ACTIVE CONTROL METHODS FOR DRAG REDUCTION IN FLOW OVER BLUFF BODIES (Generation-Sustenance Mechanism and Statistical Law of Turbulence)

ACTIVE

CONTROL METHODS FOR DRAG REDUCTION

IN

FLOW

OVER

BLUFF

BODIES

Haecheon Choi

Schoolof Mechanicaland AerospaceEngineering,SeoulNational University,Seoul 151-742,Korea

ABSTRACT

In this

paper,

we

present twosuccessful results from activecontrolsof flows

over

acircular cylinderand

a

spherefor drag reduction. TheReynoldsnumber

range

consideredfortheflow

over

acircular cylinder is40\sim 3900

based

on

the free-stream velocity andcylinderdiameter, whereasfor the flow

over

asphereit is 105 based

on

the free-streamvelocity and sphere diameter. The successful

active

control methods

are

adistributed

(spatially

periodic) forcingandahigh-frequency(timeperiodic)forcing. With thesecontrol methods,the

mean

drag and

liftfluctuations decrease andvorticalstructures

are

significantlymodified. Forexample,thetime-periodic forcing

with ahighfrequency(largerthan20times thevortexsheddingfrequency)produces50% drag reduction for the flow

over

asphere at$Re$ $=10^{5}$

.

Thedistributed forcing applied to the flow

over

acircular cylinder results in

a

significant drag reductionatalltheReynolds numbers investigated.

INTRODUCTION

Thedrag andnoise increase

very

rapidlywithincreasing speed ofvehicles. Therefore,controlof flow

over

abluff body for drag andnoise reductionhas been considered

one

ofthemajor issues influid mechanics. In the present study,

we

consider two kindsofbluff-body flows:

one

isthe flow

over

acircular cylinder and the other is the flow

over

asphere. These two flows contain mostof the characteristics observed in flows

over

tw0-and three-dimensionalbluffbodies,respectively.

So far,

many

researchers have applied three kinds of control methods to flow

over

abluff body: passive, activeopen-loop(i.e. non-feedback)andactivefeedback controls. Amongthem,

we

restrict

our

control method

to acategory ofthe active open-loop control method in thispaperand considertwo typesofactive open-loop

control methods. The firstis atime-periodicforcing whose frequencyiseither

near

thevortexshedding frequency

(low-ffequency forcing)

or

similar to

or

larger than the ffequencycorresponding to the shear-layer instability

(high-frequency forcing). The secondisasteady but distributed(i.e. spatiallyvarying)forcing.These two control

methods

are

appliedtoflows

over

circular cylinderandasphere, inorder toinvestigatethe controleffect

on

the

drag,liftandflowstructures.

The Reynolds number

ranges

considered

are

$Re$ $=u_{\infty}d/\mathrm{v}=40\sim 3900$forflow

over

acircularcylinderand $Re$$=u_{\infty}d/\mathrm{v}=425\sim 10^{5}$for flow

over

asphere, respectively,where$Re$istheReynoldsnumber,$u_{\infty}$ isthe

free-stream velocity, $d$isthe cylinder

or

spherediameter, and$\mathrm{v}$ is thekinematic viscosity. Forflowoveracircular

cylinder, numerical simulations

are

conducted for all the Reynolds numbers investigated. On the otherhand, for flow

over

asphere, numerical simulations

are

conductedat$Re$$=425\sim 3700$and

an

experimental studyiscarried

outat$Re$ $=10^{5}$

.

NUMERICAL AND EXPERIMENTAL METHODS

Flow

over

aCircular Cylinder

Flow

over

acircular cylinderisstudied at $Re$$=40\sim 140$ and

3900

using anumerical method. For$Re$$=$

40\sim 140,the flowislaminarand thus

no

turbulence model isused. For$Re$$=3900$,largeeddy simulation with

adynamic subgrid-scalemodel(Germanoet al. 1991;Lilly 1992)is carriedout. The numericalmethodused

is

based

on

fully implicit fractionalstepmethod(ChoiandMoin 1994)in generalizedcoordinates with the

second-ordercentral difference scheme for the discretization of thespatialderivatives. The numbersof gridpointsused

are

$320\cross 120\mathrm{x}$ $16$(spanwisedirection)for$Re$$=40\sim 140$and

672

$\mathrm{x}160\mathrm{x}64$(spanwisedirection)for$Re$$=3900$

.

