E ect of In Phase and Out of Phase Forcing on Circular Cylinder Wake by Michael H. Moore Jr. A thesis submitted to the Graduate Faculty of Auburn University in partial ful llment of the requirements for the Degree of Master of Science Auburn, Alabama May 4, 2013 Keywords: Circular cylinder, Flow control, Periodic forcing Copyright 2013 by Michael H. Moore Jr. Approved by Anwar Ahmed, Chair, Professor of Aerospace Engineering Roy Hart eld, Walt and Virginia Woltosz Professor of Aerospace Engineering Jay Khodadadi, Alumni Professor of Mechanical Engineering Abstract Using periodic forcing, the control of instabilities in the wake of a circular cylinder was investigated. The cylinder model had two straight slits, one on each side, that were connected to separate low frequency and high frequency acoustic drivers. In order to provide equal periodic forcing, the top and bottom slits were separated by a partition located in the middle of the cylinder. This feature also allowed the implementation of in-phase (IP) and out-of-phase (OP) forcing. The experiments were conducted at six di erent forcing frequencies and Reynolds numbers of 12,000 and 24,000. Excitation frequencies (fe) ranging from 12fs0 to 4fs0 were utilized in an attempt to decrease and eliminate the amplitude of von K arm an vortex shedding. A unique random noise frequency excitation was also investigated and was found to similarly suppress the oscillatory wake. Forcing from the two dimensional slit was able to disrupt the formation of the von K arm an instability, therefore reducing the oscillatory wake and the pressure drag. A maximum reduction of 28% was observed for the in-phase driver mode and 26% for out-of-phase. At the lower Reynolds number the wake was more responsive to the periodic forcing and required a lower blowing coe cient. It was found that the out-of-phase excitation caused the shedding frequency to lock on to the corresponding excitation frequency until approximately 4fs0. In-phase forcing was more e cient at suppressing the cylinder wake, while the out-of-phase driver mode had more control authority. ii Acknowledgments The author would like to thank Dr. Anwar Ahmed for his guidance, patience, and expertise in the development of this thesis. You have taught me many valuable lessons, and for that I am forever thankful. Thanks are also due to Mr. Andy Weldon for his advice and expertise in machining each part of the experimental apparatus. I would also like to thank Mr. AJ Weiner and Brian Davis for their support and encouragement while working in the wind tunnel. Last, but not least I would like to acknowledge my family and loving wife for their patience, encouragement, and emotional support through this long and challenging process. iii Table of Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii List of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Blu body ow characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Flow control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Passive ow control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3.1 Body geometry and surface alterations . . . . . . . . . . . . . . . . . 5 1.3.2 Surface alterations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 Active ow control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.5 Present research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2 Experimental Set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.1 Details of cylinder and test set-up . . . . . . . . . . . . . . . . . . . . . . . . 10 2.1.1 Drivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.1.2 Data acquisition system . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.1.3 Constant temperature anemometers . . . . . . . . . . . . . . . . . . . 13 2.1.4 Wake pressure survey . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.1.5 Particle image velocimetry (PIV) . . . . . . . . . . . . . . . . . . . . 14 3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.1 Wake power spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.2 Mean wake quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 iv 3.3 Time-averaged turbulent quantities . . . . . . . . . . . . . . . . . . . . . . . 31 3.3.1 Time-averaged mean ow . . . . . . . . . . . . . . . . . . . . . . . . 32 3.3.2 Turbulence intensity . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.3.3 Reynolds shear stress . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.3.4 Turbulent kinetic energy . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.3.5 Vorticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.3.6 POD modal energy distribution . . . . . . . . . . . . . . . . . . . . . 36 4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 A Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 A.1 Constant temperature anemometer calibration . . . . . . . . . . . . . . . . . 80 A.2 Power ampli er calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 B Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 B.1 Drag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 C Uncertainty analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 v List of Figures 1.1 Periodic laminar wake: (a) Re = 54, (b) Re = 65, (c) Re = 102 [1] . . . . . . . 3 1.2 Vortex-formation showing entrainment ows [2] . . . . . . . . . . . . . . . . . . 3 2.1 Cylinder model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 Cross section of hollow partitioned cylinder . . . . . . . . . . . . . . . . . . . . 11 2.3 Periodic forcing (IP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.4 Periodic forcing (OP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.5 Side view of PIV wall set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.6 periodic forcing set up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.7 Particle image velocimetry test set-up . . . . . . . . . . . . . . . . . . . . . . . 16 3.1 Time history of random noise signal . . . . . . . . . . . . . . . . . . . . . . . . 18 3.2 Power spectra of random noise signal . . . . . . . . . . . . . . . . . . . . . . . . 19 3.3 Power spectra for Re = 12,000, IP . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.4 Power spectra for Re = 12,000, OP . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.5 Power spectra for Re = 24,000, IP . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.6 Power spectra for Re = 24,000, OP . . . . . . . . . . . . . . . . . . . . . . . . . 22 vi 3.7 Description of the wake half-width . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.8 Mean velocity pro le (x/D = 4, Re = 12,000) . . . . . . . . . . . . . . . . . . . 26 3.9 Mean velocity pro le (x/D = 4, Re = 24,000) . . . . . . . . . . . . . . . . . . . 27 3.10 Variation of wake half-width (Re = 12,000) . . . . . . . . . . . . . . . . . . . . 29 3.11 Variation of wake half-width (Re = 24,000) . . . . . . . . . . . . . . . . . . . . 30 3.12 Cartoon of in-phase forcing e ect . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.13 Cartoon of out-of-phase forcing e ect . . . . . . . . . . . . . . . . . . . . . . . . 31 3.14 Streamline topology (Re = 12,000, No forcing) . . . . . . . . . . . . . . . . . . . 37 3.15 Streamline topology (Re = 12,000, fe = 11.5 Hz) . . . . . . . . . . . . . . . . . 37 3.16 Streamline topology (Re = 12,000, fe = 23 Hz) . . . . . . . . . . . . . . . . . . 38 3.17 Streamline topology (Re = 12,000, fe = 46 Hz) . . . . . . . . . . . . . . . . . . 38 3.18 Streamline topology (Re = 12,000, fe = 69 Hz) . . . . . . . . . . . . . . . . . . 39 3.19 Streamline topology (Re = 12,000, fe = 92 Hz) . . . . . . . . . . . . . . . . . . 39 3.20 Streamline topology (Re = 12,000, fe = Random noise) . . . . . . . . . . . . . . 40 3.21 Streamline topology (Re = 24,000, No forcing) . . . . . . . . . . . . . . . . . . . 40 3.22 Streamline topology (Re = 24,000, fe = 23 Hz) . . . . . . . . . . . . . . . . . . 41 3.23 Streamline topology (Re = 24,000, fe = 46 Hz) . . . . . . . . . . . . . . . . . . 41 3.24 Streamline topology (Re = 24,000, fe = 92 Hz) . . . . . . . . . . . . . . . . . . 42 vii 3.25 Streamline topology (Re = 24,000, fe = 138 Hz) . . . . . . . . . . . . . . . . . . 42 3.26 Streamline topology (Re = 24,000, fe = 184 Hz) . . . . . . . . . . . . . . . . . . 43 3.27 Streamline topology (Re = 24,000, fe = Random noise) . . . . . . . . . . . . . . 43 3.28 Turbulence intensity contour (Re = 12,000, No forcing) . . . . . . . . . . . . . . 44 3.29 Turbulence intensity contour (Re = 12,000, fe = 11.5 Hz) . . . . . . . . . . . . 44 3.30 Turbulence intensity contour (Re = 12,000, fe = 23 Hz) . . . . . . . . . . . . . 45 3.31 Turbulence intensity contour (Re = 12,000, fe = 46 Hz) . . . . . . . . . . . . . 45 3.32 Turbulence intensity contour (Re = 12,000, fe = 69 Hz) . . . . . . . . . . . . . 46 3.33 Turbulence intensity contour (Re = 12,000, fe = 92 Hz) . . . . . . . . . . . . . 46 3.34 Turbulence intensity contour (Re = 12,000, fe = Random noise) . . . . . . . . . 47 3.35 Turbulence intensity contour (Re = 24,000, No forcing) . . . . . . . . . . . . . . 47 3.36 Turbulence intensity contour (Re = 24,000, fe = 23 Hz) . . . . . . . . . . . . . 48 3.37 Turbulence intensity contour (Re = 24,000, fe = 46 Hz) . . . . . . . . . . . . . 48 3.38 Turbulence intensity contour (Re = 24,000, fe = 92 Hz) . . . . . . . . . . . . . 49 3.39 Turbulence intensity contour (Re = 24,000, fe = 138 Hz) . . . . . . . . . . . . . 49 3.40 Turbulence intensity contour (Re = 24,000, fe = 184 Hz) . . . . . . . . . . . . . 50 3.41 Turbulence intensity contour (Re = 24,000, fe = Random noise) . . . . . . . . . 50 3.42 Reynolds shear stress contour (Re = 12,000, No forcing) . . . . . . . . . . . . . 51 viii 3.43 Reynolds shear stress contour (Re = 12,000, fe = 11.5 Hz) . . . . . . . . . . . . 51 3.44 Reynolds shear stress contour (Re = 12,000, fe = 23 Hz) . . . . . . . . . . . . . 52 3.45 Reynolds shear stress contour (Re = 12,000, fe = 46 Hz) . . . . . . . . . . . . . 52 3.46 Reynolds shear stress contour (Re = 12,000, fe = 69 Hz) . . . . . . . . . . . . . 53 3.47 Reynolds shear stress contour (Re = 12,000, fe = 92 Hz) . . . . . . . . . . . . . 53 3.48 Reynolds shear stress contour (Re = 12,000, fe = Random noise) . . . . . . . . 54 3.49 Reynolds shear stress contour (Re = 24,000, No forcing) . . . . . . . . . . . . . 54 3.50 Reynolds shear stress contour (Re = 24,000, fe = 23 Hz) . . . . . . . . . . . . . 