2-D URANS vs.experiments of Flow Induced Motion Softw o Circular Cylinders in Tandem With Passive Turbulence Control for 30,000oReo105,000

7232019 2-D URANS vsexperiments of Flow Induced Motion Softw o Circular Cylinders in Tandem With Passive Turbulence hellip

httpslidepdfcomreaderfull2-d-urans-vsexperiments-of-flow-induced-motion-softw-o-circular-cylinders 112

2-D URANS vs experiments of 1047298ow induced motions of two circularcylinders in tandem with passive turbulence controlfor 30000oReo105000

Lin Ding ab Michael M Bernitsas bcdn Eun Soo Kim bc

a College of Power Engineering Chongqing University Chongqing 400044 Chinab Marine Renewable Energy Laboratory Dept of Naval Architecture amp Marine Engineering University of Michigan 2600 Draper Road Ann Arbor

MI 48109-2145 United Statesc Department of Mechanical Engineering University of Michigan MI United Statesd CTO of Vortex Hydro Energy Ann Arbor MI United States

a r t i c l e i n f o

Article history

Received 10 January 2013

Accepted 2 June 2013Available online 15 August 2013

Keywords

Two cylinders

URANS

Flow induced motions

Vortex induced vibrations

Galloping

Passive turbulence control

VIVACE Converter

Surface roughness

Hydrokinetic energy

a b s t r a c t

The 1047298ow induced motions (FIM) of two rigid circular cylinders on end linear-springs in tandem are

studied using two-dimensional Unsteady Reynolds-Averaged Navier-Stokes (2-D URANS) simulations

veri1047297ed by experimental data Passive turbulence control (PTC) is being used in the Marine Renewable

Energy Laboratory (MRELab) of the University of Michigan to enhance FIM of cylinders in the VIVACE

(Vortex Induced Vibration for Aquatic Clean Energy) Converter to increase its ef 1047297ciency and power

density in harnessing marine hydrokinetic energy Simulation is performed using a solver based on the

open source CFD tool OpenFOAM which solves continuum mechanics problems with a 1047297nite-volume

discretization method The simulated Reynolds number range for which experiments were conducted in

the MRELab is 30000oReo105000 which falls in the TrSL3 regime (Transition in Shear Layer) where

the shear layers are fully saturated and consequently lift is high The amplitude and frequency results are

in excellent agreement with experimental data showing the initial and upper branches in VIV transition

from VIV to galloping and galloping Vortex structures are studied using high-resolution imaging from

the CFD results showing typical 2S structure in the initial branch and both 2P +2S and 2P in the upperbranch of VIV In the galloping branch amplitudes of 35 diameters are reached before the channel stops

are hit

amp 2013 Elsevier Ltd All rights reserved

1 Introduction

Elastically mounted rigid circular cylinders exposed to 1047298uid 1047298ow

perpendicular to their axis experience 1047298ow induced motions (FIM)

excited by the alternating vortices shed in the cylinder wake and

forming the von Kaacutermaacuten street Vortex shedding occurs over the

entire range of Reynolds numbers (Re) with the exception of very

low Reo40 the Tritton (1977) transitions region (200oReo400)and the laminar to turbulent 1047298ow transition The cylinder would be

excited to signi1047297cant amplitudes when the frequency of the vortex

shedding mode locks onto the vibration frequency thus synchroniz-

ing the natural frequency and the excitation frequency For a smooth

or rough cylinder the oscillatory lift forces on the body lead to

vortex-induced vibration (VIV) When the cylinder is not rotationally

symmetric for example by using turbulence stimulation strips

galloping may be induced as shown experimentally (Chang et al

2011 Kim et al 2011 Lee and Bernitsas 2011) VIV and galloping

are the most commonly observed FIM phenomena A comprehen-

sive review of research on VIV can be found in the article by

Williamson and Govardhan (2004)

FIM is typically treated as a destructive phenomenon because

of the fatigue damage it may cause The effective control of vortexshedding is important in engineering applications Unlike previous

efforts to alter vortex shedding and suppress the occurrence of

FIM Bernitsas et al (2008) and Lee and Bernitsas (2011) have been

successful in utilizing this potentially disastrous phenomenon

to generate power with the VIVACE (Vortex-Induced Vibration

for Aquatic Clean Energy) Converter The VIVACE Converter is a

hydrokinetic power generating device invented by Bernitsas and

Raghavan in 2005 (Bernitsas and Raghavan 2009) and further

developed by the Marine Renewable Energy Laboratory (MRELab)

at the University of Michigan (Bernitsas et al 2009 Lee et al

2010 2011 Lee and Bernitsas 2011 Raghavan and Bernitsas

2011) The simplest form of VIVACE is a single cylinder suspended

Contents lists available at ScienceDirect

journal homepage wwwelseviercomlocateoceaneng

Ocean Engineering

0029-8018$ - see front matter amp 2013 Elsevier Ltd All rights reserved

httpdxdoiorg101016joceaneng201306005

n Corresponding author at Department of Naval Architecture amp Marine Engineer-

ing University of Michigan Ann Arbor MI 48109-2145 United State Tel +1734

764 9317 fax +1 734 936 8820

E-mail addresses lindingcqueducn (L Ding)

michaelbumichedu (MM Bernitsas)

Ocean Engineering 72 (2013) 429 ndash 440



by springs with a power-take-off (PTO) system It can harness

hydrokinetic energy from ocean and river currents as slow as

04 ms frac1408 knots (Chang et al 2011) The goal of the VIVACE

team is to enhance the oscillation amplitude and maximize the

hydrokinetic energy converted to mechanical energy in the oscil-

lating cylinder One way to improve the performance of VIVACE is

to use multiple cylinders as would be the case in multi-blade

propellers or windmills Two rigid circular cylinders in tandem

mounted on end linear-springs with passive turbulence control(PTC) to enhance FIM are studied in this paper

Roughness on the cylinder can effectively change the 1047298ow

properties Extensive literature is available on using roughness to

alter FIM of cylinders on springs There are different roughness

parameters that affect 1047298ow-induced motion such as roughness

location roughness height and roughness coverage (Chang et al

2011 Park et al 2012) PTC was introduced in the MRELab to

enhance cylinder FIM and extract more hydrokinetic energy from1047298uid 1047298ows PTC consists of selectively located surface roughness

with thickness on the order of the boundary layer thickness and

depending on its location it can induce galloping hard galloping

weak suppression or strong suppression as shown in the FIM-to-

PTC Map (Park et al 2012) With the application of PTC cylinder FIM

can be enhanced In addition back-to-back VIV and galloping are

achieved The maximum power density of a single-cylinder VIVACE

(349 Wm3) was ampli1047297ed 138 times in comparison to that of

VIVACE with a smooth surface cylinder (253 Wm3) at 1047298ow speed

U frac14145 ms (Chang et al 2011) Amplitudes as high as 27 diameters

have been achieved by using passive turbulence control (Chang

et al 2011 Kim et al 2011 Raghavan and Bernitsas 2008) The

effects of PTC were studied in detailed by Chang et al (2011) and

Park et al (2012)

To further improve the power density of VIVACE multiple

cylinder systems are investigated experimentally in the MRELab

Multiple cylinder systems are used in many applications in civil

offshore aeronautical engineering etc The interference between

cylinders strongly depends on the arrangement of cylinders and

their orientation with respect to the free stream (Zdravkovich

1997b) Two-cylinder systems have been studied the most becausethey are the simplest multi-cylinder arrangement (Assi et al 2006

King and Johns 1976 Sumner et al 2000 Zdravkovich 1985 1987)

For two cylinders in tandem the downstream cylinder is subjected

to high level of turbulence generated from the upstream cylinder in

addition to impingement of Kaacutermaacuten-size shed vortices Most of

studies performed in the past on two-cylinder arrangements were

on smooth cylinders Moreover in most studies the cylinders were

1047297xed or at very low Reynolds number (Borazjani and Sotiropoulos

2009) FIM of two-cylinders with surface roughness (PTC) for high

Re has been studied only by the MRELab to the best of the authorsrsquo

knowledge (Kim et al 2011)

In this paper two rigid PTC-cylinders in tandem mounted on end-

springs are simulated using two-dimensional Unsteady Reynolds-

Averaged Navier-Stokes (URANS) equations with the Spalart ndash Allmarasone-equation turbulence model The 1047298ow is simulated in the range of

30000oReo105000 which falls in the high-lift TrSL3 regime and

for which experiments were conducted in the MRELab TrSL stands

for Transition in Shear Layer and ldquo3rdquo indicates the third region where

the shear layer is fully saturated resulting in stronger vortices shorter

formation length and highest lift (Zdravkovich 1997a) There are

numerous studies of using URANS for simulation of 1047298ow past a

circular cylinder From the published literature URANS results of the

Strouhal number agree very well with other numerical and experi-

mental results Lift and drag coef 1047297cient CFD results at low Reynolds

numbers (Wanderley et al 2008) also agree well with experiments

Researchers mostly apply URANS at low Reynolds number Applica-

tions at higher Re show that prediction for Re412000 is still a

challenging task for URANS Prediction is even poorer near the drag

crisis (Catalano et al 2003) As explained by Wu et al (2011) the 1047297rst

manifestation of failure lies in the fact that for Re410000 the

separation point is not predicted properly Speci1047297cally CFD using

2-D URANS predicts that the separation point hardly oscillates around

901 while experimental data show that it oscillates around 811 in

laminar 1047298ow with amplitudes as much as 5 ndash 101 This is a most

important characteristic of 1047298ows past a circular cylinder It is also a

local property of the 1047298ow as opposed to integral 1047298ow properties such

as the Strouhal number and the liftdrag forces Some integralproperties are easier to predict as integration 1047297lters local errors

