Sensible Performance Analysis of Multi-Pass Cross Flow Heat Exchangers

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1 108, (2017) DOI: / mateccnf/ Sensible Perfrmance nalysis f Multi-Pass Crss Flw Heat Exchangers 1 Karthik Silaipillayarputhur, awfiq l-mughanam 2, bdulelah I l-niniya 2 1 PO Bx 380, King Faisal University, Dept f Mechanical Engineering, l-hsa, Kingdm f Saudi rabia 2 PO Bx 380, King Faisal University, Cllege f Engineering,, l-hsa, Kingdm f Saudi rabia bstract In this paper, a steady state sensible perfrmance analysis f a multi-pass crss flw exchanger exhibiting varius flw circuiting is cnsidered Cunter crss flw, parallel crss flw and pure crss flw (where the flw circuiting is neither in parallel nr in cunter flw) are cnsidered in this paper previusly develped matrix apprach is used t study the heat exchanger perfrmance at each individual pass he equatins required fr mdeling a crss flw heat exchanger fr each flw arrangement are presented hereafter, a baseline heat exchanger gemetry was selected and perfrmance f the heat exchanger fr each flw circuiting was described s expected, the best thermal perfrmance was seen in a cunter crss flw heat exchanger and the perfrmance f pure crss flw was intermediate between that f a parallel and a cunter crss flw heat 1 Intrductin his paper presents results frm a steady state sensible perfrmance investigatin f a multi-pass crss flw exchanger pssessing varius flw circuiting he analysis is based n the matrix apprach previusly reprted in Silaipillayarputhur and Idem [1] Silaipillayarputhur and Idem [2] cnsidered practical validatin f the matrix perfrmance mdel In that study the gverning equatins required t mdel a multi-pass cunter crss flw heat exchanger with cntinuus wavy fins were presented he heat exchanger selected fr validatin was a chilled water cil used at a chemical facility in Chattanga, N, US he predictins btained frm the perfrmance mdel were cmpared with actual data frm the chilled water cil and the theretical perfrmance data frm the manufacturer Based n the cmparisns, it was cncluded that the matrix heat exchanger perfrmance mdel predicted the perfrmance f a cunter crss flw heat exchanger with at least 95% accuracy In prcess industries, several heat exchanger flw cnfiguratins ccur, due t existing piping cnnectins and space cnstraints Hwever, the thermal advantage f using cunter flw heat exchangers is well knwn In the present paper a baseline, finned six-pass crss flw heat exchanger presented in [2] is cnsidered fr further analysis steady state thermal perfrmance cmparisn is cnducted between verall cunter flw, verall parallel flw, and pure crss flw In each instance, the matrix apprach is emplyed t study the heat exchanger perfrmance fr each individual pass hereafter, a parametric study is perfrmed n the same six-pass crss flw heat exchanger subjected t cunter, parallel, and pure crss flw circuiting by varying the NU and capacity rate ratis Fr each case, the effectiveness f the heat exchanger is pltted against the significant dimensinless parameters Numerus ther papers have been reprted in the literature pertaining t steady state heat exchanger perfrmance mdeling, and nly the mst relevant papers are reprted herein Pigntti and Shah [3] cnsidered the effectiveness and NU relatinships fr heat exchangers with cmplex flw arrangements Heat exchanger terminal temperatures, surface area, and fluid flw rates were presented in dimensinless frm in terms f heat exchanger effectiveness, number f transfer units, and heat capacity rate ratis Explicit effectiveness-nu relatinships were btained fr a ttal f 18 cmplex heat exchanger flw arrangements, and the results were summarized in tabular frmat Dmings [4] presented general methd fr calculating the ttal effectiveness and intermediate temperatures f assemblies f heat exchangers he assemblies culd cnsist f assciatins f any types f heat he methd utilized a transfrmatin that related the inlet and utlet temperatures f the fluid streams, and thus permitted the derivatin f clsed frm expressins Shah and Pigntti [5] examined cmplicated heat exchanger flw arrangements and related them t simple frms fr which either a slutin existed, r an apprximate slutin culd be btained Chen and Hsieh [6] develped a simple and systematic prcedure t determine the effectiveness and exit fluid temperatures f cmplex he uthrs, published by EDP Sciences his is an pen access article distributed under the terms f the Creative Cmmns ttributin License 40 (

