Granular flow in static mixers by coupled DEM/CFD approach

Gra ular flo i stati i ers oupled DEM/CFD approa h

U i e sit of Belg ade, I stitute of Ge e al a d Ph si al Che ist , Belg ade, Se ia

U i e sit of Belg ade,La o ato fo The al E gi ee i g a d E e g , I stitute of Nu lea S ie es “Vi ča“, Belg ade, Se ia

U i e sit of Belg ade, Fa ult of Me ha i al E gi ee i g, Belg ade, Se ia U i e sit of No i Sad, Fa ult of Te h olog , No i Sad, Se ia

A st a t

The i i g p o ess g eatl i flue es the i i g effi ie , as ell as the ualit a d the p i e of the i te ediate a d/o the fi al p odu t. Stati i e is used fo p e i i g a tio

efo e the ai i i g p o ess, fo sig ifi a t edu tio of i i g ti e a d e e g o -su ptio . This t pe of p e i i g a tio is ot i estigated i detail i the ope lite atu e. I this a ti le, the o el u e i al app oa h alled Dis ete Ele e t Method is used fo

odelli g of g a ula flo i ultiple stati i e appli atio s – Ko a o Ross i i g ele e ts e e utilized , hile the Co putatio al Fluid D a i Method as hose fo fluid flo odelli g, usi g the Eule ia ultiphase odel. The ai ai of this a ti le is to p edi t the eha io of g a ules ei g g a itatio all t a spo ted i diffe e t i e o -figu atio a d to hoose the est o -figu atio of the i e taki g i to a ou t the total pa ti le path, the u e of i i g ele e ts a d the ualit of the o tai ed i tu e. The esults of the u e i al si ulatio s i the stati i e s e e o pa ed to e pe i e tal esults, the i i g ualit is e a i ed RSD elati e sta da d de iatio ite io , a d the effe ts o the i e t pe a d the u e of i i g ele e ts o i i g p o ess e e studied. The effe ts of the i e t pe a d the u e of i i g ele e ts o i i g p o-ess e e studied usi g a al sis of a ia e ANOVA . Mathe ati al odelli g is used fo opti izatio of u e of Ross a d Ko a seg e ts i i e i o de to gai desi a le

i i g esults.

Ke o ds: DEM/CFD, p edi tio , stati i e , Ko a , Ross, pa ti le t a ki g.

SCIENTIFIC PAPER

UDC : :

He . I d. –

doi: . /HEMIND P

A aila le o li e at the Jou al e site: http:// .a he.o g. s/HI/

Stati i e s a e lo e e g o su i g e uip e t due to the g a itatio al flo of the ate ial a d effi ie tl i i g de i es, that a ha dle a ide a ge of appli atio s. Detailed e ie o stati i e s, o

-e i g th-e -e ha is s, appli atio s, lassifi atio a d ha a te izatio ethods fo usi g o i i g p

o-ess a d ass t a sfe pe fo a e is gi e a ious esea he s [ – ]. The i i g p o ess is e o ple a d se siti e, a d it ust e opti all o figu ed. Too lo g i i g p o ess a ause defo atio of the pa ti les that a e i ed, to edu e the ualit of the i -tu e a d a also ause the i ease i the p i e of te h ologi al p o ess a d the fi al p odu t. The i i g p o ess is a esult of diffusio , o e tio a d shea , hi h a e the ai e ha is s of the ho oge izatio [ – ].

The p o le s elated to the opti izatio of the i i g p o esses a e o e o e usi g a athe-ati al odelli g. E pe i e ts a e usuall o ple a d e ui e o e fi a ial esou es. The odels a

Co espo de e: L. Pezo, U i e sit of Belg ade, I stitute of Ge e al a d Ph si al Che ist , Stude tski t g /V, Beog ad, Se ia. E- ail: latopezo@ ahoo. o.uk

Pape e ei ed: O to e , Pape a epted: O to e ,

d asti all edu e the e pi i al o k e essa fo p e-di ti g pa a ete s of the i i g p o ess.