With proper modeling of PTC however 2-D URANS simulations

exhibit several of the salient local features of the 1047298ow resulting is

excellent agreement with experiments as proven by Wu et al

(2011) They developed a CFD code based on OpenFOAM to solve

the problem of a single cylinder with PTC They showed that the

presence of PTC results in very good agreement between experi-

ments and CFD simulations up to Refrac14135000 for which experi-

mental data were available from tests in the MRELab Without PTC

such agreement was limited to Refrac1410000 ndash 12000 (Wanderley

et al 2008 Wu et al 2011) when 2-D URANS is used

Thus the code developed by Wu et al (2011) for a single

cylinder in FIM and in this paper for two cylinders in tandem

predict very well the experimentally measured data including

vortex streets transition from VIV to galloping and shear layer

oscillation Consequently the developed tool can be used with

con1047297dence to predict 1047298ow properties that are more challenging to

measure experimentally at such high speeds and turbulence levels

In the present study the FIM of two rigid circular cylinders on end

linear-springs in tandem are studied using 2-D URANS simulations

veri1047297ed by experimental data The objective of this study is to

establish the capability of a numerical tool to simulate the VIVACE

system with two PTC-cylinders in FIM and investigate the system

parameter effects on the cylinder dynamics The physical model and

running parameters are presented in Section 2 In Section 3 the

numerical approach and grid generation are described The simulation

results of amplitude and frequency for the two PTC-cylinders are

shown in Sections 4 and 5 respectively Numerical results are

compared with experiments conducted in the Low Turbulence FreeSurface Water (LTFSW) Channel of the MRELab Vortex structures of

four typical cases are discussed in Section 6 Conclusions are presented

at the end based on the analysis of amplitude and frequency response

and vortex structures

2 Physical model

The physical model considered in this paper consists of two

oscillatory systems as depicted in Fig 1 The elements of each

oscillatory system are a rigid circular cylinder of diameter D and

length L two supporting linear springs of stiffness K and the

Fig 1 Schematic of the physical model

L Ding et al Ocean Engineering 72 (2013) 429ndash440430



system damping c due to friction Two cylinders arranged in

tandem are constrained to oscillate in the y-direction which is

perpendicular to the 1047298ow velocity direction ( x) The center-to-

center distance d between the two cylinders is set at 2D Two

straight roughness strips are attached to the surface of each

cylinder symmetrically one on each side of the cylinder (Chang

et al 2011) The angle α PTC is measured in degrees from the

forward stagnation point in the corresponding ideal 1047298ow The

coverage provided by each sand-strip is 161In the present study simulations are veri1047297ed by experimental

measurements of the 1047298ow induced motion of two circular cylin-

ders with PTC in tandem The system parameters in the 2-D

URANS simulation are the same as those used in the correspond-

ing experiments in the MRELab as listed in Tables 1 and 2 The

stiffness of the springs and the system damping are measured

using a series of free-decay tests in air where linear viscous

damping was assumed All the experiments were conducted in the

LTFSW Channel located in MRELab Details on the LTFSW Channel

are provided by Bernitsas et al (2009)

The test-section of the channel is 1 m wide and 08 m deep The

ratio of cylinder diameter D to channel depth is about 12 The ratio

of cylinder length L to channel width w is nearly 1 Analysis of four

potential blockage effects (a) side-to-side blockage (b) top-to-

bottom blockage (c) free-surface effect and (d) bottom-boundary

effect are discussed by Chang et al (2011) The last two are studied

in detail in Raghavan (2007) and Raghavan et al (2009)

Passive turbulence control (PTC) is being used in the MRELab of

the University of Michigan to enhance FIM of cylinders in the

VIVACE Converter to increase its ef 1047297ciency and power density in

harnessing marine hydrokinetic energy The strips with roughness

designation P60 have been used as PTC for the research in this

study All modeling parameters of PTC are de1047297ned in Fig 2 (Chang

et al 2011) The strips are attached running along the entire

length of the cylinder parallel to the cylinder axis Waterproof

sandpaper strip is cut into speci1047297c width which covers 161 of the

surface of the circular cylinder The strip thickness is about equal

to the thickness of the boundary layer and affects profoundly FIM

The FIM-to-PTC Map developed by Park et al (2012) shows the

effect of selective surface roughness in the form of strips on the

FIM of circular cylinders Table 3 shows the details of the rough-

ness strip P60 used in this study

3 Mathematical and numerical modeling

In this section the mathematical modeling for the 1047298uid

dynamics and the two oscillators is provided 1047297rst The integration

scheme the computational domain the grid generation and the

computational time are presented as well

31 Governing equations

The mathematical model consists of the 1047298uid dynamics equa-

tions the turbulence model for the 1047298uid and the body dynamics

equations Those are described in the following subsections

311 Fluid dynamics

In the present study two-dimensional URANS 1047298ow simulations

are performed by developing a solver built into the open source CFD

tool OpenFOAM to predict 1047298ow properties past two circular cylin-

ders with PTC The cylinders are rigidly supported by two end linear-

springs and allowed a single degree of freedom motion transversely

to the 1047298ow direction OpenFOAM is a collection of C++ library

subroutines that are developed for solving continuum mechanics

problems with the 1047297nite-volume discretization method The 1047298ow is

assumed to be two-dimensional and unsteady and the 1047298uid is

incompressible The 1047298uid 1047298ow is modeled using the Unsteady

Reynolds-Averaged Navier-Stokes (URANS) equations together with

the one-equation Spalart ndash Allmaras (S ndash A) turbulence model The

basic URANS equations are

partU ipart xi

frac14 0 eth1THORN

partU ipartt

thorn part

part x jethU iU jTHORN frac14 minus

1

ρ

part p

part xithorn part

part x jeth2νS ijminusuprimeiuprime j THORN eth2THORN

where ν is the molecular kinematic viscosity and S ij is the mean

Table 1

Nomenclature

Apeaks Mean amplitude of the peaks

C a Added mass coef 1047297cient

C d Drag coef 1047297cient

C l Lift coef 1047297cient

D Cylinder diameterK Spring constant

L Cylinder length

P Thickness of sand paper

Re Reynolds number

St Strouhal number

T Total thickness of PTC

T 1nfrac141 f nwater Natural period in water for the 1st cylinder

U Mean 1047298ow velocity

U nair frac14U ( f nairD) Reduced velocity in air

U nwater frac14U ( f nwaterD) Reduced velocity in water

c structure Structural damping

c harn Added damping to harness energy

c frac14c strucure+c harn Total damping of system

D Center-to-center distance of cylinders

f nwaterfrac14 ffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffi

K =ethmosc thorn ma THORNp

=2π System natural frequency in water

f nairfrac14 ffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiK =mosc p =2π System natural frequency in air

f osc Oscillating frequency of cylinder

K Average height of sandpaper grit

md Displaced 1047298uid mass

mafrac14C amd Added mass

mosc Oscillating system mass

mnfrac14mosc md Mass ratio

P Pressure

W Channel width

y(t ) Displacement of cylinder

y+ Nondimensional 1047297rst grid spacing

α PTC PTC placement angle

z Damping ratio of system

θ Angular coverage of strip

μt Turbulent eddy viscosity

v Kinematic molecular viscosity

~ν Intermediate working variable

ρ Density of the 1047298uid

Table 2

Physical model parameters

Item First cylinder Second cylinder

Diameter D [m] 00889 00889Length L [m] 091441 09144Oscillating system mass mosc [kg] 95121 95756Spring const K [Nm] 75811 72684Damping ratio of system ζ 00161 0017

Damping c [N sm] 27274 28434Natural freq in water f nwater 11246 10989Natural freq in air f nair 1 4209 13866Mass ratio m

16774 16886Added mass coef C a 1 1Displaced mass md [kg] 56707 56707Added mass ma [kg] 56707 56707

