Transition phenomena in the wakes of cylinders

TRANSITION PHENOMENA IN THE WAKES OF CYLINDERS TONG XIAOHU NATIONAL UNIVERSITY OF SINGAPORE 2003 FOUNDED 1905 TRANSITION PHENOMENA IN THE WAKES OF CYLINDERS TONG XIAOHU (B.Eng, M.Eng) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY NATIONAL UNIVERSITY OF SINGAPORE 2003 ACKNOWLEDGEMENT Acknowledgement I wish to take this opportunity to express my deep and sincere gratitude to my supervisors A/Prof. S.C.Luo and A/Prof. B.C.Khoo for their valuable guidance, advice and suggestions throughout this study. Without their consistent support and patient instruction, this work would have been impossible to accomplish. I would also like to thank Prof. J. Soria from Monash University and A/Prof. T.T. Lim for their valuable discussions on PIV measurements. I would also like to thank to Mr. C.S. Yap, Mr. K.S. Yap and Mr. K.W. Tan for their technical support during the present research. I would also like to express my gratitude to all my fellow postgraduate students in the Fluid Mechanics Laboratory, National University of Singapore for their help and valuable discussions during the present research. I would also like to thank the National University of Singapore for the award of the postgraduate research scholarship. Last but certainly not least, I would like to express my gratitude to my father and mother for their support and encouragement. I TABLE OF CONTENTS Table of Contents Acknowledgement I Table of contents II Summary V Nomenclature VII List of Figures IX XVI List of Tables Chapter One Introduction and Literature Review 1.1 Background 1.2 Literature Review 1.2.1 Experimental works on circular cylinder wake transition 1.2.2 DNS and Linear Instability Analysis 1.2.3 Different Explanations For Circular Cylinder Wake Transition 1.2.4 Influence of Aspect Ratio, End Condition and Other Factors 1.2.5 The Square Cylinder Wake at Low Speed Flow 13 1.3 Objectives and Scope of Present Investigations 15 1.4 Organization of the Thesis 16 Chapter Two Experimental Setup and Techniques 23 2.1 Experiment Set-up 23 2.1.1 The Vertical Water Tunnel 23 2.1.2 The Horizontal Water Channel 25 2.2 Experimental Models and Measurement System 26 2.2.1 Hot-film Measurement 26 2.2.2 Flow Visualization Techniques 27 2.2.3 Particle Image Velocimetry (PIV) 28 II TABLE OF CONTENTS 2.2.3.1 Background of PIV techniques and Current PIV System 28 2.2.3.2 Data Processing 30 Chapter Three The Transition Process of the Wake of a Circular Cylinder 36 3.1 Introduction 36 3.2 End effects on transition process of the wake of circular cylinder 36 3.3 Time traces of streamwise velocity and spectral patterns 40 3.4 Concluding Remarks for this Chapter 42 Chapter Four Hot Film Anemometry Measurements 46 4.1 Introduction 46 4.2 The effects of end conditions and aspect ratio on the transition process of a square cylinder wake 47 4.3 The transition process of the wake of a square cylinder at α=0° 51 4.4 The effects of angle of attack on the transition process of a square cylinder wake 4.5 The characteristics of the wake of a square cylinder at α=0° 57 61 4.6 Concluding remarks for this chapter 66 Chapter Five Flow Visualization 95 5.1 Introduction 95 5.2 The Formation of von Karman Vortices in Circular Cylinder and Square Cylinder Wake 5.3 Various flow regimes identified through flow visualization 96 5.3.1 End Effects on Cylinder Wake 5.3.2. The Existence of Mode A and Mode B Instabilities in the Wake of a Square Cylinder 5.3.3. The Evolution of Streamwise vortices 5.4 Concluding Remarks for This Chapter 98 98 100 101 104 III TABLE OF CONTENTS Chapter Six PIV Measurements 119 6.1 Introduction 119 6.2 Vorticity Measurements in the Very Near Wake of a Square Cylinder at an incidence of 0° 6.2.1 A Study of the Vortex Shedding Process 120 121 6.2.2 Cross Flow Velocity Variations at X=1D and X=2D 127 6.2.3. Mean Flow Fields and Some Comments on Regimes Based on Cpb-Re Plot 6.3 Measurements of Vortex Street Parameters in the Wake of a Square Cylinder at Different Incidences 6.3.1 Vortex Spacing Ratio of Vortex Street 6.3.2. Vortex Convection velocity and Vortex Strength in the Near wake 6.4 The Study of Secondary Vortices in the Cylinder Wake 130 133 134 137 139 6.4.1 Measurements of Secondary Vortices 140 6.4.2 Discussions on the origin of Secondary Instabilities 148 6.5 Concluding Remarks For This Chapter 153 Chapter Seven Conclusions 209 7.1 Summary and Conclusions 209 7.2 Recommendations