THEORETICAL AND EXPERIMENTAL STUDY ON DROPWISE CONDENSATION IN PLATE HEAT EXCHANGERS

Transcription

1 Abstat THEORETICAL AND EXPERIMENTAL STUDY ON DROPWISE CONDENSATION IN PLATE HEAT EXCHANGERS V. Bendt, S. Zunft and H. Mülle-Steinhagen Geman Aeospae Cente (DLR), Stuttgat, Gemany This pape desibes the outline of a simulation model fo an oil-ooled flat-plate ondense and summaises the main esults fom its appliation. Mass and enegy balanes ae solved fo a speifi Alfa Laval plate heat exhange with thee hannels. Dopwise ondensation on the ougated plate sufae is desibed using a modified model fom the liteatue, and studied though high-speed imaging. Paamete vaiations show the most elevant paametes of the model. The influene of tempeatue diffeene, oil flow, pessue and some model paametes on the simulation esults is analysed. The esults of the simulations ae ompaed to expeimental data, showing that the model is useful ove a etain ange of paametes, but has to be impoved fo high heat fluxes to ahieve a bette fit to the expeimental data. Intodution Dopwise ondensation ealises heat tansfe oeffiients whih ae about one ode of magnitude highe than those fo filmwise ondensation (Koh, 997). Fo a long time, howeve, no adequate sufaes fo dopwise ondensation of steam had been found whih satisfied industial equiements with espet to stability and ost. In the last deades new oating tehnologies have been developed, and today good pospets exist fo the podution of duable and affodable hydophobi oatings (Rose, 2002). With these new tehnologies dopwise ondensation may be implemented in industial appliations. Pope design of industial ondenses equies the auate knowledge of the undelying heat tansfe oeffiients. To fully exploit the potential of the enhaned heat tansfe, the basis of suh design alulations needs to be efined. This wok outlines expeiments and poposes a model that an fom the basis of an adequate design poedue. Fo pefoming the expeimental tests fo steam ondensation on vaious oated plates, a heat exhange test ig is set up at the Institute of Tehnial Themodynamis of the Geman Aeospae Cente (DLR). The dopwise ondensation poess with its highly unsteady natue, whee aound a million oalesenes an ou in one seond on a squae entimete of the ondensing sufae, an not be modelled in detail. The exellent ageement between theoetial esults and heat-tansfe measuements justifies the assumption of a steady heat tansfe ate fo a dop of given size and a steady distibution of dop sizes (Rose, 976). The suggested appoah is based on the enegy and mass balanes fo steam and oolant flow ate with the assumption of a onstant dop size distibution and dop gowth ate duing a patiula inteval. Fo a bette adaptation of the model to the onditions in industial plate heat exhanges, and as an impovement ove pevious models, the effet of the shape of the ondense plate is onsideed.

2 2 Modeling and Simulation Based on the mass and enegy balanes ove the plate heat exhange the alulation is efined by the detemination of heat tansfe fo the ondensation and fo the ooling side depending on the loal tempeatue onditions. Likewise, the heat ondution though the plate heat exhange is onsideed. Patiula emphasis is plaed on the detailed onsideation of the dopwise ondensation poess. Steady state mass and enegy balanes fo the ondensing steam and fo the oolant flow fom a system of non-linea, odinay diffeential equations. The tempeatue of the oolant (themo-oil) flow and the steam quality ae the dependant vaiables. The oveall heat tansfe oeffiient U is alulated fom the loal ondensation heat tansfe oeffiient, the oolant heat tansfe oeffiient and heat ondution though the oated plate, and theefoe depends on the loal tempeatues and steam quality. This model is ompiled fo a symmeti plate heat exhange with only thee hannels; in the middle the ondensing steam and on both sides the themo-oil flows. The dietion of the oil flow an be o-uent o ounte-uent to the steam flow. 2. Model of the Plate Heat Exhange The pesent ontibution poposes a model fomulation fo a plate heat exhange opeated with ondensing steam and themal oil in adjaent hannels. The onsideed setup is depited in Figue. The enegy balanes fo oil and steam fom a set of equations that an be solved numeially. Equations () and (2) ae the basi equations fo the oil tempeatue and the steam quality. Mass flow is the same as mass flow. dϑ da p = U,2 ( ϑ ϑs ) () dz m p, dx 2 da S p = U,2 ( ϑ ϑ ) = 0 s (2) dz Δh m 2 V The heat tansfe oeffiient depends on the oil and steam tempeatues, the steam quality and the oil flow, theefoe it also depends on the vaiable z: U,2 = f,, m, x ϑs ϑ S = f ( z). z=0 OIL STEAM OIL z m m 2 z x s m (z) d Q d Q z + dz, 2 2, x s (z+dz) m 2 m m z=l Figue : Model of the plate heat exhange.

