Heat tranfer and aborption of SO of wet flue ga in a tube ooled L. Jia Department of Power Engineering, Shool of Mehanial, Eletroni and Control Engineering, Beijing Jiaotong Univerity, Beijing 00044, China Abtrat The heat tranfer mehanim of wet flue ga and it influene on SO aborption when ondenation our were theoretially analyzed with vapor fration of 8% to 8%. A modified film model and Nuelt theory were ued to deribe the harateriti of ma, momentum and energy tranfer at the phae interfae. The effet of the veloitie indued by ma tranfer (vapor ondenation and SO aborption) were inluded in onduting governing equation. Vapor ondenation indue the SO aborption in the wet flue ga. For high ma fration of vapor the SO aborption will be an important phenomenon in the ondenation proe. Another important fator influening the SO aborption i the Re number of bulk flow of wet flue ga. Keyword: heat tranfer, ondenation, SO aborption. Introdution The onvetive ondenation heat tranfer of mixture ga with ondenable ga i an important proe in the hemial and power indutrie and ha been extenively tudied [-3]. Determination of total heat tranfer oeffiient i important and intereting topi for mixture ga, ine thi kind of heat tranfer proe i omprehenively enountered in the utilization of wate or low temperature energy [4]. For the ondenation of vapor inluding a non-ondenable ga when the vapor fration i mall the ga mixture flow doe not obviouly deelerate. Therefore a new analyi whih hould onider low fration of water vapor i needed to tu. Although the ondenation of vapor from a vapor-ga mixture in tube ha been tudied hitorially [5,6], the main interet of thee tudie i Advane in Fluid Mehani V, A. Mende, M. Rahman & C. A. Brebbia (Editor) 004 WIT Pre, www.witpre.om, ISBN -853-704-3
58 Advane in Fluid Mehani V not to detet the effet of ondenation of vapor on onvetion heat tranfer, but to predit the effet of non-ondenable ga on ondenation heat tranfer. For the mixture ga with low vapor fration, a earh of the literature ha revealed that no muh work ha been publihed to indiate the remarkable influene of ondenation affeting upon onvetion heat tranfer in tube, exept for a few report on wet air phenomenon [7]. Conidering the real mixture ga with SO, the ituation will be more omplex than laial vapor with non-ondenable ga. But it an be enountered in the hemial and power indutrial proe. So the onvetive ondenation phenomenon of the mixture ga ompoed of water vapor, SO and dry flue ga wa diued in thi paper. Beaue of the omplex mehanim and widepread appliation of the phyial ae, the tu on ondenation heat tranfer phenomenon ha reeived growing attention ine Colburn and Hougen pioneer work[-3]. In thi paper the theoretial and experimental invetigation are foued on the onvetive ondenation heat tranfer and SO aborption in the mixture ga exhauted from hemial indutrial proe and ombution devie. The regular pattern of the fored onvetion heat tranfer of the bulk flow of mixture ga and onvetive ondenation of the ondenable gae and SO aborption are diued and the fator influening the ombined heat and ma tranfer phenomena are illutrated. Thi paper preent a mathematial model obtained by mean of modified film model and Nuelt ondening theory and the onvetive ondenation phenomenon of vapor-ga mixture and SO aborption by ondenate were invetigated. The theoretial predition agree well with experimental reult. It i illutrated that the theoretial olution i lightly higher than experimental data, but better than that of vapor-phae reitant method. Nomenlature : peifi heat apaity J/(kg.K), ma fration D: diffuion oeffiient m / d: diameter m g: ma tranfer oeffiient kg/(m. ) h: heat tranfer oeffiient w/(m.k) k: thermal ondutivity w/(m.k) m: ma flux to wall kg/(m.) M: ondening ma flux kg/ r: radiu m t: temperature u: veloity m/ v: indued veloity m/ x: oordinate in diretion of ga flow m y: oordinate per diretion of ga flow m δ: thikne of ondenate film m η: nami vioity Pa. τ: hear tre N/m ρ: denity kg/m 3 Advane in Fluid Mehani V, A. Mende, M. Rahman & C. A. Brebbia (Editor) 004 WIT Pre, www.witpre.om, ISBN -853-704-3
