9
507 HWAHAK KONGHAK Vol. 40, No. 4, August, 2002, pp. 507-515 * ** * ** (2002 3 23 , 2002 5 8 ) Calculation of Spray Drying Using Computational Fluid Dynamics Ka-Ram Park, Kyun Young Park , Ji-Sun Ju* and Jun Taek Park** Department of Chemical Engineering, Kongju National University, Gongju 314-701, Korea *Plant Engineering Center, Institute for Advanced Engineering, Yongin 449-860, Korea **Department of Energy Systems, Korea Institute of Energy Research, Daejeon 305-343, Korea (Received 23 March 2002; accepted 8 May 2002) CFX4 140 cm, 170 cm , , . . . . . 0 o , 30 o , 45 o . , . Abstract - Using CFX4, a computational fluid dynamics program, the gas flow pattern, the droplet trajectory and the extent of drying were calculated for spray drying of a milk with a rotary disk in a spray chamber of 140 cm in diameter and 170 cm in height. Due to the cone of the chamber, whose cross sectional area became smaller toward the outlet, a recirculation flow was formed in the chamber pointing downward in the center and upward near the wall. The gas flow pattern was significantly affected by the droplets ejected from the rotating disk. The smaller droplets descended downward not far from the axis, medium sized droplets were swept into the recirculation flow, and even larger ones were little affected by the recirculation flow, travelling downward near the wall. The center of recirculation flow moved upward and toward the wall as the vane angle of the air disperser was increased from 0 to 30 and 45 o . An increase of the vane angle increased the swirling intensity and conse- quently the droplets flew in a larger circle resulting in an increase of the residence time. On the other hand, the droplets became more likely to hit the wall with the vane angle increase. Key words: Spray Drying, Computational Fluid Dynamics, Milk Powder 1. . , , , , , , . . , . . (swirling) To whom correspondence should be addressed. E-mail: [email protected]

Calculation of Spray Drying Using Computational Fluid Dynamics · 2002-08-22 · Calculation of Spray Drying Using Computational Fluid Dynamics Ka-Ram Park, Kyun Young Park †, Ji-Sun

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HWAHAK KONGHAK Vol. 40, No. 4, August, 2002, pp. 507-515

������� � �� ���

�������†���*���**

����� �����*��� � ����������

**������� � ������� �(2002 3! 23" #$, 2002 5! 8" %&)

Calculation of Spray Drying Using Computational Fluid Dynamics

Ka-Ram Park, Kyun Young Park†, Ji-Sun Ju* and Jun Taek Park**

Department of Chemical Engineering, Kongju National University, Gongju 314-701, Korea*Plant Engineering Center, Institute for Advanced Engineering, Yongin 449-860, Korea

**Department of Energy Systems, Korea Institute of Energy Research, Daejeon 305-343, Korea(Received 23 March 2002; accepted 8 May 2002)

� �

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Abstract − Using CFX4, a computational fluid dynamics program, the gas flow pattern, the droplet trajectory and the extent

of drying were calculated for spray drying of a milk with a rotary disk in a spray chamber of 140 cm in diameter and 170 cm in

height. Due to the cone of the chamber, whose cross sectional area became smaller toward the outlet, a recirculation flow was

formed in the chamber pointing downward in the center and upward near the wall. The gas flow pattern was significantly

affected by the droplets ejected from the rotating disk. The smaller droplets descended downward not far from the axis,

medium sized droplets were swept into the recirculation flow, and even larger ones were little affected by the recirculation flow,

travelling downward near the wall. The center of recirculation flow moved upward and toward the wall as the vane angle of the

air disperser was increased from 0 to 30 and 45o. An increase of the vane angle increased the swirling intensity and conse-

quently the droplets flew in a larger circle resulting in an increase of the residence time. On the other hand, the droplets became

more likely to hit the wall with the vane angle increase.

Key words: Spray Drying, Computational Fluid Dynamics, Milk Powder

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� ��0 �� õ�� x(f.g), r(Ue.g), w(��.

g) 4�� ,²� ¤+ Ð�µ,.

