Mitigation of Vortex-Induced Vibrations Using Macro

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2012 Mitigation of Vortex-Induced Vibrations in Cables Using Macro-Fiber Composites Gustavo J. Munoz

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FSU-FAMU COLLEGE OF ENGINEERING

MITIGATION OF VORTEX-INDUCED VIBRATIONS IN CABLES USING MACRO-FIBER COMPOSITES

GUSTAVO J. MUNOZ

A Thesis submitted to the Department of Civil and Environmental Engineering in partial fulfillment of the requirements for the degree of Master of Science

Degree Awarded: Spring Semester, 2012

Gustavo J. Munoz defended this thesis on March 30, 2012.

The members of the supervisory committee were:

Sungmoon Jung Professor Directing Thesis

Michelle Rambo-Roddenberry Committee Member

Lisa K. Spainhour Committee Member

The Graduate School has verified and approved the above-named committee members, and certifies that the [thesis/treatise/dissertation] has been approved in accordance with university requirements

I dedicate this manuscript to my mother, father and wife. I love you.

iii

ACKNOWLEDGMENTS

This thesis is a combination of efforts in different ways from many special people. To begin, my advisor, Sungmoon Jung has worked tirelessly and constantly in ensuring my complete understanding of the work needed to complete this project. Not only did he guide me through my thesis work, he pushed me to reach further than minimum requirements -- arguing that we should tap into all of our potential. He also taught me and guided me through a very particular way of analytical thought while stimulating me to blossom in my own way of scientific thinking. I thank him dearly for being an excellent advisor, engineer, and friend. Special thanks to Michelle Rambo-Roddenberry and Lisa Spainhour, my two committee members. It is my aspiration to be as ethical and successful in my work as my advisors are with theirs'. A very warm and special thanks to my mother, Adelina Munoz, father, Gustavo Munoz, sister, Emily Munoz, two beautiful nieces, Samantha and Victoria, godmother, Tualina Matthews, family, Cristi Pertot, Aida Campos and Jorge Ortiz. Without their support and constant encouragement, my thesis would not have been completed with so much enthusiasm and concentration. My mother constantly pushed me to understand the importance of my success and my father was never too tired to help me -- even when it came to constructing portions of my project or giving technical advice. Finally, my friends do not come anywhere far from deserving an enormous amount of gratitude. Edmund P. Rita, my unofficial "professor", was the engine behind my belief in being able to construct a full-scale wind tunnel and have it function as a sophisticated machine. Thanks to him, my department has the immediate facilities to work with wind phenomena. Kunal Joshi, one of my best friends, spent countless hours constructing, troubleshooting and experimenting with me -- much thanks to him. Thanks to Christopher Roberts, Jeyre Lewis and Steven Sullivan, whom all helped in construction of the tunnel. To all others who supported me, Belinda Morris, Rosa Booker, Tom Trimble, Duo Liu, Braketta Ritzenthaler, John Collier, Ching-Jen Chen, Kamal Tawfiq, Amy Chan Hilton and Kirby Kemper, sincerely, thank you very much. This project was funded by a Graduate fellowship through the Florida Space Grant Consortium, NASA. iv

TABLE OF CONTENTS

List of Figures vi Abstract viii

1.0 Introduction 1

2.0 Literature Review and Motivation 2 2.1 Vortex-Induced Vibration 2 2.2 Vortex-Induced Vibration Control Methods 3 2.3 Macro-Fiber Composite 4 2.4 Motivation for Study 7

3.0 Construction of Wind Tunnel 8

4.0 Experimental Setup 12 4.1 Idealization of Problem 12 4.2 Instrumentation 13 4.3 Method of Perturbation 13 4.4 Calculation of Wind Speed for VIV 15 4.5 Variable Angle Test 17 4.6 Actuation Phase Test 19

