F CHi KHOA HQC & C6NG NGHp CAC TRUdNG DAI HQC K^ THU^T * S6 91 - 2012
M 6 HiNH TOAN M 6 TA QUA TRINH TRAO D 6 I NHIIT
TRAO o6i CHAT H6N Hgfp TRONG cAc THAP GLAI NHIETMATHEMATICAL MODEL DESCRIBING THE MIXED HEAT AND MASS TRANSFER IN THE COOLING TOWERS
Dgng QuSc Phu, DSng Trhn Thg Tru&ng Dgi hgc Bdch khoa Hd Ngi Den Tda soan 03-4-2011, chip nhdn ddng 28-82012
T6M TAT
Bdi bdo trinh bdy kit qud nghidn c&u. xdy diyng md hinh todn md td qud trinh trao dil nhidt - trao dii chit (TDN - TDC) hdn hgp trong thdp gidt nhiit (TGN). Trdn co sd cdc qud trinh tmyin nhl$t - iniyin chit co bdn. v&i vi$c di xuit su dung hd si truyin chitp [kg/m'hPa] cung thi truyin chitAP [Pa] dd xdy di/ng dugc md hinh todn hgc md td qud Irinh biin ddi trang thdi cua nu&c, khdng khi trong TGN Dd tin c$y cua md hinh todn dugc phdn tich, ddnh gid vd so sdnh v&i kit qud nghidn cuv thirc nghidm.
ABSTRACT
The article presented research results, establishing the mathematical model desenbing the mixed heal and mass transfer in the cooling towers. On the reason of the basic heat and mass transfer in cooling tower, with the use of mass transfer coefficient p kg/m2hPal and the mass potential AP [Pa], had built mathematical models that describe the change of status water and air in the cooling tower The reliability of the mathematical model was analyzed, evaluated and compared with the experimental results.
1. DAT VAN DE
Trao ddi nhiet - trao ddi chat hdn hgp Id mot trong nhung ITnh vuc ca ban ciia ly thuyet truyen nhiet - truyen chdt vd la co sd cho viec nghien cim, thiet ke, che tao cac thiet bj nhiet lanh. Trong dd, c6 cdc thdp 1dm mdt nudc, mpt trong nhung phan td quan trpng ciia cdc he thdng lanh vd dieu hod khdng khi. Trong cdc TGN qud trinh trao ddi nhiet dugc thuc hien dudi hai phuang thirc: trao ddi nhiet ddi luu giSa nudc - kliong khi va trao ddi nhiet do bay hai nudc vao khdng khi. Hieu qud ciia qua trinh phu thudc rat nhieu vdo nhiet dp, dp dm khdng khi ciia mdi trirong [1], [2]. De ldng qudt hod qua trinh trao ddi nhiet - trao ddi chdt trong cdc TGN phai xay dung cdc md hinh toan hpc mo td qud trinh truyen nhiet - truyen chdt trong TGN.
KII hgp ly thuyet vdi thuc nghiem sfi cho phep ddnh gid mpt cdch tdng qudt hieu qud Idm mdt nudc cua TGN trong dieu kien kill hau ndng am.
2. MO HINH T O A N HQC MO T A Q U A TRINH TDN - TDC H 6 N H Q P TRONG TGN
Qud trinh 1dm mat nudc dien ra trong thdp Id mdt qud trinh truyen nhiet truyen chat hdn hgp. Vl vdy, md ta qud trinh bien ddi trong TGN phai la he phuang trinh bieu dien qud trinh truyen nhiet - truyen chit ket hgp.
Theo quan diem cua Pope [10], cd xudt hien viing qud bdo hod trong thdp sau khi den trang thdi bao hoa, dieu ndy ndy da dugc chiing minh bang ly thuylt vd thuc nghiem trong [3].
Do dd, de bieu dien su bien ddi trang thdi khdng khi, nudc trong thdp sg Id cdc h& phuang trinh cho vung khdng khi chua bdo hod, viing bdo hod vd qud bao hoa. Tuy nhien, khi khdng khi dat den trang thdi bdo hoa thi lugng nhiet trao ddi giCra nudc vd khdng khi giam manh.
Lugng nudc bay hoi vao khdng khi Id rit nho, chii yeu hod quyen vao khdng khi d dang suong mil nen lugng nhiet trao ddi Id khdng dang ke [3].