55 3.51 Reynolds shear stress contour (Re = 24,000, fe = 46 Hz) . . . . . . . . . . . . . 55 3.52 Reynolds shear stress contour (Re = 24,000, fe = 92 Hz) . . . . . . . . . . . . . 56 3.53 Reynolds shear stress contour (Re = 24,000, fe = 138 Hz) . . . . . . . . . . . . 56 3.54 Reynolds shear stress contour (Re = 24,000, fe = 184 Hz) . . . . . . . . . . . . 57 3.55 Reynolds shear stress contour (Re = 24,000, fe = Random noise) . . . . . . . . 57 3.56 Turbulent kinetic energy contour (Re = 12,000, No forcing) . . . . . . . . . . . 58 3.57 Turbulent kinetic energy contour (Re = 12,000, fe = 11.5 Hz) . . . . . . . . . . 58 3.58 Turbulent kinetic energy contour (Re = 12,000, fe = 23 Hz) . . . . . . . . . . . 59 3.59 Turbulent kinetic energy contour (Re = 12,000, fe = 46 Hz) . . . . . . . . . . . 59 3.60 Turbulent kinetic energy contour (Re = 12,000, fe = 69 Hz) . . . . . . . . . . . 60 ix 3.61 Turbulent kinetic energy contour (Re = 12,000, fe = 92 Hz) . . . . . . . . . . . 60 3.62 Turbulent kinetic energy contour (Re = 12,000, fe = Random noise) . . . . . . 61 3.63 Turbulent kinetic energy contour (Re = 24,000, No forcing) . . . . . . . . . . . 61 3.64 Turbulent kinetic energy contour (Re = 24,000, fe = 23 Hz) . . . . . . . . . . . 62 3.65 Turbulent kinetic energy contour (Re = 24,000, fe = 46 Hz) . . . . . . . . . . . 62 3.66 Turbulent kinetic energy contour (Re = 24,000, fe = 92 Hz) . . . . . . . . . . . 63 3.67 Turbulent kinetic energy contour (Re = 24,000, fe = 138 Hz) . . . . . . . . . . 63 3.68 Turbulent kinetic energy contour (Re = 24,000, fe = 184 Hz) . . . . . . . . . . 64 3.69 Turbulent kinetic energy contour (Re = 24,000, fe = Random noise) . . . . . . 64 3.70 Vorticity contour (Re = 12,000, No forcing) . . . . . . . . . . . . . . . . . . . . 65 3.71 Vorticity contour (Re = 12,000, fe = 11.5 Hz) . . . . . . . . . . . . . . . . . . . 65 3.72 Vorticity contour (Re = 12,000, fe = 23 Hz) . . . . . . . . . . . . . . . . . . . . 66 3.73 Vorticity contour (Re = 12,000, fe = 46 Hz) . . . . . . . . . . . . . . . . . . . . 66 3.74 Vorticity contour (Re = 12,000, fe = 69 Hz) . . . . . . . . . . . . . . . . . . . . 67 3.75 Vorticity contour (Re = 12,000, fe = 92 Hz) . . . . . . . . . . . . . . . . . . . . 67 3.76 Vorticity contour (Re = 12,000, fe = Random noise) . . . . . . . . . . . . . . . 68 3.77 Vorticity contour (Re = 24,000, No forcing) . . . . . . . . . . . . . . . . . . . . 68 3.78 Vorticity contour (Re = 24,000, fe = 23 Hz) . . . . . . . . . . . . . . . . . . . . 69 x 3.79 Vorticity contour (Re = 24,000, fe = 46 Hz) . . . . . . . . . . . . . . . . . . . . 69 3.80 Vorticity contour (Re = 24,000, fe = 92 Hz) . . . . . . . . . . . . . . . . . . . . 70 3.81 Vorticity contour (Re = 24,000, fe = 138 Hz) . . . . . . . . . . . . . . . . . . . 70 3.82 Vorticity contour (Re = 24,000, fe = 184 Hz) . . . . . . . . . . . . . . . . . . . 71 3.83 Vorticity contour (Re = 24,000, fe = Random noise) . . . . . . . . . . . . . . . 71 3.84 Energy distribution, (Re = 12,000, xD=4) . . . . . . . . . . . . . . . . . . . . . . 72 3.85 Energy distribution, (Re = 24,000, xD=4) . . . . . . . . . . . . . . . . . . . . . . 72 A.1 Hot wire calibration curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 xi List of Tables 3.1 Coe cients of drag at di erent downstream locations . . . . . . . . . . . . . . . 28 3.2 Coe cients of drag at di erent downstream locations . . . . . . . . . . . . . . . 28 A.1 Hot wire calibration data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 A.2 Ampli er calibration data at Re = 12,000 . . . . . . . . . . . . . . . . . . . . . 83 A.3 Ampli er calibration data at Re = 24,000 . . . . . . . . . . . . . . . . . . . . . 83 xii List of Abbreviations ! Vorticity, = !dU1 b Wake half-width Cd Drag coe cient C Blowing coe cient ujU1 fe Excitation or forcing frequency fs0 Natural shedding frequency IP In-phase forcing k Turbulent kinetic energy, u02+v02+w02U2 1 L Formation length OP Out-of-phase forcing Ps static pressure Pt Total pressure q Dynamic pressure Rij Reynolds shear stress, u0v0U2 1 u0i Fluctuation component of velocity in the streamwise direction u0j Fluctuation component of velocity in the normal direction U1 Free stream velocity xiii vs periodic excitation velocity D Cylinder diameter St Strouhal Number fDU1 xiv Chapter 1 Introduction Circular cylinders are classi ed as canonical blu bodies due to the substantial amount of separation that occurs over the surface and are seen today in many practical applications. These geometric shapes are used readily due to their simple structural characteristics and ease of manufacturing. However, very unique and complex ow characteristics are produced in the wake of the body, that can cause premature fatigue or even structural failure due to vortex induced vibrations. Research on this topic has been conducted for many years to gain a better understanding of the ow instabilities associated with the blu body and to improve or control their detrimental e ects. A number of review articles on the subject of blu body ow characteristics have been written, notably those of Berger and Wille (1972) [3], Bearman (1984) [4], Oertel (1990) [5], Williamson (1996) [6], Rockwell (1998) [7], Roshko (1955) [8] and Williamson and Govardhan (2004)[9]. 1.1 Blu body ow characteristics A very comprehensive description of the behaviour of cylinder wake is described by Zdravkovich in his book on circular cylinder ow [1]. At extremely low Reynolds numbers (Re < 1), called a creeping ow, the inertial forces are very small compared to the viscous forces as a uid encounters a body allowing separation to occur at the rear stagnation point creating a symmetric ow with no vortex shedding. At a Reynolds number of approximately 4 to 5 a closed, symmetric near wake is formed with the free shear layers meeting at the end of the near wake called the con uence point. Figure 1.1a shows a steady separation regime that occurs at Reynolds numbers from 4 to 48 and is characterized by the closed near wake becoming elongated and unstable near Re = 30 due to the Helmholtz instability. The onset of 1 sinusoidal oscillations of the shear layer begins at the con uence point causing the shear layer to roll up into Helmholtz vortices at crests and troughs, shown in Figure 1.1b. These vortices are then shed periodically from either side of the body, creating what is famously known as the von K arm an vortex formation [4] [10]. Gerrard studied the e ects of vortex induced vibrations and described the process of uid entrainment in the near wake of a blu body. It was postulated that the circulation from the connected shear layer increased the strength of the growing vortex until it was strong enough to attract the opposing shear layer across the near wake. The vortex was then separated from the shear layer due to the approach of oppositely signed vorticity and shed downstream as Helmholtz vortices [2]. An illustration of the shear layer entrainment can be seen in Figure 1.2. The entrained shear layer may separate in three directions: (a) the largest part is engulfed into the growing vortex, (b) while another portion gets pushed into the developing shear layer, and (c) the nal portion is temporarily entrained into the body causing a low pressure region of circulation. Flow over a blu body is known to be predominantly two-dimensional until three-dimensional e ects are introduced with Reynolds numbers greater than 180 [10]. At increasing Reynolds numbers up to 200 a fully periodic wake is formed with staggered laminar eddies shown in Figure 1.1c. As Reynolds number increases above 200 a transition in the wake begins. Farther downstream, the laminar periodic wake becomes unstable and the transition gradually moves upstream until the eddy becomes turbulent during its formation. Typically the shedding frequency of the Helmholtz vortices can be quanti ed using the Strouhal number, which relates the shedding frequency (fs0), body diameter (D), and free stream velocity (U1) and is de ned in equation 1.1. For cylinders at sub-critical Reynolds numbers, the average value of St 0:21. St = fDU 1 (1.1) 2 Figure 1.1: Periodic laminar wake: (a) Re = 54, (b) Re = 65, (c) Re = 102 [1] Figure 1.2: Vortex-formation showing entrainment ows [2] Reynolds numbers ranging from 400 to approximately 20,000 are classi ed as a sub- critical state and experience a transition in the shear layers themselves. In this state the instability of the separating shear layer develops, decreasing the formation length and moving the transition point forward. Increasing the Reynolds number further causes the shear layers to become stronger and the instabilities farther downstream to increase in strength, pushing the transition to turbulence gradually upstream until the eddy becomes turbulent during its formation [1]. Above this range is a regime known as the critical state characterized by a transition in the boundary layers.[1] 3 The present research focuses on the sub-critical or shear layer transition regime with the Reynolds numbers used ranging from 12,000 to 24,000. The basic structure of the ow develops as the boundary layer encounters an adverse pressure gradient due to the divergent geometry of the cylinder and separates from the surface, forming a free shear layer. The boundary layer feeds vorticity into the free shear layer downstream of the cylinder causing it to roll up into Helmholtz vortices on the top and bottom of the cylinder which grow larger resulting in the formation of the von K arm an vortex formation. A region of slowly recirculating ow is formed directly behind the body called the near wake separation bubble. The separation bubble is bounded by the interacting shear layers from the top and bottom of the cylinder and is at a signi cantly lower pressure compared to the free stream pressure. This region is responsible for a large portion of the pressure drag associated with blu bodies. The separation bubble ends at a downstream closure point that may be identi ed as a point where the shear layers cross the center line in the wake and begin to interact, or more accurately, at a point where the mean velocity is zero along the wake center line. [11] 1.2 Flow control A large part of uid mechanics research consists of attempts to control a uid as it moves passed a body. Viscous e ects dominate most practical applications and give rise to many complicated ow regimes. At lower Reynolds numbers the dominant force on a body is mainly attributed to skin friction, but as the Reynolds number exceeds a critical value, vortex shedding occurs generating a signi cant amount of pressure drag. Vortex shedding gives rise to a plethora of challenging ow characteristics to combat. A few of the major issues include structural vibrations, acoustic noise, and large increases in the mean drag and lift uctuations. Many areas that could bene t from e ective ow control include o shore platforms, bridge pylons, cables and ropes used for mooring, heat exchanger tubes, cooling towers, smoke stacks, tall buildings, and aircraft control surfaces and antennae to name a few. In an attempt to improve the ow characteristics over blu bodies, a variety of ow 4 control techniques have been developed and are reviewed by Choi et al [12]. The two main categories of ow control are: (1) Passive ow control (2) Active ow control 1.3 Passive ow control Passive ow control techniques are classi ed by a modi cation of the body or surface geometry to alter the ow characteristics. 