5.0 Results and Discussion 21 5.1 Variable Angle Test 21 5.2 Actuation Phase Test 29

6.0 Conclusion and Future Work 34 6.1 Variable Angle Test 34 6.2 Actuation Phase Test 34

APPENDIX 36 REFERENCES 51 BIOGRAPHICAL SKETCH 53

LIST OF FIGURES

1 Macro-Fiber Composite Schematic 5

2 M-8528-P1 Macro-Fiber Composite Actuator 5

3 Schematic of MFC motion at rest (top) and under actuation (bottom) 6

4 Wind Tunnel Design 9

5 5’ x 5’ Aluminum contraction cone followed by flow straightening section 10

6 Test Section & Diffuser Section 11

7 Open-Circuit Wind Tunnel 11

8 Setup of idealized cable section inside test section of wind tunnel 12

9 Side view of cylinder section placement in wind tunnel 13

10 Schematic of Displacement due to MFC Actuation 14

11 MFC Mechanism mounted inside Cylinder at 60-degree Orientation 14

12 Aluminum Plates with MFC glued on both sides 14

13 Schematic of Cylinder with Actuator mounted inside 15

14 Free Vibration Cylinder at 12 seconds 16

15 Free Vibration Cylinder at 1 second 16

16 Boundary Layer Separation 18

17 4 Angles of Perturbation 18

18 Detailed Schematic of Cylinder System at 60 degrees 19

19 Schematic of phase difference 20

20 0-degree Orientation Spectrum 21

21 Average Maximum Displacement @ 2.2 m/s and 0 degrees 22

22 Maximum Displacement @ 2.2 m/s and 0 degrees 22 vi

23 VIV undergoing 5.5 Hz actuation at 2.2 m/s 23

24 VIV undergoing 6.0 Hz actuation at 2.2 m/s 23

25 VIV undergoing 6.5 Hz actuation at 2.2 m/s 24

26 Average Maximum Displacement @ 2.35 m/s and 0 degrees 24

27 Maximum Displacement @ 2.35 m/s and 0 degrees 25

28 VIV undergoing 5.5 Hz actuation at 2.35 m/s 25

29 VIV undergoing 6.0 Hz actuation at 2.35 m/s 26

30 VIV undergoing 6.5 Hz actuation at 2.35 m/s 26

31 Average Maximum Displacement @ 2.6 m/s and 0 degrees 27

32 Maximum Displacement @ 3.0 m/s and 0 degrees 27

33 VIV undergoing 5.5 Hz actuation at 2.6 m/s 28

34 VIV undergoing 6.0 Hz actuation at 2.6 m/s 28

35 VIV undergoing 6.5 Hz actuation at 2.6 m/s 28

36 Effect of Frequencies Near fv on Vortex-Induced Vibrations 29

37 VIV Magnitude at Re = 6400 30

38 Cylinder undergoing VIV with 3 Hz perturbation at Re = 6400 (Trial 1) 30

39 Cylinder undergoing VIV with 3 Hz perturbation at Re = 6400 (Trial 2) 31

40 Cylinder undergoing VIV with 3 Hz perturbation at Re = 6400 (Trial 3) 31

41 Phase difference between 180o and 270o (Trial 1) 32

42 Phase difference between 180o and 270o (Trial 2) 32

43 Phase difference between 180o and 270o (Trial 3) 33

vii

ABSTRACT

Vortex-Induced Vibration (VIV) in cables is a prevalent phenomenon affecting the structural health of bridges and their components. Past studies have shown both passive and active methods are beneficial in the reduction of vibrations, however, a number of issues such as excessive base moment, transformation of geometry, intrusive implementation and fatigue limit the effectiveness of current engineering. A method involving no intrusion, no geometrical manipulation and a mechanism to prevent and mitigate VIV is needed. A "skin" of material embedded with Macro-Fiber Composite (MFC) material and with the capabilities of perturbing the surface near the separation point of vortex shedding is explored and tested. Simplifications of the proposed material are made in order to understand the effects of the capabilities of a perturbing skin of MFC material. Construction of a 17-ft Open-circuit wind tunnel is done in order to make the VIV condition to be tested with the near method of VIV control. The VIV on cables is recorded. Experiments are run inside the tunnel at a Re of 11400 and 6400. In order to see the effects of surface perturbations, an MFC actuation mechanism is made and a cable section effectively able to cause surface perturbations is built. A test is then run to find the effect of different angles of perturbation. Finally, a testing and analysis of a phase- difference of a signal, at prescribed perturbation frequencies is done. This is analyzed against surface vortex formation theory. The data are analyzed in order to see the capabilities of an MFC skin on VIV of cables. The mechanism shows promise in both reducing VIV and providing for a low-key, non-intrusive control mechanism.

viii

CHAPTER 1

INTRODUCTION

Structures, heavily or partially supported by cables may undergo Vortex-Induced Vibrations (VIV) when subject to wind or other fluid flow, due to boundary layer flow separation. This characteristic of flow behavior may cause detrimental effects to the support cables of bridges. Several issues arise with modern bridge structures being subject to wind. Long span slender structures are affected by VIV as well as the inclined cables supporting them. Due to very low damping of the cables, VIV are fairly common [Matsumoto et al, 2003]. Although many control methods have been used in prototypes and have been implemented in real cable-stayed bridges, fatigue from constant vibrations is found in connections of cables to damping mechanisms. Certain bridges such as two cable-stayed bridges in Shanghai and Nanjing China have suffered from heavy cable vibrations due to rain-wind-induced vibrations, causing severe damage to the outside protective casing of the cables [Gu et al, 1998]. Hikami reproduced wind induced vibration of cables which had occurred naturally on the Meiko Nishi Bridge to demonstrate the effects of VIV [Hikami, 1986]. Matsumoto demonstrated, under natural wind, that vibrations of amplitudes up to 2 m were possible in full scale cable-stayed bridges [Matsumoto et al, 1998]. These amplitudes cause fatigue in the cable members as well as safety issues in the structure itself. Active and passive control methods are used in mitigating the effects of VIV and are generally intrusive to the cables. Methods utilizing a novel and non-intrusive approach should be investigated to implement forms of preventing VIV from initializing while at the same time avoiding the continuance and danger of already induced vibrations. Exploration of the use of Macro-Fiber Composites (MFC), a composite piezoelectric material, in structural engineering is common. Uses such as acoustic sensing, crack detection, and VIV control have been tested and recorded. The following investigation involves the use of MFC in perturbing the surface of circular cylinders to understand the effects and behavior of cables undergoing VIV and the possibilities of this method in the control and mitigation of cable vibrations.

CHAPTER 2

LITERATURE REVIEW AND MOTIVATION

2.1 Vortex-Induced Vibration

Vortex-Induced Vibration (VIV) is a phenomenon in fluids in which the shedding frequency of vortices, due to separation from a bluff body, is very close to the natural frequency of the structure being affected. This causes the structure to dominate vibrations in a “lock-in” state and resonate due to oscillatory forces. The Strouhal number is related to the shedding frequency of fixed cylinders. This dimensionless number is:

S = fv D/U (1)

where U is the velocity of the fluid flow, fv is the vortex shedding frequency, and D is the diameter of the cylinder. Strouhal numbers near the value of 0.2 are common for many different Reynolds numbers causing VIV in cylinders [Gabbai and Benora, 2005]. For VIV to occur, the shedding frequency of the separating vortices must be very close to the natural frequency of the body. The natural frequency is found using either of two different methods: using the structural mass and stiffness or measured experimentally from free-vibration tests. The method for structural stiffness and mass would be using the equation:

= (2) �

fn = cycles/Δt , (3)

Another important component of VIV analysis is the Reynolds Number (Re). The Reynolds number separates different flow categories, such as laminar flow or turbulent flow. For Re > 10,000 the flow is considered turbulent, while for Re < 10,000 flow is considered laminar. [Sieve et al, 1995]

Re = UD/n, (4) n = μ/ρ, where μ is the dynamic viscosity of the fluid and ρ is the density of the fluid. The amplitude of vibrations is dominate d by another dimensionless number called the Scruton number (reduced damping):

2 Sc = 2m(2πξ)/ρD , (5)

where ξ = (1/2πj)ln(ui/ ui+j). (6)

Equation 6 is computed by looking at the ratio of how many cycles, j, have gone by for a certain reduction in displacement, u. Less mass of the mechanism would require lower Re while higher mass would require higher Re, but as long as the Scruton number is less than 64, significant resonant displacement will occur [Blevins, 1990]. A very important area of VIV control and mitigation is that of cable vibrations due to VIV (Williamson and Govardhan, 2004). Cable-stayed bridges and suspension bridges may both have VIV effects on the support cables which may reach large and dangerous amplitudes.