2 108, (2017) DOI: / mateccnf/ assemblies f identical heat exchangers hree cmplex assemblies were chsen t illustrate the prcedure he assembly with nn-identical heat exchangers was als studied t examine the general applicability f the present prcedure Baclic [7] prpsed a simplified frmula fr crss flw heat exchanger effectiveness he frmula related effectiveness NU and heat capacity rate rati fr crss flw heat exchangers when bth the fluids are unmixed 2 Nmenclature Heat transfer surface area C Heat capacity rate f a fluid c Specific heat at cnstant pressure m - Mass flw rate n Number f passes NU Overall number f transfer units r Capacity rate rati - emperature f the external (ht) fluid - Inlet temperature f the external (ht) fluid - Outlet temperature f the external (ht) fluid w - emperature f the tube-side (cld) fluid wi - Inlet temperature f the tube-side (cld) fluid w - Outlet temperature f the tube-side (cld) fluid U - Overall heat transfer cefficient Greek Letters - Effectiveness, matrix apprach Subscripts External fluid (ht fluid) i running index (1 thrugh n) i - Inside j running index (1 thrugh n) min Minimum max Maximum - Overall r Rw sum - Sum w ube-side fluid (cld fluid) Superscripts Quantity expressed n per pass basis 3 Steady state perfrmance mdel baseline heat exchanger presented in [2] is cnsidered fr further analysis able 1 presents the gemetry f the baseline heat exchanger, as well as ther fundamental perating characteristics he baseline heat exchanger is a six-pass crss flw heat exchanger, and it is emplyed fr a quenching prcess in a chemical plant in Chattanga, N he baseline heat exchanger has air in the gas-side f the heat exchanger and has chilled water in the tube-side f the heat In this paper, the thermal perfrmance f the baseline heat exchanger is cmpared between verall cunter and parallel flw, and pure crss flw Only sensible heat transfer between the fluids is cnsidered, and there is n phase change he number f transfer units is assumed t be unifrmly distributed amng the heat exchanger passes lthugh fuling is a cmmn ccurrence in practice, the effects f fuling are nt cnsidered in the current study Fr the verall heat exchanger, the external fluid is assumed t be the minimum capacity rate fluid, since this is a cmmnly encuntered situatin in prcess industries Fr a parallel and cunter crss flw heat exchanger, the verall capacity rate rati is equal t the capacity rate rati per pass his is because each pass encunters the same full mass flw rate f the external fluid and the tube side fluid Hwever, fr a pure crss flw heat exchanger, the tube-side fluid is assumed t be evenly split amng the tube passes Cnsidering the baseline heat exchanger with six passes, fr a pure crss flw cnfiguratin n a per pass basis the tube-side fluid encunters ne-sixth f the verall mass flw rate hus fr a pure crss flw cnfiguratin, n a per pass basis the tube-side fluid can be the minimum capacity fluid Heat exchanger verall perfrmance Fr the verall heat exchanger, the external fluid (air), designated thrugh subscript is the minimum capacity rate fluid and while the tube-side fluid (chilled water) designated thrugh subscript w is the maximum capacity rate fluid he capacity rate rati fr the verall heat exchanger is given by [8,9] m c r Cmax m c w (1) Likewise, the verall NU fr the heat exchanger is expressed as [8,9] U U NU m c (2) he effectiveness fr the verall heat exchanger, assuming bth fluids t be unmixed, may be calculated as [8,9] 022 NU exp exp rnu 1 r (3) he calculated effectiveness f the heat exchanger is related t rate f heat transfer by q q max (4) he heat transfer is determined by means f the fllwing energy balance expressins [8,9] and: q m q m w c c w w wi (6) he inlet temperatures f bth fluids are knwn quantities In that case the maximum heat transfer is given by [8,9] q C m c max min wi wi (7) Emplying Equatins 4 and 7, the rate f heat transfer between the tw fluids in the heat exchanger can be (5) 2

