ASSESSMENT OF THE TWO PHASE HEAT TRANSFER COEFFICIENTS IN THE VAPORIZER TUBES BY SEVERAL MODELS

Transcription

1 ASSESSMENT OF THE TWO PHASE HEAT TRANSFER COEFFICIENTS IN THE VAPORIZER TUBES BY SEVERAL MODELS Dalila KHALFA *, Abdelouaab BENRETEM *, Racid CHAIB ** * Laboratory o te Electromecanics Systems, University o Annaba, Algeria ** Laboratory o Mecanics, University o Constantine, Algeria Abstract. Flowing luids undergo boiling in many o case in wic we transer eat to luids moving tubes. Wen we use te terms boiler, steam generator, or evaporator we usually reer to equipment tat involves eat transer witin tubes.te prediction o eat transer coeicients in tese systems is oten essential. Te object o tis researc is aimed to te assessment o te eat transer coeicient in te vaporizer tubes in saturated regime by several models. Two mecanisms appear in tis regime: te nucleate boiling and te convection boiling; tese two mecanisms can coexist or one can be dominant. Every model gives te interaction between te two mecanisms and precise teir variations according to te dierent termoydraulics parameters. Te inalized trial program concerns te prevision o te eat transer coeicients; and te evaluation o te nature o two pase low in te vaporizer tubes. Te application on te vaporizer tubes o te dynamic boiler o te termal power station Sonelgaz Annaba, Algeria and te comparison between te models gave us a very important databank. Keywords: two pase low, saturation, eat transer coeicient, convective boiling, nucleate boiling 1. Introduction Te transer penomena putting in play te evaporation; ebullition is very answered in many domains o te energy [1]. He is sometimes o an important capital in industrial problems. In particular, te knowledge o te eat transer coeicients in nucleate boiling, wo depends on crucial manner o microscopic caracteristics, tese caracteristics are sometimes diicult to determine experimentally and te direct numeric simulation appears ten like an alternative permitting to ave access to tis inormation. Te main interest o tis researc is to study te models o two pase low liquid/vapour in saturated regime in te vaporiser tubes, wic constitute te surrounding wall o te dynamic boiler. Tis last participates in te electric energy production process; providing dry steam to drag te group turboalternateur. 2. Nucleate boiling in te vaporiser tubes Consider again a tube eated uniormly over its lengt wit a low eat lux and ed subcooled liquid at its base at suc a rate tat te liquid is totally evaporated over te lengt o te tube, igure 1 sows, in diagrammatic orm. Te various low patterns encountered over te lengt o te tube, togeter wit te corresponding eat transer regions [2]. Wile te liquid is being eated up to te saturation temperature and te wall temperature remains below tat necessary or nucleation, te process o eat transer is single pase convective eat transer to liquid pase (Region A) at some point along te tube, te condition site can occur. Initially vapour ormation takes place in te presence o subcooled liquid (Region B) and tis eat transer mecanism is known as subcooled nucleate boiling. In tis region te wall temperature remains essentially constant a ew degrees above te saturation temperature. Figure 1. Te development o a two pase low in vertical tube wit a uniorm wall eat lux RECENT, Vol. 8, no. 2 (2), Iulie, 27 19