for Further Studies 211 Reference 213 IV SUMMARY Summary Square cylinders, along with circular cylinders, are very commonly used in civil engineering constructions and industrial applications. However, when compared with the wake of a circular cylinder that has been extensively studied, a square cylinder’s wake is somewhat less thoroughly investigated, and unresolved problems remain. The present research on the flow past a square cylinder at moderate Reynolds numbers consists of three main parts. They are (1) hot film anemometry measurements, which identified the critical Reynolds numbers as well as certain wake’s characteristics. (2) The flow visualization of the structures of secondary vortices. (3) PIV measurements of the secondary vortices. The hot film anemometry measurements on the S-Re relation identified the critical Reynolds numbers for the wake of square cylinder at different angles of attack. The critical Reynolds numbers (Rec1 and Rec2) mark the inception of mode A and mode B instabilities and correspond to the points of discontinuity in the S-Re curves. Besides the existence of two discontinuities in the S-Re curves, the spectra and time traces of the wake streamwise velocity component were observed to exhibit three distinct patterns in different flow regimes. The existences of mode A and mode B instabilities at three different angles of attack were identified by flow visualization and PIV measurements. Streamwise vortices with different spanwise wavelength at various Reynolds numbers were observed, with the wavelength in the mode A regime being the larger of the two. The symmetries and evolution of the secondary vortices at α=0° were explored by using Laser-Induced-Fluorescent dye. It was found that just like the case of circular cylinder, the secondary vortices from the top and bottom rows of primary vortices are out-ofV SUMMARY phase with each other in the mode A regime, but in-phase with each other in the mode B regime. Also, from the flow visualization, it was qualitatively proven that there is stronger interaction between braid regions in the mode B regime. Analysis of PIV measurements indicates a stronger cross flow in mode B regime when compared to the mode A regime. It suggests that the in-phase symmetry of the mode B instability is the result of interaction between the top and bottom vortex rows. It also observed that although the intensity of secondary vortices (peak value of vorticity) is smaller in mode A regime, its strength (circulation of vortex) is more than twice of that of mode B instability. Compared to primary vortices, the strength of both mode A and mode B streamwise vortices is much smaller which indicates that the secondary vortices may be part of the primary vortices and originated from them. Similar findings had already been reported for the circular cylinder wake in the literature (Wu et. al. (1994b)). From the present investigation, mode A instability is likely due to the jointeffects of the deformation of primary vortex cores and the stretching of vortex sheets in the braid region. On the other hand, mode B instability was thought to originate from the shear layers. Further work (both experimental and DNS) is needed before more detail information can be made available. VI NOMENCLATURES Nomenclatures English alphabets a Inter-vortex spacing in one row b Distance between vortex rows Cpb The coefficient of base pressure D The diameter of circular cylinder or the projected width of a square cylinder D’ The side length of a square cylinder f Shedding frequency I Light intensity k Critical number for rejecting vector in PIV processing K The circulation of vorticity (dimensional) L Length of cylinder; Length between the leading edges of endplates m The pixel number of interrogation area along the X direction n The pixel number of interrogation area along the Y direction; Decibel P The power of spectrum density P0 The power of spectrum density at predominant frequency R Coefficient of cross-correlation Re Reynolds number (=UD/υ) Re’ Reynolds number (=UD’/υ) Rec The critical Reynolds number for primary instability Rec1 The critical Reynolds number for the mode A instability Rec2 The critical Reynolds number for the mode B instability S0 The Strouhal number for parallel shedding Sθ The Strouhal number for oblique shedding S Strouhal number (=fD/U0) S’ Strouhal number (=fD’/U0) t Time T The cycle of vortex shedding VII NOMENCLATURES