N G H I S N CLTU-TRAOeOi MO HINH TOAN XAC DINH CHIEU DAY MANG LONG NGUlVG TRONG VI ONG d CHE DO HINH XUYEN MATHEMATICAL MODEL FOR DETERMINATION OF CONDENSATION FILM THICKNESS IN MICRO TUBE IN ANNULAR REGIME ThS Hoang Anh Tnin', PGS,TS Nguyin Nguyen An^ 'Tmdng Cao ding nghd Cdng nghiep Thanh Hoa ^Tnrdng Dai hpc Bich khoa Hi Npi TOM TAT Bdi bdo trinh bdy viec xdy dung mgt mo hinh todn giup xdc dinh chieu ddy mdng long ngung vi ong cr che hinh xuyen Mo hinh diroc xdy dung dua tren vi^c thiet lap he phinmg trinh viphdn bdo todn dgng lufrng, bdo todn khoi vd cdn bdng ndng Ittfmg Ap tog trg hai chieu CO ki den dg cong ciia mdng long ngimg cUng nhu hi^n tuong truot tgi be mat phdn pha long - hai Vifc tich phdn he phuong trinh viphdn ndy theo tiet dien ngang vi ong dd duoc thttc hifn, gidp xdy dung mgt mo hinh todn chi gom cdc phep tinh dgi so vd tich phdn xdc dinh, hodn todn co the gim duoc bdng cdc phuong phdp so thong dung hien Bdy Id co so de xdy dung mgt phucmg phdp ly thuyet giup xae dinh chinh xdc hem chieu ddy mdng long ngung ciing nhu he so trao ddi nhtft doi luu Irong vi ong a che dg hinh xuyen Tir khoi: Mdng long ngtmg, ngung Ut, vi Sng ABSTRACT This paper presents Ihe development of a mathematical model to determine the thickness of condensed liquid layer during condensation in micro tube in annular regime The model was developed based on the establishment of the differential equations for momentum, mass and energy conservations in two - dimensional cylindrical coordinate system Theses differential equations are took into account the effects of cultivation of the liquid layer as well as the slip phenomenon al Ihe liquid - vapor interface surface The integrating the differential equations in the cross - section c Ihe lube was performed that converted these differential equations to the algebraicform which can be solved easily by popular numerical methods This is basic ofdevelopment ofa theoretical method for precisely determine the thickness of the liquid layer as well as the convective heat transfer coefficient during condensation in micro tube in annular regime Kcyivords: Condensed liquid layer, condensation, micro Uibe ISSN 0866-7056 TAPCHlCaKHlVl6TNAM,Sd I0nam2016 www.cokhivietnam.vn NGHIEN CU'U - TRAO 06l l.DATVANDE Qua trinh ngung ty cua ddng mdi chdt Uong vi dng (nhirng dng cd dudng ldnh nhd hon 2mm) dang rdt duoc quan tdm khd nang tiet kipm nguyfin vdt lieu chl tgo thiet hi, cDng nhu gidm dupc ddng ke Iupng mdi chdt su dyng Trong qud trinh ngung ty bfin dng, che dp hmh xuyen Iudn xdy vdi tdn suat cao hon cdc chfi dp Ididc Doi vdi vi dng, cd kich thudc nhd, che dp hinh xuyfin xdyraUong phan ldn cdc trudng hpp [1,2] Do vay, nghien ciiu ve qud trinh ngimg ty Uong dng d che dp hinh xuyen ludn dupc quan tam, dac biet la ddi vdi vi dng Qud trinh ngung ty bfin Uong vi dng ndi chung, d che dp hinh xuyfin ndirifing,dupc nghifin ciiu cd d phuong di^n Iy thuyet lan thyc nghifm Cdc nghien cim thyc nghipm thudng dupc tifin hdnh cho mpt sd ttudng hpp cy the vfi kich cd vi dng, chung logi mdi chdt va dai nhipt dO, dp