effect on em cells

8/11/2019 Effect on EM cells

1/9

Pergamon

Chemi al Engineering Sctence. Vol. 52. Nos. 21.'22, pp. 3843 3851. 1997

, 1997 Elsevier Science Ltd. All rights reserved

Printed in Great

Britain

P I I : S0009-2509(97)00090-0 ooo9 2509.'97 $17.00 + 0.(~

Effect s o f baf f le des ign on the l iqu id mix ing

in an aerated s t irred tank wi th s tandard

Rushton turb ine impe l l er s

Wei-Ming Lu,* Hong-Zhang Wu a nd Ming-Ying Ju

De par tm ent o f Chem ica l Enginee r ing , Na t iona l Ta iw an U nive r s i ty , Ta ipe i , Ta iw an 10617,

R.O .C.

(Accepted 1 Ju ly 1997)

Abstract-

Th e ef fects of width and nu m be r of baf fles in mec hanica l ly agi ta ted vesse ls wi th

s tand a rd Ru sh ton tu rb ine impe l le rs a r e exam ined fo r sys tems w i th and w i thou t ae r a t i on . The

inse r t ion o f the appro pr i a te num ber o f baf fles c lea r ly imp roves the ex ten t o f li qu id mixing .

How eve r , excess ive ba f f li ng (i .e . nb > 8 o r

B / T

>0.2) and spa rg ing gas th rough the impe l le r

would in te r rup t l i qu id mixing and leng then the mixing time. Th i s s tudy found tha t spa rg ing gas

th ro ugh the impe l le r le ads to an inc r ea se in the mixing time o f mo re than 20% because i t

r educes the l iqu id pu mp ing capac i ty o f the impel le r. A numer i ca l t e chn iq ue was appl i ed to

exam ine the same e f fec t on seve ra l ex t r eme ba ff le con d i t i ons an d the ca se s o f h ighe r ga s f low

ra te s and ro ta t i ona l speeds . To gene ra l i ze our r e su l t s ob ta ined , the numer i ca l t e chn ique was

appl i ed to s imula te fo r a sys tem w i th t r ip le impe ller s. The t r ends o f the m ixing t ime w ere found

to be ve ry s imi lar to the s ing le impe l le r sys tem. By cor r e la t i ng the m ixing t ime w i th nb ,

B / T ,

Q0 and N , the fo l lowing cor r e la t i on i s ob ta ined fo r the sys tem wi th s ing le Rush ton tu rb ine

impe l le r unde r non-gassed and ae r a ted sys tems .

N t M = 5 5 . 7 ( n b ) - o . 3 o ( B / T

)- o.1 s35

( Q g / N D 3 ) 2 9 6

and the s imi la r co r r e la t i on fo r the t r i p le impe l le r sys tem can be g iven a s

N t M

= 46.5(nb)- o

29 5(B /T ) - o.327(Qg/ND3)O.OlO

( 1997 Elsevier Science Ltd.

K e y w o r d s :

Liquid mixing; baf f le design; mixing t ime; mult iple impellers : s t i r red tank; power

c o n s u m p t i o n .

I N T R O D U C T I O N

Th e role o f baf fles in a me chan ica l ly agi ta ted Vessel i s

t o p r o m o t e t h e s ta b i li ty o f p o w e r d r a w n b y t h e i m p e l-

ler and to p r even t sw i r li ng and vor tex ing o f l iqu id ,

thus , g r ea t ly im prov ing the m ixing o f l iqu id . I n the

com me rc i a l l a rge sca le tanks , the i nse r t i on o f ex t r a

baf f les to obta in more heat t ransfer area i s a very

common prac t i ce . Howeve r , excess ive ba f f l i ng may

cause a r ed uc t ion o f mass f low and loca l i z ing f low

wi th in the sys tem. By ex tend ing Na ga ta ' s ( 1975)

w o r k , N i s h i k a w a

et a l .

(1979) presented a re la t ionship

be tween the n um ber o f ba ff le s and m ixing t ime fo r

a s ingle four- and s ix-blade f la t-paddle impeller . They

a lso de f ined the prod uc t o f mixing t ime and pow er

draw n b y the impe l le r a s mixing ene rgy as an index to

cha rac te r i ze the mixing in a mechan ica l ly ag i ta ted

vesse l . From thei r results , Nishikawa

et al .

(1979)

*Corresponding author. T el. : 008862 3622707 . Fax:

00 886 2 362 3040.

3843

poin ted ou t tha t i f the w id th o f the ba ff le i s l arge r than

0.1 T, the ful ly baf fled co ndi t ion w i ll be obta ined as

nb - -3 o r m ore .

