Entropy Generation in a Plate-Fin Compact Heat Exchanger with Louvered Fins

Transcription

1 International Journal of Energy Engineering 01, (): DOI: 10.59/j.ijee Entropy Generation in a Plate-Fin Copact Heat Exchanger with Louvered Fins Masoud Asadi 1,*, Rain Haghighi Khoshkho 1 Departent of Mechanical Engineering Azad Islaic UniversityScience and Research branch,tehran, Iran Departent of Mechanical Engineering & Energy engineeringpower and Water University of Technology,Tehran, Iran Abstract This study explores the generation of entropy in a plate-fin heat exchanger with Louvered fins. The objectives are finding the nuber of total entropy generation units under a given heat duty and pressure drop constraints. To clarify ethod, a heat exchanger for cooling water is designed. The overall assessent of cooling syste requires a trade-off between theral perforance and pressure drop. Entropy generation iniization (EGM) ethod is based on the theory that a therodynaically optiized syste is the least irreversible, or iniu entropy generation in the syste. At air side, ten types of fins are eployed. Eventually, based on the entropy generation and theral perforance a type of fin is selected for designing. To optiize the perforance of selected heat exchanger, a equation for finding optial ass flow rate is offered. Using this optial ass flow rate, the entropy generation decreased up to 1% and also energy consuption about 5%. Keywords Entropy Generation, Plate-Fin Heat Exchanger, Louvered Fin 1. Introduction Copact heat exchangers are used in a variety of autootive, residential air-conditioning, oil industry and refrigeration. For air-side heat transfer augentation, louvered fin are quite popular. Beauvais[1] was the first to conduct flow visualization experients on the louvered fin array. He deonstrated that louvers, rather than acting as surface roughness that enhanced heat transfer perforance, acted to realign the airflow in the direction parallel to theselves. Davenport[]perfored flow visualization experients identical to those of Beauvais and further deonstrated two flow regies, duct directed flow, and louver directed flow. Zhang et al. (1997) observed siilar vortex shedding phenoena in a two-diensionalcoputational study. Inline and offset parallel plate odels were created with periodic boundary condit ions to s iu lat e an in fin ite array in all directions, thus ignoring entrance and exit effects. It was deterined that the vortex shedding served to increase the overall heat transfer of thelouver. Unsteady solutions to the odels showed that the vortices alternated shedding off the topand botto of the plate and, correspondingly, had the effect of alternately increasing and decreasing the convective heat transfer along the plate surface. However, the tie-averaged result of the vortices resulted in a sooth, * Corresponding author: asoud471@gail.co (MasoudAsadi) Published online at Copyright 01 Scientific & Acadeic Publishing. All Rights Reserved decreasing heat transfer curve fro the leading edge to the trailing edge. This result disagrees with the DeJong et al. (1997) finding that showed a local heat transfer axiu at a location where the separated flow fro the leading edge reattached to the plate at high Reynolds nubers. Both studies agreed, however, that the overall effect of vortex shedding was to increase the heat transfer in the array. Kurosaki et al. (1988) studied the effects that theral wakes have on the heat transfer of downstrea louvers in various arrangeents of parallel plates. Using laser holographic interferoetry to visualize isotheral contours of the wakes off the back of the plates, they were able to observe the anner in which the wakes fro upstrea plates progressed downstrea and interacted with downstrea louvers. Theral wake visualization showed that increasing the Reynolds nuber caused the wake to narrow and a intain for further downstrea, in agreeent with the data of Springer and Thole (1998a) and the predictions of Zhang et al. (1997). Heat transfer easureents on downstrea plates indicated that direct interactions with wakes had an adverse effect on the convective heat transfer of the plates. By shifting the louvers such that they avoided the wakes of upstrea plates for as long as possible, the heat transfer of the downstrea louvers was increased due to the relatively cooler fluid surrounding the louvers. Additionally, increasing the streawise distance between aligned louvers was shown to have a inial effect on the heat transfer of the downstrea louver except at high Reynolds nubers. At high Reynolds nubers, the difference in thickness between the theral boundary layer on the upstrea and downstrea louver becae ore significant, causing decreased heat