L Ding et al Ocean Engineering 72 (2013) 429ndash440 431



strain-rate tensor

S ij frac14 1

2

partU ipart x j

thornpartU jpart xi

eth3THORN

and U i is the mean 1047298ow velocity vector The quantity τ ij frac14 minusuprimeiuprime j is

known as the Reynolds-stress tensor In order to solve the URANS

equations for the mean-1047298ow properties of the turbulence 1047298ow the

Boussinesq eddy-viscosity approximation is employed to relate the

Reynolds-stress to the mean velocity gradients as

minus ρuprimeiuprime j frac14 2 μt S ij eth4THORN

where the μt is turbulence eddy viscosity

312 Turbulence model

The Spalart ndash Allmaras (S ndash A) turbulence model is a one-equation

model which solves a transport equation for the kinematic eddy

viscosity This model has been shown to give acceptable results for

a wide variety of situations and is known for its stability Several

modi1047297cations of the S ndash A model exist (Allmaras et al 2012 Aupoix

and Spalart 2003 Edwards and Chandra 1996) but the original

model (Spalart and Allmaras 1994) is employed in this work In

the Spalart ndash Allmaras model the turbulent eddy viscosity is com-

puted from

μt frac14 ρ~ν f ν1 eth5THORN

where

f ν1 frac14 χ 3

χ 3

thorn c 3ν1

eth6THORN

χ frac14 ~ν

νeth7THORN

~ν is an intermediate working variable of the turbulence model and

obeys the following transport equation

part~ν

partt thorn u j

part~ν

part x jfrac14 c b1

~S ~νminusc w1 f w~ν

d

2

thorn1

s

part

part x jethν thorn ~νTHORN

part ~ν

part x j

thorn c b2

part~ν

part xi

part~ν

part xi

eth8THORN

Additional de1047297nitions of functions and constants are given by

Spalart and Allmaras (1994) The trip terms f t 1 and f t 2 are turned

off and the ldquotrip-lessrdquo initial condition (Shur et al 1996 Travin

et al 2000) for ~ν which was successfully used in earlier work for a

single circular cylinder (Wu et al 2011) is used in this study

313 Oscillator dynamics

The dynamics of the two oscillators is modeled by the classical

linear oscillator model

mosc euro y thorn c _ y thorn K y frac14 f etht THORN eth9THORN

where mosc is the total oscillating mass of cylinder and attach-

ments including 13 of the spring mass c is the linear viscous

damping and K is the linear spring constant

It should be noted however that there is signi1047297cant difference

between the mathematical modeling of damping in Eq (9) and the

real physical damping in the oscillators used in the experiments

This difference is more pronounced in low oscillator speeds Using

extensive system identi1047297cation the damping model in the physical

oscillators was found by Lee et al (2011) to be

f frac14 uSTEP ethj_ ynjminusυthresTHORNsdotΨ eth_ ynTHORN thorn uSTEP ethυthresminusj_ ynjTHORN sum4

kminus1

ak f nminusk eth10THORN

where the velocity threshold is υthresfrac140001 uSTEP is the unit step-

function Ψ eth_ ynTHORN is a symbolic representation of the nonlinear static

dependence of the friction force upon the current velocity and ak

is a coef 1047297cient determined experimentally as explained by Lee

et al (2011) This damping model is capable of predicting well the

VIV response even in low oscillator velocity for the virtual damper

spring VIVACE system in the experiments (Lee and Bernitsas

2011) Lee et al (2010) also showed that at low oscillation speedsdiscrepancies exist between experiments conducted with real

springsdampers and experiments conducted with a virtual sys-

tem using only linear viscous damping Low oscillator speeds exist

at the beginning of the initial branch in VIV and near the end of

VIV in the desynchronization range This is observed also in the

results in this paper since the experiments were conducted with

springsdampers while the CFD oscillator modeluses the classical

linear viscous damping model in Eq (9)

32 Integration scheme

A second-order Gauss integration scheme with a linear inter-

polation for the face-centered value of the unknown is used for the

divergence gradient and Laplacian terms in the governing equa-tions The second-order backward Euler method is adopted for

time integration Thus the numerical discretization scheme gives

second order accuracy in space and time A pressure implicit with

splitting of operators (PISO) algorithm is used for solving momen-

tum and continuity equations together in a segregated way The

equations of motion for the two cylinders are solved using a

second-order mixed implicit and explicit time integration scheme

33 Computational domain

The computational domain is 52D 9D for the two PTC-cylinders

As shown in Fig 3 the entire domain includes 1047297ve boundaries

in1047298ow out1047298ow top bottom and the two cylinder walls The distance

between the inlet boundary and the center of 1st cylinder lup is set

Fig 2 Con1047297guration of the passive turbulence control (PTC) on the cylinder (Chang et al 2011)

Table 3

PTC Parameters (P60 sand paper)


Strip placement angle α PTC [degree] 20 30

Angular coverage of strip θ [degree] 16 16

Sand paper thickness P [mm] 0587 0587

Average grit height k [mm] 026 026

Total thickness of strip T frac14 P +k [mm] 0847 0847




at 25D The downstream length of the domain ldown is also set at

25D The in1047298ow velocity is considered as uniform and constant

velocity At the out1047298ow boundary a zero gradient condition is

speci1047297ed for velocity The bottom condition is de1047297ned as a wall boun-

dary to match the experimental conditions In the present numerical

study the free surface is simpli1047297ed by modeling it as a wall

A moving wall boundary condition is applied for the cylinders when

the cylinders are in FIM For the roughness strips due to the

speci1047297cally modi1047297ed surface geometry a wall function type bound-

ary condition is used for vt and ~ν in order to account for the effect of

surface roughness Thus the separation point can be predicted accur-

ately during the calculation In addition similar to the ldquotrip-lessrdquo

initial condition for the one-cylinder simulation (Wu et al 2011) the1047298uid domain is divided into two regions (a) from the upstream inlet

to the center of the 1st cylinder a zero value is applied for the eddy

viscosity and (b) a nonzero value is used for the downstream-half of

the 1st cylinder through the 2nd cylinder to the outlet of the 1047298ow

domain The nonzero value is set equal to the molecular eddy

viscosity for all the simulations in the present study The water

properties for testing and simulations are also shown in Fig 3

The body and channel boundary conditions in the numerical

model match the physical model conditions as described in

Section 2 with the exception of the free surface which is modeled

by a wall

34 Grid generation

Two-dimensional structured computational grids were gener-

ated for all cases using the Gambit grid generating software The

grid domain size is 52D 9D The distance between the down-

stream boundary edge and the center of the 2nd cylinder is 25

times the cylinder diameter This is to ensure that the results of the

numerical model are accurate and that the conditions at the 1047298ow

outlet are close to the assumed conditions The distance from the

upstream boundary to the center of the 1st cylinder is also set at

25D The computational domain in the vicinity of each cylinder is a

2D 2D square where the grid density for the near-wall region is

enhanced to solve for high resolution in 1047298ow properties For the

cylinder with PTC the standard rough wall function is used to

account for the effect of surface roughness Due to the nature of the wall-function for the roughness model used in this study the

near-wall grid-spacing was selected to produce a y+ between 30

and 70 depending on the Reynolds number

In order to determine the overall grid resolution to achieve a

convergent and accurate solution in reasonable computational-

time three different grid densities were considered In earlier

work a similar grid sensitivity study was conducted and the

medium grid was successfully used to simulate a single cylinder

with PTC in FIM (Wu et al 2011) In this paper the grid sensitivity

study was conducted using three different grid densities for two

stationary PTC-cylinders The grid parameters and selected results

are listed in Table 4 where C d is the time-average value of the drag

coef 1047297cient C l is the average value of the absolute values of the lift

coef 1047297cient peaks and St is the Strouhal number

As shown in Table 4 the three grids produce similar results

Thus in the present work the medium grid resolution for the two

PTC-cylinders was selected as well A close-up of the medium grid

is shown in Fig 4

In the present work the 1047298ow is simulated in the range

30000oReo105000 which falls in the high-lift TrSL3 regime

and for which experiments were conducted in the MRELab where

TrSL indicates Transition in Shear Layer (Zdravkovich 1997a) In

these experiments galloping was observed and the maximumamplitude reached was 28D where the safety stops were placed

(Kim et al 2011) In those cases in the CFD simulations large

mesh deformations occur with the cylinders undergoing galloping

In order to minimize the mesh deformation a dynamic mesh

technique of topological change was used in the present study

Comparing Fig 5 with Fig 4 when the cylinders are in FIM the

2D 2D square which is part of the grid is moving up and down

with the cylinder The cell layers which are located at the top or

bottom of each square are removed when the mesh is compressed

and added when the mesh is expanded Thus there is little

deformation in the mesh when the cylinders undergo large FIM

Fig 3 Computational domain

Table 4

Grid resolution study (Refrac1430000)

Grid (central square

circumferential radial)