3 108, (2017) DOI: / mateccnf/ determined, and frm that calculatin the discharge temperatures f bth the fluids can readily be evaluated Intermediate thermal perfrmance fr parallel and cunter crss flw heat exchangers using the matrix apprach he baseline heat exchanger as described in able 1 is a six-pass crss flw heat Figures 1 and 2 depict the flw circuiting f a six-pass parallel and cunter crss flw heat exchangers able 1 Baseline heat exchanger perating characteristics Item Descriptin Number f passes 6 Fin material Fin thickness Baseline heat exchanger luminium m Fin density 315 fins/m ube material Cpper ube OD 0016 m ube thickness m Number f rws per pass 1 Number f tubes 46 ube length Lngitudinal pitch ransverse pitch Mass flw rate f water Mass flw rate f air Inlet air temperature ( ) Inlet water temperature ( wi ) w4 6 w2 5 4 wi 165 m 0038 m 0033 m 9396 kg/hr kg/hr 2963 K 2841 K Figure 1 Flw circuiting fr a six-pass parallel crss flw heat wi w2 6 w4 5 4 Figure 2 Flw circuiting fr a six-pass cunter crss flw heat Each pass f the crss flw heat exchanger encunters the full mass flw rate f the external fluid and tube-side w1 1 1 w3 w3 w1 fluid Hence, the capacity rate rati per pass may be given as m c r" r m c w (8) he surface area f the heat exchanger is assumed t be unifrmly distributed amng the heat exchanger passes herefre, the NU per pass may be expressed as U / n U NU" nm c (9) hus by Equatin 3 the heat exchanger effectiveness per pass is 022 NU exp exp r NU 1 r (10) he matrix apprach [1] uses the cncept f an energy balance and effectiveness applied t each pass f a crss flw heat hus if a crss flw heat exchanger has n number f passes, there will be 2n simultaneus equatins t be slved Fr every pass there are tw unknwns, namely the discharge temperature f the external fluid and the discharge temperature f the tube-side fluid By slving the system f simultaneus linear equatins the unknwn discharge temperatures exiting each pass can be readily determined Fr a multipass parallel crss flw heat exchanger, the fllwing generalized equatins are emplyed t determine the intermediate and final temperatures f bth the fluids in the heat If m crrespnds t the number f passes, n crrespnds t twice the number f passes, and j crrespnds t anywhere between 1 and n, then referring t [1]: Fr j = 1 r j,j 1 Bj,j1 r wi (11) Fr j = 2;m-1 r j 1,j r j,j1 wj1,j wj,j1 0 (12) Fr j = m r j 1,j r wj1,j w 0 (13) Fr j = m r1 r1wi (14) Fr j = m+2;n-1 1 rj m j m1,jm jm,jm1 rj mwj m1,jm (15) Fr j = n 1 rj m jm1,jm rjmwjm1,jm 0 (16) Likewise, fr a multi-pass cunter crss flw heat exchanger, the fllwing generalized equatins can be utilized [1] t determine the intermediate and final temperatures f bth the fluids in the heat exchanger: Fr j = 1 j,j 1 rj wj 1 rj (17) Fr j = 2;m-1 rj 1 j 1,j j,j1 rjwj,j1 0 (18) Fr j = m rj 1 j 1,j rjwi (19) 0 3

4 108, (2017) DOI: / mateccnf/ Fr j = m+1;n-2 r jm,jm1 r jm1,j m2 wjm,jm1 wjm1,j m2 0 (20) Fr j = n-1 r j m,jm1 r jm1,j m2 wjm,jm1 wi (21) Fr j = n r 12 w12 w r (22) Intermediate thermal perfrmance fr pure crss flw heat exchangers using the matrix apprach Figure 3 depicts the flw circuiting f a six-pass pure crss flw heat Each pass f the crss flw heat exchanger encunters the full mass flw rate f the external fluid and ne sixth f the verall mass flw rate f the tube-side fluid w4 Or: U NU" C NU" min U / n U / n m c / n w (24) NU r m cw (25) ssuming bth fluids t be unmixed in a given pass the heat exchanger effectiveness per pass may be calculated using Equatin 10 Fr a multi-pass pure crss flw heat exchanger, the fllwing generalized equatins [1] are applied t determine the intermediate and final temperatures f bth the fluids in the heat exchanger: Fr j = 1 Fr j = 2;m r r j,j 1 wj wi (26) r r j 1,j j,j1 wj wi (27) Fr j = m+1 w1 1 r1 wi r1 Fr j = m+2;n rjmjm1,jm wjm wi rjmwi (28) (29) wi Figure 3 Flw circuiting fr a six-pass pure crss flw heat In his analysis, it is reasnable t assume that n a per pass basis, the tube-side fluid is the minimum capacity rate fluid hus, the capacity rate rati per pass is given by m c 1 1 r" nm c w n r (23) Likewise, the NU per pass can be expressed as 1 w3 w2 w1 w 4 Baseline heat exchanger perfrmance he baseline six-pass crss flw heat exchanger perfrmance was studied fr verall cunter and parallel flw and pure crss flw circuiting cnfiguratins herein, the heat exchanger verall perfrmance was described thrugh the heat exchanger effectiveness he matrix apprach was emplyed t study the intermediate thermal perfrmance f the heat Matlab cde was develped t slve the system f simultaneus linear equatins and t determine the intermediate and the verall thermal perfrmance f the crss flw heat In every instance, the external fluid was assumed t be the minimum capacity rate fluid he external fluid and the internal fluid were cnsidered unmixed in the analysis able 2 Perfrmance f baseline crss flw heat exchanger Baseline crss flw heat exchanger 6 pass Cunter Flw 6 pass Parallel Flw 6 pass Pure Crss Flw emp Label emp (K) emp Label emp (K) emp Label emp (K) wi 2841 wi 2841 wi 2841 w w w w w w w w w w w w ε verall 086 ε verall 067 ε verall 080 4