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r--- ∂

∂r----- ρrUr( )+ SP=

∇ ρUU⋅[ ] ∇ τ⋅[ ]+ ∇P– ρg SP+ +=

∇ ρUU⋅[ ]Fig. 1. Schematic drawing of drying chamber.

Fig. 2. Sketch of air disperser and rotating disk.

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¾� 8!, (2) õ�(constant rate) ��8!, (3) ��(falling rate) ��8!.

∇ ρUU⋅[ ]x1r--- ∂

∂r----- rρUxUr( ) ∂

∂x------ ρUxUx( )+=

∇ ρUU⋅[ ]r1r--- ∂

∂r----- rρUrUr( ) 1

r---– ρUw

2 ∂∂x------+ ρUrUx( )=

∇ ρUU⋅[ ]w∂∂r----- ρUrUw( ) ∂

∂r----- ρUrUw( ) ∂

∂x------ ρUxUw( )+ +=

∇ τ⋅( )x1r--- ∂

∂r----- rτrx( )

∂τxx

∂x---------+=

∇ τ⋅( )r1r--- ∂

∂r----- rτrr( )

∂τrx

∂x---------+=

∇ τ⋅( )w

∂τrw

∂r----------

2r---τrw

∂τwx

∂x----------+ +=

τrr µeff 2∂Ur

∂r--------- 2

3--- ∇ U⋅( )––=

τrx µeff

∂Uw

∂r----------

∂Ur

∂x---------+–=

τxx µeff 2∂Uw

∂x---------- 2

3--- ∇ U⋅( )––=

τrw µeff r ∂∂r-----

Uw

r-------

1r---

∂Ur

∂w---------+–=

µeff µt µl+=

µt Cµρk2

ε-----=

∂∂x------ ρUxk( ) 1

r--- ∂

∂r----- rρUrk( ) ∂

∂x------

µt

σk

-----∂k∂x------

1r--- ∂

∂r-----

rµt

σk

-------∂k∂r------

Gk ρε–+ +=+

∂∂x------ ρUxε( ) 1

r--- rρUrε( ) ∂

∂x------

µt

σε-----∂ε

∂x------

1r--- ∂

∂r-----

rµt

σε-------∂ε

∂r-----

εk--- C1Gk C2ρε–( )+ +=+

Gk µt 2∂Ux

∂x---------

2 ∂Ur

∂r---------

2 Ur

r------

2

+ + ∂Uw

∂x----------

2

+=

+ r ∂∂r-----

Uw

r-------

2 ∂Ux

∂r---------

∂Ur

∂x---------+

2

+

∂∂x------ ρUxH( ) 1

r--- rρUrH( ) ∂

∂x------

µt

σH

------∂H∂x-------

1r--- ∂

∂r-----

rµt

σH

-------∂H∂r-------

+=+

Y iH i∑

mddvx

dt-------- CDρ Ux vx–( ) U v–

Ad

2------ mdg+=

mddvw

dt--------- CDρ Uw vw–( ) U v–

Ad

2------ md–

vrvw

r----------=

mddvr

dt-------- CDρ Ur vr–( ) U v–

Ad

2------+md

vw2

r-----=

U v– Ux vx–( )2 Ur vr–( )2 Uw vw–( )2+ +=

Ad

6rβdp

-------=

CD

CDo

1 B+------------=

B Cv

Tg Td–L

----------------=

CDo

24Re------ 1 0.15Re0.687+( )=

Re ρU v– dp

µ-------------------=

xd xd 0, v v0+( ) t∆2-----+=

xd 0, xd

v0

v

Table 1. Values for coefficients in κκκκ−−−−εεεε model

Constant Cµ C1 C2 σk σε

Value 0.09 1.44 1.92 1.0 1.3

HWAHAK KONGHAK Vol. 40, No. 4, August, 2002

510 �������������

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(32)

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antoine /��Êô 8�,.

Pvap=exp(A− ) (33)

A=23.196

B=3816.4

C=−46.13

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¡�0 vC ��hij ùù �X)� �� ��8!0 i{�,. +

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ij 1 Í��� �ë"� ï�� j`"# ,²� ¤� /0 �2 �

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#l0É, md� ��� ©ª, cd� ��� 1�, Td� ��� �i, Qc

� ��� ls0É ���� S{N� �+�, QM� ����Êô :

�+ �}. m /b� "� �}��+< (−)Ö' jY,.

