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VORTEX RINGS IN A HELE-SHAW CELL. NUMERICALSIMULATIONS AND EXPERIMENTS

TEFAN - MUGUR SIMIONESCU- PhD. Student, "Politehnica" University of Bucharest, Romania, ReoromLaboratory, Faculty of Poer !nineerin, e-mail# stefan$simionescu%yahoo.com

CONSTANTIN - RZVAN ANTON- Student, "Politehnica" University of Bucharest, Romania, ReoromLaboratory, Faculty of Poer !nineerin

NICOLETA - OCTAVIA TNASE- &ssistant, PhD, "Politehnica" University of Bucharest, Romania, ReoromLaboratory, Faculty of Poer !nineerin

Abstrat!'his study is focused on the numerical simulations reardin vorte( rins formationin a )ele-Sha cell, due to the im*inin ater +et on a smooth obstacle. e investiated thetime evolution of the vorte( rin and its im*act on the surface. 'he all shear stress and*ressure distribution ra*hics on the solid *late ere com*uted too. For the validation of the

numerical results, an e(*erimental setu* as realied, consistin of a lass-made )ele-Sha

cell ith a mm a*, immersed in a ater tan/. 'he e(*eriment as *erformed by the in+ectionith a constant rate of dyed ater throuh a needle in the )ele-Sha cell. Flo characteristics#needle inner diameter 0 mm1 Reynolds number 0221 ambient fluid# ater1 im*ined fluid# dyedater.

"#$%&r's!Reynolds number, all shear stress, solid interface, mesh.

(. I)tr&'*t+&)

3orte( rins are one of the fundamental *henomena that have been studied intensely by many authors,

startin ith ). )elmholt, u* to noadays scientists. 3ortical motions are characteriin almost all

*henomena of fluid mechanics, startin ith hurricanes, ty*hoons and tornadoes and oin to the

hirl*ools in /itchen and bathroom sin/s 40-56.

3orte( rins are *articular vortical flos, hich are characteried by the im*inin +et of one fluid in

another fluid in an o*en atmos*here or closed eometry 47-86.

9n literature, the most re*resentative studied cases are the folloin# :i; vorte( rin is formed usin the

same fluid for the im*inin +et and as ambient fluid1 :ii; the e+ected fluid is more dense then the

ambient one, ith in+ection from the to* or the bottom of the tan/ and :iii; the case here the e+ected

fluid is less dense than the ambient one, and usually in+ected from the bottom of the tan/.

&lmost all the *revious studies ere focused on vorte( rins eneration by immersed +ets usin the

same li

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,. N*#r+a s+*at+&)s a)' r#s*ts

'o achieve the numerical calculation usin the Fluent code, a eometry that re*roduces the actual flo

as built :Fiure 0; and then a discretiation of the domain into a s*atial rid :"mesh"; consistin of

finite elements as used.

'he construction of the eometry and the mesh of the flo field have a reat influence on the obtained

results. For the *resent study, the construction of the flo field and its mesh ere carried out usin the*re-*rocessor =ambit .>, hich *rovides a common set of ?&D functions for creatin fields, and

features im*lemented s*ecifically for ra*id creation of *redefined and structured@unstructured

eometries and meshes.

'he time evolution of the ater +et and the vorte( rin formation ere folloed usin the 3iscous -

laminar model of &nsys-Fluent. 'his model can be used for lo Reynolds numbers, such as the

current case.

Fi. 0. )ele-Sha cell eometry and dimensions. a; e(*erimental1 b; numerical com*uted domain and mesh

9n the studied case, the flo domain as divided into to areas, for a sim*lification of the meshin

*rocess# the needle and the actual )ele-Sha cell. 'he flo field mesh as built usin s-bit com*uter ith Dual .55 =) *rocessor and 05 =B R& memory.

'he numerical simulations ere *erformed ith laminar model and unsteady solver. For the model

discretiation, the S9PL! scheme as em*loyed for *ressure-velocity cou*lin, AU9? for the

momentum and the trans*ort e

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Table 1

F&% &)'+t+&)s /&r )*#r+a s+*at+&)s

Go.

4-6

v4m@s6

Q4m@s6

Q4ml@min

6

d4mm6

4/@m6

4PaHs6

0 2 2.2 0.E70 e-C 2.8> 0 0222 02-

E2 2.2E .87 e-C .E5 0 0222 02-

022 2.0 7.CE> e-C >.70 0 0222 02-

> 22 2. 0E.72C e-C 8.>> 0 0222 02-

Fi. . Gumerical or/in domain, )ele-Sha cell boundary conditions

9n Fiure the stream lines s*ectrum for the flo in the )ele-Sha cell are *resented.

