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Effects of turbulence on wind induced vibrations of bluff cylinders Laneville, André 1973

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1 11 3 EFFECTS OF TURBULENCE ON WIND INDUCED VIBRATIONS OF BLUFF CYLINDERS by ANDRE LANEVILLE B.A., Laval University, Quebec, Que, 1965. B.Eng., University of Western Ontario, Ont., 1969. A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENT FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of Mechanical Engineering We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA May 1973 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l l m e n t o f t h e r e q u i r e m e n t s f o r an advanced d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h Columbia, I a g r e e t h a t t h e 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 r e f e r e n c e and s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r poses may be g r a n t e d by t h e Head o f my Department o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t p u b l i c a t i o n , i n p a r t o r i n whole, o r t h e c o p y i n g o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . ANDRE LANEVILLE Department o f M e c h a n i c a l E n g i n e e r i n g The U n i v e r s i t y o f B r i t i s h C olumbia, Vancouver 8, Canada. Date ABSTRACT x a" L This thesis studies the effects of turbulence, i n an otherwise uniform a i r flow, on the s t a t i c forces and vibrations of b l u f f cylinders. The main purpose was to investigate i f the quasi-steady theory could give correct pre-dictions when two additional variables, the scale and the in t e n s i t y of turbu-lence, were introduced. Turbulence was produced by grids of bars of rectangular section and the measurements of i t s properties, with hot wires, gave r e s u l t s i n good agreement with those of other experimenters. Then, dynamic and s t a t i c models of rectangular section with H/d=0.5, 1.0, 2.0 and of D-shape, were exposed to different i n t e n s i t i e s and to d i f f e -rent scales of turbulence. A pyramidal.strain-gauge balance and an air-bearing system were used to measure the s t a t i c forces and the amplitudes of o s c i l l a t i o n s respectively. The s t a t i c force r e s u l t s indicated that an increased i n t e n s i t y of turbulence would turn a hard o s c i l l a t o r into a soft o s c i l l a t o r and a soft o s c i l l a t o r into a stable system. The results of the dynamic tests agreed, and i n addition, indicated that the quasi-steady theory gave good quantitative r e s u l t s . The effect of the scale of turbulence did not appear important. In an attempt to understand the physical mechanism involved i n the change of behaviour of the o s c i l l a t o r s , shadowgraph and hot wire experiments on the separated shear layers were performed. The shadowgraph res u l t s i n d i -cated that an increased mixing, causing an e a r l i e r reattachment, existed i n s i -de the shear layer exposed to turbulent flow while a spectral analysis of the hot wire signals showed that t r a n s i t i o n occurred sooner i n turbulent flow. i v TABLE OF CONTENTS / Page INTRODUCTION 1 CHAPTER I 4 1.1 Turbulence Generators: Square Mesh Grids . . . . 4 1.2 Properties of Grid Turbulence 6 1.3 Measurement of the Turbulence Properties . 7 1.3.1 Instruments 7 1.3.2 Wind Tunnel 9 1.3.3 Calibrations . 10 1.3.4 Results 12 1.3.4.1 In t e n s i t i e s of Turbulence, Reynolds Stresses, Uniformity 12 1.3.4.2 Scales of Turbulence 15 1.3.4.2.1 Low Frequency Cut-Off and Base Line Shift Errors 15 1.3.4.2.2 V e r i f i c a t i o n of Taylor's Hypothesis . . 16 1.3.4.2.3 L , L Data 17 x y 1.3.4.3 Spectral Analysis . . . 18 1.4 Conclusion . 19 CHAPTER I I 20 I I . 1 Quasi-Steady Theory 21 11.2 Apparatus and Instrumentation . . . 25 11.2.1 Wind Tunnel Balance 25 11.2.2 A i r Bearing System 26 11.3 Results 27 II.3.1 S t a t i c Results 27 II.3.1.1 Effect of Reynolds Number at a = 0 27 Page 11.3.1.2 Effect of Wind Tunnel Blockage and Scale of Turbulence at a = 0 28 11.3.1.3 Effect of the Intensity of Turbulence at a = 0 29 11.3.1.4 Effect of Intensity of Turbulence on C , C and Cv 30 y 11.3.1.4.1 Section with H/d = 0.5 30 11.3.1.4.2 Section with H/d = 1.0. . . . . . . 31 11.3.1.4.3 Section with H/d = 2.0 31 11.3.1.4.4 D-Section . . . . . . 32 11.3.1.5 Effect of the Scale of Turbulence on C ^ J C ^ and C-p 33 11.3.1.5.1 Section with H/d = 0.5 33 11.3.1.5.2 Section with H/d = 1.0. . . . . . . 33 11.3.1.5.3 Section with H/d = 2.0 33 11.3.1.5.4 D-Section . 34 II.3.2 Dynamic Results 34 11.3.2.1 Vortex-Induced Vibrations of the D-Section. . . 34 11.3.2.2 Galloping O s c i l l a t i o n s of Rectangular Sections. 35 11.3.2.2.1 Section with H/d = 1.0 35 11.3.2.2.2 Section with H/d = 2.0 36 11.3.2.2.3 Section with H/d = 0.5 36 I I . 4 Conclusion 37 CHAPTER I I I . . 39 I I I . l Flow V i s u a l i z a t i o n . . . . . 40 I I I . 1.1 Method 40 III.1.1.1 Wind Tunnel, Optical Apparatus and Models. . 40 I I I . 1.1.2 J u s t i f i c a t i o n 42 I I I . 1.2 Results 43 v i Page III.1.2.1 Estimation of the Angle of Reattachment. . . 43 III.1.2.2 Behaviour of the Shear Layer 44 111.2 Spectral Analysis 45 111.2.1 Apparatus and Models 45 111.2.2 Results. . . . 46 111.2.2.1 Results of the F i r s t Experiment . . . . . . 46 111.2.2.2 Results of the Second Experiment 47 111.3 Conclusion 48 APPENDIX I : 50 BIBLIOGRAPHY 53 v i i LIST OF FIGURES Figure Page 1.1 Graph of the Grid Drag Coefficient as a Function of M/b 56 1.2 Outline of the Wind Tunnel 57 1.3 Graph of K g e t 2 as a Function of Temperature 58 1.4 Typical Hot Wire Anemometer Calibration Curve . 59 1.5 Decay of the Longitudinal Intensity of Turbulence 60 1.6 Decay of the Ratio RMS/DC for Slanted Hot Wire at -k}> and -(f) .. . 61 1.7 Decay of Siddon's Probe Output f o r the v' and w' Components of Turbulence 62 1.8 D i s t r i b u t i o n of U/U Across the Tunnel 63 av 1.9 D i s t r i b u t i o n of u'/U Across the Tunnel . 64 1.10 D i s t r i b u t i o n of U/U Across the Tunnel Downstream the 9" Mesh Grid. . . .aV.BT.g. . 65 1.11 D i s t r i b u t i o n of u'/U Across the Tunnel Downstream the 9" Mesh Grid 66 1.12 Error Due to Low Frequency Cut-Off on Normalized Correlation Function. . 67 1.13 V e r i f i c a t i o n of Taylor's Hypothesis 68 1.14 Graph of f (x) as a Function of x/L x 69 1.15 Graph of g(y) as a Function of y/L^ 70 1.16 Growth of the Lateral Macro-Scale of Turbulence 71 1.17 Growth of the Longitudinal Macro-Scale of Turbulence 72 1.18 Turbulence Spectra for Large Mesh Grid 73 1.19 Turbulence Spectra for Small Mesh Grid 74 I I . 1 C a l i b r a t i o n Curves for Model .Testing 75 11.2 Ca l i b r a t i o n Curves for Model Testing 76 11.3 Effect of Reynolds Number at a = 0, for Section with H/d = 0.5. . 77 11.4 Effect of Reynolds Number at a = 0, for Section with H/d = 1.0. . 78 v i i i . Figure Page 11.5 Effect of Reynolds Number at a = 0, for Section with H/d =2.0. 79 11.6 Effect of Reynolds Number at a = 0, for D-Section 80 11.7 Effect of Wind Tunnel Blockage for Section with H/d =1.0. . . . 81 11.8 Effect of Wind Tunnel Blockage for Section with H/d =2.0. . . . 82 11.9 Effect of u'/U on C Q for Rectangular sections at a = 0 83 11.10 Effect of u'/U on C D for Rectangular Section at a = 0. . .. . . .84 11.11 Effect of H/d on the Drag Coefficient of Long Prisms at a=0. . . 85 11.12 Effect of Intensity of Turbulence.on C ( a ) for section with H/d = 0.5. . 86 11.13 Effect of Intensity of Turbulence on C (a) for section with H/d =• 0.5. 87 11.14 Effect of Intensity of Turbulence on Cj ( a ) for section with H/d = 0.5 88 11.15 Effect of Intensity of Turbulence on C (a) for section with H/d = 1.0. 89 11.16 Effect of Intensity of Turbulence on C (a) for section with H/d = 1.0 : 90 11.17 Effect of Intensity of Turbulence on Cjr ( a ) for section with H/d = 1.0 y 91 11.18 Effect of Intensity of Turbulence on C (a) for section with H/d = 2.0 ' 92 11.19 Effect of Intensity of Turbulence on C (a) for section with H/d = 2.0 93 11.20 Effect of Intensity of Turbulence on Cp ( a ) for section with H/d = 2.0. • . . . y 94 11.21 Effect of Intensity of Turbulence on C (a) for D-Section . . . . 95 11.22 Effect of Intensity of Turbulence on C D ( a ) for D-Section . . . . 96 11.23 Effect of Intensity of Turbulence on C F ^(a) for D-Section. . . . 97 11.24 Effect, of the Scale of Turbulence on C ( a ) f o r Section with H/d = 0.5 98 11.25 Effect of the Scale of Turbulence on C ( a ) for Section with H/d = 0.5 . 99 • IX Figure . Page 11.26 Effect of the Scale of Turbulence on C F (a) for Section with H/d = 0.5 y. 100 11.27 Effect of the Scale of Turbulence on C (a) for Section with H/d = 1.0 101 11.28 Effect of the Scale of Turbulence on C (a) for Section with H/d = 1.0 102 11.29 Effect of the Scale of Turbulence on Cp (a) for Section with H/d = 1.0. . y. 103 11.30 Effect of the Scale of Turbulence on C (a) for Section with H/d = 2.0 . 104 11.31 Effect of the Scale of Turbulence on C (a) for Section with H/d = 2.0 105 11.32 Effect of the Scale of Turbulence on Cp (a) for Section with H/d = 2.0 y. . 1 0 6 11.33 Effect of the Scale of Turbulence on C (a) for D-Section . . . 107 11.34 Effect of the Scale of Turbulence on C D(a) for D-Section . . . 108 11.35 Effect of the Scale of Turbulence on C F y(a) for D-Section. . . 109 11.36 Vortex-Induced Vibrations of a D-Section i n Turbulent Flows. . 110 11.37 Galloping Amplitude of the Square Section I l l 11.38 Steady-State Plunge Amplitude for Models with H/d - 1 Section (Small 3). . 112 11.39 Steady-State Plunge Amplitude for Models with H/d = 1 Section (Small 2) 113 11.40 Steady-State Plunge Amplitude for Models with H/d = 1 Section (Small 1) 114 11.41 Steady-State Plunge Amplitude for Models with H/d = 1 Section (Large) 115 11.42 Galloping Amplitude of the H/d = 2 Section 116 11.43 Steady-State Plunge Amplitude f o r Models with H/d = 2 Section (Small 3) 117 11.44 Steady-State Plunge Amplitude for Models with H/d = 2 Section (Small 2) . 118 X Figure • Page I I . 45 Steady-State Plunge Amplitude for Models with H/d =0.5 Section 119 I I I . 1'- Photograph of the Models for the Flow V i s u a l i z a t i o n 120 111.2 S t i l l Photographs of Model with H/d =0.5 Section, at 121 Different .Angles of Attack 122 111.3 Summary of the Flow V i s u a l i z a t i o n Results Concerning the Estimated Angle for Reattachment . . . 123 111.4 S t i l l Photograph of Model with H/d = 2.0 Section, at a = 0 i n Turbulent and Smooth Flows. 124 111.5 Power Spectra for a Square Section . . . . . 125 111.6 Spectra for H/d = 0.5 Section 126 111.7 Oscilloscope Photographs of the Hot-Wire Output 127 111.8 Spectra for Square Section+Splitter Plate i n Smooth Flow . . . 128 111.9 Spectra for Square Section+Splitter Plate i n Turbulent Flow. . 129 x i NOMENCLATURE y = Lateral displacement of o s c i l l a t i n g cylinder. d = Lateral dimension of cylinder section. H = Streamwise dimension of cylinder section. £ = Length of cylinder. m = Mass of o s c i l l a t i n g system. c = Coefficient of viscous damping of o s c i l l a t i n g system or tunnel width, k = Spring constant. U) = (k/m) 2 = Cir c u l a r frequency of free undamped o s c i l l a t i n g system. U = A i r v e l o c i t y (mean). U e^^ = A i r v e l o c i t y r e l a t i v e to o s c i l l a t i n g cylinder. a = Angle of attack of r e l a t i v e wind to cylinder section. a,ot'= Decay exponents i n c o r r e l a t i o n function. p = A i r density. L = Aerodynamic l i f t on cylinder. D = Aerodynamic drag on cylinder. Fy = Lateral Aerodynamic force on cylinder. L (p/2) u; .2 r e l D F Y (p/2) U 2d£ U r U/(wd) = Dimensionless flow v e l o c i t y . Y y/d = Dimensionless displacement. Y Dimensionless o s c i l l a t i o n amplitude. (x,y,z,T) = u(0,0,0,0) u(x,y,z,T) X l l $ = c/(2ma)) = Dimensionless damping c o e f f i c i e n t . 2 n = pd £ = Dimensionless mass parameter. 2m U = 2$L ~ C r i t i c a l a i r v e l o c i t y . nA^ t = Time. T = 0)t = Dimensionless time (Chapter II) . T = Time delay (Chapter I) . (*) = Derivative with respect to T or t . V = Kinematic v i s c o s i t y . S = fd/U = Strouhal number. M = Grid mesh s i z e . b = Grid bar s i z e . u' = RMS value of the longitudinal f l u c t u a t i n g v e l o c i t y component. v' = RMS value of the l a t e r a l f l u c t u a t i n g v e l o c i t y component. w' = RMS value of the l a t e r a l f l u c t u a t i n g v e l o c i t y component. q = pressure drop across the wind tunnel nozzle. 2 q = pU (smooth flow). 2 uv = Reynolds stress. uw = Reynolds stress. vw = Reynolds stress. e g = RMS output" of Siddon's probe. S = Siddon's probe s e n s i t i v i t y (mvolts/mm HO), s e ( x ) = Error i n normalized c o r r e l a t i o n function due to the low-frequency cut-off of the correlator. = Longitudinal macroscale of turbulence. L = Lateral macroscale of turbulence. y. f(x) = R n (x,0,0,0). g(y)= R^ (0,y,0,0). x i i i ACKNOWLEDGEMENTS The author wishes to express h is gratitude to Dr. G.V. Parkinson for his expert advice and guidance, as well as for his relaxed and amiable a t t i -tude; working with him was a pleasant and rewarding experience. Many d i s -cussions with Dr. I.S. Gartshore, Dr. T.E. Siddon and Dr. E.G. Hauptman concerning t h i s research were most he l p f u l and the author wants to thank them for t h e i r i n t e r e s t . Also most appreciated were the s k i l l and patience of P. Hurren and J . Hoar, chief technicians, and the collaboration of the Mecha-n i c a l Engineering Staff. And I want to express my appreciation to P i e r r o t , my wife, for her presence and her help during t h i s period of time. Fin a n c i a l assistance was received from the National Research Council of Canada, Grant A-586. I Introduction. This project was a part of a continuing programme studying the a e r o e l a s t i c i n s t a b i l i t i e s of b l u f f c y l i n d e r s , when e l a s t i c a l l y mounted in a flow of a i r : vertex resonance and galloping o s c i l l a t i o n s . As known, vortex resonance occurs when the freguency at which the eddies are shedding away from a c y l i n d e r ; i . e . ,the Strouhal frequency, matches the natural frequency of the cylinder's e l a s t i c system . This resonance i s obviously r e s t r i c t e d to a small discrete range of wind speeds and the Strouhal No. i s a s u f f i c i e n t tool to predict i t s occurrence. The amplitude of vib r a t i o n can be of the order of the c y l i n d e r diameter. Galloping o s c i l l a t i o n s could be considered as a negative aerodynamic damping phencrcenon since t h e i r inducing forces are i n i t i a l l y proportional to the v e l o c i t y of the cylinder's e l a s t i c system and therefore, p a r a l l e l the viscous damping forces. In the case of galloping, because of i t s aerodynaraically unstable cross section, the cylinder, and i t s e l a s t i c system, i s fed the wind stream energy in amount more than reguired to overcome i t s viscous damping so that the net damping becomes negative. Contrary to vortex induced vibrations, the occurrence of t h i s aerodynamic i n s t a b i l i t y i s not r e s t r i c t e d to a small range of wind speeds and the amplitudes of o s c i l l a t i o n can reach many cylinder diameters. 