QC=Nuπ k(Tg−Td) (40)

QM=L (41)

�}� 0 () 8!0É� ��+ ¾�N�, õ� ��8!0É� �

�3 �l�Êô ����� �S{ hij ¦� �}0 /b� �ª

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� �"� �¹ N<, �� ��8!0É� �s�¢ �ij ��"¹

µ,.

dmd

dt---------- Sh ρD( )πd

WC

WG

--------1 XV–

1 XG–---------------

log=

Sh 2 0.6Re0.5 µρD-------

1 3⁄

+=

XVWGPvap

WGP WG WC–( )Pvap–-----------------------------------------------------=

BTd C+---------------

dmd

dt----------

Nuπk Tg Td–( )L

-----------------------------------=

Nu 2 0.6Re0.5 µCp

k------

1 3⁄

+=

dmd

dt----------

dmd

dt----------–

dmd

dt----------

cr

md md eq,–md cr, md eq,–-----------------------------

–=

dmd

dt----------

cr

Md i,∆ πρpη· ivi out, di out,

3 vi in, di in,3–

6----------------------------------------------=

η· i

vi out, di out,

vi in,

Md∆ Md i,∆i

∑=

mdcd

dTd

dt--------- QC QM+=

dmd

dt----------

Fig. 3. Drying characteristics of droplets during spray drying.

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� ý ©ª�� Q8 Ö+ 10−3³, �M�)+ (9. m:� �h�

,. Ù Â80 r3µ Ï¢� f .g�� 76 °, U�u.g�� 47°

,(Fig. 4). Ï¢ :� �j� �K� `÷i� g����(, �K�!

' �j�;,. ¾1 <�Þ _�, + `i� Ï¢ : +��� "#i

�K_�0 � Í+j �´,. Kim[7]� 5r� �K0É f .g��

30°, U�u .g�� 19°� Ï¢� r3"��d, + `i� Ï¢ :

0É� Ù Â80É ®`µ :Òl50 �[� ="� ï�� Q�>,.

Ù Â80 r3µ T5� :��ª� 87 wt%+< l� T5� ¦4

� �l� ¦4' Table 20 Q��´,. �K0 /b� ��� ?l �

e�à, ��� ?lhi, Æc Çi0 v- 5� �l� hi4�� ,

²� ¤+ @`"# r3"�,.

3-1. � ���� ��

�� �åª, �� ¦4, RSTU� %T��Êô ��N�

��� �i� ,²� ¤� ZÃ/ [13]0 �2 dp,50%, dp,95%� @`"

�,.

dp,50%= (42)

dp,95%=2Adp,50%(dp,50%<60µm) (43)

dp,95%=2.5Adp,50%(60<dp,50%<120µm) (44)

dp,50%� l" ��e+<, M� �� 5ª(kg/h), N� TU� R

Shi(rpm), d� ú�k� pe(m), n� Æc� °:, h� Æc� Ô

+(m)+,. K Ö� a, b, c, d� TU� RShi\ Æc� �Ê"(liquid

loading)0 vC {C��d Ù Â8� �S�� IJ0É� a=0.24,

b=0.82, c=0.6, d=0.24, K=1.4+,.

��� kl�àj �:`ß�à� Q��,� j`"È, ,²� ¤

� /�� Q�� : ;,.

(45)

φ� �e dp\ dp+∆dpr+� kl� ¤� �¢� °:�Õ, z =log dp,50%,

z=log dp, σg� l"Ð5¸Í� Q��,. l"Ð5¸Í� dp,50%, dp,95%

�Êô B¹ 89 : ;,. Z% Ú��Û0É� / (45)� Âh� k

l�à �C, 13°� kl'º�� �9"# r3"�,.

3-2. � �� ��

RS TU��Êô ��N� ��� pe.g ?lhi(vr)� ��.

g ?lhi(vw)� ÇÇ ,²� ¤+ @`"�,[13].

(46)

(47)

ρL� �� ói(kg/m3), d� TU pe(m), Q� �5ª(m3/h), N

� RShi(rpm), µ� ùi(cP), n� Æc� °:, h� Æc� Ô++,.

