discrete range of wind speeds. (a) Frequency of fluctuating pressures and cylinder oscillations Typical oscilloscope traces of cylinder oscillation and fluctuating pressures (90°), obtained as described i n section 3.2.3, are shown in f i g . 37. It i s seen in (figs. 37 (a) and (b) ) that an amplitude modulation i s experienced by the cylinder at wind speeds i n i t i a t i n g cylinder oscillation. The modulation shows a beat phenomenon, i t s frequency being approximately the difference between the fluctuating pressure frequency and the cylinder oscillation frequency. At higher wind speeds in the cylinder oscillating range, the amplitude modulation disappeared (fi g . 37 (c) to (e) )„ Frequency of the fluctuating pressure together with cylinder oscillation amplitude and frequency are plotted on a base of wind speed in f i g . 38. The frequency of the fluctuating pressure follows the familiar pattern of the 'capture1 phenomenon. While the transition from the 'stationary' Strouhal frequency line to the 'lock-in' region (at approximately the natural frequency of the model-spring system) i s clearly defined, the departure from this region proves to be less organized and considerable scatter of data i s present. The natural frequency of the system was determined by means of a 30 streamline model (section 2.3 and Appendix A)„ The dynamic response of the model i s seen to he t y p i c a l of a resonance phenomenon. Model amplitude-wind speed data from several tests showed reasonable agreement, the s l i g h t scatter of data following maximum model amplitude being credited to the s e n s i t i v i t y of a i r bearing alignment and a possible change i n damping r e s u l t -ing from small changes i n configuration of the pressure transducer tube connection. Frequency measurements from t h i s investigation along with previous measurements (22) are plotted i n f i g . 43; c o r r e l a t i o n i s discussed i n section 5° (b) Phase r e l a t i o n of flu c t u a t i n g pressure and cylinder o s c i l l a t i o n Phase r e l a t i o n data taken from f a s t sweep oscilloscope traces (as shown i n f i g . 37) are plotted i n f i g . 38. The phase shown i s between the maximum negative pressure at the 90° tap and the maximum cylinder displace-ment i n the 90° tap dir e c t i o n . Phase lag due to the transducer tube connection to the 90° tap was accounted for as described i n sections 3.1.3 and 3.1.4 and the appropriate correction applied. Considerable scatter of data i s evident i n f i g . 38, but the change of phase which occurs i n the wind speed range giving maximum cylinder amplitude i s c l e a r l y defined. Reasonable agreement from several runs was obtained and i t was noted that the phase change was a sudden occurrence, extremely sensitive to wind speed. Phase data from t h i s investigation along with previous phase measurements (23) are plotted i n f i g . 44; c o r r e l a t i o n i s discussed i n section 5» (c) Fluctuating pressures on o s c i l l a t i n g cylinder As i n the case of the stationary cylinder, pressure signal amplitude modulation was evident ( f i g . 39); i t was observed that the 31 behaviour of the modulation was dependent upon wind speed. Fig. 39 (a) shows a fluctuating pressure signal for the 90° and 180° positions on the model as the wind speed was increased through the resonant range. It is seen that in a particular range of wind speed, both the signal amplitude and amplitude modulation are affected; a similar effect was produced by a decrease of wind speed through this range. Fig. 39 (h) and (d) show that the amplitude modulation i s i n phase around the cylinder and that the phase of the fundamental i s as for the stationary cylinder. Fig. 39 (c) shows less modulation of the pressure signal and a slight asymmetry of the wave form is apparent. Pressure signal asymmetry was observed i n the region of maximum cylinder amplitude, i t s occurrence having a c r i t i c a l dependence on wind speed. In f i g . 39 (d) the asymmetry of the 90° pressure signal i s clearly shown. Mean signal amplitudes and their ratios were obtained as described i n section 4«1« Fluctuating pressure signals from the 180° position showed the second harmonic effect. Fluctuating pressures were observed at 0°, but neither the fundamental nor the second harmonic was clearly defined; such pressures were of a lower order of magnitude than those measured at other points on the model. Fluctuating pressures at the fundamental frequency are plotted in f i g . 40 (b) in the form of the fluctuating pressure coefficient C• . The c r i t i c a l dependence of pressure amplitude on wind P o speed i n the resonance range i s seen i n the abrupt decrease of C •^o Pressures around the cylinder, shown in f i g . 40 (a) in terms of the fluctuat-ing pressure at 90°, are seen to experience a redistribution as the wind speed is varied through the resonance range. The cylinder amplitude and phase data from fig.. 38 are repeated i n f i g . 40 (c) for correlation. Fig. 41 shows model oscillation and 90° pressure fluctuation as the model amplitude is allowed to build-up from rest to a steady-state condition, wind speed being kept constant. A similar effect on fluctuating pressures was exhibited 32 at a l l pressure tap positions. C 1 and C are plotted on a base of wind r P s Po speed in f i g . 42; relevant discussion is included in section 5» 4.4 Wake Survey - Oscillating Cylinder The survey was performed at several wind speeds in the range of cylinder oscillation. The coordinate axes referred to in the following text and figures are defined in f i g . 