2 In e a r l i e r . phases of the programme, the works of N.P.H, Brooks (1) , J . D. Smith (2) and T.V. Santcshan (3) • have shown t h a t , i n smooth flow, G.V. Parkinson's q u a s i - s t e a d y theory |4) p r e d i c t s c o r r e c t l y the behaviour of the g a l l o p i n g c y l i n d e r s . F i r s t , N.P.H. Brooks i n v e s t i g a t e d the i n s t a b i l i t y of b l u f f bodies of r e c t a n g u l a r and D s e c t i o n s . Be showed that f o r plunging o s c i l l a t i o n , the D s e c t i o n and the sh o r t r e c t a n g l e s are s t a b l e a t r e s t while the square s e c t i o n i s s t r o n g l y u n s t a b l e . Then J.D. Smith, with improved i n s t r u m e n t a t i o n , extended E r o o k s 1 i n v e s t i g a t i o n of r e c t a n g u l a r s e c t i o n s and h i s t h e s i s i n c l u d e s an e x t e n s i v e examination of the u n s t a b l e behaviour of the square s e c t i o n . Using a qua s i - s t e a d y theory, G.V. P a r k i n s o n a n a l y 2 e d the o s c i l l a t i o n of the given r e c t a n g u l a r c y l i n d e r s and found good agreement with Smith's data f o r the square s e c t i o n but not f o r the 2 :1 r e c t a n g l e . T.V. Santcsham e x p l a i n e d t h i s d i s c r e p a n c y by the wake v o r t i c e s not accounted f o r by the q u a s i - s t e a d y theory i n the p r o x i m i t y of the vortex-induced v i b r a t i o n s . High o r d e r curve f i t t i n g of f o r c e c o e f f i c i e n t s gave Santoshara a good agreement between Parkinson's theory and experimental data. His t h e s i s c o n t a i n s e x t e n s i v e measurements of f o r c e data f o r 1:2, 2 :1 and D s e c t i o n s . F i n a l l y C. C. Feng (5) i n v e s t i g a t e d the dynamical behaviour of c i r c u l a r and D s e c t i o n s e x p e r i e n c i n g vortex-induced v i b r a t i o n s . His t h e s i s , i n a d d i t i o n , c o n t a i n s s u b s t a n t i a l 3 measurements of the pressure d i s t r i b u t i o n around the models and i t s spanwise c o r r e l a t i o n . The present research extends t h i s programme to turbulent flows, one of i t s main objects being to v e r i f y i f the guasi-steady theory s t i l l holds when two additional variables such as a l e v e l and a scale of turbulence are introduced, accordingly t h i s research programme consists of generating an appropriate turbulent flow and measuring the s t a t i c and dynamical c h a r a c t e r i s t i c s of the b l u f f bodies i n the known flow. This i n v e s t i g a t i o n does not deal with the d i r e c t dynamical ef f e c t s on e l a s t i c bodies of the turbulence in a flow, known as bu f f e t t i n g o s c i l l a t i o n s , such as those studied by Campbell and Etkin (12). CEAPTFR I lM£tulence Generators 2 Square Mesh Grids The choice of square mesh grids tc create turbulence rested on d i f f e r e n t f a c t o r s . F i r s t , the q u a l i t y of the resultant flow at some distance downstream of the g r i d , which has been shown (see for instance Eaines and Peterson (6) ) tc be nearly i s o t r o p i c homogeneous turbulence superimposed on a uniform mean flow, fts the f a c i l i t i e s at that time at U.B.C. were intended for two dimensional tests, g r i d turbulence appeared to be the closest to two dimensional flow with i t s f l a t v e l o c i t y p r o f i l e and i t s uniform turbulence i n t e n s i t i e s d i s t r i b u t i o n . Another advantage of grid turbulence becomes evident as the number of variables i s reduced to a minimum of three: the mesh size M, the bar size b and the distance downstream at which measurements w i l l be made. These variables enable the scale of turbulence and the levels of turbulence to be chosen. Cn the other hand, the choice of the dimensions M and b of a p a r t i c u l a r g r i d i s governed by the resultant drag of the grid and the avai l a b l e test section length. F i r s t , the working section should be long enough tc ensure that decay i s the dominant process. The point where the decay becomes predominant and hence where the intensity s t a r t s to decrease, occurs between 2 tc 3 mesh lengths behind the g r i d . Some distance beyond t h i s point but ahead of the point" where the 5 v e l o c i t y d i s t r i b u t i o n i s even across the tunnel, the conversion of mean flow energy becomes n e g l i g i b l e and the decay i s the important process remaining. In this respect, Baines and Petersen found that, i f the flow i s to be nearly uniform, the model can be no closer than 5 to 10 mesh widths from the g r i d . B.J. Vickery(7) suggests, i n order to obtain turbulence conditions f a i r l y representative of atmospheric turbulence ( i n t e n s i t y ) , that M = ( A v a i l a b l e length of working section)/8. The choice of the bar s i z e i s regulated by the blockage of the grid and the desired scale of turbulence. The l a t t e r i s roughly proportional to b and, i n practice, should be as large as possible to avoid instrumentation problems with the models and possible scale e f f e c t s . But as the bar size increases as shown by the following equation, ( r e f . 8 ) C = b/M * (2 - b/M) (c.f. f i g . 1.1 ) i t can be seen that for K/k<U the grid drag c o e f f i c i e n t increases at a dr a s t i c rate. Baines and Peterson recommend that M/b should be greater than 3.(1 while Vickery suggests M/b = U.O which gives a drag c o e f f i c i e n t of 1.4. With those recommendations and the avail a b l e length of working section of the wind tunnel at U.B.C. ( 72 inches) , a 6 f i r s t g r i d with fc = 2.25" and H = 9" was designed to create the largest possible scale of turbulence and a second one with b = 1.125" and H = 4.5" to generate half of that scale. The smaller mesh siz e grid was used to investigate the e f f e c t of i n t e n s i t y of turbulence since i t was estimated that i t would require the whole working sectionfor the large mesh grid to reach a stable flow. The grids were made of wood with rectangular bar section of dimensions b x 3/4". I_. 2 Properties of Grid Turbulence A turbulent flow i s defined as homogeneous when i t s mean properties at a point are the same throughout the flew and when i t s two-point c h a r a c t e r i s t i c s such as the double-velocity c o r r e l a t i o n s depend only on the r e l a t i v e d i s p o s i t i o n of the two points and not on the position of cne of the points i n space. Homogeneous turbulence i s i s o t r o p i c i f the ve l o c i t y c o r r e l a t i o n tensor i s symmetric or independent of the d i r e c t i o n of r, the l i n e joining the two v e l o c i t y points, and therefore unaffected by the interchange of positions. Grid turbulence has been often quoted as nearly i s o t r o p i c turbulence and thi s was based on the v e r i f i c a t i o n of the rel a t i o n s : u' = v' = w' and uv = uw = vw = 0 7 At the same time, u, the mean v e l o c i t y , was measured constant and the i n t e n s i t i e s u'» v' and w' presented a uniform d i s t r i b u t i o n for the cross section of the flow-Grid turbulence, in addition, has been observed as a flow where Taylor's hypothesis applies. This implies that the ve l o c i t y at which the eddies convect downstream i s equal to the mean stream v e l o c i t y , and requires a frozen type of pattern with no decay. This i s approximately the case for grid turbulence when the separation between two points i s small. Taylor's hypothesis i s p a r t i c u l a r l y useful when computing the lo n g i t u d i n a l scale of turbulence by the autocorrelation method. . I...2 Measurement of the Turbulence Properties Ij. 3_.J Instruments The c h a r a c t e r i s t i c s cf the turbulence achieved by the designed grids were e s s e n t i a l l y measured by single hot wires with l i n e a r i z e d response. The wires were cf tungsten with a diameter of 5 microns. In the case of incl i n e d fact wires, <J> ; the angle between the mean ve l o c i t y d i r e c t i o n and the wire i t s e l f was never less than 50° and never larger than 54° to ensure a good cosine response. The hot wire system used was a Disa type 55D01. The sign a l coming from the sensing element, aft e r having been translated 8 into a voltage by the anemometer unit, was fed to a Disa l i n e a r i z e r of the type 55D10 and then f i l t e r e d by the Lisa unit 55D25 to remove any frequency higher than 10 kcps. The in s t r u c t i o n manual {9) gives complete information on the c h a r a c t e r i s t i c s of the Disa system. A probe of the l i f t type, designed by T-E.Siddcn (10) was made available i n order to measure the v* and w» components of the turbulence and to eas i l y obtain t h e i r spectra. Unfortunately the probe s e n s i t i v i t y had not been accurately determined and further modifications of the probe made impossible i t s evaluation. The r e s u l t s obtained with Siddcn's probe w i l l be included l a t e r and by a comparison with hot wire data, i t s s e n s i t i v i t y w i l l be evaluated. A traverse mechanism with three degrees of freedom was designed in order to support the probes. The basic system was made heavy so as to ensure a low natural frequency and prevent any unwanted motion. Two probes could be i n s t a l l e d simultaneously so that l a t e r a l c o r r e l a t i o n could be computed. The probes were located 10 diameters upstream from the main supporting cylinder and, in addition, a test was run to check for possible upstream e f f e c t due to the mechanism. As the vel o c i t y p r o f i l e was measured as being f l a t for the main core of the flow, t h i s mechanism was accepted. In order to measure the longitudinal c o r r e l a t i o n function, one hot wire probe was fixed to the f l o o r , the sensing element 9 being located i n the center of the tunnel, and the second probe, at the same height, was displaced l o n g i t u d i n a l l y along with the mechanism. The c o r r e l a t i o n functions necessary to get the scales cf turbulence were computed by a P.A.R. 101 co r r e l a t o r using . the A.C. output of the l i n e a r i z e d anemometer output. The low frequency cut-off of t h i s instrument i s f a i r l y low { 1 rad./sec. ). A B. and K. 1/3 octave bandwith f i l t e r ( type 1614 ) in connection with a B. and K. true B.M.S. voltmeter ( type 2606 ) was used to analyse the l i n e a r i z e d hot wire output and get the turbulence l o n g i t u d i n a l energy spectrum. The spectra cf v* and w' were obtained via the same instrumentation but using Siddon's probe. I-3__.2 Wind Tunnel Except for the flow v i s u a l i z a t i o n , a l l the experiments were conducted in the U.E.C. low speed, low turbulence, return-type wind tunnel in which the ve l o c i t y can be varied between 3 fps and 150 fps with a turbulence l e v e l of less than 0.1?. Three screens smooth the flow at the entrance of the s e t t l i n g chamber and a 7:1 contraction accelerates i t , improving i t s uniformity as i t reaches the test section. The test section i s 9 feet long with a cross section of 36" by 27". Four 45 degree f i l l e t s , decreasing from 6" at the upstream end to 4.75" at the 10 downstream end o f f s e t the e f f e c t of boundary l a y e r growth i n the t e s t s e c t i o n . The t u n n e l was powered by a 15 horsepower d i r e c t - c u r r e n t motor, d r i v i n g a commercial a x i a l - flow f a n with a Ward Leonard system of speed c o n t r o l . The p r e s s u r e drop, g, a c r o s s the c o n t r a c t i o n was measured, by means of r i n g s of s t a t i c pressure t a p s , on a Betz micromancmeter with a p r e c i s i o n of 0.05 m i l l i m e t e r of water. The a i r v e l o c i t y i n the t e s t s e c t i o n was c a l i b r a t e d a g a i n s t the above pr e s s u r e drop. F i g u r e 1.2 shows the o u t l i n e of the t u n n e l . 1.3.3 C a l i b r a t i o n s For both i n c l i n e d and normal hot wires, the c a l i b r a t i o n curve was made to f i t the equation DC(volts) = .[q(mm H 0)]^' so t h a t U(fps) = K(T) * DC T y p i c a l l y K (T) = 13.25 f o r an a i r temperature of 70 degrees F. ( c . f . f i g . 1.3 ) . The c a l i b r a t i o n was done i n the empty wind t u n n e l , the same used f o r the t e s t s , using the Eetz micro manometer as the i n d i c a t o r of the g. F i g u r e 1.4 shows a t y p i c a l c a l i b r a t i o n curve. In cases where i t was necessary to remcve the ,hct wires and 11 t h e i r supporting mechanism from the tunnel, and s t i l l know accurately the mean vel o c i t y of the turbulent flow, (as when measuring the forces acting on a cylinder) , another type of c a l i b r a t i o n was used, since the introduction of grids causes an erroneous measurement of the q by the pressure tap rings. Immediately after the c a l i b r a t i o n of the hot wires i n smooth flow, the g r i d was introduced at i t s proper location and the modified dynamic head read by the Betz micromanometer was ca l i b r a t e d against the hot wire DC response for d i f f e r e n t a i r v e l o c i t i e s . This method, the c a l i b r a t i o n being repeatable, appeared successful when the gr i d was not tec close to the pressure taps. Yet, in two cases, when the grid was mounted d i r e c t l y over the taps, a small misalignment of the grid could cause a s h i f t of up to 5% in the c a l i b r a t i o n curve. Because of th i s defect, a c a l i b r a t i o n was done before each test with the grids positioned i n t h i s manner. At a l a t e r stage, a P i t o t -s t a t i c tube, located halfway in the nozzle, was used to monitor the g. This g was measured to be 3.46 times smaller than the g i n the tes t section for smooth flow. For a l l hot wire measurements, care was taken to avoid any d r i f t of the c a l i b r a t i o n curve. For that reason, the wires were washed i n chlorothene and then dipped in alcohol. This procedure, as well as the c a l i b r a t i o n in smooth flow, was repeated every hour or more often whenever noticeable increase of the a i r temperature occurred. In the case of the measurements of the turbulence properties, t h i s temperature d r i f t which affe c t s the anemometers* response, i s not c r i t i c a l since only 12 r a t i o s of RMS/DO are of i n t e r e s t , When absolute values cf the DC were required, very short tests were run to avoid this temperature d r i f t . 