MODULE 7 HEAT EXCHANGERS

Transcription

1 MODULE 7 HEAT EXCHANGERS 7. What are heat exchangers? Heat exchangers are practcal devces used t transfer energy frm ne flud t anther. Arund the husehld, we are accustmed t seeng the cndensers and evapratrs used n ar cndtnng unts. In autmbles we see radatrs and l clers. In the pwer ndustry we see blers, cndensers, ecnmzers, pre-heaters and numerus ther heat exchangers. Wthn the prcess ndustry, we fnd heat exchangers used extensvely fr a varety f purpses. Because f the wde varety f uses fr heat exchangers, ther cnstructn may vary wdely. We wll cnsder nly the mre cmmn types here, but the cnsderatns ncluded are cmmn t all types. In ndustral drawngs t s cmmn t use the abbrevatn HX t ndcate heat exchangers. We wll use ths termnlgy here t shrten the dscussns. 7. Heat Transfer Cnsderatns The energy flw between ht and cld streams, when vewed frm ne end f the heat exchanger, wll appear as shwn n Fgure t the rght. Heat transfer wll ccur by cnvectn t the utsde f the nner tube, by cnductn acrss the tube and by cnvectn t the cler flud frm the nsde tube surface. Snce the heat transfer ccurs acrss the smaller tube, t s ths nternal surface whch cntrls the heat transfer prcess. By cnventn, t s the uter surface, termed A, f ths central tube t d d T

2 whch s referred t n descrbng heat exchanger area. Applyng the electrcal analgy, an equvalent thermal resstance may be defned fr ths tube. r ln r R + ha π kl + h A If we defne the heat exchanger ceffcent, U c, as: U c RA Substtutng the value f R abve ths yelds: r + U h c r ln r k A + ha Bth cnvectve ceffcents, h and h, can be evaluated frm expermentally develped cnvectve crrelatns. Areas and rad are determned frm the gemetry f the nternal tube. The thermal cnductvty, k, crrespnds t that fr the materal f the nternal tube. In ths fashn each f the terms are generally avalable fr determnng U c and the term s well defned fr mst heat exchangers. 7.3 Fulng Materal depsts n the surfaces f the heat exchanger tube may add further resstances t heat transfer n addtn t thse lsted abve. Such depsts are termed fulng and may sgnfcantly affect heat exchanger perfrmance. The heat exchanger ceffcent, U c, determned abve may be mdfed t nclude the fulng factr R f. + U U R " d c Scalng s the mst cmmn frm f fulng and s asscated wth nverse slublty salts. Examples f such salts are CaCO 3, CaSO 4, Ca 3 (PO 4 ), CaSO 3, Ca(OH), Mg(OH), MgSO 3, Na SO 4, LSO 4, and L CO 3. The characterstc whch s termed nverse slublty s that, unlke mst nrganc materals, the slublty decreases wth temperature. The mst mprtant f these cmpunds s calcum carbnate, CaCO 3. Calcum carbnate exsts n several frms, but ne f the mre mprtant s lmestne. The materal frequently crystallzes n a frm clsely resemblng marble, anther

