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On the experimental investigation of vortex excited pressure fluctuations Heine, Walter 1964

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ON THE EXPERIMENTAL INVESTIGATION OF VORTBX EXCITED PRESSURE FLUCTUATIONS by WALTER HEINE B.A.Sc, University of B r i t i s h Columbia, 1963 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of Mechanical Engineering We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August, 1964 In presenting this thesis in p a r t i a l fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make i t freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed v/ithout my written permission. Department of Mechanical Engineering The University of British Columbia, Vancouver 8, Canada. D a t e Septpmher A, 1964 ABSTRACT Construction and c a l i b r a t i o n of a piezoelectrio transducer capable of measuring acoustic l e v e l pressure fluctuations occurring on the surface of a body due to shed vortices i s described. The application of the transducer as a wake survey equipment i s also explained. The fluctuating pressure and wake geometry study carried out using two dimensional models of several b l u f f and:.streamlined bodies indicate that (1) Fluctuating l i f t c o e f f i c i e n t decreases with reduction i n bluffness of the body0 (2) For square and rectangular cylinders^ as well as f o r the e l l i p t i c cylinder at large angles of attack, the amplitude of fluctuating pressure i s minimum at the points where s t a t i c pressure is-maximums (3) Fluctuating l i f t c o e f f i c i e n t for the bodies with sharp leading edge (e„g0 square and rectangular cylinders) i s considerably larger than the corresponding s t a t i c value, while f o r the c i r c u l a r cylinder, . e l l i p t i c cylinder and the wing, the fluctuating coefficients were found to be smaller than their s t a t i c counterpart,, (4) The s e l f excited motion of the. body, pa r t i c u l a r l y a b l u f f body, does not affec t either the frequency of shedding vortices or the fluctuating pressure* for frequencies above vortex resonance. ACKNOWLEDGEMENT I would l i k e to express my sincere thanks and appreciation to Dr„ V. J. Modi for the guidance and assistance he has given me i n the presentation of this thesis. Thanks are also due to Mr. P. Hurren for his continued assistance i n the experimental work, especially i n the design, and construction of the pressure transducer* Also, I would l i k e to thank the Department of Mechanical Engineering f o r the use of their f a c i l i t i e s , and the National Research Council of Canada for f i n a n c i a l assistance given through grants i n aid of research. TABLE OP CONTENTS Page I. Introduction 1 II . Statement of Problem 3 III . Instrumentation Calibration and Experimental Setup 4 3.1.1 Wind Tunnel 4 3.1.2. Calibration of Betz Manometer 5 3.2. Models 5 3.3. Model Mounting System 8 3.4. Pressure Transducer 16 3.4.1. Calibration of Pressure Transducer 24 3.5. Wake Survey Equipment 30 3.6. Bending and Torsional Displacement Transducers 1 33 3.6.1. Calibration of Displacement Transducers 33 3.7. Electromagnetic Darning 34 3.8. Experimental Test Procedures 38 3.8.1. Static and Os c i l l a t i n g Pressure Measurements 38 3.8.2. Amplitude Measurements 40 3.8.3. Wake Measurements 40 3.8.4. Strouhal Numbers 41 3.8.5. Static L i f t Coefficient versus Angle of Attack 42 3.8.6. Dynamic L i f t Coefficients Page IV. Experimental Results 46 4.1.1. Stationary Square Cylinder 46 4.1.2. O s c i l l a t i n g Square Cylinder 47 4.2.1. Stationary Rectangular Cylinder AR=2 60 4.2.2. O s c i l l a t i n g Rectangular Cylinder JBO 2 74 4.2.3. Stationary Rectangular Cylinder ARo 1/2 74 4.3.1. Stationary Circular Cylinder 79 4.3.2. O s c i l l a t i n g Circular Cylinder 81 4.4.1. Stationary E l l i p t i c Cylinder (a • 3 inches, e m 0.985) 8 9 4.5.1. Stationary and O s c i l l a t i n g A i r f o i l 100 V. Discussion of Results and Concluding Remarks 103 VI. Bibliography "' 107 LIST OP FIGURES ^fiHEe Pa$e. 1. Aerodynamic Outline of Wind Tunnel 6 , 2. Calibration Curve: Wind Tunnel 7 3. Experimental Models 9 4. Location of Pressure Taps on Models 10, 11 5. Details of Model Mounting System 12, 13 6.. Cross-section of A i r Bearings 15 7. Pressure Transducer 18, 19, 20 8. Effeot of Tube Length on Phase %2. 9. Pressure Transducer as Located i n Acoustically Dead Chamber 23. 10. Calibration Setup 26, 27 11. Calibration Curve: Variation of Output with Frequency (Pressure Transducer) 28 12. Calibration Curve: Variation of Output with Pressure (Pressure Transducer) 29 13. Wake Measurement Probe 32 14. Calibration Curve: Lateral Displacement Transducer 35 15. Calibration Curve: Torsional Displacement Transducer 36 16. Calibration Curvet Electromagnetic Damper 37 17. Equipment and Test Section 39 18. Numbering of Surfaces of Square and Rectangular Cylinders 43. Figure 19. 20. 21. 22. 23. 24. 25. 26, 27. 28. 29. 30. 31. Integration about E l l i p t i c Cylinder Variation of Static Pressure Distribution with a: Square Cylinder Variation of Static L i f t Coefficient with at Square Cylinder Variation of Strouhal lumber with Reynolds : Number f o r Square Cylinder Variation of Fluctuating Pressure Distribution with a: Square Cylinder Variation of Fluctuating L i f t Coefficient with ai Square Cylinder Pressure Oscillations on the Surface of the Square Cylinder Amplitude Modulations of Pressure Fluctuations on the Surface of The Square Cylinder Slowly Varying Amplitude and Frequency of Square Cylinder Motion Effect of Motion on Pressure Fluctuations on the Surface of Square Cylinder Variation of Static Pressure Distribution with a: Rectangular Cylinder AR=2 Variation of Static L i f t Coefficient with a; Rectangular Cylinder £R=2 Variation of Strouhal Number with Reynold^; Number; Rectangular Cylinder AR=2 Page 44 49, 50, 51 52 53 54, 55, 56 57 58. 59 59 59 62, 63, 64, 65 66. 67 Variation of Fluctuating Pressure Distribution with a: Rectangular Cylinder AR=2 Variation of L i f t Coefficient with a: Rectangular Cylinder ARo2 Pressure O s c i l l a t i o n on the Surface of the Rectangular Cylinder M =2 PressureTsyfluctuations as Recorded by Probe and Tap 1 of Rectangular Cylinder ARB2, Probe 17.3 inches Downstream of Model Effec t of Motion on Pressure Fluctuations on the Surface of Rectangular Cylinder AR=2 Pressure Distribution oyer Rectangular Cylinder M «=l/2 Variation of Strouhal Number with Reynolds^ Number: Rectangular Cylinder AR=l/2 Static Pressure Distribution; C i r c u l a r Cylinder Variation of Strouhal Number with Reynold&'s Number f o r Circular Cylinder Fluctuating Pressure Distribution: Circular Cylinder C s i n & versus for Circular Cylinder P f l Pressure Oscillations on the surface of Circular Cylinder Amplitude Modulation of Pressure O s c i l l a t i o n on the surface of Circular Cylinder Figure Page 45. Variation of Phase on the Surface of Circular Cylinder 87 46. Pressure Fluctuations as recorded by Probe 9.7 inches Downstream of Model 88 47. Double Frequency Effect at the Center of Wake of Circular Cylinder 88 48. Pressure Fluctuations on the Surface of Circular Cylinder as affected by i t s motion 88 49. Variation of Static Pressure Distribution with o: E l l i p t i c Cylinder 91, 92, 93 50. Variation of Static L i f t Coefficient with a» E l l i p t i c Cylinder 94 51. Pressure Oscillations on the Surface of E l l i p t i c Cylinder 95 52. Variation of Fluctuating Pressure D i s t r i -bution with as E l l i p t i c Cylinder 96, 97 53. Variation of Fluctuating Lift Coefficient with a: E l l i p t i c Cylinder 98 54. Variation of Strouhal Number with Reynoldss Number for E l l i p t i c Cylinder 99 55. Self-Excited Motion of the A i r f o i l 101 56. Lissajous Figure During Self. Excited Motion of the A i r f o i l 101 Figure Page \ 57.a Tap 3 and Lateral Displacement of A i r f o i l 101 57. b Tap 3 and Torsional Displacement of A i r f o i l 101 i 58. O s c i l l a t i n g Pressure on the Surface of A i r f o i l Undergoing Flutter 102 59. Effect of Streamlining on 104 f l ; max LIST OP SYMBOLS a Lateral spacing of vortices a Semimajor axis of e l l i p s e & Aspect r a t i o b Length of face of rectangular cylinder p a r a l l e l to flow c Characteristic chord C Coefficient per unit span ds Elementary length e Eccentricity of e l l i p t i c cylinder h Length of face of rectangular cylinder perpendicular to flow h Longitudinal spacing of vortices I Current i n electromagnetic dampers L' L i f t per unit span P Pressure at a point Vc He — , Reynolds Number r Damping coe f f i c i e n t Kt ~ , Strouhal Number V Free stream velocity x Coordinate, abscissa y Coordinate, ordinate a Angle of attack T Angle between pressure and l i f t f or e l l i p t i c cylinder * Angular spacing of taps of c i r c u l a r cylinder V Kinematic v i ^ , • (p Density u) Strouhal frequenoy, i . e . , frequency of shedding vortices Subscripts* f l Fluctuating measurement £ Lower surface L Pertaining to l i f t max Maximum value P Pertaining to pressure rms Root mean square value st S t a t i c measurement u Upper surfaoe Value at i n f i n i t y I. INTRODUCTION The nature of the excitation i n the study of aeroelastic insta-b i l i t y i s an important factor governing the response of a system. Hence precise determination of fluctuating pressure on e l a s t i c bodies i s essential i n the study of their i n s t a b i l i t y characteristics., A survey of existing l i t e r a t u r e reveals that problems involving vortex-excited fluctuating pressure characteristics have received comparatively l i t t l e attention. The situations involving separation (over part of the body or during part of the cycle) have been i n v e s t i -gated to some extent by Duncan ( l ) , * Van de Vooren (2), Mendelson ( 3 ) , Slsto ( 4 ) , Sttider (5) and others. The characteristics of the wake, which forms one of the important parameters i n the aeroelastic i n s t a b i l i t y study, were investigated theoretically by von Karman in his c l a s s i c a l ; papers ( 6 ) , (7). Studies of the flow pattern i n the wake of bluff c y l -inders using hot wire anemometers and similar flow measuring apparatus were carried out by Cometta (8) and Roshko (9), while Chuan; and Magnus (lO) investigated the vortex shedding as related to s e l f excited tor-sional o s c i l l a t i o n s of an a i r f o i l . The measurement of o s c i l l a t i n g pressure on a stationary c i r c u l a r cylinder was carried out by McGregor ( l l ) and Prendergast (12). The experimental arrangement required external rotation of the model to obtain a complete d i s t r i b u t i o n of fluctuating pressure. * Numbers i n brackets refer to bibliography 2 A t e c h n i q u e i n v o l v i n g a m i n i a t u r e s t r a i n g a u g e t y p e t r a n s d u c e r f o r o s c i l l a t i n g p r e s s u r e m e a s u r e m e n t was d e v e l o p e d b y M o l y n e u x (13) a n d l a t e r m o d i f i e d by M o l y n e u x a n d R u d d l e s t o n ( 1 4 ) . The d e v i c e was u s e d f o r t h e e x p e r i m e n t a l d e t e r m i n a t i o n o f a e r o d y n a m i c d e r i v a t i v e s by m e a s u r e m e n t of o s c i l l a t i n g p r e s s u r e a n d i t s i n t e g r a t i o n o v e r t h e s u r f a c e o f t h e a i r f o i l . T h e i r w o r k , h o w e v e r , r e m a i n e d s o l e l y f o r a i r f o i l s a s t h i s was t h e i r m a i n f i e l d o f i n t e r e s t . The m o d e l s w e r e e x p o s e d t o e x t e r n a l l y a p p l i e d f o r c e d v i b r a t i o n s r a t h e r t h a n o s c i l l a t i o n s r e s u l t i n g f r o m t h e f l u t t e r p h e n o m e n o n . W i t h a l l t h i s i n f o r m a t i o n a n i m p o r t a n t t a s k o f c o r r e l a t i o n b e t w e e n c h a r a c t e r i s t i c s o f t h e w a k e , o s c i l l a t i n g p r e s s u r e d i s t r i b u t i o n on a b o d y a n d t h e a e r o e l a s t i c i n s t a b i l i t y o f t h a t b o d y r e m a i n s . 3. I I . STATEMENT OF THE PROBLEM The measurement of unsteady aerodynamic pressure on a body and a survey of the associated wake and the aeroelastic i n s t a b i l i t y of the body forms the subject of this experimental investigation. The projeot may be c l a s s i f i e d into four stages: ( i ) Measurement of o s c i l l a t i n g pressure on bluff as well as streamlined bodies, stationary and vibrating, when located i n steady flow. ( i i ) Experimental study of wake to associate fluctuating pressure with the wake configuration, ( i i i ) Measurement of c r i t i c a l f l u t t e r speed for the bluff and aerodynamic bodies i n two degrees of freedom, plunging and tor-sion. (iv) Correlation of information obtained i n ( i ) , ( i i ) , and ( i i i ) . 4. III. INSTRUMENTATION, CALIBRATION AND EXPERIMENTAL SETUP The instrumentation used i n the experimental investigation cor-responds as follows to the f i r s t three stages of the project mentioned i n Chapter II: (i) a pressure measuring device, a transducer, and the arrange-ment for calibrating i t ( i i ) instrumentation for wake survey ( i i i ) mounting of model i n the wind tunnel to provide freedom of motion i n plunging, and torsion, system for providing de-sirable s t i f f n e s s and damping, arrangement for measurement of c r i t i c a l velocity, frequency, and amplitude during aero-e l a s t i c i n s t a b i l i t y of the model* Each of these systems i s described i n some d e t a i l below. 3.1.1 Wind Tunnel The wind tunnel used for the test program was of the standard low speed, low turbulence return type with velocity control over the range of 4 to 150 feet per second and a turbulence l e v e l of less than 0.5$ as indicated by sphere drag test. The tunnel was powered by a 15 horsepower direct current motor driving a commercial axiflow fan with a Ward-Leonard system of speed control. The tunnel velocity i s calibrated against the pressure d i f f e r e n t i a l across the contraction section of 7:1 r a t i o . This pressure was measured on a Betz micromano-meter which can be read to 0.02 millimeter of water. The test section 5. was 36 inches by 27 inches with corner f i l l e t s varying from 6 inches by 6 inches to 4 3/4 inches by 4 3/4 inches to compensate f o r boundary layer growth. The s p a t i a l variation of velocity was found to be less than 0.25$. The aerodynamic outline of the tunnel i s given i n Figure 1. 3.1.2-Calibration of Betz Manometer A standard pitot tube placed i n the test section was used i n conjunction with a Lambrecht Manometer to measure the dynamic pressure head. The readings obtained from these measurements were then compared with the readings of the pressure d i f f e r e n t i a l across the contraction section as measured by the Betz manometer. The accuracy of Betz mano-meter was found to be adequate for the purpose (Figure 2). 3.2 Models The models used were a l l of a light weight balsa construction. Five different models were made: (i) a 2 inch sqare cylinder ( i i ) a 1 1/2 by 3 inch rectangular cyliner ( i i i ) a 2 inch diameter c i r c u l a r cylinder (iv) an e l l i p t i c cylinder with semimajor axis of 3 inches and semiminor axis of 3/8 inch (v) a 6 inch chord NACA 4412 a i r f o i l section wing A l l models were constructed to span the entire wind tunnel test section thus simulating two-dimensional flow. The models were made out of s o l i d balsa with the exception of the wing which was made up of st i f f e n i n g ribs with stringers and covered with a 1/16 inch balsa sheet. The models are F i g u r e 1. Aerodynamic O u t l i n e of Wind Tunnel 0 15 30 45 60 75 90 105 Wind Velocity, Pltot Tube, f p s . Figure 2. Calibration, Curve: Wind Tunnel 8. shown i n Figure 3» A copper s t r i p 3/4 inch wide, was placed at midspan to accommodate the pressure taps i n the e l l i p t i c cylinder and a i r f o i l . For the c i r -cular cylinder, a copper ring of 2 inch diameter and 3/4 inch width was used, while the square and rectangular cylinders used 3/4 inch wide aluminum blocks for positioning the s t a t i c pressure holes. Models with the location of the pressure taps are shown i n Figure 4. Each model was supported by a l/2 inch diameter shaft which extended beyond the tunnel walls, the shaft i n turn being supported by a system of a i r bearings. (Figure 5a). 3.3 Model Mounting System The mounting system essentially consisted of a channel section, a steel frame supporting the a i r bearings at the top and bottom of of the tunnel section which provided the plunging degree of freedom to the model. Positive alignment between upper and lower a i r bearings was achieved by the use of 2 1/2 by 2 1/2 inch angle irons bolted at the ends, while the several adjusting bolts provided along the frame side helped i n v e r t i c a l positioning of the model. The upper and lower channels were machined to provide accurate alignment between the a i r bearings supporting the l a t e r a l shafts. The above arrangement was i d e n t i c a l to that used by Smith (15). For the study of f l u t t e r phenomena i t was essential to incorporate the torsional degree of freedom. This was achieved by providing a set of torsional a i r bearings which were similar to the l a t e r a l a i r bearings but on a smaller scale. The torsional a i r bearings were designed to be mounted i n the upper and lower l a t e r a l support shafts (Figure 5b). F i g u r e 3. Experimental Models. 