3 The following bounday onditions ae used: Satuated steam at the entane of hannel 2: ( z = 0 ) = Same inlet tempeatue fo both oil hannels and same mass flow ate 0, =,4 = Fist and last plate adiabati: Q Q 0 The oveall heat tansfe oeffiient vaies with the height z of the heat exhange and is alulated fom the ondensation and the oolant (oil) heat tansfe oeffiients h and h oil and the heat esistanes of the plate and the oating, F pl and F, as shown in equation (). = + Fpl + F + () U h hoil s pl s With Fpl = F = (4) λ λ pl s pl and s in equation (4) ae the thikness of the ondense plate and of the oating and λ pl and λ is the espetive themal ondutivity of the plate and the oating. Heat flux and heat tansfe oeffiient ae onneted as pesented in equation (5). ( ϑs ϑwall s ) = oil ( ϑwall, oil ϑoil q = h, h ) (5) The heat tansfe oeffiient of the themal oil is alulated with an equation by Matin (2002). The alulation of the ondensation heat tansfe is desibed in detail in the following setion. 2.2 Model fo Dopwise Condensation Vaious attempts have been made to estimate the heat tansfe ate duing dopwise ondensation. Fatia and Katz (949) wee the fist who poposed a model fo the heat flux by assuming that all dops on a given aea ae of the same size and gow by ondensation on thei sufae. Late, diffeent eseahes have dealt with the poblem of dop size distibution, see fo example Rose and Gliksman (97), Tanaka (975) and Wu and Maa (976). All these eseahes developed thei models on the basis of the mass and enegy balanes fo a single dop with adius. Integating the veloity of the ondensation poess - ondensate volume pe unit time and unit aea - ove the adius inteval fom the minimum (emeging o nuleation) adius min to the maximum (sweeping) adius max (befoe it slides down) yields the following equation (assuming a ontat angle of 90 degees) fo the heat flux max V 2 q = ρ ΔhV = ρ ΔhV 2 π R() N() d (6) A min d The dop gowth ate R () = depends on the dop adius, the steam pessue and theefoe the dt ondensation tempeatue as well as the wall subooling Δ T = ϑs ϑwall. The dop size distibution n () (, + Δ) N = aounts fo the numbe of dops of a speifi adius o adius ange Δ. Δ A Rose (976) analysed vaious expeimental data fom diffeent authos and found the following equations to desibe dop gowth ate and dop size distibution, see equations (7) and (8) below. Heein, K = 0,67, K 2 = 0,5, K = 0,4 ae empiial onstants. min ΔT R() = (7) 2 ρ T fl ΔhV s K + K 2 + Fpl + F λ O fl x S

4 N () = π max max 8 (8) The minimum and maximum adius min and max and the sufae O ae alulated fom equation (9). 0,5 2 σ v f = σ min max = K ΔhV ΔT ( ) g ρ fl ρ g 0,5 2 κ + 2 σ O = ρ Δ g hv (9) κ RG Ts Peviously published oelations assume a sufae inlination of 90 with an idealized spheial dop shape. Consideing a plate heat exhange with ougated hannels, the influene of the shape of the sufae must also be evaluated. Expeimental data of Koh et al. (997) ae used to alulate the dependene of the heat tansfe oeffiient on the angle of inlination of the heat exhange sufae, see Figue 2. A polynomial equation is fitted to the expeimental data. h h ( β ) ( 90 ) = -, β + 5, β - 7, β + 4, β +, (0) 2. Simulation Results In the following, some esults fom the simulation of the plate ondense with ounte-uent oil flow ae pesented. Figue (left gaph) shows the vaiation of the opeational paametes tempeatue diffeene between steam and oil and satuation pessue that have also been vaied in the expeiments. With ineasing satuation pessue the heat flux ineases. Also with ineasing the tempeatue diffeene highe heat fluxes an be eahed. To hek the influene of the model paametes, the dop adii wee also vaied. The value of the minimum dop adius has almost no influene on the total heat flux. Only when it eahes the same ode of magnitude as the maximum adius, it influenes the alulated esults. This an be lealy seen in Figue (ight diagam). The influene of the value of the maximum adius is muh moe signifiant; thus its estimation, and patiulaly the estimation of paamete K, have to be pefomed aefully in ode to obtain good simulation esults. Figue 2: Dependene of the heat tansfe oeffiient on the sufae inlination (Soue: Koh 997).