1.3.4 Results I.3..4_._1 I n t e n s i t i e s of Turbulence, Reynolds Stresses, Uniformity The i n t e n s i t i e s of turbulence as well as the Reynolds stresses were evaluated on an IBM 360 computer according to the equations: { for x-y plane ) " ^ >* = 90° U uv 2 U 2F2(<M 1 4F(<j>) L DC 0 * 1 DC " /RMSx2 DC + * DC ^ I ( 1 ) ( 2 ) ( 3 ) When the i n c l i n e d hot wire was i n the x-z plane, w»/U and 2 uw/U were obtained. These r e l a t i o n s h i p s for hot wires with l i n e a r i z e d response are derived i n appendix 1. On the lo n g i t u d i n a l centre axis cf the test section, the decay cf the i n t e n s i t i e s can be represented by the formulae : "1 K 2.58 ( x / b ) ~ 8 / 9 . . . ( 4 ) U 13 ^ = * U 2.52 ( x / b ) - 8 / 9 < 5 > U U Figure 1.5 shows the decay of the lon g i t u d i n a l component fo r the range 15 < x/b < 70 while, for the same range, figur e 1.6 shows the decay of the r a t i o RMS/DC for an i n c l i n e d hot wire. The r a t i o did cot vary s i g n i f i c a n t l y when the wire was in c l i n e d at + <}> and - 4> , in both the x-y and the x-z planes. From the curve f i t t i n g of the points, equation 5 was obtained using equations 2 and 4. Data for uniplanar grid obtained by B . J . Vickery agree very well, while the re s u l t s obtained by Surry (11) and Campbell and B. Etkin{12), depart from the present ones. This discrepancy could be attributed to the location of the i r test section i n the wind tunnel d i f f u s e r . Data for a grid with s i m i l a r blockage were extracted from Baines* and Peterson's a r t i c l e and are somewhat lower. S i m i l a r l y , the curve ^ = 1.12 &~ 5 / 7 , \ U b which i s a best f i t to Baines' and Peterson's data for d i f f e r e n t blockage grids> i s lower than the present curve. Vickery attributes t h i s discrepancy to the fa c t that his grid was uniplanar, and, tc the limited frequency response of the voltmeter used. It shculd be added that over an in t e n s i t y of 105?, the use of l i n e a r i z e r s becomes a prerequisite tc ensure a correct RMS/DC r a t i o . Data from McLaren et a l . (13) agree very well. 14 Comte-Bellot(14) observed approximately equal i n t e n s i t i e s v' and w' in a region further downstream than the present range while Surry, Campbell and Etkin measured a reduction of 20? from u'/E for v'/U a n u w'/U. Many factors could influence the value of v'/U a n d w*/D in addition to the ones already mentioned. A c r i t i c a l one i s , i f cross hot wired are used, the d i s p o s i t i o n of the f i r s t wire which could influence the one behind. , 2 . 2 The Reynolds stresses,or more appropriately uv/u' and W/u'; were ranging between +0.01 and -rO.01. In the experiments using Siddon's probe, e s , the BMS output of the probe, was found to f i t the curve (cf f i g . 1.7 ) . . . • ( .6 ) _s = 50.7 * 10 (^) - 8/ 9 o b (DC) A normal hot wire measured the DC component because Siddon's probe reacted only to A.C. ccmponents and accordingly gave only an A.C.. output. As v 1 = w' = e S q s SL ( 7 ) where S = probe sensitivity s 2 ( o c r i t was possible to calculate S s by comparing equations 7 and 5, and using 6. S g was 2.01 mv/mm H20. This s e n s i t i v i t y w i l l be used l a t e r for the v* and w' spectra. A point to notice here, i s that the rate at which v'/D and w'/U decay l o n g i t u d i n a l l y , corresponds to the one measured, with hot wires. Thus Siddon's 15 probe reacts consistently with the hct wire anemometers. With respect to the uniformity of the flow, figures 1.8, 1.9, 1.10, and 1.11 show that, for both grids, the v e l o c i t y p r o f i l e and the l o n g i t u d i n a l i n t e n s i t y d i s t r i b u t i o n s become f a i r l y f l a t a f t e r x/b = 28. This confirms the c r i t e r i a set forward by B.J. Vickery, Baines and Petersen. I. 3.4. 2 Scales of Turbulence For the measure of both the l o n g i t u d i n a l and l a t e r a l scales of turbulence a c o r r e l a t i o n technique was used. I-.3.4.2.J. Low Frequency Cut-off and Base Line S h i f t Errors F i r s t , as the influence of the low frequency cut-off of the c o r r e l a t o r was thought to be of importance for the experiments, programs were run to evaluate t h i s e f f e c t according tc the equations derived by Hayar,Siddon and Chu(15); only the exponential and Gaussian types of autocorrelation function were considered and the resultant error was estimated according to the followinq expressions: Exponential case (not v a l i d at T = 0) , v -ax (a/ai ) r , , a c . , 2ax c ,a c *, e(x> = e_ e w c' [erfc ( j- ) + e erfc (- H- — '1 2 c c Gaussian case a'x^ e , 2 e (aiz/ 4a' + 1) , N -a'x c  e(x) = e [ aiz 16 For T <50msec, i t was found that e ( T ) did not vary s i g n i f i c a n t l y in both cases. Figure 1.12 shows the eff e c t of 2 ( a/oO and (a'/ to ) respectively on e ( x ) for the exponential c c and Gaussian autocorrelation functions and as i n the actual experiment a/u) - 100 » the influence of the instrument c cut-off was shown to be i n s i g n i f i c a n t . I t should be mentioned though that the c o r r e l a t i o n functions, because of a s h i f t cf the base l i n e during computation (due to improper trimming of the r e s i d u a l D.C. in the correlator) had to be corrected. Fortunately enough, th i s negative s h i f t was constant and the correction was done by re e s t i u a t i n g the normalized c o r r e l a t i o n function taking t h i s a dditional height into account. 1.3.4.2.2 V e r i f i c a t i o n of Ta^lor^s Hj£cthesis Taylor's hypothesis was v e r i f i e d with a method independent of the errors introduced by the co r r e l a t o r : with tuc hot wires located on the lo n g i t u d i n a l centre axis cf the tunnel, the convective speed at which the turbulent structures (eddies) moved downstream, was measured and then compared to the mean flow v e l o c i t y . Thus, for d i f f e r e n t x, the time delay for which a maximum co r r e l a t i o n between the two hot-wire signals occurs, was determined and then, dx/dx , a convective v e l o c i t y was obtained. As dx/d x was found equal to the mean v e l o c i t y , half of Taylor's hypothesis was v e r i f i e d ( cf f i g . 1.13 ) . As mentioned previously, the fac t that u* decays l o n g i t u d i n a l l y 17 r e s t r i c t s the f u l l use of the h y p o t h e s i s . T h i s r e s t r i c t i o n can be v i s u a l i z e d i n f i g u r e 1.14 where f o r l a r g e r x, the t a i l s of the c o r r e l a t i o n f u n c t i o n s dc not c o i n c i d e . T h i s d i s c r e p a n c y a c t u a l l y does not i n t r o d u c e a s i g n i f i c a n t e r r o r ( 5 % ) when comparing the r e s p e c t i v e i n t e g r a t e d areas f o r the macrcscale of t u r b u l e n c e . Ccnseguently, the l o n g i t u d i n a l s c a l e s of t u r b u l e n c e , t x , were mainly computed by simple a u t o c o r r e l a t i o n technique. T h i s method i s c e r t a i n l y most p r a c t i c a l and e l e g a n t . In a d d i t i o n , the p o s s i b i l i t y of l o s s e s of coherence due t o an upstream probe i n a two hot-wire montage i s completely avoided. I . 3.4_. 2^3 L x X I Data The normalized l a t e r a l c o r r e l a t i o n f u n c t i o n s g (y) are presented i n f i g u r e 1.15 f o r both g r i d s and the r e s u l t a n t l a t e r a l s c a l e s , L y , were 0.96 i n c h f o r the s m a l l mesh g r i d at x/b = 42 and 1.80 inch f o r the l a r g e mesh one at x/b = 30. As p r e d i c t e d , L y i s roughly equal t o the g r i d bar s i z e . These o b s e r v a t i o n s of g <y) agree c l o s e l y with the ones of V i c k e r y , Baines and P e t e r s o n and so do the data of I as shown i n f i g u r e 1 . 1 6 . S i m i l a r l y f i g u r e 1.17 shows the growth of the l o n g i t u d i n a l s c a l e of t u r b u l e n c e with downstream d i s t a n c e . The data of I compare f a i r l y w e l l with that of other experimenters. 18 In i s o t r o p i c turbulence, i t can be shewn that L = 2 L x y Vickery measured as 3.3 times L using the l o n g i t u d i n a l component co-spectrum. In the present work, L was 2.15 I . x y Comte-Bellot obtained for 224 < x/b < 9 14 lo n g i t u d i n a l scales of 1.83 to 2.15 times the l a t e r a l ones. S i m i l a r l y , considering only the scales obtained from the u component, Surry measured Lx as 1.83 to 2.28 times L y. It should be pointed out that some scatter could be caused by the technigue used, e s p e c i a l l y i f an extrapolation to the zero frequency from the spectrum i s employed. 1.3.4.3 Spectral Analysis Even i f the RMS values of the f l u c t u a t i n g v e l o c i t y components were i d e n t i c a l , as found before, a Fourier Analysis was performed to investigate how the energy of these v e l o c i t i e s was d i s t r i b u t e d over a standard range of frequencies . Resultant spectra are shown in Figures 1.18 and 1.19 and appeared f a i r l y i d e n t i c a l . At higher frequencies, the response of Siddon's probe s t a r t s tc f a l l , as i t can be predicted from i t s c h a r a c t e r i s t i c s , but enough evidence is given to prove the spectra s i m i l i t u d e . It i s i n t e r e s t i n g to note that the spectra data fellow the -5/3 slope of the i n e r t i a l subrange (Kolmcgorcff spectrum, r e f . 8 ). 19 i i i Conclusion The choice of grids was made according to the results of previous experiments and, as expected, the resultant flow was nearly i s o t r o p i c turbulence superimposed on a mean flew. Also, f a i r l y good agreement with other data was encountered. 20 CHAPTER II The properties of grid turbulence having been determined, t h e i r e f f e c t s on the s t a t i c and dynamic behaviour of b l u f f cylinders were then investigated. For that purpose, the models were exposed, f i r s t , to three i n t e n s i t i e s of turbulence with approximately i d e n t i c a l scales, and then, tc two scales of turbulence with i d e n t i c a l i n t e n s i t y . The loading dispositions were as follows : GRID ID x/b M b u'/U L / b x ' Small 3 58.5 4 1/2" 1 1/8" .07 2.3 Small 2 43.5 4 1/2" 1 1/8" .091 2.15 Small 1 30.5 4 1/2" 1 1/8" .125 1.85 Large - 30.6 9" 2 1/4" .127 1.85 For these grid locations, the c a l i b r a t i o n curves expressing the true g, using the rings of s t a t i c pressure taps, are shown in figures II-1 and II-2. Models of rectangular section, with H/d = 0.5, 1.0 and 2.0, were used tc investigate the e f f e c t s of turbulence on galloping, while a model of D-secticn was used to study the vortex-induced vibrations. At a l a t e r stage, because of the conclusions reached by McClaren et al.(13 6 16), concerning the e f f e c t s cf the scale of turbulence on square prisms, i t was decided to investigate these 21 e f f e c t s mere thoroughly by exposing 8 square prisms of d i f f e r e n t sizes to an i d e n t i c a l scale of turbulence. This experiment was repeated for the three l e v e l s of turbulence. d-Ii-l Quasi-Steady Theory. The quasi-steady theory assumes that instantaneous aerodynamic forces, acting on the o s c i l l a t i n g c y l i n d e r , may be approximated by the forces acting on the stationary c y l i n d e r , at an angle of attack, a , equal to the apparent angle of attack cf the o s c i l l a t i n g c y l i n d e r . The extension to turbulent flow implies the introduction of mean and fluc t u a t i n g components i n the v e l o c i t i e s . However, t h i s complex s i t u a t i o n can be s i m p l i f i e d by considering only the mean components. H. Novak (17) used t h i s s i m p l i f i c a t i o n successfully in three dimensional flow conditions (models with f i n i t e length, exposed to simulated earth boundary layer and grid turbulence). In the present experiments, the flew conditions were kept two-dimensional, as much as that was possible. , For a s t a t i c model exposed to a turbulent flow, the time mean force in the X di r e c t i o n i s F = C F (a) id * pU2/2 22 where, in terms of l i f t and drag c o e f f i c i e n t s C L and C Q , C-p (a) = -(CT + CL tana) seca r y L D As the drag and the l i f t forces can be measured for the stationary body as a function of the angle of attack, one can f i t a polynomial curve tc the data in the form j Cp (a) =23 A- tan xa y i=0 1 This curve f i t t i n g enables the generation cf a continuous loading function. A Chebyshev polynomial technique (19) i s excellent f o r t h i s type of approximation. Since the l i f t i s an odd function of a for symmetrical sections, a l l the even powers of tan a must vanish, and consequently, A. = 0 for i = 0, 2, 4...even As the quasi-steady theory implies that { see nomenclature for the d e f i n i t i o n of a l l the terms ) Tan a = y/U the equation of motion of the vi b r a t i n g model, with a cce-degree-of-freedom li n e a r e l a s t i c system, my + cy + ky = F , after non-dimensionalizaticn, can be rewritten as 23 Y + 2 3Y + Y = n£_ A. Y_ odd r The l a t t e r equation, after rearrangement, becomes Y + Y = nA i [ ( r n \ i=3 A x U r 1 - 2 This i s a quasi-linear d i f f e r e n t i a l equation, of the autonomous type, of the form Y + Y which can be solved for u << 1 using the quasi-harmonic theory of K r y l c f f and Bogoliuboff (19). G.V. Parkinson ( 4 ) , f i r s t , solved the equation and obtained the following equation for the steady-state s o l u t i o n : A xt U - 2 nA x [( r - H j - ) C±Y + T C. A. Y 1 odd 1 r ] = 0 • • !• • • equation I I . 1 where C = ( i - _ ) C. , X 1+1 1-1 C0= 1 and Y = Steady State amplitude of galloping. Thus, for a system with given parameters n, 8 and A i # equation n . i predicts the amplitude Y as a function of the reduced mean v e l o c i t y . For a given U r, each r e a l Y root 24 represents the radius cf a c i r c u l a r l i m i t cycle in the i-Y phase plane. As far as s t a t i l i t y i s concerned, when < 2 3 / nA^  , Y = 0 i s a stable focus and consequently small o s c i l l a t i o n s w i l l die out, whereas i f > 2 8 / nA , the point Y = ¥ = 0 becomes an unstable focus and galloping w i l l s t a r t . The s t a b i l i t y of the next l i m i t cycles i s determined by the sequence stable-unstable-stable. Since the f i r s t c o e f f i c i e n t cf the curve f i t t i n g can be defined as A. = ( dCF / da ) 1 *y small a i t follows, that cylinders of secticn with negative dC„ /da F y cannot gallop. This i s well known as the Een Hartog c r i t e r i o n ( 2 0 ) . So, as seen, the guasi-steady theory, in order tc be v e r i f i e d , requires twc types cf measurements: the input, drag and l i f t c o e f f i c i e n t s measured on the stationary body at di f f e r e n t angles of attack (frcm which an amplitude of o s c i l l a t i o n i s predictable), and, the displacement Y as a function of v e l o c i t y 0. 