2.2 Vortex-Induced Vibration Control Methods

Many control strategies for VIV have been employed, specifically in the area of cable vibrations. Passive, active and semi-active control methods are used. Scruton and Walshe demonstrate a passive approach by the use of helical strakes in steel chimneys [Scruton Walshe, 1957], which proved useful but cause a large base moment on the structure. Vortex Generators (VG) have also been used to suppress vortex formation and reduce VIV effects [Barret and Farokhi, 1996]. This involves applying tabs to the exterior of the cylinder in order to promote creation of different vortices and reduce boundary layer separation. Internal and external damping systems are used in cable-stayed bridges but are subject to fatigue due to constant vibrations at the connections [Bosch, 2011].

Active control techniques such as Smart VG (SVG) are used also. This technique uses shape-memory-alloy actuators, sensors and an optimal controller to optimize the lift to drag ratio by adjusting its height [Barrett and Farokhi, 1996]. Blowing and suction techniques using different signals used as well. They function by blowing jets of air through the body near the separation points. Pulsed air blowing/suction worked the most due to high-momentum air causing vorticity in the boundary layer [Seifert, Nishri, Wygnanski, 1993]. Another active control method used for controlling VIV is the use of Macro-Fiber Composites - a type of piezoelectric actuator. This method has been investigated with respect to square sections, by causing surface perturbations on the top surface of a square section undergoing VIV. The method reduced VIV significantly but has not been investigated further in the scope of cable vibrations and behavior under different perturbation signals.

2.3 Macro-Fiber Composite

Macro-Fiber Composite (MFC) is a type of piezoelectric composite material made of fibers which when under mechanical stress, generates an electric field (Direct Piezoelectric Effect). The sensor also has the property of actuation when an electric field is applied (Converse Piezoelectric Effect) [Giurgiutiu, 2007]. This material is known to have very high structural stiffness and is able to reach very high frequencies: approximately between 1 Hz and 2 kHz [Inman et al, 2003]. The flexible nature of the material allows it to be attached to curved surfaces at a maximum of 0.0889 m in the fiber direction. The material also pushes with a force of 4 kN/cm2 for the active cross-section.

Figure 1: Macro-Fiber Composite Schematic [Zhang et al, 2005]

Figure 2: M-8528-P1 Macro-Fiber Composite Actuator

The behavior of the material under actuation is shown through the coupled equations:

{S} = [s]{T} + [d]t{E} (7) {D} = [d]{T} + [ε]{E} (8) where [S] and {T} are the strain and stress, {E} and {D} are electric field and electric displacement, [d] is the charge per unit stress, and [d]t is the strain per unit electric field. [s] is the compliance, which is the strain per unit stress and [ε] is the permittivity [Giurgitiu, 2007].

Aluminum plate on top and bottom

Direction of motion MFC attached to top and bottom

Figure 3: Schematic of MFC motion at rest (top) and under actuation (bottom)

Fig. 3 illustrates the use of 2 aluminum plates attached at both ends and combined with a MFC on top and on the bottom. The MFC move in synchronization in order to induce an equal- magnitude moment, causing displacement in the y-direction. A similar form was used by Zhang et al to perturb a square cylinder surface [Zhang et al, 2005]. MFC is used in various applications in engineering such as Structural Health Monitoring, and control of wind turbine vibration. Giurgiutiu et al studied the use of piezoelectronics for active sensing of aerospace structures [Giurgitiu, 2003]. Zhang et al used embedded piezoceramics to eliminate VIV from a freely vibrating square section by means of surface perturbations. Although MFC have been investigated for their potential VIV control capabilities in square sections, they have not been studied for cable vibrations. The perturbation strategies used by Zhang et al, for square sections, can be further studied to understand the signal effect as well as the effect of the perturbation mechanism on vortex formation and VIV mitigation.

2.4 Motivation for Study

Many methods for VIV control require the modification of the body’s geometric properties. For example, helical strakes require circular sections to have physical strakes either manufactured or retrofitted onto them. Vortex Generators are applied in a similar fashion; by adding small bumps to the existing surface. Another method mentioned earlier - Smart VG - requires a shape-memory alloy to adjust the geometry of the structures by applying the material to the exterior of the body and allowing for actuation to cover the backside of the circular section [Barret and Farokhi, 1996]. While many methods currently exist, they involve invasive control techniques. The use of Macro-Fiber Composites has not been explored in the area of cable VIV. MFC can provide a material that does not invade the current geometry of cables being affected by VIV. Micro-Fiber Composites (MFC) have been used in this area, especially by M.M. Zhang et al in mitigating VIV on square cylinders, but the effect it may have on circular cylinders is not known [Zhang et al, 2005]. While Shape-Memory-Alloy is used in exterior portions of cylinders to change the boundary layer separation characteristics or lift to drag ratio, close effects of surface perturbations using MFC have not been explored. Zhang, Chen and Zhou, in a paper titled Control of vortex-induced non-resonant vibration using piezo-ceramic actuator embedded in a structure experimented with the use of piezoelectric actuators to perturb a square cylinder. This provided evidence that by using surface perturbation on a square cylinder surface, significant decrease in VIV amplitude is possible [Zhang et al, 2005]. The paper also noted that using frequencies near the natural frequency of the bluff body significant changes to the amplitude. The study provided evidence of MFC perturbation usage at Reynolds numbers of 8000 and 2800, with sinusoid signals ranging around the area of natural frequency. This study provided basis for further exploration into the usage of this method in circular cross-sections leading to cable vibrations. It is also imperative to study the behavior of VIV when actuated at various phase differences of synchronization between the actuation pattern and the frequency of vibration.