1. E l l i p t i c C y l i n d e r 2. Square C y l i n d e r 3. NACA 4412 Se c t i o n Wing 4. C i r c u l a r C y l i n d e r 5. Rectangular C y l i n d e r Mm 1/2,2 15 16 1 2 > 1 1 (-14 13-h 12 2 i n . x 2 i n . y—A—i—h V •• 6 7 IS 6 11 10 9 8 (a) Square Cylinder -*j akin 16 --15 r 14 13 12 11 10 9 (b) Rectangular Cylinder (c) Circular Cylinder (d) E l l i p t i c Cylinder (e) NACA 4412 A i r f o i l Figure 4., Location of Pressure Taps on Models Figure 5a. 1. Lateral Displacement Transducer 2. Lateral Stiffness Spring 3. Lateral A i r Bearing 4. Lateral Support Shaft 5. Lateral Damper 6. Torsional A i r Bearing 7. Model Shaft 13 Figure 5b. 1. Lateral A i r Bearing 2, Lateral Stiffness Spring 3. Lateral Support Shaft 4. Model Shaft 5. Torsional A i r Bearing 6. Torsional Displacement Transducer 7. Torsional Stiffness Spring Figure 5» Details of Model Mounting System 14. The a i r bearing carries a load on a shaft passing through the bearing i n a similar manner to an o i l journal bearing. Air i s supplied through an o r i f i c e (Figure 6) at a pressure P o. Due to viscous forces acting along the sides of the shaft and bearing walls the pressure drops to some value P^. Application of a load causes the shaft to position i t s e l f ec-ce n t r i c a l l y with respect to the bearing. The distance between shaft and bearing:now becomesiless on the side opposite to the load. The reduction i n distance' between shaft and journal 1on the side opposite to the load increases the viscous forces on the a i r flowing through the bearing thus decreasing the flow out of the bearing. Since the volumetric flow i s now decreased, the pressure drop (P - P^) i s de-creased and since P i s constant P., must increase. The opposite effect o 1 y y occurs on the load side where the distance increases. A pressure d i f f e r e n t i a l i s therefore set up which supports the load. A quanti-tative analysis of a i r bearings i s given by Laub (16). Air for the bearings was supplied by an Ingersoll-Rand 2-stage compressor, pumping into a 250 cubic foot storage tank. Air was carried from the tank by a f l e x i b l e hose to a t h r o t t l i n g valve which distributed a i r at 60 pounds per square inch to a l l a i r bearings from the main supply at 118 pounds per square inch. Lateral s t i f f n e s s was supplied by springs attached between the mounting frame and the torsional a i r bearing. For torsional s t i f f n e s s , cantilever springs were used. This was done by taking a s t r i p of beryllium-copper and attaching i t at one end to the torsional fair bearing serving as the root and at the other end i n such a way as to r e s t r a i n torsional \ V Y/////////A V///////2 Model Support Shaft 77mY7777777, 7 O r i f i c e r s Figure 6 , CrosB-section of Ai r Bearing 16. motion. The details of the two mode stiffnesses are shown i n Figure 5. 3.4 Pressure Transducer The main problem encountered i n the investigation was the design and c a l i b r a t i o n of a dynamic pressure transducer suitable for the measure-ment of fluctuating pressure on the surface of the models, which may be stationary or o s c i l l a t i n g and may be located i n unseparated or separated flow. Acoustic l e v e l pressure variations i n the frequency range of 2 to 200 cycles per second made most of the commercially available trans-ducers unsuitable for the purpose. The ide a l transducer would be one with high s e n s i t i v i t y , linear response, and neutral to variations i n atmospheric conditions. With this ideal i n mind a variety of trans-ducers involving the principle of strain gage, capacity change, resistance change and pi e z o e l e c t r i c i t y were designed. The r e s i s t o r and capacitor type transducers f a i l e d to provide enough s e n s i t i v i t y f o r the size of the transducer intended. A s t r a i n gage type of transducer designed according to the arrangement suggested by Perry (l6) was found to be quite sensitive to s t a t i c pressures but r e l a t i v e l y insensitive to pressure fluctuations of acoustic l e v e l . The tests conducted with a diapnragm of 2 inches diameter and 0.002 inch thickness revealed.rather extreme s e n s i t i v i t y of the transducer output to the minor imperfections i n the diaphragm. Increase i n diaphragm thickness only reduced the s e n s i t i v i t y without improving the situation substantially. It i s believed that with a r e l a t i v e l y s t i f f diaphragm the str a i n gage transducer suggested by Perry may be used for measurement of s t a t i c or 17.* large amplitude dynamic pressure but further investigation i s necessary to make i t suitable for minute pressure fluctuations. Transducers using Rochelle s a l t , quartz, and ceramic piezoelectric crystals i n the form of a phonograph cartridge as used i n the arrange-ment shown i n Figure 7 were found to be highly sensitive and capable of measuring intended low l e v e l pressure changes on a body. The insensi-t i v i t y of the device to s t a t i c pressure did not present any problem as the intention was to measure fluctuating pressure rather- than s t a t i c pressure. Crystals of Rochelle salt and quartz were discarded i n preference to the ceramic type because of their s e n s i t i v i t y to temperature changes. Thus the piezoelectric transducer using a ceramic crystal i met the necessary requirements adequately and hence was used for the pressure measurement throughout the experiment. In a piezoelectric device i t can be shown that the voltage output i s d i r e c t l y proportional to the force applied across one of the sensitive dimensions of the c r y s t a l (17). This phenomenon is due to the character-i s t i c s of the cr y s t a l structure and advantage was taken of this property to provide a linear pressure transducer. The o s c i l l a t i n g pressures at the surface of the body were sensed by pressure taps and transmitted by polyethylene tubing to the transducer. It was important to determine the effect of length and diameter of the tubing on s e n s i t i v i t y and phase lag. Experiments carried out with tubing of different diameter and lengths revealed considerable depend-ence of s e n s i t i v i t y on the diameter of the tube. With very fine tubing (0.010 inches diameter) response of the 18. Figure 7a. Sohematic Figure 7b. Exploded View F i g u r e 7ff. Assembly Fi g u r e 7. Pressure Transducer (V) o I 21. transducer was almost negligible while with a large diameter tubing (l/8 inch inside diameter) the transducer response was observed to be turbulent. The tube size of 0.07 inch inside diameter showed no loss i n the s e n s i t i v i t y and hence was used i n the experiment. To study the effect of length of the tubing on phase s h i f t , the fluctuating pressure at a point on a model was transmitted to two ide n t i c a l pressure transducers, one located within the model and the other located at the end of 30 inches of 0.07 inch diameter tube. No measureable phase lag was observed i n the frequency range of 10 cycles per second to 70 cycles per second (Figure 8). This made i t possible to locate the pressure transducers outside the tunnel thus eliminating i n e r t i a effects which would be present i f the transducer were located inside the model. To establish the technique of construction giving transducers of i d e n t i c a l performance three units were constructed and c a l i -brated although only one of them was used. The arrangement was made to connect the pressure taps separately. This was accomplished by allowing the pressure tubes to hang freely from the bottom of the model and to be indi v i d u a l l y connected to an acoustically dead chamber designed to eliminate the interference from external noise. The acoustically dead chamber was construoted from 3/4 inch plywood lined with 1 inch thick foam rubber. The chamber was then placed on a 1 inch foam rubber pad to eliminate mechanical vibrations transmitted through the f l o o r . The acoustically dead chamber with transducer i n place i s shown i n Figure 9. 22. Figure 8 . E f f e c t of Tube Length on Phase, 67 cycles per second 24. 