25 11-.2 An_naratus and Instrumentation The drag and l i f t c o e f f i c i e n t s were determined from measurements with a 6-ccmponent balance, while the amplitudes of vibrati o n were recorded from an air-bearing system designed by J.D. Smith. II.2.1 Wind Tunnel Balance Force measurements were taken from an Serclab pyramidal s t r a i n gauge balance' system. The balance' system i s designed to support a model in the wind tunnel and vary i t s angle of attack by 30° and i t s angle of yaw over a 360° range with a precision of 0.1°. Links separate the six force and moment components, so that each can be measured through an i n d i v i d u a l s t r a i n gauge load c e l l . Read out can be obtained by the use of appropriate e l e c t r i c a l equipment. Since the two-dimensional models were mounted with axis v e r t i c a l i n the wind tunnel, the l i f t force, as a function of the angle of attack, was measured via the side force, as a function cf the angle of yaw on the balance. Using the balance recorder output, two d i g i t a l voltmeters, one (Disa type 55D31 ) with integrating time constant varying from 0.1 tc 100 s e c , and the second with a servo motor equipped with variable damping (Disa type 55D30 ), gave more precise data. 26 11-_22 Air Bearing System For the present i n v e s t i g a t i o n , the a i r bearing model mounting system designed by J. D. Smith was found suitable when rotated by a 180 ° yaw angle and i n s t a l l e d at 36" from the downstream end of the test s e c t i on. This was done by rotating the wind tunnel c e i l i n g and f l o o r . This mounting system consists of two iron channels, one at the top and one at the bottom of the tunnel test section, to each cf which are bolted two a i r bearings. Two 2 1/2 inch angle irons connect the channels by bolts located at their ends. The para l l e l i s m of the two sets of bearings i s adjustable by screws located at the Intersections of the lower channels and the angles. To ensure that the attached model i s v e r t i c a l , the lower channel can be displaced h o r i z o n t a l l y . The whole assembly just described i s attached to the outside of the wind tunnel section and forms a v e r t i c a l plane allowing only for transverse displacement of the model. Each a i r bearing supports a tube, by means cf pressure forces r e s u l t i n g from the introduction cf high pressure a i r between the load carrying surfaces. Equidistant holes around their inner circumference allow high pressure a i r to be introduced into the journal-type bearings. Details of the design and construction of the bearing are given in ref. 2 . 27 The model was attached to the tube by means of l i g h t soldered aluminum clamps. Holes i n these clamps permitted the attachment of four springs, the other ends of the springs being fastened to the top and bottom of the two angles with adjustable hooks. An Ingersoll-Band 2-Stage compressor, Rodel 11 3/4 S 7 x 8 VHB-2, pumping into a 250 cubic foot storage tank prcvided a i r for the bearings. A f l e x i b l e hose carried the a i r at 118 psig from the tank to a t h r o t t l i n g valve which d i s t r i b u t e d i t at 60 psig to a l l bearings. I I . . 3 Results II.3.1 S t a t i c Results II_.3_.JU1_ E f f e c t of Reynolds J umber at a =0 As shown i n figures II-3, II-4, II-5, and II-6, for a l l the sections tested, the drag c o e f f i c i e n t (corrected for blockage e f f e c t by the method of E l Sherbiny(21) ) did not undergo any serious change for the tested range cf Reynolds number (20,000 -50,000). This confirms Vickery's results (22) for a square section. Some e f f e c t can be noticed for the range <30,000 and this e f f e c t i s not r e s t r i c t e d to a p a r t i c u l a r section. Soberscn et a l . (23) observed a s i m i l a r trend in turbulent flow; so did Delany (24) i n smooth flow. Since i t i s not l i k e l y that the 28 boundary layer (lying on the upstream face of the b l u f f body ) goes turbulent because of the l o c a l pressure gradient, a possible explanation i s that the shear layers go into t r a n s i t i o n , thereby modifying the base pressure as well as the f r i c t i o n on the sides of the c y l i n d e r . 11.3. 1.2 Effect of Wind Tunnel Blockacje and Scale cf Turbulence at a =0 The e f f e c t s of wind tunnel blockage* and the scale of turbulence at a=0 , were investigated using 9 cylinders with B/d=1.0 and 5 cylinders with H/d=2.0. As shown i n figures II-7 and II-8 , the drag c o e f f i c i e n t , for any given s e c t i o n , follows the curve for wall correction proposed by S. El Sherbiny (for normal f l a t plates i n smooth flew). This indicates that, for a given scale of turbulence, the corrected drag c o e f f i c i e n t dees not change with model s i z e . In the experiments, the r a t i o l x / d was varied from 0.6 to 5.0. On the other hand, r e s u l t s for Small 1 and Large show that C D changes with grid mesh s i z e . For the range .24 < L /d < 1.28* Hcberscn et a l . did not f i n d any scale e f f e c t , while McClaren et a l . found some in the region of L /d = 1.0. In the experiments by McClaren, end plates were used, and misalignment of those plates, as mentioned by Cowdrey(25), could introduce serious errors in the drag, when small models are tested. McClaren et a l . support their curve for a 9.8% i n t e n s i t y of turbulence with a point (CD= 2.1 for u'/U =10% and L /d= 1.33) obtained by integration of Vickery's data. 29 However, th i s value cf C D contradicts Vickery's conclusion that a drop of up to 305? i n the mean drag c o e f f i c i e n t i s to be expected for a 10% inte n s i t y cf turbulence. The data of HcClaren et a l . i s included in Fig . II-9 and i t w i l l be noted that except for one point (which supports t h e i r whole scale e f f e c t argument), t h e i r data compare f a i r l y well with the r e s u l t s from other experimenters and with those of the present experiments. II. 3. 1.3 Effe c t of the IntensjLj_J_ of Turbulence at a =0 As shown in figures II-9 and 11-10, the e f f e c t of increasing the l e v e l of turbulence r e s u l t s in a general decrease of the mean drag c o e f f i c i e n t . For the square and E/d=2.0 sections, the drop, although at d i f f e r e n t rates, seems approximately l i n e a r while a d i f f e r e n t behaviour i s to be suspected for the H/d=0.5 section. An explanation of the l a t t e r behaviour and also cf the d i f f e r e n t rate of decaying for the drag c o e f f i c i e n t i s given by examining the re s u l t s of Eearman and Trueman(26), Bostock and Mair(27), and Nakaguchi et a l . (28) (cf figure 11-11). These r e s u l t s shew, that increasing H/d for rectangular sections with H/d>0.6 in smccth flew produces a reduction of C D at a rate depending on the value of the i n i t i a l H/d. Further, the decreasing rate i s slower from a section with H/d=2.0 than the one from a section with H/d=1.0. Considering f i r s t a section with H/d=0.5, an increase in H/d re s u l t s (up to H/d=0.6) in an increase in C D , followed by a maximum at H/d=0.6 and then, by a decrease for H/d>0.6. This behaviour*is l i k e that 30 of Figures II-9 and II-1C except for the fact that u'/U replaced the variable H/d. This leads tc the conclusion that the e f f e c t cf an increasing i n t e n s i t y of turbulence i s s i m i l a r to that of an increasing H/d. So, one could expect a rectangular section in turbulent flow to behave as a rectangular section with increased H/d i n smooth flow. 11.3.1.4 Ef f e c t of i n t e n s i t y of Turbulence on ^ C_L and Hs.ls.1 .4^1 Section with H^ /d = 0._5 As shown by figure 11-12, the e f f e c t of increasing the turbulence i s to progressively reduce the maximum negative l i f t , leaving the i n i t i a l trend at small angles cf attack ( <15° ) unaltered. This reduction i s accompanied by a s h i f t towards smaller angles of attack for the angle cf maximum l i f t . This s h i f t towards smaller angles cf attack i s repeated for the minimum drag, as shown by fi g u r e 11-13. At small angles cf attack, an increase of turbulence causes a decrease in drag, whereas no serious i n t e n s i t y e f f e c t can be found a f t e r the angle of minimum drag. As a consequence cf the drag reduction, the i n i t i a l slope of the C F (a) w i l l be more positive with increased turbulence. y 31 This can be seen from figure 11-14, along with the expected s h i f t towards smaller angles for the occurrence of maximum l a t e r a l force. This leads to the p o s s i b i l i t y for a cylinder with H/d=0.5 to gallop, or presumably, tc behave as a cylinder with H/d > 0.5 in smooth flow, since i n smooth flow, a section with H/d = 0.5 does not gallop by i t s e l f (hard o s c i l l a t o r ) . Kovak{17) observed s i m i l a r behaviour of the force data. I l i l i l i i y 2 Section with H/d ~ _1__0 As in the case of the section with H/d = 0.5, increased turbulence progressively reduces the maximum l i f t as well as the drag at small angles of attack. This trend can he seen in figures 11-15 and 11-16 for the case cf a square section. Figure 11-17 shows hew the l a t e r a l force c o e f f i c i e n t experiences a reduction i n i t s maximum, accompanied by no s i g n i f i c a n t change in i t s i n i t i a l range. This implies that the square section should s t i l l gallop i n turbulent flew but with a reduced amplitude because of the reduction in i t s maximum C F . In addition, by comparison with smooth flew, the Cv curve loses y i t s point of i n f l e c t i o n , and thi s suggests the loss of one stable l i m i t cycle in the phase plane. II. 3 . 1.4.3 Section with H/d = 2 . 0 Figure 11-18 shows how d r a s t i c a l l y the l i f t c o e f f i c i e n t i s reduced by increased turbulence. In contrast > with t h i s 32 destruction of l i f t , the drag c o e f f i c i e n t remains r e l a t i v e l y unchanged, (cf f i g u r e 11-19). Consequently, the l a t e r a l force c o e f f i c i e n t i s considerably affected by an increased l e v e l of turbulence, as f i g u r e 11-20 shows. A l e v e l of turbulence of 12.5?, because of the negative i n i t i a l slope dC F /da , w i l l presumably stop the H/d = 2.0 y section from galloping, behaviour which p a r a l l e l s that of sections with H/d > 3.0 i n smooth flow. This d r a s t i c change of C„ was also observed by Novak (17) . y II.3.1.4.4 D-Section In turbulent flows, as shown i n figures 11-21 and 11-22 no serious change could be discerned for a <25° in the drag and l i f t forces f o r the D-section. Accordingly, the l a t e r a l force c o e f f i c i e n t i s only s l i g h t l y altered by d i f f e r e n t l e v e l s of turbulence, as shown in figure 11-23. Yet, when compared with the smooth flow data, the i n i t i a l slcpe (negative i n smooth flow) becomes s l i g h t l y p o s i t i v e in turbulent flews, i n d i c a t i n g that the D-section should remain a hard o s c i l l a t o r but with a tendency to become a soft o s c i l l a t o r - Very recently, Uovak(29) pointed cut a s i m i l a r p o s s i b i l i t y . 33 II. 3. 1.5 Effect of the Scale cf Turbulence cn ^ ^ a n d C p I l i l i l i S i i Section with H/d = 0.5 As shown i n graphs 11-24, 11-25 and 11-26, no s i g n i f i c a n t e f f e c t of the scale of turbulence could be detected for the three force c o e f f i c i e n t s . II.3. 1.5.2 Section with H/d 1.0 I t i s i n t e r e s t i n g to note that the drag c o e f f i c i e n t at zero angle of attack (cf figure 11-28), for the loading using the large mesh, d i f f e r s from the one using the small mesh. This r e s u l t again contradicts the ones obtained by exposing d i f f e r e n t models to the same flow. This e f f e c t i s f e l t by the l i f t force (cf f i g u r e 11-27) and the resultant l a t e r a l force c o e f f i c i e n t would indicate a difference close tc 151 (cf Figure 11-29 ). II.3.1.5.3 Section with H/d 5 2..0 Similar to the previous case, there i s a s l i g h t difference in the l i f t forces (figure 11-30) and i n the drag forces (figure 11-31). Even i f the resultant Cv curves d i f f e r (cf figure 11-32), in both cases they indicate that an i n t e n s i t y of 12% would transform t h i s soft o s c i l l a t o r (in sasccth* flow) into a 34 stable system. II. 3.. U 5.4 C-Section As for the H/d = 0.5 section, no s i g n i f i c a n t e f f e c t of the scale of turbulence could be detected in the c o e f f i c i e n t s of the D-Section (cf figures 11-33, 11-34 and 11-35). II.3.2 Dynamic Results 11. 3.. 2 . 1 Vortex-Induced Vibrations of the C-Secticn As shown in fig u r e 11-36, no ef f e c t of the scale , nor of the l e v e l of turbulence, i s r e f l e c t e d in the vertex-induced vibrations of the D-Section. As the inherent danping,g , was estimated as .00237, these r e s u l t s compare very well with Feng's results(5) for smooth flow with g = .00257. Thus, since the dynamic behaviour of the D-Section i s t o t a l l y unaffected by turbulence in the region of Ur = 1,0, i t s i g n i f i e s that the vortex formation on the side of cylinders with very short afterbody length i s not s i g n i f i c a n t l y affected by the presence of oncoming turbulence. 35 IIi.li.2.2 Galloping O s c i l l a t i o n s of Bectan_gular Sections In previous sections, the s t a t i c force c o e f f i c i e n t , Cv , y has keen used to forecast that the hard o s c i l l a t o r (H/d =0.5) becomes a soft o s c i l l a t o r under increased turbulence, while a soft o s c i l l a t o r has i t s amplitude of o s c i l l a t i o n reduced (H/d = I, 0) and w i l l even stop galloping (H/d = 2.0). II . 3_. 2__2.J Section jwith H/d = Jk 0 &s predicted, the amplitude cf vibration, i , reduces with increased turbulence as shown i n figure 11-37. In addition, the data for the larger scale of turbulence and f o r Small 1 agree very well. The q u a l i t a t i v e predictions are thus v e r i f i e d . Figures 11-38, 11-39, 11-40 and 11-41 show the quantitative agreement between the quasi-steady theory and the data. Considering the d i f f i c u l t y in estimating precisely the amount of equivalent viscous damping and how a small misalignment of the air bearing can introduce undesired f r i c t i c n , the agreement i s very good. The value of 3 was estimated from the o s c i l l a t i o n record of a normal f l a t plate in s t i l l a i r , which could d i f f e r from the damping of the exposed model. The data for the 1.8" model seem to indicate the presence of two l i m i t cycles for a certain range of v e l o c i t i e s . The guasi-steady theory did not forecast t h i s behaviour but, i t i s i n t e r e s t i n g tc ncte that the larger amplitudes cf o s c i l l a t i o n cf the 1.8" model agree f a i r l y well with the ones predicted. 36 II-.3o.2_. 2^ ,2 Section with H/d = 2 . 0 Figure 11-42 shows that the long rectangular section experiences o s c i l l a t i o n s with reduced amplitude when compared to smooth flow. The q u a l i t a t i v e prediction i s stressed even more by the fact that t h i s cylinder did net gallop when exposed to an i n t e n s i t y of turbulence cf 12.5?. Figures 11-43 and 11-44 show a very good quantitative agreement under the loading Small 3 while for the loading Small 2, the agreement i s not as good. This discrepancy can perhaps be attributed to a possible misalignment of the a i r bearing. In view of the other r e s u l t s , there i s no reason to suspect that the quasi-steady theory i s unable to predict c o r r e c t l y the amplitude of o s c i l l a t i o n when buffeting i s present. I I i l i 2 _ . 2_. 