34« Wake survey procedure is outlined i n section 3.2.4. Phase and signal amplitude data plotted i n the following figures refer to signals at the fundamental frequency only; a correction for relative probe lag, as discussed i n section 3.1.5, has been applied. Signal amplitude data were taken from oscilloscope traces after a coherent build up had been attained, phase data were taken from single sweep traces. Longitudinal traversing at y/h = 0.47 gave phase and probe signal amplitudes shown in f i g . 45» The lack of a clearly defined fundamental and a reduction of signal amplitude prevented phase observation for x/h >5.0. The absence of phase data at wind speeds of 13.88 and 14.79 feet per second is due to the lack of a coherent signal i n the wake; no fundamental signal was detectable from either single sweep traces or after long build-up periods. Results of lateral traversing at x/h = 1.33 and x/h = 2.67 are plotted i n f i g . 46. Lateral traversing at wind speeds of 13.88 and 14.79 feet per second provided an indication of lateral vortex spacing immediately behind the cylinder. From f i g . 46, i t i s seen that the probe signal amplitude at x/h = 1.33 increases with wind speed (and cylinder oscillation amplitude) up to 13.28 feet per second, after which a decrease occurs: this may be correlated with C* (f i g . 40). The position of the f i r s t 'in phase' P o signal ( f i g . 45) i s seen not to vary significantly with wind speed and correlates with the amplitude of the probe signal. Longitudinal spacing of 33 the vortices, as indicated by the constant slope portion of the phase curves in f i g . 45» is plotted on a base of wind speed i n f i g . 47; lateral vortex spacing at x/h = 1.33 and cylinder amplitude (Y) are also shown. Up to the limit of available data, i t i s seen that as the resonant wind speed, i.e., the wind speed corresponding to maximum cylinder amplitude, i s approached, the longitudinal spacing of the vortices increases while no significant change occurs i n the lateral spacing. In the immediate v i c i n i t y of resonance, however, a sharp decrease of lateral spacing i s evident. Accurate determination of the wind speed corresponding to the above occurrence was prevented by i t s abruptness, the extreme sensitivity to wind speed being similar to that found during investigation of fluctuating pressures. The velocity of vortices, given by V^ = (fa), ( f i g . 47) appears to increase as resonance is approached. Velocity V^ is calculated for two longitudinal positions, x/h =1,0 and x/h = 3.0, the latter position corresponding to the region of linear phase relation (fig, 45). 34 V. DISCUSSION OF RESULTS Fluctuating Pressure - Stationary Cylinder The random amplitude modulation of the fluctuating pressures shown in f i g . 31 has been observed i n earlier investigations (lO) ( l l ) (12). Direct measurements of l i f t and drag forces i n the Reynolds number range 3.6(10^) to 11 (10^) made by Bishop and Hassan (13) and Humphreys (7) at Reynolds number 4(l0 4), show similar amplitude modulations. While frequent mention i s made of such amplitude modulation, no reference to i t s phase round the cylinder could be found. During the investigation, however, the 'in-phase' characteristic of this modulation was observed on numerous oscilloscope traces. At higher wind speeds than those for which data are included i n this report, the amplitude modulation persisted, but a random, low frequency effect on the mean pressure was observed. Quantitative measure-ments were not made since this would have entailed further work on the transducer calibration: a typical qualitative pressure signal i s shown in f i g . 3l(h)tBoth Gerrard and McGregor employed a wave analyser, thus permitting separation of the fundamental and second harmonic signals. It i s reported, however, that the signal at ©<120° was a well defined fundamental; this i s substantiated by the results of this investigation. The second harmonic showed clearly at Q = 180°. While others (10) ( l l ) report the presence of a relatively small signal at 0°, no significant signal could be interpreted from this investigation. The phase of the fundamental was found to be as assumed by McGregor and as found experimentally by Heine. The inclusion of a wave analyser i n the c i r c u i t r y would permit a more refined investigation of both the fundamental and the second harmonic at the 0° and 180° positions. It i s seen from f i g . 32 that over the Reynolds number range investigated, there i s no appreciable change in the fluctuating pressure distribution. Pressure 35 distributions at 30° and 60° agree with Gerrard, indicating the fluctuating pressure amplitude at these positions to be greater than that found by McGregor. At 120° and 150°, the pressure distribution i s more in agreement with McGregor's findings. No fundamental signal was detectable at 180° and data plotted i n f i g . 32 for that position are second harmonic values. Fig. 33 shows agreement of C' with Gerrard, both i n the amount p s of scatter of the data, as shown by the shaded bands, and in a consistent trend of C 1 increasing with Reynolds number. An estimate of C 1^ was p s obtained from integration of C around the cylinder. Although these data p s are not presented i n this report, rough calculations indicate C'£b0.42 at N R = 1„5(104) McGregor (10) finds C^O.58 at N R = 5(l0 4), the higher value being consistent with the upward trend of C with increasing N D. p a. Frequency of fluctuating pressures and cylinder oscillations From f i g . 38, i t i s seen that 'capture' of the surface pressure frequency occurs at an amplitude Y=a»0.03. Brooks (2) finds this phenomenon occurring later i n the resonance region (1^0.15). Eagleson et a l . (2l), find similar characteristics i n the behaviour of f l a t plates placed parallel to a uniform water stream and allowed one degree of freedom torsional oscillation around a vertical axis along their leading edge. Their measure-ments of frequency and vibration amplitude show that over the 'capture' range of flow speed, the vibrational frequency increased slightly but remained below the 'stationary' Strouhal value. An investigation by Smirnov and Pavlihina (22) shows further evidence of the capture phenomenon. Circular cylinders of 41 nnn and 65 mm diameter were immersed in a water channel and forced to vibrate at a variable frequency with a constant amplitude of 15 mm. Water velocities were 12 cm/sec and 16 cm/sec. Their results are shown i n f i g . 