SIMULATION OF UNSTEADY COMBINED HEAT AND MASS TRANSFER PROCESSES IN EVAPORATORS

Transcription

1 V Msk eol Sem He Ppes He Pumps efgeos Msk Belus Sepembe -7 SMULAON OF UNSEADY COMBNED HEA AND MASS ANSFE POCESSES N EVAPOAOS G. Mlusks. Movls Depme of heml Nule Eegy Kus Uvesy of ehology Kus Lhu Abs Combe sfe poesses he evpoos of he spye lu e smule by gl pemes. he mheml moel evlues useess of he poesses he spel peules of lu opl popees he eo of eegy sfe poesses semspe ople lso he fluee of he Sef flow o eegy mss sfe ople s suougs. he euos of eegy ble o he ople sufe of eegy osevo he selee ool volume of spese flow e solve umelly. sfe poesses wh he ople s suougs e lose muul eloshp. he mpoe of useess he evpoos s show. KEYWODS Evpoos spese flow ople semspe lu se of usey ombe sfe. NODUCON Evpoo of he lu spye fom kes ple subbes evpoos oeses ohe he eves. sllo opeo of hs eupme les o hghe oss of ol ouly fo bulg mee of heml usl sysems. [] oepul pple fo esfo of he sfe poesses s evelope whe see- mpulse supply of eegy o he ples s pove whh ems esy of he mss sfe. hese lol ees of hgh poel eegy mos eve fom eulbum se e fome. he sfe poesses suh ees e vey usey fluee he se of he whole spese sysem. efl o sufes be suh ples fo spese flow. he el soues of eegy be lse o o flux fom he ho sufes of he hel. Plly hs e be e ou by eful vesgo of ompl sfe poesses he gs phse he spye lu phse wh oully vyg bouy oos of he he mss sfe. hs wok s evoe o he vesgo of ombe sfe poesses evpog we oples he suougs. ESEACH ECHNQUE he se of spese flow l oss-seo of he hel s well kow. hee s o bek up olesee of oples. he o flux eme by blk boy of peeme empeue. hee beg o heml eos. he effes of heml ffuso vsosy sspo e eglee. he see me of he oese phse of he flow e ve he J umbe of ffee sze ople goups. he se sfomos of gseous phse e eeme by he eegy peues fo he se heg phse hges of oples. f he sbuo of oples he oss-seo of he hel s ufom he me mss empeue he volume oe of flow ves log he legh of he hel oly. Se o-ufom sze oples uego ffee esy of ol eegy fluxes gs he heg evpoo e of evey goup s ogl. he esy of he sfe bewee he gs lu oples ue he veloy of gs ehlpy hge: ( ρ g hg ) J N j j g j. () j G. Mlusks

2 he esy of ve soue hs o fluee o he vlue of gj euo (). hough he Sef flow effe he oveve he sfe esy of he evpog sphee oes o oespo o he esy of he sol sphee. he o of he bove eses be evlue og o he Splg he sfe umbe []. he vlue of hs sfe umbe epes o he physl popees of gs lu o he gs lu empeue ffeees he empeue evve se he lu []. he hel wh movg spese flow s ve he A umbe of ool oss-seos. he umbe V - of fe ool volume s efe og o he bove meoe oss-seos he wll of he hel. he hes pmees of he spese flow movg oss he ool volume be eeme og o ee oule oos of he ool volume: k j k j.( ) j.( ) p.( ) ρ.( ρ ρ ) () j j j p g p g g g sml he posue me j j j of eh goup of oples ool volume he me mss empeue of gs flow he oss-seo of he hel be efe by he followg lgeb euo: J g g NV j j j j. () j V ρ g p Evlug he effe of lu oples o he se of gseous mxue ool volume he osevo of momeum s pesse by he euo: lkewse ouy s eul: [ Fw ] [ FL ] p A () Gg wg p A Gg wg J j L j J Gg G Gg G. () he ls bu oe em euo () evlues he effe of fo o he wll gseous flow he ls em euo () evlues he ol g foes of ll oples he ool volume: J [ F ] N C w g w w g w j L V j L j AL j g L j j L j ρ L j. () Due o he eoym g he veloy of oples ppoh he veloy of gs lle by lle. he eleo of oples epes o he sze he slp veloy he ol g oeffe of oples C L 7e -.8. he sysem of euo ( ) s ue oly whe he se of he spese flow A oss-seo of he hel s kow he yms of heg evpog oples pesee he ool volume s eeme. Fo hs pupose boh he poblem of ople el mss he sfe he usey ombe he sfe poblem se he ople mus be solve. he smple soluos of he le poblems be eeve oly whe he empeue he oule ossseo of he ool volume s efe. e. whe he soluo of he sysem euo ( ) s kow. heefoe he ompl ouplg bewee gs lu ople poblem whh esbes he sfomos of spese flow mus be solve umelly by he meho of eo. he evpoo yms of sphelly symme ople o he efl sufe s efe by he Sef flow effe o he e of phse hges [] euo: D µ g µ p p v v ρ L m pv s pv p l p v s pv. (7) vg µ µ g p pv s As he Kuse umbe fo he ople s K l / <. he effe of he Kuse lye o he sfe poesses s eglgble []. h se vg p s he vpou suo pessue empeue. he pessue p v epes upo he elve humy of. he evpog oples ve evome e fluee by el ompl he flux. he bsopo oeffes of semspe lus e fe heefoe he el o he flux s bsobe by he whole v s G. Mlusks