C d C l St

1st 2nd 1st 2nd 1st 2nd

Coarse (180 40) 1029 minus0 0 60 0 2 87 0 537 015 2 015 2

Medium (240 70) 1039 minus0 0 65 0 2 99 0 561 015 2 015 2

Fine (360 100) 1038 minus0 0 67 0 2 98 0 55 9 015 0 015 0

Fig 4 Close-up of the medium resolution grid for 2 cylinders with PTC

Fig 5 Close-up of the grid for two PTC-cylinders in FIM




35 Computational time

Table 5 provides information on the computational time used

in the CFD simulations as one-processor equivalent with reference

to simulated real time The processor used was an AMD Opteron

64-bit cluster The operating system was Red Hat Linux The

memory used was 3 GB

4 Amplitude ratio results

In earlier work it was shown that FIM can be enhanced to

achieve back-to-back VIV and galloping by introducing PTC (Chang

et al 2011 Wu et al 2011) For a single cylinder with PTC the

amplitude exceeds three diameters and the synchronization range

remains open-ended due to facility limitations Results within the

capability of the LTFSW Channel show more than doubling of the

synchronization range compared to that of VIV of a smooth cylinder

The present study aims at modeling and simulating numeri-

cally the 1047298ow and cylinder dynamics for two rigid PTC-cylinders in

tandem supported by linear springs in a steady uniform 1047298ow in a

1047298uid domain similar to the test section of the LTFSW Channel

Cylinder oscillations are constrained to the direction perpendicular

to the 1047298ow and the cylinder axis A series of simulations are

conducted for validating the responses of the two cylinders

undergoing 1047298ow induced motion The numerical simulations use

the values of the system parameters used in the model tests ( Kimet al 2011) The Reynolds number range is 30000oReo105000

which is in the high lift TrSL3 regime the corresponding reduced

velocity ranges are 384oU nwatero1345 for the 1st cylinder and

393oU nwatero1377 for the 2nd cylinder In this section the

amplitude response of the two cylinders is discussed The simula-

tion results are compared with the experimental data derived in

the LTFSW Channel of the MRELab (Kim et al 2011) In the present

study both cylinders start from the neutral position with zero

initial velocity and displacement The amplitude Apeaks of each

cylinder is calculated by averaging the absolute values of the 60

highest positive or negative peaks

41 First (upstream) cylinder

The amplitude ratios ( ApeaksD) for the numerical study and

experimental data for the 1st cylinder are plotted in Fig 6 Within

the test range of experiments and simulations 1047297ve regions are

observed in the amplitude ratio curve

(a) Reo30000 No FIM takes place in this range experimentally

or numerically

(b) 30000oReo40000 This is the initial branch in VIV FIM

using simulations starts at Refrac1430000 (U nair frac14304 U nwater frac14

384) and the amplitude ratio vs U =U nwaterRe follows closely

the experimental data with one exception Speci1047297cally the

initial branch is initiated numerically (Refrac1430000) earlier than

in the experiments (Refrac1440000) This is attributed to the

difference between the mathematical damping model in the

numerical simulations in this paper and the actual physical

damping model in the experimental apparatus which is

modeled more accurately by Eq (10)

(c) 40000oReo80000 This is the upper branch in VIV In the

amplitude curve for 40000oReo80000 (512oU nwatero1025)

the URANS results follow closely the upper branch of the

experiments The amplitude increases steadily as the velocity

increases for 40000oReo80000 and the amplitude ratio

increases from 089 to 140 For Reynolds numbers less than

10000 typical VIV response consists of an initial branch

followed by a constant amplitude upper branch and a lower

branch (Williamson and Govardhan 2004 2008) For higher

Reynolds numbers following the initial branch is a strong

upper branch increasing in amplitude and overtaking the

lower branch nearly completely prior to desynchronization

(Bernitsas et al 2008 2009)(d) 80000oReo95000 This is the region of transition from VIV

to galloping For cylinders with PTC transition to galloping

was successfully initiated at U nwaterasymp1025 that is back-to-back

with VIV (Chang et al 2011) instead of the typical U nwaterasymp20

Fig 6 shows this rapid rise in amplitude for Re480000

(U nwater41025) In this region both forcing mechanisms co-

exist as is further explained in Section 6

(e) Re495000 This is the galloping region By the end of

the experimental range U nwaterasymp13 the amplitude ratio con-

tinues to increase and approaches a maximum value of 286

for the 1st cylinder In the range of transition from VIV to

galloping and the galloping range the agreement between

CFD calculations and experimental data is excellent In

the experiments the maximum amplitude ratio is about2797 occurring at Refrac14104356 (U nwater frac141337) for the 1st

cylinder

42 Second (downstream) cylinder

For the 2nd cylinder PTC is applied at 7301 as shown in

Table 3 The amplitude ratio results are shown in Fig 7 FIM results

calculated by CFD fall into one of 1047297ve branches as was observed in

the 1st cylinder no FIM branch the initial branch of VIV the

upper branch of VIV transition from VIV to galloping and

galloping


or numerically

Table 5

Computational time

Re (104) 3 4 5 6 7 8 9 10

Computational time (h) 62 96 180 240 487 523 690 Hits channel

boundariesSimulated real time (s) 20 20 20 20 20 20 20

Time step Automatic time step adjustment (maximum Courant

number is 02)

Fig 6 Amplitude ratio of the 1st cylinder with PTC




(b) 30000oReo40000 In this initial branch of VIV the 2nd

cylinder has nearly zero amplitude with an amplitude ratio of

less than 01 at Reasymp30000 (U nwaterasymp393) This is also observed

in the corresponding experiments

(c) 40000oReo80000 At Refrac1440000 (U nwaterasymp524) where the

upper branch in VIV begins the amplitude of oscillation

increases sharply and agrees well with the experiments until

Refrac1442300 At the 1047297rst part of the upper branch that is for

40000oReo56400 (524oU n

watero740) experimentalresults show a drop in the amplitude of the 2nd cylinder to

nearly zero Simulation cannot predict this phenomenon Past

this discrepancy at the beginning of the upper branch agree-

ment between CFD and experiments is very good The ampli-

tude ratio increases at a relatively slow rate picking up from

080 at Reasymp40000 (U nwaterasymp524) and reaching 139 around

Refrac1480000 (U nwater frac141049)

(d) 80000oReo95000 Next comes the transition from VIV to

galloping a range that has hardly been studied in the litera-

ture and is discussed further in Section 6 based on vortex

structures The amplitude increases rapidly for U nwater 41049

(e) Re495000 A maximum value of 35 in amplitude ratio is

reached in galloping at U nwaterasymp1331 which is higher than the

maximum value of 276 measured experimentally for the 2nd

cylinder This is due to the fact that in the CFD simulations the

free surface was replaced by a wall In the experiments as

energy is converted from hydrokinetic to mechanical the two

cylinders create a dam effect thus lowering the water level

above the 2nd cylinder That limits the achievable amplitude

experimentally which is observed as a plateau in the experi-

mental results in Fig 7 The safety-stops are placed on both

sides of the mean position with a distance of around 28 times

the diameter in the experiments in the MRELab Consequently

the cylinder would hit the safety stops and limit the travel

when it was undergoing galloping In CFD simulation would

stop when the distance between the bottom wall boundary

and the center of each cylinder would reach one diameter

which is the distance between the bottom side of the 2D-by-

2D square grid of higher resolution for near wall calculations

Therefore in both simulations and experiments the limits of

the tools for analysis are reached as expected for the case of

galloping It should be reminded that galloping is an instability

phenomenon which stops only with the collapse of the structure

unless stops or higher damping are imposed

5 Frequency ratio results

The simulation records for each run and for each cylinder are

processed using Fast Fourier Transform (FFT) Thus the frequency

of oscillation is calculated and the frequency ratio is plotted versus

reduced velocity U nwater Reynolds number Re and 1047298ow velocity U

for the 1st PTC-cylinder in Fig 8 and for the 2nd PTC-cylinder in

Fig 9 The frequency of oscillation for each cylinder is non-

dimensionalized by the corresponding system natural frequencyin water f nwater The results are compared with the experimental

data from the LTFSW Channel (Kim et al 2011)


As shown in Fig 8 the frequency ratio curve exhibits variations

as FIM transitions between branches similar to the experimental

results


or numerically

(b) 30000oReo40000 The major harmonic frequency in the

VIV initial branch is higher in the numerical simulations than

in the experiments due to the viscous damping model asexplained in Section 4 on the basis of the response amplitude

Speci1047297cally in the numerical model only the linear viscous

damping is modeled while the physical model exhibits a very

complex viscous model see Eq (10) as identi1047297ed by Lee et al

(2011) As a result the experimental initial branch starts later

at Reasymp40000 There is a small increase in frequency ratio

around Reasymp40000 (U nwater frac14512) numerically matching the

experimental jump

(c) 40000oReo80000 The large jump of frequency observed

in the experiments at Reasymp40000 indicates the oscillation of

the 1st cylinder transitions from the VIV initial branch to the

VIV upper branch In the upper branch simulations and

experiments match very closely As the Re increases from

40000 to 60000 (U n

water frac14512 ndash

769) the frequency ratio of the 1st cylinder decreases from 120 and reaches 103 After