Sano and H i romoto (1987) have s tud ied the r e la -

t i onsh ip be tween c i r cu la t i on r a te and mixing t ime fo r

va r ious padd le impe l le r s and have r e la ted the mixing

t ime w i th the o the r ope ra t ion va r i ab le s a s

NtM = (NtMjF.B.C/ ( I

--0 .62 e -6 8~) (1)

whe re

~ = n b B / T

a n d

( N t . ~ t) F H c = 2 . 3 ( D / T ) - 1 ~ 7

( w / T )

0.7 4 n~;-0.4~.

Pand i t and Josh i ( 1982) , ex tend ing the mode l pro-

p o s e d b y J o s h i et a l . ( 1982), e s t ima ted the mixing t ime

of the gassed s ti r red tan k and o bta ined the fo l lowing

equa t ion to pr ed i c t mix ing t ime in such a sys tem

N tM = 2 0.4 1 ( ~ - f - ) ( T ) t 3 ' 6 ( W ) ( N ~ ) ' 2

/ 2 1


2/9

3844 W.-M.

where the constant

'a

depended on the size of the

circu latio n loop and was equal to 1 for a centrally

located impeller.

In retrospect, we see that little research has been

done on the effect of baffle design on mixing time in

the gassed stirred tank with Rushton impellers in the

previous works. In this study, both tracer technique

and computational fluid dynamic approach are used

to discuss how the baffle width, baffle number, rota-

tional speed, aeratio n rate an d impel ler numbe r affect

the extent of liquid mixing in a mechanical ly agitated

tank with Rushton turbine impellers.

DETERMINATION OF MIXING rIME AND ENERGY

Tr ac e r t e s t t o de t e r mi ne t he m i x i ny t i m( ,

Tracer test was carried out in a fiat-bottomed

transpar ent acrylic tank. The maj or dimensions of the

vessel and the equipment used in this study are both

shown in Fig. 1. The power drawn by the impeller

under various conditions was det ermined carefully by

a torsion angle-type torque meter. Baffles were fixed

in a multislot ring which enabled us to change the

number and width of the baffles. The tracer used in

L u et al.

this study was 100 ml 40% NaCI sol ution for each

measurement and was added into stirred vessel along

the shaft ins tanta neous ly. To detect the mixing time,

an electrode as proposed by Lamb et al . (1960) was

located at various positions, from which the longest

time was chosen as the mixing time under the given

condition. The error indu ced by the dosing time was

found to be less than 0.5 s which was qui te small

compared to most of the measured mixing time and

was neglected in this study. The termination point of

the tracer experiment or the cut point for mixing time

was taken when the response curve has reached

c ( t ) - ( ,

i - - C

- - ~< 5 % ( 3 )

where c~, q and

c ( t )

are tracer equilib rium concentra-

tion, initial concen tratio n and concent ration at time t,

respectively.

S i m u l a t i o n q f m i x i n y t i m e s

To determine the mixing time under extreme

baffle conditions, other rotational speeds (N = 5 and

6.66 rps) and the mixing time for multiple impeller

l.motor 2.torque meier

4.tracer inlet 5.gas inlet

3.mixing time measured instrument

6.water inlet

(~ ~

] J

a v

e 1

i | i

' I

r: [] = ~ ( ~)

t ~

ho

=

T/3

D=T/3

C=2T/3

L=D/4

W = D/5

B =case by case

T=0.288m

c

a

-'-0 ~I,,,

'~1.


3/9

Effects of baffle design on the liquid mixing in an aerated stirred tank

3845

s y s t e m , a n u m e r i c a l s i m u l a t i o n p r o g r a m w a s d e v i s e d

t o e s t i m a t e t h e m i x i n g ti m e o f t h e s y s t em w i t h a n d

w i t h o u t a e r a t i o n . T h e c o m m e r c i a l ly a v a i l a b l e c o m -

p u t e r s o f t w a r e ' F l u e n t ' w a s u s e d t o c a l c u l a t e t h e

s ing le -phas e f low f ie ld o f the ag i t a t ed ves s e l . Du r ing

t h e s i m u l a t i o n , t h e i m p e l l e r w a s a l w a y s c o n f i n e d i n

a b l a c k b o x a n d t h e b o u n d a r y c o n d i t i o n s w e r e s e t o n

t h e e d g e s o f t h i s b o x . T h e b o u n d a r y c o n d i t i o n s i n -

c l u d i n g t h e k i n e t i c e n e r g y , r a d i a l v e l o c i t y , t a n g e n t i a l

ve loc i ty and ver t i c a l ve loc i ty were s e t a f t e r the l a s e r

d o p p l e r a n e m o m e t e r ( L D V ) m e a s u r e m e n t s , h o w ev e r ,

t h e e n e r g y d i s p a s s i o n r a t e w e r e e s t i m a t e d f r o m a n

e x p r e s s i o n p r o p o s e d b y W u a n d P a t t e r s o n ( 1 9 8 9 )

c , = A K 3 / 2 / L , ~ ) .

