parametric study concentric048

7/28/2019 Parametric Study Concentric048

1/6

S f l G E P U B L I C f l T I O N S F R X NO . s 4990871 11-16-98 09:37 P.03

A Parametric Study of Horizontal Concentric HeatExchangers for Storage Tanksby A, Nasr, G. L Morrison, and M. BehniaABSTRACTHeat exchanger based l i qu id storage systems havenumerous applications such as solar water heating systems an dchemical processes. One of the most common heat exchangerbasedstorage systems uses a. concentric or man t le hea t exchanger a roundth e storage tank. In this configuration, fluid f rom a heat source t rav-els aroun d the a n n u l a r gap enclosing th e central storage t ank andtransfers heat to the l iqu id in the central storage t ank . Due to thesimultaneous occurrence of both cooling and heat ing processes, th eperformance of a concentric heal exchanger is qui t e complex andit s characteristicsdiffer significant ly from t radit ional heat exchang-ers. The flow and heat t ransfer characteristics of an a n n u l a r h e a texchanger were investigated numerically, and the ca lcu la t ed H owpatterns and h e a t t ransfer were compared with experimental data ,A hea t exchanger deficiency coeff ic ient was developed to quan t i f yth e degrada t ion of thermal s t r a t i f i ca t i on in the inner storage t?nVcaused by the flow in the annulus .

1. IntroductionThere have been num erou s appl icat ions of heat exchang -er s fo r the rmosyphon solar water heating systems, Morrison

(1995) and Webster, Coutier, Place, an d Tavan (1987) pro-posed a horizontal storage tank consisting of a number ofhorizontal tubes located near the bottom of the storage tankin a solar water heater. Their experimental and numerica lresults indicated that in such a system there was very l i t t lethermal stratificatio n developed in the tank as a result of thedisturbance caused by heat inp ut into the bottom of the tank .This effect causes a loss of the benefit of thermal stratifica-tion an d could be one of the consequences of using an y typeof beat exchanger in thermosyphon systems w i th hor izon-tal storage tanks . However Webster observed a performancedegradation of less than 10%, which was regarded as smallenough to make th e system technically feasible.To overcome problems with heat exchanger based solarhot w a t e r storage tanks . Parent, V an Der Meer , and H o l l ands(1987) investigated the perform ance of systems emp loying asingle pass side arm heat exchanger installed cither ins ide orouts ide th e storage tank (immersed type and external type,respectively). In both systems, a vertical t ank w as used to en-hance th e buoyancy-induced convection on the storage tankside of the heat exchanger and a pum p was used in the collec-to r loop on the other side of th e side arm heat exchanger Al-though the stratification performance was preserved in bothcases, th e manufac tu r ing cost and installat ion problems were

A. Nasr , C. L . Morrison, ondM. Bchnia, School o f Mcchunicel an d M anufa-turing Engineering, University of'M?w South Wales. Sydney 2052, Australia.Communicated byS. N .

considered to be major disadvantages, M ertol, Place, Web-ster, and Grief (1981) numerically investigated a heat ex -changer consisting of copper tubes immersed in the bottomsection of a vertical storage tank and showed tha t the systemwas capable of 90% of the performance of a direct -coupledcollector heating system (w i t hou t heat exchanger) .Baur , K le in , an d Beckman (1993) studied a vertical con-centric heat exchanger based system for pumped circula-tion solar water heaters an d concluded t ha t there w as l i t t ledifference in annual performance between a vertical man-tl e tank and an external hoat exchanger tank in solar waterheaters. The advantages of the i r design over other designswere claimed to be simplicity, larger heat transfer area, an dhigher efficiency. More recently, F u r b o (1993) showed thatfo r a vertical tank w i t h a ma ntle heat exchanger , th e temper-ature stratification in the i nne r t a nk is not d i s t u r b e d by heattransfer from the fluid in the annu lus , s ince th e in le t fluid inth e annu lus moves directly to a level just above it s the rm a le q u i l i b r i u m level with the wa te r in the i n n e r t a n k .