Even though the base flows at $Re=40\sim 140$

are

tw0-dimensional, thecomputations

are

carried out in three dimension because of the distributed forcing applied in thespanwisedirection

数理解析研究所講究録 1285 巻 2002 年 84-91

Figure 1. SCHEMATICDIAGRAM OF THE EXPERIMENTALSET-UP.

Table1. FORCINGCASES.

Cylinder Sphere

Low-frequency Re=100&3900 $Re=3700$(NUM)

forcing (NUM)

High-frequency Re=100&3900 $Re=3700$ (NUM)

forcing (NUM) &10 (EXP)

Distributed $Re=40\sim 140$ $Re=425$ (NUM)

forcing

&3900

(NUM)

Here NUM and EXP denote the numerical and experimentalstudies,respectively.

Flow

over

aSphere

Flow

over

asphereisstudied at$Re=425$and

3700

usinganumerical method and

10

using

an

experimental

method,respectively.

For$Re=425$,theflowislaminar unsteady and thus

no

turbulencemodelisused. For$Re=3700$,large eddy

simulation with adynamic subgrid-scale model (Germanoetal. 1991;Lilly 1992)iscarriedout. The numerical method usedis based

on

anewly-developed immersed boundary method by Kimetal. (2001)with the second-order central difference scheme for the discretization of the spatial derivatives. The number of gridpointsusedfor

$Re=425$is$449\cross 161\cross 40$_,and that for_$Re=3700$is$577\cross 141\cross 40$_,respectively, in the streamwise,radial and

circumferentialdirections.

For $Re=10^{5}$_,

an

_{experimental study is conducted. Figure 1shows the schematic diagram of the present} experimental set-up, consistingof

an

open-type windtunnel, sphere, supporter, speaker, load cell andtraversing unit. The diameter of asphere is 150$\mathrm{m}\mathrm{m}$, and the free-stream velocity is 10 $\mathrm{m}/\mathrm{s}$

.

AtwO-dimensional slit of

0.65

mm

(about$0.5^{o}$) widthis located

on

the sphere surface at the angle of$76^{o}$from thestagnation point,which

is

an

upstream location ofthe separation line. Asupporter attached to the sphere base

is

linked to aspeaker chamber through latex. Then thespeaker induces atime-periodic blowingand

suction

ataspecified frequencyat the slit. Theforcing frequencies(/)applied

are

from 10Hz to370Hz by

increments

of10Hz,correspondingto

$S\mathrm{r}(=fd/u_{\infty})=0.15$ to 5.55by incrementsof0.15. For all thefrequencies, the maximumvelocityatthe slitis

tuned to be 1 $\mathrm{m}/\mathrm{s}$(10%of the free-streamvelocity).The drag

on

thesphereis directlymeasuredusingaload cell

(CassBCL-IL),and the velocity fieldismeasured with

an

in-ho

se

$\mathrm{x}$-typehot-wire probe and atw0-dimensional

traversing unitthat operates at variable horizontal angles. We also separately placeatripcomposed of two

0.5

$\mathrm{m}\mathrm{m}$-thick wires,respectively,at$55^{o}$and$60^{o}$toexaminetheeffect of trip

on

thedrag

$\frac{C_{D}}{C_{Dp}}$

Figure2. VARIATION OFTHEDRAG COEFFICIENTWITHTHEFORCINGFREQUENCY.

CONTROL

METHODS

The control methods usedin this study

are

explainedinthis section:

one

is atime-periodic forcing andthe otherisadistributed forcing. For atime-periodic forcing, the disturbanceisprovided to the base flow either from thefree-stream

or

from aslot

on

abluff-body(cylinder

or

sphere)surfacein afollowing

manner:

$\phi(t)=\mathrm{a}\sin(2\mathrm{y}\mathrm{c}f\mathrm{r})$, (1)

where$t$is thetime, $\alpha(=0.1u_{\infty})$ istheforcing amplitude and_$f$isthe forcing ffequency. The forcing frequency $f$ is selected to be either

near

the vortex-shedding frequency (low-frequency forcing)

or near

or

larger than the

frequency correspondingtotheshear-layer instability(high-frequency forcing).