1.3.1 Body geometry and surface alterations Research conducted by Owen and Bearman [13] showed a signi cant reduction in drag of up to 47% for a cylinder with a sinuous axis and about 25% for a cylinder with hemispherical bumps along the span. It was shown that if the separation line of a blu body is forced to be sinuous , then there is a suppression of the vortex shedding and consequently a reduction in drag. Nakamura and Igarashi [14] achieved a reduction in drag and uctuating forces for a cylinder in a cross- ow by attaching cylindrical rings along its span. Separation bubbles on both sides of the ring allowed the recovery of the low pressure region behind the cylinder. A wake comparison between a smooth cylinder and grooved cylinder was conducted by Liu, Shi, and Yu [15]. The length of the recirculation zone in the near wake was shown to be extended by 18.2% for the grooved cylinder due to the small-scale recirculating zones produced by the cavities, decreasing drag. Shoa, Wang, and Wei [16] added a narrow strip parallel to the cylinder surface at varying angles from the trailing stagnation point. It was found that at a range from 30 to 50 degrees the obstructive strip successfully suppressed the periodic wake. Ahmed et al [17] investigated the ow characteristics over a wavy cylinder. The wake behind the nodal points of attachment was found to be more narrow and have a faster rate of velocity recovery compared to the saddle points of attachment. A splitter plate was investigated by a number of researchers, Anderson and Szewczyk [18], Bearman [19], Hwang 5 et al. [20], Kwon and Choi [21], Ozono [22], and Roshko [8]. The interaction between the top and bottom shear layers was delayed in the wake, suppressing vortex shedding. As a result, the base pressure behind the blu body increased, resulting in a drag reduction. 1.3.2 Surface alterations Helical strakes have been implemented by Scruton and Walshe [23], Woodgate and Mabey [24], Hirsch, Ruscheweyh, and Zutt [25], Wong and Kokkalis [26], and Every, King, and Weaver [27]. This method of passive ow control is able to reduce the force uctuations, which decreases the vibration induced by K arm an vortex shedding. Eckmekci and Rockwell [28] placed a single span wise wire in the upper shear layer on a circular cylinder and observed the e ects on the near wake. The wire was able to decrease the impact of the K arm an instability when it was placed at certain critical angles, which led to a contraction of the time-averaged ow characteristics of the wake. Kareem and Cheng[29] investigated the pressure and force uctuations on roughened cylinders by placing a trip wires at 65 degrees and separation wires at 115 degrees. With the wires positioned at the optimal locations, the surface pressure measured was characteristic of higher Reynolds number ows with three dimensional features. By placing rectangular tabs spanwise at optimal locations along the separation point of a circular cylinder, Yoon [30] achieved a drag reduction. The tabs caused a phase mismatch in the vortex shedding process, which broke up the naturally two dimensional vortices creating high levels of mixing in the wake. 1.4 Active ow control Active ow control methods are characterized by introducing additional energy to the ow. Generally, when time-periodic forcing is applied, the vortex shedding in the wake becomes locked in-phase with the forcing that is applied [31]. A few techniques, however, have been successful in reducing drag and attenuating the von K arm an vortex shedding. 6 Tokumaru and Dimotakis [32] experimented with the e ects of a circular cylinder at an oscillatory high-frequency of rotation to control the wake. The sinusoidal rotation was performed at speci c frequencies, f and a normalized peak rotational rate of . The peak rotation rate was chosen so that the circumferential velocity of the cylinder would be com- parable to the velocity just outside the boundary layer. The Strouhal number was varied between 0.17 and 3.3. The greatest control authority was observed when the forcing fre- quency was in sync with the shedding structures. They concluded that the mechanism by which the wake can be controlled have more to do with the ejection of circulation into the ow instead of the behavior of the ow in the absence of forcing. A base bleed technique was implemented by Bearman [33] and Wood [34]. It was found that the bleed decreased the strength of the vortex formation which decreased the pro le drag. As the strength of the base bleed increased, the formation of the vortices formed farther downstream. An examination of the wake of a transverse vibrating cylinder was performed by Koopman [35], showing that the coherence of separation points along the span is induced when the vibration is driven at the vortex natural shedding frequency. As a certain amplitude of vibration was reached, the vortex formation experienced a dramatic change. Originally, the vortex laments of the non-vibrating cylinder shed in a slanted direction and when the cylinder was vibrated, the vortex laments jumped to align themselves parallel with the cylinder, reducing the lateral spacing between the wake vortices. This phenomenon required a displacement of about 10% of the cylinder diameter for each tested Reynolds number. A similar study was conducted by Ongoren and Rockwell [36] using cylinders of various cross-sectional geometries. The excitation frequency, fe, was at a frequency relative to the formation frequency, fo. At a critical amplitude, both the subharmonic frequency ratio of 0.5 as well as 1, the near wake structures became phase-locked to the cylinder motion, but in two di erent synchronization mechanisms. Oscillations at a frequency close the that of the shedding frequency resulted in a phase shift of approximately . The formation length was signi cantly reduced and an increase in the angle of inclination of shedding was seen in the base region. Just above this 7 frequency ratio the shedding switches phases to the opposite side of the cylinder including a decrease in inclination of the base region to about zero. Over a wide range of forcing frequencies, the near wake rapidly recovered to a large scale antisymmetric mode similar to the K arm an vortex formation through the interaction of the cylinder?s own vortices of alternate signs. A study was done by Fransson, Konieczny, and Alfredsson [37] on the ow around a circular cylinder subjected to continuous suction or blowing. The blowing and suction rate was varied compared to the free stream velocity and given as . The maximum suction was 40% of the free stream and the maximum blowing was 60% of the free stream velocity. It was shown that relatively low levels of suction or blowing had a large e ect on the ow around the cylinder. Suction strengths above -2.5 moved the separation line farther aft resulting in a smaller wake and a drag reduction of up to 70%. When blowing was applied through the porous cylinder, the opposite e ect was observed and an increase in drag occurred. A di erent method of active ow control that has been used in the past involves ap- plying sound waves to the ow. Blevins [38] and Detemple-Laake and Eckelmann [39] are a few of the researchers that have conducted this type of research. Blevins? research was conducted in the Reynolds number range of 20,000 to 40,000. The results showed a cor- relation between sound and span-wise vortex shedding detected by four ush lm sensors placed on the cylinder at di erent span-wise locations. Irregular signals were obtained when the excitation was absent, but when a 143.5 dB sound wave was applied to the ow at the shedding frequency, the four signals were approximately in-phase with less irregularity. This showed that the application of the periodic excitation was able to synchronize the shedding frequency and increase its strength. Detemple-Laake and Eckelmann superimposed sound waves on the ow over a cylinder in the mean ow direction to investigate the coupling mech- anism. The Reynolds number range was selected to be between 53 and 250 with the ratio of sound frequency to natural shedding frequency ranging from 0.5 to 4. Twelve di erent wake 8 structures were found depending on the sound frequency and amplitude that were catego- rized into three groups: structures independent of the ratio of sound frequency and natural shedding frequency, synchronization, and the natural shedding frequency locking onto the sound frequency. 