A heat exchanger based solar water heater storage systemcomm only used in the rmosyphon so l a r wa te r hca t ing sys t cmsuses two horizontal concentr ic cyl inders. In th is configura-t ion, the inner cylinder serves as th e storage t an k and th e hotl iquid flows in the ann ular cavi ty between the two cyl inders.The performan ce of this type of heat exchanger is com plex,since th e flow in th e ann ulu s undergoes both cool ing an d heat-in g processes during one pass, The object ive of the presentwork is to investigate the f low and heat t ran sfer character is-t ics in such a heat exchanger (Figure 1). The collector loopin le t an d outlet connection points to such an annular hea texchanger in a solar water heater ar c norm al ly made to thebonom of the ann ula r cavi ty in order to m i n i m i z e heat lossdue to reverse circulat ion be tween th e tank and the collectorat night t im e . Th e bottom posi t ion of the hot inle t penal izesthe performance d u e to los*of stra t i f ica t ion from heat i np u t toth e bottom of the t ank ra the r than to the t he rm al e q u i l i b r i u mposit ion. Stratification in the s torage tank could he improved.i f th e collector re turn point were just below th e level of theinte rna l electric or gas booster clement in the tank. H ow-ever, high connections to th e tank require careful insu la t ionof the collector to tank pipes in order to m i n i m i z e reverseci rculat ion at night .To unders tand th e t rade-off between improved stratifica-t ion and increased losses due to reverse c i r cu l a t i o n , thi s paperreports an e x p e r i m e n t a l and numerical s tudy of the flow an dtemperature characteristics of these systems. For the exper i -ment , a half-scale model of a typ ica l hor izon t a l t ank m a nt l eheat exchanger w as constructed w i t h a Pcrspcx ou te r wallto allow visual izat ion of the flow in the a n n u l a r passageway

Computer Model ing and Simulation in Engineering 269


2/6

R O M : S f l G E P U B L I C f l T I O N S F f l X NO . : 4990871 11-16-98 89:38 P .0 4

Flow to !Fk m f aacolkcMrFigure 1, Mantle heat exchanger used with horizontal tanksolar water heating systems (width of annular gap exagger-ated),

Pcrjpcx outer cylinder end flange

y > x

v ,i\nmetal inner tank

_ X1 Heat exchangerCold outlet flow Hot inlet flow omukr passageFigure 2, Horizontal tank annular heat exchanger test model.

(Figure 2). The concentric heat exchanger in the presentstudy has an outer cylinder diameter D0 of 300 mm and aninner cylinder diameter D\f 290 rom (D(/D0 = 0,97). Thef low enters th e annulus through an inlet port at the bottomof one end and exits from a port at the bottom of the otherend. Both the in le t and outlet pipes have an internal diameterof Dp = 44 mm (DP/D0 = 0.15) w i t h a spacing -frew-th*

.end wall of th e annulwof S = 700 mm (S/D0 = 2.3) (seeFigure 2). The inlet and outlet pipes enteredver t ical ly into thebottom of the annulus between the inner and outer cylindersas commonly used in thermosyphon solar water heaters. Thelaboratory model heat exchanger had an overall length I of916mm,Flow visualization using dye injection into th e a n n u l a rcavity was used to determine the flow structure. Significantunsteadiness in the flow near th e inlet port w a s observed du elo impingement of the inlet flow onto the inner tank wa l lopposite th e inlet port. Although this geometry introducescomplications into the f low, i t was invest igated f i rs t becauseit is the most commonconfiguration used in commercial solarwater heaters. Flow v i sua l i z a t i on and simulation of th e f lowand heat transfer in the a n n u l u s is dif f icul t due to the curvatureof the working space- This project presents some resultsfo r th e curved annulus and details of flow in a vertical slotconf igura t ion in order to investigate th e effect of dif ferentboundary conditions, including th e impingement inlet shownin Figures 1 and 2 and an inlet parallel to the annulus wal l s .

2. Numerical SimulationThe analysis of this problem is complicated by the mixedforced and free convection processes in the a n n u l u s and thei m p i n g i n g w a l l jet effect a t the inlet due to the location o f

the inlet pipe at right angles to the bottom of the a n n u l a r gap.The aim of this investigation is to understand the flow andheat transfer phenomena i n a n n u l a r heat exchangers for thedesign and optimization of solar water heaters. The focus ofth is report is on the design of solar water heaters rather thanthe development of new simulation procedures; hence , a re-l iable , widely used CFD code (FLUENT, Release 4.4)was