3 G. Mlusks volume of ople oly fews p of eegy s sfee o he ople sufe. he empeue of he ople sufe mus ssfy he ble of eegy fluxes o he sufe of he efl o: ( ) ( ) ( ) ( ) ( ) ( ) k f s k g. (8) he lulo meho of he o he flux esy he semspe ople kg o ou he spel popees of he lu s fou ou [7]. se of he ve-ouve he sfe he empeue fel of he ople be pesse by suh sysem of egl euo: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) [ ( ) ( ) ( ) ( ) ( ) ( ) ] ( ). s / p p p p p s os os s p s s s s s s / z y z y z y p f f χ ρ (9) Euo sysem (9) s eeme f he l bouy oos e vl: () ) ( ( ) ( ) ) ( ) ( ( ) ( ) ( ) ( ) [ ]. () A evve of sufe empeue s evlue esy by og o () oos. Whe boh he soluo of ople el he sfe he soluo of ople el he mss sfe ss he foml pesso of eegy ble (8) he oee fom be lule follows: ( ) ( ) ( ) ( ) ( ) ( ) ( ) p os s ml Nu s g vg v pl L e λ ρ λ () he fluee of oveo se he ople evlues he oeffe of effeve ouvy λ e f(pe L ) [9].he pesee sysem of euos esbes he se sfomos of he spese flow he yms of gseous phse ople flow efes he peules of semspe lu opl hess he eo of ompl eegy sfe poesses se he ople he effe of he Sef flow o he eegy mss sfe he ople suougs. he gl peme s e ou begg wh he fs ool volume se he spese flow s eeme fully he l oss-seo of he hel. he oule oss-seo he empeue of gseous flow s selee he followg eos e spefe. Hvg peeeme empeue j he euo sysem (7-) s oe fo eh goup of he oples. Mmsg he ble of eegy () by he fses ese meho he empeue of ople sufe j eh goup s eeme. he oples e ppooe o he M oe us. hee he he flux s lule by he empeue of el soue og o he empeue fels of oples s efe moe ly he fome eo. he umel ego ws me ove he gle by he Guss meho ove he wve umbe by he