3 frm f calcum carbnate. Such materals are extremely dffcult t remve mechancally and may requre acd cleanng. Crrsn fulng s classfed as a chemcal reactn whch nvlves the heat exchanger tubes. Many metals, cpper and alumnum beng specfc examples, frm adherent xde catngs whch serve t passvate the surface and prevent further crrsn. Metal xdes are a type f ceramc and typcally exhbt qute lw thermal cnductvtes. Even relatve thn catngs f xdes may sgnfcantly affect heat exchanger perfrmance and shuld be ncluded n evaluatng verall heat transfer resstance. Chemcal reactn fulng nvlves chemcal reactns n the prcess stream whch results n depstn f materal n the heat exchanger tubes. When fd prducts are nvlved ths may be termed scrchng but a wde range f rganc materals are subject t smlar prblems. Ths s cmmnly encuntered when chemcally senstve prcess fluds are heated t temperatures near that fr chemcal decmpstn. Because f the n flw cndtn at the wall surface and the temperature gradent whch exsts acrss ths lamnar sub layer, these regns wll perate at smewhat hgher temperatures than the bulk and are deally suted t prmte favrable cndtns fr such reactns. Freezng fulng s sad t ccur when a prtn f the ht stream s cled t near the freezng pnt fr ne f ts cmpnents. Ths s mst ntable n refneres where paraffn frequently sldfes frm petrleum prducts at varus stages n the refnng prcess, bstructng bth flw and heat transfer. Blgcal fulng s cmmn where untreated water s used as a clant stream. Prblems range frm algae r ther mcrbes t barnacles. Durng the seasn where such mcrbes are sad t blm, clnes several mllmeters deep may grw acrss a tube surface vrtually vernght, mpedng crculatn near the tube wall and retardng heat transprt. Vewed under a mcrscpe, many f these rgansms appear as lsely ntertwned fbers much lke the frm f fberglass nsulatn Tradtnally these rgansms have been treated whch chlrne, but present day cncerns n pssble cntamnatn t pen water bdes has severely restrcted the use f xdzers n pen dscharge systems. Partculate fulng results frm the presence f Brwnan szed partcles n slutn. Under certan cndtns such materals dsplay a phenmenn knwn as thermphress n whch mtn s nduced as a result f a temperature gradent. Thermdynamcally ths s referred t as a crss-cupled phenmenn and may be vewed as beng analgus t the Seabeck

4 effect. When such partcles accumulate n a heat exchanger surface they smetmes fuse, resultng n a buldup havng the texture f a sandstne. Lke scale these depsts are dffcult t remve mechancally. Mst f the actual data n fulng factrs s tghtly held be a few specalty cnsultng cmpanes. The data whch s cmmnly avalable s sparse. An example s gven belw: Flud R, m K/Watt Seawater and treated bler feedwater (belw 50 C) Seawater and treated bler feedwater (abve 50 C) Rver water (belw 50 C) Fuel Ol Regrgeratng lquds Steam (nn-l bearng) Table: Representatve Fulng Factrs r ln( r ) U r k h d h r R" 7.4 Basc Heat Exchanger Flw Arrangements Basc flw arrangements are as shwn n the Fgure belw. Parallel and cunterflw prvde alternatve arrangements fr certan specalzed applcatns. In parallel flw bth the ht and cld streams enter the heat exchanger at the same end and travel t the ppste end n parallel streams. Energy s transferred alng the length frm the ht t the cld flud s the utlet temperatures asympttcally apprach ne anther. In cunter flw the tw streams enter at ppste ends f the heat exchanger and flw n ppste drectns. Temperatures wthn the tw streams tend t apprach ne anther n a nearly lnearly fashn resultng n a much mre unfrm heatng pattern. Shwn belw the heat exchangers are representatns f the axal temperature prfles fr each. Parallel flw results n rapd ntal rates f heat exchange but rates rapdly decrease as the temperatures f the tw streams apprach ne anther. Cunter flw prvdes fr relatvely unfrm temperature dfferences and, cnsequently, lead tward relatvely unfrm heat rates thrughut the length f the unt.

5 t t t t T T Parallel Flw T T Cunter Flw Temperature t t Temperature t t Pstn Pstn Basc Flw Arrangements fr Tube n Tube Heat Exchangers. 7.5 Lg Mean Temperature Dfferences Heat flws between the ht and cld streams due t the temperature dfference acrss the tube actng as a drvng frce. As seen n the Fgure belw, the dfference wll vary wth axal pstn wthn the HX s that ne must speak n terms f the effectve r ntegrated average temperature dfferences. T Cunter Flw T Parallel Flw t t t t Pstn Pstn Temperature Dfferences Between Ht and Cld Prcess Streams Wrkng frm the three heat exchanger equatns shwn abve, after sme develpment t f fund that the ntegrated average temperature dfference fr ether parallel r cunter flw may be wrtten as: θ θ Δθ LMTD θ ln θ The effectve temperature dfference calculated frm ths equatn s knwn as the lg mean temperature dfference, frequently abbrevated as LMTD, based n