5 108, (2017) DOI: / mateccnf/ cmparisn f steady state perfrmance was cnducted fr cases where the baseline heat exchanger was perated either with verall parallel r cunter flw circuiting, r therwise fr pure crss flw circuiting he specific input cnditins are utlined in able 1 cmplete accunting f the equatins used t characterize the heat exchanger gemetry, and t evaluate such dimensinless parameters as the particular capacity rate rati and NU, are prvided in [2], and are nt included herein he results f the present study are presented in able 2 in terms f the verall and intermediate steady state sensible perfrmance f the baseline heat s expected the cunter crss flw heat exchanger yielded the best heat exchanger perfrmance, ie, the maximum verall effectiveness Likewise, the perfrmance f the pure crss flw heat exchanger was intermediate between that fr verall cunter and parallel crss circuiting 5 Summary Steady state sensible perfrmance f a crss flw heat exchanger was studied in this paper baseline heat exchanger presented in [2] was analyzed subject t varius flw circuiting cnsideratins, ie, verall parallel and cunter flw, as well as pure crss flw he baseline heat exchanger s perfrmance was determined fr each flw circuiting, assuming perating cnditins typical f design cnditins In every instance, the heat exchanger cnsidered in this study had six passes Hwever, the number f passes cnsidered is arbitrary (subject t mandatry perfrmance requirements), and the analysis can be readily extended t any number f passes by emplying the matrix apprach he matrix apprach uses fundamental analytical relatinships t study the intermediate and the verall perfrmance f a crss flw heat he matrix apprach is very simple t use, and by slving a set f generalized equatins, the intermediate and the verall perfrmance f the heat exchanger can be readily determined Matrix analysis uses physically significant parameters such as NU and capacity rate rati t evaluate verall heat exchanger effectiveness, and thus prvides clear infrmatin t the engineers during the initial design r selectin f the crss flw heat With the availability f intermediate temperatures, the matrix apprach can be utilized t ptimize size, material, weight, and initial cst f the crss flw heat Furthermre, the matrix methd can assist with thermal stress analysis f heat exchanger, since it prvides detailed infrmatin pertaining t lcal temperature variatins in the heat References 1 K Silaipillayarputhur and S Idem, 2013, general matrix apprach t mdel steady state perfrmance f crss flw heat exchangers, Heat ransfer Engineering, Vl 34, N 4, pp K Silaipillayarputhur and S Idem, 2013, Practical Validatin f a Matrix pprach Steady State Heat Exchanger Perfrmance Mdel, Jurnal f pplied Glbal Research, ISSN: , Vl 6, N 17, pp Pigntti and R K Shah, 1992 Effectivenessnumber f transfer units relatinships fr heat exchanger cmplex flw arrangements, Int J Heat Mass ransfer, Vl 35, N 5, pp J D Dmings, 1969, nalysis f Cmplex ssemblies f Heat Exchangers, Int J Heat Mass ransfer, Vl 12, pp R K Shah and Pigntti, 1993, hermal nalysis f Cmplex Crssflw Exchangers in erms f Standard Cnfiguratins, J Heat ransfer, Vl 115, pp J D Chen and S S Hsieh, 1990, General prcedure fr effectiveness f cmplex assemblies f heat exchangers, Int J Heat Mass ransfer, Vl 33, N 8, pp B S Baclic, 1978, Simplified Frmula fr Crssflw Heat Exchanger Effectiveness, rans SME, Vl 100, pp W M Kays and L Lndn, 1984, Cmpact Heat Exchangers, 3rd Ed, McGraw-Hill, New Yrk 9 F P Incrpera, D P Dewitt, L Bergman, and S Lavine, 2006, Fundamentals f Heat and Mass ransfer, 4th Editin, Jhn Wiley & Sns, Inc, New Yrk 5

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