4 egul ehue. he he flux s evlue m - ge of he speum whh s ve by peules of he opl popees of we o gps s s show Fgue. he fomul of empeue fel s eessy o evlue he les ems he fve sum. By solvg umelly euos (7 ) he yms of ople evpoo s evlue by he se bove euos he hges ople veloy he ool volume e eeme. he he posue me of oples he ool volume ws fou summy mou of he evpoe lu eeme. Aog o meho [] he omposo of gseous mxue s spefe he pl pessue of we vpou he gseous mxue p s s efe. he flow e of gseous phse G g he oss-seo of hel A s evlue he veloy of gs w g s efe moe ly. he elve humy of ϕp /p s ( g ) s pove. A moe pese efo of he empeue of he gseous flow he oule oss-seo of he ool volume ws me by solvg umelly euo () moe pesely. f he ffeee bewee he lule selee empeue s moe h.k he he lulos e epee he ool volume oug ohe selee empeue. ESULS OF HE ESEACH he se hges of movg he sble oss-seo hel wee lule umelly whle he spye we oples l 8K empeue l veloy w L m/s keep evpog. A K empeue. MP pessue w g.9 m/s he l veloy y flows o he hel. A he l oss-seo g s.;.. he sfe poesses e moelle fo he moospese flow wh he ople ; ; 7 µm. he polyspese flow osss of he bove meoe h goup of oples whe ps of he flow e oespogly o 8 % fomg he whole spese flow. he effe of ol eegy flux fom he epee el o soue o he se vo egules he lu oples he e vesge. he ses whe blk boy soue ems s empeue e smule (Fgue.). he we oples he flow of e hee keep evpog whle he volume oe of he gseous mxue uegoes hge. Some we vpou he e phse ses heefoe he humy eses (Fgue.). he gl peme s soppe whe he elve humy of he heves he vlue of 98±. % s ofme f he s flows ou of he hmbe. Hvg he sme g smlle spye oples hve lge efl sufe e o he sfe poesses fom he sufe e moe esve beuse he s se wh mpess fse he legh of he evpog hmbe beome smlle. he moelle ses of he spese sysem he fluee of he o soue esuls esy of he ll sfe poesses heefoe s sgf o he weg poess of he. he se of he ombe heg s possble o pk ou χ m - W m se φ %. g.. m - x m....8 Fg.. Absopo oeffe of we C Fg..Dyms of he weg: µm: esy of blk boy: s K: ; ; 7. ; : ; 8. s K: 8. 8 G. Mlusks

5 K 8 8. K K 9. b Fg. he empol vos of he empeue se he ople by he ve-oveve heg. x m:.; b.;.. 7µm. s 8 K. ϕ %. hee peos of ople se hge: l whe mx se whe ( )< mx > fl whe mx ( ) (Fgue ). he vos of we se epe o oly o speso of he g. g xm b Fg. he epeey of he he ( ) mss (b ) sfe oos fom he wy of eegy supply o oples: b oveve; ve-oveve. µm: 7 ; 8 ; 9 7. : g ;. b : p p s ( g ); p p v ; 7 9 p p s ( ). oples bu lso o he heg wy (Fgue.). he se of he oveve heg he gs ople empeue ppohes sympo eh ohe. he oole he hee we oples flow ou of he evpog hmbe beg hghe empeue he e phse (Fgue. ). A moooous eese of he vg foe fo ffuso of we vpou fom he ople sufe o he se of he oveve heg s obseve ug he poess of he weg (Fgue. b). h foe s popool o he ffeees bewee he pessue of we vpou he ople h he gseous mxue. Due o he ese of humy he esy of he sfe poesses fll he hge of he elve humy log he legh of hmbe beomes o-ufom. A shp ese he l p of he hmbe s eee he es of he hmbe sgf hges. Geelly he opeos of evpog hmbe s o vey effeve. A ol eegy of ve soue s employe fo he heg of he ople he sfe poesses he evpog hmbe e ulvely ffee. he evpog ople empeue ply ppohes gs empeue eve ees (Fgue. ). Dug he weg poess he fs ools ow le begs o wm. he se of he ombe eegy supply o he g. s 8K..... g. s 8K xm 8 G. Mlusks

6 ( ) ( ).....x m Fg..he epeey of he o-soheml o Fg.. he bsopo sbuo fo opfo ople fom he heg wy: o- le: µm: 7;. s veve; ve-oveve. 7µm. K: 8; ;. oples he evpog hmbe wh he popely selee powe of ve soue s possble o mose he o wm s esbly.e. o ge he eessy se of he oe eve. Se he vg foe fo he we vpou ffuso o he elly oes o eese he sfe poesses he evpog hmbe em moe effeve (Fgue. ). Due o he wy of he heg he se empeue pofle se we ople s ffee (Fgue.). Whe he ople s hee by oveo he heg eegy s supple o he ople sufe. Some he fom gs wll be eue fo evpoo whle some s sfee o he eo of he ople fo heg. he hghes ople empeue ous o s sufe. he ople beomes soheml g he mome of evpoo eulbum selg. Dug he weg poess fs he o of ople o-soheml eses bu le eeses. he ople s lwys o-soheml (Fgue.) s ombe heg ffes fom oveve heg. Beuse he esy of he flux he sufe of he lge ople s hghe (Fgue.) hus he eulbum evpoo s possble he hghe empeue. heefoe he sme g s he se of he empeue s lge fo spese flow wh he lge oples (Fgue. ). he sbuo of he o bsopo ees fom he opl hkess. epes o he peules of he we spel popees he ople sze. As he slp veloy of he ople s ppohg o zeo (Fgue 7.) he ve oveve heg gully pss o o he ve ouve heg. he se of he oveve heg he ble of eegy o he sufe of he evpog oples ompleely evlue by summg up he hee ompoes (Fgue 7. ) lwys h fluxes e eesg. he se of he ombe heg (Fgue 7 b) s eessy o lule he ol he flux ± k ol he flux se he ople ± k. h se he esy of he ople heg s lso eesg bu he he flux fo he evpoo s ouously esg g Fg.7.he he sfe o he ople sufe: oveve heg; b ve-oveve heg. 7µm. : ; ; ; ; ;. k k f..... x m g. s 8K b G. Mlusks