3 Section wjth H/d 5 0_.5 As predicted by the force data, this short rectangular section, a hard o s c i l l a t o r in smooth flow, should have a tendency to become a soft o s c i l l a t o r . Figure 11-45 shows the th e o r e t i c a l curves for the o s c i l l a t o r y motion and indicates that for the loading Small 1, very low damping and/cr very small mass are required to observe possible galloping o s c i l l a t i o n s . Since, i n the e a r l i e r stages of the experiments, B /n was larger than 3 and also because of the limited' amplitude of 37 o s c i l l a t i o n possible in the a i r bearing, no galloping was observed. Yet, by increasing s l i g h t l y the l e v e l cf turbulence, the model with H/d = 0.5 exhibited galloping o s c i l l a t i o n s , as shown by the experimental points. It should pointed cut that the amplitude reached was the maximum allowable by the a i r bearing system. Therefore, the o s c i l l a t o r y motion, even i f steady, could have perhaps reached larger values (the a i r flowing out a x i a l l y from the a i r bearing acted as a force against the mcticn cf the clamp). II.U Conclusion The e f f e c t of in t e n s i t y cf turbulence on the force c o e f f i c i e n t s as well as on the galloping behaviour of rectangular sections i s the same q u a l i t a t i v e l y as the effect of increasing the afterbody length or H/d. The vortex-induced vibrations cf a D-secticn were net affected whatsoever by the l e v e l s and scales of turbulence used. The e f f e c t of the scale of turbulence for the range L /d < 5 seems ne g l i g i b l e on the s t a t i c as well as on the dynamic behaviour cf rectangular sections. This r e s u l t , in the case of the s t a t i c forces, i s not strongly conclusive as in the galloping o s c i l l a t i c n s . > 38 F i n a l l y , the quasi-steady theory predicted correct quantitative amplitudes and should apply at s u f f i c i e n t l y low reduced frequencies as long as the dynamic models are submitted to the same loading as that which the s t a t i c mcdels experienced. 39 CHAPTER III At t h i s stage, i t i s necessary tc define the physical mechanism involved i n the change of cylinder behaviour with increased turbulence, or hew, for a given section, an increased l e v e l cf turbulence leads to a behaviour t y p i c a l cf a longer section i n smooth flow. It .seems very unlikely that three dimensional e f f e c t s could create such a s p e c i f i c behaviour. These e f f e c t s , most c e r t a i n l y , would reduce the degree cf spanwise c c r r e l a t i o n . yet, they would have to increase i t i n order to explain the behaviour cf the H/d=0.5 section. Since the forces on a bedy are dominated by the r e l a t i o n s h i p between the separated shear layers and the adjacent body surfaces, i t leads to the question of the e f f e c t s cf v« on the shear l a y e r s . It i s already known that increasing Reynolds number and turbulence a f f e c t a free shear layer, making i t go into t r a n s i t i o n sooner and increasing the mixing within i t . The work by Sato( 30 & 31 ) gives some information on separated shear layers and on the disturbance waves inducing t r a n s i t i o n in them,but,it should be added that i t i s r e s t r i c t e d to f l a t plate models. Thus, for a better understanding, t h i s research was extended to a flow v i s u a l i z a t i o n and a spectral analysis of the energy in the shear layer of bluff bodies. 40 IIIiJLs. Flow V i s u a l i z a t i o n The flow v i s u a l i z a t i o n was carried out in an cpeft-circuit wind tunnel, with models and grids reduced in order to obtain the same r e l a t i v e scales. The purpose was to see i f an important change occurs in the shear layers due to turbulence, as well as to see how they reattach on the cylinder walls. III.1.1. Method A simple shadowgraph technique was used to make the shear layer v i s i b l e . A small c a l o r i f i c ribbcn (1/8 n wide and 1/3 of the models' length) located in the center of the models' upstream face, heated the stagnant a i r of the boundary layer and the resultant temperature gradients allowed the v i s u a l i z a t i o n of the shear layers. III.1.1.1. Wind Tunnel^ Optical Apparatus and Models As previously mentioned, the wind tunnel used was of the open-circuit type with a rectangular test section 6 inches by 12 inches. In order to expose the heated a i r to p a r a l l e l l i g h t rays, a point source of l i g h t (Polarizing Instrument Co. Inc. ,mercury lamp rated at 1000 watts ) was located at the focal, point of a 41 convergent lens { f l = 24",f/6.0 ). Then, after passing through the f i r s t wall (1/2" plate g l a s s ) , the width of the test section and the second wall (1/2" plate glass) cf the wind tunnel, the l i g h t rays were either recorded on a photographic plate (Polaroid f i l m PN 55 ) or shone on a ground glass in order tc be filmed (Eolex camera type H 16 Reflex ). The models were f i t t e d in the test section through two holes in the plate glasses and care was taken to a l i g n the l i g h t rays with the model sides when not heated. Except f o r the H/d=2.0 model, a l l the models had d=0.75" and a 6" span of rectangular section. Each end of the models was turned in order tc f i t the plate glass holes, fl c i r c u l a r hole, in the center of the section, running fEom one end tc the middle of the model span, was d r i l l e d , and a s l o t (larger than the c i r c u l a r hcle) on one of the faces of the models was then machined. The s l o t located in the middle of the span allowed for the i n s t a l l a t i o n cf an i n s u l a t o r cf the ceramic type (brand name:LAVfl) on which the c a l o r i f i c ribbon (type Kandhall) was attached by two nuts with heads reduced tc minimal thickness. The two nuts, through holes i n the i n s u l a t o r , were the ends of the resistance, and the e l e c t r i c a l pcwer was applied via teflon wires running in the hole. The current required was of approximately 15 amps for 10 volts of potential difference. The other c i r c u l a r end of the models was eguipped with a rod ind i c a t i n g the angle cf attack. Fcur models were designed. They were of rectangular section 42 with H/d=0.5, 1.0 and 2.0 and of D section. In addition, the model of H/d=0.5 section could have i t s H increased by 1/8", 3/16" or 1/4" by means cf plates attached tc i t s downstream face. Figure III-1 shows a photograph cf the models and of the int e r n a l arrangement. The model with H/d=2.0 was i d e n t i c a l l y designed with d=3/8". III.1. 1.2. J u s t i f i c a t i o n This flow v i s u a l i z a t i o n can be j u s t i f i e d by considering the Prandtl number and the r a t i o of the Grashof number over the square of the Reynolds number. In the case of a i r , the Prandtl number i s very close to one (0.7) so that the heat transfer phenomena are f u l l y correlated to the f l u i d mechanics phenomena. In order to insure that buoyancy forces or free convection are unimportant when compared to forced convection, the r a t i c of the Grashof number over the square of the Reynolds number has to be <1.0. In the actual case, for an estimated temperature cf the 0 o ribbon of 320 F and a i r temperature cf 80 F , t h i s r a t i o was -3 approximately 10 i 43 I l l i l i i i J e s u i t s From the s t i l l photographs, the reattachment was c l e a r l y observed although the shape cf the wake vertices was not c l e a r l y distinguishable. Even with t h i s crude method of v i s u a l i z a t i o n , some r e l a t i v e differences could be observed between the behaviour of the shear layer in smooth flow and i n turbulent flow. I I I . 1 . 2 . 1 . Estimation of the Angle of Reattachment From the s t i l l s of the models at d i f f e r e n t angles cf attack (cf Figure I I I - 2 for an example), the angle at which the shear layer f u l l y touches one side of the model was estimated. Figure I I I - 3 gives a summary of these observations for rectangular models and indicates a clear r e l a t i o n s h i p between H/d, turbulence l e v e l and the angle for reattachment. The data for smooth flow could be extrapolated tc intercept the a t c i s s a at approximately H/d = -3 : thi s implies nc possible galloping for the section with H/d = 3 i n smooth flow, and i t agrees with the observations of Smith ( 2 ) . The H/d = 2 section, f o r a l e v e l of 0.11 cf turbulence, would experience reattachment at a = 3 0 f showing, when compared to smooth flow, how d r a s t i c a l l y i t i s influenced by turbulence. Also, by running a l i n e p a r a l l e l to the abcissa, the angle for reattachment of a given H/d section in turbulent flow can be seen egual tc the angle for reattachment of a longer section i n smooth flow. I I l i l s . 2 - 2 - . Behaviour of the Shear Layer F i r s t , i t can be seen from the photographs (Figure III-U) of the section with H/d=2.0 at a= 0# that the shear layers in turbulent and smooth flows d i f f e r considerably, when exposed to turbulent flow> the shear layers are v i s i b l e ever a shorter length than they are i n smooth flew. Since the Reynolds number in smooth flow was three times larger than in turbulent flew, and since the heating power was kept constant, t h i s means that increased mixing inside the shear layer made the temperature gradients more constant. Consequently i t can be i n f e r r e d that the shear layers i n turbulent flow grow thicker and t h i s results i n an e a r l i e r reattachment (very close tc a =0 i n t h i s p a r t i c u l a r case). As the shear layer comes in contact with the body side, the s t a t i c pressure on the model becomes po s i t i v e and the l a t e r a l forces are reduced. This i s translated into a peak i n the Cpy carve, and the angle f o r reattachment could be located from t h i s peak. As the flow v i s u a l i z a t i o n indicates e a r l i e r reattachment under turbulent loadings, i t confirms the s t a t i c data where the e f f e c t s of turbulence were a s h i f t of the Cv curve peak to y smaller angles of attack. So f a r , the influence cf turbulence can.be summarized as inducing a thicker shear layer and an e a r l i e r reattachment. Increased mixing was the l o g i c a l reason for t h i s increased thickness. A spectral analysis cf the output 45 of a normal hot wire located in the shear layer should give more information. 111-. 2_. Spectral Analysis The purpose of the Fourier Analysis of the longitudinal f l u c t u a t i n g component of v e l o c i t y was to f i n d where the t r a n s i t i o n occurred, and, whether t h i s l ocation could te influenced by on-coming turbulence. This experiment was done twice: the f i r s t time, very crudely in the open-circuit wind tunnel, and the second time in the closed c i r c u i t wind tunnel in collaboration with I.S. Gartshore. The p r i n c i p a l improvements in the second experiment are the better location cf the hot wire and the p o s s i b i l i t y cf adding a s p l i t t e r plate to the model. III_.2_.J_; Apparatus and Bedels The hot wire equipment was the same as used previously and i s described i n the f i r s t chapter. A B.K. Spectral Analyzer with extended frequency range {type 2603) was used for the analysis of the hot wire output,and the leve l s were recorded on a E. K. Chart recorder (type 2305). The bandwidth was set for the maximum s e n s i t i v i t y (6% cf center frequency) and a l l the r e s u l t s were corrected for bandwidth e f f e c t . The models used i n the f i r s t experiment were the cnes used 46 f o r the flow v i s u a l i z a t i o n . For the second experiment, a rectangular section with variable H and pressure taps was designed. The upstream face cf the model measured 3" and the t o t a l span was 27". The s p l i t t e r plate was approximately 30 inches long and was located i n the center cf the mcdel downstream side, spanning the whole mcdel. Care was taken, when i n s t a l l i n g the plate, to prevent any communication between the two separated areas. III.2.2. Results III.2.2.1. Results cf the F i r s t Experiment Figure III-5 shews the power spectra when the hot wire i s located at H/2, (1/8" from the cylinder wall). The hct wire was fixed at the same location for a l l the exposures. The graph indicates f i r s t , that for a l l l e v e l s of turbulence higher than 0.2$, the shear layer, by comparison with the shape of turbulent flew spectra ( c f . chapter I ), seemed tc have already undergone f u l l transition,while the l e v e l at higher frequencies for smooth flow was s i g n i f i c a n t l y smaller. The peak at 28 hertz represents a Strouhal number cf 0.123 . The second i n t e r e s t i n g observation i s how the Strouhal frequency peak was affected by increased turbulence. As the l e v e l of turbulence increased, the peak was reduced in magnitude and experienced a broadening. Surry (11) observed a s i m i l a r broadening trend for a c i r c u l a r cylinder. 47 Figure II I - 6 shows the spectra cf the shear layer of a section with H/d=0.5. The model was exposed to smooth flew and to 11% i n t e n s i t y of turbulence,and i n both cases, the wire was located at H/2 and H at approximately 1/8" from the wall. The cases of smooth flow and turbulent flew cannot be d i r e c t l y compared because of d i f f e r e n t gains, but the cases cf i d e n t i c a l flow can be compared. From the graph, i t i s evident that t r a n s i t i o n began at H/2 and was nearly complete at H in smooth flow. The peaks do not match frequency wise because of differences i n mean a i r v e l o c i t y , but i n both cases; the corresponding Strouhal number was 0.145 . The oscilloscope photographs (cf Figure III-7) indicate that the disturbance waves were strongly modulated by the Strouhal frequency. In turbulent flows, the spectra indicate f u l l t r a n s i t i o n i n both cases. Also, as the wire was located at H, the double Strouhal frequency can be seen. In a l l cases, the decibel l e v e l at higher frequencies grows with downstream distance. This could be due to the amp l i f i c a t i o n of the disturbance waves. 1 1 1 * 2 . 2 . 2 . .Results cf the Second Experiment The results of the second experiment are s i g n i f i c a n t in as much as they confirm the v a l i d i t y cf the f i r s t experiment and also because they show that the phenomenon already observed at higher frequencies i s net d i r e c t l y associated with the Strouhal frequency. The quantity f g represents the Strouhal frequency for the model without s p l i t t e r plate. 