T h e x - ~ t u r b u l e n t m o d e l w a s a d o p t -

e d t o d e t e r m i n e t h e R e y n o l d s s t r e s s e s . O n c e t h e

s ing le -phas e f low f ie ld be de te rmined , the l iqu id

v e l o c i t y w i t h a e r a t i o n c a n b e c a l c u l a t e d f r o m t h e

r e s u l t s o f B a k k e r a n d V a n d e n A k k e r ( 1 9 9 4 ) a s

fo l lows :

U . g

=

U t . ~ x

P g / P o ) ~

(4)

wher e U t .g and U~. , a re the l iqu id -pha s e ve loc i ty w i th

a n d w i t h o u t a e r a t i o n , P0 a n d P o a r e t h e p o w e r c o n -

s u m p t i o n w i t h a n d w i t h o u t a e r a t i o n , r e s p e c t i v e l y .

T h e n t h e l i q u i d v o l u m e t r i c fl o w r a t e c a n b e c a l c u l a t e d

as fo l lows :

q,,t .g = UJ.o x (aerai , pro) x (1 - % ) (5)

w h e r e

q~a,g

w a s t h e l i q u i d v o l u m e t r i c f l o w r a t e b e t -

ween ce l l s in the i d i rec t ion , ae ra i.p ,o was the p ro jec -

t ive a rea in the i d i rec t io n and eg i s the va lue o f loca l

g a s h o l d - u p w h i c h a r e o b t a i n e d f r o m J i a n ( 1 9 92 ) a n d

Lin (1994) . By u s ing the numer ica l s imu la t ion p ro -

g r a m , t h e m i x i n g ti m e o f t h e s y s te m u n d e r g a s s e d

a n d u n g a s s e d c o n d i t i o n s c a n b e e s t i m a t e d . T h e m o s t

s u i t a b l e e x p o n e n t ' / / ' w a s d e t e r m i n e d b y c o m p a r i n g

t h e s i m u l a t e d m i x i n g t i m e w i t h t h e e x p e r i m e n t a l

v a l u e . T h e p r o c e d u r e s o f t h i s s i m u l a t i o n i s d e p i c t e d i n

F ig . 2 . and the de ta i l s c an b e found in Wu 's thes i s

(1996). Tab le 1 com par es the s im u la ted res u l t s w i th

t h e e x p e r i m e n t a l d a t a , f r o m w h i c h i t c a n b e s e e n t h a t

t h e s i m u l a t i o n r e s u l t s c a n a g r e e w i t h t h e e x p e r i m e n t a l

d a t a w i t h i n a r a n g e o f 1 0 % d e v i a t i o n u n d e r g a s s e d

a n d u n g a s s e d c o n d i t i o n s .

/

Y e s

Input the s ingle phase ~ .

flow field data from

/

esult obtained hrough

P l u e m

D iv iding the stiffed / "

tank into several

zones and input he

local gas holdup

data, s

_ L

Input the power

consumptionvaluc , ~

with and without

aeratiou,Po , Po_~

ca lcu la t ing l iqu id ~

~ / ve locity ata from

/ / f o l l o w i n g :

/

Calculalino he volume

f lo w r a t e from folow~g:

t'U~x(areal~)x(l as)

I Ee~ , l t~g mix~g ime rom mass

i r a

balanceequd on of each cells B

RESULTS AND DISCUSSION

F i g . 3 s ho w s h o w t h e w i d t h a n d t h e n u m b e r o f

baf f l e a f fec t the ex ten t o f l iqu id mix ing o f the s ing le

i m p e l l e r s y st e m u n d e r u n g a s s e d c o n d i t i o n s f o r

N = 3 . 3 3 r p s i n t e r m s o f ' m i x i n g t i m e ' . T h e r e s u lt s

c lea r ly ind ica te tha t in s e r t ion o f ba f f l es in the s ys tem

c a n g r e a t l y i m p r o v e t h e l i q u i d m i x i n g e v e n w h e n t h e

r a t i o o f

B / T

i s l e s s than 0 .05 . However , the fu l ly

baf f l ed cond i t ion i s d i f f icu l t to ach ieve i f the ba f f l e

number i s l e s s than th ree , wh ich can be s een f rom the

deca y cu rves fo r nb = 2 and 3 in th i s f igu re. Th is res u l t

i s d i f f e r e n t f r o m w h a t w a s o b s e r v e d b y N i s h i k a w a

et a l .