Refrac1460000 (U nwater frac14769) frequency ratio stabilizes around

105 and the curve shows a nearly constant slope with the

oscillation frequency of the 1st cylinder being very close to the

system natural frequency This good agreement between

experiments and simulations is attributed to the following

two facts

Fig 7 Amplitude ratio of the 2nd cylinder with PTC Fig 8 Frequency ratio of the 1st cylinder with PTC




i The classical linear viscous damping model used in the

simulations matches well with the physical damping model

because the velocity of oscillations is not near zero Thus

the damping dynamic memory effect and the nonlinear

static damping effect are small compared to the linear

viscous damping term as identi1047297ed by Lee et al (2011) This

was further veri1047297ed by Lee and Bernitsas (2011) where

experimental data with physical springs and dampers were

compared to experimental data with virtual springs and

dampers emulated by a controller The virtual system

provided an oscillator which matched perfectly the math-

ematical model on the linear oscillator

ii The amplitude of oscillation in the upper branch remains

below 15D and thus the cylinder is not close to the free

surface experimentally which numerically has been

replaced by a wall The effect of this discrepancy does notcome into play until Reasymp100000 as shown in Figs 6 and 7

when the amplitude experimental data start exhibiting a

plateau(d) 80000oReo95000 As the Reynolds number reaches about

80000 (U nwater frac141025) a small jump in the frequency ratio

occurs right at the point of switching from the VIV upper

branch to the transition region from VIV to galloping

(e) Re495000 The frequency ratio reduces at a relatively slow

rate after the oscillation mode transition into the galloping

branch has occurred and then its value remains in the vicinity

of 1 In the experimental results the frequency ratio of the 1st

cylinder slowly rises with the increase of 1047298ow velocity and

drops around the transition between the upper branch and the

galloping branch and then increases again The frequencyratio holds around 1 in the galloping branch In summary the

simulation results of the oscillation frequency for the 1st

cylinder are similar with the experimental data


In Fig 9 the frequency ratio f osc f nwater for the 2nd cylinder is

plotted along with experimental results for comparison The

motion of the 2nd cylinder is affected by the upstream cylinder

and exhibits unique response which is veri1047297ed both numerically

and experimentally The FFT of the 2nd cylinder (see Figs 11 and

12) shows two frequencies in the response of the 2nd cylinder one

due to the oscillations and wake frequency of the upstream

cylinder and one due to its own vortex shedding The following

observations can be made regarding the 1047297ve regions of FIM


or numerically

(b) 30000oReo40000 As shown in Fig 7 the amplitude ratio

of the 2nd cylinder is low for Re frac1430000 (U nwater frac14393) for the

same reasons as those discussed regarding the 1st cylinder

The numerical frequency ratio of the 2nd cylinder remainsobviously higher than that in the experiment and almost the

same value as the 1st cylinder which is shown in Fig 9 This

difference in general reduces as FIM moves into the upper

branch where the cylinder speed is higher and thus the

discrepancy between the physical damping model in Eq (10)

and the mathematical linear damping model in Eq (9)

weakens

(c) 40000oReo80000 In the numerical simulation results the

frequency ratio of the 2nd cylinder follows the experimental

results trend For reduced velocity 5oU nwatero7 the simulated

frequency ratio of the 2nd cylinder follows the same trend but

over-predicts the experimentally measured value by about

5 ndash 15 As shown in Fig 9 for the 2nd cylinder a prominent

drop occurs in both curves of numerical data and experimental

results around U nwater frac147

(d) 80000oReo95000 At Re frac1480000 (U nwater41049) the VIV

to galloping transition occurs The frequency ratio gradually

drops to about one at the beginning of galloping

(e) Re495000 In the galloping range the frequency ratio is very

close to 1 and the results of simulation and experiments are

nearly identical

6 Near-wake structures

The 2-D URANS results of amplitude and frequency response

for two PTC-cylinders match well with experiments The ampli-

tude and frequency response are closely related to the vortex

dynamics and wake pattern Actually amplitude and frequency areintegral properties of the 1047298uid ndash structure dynamics in the sense

that the pressure is integrated to give a force to which the cylinder

responds Typically integrals reduce error compared to non-

integral properties such as pressure distribution or location of

the separation point Thus it is harder for a URANS code on

cylinder 1047298uid dynamics to predict accurately local properties such

as vorticity and pressure distribution than it is to predict integral

properties such as Strouhal number drag and lift forces or

amplitude and frequency of response A very important local

property is that of the vorticity distribution which results in vortex

structures in the near-wake The vortex structures around the two

PTC-cylinders in FIM are presented and discussed in this section

In the numerical and experimental results presented by Wu

et al (2011) and Chang et al (2011) the near-wake structures andmode transition for one PTC-cylinder in FIM were discussed and

the salient features of the 1047298ow in the different branches of VIV and

galloping were achieved numerically For one cylinder in FIM the

transition between branches is accompanied by vortex pattern

change and the vortex pattern is stable when the cylinder is in a

branch (Wu et al 2011)

It should be reminded here that the reason for this successful

numerical prediction of the experimental results lies in the

application of the turbulence stimulation in the form of the PTC

Speci1047297cally 2-D URANS results for a stationary smooth cylinder

match well basic integral experimental results such as Strouhal

number and drag and lift coef 1047297cients for Reo10000 For a

smooth cylinder in VIV this agreement between experiments

and CFD extends to Re about 12000 (Wanderley et al 2008 Wu

Fig 9 Frequency ratio of the 2nd cylinder with PTC




et al 2011) The failure of agreement for Re412000 can be traced

to the inaccurate prediction of a very important local property for

1047298ows past a cylinder stationary or in FIM That is the point of

separation of the 1047298ow and its oscillation as vortices shed in an

alternating manner Speci1047297cally the separation point in laminar1047298ow (Reo300000) is located at 811 and oscillates around it up to

75 ndash 101 For Re410000 2-D URANS methods fail to predict that

motion correctly Typically the separation point for Re410000 is

predicted by 2D-URANS to be stationary at 901 With the additionof the PTC in the experiments and in the 2-D URANS simulations

the location of the separation point is predetermined resulting in

accurate prediction of the separation point That resulted in very

good agreement between simulations and experiments in Wu

et al (2011) for Reynolds numbers at least up to 135000 for which

experimental results were available for a single PTC-cylinder in

FIM This successful agreement extended not only to integral

properties but also local properties such as the vortex near-wake

structures This agreement is also evident in the results in this

paper for two PTC-cylinders in FIM

For the two PTC-cylinders in tandem cases the upstream

cylinder (1st cylinder) has great in1047298uence on the motion and

vortex shedding of the downstream cylinder (2nd cylinder) and

the vortex pattern becomes more complex than in the single

cylinder cases The simulation results of four typical Reynolds

numbers which correspond to the VIV initial branch upper

branch transition from VIV to galloping and galloping branch

are presented in this section The vortex patterns for two PTC-

cylinders at Re frac1430000 Re frac1459229 Re frac1493074 and Re frac14 100000

are shown in Figs 10 ndash 13 respectively The displacement ratio and

its FFT analysis for each cylinder are shown in Figs 10 ndash 12 as well

61 Reynolds number of 30000 (initial VIV branch)

As shown in Fig 10 the 2S mode of vortex shedding can be

clearly observed for the 1st cylinder Here 2S indicates two single

vortices shed per cycle Two vortices are shed from the 1st cylinder

per cycle of oscillation one by the top shear layer and another one

by the bottom shear layer When the two vortices move down-

stream and cross into the domain of the 2nd cylinder the clock-

wise rotating vortex passes right above the 2nd cylinder and the

counter-clockwise vortex passes below it This phenomenon

due to the speci1047297c spacing between the two cylinders causes

the vorticity from the 1st cylinder to absorb the same-rotation

vorticity from the 2nd cylinder preventing formation of large von

Kaacutermaacuten vortices forming behind the 2nd cylinder mdash thus suppres-

sing its FIM Shed vortices of the 1st cylinder allow only gene-

ration of small scale and very weak vortices in the 2nd cylinder

In addition the motion of the 1st cylinder has a strong regular

form which can be observed in the displacement ratio curves and

FFT analysis in Fig10 The displacement of the 2nd cylinder is very

small with average value of the 60 maximum peaks about 01 D

and a maximum displacement of about 013D Therefore the

motion of the 2nd cylinder is almost suppressed For the cases in

the VIV initial branch the suppression of the 2nd cylinder was alsoobserved in the experiments Visualization of the near wake vortex

structures using CFD has helped understand and explain this

phenomenon

62 Reynolds number of 59229 (upper VIV branch)

The time sequence of vortex shedding is shown in Fig 11 In the

vortex structure of the near-wake of the 1st cylinder two modes of

vortex shedding are observed in the simulation results (a) When

the two PTC-cylinders move in opposite direction (out of phase) a

2P vortex pattern is observed behind the 1st cylinder where 2P

means two pairs of vortices shed per cycle (b) When the two

cylinders move in phase the vortex mode of the 1st cylinder is 2P

+

2S The vortex pattern of the 1st cylinder switches between thesetwo modes over time Thus the motion of the 2nd cylinder

in1047298uences the vortex shedding of the 1st cylinder For the 2nd

cylinder the 2P vortex pattern is shown in the simulation results

The upstream vortices directly and closely interact with the

downstream cylinder As can be seen in the displacement ratio

curves in Fig 11 the motion of the 1st cylinder shows a periodic

pattern while small displacement is observed in certain cycles for

the 2nd cylinder The reason for the small displacement in those

cycles is that the vortex development of the 2nd cylinder is

weakened by the shed vortices from the 1st cylinder which is

similar to the phenomenon of the 2nd cylinder at Re frac1430000 The

drop-off in displacement of the 2nd cylinder is associated with the

variation of the phase difference between 1st and 2nd cylinder

which means the relative position of the two cylinders changes

periodically from out-of-phase to in-phase At the same time the

vortex structure of the 1st cylinder switches between 2P and 2P

+2S Relatively large difference of oscillation frequencies between

1st and 2nd cylinder could be found in the FFT analysis of the

displacement ratio Three peaks appear in the result of FFT analysis

for the 2nd cylinder as shown in Fig 11 The frequency values of

these three peaks are close to each other The frequency of the

highest peak is larger than those of other two peaks The

Fig 10 Vortex structures displacement history and frequency spectrum in the initial VIV branch at Re frac14 30000 (T n1frac140889 where T nfrac141 f nwater and T n1 is for the 1st

cylinder)




frequency of the peak in the middle which has the smallest

amplitude among these three peaks equals to the one of the FFT

analysis for the 1st cylinder

63 For Reynolds number of 93074 (VIV to galloping transition)

As shown in Fig 12 both cylinders shed vortices following the

2P+2S mode By the preceding analysis in Section 4 the two PTC-

cylinders are in the region of transition from VIV to galloping There

is variation in the vortex shedding structure for the 1st cylinder

The 2P+2S pattern is observed in most cycles occasionally though

one additional vortex is shed during the upward travel That is a

cycle-to-cycle variation in shedding exists For the 2nd cylinder the

vortex pattern is hard to identify as the shed vortices are strongly

disrupted and modi1047297ed by the vortices shed by the upstream

cylinder In the displacement ratio curves in Fig 12 the amplitudes

have strong and weak values and the maximum displacement

reaches 3D in some cycles for both cylinders

Fig 12 Vortex structures displacement history and frequency spectrum in the VIV-to-galloping transition region at Re frac1493074

