MALAYSIA-JAPAN INTERNATIONALINSTITUTE OF TECHNOLOGY

RESEARCH PROPOSAL

June 26, 2013

Mechanism For Vortex-InducedVibration of A Bluff Body With A

Downstream Flat Plate

PhD Candidate:MOHAMAD HAFIZ ISMAIL

Supervisors:Dr. Mohamed Sukri Mat Ali

Dr. Sheikh Ahmad Zaki Shaikh Salim

Prof. Dr. Masataka Shirakashi

Abstract

Vortex induced vibration (ViV) is one of the common phenomenon found in manyfields of engineering. It received much attention especially when it causes a concernin the dynamics of long slender cylindrical (bluff body) structures such as riser tubesin the offshore oil industry. Bluff bodies are very efficience vortex generator.

When a secondary body (not necessary a bluff body) is placed in the wake of thebluff bodies, a complex flow-structure interaction in the vacinity of the gap betweenthe two bodies arranged in tandem instigates a strong dynamics response. Addi-tionally, the hydrodyamics forces generated on the downstream body can reach upto two order of magnitude larger than the forces acting on the upstream body (vor-tex generator) itself. Despite of that, the downstream body can suprisingly suppressthe vortex shedding of the upstream body when the geometry and location for thedowstream body are carefully designed. Without the vortex shedding, the problemof vortex induced vibration can be passively controlled.

This research involves the investigation of flow around a finite square cylinder ar-ranged in tandem with a downstream flat plate. The cylinder and the plate are freeto oscillate in crosstream direction with the support of a one degree mass-spring-damper system. The location and size of the plate are changed to evaluate the sen-sitivity of these parameters to the flow fields and consequently the vibration of thebodies. The main objective of this research is to find the optimal square cylinder-flat plate configuration that can give the lowest vibration level. It is expected thatfrom this research, a new concept and approach of passive vortex-induced vibrationcontrol can be adopted as an alternative to less efficient of active and passsive vibra-tion control for the application of a long slender cylindrical structures immersed ina hydrodynamic flow.

1

Contents

1 Introduction 31.1 Research Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Aims and Significance of The Research . . . . . . . . . . . . . . . . . . . 81.3 Problem Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.4 Execution Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2 Literature Review and Gap of Research 112.1 Flow Interaction with Bluff Bodies . . . . . . . . . . . . . . . . . . . . . 112.2 Flow over Bluff Bodies with Wake Interferences . . . . . . . . . . . . . 132.3 Vortex-induced Vibration . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.3.1 Flow-induced vibration of an isolated bluff body . . . . . . . . 162.3.2 Flow-induced vibration of bluff bodies with a wake interference 17

2.4 Wavy trailing Edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3 Numerical Simulation 183.1 Numerical simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.1.1 Flow Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.1.2 Turbulence Model . . . . . . . . . . . . . . . . . . . . . . . . . . 243.1.3 Motion analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2 Arbitrary Lagrangian-Eulerian formulation . . . . . . . . . . . . . . . . 253.2.1 Grid Independent . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.3 Wind Tunnel Testings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.3.1 Measurement Equipments . . . . . . . . . . . . . . . . . . . . . . 263.3.2 Samples of Data for Comparisons . . . . . . . . . . . . . . . . . 27

4 Numerical Simulation of Flow Over A Finite Square Cylinder 27

5 Conclusion 27

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1 Introduction

This chapter presents a brief overview of the research. The chapter begins with somebackground in section 1.1, where the motivation of the research is discussed. Then,the aims and significance of the research are stated in section 1.2. The test cases underinvestigation are described in section 1.3. Section 1.4 described the tasks required toachieve the research aims.