1.5 Present research Past research on internal periodic forcing has been reported by Huang [40] and Fujisawa and Takeda [41]. Huang?s work mainly focused on Reynolds numbers in the range from 4,000 to 8,000. It was found that only weak excitation was needed to suppress the formation of periodic vortex shedding. It was also found that vortex shedding on both sides of the cylinder may be suppressed even when only one shear layer was a ected. This observation showed that the vortex shedding instabilities were a result of the interaction between parallel shear layers. Fujisawa and Takeda [41] focused on periodic forcing through a slit at Reynolds number of 9,000. They altered the location of the slit relative to the attachment point and forcing amplitude to obtain a drag reduction of up to 30%. The optimum placement of the slit was found to be just behind the separation point and an excitation frequency near the unstable frequency of the separating shear layer. Bhattacharya [42] conducted research on the e ect of three dimensional forcing on the wake of a circular cylinder at higher Reynolds numbers of 24,000 and 45,000, which introduces global modes with larger amplitudes. A hollow circular cylinder with diametrically opposite sinusoidal slits were used to introduce three dimensional forcing to e ect the shear layers and a drag reduction of almost 50% was obtained for a Reynolds number of 24,000. The objective of the present work was to explore the e ects of in-phase and out-of-phase forcing on the turbulent wake behind a circular cylinder using two-dimensional forcing. The forcing provided by the acoustic driver diaphragms acted as a synthetic jet that added momentum to the shear layer at the onset of separation through the slits and modi ed the ow in the wake. 9 Chapter 2 Experimental Set-up The cylinder model used in this study had two straight slits on opposite sides. Each end of the cylinder was connected, via copper tubing, to a sub-woofer to apply the periodic forcing at the desired frequencies and blowing coe cients. Tests were performed at Reynolds numbers of 12,000 and 24,000. A constant temperature anemometer (CTA) was used to measure the air speed of the ow through the slits ensuring the proper blowing coe cient, and measure the wake power spectra by computing PSD. This illustrated the a ect of the periodic forcing on the natural shedding frequency of turbulence statistics, vorticity, and energy distributions in the wake. Particle image velocimetry (PIV) was also performed to document the formation of complex wake structures. Post processing of PIV data consisted of proper orthogonal decomposition (POD) to quantify the dominant modes in the wake. The drag coe cient for each case was calculated from pitot surveys of the wake using the momentum de cit method. All experiments were conducted in the Auburn University 3 ft x 4 ft, closed circuit, low speed wind tunnel. The tunnel speed was monitored electronically and also with a manometer. The free stream turbulence level was found to be approximately 0.5% and the non-uniformity was less than 1%. 2.1 Details of cylinder and test set-up The model used was a hollow resin cylinder made on a three-dimensional printer in the Air Force Research Lab at Wright Patterson Air Force Base. A partition in the middle of the cylinder allowed the periodic forcing from each driver to individually exit the slits on either side. Figure 2.1 shows the cylinder model which had an e ective aspect ratio of 23 and 10 slit lengths of 6.5 inches. Figure 2.2 show a cross section view of the cylinder and Figures 2.3 and 2.4 illustrate the in-phase and out-of-phase forcing, respectively. The model was installed between two walls mounted in the test section shown in Figures 2.5 and Figure 2.6. 9.0001.630 1.450 .090 6.500 .025 Figure 2.1: Cylinder model Figure 2.2: Cross section of hollow partitioned cylinder Figure 2.3: Periodic forcing (IP) 11 Figure 2.4: Periodic forcing (OP) The wall inserts were made out of 1 inch thick particle board with large acrylic windows for PIV measurements. The walls were held in place with the help of aluminum L-brackets bolted to the test section oor. The periodic forcing supplied by the drivers traveled through copper piping that was attached to each end of the cylinder, through a round opening in the front end of the acrylic wall, and up through the ceiling of the test section to the drivers. 2.1.1 Drivers The periodic forcing applied to the ow was supplied by two sets of drivers. The low frequency forcing (11.5 Hz { 46 Hz) was generated from two In nity Reference 12 inch sub woofers and the high frequency forcing was generated from two In nity Reference 8 inch (1000 watt max). drivers. The drivers were connected to wave form generators (Wavetek model 182A and 132) to provide a sinusoidal wave signal and desired frequencies. The signal was monitored on an oscilloscope and passed through separate external power ampli ers (MB Dynamics SS250VCF for the 12 inch drivers and an MBIS Model SS500 for the 8 inch drivers) requiring a range of nine to sixteen volts. A polarity reversing box was constructed from two switches in order to change the phase of the drivers. It was found that at the higher frequencies, a larger voltage was required to generate the desired periodic forcing. Special care was taken to prevent any damage to the driver voice coils. 2.1.2 Data acquisition system A National Instruments data acquisition board (NI USB-6210) was used to acquire all of the data generated by the constant temperature anemometers. The raw data was then 12 processed in LabVIEW 10.0.1 using a continuous voltage acquisition program and recorded to a text le for spectrum analysis using MATLAB. 2.1.3 Constant temperature anemometers Constant temperature anemometry was used to the determine the Strouhal number of the wake. A single bridge miniCTA system from DANTEC Dynamics was used to acquire wake spectra. The frequency response of the system was approximately 6 kHz at 30 m/s. The wire was made of platinum plated tungsten with a diameter of 5 microns and a length of 1.25 millimeters. A maximum operating temperature recommended by the manufacturer was 300 C, but a temperature of only 200 C was selected to ensure the longevity of the wire. A two degrees of freedom Velmax traverse was placed above the test section to provide axial and transverse probe movement along the test section. Probe access to the test section was available through a slot cut in the acrylic ceiling. The traverse was manually controlled, via Velmex VP9000 controller, to speci c locations measured in the test section. The CTA probe holder was attached to a streamlined support to reduce the vibration, which was securely fastened to the traverse controller. 2.1.4 Wake pressure survey A pitot probe was secured to the traverse system and connected to a Validyne DP45-16 pressure transducer to obtain the dynamic pressure required to calculate the drag coe cient (Appendix B.1). The transducer was read by a volt meter which sent the pressure data to a National Instruments USB-6008 data acquisition board. A LabVIEW program was developed to record the pressure measurements as the traverse moved in increments of one- tenth of an inch in the transverse direction throughout the wake of the cylinder from two to ten diameters downstream. 13 2.1.5 Particle image velocimetry (PIV) Particle image velocimetry is a well known ow diagnostic technique. The system uses a high energy light source, in this case, a YAG laser, to form a thin light sheet in the desired plane of interest to illuminate the particulates in the ow shown in Figure 2.7. A high speed camera is integrated into the laser timing system to capture successive images to be analyzed. A New Wave Research Solo III dual pulse laser was used for PIV measurements. The light beam was passed through three lenses consisting of a diverging lens, a converging lens to focus the beam, and nally a cylindrical lens to generate the light sheet. The images were captured using a Cooke Corporation Sensicam high speed camera of 1376 x 1040 pixel resolution with a Tamron 75mm lens. The interrogation window was 32 x 32 pixels. The camera timing was synced with the laser pulses using two quantum composer pulse generators (Model 9514). One generator was used to control the laser pulses and the other was used to control the camera shutter. The timing between images was set to 50 s. 1155 image pairs were taken for each case. An Antari Z-800II smoke generator was used to seed the ow with smoke particles and was placed in the di user section of the closed circuit wind tunnel. A remote control was used to trigger the production of smoke. The fog liquid mixture (glycol and water) was heated and vaporized by passing through a heat exchanger and then dispersed into the ow. By placing the smoke generator in the di user, the particles had time to disperse throughout the ow before they reached the test section. CamWare 2.19 software was used to record the captured image pairs on a computer system and Fluere version 0.9 was used to process the image data using cross correlation. 14 Low frequency driver High frequency driver Transparent insert for PIV U Figure 2.5: Side view of PIV wall set-up Low frequency driver High frequency driver Cylinder Tunnel floor Tunnel ceiling Phase Switch Amplifier Waveform Generator Oscilloscope Tunnelceiling Test section Figure 2.6: periodic forcing set up 15 Laser Traverse Cylindrical lens Light sheet Figure 2.7: Particle image velocimetry test set-up 16 Chapter 3 Results and Discussion The tests were conducted at free stream velocities of 15 ft/sec and 30 ft/sec resulting in Reynolds numbers of approximately 12,000 and 24,000, based on the cylinder diameter. The cylinder was positioned between the two support walls with the straight slit 90 degrees from the forward attachment line, which was discovered to be the optimal angle by Fujisawa and Takeda [41]. The single wire constant temperature anemometer was placed directly above the slit to measure the slit jet velocity. At each forcing frequency the blowing coe cient was calculated and the required voltage was recorded to ensure repeatability. The C values and corresponding voltages were listed in Tables A.2 and A.3. 