3-3. �� �� ��

Fig. 20 Q�½ �\ ¤+ �l �Kl0� Æc+ ®[NX ;X �

lj �R"ÈÉ ��Z� 5�µ,. f.g hi� �åN� �l�

5ª' �l �Kl ºÈ��� Q%X 8"�, �R0 v- Çhi

(angular velocity)� / (48)� Êô _`"�,[14].

(48)

ω� Çhi, Rh� iD ÁÎ �l�Kl� B� U�u, R� �E U

�u, Ux� f .g hi, α� Æc� Çi+,.

K M( )a

Nb( ) dc( ) nh( )d---------------------------------- 104×

dφd dplog---------------- 1

σg 2πlog------------------------ z z–( )2

2 σglog( )2-----------------------–exp=

vr 0.0024ρLπ2N2dQ2

µh2n2----------------------------

1 3⁄

m s⁄( )=

vw πdN m s⁄( )=

ω r3 rdRh

R

∫ Ux αR3 Rh

3–3

-----------------tan=

Fig. 4. Computational grid for spray chamber.

Table 2. Physical properties used for calculation

Item Properties Value

continuous phase

air Specific heat [J/kg K] 1,006Thermal conductivity [W/m K] 0.0224Humidity [kg H2O/kg dry air] 0.02

water vapor Specific heat [J/kg K] 2,000Diffusivity [m2/s] 0.00025

dispersed phase

water Specific heat [J/kg K] 4,200Latent heat for vaporization[J/kg] 2,501,000Density [kg/m3] 1,000

dry milk Average moisture content[kg H2O/kg dry solid]

0.03

Density [kg/m3] 400

HWAHAK KONGHAK Vol. 40, No. 4, August, 2002

512 �������������

4. �� ��

4-1. �� ! ��"# ��

�l 5ª 5 m3/min, �l 5��i 453.15 K, �l �Kl Æc Çi

30o� ��0É ��+ FG"� �' eG ��Z � 5s� tu�à

� Fig. 5(a)0 Q��´,. G¿� �HÐ� Ð�µ Ê�� 5s� tu

.g', ð¿� f.g hi�à� ³#5,. ��Z "Ê� 5�j I

��� Ê�0É ØÊ� 5sj J��� G J"� ï' ¼ : ;,.

Fig. 5. Effect of spraying on gas flow distribution.(air velocity: 5 m3/min, air temperature: 453.15 K, vane angle: 30o)

Fig. 6. Effect of vane angle on gas flow pattern.(air velocity: 5 m3/min, air temperature: 453.15 K, rotating velocity of disk: 21,000 rpm).

���� �40� �4� 2002� 8�

� ����� ��� ���� 513

+� 5s� G J ��� � Â8¢¶0 �2Éi ³� µ � ;,.

J� ��0 Êj"# �� 13.2 L/hr� �å9 eG 5stu�

à0 �[� �g' û�³Ì,. � � :��ª� 87 wt%, RST

U RShi 21,000 rpm�� "�,. Fig. 5(b)0É ³� �\ ¤+ 5

s� G J �3+ ��Z �Ê ��� +6"�,. � +5� ��+

RSTU��Êô ��Z aì0É z ��� : .g�� ,- hi

� RS"ÈÉ �ã���K ��+ j�� : .g� �6ª+ 5s

0 S{N´l mn�� ~ǵ,(�l ��0É ��� �ãhi�

110 m/s�).

5�N� ��3 �l� �R`ij 5stu�à0 �[� �g'

û�³l J2 l� ZÃ��� Ø`"¹ 5�� ñ �l�Kl� Æ

c Çi� 0, 30, 45o� ���L,. Fig. 60É ³� �\ ¤+ Æc Ç

ij �j9:ç G J �3+ �� ��Z wx ��� ��� z �

�� +6"�,. Å�, Æc Çij �j9:ç ��Z �Ê aìÊ�

0É 5s� tu.g+ J��� Q�Q� � áij �j�' û :

;,. Æc� Çij �j"È �l� �Ráij MXQ ��� ��

��Z � s��!+ MXQ� xù+ ;�(, 5s� tu' vC �

�+ NpØ eG ��j ñ Nli S0 ��+ ��Z z+Q wx0

{C|� n%j ~o :i ;²' �r2 �� ;,.