Models ased o Dis ete Ele e t Method DEM ha e ee de eloped i the past a d sho to e eli-a le eli-a d effi ie t i eli-at hi g peli-a ti le i te eli-a tio s eli-a d p edi ti g i i g p o ess fo i estigatio of pa ti le i i g. The soft-sphe e ethod o igi all de eloped Cu dall a d St a k [ ], as the fi st g a ula d a i s si ulatio te h i ue pu lished i the ope lite atu e. The de eloped the li ea sp i g a d the dashpot odel he e the ag itude of the o al fo e et ee t o pa ti les as the su of sp i g fo e a d da pi g fo e. Lag a gia t a ki g te h i ues ha e ee used i a studies i o de to ha a te ize the i i g pe -fo a e i diffe e t s ste s [ – ]. A detailed e ie a d defi itio s of the ualit of a i tu e, the i i g e ha is s, the possi ilities fo the hoi e of solid i e , the e pe i e tal assess e t of ho oge eit a d i i g i de es a e p ese ted i Pou et al. [ ].

The fo us of this pape as to opti ize the geo-et a d to o pa e diffe e t stati i e de i es. Ko a a d Ross a e o e ial p odu ts, ith k o geo et , used idel i a ious a hes of i dust .

I this pape , e pe i e tal a d u e i al o pa -iso et ee a ious ultiple Ko a a d Ross i i g

o figu atio s has ee pe fo ed. The fluid is t eated as a o ti uu hile the solid phase is odelled usi g the DEM. The fluid ai elo it a d p essu e field a e o puted usi g the Co putatio al Fluid D a i CFD app oa h. I the DEM, pa ti le–pa ti le a d the pa ti le– all i te a tio s a e esol ed a d the ti e i teg atio is pe fo ed usi g Ne to ’s se o d la of otio . DEM odelli g gi es i fo atio a out pa -ti le-pa -ti le i te a -tio s, pa -ti le- all i te a -tio s, positio , elo it a d a ele atio of pa ti le a d fo es a ti g o the pa ti le. This i fo atio a e useful fo o st u tio a d desig of the i i g de i es. App op iate odelli g a o t i ute ette i -i g ual-it a d o e o e defe ts a d p o le s that

a o u du i g the i i g p o ess. The ualit of the i i g p o ess is a al sed usi g elati e sta da d de i-atio RSD ite ia [ ]. The effe ts of the i e t pe a d the u e of i i g ele e ts o i i g p o ess e e studied usi g a al sis of a ia e ANOVA . The ai ai of this stud as to de o st ate the use of DEM/CFD si ulatio oupli g i pla i g the u e of Ko a o Ross ele e ts i o de to gai desi a le

i i g esults.

MATERIALS AND METHODS Mathe ati al odel

This pape studies the flo i t o t pes of t isted- - lade stati i e s Ko a o Ross i i g ele e ts, li ked i a se ies of – pie es . It e aluates the i i g pe fo a e al ulati g the t aje to of suspe ded pa ti les th ough the i e . The athe ati al odel is sol ed i t o stages, fi st the fluid elo it a d p es-su e field a e dete i ed CFD, a d the , usi g a sepa ate stud , the pa ti le t aje to ies of the g a ula ate ials a e o puted DEM. The o se atio s of ass a d o e tu i te s of the lo al ea a i-a les o e i-a o puti-atio i-al ell i-a e gi e Ni-a ie – –Sto ks e uatio s [ ]:

(

)

(

)

(

)

(

)

( )

p F g

ρ ε

ρ ε

ετ ρ ε

∂

+ ∇ ⋅ =

∂

−∇ − + ∇ +

he e ε, u, t, ρf, p, Fp-f, τ a d g a e: po osit , ea fluid

elo it , ti e, fluid de sit , p essu e, olu et i fluid– –pa ti le i te a tio fo e, fluid is ous st ess te so , a d a ele atio due to g a it . Fluid pa ti le i te -a tio fo e is defi ed :

p-f p-f, ell i k i i F

V = ρ

=



he e Fp-f,i is the total fluid fo e o pa ti le i a d ki is

the u e of pa ti les i a CFD ell. The solid phase is t eated as a dis ete phase a d des i ed the so- alled DEM [ ]. A o di g to this odel, the t a s-latio al a d otatio al otio s of a pa ti le at a ti e t, a e des i ed Ne to ’s la of otio :

(

)

p-f, , d, d

d

i k i

i i ij ij i

j

f f f g

t = +



a d

(

)

i ij ij

j

I T M

t

ω

=

=



he e i, Ii, i a d ωi a e: the ass, o e t of i e tia,

t a slatio al a d otatio al elo ities of pa ti le i, es-pe ti el . The fluid flo field a e o tai ed sol-i g E s. use of a sta da d CFD ethod. The pa ti le eha iou a e o tai ed sol i g E . a e pli it ti e i teg atio ethod.