1.1 Research Background

The fluid mechanics of the flow around a bluff body, the forces induced on the bodyand the dynamic response experienced naturally by it have been extensively stud-ied for a very long time. It was reported that Leonardo da Vinci pioneered the flowvisualization of swirling water motion behind a bluff body around the year of 1500[1]. Strouhal in 1878 [2] described the interesting phenomenon known as aeoliantones emanating from a wire moving through air. von Karman in 1911 [3] publishedthe first theoretical study of prominent vortex streets behind a bluff body. Interest-ingly, despite that many advances and insights gained through the efforts of manyresearchers over the years, the study on this subject still receiving a great attention todate. This is because for every research being done, there are still remain questionsto be answered wisely and new fascinating facets to be explored in great details.

The understanding of flow over bluff bodies is not only important for exploringnew fundamental knowledge but also it concerns to many engineering applications.Heavy road vehicles that are moving at high speed for example, experience a largeamount of pressure drag due to flow separation that occurs at an early stage of theboundary layer [4]. An experimental study of a full scale truck by Rose [5] showedthat a drag reduction as much as 36% to resulted in a 16% fuel saving. Another exam-ple is the hydrodynamic flow around bridge piers. Free shear layers that originatefrom the separated flow generate a complex flow in the wake that consequently in-teract with a horseshoe vortex in the channel bed. As the process continues, a scour(a hole due to the removal of sediment) is created around the pier [6]. Additionally,study by Tseng et al. [7] found that a square pier have a greater effect in producingthe scour if compared to a circular pier.

There is also primary concerns in mixing effects for a bluff body burner about thewake of a bluff body. Martins and Ghoniem [8]; Ma and Harn [9] stated that, thegeometry of the bluff body is one of the importance parameters in determining the

3

mixing condition of the burner. This is because, the formation of recirculation zonebehind the bluff body can provide a good mechanism for the fuel and air of a burnerto mix efficiently.

Flow around bluff bodies can also radiate acoustic sound. The noise radiatedfrom bluff bodies is always an unwanted element of many engineering applications.Addressing this problem currently receiving much research attentions, e.g; Talotte[10]; Williams [11]; Juve [12]. This trend is in response to noise complaints as well asthe negative impacts noise from the bluff bodies such as; degrading human healthand interfering with the acoustic wave produced and used by some animals to nav-igate or communicate [13].

The collapse of the Tacoma Narrows suspension bridge in 1940 is one of the mostremembered engineering disaster due to flow interactions. Even though there weresome disagrement among engineers on the cause of the collapse, they were agreedthat the vibration of the bridge was started initially by the vortex shedding [14, 15].Figure 2 illustrates the vortex generation around the deck of Tacoma bridge.

Flow induced vibration also getting attention in designing deep sea water risers.Currently, helical strakes has been used to minimise vibration of risers in deep seawater. However, helical strakes are known to increase drag and also at a given strakeheight its effectiveness as a passive vibration control is reduced with the decreamentof response parameter, i.e , mass-damping ratio (m) [16]. There also other meansof vortex suprression used for deep sea risers, such as perforated shroud, axial slats,streamlined fairing, splitter, ribbon, guided vane and spoiler plates. Except for split-ter and streamlined fairing, these vortex supression mechanisms increase the drag ofthe risers significantly that consequently compromise the safety of the platform [17].

The understanding of flow-induced vibration is also becoming the interest of ar-chitects and structural engineers who designing super tall buildings. Figures 3(a)and 3(b) show the results of Tingting et al. [18], who experimentally investigated thedynamic response of a scaled super tall building. They found that the self excitationof dynamics response of the building is due primarily to the vortex generation. An-other study by Cheng [19] found that the dynamic response experienced by the tallbuilding due to the crosswind can be catogerised into three regions according to itsmass-damping coefficient.

The undertanding of the flow and dynamic response behaviour of flow-inducedvibration is important for designing energy harvesting system using a pizoelectricenergy converting mechanism [21, 20]. Figures 4(a) and 4(b) show how the wake

4

Figure 1: Fairing installation on drilling riser.

Figure 2: Sketches of vortex pattern over rotating deck section of Tacoma bridge.

5

(a) Model of a tall buildings in the wind tunnel test section.