Vi vdy, phin dnh hudng manh nhat tdi hi?u qua qud trinh TDN - TDC trong TGN la qud trinh bien ddi trong vimg khdng khi chua bdo hod. Ddy id vimg cd y nghia nhdt vl hieu qua lam mdt trong TGN. Thilt lap hfi phuong
TAP CHi KHOA HOC & CONG NGHf CAC TRU'NG DAI HOC KY THUAT * S6 91 - 2012 trinh vi phdn bifiu di6n qud trinh bien ddi trang
thdi ciia khdng khi, nudc trong viing bdo hoa vd qud bao hod dd dugc thirc hien trong [3]. 6 day se xay dung md hinh toan hgc bieu diin qud trinh biln ddi trang thdi cua khdng khi, nudc trong viing chua bdo hod vd hudng tog dung ciia nd.
Cdc gid thiel
Khi khdo sdt ly thuyet cdc qua trinh TDN - TDC trong thilt bi kidu ti6p xiic ngugc chieu thudng phdi chap rihan mdt sd gid thiet sau:
- Qud trinh dugc coi Id qud trinli doan nhiet.
- Bd qua su phu thudc cua nhiet dung riSng vao nhidt dp. Nhiet dung rieng cua khong khi kho, hai nudc, nudc dugc xem la khdng ddi vd CO cac gid tri:
Cpk = 1,004 kJ/kgK; Cpi, = 1,842 kJ/kgK;
Cn= 4,186 kJ/kgK
- Qud trinh la lien tuc, dn dinh.
- Nhiet dd bd mat vd tam ciia gipt nudc bang nhau.
Cdc qud trinh truyin nhit - truyen chdt ca bdn Xet mot phan td dien tich be mat tiep xuc dF, hinh 1. Khi tn > t^ ta cd cac phuang trinh TDN - TDC CO ban gdm:
Gn + d G „ jfl + d i n
1
* _ J .
1
1
\
G„, i„
GK d + d ( d ) k + dik
f
- d Q d , dF , d Q „
t
k, d G l
Htnh 1. Md hinh TDN - TDC trong phdn td dF Trao ddi nhiet doi luv giu-a nu&c vd khong khi Lugng nhiet do trao ddi bang ddi luu qua phdn td dF dugc xdc dinh:
dQdi = a.{V tk)dF - a.At.dF (1)
Trao doi nhiit bdng trao ddi chdt do nuac bay hai vdo khong khi
Theo Merkel [9] thi tao ra qud Uinh trao ddi nhiet Id AI = lk{tn) - \{Q va nhiet trao ddi dugc xdc djnh:
dQ= p'.[(l,(g-L(t,)].dF (2) Vdi p' Id he so truyen tdng hgp, cd thd nguyen, kg/m^s
Trong [10] Pope dd sir dung the tao ra qud trinh truyin chat la dp chenh Ad = dghCtJ - d, tren co sd do lugng nudc bay hai dugc xac djnli:
dG,= p-.[d,h(t„)-4].dF (3) Lugng nhiet trao ddi bang truyen chit dugc tinh theo:
dQ,c= )l*.[d,h{tn)-4].dF.rg, (4) Vdi p' dugc Pope gpi la he so truyen chit, c6 thd nguyen kg/m^s.
Trong [4] da chimg minh p* la luu lupng khdng khi khd qua mot don vi dien tich b6 mat.