2 Assessment o te Two Pase Heat Transer Coeicients in te Vaporizer Tubes by Several Models But in te subsequent regimes o slug low and annular low (D, E, and F) te eat transer mecanism canges substantially. Nucleation is increasingly suppressed, and vaporization takes place mainly at te ree surace o te liquid ilm on te tube wall. Most eorts to model low boiling dierentiate between nucleate boiling controlled eat transer and convective boiling eat transer. In tose regimes were ully developed nucleate occurs (te later parts o C), te eat transer coeicient is essentially unaected by te mass low rate and te low quality. In convective boiling, vaporization occurs away rom te wall, wit a liquid pase convection process dominating at te wall. In te annular regions E and F, eat is convected rom te wall by liquid ilm and vaporization occurs at te interace o te ilm wit te vapour in te core o te tube. Convective boiling can also dominate at low eat luxes or ig mass quality low rates, were wall nucleate is again suppressed vaporization ten mainly on entrained bubbles in te core o te tube. In convective boiling, te eat transer coeicient is essentially independent o te eat lux, but it is strongly aected by te mass low rate and quality. Building a model to capture tese complicated and competing trends as presented a callenge to researcers or several decades [3, 4]. 3. Study on te saturated regime Every regime o eat transer possesses its proper pysical mecanism and te nucleate boiling is te most practical. Tis zone being desirable in te nuclear reactor, te dynamic boiler, in te cooling tecnical, etc. te improvement o te eat transer in tis case is essentially due to a local eect o microconvection induced by te bubbles, tis one by te requency o teir birt, te increase o teir volume and teir departure o te wall, play te role o agitators destroying te situated termal boundary layer to te contact o te wall. Tis layer presents te main resistance to te passage o te eat o te wall to te liquid. In te regions (C & D) exibited appreciably on te igure 1 te mecanism o eat transer canges. Te nucleate boiling is presented more and more, and te vaporization takes place mainly on te surace o te liquid ilm on te tube wall. Te two mecanisms can coexist or one can be predominant. Te total eat transer coeicient can be decomposed ten in one term o nucleate boiling nb ; and a term o convective boiling cb. Webb & Guptes give te classiication or te 11 RECENT, Vol. 8, nr. 2 (2), Iulie, 27 dierent models according to te manner o wic te interactions between mecanisms o eat transer are take in account and will ix te part o every mecanism according to te dierent pysical parameters: - Intensiication model: = N cb ; n cb n nb - Asymptotic model o n order: = + ; - Superposition model: = cb + nb. We give ere a correlation or every model, as well as te analysis to propose by every autor. 3.1 Intensiication model Sa correlation Sa proposed a metod to calculate te eat transer coeicients, rom te analysis o about 8 experimental data coming rom 18 independent sources [5]. Te numbers are used: - Convection number ( x / x).8 ( ρ / ρ ). 5 Co = ; (1) 1 g - Boiling number q B = G i g ; (2) - Froude number 2 G Fr = ; (3) ρ g D - Te local liquid-pase orced convection coeicient: = G D ( 1 x).4 λ.23 Pr ; (4) µ D He considered two distinct mecanisms: nucleate boiling and convective boiling caracterized respectively by te coeicients o eat transer nb and cb. But, it only considers te more important o te two coeicients, te metod is as a ollows: Calculate te dimensionless parameter N: - or te vertical tubes, and or te orizontal tubes as Fr >.4 N = C v ; (5) - or orizontal tubes wen Fr <.4:. 3 N =.38 Fr C v. (6) Ten or N > 1.: n.5 B >.3 nb / = 2. 3 B ; (7).5 B <.3 nb / = B ; (8) cb / = 1.8/ N ; (9) = max ( cb, nb)