Advane in Fluid Mehani V 59 Subript b: bulk flow : vapor i: interfaial l: liquid : ulphur dioxide w: wall urfae The film model and SO ma tranfer Conider a film ontaining non-ondenable gae, SO and vapor, a depited in Fig., through whih there i the tranfer of heat, ma and momentum in the y- diretion, and the mixture flow parallel to the wall in the x-diretion. The ooling flow i in the left ide of the wall. The ondenate film and ga film are in the right ide of the wall. On the urfae of liquid film, the vapor preure i p vi, SO preure i p i, and temperature i t i. At a ditane δ the bulk vapor preure i p v, and SO preure i p. At a ditane δ t the bulk temperature i t g At a ditane δ u the bulk veloity i u b. For the purpoe of the preent analyi the phyial propertie in the film are aumed to be ontant and the mixture to behave a an ideal and inompreible ga. Muh work ha been done relative to the ditribution of the vapor ma fration, temperature and veloity in thee film by Brouwer and Cheter[6]. In thi paper main foue are vapor ondenation at the liquid urfae and SO aborption, o ome reult mut be modified. Figure : The film model. The full Fikian diffuion equation without oure term read + u + v = D + τ x y x y () Advane in Fluid Mehani V, A. Mende, M. Rahman & C. A. Brebbia (Editor) 004 WIT Pre, www.witpre.om, ISBN -853-704-3
60 Advane in Fluid Mehani V Conidering the attention i retrited here to tea ituation and the variation of (ma frature) i mall enough in the x-diretion to be negleted a well and film model an be obtained a d d ρ v = ρd () In the equation () the onvetive veloity v i aued by diffuion of vapor and SO through the mixture v = d D D d d D (3) Beaue of mall onentration of SO ompared with vapor fration, the influene of the diffuion of SO on indued veloity i extremely mall and an be ignored. The boundary ondition on are: ( y = 0) = (4) ( y = δ ) = g (5) So the ditribution of vapor fration in the film an be obtained a y g ( y) = ( )exp{ ln } i (6) δ i Thi expreion an be found in the literature [6], but the ditribution of SO hould be derived uing the indued veloity above. Similar to equation (), the diffuion equation for SO an be redued a d d v = D (7) The boundary ondition on SO read ( y = 0) = i (8) ( y = δ ) = (9) The indued veloity that i aued by vapor ondenation hould be ued, o equation (7) an be rewritten a d D g d ln( ) = 0 (0) δds i Combining and olving equation (0), and applying boundary ondition (8) and (9), yield the ditribution of SO fration in the film a where g i ξy = i ( e ) () ξδ e i g Advane in Fluid Mehani V, A. Mende, M. Rahman & C. A. Brebbia (Editor) 004 WIT Pre, www.witpre.om, ISBN -853-704-3