(b) Self excitation of dynamic reponse of a tall building due to wind atreduced velocity of, Ur = 33.3 and mass-damping of , = 0.7%

Figure 3: Example of the investigation of a bluff body, i.e. building.

6

(a) Diagram illustrating the idea behind the operation of the harvester [20]

(b) Modeled and experimental frequency response of bender and fin. [20].

Figure 4: Example of the bluff body application, i.e. wake induced vibration forgenerating electricity.

7

from a bluff body can be exploited to create electricity. This concept may not directlyrelated to the current study, but it can provides details explanation they require tounderstand the complex mechanism in generating the high vibration system frombluff body wake.

This research examines how the flow structure around two rigid bodies (one ofthem bluff) in close proximity can influence the dynamic response of the elastic struc-ture system. The case study chosen for this research is a two dimensional squarecylinder as a primary body and a flat plate located downstream as a secondary body.The length and shape of the secondary body can be changed in order to investigatethe geometry and the location effects on dynamic response of the bluff body. There-fore, the research scope includes the flow and dynamic response alteration causedby the location and geometry modificatio of the secondary rigid body. At the end ofthis research, it is hoped that a robust explanation can be presented that justifies thepossible vibration reduction by imposing a secondary rigid body as a means of flowand vibration control mechanism.

A rigid square cylinder has been chosen as the case of study because it is one ofthe most basic forms of a bluff body. Additionally, few flow and vibration investiga-tions have been published for the square cylinder when compared with the circularcylinder (ref.), particularly at high Reynolds numbers. Furthermore, unlike circularcylinders where the separation point varies according to the Reynolds number, theseparation point of the unsteady flow around a square cylinder is fixed at the shapeedges [22]. This could bring a distinctive feature to the flow and vibration interactioneven though it is expected that the near wake flow structure for circular and squarecylinders are topologically similar to one another [23, 24].

Investigation of the flow structure on the square cylinder have been an intensefocus for a long time. It can be said the characteristics of the flow is well understoodfor all Reynolds number regimes. But, less is known about what happens when ananother rigid body is placed near to the square cylinder particularly on the aspectof sound alteration. Relevant investigation on this problem is described in the nextchapter and it is shown that there are many unresolved aspects that require furtherinvestigations.

1.2 Aims and Significance of The Research

The main aims of the proposed study are to investigate the flow interaction and thedynamic response of flow over a square cylinder with a downstream flat plate that

8

are freely to move in the cross-stream direction under the support of one degree offreedom elastic system.

The specific objectives of the proposed study are;

1. to obtain robust explanation of the fluid dynamic mechanisms that control thewake properties of a bluff body when a flat plates of various length are placeddownstream.

Previous related work has explained the flow interaction between a squarecylinder with a downstream flat plate. However, the study is limited to two-dimensional flow and the bodies were fixed in position. Another related studyhas considered three-dimensional flow and dynamic response from the wake-body interaction. However, the study was limited to identical bluff bodies thatwere arranged in tandem.

2. to assess the possibility of using a flat plate as a passive vibration control forthe application of slender cylindrical structures.

Previous works have proved that a flat plate located downstream of a bluffbody can supress the vortex shedding of the upstream body. However moststudies were limited to two-dimensional flow and the bodies were assumedstatic. No study has been done to propose a mechanism to control passivelythe vibration of a bluff body using a flat plate.

These are related to each other but focused on different aspects: prediction,understanding and prevention

1.3 Problem Geometry

The problem geometry under investigation is a finite square cylinder immersed inthe freestream velocity of U and of Reynolds number based on the side length ofthe cylinder D of Re=UD/= 22104. A flat plate with the same spanwise lengthwith the square cylinder is placed in the wake of the square cylinder.