For distributedforcing,thedisturbanceisprovided ffom

a

slotlocated

on

abluff-bodysurface:for acylinder

$\phi(z)=a\sin(2\pi\frac{z}{\lambda_{\mathrm{z}}})$ (2)

andfor asphere

$\phi(\Theta)=\alpha\sin(m9)$, (3)

where$z$isthespanwisedirectionof the cylinder,$\Theta$ isthe circumferential direction of the sphere,

$\lambda_{z}$isthe

wave-length of the forcing in the spanwisedirection,and$m$is

an

integer$(m =\mathrm{I},2, \cdots)$

.

RESULTS

Table1illustratestheforcing

cases

investigatedinthis study. In thebelow,

we

briefly describe the results ffom the controls listedin Table1.

With low- andhigh-frequency forcings appliedtotheflows

over

acylinder and asphere

were

notsuccessful

in producing drag reductionatlow Reynolds numbers$(<O(10^{4}))$_{because the low-ffequency forcingenhanced} the vortexsheddingandthehigh-frequency forcing increasedtheshear-layer instabilityafterflow separation. On

theotherhand,thehigh-frequency forcing appliedto theflow

over

asphereat$Re=10^{5}$_reducedthe

mean

_{drag by}

50%.Thisresult will bedescribed

in

more

details later

in

this

section.

The distributed forcing(spatiallyperiodic forcingin the spanwise direction)

was

applied to the flow

over

a

circularcylinder

as

shownin Table 1with varyingtheforcing wavelength. With thiscontrol,thedrag

was

signif-icantly reduced when the baseflowcontained vortexshedding(i.e. $Re\geq 47$). This result will also be presented

laterin this

section.

Unlikethe

case

ofcylinder,the

distributed

forcing appliedtotheflow

over

asphere slightly

increased the drag for$m=1,2$and3(Equation3). Thisdifferenceinthe control results between the

cases

of the

0.6

0.5

0.4

$C_{\mathit{0}}0.3$

0.2

0.1

0.0

Figure3. VARIATIONS OF THEDRAG COEFFICIENT DUETOACTIVE ANDPASSIVE DEVICES ASAFUNCTION OFTHE

REYNOLDS NUMBER:

.,

PRESENT STUDY; DIMPLE (GOLF BALL), BEARMAN AND HARVEY(1976); ROUGHNESS(K),

ACHENBACH(1974).

cylinder andsphere is mainly attributed to the

very

different vortical structures between two flows, indicating

a

significantdependence of the control method

on

the shape of abluff body.

In the below,

we

present the results from two successful controls appliedto the flows

over

asphere and

a

cylinder.

Flow

over

aSphere: High-Frequency Forcing

at

${\rm Re}=10^{5}$

Figure 2shows the variations of the drag coefficient$(C_{D})$with respecttotheforcing frequency in the absence

and

presence

oftrip. Here the dragcoefficient is normalized by that of the basic sphere(i.e. without forcing in the absenceoftrip;$C_{D,b}$) and$St=0$corresponds to the

case

of

no

forcing. The drag coefficient measured

on

the

basic sphere is about0.51,whichis in good agreement with the result of Achenbach(1972). In the absenceoftrip,

the drag abruptly decreases by about50% atacritical forcing frequency of$St_{c}(=f_{c}d/u_{\infty})=2.85$and becomes

nearly constant for$St>Stc$

.

Ontheotherhand,thedrag isreduced by30%inthe

presence

oftrip, but theforcing

does not reduce the drag further. Strikingly, the amount of drag reduction from the forcinginthe absence oftripis

larger than that from the forcinginthe

presence

oftrip. The

reason

for this will be explained laterinthissection. Figure3shows the variations of the dragcoefficient due to active andpassivedevices

as

afunction of the Reynolds number. It

was

shown in Achenbach(1974) thatwith surface roughness the drag coefficient rapidly decreases and then increases withincreasingReynoldsnumber, showing alocal minimum at acritical Reynolds number(Rec). This critical Reynolds number decreases with increasing roughness. Also, thedrag coefficient at$Re>Re_{c}$ increases

more

sharplyatlarger roughness andapproaches 0.4. On the otherhand, dimples reduce the dragcoefficient

even

atalower Reynolds number than surface roughness does(Bearmanand Harvey 1976).