The odelli g te h i ue is ased o the assu p-tio that the pa ti le is soft soft pa ti le ethod , a d that pa ti les a e allo ed to o e lap [ ]. The a ou t of o e lap is la elled as Δ , a d the o al a d ta ge tial

elati e elo ities dete i e the ollisio fo es F a d Ft, ased o the Kel i –Voigt odel [ , ]. Figu e

illust ates the ollisio fo e as the esult of o al a d ta ge tial fo es. The o al fo e F is o side ed as the epulsi e fo e that pushes the pa ti les apa t o pa ti le f o ou di g geo et , depi ted as the a t-io of the sp i g, a d also dissipatt-io a tt-io , esulti g i a effe ti e oeffi ie t of estitutio , sho as dash-pot a tio . Ta ge tial o po e t is o side ed as a i e e ti g sp i g a tio a d dashpot a tio that is su je t to f i tio al li its.

Figu e . Kel i –Voigt o ta t odel.

(

)

ij ij

F = −kδ −η a d

(

)

ij

t t s

ij ij

F = −kδ −η The odelli g of the fluid flo CFD is pe fo ed at the o putatio al ell le el, hilst the odelli g of the solids flo DEM is a o plished at the i di -idual pa ti le le el. Coupli g DEM a d CFD is a hie ed as follo s: DEM gi es i fo atio a out positio s a d elo ities of i di idual pa ti les at ea h ti e step, fo the e aluatio of po osit a d olu et i fluid–pa ti les i te a tio fo e i a o putatio al ell. I o po atio of the esulti g fo es i to DEM ill p odu e i fo -atio a out the otio of i di idual pa ti le fo the

e t ti e step [ ].

E peri e tal ethod

The e pe i e tal appa atus as spe iall desig ed fo this stud , usi g t a spa e t Ple iglass o sisted of th ee seg e ts Ross a d Ko a o figu atio s , Fig. a. The uppe seg e t of the i e a ked ith is di ided i to the t o o pa t e ts ith a a ie a d a o ile pa el. Sphe i al pai ted s theti zeolite A g a ules app o . . a e pla ed i oth o pa

t-e ts, t-ed g a ult-es i tht-e fi st o pa t t-e t a d lut-e g a ules i the se o d o pa t e t. The ha a te -isti s of the zeolite g a ules a e gi e i the lite atu e [ ]. This o pa t e t is used o l fo the i itial sep-a sep-atio of the g sep-a ules efo e the p e i i g. The fi st a d last o pa t e ts a e used to olle t the g a ules efo e a d afte the p e i i g is do e. These o pa

t-e ts a t-e also adt-e of t a spa t-e t plt-e iglass ith a

height of . The se o d o pa t e t is a p e i -i g de -i e, -ith seg e ts a ked as , a d , ea h ith a height of , a d the outlet dia ete of . The seg e ts a e o e ted i the a that the outlet of the fi st ightha ded seg e t is o

-e t-ed ith s-e o d, l-eft-ha d-ed s-eg -e t, at a a gl-e of deg ees elati e to the e ti al a is, Fig. –d. Figu e sho s the o pute odel of Ross i e .

Fig. p ese ts the spe ial desig of the Ko a stati i e used fo this e pe i e t. It o sists of th ee i i g ele e ts, t o ight-ha ded Ko a

seg-e ts a d o seg-e lseg-eft-ha dseg-ed Ko a sseg-eg seg-e t. Thseg-e seg-elseg-e- ele-e ts a ele-e adele-e of hitele-e plasti ABS , i thi k ele-ess of . , usi g a D p i ti g de i e Cu eP o T io, used fo apid p otot pi g . The tu e i hi h the

seg-e ts a seg-e pla seg-ed is adseg-e of t a spa e t ple i-glass. Afte passi g th ough th ee seg e ts of the stati i e , g a ules fall at the otto of the lo e o -pa t e t of the p e i e .