The length of the plate is initially set the same as the side length of the cylin-der (L = D) and the gap distance between the plate and cylinder is varied between0 G 6D. After the location for the downstream flat plate for the best reduction

9

U cylinder

plate

vertical spring

damper

axial spring

Figure 5: Problem geometry and annotations for crosswind over a train bridge. Theratio of h/ho is varied from 0,1/2 and 1.

on vibration of the squre cylinder has been identified, the length of the plate willbe changed so that further vibration reduction can be obtained. Finally, the trailingedge of the plate will be modified to waviness to see if any further improvementcan be made in an final effort in this study to reduce the vibration of the upstreamcylinder.

The rigid bodies are supported with a one degree of freedom (1 dof) mass-spring-damping system (or preferably called elastic system). This allow for thesquare cylinder and the flat plate to move freely in the cross-stream direction. Theparameters for the elastis system are fixed, with mass ratio, m = mbodym f luids , of 2.4 andmass-damping parameter, m= m csystemccritical , of 0.013.

1.4 Execution Plan

Table ?? lists the task to be completed in order to achieve the objectives of this re-search. Thirty six months (3years) have been allocated to successfully complete allof the tasks.

1. Literature reviews: flow over a bluff body, flow over bluff body with wake in-terference, vortex induced vibration for single and two bodies in a tandem ar-rangement, the effect of trailing edge waviness on flow structure of bluff body.

2. Grid independence study, choice of turbulence models and discretisation schemes.A conference paper is ecpeted from this study.

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3. Comparison study of single circular cylinder that vibrate in the freestream dueto vortex induced vibration between current numerical simualtion and previ-ous publised data. A conference paper is ecpeted from this study.

4. The effect of gap between the cylinder and plate on flow structure and vibra-tion of the upstream body. Identify the location of the downstream for thelowest vibration. A journal paper is expected from this study.

5. The effect of chord length of the plate on the flow strcuture and vibration of theupstream body. Identify the suitable chord length of the plate for the lowestvibration. A journal paper is expected from this study.

6. The effect of waviness design of the trailing edge of the plate in vibration of theupstream body. A journal paper is expected from this study.

Figure ??: Gantt chartFigure ??: Flow chart

2 Literature Review and Gap of Research

The current study is part of a general investigation of flow over bluff bodies and itsassociation with vibration. This chapter reviews previous investigations that bringto the gaps of this study determine to address.

2.1 Flow Interaction with Bluff Bodies

Flow over bluff bodies are proned to flow separations. These separations take a sig-nificant portion of the body surfaces, leaving the upstream surface of the body witha high pressure region, where it is due to a stagnation point, and the downstreamsurface with a low pressure region. This briefly explain why the drag acting on bluffbodies is higher than the streamline bodies.

The cause for flow separation is the same between the bluff and streamline bod-ies. However, due to the bluntness surface of the bluff body compared to the stream-line body, high pressure gradient is generated by the geometry of the bluff body. Theboundary layers that are started to grow from the stagnation point slowly not ableto stand the high adverse pressure gradient downstream. Consequently, they flow

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Tabl

e1:

Gan

ttch

art

TASK

Year

2012

2013

2014

2015

Mon

th9

1011

121

23

45

67

89

1011

121

23

45

67

89

1011

121

23

45

67

8Li

tera

ture

Rev

iew

Gri

dR

efine

men

tStu

dy

Turb

ulen

ceM

odel

sBo

unda

ryC

ondi

tion

sG

rid

Con

verg

ence

Inde

xV

alid

atio

nSt

udy

Wri

ting

AC

onfe

renc

ePa

per

Vort

ex-I

nduc

edV

ibra

tion

(ViV

)of

An

Isol

ated

Squa

reC

ylin

dera

tLow

-M

ass

Dam

ping

.

