mixing sys desgin

8/11/2019 Mixing Sys Desgin

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kL a

kL a

3

kL a


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1

k

k

kL a a kL

k


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kL a

kL a kL a kL a

kL a


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k L a


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kL a


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2

2


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1

1

1

kL a 1

kL a

kL a


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kL a

kL a kL a


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k kL a

1

1

kL a 1

1

1

1

kL a 1 kL a

1

kL a 1


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u i 1

a 2 F q F lift,q R pq p q

v pq

1

a 1

B l

B r 3 1

C 3

C 3

C D

Dc

D l 2 1

d p

D r 3 1

d32

F

F

f

g 2

Gk,q 1

3

I

J 2 1

k 1

kL 1

K pq 3 1

kq 2 1

m

N 1

n 3

p

P g


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RA

Re

t

U 1

u i 1

u i 1

V 3

1 1

1 1

1

1 2

w

3

e

p

2 3


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kL a


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3


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3 4 4 + 4 + 3 2+ + 2

4 + 4 2

3 4 4 + 4 + 3 2+ + 2

4 + 4 2

9 5 + 8 + + 2 2 5 + 4 2+ + 4 2 + 2 2 2+ + 2

4

3 4 + 7 .5 2 + 2 3 2+ + 4 2

4 + 2 +

3 3+ + + + 2 24 + 6 2 [ 3 6 4)2 ] + 6 + ( , ) 2 3+ + 3 2 4 2 3 + 6 + ( , )


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t

+ (v ) = S m S m

(v )

t + (vv ) = p + + g + F

p


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g

F

= v + v T 23 vI

I

u i = ui + u i

u i ui i

t

+ x i

(u i ) = 0

(u i)t

+ (u i u j )

x j=

px i

+ x j

u ix j

+ u jx i

23

iju lx l

+ x j u iu j

u i u j


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q q

n

q=1 q = 1

q

q = qq

q q

q

t

( qq) + ( qqv q) =n

p=1( m pq mqp) + S q

v q q m pq pth q th

mqp q pS q

q

t

( qqv q) + ( qqv qv q) = q p + q + qqg +n

p=1

R pq + m pqv pq mqpv qp + F q + F lift,q + F vm,q

q q th

q = qq v q + v T q + q q 23q v qI

q q

q q F q F lift,q F vm,q R pq

p

v pq


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n

p=1

R pq =n

p=1

K pq (v p

v q)

K pq (= K qp)

K pq

K pq = q p pf

p

f

p

p = pd2 p18q

d p p

C D

Re

f = C D Re

24

C D = 24 1 + 0 .15Re 0.687 /Re Re 10000.44 Re > 1000

q p

Re = q|v p v q|d p

q

p r

Re = rp |v r v p|drp

rp

rp p r

rp = p p + r r


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Re = q|v p v q|d p

= q + Ck2

k

k k

t = qk2qq

= q + C t,q

k

k

q = 23

qkq + qt,q U q I + qt,q U q + U T q


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U q

t,q

kq

k

t

(qqkq) + qq U qkq = qt,q k

kq + qGk,q qqq + qqkq

t

( qqq) + qq U qq = qt,q

q + qqkq

(C 1Gk,q C 2qq) + qqq

Gk,q

t,q = qC k2qq

kq q

kq =M

p=1

K pqqq

(k pq 2kq + v pq v dr )

v pq

v dr

k pq q l

q = C 3kq kq

k

C 1 C 2 C 3 C k

k


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q p


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m m

t dR

dN = ndr

n

R1

N (R1 ) =

R 1

ndR

= +

u


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t

[n(v, t )] + [un (v, t )] + v[Gvn(v, t )]

=

12 v0 a(v v , v )n(v v , t )n(v , t )dv

0a(v, v )n(v, t )n(v , t)dv

+ v pg(v ) (v|v )n(v , t )dv

g(v)n(v, t )

n(v, t = 0) = nv; n(v = 0 , t )Gv = n 0

g(v )n(v )dv pg(v )n(v )dv (v|v )dv

p

v v v v


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mk (t) =

+

0n(L; t)LkdL

n(L; t)


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mk = +

0n(L; t)LkdL

N

i=1wi Lki

wi Li

g(v ) (v|v ) g(v ) v

(v

|v )

v v (v|v )