(1979) fo r padd le imp e l l e r s ys tem w h ich s t a t es

tha t i f n~ > /2 , the fu l ly ba f f l ed cond i t ion can be

o b t a i n e d . I n t h e s y s t e m s f o r w h i c h t h e b a f f le n u m b e r

Fig. 2. The f low diagram of the simulated procedure for

estimating the mixing time in gas-liquid agitated vessel.

i s m o r e t h a n f o u r, t h e m i x i n g t im e d e c r e a s e s s t e e p l y

wi th the inc re as e o f the w id th o f the ba f f l e f i r st , t hen i t

s o o n r e a c h e s a c o n s t a n t v a l u e a s

B / T

exce eds 0 .1 . I t is

in te res t ing to no te tha t th i s l eve l ing of f va lue t end s to

dec reas e as the number o f ba f f l es inc reas es in the

range o f nb < 8 and B / T < 0 . 2 0 . T h i s f a c t i m p l i e s th a t

wi th in th i s range , the inc reas e o f nh and B / T wil l

i m p r o v e t h e e x t e n t o f l i q u i d m i x i ng . H o w e v e r , t h e

s imu la ted res u l t s a s s hown in the f igu re by do t t ed

l i ne s a l s o p o i n t o u t t h a t t h e q u a l i t y o f l i q u id m i x i n g

wi l l becom e w ors e i f n~ i s m ore than e igh t o r

B / T

is


4/9

3846

W.-M. Lu et al.

Table 1 . Com par ison of mixing timc ( t~f ) be tween exper im cnta l and s im ula ted methods

Baffle width

Mixing t ime 0 .05T 0 .075T 0 . 1 T

0.15T 0 .2T

Single impeller

system nh = 2

Q~ = 0 L/rain

Single impeller

system nh = 2

Qg = 5 L/m in

Tr iple impe l le r

sys tem B =0.15T

Qg = 0 L ;min

Tr iple impe l le r

sys tem B =0.157 '

Q~ = 13 L/m in

Exper imenta l da ta

(sl

14.6 13.7 13.0

Sim ulate d dat a (s) 14.8 14.2 13.4

D evi atio n (% ) 1.30 3.60 3.(X1

Ex per im enta l dat a (s) 17.2 16.1 15.2

Sim ulated dat a (s) 18.4 17.3 16.6

De viati on (%) 6.98 7.45 9.21

Baffle width

2 3 4

Ex per im enta l dat a (s) 13.7 13.6 10. I

Sim ulate d dat a (s) 13.3 13.2 10.3

De viati on (%) 2.92 2.94 1.98

Ex per im enta l dat a (s) 15.1 14.9 11.3

Si m ula ted da ta (s) 14.0 14.11 1(I.2

De viatio n (%) 7.28 6.04 9.73

12.1 11.5

12.0 11.7

0.83 1.74

14.7 13.5

15.3 14.2

4.(18 5.19

6 8

9.20 8.10

9.(X) 8.40

2.22 3.70

10.4 9.20

9.40 8.50

9.62 7.61

2

E

c

.M

E

30

_ _

i

25

2 0 1

15

k ~

.5

0.00

e x p e i m e n t a l d a t a

s i m u l a t e d d a l a

l.bartl~

J.I,arne,

4-l.alleo

0 6-bame,

X 1 1 - ' ~ t / l l ~

1 / f +

. . . .. _ . . _ . / / i

c _ ~ 3 - . - ~

I / / '

L.... . .,_ ~ [ :

0 .0 5 0 . 1 0 0 . 1 5 0 . 2 0 0 . 2 5 0 . 3 0

B / T

0.35

Fig. 3. Effect of baffle width on t .~t for va rious num ber of

baffles under ungassed condition for singlc impeller system

with N =3.33 rps.

11

o

E

on

E

10

~ ~ 4-b~ m es

Ra~U n, l s p e e

3 33fUS

5 oo

7r~

5

0.05 0.10 0.15 0.20

B / T

Fig. 4. Effect of baffle width o11 tM with n~ =4 for various

rotational speeds under ungassed condition.

l a r g er t h a n 0 .2 5 . T h e t r e n d o f g r o w i n g w o r s e i n m i x i n g

i s d u e t o t h e l o ca l i z in g e f f ec t o f e xce s s ive ba f f l in g .

