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Flow interference effects between two circular cylinders of different diameters Seto, Mae L. 1990

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F L O W I N T E R F E R E N C E E F F E C T S B E T W E E N T W O C I R C U L A R CYLINDERS OF D I F F E R E N T DIAMETERS by Mae L. Seto B.A.Sc, The University of British Columbia, 1987 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF PHYSICS We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October, 1990 ©Mae L. Seto 1990 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of PH^SicS The University of British Columbia Vancouver, Canada Date O C T [2. /t)0 DE-6 (2/88) A B S T R A C T This thesis investigates different examples of action at a distance, namely the in-teraction of two circular cylinders of different diameters and the interaction of a cylinder with a wall in various arrangements. Action at a distance modifies both the lift and drag of each one of the objects. The fluid flow interaction between a circular cylinder (of diameter D) with a wall, and a circular cylinder with a smaller (\D) circular cylinder at Reynolds numbers of w 10,000 were of interest. Man-ifestations of the interactions include mutual changes in the lift and drag forces, phase, onset and frequency of vortex shedding on the circular cylinders/wall. A novel force measurement device for lift and drag of circular cylinders and a data acqusition system was built to realize the above experiments in a water towing tank. The system was capable of simultaneously measuring lift and drag on two circular cylinders with time resolution and correlating these measurements with flow field pictures. Measurements of the lift and drag and phase, onset and frequency of vortex shedding were taken on the large and small cylinder simultaneously as a function of the relative position between itself and the smaller cylinder as the two are towed. These measurements make it possible to map out the areas within the cylinders' sphere of influence and measure the intensity of this influence as a func-tion of the distance between the two cylinders. Every quantity that was mutually altered by the presence of another cylinder is used as measurements of the area of influence for a circular cylinder. It was found in general that the forces act up to a distance of about 3 diameters in the lateral direction. It was also noted that pressure fluctuations at the vortex shedding frequency penetrate into the laminar flow region up to about 3D in the lateral direction. The results agree with existing ii results for wall/cylinder proximity experiments and flow interference between iden-tical circular cylinders. A novel method to trigger the onset of vortex shedding for towing tanks was also discovered. iii T A B L E OF CONTENTS ABSTRACT ii LIST OF TABLES AND FIGURES . vii NOMENCLATURE xi CHAPTER 1: INTRODUCTION 1 CHAPTER 2: Fluid Dynamics of Cylinders in a Flow 7 2.1 A Single Circular Cylinder 7 2.2 Two Identical Circular Cylinders 12 2.3 Two Circular Cylinders of Different Diameters 18 2.4 Thesis Strategy 21 CHAPTER 3: EXPERIMENTAL ARRANGEMENT 26 3.1 Experimental Requirements 26 3.2 Data Acquisition System 28 3.3 Software 34 CHAPTER 4: MEASURING FORCES ON CYLINDERS 38 4.1 Design Criteria for Transducers 38 4.2 Methods for Measuring Forces on Circular Cylinders 39 4.3 Design of the Principal Cylinder Transducer 44 4.4 Testing and Calibration of Principal Cylidner Transducer 49 4.5 The Control Cylinder 56 iv 4.6 System Integration 56 CHAPTER 5: INITIAL SINGLE CYLINDER EXPERIMENTS 60 5.1 Phase of the Lift Force Correlated with Visualization 61 5.2 Cylinder Near a Wall Experiment 61 5.3 Triggering the Vortex Street 63 CHAPTER 6: Flow Interference Between Cylinders of Different Diameters . 72 6.1 Data Collection 72 6.2 Data Reduction 77 CHAPTER 7: RESULTS AND DISCUSSION 83 7.1: Drag of Principal Cylinder 83 7.2 Interference Lift of the Principal Cylinder 86 7.3 Vortex Shedding of the Principal Cylinder 89 7.4 Phase Locking and Vortex Shedding Onset of Principal Cylinder . . 91 7.5 Frequency Variation of Principal Cylinder Lift 93 7.6 Interference Lift and Drag of Control Cylinder 97 7.7 Frequency Variation of Control Cylinder Lift 108 7.8 Fourier Spectrum of Control Cylinder Lift 109 7.9 Action at a Distance 115 CHAPTER 8: Conclusions and Recomendations 119 REFERENCES 123 APPENDIX 1: Listing: ACAD Program written to Generate Potential Plot. 127 APPENDIX 2: Listing: MATLAB programs written: trial, proc, acamp. . 130 APPENDIX 3: Copy of paper (vortex triggering) in press 134 v A P P E N D I X 4: Strain Gauge Specifications vi LIST OF TABLES 5-1 Summary of triggered vortex street experimental conditions 71 5- 2 Time and position of maxima of lift signals for x0 = 8.3D 71 6- 1 Summary of two cylinder experimental conditions . . 76 7- 1 A(f0),(jfM) x 100 vs control cylinder position 115 vi i LIST OF FIGURES 1-1 The potential flow around a circular cylinder 4 1-2 Flow around a flat plate at subcritical Reynolds numbers 4 1- 3 The UBC Physics tow tank 6 2- 1 Fluid dynamic quantities of a circular cylinder 11 2-2 Flow past a circular cylinder at different regimes of Reynold's numbers. 13 2-3 Lift and drag force on a circular cylinder 14 2-4 Interference force coefficients for two identical cylinders 14 2-5 Schematic of setup for two cylinder experiment 20 2- 6 Block diagram of experimental approach 25 3- 1 Tow tank and camera arrangement 27 3-2 Block diagram of data acquisition system 29 3-3 Example of superposition of frames used in video analysis 32 3- 4 Menu screens of programs used 36 4- 1 Blueprints of principal cylinder transducer 45 4-2 Wiring of electronics for one channel of transducer 50 4-3 Setup of static calibration for principal cylinder . 50 viii 4-4 Calibration of the principal cylinder 51 4-5 Response of principal cylinder to an impulse 52 4-6 Typical signals and their spectra of the principal cylinder 54 4-7 Blueprints of the control cylinder 57 4- 8 Moment calibration of control cylinder lift 57 5- 1 Phase of lift force correlated with flow visualization 62 5-2 Setup schematics for cylinder/wall interference experiments 64 5-3 Results of lift and drag from wall proximity experiment. . . . . . . . 65 5-4 Triggering the vortex street at different points 67 5- 5 Photograph of triggered vortex street 70 6- 1 Relative positions of cylinders where data is collected . . 74 6-2 Example of four signals collected in a run . 75 6-3 Information extracted from signals 78 6-4 Examples of unperturbed forces on both cylinders 80 6- 5 Example of how relative FFT amplitudes are obtained 82 7- 1 Drag on the principal cylinder vs relative positions of both cylinders. . 84 7-2 Interference lift of principal cylinder vs positions of both cylinders.... 87 7-3 Shedding frequency of principal cylinder vs relative positions of cylinders. 94 7-4 Principal cylinder lift vs control cylinder positons at yc = Q.OD 98 ix 7-5 Principal cylinder lift vs control cylinder positons at yc = 0.5D. . . . 100 7-6 Principal cylinder lift vs control cylinder positions at yc = I.O.D. . . 102 7-7 Principal cylinder lift vs control cylinder positions at yc = 1.5D. . . . 104 7-8 Principal cylinder lift vs control cylinder positions at yc = 2.0D. . . . 106 7-9 A(f0) from FFT of control cylinder vs relative positions of both cylinders.Ill 7-10 FFT of control cylinder vs control cylinder positions for xc = 0.0D. . 112 7-11 FFT of control cylinder vs control cylinder positions for for yc = 1.0D. 113 7-12 FFT of cc vs relative position between cylinders for misc separations. 114 7-13 Sphere of influence of principal cylinder 116 x N O M E N C L A T U R E Uoo velocity of fluid at infinity D diameter of the principal cylinder D* effective diameter of compound body 8 phase constant d diameter of the control cylinder p fluid density v viscosity of fluid Re Reynold's number: (^) S Strouhal number: ) Fry perturbed drag force on the large cylinder Ft drag force on the small cylinder CD drag coefficient Fi offset (interference) lift Fi perturbed lift force on the large cylinder F\ lift force on the small cylinder f0 lift frequency on large cylinder fi lift frequency on smaller cylinder t* nondimensional time (^jjr) xc the x coordinate of control cylinder yc the y coordinate of control cylinder xi Chapter 1 Introduction 1 C H A P T E R 1 INTRODUCTION All solid objects moving through a fluid at some relative velocity Uoo expe-rience drag forces parallel to the direction of relative motion, ^f•. Depending on its geometry and the magnitude of UQO, an object may also experience a constant or time varying lift force. For circular cylinders of diameter D, which are towed in a certain velocity range, a wake flow develops where vortices are shed on alter-nate sides and the lift force consequently oscillates at the vortex shedding frequency Lift and drag affect both animals and man made objects profoundly since most activities of living beings and technical structures interact with flow fields in air, water or some other fluids. Lift and drag allow birds to fly, make flags flutter in the wind, slow down fast cars, toss boats around in swift currents, give action to fans and propellers and let aquatic animals move through the water. As lift and drag act on a body, a reaction force is exerted onto the surrounding fluid, which deflects fluid elements out of their paths and modifies the flow in the vicinity of the object. The perturbed flow extends in all directions around the object to some distance, A(x,y,z). For instance to the side of the object, the speed of the fluid might be modified up to a few body diameters before it returns to the Chapter 1 Introduction 2 velocity of the free stream. One may think of this perturbed region as a volume with a surface described by A(x,y,z). Outside of this sphere of influence, the fluid behaves as if no object was present, but inside this sphere of influence, the flow differs from the free flow conditions. However, the lift and drag on the object are uniquely associated with the free stream velocity Uoo. When two objects are made to travel within each other's sphere of influence, they no longer experience the free stream conditions and their lift and drag may be modified. The effect of two objects close together cannot be determined by superposition of their individual isolated flow fields. The two objects therefore interfere with each other's motion over a distance. They no longer move as if they were isolated in the free stream. Motion in a fluid therefore implies action at a distance. Action at a distance is known from the interference of two objects of equal size and similar geometry, as well as from the phenomenon of blockage. This thesis looks at different examples of action at a distance, namely the interaction of two circular cylinders of different diameters and the interaction of a cylinder with a flat plate in various arrangements. Action at a distance modifies both the lift and drag of each one of the objects. For the drag, this implies a variation in magnitude. For the oscillating lift, action at a distance can change the amplitude, the frequency and the phase. The lift signal may also be offset by a certain amount due to interference effects between objects. Action at a distance is a hallmark of all force fields. For instance, the field of an electric charge extends to infinity. However, in many physical situations, fields are not extended to infinity. The fields of electrons in a plasma are shielded over a distance called the Debye length. The viscous force field in a real fluid decays over the width of the velocity boundary layer. At large Reynolds numbers viscous effects Chapter 1 Introduction 3 become negligible. According to potential flow theory, an object imbedded into a flow should make its presence felt up to infinity in the lateral direction. Figure 1-1 shows the streamlines for the potential (inviscid) flow past a circular cylinder. The streamlines clearly have a radius of curvature of and do not become exactly straight lines or freestream streamlines until infinity. However, it is likely that there is a practical cut off distance beyond which no signals from an object penetrate into the surrounding fluid, corresponding to the Debye length in plasmas or the collision cross section of kinetic theory. As an illustration, Figure 1-2 shows the flow field around a cylinder at a Reynolds number of « 10,000. To the knowledge of the author and collaborators, there has not been any reported experimental investigation into the nature of action at a distance. No one has attempted to determine the radial dependence of a force field in the fluid flow around an object. Nor has anyone examined the phase relation between lift and drag forces on two objects, the variations of amplitudes of the lift and at its effects on frequencies of vortex shedding. Only very few experiments have been done at all with two objects of different sizes. They are reported in section 2.3. An understanding of action at a distance in fluid flow would fundamentally explain blockage, why tall buildings should not be built too close together and other engineering problems like the galloping transmission lines and twin smokestacks in the wind. In this thesis, action at a distance was studied by measuring from startup in a towing tank, the lift and drag of two cylinders of different diameters. By defining amplitudes, offsets, frequencies and phases, various aspects of action at a distance were mapped out, namely the region where the onset of vortex shedding can be affected, the region where drag changes from its isolated free stream value, Figure 1-2. Flow around a flat plate at subcritical Reynolds numbers. Chapter 1 Introduction 5 and the region into which signals of pressure fluctuations of the vortex shedding penetrate into the laminar flow outside the wake. There is nothing to suggest that these surfaces are identical in shape. In fact, Zradkovich [31] noticed that the interference lift and drag of two circular cylinders extend out to different distances. These regions are in general three dimensional surfaces. For cylindrical objects they become cylindrical surfaces with cross sections elongated in the flow direction which could be shown as a contour line as in Figure 7-2. As the simplest figure of merit of these regions, one may define an impact radius, A, sketched in Figure 1-2, outside of which free stream conditions are found. The experiments were carried out in a 1 x 1 x 5m towing tank system (Figure 1-3) which is described in Chapter 3. A novel lift and drag .measurement system was developed to measure these forces with good time resolution. This is described in Chapter 4. This system was tested initially on a single cylinder the results of which are described in Chapter 5. The results of this thesis are based on the analysis of about 800 runs which are detailed in Chapters 5 and 6. In order to appreciate the mutual interaction between the two objects it was considered necessary to first review what is known about related topics. First the large body of knowledge on the fluid dynamics of single cylinders (Chapter 2) is summarized, secondly, the case of flow around two cylinders of equal size is examined and finally, the much sparser results of flow around cylinders of unequal diameters are reviewed. Chapter 2 Fluid Dynamics of Circular Cylinders 7 C H A P T E R 2 FLUID DYNAMICS OF CIRCULAR CYLINDERS 2.1 A Single Circular Cylinder As a starting point for the study of the interaction of two circular cyinder of different sizes, the flow around single cylinders must be well understood. The fluid dynamics of a single circular cylinder has been studied extensively for over a hundred years. Here, reference is made to the recent works of Gerrard [10] and Roshko [21]. Flow past a circular cylinder can be produced by moving a fluid past a sta-tionary cylinder as in a wind tunnel or by a cylinder moving through a stationary fluid in a towing tank. The flow in this experiment is produced by towing a circular cylinder through the length of a water tank (see Figure 1-3). Information has been gathered about the flow by pressure/force measurements and by direct visualization. The best understanding comes from correlating the information from both types of experiments. The flow in this work is described by a coordinate system with the s-axis in the towing direction, the z-axis parallel to the cylinder axis (spanwise direction) and the y-axis perpendicular to the plane formed by the x and z axis. Therefore, the two dimensional flow fields studied here are in the x — y plane. Chapter 2 Fluid Dynamics of Circular Cylinders 8 Parameters of Flow Experiments Flow fields can be generally characterized by the nondimensional Reynold's number, Re = (^p) , where U is the free stream velocity, v is the viscosity of the fluid and D is some length measurement (diameter in this case). The resulting flow downstream of the circular cylinder is strongly dependent on Reynolds number. Usually, the following regimes are distinguished: Re < 5: The flow is described as creeping motion with no eddies or vortices downstream of the cylinder. The fluid goes around the fluid smoothly and closes again immediately behind the cylinder. 5 < Re < 50: The laminar flow separates on the cylinder and encloses a stable vortex pair (the Foppl vortices) attached to the cylinder followed by a laminar wake of low amplitude and frequency 40 < Re < 150: The regime where the vortex street is laminar. 60 < Re < 5000: Starting at a He number of about 60 an oscillating wake appears as the Reynolds number is larger . This oscillating wake increases in amplitude and starts to roll up into distinct vortex patterns. The wake is not stable anymore. If the cylinder starts from rest, there is initially a large spike in the drag force which is asociated with the formation of a pair of vortices (Foppl vortices) behind the cylinder. An instability in the flow will cause one of them to shed first and the other to follow and swim away with the flow. New vortices then form alternately and also detach as the lift and drag forces settle down to the steady state values. This is the Karman vortex street. Chapter 2 Fluid Dynamics of Circular Cylinders 9 Re > 5000: The wake behind the cylinder can no longer sustain the laminar shed vortices, it is completely turbulent. The experiments in this thesis fall into the Reynolds number range 2000 — 8000. Figure 2-2 shows what visualization experiments would yield for the above ranges of Reynolds numbers. Force Measurements As a circular cylinder is towed through a fluid the motion of the fluid around the cylinder produces lift and drag forces. The drag force is the integral of the streamwise, x, components of the surface pressure and the lift is the integral of the transverse, y, forces. Similarly, the integration of the streamwise component of the shear force over the cylinder is the skin friction drag. In the Reynolds number range of this work, pressure drag dominates over skin drag so that the measured drag is assumed due to pressure forces. Figure 2-3 is an example of the lift and drag measured on a circular cylinder of diameter D which is started from rest and is quickly accelerated to the speed Uoo • The time scale is divided into units of t* = ^ and is measured from the start of the cylinder's trip across the tank. The drag and lift forces acting upon the cylinder are assumed to be propor-tional to the dynamic pressure, \pUl0 of the undisturbed flow and the projected area of the cylinder to the flow. The proportionality constants Cry and CL, are called the drag and lift coefficients respectively. The relationship for these average forces can then be given in the form: FA 'rag — x projected area x CD (2.1a) Flift = x projected area x Ci (2.1b) Chapter 2 Fluid Dynamics of Circular Cylinders 10 These lift and drag coefficients are empirically obtained and are influenced by such factors as end effects, surface roughness, body bluffness, geometry, Reynolds numbers and other macroscopic effects. Figure 2-l(a) shows the drag coefficient CD over a wide range of Reynolds numbers for an infinitely long cylinder (a cylinder with a length to diameter ratio of 12 or greater). In the intermediate range of Reynolds numbers where a steady von Karman street is generated, the lift is a periodic force that oscillates at the vortex shedding frequency with amplitude F. Its average value is zero for a single cylinder, but it differs from zero if there are other objects nearby. It is this amplitude that is obtained from equation (2.1b). Equation (2.1b) does not reveal the details of the lift force's sinusoidal character. When the cylinder is started from rest initially, the lift signal has a low frequency and low amplitude but as the flow becomes more developed 4ts sinusoidal character is revealed. The lift signal builds in amplitude and frequency until it reaches its steady state in amplitude and frequency. This may occur within a few units of t* or it may be entirely suppressed. The startup time is highly dependent on flow conditions like turbulence level and viscosity. Through many experiments, it has been found that the vortex shedding fre-quency, f0 is proportional to ^fr, that is: / • = T T (2-2) The proportionality constant S is often called the Strouhal number. S has been measured over a wide range of Reynolds numbers, from Figure 2-1(b) it is noted that S changes very little in the range 102 < Re < 106. It is easily treated as a constant. Reynolds number Figure 2-1. Fluid dynamic quantities of a circular cylinder (a) CD VS Re (b) S vs Re. Chapter 2 Fluid Dynamics of Circular Cylinders 12 When the vortex street is fully developed the drag force is mainly constant with small fluctuations superimposed on it. These fluctuations have a predominant frequency component of two times the lift frequency [10]. One must keep in mind that the cylinder is towed across the tank starting from rest. This means that until the cylinder reaches its final velocity, Uoo, it is in an accelerated flow. The lines of action of the drag and lift may not always go through the cylinder axis so that a moment may result producing a torque on the circular cylinder. The torque however, is small and could not be measured with the available equipment. 