suat Idm viec [1-12] Tuy khdng chi dupc bdn chdt ciia cdc qud trinh xdy ben nhirag ket qud nghien ciiu thyc nghifim tiiudng cho ket qua khd chinh xdc, ddp iing dupc nhu cdu tinh toan Uong thuc te De md rpng phgm vi dp dyng ciia cdc kfit qud nghien Cliu thyc nghipm, mdt sd nghifin ciiu ly thuyfit da dupc din hanh Trong dd, hudng nghien ciiu dau tien dupc thyc hipn Id su dyng cdc cdng thiic da dupc xdy dyng cho ong thudng [1317], dp dyng cho vi dng vd so sdnh vdi cdc ket qua thyc nghipm de ddnh gid dp chinh xdc cung nhu phgm vi dp dyng ciia cdc cdng thiic ndy Theo dd, cdng thiic ciia Akers vd cpng sy [13] cho kit qud phu hpp nhdt dp dung de tinh hp sd trao ddi nhipt ddi luu trung binh cho todn bp dogn vi dng dang khdo sdt, vdi sai lech cao hon tii 10% den 20% so vdi sd lipu thuc nghifm Tuy nhien, so sdnh vdi sd lipu thyc nghipm vfi hp sd trao ddi nhiet ddi Iim cue bp Uong vi dng, Baird va cpng sy nhdn thdy, tdt cd cac cdng thiic hien cd dlu cho kit qua rdt sai lech [1] Vi vdy, Baird vd cdng sy da tien hdnh xdy dung mdt md hmh ban thuc nghiem de xdc dinh he sd trao doi nhifit ddi luu cyc bd ttong vi dng cho chl dp hinh xuyln, cd ke den dnh hudng cua tdc dp khdi, dp khd mdi chdt, kich CO vi dng vd dp sudt cua qud trinh ngimg ty [1] Cdc nghien ciiu ly thuyet vfi qua trinh ngung ty Uong vi dng, nhu vua trinh bay, cd ddc difim la dlu kl thira ly tiiuylt ogimg mdng Nusselts vdi chieu ddy mang ldng ngung dupc coi Id rdt nhd so vdi dudng kinh dng va dnh hudng cua lyc trpng trudng Ifin chuyen dpng cua mang ngung Id khdng the bd qua ttong mdt sd trudng hpp Ddi vdi vi dng, cd dudng kinh rdt nhd nfin nhimg ddc difim Iy thuylt ngung mdng Nusselts Ud nen khdng phu hpp Vi vgy, bdi bao se Uinh bdy mpt md hinh todn giiip xdc dinh chifiu ddy mang ldng ngung vi dng d chfi dp hinh xuyen tuong ty nhu ly thuyet ngung mdng Nusselts vdi diem khac bidt Id cd ke den dp cong cua mdng Idng ngung vd bd qua tdc d^ng cua lyc ttpng trudng Ngodi ra, md hinh ciing ke den sy trupt giiia bl mgt phdn pha Idng - hoi, mpt dac diem rdt quan Upng, khdng the bd qua ttong qud trinh luu dpng cua ddng pha bfin Uong vi dng Day Id CO sd de hieu rd hon bdn chdt cung nhu xdc dinh chinh xdc hon chieu ddy mdng Idng ngung vd he sd trao ddi nhiet ddi luu cua qua trinh ngung ty bfin vi dng CO s d LY THUYET 2.1 Hfi phuong trinh vi phdn md ta qud trinh Qud trinh ngung ty ben Uong vi ong d che dp hinh xuyen dupc trinh bay ttfin hinh Theo do, ddng hoi mdi chdt d Ugng thdi bao hod khd di vdo mpt ddu cua doan vi dng dang khdo sdt Tai ddy, qud trinh ngung ty bdt ddu xay vdi chieu day vd tdc dp mdng long ngung dupc coi Id bdng Qua trinh ngung hi ^ ISSN 0866 - 7056 TAP CHl CO KHl V I £ T NAM Sd 10 ndm www.coldiivietnam.vn 2016 NGHlfN CUU - TRAO D6\ ctia hoi mdi chdt dpc theo chieu chuyen dpng se lam cho chifiu ddy ciia mdng Idng ngung tang Ifin vd hmh tiidnh mot ldp mdng Idng ngung hmh xuyln bao quanh chu vi dng Chilu day vd phdn bd tdc dp ldp mdng Idng ngung hinh xuyln nay, vl co bdn, se chiu dnh hudng cua Iyc ma sdt vdi thdnh dng, lyc keo bdi ddng hoi loi dng (loi hoi) vd