Num

eric

alSi

mul

atio

nsV

alid

atio

n

Prop

osal

Def

ense

ViV

ofA

Squa

reC

ylin

der

wit

hA

Fixe

dD

owns

trea

mFl

atPl

ate

(L=D

)

Num

eric

alSi

mul

atio

nsI

niti

albr

anch

Upp

erbr

anch

Low

erbr

anch

Expe

rim

enta

lInv

esti

gati

ons

ViV

ofA

Squa

reC

ylin

der

wit

hA

Fixe

dD

owns

trea

mFl

atPl

ate

ofV

ar-

ious

Leng

th(0L/

D

7)

Num

eric

alSi

mul

atio

nsP

hysi

csof

fluid

sF

luct

uati

ngFo

rces

Vib

rati

onW

riti

ngA

Jour

nalP

aper

ViV

ofA

Squa

reC

ylin

der

wit

hA

Fixe

dD

owns

trea

mFl

atPl

ate

ofV

ar-

ious

Gap

Dis

tanc

e(0G/D

5)

Num

eric

alSi

mul

atio

nsP

hysi

csof

fluid

sF

luct

uati

ngFo

rces

Vib

rati

onFi

ndTh

eO

ptim

alC

onfig

urat

ion

(Lop

timal

andGop

timal

)for

The

Low

estV

ibra

tion

Leve

lW

riti

ngA

Jour

nalP

aper

ViV

ofA

Squa

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ylin

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trea

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atO

p-ti

mal

Con

figur

atio

nan

dw

ith

wav

i-ne

sstr

ailin

ged

ge

Num

eric

alSi

mul

atio

nsP

hysi

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fluid

sF

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ngFo

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nalP

aper

Thes

isW

riti

ng

12

get separated from the surface body. For the bluff bodies having sharp edges like asquare cylinder, the flow is separated due to the sudden change in the geometry.

The level of the boundary layer to sustanin the adverse pressure gradient can berepresent as the balance between inertial and viscous forces, or know as Reynoldsnumber.

Re=UD

(1)

The boundary layers are able to remain attached if the Reynolds number is low. Forhigh Reynolds number, the flow is governed by high inertial force that responsiblefor generating vorticity in the separation flow.

The flow detaches from the surfaces of the bluff bodies in the form of free shearlayers. The periodic shedding of the shear layers are responsible for many flow-induced engineering problems such high pressure drag, fluctuations of lift and drag,aerodynamic noise and structural vibration. Figure 1 shows the illustration of two-dimensional structure of flow over a bluff body.

Figure 1: The flow over a bluff body exhibits various important physical phe-nomena such as flow separations, vortex shedding and turbulence in the wake.

For a given fixed bluff body geometry, the vortex shedding frequency is charac-terised by the instability of the shear layers. Figure 2 shows the variation of Strouhalnumber (St = f DU ) with Reynolds numbers (Re =

UD ). All the bluff body shapes

have the same trends, but they are different in magnitude or the level of sensitiv-ity in the flow instability. For real industrial applications (high Reynolds number),spanwise instability become important. There are six different flow regimes with theincreasing Reynolds number within that exhibit spanwise instability [WilliamsonC.H.K,1997].

2.2 Flow over Bluff Bodies with Wake Interferences

When the wake of bluff bodies is disturbed with interference elements such as a flatplate or bluff body (not necessaraly identical), a complex flow structure is observed.This flow structure is strongly influenced by the location of the interference elementfrom the primary body. Zdravkovich [1988] classified the flow structure accordingto interference regions, see Figure 3.

The understanding of the complex flow structure generated from the wake in-terference is important for the fundamental aspect of physics flow and also for thebenefit of real engineering applications. Recently, a study by Ali 2013 et al found that

13

Figure 6: Variation of lift and drag coefficients with Reynolds number for a circularcylinder. CD represent mean drag; CL and CD represent the magnitude of fluctuatinglift and drag. A small p and f indices represent terms due to pressure and frictiondrag. Dashed regions represent the scatter of experimental data. Figure is takenfrom ref.[25], where was the data was adapted from Zdravkovich (1997) [26] .

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Figure 7: Strouhal number versus Reynolds number: 5; Bearman [27]; Norberg [28,29]:; laminar shedding;; wake transition;4; turbulent shedding;, Barkleyand Henderson [30], 2-D; ; Kwon and Choi [31], 2-D; ; Posdziech and Grundmann(2000), 2-D; , formulas in Appendix A of ref. [32]. Shaded region corresponds to thebandwidth (-3 dB) of the shedding peak frequency. Data are taken form ref.[32].