2.2 Two Identical Circular Cylinders The circular cylinder discussed in the last section could represent a chimney buffetted by winds, the pole of an offshore rig in an ocean current or a similar fluid problem. The single cylinder model would describe the situation correctly if the chimney or pole was isolated in the flow and all other structures were located far away. Far away means that all other objects must be located outside the sphere of influence. When objects are too close together their force fields interfere mutually. The early work in flow interference was driven by interest in aeronautics in such areas as fuselage-tail interference, mutual interference between parts of aircraft, interference drag of fuselage bodies, body-wing interference, wing-nacelle configu-rations, etc. A very good perspective of flow interference between two cylinders is given by Zradkovich [32] to 1977. Other workers in this field include Spivack[27], Hori [12], Bearman and Wadcock [7], The bulk of the work done by these researchers is for identical circular cylinders. Strykowksy and Sreenivasan [28] used cylinders of different diameters but at laminar Reynolds numbers. These papers contain Chapter 2 Fluid Dynamics of Circular Cylinders 13 Re < 5: regime o f unsepara ted o r potential flow 5 < Re 40: a pair o f Foppl v o r t i c e s in the wake and a t t a c h e d t o the cylinder 40 < Re < 150= v o r t e x s t r e e t is laminar 300 < Re < 300,000 v o r t e x s t r e e t is completely turbu lent 300,000 < Re < 3,500,000 • laminar boundary layer undergone turbulent transit ion and wake is narrower and disorganized Re > 3,500,000* turbulent v o r t e x s t r e e t is r e - e s t a b l i s h e d Figure 2-2. Flow past a circular cylinder at different regimes of Reynold's numbers. Figure 2-3. The forces on a circular cylinder: (a) lift (b) drag. now 7 %-\ © *-<^ ® / A"\ - \ \ /V®V © / © W *«>• • to* - - 1 a L / D / ® \ k~L • \ © / ^ ^ ^ Figure 2-4. Interference force coefficients for two identical cylinders from reference [12]. Chapter 2 Fluid Dynamics of Circular Cylinders 15 some important background which is summarized in the following sections on equal diameter cylinders and unequal diameter cylinders. There are many ways that two identical cylinders can be arranged in a flow configuration. They can be divided into two groups according to their spacing. In the tandem arrangement, one cylinder is directly behind the other with some longitudinal spacing between them. In the side by side or transverse configuration, both cylinders face the incoming flow sided by side with some transverse spacing between them. All other configurations which are combinations of the side by side and tandem are referred to as staggered. Researchers define an interference drag coefficient as a measure of the mutual interference between the two cylinders. Two cylinders, 1 and 2, that are in close proximity to one another, usually present a combined drag D\+z which may be larger or smaller than the sum of the individual drag components (D\ + D2), each measured in a free flow. The difference AD = D1+2 — (Di + Di) is the interference drag. In the most general arrangement, the cylinders are staggered, (Figure 2-5), and have different diameters. Unfortunately, the least amount of work has been done in this configuration. Hori [12] has produced some extensive systematic results for the lift and drag coefficients from surface pressure measurements. His results are summarized in Figure 2-4. For cylinders of equal diameters, he rotated the cylinder pairs and presented them in staggered arrangements to the flow for the spacings L overD = 1.2,2 and 3D (where L = \Jx2 + y2 is the total center to center separation between cylinders) . Depending on the relative position of both cylinders, he found that the interference forces between them may have attractive or repulsive components. To summarize his results, Figure 2-4 shows one of the Chapter 2 Fluid Dynamics of Circular Cylinders 16 cylinders location at the origin of the coordinate system while the other is centered at various point in the surrounding plane. At some points, the drag is greater and at others the drag may be smaller than that of an isolated cylinder. Likewise the lift may be positive (repulsive) negative or negligible. The upstream cylinder can be in one of three possible regimes: 1. negligible lift, reduced drag 2. small repulsive lift, reduced drag 3. repulsive lift, increased drag The downstream cylinder can be placed in any of the aforementioned three positions and: 4. negligible lift, increased drag (a very small region beyond which there is no interference 5. negative lift, decreased drag (main region downstream) A special case of staggered cylinders is the tandem arrangement when one cylinder is directly in front of the other. Hori found only the rear part of the upstream cylinder is affected by the presence of a downstream cylinder. The base pressure coefficient (namely the average pressure, p at the rear stagnation point) increases with longitudinal spacing between both cylinders. As a result, the drag of the upstream cylinder decreases. For the downstream cylinder, the side facing the upstream cylinder has a low negative pressure with a magnitude roughly equal to p. This is an indication that the flow activity in the gap is very small. The downstream cylinder experiences a negative drag or thrust force that pulls it toward the upstream cylinder. Chapter 2 Fluid Dynamics of Circular Cylinders 17 The lift on cylinders in tandem reflects the formation of vortex streets on each one of them. At low Reynolds numbers (60), a vortex street forms behind the downstream cylinder only for spacings greater than about 4 diameters. Beyond that spacing, the vortex shedding appears suddenly and quickly reaches its single cylinder state. In the intermediate subcritical Eteynolds numbers, the upstream cylinder was not observed to be shedding vortices within the 4 diameter separation. For the downstream cylinder, at the same Reynolds numbers, vortex shedding always oc-curred. For longitudinal separations in the range 1 < ^ < 3.8, the Strouhal number was observed to decrease from values much higher than the single cylinder to much lower than the single cylinder. A discontinuity occurs in the Strouhal number of the downstream cylinder at the spacing where the upstream cylinder starts to shed vortices. Therefore, there are two flow patterns: 1. No vortex shedding behind the mjpstream cylinder and strong influence on the shedding of the downstream cylinder. The flow separating from the upstream cylinder reattaches to the downstream one and inhibits vortex shedding behind the upstream one. 2. Vortex shedding behind both cylinders with the shedding of the upstream cylinder strongly affecting and .synchronizing sihedding behind the downstream one. Another special case of staggered cylinders is the side by side arrangement. Biermann and Herrnstein |8] jneasured the drag force on the two cylinders in the transverse configuration. They found that the interference drag coefficient became Chapter 2 Fluid Dynamics of Circular Cylinders 18 zero for spacings greater than 5 diameters. From 5 to 2.5 diameters, the interference drag coefficient increases. At less than 2.5 diameters the flow pattern acquires a bistable nature and may not duplicate itself from run to run even at a constant spacing. Information about vortex shedding and lift was obtained by Spivack [27]. He found that for spacings greater than 2 diameters a single frequency existed in the wake of both cylinders which was the same as that for the single cylinder. The shedding was in phase across the two cylinders. At less than 2 diameters, 2 frequencies were found in both wakes. The upper frequency disappears for spacings of less than 1.4 diameters and the lower one remains until the two cylinders touch. In the 1.4 to 2 diameter spacing the gap flow is biased to one side. As a result, wide and narrow wakes are formed behind the cylinders, the wider wake giving lower frequencies and the narrower wake giving higher frequencies. When the spacing becomes less than 1.4 diameter, the two cylinders behave like a single body and shed at one frequency. This frequency is half that of the single cylinder so effectively the diameter of the object has been doubled. At such small diameters, the gap flow is very weak. 2.3 Two Circular Cylinders of Different Diameters The work on staggered cylinders of equal size extends over a large Reynolds number range. In contrast, for cylinders of different diameters, there are the experi-ments by Strykowski and Sreenivasan [28] who worked at very low Reynolds numbers Chapter 2 Fluid Dynamics of Circular Cylinders 19 and Novak[19] who investigated tandem cylinders at higher Reynolds numbers. No experiments on staggered cylinders at higher Reynolds numbers have been done. Strykowski and Sreenivasan used cylinders with diameters that differed by factors of 4, 8 and 16. They were interested in the complete suppression of vortex shedding from the large cylinder caused by placing the smaller cylinder downstream at low transitional Reynold's numbers of 40-80 (with Reynolds number based on the larger cylinder). These regions of suppression widened with increasing D/d. They referred to the larger cylinder as the vortex shedding cylinder and the smaller one as the control cylinder. They did not measure the drag force of the large cylinder or the drag or lift on the small cylinder. They viewed the smaller cylinder as a perturber rather than a body causing its own flow field. The presence of this perturbing cylinder has the effect of locally reducing the Reynold's number, hence the total suppression of vortex shedding. In this thesis, freestream velocities are used where both cylinders shed vortices, therefore, Sreenivasaan and Strykowsky's terminology has been modified in this thesis. The small cylinder is called the control cylinder but the large cylinder here is referred to as the principal cylinder (see Figure 2-5). Novak [19] reported, his tandem measurements in the range 4500 < Re < 14,000 for two cylinders with relative diameters of 2. He found that when the small cylinder was upstream, it did not start shedding vortices until it was 2.25D away from the big cylinder. A big downstream cylinder would shed vortices at all longitudinal spacings. In the reverse experiment, with the large cylinder upstream, the small cylinder could not suppress the bigger upstream cylinder's shedding no matter how close it was. On the other hand, the big cylinder upstream would suppress vortex shedding of the small one for longitudinal spacings up to 7D. Lefrancois [16] reproduced some of the results of Sreenivasan and Strykowski at higher Reynold's numbers. He measured drag at a few points only. His results Chapter 2 Fluid Dynamics of Circular Cylinders 20 c o n t r o l c y l i n d e r <diameter=0.25D> <d iameter=D) Figure 2-5. Schematic of setup for two cylinder experiment. Chapter 2 Fluid Dynamics of Circular Cylinders 21 indicate regions of suppression occurring downstream and found regions of increased drag for cylinders arranged side by side for Reynold's numbers of 2200, 4500, and 5400. However, his measurements suffered from low sensitivity. This thesis is an extension of his work. 2.5 Thesis Strategy This short review shows that two objects in a flow can affect each other's lift, drag and vortex shedding. The objective of this thesis is to measure these 'actions at a distance' with good time resolution for two cylinders of different diameters placed in each other's vicinity. No similar work has been reported in the literature. Before embarking on a measurement program of staggered cylinders in a towing tank the theme of this thesis must be more clearly developed. Action at a dis-tance or interference between objects in a flow requires a good understanding of the sphere of influence mentioned in the introduction. The phrase refers to the range of separations over which a particular object can affect or be affected by another. In plasma physics this would correspond to the Debye sphere which determines how closely two charges can be placed without affecting one another. Where is infinity? The sphere of influence of a circular cylinder in a two dimensional flow could be denned as the locus of all such closest points of noninterference in all directions. This would map out a generalized surface rather than a sphere since the location of infinities is not necessarily symmetric. The sphere of influence is seen in the phenomena of blockage whereby the proximity of walls affects the drag and lift forces of an airfoil in a small wind tunnel Chapter 2 Fluid Dynamics of Circular Cylinders 22 or a large ship in a small canal. Blockage is a phenomena that has been treated empirically. There are methods to calculate corrections for blockage but a more fundamental understanding is lacking. The sphere of influence of a single cylinder can be determined to some ex-tent from existing data. Drag coefficients have been compiled to show the single cylinder's changing drag as it approaches a wall [24]. This information shows that the single cylinder can feel the wall as far away as about 3-5 cylinder diameters in the transverse direction. With proximity to a cylinder of the same diameter, the circular cylinder can feel out to 3 cylinder diameters for angles from 0 to 50 degrees measured from the forward direction. The aim of this thesis is to gain an understanding of action at a distance. To that end, lift and drag on staggered cylinders of different diameters have been determined. These force measurements are augmented with time correlated flow visualization. The usual approach is to measure averages of the drag and the lift. An average of the drag force will give its dc component and a rough idea of the force. An average of the lift force is does not reveal anything about the ac component. There is too much information lost when the relative phases of the forces are disregarded. The lift force amplitude may be very large but its average will not reveal that. For that reason in this thesis, Fuft and Firag are measured as function of time with good frequency resolution so that amplitude, phase and phase lags can be resolved. There are three components to the experimental approach: flow visualization, force measurements and correlation. Chapter 2 Fluid Dynamics of Circular Cylinders 23 Flow visualization is concerned with the acquisition and processing of flow field pictures. Flow visualization data will determine the sequence of events in terms of vortex dynamics. Interpretations of CD and CL nxay be made in terms of the flow activity. The information will be mostly qualitative in nature. Force measurements are concerned with the measuring of lift and drag forces on both cylinders simultaneously. The action of the flow on the cylinder is directly transduced to an electrical signal The final result is time resolved simultaneous traces of lift and drag on both cylinders. These measurement would relate the phase of the lift and drag forces, determine Strouhal number and vortex shedding frequency. The spectra of the signals will yield useful information about the fre-quency components in the flow field. The information here is mainly quantitative. Both flow field pictures and time resolved force measurements must be corre-lated in time. To follow this general approach, lift and drag on both cylinders have been mea-sured in a flow of Reynolds numbers = 8000 (based on the diameter of the larger cylinder) with diameter ratio, ^ = 4. The measurements have been done sys-tematically for tandem, transverse and staggered arrangements for both upstream and downstream configurations. They were time correlated with flow visualization information. To achieve these ends, a force measuring system with accuracy im-proved over Lefrancois' [16] was developed. A data acquisition system was built and assembled around this force measuring system. With the results of about 800 individual runs, it was possible to 1. map out the force regions around the large cylinder when the smaller one is close by; 2. to see if the small cylinder takes on a disproportionately large force when the large cylinder shows a suppression in drag or vortex shedding, so that the sum of the drag on both cylinders is independent of their mutual positions; 3. to compare these results with Hori's [12] identical Chapter 2 Fluid Dynamics of Circular Cylinders 24 cylinder experiments; and 4. to study the phase relations of vortex shedding off both objects and to develop further the concept of sphere of influence in fluid flow. The results can be presented as contour maps in the x — y plane which show the magnitude of the particular action at a distance as a function of the relative position of the two cylinders. Usually, the principal cylinder is shown at the center of an x — y plot and a number at any point in the four cartesian quadrants indicates the magnitude of the effect on the principal cylinder if the control cylinder is located at that particular point. Figure 2-6 is a summary of the experimental approach to be taken. The ex-periment requires a versatile towing tank and an extensive data acquisition system. The next chapter describes how the data acquisition system was developed and incorporated into the existing tow tank at the UBC Physics Department. DATA ACQUISITION PROCESSING RAW DATA FINAL PRODUCT FLOW VISUALIZATION Records flow field activity on filn Digitize franes and store in memory Picture of the flow field CORRELATION Counters and switches used in film and trace of the forces Computer matches up each frame with points on force traces Flow field correlated with forces FORCE MEASUREMENT Record lift & drag in memory Filter and threshold Simultaneous trace of lift & drag Figure 2-6. Block diagram of experimental approach. Chapter 3 Experimental System 26 C H A P T E R 3 EXPERIMENTAL SYSTEM 3.1 Tow Tank System The two dimensional turbulent flow field for these experiments is generated by towing circular cylinders, with their axes perpendicular to the direction of travel through the fluid . The fluid is water at room temperature, one atmosphere, and contained within a rectangular towing tank of dimension 1 x 1 x 5 m. What must be measured are lift and drag forces on the towed cylinder(s); these measurements correlated with either videos or long exposure photographs of the flow around the cylinder(s). In addition, veloctiy, U<x>, and fluid quantities like temperature are monitored. The tow tank system and camera system is shown in Figure 3-1. Straddling the top of the tank is a cart on a pair of guide rails. This cart is driven by a 1/2 Hp variable speed motor via pulleys and can tranverse the entire 5m length of the tank in both directions. Through a proportional control of the motor speed and by changing the belt sheaves on the gear system, towing speeds ranging from 2 to 60 cm/s are possible. Chapter 3 Experimental System 28 Along the bottom of this tank runs the underwater platform. It is driven by the same 1/2 Hp motor and gearing system as the cart above. It can be made to run either parallel or antiparallel to the cart at the same speed. The cart and underwater platform can also each be run alone. At either end of the tank are photo-eye limit switches in the normally open (NO) position and dead stops. When the photo-eye is blocked by the wheel of the upper cart it turns off the motor. The dead stops physically prevent the upper cart from getting too close to the walls of the tank. These safety devices are mainly a protection against operator inattention. The limit switches can also be placed at different points along the tank making it possible for the cart and/or underwater platform to travel the same distance repeatedly when necessary. The cylinders can be attached to the cart and/or fixed to the underwater platform to reduce pressure losses due to end effects. If the cylinder is mounted at the bottom, it has for all purposes no 'free end' and can be treated as an infinite cylinder. 