43 along with data from the current investigation. Valid comparison can he made for the 'capture' region only, as the cylinders used in the investigation were not allowed to exhibit self-induced oscillations. It i s interesting to note, however, that the limits of the 'capture' region agree favourably. Bishop and Hassan (23), using apparatus similar to that of Smirnov and Pavlihina,, observed 'capture' i n measurements of l i f t force frequency (Reynolds Number 3 .6(lO^) ). When the oscillation frequency of the cylinder approached the frequency of the l i f t force, the latter suddenly changed to that of the cylinder oscillation. Phase relation of fluctuating pressure and cylinder oscillation The sensitivity of the relative phase of cylinder surface pressure and displacement to wind speed i s clearly seen i n f i g . 38s a similar sensi-t i v i t y of relative phase of l i f t force and cylinder displacement to cylinder oscillation frequency i s reported by Bishop and Hassan (23). Measurements of phase made during this investigation along with data on phase of l i f t force with respect to cylinder motion from (23) are shown in f i g . 44 on a base of 'cylinder Strouhal number', f h/v„ For reasons explained in the preceding paragraph, detailed comparison i s not valid, but i t i s interesting to note that the sudden phase change experienced by the l i f t force i s of the same sense as that experienced by the fluctuating pressures. Further comparison of these results can be made in the form of the ' c r i t i c a l non-dimensional frequency', i.e., the frequency at which the phase and l i f t undergo a sudden change. From the current investigation, the phase changes at Y=^0.29, frequency ^ 8 , 9 8 c.p.s. Dividing by the 'stationary" Strouhal frequency (approx. 10, 7 c.p.s.) for that particular wind speed (approximately 13.8, f.p.s.) gives a non-dimensional frequency of 37 approximately O.84; this value compares favourably with that of ref, (23), (approximately 0,83), The above comparison is made with regard to phase shift only as i t i s seen from f i g . 40 that the decrease in pressure amplitude occurs at a wind speed lower than the resonant wind speed. Fluctuating pressures on an oscillating cylinder The increase and subsequent abrupt decrease of fluctuating pressure amplitude shown in f i g . 40 (b) i s in keeping with the behaviour of l i f t force measured by Bishop and Hassan (23). The latter investigators report that in the "range of synchronisation", i.e., 'capture', the wave form of the f l u c -tuating forces becomes f a i r l y constant; a similar effect on the fluctuating pressure wave form i s seen i n f i g . 37 (d). The sensitivity of this phenomenon to wind speed (cylinder oscillation frequency i n the case of ref, (23) ), cannot be over-emphasised. It is seen from f i g . 40 (b) that the decrease in C occurs before the cylinder reaches i t s maximum oscillation amplitude and po approximately at the mid-point of the 'capture' region. Since C is the Po excitation which produces cylinder maximum amplitude, i t s decrease might be expected to correlate with a reduction of cylinder amplitude. It appears that the subsequent phase change (fi g . 38) is an associated factor and more refined measurements of phase and frequency might be the basis of an under-standing of the phenomenon. A similar relationship between phase and maximum amplitude is i n the case of forced vibrations with viscous damping. The variation of pressure distribution shown in f i g . 40 (a) correlates with the C variation. The region of increasing C which occurs before Po Po maximum cylinder amplitude, includes no significant change in pressure dis-tirbution. Following this region, however, the sudden decrease in C' is Po accompanied by a distinct pressure redistribution., Although continuous 38 curves are drawn through the pressure distribution data, there i s a possibility that the pressure distribution, l i k e C and phase, changes Po suddenly. The sensitivity of the flow characteristics to wind speed pointed out the need for refinements in the apparatus which would permit further investigation of this resonance region. Comparison of C* and C is made P s Po in f i g . 42. The shaded bands enclose the scatter of C' data. The increase P *s of C with increasing wind speed and the subsequent decrease to stationary po cylinder values i s clearly seen. For correlation, the data from f i g . 38 has been included. D-Section Although the measurements made on the D-section cylinder were not analysed in de t a i l , to the extent they were analysed they tended to confirm the following phenomena previously discussed for the circular cylinder. For both the stationary and oscillating cylinder, modulation of the fluctuating pressure amplitude was i n phase around the cylinder and the fundamental was in phase on one side of the model and 180° out of phase with the opposite side. At the i n i t i a t i o n of vortex-excited oscillation, the cylinder experienced a beating amplitude modulation, which at higher wind speeds disappeared. Fluctuating pressures experienced a severe amplitude modulation at wind speeds corresponding to cylinder amplitude modulation, but this was almost completely eliminated with the disappearance of cylinder amplitude modulation. Wake Survey - stationary and oscillating cylinder Several investigators ( l ) , (15), (IT) have made measurements in the wake of stationary cylinders, but their efforts have been concentrated in the low Reynolds number range (20 to 1000). More relevant are measurements 39 of velocity, frequency and longitudinal spacing of vortices i n the wake of a variety of bluff body shapes made by Page and Johansen (14). Results of these experiments for a circular cylinder = 2„76(l04)^J are, in part, Vy/V = 0.80(0.796), b/a = 0.234(0.269). The numbers in the brackets are from the current investigation |jJR = 2,0(l04)]J . Reference (14) does not provide data regarding the variation of vortex spacing with increasing distance from the cylinder. It is assumed that measurements were made as in a previous investigation (26), i.e., in the region 2.0<x/h <12.0: this being the case, the curvature on a phase - x/h plot, such as shown in f i g . 