6 the type f mathematcal average that t descrbes. Whle the equatn apples t ether parallel r cunter flw, t can be shwn that Δθ eff wll always be greater n the cunter flw arrangement. Ths can be shwn theretcally frm Secnd Law cnsderatns but, fr the undergraduate student, t s generally mre satsfyng t arbtrarly chse a set f temperatures and check the results frm the tw equatns. The nly restrctns that we place n the case s that t be physcally pssble fr parallel flw,.e. θ and θ must bth be pstve. Anther nterestng bservatn frm the abve Fgure s that cunter flw s mre apprprate fr maxmum energy recvery. In a number f ndustral applcatns there wll be cnsderable energy avalable wthn a ht waste stream whch may be recvered befre the stream s dscharged. Ths s dne by recverng energy nt a fresh cld stream. Nte n the Fgures shwn abve that the ht stream may be cled t t fr cunter flw, but may nly be cled t t fr parallel flw. Cunter flw allws fr a greater degree f energy recvery. Smlar arguments may be made t shw the advantage f cunter flw fr energy recvery frm refrgerated cld streams. 7.6 Applcatns fr Cunter and Parallel Flws We have seen tw advantages fr cunter flw, (a) larger effectve LMTD and (b) greater ptental energy recvery. The advantage f the larger LMTD, as seen frm the heat exchanger equatn, s that a larger LMTD permts a smaller heat exchanger area, A, fr a gven thermal duty, Q. Ths wuld nrmally be expected t result n smaller, less expensve equpment fr a gven applcatn. Ths shuld nt lead t the assumptn that cunter flw s always a superr. Parallel flws are advantageus (a) where the hgh ntal heatng rate may be used t advantage and (b) where the mre mderate temperatures develped at the tube walls are requred. In heatng very vscus fluds, parallel flw prvdes fr rapd ntal heatng. The quck decrease n vscsty whch results may sgnfcantly reduce pumpng requrements thrugh the heat exchanger. The decrease n vscsty als serves t shrten the dstance requred fr flw t transtn frm lamnar t turbulent, enhancng heat transfer rates. Where the mprvements n heat transfer rates cmpensate fr the lwer LMTD parallel flw may be used t advantage. A secnd feature f parallel flw may ccur due t the mderatn f tube wall temperatures. As an example, cnsder a case where cnvectve ceffcents are apprxmately equal n bth sdes f the heat exchanger tube. Ths wll result n the tube wall temperatures beng abut the average f the tw stream temperatures. In the case f cunter flw the tw extreme ht temperatures are at ne end, the tw extreme cld temperatures at the ther.

7 Ths prduces relatvely ht tube wall temperatures at ne end and relatvely cld temperatures at the ther. Temperature senstve fluds, ntably fd prducts, pharmaceutcals and blgcal prducts, are less lkely t be scrched r thermally damaged n a parallel flw heat exchanger. Chemcal reactn fulng may be cnsdered as leadng t a thermally damaged prcess stream. In such cases, cunter flw may result n greater fulng rates and, ultmately, lwer thermal perfrmance. Other types f fulng are als thermally senstve. Mst ntable are scalng, crrsn fulng and freezng fulng. Where cntrl f temperature senstve fulng s a majr cncern, parallel flw may be used t advantage. 7.7 Multpass Flw Arrangements In rder t ncrease the surface area fr cnvectn relatve t the flud vlume, t s cmmn t desgn fr multple tubes wthn a sngle heat exchanger. Wth multple tubes t s pssble t arrange t flw s that ne regn wll be n parallel and anther prtn n cunter flw. An arrangement where the tube sde flud passes thrugh nce n parallel and nce n cunter flw s shwn n the Fgure belw. Nrmal termnlgy wuld refer t ths arrangement as a - pass heat exchanger, ndcatng that the shell sde flud passes thrugh the unt nce, the tube sde twce. By cnventn the number f shell sde passes s always lsted frst. The prmary reasn fr usng multpass desgns s t ncrease the average tube sde flud velcty n a gven arrangement. In a tw pass arrangement the flud flws thrugh nly half the tubes and any ne pnt, s that the Reynld s number s effectvely dubled. Increasng the Reynlds s number results n ncreased turbulence, ncreased Nusselt numbers and, fnally, n ncreased cnvectn ceffcents. Even thugh the parallel prtn f the flw results n a lwer effectve ΔT, the ncrease n verall heat transfer ceffcent wll frequently cmpensate s that the verall heat exchanger sze wll be smaller fr a specfc servce. The mprvements achevable wth multpass heat exchangers s suffcently large that they have becme much mre cmmn n ndustry than the true parallel r cunter flw desgns. The LMTD frmulas develped earler are n lnger adequate fr multpass heat exchangers. Nrmal practce s t calculate the LMTD fr cunter flw, LMTD cf, and t apply a crrectn factr, F T, such that