Figure 8: Distributed forcing (a) schematic of the forcing, (b) Re = 100( = 5d), and(c) Re = 3900( = pid). Shown in panels b and c are the instantaneous vortical struc-tures without (left column) and with (right column) control. Figure taken from KimChoi [33]

15

Figure 9: Sketch of wake interference regime by Zdravkovich [34].

an interference element can be used to cancell the noise generated aerodynamicallyfrom the upstream bluff body. They used a thin rigid flat plate as the interferenceelement and a square cylinder as the bluff body. Another study by Ali 2011 et al alsofound that a long flat plate located downstream can supress the vortex shedding ofthe upstream bluff body.

2.3 Vortex-induced Vibration

2.3.1 Flow-induced vibration of an isolated bluff body

For a long slender cylindrical structure, such as risers tube in the offshore oil indus-try, the periodic oscillation of the fluctating forces instigates the elastically cylinder tovibrate. When the elastically cylinder is support with a mass-spring-damper system,the dynamic response of the body change according to the reduced velocity,U= UfnDand mass-damping, m, where m = mcylmdisplaced and is damping ratio. Figure 4 showthe response of a circular cylinder with reduced velocity.

16

Figure 10: Response of amplitude and frequncy for a single circular cylinder [ref.]

2.3.2 Flow-induced vibration of bluff bodies with a wake interference

The dynamic response of downstream body is more severe then the upstream body.This is due to the wake that amplify the forces generate don the downstream body.They are many study on the two circular cylinder in tandem arrangement but thereis avery limited no study on the case of a bluff body with a flixible downstream flatplate.

A series of studies by Assi et al. [35, 25, 36] found various mechanisms of flow-induced vibration when a parallel plates are placed in various arrangement for cir-cular cylinders arranged in tandem. Figure 13 shows the type of configurations theyused in their investigations. The upstream cylinder was fixed while the downstreamcylinder was free to move in the cross-stream direction.

For configuration I, the dynamic response of the downstream cylinder was re-duced when U/ f0D 10. At U/ f0D= 30, the dynamic responses were one and 1.5diameters for configuration I and plain configuration, respectively. This reductionwas due to the plate that weakeaning the wake by delaying the vortex formation.However, the dynamic response increased with the increasing U/ f0D 10, simi-lar to the case of plain cylinders in tandem. Configurations II and III gave more

17

Figure 11: Configurations tested as reference and to investigate strake effectiveness.Cylinders marked with a cross are not free to oscillate. (a) Static single; (b) VIV plain;(c) VIV with strakes; (d) static tandem; (e) WIV plain; (f) WIV with strakes [36]

promosing in reducing the downstream vibration. The vibration of the downstreamcylinder was only 10% of diameter when U/ f0D 10.

2.4 Wavy trailing Edge

Surface modifications such as a spiralling arrangement of surface control bumps onthe surface of long cylinders can be used to control of the flow-induced vibration.Bumps work by instigate three-dimensional separation that then eliminates vortexshedding. However, it allow effective for high mass-damping ration, where fow lowmass-damping ratio the flow-induced vibration is similat to the plain cylinder [37].

Helical strakes [16] only effective for high mass-damping ratios, and it increasesthe drag of the system.