35 could have been overlooked and a straight line relationship accepted. The position of the f i r s t in-phase signal (x/h — 1.0) shown in f i g . 35 correlates with the position of maximum suction pressure on the wake centreline ( x / h — l . l ) measured by Roshko (19). No reference to measurements in the wake of vortex excited cylinders could be found in the technical literature. Wehrmann (24) investigated velocity fluctuations i n the wake of an obround cylinder which was forced to vibrate at 90° to a constant flow velocity (N R = 68). The frequency of vibration was controlled by a feedback system from a hot—wire anemometer ' placed in the wake. The phase of vibration was varied by changing the position of the hot-wire in the wake and the amplitude controlled by an amplifier in the feedback c i r c u i t . With the right choice of amplitude and phase, i t was found that velocity fluctuations i n the wake could be reduced by 72$. Smirnov and Pavlihina (22), whose findings on 'capture' were previously discussed in this section, make reference to visual observations of vortex formation behind a cylinder experiencing forced vibrations. At 'low' frequencies of cylinder oscillation, vortex formation was observed to be similar to that of a stationary cylinder, i.e., the f i r s t vortex being 40 formed i n line with the separating shear layers. At 'high' frequencies, i n i t i a l vortex formation occurred immediately behind the cylinder. No definition i s given to the terms 'low' and 'high* frequencies, but i t might be assumed that the phenomenon correlates with the b/h reduction shown in f i g . 47. The corresponding loss of coherent probe signal farther downstream, although at a higher N R, may be interpreted as a phenomenon similar to that observed in reference (24). Parkinson (4) has suggested that as the cylinder oscillation amplitude increases, the vortices form a wider street and on the assumption that the s t a b i l i t y requirement i s unchanged by cylinder motion, a correspond-ing increase in longitudinal spacing occurs. Comparison of b/h for a stationary and oscillating cylinder shows ( f i g . 47) a reduction of street width rather than an increase, while the longitudinal spacing of the vortices, up to the measurable limit, increases. It appears that the street width i s dependent not only upon cylinder oscillation amplitude, but on the phase relation of the vortex formation and the cylinder oscillation. The sudden decrease of street width which occurs between 13.3 and 13.9 feet per second (fig . 47) is accompanied by a phase change (fi g . 38) already discussed in this section. In an effort to establish the longitudinal spacing of vortices in the particular range of wind speeds (approximately > 13.5 f.p.s.) at which no coherent signal was detectable in the wake, the probe was positioned out-side the wake (y/h >3). A fundamental signal wa3 observed, but the phase with respect to a surface pressure signal (90°) , remained constant for a l l downstream positions. Wake data plotted i n this report refer to measurements made in the plane of the cylinder mid-span (z = 0). Longitudinal traverses made with 41 the probe in the planes z/h =1,0 and z/h = 2,0 and the surface pressure reference signal at z/h = 0 showed no coherent spanwise effect on phase. This result was thought to be influenced by the existence of cylinder end effects. Three dimensional flow was observed by Humphreys (7) in his experi-ments with fine s i l k threads fastened to a circular cylinder. Thread motion at NR<10 indicated a random spanwise irregularity, but at H^—IO , a distinct cellular pattern developed and remained u n t i l N^3(l0^). Mattingly (8) investigated the three dimensionality of flow around a circular cylinder by 4 5 means of dye techniques in a water tank. In the range 10 <HJJ<10 , the flow was found to be strongly three dimensional. It was thought that discs, similar to those.used by Keefe (9), would enable spanwise effect on phase to be measured both on the cylinder surface and i n the wake. Plastic discs were made, but time did not permit their use i n this programme. Spacing ratios b/a shown in f i g . 47 are calculated for b measured at x/h = 1.33. An increase in b for x/h>1.33 is indicated in f i g . 46. The data i n f i g . 47, therefore, should be interpreted as a trend only, not as the f u l l y developed wake ratios. VI. SUMMARY OF RESULTS Results of this investigation are summarized as follows: 1. Fluctuating pressures on the surface of both a stationary and vortex-excited circular cylinder experience amplitude modulation which is in phase around the cylinder. For a stationary cylinder, the modulation i s random, but for a vortex-excited cylinder the modulation is c r i t i c a l l y dependent on wind speed, and at the i n i t i a t i o n of cylinder oscillation, displays a beat phenomenon similar to that discussed i n 3 below. 