T* Non-dimensional time (=t/(D/U0)) U0 Free stream velocity U X-component velocity Umean The mean velocity along the X direction Urms The r.m.s velocity along the X direction v The average velocity for one point within interrogation area V Y-component velocity Vi Influencing velocity Vp Penetrating velocity Xr The length of re-circulation region Greek alphabets α Angle of attack; Acceptance factor in PIV processing φ The coefficient of auto-correlation θ Oblique shedding angle ωz Von Karman vorticity (dimensional) ζx X-component of secondary vorticity (non-dimensional) ζy Y-component of secondary vorticity (non-dimensional) ζz Von Karman vorticity (non-dimensional) Γx Circulation of X-component of secondary vortex (non-dimensional) Γy Circulation of Y-component of secondary vortex (non-dimensional) Γz Circulation of von Karman vortex (non-dimensional) VIII CHAPTER SIX: PIV MEASUREMENTS Figure 6.4.25 Schematic ‘threading diagram’ of vortex sheet in a von Karman vortex street (Perry et al. (1982)). 206 CHAPTER SIX: PIV MEASUREMENTS Vortex A Cylinder (a) (b) Vortex C Vortex B Vortex A (c) (d) Z Flow direction Y X (e) Figure 6.4.26 A sketch on the evolution of secondary vortices in mode A regime. 207 CHAPTER SIX: PIV MEASUREMENTS Cylinder Braid A (a) (b) Braid B Z Braid A Y Flow direction X (c) (d) Figure 6.4.27 A sketch on the evolution of secondary vortices in mode B regime. 208 CHAPTER SEVEN CONCLUSIONS Chapter Seven Conclusions 7.1 Summary and Conclusions The present research on flow past a square cylinder at moderate Reynolds numbers consists of three main parts. They are: (1) Hot film anemometry measurements which identified the critical Reynolds numbers and generated certain wake characteristics data. (2) Flow visualization which revealed the structures of secondary vortices. (3) PIV measurements of the primary and secondary vortices. Through these investigations, a better understanding about the wake of a square cylinder was obtained and the similarities of the transition processes in the wakes of square and circular cylinders were demonstrated. The hot film anemometry measurements on the S-Re relation identified the critical Reynolds numbers for the wake of square cylinder at different angles of attack. The critical Reynolds numbers (Rec1 and Rec2) mark the inception of mode A and mode B 209 CHAPTER SEVEN CONCLUSIONS instabilities respectively and correspond to the points of discontinuity in the S-Re curves. It can be seen that with the increase of angle of attack (α), Rec1 increases from 160 (at α=0°) to 165 (at α=5°), 166 (at 6°) and 167 (at α=10°). Thereafter the magnitude of Rec1 decreases with further increase in α and reaches a minimum of 127 at α=45°. Rec2 is around 204 ± at α=0° and the trend of the variation of Rec2 with α is similar to that of Rec1. Besides the existence of the two discontinuities in the S-Re curves, the spectra and time traces of the wake streamwise velocity display three distinct patterns in the three different flow regimes. The existence of mode A and mode B instabilities at three different angles of attack were identified by releasing ordinary dye into flow. Streamwise vortices with different wavelength at various Reynolds numbers were observed. At the same time by using Laser-induced-fluorescent (LIF) dye, the symmetries and evolution of the secondary vortices at α=0° were explored. It was found that just like the case of circular cylinder, the secondary vortices from the top and bottom rows are out-of-phase with each other in the mode A regime, but in-phase with each other in the mode B regime. Also, from the flow visualization, it was qualitatively proven that there is stronger interaction between the two braid regions in the mode B regime. Analysis of PIV measurements indicates a stronger wake cross flow in the mode B regime when compared to the mode A regime. It suggests that the in-phase symmetry of the mode B streamwise vortices is the result of the interaction between the top and bottom vortex rows. It was also observed that although the intensity of the streamwise vortices (peak value of vorticity) is smaller in the mode A regime, the strength (circulation of vortex) of the mode A streamwise vortices is more than twice that of the 210 CHAPTER SEVEN CONCLUSIONS mode B streamwise vortices. Compared to primary vortices, the strength of both mode A and mode B streamwise vortices are much smaller which indicates that the secondary vortices may be