3 Assessment o te Two Pase Heat Transer Coeicients in te Vaporizer Tubes by Several Models For.1 < N < 1. calculate te value cb rom equation (9) and nb in te bubble suppression regime as: nb.5.1 = F B exp( N ) (1) and coose te larger value o. For N.1 calculate cb rom equation (9) and nb in te bubble suppression regime as: nb.15 = F B exp( N ) (11) and coose te larger value o. Te constant F is determined as ollows: B >.11 F = 14.7; B <.11 F = Asymptotic model Cen correlation He considered two mecanisms: nucleate boiling and convective boiling and tat te contributions made by te two mecanisms are additive. Te two penomena superpose temselves. Cen propose te use a nucleate boiling suppression actor S and a convective boiling intensiication actor F [6, 7]. = + = F + S ; (12) cb nb To determine cb, te autor part rom te relation o Dattus-Bœlter:.4 λtp cb =.23 ReTP PrtP, (13) D λ TP - te termal conductivity, and Re TP, Pr TP - te numbers o Reynolds and Prandtl are te eectives values associated wit te two-pase luid. Re TP Re TP F = =. (14) Re D G ( 1 x) µ Te equation (13) can write itsel ten:.4 λ cb = F.23 Re Pr. (15) D Writing te equation or npb using te Forester and Zuber analysis wit te eective values o te supereat and te vapour pressure dierence is resulting: nb =.122 σ npb Tsat psat S He ten deines a suppression actor, S, te ratio o te mean supereat T e, to te wall supereat T sat λ C p, ρ µ i g ρg (16) RECENT, Vol. 8, nr. 2 (2), July, T = e P S e ; (17) Tsat Tsat sat g sat sat ( 1/ ρ 1 ρ ) P = i T / T /. (18) 3.3. Superposition model Kandlikar correlation He as instead pursued correlation built rom dimensional analysis and pysical reasoning and proceed wit a dimensional analysis: - we irst note tat te liquid and vapour pases may ave dierent velocities. Tus, - we avoid introducing a low speed and instead rely on te supericial mass lux, G, troug te tube. G = m / Atube [ Kg / m ² s] ; (19) - used Re to calculate Re = G D / µ ; (2) g.4 ( λ D ) =.23 (1 x) Re Pr / or a eat transer coeicient, in vertical tubes TP takes te ollowing orm ( B Co) TP / = n, ; (21) Te irst dimensionless group is te boiling number B = q / G i g ; (22) Te oter group is te convection number ( x / x ).8 ( ρ / ρ ). 5 Co =. (23) 1 g Wen a convection number is large Co.65, as or low quality, nucleate boiling dominates; in tis range TP / increases wit te increase o B and is approximately independent o Co. Wen te convection number is smaller, Co.65, as at ig quality, te eect o te boiling number declines and TP / increase wit te decreasing Co. His metod is to calculate o / rom eac o te two ollowing correlation and coose te large value nbd ( 1 x) = ; (24a).2. 7 [.6683 Co B F ] cbd ( 1 x) = ; (24b) PL.9. 7 [ Co B F ] PL `nbd` means «nucleate boiling dominant» `cbd` means «convective boiling dominant» In tese equations, te actor o orientation; is placed to te unit or te vertical tubes and F PL is a luid-surace parameter, were value is indicated in te table 1.

4 Assessment o te T wo Pase Heat Transer Coeicients in te Vaporizer T ubes by Several Models Table 1. Fluid-surace parameter F PL or rerigerants in copper or brass tubes Fluid F PL Fluid F PL Water 1. R R R R R Equation (24) can be applicable or te nucleate boiling saturated regimes (C troug F) wit a mass quality in te range < x < [8, 9, 1]. 4. Application on te tubes vaporizer o te termal power station Sonelgaz Annaba, Algeria Te experimental caracteristics o te vertical tubes o te dynamic boiler o te termal power station Sonalgaz Annaba, were used to study te comparison o te dierent models. T e conditions are given in te table 2, and te mass quality in te tubes is.2. One ad varied x o.1 to.9 and te eat lux q to see te variation o te termoydraulics parameters o every model. Table 2. Te caracteristics tube o te dynamic boiler o te termal power station Sonalgaz Annaba, Algeria Inlet Diameter: Flux = Lengt temperature: D = 65 mm; (13; 15; o tube: 34 C; mass quality: 7; 1) 2 m Inlet pressure: x =.2 kw/m² 145 bar 4. Results 4.1. Sa correlation Te igures 2, 3, 4, 5 sow te variation te Sa correlation parameters. Te igure 2 sow tat te convection number decrease wit te increasing o mass quality x, wile te Martinnelli number obtain an increasing pace wit te large value o mass quality x, igure 3, tis number represents te drop pressure in te two pase lows. T e igure 4 present te pace o nucleate boiling coeicient nb according to dimensionless number N, nb growing wit te increasing o N. Te igure 5 sows tat cb takes large values or small numbers o N and te small values or large N. T e table 3 gives te value o nucleate boiling coeicient nb and te convective boiling coeicient cb o Sa correlation. For te variation o mass quality o.1 to.9 and or te value o ollow eat lux q = (13; 15; 7) kw/m²; according to te gotten results one remark tat: nb decrease sligtly wit te increase o mass quality x; and increase wit te increasing o eat lux q, altoug cb remains constant some eiter te done variation. Figure 2. Co vs. mass quality x Figure 3. Martinnelli number vs. mass quality x Figure 4. nb vs. dimensionless number N Figure 5. cb vs. dimensionless number N 112 RECENT, Vol. 8, nr. 2 (2), Iulie, 27