employed to investigate the problem. The FLUENT CFDcode was used to solve th e flow and energy equations in thea n n u l u s of the concentric heat exchanger. The number ofnodes along the anmilus axis and in the radial and circumfer-ent ia l directions was 93, ] 7, and 42, respectively (a to tal of66,402 cells). The mesh was concentrated in the high- gra-dient regions near the walls and around the in le t and outlet .The three-dimensional laminar f low equations fo r cont i nu i ty ,Navier-Stokcs, and energy were solved. For the t rea tmentof pressure, th e SIMPLE algorithm w as adopted in conjunc-tion with a mul t ig r id scheme. For accuracy, the QUICK dis-cre t iza t ion of the convection terms was used (at least second-order accurate). The energy equation was solved in the formo f a transport equation for the static enthalpy using a mul t i g r i dscheme. The density was assumed to be constant except in thebuoyancy term, which was modeled using the Boussinesq ap-p r o x i m a t i o n . The viscous dissipation terms were neglected.Tests w i t h f iner grids showed grid dependency errors of lessthan 5% fo r velocity and 3% for temperature.

The in le t flow was assumed to be a plug prof i le type. Inthe outlet, both pressure and fu l ly developed ou t l e t condi-t ions were examined. I t was noted that the f low f ield in thea n n u l u s was no t strongly affected by the assumption of theoutle t boundary condition. The most s ign i f i can t boundaryco nd i t i o n is the thermal conditi onof the i n n e r tank w a l l . Thesurface of the inner wall of the annulus was divided into top,central , and bottom sections. The top and bot tom section;-;had the same surface area, whereas the surface area o f thecentral section wa s twice that of the top and bottom sections,To s i m u l a t e a thermal ly stratified inner t a n k , t empe ra t u re sof T J = 330 K and Tb * * 300 K were prescribed for theto p and bottom sections, respectively, and the central sec-tion w as divided into 20 horizontal strips w i t h a temperaturegr ad i en t of 1,4 K per strip. It w as assumed that the outercy l i nde r surface was adiabatic. Inlet velocities of 7.5 to .15m m / s were used, corresponding to flow rates of 0.7 to 1.4L / m i n and inlet Reynolds numbers of 300 to 600, w h i c h aret yp i c a l o f thermosyphon solar water hea t i ng systems. Thein le t t emper a tu r e was assumed to be 315 1C3. Evaluation of the CFD Code

Measu remen t s o f heat t r ans fe r between the f low in the a n -n u l u s and the water in the central t ank were performed on themode l o f a typical solar water m a n t l e hea t e xc h a n g e r (Fig-u re 2) to evaluate th e accuracy of the n u m e r i c a l s i m u l a t i o n s .The dimensionsof the heat e xc h a n g e r in the e x p e r i m e n t wereapp r ox imate l y ha l f o f those currently used i n mantle hentexchange r thermosyphon solar water heating systems. Theinner cy l i nde r was made o f 02 m m steeK a nd the ends o fthe cy l inders were closed w i t h Pcrspex f lange plates. Theo u te r cy l i nde r w as made o f Pcrspex 5 0 that due in jec t ioncould be used to v i sua l i ze the f low pat te rns in the a n n u l u s .Temperature-controlled water was pumped through the an-n u l u s to s i m u l a t e th e solar collector loop f low c i r cu l a t i on .The i nne r tank surface temperatures were measured usingt he rmocouple s f i xed on the inne r surface of the t a n k w h i l eth e outer cy l inde r was insulated. The experiments i nc l udedf low v i sua l i za t i on and t empe ra t u re measurements for a uni-form t empe ra t u re inner tank wall with f l ow i n to the a n n u l u aof 0.68 L / m i n and a range of in le t temperatures. The mea-sured and computed heat transfer fo r isothermal inner tankcond i t i ons (Figure 3) showed that the. n u m e r i c a l model givesan accurate simulation of overall heat t ransfer .