Fig 11 Vortex structures displacement history and frequency spectrum in the upper VIV branch at Re frac1459229




During transition from VIV to galloping several FIM features

change We have observed and discussed changes from the typical

VIV amplitudes of about 1-2 diameters to higher values and also

changes in the frequency ratio There is another important phe-

nomenon to be observed and studied in Fig 12 which has hardly

been studied in the literature it is the transition from the VIV

driving mechanism to the galloping driving mechanism The dis-

cussion on the driving mechanisms of FIM is presented at the end of

this section as it is better understood by comparing Figs 11 ndash 13

64 For Reynolds number of 100000 (fully developed galloping)

Fig 13 shows the vortex structures for the two cylinders in fully

developed galloping at Re frac14100000 For the 1st cylinder and there

are 8 vortices shedding in one oscillation cycle The vortex pattern

for the 2nd cylinder is not easy to identify as the vortex shedding

is severely affected by the 1st cylinder The number of vortices and

their shedding mode is of secondary importance in galloping as

explained next

65 FIM driving mechanism

The VIV driving mechanism is solely based on the oscillatory lift

resulting from vortex shedding The mode of vortex shedding ndash

whether 2S 2P or 2P+2S ndash has frequency locked onto the frequency

of oscillation of the cylinder Thus the oscillatory excitation is in

synchronization with the body motion a condition similar to linear

resonance at each frequency of oscillation as the 1047298ow velocity

changes within the synchronization range In galloping the driving

mechanism is not based on the alternating vortices but on the lift

instability caused by negative damping due to the lift force induced

by the geometric asymmetry of the circular cylinder due to the

turbulence stimulation The transition from the VIV mechanism to

the galloping mechanism can be observed by comparing Fig 11(VIV) to Fig 12 (VIV-to-galloping transition) to Fig 13 (fully

developed galloping) In Fig 11 the vortex shedding mode is in

synchronization with the cylinder oscillation In Fig 12 as the

amplitude of oscillation increases the number of vortices shed per

cycle increases resulting in more complex modes The vortex

shedding frequency is several times higher than the vortex-mode

frequency which is still in synchronization with the cylinder

oscillations In Fig 12 it can also be observed that the shear layer

motions follow the cylinder oscillations as expected Their role in

inducing oscillatory lift in synchronization with the cylinder motion

increases and becomes the dominant driving mechanism in Fig 13

where vortices no longer shed in modes synchronized with the

cylinder oscillations Vortices shed in less complex modes as the

cylinder amplitude increases and more complex modes with more

vortices cannot be developed and stay synchronized with the

cylinder motion That is some vortices increase the lift force as

they are in phase with the cylinder motion and some decrease the

lift force as they are out of phase with the cylinder motion In fully

developed galloping the shear layer motion is in synchronization

with the galloping instability motion

7 Conclusions

One degree of freedom 1047298ow induced motions transverse to a

uniform 1047298ow of two rigid circular cylinders mounted on end

linear-springs in tandem were studied using 2-D URANS simula-

tions veri1047297ed by experimental data The range of Reynolds num-

bers for which experimental data were collected in the MRELab

was 30000oReo105000 which falls in the high-lift TrSL3

regime Typical 2-D URANS results on smooth circular cylinders

stationary or in VIV are valid up to Reynolds number Recong10000 ndash

12000 In earlier work it has been shown that passive turbulence

control in the form of selectively distributed surface roughnessresults in very good agreement between 2-D URANS and experi-

ments for single cylinder FIM PTC was used in this paper and

proved to be the key factor in achieving agreement between

experimental and CFD simulations The following conclusions

can be drawn from the results presented in this paper

1 An effective method was developed to handle large-amplitude

FIM response Large mesh deformations occur when the

cylinders undergo FIM in the form of VIV or galloping In order

to minimize the mesh deformation a dynamic mesh technique

of topological change was implemented

2 The amplitude-ratio results are in excellent agreement with

experimental data showing the initial and upper branches in

VIV transition from VIV to galloping and galloping for the twoPTC-cylinders The discrepancy observed at the initiation of FIM

in the initial branch of VIV was justi1047297ed based on the difference

between the mathematical damping model implemented in the

simulations and the actual physical damping model at low

cylinder oscillatory velocity

3 The frequency results are in excellent agreement with experi-

mental data also showing the initial and upper branches in VIV

with back-to-back galloping for the two PTC-cylinders

4 Integral properties of FIM such as the Strouhal number and lift

drag forces are easier to predict using 2-D URANS Such

methods fail in predicting local features of 1047298ow past cylinders

in FIM for Re410000 and particularly the complex motion of

the separation point which is a key and unique feature in

cylinder 1047298ows With the proper implementation of PTC the

Fig 13 Vortex structures in galloping at Re frac14100000




location of the separation point is known a priori resulting in

very good agreement between experiments and simulations

An important local 1047298ow property is the vorticity generation

which results in complex vortex structures These were studied

using high-resolution imaging from the CFD results

5 For Re frac1430000 in the initial VIV branch the typical 2S vortex

structure is shown for the 1st cylinder

6 For Refrac1430000 in the initial VIV branch the 2nd cylinder

motion is almost suppressed and simulations explain thisphenomenon for center-to-center spacing between the cylin-

ders equal to two diameters

7 For Re frac1459229 which is in the range of the VIV upper branch

both 2P and 2P+2S patterns are observed for the 1st cylinder

while the vortex structure for the 2nd cylinder is only 2P The

upstream vortices shedding from the 1st cylinder directly and

closely interact with the downstream cylinder

8 The vortex structure simulation is most helpful in understand-

ing and demonstrating the differences between the driving

hydrodynamic mechanism in VIV and galloping as well as the

coexistence of the two mechanisms in the transition region

from VIV to galloping

9 In galloping amplitude of 35 diameters is achieved numeri-

cally in good agreement with experimental results The 1047298ow

domain limits are reached and the stops in the 1047298ow channel are

hit thus limiting experimental testing

Acknowledgements

The following support is gratefully acknowledged (a) DOE

contract DE-EE0003644 to Vortex Hydro Energy with subcontract

to the University of Michigan (b) ONR grant N00014-08-1-0601

to the University of Michigan Program Manager Kelly Cooper

(c) Specialized Research Fund for the Doctoral Program of Higher

Education of China (Grant No 20120191130003) and the China

Scholarship Council for Lin Ding

References

Allmaras SR Johnson FT Spalart PR 2012 Modi1047297cations and clari1047297cations forthe implementation of the Spalart ndash Allmaras turbulence model In SeventhInternational Conference on Computational Fluid Dynamics 9 ndash 13 July 2012 BigIsland Hawaii

Assi GRS Meneghini JR Aranha JAP Bearman PW Casaprima E 2006Experimental investigation of 1047298ow-induced vibration interference betweentwo circular cylinders J Fluid Struct 22 (6 ndash 7) 819 ndash 827

Aupoix B Spalart PR 2003 Extensions of the Spalart ndash Allmaras turbulence modelto account for wall roughness Int J Heat Fluid Flow 24 (4) 454 ndash 462

Bernitsas MM Ben-Simon Y Raghavan K Garcia EMH 2009 The VIVACEconverter model tests at high damping and Reynolds Number around 105 JOffshore Mech Arct Eng-Trans ASME 131 1

Bernitsas MM RaghavanK 2009 Fluid Motion Energy Converter United StatesPatent and Trademark Of 1047297ce Patent 7 493 759 B2 Issued on February 24

2009Bernitsas MM Raghavan K Ben-Simon Y Garcia EMH 2008 VIVACE (vortexinduced vibration aquatic clean energy) a new concept in generation of cleanand renewable energy from 1047298uid 1047298ow J Offshore Mech Arct Eng-Trans ASME130 4

Borazjani I Sotiropoulos F 2009 Vortex-induced vibrations of two cylinders intandem arrangement in the proximity-wake interference region J Fluid Mech621 321 ndash 364