1 48 Figures III-8 and III-9 shew the spectra of the shear layers at d i f f e r e n t streamwise locations on the side cf a sguare c y l i n d e r . The wire was located transversely at the point of maximum R.M.S. value. As shown, for the same Reynolds number ( 20,000 ), t r a n s i t i o n in smooth flew has occurred between H/6 and H, whereas i n turbulent flow, t r a n s i t i o n c e r t a i n l y occurs before H/24. It i s i n t e r e s t i n g to note that, in both experiments in smooth flow ( curves C, figures III-6 and III-8 j , there i s an important amount cf energy peaking at approximately 400 hert2 ( the a i r v e l o c i t y was 13.3 fps i n both cases ). For these spectra, the hot wire s i g n a l ( cf figure I I I - 7 , centre photograph ) shows a very regular wave form ( almost the "beating" phenomenon ) and suggests the presence cf disturbance waves cf the type observed by Sato (30). As the experiments were performed with d i f f e r e n t probes, d i f f e r e n t probe supporting systems and in d i f f e r e n t wind tunnels, these observations cannot be due to instrumentation defects. More research w i l l be needed to investigate these waves and their r e l a t i o n s h i p with the t r a n s i t i o n in the shear layer. III.. 3__ Conclusion The e f f e c t of turbulence i s to induce an e a r l i e r t r a n s i t i o n i n the shear layer , so that the l a t t e r gains mixing and thickness. A conseguence of this process i s that the shear layer 49 comes closer to the wall cf the cylinder , and, in certain cases (H/d = 2.0) reattaches. From th i s fact, i t can te inferred that a cylinder exposed to turbulent flews w i l l behave as a longer section cylinder in smooth flew. 50 APPENDIX I - HOT-WIRE ANEMOMETRY Method o f M e a s u r i n g u ' , v ' , w ' , uv , uw U U U U 2 U 2 As suming t h a t t h e h o t - w i r e o u t p u t has been l i n e a r i z e d , t h e r e s p o n s e e q u a t i o n f o r t h e h o t - w i r e can be w r i t t e n a s : E = K U + B ( 1 ) where K and B a r e c o n s t a n t s . (B was b i a s e d t o 0 a t c a l i b r a t i o n ) y F o r a s l a n t e d w i r e , t h e e f f e c t i v e c o o l i n g v e l o c i t y i s a f u n c t i o n o f b o t h t h e normal and p a r a l l e l components o f t h e mean v e l o c i t y , so t h a t t h e r e s p o n s e e q u a t i o n becomes : E = C( 4>) U . . . . ( 2 ) where C(c{>) = C^ s i n 2 * } ) + k 2 co s 2 < j> ) 1 / 2 cj) = a n g l e o f i n c l i n a t i o n o f w i r e w i t h r e s p e c t t o mean f l o w . C^= c o n s t a n t o f p r o p o r t i o n a l i t y . k = c o n s t a n t d e p e n d i n g on t h e r a t i o o f t h e l e n g t h o f h o t - w i r e t o i t s d i a m e t e r , k = 0 .2 a f t e r Champagne (32) T a k i n g t h e d e r i v a t i v e o f E, dE= , . .2, . ,2 _ _ _ 2 l X , ,1 - k ' = C j j - C s i n <j> + k cos <|>) dU + ( 2 ) s i n 2cp Udcb ^ ^ 3 ^ , . 2 A . 2 2 ^ 1 / 2 ( s i n c}> + k co s cf>) ] c o n t . / . . . and d i v i d i n g dE by E, one g e t s : , 2 dE = dU_ + E U 0 ) s i n 2 4> Ud<f> ( 4 ) 2 ( s i n cfi k 2 cos 2cJ)) U F o r c o n v e n i e n c e , l e t e = dE and 2 F(<t>) = (l : k ) s i n . 2 4) =. (1 - k 2 ) cot4» ( 5 ) 2 2 2 2 2 ( s i n <J) + k cos 4>) 1 + k c o t (j> and as f o r s m a l l d i s t u r b a n c e s , s a y u u u dU = u Udcfc = v i n x - y p l a n e , e q u a t i o n 4 c an be r e w r i t t e n a s : e = u + F(<|)) v ( 6 ) E U U F o r t h e c a s e where <J> = 90* (normal w i r e ) , F(<j>) = 0 , t h e n ^ J ' . . . . . . . . ( 7 ) A t a g i v e n a n g l e + <j> i n t h e x - y p l a n e , t h e s q u a r e o f e q u a t i o n 6 i s : . d\ - u 2 + F 2 ( * ) I 2 . 2F(<f>) uv E 2 ) * ~ U 2 U 2 U 2 and t h e t i m e mean (1) - Z + F 2 ( < i > ) " Z + 2F(4>) ~W , R ) E 9 U U U c o n t . / . But i f t h e w i r e i s a t i n t h e x - y p l a n e ( r o t a t i o n by 1 8 0 ° ) , e q u a t i o n 8 becomes d\ - M 2 + F 2 (4») y f . 2F(d>) uv , q , E 9 U U U T h u s , by a d d i n g e q u a t i o n s 8 and 9 and u s i n g 7 , 7 u 2 and by s u b t r a c t i n g '. e q u a t i o n f r o m e q u a t i o n 8 , one g e t s : uv U 2 4F(4>) * ) [ ( E 2 ) + * " ( E 2 ) - * ] • < n ) S i m i l a r l y , f o r t h e w i r e i n t h e x - z p l a n e Udcp = w and ~ 2 _ U w ,2 [ 2 2 2 ~| ^ + ^ - 2 ( p W j . . . . . ( 1 2 ) . _2 _2 uw_ U 2 1 n V i - ^ d i ••••••• { i 3 ) 4F(cJ>) | _ E Z * E In p r a c t i c e , t h e v o l t m e t e r s used t o r e a d t h e r e s p o n s e o f t h e h o t w i r e g i v e R.M.S. and D.C. v a l u e s . As e i s a measure o f t h e f l u c t u a t i o n s , a n d E, a measure o f t h e mean, e q u a t i o n s 10 and 11 c a n be r e w r i t t e n a s : 7 , r „ . . , 2 1 .-/RMSx2 n/mS\2 ~1 = 2 F 2 U ) L K 4 * ' 1 DC D C * " 9 0 O J • ( 1 4 ) 1 r ( B M S ) 2 . ( RMS)2 " j (15 ) IT 4F((}>) L DC + ( P DC ' U uv ,2 53 1. Brooks, N.P.H. 2. Smith, J.D. 3. Santosham, T.V. 4. Parkinson, G.V. and Smith, J.D. 5. Feng, C.C., 6. Baines, W.D. and Peterson, E.G. 7. Vickery, B.J. 8. Hinze, J.O. 9. 10. Siddon, T.E. 11.Surry, D. 12. Campbell, A.C and Etk i n , B. BIBLIOGRAPHY "Experimental Investigation of Aeroelastic I n s t a b i l i t y of Bluff Two-Dimensional Cylinders." M.A.Sc. Thesis, University of B r i t i s h Columbia, Jul y , 1960. 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"Turbulence: An Introduction to i t s Mechanism and Theory.", McGraw-Hill Book Co, Inc., 1959. Instruction Manual for DISA Anemometer Unit 55D01. "A Miniature Turbulence Gauge U t i l i z i n g Aerody-namic L i f t . " , The Review of S c i e n t i f i c Instru-ments, Vol.42, No. 5, 653-656, May, 1971. "The Effect of High Intensity Turbulence on the Aerodynamics of a Rigid C i r c u l a r Cylinder at S u b c r i t i c a l Reynolds Number.", UTIAS Report 142, October, 1969. "The Response of a C y l i n d r i c a l Structure to a Turbulent Flow F i e l d at S u b c r i t i c a l Reynolds Number.", UTIAS Technical Note 115, Ju l y , 1967. 54 13. McLaren, F.G. and Sherratt, A.F.C. and Morton, A.S. 14. Comte-Bellot, G. and Corrsin, S. 15. Nayar, B.M. and Siddon, T.E. and Chu, W.T. 16. McLaren, F.G. and Sherratt, A.F.C. and Morton, A.S. "Effect of Free Stream Turbulence on the Drag Coefficients of Bluff Sharp-Edged Cylinders.", Nature, Vol. 223, No. 5208, pp. 828-829, August, 1969. "Simple Eulerian Time Correlation of Full-and Narrow-Band Velocity Signals i n Grid-Generated, "Isotropic" Turbulence.", J. F l u i d Mech., Vol.48, part 2, pp.273-337,1971. "Properties of the Turbulence i n the Transition Region of a Round Jet.",UTIAS Technical note 131, January, 1969. "Effect of Free Stream Turbulence on the Drag Coefficients of Bl u f f Sharp-Edged Cylinders.", Nature, Vol. 224, No. 5222, pp.908-909, November, 1969. 17. Novak, M. 18. "Galloping O s c i l l a t i o n s of Prismatic Structures." Journal of the Engineering Mechanics D i v i s i o n , ASCE, Vol. 98, No. EMI, pp. 27-46, February,1972. "Tables of Chebyshev Polynomials.", U.S. National Bureau of Standards, App. Math. Series 9, December 1952. 19. K r y l o f f , N. and Bogoliuboff, N. 20. Minorsky, N. "Introduction to Non-Linear Mechanics.", Trans-l a t i o n by Solomon Lefschetz of Excerpts from Two Russian Monographs. "Introduction to Non-Linear Mechanics", Edwards Brothers, Inc. 1947. 21. El-Sherbiny, S.E-S. 22. Vickery, B.J. "Effect of Wall Confinement on the Aerodynamics of B l u f f Bodies.", Ph.D. Thesis, University of B r i t i s h Columbia, September, 1972. " Fluctuating L i f t and Drag on a Long Cylinder of Square Cross-Section i n a Smooth and i n a Turbulent Stream.", Journal of F l u i d Mechanics, Vol. 25, Part 3, pp.481-494, 1966. 23. Roberson, J.A. and L i n , C.Y. and Rutherford, G.S.and Stine, M.D. "Turbulence Effects on Drag of Sharp-Edged Bodies." Journal of the Hydraulics D i v i s i o n , ASCE, Vol. 98, No. HY7, pp. 1187-1203, Ju l y , 1972. 24. Delany, N.K. and Sorensen, N.E. "Low Speed Drag of Cylinders of Various Shapes." NACA Technical Note TN 3038, 1953. 25. Cowdrey, C.F., "A Note on the Use of End Plates to Prevent Three-Dimensional Flow at the Ends of Bluff Cylinders.", National Physical Lab. Aero Rep. 1025, June 1962. 55 26. Bearman, P.W. and Trueman, D.M. 27. Bostock, B.R. and Mair, W.A. 28. Nakaguchi, H. and Hashimoto, K. and Muto, S. "An Investigation of the Flow Around Rectangu-l a r Cylinders.", Imperial College Aero Report 71-15, June, 1971. "Pressure Distributions and Forces on Rectangu-l a r and D-Shaped Cylinders.", Aeronautical Quarterly, pp. 1-6, February, 1972. "An Experimental Study on Aerodynamic Drag of Rectangular Cylinders.", Journal of Japan Socie-ty for Aero and Space Sciences, Vol. 16, No. 168, 1968. 29. Novak, M. "A Note on Galloping I n s t a b i l i t y of a D-Section i n Turbulent Flow.", University of Western Ontario Research Report BLWT-3-72, December, 1972. 30. Sato, H. 31. Sato, H. 32. Champagne, F.H. "Experimental Investigation on the Transition of Laminar Separated Layer.", Journal of the Physical Society of Japan, Vol. 11, No. 6, pp.702-709, June, 1956. "Further Investigation on the Transition of Two-Dimensional Separated Layer at Subsonic Speeds." Journal of the Physical Society of Japan, Vol.14, No. 12, pp.1797-1810, December, 1959. "Turbulence Measurements with Inclined Hot-wires.", Boeing S c i e n t i f i c Research Lab. Dl-82-0491, December, 1965. 33. Van der Hegge-Zijnen, B.G. "Measurements of the Intensity, Integral Scale and Microscale of Turbulence Downstream of Three Grids i n a Stream of A i r . " , Applied S c i e n t i f i c Research, Section A, Vol. 7, p. 149, 1958. 34. Cowdrey, C F . "The Effect of a Shroud on the Time-Average Aero-dynamic Forces on a Two-Dimensional Square-Section Cylinder.", National Physical Lab., Mar. S c i . Report No. 6-72, May, 1972. i 56 3 .0 2.6 2.6 2o4 2.2 2.0 1.8 1.6 1 . 4 1.2 1.0 OrO 4J Ci a? •H o o o o ttO CiJ U ft , . j U o GRAPH OF THE GRID DRAG COEFFICIENT AS A FUNCTION OF M/b C F o r c i r c u l a r r o d ) \ \ \ \ \ \ \ 0 . 6 0.4 0.2 M/b 1 ± 3 5 J 1 ! _ J L o g 10 11 Figure 1.1 Figure 1.2 Figure 1.3 TYPICAL HOT WIRE ANEMOMETER Figure 1.4 60 0.50 _ J 0.40 DECAY OF THE LONGITUDINAL INTENSITY OF TURBULENCE 0.30 0.25 0.20 _ 0.15 0.10 . 0.09 . 0.08 -0.07 -0.06 -0.05 -0.04 . 0.03 — 0.025-0.02 v C ampbe l l and E t k i n • S u r r y A V i c k e r y A V i c k e r y ( as s een by v o l t m e t e r ) m B a i n e s and P e t e r s o n ^ S m a l l mesh g r i d ® L a r g e mesh g r i d v M c C l a r e n e t a l . A) u'/U = 2.58 ( x/b ) " 8 / 9 B) u'/U =1.12 ( x/b ) •5/7 x/b 10 15 1 I I I M M 20 25 30 40 50 60 70.80 90 100 Figure 1.5 61 Figure 1.6 Figure' 1.7 D I S T R I B U T I O N O F U. A C R O S S T H E T U N N E L U, 6 t 5.. 4 . . 3.. 2 U J u U z 2 3.. 4 . . 5.. 'av X = 6 4 . 4 X=53.8 1 = 43.! X = 3 2 . 4 X = 2 1 . 8 X = 11.1 X = 0 . 4 lh> &•» Sn l-% In 0 © © © 0 ? t • I I) • * 0 © © © 3 -CJ 0 0 15 '-© 4 9 <» eft 6 • I *^  I h •i h 4 . © © e ... H h •9 1 1.1 .9 1 1.1 .9 1 1.1 .9 1 1.1 . 9 1 1.1 . 9 1 1.1 0 .4 .8 1.2 1.6 Figure 1.8 D I S T R I B U T I O N O F ir U A C R O S S T H E T U N N E L 6 1 5 4.. 3.. to x . z .1 2 31 4 5 61 X=64.4 X=53.8 E3 52 -ft El', .06 .07 E5; 83 ft n Si! GJ Q .07 .08 X=43.1 J3 • P "35 1 S3 .08 .09 X=32.4 b a f a a" 0 S3 S3 is • iss S3 J« 13 S3 53 X=21.8 b 13 • -a — 1 f3 SI 0 E2 •53 3 E : B : E : o.i o.n o.i2 0.15 0.16 0.17 Figure 1.9 6 5 4 3 2 2 3 4 5 -6 ~ 7 DISTRIBUTION OF U ACROSS THE TUNNEL DOWNSTREAM THE 9" MESH GRID U. r = 32.2 £ =26.9 averg .1 <1 I .1 «M I .9 1 1.1 .9 . 1. 1.1 .9 1 . 1.1 = 16.2 .9. 1 1.1 ~ = 0.22 J I L .8 1.2 1.6 2.0 Figure I.10 in DISTRIBUTION OF u 1 ACROSS THE TUNNEL DOWNSTREAM THE 9" MESH GRID U jj- - 32.2 f - 26. =21.6 n m • I j c a • n I! a • EI a a Eg B a a • 3 a n Vl mm. S3 S3 a S3 • a El a B • Q a m a 9 B a El IS 13 El C a H 1 1 •1 1 1 • I 1 1 -I 1 .1 .11 .12 .13 . 14 .15 .17 . 18 .19 = 16.2 J L .23 .24 .25 .26 Figure I.11 .30 .28 .26 .24 .22 .20 .18 .16 .14 .12 .10 .08 .06 .04 .02 I— 10 20 30 40 50 60 70 80 a'Ao„ 90 100 ERROR DUE TO LOW FREQUENCY CUT-OFF ON NORMALIZED CORRELATION FUNCTION ( T < 50 msec ) A ) Exponential Autocorrelation c( T ) - e-«T (x) \ \ \ \ \ ^ \ B ) Gaussian Autocorrelation c'( T ) « e'a'^ u c = cut-off frequency (rad./ sec.) \ a / u 10 12 14 16 18 20 Figure 1.12 ) 2 4 6 8 10 i 12 14 Figure 1.13 1.0 & 0.9 L 0.8 0.7 \ 0.6 0.5 0.4 0.3 0.2 0.1 0.0 \ \ GRAPH OF f(x) AS A FUNCTION OF x/L o Large mesh grid (autocorrelation) f(x) \© ' x/b = 33.6 © Small mesh grid (autocorrelation) x/b = 31.6 Small mesh grid (true) x/b = 30.4 69 0 1 2 3 x / L ' x Figure I.14 70 o ^-t o o o o o o o o o CF5 Figure 1.15 6.0 600 800 1000 7 -6 -5 4 3 2.5 1.5 GROWTH OF THE LONGITUDINAL MACRO-SCALE OF TURBULENCE J L Scatter l i m i t for Van der Hegqe Zijnen data (33) Large mesh grid (autocorrelation Campbell and Etkin D Surry Small mesh grid (autocorrelation V Comte-Bellot A Small mesh grid (true). t v v ? c k e r y i i i i i i 10 15 ' 20 25 30 40 50 60 80 100 300 400 600 800 1000 Fi g u r e 1.17 ho 90 85 80 75 70 65 60 50 -45 40 — - 5 / 3 s l o p e | I n e r t i c U m ® • £) 0 s u b r a n g e s l o p e ) DB TURBULENCE SPECTRA FOR LARGE MESH GRID ( x/b = 32.2 ) M w ' s p e c t r u m D v 1 s p e c t r u m ® u ' s p e c t r u m U = 3 4 . 8 f p s F r e q u e n c y ( H e r t z ) ! ! 1 I l I I I 23 20 40 Figure 1.18 60 80 100 200 400 600 1000 2000 4000 6000 10000 20000 P1 Q | j "&r~-«^ _ - 5 /3 s l o p e ( I n e r t i j a l s u b r a n g e s l o p e TURBULENCE SPECTRA FOR SMALL MESH GRID ( x/b = 32 .4 ) DB J 1 I M 11 w s p e c t r u m • v 1 s p e c t r u m © u ' s p e c t r u m U = 3 8 . 3 f p s F r e q u e n c y ( H e r t z ) J I 1 1 M M J L I I I I I I P 20 ' 30 40 50 70 Figure 1.19 100 200 400 600 800 2000 5000 loooe 2 0 0 0 0 75 0 10 20 30 40 50 60 Figure II.1 — udc EFFECT OF REYNOLDS NUMBER AT a=0, FOR SECTION WITH H/d = 0.5 —0 2 . 4 _ _ V cdc • • a • B v D — 2.2 . "dc 'dc V v A A A A Ud/v l&T T.V. Santosham (Smooth Flow) 62 Smooth Flow, • Small 3 v Small 2 v Small 1 A Large 10,000 Figure II.3 20,000 30,000 40,000 50,000 1.9 1.8 1.7 'dc EFFECT OF REYNOLDS NUMBER AT a=0, FOR SECTION WITH H/d = 1.0 a a H H • ES U B E B D  m • Q Small 3 1.7 _ 1.6 1.5 1.5 1.4 1.3 'dc 'dc D C B n a a a an a a oP £?°o (Q C P ^ O O O O 0 % % o o ^ o o oo o o 0 § W O O O o_ o o o • o Small 2 o o „ ~ o n o n o o o o 0 ° 0 0 o o o o o o Small 1 1.6 __ 1.5 1.4 1 — 'dc A A A A A 1 A A Large Ud/v 1 I 1 1 J L 0 10,000 20,000 Figure II. 4 30,000 40,000 50,000 60,000 . 70,000 80,000 03 EFFECT OF REYNOLDS NUMBER AT a=0, FOR SECTION WITH H/d = 2.0 Cdc 0.9 1.2 I — 1.0 y V • • Small 3 1.3 • v T W V V • V V / V r V v • • 1.2 1 • v ^ c\ • • V • f dc 1.1 1.2 1 A 4 - A . A * A. * A * ! * - * l.o L_ A ^ A • A S M A 1 1 2 1.1 I 1.0 h r A * \  A± A A A A Ad. A A A A A Small 1 V 1.1 I — v v v v V w dc Large Ud/v 0 5,000 10,000 15,000 20,000 25,000 30,000 35,000 Figure II.5 DRAG COEFFICIENT FOR D-SECTION AT a = 0 2.3 ,— 2.2 2.1 2.0 1.9 'dc 4.8 % deviat ion Ud/v 10,000 Figure I I . 6 20,000 30,000 40,000 a A © 50,000 ;60,000 T.V. Santosham ( Smooth Flow ) Smooth Flow Small 3 Small 2 Small 1 Large EFFECT OF WIND TUNNEL BLOCKAGE FOR SECTION WITH H/d «rjl,0 Figure II.7 EFFECT OF WIND TUNNEL BLOCKAGE FOR SECTION WITH H/d=2.0 1.4 — -1.3 — 1.2 — c 1.1 — 1.3 1.2 1.1 1.0 •A-A —*L-A A 1 a 1.2 1.1 1.0 — 0.9 _ • D © Figure II.8 .01 Blockage Ratio (d/c) • I .02 Cd = C, ( 1 - 1.69d/c) .03 D Large © Small 1 m Small 2 ^ Small 3 .04 00 N) 83 EFFECT OF u'/U ON c d FOR RECTANGULAR SECTIONS AT C<= 0. 2.2 tf 1.0 u'/U ( % ) J © Present tests A C.F. Cowdrey (34) H J.A. Roberson v McClaren et a l . • Bearman and Trueman A Nakaguchi, Hashimoto and Muto O Del any V T.V. Santosham 10 12 14 Figure II.9 2.4 2.3 2.2 2.1 2.0 1.9 "dc it EFFECT OF u'/U ON C ( j FOR RECTANGULAR SECTION AT C < = 0 . A T.V. Santosham ® Present tests n Bostock and Mair a Bearman and Trueman u'/U ( % ) 0 1 3 Figure 11.10 11 13 1 2.8 2.6 2.4 2.2 2.0 1.8 1.6 1.4 1.2 * \ EFFECT OF H/d ON THE DRAG COEFFICIENT OF LONG PRISMS AT a = 0 . Experimental Data • Eeanr.an and Trueman D Bostock and Hair * Fage and Johansen T Nakaguchi .Hashimoto and Muto H/d I 1 1 1 I 1 1 I I » » 1 "1 I I » I I • 1 1 1 I I I- I 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 .figure IIJL1 ; ± , - 00 .15 W i r - i 4 i ! i i-l 1 i o.o i i ! ! H-i! nil hi I i-iti i ! 1 if?* I -!: lii-b O H 11 C) •H-C) i i n Ah O S M A L L 3 A S M A L L 2 +. S M A L L 1 1 4.0 8.0 13.0 16.0 20.0 24.0 RLPHfl (DEGREES) II 2S.0 32.0 36.0 40.0 44.0 49.0 CO Figure 11.12 11.14 EFFECT OF INTENSITY OF TURBULENCE ON C F («0 FOR SECTION WITH H/d=0.5 r H - : ~ • !' » I o— M M F T : 1 i i • ; i ; • : i; I i i.i i | ; ; j . . ! j-! 1 ; 1 i l ; , I Hi: • '• i ; i i IF f '• \ I! i i • ' It'.: j : ! i 1 i '•• - — ....... -! i !. 1 - 1 P" ' ! : i 11 • •( D.i-ii- : • 1 ! i ; ' i 1 ; i i rj I 1 • '• : i ; ! 