2. Fluctuating pressures at the fundamental frequency for both a stationary and a vortex-excited circular cylinder are i n phase over one side of the cylinder and 180° out of phase with the opposite side. 3. At the i n i t i a t i o n of cylinder oscillation where cylinder and vortex frequencies are slightly different, the cylinder experiences a beat amplitude modulation. Then the' phenomenon of 'capture' of vortex by cylinder frequency is well defined, departure from that region of wind speeds being less organized than i t s i n i t i a l occurrence. Appreciable cylinder oscillation amplitude exists at the end of the 'capture' range. 4. The amplitude of fluctuating pressure on the surface of a vortex-excited circular cylinder has a c r i t i c a l dependence on wind speed, the i n i t i a t i o n of cylinder oscillation producing pressure amplitudes similar to that for a stationary cylinder. As the wind speed approaches the resonant value (that for maximum cylinder amplitude), fluctuating pressure amplitude i s approximately doubled, but before the resonant wind speed i s actually reached, the pressure amplitude reduces abruptly to approximately i t s i n i t i a l value and the modulation, both of surface pressure amplitude and cylinder amplitude, disappears. This i s maintained for the remainder of the wind speed range for 'capture'. Similar behaviour i s observed during 43 the transient build-up of cylinder oscillation amplitude when the cylinder i s released from rest i n a constant wind speed close to the resonant value. 5. Near the resonant wind speed, the phase between cylinder motion and fluctuating pressure changes suddenly and an asymmetry i n the pressure wave form i s apparent. 6. The longitudinal spacing of vortices i n the wake of a stationary circular cylinder increases as the vortices are swept downstream from the formation zone, reaching a constant spacing at x/h^S.O. A similar increase occurs in the wake of a vortex-excited cylinder, the constant spacing value being dependent on wind speed. As the resonant wind speed i s approached, the longitudinal spacing increases, but before the speed actually reaches the resonant value, the wake loses i t s periodicity and further longitudinal spacing data are unobtainable. A narrowing of the wake occurs when the cylinder experiences vortex-excited oscillation. In the range of wind speed preceding the resonant value, the lateral spacing of the vortices does not change significantly. Before the actual resonant wind speed i s reached, however, a sudden decrease in lateral spacing occurs, the actual spacing being unobtainable due to the loss of the coherent signal in the wake; this loss corresponds to the loss of wake periodicity discussed above. The lateral spacing indicated at the resonant wind speed for a vortex-excited cylinder i s less than half the value for a stationary cylinder at the same wind speed. • APPENDIX A 44 Tension Spring particulars: Material Coil O.D. Wire diam Number of coi l s Length, of c o i l s 011 tempered steel wire 0.649 inch 0.091 inch 113 12 inch 0 The follow Lng damping lata were ob bained as d i 3cussed in S X action 2.3 t I n i t i a l cy amplitude L inder _~ = 0.69 i n / \ yy "TT TJV7I7T - I n i t i a l c y l Lnder amplitude = 0.75 in. ft Weight of Weight of Natural f oscillating model only cequency = 9 system = 1. = O.856 lb. .10 c.p.s. j83 lb. • 10 15 t, (sees.) 20 25 30 APPENDIX B 45 PIEZOELECTRIC CRYSTAL RESPONSE DATA (Astatic No. 445-A) Link Displacement = A sin cot Link Velocity = Aco cos cot Max. Link Velocity = Aco 0 20 40 60 80 100 Frequency (c.p.s.) APPENDIX C TRANSDUCER COMPONENTS Light dependent resistance: Shunt resistance Light bulbs Voltmeter Ammeter Potentiometer Diaphragm Shutter Phillips type No. B 8 731 03 Budd Metalfilm strain gauges Type C 6 - 141 - 1000 resistance 1000 ohms Westinghouse No. 605 6.15 volt, 0.50 amp Triplet, 0-5 volts d.c. Triplet, 0-400 m.a. Wire wound 0-10 ohm linear taper Dental Dam, Dark Extra Heavy, Pure Latex (.015 in.) .002 brass shim stock. APPENDIX D WAVE PROPAGATION IN A TUBE The pressure developed by the piston (Section 3.1.3) at the input end of the tube was calculated from elementary one-dimensional acoustic theory (29). At the piston, p'(t) = oL^Sl S c o s J T t where piston displacement = 6 sin i l t APPENDIX E  DISC STATIC PROBE The following data are taken from R e f , (27) c\j> Yaw +ve. Pitch 0,30 Vari atior wit! 1 yaw Vari atior witl L p i t :h r\ / J - „ -20 -15 -10 -5 0 5 10 15 20 Pitch and Yaw (degrees) 0.15 0^ 0.10 Q. <|cvi 0.05 20 40 .60 30 Velocity (f.p.s.) 100 120 49 APPENDIX F TUNNEL CORRECTIONS TO WIND SPEED Wind speeds were corrected according to Ref. (28). In the absence of better data, corrections to wind speed for the os c i l l a t i n g cylinder were the same as for the stationary cylinder. Solid Blockage: V = V uncorr. where C = 0,822 for a closed tunnel ^ = 1.0 (model shape factor) h = model width H = tunnel width Wake Blockage: V = V ( l + 0.25 (£) n ~1 uncorr. \_ y VH' C, J where C^ = measured drag coefficient (assumed 1.25) Therefore V = V f l + 0.82 fc|)2 + 0.25 (l .25) - 1.032 V uncorr. L 36' ^ x x 3o'J i uncorr. 