Numerical study of the effect of velocity perturbations on the mechanics of vortex shedding in synchronized bluff-body wakes

S. BALABANI1 E. KONSTANTINIDIS1,2 C. LIANG3 G. PAPADAKIS1

1Department of Mechanical Engineering, Kings College London, WC2R 2LS, UK

2Department of Engineering and Management of Energy Resources, University of Western Macedonia, Kozani 50100, Greece

3Department of Mathematics, University of Glasgow, Glasgow G12 8QW, UK

Outline

Background and motivation Computational details Comparison with experiments Observations from a typical simulation Effect of excitation frequency Summary and remarks

Wake and vortex shedding control by periodic excitations

Rectilinear cylinder oscillations Rotational cylinder oscillations Flow pulsation Acoustic forcing Vibration of control rod in wake Surface suction/blowing Surface modulation/deformation

Question: are there any universal features among the different methods?

Flow configuration

0.21 /o mf U d Inflow with superimposed periodic velocity oscillations

Circular cylinder perpendicular to the oncoming flow

( ) sin(2 )m eU t U U f t= +

Main parameters:

2 e

m

A UD f d

UU

=

*

0

e

e

UUf d

ff

=UDRe =

Forced oscillation studies (inline)

0.5 1.0 1.5 2.0 2.5 3.00.0

0.1

0.2

0.3

0.4

=

Flow Oscillations Cylinder OscillationsArmstong et al. (1986), Re = 21

500 Griffin & Ramberg (1976), Re = 190Barbi et al. (1986), Re = 3

000 Tanida et al. (1973), Re = 80Barbi et al. (1986), Re = 40

000 Tanida et al. (1973), Re = 4

000Konstantinidis et al (2003), Re = 2 150 Tatsuno (1972), Re = 100Konstantinidis et al (2005), Re = 2 150 Nishihara et al (2004), Re = 17000

A UD 2 feD

fundamentalsynchronization

region

fe / fo

Vortex-induced inline vibration

Okajima et al (2004) Eur J Mech B/Fluids 23: 115-125

Forced vs. free streamwise vibration

In the middle of the lock-on region associated with no excitation, i.e. zero energy transfer from the fluid to the structure (Konstantinidis et al. 2005, JFM)

1.5 2.0 2.5 3.0 3.5 4.0

4 3.5 3 2.5 2 1.50.00

0.05

0.10

0.15

0.20

2nd responsebranch

1st responsebranch

A D

lock-onregion

fe / fo

U *= U/feD

fefnfefw

Objectives

Compare LES to PIV data at moderate Reynolds numbers

Determine forces (magnitude and phase) exerted on the cylinder within lock-on range

Determine sign of energy transfer Improve understanding of flow physics for

this class of problems by generalization of the results

Present simulations & previous experiments

1.5 2.0 2.5 3.0 3.5

4 3.5 3 2.5 2 1.50.00

0.05

0.10

0.15

0.20 PIV (Konstantinidis et al 2005) LES (present)

2nd responsebranch

1st responsebranch

A D

lock-onregion

fe / fo

U *= U/feD

Computational details

Unstructured collocated grid (746,688 cells)

3D LES (standard Smagorinsky model)

33 planes along span (L=D) Liang & Papadakis (2007)

Comp. Fluids

Flow statistics

Mean flow streamlines Mean vorticity

Streamwise mean velocity Reynolds stress

LES

PIV LES

Re 2150 2580

fe/fo 1.87 1.88

u/U 0.045 0.050PIV

Instantaneous flow

SimulationExperiment

3-D flow structureSpanwise vorticity

z /UD = 3

Streamwise vorticity (Mode B instability)

x /UD = 1

Spanwise correlation of velocity fluctuations in separating shear layerAspect ratio effectsexperiment: 10D (end walls)simulation: D (periodic b. condition)

Typical simulation

0

1

2

3

-1

0

1

0 10 20 30 400

45

90

135

180

0 10 20 30 400

45

90

135

180

CD CL

drag

t /Te

lift

t /Te

fe/fo =

1.88

Lissajous figures

1.0 1.5 2.0-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

1.0 1.5 2.0 1.0 1.5 2.0 1.0 1.5 2.0

2.092.001.88fe / fo = 1.77

CD

CL

Timing of vortex shedding

U(t)

fe/fo = 1.77

1.88

2.00

2.09

Force phase and energy transfer

1.7 1.8 1.9 2.0 2.1 2.2 2.30

60

120

180

E < 0

E > 0

fe/fo

drag (LES) lift (LES) Vmax(PIV)

U()

V()

Mean drag vs. excitation frequency

1.0 1.5 2.0 2.5 3.01.0

1.2

1.4

1.6

present LES, Re = 2580 Nishihara et al, Re = 17000

M

e

a

n

d

r

a

g

fe/fo

Drag amplification vs amplitude

Flow forcing

Present study

Jarza & Podolski (2004)

Konstantinidis et al (2005)

Streamwise oscillations

Tanida et al (1973)

Nishihara et al (2005)

Transverse oscillations

Tanida et al (1973)

Sarpkaya (1978)

Gopalkrishnan (1993)

Dong & Karniadakis (2004)0.0 0.2 0.4 0.6 0.8

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.00 0.05 0.10 0.15

Streamwise, Ax /D Transverse, Ay /D1+

8.2(

A x /D

)

C

D

m

a

x

/

C

D

o

1+2.1

(A y /D)

A/D

A/D

Effect of velocity perturbation

0.0 0.1 0.2 0.31.0

1.5

2.0

2.5

C

D

m

a

x

/

C

D

o

U/Uo

Summary

Comparison between computations and experiments shows agreement on flow statistics instantaneous flow structure spanwise correlation

Simulations revealed 3-D flow structure (Mode B type) primary vortices fully-correlated along span (D) vortex-induced drag in-phase with relative displacement (zero

energy transfer) Equivalence between inline cylinder oscillations and inflow

fluctuations lock-on limits phase between induced forces and relative flow/cylinder oscillation drag amplification

Closing remarks

Within lock-on region vortex shedding frequency is controlled by the excitation frequency

Energy transfer between the fluid and the structure is controlled by the timing of vortex shedding which is imposed by the velocity perturbation

Zero-phase difference between force and relative displacement when fe = 2fo for streamwise and fe = fo for transverse oscillations

Drag amplification appears more pronounced in streamwisethan in transverse oscillations

Acknowledgement

Financial support from the ECLAT group at Kings College London for attending this conference

Numerical study of the effect of velocity perturbations on the mechanics of vortex shedding in synchronized bluff-body wakesOutlineWake and vortex shedding control by periodic excitationsFlow configurationForced oscillation studies (inline)Vortex-induced inline vibrationForced vs. free streamwise vibrationObjectivesPresent simulations & previous experimentsComputational detailsFlow statisticsInstantaneous flow3-D flow structureTypical simulationLissajous figuresTiming of vortex sheddingForce phase and energy transferMean drag vs. excitation frequencyDrag amplification vs amplitudeEffect of velocity perturbationSummaryClosing remarksAcknowledgement