part of the primary vortices and originated from them, which had previously been suggested by Wu et al. (1994b) for a circular cylinder wake. As for the intensity of secondary vortices, while the secondary vortices in the mode A regime have intensity smaller than that of primary vortices, the mode B secondary vortices actually have larger intensity than the primary vortices. Besides these differences, the wavelength of the streamwise vortices in the mode A regime is larger than that of the mode B regime. For example, from the present measurements and at α=0°, in the mode A regime the spanwise wavelength (λz) is about 5.12 times of the projected width of the cylinder and λz is only about 1.2 D in the mode B regime. From the present investigation, mode A instability is likely to be caused by the joint-effects of the deformation of primary vortex cores and the stretching of vortex sheets in the braid region. On the other hand, mode B instability was thought to originate from the shear layers. 7.2 Recommendations for Further Studies The results of the present study give rise to several questions, which require further investigation. The simultaneous measurements of hot film anemometer and PIV, as well as the flow visualization would explain the relationships between the presence or absence of “glitches” and the streamwise velocity and the wavelength of secondary vortices in 211 CHAPTER SEVEN CONCLUSIONS different Reynolds number regimes, thus allowing us to further verify the method of detecting critical Reynolds numbers through S-Re curve measurement. For PIV measurements, the secondary vortices obtained from X-Y planes could provide the necessary information for the space-time re-construction of the streamwise vortices (as done by Brede et al (1996)). Through this process, the existence of mode S in the wake of a square cylinder proposed by Robichaux et al (1999) could be further investigated. Lastly, a carefully carried out DNS investigation might provide some information on how the streamwise vortices evolve and grow from small disturbances, thus providing some direct explanations to the origin of the secondary instabilities. 212 RFERENCE Reference Albardede P., Monkewitz P.A. 1992 A model for the formation of oblique shedding and chevron patterns in cylinder wakes. Phys. Fluids A 4, 744 Bays-Muchmore B. and Ahmed A. 1993 On streamwise vortices in turbulence wakes of cylinder. Phys. Fluids A (2), 387. Barkley D., Henderson R. D. 1996 Three dimensional Floquet stability analysis of the wake of circular cylinder. J. Fluid. Mech. 322, 215. Bearman P. W., Trueman D. M. 1972 An investigation of the flow around rectangular cylinders. Aero. Quart. 23, 229. Bloor S. 1964 The transition to turbulence in the wake of a circular. J. Fluid Mech. 19,290. Braza M., Faghani D. and Persillon H. 2001 Successive stages and the role of natural vortex dislocations in three-dimensional wake transition. J. Fluid Mech. 439, 1. Brede M., Eckelmann H., Konig M., Noack B. R. 1994 Discrete shedding modes of the cylinder wake in a jet with a homogeneous core. Phys. Fluids vol.6, 8, 2711. Brede M., Eckelmann H., Rockwell D. 1996 On secondary vortices in the cylinder wake. Phys. Fluids. A 8, 2117. Chen J.M., Liu C.H. 1999 Vortex shedding and surface pressures on a square cylinder at incidence to a uniform air stream. Int. J. Heat and Fluid Flow 20, 592. Coutanceau M., Defaye, J-R. 1991 Circular cylinder wake configurations: a flow visualization survey. Appl. Mech. Rev. 44, 255. 213 RFERENCE Cowdrey C.F. 1963 A note on the use of endplates to prevent three-dimensional flow at the ends of bluff cylinders. ARC. Current Papers 683. Diao C. G. 1998 A study of low Reynolds number flow bluff bodies wake dynamics. M.Eng. thesis, National University of Singapore. Eisenlohr H., Eckelmann H. 1984 Vortex splitting and its consequences in the vortex street wake of cylinders at low Reynolds numbers. Phys. Fluids A 1:189. Ferre F. A., Mumeord J. C., Savill A. M. & Ciralt F.1990 Three-dimensional largeeddy motions and time scale activity in a plane wake. J. Fluid Mech. 210, 371. Fey U., Konig M. and Eckelmann H. 1998 A new Strouhal-Reynolds-Number relationship for a circular cylinder in the range 47[...]