1 | II! •i •--i' i I-I ! i F I i • III! I ;-i '-1 i-l i ! j r j ; j ; ~-: -I CD n i l ; : i | Mi -i I t I 1 1 1 I i-i' f l " M - ;'! M i F ! 1 F F i I • I 1 ! i » I ~ - - ---:1 -ri \l M 11 l l i l ! ] i I Mil ft ! i MM Mi -M1 • i f'l-,|, . . 1 |" -• | 1 j ! ;-| i i r; . J i I; : i 1 i i . . jjl< D- i ! 1 J i l l i H i j.i.i i- t \' 1 j i M|:|i 1 . i- l " I I •j . i i ITii ' i : 1 i i l ; ; j ,' , " j O— j ! m 1 n — ;_ : : / V +• 1- i 1 i j I Ji 11 j j r • i i § IM : i n hi t i y HI ! 1 •i 1 ' M l-i 1 fi'H Ml •-\ i F l • ' i i I i.i'-: • Hi; •l-M • "!T.!.. ; 1 l-r ' j- 1- !- r-Mi: j i i * * \ 1-1 $ ' I !'' ilil i\ IV ;; j i : : I • i ; ' IM in : M i.j.i ]-i4 l r 1 |-r- i l i i i nil .! 11 i - ~M - l ! i ! • i i j ; i ! I j-i j I 1 : i i i i ! i.i. • 1 I 1 -1--; II" I m +1" T.I: :| i-i 1 ! 1.17.1 i t i . i \ ; j 1 i • • • fe -. • I F ft" . . : 1 i i i t jL' 1. V. 1 : ! i ; '.- ! ' ' i'i-: : i-! t ! . t .... 1 r -, i.i • i >' -i-i- f" r •"Ht F l ! ! ' D i I : '. • ! i i M i 1 i i A i ( : • .-j-y 1 : ; ; i 1 ! J i -i-, I till: - • rl • ' - - r ••; O S M A L L 3 - -. t o ' <-> ' ' - J " " - \ 11 M ; i.n 1 : ' : 1 | 1 ! [. j | m | i i-i-j . • I I • .'!' : ..i'.:' — : :t -• -h- A S M A L L 2 Ml • • f i ' I'll i I ': |F-'• 1M I i 1 i F1 1 LjTi • 1 i •• F - •1 :! :!.::|-.-+ S M A L L 1 ! ! . I ri:. '. 1 ! l< E( !-"!• i y\ i i i i " MM -n i . i : j i l T 1 i \'\. •\ i ! i J I ii. 4" • i ) ' i •i • r -. . . | . . . - .(. ' .j:.:. ' \~~ •::..]:;. fjiri: | •!•{•[-il i - i i F i ~ l - - •Hr: •! M i i i i .1.1 fr-I- i I i i l l | lit I ; ; J. j- - • 1 • • r • • • •] .!. . ' i|.:.; .. .I -j-.'. .". . t J t i'i .Li Lj -I Iti •iTfV 1 - 1 • -1 -. r -i r \ !• n j r > ©t Slit ill HI--i i" .1 r i •1-r i ii !' rr| r . : . 1 1 il •1 i .)• -T "f 4 J !- 1 "j .1" i '•' i l ! M < i I'M F i 1 j i'\• j : | : T • ; ; •il M • :-• i i : ' i 1 i n : i F 11 i-l i! . i-•j 1!:' j: • -T11 I 1 I - 'i r II IT If i i '!• - i 1 M l i i i ^& l it : ! 1 1 ; ; •  "H7 M:i . a} j : p 1 D ; -I:'. 'i1 pill 1:: £ •Pi' n i l ' i I : ! i.o 1 I IIHl BUI| ; ; : t M i b i P N C mt i l ! (DEfef j : . : l <ioi ! Prl2 3.0: | -['•2 2.0: 3 r o : A : 5.0 M 4 DF: r-: •  -4.0 j < } i i : Mil ! ! I i j j i j Ill; ill] i i l! 1 rt i i i :i [f:t [if; i. - " I i l w A DM:; ••'•••!' • -; i ; rrlr 11 )-i i n ! ! i i.i Ml: 11' j III! i !• 1 j I U 1 • i ; : !! t ! IT: T Lrr MM l i i i ; 1.; i i 1 ' j i I : i +: j ; ; • .. : ;.j h:: T "rf .:.... i 1 1 :. : M ... .. 1 1:1; i i i:r ;l. ii i r Figure 11.15 EFFECT OF INTENSITY OF TURBULENCE ON CL(a) FOR SECTION WITH H/d = 1.0 w» Figure 11.16 EFFECT OF INTENSITY OF TURBULENCE ON C (a) FOR SECTION WITH H/d 92 !4 H± m --'i-'it ii i- -+— ! • 4-. j : J . i . ii riTt w IT P. TIT Mi m :e>: SI i t fli'i I 1+1 ,x H - h - j l - , L t l i O SMALL 3 ft .1 A SMALL 2 'R'i + SMALL 1 lit !:i U-1: RT MM Hit HE m i n x : I At i 1 r •Pi nil-1 l i d : fltRHa IDEGR J o !-i £ESJ lift i i-i-i-t. m iMfft Figure 11.18 EFFECT OF INTENSITY OF TURBULENCE ON C (a) FOR SECTION WITH H/d=2.0 93 -i i j'| i iii l i l t i i i i i'|ii .kill -1 i-i-i 1 f : - -Hi 1 j i i .]..... !Jt|-1 1 ! 1 i ''t!-[iiii i i # rtb :ftFi-' • f + F F lit i 1 i i iiH ifil i-rn i l i l i f i l iilrx m !-l i Sjl! i j i 1 : i i i i i iiii iiii iiii iiii ilil ! i ;• i Li ; ' '•: i r iiii i'l i I Till I I! j U K •:.' I ' : !•• ' |ii:-: l i i 'Ni' -:-::r . . . . iiii iiii i i i ! Ifff w •i+H: xfet t'ri-L tfi FM-i i i i t i l l i l l ! "L '•t +F 4 - a -f t 4+ Wi ' f} I ! i-i I " m L i i i !l i 1 Fi i 1 iiii lli • ~ : -i-i-i- •i-ril-T H I -rrrf i j11 ilil iiii [||| iiii + ttt Fit -Hi I • \\-i i • i' Iii! |! i f ii •i i I-I IX! | iiii iqi iiii 1 : 1 ! 11 Ii IT!I l i t i 1 i i 1-1+ 111 i rti i [•; •i i i ! Ii j iiii Iiii i-li-i i l-l-r iiii T i i"i. Iiii -:-r '/rt : -' • fi A : iiii i'tii -iiii ( • r» • i:i i';i i j-;: i'liii ... . Itii : i IT- t t j-l-i i iii" Hil -T— !: j i n i i i i t i i i - Fiii •i f'T Hi-; -;!tt illii r iXi d:t'i: i i'U ••i-i : ; C } A i !?::! 1 ii'i i n -ii-ii-l i f f iiii 1 i i i i r-n •FFI'T -Pil • iiii •! i i iiii: + ti-i-i- ;J i i i'l ij-i! liij :!t|x tit lit : at: ' t-f 1 Mir i iff i i i i i l ti :!.i.i:r ii'i i-! If.; O -it!-!- -.! Li:l i i i ! i i i i-i-i i •i 11' EH lit "iilt i i.| i i l i l -fit i :F Xtt'r rH'E '[tiF j:U.|- Hi i-i ii'i. "Ari FI-I-F -!-|-it i l i l iii-ii i i i ! : i ii. •! i-i i S F iii FF! • i : •  u> : i.i Lj- M r -!-iii m lit!' t: i t i t tiFt -i-i i-i :'tri:r. -i-i-i--i-Fir 'Fj 11 i i l •llli .I-FHC )i i"i:i: rhr:l -.rtj:j. it::!. i-i-i-1 iiii i i i i Fit 1 .; ! i n. i 11 • 1 i ["• W itit - ; r : r :!±ht ! |-|_| [ r. -FH i-IHi iil- .:+Li: ;t-H:t- "ijiii!' •'FFFr •!:.;l i i i i i i i i .I.Lxi. Fti ft; i i i i i i i: i! i-i Iiii I!! ! I [ j i i-i i ;• i-FF! iFFi .j i itii i i i | i Fr! Uli iiH "fti-f •m • ; i! | li-i i i l l !'il"i" |rrii Ii i-i n ii i v*. i4H i i l W llHi! t i l i ii'i \ m W tii ni l i l i l Fill l i l t -r-t-H-i i i i i l l i !.-: :J :j ri.i. iiii "fill f f i .'•ii-.!. '•!-F!"F P i f IFFI til l. Fi.i.i- WW .iiii; •• i i-l-iiii i l l £.«V & 3 Q i i ji i.rl i|i, fttt H i t t i l l :j±ff iFFi- till- i t i i i ; - i! m M :;:i±r. -Ll.it 'i'. -i1 i [• .'r'rri -l-i-i i-4:l:u: •rl;i i-I-i'i-.ill' ti i t ii i i "'•': I ' l it : 1!. i i l i l Hit Jill I l-i-s t-f-r- [it! i-liF : L i . t : 11 1 titi-IT F  i4'!i: -;-n F ml Ilil: -ii|i-["Ml l i t i • 1-rj i 'i'-rj i j - F r r -iiir' TTT . r » . ; <o : llif i-i-! ! 1 i-il' iii'!- .Li -.: it; 'SI- m W + ! . | . l . -L.Luj m i i i i -LLl-L 'rht.Li ilEii itjii :hl;t ! i ' i i l ; in 1 iii.i ni l H-!-r i it! 1 FJi Ff,-4 •'•Fi-!-ttbi i I-! Fr O SMALL 3 tiij: xbht 1 i i-r '• Fi! I Li; ! 11 ! im t'H F H+t •I&'i J!Ah. -!+F4 X + A SMALL 2 !X|.j :i-i i-i .-Itii il ; t o ' 1 III i-iic % T-FFF "Fpi-F tFrt- p p A + ft + SMALL 1 m ii'Fi. iprrt B Tit'-. *r fH-L : ! 1 I m •I-I tl! |4i:i" i-H-i- J--1.1. + :f! m W r -Tpp m rhi r t i l l i.trt-Hit xi±i: -Ftff i+FF tf+i' t-rtj-"Bfi-i-iil -|ti f r' •c ! i i I'FF-i .:.i lilt tin •I! i-i i t-h~ 'i:::!:i .1. iil HH iFii-•IF!'! - i rxr ittt m m H i ! M t'F * \ li<3G • i T+':7 :+ FH.i. iiii au '• i i i in iiii iiii Mifi if • Li i Iiii!" i iit 11 Ii iii: • FFF rt: •. •* :+:: r i-rr :::: 1 -'.:.: WB — — — i r t Ti'!'; i-i ;' flLPt4a (DEGREES) Figure EFFECT 11.19 OF INTENSITY. OF TURBULENCE ON C n(a) FOR SECTION WITH H/d=2.0 i ( i 94 -|- Small 1 Smooth flow (ref.3) 19th order curve f i t Figure 11.20 EFFECT OF INTENSITY OF TURBULENCE ON C F (a) FOR SECTION WITH H/d=2.0 95 r r ::..|::... H S •fr-rf - : ~ :;::|-::- I : .'•!.: ... i i ;::< i IB : i . 1 i ii i m i i 1 : : ^ : •: •; • r: r i-. :'i : : j -1 • •' I ' i ... ....J.; .... 1 jili ;t(f: TttF st'.t - Pi TtTT . . ' ' ! ' ' • , L . '.Q~ ffi : Hi ' If! j rttlj •EEH ~t . t -. •. • r-rr 3::: rrrf l-l i ; j-li llli ..i i I . rH r ij ii !•; i i'i i Hi-! ffii ! ! i-| ; j 11 l.i I'j Pi -TTT l i i i 1 i : i] j ffti i | ;:rr| ! i l.i •i ;• r ! Fl'i ! ! i ; i! F III! l:ii i f jirj-: r.t!:r i i r'ri !H >• 1'fir :-i-r| j-.i i" : |: :• 3 :; |: i! i'i : ' 1 • tltl i i.t.L i|- ! Htl lllf Htf ! 1 •i ![ ; \U ; i-t-i: FFF-F M m '•r[-Tf iiiL -|:!:|-r M -i-N 1 i ; l!' |! i I-f Ml T p t •ff-ii llli: rttr !tl] |j. l i t T'i+i m im :(.T.fF m :iii~r -Eci.j: SH- 1- +1T | ' •: ii ih;f i'i | i i ! j f ifi-i ;[[[ • e» Hi+F :. !-L! t h ! :&; O: ' • •! rHF ...^.1 . «. •tii-i : ;.L-::iti ! ' !-'• 1'i-ii its'. •  i:F[ : rT"; r i . • r> -•:!.;:!. r r i ' HI-} ! ! 1 1 r f | | H - •iFi| m 1:i i; ! 111 ilji I ! Fl ilji ; 8 l- r. ; i i! lif! Tiil: *• i ii i. ;i;-| U_ J w. _J 1 » TUT -rH-r : : i ;.::;,! 5 T;. : . . . 1 nii i ilMI ..: |; .;. ' i- •' : O SMALL 3 ! i • i £k SMALL 2 •'•!! 1 i f r f -rrff ; i i; sin + SMALL 1 ; i . i • • . • 1. •! fl? — - rrr IHi ; —_o_ • i'i' jHI -ii!! . . J . : ; ; ; ! « n L tt:.t ill! l •it! • •• . . :ii:i r:f[: •M-H ! ; [ ; :ti! :;(; • i. i Li.!.:.;_, •: 1 : '-' -°.t '! -• 1 " 1 -• - ! - ! i ; : • i • ' i : 3  r_:.|_:.. .0 < .0 1 i.a , i i.o ; PLF D.D 2 Hfl ICEGR 4.0 i - : 1.0 1 : • '! !.0 | : . • • • 2 >.0 | . . . • • • •i );? ;| : • t - • • A );9 | Hi!.:.-! i i •' i : ~T | ; : l : " ! : ' i i i i i : : : : ( -Figure 11.21 i I EFFECT OF INTENSITY OF TURBULENCE ON C ( a ) FOR D-SECTION '| 96 if] i- i! 1; . : j . • 1 — . — " ;!:::i i|i! ! i:il| •! 1 " TEE: • j:::!. r-iti .L:I.L;l.i ' ' I • " • :'\- ' ! i! i iiii! "! :*!• i-l-K tin iiii iiii IIII iiii iiii •r ji n ii 1 !i Hi -1-1°*" ftr!:! Fiji -i-i 11 i I' • T:-T ! : : i HI! i-l II itti ifi! -1. i •| P! i li iii, i; i n: X •I •j:: i! -! i » i . ! | • \ ill Iiii iiii Iiii 11:!: IiH ;.;.n ifflj ha; iiii J, J •f-j-i - iil: -rr: iiii iii: : i i i i i-ii iiii :Hi! !. ILi! i.i 1 iiii t L p L| ; ; : ; % Iii: II ii pi.j lift ii-H Hit 1 t • • Mi- r; i \l iiii M L , a .- 11 i-i iil-i iiii Sclii -"IH ii'i iiii • i;: i •; 1 iiii ilil 11 i i i! i i i ! lli l| t J.' ; H t nxr •i-'-R F:|i; •l-ii! itii ifil •!*IH P&i 'hi( iiii Hi-|-i i-l i iiii-i 1 I-l i 11 i i i i-ill iiiiti I f -Htt 'pi"-FF X i iffl iiii TEi i iii; Hi! i-l ri - i l i4| ftL ulii ilil IIH iiii HH i:l i |i • i i l "Iiii i-i-l-•ii'i- lit t i | : | l i - i l •II r fi-f i hLLi iiii i hi tt-f-j. i i -iiii •iifi' J!j.ii I iiii iiii iiji iiji Ijli-! Lli -i'i ii I f ti l i. : j ;X Hi FFF ffft: :: :±t ..XL-m + m iii: mi iiii iiii t tri i i-Fi-f i i i j :i; til i ; i i i Ii I iiii .rf it iiii - r j f • t +E -ipt ± : : r :L::: m r l fiii i i ;ti itii I'l;:! •'11! • ^ D iii? M 1 -PF :FP!+ :i:L:. t i l I r r r r •nfp -. .rut ii.i i •iii ii.ii I iiii iiii jilii H-; ;• -rvn Sit -Fri-i -!-FF~ l l i it i t l :; It.; :l l It • i j i :*; i:;' iiii i I!'[ i i ii j ;:nt •|Hi •l-l-l-f iiiE PtLL - F H I il-FE .L-LEil u it: :b+h fFFPt TPFt •I-ilfii! T-rii il i i •' 11 iiii pi! PHI: TiTh Iiii -Hji #FP ijih +di tptt T.l? t i l i i i ±f "{"fit ti- iTF! ti+i i 1 ! fi fiii i f . t - i .-H.-L-j: xiir -ti-ti" "LLU '. p - i l f i -i-H-r rr:nx X -1--lift II •i 1 i'l-i i'i '. itii -i-i t-i-t ifE r r lit! i l l ii I.i. -1 U;-\ fHt 4 fr ; i! I i'j i. ! iil! .iiii i-i ii iiii i 'Pit !-i 11-: Pi .- :•(-: PPF! liiili litlfi -I . iiii 1 Pi i ; PI r Fiji n i-i tl.i.i -.j.'i; m I 1 IT i.i rr i.Rii tiii FE ii Iii? • ; r t 1. : (•Hi ii-IF •1 ri-i-iilii iiii •H '-i • i'i IL: \ liiiil If "ilil t;±L ilPF -i !-!•'• :i Mi liij •j-iii. iiii. ilil ! I ! 1 :li; . m i Ki i'ri'i -Iil i i i i.ri.t i l l l l i •Rt •. fiii iiii ; ,.Ll i ; i j-: iiii .Itti it-H •iiii Hi! till i li-i iiiI ; i: • iiii |!H< i 11!: Itii i i-i-'P O SMALL 3 •! i F 1 i - - ii-i [if! ~r:L A SMALL 2 lli i-| !•!- il i i nil' v | iii -'d-i;i-J'Jrrt + SMALL 1 il i HI | ti l -tri i • :i': .... i:iti. tHi ii-ii fit! iiM: iiii i.i ii if ri. : LIT i.LLi. :j: ,|± i i i Pfii HttiT iiii 11'' !• Tj-.if iHili xlil !-i-l-: i-rr 1 i I !-: i ri rpi ! : O L i'Si: H If i tS! P |.: -— •ptf- ii-ii iii: • : - 8 • . . j. • - --—|—:- ..: iiiiilii: - v : i ... ].... • • ! •:! • :: ;.:.:)::.: :: l -Figure 1 1 . 2 2 ' j • i EFFECT OF INTENSITY OF TURBULENCE ON C_(a) FOR D-SECTION | 97 Figure 11.23 EFFECT OF INTENSITY OF TURBULENCE ON C F y(a) FOR D-SECTION ii ;- '• 1 ; i iiii Ti 7 if '1 TT T T: i 17 - - i | T" 1 1 i-i ! i 1 i 1 1 i 7 -'IT 7T!.i il 1 iiii | \ > 1 1 |i o : : ! iiii !|ii iiii ! 1 1 j | •1 1 i i 11 i  i i il i 11 1 i 1 i i ; i : ! i hi! ! 1 i : i 1 iiii 1 \\ !>| 1 ! i I ill i • - T - llli i 1; j iiii i i : ; i i ! 1 Ji i 1 1 1 1 1 i i JI 1 i i 1 1 i-1 1 ii-il ill1 11 i i' j ! | ii | \ 1 1 ' -i-i-i 1" -; i III 1 1 1 1 • | a • . , ! ' ilji ;[ r i i r 1 -j- H n 1 i i i ! i t •I- 1" I-I 11-•I" •i-i-;!i! ;' S i ! iiii 1 "T T 1 1 |.j 1 : I 1 T " i 1 i i'i ~r 1 1 *f" i l l ! iMl n i i i I j i i i 1.1 i 7-; j ; .: i" 7-i i • • • i] • "1-iT-- iff- fiii iiii ! .• i j i- |i . 1 | . i i : i ;i.ii 1 o :: i i iiii i j ii 1 i i-l-l " i : H i .. •l-t |: ": 77 " I " 1- • ::: l-il--17-r-' ¥• "'in :i|i i 1 i7 ! ! I 1 ?" : i 1 i • i i ! ! i j !?li ; ! : t ! r "i 11: IF-f -1-i -: :| •- <f w •1 '-[ T ~Y T '1" ' ; 7;v i'i t i l : - i - r i * -[•: ;-| \. - . | i ': Mil i n i 1 ' ! ' LL4. ; j | : Iiii r* ..:: Hi T|T; Iiii 'ill -i i j i. i . 1 1 "i > 1 i •; "i"' M i l ]ti : ; i-i .Li i . . iitl •! I n t f i i -! j !' • ill • ! 1 i 1 .. r. : \ '• M|' iiii ; i i '• i ; |. ;i •• t . >:• J- -i. ji-il ;. i 1 j i 7 I 1 ' l~ \ I i i i i ' i ' i | i • ; : i ; ; ; ; ! i i: ' i i j Iiii 11 i i_ -\ < -\ "•!•: i ii I :m <i ii! it.!. i'l'i! 1 i 1''. • i i i i i ! iTi 7TTT iiii 17 11 i ! - - | f 1 : itl| i . -i \\ i i i i :i i i i "i "•171" f I i : : i 7 ' • i i iiii •!•!-!= IIII IIII i ! i i i i j i i •i : ii | i II iiii ill Ml ! i i ; I i iMl i.LL si i/> : j : 1 I'll i i M —I ji i'i i TiTt I I ! ! j j | I 11 ii * i 1 i-; i r :•! 1 j i . ! 7-i ! •I-I -I i 11 iiii Il 7 iiii ilji -ii- ill: 8 7. i : : j f - -i j 1 1 1 j 1 1! (| ; ; : :{ T Iiii i i L -1 i'j j: •r-l Hi! ii; j \ u . . _]»< i i i ti i; i | r ; -j t i i - - - -- -1 - ; - - • I J . + i -- -I-T -m •1! H-7-17! f.":: r-i-l Iiii iiii il j i ; il TT - r i •i < i - _ - — i -1 i- !" : 1 j | ii i i i i 1 i" : i : -L - ; -; ; - M i-! A \ i i • r I; jt Ti i i l I * - -- V i ADr.c -1 ; ! 1 1 i : . j I i ; i | | • - - - - 7 - - - .. 1 .11 i I 1 ; j !; i: Tj j < ; ; ; : — "7 X j x - - | - 7 i-i iiii :; 11 i j] :i -1 - - - - - -- I -- ... i- • -_ . . j : iii" t i i ' l ; i l l : 1 i ; j i <.. ; - - :F _; •- - ; 7 :7' - 7: -- T : : : : : : 1":' .1 1 i r ; r i I' i til A - - - - -- - - 7 7- • r i 1 1 I ii ill! j ! 1 f - - - - - - - j - -- ... .. _. Ii 1 ! | ! ! 1 . i ' i j! 1:1' I : i -- ... - - - - - ._ - ii i- I ill | I il i; ! !"!! i -• ; 1 t z r : - _ - 1; n : : z ~ '. ~ i " 1 - j .1 I-i : jil; j i -) i - - - - -- -- "TT- ]• [I'M i | j- t j - 1 I - : 1 - - -- — r -: P t | II [ i j §4 _ ; : 7 i; -': ; : -'• ; : : . - 7 ::. :. : : : :- : : ;7 "V i l _i. -H i ! 1 • " 0.0 4.0 8.0 12.0 16.0 20.0 24.0 28.0 32.0 36.0 40.0 44.0 48.0 ALPHA (DEGREES) i 1 Figure 11.24 EFFECT OF THE SCALE OF TURBULENCE ON C T(a) FOR SECTION WITH H/d =-0.5. . 03 0.0 4.0 8.0 17.0 16.0 ^ J h O i K s * $ S } » • » <fl.D Figure 11.25 EFFECT OF.THE SCALE OF TURBULENCE ON C (a) FOR SECTION WITH H/d = 0.5 M fit" T i I'i -:j:i::: xx _ - .. X I X - H - j - H - -- i - -.  .. _ _ xxxx X : _ : j- -- i -- 'l - i f|; j ill! j i ii ! !-. - i " ! : .oi M i l t [. •|:| i -^ - r - -X X X I f X x: x: x x x: xx: ": : - - - z X \ i i • i i i i •-I 1 ' M l ' '• I i-i -i ! r -!'-- -i .. . X - • i- -- -r - :zz:± X -- : - -- - i l i ] r; i 11 i 1 yi! i i i i -! i- i . . . -\--r v ixx xx xxx x: .:x.x:x: :xxxxbxLx >: zi w :: - -- I-'! r--i-I 1 ! 1 ' T l i l i I ; i i T T j t !i!i xi' I 1 I 1 j i ; . .a . _ I xjx. .:: :LxxTx W^M - -- - - -- i - .1 i i i I 1 1 i i i i ' ! I | T iz ix F-_±- •-•—-j--± x -KJ . -- -- • -:z -- t ~ " -x : z X - i i i i i_ i I |! :ii ! i i i : : j- j---- X -- .:" +lx: " x: x." ' < \ - -i- M } \ _ --- i I i i i i j : j" i [ ' ; i m 'i'i •i- _. . . ! . . . . X ... f - .: i i I > j : '• '. 1 \ ! • ; • t- - - -t-1- - - - v , ' F „ . ,. i • ; ' | : : i • a : r z - r 1! t - --|fx:: . . .J .L '.:[xx;M'- . - . ' X x: \ x: ; I-1 ' i i I; ii ! | ! | 1 i i 1 iiii | j } • i" i i i - j - . . .-1- !. ... r . : i : i 'j - i -:H Ii1.. xt j *~ — l r - -'i,xl-xx:xy: - / X :: - - i i j! 'in i l i l : : i : ; •: . a i. L!:i - -IH -i|i-l- XL:-I: _ 1 !.. --'|-r>V-rX'. . "F L ! X 4 X -- -- ;; : '-: ':" -i l ! i i ! I I : ; i ; •hi • I u, ' i i&a; 1 -11-•! ---Li * +>:;, - - - i — -11-- - - -—It--xjx-4Fxx x:x:xx" : : : X x X -- : - -i -I i I- "H i ! 