270 Vbf. 3, No. 4, November 1996


3/6

F R O M : SflGE PUBLICflTIONS FflX NO . : 4990871 11-16-98 09:39 P .054. Flow and Heat Transfer Characteristics

The computat ional results are presented in two sections.The flow development and heat transfer characteristics in an-nular heat exchangers are presented in this section. In th enext section, the annular cavity is approximated by a verti-ca l cavity to simpl i fy th e evaluation of the effect of cavitygeometry on th e performance of this type of heat exchanger.4, T Flow Development

The computed velocity vectors in th e midplane of the an-nu lus are shown in Figure 4. This figure indicates relativelyhigh velocities adjacent to the inlet port due to deflection ofth e inle t flow off the tank wall directly opposite th e inlet port,A flow recirculation zone above th e inlet and adjacent to thenear en d wall of the cavity is also evident in Figure 4, Itcan be seen that, due to it s in i t i a l m o m e n t u m and buoyancy ,th e m a i n flow rises up to the central region of the cavity andthen flows down toward the outlet port. D ue to the opposingbuoyancy effect caused by cooling on the inner tank wall ,flow penetration into th e to p half section of the annulus isprevented. Similar flow behavior was also observed in th eplanes adjacent to the i nne r and outer walls of the ann ulus.Figure 4 shows that the flow field adjacent to the inlet andoutlet ports differs significantly due to the j e t impingem entan d free convection effects near th e inlet port and forced con -vection near the outlet port.

" f t > examine the effect of buoyancy on th e flow field inthe annula r cavi ty, computat ions were performed fo r th ecase of forced convection only, as proposed by R a m a d b y a n i ,Zcno uzi, and Astill (1984), The computed veloci ty vectors inth e midplane of the ann ulu s, neglecting buoyancy effects , arcshown in Figure 5. Here, du e to th e absence of th e n o r m a lop -posing buoyancy effects caused by cooling on the inner tankwall, the flow pen etration in to the top of the cavity is stronger

-1000Qw a n s-2000

-3000 20 30 40 50

an d recircula tion adjacent to the en d wall is suppressed. Theflow field fo r th e forced convection only condition shown inFigure 5 i s symmetric in contrast to the mix ed convect ion caseshown in Figure 4, thus indicat ing th e importance of buoy-ancy effects on flow development in this type of concentricheat exchanger.4 .2 Therma l F i e l d

Figure 6 shows the computed temperature contours in themidp la ne of the annulus . The contours ar c more dispersedin the bottom and central sections above the inlet , imp ly ingstronger convective heat transfer than in th e to p section of thecavity. Th e existence of high-temperature gradients aroundth e inlet indicates high heat transfer or mixing of hot i ncom-ing fluid due to i m p i n g e m e n t of the inlet f low on th e t ankwall directly opposite th e effect at the inle t .For the ca$e of forced con vect ion w i t h o u t buoyancy, thecomput ed temperature contours in the midplane of the a n n u -lu s arc shown in Figure 7. Here, un l ike the mix ed convect ioncase (Figure 6), the tempe rature con tours above the in le t portindicate stronger penetration of the i n c o m i n g fluid in to th eto p region of the annulus . The top und isturbed region of thea nnu lus observed for the mixed convection case is not evi-dent in Figure 7 due to the absence of the normal tank wallcooling on the buoyancy of t h e fluid in the a n n u l u s .

uj j j i f t ^

\vhv\vtV * V V M 1 1

Figure 5. Computed velocity vectors in the midplane of theannulus (no buoyancy).

Figure 3. Comparisonof measured and computed heat trans-fer.

Figure 6. Temperature contours in the midplane of the annu-lus, 7 S B 315 K, and tank stratification from 300 to 330 K.

; :

'

~'lll\f : - : : : :Figure 4. Computed velocity vectors in the midplane of theannulus.

Figure 7. Temperature contours in the midplane of the annu-lus for forced convection only (buoyancy suppressed), T \-315 K and tank stratification from 300 to 330 K,Computer Modeling and Simulation in Engineering 271


4/6

SflGE PUBLICflTIONS F O X N O . : 4990871 11-16-98 09:40 P.06/*.3Heat Flux

The contours of heat flux through the inner tank wal l arcshown in Figure 8, The majority of the heat transfer fromthe flow in the annulus to the inner tank takes place near (hebottom of the cavity, which in practice causes mixing of theinner tank. The existence of a large region with positive heatflux (local heat removal from the inner tank) in the middle andupper sections of the annulus indicates that some of the flowin the annulus rises above its thermal equilibrium level withthe inner tank, resulting in energy removal from the innertank in this region. The heat flux in the small zone oppositethe 'nletisVCr-v W8h>about 3Xw/m*>dueto the impingingOf lJie jniet flow ont|jC opposite cold tank wall.