2 International Journal of Energy Engineering 01, (): transfer perforance on the downstrea louver as copared to the upstrea louver. Noencl ature A f : fin area A P : priary area A t : heat transfer area Nu : Nusselt nuber NTU :nuber of transfer unit n f :total nuber of fins b: tube spacing n louv :total nuber of louvers C P : specific heat D h P f :fin pitch P : hydraulic diaeter l :Louver pitch f: frict ion fact or P: pressure h: convect ive coefficient H t : tube height q :heat transfer per unit length Re : Reynolds nuber j: Colburn factor St : Stanton nuber K C :Contract ion coefficient S gen :entropy generation K e : expansion coefficient T : t eperat ure of fluids K :theral conductivity W t :tube outside pitch L louv :louver cut length Greek sybols L P :louver pitch : ass flow rate N pg :nuber of passages N s :entropy generation nuber N t :total nuber of tubes ρ µ : fluid density : dynaic viscosity Subscripts 1 : Wat er : Air Fi gure 1. Scheatic of a typical louvered fin-and-t ube heat exchanger

3 11 Masoud Asadi et al.: Entropy Generation in a Plate-Fin Copact Heat Exchanger with Louvered Fins. Theral-hydraulic Design Fi gure. Side view of a typical louvered fin geoetry In the theral design of heat exchangers, two of the ost iportant probles involve rating and sizing. Deterination of heat transfer and pressure drop is referred to as rating proble. Deterination of a physical size such as length, width, height, and surface area on each side is referred to as a sizing proble. When the heat transfer rate is not known or the outlet teperature are not known, tedious iterations with the LMTD ethod are required. In a attept to eliinate the iterations, Kays and London in 1995 developed a new ethod called the ε NTU ethod. Here, the heat capacity rate is defined as the product of ass flow rate and specific heat. The iniu capacity rate is the one that has a lesser capacity rate, and the axiu capacity rate is then the one that has a higher capacity rate. So, the heat transfer rate is, Q =εcin ( Th,i Tc,i ) =εcin Tax (1) Here ε, Tax and C are the heat exchanger in efficiency, entering teperature difference and the iniu of heat capacity respectively * 0.78 ε= 1 exp NTU exp * ( C.NTU ) 1 C () * Where C is defined by: ( Tc,o Tc,i ) for Ch = Cin ( p ) ( h,i h,o ) * C C T T in in C = = = C () ax ( C p ) ax ( Th,i Th,o ) for Cc = Cin ( Tc,o Tc,i ) The other iportant paraeter is NTU, Where it is considered as the nuber of transfer unit. UA NTU = UdA C = 1 in C (4) in A To calculate the outlet teperatures of both fluids, hot and cold, the equation of (5) and (6) can be considered. C T in ho, = Thi, ε. ( Thi, Tci, ) (5-a) C h C T in co, = Tci, + ε. ( Thi, Tci, ) (5-b) Cc One of the key stage in designing a heat exchanger is accurate calculation of fluid properties. But before doing this, it is necessary to copute average teperature of each fluid. * Here, according to shah research, if C 0.50 the average teperatures would be Thi, + Tho, Th, = (6-a) Tci, + Tco, Tc, = (6-b) Heat transfer coefficient is, h jgc...pr (7) = P G = (8) A fr In this forula, G and A fr are ass velocity and free flow cross sectional area respectively. Also, Colburn factor is, θ Pf b W t j = Re 90 L p L p L p (9) L louv P t δ L p L p L p Where L p is the louver pitch, θ the louver angle, P f the fin pitch, P t the tube pitch, b the tube spacing, W t the tube outside width, L louv the louver cut length, and δ the fin thickness.furtherore, frictional pressure drop in both sides is given by: ρin,1 S ρ 1 in,1 ( 1+ KC,1 σ1 ) f1 G1 ρ out,1 A1 ρ,1 P1 = ρ (10) in,1 ρin,1 ( 1 σ1 k e,1 ) ρ out,1 Here K c and K e are contraction and expansion coefficients. The noncircular diaeter in the flow channels are approxiated using the hydraulic diaeter for the Reynolds nuber. The hydraulic diaeter is defined as, 4A D c h = Pwetted Where Nt = Npg + 1is the wetted perieter. The theral design of a heat exchanger is aied at calculating a surface area adequate to handle the theral duty for the given