1 i i ; ; 1 • i i i ' • ; i ; ' 8°: T .:: i-i *fi - xxx:xi:: -Z : z - ~: -- H -~r ! '• i I ; . . : , . •iii. IU i; :-' ; - 4-, K'j r" - - - i - i - - - - -r +-F ------ . — - - - - -- -- - -x x i i i i _ r T" 4 i " • • i life XHX |-- r r w i f i; -4 :T i ; : .. Ji X I x r - ~ z.; z z z x x -1 - -- - - - - - : - : " 1 : - XX i 1 1 iiii i l l : I j ' i : Mi-i l l i- -!• ' "1 r: •. 1. _ ; 0 1 b; •-X xx-.-j ^ x i M i 1 xxx. r:z — I \ Z\ - ; X ;j ] I -_-J) « • _ il 0 Iiii ii'i t ; i" _xl - x l x.;_ : ix: Hi ;-l-XI- - --- - - - -- i i i iii' ; 1 • I • '• -j.'ji L •) • ' i'i- 1 j i 1 : j I 1 | X I j i 1 : - 1 -r --• X X ._ - -• — : x x x x' — — - - - - - -- - -- • - - i i iiii ! • i 1 • ( • 1 i : I- |- i \ i - i - -1.: ..(.. .. _p.. . _ . - -)— - -xx xx: + S M A L L 1 M i 1' j: Iiii ilil ; | ; i ! i ' 1 • i i i i 1: ! I i M i l i ! i i i ! • : - ri!:j. XiTj.: L - - "r' - ' ' i M i ' i i i i " X i X ] ' \ i t : •i U. X L A R G E 11 : { 1 1 ; 1 | 1 1 :~ : .a - . . . . . ii-i-l-' 1_ •\- 1-1" ::::.:: x.: - -- - i j [iil ; J ; i "i 1 : : j ; I! 11- 1 7 -i . : i ' i ' Z Z' .' . ;~ " - x xrx " xxxxExx — X - - :: - - : : - i i i i ! i ilil : i 1; : i i • ! j i i i i :Fii -1- • ... .. _ . X X "' 1 7 .'.' • - -'• - - : - iiii iil; -ti ! i .T! i I |- FT "j". ~F 'l -li-" x - - x'.xxx - xxx:: ; ; : -: i !||l • 1M ; i ' I • i i : ; i ! ; Iiii III! 11 i i ; j - ii'Fi I'-H-i-' rrr-i •i-l r -X!.:i : -ii i- t-i h'r !-!-" --- - x::::x - xxx-x"' ;* - x :x: ; X il i i x i I i i : l i lilr. - - 4-1-.!: • 1 r x : x :.|. x.x '.... -....". z: X X I : - : . i i I X ; i i i i |TH : i x ! iiii ..... [ j l-l-i-i" -| - l-i : i 1" X. - . . r i ---- -- - i i'i I i i i o o Figure 11.26 EFFECT OF THE SCALE OF TURBULENCE ON C F (a) FOR SECTION WITH H/d = 0.5 ' ; I ' i !•, • : M i 1*1 M W o : 8 Ii-h + S M A L L 1 X L A R G E • " H i I III ! I ! I u r ' " n I: > -f4-H-I : I : i i i i i I'! 11 i i ! !2ri> 53 :aui CM) 5 5LI> *l i l l ; i ! ; Figure 11.27 EFFECT OF THE SCALE OF TURBULENCE ON C (a) FOR SECTION WITH H/d = 1.0 ; ^ I + Small 1 X Large 19th order curve f i t i i WW I-C ;2 i ?7!i 1'i i!i ! ' ' i i ' i Nil; i'li I i lit' il j | 'III: i l I Figure 11.29 EFFECT OF THE SCALE OF TURBULENCE ON C„ (a) FOR SECTION WITH H/d = 1.0 o 104 - r r f — : : : : ! : : : : lii - l : - : -•: i :.. |:.:-I :: 1 •:: j .:H:IJ.: : : : | ' . : . - : • 1 : . ; : Hill i.i.i.i Hi-; i I ii ; i 11' :!•: i!i: 'i i i-i iiji : ; : : i ;n : Hi! MM Iii'! ..IILL iiii iiii Trrr i 1 ii iiii "rri*r TPPP Iiii' :• 1 i; 1! i! -iilt •i !-:•! Tfcrt! I :i-H ...-;.«». ! : l i |H | ; iil! 'iii I'M I-i I i 1 r-r i iX:i|. i i . . . : n . 1 j i i Hi! n n n i n : 1 i i • 1 F ~ Hi: xrrl iiji ti]]' !i|i iiii iiH i!! i | I i ! Ilil i ij • 11-FI 1 Hi •! iii' i ipt-iiH i i ! ! i l l ! iiii i!-ii i-i-Pi- i l i l ]: ii i iiii mm fH- 1 ilil i i i-i ilil 11 1 L i I ilil i i i i Iiji |i i.i Iiiii iipp i •F if m t "PFFE : i" V 1 i H lit] H.i! i i i i i i i ! ii- i -H: : Mi; ilil 1-Hr ti'ti i f l i " i r IF!! iii rr nix I j - •* iiH •i-i i i i'ii! 11 i-j iii'!-r r ; ]| i#i lib! fFl:^ !-FPi: :-FF!"i- ijpi Fl-t-r tiitf • :- | ; i : : - . - r ~ • H ••• . ..... --Hi : 11 i ! • i i + B iiii •iiii ffi i i i i i 1-iH' i-i-!-! ;EErS. r xtri i i •HHF i i i i - f Ttd: F-Hl itii .Ixbv r-l-r.r- mi' iixt i l l •-til , I ; i-lii M H-K fit '[in tiEi :PFFF p FTP;' IxEt i o i iI |- iHf i i f -i-i-t'r .rib. i i i-! j i t -rrVI-m "iiliE i i 'FFFF r i r r i t i i xt.rJ: 1 Lt_.. iftt xlxi i jitrt" • <o • 1: Mi i .ii'iii '!''-!•]• i!-FI l i t iiL!. !:H'r -RF: i f i i w 'HIT iEEiE rrr" xn.i. i-i i 1 i i n til} i Til .!#[• ± H t - i i ! ' :F!--I-!: i i -:-rr rrrrri j-rr;— i-FFE xi Ii i - t a "U-& o :U -r~r , , T ' • •> IFF" l i t i :|F! l i i | • i i i ! -iiii i-i'i F I ilr i f i l :i±t| ±t±r i.i-ur -ilti W 'Hiri -r-Ppl-•TPj-Hi! -Ml! 1 Ilil ilil •Hi! L i-l 1 i-iii':-' tt!.E -i'!•!-! •f rl-l- i±pE •|i:ri •M-i-l- •I H-r .tan. FI+I--.U_a •_J • _» _rf.T > X-+ rH:r t rH :! r.i.l -I'Fii + SMALL 1 +PPE i B it i i -PFi'l-> m X LARGE xrrE "t-!:|-a > ~rr> X _— •X- ; ! + ^ i H-i-+[-}•>• Ltd -R:.TT 'FFi1 •Iiii-Hii Mil riii ; [ - . ! : rx.tr +t • i i l ;+•• : ilfM i t i i xq+ i l iiii i i i ! i i i i ii'F] •I i+;---l-!-l- iXI.I • " I-i'Fi dix -• jT-F •; !-;-r M SrE -a : -+;* :+:: —•. -r-i-f-r 'FFFf xnx liti •trit-i i i i i f t i l t 7 I-l! - rrrnr. L 1 i-l-i- m tjxr i i .L-T-f-!" iFi-! ^ -H-!-[ :ixPE -H-i-i •FR-T i i i i : t-i • it; I "I: Til ij'd IEEE iEEix • 0 .—es_ .0- ; . ! 4 I ~ ' p " : _ -Pill e •: : 1 !q •: i .0 • • • 2 : ' ' : -fllF ? :MT : M ib ; i Hfl: ( .,. 2 3EGR 1 0 :ESJ til? >!<fi"; i.i i'? Il a iil? s!o r p i j;; * P ;FPP« r'xr If w lipp; • n i : : | . : :::: I:::: J_L:|:Lil - ! - • • •. • j. . . . . •Hrr . . :.. -r • «• : i:..: Mi. . ': i M • i" ! - — i — .::::!•.:: ..:.) ... Figure 11.30 EFFECT OF THE SCALE OF TURBULENCE ON C (a) FOR SECTION WITH H/d = 2.0 105 I.! I Iii i ii .ill.. ill-iiii l!H : I ! i i i! iiti 1 ii-i H: !-u:i; ih 1 ,X|. Hlrt i 114 n M I iff - H > ' m i+ iiii. BP it - i i i! iiii III! m H-ii IL£L Liti ra. 'i •m I L'L" i -H Ir.ii 1 1 H-ti + SMALL 1 m X LARGE i m ii.l:X ,!ii : i ! I • ih-i : + i * :vif. • r.rtr -1 12.0 18.0 20.0 24.0 28.0 ALPHA 1 DEGREES) —t— 32.0 — r — Figure EFFECT 11.31 OF THE SCALE OF TURBULENCE ON 0.(00 FOR SECTION WITH H/d =2.0 1 ! 1st :t:Hl .J-I.LL - i i i i ; tut :n .i.T. m I4|-i "F 1 |- r i i LI. .i Li i i i 1 i ill; ill! ijj.j j ! ! • •: i . ' i i i i •:-rrL ir:j i i i : • r i t : ;-i : I.; i . i . i'K i_ i i i i ii -• Ll r i :.: i ;[ i-i i — • Q: ; ; r i . i i !• " i l ' | 'I" i"7 i — — • .:; - - • • -" : ~ - — r : : i.'f •j l-i'i" • • ;-; r -iiii- i l l ! t L L t i i i i | I |;i i l l : i'i hi •llli •I4J4 - r r r i X T X X -| t _ r i i l l ' -1' i'i ! i • 1 ! j 1 1 iXi.'i. ! ii-1 j- mi; I T - f i - 1- • i 1 . : 1. . 'tl ;• --;-|-i !•!';-tit! T;- rr 7-H-r lilt •i i i-l •i : i-F Li h! . 1 . .Iff! i iii ;_l 1 j. -St - J X r r . C L L T iir.i" -|-• IT; r i ' LT i : - 1 -1 -; i ;.: 1 l • ;-: •; f 1-1- i i'i i ~M . l i l 1 I. sT; I-r ft H \+ i f ! ; 1 I ! :HtH-if+F TFR-.Xpi".i' •i i U |"j.ri" - | h i r r i i'i i ' ' ' ' i ; j L. iii -E i i i i.'l.'il.i. rn * 1 _ ) • : • CX : : <X_. U J •.. l. i 1. 1 i I-i i-H'-F T'FFF 1+1+4-m - i . '.'Lf-i ; I - *- —' + S M A L L 1 1 1 11 :! 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".'..'ir'x - F r i - ; --H4-|-- r r l T tiiF -EltF iF'FF ti .Ll t r 4-F 1' • f -Li: I L 1 1 I' .[ t • rv-— — s X zc + . i -.tf i :h i - ~rr iiiii 44-H <-T-F-F .LL ;_L :pi:|;j: " i T - C i : .i ri-i-i ; -i-. j . l . -i-FFF x!.,-i -H'FF T i'-FF ..r| :_|. i l l ! T r r r -1-iX . ..|.ri-L l i'. l X C i X :t±Lt -[-it i ii t • i-1- L "L ; i i I i ll. 1 FF ... .; i .. M -L Ei 1 i . ~ r r s -Ij-rL l i l r i i ; i i . 1-L.L.!. 1 — m lil 1 i - . . j . ' i iiii" X T ' t t -i-j-ir i •;;.-[; t'.tii •l-l-l-f •]i'FJ-i l m T T - r t :Ef . L 1 i :; 4 t X m - r r , r i -1-l ri+ I T . i s m ±h|i EFti +Lii m m xLi i. i i i i ; - r ! _ r i -ixfca-i i i i m 1 r r r :i±tr: itix T -B - - f --L : t V + t --r i i ^ . . : . i . i L irtl: ix i ± -L-_ -U-±ttb -ii+t :FiLT ! I I > - r r r i " tfff m s i-Fi^ -ii-i-p iixi: - h L L L •i-l-E T: r-r 1 1 . 1 ..i.rrr -U-l-!.. -i-if, L m •1 F r --r V X tF ta: X i -p- -- i -m - E "h_ -T "f~ • • i '. l.i.:. • - i ^ -itix - - Fx Ep: k - l -tH+i-l i l t +'(++ •il-rr--r___r -FF-LF' .-I; |+-iFrt -r- + Etii' \ -TF -i- u M Iiii; iiii-:i FiT :;:F;:i ••;-!• 'i-i i-[ i-i"* ti-FF !tfFF- ;LFFF - t i ; :• TTTE •FFLF-•I r r '• t 4 r -i E 1 f l - -r-h -: x[X E I-t-- f i - r i - i'i. w -L. L.I. |. +1 r; i l-.l-L- •FFTi. T-FI j iiii: ! i i i <i!i iT.:..i. -j I... 1 -U!. 1 1 .1.1..: i . m Eft -rr ii". -n i -F 1 .1 *") i - i !-;-; ;- i j T F E i i i i ; i i i. t i i i ! [rj-.r "atF i"L]';" i i i i i i i i i i; i j : : : 1 i- •: 1 i;> .':. ;."i i + .'!; r. ;• m - i - l .1-1 14 !! 1 i . L j-*|. -:.. 1 . -HiF r ; -r- r FFFF •FFE IT:' "i"r.i"":' i i i i ii i !.! • \ jit .i . : I I . . . I r l ; ''hl^" - i - | t ; "F,Ei-r r F? i T •] .1... • <*r r v , I4W .LLi. 1. ii-i-f-L •l-i-rr il+i-i-i-i-t-4-S+-H .-L.I "ii." i . . ; X I... -i| 1 i i ri-K r r r : i i - E i i i E T f 4-~r .-L -T- •t-t •r if i - E Figure 11.32 EFFECT OF THE SCALE OF TURBULENCE ON C p ( a ) FOR SECTION.WITH H/d =2.0 107 • f • 1/V • i t -j l j i I i i X it;;;'; T P -:•:•!::: . . i ' i : : . -:::[•::: •: j' • i . j . i . I . •'r'-'r Y <•:.: • +1 7 * Ttr; TJ-TT ~r . i . l i l l ' i i ••—>r::-' Iiii::! . :.:.H .:.: •:--"! : ; : : C + - ~ : -~ : : l • ; 1 •>i • I • • • 1 .:(..:• . . I .L - . i l i j l V : : : l ! : ; . l : X • • • I -rr': • •• •1 : 1 i i i ' +H-1 I i I T H : 'Trf : * l iii; iiii iiii iiii iiii i i i! III! iiii Hi; i i i i i il i Iiii iiii ii!! C. . - i'i i i nii iiii iiii i l i l i i i i iiii i l l! -iili il-H . h . ;! i • I.i 11 ill"! . i . . 1 iiii i i i i t i l ! m I.I i •: i ii i : i-i: iiii • : ; I Hit l-!i| i i i r ilil iiii - 4 : Iiii ! }f_l ' 1 i r r i:i i li-r-l: H.l I : i ; -'" iiii iiii i i H.i - tri 1 -—r -----! » iii'! i'Llij. Ii iil iiH;: & • 1 •- f ; 'iii' i i —1 — ea- • m iiii i'.f i j j i i.n i i-i I.i •>i.| . ; i; m '•'-'! iii'j , . 1 : u. •6-'• i : '.!'.:' - -~-r HI: Siiiijiji; iM]: : ! : i i i i ~ ' ~ •f-rr - ~ - — - -ir-- Hi! ! ? ! ill! ! U- • 1 _J i d . •i'i :ii 1 • < i-i ii + SMALL 1 r- :" ,lni-• ! i-Si c':' 1 i • ! X LARGE i :.: • ijsj. ( ih :— -~ -tf--i!-: i : i II i i j : :!•'•• X -r-f-... -i i i : £ i' • • .! • "TK-<---.- — _iil|.L.'i_ : l.j 1 i i i i : . . |. . I : ' •: i " :~~ - • - : i — i i i! i • * : !' •. -—I Q-' I * j. ' : — 7 1 - j—— i :•: .1 I - I ': L :'.. —rf ! '!:: _ i—_ ! : : . i-ill: • rrr i; ii iiii i i i i . . i . ». ' X • • 1 - • • X ; ( ' • i ... i • ....!_ I'i •'• - - - — : 11: L:.:. .'• i-•i • • I.: 1 .1 i |.:: j : ri] i'i;.; iii.! r f t; '1 : . . . . • •: <a.-• ; £ -.j °:: i .0 I .0' 1 1 S.B 1 HR IDEGR 4.D ! EES) i.o 1 : 2.o I • • : . 1 . s.o 1.6 • '* 1.0 ; • • • 1 • i i a ' 6* i... . ; i _ . _ • • : • :' : i : ! Figure 11.33 EFFECT OF THE SCALE OF TURBULENCE ON C (ot) FOR D-SECTION 108 I ^ I M : - . : : ( . . . i 1 :«*' :::: ;:: i !' • • • • i i • i. • • • .1 ....j ... 1 . M | M - - - . | :: • "i.i — : • • • <x ^ - i t ' : 1 I . . . . j . 1 . . 1 1 i. • • • I :: 1 ; -T i ; j :J ': tmt'i —rf^ " <*} - -i i.rrr T in iiii ; i 1 : iiii ! 11 i + ^  ;;><!> ( M M : :- . • , M | , M — 1 • • ir-i- - iEJi - i— MMjiMi M [i :M -tl i - M i — T i t 7 " iiii iiii 1 fl H d M; . • . : M 1 i i ! ! I i i i ! ; i i 1 'i ' i i'i! i i i ! MM iiii l i i ! Mil iliH i il i '' V ' \*\, {•in .• r r\ ! 1 ! j i 1 ! 1 i 1 1 h • : i i. 111: i j !lll I i i.i. :!-!! | l ih I-I 11 i* i MMJMM : i I.!-j:! | t - t - r I'll •Nil t i l .l.i M> 11 -i Lj (j|: J M M M : : iiiiJMM i: i :L:.T i i . :o 1 il-i! H i-i '! M'i i l l ! Iiii MM . r- ::: •. i:.: • -. :nl. i pi — 7 M M ! M : ; ::.:}.:.: - ~r. ". ! i U. ; i I-I i i-i i •; M ! ' . . —j 1 :: 1 "HIT j L j ] Ii I-i - — -' . ! : | i ! i - M i : ; M 1 i l 1 !•»• ..::> < - ; — i ! • I • ' i l l ! ! : ig Hi! '•! i • Hi! l-il :||jj III! : - I . : : -: 1 •:: : :: | Mi.M_ : ! i • . -1 . .-- |-::-i l l ! llli i f 1 j l.:!.| M.r) iiM I i-i 1 •1 ••: a i i . L; !. Hi' 1 i •ll! i iiii !'H; iiii ; i-i j i 1M i i i : i i i ' X 1 - - r r 1 iiii i! : |! II i-i-li-il •;.i:ij II-r 1 I i - | i -l-i-il Iii'! MM MMj .• iiii 1 ;•! I I 11 •;!-!--M-1 J I ! i i i : l-MJ !:i: I i-i i-i | j . | i I i'i 1 • • I - - . -! • ': ' :•»' + SMALL 1 ;;;;( : ' Mj -M X LARGE : i:! • • : •: <; l , , 1 — \ — ' , ; ; i ; " " j : . : : rf:-r -•rrr i p ;i ji Mil I I I -"iiii :=' : :. • .. : : : : : I I I ; MM i . i . - I M : E : . . . . . . . . . MMJiiii • M - - •H-rf :x: i-: i : . . . | . : . . MMMiT i - : |:: •: : : • : ! : . : : !:::!:•:: :::: | :;: • -.!::•• :: •: :: :: . T M -: •. | •:' : ; i i ! : : ' { M X 1 -• I . . . -. . . |. » I " : -~ i •— ':. ii 1 i • "i • + M i i -TT 1 1 1 1 1 i 1 1 \ 1 1 T T "•I! 4.0 B.O ii.o is.o ;:.o ?a.o 3j.o 38.0 o.o 4 4 . 0 «-o Figure 11.34 EFFECT OF THE SCALE OF TURBULENCE ON C_(a) FOR D-SECTION 109 :t±ti m xi+; Ten ffi+t- rf-H i± 4±t! ££L i * tth[ .1- L i . i l-H-r h i t T F P ± i ± - r r r ) -t Iti S B ±t i j T i •PM-•F:(; i i i i ! X i l hi-H" H i -P i . rr • PRT LTS?x i i u :;g. -! u.»-t:x. it Xix ti± t 4 - r r •rfl- -H-H r: LLi !±!:r f-ptp hi-!. tht tfcp Til r P r LL+t i i i ILLU + S M A L L 1 X L A R G E r.rx! t F f t ix: T f ; l - r f - i - - - f l j J r <5S pi i j C . 0 - \ H O.B ; ! D.9-u t t r m m Figure 11.35 EFFECT OF THE SCALE OF TURBULENCE ON C F (a) FOR D-SECTION r VORTEX-INDUCED VIBRATIONS ta Small 1 $ A Small 2 © Small 3 f O Large .9 .95 1.0 1.05 1.10 . 1.15 1.20 1.25 1-11 Y 2 . 0 1 .5 . . 1.0 .. 0 . 5 0 . 4 0 . 3 0 . 2 0 . 1 GALLOPING AMPLITUDE OF THE SQUARE SECTION Experimental Data J.D. Smith (Smooth Flow) Small Small Small 1 2 3 4 Figure 11.37 5 6 7 8 9 10 112 Figure 11.38 STEADY-STATE PLUNGE AMPLITUDE FOR MODELS WITH H/d = 1 SECTION (Small 3) 113 0 1 2 3 4 5 6 7 8 9 10 Figure 11.39 STEADY-STATE PLUNGE AMPLITUDE FOR MODELS WITH H/d = 1 SECTION (Small 2) 114 ure 11.41 STEADY-STATE PLUNGE AMPLITUDE FOR MODELS WITH H/d = 1 SECTION (Large) 1.4 1.2 1.0 . 9 . 8 . 7 . 6 . 5 . 4 . 3 .2 .1 Y U r Experimental Data A Smooth Flow v Small 3 © Smal1 2 GALLOPING AMPLITUDE OF THE H/d = 2 Section. -+• 1 2 Figure 11.42 8 10 Ui 0 1 2 3 4 5 6 . 7 8 9 10 11 F i g u r e 11.45 Figure I I I . l PHOTOGRAPH OF THE MODELS FOR THE FLOW VISUALIZATION u = 0 = 5 <* = 1 0 d •(I i © s - U o k - 5 t ©k - 1 0 t * = 1 5 ° <* = 1 6 ° <* = 1 7 ° It t t <* = 1 2 ° <* = 1 4 ° <X - 1 5 ° Figure I I I . 2 STILL PHOTOGRAPHS OF MODEL WITH H/d = 0.5 SECTION, AT DIFFERENT ANGLES OF ATTACK * = 18° * = 19° * ~J - 17° x =20° * <K - 10 !* i oc = 99° o< - 1/ * •s - 10 it IS) A 4 A O =19 — . — ^ e< =20 FIGURE I I I . 2 STILL PHOTOGRAPHS OF MODEL WITH H/d = 0.5 SECTION, AT DIFFERENT ANGLES OF ATTACK 22 18 14 10 Estimated angle .for reattachment ( degrees ) © u'/U = 0.11 O u'/U = 0.063 SB u'/U = 0.002 0 0.25 Figure III.3 0.50 SUMMARY OF THE FLOW VISUALIZATION RESULTS CONCERNING THE ESTIMATED ANGLE FOR REATTACHMENT H/d 0.75 1.0 1.25 1.50 1.75 2.00 ho 124 o C = 0 Figure III.4 STILL PHOTOGRAPH OF MODEL WITH H/d =2.0 SECTION, AT rx = 0 IN TURBULENT AND SMOOTH FLOWS A 30 20 10 •10 -20 -30 B,C,E DB A ) B ) C ) D ) E ) o Smooth Flow u'/U = 0.063 ( Small grid ) u'/U «= 0.077 ( Small grid ) u'/U = 0.095 (Large grid ) u'/U = 0.11 (Small grid ) as D ) I I M 10 20 Figure III.5 40 60 80 100 msxa POWER SPECTRA FOR A SQUARE SECTION ( hot wire located at H/2 ) 200 400 600 8^00 1000 2000' 4000 6000 • 10000 TURBULENT FLOW ( s i g n a l i n t h e s h e a r l a y e r , c a t i o n as c u r v e A, F i g . I l l -no f i l t e r ) l o -6, SMOOTH FLOW ( s i g n a l i n t h e s h e a r l a y e r , l o c a t i o n as c u r v e C, F i g . I I I - 6 no f i l t e r i n g ) SMOOTH FLOW ( s i g n a l o u t s i d e t h e s h e a r l a y e r , no f i l t e r i n g ) fD -J r-t-o CD O HI fD O 3 < o Q -< M O 3 in O Ol fD m fD o m C L < • D C ••no r—^ i PI: 7 ;'— / L I y — i fD -S o I/) o Ol fD en O < o Q . < O -5 N O 3 O QJ fD 1/1 fD o < If —«k— 3 . . JLI M fD o Ol m o Q> fD 3 < O C L < o -5 INI o m n 3 i n ID o 10 -10 -20 -30 -40 •50 -60 OB SPECTRA FOR SQUARE SECTION+SPLITTER PLATE IN SMOOTH FLOW ( Reynolds no.=20000, f = 7.7 cps ) Locations of the hot wire from the leading edge : A ) H/24 B ) H/12 C ) H/6 D ) H ( Frequency (cps 1 M 1 1 1 1 I .6 .8 1 4 6 8 10 Figure III.8 20 . 0.6 0.8 1 2 4 6 8 10 20 40 60 80 100 200 400 600 1000 Figure III.9 

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