I f t h e s a m e p l o t s a r e d r a w n f o r N = 5 a n d 6 . 67 r p s ,

i t w i l l b e f o u n d t h a t t h e t r e n d s o f m i x i n g t i m e a r e v e r y

s i m i l a r to F i g . 3 . H o w e v e r , t h e c o n t i n u o u s d e c a y o f

t h e m i x i n g t i m e w i t h t h e i n c r e a s e o f b a f fl e w i d t h s t i l l

e x i s t s f o r n b = 4 a n d t h e m i x i n g t i m e d o e s n o t r e a c h

a l e v e l i n g o f f v a l u e u n t i l

B / T >

0 . 15 a n d n h > /6 . F ig . 4

s h o w s t h e r e l a t i o n s h i p b e t w e e n t h e m i x i n g t i m e a n d

b a f f le w i d t h f o r n b = 4 u n d e r v a r i o u s r o t a t i o n a l

spe e d s . I t c l e a r l y in d ic a t e s t h a t ( 1} t h e in c r e a se o f

r o t a t i o n a l s p e e d w i l l i n c r e a s e t h e l i q u i d p u m p i n g

c a p a c i t y o f t h e im p e l l e r , t h u s t h e m i x i n g q u a l i t y w i l l

b e i m p r o v e d ; ( 2) t h e c o n t i n u o u s d e c a y t r e n d o f m i x i n g

t i m e w i t h t h e i n c r e a s e o f b a f f le w i d t h b e c o m e s m o r e

e v i d e n t f o r l a r g e r r o t a t i o n a l s p e e d s a n d ( 3) t h e l e v e l i n g

o f f v a l u e o f m i x i n g t i m e c a n b e s e e n o n l y f o r

N = 3 . 33 rp s , imp ly in g t h a t i t w i l l be mo re d i f f i cu l t t o

a t t a i n t h e f u l ly b a f f le d c o n d i t i o n i f t h e r o t a t i o n a l

s p e e d i s h i g h e r . T h i s p h e n o m e n o n i s c o n s i s t e n t w i t h

t h e e x p e r i m e n t a l r e s u l t s o f t h e f u l ly b a f f le d c o n d i t i o n

f o r v a r i o u s r o t a t i o n a l s p e e d s o b t a i n e d b y t h e a u t h o r s

w h i c h i n d i c a t e t h a t t h e f ul l y b a f f le d c o n d i t i o n f o r

N = 3 . 3 3 , 5, 6 . 6 7 r p s a r e n b B / T ) 12 = 0 . 4 5 . 0 . 6 7 a n d

0 . 74 , r e spe c t ive ly (L u et al. 19971.

T o e x a m i n e h o w t h e m i x i n g e n e r g y ( P h t M ) i s a f f e c -

t e d b y t h e i n c r e a s e o f b a f f le w i d t h a n d n u m b e r , t h e

p l o t s o f PhtM a g a i n s t B / T f o r va r io u s n h wi th N =

3 .3 3 r p s a r e s h o w n i n F i g . 5 . T h e t r e n d s o f th e s e p l o t s

i s v e r y s i m i l a r t o w h a t i s s e e n i n F i g . 3 . T h e v a l u e o f


5/9

Effects of baffle design on the liquid mixing in an aerated stirred tank 3847

E

II0

100

90

80

70

6o

50

40

30

20

0.00

t

' I

0.05 0.10

(arrx-)

Imlh

t t-t.,,n~

0.15 0.20

110

o o ~

90

8 0

70

~ 6 o

~ 50

40

30

20

\

b = m w i d t h

B - 0.OST

B - 0 075T

B - O I T

B OIST

B 0 T

I

]

0 1 2 3 4 5 6 7 8 9 10 11 12

nb

Fig, 5. Effect of baffle width on PbtM for single impeller

system with various number of baffles under ungassed condi-

tion and N = 3.33 rps.

Fig. 6. Effect of baffle number on PbtM for single impeller

system with various width of baffles under ungassed condi-

tion and N = 3.33 rps.

mixin g energy decreases first an d soon reaches a level-

ing off value for a given numbe r of baffles, except for

nb ~


6/9

3848 W.-M. Lu

et

a l .

B = 0 . 1 5 T

baffle umber

2 ball]es

3 barnes

4 balTles

O 6 barnes

[ ] 8 - b a f f l e s

,1

E

~

e-,

~

E

0 . 0 0 E + 0

16.00

15.00

14.00

13.00

12.00

1 1 . 0 0

10.00

9 .00

8 .00

7 .00

6 .00

0

i

0 .00

8 .33E-5 1 .67E-4 2 .50E-4 3 .33E-4 m J / s )

r

t

' F l o o d e d

I

I

I

/ i

r

J ,

5 I 0 15 20 (L/m in)

, a i ' (vv m)

0.26 0 .53 0 .79 1 .05

Q g

Fig. 7. Effect of gas f low rates on t .u for single impeller system with various width o f ba ffles and

N = 3.33 rps.

l o n g e r t h a n t h e o n e s o f s in g l e i m p e l l e r s y s t e m a n d t h e

d i f fe r e n c e b e t w e e n t h e m b e c o m e s s m a l l e r a s t h e b a ff l e

w i d t h b e c o m e l a r g e r . I t is a l s o i n t e r e s t i n g t o n o t e t h a t

t h is d i f fe r e n c e i n c re a s e s t o a l m o s t d o u b l e a s i t r e a c h e s

t h e f u l ly b a f f le d c o n d i t i o n i f i t is c o m p a r e d w i t h t h e

c a s e o f

nb

is 2 or 3.