4 International Journal of Energy Engineering 01, (): specifications. Fluid friction effects in the heat exchanger are iportant because they deterine the pressure drop of the fluids flowing in the syste, and consequently the puping power or fan work input necessary to aintain the flow. The nuber of passages N pg on the hot side is defined as the air flow passages between flat tubes. The core width L 1 is e xpressed in ters of the nuber of passages N pg as L1 = Npgb+ ( Npg + 1) Ht (11) Where b is the tube spacing and H t the tube height. Solving for the nuber of passages N pg gives L1 Ht N pg = b+ Ht (1) The total nuber of fins is nf L = Npg Pf (1) The total heat transfer area A t is generally obtained fro the su of the priary area A p and the fin area A f. The priary area A p is calculated by subtracting the fin base areas fro the tube outer surface areas, considering the circular front and end of the tubes. Ap = ( L Ht ) + πht L( Npg + 1) δln f (14) The total nuber of louvers in the core is obtained as L f nlouv = 1 n f L p (15) So, the total fin area is the su of the fin area and the louver edge area as Af = ( sf L + sf δ) nf + Llouvδnlouv (16) Here s f is the fin width. The total heat transfer area is, At1 = ( L Ht) + π ( Ht δw) LN t (17) The in iu free-flow area A c is expressed by: Ac = bl N pg δ ( δ f Llouv ) + Llouv. L h n f (18) In coolant side, the total nuber of tubes is, Nt = Npg + 1 (19) Considering the circular shapes at both ends, the total heat transfer area A t1 on the coolant side is obtained by, At1 = ( L Ht) + π ( Ht δw) LN t (0) The free-flo w area Ac1 on the coolant side is: π Nt Ac1 = L Ht Ht δw + Ht δw 4 N p (1).Entropy Generation In a large nuber of convective heat transfer situations the velocity and teperature fields are not known at each point in the ediu. This is a case when the flow regie is turbulent or when the flow geoetry is so coplicated that an exact description of velocity and teperature is not available in analytical or nuerical for. Consider the flow passage of arbitrary cross-section A and wetted perieter P. The bulk properties of the strea are T,P,H,S,ρ. In general, this heat transfer arrangeent is characterized by a finite frictional pressure gradient dp / dx 0 and when heat is transferred to the strea at a rate q ( W / ), by a fin ite wall-bulk fluid teperature difference T. Focusing on a slice of thickness dxas a syste, the rate of entropy generation is given by the second law: q dx ds gen = ds () T + T In addition, for any pure substance we write the canonical relation as: dh ds 1 dp = T + () dx dx ρ dx This forula can be relate to average heat transfer and fluid friction inforation, which ay be obtained experientally or nuerically for ust duct geoetries. The relationship between heat transfer rate q and wall-bulk fluid teperature difference is expressed in the for of Stanton nuber correlations: q / P T St = (4) CPG Here, note is that q / P T is the average heat transfer coefficient. The fluid friction characteristics of a certain duct are reported usually in the for of friction factor correlations: ρd dp f = (5) G dx In order to illustrate the dependence of S gen on Stanton nuber and friction factor inforation, we considering the case in which the heat transfer rate per unit length q and the ass flow rate are specified. So, q D f S gen = + (6) 4T C St P ρ T DA Under the present assuptions the duct configuration has two degrees of freedo. The wetted perieter Pand the cross-sectional area Aor any other couple of independent paraeters such as ( Re,D) or (G,D). Exaining this Equation, it becoes evident that ah high Stanton nuber contributes to the reduction of heat transfer share of S gen, while a high friction factor has the effect of increasing the entropy generation rate due to viscous effects. In a round tube of diaeter D, the rate of entropy generation per unit length is: q f S gen = + 5 πkt Nu π ρ T D (7) Here, the Nusselt nuber is Nu=St.Re.Pr. If the pipe flow