CHAPTER 3

CONSTRUCTION OF WIND TUNNEL

Since the dawn of the modern wind tunnel, applications are numerous, albeit the creation and use of sophisticated Finite Element Modeling and/or other computer simulation software. While Computer Fluid Dynamics software has taken up similar projects that wind tunnels do, the size and complexity of the model is limited by the computational power of today’s hardware [McAlpine, 2004]. This means that complicated geometrical structures can be placed in large wind tunnels without the concern for increasing computational power. Wind tunnels are classified into two categories of construction: Open Circuit Wind Tunnels and Closed Circuit Wind Tunnels. Open Circuit Wind Tunnels are tunnels which bring in air from the atmosphere through the front section of the tunnel and exhaust it out back into the environment while Closed Circuit Wind Tunnels are tunnels that circulate air throughout the tunnel without exhausting it. These two types of tunnels are also classified by the maximum speeds they attain: Subsonic Speed (Low speed), Transonic Speed (High Speed), Supersonic Speed, and Hypersonic speed [Barlow, 1999]. These names correspond, respectively; to the Mach number (speed) at which the tunnel can blow. In our case we are focusing on a Low Speed (< Mach 1), Open-Circuit Wind Tunnel. The tunnel design used to reach the VIV condition is based on the Wandering Wind Tunnel and the Vision in Aeronautics project [Baals and Corliss, 1981]. The tunnel has 4 main sections in which it is partitioned: contraction cone, flow straightening section, test section, and diffuser section (Fig. 4). Each of these portions plays a vital role in the proper functionality of the tunnel.

Screen & Honeycomb Structure

F Contraction A Diffuser Section Test Section Cone N

Flow-straightening Contraction

Section Ratio

Figure 4: Wind Tunnel Design

The first step is to make sure that the contraction ratio (ratio between the cross-sectional area of the contraction cone to the cross-sectional area of the test section) is 12:1. This means that a 5’ x 5’ (1.524m x 1.524m) contraction cone leads to a 1.5’ x 1.5’ (0.4572m x 0.4572m) test section. The cone is constructed with 24” x 24” x 0.04” (60.96cm x 60.96cm x 0.1016cm) aluminum sheets connected by pop rivets (Fig. 5). This material allowed for easier shaping of a smooth, non-linear transition of airflow. This transition follows the Continuity principle:

1 1 1 = 2 2 2, (9)

� � where ρ is the density of the fluid, A is the area of the section, and v the velocity of the sections. The second step involves the design of a flow straightening section. This section uses a 2” x 18” x 18” (5.08cm x 45.72cm x 45.72cm) aluminum honeycomb structure followed by a screen. The honeycomb structure is used to break apart turbulent flow so streamlines are uniform while the screen serves to equalize the speed of streamlines coming into the test section.

Figure 5: 5’ x 5’ Aluminum contraction cone followed by flow straightening section

The cross sectional area of the test section is engineered based on the result of the contraction ratio. This ratio yields a section of 4’ x 1.5’ x 1.5’ (1.2192m x 0.4572m x 0.4572m). The section is built with 19/32” (1.508cm) plywood which was filled with plastic body filler, topped with resin and finished with 320 grade sandpaper. This preparation is in hope of achieving laminar flow, by reducing frictional forces due to obstacles along the walls of the tunnel. Plexiglass windows are installed from the inside – flush to the surface – to allow for viewing of test subjects. The following section – diffuser section – is composed of the same building materials and preparation but with a pitch of 3o to allow for the velocity of the fluid to slowly reduce as it exits the tunnel. This is all powered by a 30” exhaust fan with a 3 HP motor which can blow 14,400 CFM (6.796 m3/s). The 14,400 CFM translates to approximately 73 MPH (32.624 m/s) maximum wind speed by way of the volumetric flow rate equation (Venturi Effect):

= , (10)

� where Q is the volumetric flow rate, v is the velocity, and A is the cross-sectional area.

Figure 6: (left) Test Section, (right) Diffuser Section

Figure 7: Open-Circuit Wind Tunnel

All sections are sealed tightly with bolts and clamps on the outside and flexible calking on the inside crevices. Weather stripping is used in portions where doors are placed.

CHAPTER 4

EXPERIMENTAL SETUP

4.1 Idealization of Problem

The problem of VIV on cables is idealized by inducing wind vibrations on a section of a cable inside an open-circuit wind tunnel. The cable section was constructed with a thin, plastic cylinder having dimensions: diameter = 0.0838 m, length = 0.381 m, thickness 1.2 mm. It is mounted using 2 aluminum brackets on both sides and 4 equal stiffness springs. The total mass of the setup is 0.165 kg. The entire setup is placed in the test section of the tunnel (Fig. 8).

Figure 8: Setup of idealized cable section inside test section of wind tunnel

The cable section is placed perpendicular to the wind direction (Fig. 8) which causes displacement due to VIV, in the Z-direction (Fig. 9). The cylinder was mounted on the brackets by fixing the cylinder at one point on the base of the bracket.

Figure 9: Side view of cylinder section placement in wind tunnel

4.2 Instrumentation

The instrumentation used during testing is a variable speed controller which is sensed with an anemometer. Once in motion the section is sensed using a OMRON ZX-LD300 Reflective Laser displacement sensor (placed along the Z direction). This sensor has a 300 μm resolution and a range of +/- 200 mm. Using a National Instruments Data Acquisition module, Model 9219, at a sampling rate of 100 Hz and Labview development environment, the data is recorded. In order to cause surface perturbations, two Smart Material M 8528 P1 MFCs are used at a maximum voltage capacity of -500V to +1500V. The application of the high voltage is achieved via the use of Labview and a National Instruments Data Acquisition module, Model 9263 and a Smart Material PA 05039 High Voltage amplifier with a rating of 1:200 V.

4.3 Method of Perturbation

As mentioned, invasive methods of retrofit control strategies require the geometry of cables to be tampered with. Using MFC in application settings would require adding a "skin" of MFC embedded material which would not change the geometrical properties of the cable. Since constructing a cylinder with this "skin" outer layer of MFC is costly and time consuming, a simpler yet efficient approach is used to account for the movement needed. An actuating mechanism is built inside of a thin and flexible cylinder to allow for free motion of the exterior. The actuation mechanism is composed of the two MFCs super glued onto 1 mm aluminum plates. A moment is induced on the aluminum plates which causes the inside of 13

the cylinder to actuate. The cylinder reflects the same shape that a cable would be (completely circular) and deforms to a slightly ovular shape (Fig. 10).