5 Assessment o te T wo Pase Heat Transer Coeicients in te Vaporizer T ubes by Several Models Table 3. Te value o te eat transer coeicient o te Sa correlation q = 13 kw/m² te Sa correlation x x =.1 x =.2 x =.3 x =.4 x =.5 x =.6 x =.7 x = x =.9 nb cb q = 15 kw/m² te Sa correlation nb cb q = 7 kw/m² te Sa correlation nb cb q = 1 kw/m² te Sa correlation nb cb Cen correlation Te igure 6, 7, 8, 9 sows te variation o te Cen correlation parameters. Te igure 6 present te variation o te local two pase Reynolds number Re tp according to liquid pase Reynolds number Re, Re tp increase wit te increasing o Re, as well as cb also increases wit te increase o Re (see igure 7). Te igure 8 sows tat te coeicient nb increases wit te increase o suppression actor S, itsel actor decrease wit te increase o Re tp (igure 9). Figure 6. R etp vs. R e Figure 7. cb vs. R e Figure 8. nb vs. S Figure 9. Suppression actor S RECENT, Vol. 8, nr. 2 (2), July,

6 Assessment o te T wo Pase Heat Transer Coeicients in te Vaporizer T ubes by Several Models Te table 4 present te value o nucleate boiling coeicient nb and te convective boiling coeicient cb o te Cen correlation or te variation o mass quality o.1 to.9 and or te value o ollowing eat lux: q = (13; 15; 7; 1) kw/m²; according to te gotten results one remark tat: nb takes te small values and constants some eiter te variation o q and x, and cb remains nearly constant and takes te large values. Table 4. Te value o te eat transer coeicient o te Cen correlation q = 13 kw/m² te Cen correlation x x =.1 x =.2 x =.3 x =.4 x =.5 x =.6 x =.7 x = x =.9 nb cb q = 15 kw/m² te Cen correlation nb cb q = 7 kw/m² te Cen correlation nb cb q = 1 kw/m² te Cen correlation nb cb Kandlikar correlation Te igure 1, 11, 12, 13, 14, 15 sows te variation o te Kandlikar correlation parameters. Te igure 1 presents te variation o nb according to mass quality x or te aorementioned conditions; or x between.1 and.2 te coeicient nb increases quickly, tis result justiies te speed birt o te bubbles in te regions (C and D) in te igure 1, beyond x =.2, nb decreases wit te increase o x. Result to justiy as bus in te regions superior o te D region, te nucleate boiling depart and te vaporization take place. Te igure 11 sows tat te coeicient cb takes small values or small mass quality x, and it increases wit te increase o x; or small convection numbers te coeicient cb is large (igure 12) wat justiies te good quality and te dominant o te convective boiling or (Co <.65); and nucleate boiling dominant or (Co >.65) as observe in igure 13 and te igure 14. Te igure 15 presents tat te convection number decrease wit te increase o mass quality x. Te table 5 sows te value o nucleate boiling coeicient nb and te coeicient o convective boiling cb o te Kandlikar correlation or te variation o mass quality x. O.1 to.9 and or te value o ollow eat lux q = (13; 15; 7; 1) kw/m², according to te gotten results one notices tat: te nucleate boiling coeicient nb takes ig value or small mass quality x and increase wit te increase o q in tis range "small value o mass quality x); wit te increase o x (beyond x =.2) nb commence to decrease even toug te eat lux increases. Te convective boiling coeicient cb increase wit te increase o x and wit te increase o eat lux; tese results conront wit te pysical reasoning and te existing literatures on an international scale. Figure 1. nb vs. Mass quality x Figure 11. cb vs. mass quality x 114 RECENT, Vol. 8, nr. 2 (2), Iulie, 27