Heat flux distribution for forced convection only, shownin Figure 9, indicates a much larger region of heat removalfrom the top of the thermally stratified inner tank due to thepenetration of the inlet flow to the top of the annu lus . Theseresults indicate that buoyancy effects in the annulus have asignificant effect on the flow; however, th e high heat f luxzones are due to convection effects adjacent to the inlet andoutlet ports.4.4 Heat Exchanger Deficiency Coefficient

The degradation of the thermal stratification of the innert ank by the flow in the annulus can be considered as a de-ficiency of the concentric heat exchanger for application tosolar thermosyphon systems. To quanti fy the stratificationdegradation of the inner tank, a heat exchanger deficiencycoefficient is introduced, For sections of the tank wall in thelower parts of the annulus , heat transfer is from the fluid inthe annuius to the inner tank (i,e. q" < 0). However, if thel iquid in the annulus rises above its thermal eq ui l i b r ium level,due to the effect of inlet momentum, the heal transfer direc-tion changes from th e inner tank to the l iquid in the a n n u l us(i.e., q[ ' > 0), The heat transfer into the central tank in th elower part of the annulus can be determined by

Figure 8, Heat flux contours through the inner tank wall(W/m2) for mixed convection only. rjn a s 31 5 K, and tankstratification from 300 to 330 K.

Figure 9. Heat flux contours through the inner tank wall W/m 2torforced convection only (buoyancy suppressed). rin^ 3 1 5K, and tank stratification from 300 to 330 K.

CD

where q" is theheat flux on any surface strip i,n is thenumberof strips covering the inner tank walls, with q" < 0, and Atis the area of each strip. The total heat transfer is determinedfrom

(2)where m is the total number of surface strips covering theinner tank wall.The difference between th e heat transfer in the lower partof the annulus, gj ^ and the loial heat transfer, Qf, is anindication of the energy displacement and degradation of th einner tank thermal stratification. This is used to quant i fy th eheat exchanger deficiency coefficient as

T | = (Slower -C/)/Gf (3)I n a similar fashion to equations (I) and (2), the heat trans-fer between th e bottom of the tank and a vertical location ywas calculated 2y)- Figure J O shows the var ia t ion of Qy(normalized with Q f) fo r mixed and purely forced convection

cases.The overall effectiveness of the heat exchanger, neglect-in g th e stratification degradation, ca n be q ua n t i f i ed by thestandard effectiveness e, where

where mCp(Tm - Tb0t) and rbot is the temperaturein the bottom of the tank.The total heat transfer for the mixed convection case w as-433W oreffectiveness 6 = 0.59.Forthe forced convectioncase, the heat transfer was -227W and c =0.31, indicat ingt h a t buoyancy effects in the cavity have a major effect onth e heat transfer between the collector loop and the storaget an k . It is noted that the magnitude of Qy goes i tuougha m a x i m u m at around y/R, = 0 . 1 (Figure/0). suggestingthat a s ignif icant part of the heat is transferred near th e bottomof th e annulus ,

1 .0

-1.0-1.2

Figure 10, Distribution of heat transfer with height for mixedand forced convection cases.

10

27 2 Vo l . 3, No . 4, November 1996


5/6

S f l S E P U B L I C R T I O N S F f l X NO. : 4990871 11-16-98 09:40 P .07

The heat exchanger deficiency coefficient for mixed andforced convection caseswas computed to be i \ 5 and 17%,respectively. T h u s , in the mixed convection case, 5% of thene t heat t ransfer into th e tank is removed f rom the hot topsection and downgraded to the cold bottom section of th etank.5. Effect ofGeometry on Flow and Heat Transfer

It has been shown in Nasr. Morrison, and Behnia (1996)that the f low and heat t ransfer characteristics of a horizon-ta l a nnu la r heat exchanger are similar to the f low and heattransfer in a narrow vertical cavity with th e same bo un daryconditions. Fo r this reason and for the sake of sim plicity ingrid generation, th e effect of the geometry of the cavity on theH ow and heat transfer characteristics was examined us ing anequivalent vert ical cavity with bound ary condit ions typ ical lyused in man t le hea t exchangers in solar w a t e r heaters. Thevertical cavity had the same length as the concentric an n u l u s ,an d th e height of the vertical cavity w as equal to half of theinner cylinder periphery.5.1 Ef fec t of the In le t Posit ion5-1.1 FLOW D E V E L O P M E N T