8 Δθ eff F T LMTD CF The crrectn factrs, F T, can be fund theretcally and presented n analytcal frm. The equatn gven belw has been shwn t be accurate fr any arrangement havng, 4, 6,...,n tube passes per shell pass t wthn %. F T ( R ) P R + ln R P PR+ + ln PR+ + + where the capacty rat, R, s defned as: R T T t t The effectveness may be gven by the equatn: X P R X ( R ) ( R ) / N shell / N shell prvded that R. In the case that R, the effectveness s gven by: where and P P N P N ( ) shell shell X P t t T t P R P As an alternatve t usng the frmulas fr the crrectn factrs, whch can becme tedus fr nn-cmputerzed calculatns, charts are avalable. Several are ncluded n standard texts. Experence has shwn that, due t varablty n readng charts, cnsderable errr can be ntrduced nt the calculatns and the equatns are recmmended. When charts are used, they shuld be reprduced at a suffcently large scale, and cnsderable care shuld be used n makng nterplatns. 7.8 Lmtatns f Multpass Arrangements

9 Snce the - heat exchanger uses ne parallel pass and ne cunter current, t fllws that the maxmum heat recvery fr these unts shuld be between that f parallel and cunter flw. As a practcal lmt t s mprtant that nwhere n the unt shuld the cld flud temperature exceed that f the Fgure. Temperature Prfles fr a - HX wth a Temperature Crss. ht flud. If s, then heat transfer s bvusly n the wrng drectn. Such a stuatn can arse n a multpass heat exchanger as seen n Fgure 6. Ths unt represents a cld flud, lcated n the tube sde f the heat exchanger, makng tw passes thrugh the unt, the ht flud, n the shell sde, travelng acrss the unt nly nce. Here the cld flud s heated t a temperature slghtly abve that f the ht flud near the ext fr the tw streams. At ths axal lcatn, near the left end f the unt, the temperature f the cld flud n the frst pass remans well belw that f the ht flud s that cnsderable heat transfer ccurs. The cld flud n the secnd pass s slghtly abve that f the ht flud at the same lcatn. The small temperature dfference between the secnd pass cld flud and the ht stream, ndcates that nly a small amunt f heat wll be transferred between these streams. Overall heat wll flw frm ht t cld flud, but a prtn f the heat transfer surface s beng used n a cunter prductve way. Ths cndtn s termed as a temperature crss. In the lmt the ht flud ext temperature culd be cled t the average f the cld flud nlet and ext temperature. Ths wuld, hwever, be hghly neffcent and wuld requre an excessvely large surface area. Sme engneers advcate that gd desgn shuld nt permt a temperature crss, ndcatng that the - shuld perate wth the same heat recvery lmt as a true parallel flw. The preferred methd f attanng addtnal heat recvery s t stage heat exchangers n seres s that n temperature crss ccurs n any unt. An equvalent slutn s t put multple n arrangements wthn a sngle shell. A 4 unt s the equvalent f unts prvded that the ttal heat transfer area s equal. Smlarly a 3 6 unt s the equvalent f 3 unts wth equal verall area. Other engneers suggest that a small temperature crss may be acceptable and may prvde a less expensve desgn than the mre cmplex alternatves. If ne were t plt the lcus f pnts where the temperature crss ccurs fr the - heat exchanger n the temperature crrectn chart, t wuld be fund t crrespnd t a relatvely narrw range f F T values rangng frm abut 0.78 t 0.8. Lwer values f F T may be taken as an ndcatn that a temperature crss wll ccur.