5 Heat flux / W 6,00E+0 5,50E+0 5,00E+0 4,50E+0 4,00E+0,50E+0,00E ΔT / K ba 2 ba ba 4 ba 5 ba Heat flux / W,4E+04,2E+04,0E+04 8,0E+0 6,0E+0 4,0E+0 2,0E+0 0,0E+00,0E-0,0E-09,0E-08,0E-07,0E-06,0E-05,0E-04 R min / m Rmax = 0,4 Rmax = 0,5 Rmax = 0,6 Rmax = 0,7 Rmax = 0,8 Rmax = 0,9 Rmax = Rmax =, Rmax =,2 Figue : Left: Calulated heat flux ove tempeatue diffeene with satuation pessue as paamete Right: Calulated heat flux ove minimum adius of the simulation model with the maximum adius as paamete. Expeiments Expeiments with oated heat exhange plates wee pefomed to quantify the influene of the pessue and the wall subooling on the pefomane. Plates with hydophobi Ni-P-PFA oatings wee tested at vaious pessues and diffeent oil tempeatues and volumeti flow ates, and wee ompaed with unoated plates. An Alfa Laval TS6 plate heat exhange was used fo the expeiments. The test ig allows visual inspetion of the ondensation poess (see Figue 4) and thus analysis of the elevant phenomena. A flow diagam of the expeimental set-up is shown in Figue 5. Visual obsevation of the dop lifeyle on oated plates showed exellent dopwise ondensation behaviou. High-speed videos wee eoded, showing the dependene of dop gowth ate and dop size on the opeating onditions. Oveall heat tansfe measuements show an inease in heat flux of up to 20 %, whih means an enhanement of about 00 % with espet to the ondensation heat tansfe oeffiient, see Figue 6. Figue 7 shows both simulated and measued data fo a steam pessue of 2 ba. Fo dopwise ondensation, simulation esults seem to fit the measued data vey well. Fo lowe oil tempeatues (= highe tempeatue diffeenes between oil and steam) the alulated data pedit highe heat fluxes than the measuements. The same effet an be seen fo highe steam pessues. Figue 4: Left: Dopwise ondensation on a oated heat exhange plate Right: Test ondense with windows fo visual obsevation and high-speed amea

6 This allows the onlusion that an additional model paamete is to be onsideed. A possible explanation is that the ondensate dainage may beome a limiting fato with high ondensation ates. The esulting deease of unwetted aea epesents an additional heat tansfe esistane, this in patiula at the bottom pat of the heat exhange. The measuements eveal that with dopwise ondensation a substantial enhanement of heat flux is aomplished. Howeve, the extent of this enhanement is limited by the signifiantly lowe oolant heat tansfe oeffiient. Fo low tempeatue diffeenes it auses a limitation of the wall subooling and thus a limitation of the ondensation heat tansfe oeffiient. Compaison of simulation and measued data also shows that the enhanement of the heat flux fo dopwise ondensation in a oated plate heat exhange ompaed to filmwise ondensation without tubulene, as is desibed in Nußelt theoy, is well epodued by the simulation model. h / W/m 2 K unoated = filmwise ondensation oated = dopwise ondensation ΔT / K Figue 6: Filmwise and dopwise ondensation heat tansfe oeffiient fom expeimental data in the Ni-P-PFA-oated plate heat exhange pessue = 2 ba tempeatue = 20,2 C 0000 Heat Wäme flux / in kw W Oil Öl-Tempeatu tempeatue / in C C Nußelt TK DWC Modell unbeshihtet unoated expeimental Messung DLC DWC Messung expeimental Figue 7: Simulation and expeimental esults fo heat flux with dopwise ondensation on ougated plates.

7 4 Conlusions A simulation model based on the mass and enegy balanes fo a plate heat exhange has been established. Compaisons with measued data eveal a easonable auay of the alulations fo both filmwise and dopwise ondensation. A futhe impovement of the model is expeted with extensions that aount fo anothe effet on the heat tansfe, suh as dainage limitations, the vapou shea o pessue dop effets. The model was assessed in paamete vaiations, whee the influene of tempeatue diffeene, oil flow, pessue and some model paametes on the ondensation pefomane was analysed. Effets of the impotant opeational paametes pessue and tempeatue diffeene on the heat flux have shown that the model is useful ove a etain ange of paametes, but has to be impoved fo high heat fluxes to ahieve a bette fit to the expeimental data. Conening the model paametes, the maximum ondensate doplet adius (befoe it slides o falls down) has to be known bette fo good modeling esults. Fo the nuleation adius only the ode of magnitude is elevant. It was shown that with a moden high ontat angle sufae, suh as the Ni-P-PFA oating, onsideably highe heat fluxes an be obtained while they stay in the dopwise ondensation egime, ompaed to pevious sufaes, whih quikly tansit to the filmwise ondensation egime. Refeenes Fatia, N. and Katz, D.L., 949, Dopwise Condensation, Chem. Eng. Pogess, 45, Koh, G. et al, 997, Condensation of Steam on the Sufae of Had Coated Coppe Diss, Heat and Mass Tansfe, 2, Matin, H., 2002, Dukvelust und Wämeübegang in Plattenwämeübetagen, VDI Heat Atlas, Setion Mm. Rose, J.W. and Gliksman, L.R., 97, Dopwise Condensation the Distibution of Dop Sizes, Int. J. Heat Mass Tansfe, 6, Rose, J.W., 976, Futhe Aspets of Dopwise Condensation Theoy, Int. J. Heat Mass Tansfe, 9, Rose, J.W., 2002, Dopwise Condensation Theoy and Expeiment: A Review, Po. Instn Meh Engs Vol. 26 Pat A: J. Powe and Enegy, Tanaka, H., 975, A theoetial study of Dopwise Condensation, Tansations ASME J. Heat Tansfe, 97, Wu, H.W. and Maa, J.R., 976, On the Heat Tansfe in Dopwise Condensation, Chem. Eng. Jounal, 2,