3.4.1 Calibration of Pressure Transducer Calibration of the pressure transducer was carried out i n two different ways. In the f i r s t arrangement the c a l i b r a t i o n was attempted using a fluctuating pressure source consisting of a fixed cylinder with a reciprocating piston. The piston was driven through an eccentric whose speed arid eccentricity could be varied so as to provide pressure fluctuations of varied amplitude and frequency. Two pressure taps were taken from the top dead centre of the cylinder with one connected to a sound level meter and the other to the pres-sure transducer. The arrangement was found to have some inherent li m i t a t i o n s . (i) The apparatus;iwas rather crude and would require consider-able improvement before i t could be used f o r refined c a l i b r a t i o n . ( i i ) Mechanical nature of the device introduced considerable noise thus disto r t i n g the signal, ( i i i ) With the available driving unit i t was not possible to attain frequencies beyond 30 cycles per second, while i t was necessary to obtain a calibration curve up to 100 cycles per second. Although the magnitudes of the pressures obtained from the mechanical o s c i l l a t i n g pressure source were found to be inaccurate as icompared to that predicted by the theory or measured by the Sound Level Meter, i t was observed that the output of the crystal transducer was linear i n the frequency range of 0 to 25 cycles per second. This information 25. proved to be helpful i n later calibration. The second arrangement made use of a University ID-60 horn driver i n conjunction with a General Radio 1551 sound level meter as shown i n Figure 10. The horn driver produced the o s c i l l a t i n g pressure inside the calibration box, constructed of mild steel, which was sensed by the microphone of the sound le v e l meter and by the cr y s t a l transducer. The frequency of pressure o s c i l l a t i o n s was controlled by a Hewlett - Packard 202 A low frequency generator and amplified by a Bogen 60 watt Amplifier. The calibrations were conducted by holding a constant pressure le v e l at varying frequency. This was made possible by keeping the Db sound le v e l , as detected by the sound le v e l mater, at a constant value and varying the frequency of the generator. From the data obtained curves representing variation of output with frequency were plotted as shown i n Figure 11. From these plots i t was straight forward to obtain the rel a t i o n between pressure and voltage output of the transducer for a given frequency. It was possible to relate the Db readings of the sound level meter to pressures i n pounds per square inch by the fact that the Dbs are defined as a function of pressure ratios with a reference pressure of 0.0002 microbars. The plots of pressure versus voltage output were found to be linear (Figure 12"). Due to the limitations imposed by the amplifier and horn driver the minimum frequency obtainable was 15 cycles per second. It thus remained to calibrate the transducer i n the low range of 0 to 15 cycles per second. This was achieved by extrapolation ro -J o Figure 10b. Assembly 1, Bogen Amplifier 2. Sound Level Meter 3. Horn Driver 4. C a l i b r a t i o n Box 5. Acoustically Dead Chamber Figure 10, Calibration Setup 2 8 . 320 2 8 0 Frequency, cps Figure 11. Calibration Curves Variation of Output with Frequency Figure 12. Calibration Curve: Variation of Output with Pressure 30. based on the fact that the variation of voltage output with f r e -quency was found to be linear i n the range of interest i n both of the c a l i b r a t i o n procedures. The calibration was checked by comparing the pressure f l u c t u -ations on the surface of a stationary c i r c u l a r cylinder registered by the pressure transducer with those obtained by McGregor ( l l ) . The comparison between the two sets of results i s presented i n Figure 41. 3.5 Wake Survey Equipment Preliminary surveys of the wake behind a c i r c u l a r cylinder, carried out with hot wire anemometer equipment, gave the impression that i t would be rather d i f f i c u l t to locate, precisely, the shed vortices. The fundamental signal was completely camouflaged by the random background noise which was d i f f i c u l t to suppress with the available equipment. An attempt to eliminate the background noise was made with the use of an integration oscilloscope, but i t was found that the random voltages superimposed on the fundamental signal triggered the sweep at different points i n the fundamental cycle each time so no build-up occurred. Thus the integration oscilloscope could not properly detect the fundamental signal. The Karman vortex street causes velocity fluctuations and accompanying these are pressure fluctuations. As the transducer was designed to measure fluctuating pressure,- a p o s s i b i l i t y existed that i t might serve as a wake survey instrument. 3 1 . A simple experiment showed that a pressure transducer placed i n a stationary body located i n the airstream would sense the frequency of the vortices shed from r that body..- It was surprising to note that the output from the crystal transducer gave a more clearly defined indication of the fundamental shedding frequency than the output from the hot wire anemometer. Proof that the f r e -quency was that of the shed vortices was obtained by comparison of the Strouhal number as determined from the frequency recorded by the transducer to the Strouhal numbers over a given range of Reynolds number for a c i r c u l a r cylinder as given by Fung (18). Thus the pressure transducer designed to measure the acoustic le v e l pressure variations can be used to determine the frequency of the shedding vortices behind test bodies. Further experimentation revealed that a pressure tap placed at the t i p of a slender probe when used i n conjunction with the pressure transducer could be used ef f e c t i v e l y as a wake survey de-vice (Figure 13). A 36 inch length of tubing was used to transmit the pressure fluctuations at the probe t i p to the transducer. Using the probe and the transducer i n this manner gave by movement of the probe i n the wake an indication of the vortex locations. The output signal from the pressure transducer with the probe i n the wake was much clearer than the corresponding signal from hot wire anemometer equipment. Experimentation with the probe i n the wake of a c i r c u l a r cylinder yielded a value of 0.29 for the ratio of l a t e r a l to longitudinal spacing between the adjacent vortices which is; l i t t l e higher than the theoretically;restablished value of 0.281. 32 F i g u r e 13. Wake Survey Probe 33. 3.6 Bending and Torsional Displacement Transducers The l a t e r a l displacement transducer was an inductive c o i l type developed by Smith (l5). Two" c o i l s were used, one as the primary and the other as the secondary. They were concentrically mounted so as to provide an annular region through which the l a t e r a l shaft could pass. A signal of 20,000 cycles per second was fed i n to the primary c o i l which was sensed by the secondary c o i l through inductance. The amplitude of the signal .received by the secondary c o i l was dependent on the number of primary turns cut off by the l a t e r a l shaft, i . e . on the plunging displace-ment of the model. The output from the secondary c o i l was an amplitude modu-lated signal. By f i l t e r i n g the carrier frequency; i . e . the 20,000 cps signal fed to the primary, an exact time-history of the l a t e r a l displacement was obtained. The torsional displacement was measured by sensing st r a i n i n one of the torsional cantilever springs used to provide torsional s t i f f n e s s to the model. The s t r a i n gages were mounted at the root of the- cantilever spring and the signal was fed through an E l l i s Bam-1 s t r a i n gage bridge amplifier. Both l a t e r a l and torsional displacement outputs were fed into a Tektronix 502A oscilloscope. 3.6.1 Calibration of Displacement Transducers The l a t e r a l displacement transducer was calibrated by 34. displacing the aluminum l a t e r a l support shaft i n the annular region of the transducer i n equal increments and noting the output. This calibration showed the l a t e r a l transducer to be linear within 1% (figure 14). The torsional displacement transducer was calibrated by displacing the end of the cantilever spring i n equal increments and noting the output. The tolerances of l i n e a r i t y were found to be comparable to those of the l a t e r a l displacement transducer (Figure 15). 