After its decrease by dimples, the drag coefficientremains almost constantatabout 0.25. In the present study, fordifferent Reynoldsnumbers,

we

fix theforcingfrequencytobe$f=330$Hz($fd/u_{\infty}=4.95$at$Re=10^{5}$) and

theforcing amplitudetobe 1 $\mathrm{m}/\mathrm{s}$. Itis shown in Figure 3that the result of the present forcing is

very

similar to

that with dimples. Afteritsrapid decrease due to the present high-frequency forcing, the drag coefficientremains

almost constant at about

0.24.

Figure4shows thesurface-pressure distributionfordifferent forcing frequencies in the absence oftrip,

t0-getherwiththose for the basicsphereandinthe

presence

oftrip,and theinviscid

pressure

(denoted

as

‘theoretical’ in Figure4).Unlike thecylinder, the base

pressure

itself does not contribute to the drag

on

thesphere because the

area

atthe basepointis

zero.

Consideringthe area, the

pressures

at the anglesof$45^{o}$ and $135^{o}$contribute most tothe drag. At the forcing frequencies less than the critical forcing frequency($St<St_{c}=2.85$ ,the

pressures

on

the sphere

are

similar to that

on

the basic sphere, indicating negligible

or

smalldrag reduction at these forcing frequencies. On the otherhand, for the forcing frequencieslarger than$Stc$, the surface

pressures

are

nearly the

same as

the inviscid

pressure

for$\phi_{s}<135^{o}$, indicating thatasignificantamountof drag reduction should

occu

87

Figure 4. STATIC-PRESSURE DISTRIBUTIONON THE SPHERE SURFACE.

no

forcing forcing (St$=4.95)$ Figure5. OIL FLOW$\mathrm{P}\mathrm{A}\Pi \mathrm{E}\mathrm{R}\mathrm{N}$ON THE SPHERE SURFACE.

atthesehigh forcing frequencies. Interestingly,the

pressure

on

thetrippedsphere surface approaches that of the

very

high frequencyforcingat$\phi_{s}<120^{o}$butbecomes nearly the

same

in the downstream surface

as

that

on

the basicsphere. It shouldbementionedhere that there

exists

aplateauinthe

pressure

curve

around 1$10^{o}$for the high-frequency forcing

cases

$(St>2.85)$

.

This

pressure

pattern

is

very

similarto that observed

in

the critical

region

whereaseparation bubble

exists

on

the spheresurface (Achenbach 1974; Fage 1936; SuryanarayanaandMeier

1995; Taneda1978),suggesting

an

importantclue to the presentdrag-reduction mechanismby thehigh-frequency forcing.

Figure 5shows

an

oil flow visualization

on

the sphere. In the

case

of the basic sphere, separation

occurs

around $80^{o}$,whereas for the

case

of$St=4.95$ separation is delayed to

occur

at $105^{o}-110^{o}$, andthen the flow

reattaches to thesurfaceat1$10^{o}-115^{o}$_,forming aseparation bubble there. Second separation

occurs near

$130^{o}$for

$St=4.95$

.

Inthe

presence

oftrip(notshownhere),separationoccurred around$105^{o}$and

no

separationbubble

was

observed

near

the sphere surface. Achenbach(1974)_{indicated that the low drag coefficient in the critical region is}

duetotheexistenceof separationbubble: withaseparationbubble,reattachedflowhas highmomentum

near

the wall with large turbulenceintensityandthus delays secondseparation. The phenomenon occurredin the critical

regionof the basic sphereis

very

similar to the presentobservation,suggestingthatlarge dragreduction achieved for$St>St_{c}$isessentially due to theexistenceof theseparationbubble. Theexistence_ofseparation_bubble

was

also confirmed from the velocitymeasurement

near

thespheresurface(notshownhere).