4-2. �� ! � $�

Æc Çi 30o(l� �S��� J\ 6Ø)0É 37.5µm, 97.5µm,

187.5µm E 3j� �e' jY ��� �� ��Z� y6' �r"

�,. Fig. 70É ³� �\ ¤+ 37.5µm\ 187.5µm��� É� ,

- ��' ��< ��Z "Ê� OXY,. �Q, a!kl� 97.5µm

��� J �P� �< 30?j �½ �0i �p ��Z �0 Q¦

;� ï' ¼ : ;,. 37.5µm��� ©ª+ � RSTU0É �ã

µ � R �6ª' *X+� : .g�� ·� â�j� ="� 5s

tu' vC �P� "á�,. +0 12 97.5µm��� : .g��

1 ·� â�j¹ NX G J 5stu0 ST�¹ N� ï�� ~Ç

µ,. � ��� ��+ Fig. 6� 5stu G J� ]^' ¤+"�

;� ù+ + ï' UV�,. 187.5µm ��� ©ª+ WÉ 5stu

G J �30 ¶Xj1Ci 5stu0 ST�� �� a�0 �2

X""� ï�� ~ǵ,. + S� Â80É� +\ ¤� ��� ��

Z� G J ��0 �2 ³� µ �j �,. 5s� vC G JN

� ��� � :j MXY0 vC � �� >sNX G J�3'

,ü QZ ï�� ~ÇN�d Ù Â80É� + ù' ��"� =�,.

4-3. %&'(

Fig. 8� � �å5ª 13.2 L/h, �l 5ª 5 m3/min, �l 5��

i 433.15 K, 5� �l� :�� ��Õ 0.02, Æc Çi 30o� ��0

É ��Z � �i \ 5s � :� �ª' E���� Ð�"� ;,.

�i E�� a 323 K� �8�i0 2"� �i�É � �3� +

� [0É \åµ �\ ¤+ ����� � S{� ��0 v- �}�

�+ ¤¹ N� õ� ��8!+< �� hij Ô� �3+,. Hayashi

[15]� ZÃ_�0 �"È 1]� J[0É 5s� �ij ^ëj N�

ï�� Q�½,. 5s � :� ��Õ' Q��� E��i � �30

É 0.0742� ^�ù�� Q�>�d + ï Å� ��j _4"¹ ØX

Q� ;²' U�"� ï+,. �� ��Z� aì Ê�� �ij ��

��� Ô�d � +5� ��Z aìÊ�0 FG"� ��� :j »

� �� ;, "1Ci ��� klj l mn0 :� �} `�ª+

����� l mnØ ï�� ~ǵ,.

Fig. 9� �� kla �!0 v- :��ª� ��� Q��� ;,.

37.5µm kl ��� eG y� !��� ��j �AN<, 97.5µm

kl ���  Á�:Õ:� ��N�d = 2 ?� �!+ b�<, 187.5µm

Ø eG0� = 6?� ���!+ /b� ï�� �KN´,. Fig. 10

� ���!0 v- ��kla ��� �i��� ³#�� ;,.

37.5µm ��� ��j /!0 ØX½ � R �� �¢(��� ��

0 �2 �¢� �c)� �ij 5s �i:� ��"��, 97.5µm �

�� �i� = 2? 6B �8�i� 5�",j ���:Õ0 i{�

+� �ij ��"��<, 187.5µm ��� ³, d �!6B �8

�i� 5�� � 5s� �i:� ��"�,. Ç kl a� �¢� ̂

e �ij ,- ï� �¢� J[j ¤� �� ��Z � J[a 5s

�i0 Í+j ;l mn+,.

6Ø� �� "0É è��Ël�\ �é0«�lêÂ8T �6��

:¡µ ZÃ_�\ 1Ä2 ³Ì,. ZÃd+ô� RSTU 60 cm f0Fig. 7. Behaviors of droplets depending on sizes.

Fig. 8. Contours of temperature and moisture content in drying cham-ber.