3 Numerical Simulation

The proposed study will involve detailed analyses of flow structure around the prob-lem geometries under investigations. Numerical simulations (sec. 3.1) has been iden-tified as a tool to obtain the necessary aerodynamics data. Wind tunnel testing may

18

Figure 12: WIV response (top) and mean drag coefficient (bottom) for cylindersfitted with strakes. Measurements are for the downstream cylinder of the tandempair. Configurations as shown in Fig. 11 . [36]

19

Figure 13: Configurations of downstream and upstream cylinders fitted with free-to-rotate (f-t-r) parallel plates. Centre-to-centre separation is x0/D = 4.0. Cylindersmarked with a cross are not free to oscillate. [35, 36]

20

Figure 14: WIV response in 1-dof (top) and mean drag coefficient (bottom) for cylin-ders fitted with parallel plates. Measurements are for the downstream cylinder ofthe tandem pair. Configurations as shown in Figs. 11 and 13 . [35, 36]

21

Figure 15: Instantaneous vorticity contours (a) and velocity vectors (b) for a f-t-rsplitter plate under WIV atU/Df0 = 6.0. PIV measurements at Re= 4500; x0/D= 4.0.(c) Sketch of possible competition between components of lift generated by wakeinteraction with a free-to-rotate splitter plate under WIV. [36]

22

Figure 16: 3D forcing by passive means: (a) helical strake, (b) segmented trailingedge, (c) wavy trailing edge, (d ) wavy stagnation face, (e) sinusoidal axis, ( f ) hemi-spherical bump, and ( g, h) small-size tab [38]

be carried out to validate the numerical simualtions (sec. 3.3), but it will not compro-mise the research findings due to the fact that a numerical validation technique ascarried out by ref. [39] can also be implemented.

3.1 Numerical simulation

3.1.1 Flow Simulation

The flow is treated as a continuous medium that obeys the conservation of massand the conservation of linear momentum. For an incompressible transient flow, thetime-averaged governing equations are;

t

+xi

(Ui) = 0 (2)

Uit

+x j

(UiU j) =Pxi +x j

(Uix j

+ t ji) (3)

Eqs. 2 and 3 are continuity and momentum equations, respectively. Here, indexesi and j are spatial components in two-dimensional form (x and y), and and P areviscosity and local pressure, respectively at an instantaneous time of t. The Reynolds

23

stress, t ji can be represented as;

t ji =uiuj (4)

Employing Boussinesq-viscosity hypothesis, the Reynolds stress can be approxi-mated to the fluids mean rates of deformation;

uiuj = t(Uix j

+U jxi

)+

23

(K+t

Uixi

)i j (5)

The additional terms, t and K are modelled as presented in sec. 3.1.2.

3.1.2 Turbulence Model

The turbulence flow is modeled statistically based on the Reynolds Averaged NavierStokes (RANS). RANS takes parts of the energy spectrum of the turbulence flow byaveraging the governing equations. The additional terms that due to the fluctutingproperties, are approximates using the standard K- turbulent model.

t

(K)+xi

(KUi) =x j

[(+

tK

)Kx j

]+GK YM (6)

t

()+xi

(Ui) =x j

[(+

t

)x j

]+C1

K(GK)C2

2

K(7)

where,

GK = uiujU jxi

(8)

YM = 2M2t (9)

Mt =

KC2

(10)

t = CK2

(11)

where, C is speed of sound, the model constants have the following values; C1 =1.44,C2 = 1.92,C = 0.09,K = 1.0 and = 1.3.

24

3.1.3 Motion analysis

Displacement variables are monitored in the cross-stream direction (plunge, y) andalso in the angular position (pitching, ). The equation of motion for the plungemotion can be written as;

my+ cvy+ ky= Fy (12)

where Fy is the aerodyamic force in the cross-stream direction, i.e., lift. For the pitchmotion, the following equation is used;

Im+ ca+ k=M (13)

where Im is the mass moment of inertia and M is the moment about its center ofgravity. The aerodyamics contribution to the motion, i.e., lift and moment, are con-tinuosly updated from the Navier Stokes equations and written in the followingform;

Fy =12LSU2(CDSin+CLCos) (14)

M =12L2SU2(CM) (15)

where L and S are the plate length and the plate span, respectively.