3.2 Data Acquisition System To measure lift and drag as a function of time and correlate these data with video equipment, a complex data acquisition system was developed. It is shown in block form in Figure 3-2. The system has three components: flow visualization, force measurement and time correlation Flow visualization is accomplished with video cameras and/or a 35mm camera which can either be mounted on the cart or at the ceiling of the lab. Observations can hence be made in two possible reference frames: XT C O M P U T E R n i V I D E D D I G I T I Z E R S Y N C S T R O B E C O U N T E R 1 2 B IT A D C V C R C A M E R A F O R C E S E N S O R S V E L O C I T Y Figure 3-2. Block diagram of data acquisition system. Chapter 3 Experimental System 30 1. the laboratory reference frame: fixed to a point that is stationary relative to the towing tank (since vortex dynamics are of interest , the camera will mostly be in this reference frame) like the laboratory ceiling. 2. the object reference frame: fixed to the upper moving cart The flow patterns of the towed cylinder(s) are made visible by sprinkling aluminum filings (« 0.5mm length) as tracers on the surface of the water. The illuminiation is provided by 4 flood lamps (75W 120V). They are mounted just outside the field of view and close above the water surface so that glare and reflection from the bottom of the tank is minimized. The flood lamps' intensity can be individually varied through VARIAC power supplies. Two Minolta photographic cameras (models 570 and 700) are used for long exposure pictures of the flow field. They are equipped with motorized rewinds so that consecutive pictures of a set exposure time can be taken as rapidly as 0.42 seconds apart; 400 ASA film is used. A Hitachi Color (VK-C830) and a Hitachi Solid State black and white (B/W KP-120) video camera were used. The video camera proved convenient in the early stages of correlating force measurements and flow observations since it records at 30 frames per second thereby improving the resolution of the time correlation with forces measurements. Video films also facilitate the superposition of the frames to achieve long time exposures whereas this is not possible with a photographic camera. In the end, what is produced is a binary black and white "picture" of the flow that can be easily recorded and photocopied. By varying the lighting conditions, camera aperture and tracer density it is possible to obtain streaks that appear at the same intensity to the camera. Figure 3-3 is an example of the vortex shedding sequence of a single cylinder. Six frames were serially superimposed to produce Chapter 3 Experimental System 31 the sequence of binary images shown. Experimentally, the tracers often reflected towards the camera at uneven intensities. However, the digitizer compensates for this by selecting a band of pre-set intensities so that the digitized pictures neither look too exposed or underexposed. The video cameras are interfaced with a Hitachi VHS video cassette recorder (VCR) in order to record the flow activity. The VCR records flow pictures at a rate of 30 per second onto 60 minute length Fuji videocassette tape. The VCR is also used in the editing and digitizing stage of the data reduction . During the digitizing process, the VCR is interfaced with the computer so that the experimenter can select the frames which are to be processed. An 8 bit gray scale video digitizer with 64 grey levels and a resolution of 244 X 256 pixels coupled with the computer is used to digitize the film recorded on VCR tape so that it can be stored on the hard disk drive of the computer as an ASCH or binary file. Then, the computer is used for the image processing of the final picture. It is also easier to store and recall the frames if they are stored in the computer memory. The flow visualization equipment complements the main objective of this the-sis which is the measurement of lift and drag on the two cylinders. Two different systems were built to measure lift and drag of the vortex shedding cylinder and the control cylinder. They are described in detail in the next chapter. Here it suffices to mention that there are four forces to measure simultaneously at any one time. The mechanical forces are transduced to an electrical signal. The four electrical analog signals are digitized and stored by the computer. A good measuring system is required to minimize noise, end effects, flow interference etc. The information from force measurements and flow visualization must be time correlated. This was accomplished by a 30 Hz counter and LED synchronizing Figure 3-3. Example of superposition of frames used in video analysis. Chapter 3 Experimental System 33 strobe. If video cameras are used for the flow visualization, the LED display of a 30 Hz counter appears in the field of view. This allows each frame of the video to be uniquely labelled with a number up to 5 digits long. In addition a red LED can be strobed ON in the camera's field of view for a designated duration. The red LED sets the counter since the computer receives a pulse for the duration the LED is turned on in the field of view with whatever 5 digit number that appears. The computer simulataneously digitizes the signal from the 30 Hz counter, the LED strobe, and all four transducer signals. The computer then matches up the counter pulses and the signals and in effect matches up the flow field pictures with a point on the four traces. At the heart of the data acquisition system is the data acquisition computer, an 8088 XT compatible with 10 MHz clock, 640K RAM, and math co-processor. The computer ties together the flow visualization, force measurement and correlation branches of the experiment. It is used to digitize and store the analog signals transduced by the cylinders, the counter and synchronization pulses, and the frames from the VCR tape. It is also used for later analysis and intrepretation of the data. The 10 bit analog to digital converter with 8 A/D and 2 D/A channels (DT2805) is a card that resides on the motherboard of the data acquisition com-puter. This card makes the data acquisition system powerful by letting it store electrical signals from many different channels simultaneously for later analysis. The signal resolutions are no longer limited by the resolution of a plotter output or oscilloscope picture. This analog to digital converter has 8 channels which it can digitize at a cumulative maximum frequency of 1200 Hz. The digitizing of the channels are multiplexed. The allocation of A/D channels for the card are: 1. drag on principal cylinder; 2. lift on principal cylinder; 3. drag on perturbing cylinder; Chapter 3 Experimental System 34 4. lift on perturbing cylinder; 5. 30 Hz counter; 6. sync pulses; and 7. velocity sensor. The towing velocity of the cylinders is determined for every run taken by the 'time of flight'. It provides only an average velocity but for this experiment, it is adequate. An optical pickup with a 10 msec counter is used to determine the time taken for the moving object to travel a known distance. The points are chosen far enough downstream that the acceleration is constant. The points are marked out with two highly reflective bands on a pulley wire (that passes over the optical pickup) that is driven by the \ Hp motor. The counter is toggled ON by the first reflective band and OFF by the second. The clock once stopped cannot be restarted by another band. It is restarted again by toggling an SPST mechanical switch. The signals from the optical pickup are also used to strobe the shutters open on the photographic cameras. The level of turbulence in the tank has never been measured but, the turbu-lence level in the towing tank can be kept constant from run to run by waiting a constant interval between runs. One can also wait a very long period of time to have an almost zero turbulence level. In general, most runs are performed 10 minutes apart. The viscosity of the water in the towing tank is determined by monitoring the temperature of the water every hour. From the temperature, the viscosity is obtained by looking up the viscosity tables for water [9]. Temperature is measured with a regular mercury thermometer which is always suspended under water. The water in the tank is changed every day when experiments are performed. 3.3 Software Chapter 3 Experimental System 35 Data acquisition software was needed to control the analog to digital card used in data collection. The needs were highly specific so they were developed within the group by M. Lefrancois. The program Collect coordinated the multiplexing and timing of digitizing 4 data channels, 2 synchronization channels and the velocity channel. It allowed control over parameters such as sampling frequency, channel selection, sampling interval, gain control, saving of data files, viewing of last and collected data files. In addition, it can do a fast Fourier transform to show the frequency spectrum all data channels. See Figure 3-4(a) for the of menu screen. Digit is used in interfacing between the video digitizer, VCR and computer. This program was also highly specific in need and was developed by M. Lefrancois. Digit is used when video data are to be digitized frame by frame and saved onto computer memory. It is used as an editor to control which frames are to be displayed to the video digitzer. Option VCR emulates the hand control that comes with the VCR. Grab does the job of frame grabbing, viewing and storing. There is also some image processing facilities in the program like thresholding, pixel removal, filtering, etc. Figure 3-4(b) is the menu screen of this program. A data reduction program was needed that allowed easy viewing, database like abilities for the transduced force signals, easy manipulation of ASCII files and demultiplexing of the individual channels. LOTUS 123 © was used to this end. Another data reduction program was necessary to perform 4096 point FFTs and easily plot and access ASCII files. In addition, other facilities like curve fitting, matrix operations, etc. were needed. The commerically available mathematical scatchpad program Matlab ©was used. Program proc, trial, acamp were written in Matlab to automate the data analysis. Program avgmax was used to automate the amplitude finding of the drag signals. Their listings can be found in Appendix 2. SE1 GAIN'- 100 SET CHANNELS: 12345 SET FREQUENCY: 300 SET TIME: 18 EXTERNAL TRIGGER: OFF EXTERNAL CLOCK: OFF ANALOG 0: 0.000 ANALOG 1: 0.000 MONITOR INPUTS COLLECT DATA FFT VIEW .DATA VIEW AMPLITUDE VIEW PHASE AXIS ON WINDOW: SQUARE EXIT: ( e s c ) PRINT SCREEN FILE TYPE: BINARY INPUT F I L E : 22-bbase.724 OUTPUT F I L E : DIRECTORY: *.724 19-BBASE.724 4- 00X-10.724 2- 05X-10.724 1-10X-1C.724 6-10X-10.724 5- 10X-05.724 3- 05X05.724 21-BBASE.724 20-BBASE.724 5- 0OX-1O.724 3- 05X-10.724 2-10X-10.724 1-10X-05.724 6- 10X-05.724 4- 05X05.724 22-BBASE.724 1- 0OX-1O.724 fe-OOX-10.724 4- 05X-10.724 3-10X-10.724 2- 10X-05.724 7-10X-05.724 5- 05X05.724 2- 00X-10.724 7-OOX-10.724 5- 05X-10.724 4-10X-10.724 3- 10X-05.724 1-05X05.724 6- 05X05.724 3- 0OX-1O.724 1- 05X-10.724 6- 05X-10.724 5-10X-10.724 4- 10X-05.724 2- 05X05.724 7- 05X05.724 STRIKE HI-LITED CHARACTER TO ISSUE COMMAND d i g i t i z e vcr f i l e s s e t t i n g s gray image b i n a r y image image p r o c e s s superimpose undo p r i n t q u i t c i e a n image edge f i n d b i t s t r i p f i l l / s w e l l wipe a r e a show image le a v e p i x e l q u i t scan backward pause frame advance slow f o r w a r d t h r e s h o l d : 10 upper bound; 50 b i n a r y : OFF c o m p r e s s i o n : OFF q u i t d i r e c t o r y : i n p u t f i l e : o u t p u t f i l e : e r a s e f i l e : s c a n f i l e s : q u i t 19- bbase.724 20- bbase.724 1- OOx-10.724 2- OOx-lO.724 3- 00X-10.724 4- OOx-lO.724 5- O0X-10.724 6- 00X-10.724 7- 00X-10.724 1- 05X-10.724 2- 05X -10.724 3- 05X -10.724 4- 05X-10.724 5- 05X-10.724 6- 05X-10.724 1- lOx-10.724 2- lOx-lO.724 3- 10X-10.724 4- lOx-lO.724 5- lOx-lO.724 6- lOx-lO.724 Figure 3-4. Menu screens of programs used, (a) Collect (b) Digit. Chapter 3 Experimental System 37 The tow tank integrated with the data acquisition system provides the facility in which the main task of this thesis can be carried out: to measure with time correlation, the lift and drag on two objects towed in a staggered arrangement. A major experimental part of this thesis was to design, build and apply a lift and drag measuring system with good sensitivity and time resolution. Chapter 4: Measuring Forces on Cylinders 38 C H A P T E R 4 MEASURING FORCES ON CYLINDERS Many methods have been developed to measure forces in fluid flow. In this study, lift and drag forces have to be measured with time resolution, on both the principal cylinder and the control cylinder, that are towed through the water tank. 4.1 Design Criteria of Transducers Lift and drag measurements must satisfy two fundamental criteria. They must cover the frequency range of signals generated by the fluid and they must not disturb the fluid motion. Firstly, the frequencies of interest in the flow at the Reynolds numbers studied are typically on the order of 0.5 to 4 Hz. The measurement device should allow for possible information up to the second or third harmonic. This means the device should have good dynamic responses at frequency levels up to about 10 Hz. Secondly, the measurements have to be made in such a manner that the setup of the instrumentation does not perturb the flow too much since the vortex dynamics are simultaneously studied. Instruments that are bulky and intrusive and block off the flow field from the cameras cannot be easily used. In addition to these two fundamental requirements, there are some practical limitations of the system. These include (but are not limited to): (a) the device Chapter 4: Measuring Forces on Cylinders 39 must give reproducible results and optimal performance in the Reynolds number range of interest. The forces will be on the order of 0.1 - I N and the sensitivity should be good to 0.02 N (20 g). Ideally, the device should be fast and sensitive; (b) the device must fit into the existing tow tank system with minimal alterations to the system itself; (c) the output signals should be relatively large, linear, hysteresis free, noise free and easily calibrated. Minimal signal processing is preferred since all the physics involved is not fully understood; (d) mV output type resistance bridge force transducers are desired to make it possible to interface with most chart recording systems and so that a voltage source power supply can be used; and (e) the force measuring device must tolerate aluminum tracers in the flow since the force measurement is done simultaneous with the flow visualization. Fortunately, the temperature of the system is constant hence temperature sensitive equipment can be used. Several methods have been used in this lab where strain gauges are the prin-cipal transducing element. However, there have been problems in the past with noisy signals and undesireable vibrations contaminating the signal. In addition, past methods have not allowed both lift and drag to be measured simultaneously and have had problems with end effects. Any new device must resolve some of these past problems. With these de-mands in mind, the traditional systems for force measurements were investigated. 