10 A secnd cnsderatn s that at lwer F T values the slpe, df T /dp, becmes extremely steep. Ths s an ndcatn that the temperature effcency, P, s asympttcally apprachng ts upper lmt and the desgn has n margn t accmmdate uncertantes. A gd rule f thumb s that the mnmum slpe f df T /dp, whch s negatve, shuld nt fall belw -.5. Instead a -4 r even a 3-6 shuld be selected t prvde the needed peratnal desgn margn.. Smlar restrctns exst fr these desgns as well. In the lmt a cunter flw desgn may be the nly sutable selectn fr hgh heat recvery applcatns. 7.9 Effectveness-NTU Methd: In ur prevus dscussns, we have been lkng at practcal HX desgns usng the LMTD CF wth a F t crrectn factr t accunt fr the mxed flw cndtns. Nw we wsh t cnsder an alternate, mre recent apprach that s n cmmn use tday. Ths s the effectveness-ntu methd. Effectveness, ε Cnsder tw cunter-flw heat exchangers, ne n whch the cld flud has the larger ΔT (smaller m c p ) and a secnd n whch the cld flud has the smaller ΔT (larger m c p ): Δt > ΔT T ΔT > Δt T M C p > m c p m c p > M C p t t t t We may see n the frst case that, because the cld flud heat capacty s small, ts temperature changes rapdly. If we seek effcent energy recvery, we see that n the lmt a HX culd be desgned n whch the cld flud ext temperature wuld reach that f the ht flud nlet. In the secnd case, the ht flud temperature changes mre rapdly, s

11 that n the lmt the ht flud ext temperature wuld reach that f the cld flud nlet. The effectveness s the rat f the energy recvered n a HX t that recverable n an deal HX. mc & ( t t) M& C p ( T T p ) ε Δt > ΔT ε mc & p ( T t) & ΔT > Δt M Cp ( T t) Cancelng dentcal terms frm the numeratr and denmnatr f bth terms: ε ( t t) ( T t ) Δt > ΔT ε ( T T) ( T t ) ΔT > Δt We see that the numeratr, n the tw cases, s the temperature change fr the stream havng the larger temperature change. The denmnatr s the same n ether case: ε Δ T max ( T t) In the LMTD-F t methd an effectveness was defned: P t t T t Nte that the use f the upper case T n the numeratr, n cntrast t ur nrmal termnlgy, des nt ndcate that the ht flud temperature change s used here. The max subscrpt ver-rdes the nrmal termnlgy and ndcates that ths refers t the sde havng the larger temperature change. Number f Transfer Unts (NTU) Recall that the energy flw n any HX s descrbed by three equatns: Q U A Δθ eff Q -M C p ΔT Q m c p Δt HX equatn st Law Equatn st Law Equatn We may generalze the latter tw expressns, usng ε-ntu termnlgy as fllws:

12 Q (M C p ) mn ΔT max Q (M C p ) max ΔT mn Agan the use f the upper case letters s ver-rdden by the use f the subscrpts. If we elmnate Q between the HX equatn and ne f the st Law equatns, U A Δθ eff (M C p ) mn ΔT max Ths expressn may be made nn-dmensnal by takng the temperatures t ne sde and the ther terms t the ther sde: NTU U A ( M& Cp ) mn Δ T Δ θ max eff Physcally we see that a HX wth a large prduct U A and a small (M C p ) mn shuld result n a hgh degree f energy recvery,.e. shuld result n a large effectveness, ε. Capacty Rat, C R The fnal nn-dmensnal rat needed here s the capacty rat, defned as fllws: C R ( M C ) p ( M C ) p mn max Δ T Δ T mn max In the LMTD-F t methd a capacty rat was defned: R T T t t

13 ε-ntu Relatnshps In the LMTD-F t methd, we fund a general equatn whch descrbed F t fr all -N, -4N, 3-6N, etc. heat exchangers. Anther relatnshp, nt gven here, s requred fr crss flw arrangements. In a smlar fashn, we may develp a number f functnal relatnshps shwng ε ε (NTU, C R ) r, alternatvely: NTU NTU(ε,C R ) These relatnshps are shwn n tables n standard text bks. Fr example, we fnd that the relatnshp fr a parallel flw exchanger s: ε e C e R NTU ( CR ) NTU ( CR ) Nte: These crrelatns are nt general. Specfc crrelatns wll be gven fr dfferent knd f HX. The ε-ntu methd ffers a number f advantages t the desgner ver the tradtnal LMTD-F t methd. One type f calculatn where the ε-ntu methd may be used t clear advantage wuld be cases n whch nether flud utlet temperature s knwn.