HWAHAK KONGHAK Vol. 40, No. 4, August, 2002

514 �������������

m]

É ñg� �¢� SMD(sauter mean diameter)�É � �åª+

10.6 L/h Ø m 30.1µm, 13.2 L/h Ø m 32.5µm(Fig. 110 Z��� Ð

�)+´,. Fig. 110É ³� �\ ¤+ �Kµ �¢� kl(ù��� Ð

�)� = 15µm ̀ i 1 k¹ Qh�<, � 5ª �j0 v- �e

�� @?� Zà _�\ 1]"�,. i�� /0 �2 @`"# �K

0 r3µ ��� ?lpe' Fig. 110 �� Ð�"�,. �� ?lp

e0 �� ZÃd+ô� 89 : �´,. ZÃÖ� �Kµ ���¢ k

l� Í+� ?l �� kl� Í+0 lc�,� ~ǵ,. �K0 �

"È, RSTU "Ê 60 cm �ù0É �¢� ��Õ� y�  Á�:Õ

0 i{"��d, ZÃd+ô� �:Õ 10% �(�� ³� N´,. �

�Õ 1Ä� J2 ³, 8s�c ZÃd+ôj /b",� ~ǵ,.

ZÃd+ô� Ê9�� c"# �K_�\� 1Ä �#+ j+ +WX

�� =� ù+ �kG<, [�� Z¿ d+ô\� 1Ä Â8j �hN

XM 9 � ~ǵ,.

5. � �

SK5s �K Ú��Û a "Qc CFX4� +3"# ����l�

��Z� 5stu �à, ��� y6, �� �� E' Hl³Ì,. �

�Z�� 5s� �P�+ I��� 8�� c"# aì0É ��\É

z ��� ZCj� W,m G J �3' Á4"�,. lsx �0 �

�+ FG"¹ ���K 5s� tu0i �g' �� ï' û : ;´

,. ��+ G J �3�� ¶Xj� �' (� jn� eG� aì

0É k¹ oXQ� �� �P� OXp� �q 1 �y� ï� G

J �3' vC Np�,. + ³, 1 ©ª+ r eG 5s tu0 �

�g' � �� �P��� +6"�,. �R� �l J2 �l�K

l� vane� Çi� 0o, 30o, 45o� ���L' m 5s� G J �3

+ J��� +6"��< ��µ ��i G J �3' vC Np�

,. Å� �Rj � eG ��N� ��� �Ê0É k¹ T' ��<

�P� OXü s��!+ oX�� ø�j ;´,. Æc Çij «�

W�È G J �3+ �Ê0 Á4Nl mn0 ��N� =� ��+

z0 Êst G�j ;,. vCÉ Æc Çi� �`"¹ 5��± /b

j ;,� ~ǵ,. ��Z �Ê0É jx u� �ij Á4N� ï�

� ³� ��+ + ÊÑ' �â m �8 �i0 i{"# »� ^� :

�+ �}N� ï�� ³c,. �� 5ª 10.6, 13.2l/h, TU RS

hi 21,000 rpm, Æc Çi 30oØ m RSTU ". 60 cm0É �Kµ

���  � �e� ZÃ Ö ³, � Ö' ³��d, +� ?l ���

e ¾¿�`0É }~µ Í0 lc"� ï�� @¿µ,. Ù ���

��K� `÷4' v�"l J2É� ³, »� ZÃ_�\� 1Ä�

#+ !vCM 9 � ~ǵ,.

� �

Ù wn� 0«�­��º �T Â8 _�� ØÊ���É Â81 �

Tl­0 �r)�x,.

����

Ad : surface area of droplets per unit volume of drying chamber [1/

B : Spalding number

Cp : specific heat of air [J/kg/oC]

CD : drag coefficient

C1 : coefficient in Eq. (16)

C2 : coefficient in Eq. (16)

Cµ : coefficient in Eq. (14)

Cv : specific heat of water vapor [J/kg/oC]

cd : specific heat of droplet [J/kg/oC]

D : diffusivity [m2/s]

d : diameter [m]

g : gravitational acceleration [m/s2]

H : enthalpy of gas [J]

Hi : enthalpy of ith component

h : vane height [m]

k : thermal conductivity [W/K/m]

K : coefficient in Eq. (42)

Fig. 9. Variation of moisture content with time for varying droplet sizes.