4.2 Methods for Measuring Forces on Circular Cylinders A number of methods have been developed to measure the forces on a circular cylinder when it is in relative motion in a fluid. The forces on cylinders can be ob-Chapter 4: Measuring Forces on Cylinders 40 tained indirectly through a measurement of local velocity or more directly, through the measurement of pressure. The velocity in a flow field is often measured by small point probes to de-termine the velocity profile. This velocity profile is useful in calculating discharge rates or for estimating the drag force by means of the momentum theorem: F = £ ( M 0 - M ) (4.1) Pitot tubes and hot wire anemometers serve as such point probes. The pitot static tube is the basic instrument for measuring fluid stagnation pressures which can be converted into free stream velocities by Bernoulli's principle. In aerodynam-ics, the drag on a particular airfoil is found by drilling small holes on the airfoil surface and measuring the differential pressure, between the stagnation point and the point of interest, using a Pitot static tube. Local velocities in a fluid flow can be measured by hot wire anemometers. The important part of these devices is an electrically heated wire which is normal to a gas stream. The wire cools at a rate that depends on the velocity of the flow normal to the wire. The actual sensing unit is a fine tungsten or platinum wire that is about 6-12 mm long and a few microns in diameter. The-wire is held by a forked probe. The hot wire is connected as a resistor to one arm of a Wheatstone bridge circuit. Hot wire anemometry is useful in measuring small scale fluid motion. It is also used in measuring velocity profiles in the boundary layer because its very small diameter makes any disturbance upstream and to the side of "the probe negligible. However, many velocity probes are needed in order to produce a velocity profile and to yield enough information to calculate a drag -force. Also, the probe Chapter 4: Measuring Forces on Cylinders 41 mounts alter the flow field downstream signifigantly so that these probes are not suitable to measure flow fields upstream of objects. Both Pitot tubes and hot wires are unsuitable for the experiment in mind. The probe points would become major obstacles for the flow field downstream and too many Pitot tubes or hot wire anemometers around the cylinder will cause too much of a disturbance and interfere with the visualization. In summary, there is no suitable method to extract the time resolved velocity field. Hence attention is directed to devices that can measure the lift and drag force acting on the principal and control cylinders directly. Required are transducer elements that transduce forces into electrical signals. Two sensor elements may be considered in this group, piezoelectric transducers and strain gauges. Pressure measurement instrumentation tends to be customized for a particular tank, tunnel or experimental setup. Often researchers purchase a pressure sensor and design/build their own mounts, etc. Commericially available instruments are very bulky and expensive. They are designed to measure relatively high pressures (7 to 200 psi). Some researchers have had some success with commercially available instruments that are very small and can be recessed into the body of the cylinder. The piezoresistance of a semiconductor is described as the change in resistance resulting from an applied strain. This property is exploited to create piezoelectric transducing elements. The semiconductor is in the form of a thin diaphragm namely a thin circular piece of silicon with 4 piezoresistive elements buried in it. Gold pads attached to the silicon allow access to the buried piezoresistive elements. The resistance of the elements changes according to the amount of pressure applied to the diaphragm. The piezoresistor is diffused into a homogeneous single crystalline silicon medium. This integrates the resistive elements into the silicon Chapter 4: Measuring Forces on Cylinders 42 force sensing diaphragm. Silicon is a perfect crystal and does not become perma-nently stretched. After being strained, it returns to its original shape. The silicon diaphragm fails only by rupturing. Their advantages include their compact size and good reproducibility. Their disadvantages include slower response time, high internal resistance, susceptibility to stray electrical signals and they are not appro-priate over large ranges of deflection. The deflections have to be scaled down to the order of the crystal's dimensions. The piezoresistors could be replaced by strain gauges which have a good response time and low internal resistance. However strain gauges have a much lower sensitivity and they would have to be bonded onto the diaphragms. This bond is inherently unstable. Strain gauges have been successfully incorporated into load cells that convert a load into an analog electrical signal. This conversion is realized by the physical deformation of strain gauges which are bonded to the load cell beam and wired in a Wheatstone bridge configuration. Weight, either compression or tension, applied to the load cell produces a deflection of the beam which introduces strain to the gauges. The strain produces an electrical resistance change proportional to the load. Load cells are used to measure forces incident on cylinders by mounting the base of the cylinder on top of the load cell. Their disadvantage for the experiment of interest is that only one load cell can be mounted at a time so that one cannot get both lift and drag. In addition, the cylinders will be towed across the tank so the load cell will also be moving across the tank with the cylinders. This means the load cell will be picking up the noise of the trip superimposed on top of the desired signals. Load cells work very well in wind or water tunnels where the objects are stationary with respect to the lab frame. In the most common application of strain gauges, the resistive element is bonded onto a flexible diaphragm which is strained under the influence of an applied Chapter 4: Measuring Forces on Cylinders 43 pressure or force. This strain produces a change in electrical resistance that is proportional to the force. This change in resistance is measured with a Wheatstone bridge^  To find the drag force on a cylinder, the strain gauges may be bonded onto some member holding the object. The cylinder is then clamped to a mount and towed through the fluid. The forces on the cylinder are transmitted to the mount and the mount senses the forces through strain gauges mounted on it. Lefrancois and Loewen used such drag force measurements in this laboratory. The strain gauge was mounted on a member holding the cylinder. This member was fixed to the cart as it was towed across the tank. Unfortunately, the voltage signals contained too much high frequency noise. In order to remove this strong high frequency noise the signals have to be filtered so much that all pertinent information in the signal is lost. In order to increase the sensitivity, the member that their strain gauges are mounted on would have to be made more flexible. This lowers the resonance fre-quency and it may bring it into the range of expected fluid signals. Also, a flexible support is more susceptible to flow induced vibrations. The alternative is to make the member shorter but the deflections are then, very small producing small signals that require huge amplification and hence are prone to noise again. The problem with this setup is that the strain gauges are mounted on the member that at the same time must bend to yield a strain gauge signal and be stiff enough to resist flow induced vibrations. The noise observed by Lefrancois was due in part to the memory character-istics of the member used. Ideally, the support should be stiff yet the strain gauge should be mounted on a member that ought to be quite flexibe and the whole Chapter 4: Measuring Forces on Cylinders 44 system should have a mechanical resonance well separated from vortex shedding frequencies. In the basic design of Lefrancois, the strain gauge is mounted near or on the member holding the cylinder and is exposed to a three dimensional flow. The flow around the end of the cylinder tends to reduce the pressure upstream and increase it downstream. The drag force decreases as the length is reduced and end effects become more significant. The strength of end effects on a cylinder drag depends on its length to diameter ratio. The cylinder is considered infinite if this ratio is 12 or greater. But because of the coupling of the resonance frequency and the sensitivity, a long cylinder is not desired. A towing tank by its very nature is a mechanically noisy system. Objects are towed for a distance so there is much movement and rattling. The idea is to keep the force instrumentation from picking up this noise and allowing it to override the actual signals from the transduced forces. The points of contact between the transducing elements and the tank were all metal, facilitating noise transmission from tank to transducing element. This is another consideration in any new design. All these facts and considerations lead to a novel design of a lift-drag trans-ducer bar which is described in the next section. 4.4 Design of the Principal Cylinder Transducer The ideal lift and drag transducer should measure a force rather than a mo-ment, have a stiff support, have a small spring constant in the strain gauge di-aphragm, have a resonance frequency well outside the frequency range of interest and require simple or no end corrections. No such system was in existence before this work had started. Figure 4-1 shows the important elements of the chosen design: springs rubber seals spacers core shell s t ra in gauge hragn strain s t e e l gauge ball rubber gaske t shell mylar "sheet 8 C CK) O Co § a. 0) underwater carriage Figure 4-1. Schematic of principal cylinder transducer. Chapter 4: Measuring Forces on Cylinders 46 Two coaxial cylinders with sensing units between them. The inner cylinder can be rigidly attached to the underwater platform at the bottom or at the top by the cart. The outer cylinder/shell is spring loaded onto the inner one. Forces in the flow act on the outer cylinder. The sensing unit in the space between inner and outer cylinder transduces the force. The spring loading allows the cylinder to resist, flexibly, the forces in the flow. To minimize interaction with the flow, the response of the outer cylinder to the flow will be more a reaction force rather than a force that does any actual displacement. Before settling for the standard strain gauge, some time was spent on the use of conductive foam as a sensing element. These foams are spongy material impreg-nated with conducting carbon particles. Compressing the material at any point increases the particle density and hence decreases the resistance. Their advantages include ability to conform to surfaces of various geometries, their fast responses and huge signals. A transducer was built with a piece of foam embedded between the outer and inner rigid cylinder . Unfortunately, this design had a very large hysteresis. In addition, the signal tended to drift unpredictably. These effects were traced to the foam material itself. Also, it became clear that the foams are not very directional. Response to shear and compression could not be distinguished. The ideal transducing element should have a high side force rejection to prevent coupling of the drag and lift forces. This use of conductive foams for a transducing element could yet yield a good, sensitive system but, more development work is needed [26]. In the end, it was decided that a sensor unit should consist of a foil grid strain gauge bonded onto a phosphor bronze diaphragm. The strain gauges chosen (HBM Chapter 4: Measuring Forces on Cylinders 47 6/120 LY 11) are general purpose strain gauges for either static or dynamic appli-cations. Phosphor bronze is a fairly elastic metal with good memory characteristics so it is a good pressure sensitive diaphragm. The strain gauges are bonded onto diaphragms that are 0.030" thick, 1.5 inches long and barely wide enough for the strain gauges to fit on. A strain gauge changes its resistance when the diaphragm is bent. A figure of merit is the change of the local radius of curvature. The change can be much larger for the short diaphragms used in this design compared to the cantilever arrangement used by Lefrancois. This much reduced length of the diaphragm makes it possible to have a very high resonant frequency and greatly increased signal to noise ratio (SNR). One end of the diaphragm is screwed tightly onto the inner cylinder, a 1 inch diameter, 3 ft long stainless steel rod. The other end of the diaphragm, which is in contact with the outer cylinder shell, is dimpled and a ball (3/32" diameter) from a ball bearing is glued onto it. The acts as the contact point for the outer sleeve which consists of a cylindrical metal shell with a thin mylar sheet on the inside. The bearing ball of the diaphragm is always in contact with the mylar sheet of the cylindrical shell. Four such sensing units are mounted on the inner cylinder, one for each of the four directions that the forces are measured in. Two diametrically opposed sensing units are arranged and connected to the two arms of a Wheatstone bridge to measure the net force in either the streamwise or transverse direction. The phosphor bronze diaphragms have a good elasticity but are much too soft (springy) to center the core and shell of the principal cylinder. The restoring force Chapter 4: Measuring Forces on Cylinders 48 must be so strong that the elasticity of the diaphragms is completely overridden. The recovery should be independent of the diaphragm elasticity. To achieve this, the outer cylindrical shell was spring loaded onto the inner rigid cylinder. This was accomplished by using two sets of tension springs, one at the top of the shell and one near the bottom. Each of the four springs in one set is anchored at the inner rigid cylinder at one end and hooked onto the outer cylindrical shell at the other. All the springs are under tension. The four springs of each set are mounted either directly above or below the four sensors. The springs have a spring constant of about 8000 N/m which is very much larger than the spring constant of the bronze phosphor diaphragms. The mechanical resonance of the system is governed by the mass of the outer shell and the linear extension constants of the springs. Both can be chosen independently. The sensitivity of the device depends on the bending of the phosphor bronze diaphragms. Thus the sensitivity and the resonance frequency are uncoupled. The end result is a very sensitive instrument with relatively little noise. The sensors are arranged so that two of them are used differentially for mea-suring forces in the streamwise direction and similarly the other two for measuring forces in the direction transverse to the streamwise. Each pair is electronically wired to be two arms of a Wheatstone bridge. The output of the bridge is amplified by a single stage differential amplifier which contains only operational amplifiers and resistors with no active components that might affect the phase of the signals. There are two channels, one for the transverse and one for the streamline sensors. One such channel is shown in Figure 4-2. The electronics are sitting on a bus card inside a metal box. This box rides on the cart in order to shorten the cable length between sensor and electronics. The inputs to the box are signals from the principal Chapter 4: Measuring Forces on Cylinders 49 cylinder and the control cylinder and the output signals are the transduced force signals sent to the recording devices. 4.4 Testing and Calibration of the Prototype Principal Cylinder Static weight loading is used to calibrate the principal cylinder. A weight is hung from a pulley by a string which is tied around the cylinder. The force is applied at the centroid of the moving section (see Figure 4-3). The principal cylinder's response is recorded with the weight as a function of output in millivolts. The response does not differ if the string is shifted up or down the cylinder as long as it is between the two sets of springs. It is therefore, not necessary to determine the center of force in the lift and drag measurements. It turned out that the sensors in the streamwise direction are more sensitive than that in the transverse direction. This means that both directions have to be independently calibrated but the results for the individual channels are still very reproducible. The agreement from repeated calibrations is good with an error of less than 10 per cent. The calibration points of both channels are fitted to a least square fit, see Figure 4-4. The results of the static calibration is checked by running the cylinder at a preset velocity and determining the force from knowledge of the velocity and projected surface area using equation (2.1a). The natural frequency of the cylinder was obtained by striking it sharply with a hammer, recording the response and then performing a fast Fourier transform (FFT) on the response. Figure 4-5 shows that the natural frequency of the principal cylinder is at 37.5 Hz with a spread from 30 to 45 Hz. This result shows that the resonant frequency of the cylinder is far away from the fluid dynamic frequencies of interest (that is, in the range of vortex shedding frequencies). 50 O 6 V o u t - 5 V W h e a t s t o n e b r i d g e a m p l i f i e r Figure 4-2. Wiring of electronics for one channel of transducer. /////////// vortex shedding cylinder centroid of moving section beneathe the water line \ _ rigidly f attached ( W ) ng Y777777? Figure 4-3. Setup of static calibration for principal cylinder. Chapter 4: Measuring Forces on Cylinders 51 2.5 2-1.5 -1 -0.5 -0 0 F(v)=0.0712v + 0.0551: forces in Newtons and voltage in mV 10 15 20 signal output (mV) 25 30 F(v)=0.1206v + 0.0368: forces in Newtons and voltage in mV (b) o jer\ >»0 i > 6 8 10 12 14 16 signal output (mV) 18 Figure 4-4. Calibration of the vortex shedding cylinder: (a) channel in the stream-wise direction (b) channel transverse to streamwise direction. 0.8 0.7 -0.6 0.5 -0.4 0.3 0.2 0.1 0 -0.1 "52 11 ! ! (*)' 0 0.5 1.5 2 time (seconds) 20 30 frequency (Hz) 40 2.5 50 60 Figure 4-5. Response of principal cylinder to an impulse: (a) time domain (b) spectrum of the response. Chapter 4: Measuring Forces on Cylinders 53 The hysteresis of the system was tested by driving the principal cylinder at a known frequency and observing the phase lag of the response. This is to ensure that the principal cylinder works well in the range of frequencies to be measured. Hysteresis was not detectable for frequencies up to 4 Hz. The principal cylinder is screwed onto the underwater platform and clamped at the top to the cart. The connections between the cart and inner rod of the principal cylinder is buffered by rubber gaskets. The gaskets helps greatly to reduce mechanical noise transmission from the cart to the principal cylinder. Figure 4-6(a) is an example of a typical run with the principal cylinder towed at 15 cm/s. Figure 4-6(b) and Figure 4-6(c) are the FFT spectra of the lift and drag signal respectively. Note the large peak in Figure 4-6(b) for the vortex shedding frequency. The vortex shedding frequency and its first overtone is detected in the drag signal These results show that the prototype principal cylinder with internally mounted strain gauges, behaves as it was designed to. The advantages of this novel design for the principal cylinder may be summed in six points: (1) A true force measurement (not moment) is made directly at the cylinder. (2) Perturbation and interaction with the flow is minimized. The transducer has good axial symmetry and is more sensitive to the geometry of the body. (3) The transducer is rugged and simple to build, there is no ultra precise machining or expensive parts (survived over 800 runs to date). (4) In the present arrangement, there are no end effects to contend with. (5) The resonances of the transducer (occurs at about 37 Hz) are far from frequencies of interest. (6) Time resolution of lift and drag is achieved simultaneously. 1.5 -1 -0.5 F 0 -0.5 -1 -54 0 0.4-0 drag (a) 10 15 20 25 t* (tU/D) 30 35 40 1 45 vortex she< iding frequej 1 — T " " " acy | (b) 2 3 4 5 6 frequency (Hz) Figure 4-6. Typical signals and their spectra (principal cylinder), (a) raw signal (b) spectrum of lift Chapter 4: Measuring Forces on Cylinders 55 Figure 4-6. Typical signals and their spectra of the principal cylinder, (c) spectra of drag. Chapter 4: Measuring Forces on Cylinders 56 4.5 Control Cylinder The control cylinder ideally should have the same specifications. However, it is not possible to use internal sensors since the diameters of interest range from one eighth to one quarter of an inch. To allow for small diameters, the sensing section was kept above the water and a cantilever arrangement with only one set of springs was used. The design is illustrated by Figure 4-7, makes use of the sensing elements developed for the principal cylinder. Again, strain gauges are mounted on thin phosphor bronze disphragms which rest between an outer shell and an inner cylinder. Again, the restoring force is provided by springs under tension. Here again, the sensitivity is decoupled from the resonant frequency. The detecting section is designed so that various diameter rods can be attached as control cylinders. The sensing electronics are identical to that of the principal cylinder transducer. Figure 4-8 is the results of the moment calibration on the control cylinder. The design of the principal cylinder and the control cylinder took the better part of a year. The investigation of flow phenomena can start when all parts work together in an integrated system. 4.6 System Integration Any system composed of various componenets must undergo testing of the whole before the real work can begin. The principal cylinder and the control cylinder were both individually tested in the tank. Some unexpected mechanical noise and signal offsets were discovered and partially resolved. In the initial tests, the principal cylinder is screwed into the underwater plat-form plate and clamped to the carriage and towed across the tank. One thing stainless steel body Sin aluminum rings teflon flange teflon cap-1.5ln 57 aluninun plug springs threaded rod steel ball Inner teflon ring strain gauge collar brass sections welded onto steel ball threaded section for control cylinder mounting Figure 4-7. Schematic of the control cylinder transducer. 0.24 0.22 0.2 0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 1 1 ! j j ' M(v)=0.018v + 0.0346: moment in Newton-metres and voltage in mV > o AO jo O JO o _5?