Tren co sd do chiing tdi de xudt n^n sir dung he sd truyin chit p [kgh/m^sPa] Id luong nudc bay hoi qua 1 don vi dien tich trong mot dan vi thdi gian khi dp chenh phdn dp sudt hai giua be mat bay hoi vd khdng khi la 1 Pa. Vdi viec su dung he sd truyin chit p nay, lugng nudc bay hai tir nudc vao khdng khi dugc tinh nhu sau:
dG„=p.(Ph,h-Ph)-dF=p.AP.dF=G,.d(d) (5) Trong dd: Phgh [Pa] - Phan dp suit hai nudc ciia ldp khdng khi tai be mat gidi han co nhiet dp bdng nhiet dp nudc t^, Phgh = Ps(tn)
Ph [Pa] - Phdn ap suit hoi nudc trong khdng khi d nhiet dp tt
d(d) - Biln thien do chda hai ciia khdng khi, kgh/kgkk
Khi dd, lugng nhiet trao ddi giira nudc vd khdng khi thuc hien bang truyin chdt dugc xac dinh bdng:
dQ,c = dG„.rgh = p.AP.r^h-dF (6) r^h Nhiet an hod hai tren be mat gidi han, xac dinh theo rJiiet dn hod hai ciia nudc d O^C va nhiet dung rieng ciia hai Cpj,:
rgh^Cph.tn + ro (7)
TAP Cllf KIIOA IIQC * C 6 N C ^GH(: CAC TRirdNG D*I HQC K ? THllAT * S 6 91-2012 aAt
Phwang trinh can bang nhi^l
• Phirong trinh cSn bang nSng lirgng:
dQ = MQJ = MQkl (8) Trong d6:
- BiSn thien nang lui;mg ciia d6ng nirdc:
d Q . = d(G..i.) = G„.di. + i„.dQ. (9) - Bign thien nSng iirgng ciia ddng IdiQng lihl:dQ» = Oi.d(li)
(10)
* Pliirang trinh truydn nhi^t - truygn chat lion hop
d Q = d Q d , + dQ,. ( I I ) TliS phuong trinh (1) va (6) vao (11) ta
nhan dugc:
dQ = [a.At + / ? .AP.r,i,].dF (12) PTVP qua Irinh biin doi trang ihdl khong khi.
mroc trong TGN
K6t hgp cac phirong trinh (8), (2) va (12) ta co:
Ci.[(Cp. + d.C,K).dti + (r„ + ti.Cfi ).d(d)] =
[ a , A t + ^ . A P . r J . d F (13) Vcri dp tinh tir phirong trinh (5), khi do
( 1 3 ) t r a thanh:
(C,i + d.C, ,a.&l
,dtj + r„+C.,
+ (ro + t..C„, ).d(d) (14) /3.AP
Sau mgt so bi6n doi nhan dugc phirong
dt, d(d)
a.AI BAP_ + C,,,.M
C „ +d.C^, Tir phuong trinh (9) va (5) ta c6:
a.A/
(15)
G . . C . . d t „ = G . . ( - ^ ^ ,
H a y i S f 5 = ^ [ ^ rfr„ O. o A ;
/J.A/'
i„).</(</)(16)
- 1 (17)
Ket hgp (15) voi (17) ta nhan dugc phuong trinh:
dtt_^G^, dt, Gj , a : A ;
0.AP '
- ] (18)
P h u a n g trinh (17) vd (18) tao thdnh hS p h u a n g trinh vi phdn:
dt„ Gr,a-^ , /3.AP
B.AP '^
- ] -i„).(C;^+d.C^)
(19) d{d) _ G„
dl,.
pAP '^'' '•
He (19) Id h? p h u a n g trinh vi phdn thudng bieu dien bien thien nhi^t dg vd dp chira hoi cua khdng khi theo nhiet d0 nudc. Dk gidi dugc he p h u a n g trinh vi phdn ndy ngodi cdc d i l u kien ban dau, dieu kien bien cdn phdi xdc djnh mpt sd dai lugng va cac quan he lien quan den he phuang trinh:
- Bien thien do chua hai theo nhi§t dp: d = fl^t) - Dg chenh nhiet do At = tn- tk
- Do chenh phdn dp sudt AP = Phgh - Ph - Ti le luu lugng khdi lugng giijra nudc vd khdng khi G ^ G t
Ty le ddc trung cua qud trinh a.At/p.AP Xdc dinh cdc dgi lugng quan h4 Quan hf d =f(t)
Ddi vdi khdng khi do chira hoi d duac tinh theo cdng thirc [1]:
P-^AUk) , kgh/kgkk (20) Ps(tk) dp suat bao hod cua hai nudc trong khdng khi dm.
