Study Group Report: Plate-fin Heat Exchangers: AEA Technology

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1 Study Grup Reprt: Plate-fin Heat Exchangers: AEA Technlgy The prblem under study cncerned the apparent discrepancy between a series f experiments using a plate fin heat exchanger and the classical thery f Nusselt. A plate fin heat exchanger invlves the flw f a stream f cndensing nitrgen vapur in ne flw channel and a cunterflwing stream f liquid nitrgen in an adjacent flw channel. The liquid nitrgen is at a lwer temperature and pressure and bils. The classical thery f Nusselt treats the flw f the cndensing vapur using lubricatin thery. A liquid film f cndensate frms n the walls f the flw channel, and drains under gravity. As the flw cntinues alng the channel, further cndensatin ccurs and the flux f liquid increases (figure 1). Simple lubricatin thery analysis suggests that the mass flux f the liquid per unit width n a flat plate is This may be used t determine the quality, Q, which i~ a measure f the vapur flux divided by the ttal flux. where M is the ttal mass flux. Nte the quality may alternatively be defined as a thermdynamic quality, in which case the rati f the enthalpy (rather than mass) fluxes is used in the definitin, with the liquid and vapur enthalpies being evaluated at the cndensatin temperature. The relatinship between the quality and the mass flux f liquid enables ne t determine the heat transfer cefficient as a functin f the quality. The heat transfer thrugh the liquid film n the walls has the frm, apprximately, where T; is the cndensatin temperature f the vapur and Tw is the wall temperature, and K is the thermal cnductivity. The film thickness h may be recast in terms f the quality, using the abve analysis, t yield the result This simple thery was applied t understand the variatin f the heat transfer cefficient with quality alng ne f the rectangular plate fin passages in a test heat exchanger at 1

2 Harwell. The thery was adapted t include the effects f the gemetry f the rectangular cavity and the reduced efficiency f the secndary fins, which are nt directly in cntact with the cunterflwing channel. Hwever, in spite f these crrectins t the simple thery, the variatin f the experimental heat transfer cefficients with quality differed frm the scaling suggested abve (figure 2). At high flw rates the dimensinless heat transfer cefficient varied smewhat mre slwly than predicted by the Nusselt scaling, while at lw flw rates the heat transfer cefficient decreased mre rapidly than predicted by the Nusselt thery. The scaling parameter, which includes the effect f the gemetry may be fund frm the data at imtermediate flw rates (figure 2). At the study grup, varius explanatins as t the surce f the discrepancy between the Nusselt thery and the data were explred. Tw appraches taken were t assess the data cllectin methd and t assess the relevance f the mdel t the experiments. Experimental assessment. The quality is calculated by measuring the heat flux thrugh the walls f the channel and then assuming that this heat flux is supplied by the latent heat released n cndensatin f the vapur. Therefre, at any distance dwn the pipe, the ttal flux f cndensed vapur may be estimated. Hwever, in analysing the data cllectin methds, it was fund that there is sme superheating f the nitrgen vapur n entry t the channel. This superheat remains in the vapur fr sme time, and affects the estimate f the pint at which cndensatin ccurs since the superheat is cnducted thrugh the wall in additin t the latent heat. In turn this affects the estimate f the quality. Hwever, frm the enthalpy balance, this superheating nly amunts t a quality errr f a few percent. Further, it was fund that the heat flux in the wall was nt in fact cnstant but varied significantly near the entry pint. The heat flux measurements in the wall were quite far apart, and did nt seem sufficient t reslve this variatin and thereby accurately estimate the ttal heat flux thrugh a given length f the wall. Indeed in sme experiments, nly ne r tw thermcuples were lcated in this entry regin. One cnclusin f the study grup is that the accuracy f these estimates culd be checked. Theretical Assessment. In additin, during the study grup week, we examined the assumptins implicit in the Nusselt thery, and their relevance t the flw in questin. A majr issue which was addressed was the rle f any indentatins in the walls, as arise fr example near sites f brazing between adjacent channel walls. In such narrw grves, the actin f surface tensin is t fill the grve with fluid, and thereby pssibly create a flw path f lwer resistance than n the smther walls f the flw channel. This can increase the flux f 2