T o o b t a i n a m o r e c o m p r e h e n s i v e a n d r e l i a b le re l a -

t i o n s h i p f o r t h e o p e r a t i n g p a r a m e t e r s , t h e m i x i n g t im e

d a t a o b t a i n e d e x p e r i m e n t a l l y a re c o r r e l a te d w i t h

n b a n d B I T a n d Q g u n d e r v a r i o u s r o t a t i o n a l s p e e d s

a n d a d i m e n s i o n l e s s c o rr e l a t i o n c a n b e g i v e n a s

N t M = 5 5 . 7 ( n b ) - 3 ( B / T

-

I535(Qg./ND3) 29~ 6 )

f o r th e s i n g l c R u s h t o n i m p e l l e r s y s t e m . I f t h e

s i m u l a t e d v a l u e o f m i x i n g t i m e f o r t r i p l e i m p e l l e r

s y s t e m a r e c o r r e l a t e d w i t h t h e s a m e p a r a m e t e r s a s t h e

t h e s i n g l e i m p e l l e r s y s t e m , t h e n t h e s i m i l a r c o r r e l a t i o n

f o r th e t r i p l e i m p e l l e r s y s t e m c a n b e g i v e n a s

N tu 46 .5 (nh ) -o .295(B/TX-O.327 ,r l

;~rn31o.oH) (7 )

T h e s t a n d a r d d e v i a t i o n o f t h es e t w o e q u a t i o n s a r e

a b o u t 1 5 a n d 2 0 % , r e s p e c t i v e ly . F r o m t h e s e t w o

e q u a t i o n s i t c a n b e s e e n t h a t t h e d i m e n s i o n l e s s m i x i n g

t i m e d e c r e a s e s w i t h t h e i n c r e a s e o f n b , B / T a n d N ,

h o w ever , i t i n c r eases as Q g in c r eases . Th e e f f ec t o f

b a ff le n u m b e r o n m i x i n g t i m e i s m o r e s i g n if i c a nt th a n

b a f fl e w i d t h i n t h e s i n g l e i m p e l l e r s y s t e m , h o w e v e r , t h e

i n v e r s e s i t u a t i o n s a r e f o u n d i n t h e t r i p l e i m p e l l e r

s y s t e m . F r o m t h e s e t w o e q u a t i o n s i t m a y b e m i s u n -

d e r s t o o d t h a t t h e e ff ec t o f ga s f l ow r a t e o n m i x i n g t im e

i s s m a l l , h o w e v e r , i f t h e d i m e n s i o n a l g r o u p s a r e u s e d ,

t h e a b o v e t w o e m p i r i c a l e q u a t i o n s c a n b e r e w r i t te n a s

N tM = 32 .4 (nh ) - z 75 (B/T )-o.14O(Q.)O.2O8 (6')

a n d

N t M = 31.1(n~) . . . . 2 8 9 ( B / T ) - O . a z o ( Q )o.171

(7'),

w h i c h w i l l l o o k m o r e r e a s o n a b l e t h a n t h e o r i g i n a l

d i m e n s i o n l e s s e q u a t i o n s . W i t h t h e s e t w o c o r r e l a t io n s

t h e m i x i n g q u a l i ty u n d e r a g i v e n o p e r a t i n g c o n d i t i o n


7/9

E f f e c ts o f b af f le d e s i g n o n t h e l i q u id m i x i n g i n a n a e r a t e d s t i r r e d t a n k

4-baftle,L B=0.1T

3849

l o o d i n g ~rated r a t e

o b s e r v e d b y

the

r c s u h s o f I bi s t u d y

csl im i~ d by Grcaves argl Kobbacy corrclation(198 I)

Rota6o~al speed

3 . 33q~s

5 o o ~ , ,

6 6 7 ~ s

12 .00

I 1 . 0 0

lO.O0 / / /

9 . 0 0 ' x

: _ . . .

I o . . . . . . . . < o < . > /

.= 8 .00 / - , ' ~

E 7 .00

I

6.00

/

5 0 0

0 . 0 0 E + 0 8 . 3 3 E -5 1 . 6 7E - 4 2 . 5 0 E - 4 3 . 3 3 E - 4

gas f low rate (m3/s)

F i g 8 . E ff e ct o f g a s f lo w r a t e o n f o r s i ng l e i m p e l l e r s y s t e m w i t h % = 4 a n d B = 0 . I T u n d e r v a r i o u s

r o t a t i o n a l s p e e d s a n d t h e c o m p a r i s o n o f th e f l o o d i n g a e r a t e d r a t e b e t w e e n t h i s s t u d y a n d o t h e r c o r r e l a t i o n .