3.1 Wake power spectra The DANTEC single hot wire was placed at a position of yD = 0:5 and xD = 4, which was veri ed to be the optimal position for the upper shear layer using a Hewlett-Packard spectrum analyzer. The natural shedding frequency was found to be 23 Hz for a Reynolds number of 12,000 and 46 Hz for a Reynolds number of 24,000. The forcing frequencies were chosen based on multiples of the natural shedding frequency. The maximum frequency tested was 184 Hz, which was 4fs0, due to driver e ectiveness and power limits. The calculated power spectra for each Reynolds number is based on a DC signal level. Figure 3.3 compares the e ect of the di erent forcing frequencies while operating in the in-phase forcing mode. For the no forcing case the slits were sealed to ensure there was no momentum loss due to the openings. A sharp peak can be seen at the top of the gure at 23 Hz indicating the natural shedding frequency of the cylinder. A sub-harmonic driver frequency of 11.5 Hz, or 12fs0, produced a decrease in the magnitude of the natural shedding 17 frequency, but also introduced a small harmonic peak at the excitation frequency. As the forcing frequency was increased to a value equal to the natural shedding frequency of 23 Hz, an increase in the magnitude of the spectral peak was observed. At 46 Hz the magnitude of the shedding frequency began to decrease indicating an attenuation of the natural shedding frequency. This was also observed in the frequencies greater than 2fs0, where the shedding frequency was damped out almost entirely. A special case using a random noise input was also tested with surprising results. The broadband wavelength of the signal was able to completely eliminate the shedding peak as can be seen in each case. A plot of the random noise time history and power spectrum can be seen in Figures 3.1 and 3.2. 0 200 400 600 800 1000 1200 1400 1600 1800 2000 ?15 ?10 ?5 0 5 10 15 Number of samples Amplitude Figure 3.1: Time history of random noise signal The results of the forcing cases with the drivers in the out-of-phase mode can be seen in Figure 3.4. In this con guration, a spectral phase shift occurred indicated by the peaks in the spectral plot matching or locking on to the excitation frequency. At fe = 92Hz, 18 0 50 100 150 200 250 300 350 400 450 500 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Frequency Hz Magnitude Figure 3.2: Power spectra of random noise signal the spectral peak was eliminated all together, signifying a successful suppression of the von K arm an vortex formation. Similar results were seen in the random noise forcing as well. The spectral plots for the in-phase and out-of-phase driver modes for a Reynolds number of 24,000 are shown in Figures 3.5 and 3.6. Similar trends were observed at this Reynolds number with larger peak magnitudes. However, higher ampli er voltages were required to supply enough power to generate the correct blowing coe cient. From the data analyzed, it is clear that with in-phase forcing at frequencies greater than 2fs0 at a Reynolds number of 12,000 and 4fs0 at a Reynolds number of 24,000, the excitation frequency was able to successfully suppress the natural shedding frequency. Detemple-Laake and Eckelmann?s work [43] investigated the coupling mechanisms of the generation of cir- cular cylinder wake as sound was superimposed in the mean direction of the ow. It was observed that the natural shedding frequency would actually lock on to the sound frequency, which was supported by the out-of-phase forcing cases in the present research. The ow visualization study by Hsiao [44] supports this observation as well by showing that the basic 19 mechanism for the elimination of von K arm an vortices in the shear layer was by disrupting their formation. The periodic forcing technique was able to accomplish this task by breaking up the strengthening vortices into smaller eddies near the cylinder. Also, depending on the phase the forcing was applied, the vortex formation occurred at the same frequency as the excitation frequency, as seen in the out-of-phase periodic forcing. Bhattacharya?s [42] results showed that using three dimensional forcing with a sinusoidal slit the natural shedding peak of a circular cylinder can be eliminated with forcing frequencies greater than or equal to 2fs0 at Reynolds numbers of 24,000 and 45,000. His research concluded that the main factor for the cancellation of shedding vortices was the three dimensionality introduced through the sinusoidal slit which depends on the slit geometry, bowing coe cient, and the excita- tion frequency. The present case used a straight slit geometry, which introduced only two dimensional disturbances to the growing shear layers. 20 0 50 100 150 200 250 300 350 400 450 500 Frequency Hz Magnitude Random noise 92 Hz 69 Hz 46 Hz 23 Hz 11.5 Hz No Forcing Figure 3.3: Power spectra for Re = 12,000, IP 0 50 100 150 200 250 300 350 400 450 500 Frequency Hz Magnitude Random noise 92 Hz 69 Hz 46 Hz 23 Hz 11.5 Hz No Forcing Figure 3.4: Power spectra for Re = 12,000, OP 21 0 50 100 150 200 250 300 350 400 450 500 Frequency Hz Magnitude Random noise 184 Hz 138 Hz 92 Hz 46 Hz 23 Hz No Forcing Figure 3.5: Power spectra for Re = 24,000, IP 0 50 100 150 200 250 300 350 400 450 500 Frequency Hz Magnitude Random noise 184 Hz 138 Hz 92 Hz 46 Hz 23 Hz No Forcing Figure 3.6: Power spectra for Re = 24,000, OP 22 3.2 Mean wake quantities Pressure surveys were taken using a pitot probe connected to a pressure transducer and traversed vertically 5 diameters at each downstream location, up to 10 diameters. Mean velocity pro les of the wake were formed at each excitation frequency, and wake half-width and drag coe cient values were calculated to describe the excitation e ects. Mean velocity pro les at x/D = 4 can be seen in Figures 3.8 and 3.9. The drag coe - cients were calculated using the wake momentum de cit method, described in Appendix B.1, and are presented for Reynolds numbers of 12,000 and 24,000 in Tables 3.1 and 3.2 respec- tively. One would deduce that the in-phase driver mode would be more e ective at reducing the cylinder drag due to the superior results illustrated in the power spectrum density plots discussed earlier. This was also supproted by the wake velocity pro les. The drag data shows a larger reduction using the in-phase forcing technique as opposed to the out-of-phase mode due to a more successful suppression of the von K arm an vortex formation. In the near wake of the cylinder at Re = 12,000, and at 2 diameters downstream a drag reduction of 5.5% was observed for the in-phase case and 4% in the out-of-phase mode. At a location of 4 diameters downstream a more signi cant drag reduction was observed with 28% for in-phase and 26% for out-of-phase. The sub-harmonic excitation frequency ampli ed the instabilities present in the ow, resulting in a 1% increase in drag with the in-phase excitation and a 1.2% increase for the out-of-phase mode. As the excitation frequency was increased the drag continued to decrease until it reached a minimum at fe = 92 or 4fs0. 6 cylinder diameters downstream a decrease in drag of 20% and 18% was seen for the in-phase and out-of-phase modes respectively. The in-phase mode had less of an e ect farther downstream at 8 diam- eters with a drag reduction of 16%. The out-of-phase case produced a 10% reduction. At 10 diameters downstream the in-phase mode improved the drag characteristics by 27% and 25% for the out-of-phase mode. The tests performed at a Reynolds number of 24,000 showed an interesting trend. In analyzing the drag coe cients at each location and comparing them to the lower Reynolds 23 number case (in-phase: 5.5%, out-of-phase: 4%) it was found that at downstream locations closer to the cylinder, for example 2 diameters downstream, the periodic forcing had a greater e ect in the reduction of drag with a 9% reduction using in-phase forcing and 6% reduction using the out-of-phase forcing. However, at downstream locations greater than 8 diameters the drag reduction decreased. This was in part due to the increased amount of kinetic energy in the higher speed ow causing the positive e ects of the periodic forcing to be less at greater downstream locations. The wake half-width was calculated from the wake de cit data. The wake half-width, illustrated in Figure 3.7, is de ned as the distance from the center of the wake to a location where the velocity defect is half of the maximum. Figures 3.10 and 3.11 show the variation of the wake half-width at each Reynolds number and excitation frequency. It is known that as the wake progresses downstream, the wake width increases. This was evident by the positive slope of the no forcing case seen at each Reynolds number. In Figure 3.8a the 11.5 Hz excitation frequency was shown to increase the half-width at each downstream location, which occurred with fe 2fs0. When an excitation frequency of fe > 2fs0 was applied, seen in Figure 3.8d, the half-width was smaller when compared to the no forcing case, which indicated a narrowing of the wake. U U Uc b, Wake half-width Figure 3.7: Description of the wake half-width 24 Figures 3.12 and 3.13 illustrate the possible e ects of the periodic forcing for each forcing mode. When utilizing the in-phase driver mode, the periodic forcing e ects both shear layers at the same time either by sucking air in through the slits or blowing it out. This could either shrink or expand the wake by subtracting or adding momentum to the forming eddies in the shear layers. The natural tendency for vortex shedding is to shed alternately. If the side of the shear layer that is about to shed an eddy is submitted to suction, energy is taken from the shear layer and the forming eddy will be weaker. If the side of the shear layer that is not shedding an eddy is subjected to blowing, momentum is added to this side and may compete and disrupt the opposite shear layer, reducing the wake periodicity. Figure 3.13 shows the possible e ect of out-of-phase forcing. An ampli cation of the natural instability may occur depending on the side the vortex sheds and the natural shedding frequency may also coincide or lock-on to the excitation frequency. If the excitation occurs in the opposite phase of the natural vortex shedding, the shear layer experiences a reduction in energy due to suction while the opposite shear layer experiences an increase in uid momentum. In a case where the excitation frequency is equal to the natural shedding frequency, the periodicity is disrupted with the opposite phase of the natural shedding frequency, dampening out the vortex formation. 