_ i i i i 0 20 40 100 60 80 signal output (mV) Figure 4-8. Moment calibration of control cylinder lift. 120 Chapter 4: Measuring Forces on Cylinders 58 becomes evident, the signal looks noisier than what would be expected from the flow. This was probably the noise encountered by Loewen and Lefrancois. A fre-quency analysis on the tank's natural resonance was carried out. This was done by mounting the principal cylinder in the tank as if a run were to be taken. Then, various sections of the tank, carriage, mounts, etc. were impulsively struck with a hammer and the responses of the cylinder to the impulses were recorded. Then, an FFT was performed on the responses. The results shows that the cylinder is picking up the natural noise (approximately 12 hz) from the towing tank. This is not a frequency expected in the flow vortex shedding frequencies of interest but it is large enough that it rides on the recorded signals. This problem was reduced by fitting 1/4" rubber gaskets to all areas of contact between the towing tank and the cylinder. The transduced drag signals in these runs came out larger than initially ex-pected. This was eventually traced to the mounting style used. When the principal cylinder is mounted simultaneously on the underwater platform and the cart, a slight misalignment between the underwater platform and the cart skews the cylinder axis from the vertical direciton and puts additional tension onto the strain gauges in the x (streamwise) direction. This distortion appears as an addition to the drag force. This is a design flaw that was not anticipated or revealed in the early testing of the device. If its inner rod is flexed, the principal cylinder picks it up. To remedy this problem, one of the underwater rails is released so that it is only held at one point in the tank and the cylinder was attached only to the underwater platform. This reduces the end force to 0.05N which is unfortunately shghtly larger than the Chapter 4: Measuring Forces on Cylinders 59 designed sensitivity of the principal cylinder transducer. The oscillating lift signal is fortunately, not affected by an offset. The fully integrated system was first tested in experiments involving a single cylinder. Chapter 5: Initial Single Cylinder Experiments 60 CHAPTER 5 INITIAL SINGLE CYLINDER EXPERIMENTS The objective of this thesis is to look at action at a distance in fluid flow by measuring lift and drag forces with time resolution. Drag force measurements (especially those that do not have any time resolution) are routinely performed in many laboratories. However, time resolved lift force measurements are more difficult and only a few have been reported. In general, the lift signal of a cylinder in a towing tank may be approximated as FL = Fi + F C O S ( 2 V T / < + S) (5.1) where Fi is the offset due to the interference of a nearby object, which was denned earlier in equation (2.1b) as: Fuft = ^pU<x>2 xprojected area x C x , F is the lift fluc-tuation amplitude, / the vortex shedding frequency, and 8 the phase constant that specifies the time of onset of vortex shedding. In experiments where the cylinder is started from rest, F{, F, and / may be functions of time and S is undetermined. In the case of an isolated cylinder in a flow, Fi = 0. Otherwise, Fi is an indication of the strength of the repulsion or attraction of two objects. F is a measure of Chapter 5: Initial Single Cylinder Experiments 61 the strength of the vortex shedding. Most previously reported measurements have dealt with time averaged signals. The sensitive lift and drag detection equipment developed in this thesis allowed measurements of F, Fi, f, and 8 in a variety of configurations and permitted to extract various aspects of the interaction of objects that are imbedded in a flow at close distances. 5.1 Phase of the Lift Force As a first test of the fully integrated system, the lift force of a towed circular cylinder was measured and instantaneously correlated with digitized pictures of the flow field activity. This allows one to correlate the phases of the lift signal with the activity in the von Karman vortex street. Digitized video pictures of the flow field were integrated for one sixth of a second by consecutively superimposing 5 digitized pictures at a time. Figure 5-1 shows an example. The lift reaches an extremum as a vortex is formed on one side of the cylinder. The lift force is pointing in the direction of the newly formed voxtex. That is a vortex 'pulls' on the cylinder rather than pushing it before detachrng from the cylinder. This agrees quite well with established results from periodic vortex shedding [17]. These force and flow field correlations confirm previously known results. The intent of this thesis is to look beyond previously known results, and search for action at a distance. 5.2 Cylinder Near a Wall The first indication of action at a distance in fluid dynamics were obtained by generating a vortex street close to a wall. In these experiments, a flat plate is encountered parallel to x at an arbitrary distance (see Figure 5-2a). The drag Chapter 5: Initial Single Cylinder Experiments 62 — ^ y — * > s S . 1 Figure 5-1. Phase of the lift force on a circular cylinder correlated with flow visualization. Chapter 5: Initial Single Cylinder Experiments 63 and lift force of the cylinder are altered because of the -wall's proximity. These effects are more commonly known as blockage. Similar experiments have been tabulated for Reynolds numbers much higher and lower than those studied here. In this experiment it was to be determined, how far away a wall would still affect the cylinder. The lift signal was used as a criterion for detecting the presence of the wall. If the wall is very far away, the lift develops gradually and grows in amplitude over some 3 or 4 vortex shedding cycles until it reaches some steady state amplitude F. If the wall is located close by, at say y0 = ID , the lift signal is offset by an amount Fi, as soon as the cylinder starts to pass the wall. In this set of experiments the lift and drag of the big cylinder was measured as it was towed across the tank. The distance y0 of the "the cylinder from the wall was varied in these runs. By the use of equation of (2.1a), the drag coefficient was calculated and the results are displayed in Figure 5-3- While the lift drops off gradually, the drag shows a maximum at y0 = D. A similar effect was already observed for the drag by Lefrancois. The diameters of the sphere of influence in this experiment may be defined as the distance y0 where the offset is just noticed. From Figure 5-3, it can be seen that the sphere of influence of lift and drag modification extends to at least 1.5D in the lateral direction. The trends observed here correspond to Roshko's [21] results at Reynolds number 2000. 5.3 Triggering the Vortex Street For a single circular cylinder towed through a fluid, instabilities in the flow determine which of the two startup Foppl vortices from a circular cylinder will shed first and hence determine the phase and to some extent, the amplitude, of the steady Chapter 5: Initial Single Cylinder Experiments 64 U Yo Ym/mi/mmtm/tm/iimmimiitimq wall (a) wall parallel to freestream direction. Xo U T Yo 1 triggering plate (b) triggering wall perpendicular to freestream direction. Figure 5-2. Schematic of setup for cylinder/wall experiments, (a) wall parallel to the freestream direction (b) wall perpendicular to the freestream direction. Figure 5-3. Results of lift and drag from wall proximity experiment: Chapter 5: Initial Single Cylinder Experiments 66 state lift force. This makes it difficult to superimpose phase correlated data of the lift force. A means to start the vortex shedding at an arbitrary point and hence synchronize the lift oscillations is often desired. A series of experiments were performed where a circular cylinder was towed past a plate placed perpendicular to the direction of the cylinder's travel (Figure 5-2(b)). The plate was bevelled from both sides at 45 degrees and the cylinder passed within half a diameter of the plate edge. The distance, x0, between the plate and the startup position, was varied. Force measurements were time correlated with flow visualization. Details of these experimental conditions are given in Table 5-1. The lift signals show that the presence of the trigger plate affects both lift fluctuation amplitude, F, and phase constant, 8, denned by equation (5.1) In cases where the circular cylinder was still in the symmetric mode of vortex shedding before reaching the plate, the plate edge initiates the asymmetric vortex shedding mode by causing the vortex closest to the plate to be shed. The amplitude of the lift force reaches its steady state value almost immediately downstream of the plate edge. In addition, the phase of the lift signal is set at that point to start with a maximum. (Figure 5-4 (c) and (d)) In the case where the plate is encountered late in the run, after the assymmet-ric vortex shedding has already started, the plate resets the phase of the lift signal so that it looks identical to the lift signals of early triggered runs. As well, the lift force amplitude reaches its steady state value almost immediately downstream of the plate edge (Figure 5-4(b)). In both cases, the lift force has the same phase and amplitude once the cylinder is downstream of the plate. The lift signals can then be superposed from repeated runs with identical conditions. 0 5 10 15 20 25 30 35 40 t* (WD) Figure 5-4. Triggering the vortex street at different points, (a) untriggered (b) triggered 14.2D from the starting point. t* (Ut/D) Figure 5-4. Triggering the vortex street at different points: (c) triggered 8.3 D from the starting point (d) triggered 5.9 D from the starting point. Chapter 5: Initial Single Cylinder Experiments 69 For comparison, a series of runs without the trigger plate are shown in Figure 5-4(a) where the vortex street is initiated randomly due to flow instabilities. The drag force was also monitored throughout and it was found to change very little. Figures 5-4(b)-(d) are each the superposition of three runs for different positions of the triggering plate from the starting point. To control the level of turbulence in the tank, which would contribute to the initiating of vortex sheddding, the time between runs was kept constant. This allowed the tank to settle to the same level of turbulence from run to run. In order to asses the variation in phase angle, S, of triggered vortex streets, the time U and position x{ of the first seven maxima of the lift signal was measured from 20 runs. Of interest was the variance of the averages a*, and o~x. The results are presented in Table 5-3. A is defined as the 'wavelength' in space for a cycle of vortex shedding. It may be seen that the location of the first maxima can be predicted with an uncertainty of only a few percent of the cycle period. The results for the position x0 = 8.2D show how strong the correlation of the lift force is from run to run when the triggering plate is used. Figure 5-5 is a photograph of the vortex street in the vicinity of the triggering plate. These experiments have confirmed the relation of the lift phase and vortex shedding activity, given a measure of the lateral extent Aj_, of the sphere of influence and provide a means to trigger a vortex street. They further show that the apparatus is ready to perform more complex experiments with staggered cylinders. The problem of random startup of vortex shedding has plagued other re-searchers as well. A short paper about the trigger plate technique was recently submitted to Physics of Fluids and it was accepted in principle. A copy of the revised manuscript is given in Appendix 3. Chapter 5: Initial Single Cylinder Experiments 70 Chapter 5: Initial Single Cylinder Experiments 71 cylinder diameter = D = 5.08 cm velocity = Uoo = l&cm/s water temperature = 63 degress F cylinder draft= 58 cm Re = 7000 - 9000 y0 = clearance between plate and cylinder at closest approach = 0.5D x0 = distance from startup position of cylinder to plate in cylinder diameter, D Table 5-1: Summary of vortex triggering experimental conditions. vortex,i *\ Of Ox" 1 7.87 0.14 8.10 0.16 3.8 2 11.76 0.21 12.08 0.22 5.3 3 15.70 0.31 16.12 0.31 7.8 4 19.63 0.31 20.17 0.30 7.8 5 23.38 0.31 24.26 0.30 7.8 6 27.42 0.35 28.0 0.35 9.9 7 31.43 0.39 32.32 0.39 10.0 TABLE 5-2: Time and Position of Maxima of Lift Signals for x0 = 8.27/J Chapter 6: Flow Interference Between Cylinders of Different Diameters 72 C H A P T E R 6 TWO CYLINDERS OF DIFFERENT DIAMETERS 6.1 Data Collection The main goal of this experiment is to collect information about action at a distance associated with objects that are towed through a fluid. For this purpose, the principal or "main" cylinder was mounted on the underwater platform and the control "or perturber" cylinder was mounted on the cart. Both underwater platform and cart travel across the tank together at the same speed with the two cylinders at various separations but mechanically decoupled. The immediate objective was then to measure both lift and drag forces on the principal cylinder and the control cylinder in a flow of Reynolds number = 8000 (with Reynolds number based on the diameter of the principal cylinder) with relative diameters of 4 and to time correlate these forces with flow visualization information. The measurements were done systematically for tandem, transverse and staggered arrangements for both upstream and downstream configurations. The relative positions of the principal cylinder and the control cylinder to the towing direction for these experiments is shown in Figure 6-1. Data are collected to map out the drag forces around the principal cylinder when the control cylinder Chapter 6: Flow Interference Between Cylinders of Different Diameters 73 is nearby. A 2D x AD diameter region (with a few more distant points) was studied with the principal cylinder centered at the bottom middle. This allows regions of 2D x 2D to be investigated both upstream and downstream. The grid spacing of the data points is | D implying a total of 40 points in the 2D x4D region. An additional 15 distant points outside the 2D x 4Z> region brings the total to 55 data points. For each of the points, six runs are performed. The first run is usually ignored since its purpose is to stir up the water to some arbitrary level of turbulence. The remaining five runs are taken at equal time intervals and are used to check against each other to find an average signal. In each run, the cylinders traverse the entire length of the tank. The effective travel length is 3 metres. During the run, the four forces, Fr),Fi,Fd,Fi along with velocity (and if applicable, the sync strobes and 30 Hz counter) are digitized and recorded on the computer with the program Collect. A typical run is shown in Figure 6-2. Simultaneously, the cameras record the flow activity. Temperature and water height are always monitored for any changes and adjusted to a constant value. The time intervals between all runs were set at 3 minutes for the experiments with a cylinder diameter ratio of ^ = 4. This time is an optimization of the tank settling time and a practical waiting period. Chapter 6: Flow Interference Between Cylinders of Different Diameters 74 ro OJ ooooo ooooo ooooo ooooo 1 h. O O O Q ooooo ro OJ oooo ooooo ooooo oooo ru 8 CD 2 o a 09 o CO O a, . r t S • © u 3 O O O O O o o ro control cylinder drag \j i control r.vlinder lift • " cyliprincipal cylinder drag - A M principal cylinder lift I I," v V * 4-0 f t U / D " ) VX Figure 8-2. Example of four signals collected in a run: principal cylinder drag and lift; control cylinder drag and lift. Chapter 6: Flow Interference Between Cylinders of Different Diameters U D d D/d water temperature Re cylinders drafts distance traversed data collection period per run area mapped resolution of mapped area runs / point time interval between runs 15 cm/s 2 in 0.5in 4:1 65 deg F 7640 65 cm (100 %) 3m 18 seconds 2D x 2D upstream and downst 0.5D 6 3 minutes Table 6-1: Summary of Two Cylinder Data Collection Chapter 6: Flow Interference Between Cylinders of Different Diameters 77 6.2 Data Reduction During an experimental run, 2 lift and 2 drag data traces are recorded, which contain a number of parameters as illustrated in Figure 6-3. The lift and drag traces in the figure could refer to either that of the principal cylinder or the control cylinder. The raw digitized signals are stored in computer memory or on data cassette cartridges. Averaging and demultiplexing routines are used to extract the individual signals from the raw data. From a lift signal (Figure 6-3 (b)), offset lift, F{, lift fluctuation amplitude F, vortex shedding frequency, w and phase angle, S, and a signal baseline (where the zero is defined) may be extracted. From a drag signal (Figure 6-3 (a)), a signal baseline and average signal amplitude is usually extracted. A signal baseline is obtained by examining the beginning and end of a signal, if the recovery is very good then they will be equal. If they are different, a linear interpolation is used. The dc or offset amplitude is measured with reference to the baseline. Once it appears that the flow is fully developed, the signal is averaged to obtain a dc level. For a typical run, this is usually 4 to 5 seconds of fully developed flow. This level would then be compared with the signal baseline. The interference lift, F\, for example, is determined with reference to the signal baseline. The difference of the average of the oscillating section with the signal baseline gives the amplitude of the interference lift. The voltage signal amplitude is then converted to forces in Newtons. The ac amplitude was obtained by a 10 point box car average of each point of the oscillating section of the lift (5 points of the signal before the point of interest 20 25 t* (tU/D) 1.5 0.5 0 -0.5 1 ! ! ! ! ! '! n M M (b) vyv*-H y\j\r I] i — i i i i i i i 0 10 15 20 25 t* (tU/D) 30 35 40 45 Figure 6-3. Information extracted from signals, (a) from the lift: Fi, F, At, f (b) from the drag: amplitude Fr). Chapter 6: Flow Interference Between Cylinders of Different Diameters 79 with 5 points after the point of interest). The maxima and minima of this new averaged signal were used in the selection of the ac amplitude. The forces measured on the principal cylinder without the control cylinder present, Fj)0 and Fi0 (Figure 6-4(a)) are used to normalize all lift and drag mea-surements in staggered configuration. Similarly, the drag and lift, F&0 and F\0 of the isolated control cylinder (Figure 6-4(b)) serve as a measure of interference effects on the small cylinder in staggered configurations. In this manner, the following quantities are determined: •£D-,-r<L-, and To survey the interference effects and look for trends and irregularities, all data were plotted in the x — y parameter plane as defined by Figure 6-1. Since all data can be given a scaler number such as jfi-, contour maps can be drawn. The program MATLAB is given the information and it produces a contour plot. Each data point is an average of 4 to 5 runs for a given relative position between cylinders. Matlab is used to produce contour plots from these data points. In order to asses how vortex shedding of one cylinder influences the flow of the other cylinder, the lift signals were Fourier analyzed to obtain a frequency spectrum. Of particular interest were the amplitudes of the Fourier spectrum at the vortex shedding frequencies of the principal and control cylinders. Some smoothing and processing was performed on the spectra to average out noise and correct for 1/f noise. This was accomplished in several steps: (1) A cublic spline is fit through the function / x FFT through all points except the frequencies of interest (/ x FFT is used instead because it is is a monotonically increasing function and fits easily to a low order polynomial whereas the FFT itself does not). Then, the cubic splined curve is divided by / to recover the original tendency of the spectra. (2) This tendency is subtracted from the FFT. (3) The result is a straightened FFT from Chapter 6: Flow Interference Between Cyhnders of Different Diameters 80 3.S 1.SH f\ n A i A H r I — 4 0 6 0 (a) T i i r 2 0 4 0 (b) Figure 6-4. Example of unperturbed forces on both cylinders, (a) principal cylin-der drag and lift (b) control cylinder drag and lift. Chapter 6: Flow Interference Between Cylinders of Different Diameters 81 which the relative amplitudes can be directly obtained. Figure 6-5 is an illustration of how the above process was carried out. In particular, the lift of the control cylinder was analyzed in this manner and the amplitude A(f0) at the vortex shedding frequency of the principal cylinder was determined. Unexpectedly, the vortex shedding frequency imprinted onto the flow field outside the wake of the principal cylinder. However, the amplitude decays quickly as the control cylinder is positioned away from the wake region. 