50 BIBLIOGRAPHY 1. Roshko, A. 2. Brooks, N.P.H. 3. Smith, J.D, "On the Development of Turbulent Wakes from Vortex Streets," National Advisory Committee for Aeron-autics, Report 1191, 1954» "Experimental Investigation of the Aeroelastic Instability of Bluff Two-Dimensional Cylinders," M,A0Sc„ Thesis, University of Br i t i s h Columbia, July, I960. "An Experimental Study of the Aeroelastic Instability of Rectangular Cylinders," M0A.Sc. of Br i t i s h Columbia, August, 1962. Thesis, University 4. Parkinson, G„V. 5. Morkovin, M.V« 6. Kuchemann, D„ 7. Humphreys, J.S. 8. Mattingly, G.E. 9. Keefe, R.T. 10. McGregor, D„M. 11, Gerrard, J.H, "Aspects of the Aeroelastic Behaviour of Bluff Cylinders," Engineering Institute of Canada, Annual General Meeting Paper No, 58, 1962. "Flow Around Circular Cylinder - A Kaleidoscope of Challenging Fluid Phenomena," Symposium on Fully Separated Flows, The American Society of Mechanical Engineers, May, I 9 6 4 . "Report on the I.U.T.A.M. Symposium on Concentrated Vortex Motion in Fluids," Journal of Fluid Mechanics, vol, 21, part 1, January, 1965, pp. 1=?20. "On a Circular Cylinder in a Steady Wind at Transition Reynolds Numbers," Journal of Fluid  Mechanics, vol. 9, i960, pp, 603-612. "An Experimental Study of the Three Dimensionality of the Flow Around a Circular Cylinder," The Institute for Fluid Dynamics and Applied Mathematics, Technical Note BN-295, June, 1962. "An Investigation of the Fluctuating Forces Acting on a Stationary Cylinder in a Subsonic Stream and of the Associated Sound Field," Institute of Aero-physics, University of Toronto, UTIA Report No, 76, September, 1961. "An Experimental Investigation of the Oscillating Pressures on a Circular Cylinder in a Fluid Stream," Institute of Aerophysics, University of Toronto, UTIA Technical Note No. 14, June, 1957. "An Experimental Investigation of the Oscillating L i f t and Drag of a Circular Cylinder Shedding Turbulent Vortices," Journal of Fluid Mechanics, vol. 11, 1961, pp. 244-256. 51 12. Heine, W. 13. Bishop, R.E„D. Hassan, A„T. 14„ Fage, A. Johansen, F.C. 15. Thorn, A. 16. Kovasznay, L. S. G. 17. Rosenhead, L. 18. Shair, F.H. Grove, A.S. Petersen, E.E, Acrivos, A. 19. Roshko, A, 20. Bloor, M.S. 21. Eagleson, P.S. Daily, J.W. Noutsopolous, G.K. 22. Smirnov, L.P. Pavlihina, M.A. "On the Experimental Investigation of Vortex Excited Pressure Fluctuations," M.A.Sc, Thesis, University of British Columbia, August, 1964. "The L i f t and Drag Forces on a Circular Cylinder in a Flowing Fluid," Proceedings of the Royal Society  of London. Series A, vol, 277, 1964, PP . 32-50. "The Structure of Vortex Sheets," Philosophical izine, Series 7, vol. 5, January-June, 1928, pp, 417-440, "The Flow Past Circular Cylinders at Low Speeds," Proceedings of the Royal Society of London. Series A, vol. 141, 1933, P P . 651-669. "Hot Wire Investigation of the Wake Behind Cylinders at Low Reynolds Numbers," Proceedings of the Royal  Society of London, Series A, vol. 198, 1949, pp. 174-190. "An Experimental Investigation of the Flow Behind Circular Cylinders i n Channels of Different Breadths," Proceedings of the Royal Society of  London, Series A, vol. 129, 1930, pp, 115-135. "The Effect of Confining Walls on the Stability of the Steady Wake Behind a Circular Cylinder," Journal of Fluid Mechanics, vol, 17, 1963, pp, 546-550. "On the Drag and Shedding Frequency of Two-Dimensional Bluff Bodies," National Advisory Committee of Aeronautics, Technical Note 3169, July, 1954, "The Transition to Turbulence i n the Wake of a Circular Cylinder," Journal of Fluid Mechanics, vol, 19, part 2, June, 1964* pp. 290-304. "Flow Induced Vibration of Flat Plates," Massachusetts Institute of Technology, Department of C i v i l Engineering, Report No. 58, February, 1963. "Vortical Traces for Flow Around Vibrating Cylinders," Studii s i Cercetari Mecan, Appl, 1958. v.9, 23. Bishop, R.E.D. Hassan, A.Y. "The L i f t and Drag Forces on a Circular Cylinder Oscillating in a Flowing Fluid," Proceedings of the  Royal Society of London, Series A, vol, 277, 1964, pp. 51-75. 52 24. Wehrmann, O.H. 25. Santosham, T.V. 26. Page, A. Johansen, P.C, 27. Bryer, D.W, Walshe, D.E. Garner, H.C. 28. Pankhurst, E.C, Holder, D.W. 29. Liepmann, H.W. Roshko, A. "Reduction of Telocity Fluctuations i n a Karman . Vortex Street hy a Vibrating Cylinder," Boeing Scientific Research Laboratories, Seattle, Washington, August, 1964. "Non-Linear Characteristics of Rectangular Sections and Force Measurements on a D-Section," M.A.Sc. Thesis, University of British Columbia, I965. "On the Flow of Air Behind an Inclined Flat Plate of Infinite Span," Proceedings of the Royal Society  of London. Series A, vol. 116, 1927, pp. 170-197. "Pressure Probes Selected for Three-Dimensional Flow Measurement," Aeronautical Research Council Reports and Memoranda, R. and M. No. 3037, 1958. "Wind Tunnel Technique," Pitman, 1948. "Elements of Gas Dynamics," Wiley, i960, Chapt. 3. AERODYNAMIC OUTLINE OF WIND TUNNEL ' F i g . l 54 Set Screw Plastic 0.022 Aluminum Adhesive Bond Groove Mounting Bracket (Plastic) PLASTIC END FITTINGS FOB CIRCULAR CYLINDER Fig. 3 MID-SPAN BULKHEAD OF D-SECTION MODEL BEFORE ALUMINUM SKIN WAS ATTACHED Fig. 4 Tap No. Deg. Tap No. y A 1 2 1/2 18 0.490 2 5 19 0.469 3 10 20 0.427 4 20 21 0.375 5 30 22 0.292 6 45 23 0.208 7 60 24 0.104 8 75 25 0 9 90 26 -0.104 10 105 27 -0.208 11 120 28 -0.292 12 135 29 -0.375 13 150 30 -0.427 14 160 31 -0.469 15 170 32 -0.490 16 175 , 17 177 1/2 33 2 l/2,3 in. "below mid-span 34 2 1/2,6 in. below mid-span V PRESSURE TAP POSITIONS FOR D-SECTION MODEL Fig. 5 VJ1 G3 Helical Tension Spring C S S Air Bearing 1 Model ARRANGEMENT OP MODEL MOUNTING SYSTEM Pig. 7 60 TRAVERSING GEAR - LOOKING DOWNSTREAM INTO WIND TUNNEL TEST SECTION Fig. 8 61 TRAVERSING GEAR IN TEST SECTION SHOWING WORKING AREA SIDE PANEL Fig. 9 62 Low Frequency Function Generator Hewlett Packard Model 202A Vibration Generator \Goodmans \ i! Bogen-Presto Model M060 , Strain Gauges Cantilever Beam Rigid Link Crystal Cartridge Astatic No. 445 Bridge Amplifier and Meter E l l i s Associates BAM-1 C.R.O. Tektronix No. 502A DIAGRAMMATIC LAYOUT OF APPARATUS USED IN CRYSTAL RESPONSE INVESTIGATION Fig. 10 63 VIBRATION GENERATOR AND CANTILEVER BEAM MOUNTED IN FRAME Fig. 11 64 S t r a i n gauge s i g n a l C r y s t a l s i g n a l S inuso ida l Wave Form - 20 cps S t r a i n gau^e s i g n a l C r y s t a l | s i g n a l . Non -s inuso ida l Wave Form - 20 cps TYPICAL OSCILLOSCOPE TRACES . . . RESPONSE F i g . 