calculation of spray drying using computational fluid dynamics · 2002-08-22 · calculation of...
TRANSCRIPT
HWAHAK KONGHAK Vol. 40, No. 4, August, 2002, pp. 507-515
������� � �� ���
�������†���*���**
����� �����*��� � ����������
**������� � ������� �(2002 3! 23" #$, 2002 5! 8" %&)
Calculation of Spray Drying Using Computational Fluid Dynamics
Ka-Ram Park, Kyun Young Park†, Ji-Sun Ju* and Jun Taek Park**
Department of Chemical Engineering, Kongju National University, Gongju 314-701, Korea*Plant Engineering Center, Institute for Advanced Engineering, Yongin 449-860, Korea
**Department of Energy Systems, Korea Institute of Energy Research, Daejeon 305-343, Korea(Received 23 March 2002; accepted 8 May 2002)
� �
���� �� ��� �� CFX4� ���� �� 140 cm, �� 170 cm� ���� ������� �� !"
#� �� ��$ % ��&' �(, )*� +,, �� -" ./ 012 345. ��$ %� ��6 789� :7;6 <
�� �� =�� %>?� @ 9#� ABC6 D5E F GH IJ/ KL�M5. ��N %� )*� ��O#�P
��� &'� "QR IS/ T6 U/ V W XY5. )*� F GH IJ#� Z[C; \/ ]^ C_` � 6 =�
� ab c[�; \d 78� e[fd �g h �+` Ui F GH IJ/ jB k�M5. � 35 h lm� n � �
� &'� o IS/ p; \d 789#� �,�M5. q�� T� r2 s����� t uv� 0o, 30o, 45o� wxy
z� jB ��� F GH IJ� r9#� �,�M5. t uvC D;{ q� |vC }C�� )*� "~�� �/ a
b ��� 78� e[;� ��� ��y�� �[;6 ��C X#�, F GH IJ� "~� �,�� jB ���; �
R )*� @� ~�� r�L� }C�M5.
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
1. � �
����� ��� �� � ���� ���� � ��� ��
� ���� !��� ��"# �$%&' ()� ��*+,. ,-
��./0 12 324, 564+ 7� 8� �$ %&' %�9 : ;
�< /&, �=&, >4?%, @A, BA, ?CD E FG HIJ� K
L�M0 +3N� ;,.
�� ��� OP+Q RSTU' V2 +WXY,. �� ./�
��Z� [:\ ]^' _`"� ab� bc+ N�d, OP� eG
� ����� f.g hij kl mn0 ��Z+ oXM "< RS
TU� eG� ��� Ue.g hij kl mn0 ��Z pe+ q
XM �,. RSTU' r39 eG �� ��+ ls� tu' vC w
x' [yQ ��Z z0 {C|� n%j }~"li �,. ��� �
�Z � s��!' �j��l J2 ��3 j� 5� � �R(swirling)
� �l mn0 ��Z � �� � 5s� y6� FG ��� ^�'†To whom correspondence should be addressed.E-mail: [email protected]
507
508 �������������
Q��,.
���� �K� ��� 56��� �� �� ��� ��, �i�
�, �� E' 6�0 ��"#M "�� FG X�� n%� "Q+,.
Dickinson� Marshall[1]� �lj �� tu�' j`"� ��� h
ij � S{ hi0 �g' �� �' (� � eG\ FG � eG
0 �2 �} hi� �K"��<, Parti\ Paláncz[2]� ��� hij
��Z� f.g�� ¡"� �¢� pe+ ]£ ¤,� j` "0
��0 �� ��� kl ��� �K"�,. Chow\ Chung[3]� �
l\ :�l� tu+ ¥�(laminar flow)C� j` "0 ¦.§� �}
hi� �K"�,. Crowe E[4]� PSIC(particle source in cell) ]¨'
%�"# l-� 2� !� ¦©, �6ª, 0«� S{� �¬ �� ®
¯"��, +� +3"# ���� �K' �¥ °��± : ;²' ³
# �´,.
J0 �yµ ]¨¶0 i�µ j`¶� Z% ����Z�� 5st
u ���� y�j ·�, �K ¸�� �Q[¹ º ��� rZ4+
»+ _#NX ;,� ¼ : ;,. Launder\ Spalding[5]� ��Z �
5stu� ½���' �Z��� ¾¿9 : ;� κ−ε]¨' %�"
�,. Sano[6]� 5stu �K0 κ−ε]¨, l-� !� �, �6ª, ¦
©S{ �K0 PSIC ]¨' i�"# À�Á ����l� �K"�
,- Â8¢� Zà _�\ 1Ä"�,. Kim[7] Å� κ−ε ]¨, PSIC
]¨' +3"# �l ��8� Æc(vane) Çi� ����ÈÉ ��
��Z � 5s tu� ��\ �¢� ��' �K"�,. Sano[6]\
Kim[7]� ��Z �Ê0É ��3 j� i�Ê�� Z% l"Ë� 8
�� ��"� �Ì�, �K ¸�� ��Z� "Ê0Éi Z%� l"
Ë� 8�\ Í+j ;� ÁÎ� Ï¢(grid)� r3"�,. �¸ Oakley
E [8]� ����Z� Z% l"� 8�� U�"# 2j� ��
½�]¨c κ−ε]¨� Reynolds stress ]¨' 1Ä"��d, Reynolds
stress ]¨+ Z%0 ³, Ñr"¹ ¾¿9 : ;�Q :Ò+ XÓ,�
³�"�,. Livesley E[9]� FLOW3D� r3"# ����l� pe
� Ô+ ��, ��l8� ��, �Á� �ª ��0 v- ��Õ' �
K� _� Z% Ö� 1Ä� × Ø[�,� ³�"�,.