Do chinh phdn dp sudt AP A P - P h , h - P h
- Ap suat Phgh d bd mat gidi han tai nhi^t ddtn
- A p s u i t h a i n u d c Ph trong khong khi tai nhi^t dp tk
TAP CHt KHOA HOC & C6NG NGH? CAC TRlTdNG 0^1 HQC KY THU^T * S6 91 - 2012 Ti li ltru lugng khoi lugng nu&c vd khdng khi
Trong TGN, luu lugng nudc thay ddi do mdt phdn nudc baj; hoi vdo khdng khi. Vi vay, ty Id luu lugng khdi lugng Gn/Gk thay ddi theo su bay hai ciia nudc. Trdn ca sd can bdng chdt cho mdt phdn td dF, xdc dinh dugc ty le GJGk theo su thay ddi ciia d nhu sau:
(21)
„ '=^.V*^-(d-d,)]
Td hgp hi sd trao ddi nhiet - dm hdn hgp a.Nt
JAP
Viec xdc dinh cdc he s6 TDN - TDC khd phdc tap vi a vd p phu thupc vdo khd nhieu yeu to.
Lewis [8] da dua ra quan he:
r - C „ (22)
Day dugc gpi Id dinh luat Lewis, da dugc thuc nghiem kiem dinh dung trong dieu kien doan nhiet, nhung d cdc dieu kien khac, trong mdt s6 trudng hgp lai cd sai khdc khd ldn. Cdc do dac sau dd cung nhu nghien ciiu ly thuyet ciia mpt sd nhd nghien cuu khdc da chi ra rang ty so nay nam trong khodng 0,8 - 1,2
Theo Bosnjakovic [7], neu coi qua trinh ddn nhiet vd khulch tdn la nhung qud trinh tuang tu vd luu y den be mat gidi han bdn tham thau vd dd chenh dp Idn Bosnjakovic da de xuat mpt phuang phdp xdc dinh td hgp cdc he so trao ddi a/p*.Cp nhu sau:
:lzl
-, = 0,9085.^
•C, ln,f vdi ^ =
(23)
(24) Khi kgt hgp phuong trinh (I) voi phuong trinh (10) va luu y:
ilQdi=a.(V ti)dF=a.At.dF=Gi.Cpi.dti (25) taco:
dQ„ = Gi.d(d).rgi
=Gi.[d.C,H.dtk+(r„+ti..Cpi).d(d)] (26) Ti^ phucmg trinh (7) va (26) ta nhan dugc:
4C,i.dti= (C,i,.t.-tk.C,H).dd
= C,H.At.d(d) (27) hay: dl, _ At
(28) d(,d) d
Chia vl vdi vB ciia (25) cho (6) thu dugc:
a.At dt, fl.AP~ ''U Kit hgp (26) vdi (27) ta c6:
a-Ar Ar « _ ^ ^ tl.AP~ '''~d^~J3~ '*'~T
The (30) vao hS (19) nhan dugc he mdi nhu sau:
Idt^a^ C„.Ar
\dl,^G,' (C,..A( + (r,„-,„).</) (29)
(30)
ldd_
\dt. ' G.'^C,. .Ar + (r,,
(31)
- ' . ) • ' '
dt, dd dt.
dd At
d
G,
c,.
Ar d *''' '"C,
Trong mot sd trudng hpp dd chiia hai ciia khdng khi ra (d2) biit trudc, tir phucmg trinh (19) ket hop vdi (28) ta thu dugc he phuang trinh vi phan md td nhiet dp nudc, nhiet dp khdng khi ra theo d nhu sau:
(32)
Cd the thay he (31), (32) Id cac he phuong trinh vi phan thudng cd the gidi dupc bdng phuang phdp sd. Ve true quan cdc he (31), (32) dan gian vd cd it dai lugng cdn xdc dinh ban he phuang trinh vi phan TDN - TDC trong TGN [3] thiet lap theo quan diem ciia Pope.
Dieu nay se rdt thudn tien khi gidi he (31) vd (32).
So sdnh, ddnh gid md hinh todn hoc Da tien hdnh giai he PTVP (31), (32) bang phuang phdp sd Range - Kutta cip 4 vdi viec su dung ngdn ngu lap trinh Visual Basic.
Dilu kien bien la gidi han cua 265 che dp thuc nghiem tii cdc che dp thuc nghiem da thuc hien tren md hinh va cac TGN hoat ddng ngoai thuc te. Kit qud so sanh dugc bieu dien Uen dd thi hinh 2.