3.7 Electromagnetic Damping The damping, i n addition to inherent damping withinthe system, was introduced by means of electromagnetic eddy current dampers. The dampers created a magnetic f i e l d to which the aluminum shaft carrying the model was exposed. Eddy currents induced i n the shaft dissipated energy from the o s c i l l a t i n g system. The damping was found to be almost viscous. For higher currents the damping was s t i l l as close to viscous as i t was for lower currents. Damping levels were controlled by the amount of D. C. current passing through the electromagnet. The c a l i -bration curve i s shown i n Figure 16. 37. 0.Q3Q 0.025 0.020 0.015 0.010 0.005 0 0.10 0.20 0.30 0.40 0.50 I, amps Figure 16. Calibration Curve: Electromagnetic Damper 38. 3.8 Experimental Test Procedures 3.8.1 Static and Oscill a t i n g Pressure Measurements Measurements of st a t i c and o s c i l l a t i n g Pressures were made separately for each individual pressure tap. The tubings from the taps were connected individually f i r s t to a Lambrecht manometer for s t a t i c pressure measurements and second to the pressure transducer for o s c i l l a t i n g pressure measurements. The transducer output was fed di r e c t l y to the Tektronix 502A oscilloscope. The grid inscribed onthe oscilloscope screen made i t possible to read with the accuracy of less than 1% f u l l scale. A l l readings of pressure fluctuations were made peak to peak and i n the ease of amplitude modulated signals the maximum amplitude only was recorded and taken to be the maximum pressure fluctuation at that point. The readings from the os-cilloscope were recorded i n m i l l i v o l t s and conversion to pounds per square inch was made using the calib r a t i o n curves. The frequency of pressure o s c i l l a t i o n s was noted during each test as output of the pressure transducer was a function of frequency. The experimental test setup i s shown i n Figure 17. Pressure measurements were made with a l l the models i n i t i a l l y stationary. The square, rectangular, e l l i p t i c a l cylinders and wing were tested at various angles of attack and the variation of s t a t i c and fluctuating pressure d i s t r i b u t i o n was noted. These measurements with stationary models were carried out as several values of Reynolds number. Figure 17* Equipment and Test S e c t i o n 4 0 . Once the models were tested when stationary, a i r was supplied to the bearings, and tunnel speed was varied u n t i l the model executed self excited o s c i l l a t i o n s . The effect of motion on the o s c i l l a t i n g pressure d i s t r i b u t i o n was noted. The o s c i l l a t i n g pressures as well as the model os c i l l a t i o n s were recorded photographically. 3.8.2 Amplitude Measurements The individual model was made free to o s c i l l a t e by supply-ing a i r to the l a t e r a l and torsional a i r bearings which permitted two degrees of freedom. Once the body was i n motion, the nature of o s c i l l a t i o n s was. observed on the oscilloscope. Since the oscilloscope was of the dual beam type i t was possible to display and photograph the two degrees of freedom of motion simultaneously. It was also possible to observe the effect of torsional and l a t e r a l displacements on the o s c i l l a t i n g pressure d i s t r i b u t i o n by the dual beam feature. 3.8.3 Wake Measurements The probe connected to the pressure transducer was placed i n the wake of each body and s l i g h t l y to one,side. The pressure fluctuations produced by the wake were displayed on the screen of the oscilloscope along with tiujse produced at a point on the surface of the model. The probe, located on the same side of the model as the point, was then moved from the v i c i n i t y of the body down stream u n t i l the two signals were i n phase. 41. The procedure was repeated with the probe ongthe opposite side. Twice the difference between the two readings gave the vortex spacing i n the flow direction. It was found that this measure-ment could be made with a f a i r degree of accuracy. For example, Figure 35 shows two such traces i n phase, the upper trace being the pressure o s c i l l a t i o n s at the surface of the body (tap l ) and the lower trace the o s c i l l a t i o n s at the probe t i p . The probe was moved across the wake of the models to obtain the spacing i n the direction perpendicular to the airstream. The measurements were made by noting the distance between the maximum fluctuations to either side of the wake. This measure-ment could be made but not with the accuracy of the longitudinal distance since the maximum fluctuations appeared over a sub-s t a n t i a l distance rather than attaining a well defined peak. 3.8.4 Strouhal Numbers Comparison (of the frequency of the pressure o s c i l l a t i o n s of the c i r c u l a r cylinder with published data on Strouhal frequencies showed the two frequencies to be i d e n t i c a l . The trace obtained by the pressure transducer sensing the o s c i l l a t i n g pressures at the surface of the model displayed the frequency of vortex shed-ding i n a more defined manner than was obtainable with hot wire anemometer equipment. A l l Strouhal frequency measurements were there-fore made from the fluctuating pressure trace at the surface of the model. 42. Strouhal frequencies were recorded at various Reynolds numbers for the c i r c u l a r , square, rectangular and e l l i p t i c cylinder at high angles of attack (no pressure fluctuations were observed at low angles of attaok in the case of the e l l i p t i c cylinder). 3.8.5 Static L i f t Coefficient Versus Angle of Attack Circ u l a r Cylinder and MACA 4412 Section Wing Pressure distributions and s t a t i c l i f t coefficients on the circ u l a r cylinder and NACA 4412 a i r f o i l are well established and i t was not necessary to measure them during this experiment. Square and/ Rectangular Cylinders Static l i f t coefficients were determined by graphical in t e -gration of the pressure distributions about the model. The l i f t f or a square or rectangular cylinder can be obtained from the r e l a t i o n ^ ^ L'=[ (^--?,)dS, Cos* +${%-Vj cL$^ sJ^oi Defining l i f t coefficient as: c' •= (where c i s the length of a face on the square cylinder and the length of -the"longest face on the rectangular cylindejO gives: 4 3 . i . e . | ( Here the subscripts 1, 2, 3, and 4 denote the value of the parameter at the faces as shown i n Figure 18. " t Figure 18 here a - angle of attack. E l l i p t i c Cylinder The l i f t for the e l l i p t i c cylinder can be obtained from the following r e l a t i o n : / 44. ft C O S©< giving the l i f t c o e f f i cient per unit span as: C=( f c a - T Q __ er>^- no)! *L/S\ i . e . ,C0So< The subscripts I and u denote the lower and upper surfaces respectively of the e l l i p t i c cylinder as shown i n Figure 19. 3.8.6 Fluctuating L i f t Coefficients From phase difference measurements around a model under test i t was observed that: (a) a l l pressure fluctuations occurring on the same surface, 45. j i . e . the lower or the upper Burfaoe, were.in phase with one another (b) pressure fluctuations on the upper surface were 180° out of phase with those on the lower surface. The: Ct i , : graphical integration was performed i n a manner similar to the one presented before with the exception that here the os-d i l a t i n g pressure d i s t r i b u t i o n was integrated over the top and bottom surfaces separately and the two results were added to get the t o t a l fluctuating l i f t c o e f f i c i e n t . A l l measurements of o s c i l l a t i n g pressures and l i f t co-e f f i c i e n t s as presented here are peak to peak. Thus«... , " fluctuating l i f t per unit span 46. IV. EXPERIMENTAL RESULTS 4.1.1 S t a t i o n a r y Square C y l i n d e r The square c y l i n d e r was provided with s i x t e e n pressure taps. The pressure d i s t r i b u t i o n , v a r i a t i o n of l i f t c o e f f i c i e n t with angle of a t t a c k , and v a r i a t i o n of S t r o u h a l number with Reynolds number showed very good agreement with the r e s u l t s obtained by other i n v e s t i g a t o r s (l5")> (20). The recorded r e s u l t s are presented i n f i g u r e s 20, 21 and 22, The S t r o u h a l number was found to be constant at the approximate value of 0.12. At hi g h e r Reynolds number the r e s u l t s were considerably s c a t t e r e d y e t the average value appeared t o be the same. The value i s s l i g h t l y lower than that obtained by Brooks (20X. The f l u c t u a t i n g pressure d i s t r i b u t i o n data were recorded f o r the angle of a t t a c k range of 0° - 17° 30' with Reynolds number he l d constant at 41,000. The r e s u l t s are presented i n Figure 23. The p l o t of C' versus angle of a t t a c k (Figure 24) shows the L f l maximum value to be 2.4 at an angle