7 CONCLUSONS he ve eegy of he ol soue oue o he evpoos of he -oog sysems s he m sfom he sfe poesses: hey e lwys usey he esy ese he empol vos lee ulvely. Wh he pope seleo of he esy of he el o he s o oly beg wee evpoos bu geelly be hee up o eessy empeues. Coseuely ph s opee o esgg ew moel of he oog sysem. Nomelue A e m ; - heml ffusvy m /s; B he sfe umbe; C L g oeffe; p mss spef he J/K kg; D mss ffusvy m /s; F fo foe N; gg L /G g mesoless flow e; G flow e kg/s; h ehlpy J/kg; umbe of hel oss-seo; spel esy of o W/m. se; spel esy of blkboy o W/m. se;j umbe of ople goups; K Kuse umbe; k spel bsopo ; L le he of evpoo J/kg; m mss flux esy kg/m s; N oeo of oples; m - ; N V umbe of oples wh he ool volume; umbe of he em fe sum; spel of efo; Nu Nussel umbe; p pessue P; P Pl umbe; he flux esy kw/m ; us of ople m; ooe of sphee m; µ uvesl gs os J/kg kmol; e eyols umbe; me s; empeue K; V volume m ; w veloy m/s; x ooe of hel m; y z he symbol oes of he opl hkess () of he egl lms; χ spel bsopo oeffe m - ; gle; λ heml ouvy W/K m; µ moleul mss kg/kmol; ρ esy kg/m ; wve umbe m -. Subsps: f evpoo; g gs; of hel oss-seo; j of ople goups; oveve; L lu; m me mss; o; ople sufe; s ` sue; s -o soue; ol; v vpou; vg gs vpou mxue; w wll; l se; f fom ople. Supesps: ee e; vble; vege. efeees. Dolskj A.A. Bsok B.. Gulyj B.C. Nkoevskj A.. SukovJ.. he see-mpulse supply of eegy ehology (uss.) F NANY 99 p. 8.. Splg D.B. Coveve mss sfe (uss.) Eegj 9 p. 8.. ekszbulu M. Nfzge. L X. A mss sfe oelo fo ople evpoo hghempeue flows Cheml Egeeg See. Vol. No pp Kuzkovskj A.V. Dyms of sphel ple poweful opl fel (uss.) zv. VUZ Fzk. No. 97 pp Elpe. Ksovov B. o heml ffuso ke effes evpoo ombuso of lge moee sze fuel oples. J. He Mss sfe. Vol. 8 No. 99 pp mos M. o Combe He sfe Chels Hemsphee 987 p Mlusks G. Nosey he mss sfe g spese flows. Spel bsopo of o flux we oples (Lh.) Eegek. No. 99 pp Mlusks G. Nosey he mss sfe g spese flows. Combe eegy sfe semspe ples (Lh.) Eegek. No. 997 pp Abmzo B. Sgo W.A. Dople vpozo moel fo spy ombuso lulos. J. He Mss sfe. Vol. No pp Mlusks G. Opmso of ompuo osey ombe he sfe sphel volume (Lh.) Mehk. No. 997 pp. -.. Hpole G. M. Dople evpoo hgh empeue evomes (uss.) Vol. No. 98 pp. -.. Hle G.M. Quey M.. Opl oss of we he -m o -µm wvelegh ego Appl. Ops. Vol. No. 97 pp G. Mlusks