Ù Â80É� �3 5s�K Ú��Û� "Qc CFX4� +3"#
RSTU' ��i8� r3"� Ü+ÝÞ ß]� ����Z �0É
lsx� 5h, �i�à\ ��� ��, ��Õ E' �K"�,. ��
��¦©� G5+<, ��0 r3µ j�� �l+,. �� ��Z�
]^, [:� Fig. 10 �� �l �Kl � RSTU� ]^, [:�
Fig. 20 Q��´,. ��� 2°� �l �Kl� V2 ��l� ��
N< �l �Kl0 {�;� Æc0 �2 �R�j Á4µ,. Æc�
Çij {C�È �Ráij {C�¹ µ,. �� 12°� â°j
{� ;� TU(disk)' V2 ��Z �� ��N< TU� pe� 10 cm,
Ô+� 1.5 cm+,. ����l� ��µ �l\ �¢� ]£ ��Z
"º� ã8� äãµ,. ��3 �l �Kl0 ®[µ Æc� Çi, R
STU� RShi, � �� ��j ��Z� 5s tu, ��
� ��0 �[� �g' �r"�,. +� Livesley E[9]� +S Â8
0É� ,WX�� �Ìæ Ê�+<, 1ç %��+l� "Q Ù Â8
� �K_�� è��Ël�\ �é0«�lêÂ8ë0É :¡µ Ü+
ÝÞ ���� ZÃ_�[10]\ 1Ä2 ³Ì,.
2. � �
�� ��Z � 5s, ��� y6� aìf0 �"# �í' +î ï
+�� 2 ÍT TV ðÐ�� ñò"��<, ÇÇ0 �� �ä.`/�
2 �(5s\ ��) !� ¦©, �6ª, 0«� S{/' ,²� ¤+ Ð
�"�,.
2-1. �� �����
2-1-1. Âh .`/
(1)
ρ� 5s� ói, Ux� f.g, Ur� Ue.g hi4�, SP� ���
�Êô 3F(¦)� �}0 �� 5s� ©ª ~4õ+,.
2-1-2. �6ª .`/
(2)
� ��0 �� õ�� x(f.g), r(Ue.g), w(��.
g) 4�� ,²� ¤+ Ð�µ,.
∂∂x------ ρUx( ) 1
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.
���� �40� �4� 2002� 8�
� ����� ��� ���� 509
(3)
(4)
(5)
Uw� ��.g hi� ÇÇ Q��,. / (2)� [ öτ]� ÷K0 ��
õ��É τ� stress tensor� Q��< ? .g� 4�� ,²� ¤+
Ð�µ,.
(6)
(7)
(8)
(9)
(10)
(11)
(12)
µeff� ½�� �g' ��� 5ø ùi(effective viscosity)�É 0ú
ùi(eddy viscosity) µt\ ¥� ùi(laminar viscosity) µl� >�� �
Kµ,.
(13)
(14)
0ú ùi� �K"� / (14)� κ−ε]¨� û�ü ;�< κ, εÖ�,²� �� .`/��Êô 8�,[5].
(15)
(16)
(17)
J /¶0 à�µ �: Cµ, C1, C2, σk, σε� ½�0 �� ZÃ0 �2
8� Ö�� Table 10 Q��´,.
2-1-3. 0«� .`/
(18)
#l0É, σH� ½�]¨ �:� 0.9+�[5], ý þÿ� H� ,² /
0 �2 �Kµ,.
H= (19)
Hi� i 4�� þÿ�+� Yi � ls x0 à�µ i 4�� ��Õ+,.
2-2. � �����
��� ]^� �S� 8Á+� ��N� 6B 8Á� ]^' 5�"
< l�� ��� Ê��Õ+ �É ��¶ �¬!� �� >s� �
� ï�� j`"�,. ��� hi� õ�� a�0 �2 �g' �
< ,²� ¤� /0 �2 _`µ,[11].
(20)
(21)
(22)
(23)
md� ��� ©ª, ρ� ls� ói, vx, vr, vw� ��� f.g, Ue
.g, ��.g hi� Q��< CD� õ��:, Ad� ��Z ºJ Ê
� ��� ÐÈ���É, ��� pe(dp)� ��Z� ��+ Í�"
� Ê��Õ(rβ)� Q�� : ;,.
(24)
õ��: CD� ,²� ¤� /0 �2 �K�,[4].
(25)
(26)
B� Spalding number, Cv� :�l� 1�, Tg\ Td� ÇÇ ls\ �
�� �i+<, L� �}��+,. / (25)� CDo� ,² /��Êô 8�,.