25 0 0.2 0.4 0.6 0.8 1 ?6 ?4 ?2 0 2 4 6 u/U ? y/D No forcing 11.5 Hz IP 11.5 Hz OP (a) 0 0.2 0.4 0.6 0.8 1 ?6 ?4 ?2 0 2 4 6 u/U ? y/D No forcing 23 Hz IP 23 Hz OP (b) 0 0.2 0.4 0.6 0.8 1 ?6 ?4 ?2 0 2 4 6 u/U ? y/D No forcing 46 Hz IP 46 Hz OP (c) 0 0.2 0.4 0.6 0.8 1 ?6 ?4 ?2 0 2 4 6 u/U ? y/D No forcing 69 Hz IP 69 Hz OP (d) 0 0.2 0.4 0.6 0.8 1 ?6 ?4 ?2 0 2 4 6 u/U ? y/D No forcing 92 Hz IP 92 Hz OP (e) 0 0.2 0.4 0.6 0.8 1 ?6 ?4 ?2 0 2 4 6 u/U ? y/D No forcing Random noise IP Random noise OP (f) Figure 3.8: Mean velocity pro le (x/D = 4, Re = 12,000) 26 0 0.2 0.4 0.6 0.8 1 ?6 ?4 ?2 0 2 4 6 u/U ? y/D No forcing 23 Hz IP 23 Hz OP (a) 0 0.2 0.4 0.6 0.8 1 ?6 ?4 ?2 0 2 4 6 u/U ? y/D No forcing 46 Hz IP 46 Hz OP (b) 0 0.2 0.4 0.6 0.8 1 ?6 ?4 ?2 0 2 4 6 u/U ? y/D No forcing 92 Hz IP 92 Hz OP (c) 0 0.2 0.4 0.6 0.8 1 ?6 ?4 ?2 0 2 4 6 u/U ? y/D No forcing 138 Hz IP 138 Hz OP (d) 0 0.2 0.4 0.6 0.8 1 ?6 ?4 ?2 0 2 4 6 u/U ? y/D No forcing 184 Hz IP 184 Hz OP (e) 0 0.2 0.4 0.6 0.8 1 ?6 ?4 ?2 0 2 4 6 u/U ? y/D No forcing Random noise IP Random noise OP (f) Figure 3.9: Mean velocity pro le (x/D = 4, Re = 24,000) 27 Table 3.1: Coe cients of drag at di erent downstream locations Re = 12,000 Location downstream Frequency 2D 4D 6D 8D 10D (Hz) In Out In Out In Out In Out In Out NoForcing 1.837 1.812 1.8123 1.7923 1.7784 11.5 1.93 1.9846 1.829 1.834 1.7599 1.8315 1.8381 1.8914 1.827 1.9033 23 1.9023 1.9452 1.4185 1.4003 1.7298 1.7353 1.7845 1.8595 1.7854 1.8105 46 1.8364 1.8682 1.3845 1.3848 1.6945 1.7157 1.7324 1.7221 1.762 1.7617 69 1.7377 1.7857 1.3092 1.3273 1.4632 1.4808 1.5903 1.6066 1.7184 1.7428 92 1.7501 1.76 1.3048 1.3266 1.4577 1.4791 1.5964 1.6171 1.2929 1.3223 Noise 1.7967 1.8218 1.4601 1.4769 1.4468 1.4806 1.4922 1.6547 1.6280 1.6490 Table 3.2: Coe cients of drag at di erent downstream locations Re = 24,000 Location downstream Frequency 2D 4D 6D 8D 10D (Hz) In Out In Out In Out In Out In Out NoForcing 1.9621 1.7614 1.6984 1.6349 1.6464 23 1.8964 1.8909 1.2589 1.2485 1.7215 1.7026 1.7396 1.7225 1.7587 1.7346 46 1.8369 1.8427 1.3154 1.4030 1.8031 1.8514 1.8044 1.8341 1.8180 1.8319 92 1.8618 1.8581 1.2448 1.2525 1.5553 1.4546 1.9036 1.9158 1.8905 1.9055 138 1.8397 1.875 1.1721 1.189 1.334 1.391 1.397 1.4224 1.8122 1.858 184 1.7868 1.8863 1.1332 1.1748 1.3494 1.3698 1.7328 1.4486 1.7174 1.5552 Noise 1.8559 1.8421 1.1463 1.1457 1.3334 1.3346 1.517 1.5081 1.5175 1.5126 28 0 2 4 6 8 10 12 0 0.5 1 1.5 2 2.5 x/D b/D No forcing 11.5 Hz IP 11.5 Hz OP (a) 0 2 4 6 8 10 12 0 0.5 1 1.5 2 2.5 x/D b/D No forcing 23 Hz IP 23 Hz OP (b) 0 2 4 6 8 10 12 0 0.5 1 1.5 2 2.5 x/D b/D No forcing 46 Hz IP 46 Hz OP (c) 0 2 4 6 8 10 12 0 0.5 1 1.5 2 2.5 x/D b/D No forcing 69 Hz IP 69 Hz OP (d) 0 2 4 6 8 10 12 0 0.5 1 1.5 2 2.5 x/D b/D No forcing 92 Hz IP 92 Hz OP (e) 0 2 4 6 8 10 12 0 0.5 1 1.5 2 2.5 x/D b/D No forcing Random noise IP Random noise OP (f) Figure 3.10: Variation of wake half-width (Re = 12,000) 29 0 2 4 6 8 10 12 0 0.5 1 1.5 2 2.5 x/D b/D No forcing 23 Hz IP 23 Hz OP (a) 0 2 4 6 8 10 12 0 0.5 1 1.5 2 2.5 x/D b/D No forcing 46 Hz IP 46 Hz OP (b) 0 2 4 6 8 10 12 0 0.5 1 1.5 2 2.5 x/D b/D No forcing 92 Hz IP 92 Hz OP (c) 0 2 4 6 8 10 12 0 0.5 1 1.5 2 2.5 x/D b/D No forcing 138 Hz IP 138 Hz OP (d) 0 2 4 6 8 10 12 0 0.5 1 1.5 2 2.5 x/D b/D No forcing 184 Hz IP 184 Hz OP (e) 0 2 4 6 8 10 12 0 0.5 1 1.5 2 2.5 x/D b/D No forcing Random noise IP Random noise OP (f) Figure 3.11: Variation of wake half-width (Re = 24,000) 30 Unforced (a) (b) Figure 3.12: Cartoon of in-phase forcing e ect Unforced (a) (b) Figure 3.13: Cartoon of out-of-phase forcing e ect 3.3 Time-averaged turbulent quantities Particle image velocimetry (PIV), data was collected for each excitation frequency and driver mode from the near wake up to 10 diameters downstream. Through post process- ing, instantaneous velocity vector eld data was produced for each of the 1155 image pairs recorded and later averaged. Additionally, snapshot proper orthogonal decomposition (POD) was implemented to extract the modal energy distributions of the ow. The velocity vector eld at each location was combined and stitched together using a MATLAB program to form a continuous data range up to 10 diameters downstream in order to view the e ects of forcing as the ow established over several diameters. Flow statistics such as the turbulence intensity, Reynolds shear stress, turbulent kinetic energy, and vorticity were calculated for each case. The Reynolds shear stress is de ned as Rij = u0iu0jU2 1 . Turbulent kinetic energy was calculated, using the mean of the turbulence 31 normal stress, k = 12 ((u01)2+(u02)2+(u03)2)U2 1 . The TKE quanti es the mean kinetic energy asso- ciated with the eddies in the turbulent ow, making it easy to recognize the e ectiveness of ow control. Large eddies carry large amounts of energy downstream, therefore a wake with a lower distribution of kinetic energy signi es an absence of large turbulent structures. Vorticity is de ned as the curl of velocity and was an essential part in describing the e ects of the applied forcing, = !dU1. By illustrating the vorticity of the ow, the vortices in the wake can be revealed on an average basis to aide in assessing the e ectiveness of wake suppression. PIV results are presented in Figures 3.14 through 3.83. 3.3.1 Time-averaged mean ow The streamlines are presented in Figures 3.14 through 3.27. These gures represent the time-averaged trajectories of the seeded ow as it passed over the cylinder and provide a good indication of the e ect of forcing. Figure 3.14 and 3.21 show the baseline, no forcing cases for Re = 12,000 and Re = 24,000 respectively. In each gure, two well de ned foci can be seen in the center of the large, symmetric regions of circulation located in the near wake. A saddle point can also be seen where the streamlines intersect and mark the end of the near wake. The distance between the cylinder surface and end of the near wake is known as the formation length (L). As forcing was applied, it was apparent that there was a signi cant e ect on the near wake and modi cation of the von K arm an vortices as evident from the deformation of the regions of circulation and reduction in formation length. In Figure 3.15b the top focal point was shifted out of the eld of view and the near wake shrank signi cantly. The circulation region in Figure 3.18a is severely dampened and eludes to a successful suppression of the primary instability present in the no forcing case. The Re = 24,000 case showed similar patterns, but appeared to be less e ective. 32 3.3.2 Turbulence intensity Figure 3.28 shows a symmetric distribution of velocity uctuations in the streamwise direction for the no forcing case at a Reynolds number of 12,000. On either side of the cylinder, the contour plot shows regions of large velocity uctuations about 1.5 diameters downstream. This large velocity gradient appears near the location of the separating shear layers, indicating the formation of strong von K arm an vortices. Figure 3.29 compares the in-phase and out-of-phase excitation modes at 11.5 Hz, which is 12fs0. It should be noted that the magnitude increased dramatically from the no forcing case, indicating a strengthened shear layer and subsequently, higher energy eddies. The in-phase excitation portrayed lower velocity uctuations than the out-of-phase case indicating a more e ective disruption of the vortex formation. When the forcing frequency was equal to the natural shedding frequency of the cylinder, fe = fs0, the out-of-phase case produced smaller velocity uctuations relative to in-phase. At 2fs0, a signi cant decrease in magnitude of the uctuating velocities was seen, which was in concordance with the power spectral density analysis, showing wake suppression. A lower degree of velocity uctuations was seen in the out-of-phase driver mode when compared with the in-phase mode. This trend continued until the random noise case, where the in-phase mode saw a lower magnitude of uctuations. Generally, for the higher Reynolds number cases, the in-phase forcing mode had lower velocity uctuations relative to out-of-phase shown in Figures 3.35 through 3.41. Note that the magnitude increased compared to the lower Reynolds number case. This was to be expected due to the larger free stream velocities associated with a higher Reynolds number. Also in the Re=24,000 cases at forcing frequencies of 12fs0 and fs0, a large increase in the magnitude of velocity uctuations due to the apparent strengthening of vortex formation was observed. It was also apparent here due to the lower Turbulence intensities, that as the excitation frequency increased, the formation of the von K arm an vortices were disrupted by the two dimensional disturbances introduced. 33 3.3.3 Reynolds shear stress The distribution of Reynolds shear stress in the wake of the circular cylinder is illustrated in Figures 3.42 through 3.55. Figure 3.42 displays the Reynolds stress for the no forcing case. The pockets of oppositely signed Reynolds stress were relatively high in magnitude and symmetric, which corresponds to the large velocity gradients seen in the separating shear layers in Figure 3.42. Reynolds stress has a direct relationship with the streamwise uctuating velocities and therefore, similar increases in magnitude were seen with periodic forcing frequencies of 12fs0 and fs0. For fe 2fs0 at both Reynolds numbers, there was a decrease in Reynolds stress along the shear layer region in the cylinder wake. According to Williamson [6], this behavior is indicative of an elongation of the near wake, which in turn, leads to the conclusion that a successful attenuation of the primary instability occurred. When forcing was introduced, an asymmetry developed in the near wake due to the disruption of the shear layers on the top and bottom of the cylinder. Naturally, the unforced cylinder had a pure sinusoidal wake that, when averaged, formed a symmetric contour as seen in Figures 3.42 and 3.49. The in-phase case created an asymmetry in the ow and was re ected in the contour plots as having a larger magnitude on either the top or bottom of the cylinder. According to the wake power spectra, the vortex shedding frequency appeared to lock on to the out-of-phase forcing mode creating less of an asymmetry, but still successfully disrupting the shear layers and decreasing the Reynolds stress. On average, the in-phase forcing mode was more e ective at decreasing the Reynolds stress in the near wake region for both the Re=12,000 and Re=24,000 cases. 