Figure 10: (left) Schematic of Displacement Figure 11: (right) MFC Mechanism mounted due to MFC Actuation at Equilibrium (black) inside Cylinder at 60-degree Orientation and at Maximum Displacement (red) (red arrows indicate displacement direction)

Figure 12: Aluminum Plates with MFC glued on both sides

Extensions to push on cylinder surface (attached to MFC/aluminum plate actuator MFC actuator)

Deformed shape of cylinder

Figure 13: Schematic of Cylinder with Actuator mounted inside

The mechanism is mounted inside the cylinder at the minimum position and expanded to a maximum of 8% of the cylinder’s diameter. Fig. 13 shows a schematic of the cylinder at its equilibrium position and at the maximum position after MFC actuation. The actuator is attached to extensions and glued to the inner surface of the cylinder to allow full motion contact with the cylinder. Once the MFC pushes out (as illustrated in Fig. 3) the cylinder move to the position designated as red (Fig. 13). This motion also retracts to the original position when the actuator returns to rest.

4.4 Calculation of Wind Speed for Vortex-Induced Vibration

In order to reach VIV, a few values must be calculated. Based on the free vibration of the cylinder (Fig. 15), it is seen that within 1second, the cylinder displaces a total of 5.5 cycles.

-1.5 6 7 8 9 10 11 12 -1.6

-1.7

-1.8

-1.9 Displacement Displacement (V)

-2

-2.1 Time (s)

Figure 14: Free Vibration Cylinder at 12 seconds

-1.5 6 6.2 6.4 6.6 6.8 7 -1.6

-1.7

-1.8

-1.9 Displacement Displacement (V)

-2

-2.1 Time (s)

Figure 15: Free Vibration Cylinder at 1 second

The damping ratio is approximately = 1.5%. This makes ωD and ωn very close in value, based on the equations: � 2 1 2 D = (11) −� and ω � 2 n = (12) � ω 16

Since the difference is minimal, Equation (3) is used to calculate the natural frequency. The natural frequency is calculated to be 5.5 Hz. In order to reach VIV, the natural frequency of the section must be equal to the vortex shedding frequency. The Strouhal Number described earlier is an important indicator of VIV. As stated earlier, at a Strouhal number near 0.2, VIV occurs. This yields a wind velocity of U = 2.30 m/s. This velocity is used in order to achieve VIV. The Reynolds number is calculated to be Re = 11,400, where U = 2.30 m/s, D = 0.0838 m, fluid density, ρ = 1.204 kg/m3 and dynamic fluid viscosity, μ = 1.983 x 10-5. Based on Equation (6) the damping ratio for the system is ξ = 0.014644 which yields a reduced damping of 0.041376.This number calculated by Equation (5) justifies that VIV is possible.

4.5 Variable Angle Test

Due to boundary layer separation, a free shear layer forms into vortices and eventually detaches from the bluff body. The 2 points at which separation begins to occur are located on either side of the body depending on the Reynolds number described above. For Re < 2 x 105 boundary layer separation occurs at Θ ≈ 80o and for Re > 2 x105, boundary layer separation occurs at Θ ≈ 140o [Smith, 2005] (Fig. 16). It is hypothesized that by applying the actuation patterns at angles that may contain separation points, disruption of boundary layer separation may be induced.

Figure 16: Boundary Layer Separation [Smith, 2005]

The first set of tests involves testing sinusoidal surface perturbations at 0o, 30o, 60o, and 90o with respect to the y-axis (Fig. 17). This involves free deformations along both the relative-x and relative-y axes. The angles represent the direction along which the cylinder maximizes and minimizes. Accordingly, the perpendicular direction also deforms. Fig. 10 shows the direction the cylinder would move when set up for a 0o test. Fig. 11 is the setup for a 60o test. The aluminum brackets sustaining the spring system contain angled sides corresponding to the 4 angles for testing (Fig. 18).

o 0 30o

60o

90o

Figure 17: 4 Angles of Perturbation

Springs (4)

Aluminum Brackets Fishing Line for range of perturbation (2)

1 mm plastic cylinder (1)

Figure 18: Detailed Schematic of Cylinder System at 60 degrees

4.6 Actuation Phase Test

Based on the observations of the Variable Angle Test, the same type of test is run at a lower Reynolds number in order to understand the behavior further. This is inspired by the Navier-Stokes equation written for the surface of the cylinder [Gad-el-Hak, 2000]:

2 + = 2 (13) � � − � where u is the dimension along the wall, y is the dimension perpendicular to the wall, Vw is the suction velocity through the wall, P is the thermodynamic pressure and μ is the wall viscosity.

Manipulating this equation by means of Vw would cause the right side of the equation to be 2 2 negative or positive. In order for separation to be prevented, 2 < 0 should be met. For 2 > 0 separation will proceed.

The Variable Angle Test showed that at 0-degree orientation, the effects of MFC perturbation were largest – specifically at frequencies near the natural frequencies. With this observation, a sinusoidal signal at 3 Hz is used to perturb the upper portion of the cylinder just as in the Variable Angle Test. The signals act with magnitude of 0.08D, that is, 8% of the cylinder diameter. This direction of movement in the signal causes a “push” or “pull to occur at the frequency prescribed. If both the vortex shedding frequency and signal spikes are synchronized, it is assumed that the VIV should act as the Navier-Stokes equation suggests based on either –Vw or +Vw. If the synchronization is offset by some phase difference δ, then the effect will be a combination or influence of both +/-. The objective of the additional testing is to understand the relationship between the phase of the actuation and reduction of the vibration. The test is run at Re = 6400.The hypothesis is that a pushing action will cause separation to continue whereas a pulling motion will reduce the separation mechanism, leading to reduced VIV. Based on the Navier-Stokes equation and the cylinder/actuation system, a sinusoidal signal that is in-phase with the vibration position (Fig. 19) will cause a pushing motion whereas an out-of-phase condition will cause no pushing. As the cylinder reaches its maximum position, the upper surface pushes out (in-phase). This motion theoretically should cause an increase of VIV. Complications exist due to the fact that the actuator can only "push" the surface. This would theoretically not prevent separation. However the goal of this test is to quantify the effect of various phase differences on the magnitude of the vibrations.