Fig. 10. Variation of droplet temperature with time.

Fig. 11. Comparison in particle size between model prediction andexperimental data.

���� �40� �4� 2002� 8�

� ����� ��� ���� 515

rs,

493

t

in

er-

-

L : latent heat of water vaporization [J/kg]

M : slurry mass flowrate [kg/hr]

m : mass [kg]

∆ : loss of momentum of droplets per cell [kg m/s]

n : number of vanes

N : rotation speed of disk [1/min]

Nu : Nusselt number

P : pressure, pascal

Q : volumetric flow rate of slurry [m3/hr]

QC : flux of heat transfer from gas to droplet [J/s]

QM : rate of heat consumed by vaporization of water [J/s]

rβ : volume of droplets per unit volume of drying chamber

R : outer diameter of vane of air disperser [m]

Rh : inner diameter of vane of air disperser [m]

Re : Reynolds number

SP : source term in Eq. (1) and (2)

Sh : Sherwood number

t : time [s]

T : temperature [K]

: gas velocity [m/s]

: droplet velocity [m/s]

Wc : molecular weight of water [kg/kmol]

WG : average molcular weight of gas phase [kg/kmol]

Xv : mole fraction of water vapor at the surface of droplet

XG : mole fraction of water vapor in the gas phase

X : weight fraction of water in droplet

X i : mole fraction of ith component in the liquid phase

Yi : mole fraction of ith component in the gas phase

)*�+ ,-

α : vane angle

σg : geometric standard deviation

k : turbulent kinetic energy [m2/s2]

µ : viscosity [kg/m/s]

i : number of particles of ith size group passing through a cell per

unit time [1/s]

ρ : density [kg/m3]

τ : shear stress [kg/m/s2]

ε : turbulent energy dissipation rate [m2/s3]

ω : angular velocity [rad/s]

./-

cr : critical point

d : droplet

eq : equilibrium point

eff : effective

g : gas

l : laminar

p : particle

r : in radial direction

t : turbulent

vap : vapor

w : in tangential direction

x : in axial direction

����

1. Dickinson, D. R. and Marshall, W. R.: AIChE J., 14, 541(1968).

2. Parti, M. and Paláncz, B.: Chem. Eng. Sci., 29, 355(1974).

3. Chow, L. C. and Chung, J. N.: Int. J. Heat & Mass Transfer, 26, 373

(1983).

4. Crowe, C. T., Sharma M. P. and Stock, D. E.: J. Fluids Eng., 99, 325

(1997).

5. Launder, B. E. and Spalding, D. B.: Computer Methods in Applied

Mechanics and Eng., 3, 269(1974).

6. Sano, Y.: Drying Tech., 11, 697(1993).

7. Kim, H. J.: Master Thesis, KAIST, Daejeon(1991).

8. Oakley, D. E. and Bahu, R. E.: Computational Modeling of Spray Drye

European Symposium on Computer Aided Process Engineering-2,

(1992).

9. Livesley, D. M., Oakley, D. E. and Yeoman, M. L.: “Developmen

and Validation of a Computational Model for Spray-Gas Mixing

Spray Dryers,” AEA Report, AEA-InTec-0759(1991).

10. Ministry of Commerce, Industry and Energy: “The Study of the D

elopment of a High Efficiency Dise Type Spray Dryer,” 1997-E-ID01-

49(2000).

11. Katta, S. and Gauvin, W. H.: AIChE J., 21, 143(1975).

12. CFX4 Solver Manual, AEA Technology(1997).

13. Master, K.: “Spray Drying Handbook,” 4th ed., George Godwin, London

(1985).

14. Beer, J. M. and Chigier, N. A.: “Combustion Aerodynamics,” Hal-

sted Press Division, Wily, New York(1972).

15. Hayashi, H.: “Studies on Spray Drying Mechanism of Milk Pow

ders,” Rep Res Lab Snow Brand Products, Japan, 66(1962).

Md

U

v

η·

HWAHAK KONGHAK Vol. 40, No. 4, August, 2002