tdc dp ngung hoi Tat cd cdc qud trinh ndy se dupc the hifin he phuong trinh vi phdn md td qud trinh nhu trinh bdy d phdn tiep theo cua bdi bdo r 4W^ ^ ^ai/ hoi mdi chit j~ pfain td xem x£t i-Iwigngirag ° ^ ^ ^ / / /1 / / L / y i-il Do tmh ddi xiing quanh trvic ciia vi dng, d day, ta xet hien tupng h$ toa dp h\i chidu 1, r vdi true dupc chpn triing vdi tryc dug vi cd gdc d diu vio dng Vdi hp t09 dp t^i nhu vira md ti, hp phuong trinh viphinsaudiy se duoc xay dimg cho mpt phin td ldng ngung hinh xuydn cd kich thudc dr x dl, nhu trinh bay tren hinh r/ —,T J y / - Do vi dng cd dudng kinh nhd, khdng Idn hon nhidu so vdd chidu day ming ldng ngimg nen ming Idng ngung hinh xuydn d diy dupc coi li vich tru, sau bd qua sv khdng dong dJn vd chidu diy quanh chu vi ong / t u Hmh Qud trinh ngung hf ben vi ong ache Hinh Cdn bdng luc phan td dang khdo sdt dg hinh xuyen 2.1.1 Cdc gid thiet ban dau 2.1.2 Phittmg trinh viphdn dgng lltgrng De phu hop vdi die diem ciia vi dng cung nhu de don giin vi?c giii h? phuong trinh vi phan, can chap nhan nhiing gii thiet sau diy: Phuong trtnh vi phin d$ng lupng bieu thi su can bang lire cho phan td dr x dl, nha trinh biy tren hinh Theo dd, bd qua lire trpng trudng, cic thinh phan lire tham gia vio su can bang niy chi bao g6m cic ling suit tnrpt giy bdi su chdnh Ipch tdc dp giOa be mjt phan td dang xdt vdi cic phin tu ldng ngung xung quanh Trong hp toa dp trvi, cin bing niy dupc bi^u dien qua bieu thirc (1), sau dd dupc bidn ddi thinh bieu thiic (2) - Bd qua inh hudng cua l\rc trpng trudng; Bd qua phin bd tdc dp ldi hoi vi coi ldi hoi li ddng nhit vd trjng thii nhiet dpng; - Mdi chat ming ldng ngimg hinh xuydn dupc xem li chit ldng Newton (Newtonian iiuid); - Ldp ldng ngung mdi chit d sit bd mat vi dng dupe coi la khdng chuySn dpng, ma sit vdi vich 6ng; - Qui trinh dupc coi li cd hi$n tupng trupt tai mat phin pha ldng - hoi giua ming Idng ngung hinh xuydn vdi ldi hoi; Bd qua thay ddi ip suit dpc theo chidu dai ong; 2ii(r + dr)dl(T+dT) = 2iirdk n; + rdr + rdr+dtdr = rt (1) (2) BChi bd qua vi phin bic 2, dr dr, bife thirc (2) cd thd dupc bidn ddi thinh djuig (3) vdi kdt qua, sau tich phin, dupc bi^u diln hidu thurc (5) ISSN 0866-7056 TAP CHI CO KHI VIET NAM, Sd lOnim 2016 www.eokhivietnam.vn NGHIEN CCrU - TRAO D O I •ff \ ~ (3) hi(r) = hi(C/r) (4) T = Clr (5) Neugiithietiingsuit trupt tai mat phin pha long - hoi, T, - h, da biet, hing sd tich phan C se dupc xic dinh va bieu thuc (5) cd the dupc bien ddi sang dang (6) R-S (6) Luu ^ ring, vdi chit long Newton, ung suit trupt ti lp vdi dp thay ddi tdc dp theo phuong vudng gdc, vdi hp sd ti le chinh li dp thilt d^ng l\rc hpc p, Khi gii thidt (i, khdng phu thudc vio nhipt dp, cd the bidn ddi bieu thiic (6) sang dang (10) R-S r tlm, dr (R-S)T,_, dr da f^i f (R-S)T,_, [dr Ml o\=- IT 0) cung li cac bidu thiic (11,12), x, - hdupc coi la da bidt Tuy nhien, theo [18] cd thd xae dinh gii tri ciia dai lupng niy dua vao bieu thiic (13) f )V Vdi ij - h li hp sd ma sit tai bd mat phin pha ldng - hoi, duoc xic djnh theo cac bieu thiic (14) - (17) / ^ = 16/Re^, Re,