3.3.4 Turbulent kinetic energy As discussed earlier, the successful suppression of the von K arm an vortex formation is accomplished by breaking up the forming vortices into smaller eddies as they develop near the surface of the cylinder. Smaller eddies inherently contain less energy than larger eddies, therefore the frequencies that successfully suppress the formation of K arm an vortices will 34 show a decrease in kinetic energy throughout the wake. Figures 3.56 through 3.69 show the distribution of the time-averaged turbulent kinetic energy in. Figure 3.56 shows a large concentration of kinetic energy in the near wake at about xD = 1:5. As the vortex was shed downstream the kinetic energy decreased due to dissipation. The kinetic energy distribution seen in Figures 3.57 and 3.58 was greater than that of the no forcing case due to the higher magnitude of turbulence intensity as discussed earlier. So, as u0 decreased with higher forcing frequencies, there was an increase in the uniformity of the ow velocity illustrated as a decrease in turbulent kinetic energy. For Re=12,000, the sub-harmonic and natural forcing frequencies had a greater bene t from the forcing mode being in-phase, where as the remaining forcing frequencies showed the out-of-phase mode as being more e ective at decreasing the kinetic energy. However, the in-phase random noise case was seen to decrease the kinetic energy more e ectively. For Re=24,000, the in-phase driver mode produced a larger decrease in Turbulent kinetic energy distribution. 3.3.5 Vorticity Contour plots of time-averaged vorticity are given in Figures 3.70 through 3.76 for Re = 12,000 and Figures 3.77 through 3.83 for Re = 24,000. The plots display oppositely signed vorticity spanning the wake of the cylinder up to 10 diameters downstream. High magnitudes of clockwise vorticity are colored blue and counter-clockwise are colored red. The vorticity was seen to be of the greatest magnitude along the shear layers aft of the cylinder and decreased as the vortices travelled downstream in Figure 3.70. The von K arm an vortex formation is easily discernible from the regions of vorticity revealed in the contour plot. The out-of-phase forcing at frequencies of 12fs0 and fs0, for both Reynolds numbers, show a higher concentration of vorticity and an increase in the wake width as illustrated in Figures 3.71, 3.72, 3.78,and 3.79. This indicated an increase in energy and vortex formation strength, which supports the previous observations. As the forcing frequency was increased to 2fs0 35 and above, it was observed that the wake narrowed and a decrease in the vorticity indicated a di usion of vorticity in the shear layer. 3.3.6 POD modal energy distribution Proper orthogonal decomposition is very useful in breaking down complex dynamical systems into low-dimensional ow elds, which is useful in characterizing the coherent ow structures of interest [45]. The energy distribution across the POD modes was found to decay exponentially and for modes above ve, the energy was very small relative to mode 1. Therefore, the rst ve proper orthogonal modes were chosen to aide in illustrating the e ect each periodic forcing frequency had on the overall ow. Figures 3.84 and 3.85 show the energy distribution at each downstream location for the rst ve modes. In the baseline case, Figure 3.84 shows mode-1 as the structure with the highest energy at about 35% and decreasing with downstream location. Modes 2 and 3 are shown to increase slightly from x/D = 2 to x/D = 4. This occurred because the structures associated with these modes in the no forcing case were stronger and more developed as they progressed downstream. It was evident for forcing of fe = 12fs0 and fe = fs0, for both Reynolds numbers, that the overall energy distribution was associated with a greater magnitude than that of the no forcing case for the out-of-phase driver mode. This indicated that the out-of-phase mode added energy to the developing instabilities of the ow and increased the strength of the von K arm an vortices. In general, the Re = 12,000 and Re = 24,000 cases exhibited a behavior in which the rst two modes in the out-of-phase case were consistently associated with a higher energy distribution than the in-phase mode. However, modes 3 through 5 had higher energies in the in-phase mode compared to out-of-phase. At forcing frequencies greater than fe = fs0, the modal energy was less than the no forcing case, indicating a successful decrease in vortex strength. It was also noted that modes 3 through 5 for all forcing frequencies contained, relatively, the same energy magnitude as the no forcing case, 36 meaning the periodic forcing had less of an e ect on lower energy turbulent structures in the wake. Figure 3.14: Streamline topology (Re = 12,000, No forcing) (a) In-phase (b) Out-of-phase Figure 3.15: Streamline topology (Re = 12,000, fe = 11.5 Hz) 37 (a) In-phase (b) Out-of-phase Figure 3.16: Streamline topology (Re = 12,000, fe = 23 Hz) (a) In-phase (b) Out-of-phase Figure 3.17: Streamline topology (Re = 12,000, fe = 46 Hz) 38 (a) In-phase (b) Out-of-phase Figure 3.18: Streamline topology (Re = 12,000, fe = 69 Hz) (a) In-phase (b) Out-of-phase Figure 3.19: Streamline topology (Re = 12,000, fe = 92 Hz) 39 (a) In-phase (b) Out-of-phase Figure 3.20: Streamline topology (Re = 12,000, fe = Random noise) Figure 3.21: Streamline topology (Re = 24,000, No forcing) 40 (a) In-phase (b) Out-of-phase Figure 3.22: Streamline topology (Re = 24,000, fe = 23 Hz) (a) In-phase (b) Out-of-phase Figure 3.23: Streamline topology (Re = 24,000, fe = 46 Hz) 41 (a) In-phase (b) Out-of-phase Figure 3.24: Streamline topology (Re = 24,000, fe = 92 Hz) (a) In-phase (b) Out-of-phase Figure 3.25: Streamline topology (Re = 24,000, fe = 138 Hz) 42 (a) In-phase (b) Out-of-phase Figure 3.26: Streamline topology (Re = 24,000, fe = 184 Hz) (a) In-phase (b) Out-of-phase Figure 3.27: Streamline topology (Re = 24,000, fe = Random noise) 43 Figure 3.28: Turbulence intensity contour (Re = 12,000, No forcing) (a) In-phase (b) Out-of-phase Figure 3.29: Turbulence intensity contour (Re = 12,000, fe = 11.5 Hz) 44 (a) In-phase (b) Out-of-phase Figure 3.30: Turbulence intensity contour (Re = 12,000, fe = 23 Hz) (a) In-phase (b) Out-of-phase Figure 3.31: Turbulence intensity contour (Re = 12,000, fe = 46 Hz) 45 (a) In-phase (b) Out-of-phase Figure 3.32: Turbulence intensity contour (Re = 12,000, fe = 69 Hz) (a) In-phase (b) Out-of-phase Figure 3.33: Turbulence intensity contour (Re = 12,000, fe = 92 Hz) 46 (a) In-phase (b) Out-of-phase Figure 3.34: Turbulence intensity contour (Re = 12,000, fe = Random noise) Figure 3.35: Turbulence intensity contour (Re = 24,000, No forcing) 47 (a) In-phase (b) Out-of-phase Figure 3.36: Turbulence intensity contour (Re = 24,000, fe = 23 Hz) (a) In-phase (b) Out-of-phase Figure 3.37: Turbulence intensity contour (Re = 24,000, fe = 46 Hz) 48 (a) In-phase (b) Out-of-phase Figure 3.38: Turbulence intensity contour (Re = 24,000, fe = 92 Hz) (a) In-phase (b) Out-of-phase Figure 3.39: Turbulence intensity contour (Re = 24,000, fe = 138 Hz) 49 (a) In-phase (b) Out-of-phase Figure 3.40: Turbulence intensity contour (Re = 24,000, fe = 184 Hz) (a) In-phase (b) Out-of-phase Figure 3.41: Turbulence intensity contour (Re = 24,000, fe = Random noise) 50 0.008 Figure 3.42: Reynolds shear stress contour (Re = 12,000, No forcing) (a) In-phase (b) Out-of-phase Figure 3.43: Reynolds shear stress contour (Re = 12,000, fe = 11.5 Hz) 51 (a) In-phase (b) Out-of-phase Figure 3.44: Reynolds shear stress contour (Re = 12,000, fe = 23 Hz) (a) In-phase (b) Out-of-phase Figure 3.45: Reynolds shear stress contour (Re = 12,000, fe = 46 Hz) 52 (a) In-phase (b) Out-of-phase Figure 3.46: Reynolds shear stress contour (Re = 12,000, fe = 69 Hz) (a) In-phase (b) Out-of-phase Figure 3.47: Reynolds shear stress contour (Re = 12,000, fe = 92 Hz) 53 (a) In-phase (b) Out-of-phase Figure 3.48: Reynolds shear stress contour (Re = 12,000, fe = Random noise) 0.008 Figure 3.49: Reynolds shear stress contour (Re = 24,000, No forcing) 54 (a) In-phase (b) Out-of-phase Figure 3.50: Reynolds shear stress contour (Re = 24,000, fe = 23 Hz) (a) In-phase (b) Out-of-phase Figure 3.51: Reynolds shear stress contour (Re = 24,000, fe = 46 Hz) 55 (a) In-phase (b) Out-of-phase Figure 3.52: Reynolds shear stress contour (Re = 24,000, fe = 92 Hz) (a) In-phase (b) Out-of-phase Figure 3.53: Reynolds shear stress contour (Re = 24,000, fe = 138 Hz) 56 (a) In-phase (b) Out-of-phase Figure 3.54: Reynolds shear stress contour (Re = 24,000, fe = 184 Hz) (a) In-phase (b) Out-of-phase Figure 3.55: Reynolds shear stress contour (Re = 24,000, fe = Random noise) 57 Figure 3.56: Turbulent kinetic energy contour (Re = 12,000, No forcing) (a) In-phase (b) Out-of-phase Figure 3.57: Turbulent kinetic energy contour (Re = 12,000, fe = 11.5 Hz) 58 (a) In-phase (b) Out-of-phase Figure 3.58: Turbulent kinetic energy contour (Re = 12,000, fe = 23 Hz) (a) In-phase (b) Out-of-phase Figure 3.59: Turbulent kinetic energy contour (Re = 12,000, fe = 46 Hz) 59 (a) In-phase (b) Out-of-phase Figure 3.60: Turbulent kinetic energy contour (Re = 12,000, fe = 69 Hz) (a) In-phase (b) Out-of-phase Figure 3.61: Turbulent kinetic energy contour (Re = 12,000, fe = 92 Hz) 60 (a) In-phase (b) Out-of-phase Figure 3.62: Turbulent kinetic energy contour (Re = 12,000, fe = Random noise) Figure 3.63: Turbulent kinetic energy contour (Re = 24,000, No forcing) 61 (a) In-phase (b) Out-of-phase Figure 3.64: Turbulent kinetic energy contour (Re = 24,000, fe = 23 Hz) (a) In-phase (b) Out-of-phase Figure 3.65: Turbulent kinetic energy contour (Re = 24,000, fe = 46 Hz) 62 (a) In-phase (b) Out-of-phase Figure 3.66: Turbulent kinetic energy contour (Re = 24,000, fe = 92 Hz) (a) In-phase (b) Out-of-phase Figure 3.67: Turbulent kinetic energy contour (Re = 24,000, fe = 138 Hz) 63 (a) In-phase (b) Out-of-phase Figure 3.68: Turbulent kinetic energy contour (Re = 24,000, fe = 184 Hz) (a) In-phase (b) Out-of-phase Figure 3.69: Turbulent kinetic energy contour (Re = 24,000, fe = Random noise) 64 Figure 3.70: Vorticity contour (Re = 12,000, No forcing) (a) In-phase (b) Out-of-phase Figure 3.71: Vorticity contour (Re = 12,000, fe = 11.5 Hz) 65 (a) In-phase (b) Out-of-phase Figure 3.72: Vorticity contour (Re = 12,000, fe = 23 Hz) (a) In-phase (b) Out-of-phase Figure 3.73: Vorticity contour (Re = 12,000, fe = 46 Hz) 66 (a) In-phase (b) Out-of-phase Figure 3.74: Vorticity contour (Re = 12,000, fe = 69 Hz) (a) In-phase (b) Out-of-phase Figure 3.75: Vorticity contour (Re = 12,000, fe = 92 Hz) 67 (a) In-phase (b) Out-of-phase Figure 3.76: Vorticity contour (Re = 12,000, fe = Random noise) Figure 3.77: Vorticity contour (Re = 24,000, No forcing) 68 (a) In-phase (b) Out-of-phase Figure 3.78: Vorticity contour (Re = 24,000, fe = 23 Hz) (a) In-phase (b) Out-of-phase Figure 3.79: Vorticity contour (Re = 24,000, fe = 46 Hz) 69 (a) In-phase (b) Out-of-phase Figure 3.80: Vorticity contour (Re = 24,000, fe = 92 Hz) (a) In-phase (b) Out-of-phase Figure 3.81: Vorticity contour (Re = 24,000, fe = 138 Hz) 70 (a) In-phase (b) Out-of-phase Figure 3.82: Vorticity contour (Re = 24,000, fe = 184 Hz) (a) In-phase (b) Out-of-phase Figure 3.83: Vorticity contour (Re = 24,000, fe = Random noise) 71 20 25 30 35 40 45 50 M oda l E nde r gy , % Mode 1 IP Mode 1 OP Mode 2 IP Mode 2 OP Mode 3 IP Mode 3 OP Mode 4 IP Mode 4 OP 0 5 10 15 0 10 20 30 40 50 60 70 80 90 100 M oda l E nde r gy , % Excitation frequency, Hz Mode 5 IP Mode 5 OP Noise Mode 1 Noise Mode 5 Figure 3.84: Energy distribution, (Re = 12,000, xD=4) 20 25 30 35 40 45 50 M oda l E nde r gy , % Mode 1 IP Mode 1 OP Mode 2 IP Mode 2 OP Mode 3 IP Mode 3 OP Mode 4 IP Mode 4 OP 0 5 10 15 0 20 40 60 80 100 120 140 160 180 200 M oda l E nde r gy , % Excitation frequency, Hz Mode 5 IP Mode 5 OP Noise Mode 1 Noise Mode 5 Figure 3.85: Energy distribution, (Re = 24,000, xD=4) 72 Chapter 4 Conclusions The wake of a circular cylinder subjected to various periodic forcing frequencies in two modes was investigated. Two pairs of acoustic drivers were used to subject the ow to the two dimensional disturbances through two straight slits on the cylinder surface in diametrically opposite locations. The experiments were conducted at Reynolds numbers of 12,000 and 24,000 in a closed circuit wind tunnel. The power spectral density plots showed a successful suppression of the von K arm an instability for fe 2fs0 for both Reynolds number cases when an in-phase forcing mode was used. It was found that for the out-of-phase forcing case, the shedding frequency locked on to the forcing frequency. For fe = 12fs0 and fs0 there was an increase in vortex strength caused by the addition of energy injected into the shear layers, which accelerated the shear layers and compounded the primary instability. The harmonic and sub-harmonic forcing frequencies built upon the instability by either syncing with the natural shedding frequency in the out-of-phase case or, in the in-phase case, adding kinetic energy to the formation of the vortex formation. The e ectiveness of the in-phase mode relative to the out-of-phase mode was also re ected in the drag calculations. On average, fe = 4fs0 provided the most relief in drag with the in-phase mode reducing drag for a Reynolds number of 12,000 by 28% 4 diameters downstream, whereas the out-of- phase mode resulted in a drag reduction of only 26%. When the Reynolds number was increased to 24,000, the near wake saw a larger drag reduction, while the positive e ects of forcing decreased farther downstream. This was, in part, due to a greater amount of kinetic energy in the higher Reynolds number ow, negating the e ects of the vortex suppression. A larger decrease in drag was seen with the in-phase forcing mode compared to the out-of- phase mode. Streamline topology, time-averaged turbulence intensity, Reynolds shear stress, 73 turbulent kinetic energy, and vorticity were calculated to provide a glimpse into the turbulent structures in the wake of the cylinder. A peak in velocity uctuations occurred along the shear layers on the top and bottom of the cylinder. Higher magnitudes indicated a stronger shear layer able to produce larger eddies, forming a more turbulent wake. A decrease was seen in the uctuating velocities as the periodic forcing took e ect above fe = 2fs0. The direct correlation between Reynolds shear stress and streamwise velocity uctuations con rmed successful ow control. The contour plots of the Reynolds shear stress also revealed the shear layer asymmetry introduced by the in-phase mode. The turbulent kinetic energy in the cylinder wake was observed to have a greater response to the in-phase mode. The vorticity contour plots showed that as the forcing was implemented, the wake narrowed and a decrease in vorticity concentration occurred, which supports evidence of the reduction of wake periodicity. The random noise forcing reduced drag and the turbulent quantities in the cylinder wake for both ow velocities. Further investigation of these e ects may prove to be bene cial due to the possible application of only a single excitation frequency over a wide range of Reynolds numbers. 74 Bibliography [1] Zdravkovich, M. M., Flow Around Circular Cylinders, Oxford University Press, 1997. [2] Gerrard, J. H., \Vortex-Induced Vibrations," Annual Review of Fluid Mechanics, Vol. 36, 2004, pp. 413{ 455. [3] Berger, E. and Wille, R., \Periodic ow phenomena," Annual Review of Fluid Mechan- ics, Vol. 4, 1972, pp. 314{ 340. [4] Bearman, P. W., \Vortex shedding from oscillating blu bodies," Annual Review of Fluid Mechanics, Vol. 16, 1984, pp. 195{ 222. [5] Jr., H. 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[45] Bernero, S. and Fiedler, H., \Application of particle image velocimetry and proper orthogonal decomposition to the study of a jet in a counter ow," Experiments in Fluids, 2000, pp. S274{ S281. [46] Jorgensen, F. E., How to Measure Turbulence with Hot-wire Anemometers: A Practical Guide, Dantec Dynamics, 2005. [47] M. Ra el, C. W. and Kompenhans, J., Particle Image Velocimetry: A Practical Guide, Springer-Verlag, 1998. 78 Appendices 79 Appendix A Calibration The content of this appendix describes the calibration procedure for the hot wire, power ampli er, and pressure transducer, which was carried out before each experiment. A.1 Constant temperature anemometer calibration The single wire was calibrated using a jet calibrator. The system consisted of an air compressor, pressure regulator, manometer, and a stagnation chamber with a series of three screens and a nozzle. The hot wire was connected to an oscilloscope and the average voltage was measured and recorded for each nozzle exit velocity speci ed as seen in Table A.1. The calibration ranged from zero to ninety six feet per second. The data was plotted and a fourth order polynomial was tted to the data and can be noted in Figure A.1. The equation was then used to obtain the voltages and velocities needed to produce the correct blowing coe cients and free stream speeds. 80 y = 1202.3x 4 -3602.4x 3 + 3527.1x 2 -902.38x -209.06 R? = 0.999560 80 100 120 V e l oc i t y ( f t / s ) 0 20 40 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 Voltage (V) Figure A.1: Hot wire calibration curve 81 Table A.1: Hot wire calibration data Pressure (inches H2O) Velocity (ft/s) Voltage (volts) 0 0.00 0.757 0.002 3.03 0.919 0.004 4.28 0.932 0.006 5.25 0.939 0.008 6.06 0.945 0.01 6.77 0.951 0.02 9.58 0.96 0.03 11.73 0.973 0.04 13.55 0.984 0.05 15.14 1.001 0.1 21.42 1.041 0.15 26.23 1.061 0.2 30.29 1.083 0.25 33.86 1.12 0.3 37.09 1.135 0.35 40.07 1.145 0.4 42.83 1.156 0.45 45.43 1.165 0.5 47.89 1.173 0.55 50.23 1.181 0.6 52.46 1.19 0.65 54.60 1.197 0.7 56.66 1.205 0.75 58.65 1.21 0.8 60.58 1.216 0.85 62.44 1.221 0.9 64.25 1.227 0.95 66.01 1.232 1 67.73 1.236 1.1 71.03 1.244 1.2 74.19 1.2505 1.3 77.22 1.259 1.4 80.13 1.266 1.5 82.95 1.272 1.6 85.67 1.278 1.7 88.30 1.282 1.8 90.86 1.2867 1.9 93.35 1.291 2 95.78 1.296 82 A.2 Power ampli er calibration The power ampli er was calibrated to obtain the correct voltages needed to produce the speci ed forcing coe cients from the drivers. The hot wire was positioned just above the slit in the cylinder to read the air velocities produced at each speaker frequency. The ampli er was connected to a wave from generator and an oscilloscope was used to measure the output voltage. At each driver frequency the peak-to-peak voltage required to generate the correct amount of forcing was recorded and the blowing coe cients were veri ed as seen in Table A.2 for a Reynolds number of 12,000 and Table A.3 for a Reynolds number of 24,000. Table A.2: Ampli er calibration data at Re = 12,000 Driver freq. (Hz) Amp. voltage (volts) C 11.5 37 0.17 23 26 0.168 46 22 0.17 69 18 0.171 92 14 0.173 Table A.3: Ampli er calibration data at Re = 24,000 Driver freq. (Hz) Amp. voltage (volts) C 23 45 0.214 46 32 0.218 92 35 0.225 138 48 0.223 184 50 0.222 83 Appendix B Calculations B.1 Drag The drag values were calculated using the wake de cit method as shown in Equation B.3. This method calculates the amount of momentum lost in the wake due to the presence of the cylinder. Pt = Ps +q (B.1) q = 12 U21 (B.2) Cd = 2D Z y2 y1 "s q q1 q q1 # dy (B.3) 84 Appendix C Uncertainty analysis An uncertainty analysis was conducted to ensure the precision of the data gathered in this investigation. The reference case selected was the Reynolds number of 12,000, which corresponds to a free stream velocity of about 15 ft/s. Several sources of uncertainty were considered: pressure transducer error, pressure transducer calibration error, hot wire cali- bration error, and A/D board resolution error. The pressure transducer error was determined from the data sheet provided by the manufacturer and was found to be 0.5%, which equates to a relative uncertainty of 0.01. Pressure transducer calibration error was rooted in curve tting errors. A linear curve t was used for the calibration and the standard deviation was calculated to be 0.7%. Using equation C.1 [46], the relative uncertainty was calculated to be 0.014. relative standard uncertainty = 2 1100standard deviation (errors, %) (C.1) A fourth order polynomial curve was tted to the hot wire data gathered, shown in Figure A.1. The standard deviation was calculated to be 0.05% which corresponds to a relative uncertainty of 0.001. The A/D data acquisition board relative uncertainty was calculated using equation C.2. relative standard uncertainty = 1p3 1U 1 EAD 2n @U1 @E (C.2) where U1 is the free stream velocity, EAD is the A/D input range, n is the resolution in bits, and @U1@E is the slope of the inverse calibration curve. EAD = 10V, n = 16, U1 = 15ft=s, and @U1@E = 153:67 Plugging in with the above values gives a relative uncertainty of 0.0009025. 85 Therefore, equation C.3 calculates the total uncertainties present in the mean velocity, which is equal to 3.45%. total standard uncertainty = 2p0:012 + 0:0142 + 0:0012 + 0:00090252 = 0:03451 (C.3) The PIV measurements were taken using a 32 pixel interrogation window with a pixel size of 2. According to Ra el et al [47] the RMS uncertainty is roughly 0.01 pixels. In this investigation, the PIV images had an overlap of 3.5%, which resulted in a 2 pixel uncertainty in the results. 86