... explain some of the significant scatter found in the many measurements of Strouhal number and the critical Reynolds number of circular cylinder wake transition The techniques mentioned above involve a slight speeding up of the flow near the ends of the cylinder Albarede & Monkewitz (1992) also suggested that it is an increase of the local Reynolds number towards the ends that produces a reduction in the. .. induce intense nonlinear breakdown and lead to the by-pass transition It is known that the same theory also applies to the transition in wake flow For the first kind of transition, linear stability can provide a great insight of the flow One of the earliest stability analysis was done by Noack et al (1993) and Noack & Eckelmann (1994) using a Galerkin projection to represent the 2-D base flow and the. .. were originally discovered as a spanwise waviness of the primary vortices from the flow visualization work of Hama (1957), performed in the Reynolds number range of 80-313 The growth of the waviness into “fingers of dye” by Gerrard (1978), and measurements by Grant (1958) and Bloor (1964) indicated the presence of pairs of counter-rotating streamwise vortices in the near wake region Due to the careful... in the wake of a square cylinder was investigated with the aid of hot film anemometer measurements Studies on both the effects of end conditions and the effects of the square cylinder’s angle of attack were carried out The characteristics of the wake of a square cylinder at two different angles of attack were also measured and presented In chapter five, the three-dimensional structures of the wake of. .. between the primary vortices, while mode B has its origin in the instability of the separated shear layers in the immediate wake of the cylinder Henderson (1997) suggested that it does not make sense to classify the instability as an elliptic instability; especially since Floquet analysis seems to indicate that the maximum amplification of disturbance occurs between the wake vortices rather than in their... Nevertheless, as pointed out by Leweke & Williamson (1998), the elliptic instability theory is surprisingly good at predicating the wavelength of the most unstable mode From earlier research works, there are some other explanations for the transitional mechanism: Wei & Smith (1986) suggested that the streamwise vortices in the wake of a cylinder are the results of three-dimensional distortion of the. .. discontinuities in the S-Re relation curve (See Figure 1.2.1) At the first discontinuity, the Strouhal number drops from the laminar curve to one corresponding to a mode A three-dimensional shedding; this discontinuity is hysteretic As Re is increased, there is a further less sharp discontinuity in Strouhal number, indicating the mode B instability This discontinuity is not hysteretic, and instead involves... suction pipe installed downstream of the cylinder (Miller & Williamson 1994) 12 CHAPTER ONE: INTRODUCTION AND LITERAURE REVIEW 1.2.5 The Square Cylinder Wake at Low Speed Flow With so much interesting results about the circular cylinder wake at low Reynolds number, it provides the motivation to investigate the wake of other geometries It is obviously interesting to find out if the wakes of other bluff... three principal directions For α=0°, the origin is at the mid-point of the rear side of the square cylinder Figure 2.2.2 A Sketch of the PIV system used in the current investigation Figure 3.2.1 Effects of endplates inclination on the circular cylinder S-Re relation Figure 3.2.2 End effects on circular cylinder wake (dye flow visualization at Re=120) Figure 3.3.1 Time traces of streamwise velocity in a... cylinder and the evolution of the streamwise vortices were investigated by using ordinary dye and laser induced fluorescent (LIF) visualization techniques In chapter six, the wake of a square cylinder at moderate Reynolds numbers was studied in details by using the particle image velocimetry (PIV) technique By analyzing the quantitative data obtained from the PIV measurements, the mechanism of the transition . 46 4.1 Introduction 46 4.2 The effects of end conditions and aspect ratio on the transition process of a square cylinder wake 47 4.3 The transition process of the wake of a square cylinder. α=0° 51 4.4 The effects of angle of attack on the transition process of a square cylinder wake 57 4.5 The characteristics of the wake of a square cylinder at α=0° 61 4.6 Concluding remarks. joint- effects of the deformation of primary vortex cores and the stretching of vortex sheets in the braid region. On the other hand, mode B instability was thought to originate from the shear layers.