Fig. d p ese ts the o pute odel of Ko a i e . Fig. e sho s Ko a i i g ele e t a d Fig. f p ese ts Ross i i g ele e t o pute odel. These

o pute odels e e used i u e i al si ulatio . The o ditio s u de hi h the e pe i e ts e e o du ted a e the sa e as i the u e i al si ulatio o ditio s.

Nu eri al odel

Nu e i al e aluatio s e e pe fo ed fo o s-e s-ed Ross a d Ko a stati i s-e o figu atio s. Ths-e

a) b) c) d)

e)

f) 0

1

2

3

4

fi st seg e t of the i e is filled ith , sphe i al pa ti les, dia ete . . The i let o pa t e t filled ith , ed pa ti les a d a se o d o pa

t-e t fillt-ed ith , lue pa ti les, outlet-p essu e outlet at osphe i p essu e a d all – the othe side of the i e a d the lades of the i e Fig. a . No slip o ditio is adopted at the all. The adia ati o -ditio s at the alls a e applied. It is assu ed that the su fa e ough ess is ideal ith f esh su fa e. The i f-lue e of the g a it is take i to a ou t a d it ep-ese ts the fo e hi h leads the pa ti les to the ot-to . The de sit of the pa ti les eleased is o alized to the ag itude of the fluid elo it at the i let. This ea s that the e a e o e pa ti les eleased he e the i let elo it is highest. It is assu ed that the gas ai elo it is lose to ze o, a d the i pa t of fluid o pa ti le o e e t is i i al. Pa ti le de sit as kg/ , fluid de sit as . kg/ , is osit . × –

kg/ s, pa ti le f i tio oeffi ie t as . , You g’s odulus as , Poisso ’s atio of pa ti les as . , hile CFD ti e step as × – s a d DEM ti e step

as × – s.

The set of ala e e uatio s E . – is sol ed usi g the o t ol olu e ased fi ite diffe e e ethod. Se i I pli it Method fo P essu e-Li ked E uatio s SIMPLE u e i al ethod is used fo

sol-i g p essu e- o e tsol-io e uatsol-io f o the o e tu a d ass ala e e uatio s [ ]. The ele e ts used i u e i al esh a e tet ahed al a d size of a ele e t is less tha – _{. A dis etizatio of pa tial diffe}

-e tial -e uatio s is a i-ed out th-ei i t-eg atio o -e o t ol olu es of asi a d stagge ed g ids. The o -e tio t-e s a -e app o i at-ed ith up i d fi it-e diffe e es, hile diffusio a d sou e te s a e app o -i ated -ith e t al d-iffe e es [ ]. The al ulat-io e o fo e e ala e e uatio a d e e o t ol ol-u e is kept ithi li its of – _{ite ati e solutio of}

sets of li ea alge ai e uatio s. CFD ti e step is te ti es la ge tha the DEM ti e step. The DEM ti e step is li ited the atu al os illatio pe iod of sp i g- ass s ste used to odel o ta ti g pa ti les. It should satisf the follo i g e uatio is pa ti le

ass a d k is stiff ess oeffi ie t :

DEM t

k

π

Δ ≤

Colour i age a al sis

I o de to he k the ualit of the i i g p o ess, usi g RSD ite ia, olou i age a al sis is pe fo ed. Colou i ages of e pe i e tal a d o pute si ul-atio esults e e aptu ed a So Po e Shot A ,

hi h is a o o digital a e a fo ho e use. The a o fu tio of the digital a e a has ee used, to o e a s e e a ea of app o i atel Ø . Sa ples e e pla ed o a hite pape apki set o a flat hite

pai ted su fa e, i side the losed ha e ,

elo the digital a e a. Pape apki s e e used i o de to a oid u desi ed efle tio effe ts f o ha

-e ’s alls. With this s-etup, it as possi l-e to aptu -e i ages ith egligi le shado s a d ithout spe ula

efle tio s.

Respo se surfa e ethodolog

The RSM ethod as sele ted to esti ate the ai effe t of the p o ess a ia les o the i i g p o ess. The i depe de t a ia les e e the t pe of the i i g ele e t Ross o Ko a a d the u e of ele e ts – , a d the depe de t a ia le o se ed as RSD ite ia. A odel as fitted to the espo se su fa e ge e ated the e pe i e t. The odel used as a fu tio of the a ia les:

i i ii i

i i

Y β βX β X β X X

= =

= +





he e: β a e o sta t eg essio oeffi ie ts.