Catalano P Wang M Iaccarino G Moin P 2003 Numerical simulation of the1047298ow around a circular cylinder at high Reynolds numbers Int J Heat Fluid Flow

24 (4) 463 ndash 469Chang C-C Kumar RA Bernitsas MM 2011 VIV and galloping of single circular

cylinder with surface roughness at 30 104leRele12 105 Ocean Eng 38 (16)1713 ndash 1732

Edwards JR Chandra S 1996 Comparison of eddy viscosity-transport turbulencemodels for three-dimensional shock-separated 1047298ow 1047297elds AIAA J 34 (4)756 ndash 763

Kim ES Bernitsas MM Kumar RA 2011 Multi-cylinder 1047298ow-induced motions

enhancement by passive turbulence control at 28000oReo120000 InProceedings of the OMAE 19 ndash 24 June 2011 Rotterdam the Netherlands44397 pp 249 ndash 260

King R Johns DJ 1976 Wake interaction experiments with two 1047298exible circular

cylinders in 1047298owing water J Sound Vib 45 (2) 259 ndash 283Lee J Chang C-C Xiros NI Bernitsas MM 2010 Integrated power take-off and

virtual oscillator system for the VIVACE Converter V CK system identi1047297cationIn ASME 2009 International Mechanical Engineering Congress and Exposition13 ndash 19 November 2009 Lake Buena Vista FL United states PART A pp 393 ndash

399Lee JH Bernitsas MM 2011 High-damping high-Reynolds VIV tests for energy

harnessing using the VIVACE converter Ocean Eng 38 (16) 1697 ndash 1712Lee JH Xiros N Bernitsas MM 2011 Virtual damper-spring system for VIV

experiments and hydrokinetic energy conversion Ocean Eng 38 (5 ndash 6) 732 ndash 747Park H Bernitsas MM Kumar RA 2012 Selective roughness in the boundary

layer to suppress 1047298ow-induced motions of circular cylinder at30000oReo120000 J Offshore Mech Arct Eng 134 (4) 041801

Raghavan K 2007 Energy Extraction from a Steady Flow Using Vortex Induced

Vibration PhD Thesis Dept of Naval Architecture amp Marine Engineering

University of MichiganRaghavan K Bernitsas MM 2008 Enhancement of high damping VIV through

roughness distribution for energy harnessing at 8 103oReo15 105 In

27th International Conference on Offshore Mechanics and Arctic Engineering9 ndash 13 June 2008 pp 871 ndash 882

Raghavan K Bernitsas MM 2011 Experimental investigation of Reynoldsnumber effect on vortex induced vibration of rigid circular cylinder on elasticsupports Ocean Eng 38 (5 ndash 6) 719 ndash 731

Raghavan K Bernitsas MM Maroulis DE 2009 Effect of bottom boundary onVIV for energy harnessing at 8 103oReo15 105 J Offshore Mech ArctEng-Trans ASME 131 (3) 1 ndash 13

Shur M Spalart P Strelets M Travin A 1996 Navier-Stokes simulation of

shedding turbulent 1047298ow past a circular cylinder and a cylinder with backwardsplitter plate In Desideri JA Hirsch C LeTallec P Pandol1047297 M Periaux J(Eds) Proceedings of the 1996 Third ECCOMAS Computational Fluid DynamicsConference Paris France pp 676 ndash 682

Spalart PR Allmaras SR 1994 A one-equation turbulence model for aerody-

namic 1047298ows Rechercheacute Aerospatiale 1 5 ndash 21

Sumner D Price SJ Paidoussis MP 2000 Flow-pattern identi1047297cation for twostaggered circular cylinders in cross-1047298ow J Fluid Mech 411 263 ndash 303

Travin A Shur M Strelets M Spalart P 2000 Detached-eddy simulations past acircular cylinder Flow Turbul Combust 63 (1 ndash 4) 293 ndash 313

Tritton DJ 1977 Physical Fluid Dynamics Van Nostrand Reinhold New York Wanderley JBV Sphaier SH Levi C 2008 A Numerical Investigation of Vortex

Induced Vibration on an Elastically Mounted Rigid Cylinder In 27th Interna-

tional Conference on Offshore Mechanics and Arctic Engineering 15 ndash 20 June2008 Estoril Portugal pp 703 ndash 711

Williamson CHK Govardhan R 2004 Vortex-induced vibrations Annu RevFluid Mech 36 413 ndash 455

Williamson CHK Govardhan R 2008 A brief review of recent results in vortex-induced vibrations J Wind Eng Ind Aerodyn 96 (6 ndash 7) 713 ndash 735

Wu W Bernitsas MM Maki K 2011 RANS simulation vs experiments of 1047298ow

induced motion of circular cylinder with passive turbulence control at35000oReo130000 In ASME 2011 30th International Conference on Ocean

Offshore and Arctic Engineering 19 ndash 24 June 2011 Rotterdam Netherlandspp 733 ndash 744

Zdravkovich MM 1985 Flow induced oscillations of two interfering circularcylinders J Sound Vib 101 (4) 511 ndash 521

Zdravkovich MM 1987 The effects of interference between circular cylinders incross 1047298ow J Fluid Struct 1 (2) 239 ndash 261

Zdravkovich MM 1997a Flow Around Circular Cylinders Volume 1 Fundamen-

tals Oxford University Press EnglandZdravkovich MM 1997b Flow Around Circular Cylinders Volume 2 Applications

Oxford University Press England




by springs with a power-take-off (PTO) system It can harness

hydrokinetic energy from ocean and river currents as slow as

04 ms frac1408 knots (Chang et al 2011) The goal of the VIVACE

team is to enhance the oscillation amplitude and maximize the

hydrokinetic energy converted to mechanical energy in the oscil-

lating cylinder One way to improve the performance of VIVACE is

to use multiple cylinders as would be the case in multi-blade

propellers or windmills Two rigid circular cylinders in tandem

mounted on end linear-springs with passive turbulence control(PTC) to enhance FIM are studied in this paper

Roughness on the cylinder can effectively change the 1047298ow

properties Extensive literature is available on using roughness to

alter FIM of cylinders on springs There are different roughness

parameters that affect 1047298ow-induced motion such as roughness

location roughness height and roughness coverage (Chang et al

2011 Park et al 2012) PTC was introduced in the MRELab to

enhance cylinder FIM and extract more hydrokinetic energy from1047298uid 1047298ows PTC consists of selectively located surface roughness

with thickness on the order of the boundary layer thickness and

depending on its location it can induce galloping hard galloping

weak suppression or strong suppression as shown in the FIM-to-

PTC Map (Park et al 2012) With the application of PTC cylinder FIM

can be enhanced In addition back-to-back VIV and galloping are

achieved The maximum power density of a single-cylinder VIVACE

(349 Wm3) was ampli1047297ed 138 times in comparison to that of

VIVACE with a smooth surface cylinder (253 Wm3) at 1047298ow speed

U frac14145 ms (Chang et al 2011) Amplitudes as high as 27 diameters

have been achieved by using passive turbulence control (Chang

et al 2011 Kim et al 2011 Raghavan and Bernitsas 2008) The

effects of PTC were studied in detailed by Chang et al (2011) and

Park et al (2012)

To further improve the power density of VIVACE multiple

cylinder systems are investigated experimentally in the MRELab

Multiple cylinder systems are used in many applications in civil

offshore aeronautical engineering etc The interference between

cylinders strongly depends on the arrangement of cylinders and

their orientation with respect to the free stream (Zdravkovich

1997b) Two-cylinder systems have been studied the most becausethey are the simplest multi-cylinder arrangement (Assi et al 2006

King and Johns 1976 Sumner et al 2000 Zdravkovich 1985 1987)

For two cylinders in tandem the downstream cylinder is subjected

to high level of turbulence generated from the upstream cylinder in

addition to impingement of Kaacutermaacuten-size shed vortices Most of

studies performed in the past on two-cylinder arrangements were

on smooth cylinders Moreover in most studies the cylinders were

1047297xed or at very low Reynolds number (Borazjani and Sotiropoulos

2009) FIM of two-cylinders with surface roughness (PTC) for high

Re has been studied only by the MRELab to the best of the authorsrsquo

knowledge (Kim et al 2011)

In this paper two rigid PTC-cylinders in tandem mounted on end-

springs are simulated using two-dimensional Unsteady Reynolds-

Averaged Navier-Stokes (URANS) equations with the Spalart ndash Allmarasone-equation turbulence model The 1047298ow is simulated in the range of