In-phase Out-of-phase

max

min

Figure 19: Schematic of phase difference

CHAPTER 5

RESULTS AND DISCUSSION

5.1 Variable Angle Test

Displacements are computed as "average displacement" and "maximum displacement". During testing, displacement is recorded at 100 Samples/sec for 50 seconds. The maximum of these data for every 50 data points (0.5 second) is recorded and a final average is taken. These are the data points being used for each figure labeled as "average". Figures labeled as "maximum" correspond to the absolute maximum value of the entire data series. Results for 30, 60 and 90 degrees are shown in Appendix, since less effective results are produced.

4 AverageDisplacement (mm) 2

0 1.5 2 2.5 3 3.5 4 Wind Speed (m/s)

Figure 20: 0-degree Orientation Spectrum

The velocity spectrum of the cylinder section has a peak velocity at 2.6 m/s and reaches a displacement of 14.88 mm (17.75% of the cylinder diameter). The two points before the peak of the spectrum are 2.2 m/s at 3.57 mm and 2.35 m/s at 7.11mm amplitude, respectively. To better

21 understand the effect of surface perturbation, these three velocities are chosen for testing. Each velocity is within lock-in and is perturbed with frequencies ranging from 1 Hz to 11 Hz.

6 Avg. Displacement 50 40 5 % Difference 30 4 20 3 10 0

2 Difference% -10 1

AverageDisplacement (mm) -20 0 -30 0 2 4 6 8 10 Actuation Frequency (Hz)

Figure 21: Average Maximum Displacement @ 2.2 m/s and 0 degrees

8 Max. Displacement 80 70 7 % Difference 60 6 50 5 40 4 30 3 20 10 Difference% 2 0 1

MaximumDisplacement (mm) -10 0 -20 0 2 4 6 8 10 Actuation Frequency (Hz)

Figure 22: Maximum Displacement @ 2.2 m/s and 0 degrees

0 Hz corresponds to the VIV condition without actuation at 2.2 m/s. It is observed that the behavior of the vibrations do not change until the frequency of the perturbation approaches

22 the frequency of vibration (~5.5 Hz). At this point the average displacement drops to approximately 22% less than the vibration at 0 Hz. However this behavior is not constant. The cylinder vibrations follow a cyclic pattern which reduces in amplitude but then increases again.

This pattern repeats as the frequency is held around fv.

10 Without Control 5.5Hz Actuation 5

-5 Displacement(mm)

-10 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time (sec) Figure 23: VIV undergoing 5.5 Hz actuation at 2.2 m/s

The behavior expressed by Fig. 23 appears to conclude that 5.5 Hz perturbation causes an increase in the VIV displacement, however, Fig. 25 shows a clear reduction of nearly 50%. This is due to the cyclic behavior described earlier. At certain intervals the vibrations are drastically reduced and at intervals between the reduction intervals, larger vibrations occur.

6 Without Control 4 6Hz Actuation

-2 Displacement(mm) -4

-6 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time (sec) Figure 24: VIV undergoing 6.0 Hz actuation at 2.2 m/s

Similar effects happen at 6 Hz and 6.5 Hz. This is an indication that the frequency is still close enough to fv to cause mitigation of VIV.

5 Without Control 6.5Hz Actuation

0 Displacement(mm)

-5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time (sec) Figure 25: VIV undergoing 6.5 Hz actuation at 2.2 m/s

8 Avg. Displacement 0 7 % Difference -5 6 -10 5 -15 4 -20 3 -25 Difference% 2 1 -30 AvgerageDisplacement (mm) 0 -35 0 2 4 6 8 10 Actuation Frequency (Hz)

Figure 26: Average Maximum Displacement @ 2.35 m/s and 0 degrees

Again, around 5.5 Hz, a clear spike in the graph is apparent. This follows the pattern of the lower velocity wind. Around synchronization a change is made in the magnitude of

24 vibrations. Interestingly, 11 Hz has a similar effect. 11 Hz is a multiple of fv which may be the reason for a similar behavior.

12 Max. Displacement 40 % Difference 10 30

8 20

6 10

4 0 Difference%

2 -10 MaximumDisplacement (mm) 0 -20 0 2 4 6 8 10 Actuation Frequency (Hz)

Figure 27: Maximum Displacement @ 2.35 m/s and 0 degrees

10 Without Control 5.5Hz Actuation 5

-5 Displacement(mm)

-10 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time (sec) Figure 28: VIV undergoing 5.5 Hz actuation at 2.35 m/s

It is observed in Fig. 28 that a similar pattern occurs. A reduction followed by a magnification of the constant VIV (red). The reduction in this plot reaches approximately 65% while reaching a magnification of 36%.

10 Without Control 6Hz Actuation 5

-5 Displacement(mm)

-10 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time (sec) Figure 29: VIV undergoing 6.0 Hz actuation at 2.35 m/s

Fig. 29 does not have any clear sign of behavioral change due to 6.5 Hz except for minor reductions and minor amplifications.

10 Without Control 6.5Hz Actuation 5

-5 Displacement(mm)

-10 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time (sec) Figure 30: VIV undergoing 6.5 Hz actuation at 2.35 m/s

Fig. 30 exemplifies the similar pattern that the initial tests exhibited. The vibrations begin with amplified magnitudes and reduce by approximately 25%.

20 Avg. Displacement 16 18 % Difference 14 16 12 14 12 10 10 8 8 6 6 Difference% 4 4

AverageDisplacement (mm) 2 2 0 0 0 2 4 6 8 10 Actuation Frequency (Hz)

Figure 31: Average Maximum Displacement @ 2.6 m/s and 0 degrees

30 Max. Displacement 70 % Difference 25 60 50 20 40 15 30

10 Difference% 20

5 10 MaximumDisplacement (mm) 0 0 0 2 4 6 8 10 Actuation Frequency (Hz)

Figure 32: Maximum Displacement @ 2.6 m/s and 0 degrees

Although Fig. 31 does not display a significant percentage of reduction but instead an amplification of the vibration magnitude, particular attention to Fig. 33 will show the decrease of vibration magnitude in similar fashion to lower velocities. 6 Hz and 6.5 Hz do not have as dramatic of an effect as when used under lower speeds.