(27)
+��: Re� ls\ ��� ��hi� r3"# ,²� ¤+ �
Kµ,.
(28)
�! ∆tj e�� � ��� J[� ,²� ¤+ �Kµ,.
(29)
� �! t00É ��� J[, � �! t+t00É ��� J[�
Q��<, ∆t6B ��� +6hi� t00É� hi \ t+t00É� h
i � ��� "�,.
2-3. 2 �� ��, ���, � ��
2-3-1. ¦© S{
�� ��Z �0É� ����Êô l� ��� ¦� �}+ ØX½,.
����Êô ¦� �}� Fig. 30É ³� �\ ¤+ 3º�� ØX½,: (1)
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 �������������
2-3-1-1. ¾� 8!
��+ ��NÈ �y� ��3 �l\ (Q �ij ��"� ¾� 8
!' y[¹ N<, + 8!0É� �� hi� ,²� ¤+ �K�,[12].
(30)
(31)
D� :�l� ÷K�:+< WC\ WG� :�l� �¢ª� Âh�0
É �>¦(��3 �l+:�l)� �¢ª+�, Xv\ XG� ÇÇ ��
ÐÈ� l�0É :�l� ��Õ' Q��,. �� ÐÈ0É :�l
� ��Õ� ,²� ¤+ �K�,.
(32)
P� lsx� ��+� Pvap� :�l� Ê� ����É ,²�
antoine /��Êô 8�,.
Pvap=exp(A− ) (33)
A=23.196
B=3816.4
C=−46.13
2-3-1-2. õ� �� 8!
����� � S{ª� ��0 v- �}��ª+ ¤��È ���
�i� Ø`2��(�8�i) + 8!0É ��hi� y� Ø`� Ö
' j�¹ N<, ,²� ¤� /0 �2 _`µ,.
(34)
k� ls� �Sii, Nu� Nusselt number, L� �}��' Q��
,. Nusselt number�
(35)
µ\ Cp� ÇÇ ls� ùi\ 1�+,.
2-3-1-3. �� �� 8!
õ� ��8!+ �â m �+È �ª� :�+ �}"# ��+
�s�¢� Á��� ��N<, ��ù0 i{� +�Êô� ��j Y
¡�0 vC ��hij ùù �X)� �� ��8!0 i{�,. +
8!0É� ��hi ��� Fig. 30É ³� �\ ¤+ �� ��¦©
� �40 vC ,^� ÁÎ� Q��¹ N�d, Ù Â80É� ��h
ij 1 Í��� �ë"� ï�� j`"# ,²� ¤� /0 �2 �
�hi(− )� _`"�,.
(36)
� ��ù0É� ��hi, md� �¢� ©ª, md, cr, md, eq
� ÇÇ ���:Õ, Á�:Õ0 i{�' m �¢� ©ª+,.
2-3-2. �6ª S{
/ (2)� 5s �6ª �ä.`/� - �0 ;� �6ª ~4õ(SP)
� �� ��� �6ª+ 5s ��� S{N� ^��É ��� �6
ª �ëª+,. !0 ®¯""�( / (2)� :[2# �`0É �� �
�Z �� # °� $(cell)� Q%¹ N�d �XY $0É ����
Êô 5s�� �6ª S{ª� ,²� ¤+ �Kµ,.
�XY $' �Q� �¢� & °� kl'º�� ��"� i() k
l'º� �¢j $' V�"ÈÉ *X+�� �6ª�
(37)
ρp� �¢� ói, � ºJ�! �Qj� kl'º i� �¢°:,
\ � $' ,ü Q � kl'º i� hi\ �¢pe,
� di, in� $� ¶Xj� hi\ �¢pe' Q��,. �XY $
0 �"# ý- �6ª S{ª�
(38)
2-3-3. � S{
��� �i� ls�Êô ����� � S{ª� :� �}���
�:�É ,²� ¤� /0 �2 _`µ,.
(39)
#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
� ¤�ü, ,� $"È Qc� QM� >� 0+ NX ��� �i� 1 +
� �"� �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.
���� �40� �4� 2002� 8�
� ����� ��� ���� 511
3. ��
J� 5s, �� �ä.`/¶' Â�"# 2l J2 �3 SK5s
3Ë Ú��Û� "Qc CFX4� +3"�,. Ù Ú��Û� �� .`
/� +K�(discretization) .*�� 5�s�*(finite volume method)
' r3"�, :Ò./��� PSIC ]¨' ñò"� ;,. �K./�
G� ��+ �,� j`"� 5sx� �ä.`/' 4 ,², � �K
_�� +3"# ��� ��, �}ª, �i� �K�,. �XY $'
V�"ÈÉ }~N� ©ª��, �� hi��, �i���Êô 5s�
�6ª.`/, Âh.`/, 0«�.`/� ~4 õ' _` ��"� 5
s x' ,� 4,. +� 5s x, �� �K�`' :Òl5(]6 $
� 5s .`/ ©ª 7� Ö(residual)� >' ��Z0 i�N� 5s
� 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