3.2 Arbitrary Lagrangian-Eulerian formulation

The movement of the body is linked to the surrounding fluids by assuming thatthe velocity of the body surface is equal to the velocity of the adjacent fluids. TheNavier Stokes equation, eqt.(3, can be re-written in a non-dimensional form follow-ing Carmo [Flow-induced vibration of a circular cylinder subjected to wake interfer-ence at low Reynolds number] as;

ut

=(um)up+ 1Re2u (16)

here, m is the velocity of the body surface.

25

3.2.1 Grid Independent

The grid solution for the numerical simualtion must be grid independent. At leastthree types of grid resolution will be evaluated for its sensitivity of the solution thethe grid size. Grid convergence index will show quantitively on the level of gridindependent. A similar grid refinement study as ref. [39] will be employed in thisproposed study.

3.3 Wind Tunnel Testings

Wind tunnel testing provides necessary information of the flow structure aroundthe scaled model of the problem geometry under investigations. Smoke visualisa-tion is one of the simplest way, but hot wire velocity probe and PIV (particle imagevelocimetry) can give more information about the flow.

Some issues that must be considered during the wind testings. The main diffcultyin using wind tunnel experiments is that the scale of the mock-up has to be suffcientin order to ensure that the geometry and flow characteristics are comparable to realconditions (Reynolds number, thickness and turbulence intensity of boundary layer).

3.3.1 Measurement Equipments

The data that is expected to be obtained can be catogerised into two;

1. Lift Fluctuation. The flow over a square cylinder becomes naturally unsta-ble and then sheds a periodic vortex downstream. This consequently createa sigificant pressure difference particularly in the cross-stream direction. Tomeasure it effects on the square cylinder and the plate, a component balancecan be used. The component balance must be connected to the both of the bod-ies (square cylinder and plate). It will be a challange to measure the lift fromthe square cylinder and from the flat plate simultaneously. Another issue is tomeasure the lift generated by the plate. The flat plate may be very thin andsmall. It might be difficult to connect the component balance to it, and theremay be also an issue on vibration (or plate flattering).

2. Instantaneous of Velocity Mapping. The info on the velocity profile particu-larly in the vacinity of the bodies is important to understand the behaviour ofthe flow structure for various experimental works being investigated. ParticleImage Velocimetry (PIV) is an advanced tool that can accurately capture the

26

instanteneous velocity vector near the square cylinder and also near the down-stream flat plate.

3.3.2 Samples of Data for Comparisons

Table 2: Previous similar studies: Flow over a square cylinder.Previous work Re % L/D Measurement Methods Turbulence Level % StNakagawa, et al. [40] 3000 20 35 LDV 6 0.13Lyn, et al. [41] 21400 7 9.8 LDV 4 0.13Durou, et al. [42] 14000 13 6 LDV 6 0.13Saha, et al. [43] 17625 6.25 16 HWA 1 0.142Shadaram, et al. [44] 8600 5 20 HWA 2 0.13Wang [45] 21400 5 pi Numerical (LES) - 0.13

4 Numerical Simulation of Flow Over A Finite Square

Cylinder

5 Conclusion

A study has been proposed to investigate the influence of bluff body wake on thegalloping level of a downstream flat plate. The galloping phenomenon creates amore complex flow structure when compared with a rigid downstream flat plate.This flow structure is calculated numerically and with the help of entensive flowvisualisations, the understanding of the physics flow can be obtained. Then the ef-fectiveness of the galloping plate on noise control can be justified.

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IntroductionResearch BackgroundAims and Significance of The ResearchProblem GeometryExecution Plan

Literature Review and Gap of ResearchFlow Interaction with Bluff BodiesFlow over Bluff Bodies with Wake InterferencesVortex-induced VibrationFlow-induced vibration of an isolated bluff bodyFlow-induced vibration of bluff bodies with a wake interference

Wavy trailing Edge

Numerical SimulationNumerical simulationFlow SimulationTurbulence ModelMotion analysis

Arbitrary Lagrangian-Eulerian formulationGrid Independent

Wind Tunnel TestingsMeasurement EquipmentsSamples of Data for Comparisons

Numerical Simulation of Flow Over A Finite Square CylinderConclusion