A al sis of a ia e ANOVA a d espo se su fa e eg essio ethod RSM e e pe fo ed usi g Stat-Soft Statisti a, fo Wi do s, e . , p og a .

RESULTS AND DISCUSSIONS

The esults of the DEM/CFD si ulatio a e o -pa ed ith e pe i e tal esults. The e ha i al p o-pe ties of zeolite g a ules a e take f o [ ]. CFD

odelli g is used to dete i e the fluid elo it field a d the p essu e field, a d DEM is used fo dete

-i -i g the pa t-i le eha -iou a d pa t-i le t aje to -ies du i g the i i g p o ess. I the follo i g, e o side t o diffe e t ep ese tati e ases , a d -seg e t Ross ele e t o figu atio a d , a d -seg e t Ko a ele e ts o figu atio . The elo it a d the p essu e field of the fluid phase e e o tai ed ia CFD al ulatio s, as ell as pa ti le t aje to ies, Fig. a–f p ese ts the i i g esults, pe fo ed ith th

ee-seg-e tee-seg-ed Ross a d Ko a o figu atio . Fig. a–d ee-seg-efee-seg-e to the fluid phase. The i flue e of fluid phase o pa -ti le eha iou a e sig ifi a t, espe iall i the ase of fo ed o tu ule t flo . Fluid phase a i flue e the elo it a d a ele atio of the pa ti les a d that a affe t o the t aje to of the pa ti les a d fo es a ti g o the pa ti les.

Fig. e a d f sho the t aje to of , pa ti les th ough o e pass of the i e . Pa ti le t aje to has i flue e o the i i g ualit . Opti al p olo gi g of the t aje to o t i utes ette ho oge eit of the

i tu e [ ].

-ti le a e sho o Fig. – t aje to , elo it a d a ele atio i , a d z di e tio of o e pa ti le du i g the i i g p o ess i side the Ko a i e . The positio of the ep ese tati e pa ti le is d a ati all ha ged ithi the i e , ith sig ifi a t tu -o e s i pa ti le el-o it a d a ele ati-o , hi h g eatl

o t i utes to the possi ilit of i eased i i g ual-it [ ].

O e all pa ti le t aje to fo th ee-seg e ted Ko a a d Ross o figu atio s, gai ed u e i al si ulatio s e e: a d , espe ti el .

I this o k, RSD as used to follo the e olutio of i i g u ifo it fo the stati i e s ith diffe e t

o figu atio s, e plai ed a o e, [ ]:

RSD= σ ,

₍

₎

M i i

M

σ −

=

=



he e M is the u e of sa ples, ithe o e

-t a-tio of sa ple i, a d -the a e age o e -t a-tio of all sa ples. Fo i sta e, o e t atio of ed pa ti les i a sa ple is al ulated as the atio of the u e of

ed pa ti les a d the total u e of pa ti les.

The esults of u e i al si ulatio s of i i g p o-esses i Ross a d Ko a i e s a e p ese ted o Fig.

. The i i g p o ess egi s afte pa ti les lea e the uppe seg e t a ked as , Fig. a, as soo as the o ile pa el is e o ed, e a li g the g a ules to fall to a d the stati i e . The pa ti les a e apidl le ded i the fi st se tio , as see f o the figu e, ea hi g the i i g deg ee of – % at the outlet. Be ause of the t isted su fa e geo et , Ko a i -i g ele e t sho s ette -i -i g esults -i th-is se t-io

– % o pa ed to Ross – % . Pa ti le elo-ities a e g eate i Ko a i e , espe iall et ee seg e t a d , as see f o Fig. . Both i e s sho s o e effe ti e i i g afte se o d a d thi d se tio . Ko a i i g ele e ts ea hes the i i g deg ee of – % a d – % at the outlets, hile the i i g ualit of – % a d – % e e o tai ed at the outlets of se tio a d , usi g Ross ele e ts. This is e pe ted, e ause of the highe pa ti le elo ities i the Ko a i e . The s all, ut stead de ease i the i i g deg ee as o se ed fo oth Ko a a d Ross le di g ele e ts du i g DEM/CFD si ulatio , Fig. afte seg e t . This is due to e t ifugal fo e affe ti g the ottio of g a ules that e tit the ti ti g o -pa t e t. The use of the uad ati g id di ide ould e a le the i i g deg ee to e ai o sta t afte g

a-ules left the thi d i i g ele e t.`

-2 -1 0 1 2 3

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

-0.2 -0.1 0.0 0.1 0.2

0.3 _{x y z}

-20 -10 0 10 20 30 40 50 60

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

x y z

x y z

Time (s)

a)

b)

c)