Flow

over

aCircular Cylinder: Spatially Periodic Forcing

Figure6showstheschematic diagramof theforcing. Duetothefactthat theforcingis applied inthespanwise

direction, the controlled flowis three-dimensional

even

ifthe baseflowis tw0-dimensional. Therefore,for$Re$$\leq$

$140$_,the computational domainsize in_thespanwise_{directionissettobe the}

same

as

_{thewavelengthof theforcing.}

In the

case

ofturbulent flow$(Re =3900)$,the computational domain

size

ofthe controlled flow is the

same as

that

of the uncontrolled flow. In this study,

we

havetwodifferent types offorcing:

one

isthein-phase forcingand the

$\ln$-phase forcing

$D$

$\mathrm{o}\mathrm{u}\mathrm{t}\cdot \mathrm{o}\mathrm{f}$-phase forcing

(a) (b)

Figure6. SCHEMATIC DIAGRAM OF THE DISTRIBUTED FORCING:(a)SIDEVIEW; (b)FRONT VIEW.

$c_{D}$

$\lambda_{z}/d$

Figure7. EFFECT OF THE IN-PHASEFORCING ONTHE MEAN DRAG AT$Re=1\mathrm{O}\mathrm{O}$.

otheristheout-0f-phaseforcing(seeFigure6).

First, the in-phase forcingis appliedtotheflow

over

the cylinder at$Re=1\mathrm{O}\mathrm{O}$

.

Figure7showsthe variation

of the drag coefficient with respecttothe forcing wavelength$(\lambda_{z}=1\sim 10d)$

.

The drag isminimumat$\lambda_{z}\approx 5d$,

resulting in about20%drag reduction. We have also applied the in-phase forcingtotheflows at$Re=80$and 140.

Inthesecases,the minimum drag occurred at$\lambda_{z}\approx 6d$and$4d$,respectively, indicating that the optimum wavelength

of the forcing decreases withincreasingReynolds number. It isinteresting to notethattheoptimum wavelength issimilar to thespanwisewavelength of the mode-A instability(Williamson 1996). The

same

in-phase forcingis

appliedtotheflow at$Re=40$,where there

occurs

no

vortex shedding in the

case

of

no

forcing. In this case, there is nearly

no

change in the drag with the forcing,

even

though three dimensional flow structure

appears

in the wake due to the forcing.

Figure 8shows the variationof vortical structures at$Re=1\mathrm{O}\mathrm{O}$(using the vortex identification method by

Jeong andHussain 1995)with the forcing wavelength. Itisclear that at theoptimumwavelength$(\approx 5d)$the flow

becomescompletely steady. The

same

observation

was

made for$Re=80$

.

However, for$Re=140$,the vortical

structures

were

still unsteady

even

attheoptimum wavelength owingtothe strong vortexstrengthshedbehindthe

cylinderatthis Reynolds number.

Second,theout-0f-phaseforcing with $\lambda_{z}=5d$is appliedto the flow

over

the cylinder at$Re=1\mathrm{O}\mathrm{O}$

.

Figure

9

shows theinstantaneousvortical structures for theout-0f-phaseforcing. Unlike thein-phase forcing,theflowwith theout-0f-phaseforcing shows aclear vortex shedding, resultinginnearly

no

changeinthe drag

as

comparedto that of the baseflow.

Lastly, the in-phase and out-0f-phase forcings

are

applied tothe flow at$Re=3900$

.

Here the base flowis three-dimensionaland turbulent afterseparation. Thesizeof thecomputational domain inthe spanwise direction

is %d, and the forcing wavelength istaken to be the

same as

the domain size. Figure 10shows the variation of

$L_{\sim}=1d\mathrm{b}^{\mathrm{b}}\circ$ $O_{\Leftrightarrow}1$

Figure9. INSTANTANEOUSVORTICAL STRUCTURES FORTHEOUT-OF-PHASE FORCING$(\lambda_{z}=5d)$AT$Re$$=1\propto$).