0.04 0.035 0.03 0.025 0.02 0.015 0.01 0.005 0 0.04 0.035 0.03 0.025 0.02 0.015 0.01 0.005 0 2 3 4 frequency (Hz) 0.04 0.035 (b) 0.025 0.02 0.015 0.01 0.005 0 2 3 frequency (Hz) 82 (a) ! ! ; j j i i o 1 o O I 0 o° i O: lo 0 ° ° o o o° ° o i 0^> 0 O O O ' ^ O * <X40„„ ^ | • f \ <w,B»n.n<>un"ut"n»""i<'6U 2 3 frequency (Hz) i ; ; ! ! A j ; j j (c) Figure 6-5. Example of how relative FFT amplitudes are corrected: (a) the raw FFT (b) the curve fitting through the calculated FFT points (c) the corrected FFT. Chapter 7: Results and Discussions 83 C H A P T E R 7 RESULTS AND DISCUSSIONS A measurement of the forces on the mutually interacting cylinders provide information about the nature of the action of the forces at a distance. Measurements from both cylinders of the lift and drag force, and frequency, phase and onset of vortex shedding can be used this way. Reported here are measurements with cylinders D = 5.1cm and d = 12.6mm towed at the velocity, Uoo — 15 cm/s. First the results of the analysis of lift and drag of the principal cylinder will be discussed and then results of the control cylinder will be given. 7.1 Drag of the Principal Cylinder As an extension of the work by Lefrancois, the drag force of the principal cylinder was measured for various positions of the control cylinder and the variation of drag Dpj} D° was determined. A contour plot can be constructed of the changes of the drag force on the principal cylinder as the relative position of the control cylinder is varied. (Figure 7-1). Regions of reductions (indicated by '-' in the plot), increase (indicated by '+') and neutrality of the drag force on the principal cylinder are identified when the Xc (D) Figure 7-1. Interference drag force, on the principal cylinder vs relative position of cylinders. oo Chapter 7: Results and Discussions 85 control cylinder is placed both upstream and downstream of the principal cylinder. This contour plot has qualitative agreement with the results from Hori [12] for identical circular cylinders at similar Reynolds numbers. If the control cylinder is placed immediately in front of the principal cylinder or behind it, regions of strong drag reduction are observed on the principal cylinder. The regions of drag reduction are not as large as that for the case of identical circular cylinders. The decrease in drag is expected. When the control cylinder is either directly upstream or directly downstream, the combined body formed by both cylinders is more streamlined with reattachment of the principal cylinder boundary layer. If both cylinders are placed side to side relative to the flow, (i.e. xc = 0) both experience strong increases in drag. The shape of the principal cylinder drag contour in this region strongly resembles that of the case with two identical cylin-ders. When the control cylinder is in positions from 0.5Z? to 1.52), the drag of the principal cylinder increases and reaches a strong maximum at 1.5D. Lefrancois [16] also observed a drag maxima at 1.5.D for similar experimental conditions. As the separation between cylinders grows larger than 1.5D, the drag on the principal cylinder gradually reaches its isolated cylinder drag value. The strong increases in drag when the two cylinders are placed closely side by side is also not surprising. The combined body of both cylinders presented to the flow (and hence the effective projected area to the flow) is largest in the side by side configuration . The drag force increases with projected area so naturally the drag on the principal cylinder is larger. Fourier analysis of the drag of the principal cylinder shows it contains the 2/ or twice the vortex shedding frequency as expected. No new information is obtained Chapter 7: Results and Discussions 86 from this since the Fourier analysis of the lift provides a stronger measure of the shedding frequency. 7.2 Interference Lift of the Principal Cylinder The interference lift, Fi, as definied in equation (2.1b) or equation (5.1) can be either positive or negative in sign. Positive means that the objects experience a mutual repulsion and negative means the objects experience a mutual attraction. The total attraction can be found by the vector operation: ( F D + F L ) . -r and the moment by the operation (FD+FL)x- r where ^ is a unit vector along a line connecting the center of both cylinders. Figure 7-2(a) shows plots of the interference lift of the principal cylinder for constant values of yc. The lift measured shows a repulsive lift for most staggered positions. Critical points, where the interference lift is a local maximum, occur when the control cylinder is both upstream and downstream for all values of yc = constant. Their signifigance is not yet understood. Figure 7-2(b) is a contour plot of the interference lift on the principal cylinder as a function of the position of the control cylinder. The most striking feature in this plot are the three 'islands' of high interference lift around the principal cylinder. The ones to the front and to the side of the principal cylinder are fairly similar in size and shape. The one in what would be considered the 'staggered' position Figure 7-2.- Interference lift of principal cylinder vs positions of both cylinders, (a) for constant yc. Figure 7-2. Interference lift (N) of principal cylinder vs positions of both cylinders (b) contour plot (arrows refer to local trends). oo oo Chapter 7: Results and Discussions 89 (a) is longer and tapers off. In these three regions, the presence of the control cylinder locally increases the freestream flow for the principal cylinder and results in a stronger repulsive lift force between the cylinders. The tapered shape of the downstream 'island' (7) suggests that the effect of a downstream control cylinder is stronger than that of the upstream or side by side position. The control cylinder in the positions a and /3 may be more involved with vortex formation and boundary layer separation. In the downstream positions, the control cylinder may be less involved with vortex formation and more affect the shedding time of the principal cylinder. Upstream of the a island, the interference lift vanishes and then becomes positive. The lift force between the two cylinders causes them to be attracted to each other. This is most strongly seen for distant upstream points at yc = 0.52?. 7.3 Vortex Shedding of the Principal Cylinder In the published results of other workers [28] [19], there are configurations where it was possible to suppress the vortex shedding of the upstream cylinder in the case of identical cylinders at low Reynolds numbers. With dissimilar cylinders (relative diameters of 2), Novak found he could not suppress vortex shedding of the large cylinder with the small one regardless of spacing . Only a few points from the data in this thesis show vortex shedding suppression. This was at (x,y) — (0.52), 0.52?) and possibly at (x,y) = (—0.52?, 0.52?) It appears that with cylinder diameter ratios of 4 at Re w 8000, complete vortex shedding suppression of the principal cylinder is only possible if the control cylinder is within a radius of 0.7D. Chapter 7: Results and Discussions 90 Usually, the amplitude of the vortex shedding F in equation (5.1) starts off very small and gradually grows to its steady state amplitude as indicated by Figure 7-4. This is the case for the principal cylinder if it were isolated in the flow. But as the control cylinder is positioned closer to the principal cylinder in both upstream and downsream configurations, the vortex shedding amplitude F reaches steady state within almost the first cycle of shedding and remains at this ampltiude for the rest of the run. As the control cylinder is positioned progresively further away from the principal cylinder, the principal cylinder starts to build its lift amplitude gradually from zero again. This is also true if the control cylinder is moved further away either upstream or downstream. These phenomena are seen in the case yc = OD quite clearly. Another interesting feature in the vortex shedding amplitude is the reduction of the amplitude as the run progresses, when the control c;ylinder is located at the 7 island defined in Figure 7-2. This is strongly illustrated in the cases of (xc,yc) = (1.0D,0.5D) in Figure 7-5 and (xc,yc) = (0.0D, 1.0D) in Figure 7-6. The vortex shedding is triggered right from the start and quite strongly. However, after about two cycles, the amplitude of the vortex shedding reduces sharply by almost a factor of two in some cases. In addition, the vortex shedding frequency also drops and in some cases by a factor of 2! During the period that the vortex shedding amplitude is strong for the first few cycles, there is no interference lift! The interference lift does not appear until the amplitude of the vortex shedding drops. This phenomena occurs mostly for cases where the control cylinder is downstream and only for one case where the control cylinder is upstream of the principal cylinder. From video film analysis, it appears that the principal cylinder initially sheds vortices as a single body until the control cylinder makes its presence known. Then, the two act together as if they were an object of diameter D* > D. The single vortex forms Chapter 7: Results and Discussions 91 behind this compound object. This may explain why the vortex shedding amplitude of the principal cylinder becomes smaller because by equation (2.2) /* ~ < f = 2j. The principal cylinder shares its vortex with the control cylinder. The immediate triggering of the vortex shedding for the first few cycles occurs because the presence of the control cylinder creates a strong gap flow that biases the immediate formation and shedding of the principal cylinder as a single cylinder. The control cylinder itself also starts immediate vortex shedding at frequency f\. But as time progresses the control cylinder's vortex shedding activity is made known to the principal cylinder and the two start to coalesce their vortices into single structures. This transition of two individual vortex streets to a single compound vortex street as well as the signals exchanged between both objects that initiate shedding, should be studied in further work. The principal cylinder's drag decreases when the vortex shedding amplitude is reduced. 7.4 Phase Locking and Onset of Principal Cylinder Lift The initial analysis of vortex shedding on the principal cylinder was made by analyzing many runs for a given position between the two cylinders. One of the remarkable features observed was a phase correlation on the lift of the principal cylinder from run to run for a given relative position between the two cylinders. The presence of the control cylinder appears to predetermine when the prin-cipal cylinder starts to shed. The phase constant 8 becomes apparently fixed by the presence of the control cylinder. This seems to be true whether the control cylinder Chapter 7: Results and Discussions 92 is placed upstream or downstream of the principal cylinder as long as it is relatively close by. The onset of shedding 8 gives an indication of when the principal cylinder has encountered the wake of the control cylinder (if the control cylinder is upstream) or when the perturbing presence of a downstream control cylinder triggers the vortex shedding of the principal cylinder. Variations of the phase lag 81 — 82 measured between two control cylinder positions can reveal signal velocities in the flow field. Figures 7-4 to 7-8 illustrates this correlation of the lift force between runs for a given relative position between the two cylinders. These figures show the lift of the principal cylinder for 3 runs at a given position for all experimental points. The correlation in phase is clear for points close to the principal cylinder. One can define a sphere of influence for the vortex shedding based on the criterion that the control cylinder when placed within this region will trigger the shedding of the principal cylinder predictably at a certain point in the run. Closely related to the phase correlation is the onset of vortex shedding. From Figures 7-4 to 7-8 the distance between the principal and control cylinder is mirrored in the onset point of vortex shedding. This onset time can be examined as a function of the relative position between the two cylinders. Clearly, for large onset times, it is no longer posssible to correlate the phases. From the visualization, it appears that the gap flow dictates which side the principal cylinder will start to shed. It may have the same effect as the trigger plate in the earlier experiments. With the control cylinder as far upstream as 2 diameters and as far down-stream as 1.5 diameters, it was possible to correlate the phase of the vortex shedding. The amplitudes of correlated runs appear to agree closely as well. At 2 diameters Chapter 7: Results and Discussions 93 downstream, the lift starts to appear with random phase and amplitudes. The small cylinder upstream also has the effect of triggering vortex shedding prematurely. Left to its own devices, the isolated cylinder does not start to shed until t* « 20. With the control cylinder upstream, the vortex shedding of the principal cylinder starts progressively earlier as the control cylinder becomes closer. It is possible to see the delay times, indicated by arrows, for example, in Figures 7-4(a), 7-5, and 7-6. to 7-8. The effect of putting the cylinder downstream is to trigger vortex shedding almost immediately. 7.5 Frequency Analysis of the Principal Cylinder Lift The principal cylinder's vortex shedding frequency, f0, changes in the prox-imity of another object. In general, a body of larger diameter has a lower vortex shedding frequency. This information will help to corroborate measurements of the drag force of the principal cylinder and can be exploited to determine how far away the control cylinder has to be in order for the principal cylinder to shed at its un-perturbed frequency. Figure 7-3(a) shows how the vortex shedding frequency of the principal cylinder varies for values of yc = constant due to interference. On these curves, a minimum in frequency is always detected with the cylinders beside each other. This is probably because, with the control cylinder in the side by side direction, the two cylinders form a compound body with an effective width, D*. The effective diameter, D*, of the object presented to the flow is larger hence their individual shedding frequencies are lower. This is quite remarkable since it implies that the two cylinders are aware of each other's presence and react to the flow Figure 7-3. Vortex shedding frequency (Hz) of principal cylinder vs relative po-sition of both cylinders (b) contour plot (f0 = 0.66 Hz when control cylinder is at infinity) ^ Chapter 7: Results and Discussions 96 like a compound body for separations as great as 2D. This minimum in frequency becomes less with increasing distance in the transverse or lateral direction. There appears to be some points where the lift frequency of the principal cylinder is a local maximum when the control cylinder is upstream. The frequency of shedding is higher because of the presence of the control cylinder. This is due to the control cylinder biasing the flow by causing a flow in the gap between the two cylinders. This gap flow increases the local freestream velocity so that by equation (2.2), the principal cylinder sheds vortices at a higher frequency. Higher shedding frequencies occurring when the control cylinder is located downstream may be due to the same mechanism, the presence of the control cylinder causes a locally higher freestream velocity for the principal cylinder. It is curious to note that these downstream critical points occur at xc « 1 tol.5P (except for yc = 0) again in the region of the 7 island of Figure 7-2. At yc = 0, the upstream shows a typical critical point but when the control cylinder is downstream, lower shedding frequencies occur for the principal cylinder. When the control cylinder is directly downstream it should be at its most stream-lined configuration. The frequencies measured do not bear this out. However, visualization shows the vortices being shed are formed from the effective body of the two cylinders and are much larger than vortices shed from the isolated principal cylinder. When the control cylinder is very close to the principal cylinder as in the (x,y)=(0.5D,0.5D) and (—0.5P,0.5D) cases, the frequency of shedding of the prin-cipal cylinder drops by a factor of 2 from its unperturbed frequency. This is under-standable since in this configuration, the two cylinders are effectively one compound assymetrical body of effective diameter D* > D. Chapter 7: Results and Discussions 97 Figure 7-3(a) is a contour plot of the interference shedding frequency or in-terference Strouhal number. The interesting features in the contour plot include the strong gradients in interference Strouhal number when the control cylinder is placed very close to the principal cylinder. But, if the control cylinder is in the direction immediately in front of the principal cylinder, the interference Strouhal number of the principal cylinder is higher and gradually decreases to lower than its single cylinder value with increasing distance between the two cylinders. This effect is not seen if the control cylinder is placed directly behind the principal cylinder. Instead, the frequency starts out much lower than the single cylinder shedding fre-quency and slowly increases with distance between the cylinders. When the control cylinder is placed in a staggered position relative to the principal cylinder there is an 'island' of slightly higher frequencies. This was already mentioned from earlier as due to an increase in the freestream flow around the principal cylinder. 