Fi. . Stream lines in the flo domain for various Reynolds numbers

'he *ressure distribution alon the 02 cm lon u**er all of the obstacle as studied for each of the

four numerical cases studied. & ra*h as com*uted :Fiure > a;, shoin the *ressure to *osition on

the obstacle. For Reynolds numbers less or e

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Fi. >. Pressure :a; and all shear stress :b; distribution on obstacleIs u**er surface

'he *ressure has a ma(imum in the im*act *oint of the +et, hile on the rest of the obstacle surface it

varies beteen *ositive and neative values.

0. E12#r+#)ta s#t-*2

'he e(*eriments are conducted in the horiontal )ele-Sha cell s/etched in Fiure 0 a;. 'o lass

*lates of C cm lon and .E cm ide are held toether by clam*s hich are reularly s*aced in order

to maintain a uniform a*. 'he a* thic/ness is fi(ed by aluminum shims : cm ide;, mm thic/,

*laced beteen the *lates at three borders. e immerse the cell horiontally in a ater tan/ ith 52

cm lenth, 2 cm idth and 5 cm de*th. 'he e(*eriment as *erformed by the in+ection ith a

constant rate of dyed ater, throuh a needle ith 0 mm inner diameter, in the )ele-Sha cell. & P)D

Ultra >>22 Syrine Pum* as used, hich maintained a constant iven florate. 'he e(*erimental

setu* is *resented in Fiure E.

Fi. E. !(*erimental setu*# &. Sony ?amera J !dmund K*tics 3 0222i Kb+ective1 B. liht source,?. )ele-Sha cell > ( 7 cm1 D. ater tan/ 52 ( 2 cm1 !. P)D Ultra >>22 Syrine Pum*

a; b;

Pressure(Pa)

Obstacle Length (m)

-0,06 -0,04 -0,02 0,00 0,02 0,04 0,06

-2

-1

0

1

2

3

4

5

6

7

8

9

Re20

Re50

Re100

Re200

-0,06 -0,04 -0,02 0,00 0,02 0,04 0,06

-0,375

-0,300

-0,225

-0,150

-0,075

0,000

0,075

0,150

0,225

0,300

0,375Re20

Re50

Re100

Re200

all!h

ear!tress(Pa)

Obstacle Length (m)

A

3

ED

C

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'he same fluid, ater, as chosen for the e(*erimental study. 'he Reynolds number for the

e(*eriment as =100 , the same ith one of the studied numerical cases. 'o ty*es of dye ere

used# food colorin :red; and methylene blue, see fi. 5 a and b.

&fter *erformin one set of e(*eriments of im*inin +ets throuh the )ele-Sha cell, e observed

the results and the corres*ondent numerical simulation. By

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R#/#r#)#s

406 3. 3. elesh/o, &. &. =our+ii, '. S. rasno*ols/aya, O3orte( rins# history and state of the art, Qournal

of athematical Sciences, vol. >, Go. 5, December 20.

46 R.Q. an, & in-eun La., !.!. &dams, K. B. Friner, OBuoyant formation number of a startinbuoyant +et, 'heoretical Physics of Fluids, 228.

46 ?. Palacios M orales, R. enit, O3orte( rin formation for Re numbers, &cta ech >, C M 87,20.

4>6 &li B. Klcay, Paul S. rueer, Oomentum evolution of e+ected and entrained fluid durin laminatvorte( rin formation, 'heor. ?om*ut. Fluid Dyn., 202.

4E6 ?. . &tta, !. Q. )o*finer, O3orte( Rin 9nstability and ?olla*se in a Stably Stratified Fluid,!(*eriments in Fluids7, 087 M 22, 08C8.

456 . Diedic, ). Q. Leutheusser, O&n e(*erimental study of viscous rins, !(*eriments in Fluids 0,

0E - >, 0885.476 Bond D., Qohari )., "9m*act of buoyancy on vorte( rin develo*ment in the near field", !(*eriments in

Fluids, 202.

4C6 &/hmetov D. =., OFormation and basic *arameters of vorte( rins , Qournal of &**lied echanics and'echnical Physics, vol. >, Go. E, 220.

486 a(orthy '., "Some e(*erimental studies of vorte( rins", Qournal od Fluid echanics, vol. C0, *art., 0877.

4026Gastase 9, eslem &, O3orte( Dynamics and !ntrainment echanism in Lo Reynolds Krifice Qets,Qournal of 3isualiation, vol. 00, Go. >, 22C.