Advane in Fluid Mehani V 6 D g ξ = ln( ) () δ DS i Although only the indued veloity aued by vapor ondenation wa onidered into the ditribution of SO fration, but it i the double-omponent ma tranfer problem. If the onentration of SO i not very mall, the expreion will be omplex. In the ame way the ditribution of temperature in the film ontaining SO an be obtained. Negleting variation of t in the x-diretion, the energy equation in the film read dt d t ρ pv = k (3) with a boundary ondition on t t ( y = 0) = t i (4) t ( y = δ t ) = t g (5) Introduing the indued veloity aued by vapor ondenation, the equation (3) beome d t ρpd g dt ln( ) = 0 (6) kδ i Solving equation (6), and applying boundary ondition (4) and (5), yield the ditribution of temperature in the film with SO a t g ti ηy t = ti ( e ) (7) ηδ t e where ρpd g η = ln( ) (8) λδ i Some orretion fator for the effet of the indued veloity were given by Brouwer [6]. But for the multi-omponent ma tranfer problem the effet of the indued veloity mut be treated arefully. In thi paper the indued veloity aued by vapor ondenation i the main fator, o for the ma tranfer of SO, ame veloity wa applied in the orretion fator a in following expreion g g ln( ) / ρ i Θ = (9) g ( ) /( ) / ρ. The film model appliation in vertial tube ooled The energy equation at the interfae an be deribed a: g i i Advane in Fluid Mehani V, A. Mende, M. Rahman & C. A. Brebbia (Editor) 004 WIT Pre, www.witpre.om, ISBN -853-704-3
6 Advane in Fluid Mehani V k ( t t ) = h ( t t ) + ml i w g b i δ l where m i the ondenate flux,l i latent heat of ondenation The ma balane of SO follow dm = πdm dx (0) () M ( x + x) = M ( x) + dm () The SO aborption i dependent on the ondenate and temperature. So the interfaial temperature and ondenate flux are important fator for SO aborption. The ondenation heat tranfer and ondenate flux an be found in literature [8]. 3 Experimental ytem The mixture of gae i produed by a natural ga boiler and a vapor generator. Fig. hematially illutrate the experimental ytem: ombution devie, ondenation apparatu, ga exhauter, olletor of ondenate and meaure ytem. The mixture of gae wa metered by an even veloity tube rate meter. SO wa injeted into flue ga to hange the onentration of the flue ga. Wet flue gae entering the vertial tube wa ooled by ounter-flow water in the ooling jaket. The tet etion wa wrapped with thermal inulation material to avoided heat lo to urrounding. Condenate wa olleted by a plexigla elbow. Figure : Experimental ytem. wet flue ga valve 3 humidifier 4 preure meter 5 data olletor 6 inlet of old water 7 outlet of old water 8 exhauter. 4 Reult and diuion The effet of Re number of mixture bulk flow and water vapor fration on heat tranfer have been fully tudied [7]. The influene of wall temperature and Re number of bulk flow on the SO aborption were diued in thi paper. The Advane in Fluid Mehani V, A. Mende, M. Rahman & C. A. Brebbia (Editor) 004 WIT Pre, www.witpre.om, ISBN -853-704-3
Advane in Fluid Mehani V 63 wall temperature and Re of bulk flow are important fator affeting the heat tranfer of mixture of gae. The interfaial temperature inreae obviouly with the wall temperature. The driving fore of ma tranfer between interfae and bulk flow dereae and the ondenation rate beome weak. Fig.3 illutrate the theoretial predition for SO aborption at different wall temperature. Fig.4 give the experimental reult when Re number i 4000. Thee reult how that the reult predited are higher than experiment.. It i hown that the higher wall temperature i orreponding to lower aborption SO abor pt i on % 30 5 0 5 0 5 3 0 0 5 30 35 40 t w ( ) Figure 3: SO aborption predited by film model. (: Re=3450; : 5000; 3:Re=7000). SOabor pt i on(%) 0 5 0 5 0 0 0 30 40 t w( ) Figure 4: SO aborption at different wall temperature. (Re=4000). When wall temperature i high, the temperature at the film urfae i high aordingly and bulk ga i in uperheated ituation. The lower wall temperature produe lower vapor fration of the mixture at the ga-liquid interfae and indue larger onentration gradient of vapor. Therefore, the vapor ondenation rate inreae with dereaing wall temperature aording to the Fik Law a hown in the Fig. 5. Fig. 6 indiate that the SO aborption rie with dereaing wall temperature. There are two fator reulting in thi. One i that the vapor ondenate a the olvent of SO inreae. The other i that the Advane in Fluid Mehani V, A. Mende, M. Rahman & C. A. Brebbia (Editor) 004 WIT Pre, www.witpre.om, ISBN -853-704-3