20 Without Control 10 5.5Hz Actuation

-10

Displacement(mm) -20

-30 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time (sec) Figure 33: VIV undergoing 5.5 Hz actuation at 2.6 m/s

20 Without Control 6Hz Actuation 10

-10 Displacement(mm)

-20 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time (sec) Figure 34: VIV undergoing 6.0 Hz actuation at 2.6 m/s

20 Without Control 6.5Hz Actuation 10

-10 Displacement(mm)

-20 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time (sec)

Figure 35: VIV undergoing 6.5 Hz actuation at 2.6 m/s

18 Without Control 16 6 Hz Actuation 14 5.5 Hz Actuation 12 10

4 AverageDisplacement (mm) 2

0 1.5 2 2.5 3 3.5 4 Wind Speed (m/s)

Figure 36: Effect of Frequencies Near fv on Vortex-Induced Vibrations

Due to the uncertain amount of reduction versus amplification, Fig. 36 may not accurately express the level of reduction that surface perturbation may have on VIV. Large reductions approaching 50% ~ 60% are common but not constant; skewing the final result of Fig. 36. Despite the change in VIV magnitude, a reduction is still apparently more significant at lower velocities. Following this observation, tests are run at lower Re to investigate the effects of various phase differences on VIV reduction.

5.2 Actuation Phase Test

For the Actuation Phase Test, three separate tests are run at the lowered Re. Each test is run for 100 seconds. The test involves a cylinder undergoing VIV and being perturbed by 3 Hz.

Since fv is slightly more or less than 3 Hz, a phase difference is constantly changing over time. This phase difference causes changes in the behavior of the vibrating cylinder.

10 8 6 4 2 0 -2 0 1 2 3 4 5 -4 Displacement(mm) -6 -8 -10 Time (s)

Figure 37: VIV Magnitude at Re = 6400

20 15 10 5 0 -5

Displacement (mm) -10 -15 -20 0 10 20 30 40 50 60 70 80 90 100 Time (s)

Figure 38: Cylinder undergoing VIV with 3 Hz perturbation at Re = 6400 (Trial 1)

Fig. 38 has 3 main sections. Each of these sections exhibits an increase from approximately 8 mm (VIV) to 15 mm which is hypothesized to be dependent on the phase angle. The displacement reduces to almost 0 mm but increases again and follows a similar behavior continuously. This behavior is similar in all 3 trials.

20 15 10 5 0 -5

Displacement (mm) -10 -15 -20 0 10 20 30 40 50 60 70 80 90 100 Time (s)

Figure 39: Cylinder undergoing VIV with 3 Hz perturbation at Re = 6400 (Trial 2)

25 20 15 10 5 0 -5 -10 Displacement (mm) -15 -20 -25 0 10 20 30 40 50 60 70 80 90 100 Time (s)

Figure 40: Cylinder undergoing VIV with 3 Hz perturbation at Re = 6400 (Trial 3)

Since all plots show a similar behavior (Fig. 38-40), going from increased VIV to dramatic reduction of VIV, further observations of the phase difference involved in regions of similar behavior should be analyzed.

20 15 10 5 0 -5

Displacement (mm) -10 -15 -20 65 70 75 80 Time (s)

Figure 41: Phase difference between 180o and 270o (Trial 1)

With a phase difference roughly beginning at 180o and ending at 270o a reduction of VIV is noticeable (Fig. 41). This reduction reaches less than the original VIV magnitude. The magnitude begins at approximately 37.5% more than undisturbed VIV and decreases by 38% of the original amplitude and 55% of the increased amplitude. This trend is consistent with all three trials.

20 15 10 5 0 -5

Displacement (mm) -10 -15 -20 65 70 75 80 Time (s)

Figure 42: Phase difference between 180o and 270o (Trial 2)

The reduction for the second trial is slightly less. It begins at approximately 56% more than VIV and reduces by 13%. However the total reduction from increased VIV to reduced VIV for this time interval is 54%. This is a similar total reduction as Figure 41.

25 20 15 10 5 0 -5 -10 Displacement (mm) -15 -20 -25 65 70 75 80 Time (s)

Figure 43: Phase difference between 180o and 270o (Trial 3)

Trial 3 has an initial increased displacement of 13 mm, which is 62.5% more than VIV. This is reduced to approximately 8.5 mm, 6.25% higher than VIV and 35% less than the increased vibration magnitude (Fig. 43).

CHAPTER 6

CONCLUSION AND FUTURE WORK

6.1 Conclusion

The use of Macro-Fiber Composites in mitigating effects of Vortex-Induced Vibration on cables proves successful. Perturbations near the separation point of a cable cause severe changes to the behavior of the vortices being formed. At surface perturbation frequencies near the vortex shedding frequency of the cable section, mitigation is observed. While amplification occurs at certain parts of the perturbation process, mitigation also occurs. Tests run at lower Re show that the phase differences affect the magnitude of the cable vibrations. Depending on the phase angle, vibrations may be amplified or reduced. These data provide insight into further design criteria of the proposed material. Other sections of the total behavior do not exhibit a clear trend. Some places follow a trend often but none as complete as the interval between 65 seconds and 80 seconds for the Actuation Phase Test. The analysis of the phase difference is not refined enough to look at smaller phase changes and therefore can limit the level of analysis and understanding. However a clear indication of the behavior between all three trials shows effects of the phase angle as well as the potential of using this knowledge in designing against VIV. The movement of the physical mechanism leads to the possibilities of designing a material which exhibits the behavior of the present study.

6.2 Future Work

Further investigation is needed in the effects of varying phase angles. This information will allow for better understanding of the mechanism that prevents or hinders the separation of vortices causing VIV. Following a refined test involving phase differences, experiments with a surface-suction mechanism will be explored. This will aid in understanding the counter effect of perturbation. With both the suction and pushing surface perturbation as well as rigorous

34 experimentation of phase angles, a much better understanding of VIV mitigation using MFC will be documented.