30000oReo105000 which falls in the high-lift TrSL3 regime and

for which experiments were conducted in the MRELab TrSL stands

for Transition in Shear Layer and ldquo3rdquo indicates the third region where

the shear layer is fully saturated resulting in stronger vortices shorter

formation length and highest lift (Zdravkovich 1997a) There are

numerous studies of using URANS for simulation of 1047298ow past a

circular cylinder From the published literature URANS results of the

Strouhal number agree very well with other numerical and experi-

mental results Lift and drag coef 1047297cient CFD results at low Reynolds

numbers (Wanderley et al 2008) also agree well with experiments

Researchers mostly apply URANS at low Reynolds number Applica-

tions at higher Re show that prediction for Re412000 is still a

challenging task for URANS Prediction is even poorer near the drag

crisis (Catalano et al 2003) As explained by Wu et al (2011) the 1047297rst

manifestation of failure lies in the fact that for Re410000 the

separation point is not predicted properly Speci1047297cally CFD using

2-D URANS predicts that the separation point hardly oscillates around

901 while experimental data show that it oscillates around 811 in

laminar 1047298ow with amplitudes as much as 5 ndash 101 This is a most

important characteristic of 1047298ows past a circular cylinder It is also a

local property of the 1047298ow as opposed to integral 1047298ow properties such

as the Strouhal number and the liftdrag forces Some integralproperties are easier to predict as integration 1047297lters local errors

With proper modeling of PTC however 2-D URANS simulations

exhibit several of the salient local features of the 1047298ow resulting is

excellent agreement with experiments as proven by Wu et al

(2011) They developed a CFD code based on OpenFOAM to solve

the problem of a single cylinder with PTC They showed that the

presence of PTC results in very good agreement between experi-

ments and CFD simulations up to Refrac14135000 for which experi-

mental data were available from tests in the MRELab Without PTC

such agreement was limited to Refrac1410000 ndash 12000 (Wanderley

et al 2008 Wu et al 2011) when 2-D URANS is used

Thus the code developed by Wu et al (2011) for a single

cylinder in FIM and in this paper for two cylinders in tandem

predict very well the experimentally measured data including

vortex streets transition from VIV to galloping and shear layer

oscillation Consequently the developed tool can be used with

con1047297dence to predict 1047298ow properties that are more challenging to

measure experimentally at such high speeds and turbulence levels

In the present study the FIM of two rigid circular cylinders on end

linear-springs in tandem are studied using 2-D URANS simulations

veri1047297ed by experimental data The objective of this study is to

establish the capability of a numerical tool to simulate the VIVACE

system with two PTC-cylinders in FIM and investigate the system

parameter effects on the cylinder dynamics The physical model and

running parameters are presented in Section 2 In Section 3 the

numerical approach and grid generation are described The simulation

results of amplitude and frequency for the two PTC-cylinders are

shown in Sections 4 and 5 respectively Numerical results are

compared with experiments conducted in the Low Turbulence FreeSurface Water (LTFSW) Channel of the MRELab Vortex structures of

four typical cases are discussed in Section 6 Conclusions are presented

at the end based on the analysis of amplitude and frequency response

and vortex structures

2 Physical model

The physical model considered in this paper consists of two

oscillatory systems as depicted in Fig 1 The elements of each

oscillatory system are a rigid circular cylinder of diameter D and

length L two supporting linear springs of stiffness K and the

Fig 1 Schematic of the physical model





















































311 Fluid dynamics














partU ipart xi

frac14 0 eth1THORN

partU ipartt

thorn part


1

ρ

part p

part xithorn part



Table 1

Nomenclature






L Cylinder length


Re Reynolds number

St Strouhal number




















P Pressure

W Channel width










Table 2









strain-rate tensor

S ij frac14 1

2

partU ipart x j

thornpartU jpart xi

eth3THORN

















puted from


where

f ν1 frac14 χ 3

χ 3

thorn c 3ν1

eth6THORN

χ frac14 ~ν

νeth7THORN



part~ν

partt thorn u j

part~ν

part x jfrac14 c b1


d

2

thorn1

s

part


part ~ν

part x j

thorn c b2

part~ν

part xi

part~ν

part xi

eth8THORN




















kminus1

































Table 3

































by a wall

34 Grid generation






























is shown in Fig 4

















Table 4




C d C l St


Coarse (180 40) 1029 minus0 0 60 0 2 87 0 537 015 2 015 2

Medium (240 70) 1039 minus0 0 65 0 2 99 0 561 015 2 015 2

Fine (360 100) 1038 minus0 0 67 0 2 98 0 55 9 015 0 015 0













































or numerically





































cylinder







galloping


or numerically

Table 5

Computational time

Re (104) 3 4 5 6 7 8 9 10




number is 02)













40000oReo56400 (524oU n















































results


or numerically










experimental jump






40000 to 60000 (U n








two facts














































or numerically










weakens














nearly identical























































































phenomenon









+
























cylinder)









































explained next

































7 Conclusions
































































Acknowledgements








References



































































































311 Fluid dynamics














partU ipart xi

frac14 0 eth1THORN

partU ipartt

thorn part


1

ρ

part p

part xithorn part



Table 1

Nomenclature






L Cylinder length


Re Reynolds number

St Strouhal number




















P Pressure

W Channel width










Table 2









strain-rate tensor

S ij frac14 1

2

partU ipart x j

thornpartU jpart xi

eth3THORN

















puted from


where

f ν1 frac14 χ 3

χ 3

thorn c 3ν1

eth6THORN

χ frac14 ~ν

νeth7THORN



part~ν

partt thorn u j

part~ν

part x jfrac14 c b1


d

2

thorn1

s

part


part ~ν

part x j

thorn c b2

part~ν

part xi

part~ν

part xi

eth8THORN




















kminus1

































Table 3

































by a wall

34 Grid generation






























is shown in Fig 4

















Table 4




C d C l St


Coarse (180 40) 1029 minus0 0 60 0 2 87 0 537 015 2 015 2

Medium (240 70) 1039 minus0 0 65 0 2 99 0 561 015 2 015 2

Fine (360 100) 1038 minus0 0 67 0 2 98 0 55 9 015 0 015 0













































or numerically





































cylinder







galloping


or numerically

Table 5

Computational time

Re (104) 3 4 5 6 7 8 9 10




number is 02)













40000oReo56400 (524oU n















































results


or numerically










experimental jump






40000 to 60000 (U n








two facts














































or numerically










weakens














nearly identical























































































phenomenon









+
























cylinder)









































explained next

































7 Conclusions
































































Acknowledgements








References


















































strain-rate tensor

S ij frac14 1

2

partU ipart x j

thornpartU jpart xi

eth3THORN

















puted from


where

f ν1 frac14 χ 3

χ 3

thorn c 3ν1

eth6THORN

χ frac14 ~ν

νeth7THORN



part~ν

partt thorn u j

part~ν

part x jfrac14 c b1


d

2

thorn1

s

part


part ~ν

part x j

thorn c b2

part~ν

part xi

part~ν

part xi

eth8THORN




















kminus1

































Table 3

































by a wall

34 Grid generation






























is shown in Fig 4

















Table 4




C d C l St


Coarse (180 40) 1029 minus0 0 60 0 2 87 0 537 015 2 015 2

Medium (240 70) 1039 minus0 0 65 0 2 99 0 561 015 2 015 2

Fine (360 100) 1038 minus0 0 67 0 2 98 0 55 9 015 0 015 0













































or numerically





































cylinder







galloping


or numerically

Table 5

Computational time

Re (104) 3 4 5 6 7 8 9 10




number is 02)













40000oReo56400 (524oU n















































results


or numerically










experimental jump






40000 to 60000 (U n








two facts














































or numerically










weakens














nearly identical























































































phenomenon









+
























cylinder)









































explained next

































7 Conclusions
































































Acknowledgements








References








































































by a wall

34 Grid generation






























is shown in Fig 4

















Table 4




C d C l St


Coarse (180 40) 1029 minus0 0 60 0 2 87 0 537 015 2 015 2

Medium (240 70) 1039 minus0 0 65 0 2 99 0 561 015 2 015 2

Fine (360 100) 1038 minus0 0 67 0 2 98 0 55 9 015 0 015 0













































or numerically





































cylinder







galloping


or numerically

Table 5

Computational time

Re (104) 3 4 5 6 7 8 9 10




number is 02)













40000oReo56400 (524oU n















































results


or numerically










experimental jump






40000 to 60000 (U n








two facts














































or numerically










weakens














nearly identical























































































phenomenon









+
























cylinder)









































explained next

































7 Conclusions
































































Acknowledgements








References

























































































or numerically





































cylinder







galloping


or numerically

Table 5

Computational time

Re (104) 3 4 5 6 7 8 9 10




number is 02)













40000oReo56400 (524oU n















































results


or numerically










experimental jump






40000 to 60000 (U n








two facts














































or numerically










weakens














nearly identical























































































phenomenon









+
























cylinder)









































explained next

































7 Conclusions
































































Acknowledgements








References


























































40000oReo56400 (524oU n















































results


or numerically










experimental jump






40000 to 60000 (U n








two facts














































or numerically










weakens














nearly identical























































































phenomenon









+
























cylinder)









































explained next

































7 Conclusions
































































Acknowledgements








References



























































































or numerically










weakens














nearly identical























































































phenomenon









+
























cylinder)









































explained next

































7 Conclusions
































































Acknowledgements








References





































































































phenomenon









+
























cylinder)









































explained next

































7 Conclusions
































































Acknowledgements








References























































































explained next

































7 Conclusions
































































Acknowledgements








References


































































explained next

































7 Conclusions
































































Acknowledgements








References










































































Acknowledgements








References
















































Documents

2-D URANS vs.experiments of Flow Induced Motion Softw o Circular Cylinders in Tandem With Passive Turbulence Control for 30,000oReo105,000