Po

si

tio

n

(m

)

V

el

oc

ity

(m

/s

)

A

cce

le

rat

io

n

(m

/s

)

2

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Figu e . T aje to , elo it a d a ele atio i , a d z di e tio of o e pa ti le du i g i i g p o ess i Ko a i e .

0.0 0.1 0.2 0.3 0.4 0.5 0.6

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Target

Pr

ed

ic

te

d

RSD Komax

Ross

Ta le sho s the i flue es of p o ess a ia les o o se ed espo se, fo u e i al si ulatio of i i g i Ross a d Ko a i e s. The a al sis e ealed that the li ea te s of oth a ia les o t i uted su sta tiall to ge e ate a sig ifi a t SOP odel. The i flue e of i i g ele e t t pe MET as sig ifi a t i SOP odel, statisti all sig ifi a t at p< . le el, hile the i flue e of the u e of ele e ts NE as the ost i po ta t i the SOP odel al ulatio p< . . The uad ati te of NE as also e i flue tial statisti all sig ifi a t at p< . le el , as

ell as the i te ha ge te MET × NE p< . .

Ta le . A al sis of a ia e ANOVA fo e pe i e tal a d u e i al esults i Ross a d Ko a i e s; +_{sig ifi a t at} p < . le el, **_{sig ifi a t at p < . le el, MET – i i g} ele e t t pe, NE– u e of i i g ele e ts, df – deg ees of f eedo , SoS – su of s ua es, F – F test

df SoS F p

MET . ** _{. .}

NE . + _{. < .}

NE . + _{. < .}

MET×NE . ** . .

E o .

.

A high is i di ati e that the a iatio as a ou ted a d that the data fitted satisfa to il to the p oposed odel. The alue as fou d e satisfa -to a d sho ed the good fit of the odel -to e

pe-i e tal esults.

CONCLUSION

Coupled DEM/CFD app oa h as used to i es-tigate e ha is s of fluid flo a d pa ti le t a ki g fo g a ula flo . I the DEM, pa ti le–pa ti le a d the pa ti le– all i te a tio s a e esol ed a d the ti e i teg atio is a ied out usi g Ne to 's se o d la of otio . Mi tu e odel as used i CFD a al sis fo the dete i atio of the ha a te isti s of the fluid phase. DEM a al sis as used to dete i e the pa ti le t aje -to ies a d the his-to of pa ti le positio s i o de -to dete i e the ualit of the i tu e. The i i g ual-it as esti ated a i i g ual-ite io , a ed RSD

elati e sta da d de iatio . The effe ts of the i e t pe a d the u e of i i g ele e ts o i i g p o ess e e studied usi g a al sis of a ia e ANOVA . The ai of this stud is to p edi t the eha iou of g a ules i diffe e t i e o figu atio a d to

opti-ize the u e of i i g ele e ts taki g i to a ou t the p i e of the fi al p odu t, the du atio of the i i g p o ess a d the ualit of the i tu e. It is o ious that the i e ased o Ko a ele e ts e a les ette i i g ualit , o pa ed to Ross,

espe-iall he the height of i stallatio is lo . Ho e e , the use of Ross is o e fi a iall a epta le, due to its si ple geo et . A o di g to the esults, the u e of i i g ele e ts is o e i flue tial pa a ete tha the t pe of i i g ele e ts. It see s that this t pe of de i e a e used o l as p e i i g de i e a d addi-tio al i e is e essa to gai the good ualit of the

i tu e. Ho e e , the p e i i g p o ess a o t i-ute ette ualit of the i tu e a d a sig ifi a tl edu e the i i g ti e a d the ost of the i i g p o-ess.

A k o ledge e ts

This o k as suppo ted the Mi ist of Edu-atio , S ie e a d Te h ologi al De elop e t of the Repu li of Se ia, g a t No. TR .