of a t t a c k of 6° and minimum value of 1.4 at 14°. I t i s of i n t e r e s t to note that the minimum f l u c t u a t i n g l i f t c o e f f i c i e n t occurs at the angle of a t t a c k f o r which the s t a t i c l i f t c o e f f i c i e n t i s maximum. Photographs showing pressure o s c i l l a t i o n s about the square . c y l i n d e r at zero angle of a t t a c k are g i v e n i n F i g u r e 25. The t r a c e s at taps 13 and 14 are purposely reproduced w i t h higher s e n s i t i v i t y " (XlO, X 2 the normal s e n s i t i v i t y r e s p e c t i v e l y ) . The 47. pressure fluctuations are nearly sinusoidal except at the rear of the cylinder. At tap 4 a high frequency signal seems to be super-, imposed on the fundamental signal while tap 5 shows marked influence of the second harmonic. Decreasing the sweep time of the oscilloscope displayed the amplitude modulation of the pressure o s c i l l a t i o n s (Figure 26). The phase study of the o s c i l l a t i n g pressure showed that a l l pres-sure fluctuations on the same side of the model were i n phase while those on the opposite side were 180° out of phase thus indicating that the breaking of a vortex from one side of the model instant-aneously affects- the pressure distribution" on that side. The wake geometry was also investigated, making use of the designed pressure transducer i n the manner explained e a r l i e r (section 3.8.3). The longitudinal spacing (h) was found to be 12.13 inches while the l a t e r a l spacing (a) was 5.75 inches thus giving an a/h r a t i o of 0.474. 4.1.2 O s c i l l a t i n g Square Cylinder The wind velocity was now increased u n t i l the model exhibited self excited o s c i l l a t i o n s . The variation i n amplitude of o s c i l l a t i o n with velocity leading to two stable l i m i t cycles as reported by Smith (l5) was observed. Figure 27 shows plunging o s c i l l a t i o n s of the model at a wind velocity of 60 feet per second (larger limit cycle). 48. The comparison of pressure fluctuations at a l l taps with the square cylinder stationary or o s c i l l a t i n g revealed that they were i d e n t i c a l . The representative photographs comparing the pressure fluctuations at tap 15 with model stationary and o s c i l -l a t i n g are shown i n Figure 26 and Figure 28. Figure 20 (cont'd). Variation of Static Pressure Distribution with as Square Cylinder 52 v i . o 0 4 8 12 16 18 20 o, deg. Figure 21 Variation of Static L i f t Coefficient with as Square Cylinder o O o o o o O v O o I o 0 O o t "--• 1.5x10 2.0 2.5 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10' He Figure 22. Variation of Strouhal Number with Reynold^: Number for Square Cylinder 54. Figure 23 (cont'd). Variation of Fluctuating Pressure Distribution with a : Square Cylinder Figure 23 (cont'd). Variation of Fluctuating Pressure Distribution with o: Square Cylinder Figure 24. Variation of Fluctuating L i f t Coefficient with Square Cylinder Figure 25. Pressure Oscillations on the Surface of Square Cylinder 59 Figure 26. Amplitude Modulations of Figure 27. Slowly Varying Amplitude Pressure Fluctuations on the Surface and Frequency of Square Cylinder Motion of Square Cylinder, Tap 15 (Stationary) Figure 28. Effect of Motion on Pressure Fluctuations on the Surface of Square Cylinder, Tap 15 60. 4.2.1 Stationary Rectangular Cylinder, J&»2 , A rectangular cylinder with AR=2 was tested f o r s t a t i c and fluctuating pressure d i s t r i b u t i o n under stationary as well as dynamic conditions. The surface of the cylinder was provided with sixteen pressure taps eaoh connected to the Lambrecht manometer for s t a t i c pressure measurements and to the designed pressure transducer for fluctuating pressure measurement. The s t a t i c pressure d i s t r i b u t i o n over a range of angle of attack i s pre-sented i n Figure 29 while Figure 30 shows var i a t i o n of l i f t c o e fficient with angle of attaok. It may be pointed out that the maximum l i f t c oefficient of 0.B3 at 10.5° ie lower than that obtained f o r the square cylinder. The measurements carried out to study variation of Strouhal number with Reynolds number showed i t to remain constant at the value of 0.081 as indioated i n Figure 31. There was less scatter of data for this case as compared to the square cylinder. The fluctuating pressure measurements at 0° and 3.5° angle of attaok were nearly i d e n t i c a l on either side of the centerline of the body as i n the case of the square cylinder. At an angle of attack of 14° the surfaoe facing the upstream; i . e . taps 9 and 14 showed signs of turbulence probably due to reattachment Of the flow while the opposite face registered sudden ri s e i n fluctuating pressure coefficients (taps 4 and 5). Fluctuating pressure coefficients on the surfaoe of the rectangular cylinder at several angles of attack are shown i n Figure 32 while the plot of fluctuating l i f t c o efficient per unit span against 61 angle of attack i s presented i n Figure 33. Photographic representation of the pressure o s c i l l a t i o n s at various points on the surface of the rectangular cylinder are shown i n Figure 34. The photographs are for the model at zero angle of attack with the oscilloscope attenuator main-tained at the same s e n s i t i v i t y . Amplitude modulation of the fluctuating pressure i n the Reynolds number range of 55,000 to 70,000 i s worth pointing out since the modulations did not appear anywhere except i n this range. No definite explanation for this can be given here. The phenomenon should be i n v e s t i -gated further. Note also the expected double frequency effect at the rear of the cylinder as shown by the photograph for tap 7. The study of phase relation between the o s c i l l a t i n g pres-sures about the rectangular cylinder showed the taps 1 to 7 and 16 to be i n phase while taps 8 to 15 to be 180° out of phase with respect to tap 1. The wake study revealed the longitudinal and l a t e r a l spacing between the consecutive vortices to be 17.3 and 5.5 inches thus giving a/h=0.318. Figure 35 shows the fluctuating pressure traces produced by the probe located 17.3 inches behind the model and that existing at tap 1. The two signals are apparently i n phase. 62. Figure 29. Variation of Static Pressure Distribution with a: Rectangular Cylinder M »2 Figure 29 (cont'd). Variation of Static fraesur© Distribution with «« R e c t a n g u l a r Cylinder Mm2 6 4 o 65. Figure 29 (cont'd). Variation of Static Pressure Distribution with OJ Rectangular Cylinder AR»2 Figure 30. Variation of S t a t i c L i f t Coefficient with o: Rectangular Cylinder JR »2 0.17 0.16 0.15 0.14 0.13 0.12 0.11 0.10 0.09 0.09 0.07 0.06 0.05 0.04 0.03 o o o o ° © < O" 1.5x10 2.0 2.5 3.0 4.0 5.0 Re Figure 31. Variation of Strouhal Number with ReynoldSs Number for Rectangular Cylinder ffi»2 Figure 32# Va?latien of fluctuating freseufe Distribution With tt: Rectangular Cylinder & «g Figure 32 (cont'd). Variation of Fluctuating Pressure Distribution with at Rectangular Cylinder JR»2 figure 32 (cont'd). Variation of Fluctuating Pressure Distribution with o: Rectangular Cylinder 43 -2 Figure 33. Variation of Fluctuating L i f t Coefficient with a: Rectangular Cylinder £Rn2 73 F i g u r e 35. P r e s s u r e F l u c t u a t i o n s as Recorded by Probe and Tap 1, R e c t a n g u l a r i, C y l i n d e r SL w2t Probe 17.3 i n c h e s downstream of the Model a. No M o t i o n , Sweep Time 50wvSh/cin. b. Motion, Sweep TimeolOOmSVcm F i g u r e 36. E f f e c t of Motion on Pres s u r e F l u c t u a t i o n s on the Surface of Re c t a n g u l a r C y l i n d e r £R «2 74. 4.2.2 Os c i l l a t i n g Rectangular Cylinder. 2 Next the wind speed was gradually increased u n t i l the model exhibited self excited o s c i l l a t i o n s . The o s c i l l a t i n g pressure at a l l taps on the surface of the model was found to be i d e n t i c a l to the corresponding pressure under stationary conditions. This i s shown for a representative pressure tap i n Figure 3 6 . 4.2.3 Stationary Rectangular Cylinder., AR= l/2 As a matter of curiosity the previous model; i . e . rec-tangular cylinder with /SR = 2, was rotated through 90° to give a rectangular cylinder with Mm l/2. The model i n this position represented a body with greater bluffness thus giving large drag particularly at higher angle of attack and speed. The i n s u f f i c i e n t s t i f f n e s s of the model caused i t to deflect under the influence of drag hence the tests were limited to zero angle of attack. The s t a t i c and fluctuating pressure distributions for this case are presented i n Figure 3 7 . The large fluctuations i n pressure on the top, bottom and rear faoe with r e l a t i v e l y small values on the upstream face are worth pointing out. Note also the comparatively large value of C'T a 4 . 