0

e-

x

B 01~]

2 balll~

3 b a f f l e s

4 . h a f l l e ~

6 balll=~

:~-ba:lles

0.67 0.83 1.00 1.17

i

. . . . ~ . . . . t . - - - - ,

0 .00 0 .17 0 .33 0 .50

70

65 -- ~- -- ,~,

6 0 . . . . . . . . . . . . . . .

s s - i - - ; -

50

4 5 ..

--4.

I

4 0

3 5

i

i i

I T

i

. ;

i . . . . . .

I

I - ~ - -

133 (Xl 04)

i ( mS / s )

I i

l 2 3 4 5 6 7 8 ( L /m in )

L - - . . ~ . . . . . t . . . . . I I . . . . L I

I

0 . 0 0 0 0 . 0 5 3 0 10 5 0 . 1 5 8 0 . 2 1 0 0 .2 6 3 0 3 1 5 0 . 3 6 8 0 . 4 2 0 ( w i n )

G as F lo w R a te Q ~

Fig . 9 . E f f ec t o f g a s f lo w r a t e o n

P~t

f o r s i n g l e i m p e l l e r s y s t e m w i t h v a r i o u s w i d t h o f b a f f l e s u n d e r

N = 3 .33 r ps .


8/9

3850 W.-M. Lu et a l .

16

14

12

10

6

4.0

~ baffle number

%-2

0

n b -

]

nb- 4

] % - 6

4.5 5.0 5.5 6.0 6.5

Pg (J )

Fig. 10. T he relation ship between Pg and t , , with v arious gas flow rates an d baffle num ber w ith a constant

baff le wid th B =0.15 T.

Table 2 . The c omp ar ison of mixing t ime ( t~) be tween the s ing le and t r ip le impe l le r sys tems under ungrassed condi t ions

Baffle width

nh Mixing t ime (s) 0 .05T 0 .075T 0 . I T 0 .15T 0 .2T

2 Single im pe lle r system (I) 14.6 13.7 13.(I 12.1 11.5

Tr iple im pelle r system (II) 18.6 16.2 14.5 13.3 12.6

Difference (II/I ) 100% 27.4 18.2 11.5 9.92 9.57

3 Single im pell er system (l) 14.5 13.8 12.8 12.0 11.6

Tr iple im pell er system (I I) 18.7 16.3 14.4 13.2 12.6

Difference (1I/I) x 100% 29.0 18. I 12.5 10.0 8.62

4 Sing le im pell er system (I) 10.4 9.7 9.1 8.6 8.6

Tr iple im pell er system (II) 16.5 14.1 12.0 10.3 9.7

Difference (11/I) x 100% 58.7 45.4 31.9 19.8 12.8

6 Sing le im pell er system (11 10.3 9.3 8.0 8.1 8.0

Tr iple im pell er system (I1} 14.8 13.2 10.5 9.0 9.0

Difference (II/I ) x 100% 43.7 41.9 31.3 11.1 12.5

8 Single im pell er system (I) 7.9 7.2 7.3 7.0 6.9

Tr iple im pell er system (II) 13.4 11.4 8.7 8.4 8.3

Difference (II/I ) x 100% 69.6 58.3 19.2 20.0 20.3

c a n b e p r e d i c t e d f o r t h e s i n g l e a n d t r i p l e R u s h t o n

i m p e l l e r s y s t e m .

CONCLUSIONS

I n t h i s s t u d y , t h e e f fe c t s o f w i d t h a n d n u m b e r o f

b a f f le s in m e c h a n i c a l l y a g i t a t e d v e s s e l s w i t h s i n g l e a n d

t r i p le s t a n d a r d R u s h t o n t u r b i n e i m p e l l e rs a r e e x a m -

i n e d f o r t h e s y s t e m s w i t h a n d w i t h o u t a e r a t i o n . T h e

i n s e r t io n o f th e a p p r o p r i a t e n u m b e r o f b af f le s c l e a r ly

i m p r o v e s t h e e x t e n t o f l iq u i d m i x i n g . H o w e v e r , t h e

e x c e s s i v e b a f f l i n g a n d s p a r g i n g g a s t h r o u g h t h e i m p e l -

l e r w o u l d i n t e r r u p t t h e l i q ui d m i x i n g a n d i n c r e as e t h e

m i x i n g t i m e .