To exa mine the effect of the in le t port relative to the endwall of the cavity, three in le t pipe positions were evaluated.T he inlet pipe center l ine w a s se t perpendicular to th e wallsfo r tw o cases, w i t h 20 and 0 cavity wid ths offset from th eright end wall A th i rd case t ha t evaluated th e effect of theinJe t H ow entering paral le l to the heat transfer wa ll was alsoconsidered. It was observed that th e size and s trength of therecirculat ion cell adjacent to the end wall beside the i n l e tport is a m a x i m u m w h en the flow enters parallel to the heattransfer surface. T he recirculat ion w a s min imized when th ef low entered normal to the heat transfer surface and in thecorner of the cavity (end wall offset 0) . The height of theflow penetrat ion into the top of the cavity w as observed to besubstantia l ly independent of the inlet port conf igurat ion, t hu sdem onstrat ing that buoyancy is the governing factor affectingf low penetra t ion.5.1,2 HEAT TRANSFER

T he normalized heat t ransfer ra tes , Qy/Qtt for the threeinlet port conf igurat ions are shown in Figure 11 . T he totalheat transfer rate w a s s i m i l a r for the three cases; however, th edegradation of stratif ication w a s highest for the case with th einlet port entering at right angles to the heat transfer surfaceand displaced from the end wa ll. For this condition, therecirculat ing flow covered a large section of the zone betweenthe end wall and th e inlet port, and this recirculat ion producedsignificant heat transport from the top to the bottom levels o fthe tank, T he heat exchanger deficiency w a s found to be 7.7and 5.9% for the inlet port set perpendicular to the t an k wa l l sand offset from th e outle t end wal l by 20 and 0 cavity wid ths ,respectively. For the paral le l en try case, th e def iciency factorw as 4.3%.5.2 Effect of the Cavi ty Wid th

T he effect of cavity width was investigated for the inletport conf igurat ion in the bottom corner of the cavity tha tresulted in mi nim um recirculat ion above the inlet por t .

5.2.1 FLOW DEVELOPMENTFo r a small cavity wid th , th e recirculation zone near th e

i n l e t was supp ressed; however, the incom ing f luid penetratedhigher into the top of the cavity above th e t h e r m a l equ i l i b r i u mlevel5.2.2 HEAT TRANSFER

T he effect of the cavity wid th on heat transfer rate i s shownin Figure 12. The heat transfer rate w as computed to be-555 W for the orig inal cavity wid th o f 5 mm (effectivenesse = 0.76), -536 W (e = 0,73) for a 10-mm w i d t h , and-560 W (s = 0.77) fo r 2.5-mm wid th . Figure 12 shows thatth e peak value o f QylQt significantly increases fo r narrowcavities. T he computed heat exchanger def iciency w as f oundto be 18. 5.9, an d 5,2% fo r cavi ty widths of 2.5, 5 , an d 10m m . respectively. Although th e to tal heat t ransfer ra te fo rth e narrow cavity is s l ightly higher, the deficiency coefficientis substantia l ly higher, indica t ing t ha t in narrow cavities th ehigher inlet velocities cause the f low to p enetrate far ther upthe cavity and to s ignif icantly degra de the in n er t an k the rm alstratification,5.3 Ef fec t of th e Cavi ty Heigh t

I n closed-loop t hermosyphon solar water hea ters using ama nt le heat exchanger, th e to p o f th e ma n t le typ ica l ly has anair pocket d u e to a ir released f rom the water in the collectorloop. To s imu late the ef fect of cavjty h e i g h t , th e f low andheat transfer were co mputed fo r cavi ty heights 25 and 50%

1 .0

Figure 11 . Effect of inlet port location on distribution of heattransfer in a vertical cavity.

-o.i Q / Q , - 0 . 0Figure 12. Effect of cavity width on the distribution of heattransfer around the inner tank wall.