8 with reference to the L f l ' narrow side, and C = £.4 with reference to the broad side. L f l The variation of Strouhal number with Reynolds number i s shown i n Figure 38. The results are quite scattered primarily due to the fact that the o s c i l l a t i n g pressure fluctuations were generally unorganized showing a large amplitude modu-la t i o n e f f e c t . 76. Figure 37a. Static Pressure Distribution Over Rectangular Cylinder iR «el/2 77. O c O o o o o o o O -l,5x!0 4 2 .0 2 .5 3 .0 4 .0 5.< 5.0 7.0 8.0 9.0 1 0,03 Re Figure 38, Variation of Strouhal Number with Reynolds;) Number f o r Rectangular Cylinder AR« 1/2 79 4.3*1 Stationary Circular Cylinder The s t a t i c pressure d i s t r i b u t i o n around a c i r c u l a r cylinder i s well known yet for completeness i t s measurement was carried out at three different values of Reynolds number (Figure 39). The measurement of Strouhal number as a function of Reynolds number gave results which were scattered around the curve obtained by ReIf and Simmons (2l), and as shown i n Figure 40. The measurement of fluctuating pressure d i s t r i b u t i o n around a stationary c i r c u l a r oylinder was carried out by McGregor ( l l ) making use of a microphone as mentioned e a r l i e r . His results served as a guide i n checking the calibration accuracy of the designed transducer. The dynamic pressure d i s t r i b u t i o n shown i n Figure 41 agreed quite well with that obtained by McGregor. The variation of Cp. s]n Q with Q The resultant fluctuating l i f t coefficient per unit span was C » 0.60 which i s comparable to that obtained by McGregor The pressure fluctuations on the surface of the c i r c u l a r cylinder are shown photographically i n Figure 43. The second harmonic effect appears to be quite prominent at pressure tap 7. The amplitude modulation of the pressure o s c i l l a t i o n s was found to be more random than that for the square cylinder as was plotted (Figure f l - 0.58, Re*53,000). 80. shown i n Figure 44. The. survey of phase between the o s c i l l a t i n g pressures re-vealed taps 2 to 7 to be i n phase and taps 8 to 12 to be 180° out of phase. Figure 45a portrays the signals of the pressure o s c i l l a t i o n s on one side of the cylinder to be i n phase and Figure 45b show 180° phase s h i f t for the pressure signals o r i -ginating from the opposite side. The effectiveness of the pressure transducer as a wake survey instrument was substantiated by applying i t to the study of wake geometry behind the c i r c u l a r cylinder and comparing the results with theoretically established values. The wake survey probe operating i n conjunction with the pressure transducer gave longitudinal spacing of 9.7 inches and l a t e r a l spacing of 2.8 inches between the adjacent vortices, thus giving the r a t i o a/h m 0.29. This i s s l i g h t l y higher than the theoreti-cally established value of 0.281. Figure 46 compares the pres-sure fluctuations sensed by the probe located 9.7 inches down-stream from the center of the model with those ocourring at pressure tap 4. The two responses are apparently i n phase. The dominance of the second harmonic fluctuations along the centerline of the wake i s shown i n Figure 47 where the upper and lower traces represent the output from tap 4 and the probe located i n the center of the wake respectively. 8 1 . 4.3.2 Oscil l a t i n g Circular Cylinder The c r i t i c a l wind speed causing s e l f excited o s c i l l a t i o n s of the circular cylinder was observed to be 26 feet per second,, Obviously this was not the vort@x excited o s c i l l a t i o n which should occur at the wind velocity of 4.9 feet per second. The o s c i l l a t i o n s therefore were attributed to imperfections i n model construction-or end effects. 0.2J 0. 0.2 0.1 0.] 0.17 ® Experimental Results Reif and Simmons (21) o o O 0 o o o o -xrr 10 1.5 2.0 2.5 3.0 4.0 5.0 6.0 7.0 8.0 Re Figure 40. Variation of Strouhal Number with Reynoldss Number! Ci r c u l a r Cylinder Figure 41. Fluctuating Pressure Distribution: C i r c u l a r Cylinder Figure 42. C s i n •& versus $ for Circular Cylinder P f l Figure 43. Pressure O s c i l l a t i o n s on the Surface of C i r c u l a r C y l i n d e r 87. Figure 44. Amplitude Modulations of Pressure Oscillations over Circular Cylinder a. Same Side. Taps 2 and 6 Figure 45. Variation of Phase on the b. Opposite Side, Taps 4 and 10 Surface of the Circ u l a r Cylinder 8 8 . Figure 46. Pressure Fluctuations as Recorded by Probe and Tap 4, Circular Cylinder, Probe 9.7 inches Downstream of the Model I H i Figure 47. Double Frequency Effect at the Center of Wake of Circular Cylinder b. Motion a. No Motion Figure 48. Pressure Fluctuations on the Surface of Circular Cylinder as Affected by i t s Motion 89. 4.4.1 Stationary E l l i p t i c Cylinder (~a=3 inches . e=0.985) Static pressure measurements on the surface of the e l l i p t i c cylinder were carried out over a wide range of angle of attack as shown in Figure 49. The st a t i c l i f t c oefficient as function of a i s presented i n Figure 50. The pressure fluctuations were not observed u n t i l an angle of attack of 9.5°. From this point oh to the angle of attack of 28.5° the pressure fluctuations though present were not well defined. But beyond 28.5° the pressure variations were observed to be quite regular. Photographs of the pressure o s c i l l a t i o n on the surface of the e l l i p t i c cylinder are given i n Figure 51. Figure 52 shows the variation i n fluctuating pressure c o e f f i c i e n t on the surface of the cylinder for several values of a. Fluctuating l i f t c o e f f i c i e n t as a function of angle of attack i s presented i n Figure 53. The study of phase difference between fluctuating pres-sures at different positions on the surface.of the e l l i p t i c cylinder at angles of attack of 28°, 38° and 48° showed taps 1 to 5 i n phase, tap 6 out of phase by 90° and taps 7 to 12 out of phase by 180° a l l with respect to tap 11 At an angle of attack of 57° the phases of the pressure o s c i l l a t i o n s with respect to tap 1 were found to be as follows: taps 1 to 5 in phase, tap 6 lagging by 45°, tap 8 lagging by 135°, tap 9 to 12 lagging by 180°. At pressure tap 7 phase difference fluctuated randomly between 0° and 180°. 90. The measurement of variation i n Strouhal number with Reynolds number at different angles of attack gave readings which were quite scattered as shown i n Figure 54. The study of the nature of the wake revealed the longi-tudinal distance between the vortices of 17.6 inches and the l a t e r a l spacing of 4.5 inches. This test was conducted only at an angle of attack of 30°. The study of s t a t i c pressure d i s t r i b u t i o n showed the presence of large twisting moment for angles of attack other than zero. This led the e l l i p t i c cylinder to exhibit pure divergence under the condition of stif f n e s s and damping present i n the system. This made measurement of fluctuating pressure under dynamic conditions of the model impossible. Figure 49. Variation of Statio Pressure Distribution with a: E l l i p t i c Cylinder Figure 49 (cont'd). Variation of S t a t i c Pressure Distribution with a: E l l i p t i c Cylinder Figure 49 (cont'd). Variation of Static Pressure Distribution with as E l l i p t i c Cylinder 94. Figure 50. Variation of S t a t i c L i f t Coefficient with a t E l l i p t i c Cylinder Figure 52. Variation*of Fluctuating Pressure Distribution with a: E l l i p t i o Cylinder Figure 52 (cont'd). Variation of Fluctuating Pressure Distribution with a: E l l i p t i c Cylinder Figure 53. Variation of Fluctuating L i f t Coefficient with o: E l l i p t i c Cylinder • >— O / - o ? o°<> n D 1 71 ° 0 <3 • v v < n n O OCs o u • n f ° <*> . 28*5° • 38° o c ^ .am 47 .5 C  ? o= 57° o < • o ' y c c DO c o u. 10 1.5 2.0 3.0 4.0 5.0 6.0 7.0 9.0 He 1.5 2.0 3.0 Figure 54. Variation of Strouhal Number with Reynolds,,- Number : E l l i p t i c Cylinder 100. 