B y c o r r e l a t i n g t h e m i x i n g t i m e w i t h n ~, B / T , Q y a n d

N , a r e l i a b l e c o r r e l a t i o n a s

N t M

= 55.7(nb)-o .30

( B / T ) - ' I 5 3 5 ( Q y / N D 3 ) ' 2 96

c a n b e o b t a i n e d f o r

t h e s y s t e m w i t h a s i n g l e R u s h t o n t u r b i n e i m p e l l e r

u n d e r n o n - g a s s e d a n d a e r a t e d s y s t e m s a n d t h e s i m i l a r

c o r r e l a t i o n f o r t h e t r i p l e i m p e l l e r s y s t e m c a n b e g i v e n

as

N t M 46.5 (n~)-o 29s -o ~2v 3 o o lo

= ( B / T ) ( Q , / N D ) .


9/9

Effects of baffle design on the liquid mixing in an aerated stirred tank

Acknowledgement

The authors are very grateful for the financial support

granted by the National Science Council NSC85-2214-E-

tX)2-0()2 for this study.

aerai ,

pr o

B

(.

Ci

( ' ~

C

D

h o

/ /

I

l h

N

t h

P , ,

P I

[ ) i . l . q

( 2

7

U i . u

V

NOT.~'IION

constant used in eq. (21

cell projective a rea in I direction, m 2

baMe width, m

tracer concentration, mol.l

initial tracer concentrat ion, mol. 1

tracer concentration at time t, mol,.l

final tracer concentration, tool 1

distance between impellers, m

impeller diameter, m

height of lower impeller from bottom, m

liquid level of stirred tank, m

length of impeller blade, m

baffle number

rotational speed of agitation impeller, l,s

power con sumpti on with baffle, kg m2's ~

power consum ption with aeration, kg m:, s~

power consumption without aeration,

kg m 2, s ~

the volumetric ltow rate between cells in

I direction, m~,s

gas flow rate, m ~ s

mixing time, s

lank diameter, m

liquid-phase velocity with aeration, m s

liquid-phase velocity without aeration, m,'s

liquid vo lume in the tank, m ~

Greek letter.s

1:~ exponent adopted in eq. (4l

~:,, local gas hold-up

R K F ' E R E N ( ' Y S

Greaves , M. and Kobba cy, K . A . H. (1981) Power

con sum pti on and impeller efficiency in gas liquid

3~51

dispersion. In Fluid Mix ing , I. Chem. Eng. Symp.

Set. No. 64, I. Chem. E., Rugby, Warks, England, l, 1.

Jian, W. J. (19921 The effect of solid co ncen tra tion on

bubble size distribution in a three phase stirred

tank. M.S. thesis, National Taiwan University,

Taiwan, ROC.

Joshi, J. B., Pandit, A. B. and Sharma, M. M. (1982)

Mechanically agitated gas-liquid reactors.

Chem.

lzmtn.q Sc i.

37 (6), 813 -844.

l,amb, D. E.. Manning, I-. S. and Wilhlem, R. H.

(1960} Measurement of c oncentra tion fluctuations

with an electrical conductivity probe. A . I . ( ' h . E . J .

614), 682.

l,in, L. C. (1994) This study of fluid flow, power and

bubble size distribution in different dual-impeller

stirred tanks. M.S. thesis, National Taiwan Univer-

sity, Taiwan, ROC.

Lu. W. M.. Wu, H. Z., Tasi, F. Y. and Wang, C. Y.

(1997) F, fects of baffle design on the fully bafl%d

condition in aerated stirred tanks with Rushton

turbine impeller. C . I . ( ' h . E . J . 28(1L 69 72.

Nagata, S. (19751 Mixinq principles and application.

Kodansha. Tokyo. Japan.

Nishikawa. M., Ashiwake, K., Hashimoto, N. and

Nagata, S. I1979) Agitation power and mixing time

in off-centering mixing.

/nt . Chem. Em#tg

19(1),

153 159.

Pandit, A. B. and Joshi, J. B. (1982) Mixing in mecha-

nically agitated gas liquid contactors , bubble col-

umns and modified bubble columns. ( 'hem. Engn 9

Sci. 37(6), 1189 1215.

Sano. Y. and I-liromoto, U. (1987) Effects of paddle

dimensions and baffle conditions on the inter-

relations among discharge flow rate, mixing power

and mixing time in mixing vessels. J. Chem. Engnq

J a p a n 20(4) . 399 404.

Wu, It. Z. (1996) Effect of baffle design on the fully

baffled con diti on and fluid mixing in aerated stirred

tank. M.S. thesis. National Taiwan University,

Taiwan, ROC.

Wu, H. and Patterson, G. K. (1989) Laser doppler

measurement of turbulent flow parameters

in a stirred rnixer. Chem. En#n# Sci . 44(10),

22O7-222 I.

effect on em cells

Documents