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IZVOD

PROTOK GRANULISANOG MATERIJALA U STATIČKOJ MEŠALICI – DEM/CFD PRISTUP

Lato Pezo , Milada Pezo , A a Jo a o ić , Ne ad Kosa ić , Aleksa da Pet o ić , Lju i ko Le ić U i e zitet u Beog adu, I stitut za opštu i fizičku he iju, Stude tski t g /V, Beog ad, S ija

U i e zitet u Beog adu, I stitut za uklea e auke Vi ča, La o ato ija za te oteh iku i e e getiku, p. p . , Beog ad, S ija

U i e zitet u Beog adu, Maši ski fakultet, K alji e Ma ije , Beog ad, S ija

U i e zitet u No o Sadu, Teh ološki fakultet, Bule a Ca a Laza a , No i Sad, S ija

Nauč i ad

P o es eša ja eo a utiče a k alitet k aj jeg polup oiz oda i/ili k aj jeg p oiz oda, a pa a et i p o esa eša ja i dizaj op e e eo a utiču a efikas-ost eša ja, k alitet p oiz oda i e u p oiz oda. U o o adu, p ikaza a je upo-t e a eupo-tode disk eupo-t ih ele e aupo-ta e gl. Dis eupo-te Ele e upo-t Meupo-thod – DEM a

odelo a je eša ja g a ula u azličiti ko figu a ija a statičkih ešača ko iš-će e su azličite Ko a i Ross ko figu a ije za eša je . Za odelo a je p otoka fluida p i e je a je etoda u e ičke eha ike fluida e gl. Co putatio al Fluid D a i – CFD , ko išće je Ojle o og d ofaz og odela. Po ezi a je ezultata o e d e etode do ijaja se pouzda , do olj o tača i adek ata odel koji daje ezultate koji odgo a aju ekspe i e tal i e e ji a. Statičke ešali e se ši oko ko iste u i dustiji p e ade h a e, fa a eutskoj ili he ijskoj i dust iji. O aj tip ešali e se ko isti ugla o kao p ed ešač, p e gla og eša ja, p i če u se z ačaj o s a juje e e eša ja i štedi e e gija. O a sta eša ja ije do olj o ispiti a a u lite atu i. K alitet eša ja g a ula zeolita u o o adu je ispiti a do o poz ati k ite iju o za k alitet eša ja, pod azi o elati a sta da d a de ija ija. Uti aj tipa ešali e i oja ele e ata za eša je ispiti a i su a alizo a ija se ANOVA . Cilj o og ada je io da se p ed idi po aša je g a ulisa og ate ijala u azličiti ko figu a ija a ešali a i da se opti izuju pa a et i p o esa uzi ajući u o zi t aja je p o esa eša ja, k alitet eša i e i e u fi al og p oiz oda. Za pot e e o og ada, ap a lje e su statičke ešali e tipa Ross i Ko a od p o id og pleksiglasa, dizaj i a e u CAD paketu, ap a lje e ko išće je CNC glodali e. Pošto su ap a lje i ele e ti ili p ozi i, p aće je p o esa eša ja g a ula je ilo i izuel o P aće e su i a alizi a e t ajekto ije,

zi e i u za ja česti a, u ilju p o e e k aliteta p o esa eša ja. Do o poz ati k ite iju za k alitet eša ja, pod azi o elati a sta da d a de ija ija RSD je ko išće za o u s hu. Opti iza ija di e zija i pa a eta a eša ja u statičkoj

ešali i je iz ede a ko išće je ate atičkog odeli a ja. Cilj o og ada je io da se p ed idi po aša je g a ula og ate ijala u azličiti ko figu a ija a ešali a i da opti izuje pa a et e p o esa uzi ajući u o zi t aja je p o esa eša ja, k alitet eša i e i e u fi al og p oiz oda eša ja. U ist aži a ju je p i eće o da su Ko a ele e ti p i e lji iji, u po eđe ju sa Ross ele e ti a, pose o kada je isi a i stala ije ala. Međuti , upot e a Ross je fi a sijski p i-h atlji ija, z og jego e jed osta ije geo et ije. Dodat i p eg ada sa k ad-at i ot o i a, koja se posta lja a izlazu iz stad-atičke ešali e, ko isti se da i se u i ilo k eta je g a ula a o odu e i, kao i da s a ji seg ega ija g a ula.

Ključ e eči: DEM/CFD • Statički ikse •