4.5.1 Stationary and Osci l l a t i n g A i r f o i l The a i r f o i l section used being standard WAEA 4412, i t was not necessary to measure s t a t i c pressure d i s t r i b u t i o n around i t s surface. When tested from 0° to 35° angle of attack i t did not show existence of any fluctuating pressure. The c r i t i c a l f l u t t e r speed of the a i r f o i l was found to be 32 feet per second. The small value of velocity was due to absence of any external damping except that provided by the airbearings. The s t i f f n e s s of the system i n plunging and torsion is indicated by i t s natural frequencies i n those degrees of freedom which were 5.3 and 5.6 cycles per second respectively. Figure 55 shows the time record of plunging and torsional displacement of the model during aeroelastic o s c i l l a t i o n s . The Lissajous figure representing the phase difference between the two degrees of freedom i s shown i n Figure 56. Under this o s c i l l a t i n g condition the a i r f o i l did exhibit fluctuating pressure on i t s surface. Figure 57 shows the o s c i l l a t i n g pressure at a representative point (tap 3) together with the plunging and torsional motion of the model. Figure 58 surveys the o s c i l -l a t i n g pressure at the surface of the model. V S M S H S S B S II iivitftfjiviivi i'iv*!iiirj,ir*v 'miiWmvaiM'A p i j i i i j M Figure 55. Self Excited Motion of the A i r f o i l 101, Figure 56. Lissajous Figure During Self Excited Motion of the A i r f o i l ftafehifcii! I iiwjiwiiBi uteri*, E S R I Figure 57a. Lateral Figure 57b. Torsion Figure 57. Pressure fluctuations at tap 3 with Lateral and Torsional Displacement of the A i r f o i l Figure 58. O s c i l l a t i n g Pressures on the Surface of A i r f o i l Undergoin Flu t t e r 103. V. DISCUSSION OF RESULTS AND CONCLUDING REMARKS It was i n t e r e s t i n g to observe the o s c i l l a t i n g l i f t co-e f f i c i e n t decrease with r e d u c t i o n i n the b l u f f n e s s of the body. For example at zero angle of a t t a c k the r e c t a n g u l a r c y l i n d e r with i t s broad side upstream (AR=l/2) had a f l u c t u a t i n g l i f t c o e f f i c i e n t of 4.6 r e f e r r e d to the fac e p a r a l l e l to the f l o w . As the body s i z e was reduced to a square c y l i n d e r the l i f t c o e f f i c i e n t dropped t o 2,4. With f u r t h e r s t r e a m l i n i n g of the body i n t o a r e c t a n g u l a r c y l i n d e r with M =2 the o s c i l l a t i n g l i f t c o e f f i c i e n t showed f u r t h e r decrease to 1,2 r e f e r r e d to the face p a r a l l e l to the flow while f o r c i r c u l a r c y l i n d e r i t was only 0.60. F u r t h e r s t r e a m l i n i n g of the body from c i r c u l a r c y l i n d e r i n t o e l l i p t i c c y l i n d e r and then i n t o a i r f o i l showed no pressure f l u c t u a t i o n at a l l at zero angle of a t t a c k . This r e d u c t i o n i n C' with s t r e a m l i n i n g of the body i s f l s c h e m a t i c a l l y shown i n Figure 59. I t i s a l s o of i n t e r e s t to note that C' i s constant f o r the r e c t a n g u l a r c y l i n d e r s L f l i f i t i s r e f e r r e d to the fac e p e r p e n d i c u l a r to the flow. For square and r e c t a n g u l a r c y l i n d e r s as w e l l as f o r the e l l i p t i c c y l i n d e r at large angles of a t t a c k the magnitude of f l u c t u a t i n g l i f t c o e f f i c i e n t was observed to be minimum at the points where s t a t i c l i f t c o e f f i c i e n t was maximum. 104. O O referred^ to b • O referred to h (c) For bodies with sharp leading edge providing well defined separation e.g. the rectangular cylinders, fluctuating pressure and l i f t coefficients were observed to be considerably larger than the corresponding s t a t i c values, while for the ci r c u l a r cylinder, e l l i p t i c cylinder and a i r f o i l the f l u c -tuating coefficients were found to be smaller than their s t a t i c counterpart. (d) Due to the model and model mounting system design, vortex excited o s c i l l a t i o n s of the bodies were not possible. Other unbalancing forces produced the self-excited motions which, particularly for a bluff body, does not seem to affect either the frequency of the shedding vortices or the f l u c -tuating pressure. 105 Probably the most s i g n i f i c a n t outcome of the project was the development of a transducer capable of measuring acoustic l e v e l pressure fluctuations over a wide range of frequency. The capability of the device to serve as a wake survey instrument further enhances i t s usefulness. 106, . RECOMMENDATION FOR FUTURE INVESTIGATION 1, Although the pressure transducer was found to be quite adequate . for the present set of experiments, further refinement i n i t s construction and calibration would make i t a more useful unit* 2, Usefulness of the transducer as a wake survey unit was described before. For precise measurement of wake geometry, a mechanical device capable of providing motion to the probe, i n three-dimension i s necessary, 3, Measurement of fluctuating pressure and wake geometry should be undertaken f o r a rectangular cylinder of AR» 1/2 over a range of angles of attack for completeness of investigation, 4, Dynamic results were not obtained i n the case of e l l i p t i c cylinder as i t exhibited pure divergence. Use of higher stiffness and/or damping should correct this tendency and provide self»excited o s c i l l a t i n g motion of the body, 5 o In the investigation presented here, the wake measurements were carried out for stationary condition of the model. Corresponding measurements during dynamic condition of the model should also be undertaken, 6, Study of pressure fluctuations and wake during vortex excited motion of the body should be of interest, 7, Similar study of I-section, T-seotion, channel and angle section, dumbbell shaped body, e t c , should prove useful, 8, Study of fluctuating pressure, wake geometry and aeroelastic i n s t a b i l i t y of a body when located i n the wake generated by another body should be of importance i n VTOL design. 107-BIBLIOGRAPHY 1, Duncan, W0J., E l l i s , DaL., Smyth, E 0, " F i r s t Report on the General Investigation of T a i l Buffeting," Br, ARC R&M 1457, 1933. 2, Van de Vooren, A 0 I 0 , and Bugh, H 0, "Spontaneous Oscillations of an Aerofoil due to Ins t a b i l i t y of Laminar Boundary Layer," Natl, Luchvaartlab, Amsterdam, Repto F96, 1951. 3, Mendelson, A,, "Aerodynamic Hysteresis as Factor i n C r i t i c a l F l u t t e r Speed of Compressor Blades at S t a l l i n g Conditions," J. Aeronaut, S c i , , 1949. 4, Sisto, F 0, " S t a l l F l u t t e r i n Cascades," J. Aeronaut. S c i 0 , 1953. 5, Studer, H.L,, "Experimental Study of Wing Flutter," B r i t , Translation ARC 2777, 1946. 6« Karman, Th. von 0, "Flussigkeits u. Luftwiderstand," Physik Z„ 13, 1911. 7.. Karman, Th. von., "Flussigkeits u. Luftwiderstand," Nachr, Ges, Wiss., Gottingen, 547, 1913. 8. Cometta, Co, "An Investigation of the Unsteady Flow Pattern i n the Wake of Cylinders and Spheres Using a Hot Wire Probe," Tech. Rept, WT-21, Brown Univ., 1957. 9. Roshko, A,, "On the Development of Turbulent Wakes from Vortex Streets," NACA TN 2913, 1953. 10. Chuan, R.L., and Magnus, R,"J,y "Study of Vortex Shedding as Related to Self-Excited Torsional Oscillations of an Ae r o f o i l , " NACA TN 2429, 1951. 11. McGregor, D.M., "An Experimental Investigation of the Os c i l l a t i n g Pressures on a Circular Cylinder i n a Fluid Stream," UTIA TN 14, 1957. 12. Prendergast, V 0, "Measurement of Two-Point Correlations of the Surface Pressure on a Circular Cylinder," UTIA TN 23, 1958, 13. Molyneux, W.G., "Measurement of the Aerodynamic Forces on Os c i l l a t i n g A i r f o i l s , " AGARD Rept, 35, 1956. 14. Molyneux, W.G,, and Ruddleston, F., "A Technique for the Measurement of Pressure Distribution on Oscill a t i n g Aerofoils, with Results for a Rectangular Wing of Aspect Ratio 3.3," Br, ARC TR 18,018, 1956, /OS, 1 5 o Smith, J.D., "An Experimental Study of the Aeroelastic I n s t a b i l i t y of Rectangular Cylinders," M,A.Sc. Thesis, Univ. B r i t . Col., 1 9 6 2 , 1 6 . Laub, J.H,, "Externally Pressurized Journal Gas Bearings," Presented at the ASIE/ASME Lubrication Conference, Boston, Preprint 6 0 1 0 - 1 5 , I 9 6 0 , 1 7 . Perry, C,C, Lissner, H,R,, "A Strain Gage Primer," McGraw-Hill Book Co., Inc., New York, 1 9 6 2 » 1 8 . Heuter, T,F,, "Sonics," John Wiley & Sons Inc., New York, 1 9 5 5 . 1 9 . Fung, Y.C., "The Theory of Ae r o e l a s t i c i t y , " John Wiley & Sons, Inc., New York, 1 9 5 5 . 2 0 . Brooks, N.P.H., "Experimental Investigation of the Aeroelastic I n s t a b i l i t y of B l u f f Two-Dimensional Cylinders," M,A,Se. Thesis, Univ. of B r i t . Col,, I 9 6 0 , 2 1 . Relf, E,P,, Simmons, L.R,G,9 "The Frequency of Eddies Generated by the Motion of Circular' Cylinders through a F l u i d , " Br. ARC, R&M 9 1 7 , 1 9 2 4 , 

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