12 (continued) 65 S t r a i n gauge s i g n a l C r y s t a l s i g n a l S i n u s o i d a l Wave Form - 50 cps ~ _" i n S t r a i n gauge s i g n a l C r y s t a l s i g n a l Non-sinusoidal Wave Form - 50 cps TYPICAL OSCILLOSCOPE TRACES OF CRYSTAL AND CANTILEVER BEAM RESPONSE F i g . 12 66 Cavity 0.50 dia, 0.25 deep Rubber Diaphragm Tube Connection LDR (active) LDR (dummy) Ground Glass Seal Set Screw Seal Set Screw (dummy shutter) Shutter Dummy Tube Connection Light Beam Translucent I Seal Aluminum Casing Bulb and Holder PRESSURE TRANSDUCER DETAILS Pig. 13 Pig. 14 68 PRESSURE TRANSDUCER F i g . 15 2 0 0 0 ohm (Strain Gauges) 2 0 0 0 ohm (Strain Gauges) To Bridge Amplifi and Meter LDR - Light Dependent Resistance (a) Bridge Circuit Voltmeter Ammeter S.P.S.T. 0 - 1 0 ohm 6 volt d.c. (b) Light Circuit PRESSURE TRANSDUCER - CIRCUIT DIAGRAMS Pig. 1 6 70 PISTON AHRANOEMENT AT UPPER END OP CANTILEVER BEAM SHOWING TUBE AND TUBE CLAMP P i g . 17 71 Disc M a t e r i a l : - M i l d S t e e l D I S C P R O B E P i g . 18 Wind Tunnel Test Section Amplifier and Meter E l l i s Associates Tektronix No. 5 6 4 DIAGRAMMATIC LAYOUT OP STEADY PRESSURE CALIBRATION APPARATUS Pig. 19 73 3000 TOTAL HEAD mmwg PRESSURE TRANSDUCER SIGNAL VS. TOTAL HEAD STEADY PRESSURE Pig. 20 74 40 20 0 1 o o o o 0 0 4 8 12 16 20 Static Pressure i n Transducer Cavity (mmwg) THE EFFECT OF A STATIC PRESSURE RISE IN THE TRANSDUCER CAVITY ON THE TRANSDUCER SENSITIVITY TO A FLUCTUATING PRESSURE Fig. 21. 75 0.040 0 50 100 150 200 Strain Gauge Signal (M.V.) CANTILEVER BEAM DEFLECTION VS. STRAIN GAUGE SIGNAL Fig. 22 76 Low frequency-function generator Hewlett Packard Model 202A Bridge amplifier and meter E l l i s Associates BAM^ -1 © C.R.O. Tektronix No. 502A DIAGRAMMATIC LAYOUT OP PRESSURE TRANSDUCER CALIBRATION APPARATUS Pig. 23 PRESSURE TRANSDUCER CALIBRATION APPARATUS Fig. 24 0 0.001 0.002 0.003 0.004 0.005 P 1 ( p . s . i . ) 79 Fig. 26 Phase lag of tube with model tap relative to tube only (degrees) Co HA m CQ o fed $ j§ ta !> •x) o tr1 o tsi CQ i-3 t ) W 1 | bd 1—1 o HH o H !2i O O < > CQ • i a >-3 H o o CD CD a o o •a CO ON O -co o o o O |> o O co r\3 Signal amplitude from tube with model tap Signal amplitude from tube only 81 • H += td r H CD u CD o U m CD CD fe CD •a S3 • H CD •§ - P o CD CO 9 id o S J3 - P - H 0). I o •3 ce CD •3 40 30 10 10 20 \ \ \ Tubes - 5.0 f t lc 0.066 inc mg h i n s i d e liameter 1 \ 9 \ \ & < \ Amp. ' r a t i o \ V • \ \ ) \ ^ )/ !r Phase/ 0 2( » \ 4 \° 3 / 6( / Fre< ) 80 Luency (c. K p.s. ) !0 1.0 CD O 0.8 : & " 0.6 0.4 0.2 PHASE AND AMPLITUDE RATIO VS. FREQUENCY DISC PROBE CALIBRATION F i g . 28 82 III n • wsiNBim •••••• Tube only Tube and d i s c probe 10 c.p.s. Tube only Tube and d i s c probe 40 c.p.s. TYPICAL OSCILLOSCOPE TRACES OP PRESSURE SIGNALS PROM DISC PROBE CALIBRATION Pig. 29 ir-Polyethylene Tube -Pressure Transducer ^ r - Bridge Amplifier and Meter E l l i s Associates BAM-1 60 watt amplifier Bogen-Presto Model M060 C.R.O. Tektronix No. 564 Voltage Amplifier DIAGRAMMATIC LAYOUT OP WAKE SURVEY APPARATUS Pig. 30 , , 1 * , I k ^ k i i , IkJi Time Base 1 sec / d i v Time Base 50 ms/div ( a ) ' TYPICAL OSCILLOSCOPE TRACES OP FLUCTUATING .... CYLINDER P i g . 31 o Time Base 50 ms/div (o) P i g , 31 (continued) Fig. 31 (continued) 88 m T h • ' ' ' ! ! ' 1 li "I' ' " M i ''I!" if' Time Base 1 s e c / d i v Time Base 50 ms/div («) P i g . 31 ( cont inued) TYPICAL OSCILLOSCOPE TRACES OP FLUCTUATING PRESSURE FROM THE SURFACE OF A 3 INCH DIAMETER STATIONARY CIRCULAR CYLINDER 00 F i g . 31 L o g 1 0 % L o % 0 % O A D D 4.1925 4.2405 4.2648 4.2825 4.3351 4.6149 + X V A X 4.10 4.30 4.80 5.20 4.64 Gerrard ( l l ) McGregor (lO) "X =* if li • X >Second Harmonic Values 90 180/T - 0 O 0 lc)0 100 60 90 120 0 Angular P o s i t i o n (Degrees) ANGULAR DISTRIBUTION OF FLUCTUATING PRESSURE AMPLITUDE AT THE FUNDAMENTAL FREQUENCY ON THE SURFACE OF A 3 INCH DIAMETER, STATIONARY, CIRCULAR CYLINDER F i g . 32 ± McGregor (l2) 93 COORDINATE AXES FOR WAKE SURVEY Fig. 34 95 • > • a, CD X) 3 20 ial amplii 10- cKJ^ * A ^ CD •§ 0 l.o -o.5 o 0.5 l.o Lateral Distance from stream axis y/h 0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 x/h Distance downstream from cylinder £ PHASE AND AMPLITUDE OF PROBE SIGNAL IN THE WAKE OF A 3 INCH DIAMETER| STATIONARY CIRCULAR CYLINDER V - 13.80 f.p.s., f o 10.52 c.p.s., S » 0.191 Fig. 35 96 jam 9 0 u Surface pressure s i g n a l Wake probe s i g n a l (a) A f t e r s i g n a l b u ild-up 9 0 u Surface pressure s i g n a l Wake probe s i g n a l (b) S i n g l e sweep x = 1.5 i n . , y = 1 .4 i n . , z - 0 TYPICAL OSCILLOSCOPE TRACES ... STATIONARY CIRCULAR CYLINDER F i g . 36 (continued) 97 w w m _ 90 Surface pressure s i g n a l Wake probe s i g n a l (c) A f t e r s i g n a l b u i l d - u p 90 Surface pressure s i g n a l Wake probe s i g n a l (d) S i n g l e sweep x ~ 6.0 i n . , y = 1,4 i n . , z = 0 TYPICAL OSCILLOSCOPE TRACES OP SURFACE PRESSURE M i l WAKE PROBE SIGNAL FOR A 3 INCH DIAMETER, STATIONARY CIRCULAR CYLINDER F i g . 36 98 MI fiPiiiiiiiniifiii • 11 ui C y l i n d e r o s c i l l a t i o n iUUIiiilliiiililH l l l l l l l l l 90" Pressure (a) Wind speed 10.57 f p s . A m p l i f i e r s e n s i t i v i t y 5 mv/div Top t r a c e 20 mv/dic Bottom tra c e Time base 0.5 s e c / d i v nu iijjiiiiiiiiiiiiiiiiiiiiiiiiiii'ii.fn im\ C y l i n d e r o s c i l l a t i o n 90" Pressure (b) Wind speed 11.09 f p s . A m p l i f i e r s e n s i t i v i t y 10 mv/div Top tr a c e 20 mv/div Bottom t r a c e Time base 0.5 cec/div. TYPICAL OSCILLOSCOPE TRACES ... VORTEX-EXCITED OSCILLATION F i g . 37 (continued) 99 fnflMiT!!1MliniMiTff!Minil uiiuiiiiuiutiiiiinfttM iHmimuiiiHii m mf immn m*mi nWlwiimlTfn iiHJiiyiiiiiyiiiiiiiiiiM, C y l i n d e r o s c i l l a t i o n 90" Pressure Time base 0 .5 s e c / d i v (c) •iiriniiiWiH •air™ L1jMMIIlfflL"JIJIIIJM:F. 10 • Time base 50 ms/div Wind speed 13.61 f p s . A m p l i f i e r s e n s i t i v i t y 50 mv/div C y l i n d e r o s c i l l a t i o n 9 0 u Pressure TYPICAL OSCILLOSCOPE TRACES ... VORTEX-EXCITED OSCILLATION P i g . 