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br (v, v ) = B (v ) v|v br 3s

1

B (v )

v 3

v 3

(v|v )

br v, v = c41/ 3d 2/ 3 1min (1 + )

2

11 / 3 12 f 2/ 3 + (1 f )

2/ 3 1 2/ 3d5/ 3 11 / 3

d

c4 min = min /d

br (v, v ) = 3c4 (1 G )11b8/ 11 n j d2 j

1/ 3

811

, tm 811

, b

+2 b3 / 11

511 , tm

511 , b + b

6/ 11

211 , tm

211 , b

br (v, v ) = 1 .191/ 3d 7/ 3 1 f 1/ 3 1

(1 + )2

13 / 3 2

2/ 3d5/ 3 f 1/ 3 2/ 3d


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a(v, v )

v v v

v

C (vi ; v j ) = C (vi ; v j )P C (vi , v j )

C

P C

vi , v j

i

j (m3

)

C = 4

(di + d j )2 n in j u ij

u ij di d j n i n j

u tij = u2i + u

2 j

1 / 2

u i = 1 .43 (d i)1/ 3

P (vi , v j ) = c0.75 1 + x2ij 1 + x

3ij

1/ 2

(g/ L + 0 .5)1/ 2 (1 + x ij )3 W e1/ 2ij

x ij = di /d j

W eij =L di u tij

2


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k k k

k

k

k


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k


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= 1

1

1

p

z+

4 w

1Dcg

z z1 z2


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p z1 z2

1 3

g

1

w

Dc

U 1 1

P P 0

= 1 P P 0


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k


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%

C D

k A p k


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x

J = DdC dx =

D

(C G C L )

D

J

dC

dx,

C G C L

J

J = K (C G C L ) K

K

kG = DG G

kL = DL L

K = 11kG

+ 1kL


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kG kL K kL kL kG K kG

J = DL L ( C ) = kL (C C L )

C L C

N A = kLAV C = kL a C

N A 3 a A V

C A1 C A2

Z F C A1 C A2


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k L a

kL a

kL a

kL a

kL a = a (U g)bP V L

c

a

P g

V L 3

U g 1

b, c

L g

b c

a

kL a

a b c


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kL

kL = 2 DL e e

DL 2 1

db/u slip

kL = 2 DL uslipdb

db

uslip 1

kL = DL s s

s

kL = F DL L LL0.25

L 2 3

L 3

L 1 1


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2 3

dC Ldt

= kL a (C C L ) C

P O 2 = H C

C C LC

= kL at kL a


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kL

kL

kL a l kL a

kL a 10 3

1

kL

kL

2 4

4

kL

kL a

kL a kL a 2 4

kL a

kL a kL

a

kL a kL a


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kL a l

kL a

kL a

kL a

kL a

kL a

kL a

kL a

kL

kL a


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kL a

kL a

kL a

kL a kL a

kL a

kL a kL a


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k


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kL a

kL a

kL a

kL a

a


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kL a

3


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1

1

1


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kL

a a kL


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kL a


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2

kL a

kL a

dC (t)dt

= kL a (C C (t))

C (t) 2 3

C 2 3


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100 150 200 250 300 350 4000

20

40

60

80

100

120

140

Impeller Speed (rpm)

P o w e r

( W )

1

100 150 200 250 300 350 4002

2.2

2.4

2.6

2.8

3

3.2

3.4

3.6

Impeller Speed (rpm)

D 3 2

( m m

)

4.37 lmin 1, 25

C


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k


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+


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0 100

0 090

0 080

0 070

0 060

0 050

0 040

0 030

0 020

0 010

0 000


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kL a

kL

kL = 2 DL uslipdb

kL = F D L L LL0.25

a = 6 G

d32

kL a kL a

kL a


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D AB = 7.4 10 8 ( B M B )12 T

B V 0.6A


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1 0.5 0 0.5 10

0.05

0.1

0.15

0.2

0.25

0.3

P o s

i t i o n , z ( m

)

Velocity in y direction (ms 1)

Numerical Grid 1Numerical Grid 2PIV

1 0.5 0 0.5 10

0.05

0.1

0.15

0.2

0.25

0.3

P o s i

t i o n , z ( m m

)