7.6 Lift and Drag of the Control Cylinder The control cylinder experiences a negative drag (i.e. thrust) force when it is downstream of the principal cylinder. This is known to be true in the identical cylinder experiments. In the experiment here with a diameter ratio of 4, the effects are much larger. At some separations it looks like the small cylinder is literally pushed forward. The natural lift frequency of the small cylinder downstream has been totally suppressed. The drag of the control cylinder also seems to mimic the principal cylinder by increasing greatly to a maximum at 1.5D in the cylinders are placed in the side by side arrangement. One of the questions posed at the start of Figure 7-4. Principal cylinder lift vs control cylinder positions at Ayc upstream = 0. (a) Figure 7-4. Principal cylinder lift vs control cylinder positions at Ayc = 0. (b) downstream Figure 7-5. Principal cylinder lift vs control cylinder positions at Ayc = 0.5D. (a) upstream Figure 7-5. Principal cylinder lift vs control cylinder positions at Ayc (b) downstream = 0.5D. t* (tU/D) F i g u r e 7-6. Principal cylinder lift vs control cylinder positions at Ayc = 1.0D. (a) upstream Figure 7 - 6 . Principal cylinder lift vs control cylinder positions at Ayc = 1.0JD. (b) downstream Figure 7-7. Principal cylinder lift vs control cylinder positions at Ay c = 1.5P. (a) upstream 0 5 10 15 20 25 30 35 40 45 t* (tU/D) Figure 7-7. Principal cylinder lift vs control cylinder positions at Ayc — 1.5D. (b) downstream Figure 7-8. Principal cylinder lift vs control cylinder positions at Ayc = 2.0D. (a) upstream Figure 7-8. Principal cylinder lift vs control cylinder positions at Ayc (b) downstream = 2.0D. Chapter 7: Results and Discussions 108 this thesis was whether the drag of the control cylinder increases enough to account for 'missing drag' from the principal cylinder when the principal cylinder's drag is reduced. The results do not suggest such 'conservation' of drag forces. An examination of the lift on the control cylinder when placed downstream of the principal cylinder shows that its frequency is mainly that of the larger cylinder. This kind of effect is a new observation which could not have been revealed by earlier experiments with identical cylinders. The amount that Fi cross talks into and Fi can be seen by looking at the relative amplitudes of the FFT's as the control cylinder position is changed from (xc,ye) = (0,0.5I>) to (2.00,0.5D). The interference lift on the control cylinder becomes increasing larger as it gets closer to the principal cylinder. This lift is strongly repulsive and the most obvious when the two cylinders are positioned side by side relative to the freestream flow. 7.7 Frequency of the Control Cylinder Lift As the control cylinder gets closer to the principal one, the control cylinder sheds at a higher frequency than it would on its own. This is a measure of control cylinder's interference Strouhal number. In addition, the principal cylinder is shed-ding at a lower frequency with its shedding appearing to be triggered or correlated in phase. In principle, the vortex shedding frequency of the control cylinder, f\ could be used to measure local velocities in flow fields around much larger objects. The velocity would be derived from equation (2.2) asu = ^ assuming S does not change much. This is a consideration for future work. Chapter 7: Results and Discussions 109 7.8 Fourier Spectrum of Control Cylinder As a tool to measure action at a distance, the control cylinder's vortex shed-ding frequency was useful. This series of analysis was performed by taking the FFT of F\ and examining the resulting spectrum. Better results were obtained by averaging FFT amplitudes from the same sets of runs. The resonances from the tank can be identified as non-eraseable noise. Depending on where the control cylinder is located, there are two peaks in the power spectrum that often stand out. The larger one is at the vortex shedding frequency of the control cylinder and the other is at the vortex shedding frequency of the principal cylinder. By examining the relative amplitudes of these peaks as a function of the relative position between control cylinder and principal cylinder, one can also see how far out the principal cylinder's influence or 'action' is felt by looking for its vortex shedding frequency in the spectrum of the control cylinder's. In this sense, the control cylinder acts as a probe to pick up the pressure (force) field generated by the principal cylinder. Interestingly, the principal cylinder's shedding frequency can be detected for a small distance, upstream. Figure 7-9 shows the amplitude A(f0) (at the vortex shedding frequency, f0 of the principal cylinder) in the frequency spectrum of the control cylinder. These amplitude values are shown as spikes above the x — y plane. Figures 7-10 to 7-12 show the actual FFT spectra obtained. The probe can pick up the principal cylinder's vortex shedding frequency in the side by side direction for as far out as three diameters. This agrees with results from the cylinder/wall experiments. The drag and lift of the cylinder is perturbed when the wall comes within three diameters. Also, in the side by side direction, the strength of the pickup increases until it reaches a point 1.5D from the center of the principal cylinder then it drops off to zero eventually. This point Chapter 7: Results and Discussions 110 of maximum amplitude also coincides with a maximum in the drag of the principal cylinder. As the probe moves further downstream, the cross-talk is quite large as ex-pected. At 2D downstream, the natural vortex sheddding of the control cylinder is completely suppressed and the control cylinder lift shows it is shedding at the shedding frequency of the principal cylinder. In fact, an examination of the probe's drag shows the shedding frequency of the principal cylinder clearly imprinted onto it. A comparison of FL and F& shows a clear phase lag while the vortices shed by the large cylinder and travel to the small cylinder. This phase lag can be used as a measure of the wake velocity. Table 7-1 shows the relative amplitudes as the control cylinder is positioned further downstream. frequency (Hz) 3 4 frequency (Ht) 5 6 Figure 7-10. Uncorrected FFT of control cylinder lift vs control cylinder positions for xc = 0.0 D. Quantity in parenthesis is coordinate location of control cylinder rel-ative to principal cylinder center. The arrows indicate the amplitudes at frequencies f0 and fi. F igu re 7-11. Uncorrected F F T of control cylinder lift vs control cylinder positions for yc = 1.0 D. Quantity in parenthesis is coordinate location of control cylinder rel-ative to principal cylinder center. The arrows indicate the amplitudes at frequencies f0 and fi. Figure 7-12. Uncorrected FFT of control cylinder lift vs control cylinder posi-tions for miscellaneous separations. Quantity in parenthesis is coordinate location of control cylinder relative to principal cylinder center. The arrows indicate the amplitudes at frequencies f0 and f\. Chapter 7: Results and Discussions 115 x(D) y(D) A(f0){mN] ^ x l O O -0.30 1.19 4.8 4.49 -0.49 1.5 0.28 0.83 0.0 1.09 1.8 4.84 0.0 1.58 3.6 12.72 0.0 1.98 1.9 4.75 -0.19 2.5 1.2 3.64 0.0 2.96 0.0 0.0 0.39 1.09 5.6 11.93 1.0 0.99 5.8 9.97 1.87 0.99 13.3 89.9 -0.19 1.5 ... 5.48 -0.69 1.09 0.0 0.0 -0.79 1.5 0.0 0.0 1.18 0.5 14.5 76.0 TABLE 7-1: A(f0), ^ | vs Position of Control Cylinder 7.0 Action at a Distance The results obtained from the various measurements could be interpreted by looking only for values where the principal cylinder behaves like a single cylinder again. In doing so, one would be denning spheres of influence for the circular cylinder based on measurements of offset lift, phase correlation, and shedding frequency, on either cylinders. Such plots were constructed of A(x,y) and are shown in Figure 7-13. The regions are all roughly about the same shape with small differences. The upstream and downstream regions are not symmetrical. It is interesting to note that phase correlation is a sign of interference in the cylinder/perpendicular wall experiment as well. The difference between the two cases is that the wall is stationary in the fluid whereas the control cylinder moves along with the principal cylinder. The wall is an obstruction at rest in the fluid and stays behind as the cylinder travels on, whereas the control cylinder moves relative to the fluid and produces constant perturbations in the flow itself. In summary, the action of force fields in fluids at a distance manifest themselves in the changes ments (b) interference l i f t o f p r i n c i p a l c y l i n d e r . Chapter 7: Results and Discussions 118 of the lift and drag forces on both the large and small cylinder. The changes in the various quantities are not the same as those stated by Zradkovich [31] for the lift and drag force on identical cylinders arranged side by side relative to the flow. Effects like phase correlation and lift fluctuation amplitude are more subtle and were not expected when this research was begun. Chapter 8: Conclusions 119 CHAPTER 8 CONCLUSION This thesis investigated the concept of action at a distance in a fluid flow. The experimental study, which was made possible by the novel construction of drag and lift transducers on circular cylinders, focussed on measuring the forces on objects in close proximity to one another when they are embedded in a flow. A change in the measured forces of the objects from their respective isolated values in the fluid, is an indication of action at a distance between the objects. Two experimental configurations were of particular interest: (1) the interaction between a circular cylinder and a stationary flate plate and (2) the interaction between a circular cylinder and a much smaller circular cylinder. The wall is an obstruction at rest in the fluid and stays behind as the cylinder travels on, whereas the control cylinder moves relative to the fluid and produces constant perturbations in the flow itself. The first set of experiments involved the interaction between a circular cylin-der and a flat plate. The plate is stationary in the fluid and is placed in one of two possible orientations. When the plate is mounted parallel to the direction of cylin-der travel, the effects of blockage on the circular cylinder was studied by varying the distance between plate and cylinder. The objective was to determine how far away the wall can be and still affect the cylinder lift and drag. The presence of the plate Chapter 8: Conclusions 120 gives rise to a repulsive lift (an offset in the lift) and both increases and decreases in the drag for cylinder/wall separations of up to 3D. Hence, the action of the wall, for distances up to 3D, on the circular cyinder is the formation of a repulsive lift and increased drag. One point of the area of influence, namely the impact radius of the circular cylinder, has now been determined. When the plate is placed perpendicular to the direction of cylinder travel, with the closest approach at 0.5D, an interesting effect was observed. If the cylinder passes the plate early in its trip across the tank (ie. vortex shedding has barely started), the plate was found to trigger the von Karman vortex street of the cylinder to its steady state conditions as the cylinder passes the plate. The triggering point in a run can be predetermined by placing the plate at the appropriate spot. This happens repeatedly so that phase correlated lift forces can be superposed. This is useful if one wants to trigger the steady state vortex shedding as soon as possible in a tank in order to have more experimental time where the cylinder is at its steady state. As the plate is placed at greater than 12 D from the cylinder's starting point, the lift force becomes more difficult to reset. The reset phases are not entirely in phase with one another any more . This is due to difficulty in overriding the strong vortex shedding that has been established by the time the cylinder has travelled 12 D . The ability of the plate to trigger the vortex shedding of the cylinder (the action) is possible only for small (< ID) gap separations. It appears the cylinder is less sensitive to the plate when the plate is mounted perpendicular to the streamwise directon. This may be due to the wall exposing less surface area to the cylinder for it to interact with. However, the momentary (almost impulsive) interaction the cylinder has as it passes the edge of the wall, is sufficient to cause a profound change in the wake of the cylinder. A short paper on the triggering of vortex streets has Chapter 8: Conclusions 121 recently been accepted by the Physics of Fluids (subject to minor modifications) (see Appendix 3). The flow interference between two circular cylinders with relative diameters of 4 were examined at Reynold's numbers of « 8000 (Reynold's number based on the larger cylinder). The flow interference was studied by simultaneously measur-ing the lift and drag forces, with time resolution, and correlating these forces with flow visualization pictures for both the large and small cylinder. The presence of the control cylinder on the vortex shedding cylinder manifests itself by affecting the amplitude of the lift and drag forces, the phase, onset and frequency of vortex shedding of the principal cylinder. Each of the affected quantities can be used to map out the circular cylinder's area of influence. The areas are not identical but overlap in general. Upstream and downstream areas are not symmetrical and there appear to-be islands where the control cylinder can be positioned, that cause in-tense activity around the principal cylinder in terms of interference lifts, drags, and shedding frequencies. The lift on the large cylinder and the correlation of phase of the vortex shedding provided the best measure of the area of influence. Frequency analysis of the control cylinder lift was also used to determine the principal cylin-der's area of influence. The detection of the principal cylinder's frequency in the spectrum of the control cylinder is a definite indication of action at a distance. It was possible for the upstream positioned control cylinder to pick up the principal cylinder vortex shedding frequency in its spectrum. In this way, the control cylinder can be interpreted as a probe to pick up the principal cylinder's actions at far away distances. Several new questions were posed upon analyzing the data and a continuation of this work could address several avenues for future work: Chapter 8: Conclusions 122 1. discuss the movement of the stagnation point on both cylinders caused by the presence of the other cylinder 2. explore the importance of gap flow dynamics in understanding flow interfer-ence effects 3. the torque on both cylinders should be mesured 4. in the experiment where the von Karman vortex street of the cylinder is triggered, measure the forces on the plate as the cylinder is passing by. 5. measure local velocities with lift probes 6. the transition from two distinct vortex streets that coalesce into one, as the two cylinders act as a compound body, merits investigation This thesis has presented a number of original contributions to the understand-ing of flow interference. The techniques developed include a novel transducer system with time resolution, good sensitivity, capable of measuring two body measurements simultaneously and time correlating these measurements with videos. Some of the more fundamental contributions include a vortex triggering plate system, upstream vortex signatures, changes of vortex shedding frequencies, interference lifts, and vortex shedding phase delays. For these we have given absolute data and shown areas of influence. References R E F E R E N C E S 123 [1] Abernathy, F.H., Kronauer, R.E., The Formation of Vortex Streets, J. Fluid Mech. 13, pp. 1-20, (1962). [2] Acrivos, A., Leal, L.G., Snowdon, D.D., Further experiments on steady sepa-rated flows past bluff objects, J. Fluid Mech. 34, pp. 25-58, (1968). [3] Ahlborn, B., F. Ahlborn and S. Loewen, A Model for Turbulence Based on Rate Equations, J. Appl. Phys 18, pp. 2127-41 (1985). [4] Apelt, C.J., West, G.S., The Effects of Tunnel Blockage and Aspect Ratio on the Mean Flow Past a Circular Cylinder with Reynolds Numbers Between 104 and 105, J. Fluid Mech. 114, pp. 361-377, (1982). [5] Baban, F., So R.M.C., and Otugen M.V., Unsteady Forces on Circular Cylin-ders in a Cross Flow Expt. Fluids (1988). [6] Baban, F., So R.M.C., and Otugen M.V., Dynamic Response of Circular Cylinders in a Turbulent Cross Flow, AIAA (1988). [7] Bearman, P.W., Wadcock, A.J., The Interaction Between a Pair of Circular Cylinders Normal to a Stream, J. Fluid Mech. 61, part 3 pp. 499-511, (1973). [8] Biermann, D. and Herrnstein, W.H. Jr., The Interference Between Struts in Various Combinations, NACA Tech. Rep. 468 (1933). [9] Blevins, R.D., Applied Fluid Dynamics Handbook, Van Nostrand Reinhold Co., (1984). [10] Gerrard, J.H., An Experimental Investigation of the Oscillating Lift and Drag of a Circular Cylinder Shedding Turbulent Vorticies, J. Fluid Mech. 2 (1961). References 124 [11] Hoerner, S.F., Fluid Dynamic Drag: Practical Information on Aerodynamic Drag and Hydrodynamic Resistance, Publ. by the Author (1965). [12] Hori, E., Experiments on Flow around a Pair of Parallel Circular Cylinders, Proc. 9th Japan National Congress for Applied Mech., Tokyo, pp. 231-234 (1959). [13] Jordan and Fromm, Oscillatory Drag, Lift and Torque on a Circular Cinlinder in a Uniform Flow, Phys. Fluids 15 (1972). [14] Kirchoff, R., Potential Flows, Marcel Dekker, Inc., (1985) [15] Kiya, M., Arie, M. Tamura, H., Mori H., Vortex Shedding from Two Circular Cylinders in Staggered Arrangement, Trans. ASME 102, pp. 166 (June 1980). [16] Lefrancois, M.E., Regions of Suppression in a Two Cylinder System, UBC Internal APSC 459 Report (1985). [17] Lugt, Hans J., Vortex Flow in Nature and Technology, David W. Taylor Naval Ship Research and Development Centre, Bethseda, Maryland (1982). [18] Milne-Thompson, L.M., Theoretical Hydrodynamics, The Macmillan Co., New York, 4th ed., (1962). [19] Novak, J., Strouhal Number for Two Cylinders of Different Diameters Ar-ranged in Tandem, Acta Technica, Czechoslovak Academy of Sciences, 3, pp 366-374 (1975). [20] Panton, R.L., Incompressible Flow, John Wiley and Sons Inc., (1985). References 125 [21] Roshko, A., et al. Flow Forces on a Cylinder Near a Wall or Near Another Cylinder Second National Conference on Wind Engineering Research, Col-orado State University, Ft. Collins, Colorado (1975). [22] Saff, E.B., Snider A.D., Fundamentals of Complex Analysis for Mathematics, Science and Engineering, Prentice Hall Inc. Englewood Cliffs, New Jersey (1976) [23] Sarpkaya, T., Kline H.k., Impulsively-Started Flow About Four Types of Bluff Body J. Fluids Eng. 104, pp. 207-213 (1982). [24] Sarpkaya, T., Vortex Induced Oscillations, J. Appl, Mech. 6, p. 244, (1979). [25] Seto, M., Ahlborn, B., Lefrancois, M., Triggering of Vortex Streets, Phys. Fluids (in press). [26] Seto, M.L., Watt, R., Williams, A.E., A Study of Interactions of Opposing Vortex Streets and the Development of a Drag Transducer for Such Studies, UBC Internal APSC 459 Report (1987). [27] Spivack, H.M., Vortex Frequency and Flow Pattern in the Wake of Two Par-allel Cylinders at Varied Spacings Normal to an Air Stream, J. Aero. Sci 13, pp. 289-297, (1946). [28] Strykowski, P.J., Sreenivasan K.R., Control of Vortex Shedding Behind Bluff Bodies, Fifth Symposium on Turbulent Shear Flows (1984). [29] Tatsuno, M., Steady flows around two cylinders at low Reynolds numbers, Fluid Dynamics Research 5, pp. 49-60 (1989). References 126 [30] Tatsuno, M., Ishi-i, K., Flow Visualization and Force Measurements on Two Cylinders at Low Reynolds Numbers, 3rd Int. Conf. Flow Visualization (1983). [31] Zradkovich, M.M., Review of Flow Interference Between Two Circular Cylin-ders in Various Arrangements, Trans. ASME I: J. Fluids Eng. 00, pp. 618-632; (1977). [32] Zradkovich, M.M., Pridden, D.L., Interference Between Two Circular Cylin-ders; Series of Unexpected Discontinuities, J. Indust. Aerodynam. 2, pp. 255-270, (1977). [33] Specifications and Tests for Strain Gage Force Transducers, Standards and Practices for Instrumentation 6ed. Instrument Society of America (1980). [34] Circuit Cellar, Byte Magazine, May (1987). Appendix 1 Listing of ACAD Lisp Program 127 Appendix 1 Listing of A C A D Lisp Program (flow.lsp). Appendix 1 Listing of ACAD Lisp Program 128 APPENDIX 1 LISTING OF A C A D LISP P R O G R A M fiow.lsp Autolisp code for Mech 502 project for potential flov past a cylinder April 19/1990 (defun cyl () (setq psi (open "psi.dat" "r")) (setq th (open "th.dat" "r")) draw the cylinder (setq th 0) (setq ptl '(5 5)) (setq pt2 '(0 0)) (while (<= th (+ (* 2 pi) (/ pi 180) )) (setq x (cos th)) (setq y (sin th)) (setq pt2 ( l i s t (eval x) (eval y))) (command "line" ptl pt2 "") (setq p t l pt2) (setq th (+ (/ pi 180) th )) ) (defun flow () ; draw psi > 0 for flow past a single cylinder (setq a 1) (setq psi (getreal "psi=? ")) (setq psif (getreal "to ?")) (setq incr (getreal "in increments of ? ")) (while (< psi (+ psif 0.001)) (if (>= psi 0) (progn (setq th pi) (setq dth (/ (* (cos pi) pi) 90)) ) ) ( i f (< psi 0) (progn (setq th 0.0001) ;(setq th (/ (*3 pi) 2)) (setq dth (/ pi 90)) ) ; calculate the f i r s t p t l (setq R (+ 1 (/ psi (sin th)))) (setq x ( * R (cos th))) (setq y ( * R (sin th))) (setq p t l ( l i s t (eval x) (eval y))) (setq th ( + th dth)) (while (> th 0) Appendix 1 Listing of ACAD Lisp Program (setq R (+ 1 (/ psi (sin th)))) (setq x ( * R (cos th))) (setq y ( * R (sin th))) (setq pt2 ( l i s t (eval x) (eval y))) (command "line" ptl pt2 "") (setq ptl pt2) (setq th ( + th dth)) ) (setq psi (+ psi incr)) (command "redraw") ) ; end psi loop ) ; end subroutine definition ; M A I H — » (defun go () flow () ) Appendix 2 Listing of MATLAB Programs 130 Appendix 2: Listing of M A T L A B programs (trial, proc, and acamp) Appendix 2 Computer Listings 131 APPENDIX 2 C O M P U T E R LISTINGS trial.m f unetion[1]=f2nois e(sum) '/.this routine rinds the tendency of the FFT amplitudes and corrects '/, for 1/f noise the FFT amplitude and its corresponding frequency are '/. the inputs '/, doesn't include points 8-11 (inclusive) load freq; */. load ; x(l:7)=f(l:7); x(8:17)=f(12:21); x(22:36)=f(68:82); x=x' • y(l:7)=sum(l:7); y(8:17)=sum(12:21); y(22:36)=sum(68:82); y=y'; z=x.