7 Assessment o te T wo Pase Heat Transer Coeicients in te Vaporizer T ubes by Several Models Figure 12. cb vs. Co Figure 13. cb and nb vs. x Figure 14. nb vs. Co Figure 15. Co vs. mass quality x Table 5. Te value o te eat transer coeicient o te Kandlikar correlation q = 13 kw/m² te Kandlikar correlation x x =.1 x =.2 x =.3 x =.4 x =.5 x =.6 x =.7 x = x =.9 nb cb q = 15 kw/m² te Kandlikar correlation nb cb q = 7 kw/m² te Kandlikar correlation nb cb q = 1 kw/m² te Kandlikar correlation nb cb Conclusion According to te results gotten by te comparison o several correlation in te two pase low; one distinguises tat: 1. Te two existing penomena in te saturated regime "te nucleate boiling and te convective boiling" develop temselves in an inverse manner; te increase o one o te two generates te decrease o te oter. 2. Te Kandlikar correlation present te more logical results, because te coeicient o eat transer reassemble te two numbers (boiling number and convection number); as it gives te nature low regime in te tube. For (Co <.65) RECENT, Vol. 8, nr. 2 (2), July,

8 Assessment o te T wo Pase Heat Transer Coeicients in te Vaporizer T ubes by Several Models ig quality, and or (Co >.65) it is te low quality); as well as te coeicient o eat transer increases wit te increase o eat lux, itsel tat is just 3. te two coeicients ( nb and cb ) o te Kandlikar correlation includes te same dimensionless groups and to coose one o te two truts value o transer coeicient don t suppress te parameters o basis used in te compreension o te penomenon mecanisms. 4. T e Cen correlation and te Sa correlation sow tat te eat lux is independent o eat transer coeicient, altoug te studies and te experiences made since te antique sow tat te increase o eat lux provokes te increase o eat transer coeicient. 5. To coose = max( nb, cb ) in te correlation o Cen or Sa, made lose quite a lot o inormation and parameters used in te process o te beginning. Nomenclatures Co: convection number C v : te Sa correlation convection number p c : speciic eat, J/kg K D: diameter, m, orientation actor F: intensiication acture o te convective Fr : Froude number g: gravitational acceleration, m/s² G: speciic mass, Kg/m²s : eat transer coeicient,w/m² C : eat transer coeicient liquid pase M: molecular weigt, kg/kmol q: eat lux, W/m² i: latent eat, J/Kg S: suppression acture o te nucleate boiling Nu: Nusselt number P: pressure, bar Pr: Prandtl number Re: Reynolds number T: temperature, C T: temperature dierence, C p: pressure dierence, bar Indices cb: convective boiling : luid g: gas g: luid/gas nb: nucleate boiling TP: two pase (liquid pase/vapor pase) Reerences 1. Frenc society o termal. Researc in termal Stakes and perspectives in 25. Tird edition, provisional documents, Iienard, J.H.: Heat transer textbook. Tird Edition, Plogiston Press, Cambridge, Massacusetts, U.S.A, Dorocenko, V.A., Tebbal, M.: Heat transer wit pase cange. Oice o te university publications, Algeria, Sacadura, J.F. et al.: Initiation to te termal transers. Edition Dunod, France Collier, J.G., Tom, J.R.: Convective boiling and condensation. Tird edition, Oxord University Press, Oxord, U.K., Sa, M.M.: Cart Correlation or saturated boiling eat transer and urter study. ASHRAE Trans., 88, Part I, p , Sawant, N.N., Vance, M., Payne, W., Domanski, P.A., Hwang, Y.W.: A Study o in-tube evaporation eat transer o carbon dioxide and water. International Congress o Rerigeration, Vol. 138, p , 23, Wasington, D.C., U.S.A. 8. Kandlikar, S.G.: Heat Transer Mecanisms during Flow Boiling in Microcanels. Journal o Heat Transer, 24, Vol. 126, p Kandlikar, S.G.: A General correlation or two-pase low boiling eat transer Coeicient inside Horizontal and Vertical Tubes. Heat Transer, 199, Vol. 12, p Kandlikar, S.G., Surong, T, Jian, Y., Sigeru, K.: Furter assessment o pool and low boiling eat transer wit binary mixtures. JAPAN, 25, Vol. 126, p. 816 Received in Marc, 27 (and revised orm in June, 27) Greek symbols ρ: density, kg/m 3 λ: termal conductivity, W/m 2 C µ: dynamic viscosity, N s/m 2 σ: surace tension, N/m Ψ: Intensiication acture χ: Martinnelli number χ = [ x / x].9 ( ρ / ρ ).5 ( µ / µ ). 5 1 g g 116 RECENT, Vol. 8, nr. 2 (2), Iulie, 27