Velocity in z direction (ms 1)

Numerical Grid 1Numerical Grid 2PIV

vy vz


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1 V 2

V 2


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3

10

9 2 9

8 57

7 86

7 14

6 43

5 71

5

4 2 9

3 57

2 8 6

2 14

1 43

0 71


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150 200 250 300 350 4000

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Impeller speed (rpm)

P o w e r

( k W )

Single phase4.37 lmin 1

7.8 lmin 1


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1.2 1 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 0.80

0.05

0.1

0.15

0.2

0.25

0.3

0.35

P o s i

t i o n ,

z ( m

)

Velocity in y direction (ms 1)

200 rpmSingle phase200 rpm4.37 lmin 1

395 rpmSingle phase395 rpm4.37 lmin 1

k


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kL

kL a

kL

kL a

kL

kL


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k

lmin 1


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128/170

150 200 225 250 300 350 3950

0.5

1

1.5

2

2.5

3

3.5

d 3 2

( m m )


ImpellerBulk


129/170

1

1


130/170


131/170

150 200 250 300 350 4001

1.25

1.5

1.75

2

2.25

2.5

2.75

3

3.25

3.5


D 3 2

( m m

)

Experimental, 4.37 lmin 1 , 25

C

CFD, 4.37 lmin 1 , 25

C


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133/170

150 200 250 300 350 4000

0.5

1

1.5

2

2.5

3

3.5


D 3 2

( m m

)

4.37 lmin 1

7.8 lmin 1

1

1

1

1


134/170

150 200 225 250 300 350 3950

0.5

1

1.5

2

2.5

3

3.5

4

d 3 2

( m m

)


WaterSynthetic leach liquor

1


135/170

2 4

10 3

1


136/170


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kL a

kL a


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a kL

kL a

kL a

kL a kL a

kL a 1

k L a 1

k L a 1

1

kL a 1


140/170

kL a

kL a

1

kL a

kL a

kL a

kL a


141/170

k L a

k L a k L a

a k L k L a

k L a

k L a

a

k L a

k L a

5.00c 02

4.50e 02

4.00e 02

3.50e 02

3.00c 02

2.50e 02

2.00e 02

1.50e 02

1.00e 02

5.00e 03

O.OOe OO


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150 200 250 300 350 4000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.01


k L

a ( s

1

)

ExperimentalCFD

k L a

k L

a

a

a

k L a

k L a k L

k L a

-

x

x

x


143/170

150 200 250 300 350 4000

0.002

0.004

0.006

0.008

0.01

0.012

0.014


k L

a ( s

1

)

4.37 lmin 1 Experimental

4.37 lmin 1 CFD

7.8 lmin1

Experimental7.8 lmin 1 CFD

k L a

k L

k L a

a

k L a

1 k L a

k L a

k L a

>-

>-

C


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145/170

0 500 1000 1500 2000 2500 30000

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

P/V (Wm 3 )

k L

a ( s

1

)

4.37 lmin 1 , Water

4.37 lmin 1 , SLL

7.8 lmin 1 , Water

7.8 lmin 1 , SLL

k L a

k L a

k L a

k L

k L a a

k L a

k L a k L a

k L a


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147/170

a b c d

#1

#2

g g 1

3

g g 3

3

2

2 kL a

0 0.005 0.01 0.015 0.02 0.025 0.030

0.005

0.01

0.015

0.02

0.025

0.03

Experimental k L

a (s 1)

P r e

d i c t e d k

L a

( s

1 )

+30%

30%

4.37 lmin 1 , 25

C

7.8 lmin 1, 25

C

4.37 lmin 1 , 50

C

7.8 lmin 1, 50

C

4.37 lmin 1 , 70

C7.8 lmin 1, 70

C

kL a kL a

kL a kL a

kL a kL a


148/170

kL a

k


149/170

k

1

1


150/170

kL a

kL

kL a

kL a

kL a

kL a


151/170

kL a


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k


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4/ 45

14th


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1

max min b 32


167/170

1

max min b 32


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1

max min b 32


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k La

kL a 1

k L a

kL a 1

kL a 1


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mixing sys desgin

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