C omp u te r Mode l ing a nd Simulat ion in Engineer ing 273


6/6

S R G E P U B L I C R T I O N S F f l X N O . : 4990871 11-16-98 09:41 P .08

.less than a f u l l cavity. Th e inlet pipe w as taken in the bot tomcorner adjacent to the end wall5.3.1 F LO W D E V E LO P M E N T

For the f u l l cavity and the 25% reduced cavity height, norecirculation w as observed near the inlet . For a 50% reduc-tion in cavity height , the inlet flow reached th e to p of th eworking section of the cavity and traveled along the top ofth e partially filled section of the cavity toward th e out le t end ,5.3.2 H E A T T R A N S F E R

Th e ef fec t of the cavity height on the heat transfer is shownin Figure 13, The m a g n i t u d e o f Qy/Qt in th e lower part ofth e cavi ty is independent o f cavity heihi , indica t ing tha t th eheat transfer at the bottom of C he cavity is not influenced bycavity depth. For the case of half -cavi ty height , th e heat ex -changer def ic iency is nearly zero, since the f low cannot reachth e upper levels of the inner tank.6. Conclusions

The flow and heat transfer characterist ics in an a n n u l a rheat exchanger with in le t and ou t le t connect ions a t the bot tomhave been s tudied numerica l ly . A recirculating f low regionabove th e inkt i$ observed. T he results show that a s ign i f ican tpart of the heat transfer occurs in the bottom of the a n n u l u s ,which, in practice, causes degradation of th e t he rma l strat i f i -ca t ion of the water in the inner lank. S imu la t ions with bu oy-ancy ef fec ts neglected reveal that the flow penetration in tothe top of th e cavi ty is stronger, bu t there is no evidence off low recircu la t ion . To ac c oun t for the degradation of t he r m alstratification of the inner tank, a heat exchanger deficiency

coeff icient r \$ def ined. F or th e ann ular heat exchanger con-f igura t ion investigated in th is s tudy , the def ic ienc y coef f ic ientw as f o u n d to range from T | = 0 to 18%, indica t ing tha t u p10 18% of th e total heat transfer is removed f rom the top andtransferred to the bottom of the i nne r t a nk (i.e., s tra t i f ica t iondegradat ion) . For f ixed in le t an d ou t le t posit ions, th e heatexchanger def ic iency coef f ic ient was fou nd to increase as th ecavi ty w id th i s reduced. For the therm al bou ndary condi t ionsinvestigated, the heat ex chang er ef fec t iveness was f o u n d t ovary f rom 50% to 77% depending on the geometry of thecavity,References ^

L Biiur. M ,, K l a i n , A. , an d Beck m a n , ;1993, " S i m u l a t i o n o f ^ a t c r t ank* Iwi th m a n t l e neat excriangers," Solar Energy. 286-291, _-J^2. Furbo, S., 1993, "Optim um design of s m al l .DHW low flow solar sys-tems." in ISES Solar World Congress, Budapest , H u n g a r y ,5 r 117-122.3. Mcriol, A., Place, W., Webster. T, an d G r e i f > R ., 1951, "Detai led loopmodel ( D LM) analysis of liquid solar t h e rmo sy ph o n s wiih h t n t exchangers/ 'Solar Energy 27 , 367-386,4. Morrison. G, L, 1995. " I n t e r n a t i o n a l Energy Agency, solar heat inga nd cooling programme,'* in D^ign an d Rating o f Solar Water Healer Stor-ag e Tanks Workshop, IEASHC/WS/2-95. San Diego, Cal i fornia .5. N H * T A,, Morrison, G. U, an d Bc hni a , M .. 1996. "Co mpula t io n * !s t ud y of f low and hea t transfer characterist ics of a n n u l a r an d vertical cav-ities," in Th e Second China-Australia Symposium on Computat ional M e-chanics. University of N ew South Wales, 185-194.6. Parent, M , G., Va n Per Mecr, R, an d Hollands, K.G.T. 1W, " N a t u -ra l convection heal exchangers in solar water heat ing systems: Theory an dexperiment Solar Energy 3*219-231.7 . Ra ma d h y a n i , $.,T c n o w i . M .. an d Asiill , K . N ., 1984, "Co mb in ed na iu r a l an d forced convcciivc heal t r an s fe r in spherical a n n u l i / V - Heai T r a n s f e j106,811-816.$. Webster, T.U,Coulter, J. P., Place, J. Wr. andTavan, M., J987, -|

pcrimemal evaluation of solar iherirnnyphons wi*h heat exchangers,"

i

274 Vol. 3, No . -4 . November 1996

parametric study concentric048

Documents