37 (continued) 100 (d) Time base 50 ms/div Wind speed 14.02 fps A m p l i f i e r s e n s i t i v i t y 50 mv/div TYPICAL OSCILLOSCOPE TRACES ... VORTEX-EXCITED OSCILLATION F i g . 37 (continued) 101 Pll i . -iiiiJi'lili.! : uiiiiiu • U H l i Cylinder oscillation 9 0 " Pressure Time base 0,5 s e c / d i v A m p l i f i e r sensitivity c y l i n d e r o s c i l l a t i o n 50 mv/div 90° pressure 20 mv/div 1 1 1 ! Ifl l M i l FJKSM ! ! ! ' M l ! C y l i n d e r o s c i l l a t i o n 90" Pressure (e) Time base 50 ms/div A m p l i f i e r s e n s i t i v i t y : c y l i n d e r o s c i l l a t i o n 50 mv/div 90 pressure 20 mv/div. TYPICAL OSCILLOSCOPE TRACES OF CYLINDER OSCILLATION AND 90° SURFACE PRESSURE FOR 3 INCH DIAMETER CIRCULAR CYLINDER EXHIBITING VORTEX-EXCITED OSCILLATION Fig. 37 102 r>5 O C CD CD 8 12 16 V Wind speed f.p.s. 20 CYLINDER OSCILLATION AMPLITUDE AND FREQUENCY, FLUCTUATING PRESSURE FREQUENCY AND PHASE VS. WIND SPEED Fig. 38 (a) F l u c t u a t i n g pressure signals-wind increased through resonant range w h i l e c y l i n d e r o s c i l l a t e d . TYPICAL OSCILLOSCOPE TRACES OF FLUCTUATING PRESSURE ... VORTEX-EXCITED OSCILLATION F i g . 39 (continued) 104 Time base 1 sec/div (b) Time base 50 ma/div A m p l i f i e r s e n s i t i v i t y 50 mv/div Wind speed 11.80 f p s . TYPICAL OSCILLOSCOPE TRACES OP FLUCTUATING PRESSURE ... VORTEX-EXCITED OSCILLATION F i g - 39 (continued) 105 ilHHIflliHIlMfffill 150^ Time base 1 s e c / d i v •120° (b continued) Time baae 50 ms/div A m p l i f i e r s e n s i t i v i t y 50 mv/div Wind speed 11.80 f p s . TYPICAL OSCILLOSCOPE TRACES OP FLUCTUATING PRESSURE ,.. VORTEX-EXCITED OSCILLATION F i g , 39 (continued) 150' -120' Time base 1 sec/div A m p l i f i e r s e n s i t i v i t y 20 mv/div Wind speed 13.35 f p s . TYPICAL OSCILLOSCOPE TRACES OP FLUCTUATING PRESSURE ... VORTEX-EXCITED OSCILLATION F i g . 39 (continued) ..itij'illiii J l i i li'. ' 11 i i n i J i > , i i i . . . i Time base 1 sec/div c continued) Time base 50 ms/div A m p l i f i e r s e n t i v i t y 20 mv/div Wind speed 13.35 f p s . TYPICAL OSCILLOSCOPE TRACES OP FLUCTUATING PRESSURE ... VORTEX-EXCITED OSCILLATION F i g . 39 (continued) 108 • • • • • M l "tiii • • • • • M M Time base • 1 sec/div 90' 120 (d) Time base 50 ms/div A m p l i f i s r s e n s i t i v i t y 20 mv/div Wind speed 14.73 f p s . TYPICAL OSCILLOSCOPE TRACES OP FLUCTUATING PRESSURE ... VORTEX-EXCITED OSCILLATION Pig- 39 (continued) 90° 120° 1 0 9 Time base 1 s e c / d i v (d continued) Time bass 50 ms/div A m p l i f i e r s e n s i t i v i t y 2 0 mv/div Wind speed 1 4 . 7 3 f p s TYPICAL OSCILLOSCOPE TRACES OF FLUCTUATING PRESSURE ON THE SURFACE OF A 3 INCH DIAMETER, CIRCULAR CYLINDER EXHIBITING VORTEX-EXCITED OSCILLATION F i g . 3 9 1.2" l.C 0 4 8 12 16 20 V Wind speed f.p.s. C' AND ANGULAR DISTRIBUTION OF FLUCTUATING PRESSURE ON THE SURFACE OF A 3 INCH DIAMETER CIRCULAR CYLINDER EXHIBITING VORTEX-EXCITED OSCILLATION Fig. 40 I l l uiikliisiiii^i ^ ^ ^ ^ ^ ^ ^ ^ M E^^^^^^^^W ^^^^^^^Wiw ^ W W ^ ^ W B i ^ ^ B W W B W I W B P W W W B W B W W K • C y l i n d e r Amplitude S i g n a l I , . i .Ul. i i ' i l . 90" Pressure S i g n a l OSCILLOSCOPE TRACE OP CYLINDER OSCILLATION AMPLITUDE AND 90° FLUCTUATING PRESSURE DURING TRANSIENT BUILD-UP OF CYLINDER DISPLACEMENT. WIND SPEED 12.4 f.p.s. P i g . 41 c« 112 V7/s P c 0 . 5 0 . 3 o.i 0.7 0 . 5 p. 0 . 3 1 0o1 CO 0 . 5 0 . 3 0 . 1 c 0 2 = 150 0 ) 0 1 o Q = 90< - c 0 Q = 6oc ft f / / 1 1 8 12 16 20 V Wind Speed f.p.s. C• AND C • VS. WIND SPEED P P *s o P i g . 42 0 . 3 0 . 2 0 . 1 113 0.3 0.2 0 Cylind Cylind er diam. = / er diam. <= ( 1 mm 6.5 mm J [NOV AND PA\r J I H I N A (22) S = 0.19 3 O j> s+ \ \ ^ " i \ & I 6 ( ) I OO N i \ \ \ \ / -0 0.1 0.2 V C O M P A R I S O N O P ' C A P T U R E ' D A T A W I T H R E P . (22) Pig. 43 114 120-\o PlUCtUJ Pressiu ,ting e °\ 0 \ ^Li: Bi Ha Force shop and ssah (13) °\? ° ° \ c o Lead 0 O.C 5 0, 1 0. fh T L5 \o ,2 COMPARISON OF PHASE DATA WITH REF. (23) Fig. 44 X 400 Y O Wine . spe< »d = 11.88 f .p, 300 Y = D.062 5 ise a A. i g l e Of Jo -« y h = 0.47 i. >- / T*1L = 0. 47 o je ai A. g l i a l amp! .itud' < O O 4C 0 v ( ( 300 0/4 5 0 PI .ase i A ingle t. A ( i / l i =* 0.47 r t > < US i n d £ peed Y = 12 n .50 f*. /h = }be E 0.47 igna] amp! .itud i — u. 1 r \ ^ 4C 0 / o ' c A ^ o /' 300 I V hase \ \ \ O y/n = : 0.4" r Ir C \ A l Win 1 spe ed = 13.2 3 f.p. of \ Y = 0.20 33 A --—Pro b e s i y/ .glial 'h = ( ampl ).47 LLudd \X/1 i Dis f r bance Dm cy dowr linde istre; r L im 115 > a CD % •P •H r - l It •I •H CQ CD •8 o 1.0 2.0 3.0 4.0 5.0 6.0 7.0 PHASE AND AMPLITUDE OP PROBE SIGNAL IN THE WAKE OP A 3 INCH DIAMETER CIRCULAR CYLINDER EXHIBITING VORTEX-EXCITED OSCILLATION (LONGITUDINAL TRAVERSE) Probe Signal Amplitude of Fundamental M.V. 116 15 15-10 £5 10 x/h = 2.67 x/h = 2, x/h = 1.33 .33 Wind speed = 11.88 f.p.s. T - 0.0625 33 Wind speed «* 12.50 f.p.s. T = 0.1250 33 Wind speed = 13.28 f.p.s. T = 0.2083 •l . o - 0 . 5 0 0 . 5 1.0 Lateral Distance from stream axis y/h Wind speed = 13.88 f.p.s. Y .= 0.2291 Wind speed = 14.79 f.p.s. Y = 0.1978 AMPLITUDE OF PROBE SIGNAL IN THE WAKE OF A 3 INCH DIAMETER CIRCULAR CYLINDER EXHIBITING VORTEX-EXCITED OSCILLATION (LATERAL TRAVERSE) Fig. 46 117 V. V , / V f o r /V far x/l> 3 x/h a/h l . C b/a Q_ A if i i 4 / i i -9-V V./V, x, Stat ~CyI Lonary inder % — : L 4 . 0 rt" 2.0 0 o c f l Pi CQ r-i I TJ +» •H 5 .0 Stationary Cylinder 0 . 3 0.2 0.1 0 13 14 15 WIND SPEED V fps LATERAL AND LONGITUDINAL SPACING AND VELOCITY OP VORTICES IN THE WAKE OP A 3 INCH DIAMETER CIRCULAR CYLINDER EXHIBITING VORTEX-EXCITED OSCILLATION Pig. 47 

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