TAP CHi KHOA HQC & C 6 N G NGHf CAC TRlTCfNG D ^ HQC KY THU^T * S 6 91 - 2012
Hinh 2. So sdnh kit qud tinh l„2 iheo ly thuyel vd thuc nghidm
Ket qud tinh todn cho thay: neu coi gid tri tn2 tir thuc nghiem Id chinh xac thi tn2 tinh theo he phuang trinh vi phan (31), (32) cd sai lech nhu sau:
Sai lech ldn nhat la: 4,65%, sai lech nhd nhdt la 0,02% va cd 165 gia tri dat sai lech nhd ban 1%. Sai lech trung binh Id: 1,4% (sai lech tuyet ddi < 0,5 K).
Tren dd thj eho thdy vi trj cac cap d i l m tn2-T>i vd tn2-LT dcu nam giao dpng xung quanh va hpi ty ve dudng cheo chinh
K i t luan
Md hinh todn hpc xdy di,mg dua tren c o sd cdc qud trinh T N - TC c a ban, cd dp chinh xdc hodn loan ddp iing dugc cac yeu cdu ky thuat. Sai Ipch trung binh giira kit qua tinh theo ly thuyet va thgc nghidm la + 1,4% (<0.5K).
Day la md hinh todn ddng tin cay vd huu ich trong vipc nghien cim, tinh loan TGN.
Cac ky hieu dung trong bai bao
D o n vj T e n d a i l u a n g N h i e t d u n g r i e n g K y
hieu
C [ k J / k g K ]
d F G h 1 Q t r a
P P
M
1 2 bh dl gh h k
[kgh/kgk]
[m^]
[kg/s]
[m]
[kJ/kg]
[W]
rc]
[kJ/kg]
[W/m-K]
[kgh/m"sPa]
[kg/m's]
[%]
Do chira hoi Dien tich be mat Luu luong khoi lugng Chieu cao Entanpy Dong nhiet Nhiet do bach phan Nhiet an
He so toa nhiet doi luu He so truyen chat He so truyen tong hgp Do am tuong doi ciia khong khi He so tudi Ky hieu chan vao
ra bay hai doi luu gioi han Hai khong khi
It ly thuyet n nuac tb trung binh tc truyen chat tn thuc nghiem u nhiet kk udt
" bao hoa
T ^ CHi KHOA HQC & CONG NCHg CAC TRUdNG D^l HQC KY THUAT • s 6 91 - 2012
TAI LIEU THAM KHAO
1. Trdn Van Phu. Cdc van de chgn Igc ve ly thuyet TN-TC hdn hpp. Bdi gidng cao hpc. Trudng DHBK-Handi 2000
2. Nguyin Dire Lgi, Pham Vdn Tuy; Ky thudt lanh ca sd; Nhd xudt ban Gido due, 1999.
3. Dang Tran Thp. Nghien cim dnh hudng cua khi hau ndng dm tdi hi^u qud trao ddi nhi^t trao ddi chat trong cdc thap 1dm mdt img dung cho ky thudt lanh va dieu hod kliong khi. Luan van Thac s y , H a n d i 2003
4. Dang Tran Thp. Nghien cim ly thuyet va thuc nghidm qud trinh trao ddi nhict - Uao ddi chat hdn hpp trong thdp gidi nhi^t ciia cac h? thdng lanh va dieu hod khdng khi. Luan an Ticn sy ky thuat. Ha npi 2007
A. F. Mill. Heat and mass transfer. Elizabeth Jones Sponsoring Editor, My 1998
Harting. Zur Einheitlichen Berechnung von Kuhlturmen. Dissertation, TU Braunschweig, 1977 F. Bonjakovic. Technische thermodyiiamik. Dressden, Due 1971
Lewis, W - In The Evaporation of a Liquid into a Gas A Corro ction. Engineering, New York 55.
USA 1933
Merkel, P., Verdunstungskiihlung, in: Verdunstungskiihlung VDI-Forschungsheft, Diisseldorf.
DLEC 1925
10. Poppe, Warme-und Stoffubertragung beider Verdungstungs- kiihlung in Gcgen- und Kreuzstrom, VDI-Forschungsheft, Dusseldorf 56. Diic 1973
Dia cbi liin hi: Dang Trdn Thp - Tel: 04.3868.2625, email: [email protected] Trudng Dai hpc Bdch khoa Ha Npi
Sd 1 - Dai Cd Viet - Hai Ba T n m g - Ha Ndi