APPENDIX

AverageDisplacement (mm) 2

0 1.5 2 2.5 3 3.5 4 Wind Speed (m/s)

30-degree orientation

14 Avg. Displacement 300

12 % Difference 250 10 200 8 150 6

100 Difference% 4

2 50 AverageDisplacement (mm)

0 0 0 2 4 6 8 10 Actuation Frequency (Hz)

Average Maximum Displacement @ 2.2 m/s for 30 degrees

18 Max. Displacement 250 16 % Difference 14 200 12 150 10 8 100

6 Difference%

4 50 2 MaximumDisplacement (mm) 0 0 0 2 4 6 8 10 Actuation Frequency (Hz)

Maximum Displacement @ 2.2 m/s for 30 degrees

14 Avg. Displacement 80 12 % Difference 70 60 10 50 8 40 6 30 4 Difference% 20 2 AverageDisplacement (mm) 10 0 0 0 2 4 6 8 10 Actuation Frequency (Hz)

Average Maximum Displacement @ 2.30 m/s for 30 degrees

16 Max. Displacement 90 14 % Difference 80 12 70 60 10 50 8 40 6

30 Difference% 4 20 2 10 MaximumDisplacement (mm) 0 0 0 2 4 6 8 10 Actuation Frequency (Hz)

Maximum Displacement @ 2.30 m/s for 30 degrees

14 Avg. Displacement 80 12 % Difference 70 60 10 50 8 40 6 30 4 Difference% 20 2 AverageDisplacement (mm) 10 0 0 0 2 4 6 8 10 Actuation Frequency (Hz)

Average Maximum Displacement @ 2.6 m/s for 30 degrees

16 70 Max. Displacement 14 % Difference 60 12 50 10 40 8 30 6 20 Difference% 4 2 10 MaximumDisplacement (mm) 0 0 0 2 4 6 8 10 Actuation Frequency (Hz)

Maximum Displacement @ 2.6 m/s for 30 degrees

6 AverageDisplacement (mm) 4

0 1.5 2 2.5 3 3.5 4 Wind Speed (m/s)

60 degree-orientation

10 14 9 12 8 7 10

6 8 5 4 6 3 4 Difference% Avg. Displacement 2 2 AverageDisplacement (mm) 1 % Difference 0 0 0 2 4 6 8 10 Actuation Frequency (Hz)

Average Maximum Displacement @ 2.20 m/s for 60 degrees

14 Max. Displacement 35 12 % Difference 30

10 25

8 20

6 15

4 10 Difference%

2 5 MaximumDisplacement (mm) 0 0 0 2 4 6 8 10 Actuation Frequency (Hz)

Maximum Displacement @ 2.20 m/s for 60 degrees

12 20 18 10 16 14 8 12 6 10 8

4 Difference% 6 Avg. Displacement 4 2 AverageDisplacement (mm) % Difference 2 0 0 0 2 4 6 8 10 Actuation Frequency (Hz)

Average Maximum Displacement @ 2.25 m/s for 60 degrees

14 Max. Displacement 35

12 % Difference 30

10 25

8 20

6 15

4 10 Difference%

2 5 MaximumDisplacement (mm) 0 0 0 2 4 6 8 10 Actuation Frequency (Hz)

Maximum Displacement @ 2.25 m/s for 60 degrees

30 Avg. Displacement 6 % Difference 5 25 4 20 3 15 2 1

10 Difference% 0 5

AverageDisplacement (mm) -1 0 -2 0 2 4 6 8 10 Actuation Frequency (Hz)

Average Maximum Displacement @ 2.4 m/s for 60 degrees

35 Max. Displacement 12 30 % Difference 10 8 25 6 20 4 15 2

0 Difference% 10 -2 5 -4 MaximumDisplacement (mm) 0 -6 0 2 4 6 8 10 Actuation Frequency (Hz)

Maximum Displacement @ 2.4 m/s for 60 degrees

10 AverageDisplacement (mm)

0 1.5 2 2.5 3 3.5 4 Wind Speed (m/s)

90 Degree-orientation

18 12 16 10 14 12 8 10 6 8

6 4 Difference% 4 Avg. Displacement 2 AverageDisplacement (mm) 2 % Difference 0 0 0 2 4 6 8 10 Actuation Frequency (Hz)

Figure x: Average Maximum Displacement @ 2.25 m/s for 90 degrees

25 Max. Displacement 30 % Difference 25 20

20 15 15 10

10 Difference%

5 5 MaximumDisplacement (mm) 0 0 0 2 4 6 8 10 Actuation Frequency (Hz)

Figure x: Maximum Displacement @ 2.25 m/s for 90 degrees

20 5 18 4.5 16 4 14 3.5 12 3 10 2.5 8 2

6 1.5 Difference% 4 Avg. Displacement 1

AverageDisplacement (mm) 2 % Difference 0.5 0 0 0 2 4 6 8 10 Actuation Frequency (Hz)

Average Maximum Displacement @ 2.40 m/s for 90 degrees

25 Max. Displacement 7 % Difference 6 20 5 4 15 3 2 10 1

0 Difference% 5 -1

MaximumDisplacement (mm) -2 0 -3 0 2 4 6 8 10 Actuation Frequency (Hz)

Maximum Displacement @ 2.40 m/s for 90 degrees

30 Avg. Displacement 0 % Difference -2 25 -4 20 -6 15 -8 -10

10 Difference% -12 5

AverageDisplacement (mm) -14 0 -16 0 2 4 6 8 10 Actuation Frequency (Hz)

Average Maximum Displacement @ 2.6 m/s for 90 degrees

35 Max. Displacement 6 4 30 % Difference 2 25 0 -2 20 -4 15 -6 -8 % Difference% 10 -10 -12 5

MaximumDisplacement (mm) -14 0 -16 0 2 4 6 8 10 Actuation Frequency (Hz)

Maximum Displacement @ 2.6 m/s for 90 degrees

Dywer Anemometer

NI 9263, NI 9219, mounted in NI chassis 47

ZX-LD300 Reflective Sensor with Controller

Labview GUI Code for control/sensing

PA 05039 High Voltage amplifier

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BIOGRAPHICAL SKETCH

Gustavo Jose Munoz

Gustavo Munoz graduated with a B.S. degree in civil engineering from Florida State University in August 2010. He has past experience in Structural Control and Structural Health Monitoring.