$C_{D}$

$tu_{\infty}/d$

Figure10. VARIATIONOF THEDRAG COEFFICIENT DUETO THEDISTRIBUTED FORCINGAT$Re$_$=3900$

.

the dragcoefficientowingto theforcing. Surprisingly,the out-0f-phase forcing

as

well

as

the in-phase forcing

reduces the drag significantly. Instantaneousvortical structures for the base flow and flowswith theforcing

are

shownin Figure 11. Inthe

case

of theout-0f-phase forcing,the vorticalstructures

are

significantly changed

near

theseparationpointbutthoseinthefurther downstream

are

similartothoseof thebase flow. Ontheotherhand,

the in-phaseforcing drasticallychanges thevorticalstructures,showingalmost

no

vortexright behindthe cylinder andfurtherdelay of vortexsheddinginthedownstream.

CONCLUSION

In this

paper, we

presented_{the results ffom both the numerical and experimental studies}

_on

_active

_controlof

flows

over

circular cylinder and aspherefordrag reduction. The Reynolds number

range

consideredfor the flow

.

uncontrolled

.

in-phase forcing

Figure11. CHANGESINTHEINSTANTANEOUSVORTICALSTRUCTURES DUE TOTHEDISTRIBUTEDFORCINGAT$Re=$

3900.

over

acircularcylinder

was

100\sim 3900based

on

thefree-stream velocity and cylinderdiameter,whereasfor the flow

over

asphereit

was

$100\sim 10^{5}$ based

on

the free-stream velocityand sphere diameter. Theactive_control

methods investigated

were

(1)aforcing with alow frequency

near

the vortex sheddingfrequency; (2)aforcing

with ahigh frequency that is much largerthan the vortex shedding frequency; (3) adistributed (i.e.

spatially

varying)forcing. The control method(1)increased the

mean

drag and lift fluctuationsatallthe Reynolds numbers

investigated for both flows. The result of the control method (2), however, showed asignificant dependence

on

theReynolds number. For example, aforcing with ahigh frequency(largerthan20 timesthevortexshedding

frequency)produced50%_{drag reduction for the flow}

_over

_{asphere at}$Re=10^{5}$_{,butincreased the dragat}${\rm Re}=3700$

.

The control method(3)applied to the flow

over

acircular cylinder resultedinasignificant drag reduction for flow

over

acircularcylinderat allthe Reynolds numbers investigated, but did notreduce the dragfor the flow

over

asphere, mainly because of the

very

different vortical structures between the flows

over

asphere andacircular

cylinder,showing asignificantdependenceof the control method

on

theshape of abluffbody.

ACKNOWLEDGMENT

This work is supported by the Korean Ministry ofScience and Technology through the National Creative ResearchInitiatives.

REFERENCES

Achenbach,E.: Experiments

on

theflow past spheresatveryhigh Reynoldsnumbers.J. Fluid Mech.54,565

(1972).

Achenbach,E.: The effect of surface roughness and tunnel blockage

on

the flow pastspheres.J.Fluid Mech.

65, 113(1972).

Bearman,P. W.and Harvey, J. K.: Golf ball aerodynamics. Aeronautical Quarterly May, 112(1976).

Choi, H. andMoin, P.: Effects of the computational timestep

on

numerical solutionsofturbulent flow. J.

Comp. Phys. 113,1(1994).

Fage, A.: Experiments

on

asphere atcritical Reynolds numbers. Aero. ${\rm Res}$

.

Counc. R.

&M.

no.

1766,

(1936).

Germano, M., Piomelli, U., Moin,P. andCabot,W. H.: Adynamic subgrid-scale eddyviscositymodel. Phys.

FluidsA3, 1760(1995).

Jeong,J. andHussain,F: Ontheidentificationof avortex. J. Fluid Mech. 285,

69

(1995).

Kim, J., Kim, D. andChoi, H.: An immersed-boundary finite volume methodfor simulations of flow in

complex geometries.J.Comput.Phys. 171,

132

(2001).

Lilly, D. K.: Aproposed modification of the Germano subgrid-scale closure method. Phys. FluidsA4,

633

(1992).

Suryanarayana, G. K. andMeier,G. E. A.: Effect of ventilation

on

theflow field around asphere. Exp.Fluids

19,

78

(1995).

Taneda,S.: Visualobservationsof the flow past asphere at Reynolds number between

10

and 10.J. Fluid

Mech. 85, 187(1972).

Williamson,C. H. K.: Three-dimensional waketransition.J.Fluid Mech.328,345(1996)