3 liquid dwn the channel, but its efect upn the relatinship between the heat transfer cefficient (HTC) and the quality was nt clear. In rder t elucidate the pssible impact f any grves upn the HTC-quality relatinship, we develped a simple mdel f a grve f size d embedded in a plane wall, and aligned with the flw. A simple scaling f the lateral surface tensin frces and the dwnward gravitatinal frce, suggests that the frce rati is and s any grve f size smaller than Irnm will draw in fluid n a shrt timescale cmpared t the dwnward flw timescale. Furthermre, the lateral flux f cndensed liquid required t fill the grve may be supplied by the enhanced cndensatin arund the grve which results frm the thinning f the film arund the grve under the actin f surface tensin (figure 3). The effect f such a grve upn the Nusselt heat transfer thery is readily calculated, and shwn t be imprtant. The reasn that a flw in a grve changes the scaling is that the liquid flux may be significantly enhanced by such a grve whereas the heat flux thrugh the wall des nt change significantly. The liquid flux is given by the sum. f the lubricatin flw dwn the wall, f lateral scale a say, plus the flw in the grve itself, giving the ttal liquid flux ver a length a (figure 3) A simple scaling analysis shws that fr a grve f width 0.1 mm, a typical film thickness f 0.05 mm, and a channel width a f 1 mm, the flux rati between the flw in the grve and that in the main film is and s the flux is increased by O(1) wing t the presence f the grve. We can then write dwn the relatin In cntrast, the heat transfer thrugh the liquid film "Cnsistsf the sum f the flux thrugh the main film and that thrugh the grve. This has the apprximate value fr the gemetry f figure 3 a d Heatflux = kt:::.t(-;;, + (h+d)) 3

4 Nw the rati f the heat flux thrugh the grve and thrugh the film prper is dh (d+h)a"'o,l and s the heat flux is nt significantly altered by the presence f the liquid filled grve. As a result, the heat flux has the apprximate value K6Ta Heatflux = h and the heat transfer cefficient scales as t(l + O( (d!~)a». Using the revised frmula fr the liquid flux, we see that the heat transfer cefficient is related t the quality by the scaling The term n the right hand side is f sme imprt, as shwn abve, and crrespnds t the enhancement f the liquid flux wing t the presence f the grves. In figure 4, we shw hw this factr differs frm the classical Nusselt thery in which the scaling is simply (1 - Q)-1/3. Nte that the effect this crrectin is greatest at lw flw rates fr which the liquid in the film cnstitutes Experimental Design. a large fractin f the ttal flux. A further feature was nted abut the present experimental cnfiguratin. This sheds sme light upn the sensitivity f the apparatus cefficient with fin blade shape. design, mst f the temperature t detect changes in the heat transfer It was identified that with the present experimental drp between the cndensing vapur and the biling liquid in adjacent flw channels actually ccurs in the metal dividing the tw flw channels rather than in the liquid film f cndensate n the wall f the channel. In particular, if we balance the flux f heat thrugh the wall with that thrugh the liquid film, then T.' Tc - TWT.' T w - n..1'../ h =.l'-a h w where hw is the thickness f the wall and Tb is the biling temperature n the far side f the wall. Since the wall thickness in the experimental set-up is apprximately 6 mm, and the typical film thickness is 0.1 mm, then the temperature drp acrss the wall is abut 10 times larger than that acrss the film f cndensed vapur. As a result, the heat flux 4

5 acrss the walls f the channel is insensitive t small changes in the mean thickness f the liquid film as the gemetry f the channel is varied fr example, since the heat flux is determined by the temperature drp acrss the wall. Fr a given psitin ~ng the flw channel, in each experiment a cmparable mass f liquid will cndense in rder t supply the heat flu."{thrugh the wall. As a result, the quality at a given lcatin alng the wall will be relatively insensitive t differences in the detailed channel gemetry, and it is difficult t accurately cmpare the efficiency f different channel designs. In the real systems, the wall thickness is much smaller, and the heat flux is therefre mre sensitive t changes in the thickness f the liquid film, since mre f the temperature difference between the biling and cndensing flws ccurs acrss the cndensed liquid film. A different apprach might be t examine the prperties f the flw at varius pints alng the flw channel, by arranging a series f different length flw channels in series, and sampling the utput frm each channel. A number f questins emerge frm this reprt, including: (i) is there a critical heat flux? (ii) what size/shape f grve is best? (iii ) can mdels be tested using the existing experimental data? 5

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7 ~:L.z-> ~ ~ ~..... c Q) u '+- '"- Q) u L- Q) '+- Vl C U L c 2-0 Vl ~ (1-3 J::. I.- (J I- \:s 2.. T Nusselt :::0-1 K uncertainty estimate in raw 6.T e e~/-vg McNaught (1987) / ~c = (1 7 I) 6. n = 0-22 In t::ql-gtin t. I... '::l n-.c -..- Vg,gas velcity + >2-0 increasing rj1<vg<2 ~ <1-0- (m/s~ PLAII'J FI N NITROGEN ALL DATA: 2-6 bar, kg I m 2 s high shear regin where ( d P ) > 1-2 x 1. (d P ) dz T g dz TV ~-'- _ ;1;s~4i~~) I I I I I I I " I I I I L.J ~_--' I I ~ film Reynlds number f1~r-...j

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