*y; speedfit(x,z,3) v=ans; curve=polyval(v,f); curve=curve./f; 8um=sum-curve; plot(f,sum) l(l)=sum(9)/max(sum); l(2)=sum(10)/max(sum); Appendix 2 Computer Listings proem funct ion[v]=f2nois e(buf) '/. this routine extracts from the raw data: the two highest amplitudes of */, the FFT and interference l i f t . '/. cen=buf(1800:4090); fini=size(buf); */. find offset l i f t st=mean(buf(1:100)); mid=mean(cen); en=mean(buf((fini-100):fini)); a(l)=8t-mid; a(2)=en-mid; a(3)=(max(cen)-mean(cen))/2; a(4)=(min(cen)-mean(cen))/2; offset=mean(cen); cen=cen-offset; clear f i n i clear buf clear st clear mid clear en clear offset z=fft(cen); mag=sqrt(z.*conj(z)); magg=mag(l:200); clear z clear mag f=300/4096*(l:200); freq(1)=f(maxel(magg)); magg(maxel(magg) )=0; freq(2)=f(maxel(magg)); magg(maxel(magg))=0; freq(3)=f(maxel(magg)); conv=200/4096*0.1206; a=a*conv; v=[a freq]; Appendix 2 Computer Listings 133 a c a m p . m '/, this program obtains the ac amplitude of an oscillating quantity '/, the quantity being array elements 1800:4090; '/, use i s : t=acamp(filename) '/, after filename has been loaded function[v]=f2noise(inparr) cen=inparr(3000:4090); offset=mean(cen); cen=cen-offset; */. for i=6:1085, buf=cen(i-B:i+5); avginp ( i) =ntean (buf); end V. v(l)=max(avginp(6:300)); v(2)=min(avginp(6:300)); v(3)=max(avginp(301:600)); v(4)=min(avginp(301:600)); v(8)=max(avginp(601:900)); v(6)=min(avginp(601:900)); v(7)=max(avginp(901:1085)); v(8)=min(avginp(901:1085)); v(9)=max(avginp); v(10)=min(avginp); Appendix S Copy of paper in press Appendix 3 Copy of paper in press Appendix S Copy of paper in press 135 A technique to trigger repeatable vortex wake configura-tions from bluff bodies by Mae Seto, Boye Ahlborn, and Marcel Lefrancois Department of Physics UBC Vancouver V6T 2A6, Canada Abstract The initial configuration of a vortex street behind an impul-sively - started cylinder in a towing tank is usually subject to small scale perturbations in the flow. We found that the pres-ence of a trigger plate, mounted normal to the towing direction on one side of the trajectory, induces an early bias to the wake vortex configuration. The phase of shedding, as inferred from lift force measurements becomes quite repeatable. Steady state wake oscillations can be induced early so that the length of vortex street in a given towing facility is increased. Appendix S Copy of paper in press 136 An impulsively started circular cylinder towed at Reynolds numbers of about 1 0 4 initially produces a pair of symmetric vor-tices. Due to some initial perturbations an asymmetry develops, so that subsequent eddies are shed alternately from opposite sides of the cylinder. After the startup interval of a few shedding cycles a steady state is reached which is known as the von Karman1 vortex street2, where the eddies are shed at the Strouhal frequency. As the eddies develop on alternate sides, the cylinder experi-ences an oscillating lift force. During the startup interval the lift force amplitude grows and it may take several cycles until the lift reaches its steady state amplitude. The vortex shedding frequency can be locked in with external effects 3 , and it may be shifted slightly away from the natural Strouhal frequency. The frequency and characteristics of the vortex street may also be influenced by the end conditions of the towed objects4. The physical perturba-tions in a given experiment determine when and on which side the first vortex of the fully developed street will shed. The issue of accurate predictions of vortex streets in nu-merical calculations of the Navier Stokes equation was raised re-cently by Anderson, who used Chorin's random vortex method 6 to investigate the impulsively started cylinder. If the scale of these computations is too fine, the vortex shedding may be sup-pressed entirely. However Anderson et. al. found that reproducible and convergent computations of vortex shedding can be accomplished if an initial perturbation, such as a vortex, is inserted into the free stream. Appendix S Copy of paper in press 137 The numerical uncertainty of the onset of the vortex shedding mirrors the expe r imenta l s i tuat ion. With the symmet r i c init ial conditions of a dragged circular cyl inder it is not obvious which s ide of the object will i ssue the first eddy of the vortex street. This makes it difficult to accumulate phase correlated experimental data using detection systems that are stationary in the lab refer-ence. In this note we show that the random start of a vortex street can be triggered immediately by an initial phys ica l asymmetry, (similar as the numerical analysis of Braza et. a l . 7 , and Anderson et. a l . 5 requires a numerical asymmetry.) A suitable bias is a trig-ger plate mounted a distance AX downstream of the starting point of a towing experiment. Fig.1. We found that such a s imple dev ice will fix the posit ion at which the first of the asymmetr ic edd ies will appear and hence phase lock the first eddies of the vortex street downstream of the trigger plate. An added advantage is the fact that the street can be triggered early so that the useful length of the towing tank is increased for vortex shedding experiments. The experiments to demonstrate this effect were carr ied out in a 1 x 1 x 5m towing tank. The object, a circular cylinder of d i -ameter D - 5.1 cm, was always towed from the same end of the tank and immediately returned after each run to the starting position. By selecting the settling time between succes s i ve runs the level of initial turbulence in the tank could be varied. The cylinder could be towed by either connect ing it to an overhead cart or to a flat sliding platform at the bottom of the tank. The trigger plate is a Appendix S Copy of paper in press 138 flat, 6mm thick a luminum plate with 45° beveled edges. It is c l amped onto the wal l perpendicu lar to the d i rect ion of travel, leaving a gap AY of typically 0.5 D for the bar to clear. The towing platforms are connected by cable to a 0.5 H P motor which allows constant towing speeds to be se lected in the range of 5 to 100 cm/sec. In these experiments a towing speed of 15- 18cm/sec was se l ec ted " (corresponding to Reynolds numbers in the range 7-9000. The bar reaches its terminal velocity within about 3 D of travel. The bar is fitted with strain gauges to detect and measure both lift FL and drag FQ. The electrical s ignals are recorded, stored, and analyzed by computer 8 . In addition a video camera or a 35 mm camera can be mounted on the ceiling of the lab to record flow pattern. Flow visual izat ion and force measurements can be time corre lated by including in the field of v iew of the camera a counter that displays a number and sends out electr ical pulses. In addition the data system records electr ical pulses which are gen-erated when the towing cart pas ses preselected points in the tank. S imultaneous observations of lift, drag, and video camera records show the c l o s e cor re lat ion between lift and vortex format ion, which has been noted before 9 . The lift force act ing on the bar is directed towards the side where a new vortex is formed. The lift s ignal is hence a good indicator of the development of the vortex s t r ee t . In a control exper iment we first measured the lift and drag s ignals a s function of t ime t for an impuls ively started cy l inder without trigger plate, Fig. 2a. The time axis may be calibrated in units of D/U = 5.1cm /18.5 cm/sec= 0.28sec. A l s o shown on the Appendix S Copy of paper in press 139 horizontal axis is a distance sca le X - U t divided into units of D, which indicates the position of the bar in the tank relative to the starting point. (Both sca les are slightly distorted near the starting point s ince the cart does not reach its terminal velocity immedi -ately.) In these runs the time intervals between s u c ce s s i v e traces is only 3 minutes, so that a significant amount uf background tur-bulence remains in the tank. Two features stand out: First the max ima of the s ignals appear with random phase, and second the signal amplitude increases gradually to reach maximum deflections after four of five cycles. However the simultaneously recorded drag reaches an approximately constant level long before the lift s ignal has attained its maximum value. The first indication of the forma-tion of a vortex street occurs at a distance of X = 8 D. The signals in Fig.2 are arranged so that a lift maximum corresponds to a force pointing in +Y direction, and a minimum indicates a force pointing in the -Y direction. Note that the trigger plate is -mounted on the -Y side of the towed bar. The other data sets of Fig. 2 show lift s ignals of towing ex-periments with the trigger plate. The start up distance AX is varied between the sets. In all ca se s the lift s ignal shows a strong min imum just after the cy l inder has p a s s e d the tr igger p late. Therefore the first eddy of the triggered regular vortex street forms just downstream of the trigger plate on the -Y s ide. Subsequent ly produced eddies are hence locked in phase by the trigger plate. Fig. 2c shows signals where the trigger plate is mounted at a distance A X «14 D where a vortex street has already started to form in exper-iment without the trigger plate, shown in F ig. 2a . ' The trigger Appendix S Copy of paper in press 140 mechanism overrides the vortex shedding initiated by random noise. It starts a new vortex street where the eddies have their location fixed relative to the trigger plate so that the positions of the first vortices in the triggered street can be predicted with good accuracy. Fig. 3 shows a photo taken with 0.5 sec exposure time of the surface flow pattern. The cyl indrical bar of D= 5.1cm diameter was towed at the speed U =18 cm/sec. Aluminium filings are used as tracers. The trigger plate in the bottom left of the picture appears to be tilted due to its horizontal offset from the optical axis of the camera lens. The magnification of the photo can be judged from the two l ines scratched 10 cm apart onto the trigger plate paral lel to its edge. In order to determine the accuracy with which a particular eddy may be predicted a series of 20 runs was analysed. The pos i -tion of maxima on the lift s ignals were measured. Each maximum correspond to a particular vortex on the +Y side (facing away from the trigger plate). The vortices are listed as function of time t and distance X from the starting point. Table 1 shows the results. Of interest are the standard deviations at of the sample and the un-certainty o x of the position at which an eddy will be formed in the next run. This quantity is obtained by multiplying ot by the towing speed U. It can be seen from the table that this uncertainty is less than 10 % of the spatial period X = x i + i - x, of succes s i ve vortices. The location of the first vortex may be predicted with an uncer-tainty a x i / D £ 2 0 % . The time starts running when the circular cyl in-der begins to move. In the triggered experiments the fluid in the tank was left to settle down for 30 minutes between runs to ascer-Appendix S Copy of paper in press 141 tain low background turbulence for each experiment. However the vortex streets could also be reliably tr iggered if the runs were taken only 3 minutes apart. At this short settling time the untrig-gered runs yield the random behavior displayed in Fig. 2a. The vortex street can also be triggered in the impulsive start up experiments by an asymmetry in the f l ow. The flow is biased when a smal l perturber is mounted in the vicinity of the cylinder, and both objects are dragged jointly. We used a small cylinder of diameter d= 1/8 D as perturber. This bias causes immediate vortex shedding. However the drag is permanently affected: Drag and vor-tex shedd ing is reduced if the perturber is mounted behind and slightly to the s ide the cyl inder at se lected d i s t a n c e s 1 0 - 8 ; the drag is increased if the perturber is mounted about 1.5D s ideways of the c y l i n d e r 1 1 . The trigger plate, on the other hand, provides an asymmetry in the flujd_which is left behind as the bar is dragged through the tank. Whi le the lift s ignal reaches the steady state magnitude immedi -ately after the bar pa s se s the trigger plate, the presence of the trigger plate cannot be noted on the drag signals at al l. Asymmetry in the flow - a s produced by the perturber cyl inder - alters the en -tire vortex street, whereas asymmetry in the initial condit ions of the fluid - as produced by a trigger plate - does not affect the flow pattern downstream of the perturbation. The triggering leads to the shedding of eddies at wel l predictable locations. They appear im-mediately behind the trigger plate so that the useful length of a vortex streets in a given towing tank can be effectively increased. Appendix 8 Copy of paper in press Acknowledgements. This work was in part supported by a research grant from National Science and Engineering Research Council of Canada Appendix S Copy of paper in press Figure Captions. Fig. 1 Towing tank with trigger plate T. 143 Fig. 2 Traces of lift force, FL, and drag force, FD, of a circular cylinder (D=5.1 cm), which is towed at U=18.5cm/sec. The horizontal axis can either be read as a time axis calibrated in units of D/U, or as position X= U t in the tank calibrated in the units of D; (a) without trigger plate, (b) trigger plate mounted at A X = 6D, (c) trigger plate mounted at AX=14D. Fig. 3. Photo of vortex street of a circular cylinder towed in the x - direction. Exposure time 0.5 sec. The lines scratched onto the trigger plate parallel to its beveled edge are 10 cm apart. Table 1. , Average time tj and space XJ positions of lift s ig-nal maxima of a circular cylinder, and standard deviations o\ and o x of 20 runs. D = 5.1cm. U=18.5 cm/sec. The street is ini-tiated by a trigger plate mounted AX « 40 cm upstream of the starting point, are the . References 1 Th. von Karman Gottinger Nachrichten Math. Phys K1. 509,(1911), Th. von Karman and H.Rubach, Phys.Z. 13, 49(1912); Appendix 3 Copy of paper in press 144 2 Lord Kelvin, Nature p. 524 ,(1894); Horace Lamb, " Hydrodynamics" 6th ed. (1932) Ch . V l l ; for further early references see also G . Birkhoff.Journal of Appl ied Physics, 24, 98-103 (1953). 3 see for instance T.Sarpkaya, Journal of Appl ied Mechanics, 46, 241-258 (1979). 4 C.H.K. Will iamson, P.FIuids, 31, 2742-2744 (1988). 5 C R . Anderson. C. Greengard, L. Greengard, V. Rokhlin, P. Fluids, A2, 883-885, (1990). 6 A.J.Chorin, J.Fluid Mech. 57, 785 (1973) and J.Comp.Phys. 27, 428 (1978). 7 M. Braza , P. Chassaing, and H.H. Minh, J . Fluid Mech. 165, 79 (1986) 8 B.Ahlborn, M.Seto, & M. Lefrangois, Bui. Am.Phys.Soc. 32, #10, 2044 (1987). 9 T.Sarpkaya and H.K.Kline, Journal of Fluids Engineering, 102, 207-213 (1982). 1 0 P.J.Strykowski and K.R.Sreenivasan, Bul.Am.Phys. Soc. 29, #9, 1557, (1984). 1 1 B.Ahlborn and M.Lefrangois, Bull. Am. Phys. Soc. 30, #10, 1727 (1985). Appendix S Copy of paper in press 145 Table 1 vortex i= 1 2 3 4 5 6 7 tj [sec] 2,22 3.32 4.43 5.54 6.60 7.74 8.87 ±c\ [msec] 40 59 87 87 87 99 110 XJ [cm] 41.13 61.35 81.89 102.5 123.2 142.2 164.2 ± ox [cm] 0.8 1.1 1.6 1.6 1.6 1.8 2.0 ox Ik 3.8% 5.3% 7.8% 7.8% 7.8% 9.9% 10% Fig. 1 5m Z - : A Y 1 M ! « - A X Appendix S Copy of paper in press FIG 3 Appendix 4 Strain Gauge Specifications 148 Appendix 4: Strain Gauge Specifications Appendix 4 Strain Gauge Specifications 149 ELEKTRISCHES ; MESSEN MECHANISCHER . GRDSSEN: DehnungsmeBstreifen Strain Gauges Jauges d'extensometrie Widerstand Resistance Resistance k-Faktor G a u g e factor Facteurk Temperaturkoefftzient desk-Faktora Twtpe iu lure coefficient ot gauge factor Coefficient d e temperature du facteurk Stuckzahl Quantity Ouantite ArtikelNr. Part No . N o d e R e i . 12 « . ZX z.zzt i y. S5 P ? S / < ie S t u c k 13 . 1 3 - 2 0 3 4 Typ 5 •' I 2 0 L Tempei aturkompensation: AngepaBt fur Temperature Compensat ion: Compensated tor Compensat ion d e tenipeiature: Compensat ion pour Stahl Steel Acier Sonstige other IX = I 1 p p Tl - 'K F o a T c O t o . N o d e F e u W e L a s Nr. Lot No. N o . d e Lot A 2 5 4 / 8 EU 4 9 4 S 1 / 5 115-1 • r N -\ --4 8 T z °cn se •-> Temperstur-verhatten der DehnungsmeBstreKen (DMS) ftppiiztert auf ainen Werk&iott mrt d e m umaerbg angegefaenon W i r n i e a u s d e h n u n o s t o e f t o o n t e r a . Temperature characteristic of strain Gauges applied to material having a temperature coefficient of linear expansion of a (see overleaf) Comporternent en temperature d'une }auge appftquee tur un materiau avec . coef. d e dilatation therrrique a voir a u verso. Afte techmsehen Daten nach V D E / V D I 2 6 3 5 . Bet Rucfcfragen bine D M S - T y p und Los-Nr angeben. Austuhrtiche tnlormatjonen iiber die HanoTiabung von D M S entnehmen Sie brlte den HBM-Broschuren und d e n Gebra ixhsanweisungen der Klebstoffe. AR technical data accordwg to V D E / V D i Standards 2635. In case of further inquiries please indicate gauge type end lot number. Comprehensive information for (he handling of strain gauges is given in various H B M brochures and in the instructions for use of the individual adhesive types. Toutes caractenstiques seton Standards V D E / V D I 2635. Pour toutes demandes cornpternentajres inotquer le type de la jauge et le numero de lot. L a brochure H B M et tes notices d'utftsaten des cofles contiennent les informations necessaires a la mane H O T T T N Q E R B A L D W I N M E S S T E C H N I K G M B H Postfach 42 35 lm Ttefen S e e 45 • D-6100 Darmstadt 1 Tel . (061 51) '803-1 Telex 419341 ELEKTRISCHES :\ MESSEN JWECHANISCHER 'j GR0SSEN E m p f o h l e n e Ktabstof fe : Z 70: Kalsftartende' £ir^Kon^xTOnteTvSc^^nel^-Webstolt. bis 120 6 C an wend bar; ertorderi gtatte Ktebeftachen. X 60: Kalthartender Zweikomponenten-Scfinellklebsiofl. bis 6 0 ' C anwendbar, E P 250: Heiflhartender ZweiKomponenten-Kleb-sioff. bis 2 5 0 e C anwendbar: vorzugs-weise fur Applikationen im Aufnehmef-bau E P 3 1 0 : HeiShartender Zweikomponenten Kleb-stoft, bis •+ 3 1 0 : C anwendbar: vorzugs-weise fur Applikationen im Aufnehmer-bau. R n o o m m a n d e d A d h e s i v e s : Z 70: R o o m temperature curing single compo-nent cement. Max. ambient temperature for the instal-led strain gauges is 120*C. Smooth sur-faces required. X 6 0 : Room temperature curing two compo-nent cement. Max. ambient temperature for the instal-led strain gauges is 8 0 ' C . E P 250: High temperature curing two component cement. Max. ambient temperature tor the instal-led strain gauges is 250 'C . Especially suitable for the construction of trans-ducers. E P 310: High temperature cunng two component cement. Max. ambient temperature for the installed strain gauges is 310 'C . Especially suitable for the construction oi transducers. C o l t e s r a c o m m a n d e e s : Z 70: Colle rapide monooomposant a froid. Temperature maxi. d'utihsation: 120 ; C. Necessite une surface polie. X 60: Col le rapide a deux composants a froid. Temperature maxi. d'utilisation: 80 C . E P 250: Col le a de J X composants a chaud Tempereture maxi. d'utilisation: 250 J C. Pariiculieremeni conseillee en fabrication de capteurs. Incompatible avec les jauges de la serie A . E P 310: Colle a deux composants a chaud. Temperature maxi. d'utilisation: 310 'C . Particulierement conseillee en fabrication d e caoteurs. 


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