64 Advane in Fluid Mehani V aborption of SO i relative with the temperature of olvent. When the temperature i lower, the aborption i more. Another important fator i the Re number of bulk flow. Alo Fig.5 and Fig. 6 how that the vapor ondenation and SO aborption inreae with the Re number. The reaon i ame a for the effet of the wall temperature. Figure 5: m(kg/h). 0 0. 8 0. 6 0. 4 0. 0. 0 3 0 5 30 35 40 t w ( ) Relation of ondenate and wall temperature. (: Re=3450; : Re=5000; 3: Re=7000). m 0 7 (kg/) 55 45 35 5 3 Figure 6: 5 0 5 30 35 40 t w ( ) Relation of SO aborption and wall temperature. (: Re=3450; : Re=5000; 3: Re=7000). ms 0 7 (kg/) 50 40 30 0 0 0 0 0. 0.4 0.6 0.8 Z/ L Figure 7: Relation of SO aborption and dimenionle length. (: g =0%; : g =%). Advane in Fluid Mehani V, A. Mende, M. Rahman & C. A. Brebbia (Editor) 004 WIT Pre, www.witpre.om, ISBN -853-704-3
Advane in Fluid Mehani V 65 Fig. 7 reveal the relation of SO aborption and dimenionle length. The reult i that the SO aborption i improved by the inreaing vapor fration. A hown in the graph, SO aborption i trengthened when the mixture ga ontaining more water vapor. It i beaue the SO onentration gradient between the bulk ga and the ga-liquid interfae goe up with the vapor ondenation. 5 Conluion. The onvetive ondenation of mixture of gae with water vapor and SO i a omplex heat and ma tranfer proe. The wall temperature ha great influene on ondenation heat tranfer and SO aborption.. The predition of film model i in good agreement with experimental reult. 3. When vapor fration and the Re number of flue ga inreae, vapor ondenation and SO aborption inreae. 4. The reearh indiate that about 8%- 8 % SO an be aborbed by ondenate. Aknowledgment Thi work wa upported by the National Natural Siene Foundation of China (No. 503600), Natural Siene Foundation of Beijing (No. 30006) and Northern Jiaotong Univerity Sientifi fund. Referene [] Colburn A.P. and Hougen O.A. Deign of ooler ondener for mixture of vapor with non-ondening gae, Ind. Engn. Chem.,934, 6: 78-8 [] Bell K.J., Chaly M.A. An approximate general lited deign method for multi-omponent/partial ondener, A.I.Ch.E. Sympoium Serie, 97, 69: 7-79 [3] Toor H.L. Fog formation in boundary value problem, A.I.Ch.E. J., 97, 7: 5-3 [4] Chaoyang Wang, Chuanjing Tu. Turbulent ondenation heat tranfer of mixture ga in irular tube, Journal of Chemial Engineering, 989, 6: 678-685 [5] MNaught J.M..An aement of deign method for ondenation of vapor from a nonondening ga. heat exhanger theory and pratie, ed. by Taborek J. Hewitt G.F. and Afgan N., 983, Hemiphere Pnb. Co. [6] Brouwer H.J.H., Cheter A.K.. Film model for tranport phenomena with fog formation the laial film model, Int. J. Heat Ma Tranfer, 99, 35():- [7] Jia L., Peng X.F. Heat Tranfer in Flue Ga with Vapor ondenation, Tinghua Siene and Tehnology,00, 7():77-8 [8] Jia L., Peng X. F. and Yan. Y., Effet of water vapor ondenation on the onvetion heat tranfer of wet flue ga in a vertial tube. Int. J. Heat and Ma Tranfer, 00, 44():457-465. Advane in Fluid Mehani V, A. Mende, M. Rahman & C. A. Brebbia (Editor) 004 WIT Pre, www.witpre.om, ISBN -853-704-3