5 114 Masoud Asadi et al.: Entropy Generation in a Plate-Fin Copact Heat Exchanger with Louvered Fins is turbulent and fully developed, the Nusselt nuber and friction factor are given by the well-known correlations(e.g., Bejan, 1995): Nu = 0.0Re Pr (8) 0. f = Re (9) If τ = T / T, in louver fins side the nuber of entropy generation is: τ J f Re Ns = + 1+ τ St τ (0) Where J and N s are respectively, J = µ q (1) ρct p Surface designation 1.5 Sgen Ns = () q / T Ta ble 1. Fin geoetries Plate spacing 10 Hydraulic diaet er 10 Fin thickness A case study A coolant to air cross flow heat exchanger is design to cool the coolant( 50 percent ethylene glycol with water). Louvered fin geoetry is eployed on the air side. Both fins and tubes are ade fro aluinu alloy with K = 117 W / K. The coolant flow in the flat tubes at / sand 95 C, and shall leave at 90 C. Air enters at 1.05 / sand 5 C. The inlet pressure of the air is at 100 Kpaabsolute and the inelt pressure of the coolant is at 00 Kpa absolute. The air pressure drop is required to be less than 500 Pa. The coolant pressure drop is recoended to be less than 7o Kpa. Louver spacing 10 Louver gap 10 Heat transfer area/volue between plate / Fin area/total area 1 / /8(a) / /(a) / /8(a) / / ¼(b) / Results and Discussions Table denotes the fluid properties. At this stage ten heat exchangers with different Louvered fins are designed and copared for different ters. Table gives this inforation. ( kg / ) Ta ble. Fluid properties ρ C ( J / Kg. K ) ( /. ) P K W K ( NS. / ) µ Pr Wat er Air In tube side, with decreasing hydraulic diaeter heat transfer and pressure drop characteristics will increase. However, the difference is not very considerable. For exaple, fro /8-6.06fin with hydraulic diaeter of 4.45 illietre to /8-11.1fin with hydraulic diaeter of.084 illietre the increase in pressure drop is just1kpa. For heat transfer coefficient and Reynolds nuber is the sae. However, in Air side there is considerable difference between different type of fins. The iportant note is that Reynolds nuber, here, is a function of Louver gap and Louver spacing. Re = f ( Louver gap, Louver spacing ) () Fins of /8(a)-6.06 and 1/(a)-6.06have the biggest Louver gap, but between the the fin of 1/(a)-6.06with 1.70 illietre Louver spacing has the highest value of Reynolds nuber. Aong cases of 1,,5,7, 8, 9 and 10 with the sae Louver gap, the fin of 1/-6.06has the highest Reynolds nuber. For the convective coefficient and ass velocity the trend is the sae as Reynolds nuber

6 International Journal of Energy Engineering 01, (): Ta ble. Designing inforation n f p A Af A t, A c, A t, A c, A fr, G1 kg /. s G kg /. s Re Re h 1 W /. K ( /. ) h W K η f η o UA ε % % % 7% 4% 7% 6% % % 6% T 1,O( C ) T,O( C ) P1 ( Kpa).5.5 P ( Kpa)

7 116 Masoud Asadi et al.: Entropy Generation in a Plate-Fin Copact Heat Exchanger with Louvered Fins Ta ble 4. Entropy generation Water Air Heat exchanger efficiency 0% 5% 0% 15% 10% 5% 0% % % % 7% 4% 7% 6% % % 6% Fi gure. Heat exchanger efficiency Pressure drop for air side(pa) Fi gure 4. Pressure drop for Air Convective coefficient Fi gure 5. Convect ive coefficient for Air

8 International Journal of Energy Engineering 01, (): Here, allowable pressure drop for Air side is 500 Pa, so the case of 7 is suitable, because it has the highest heat exchanger efficiency between all cases with allowable pressure drop. Table 4 gives entropy generation for Water and Air side. It is evident that entropy generation has a direct relation with heat exchanger efficiency, as in the case of 6 with the heat exchanger efficiency of 7% there are the largest value entropy generation in both sides. As previously entioned, the selected fin for our designing is case of 7. However, here, the entropy generation is high and it is necessary decreasing it. To reach the optial entropy generation in this case, we can change the ass flow rate. Equation of.(4) deonstrates the optial ass flow rate based on entropy iniization. Re D π opt = For Air side q (4) 5 q ρ D π opt = For Water side 96 f T k Nu Figures of (6) and (7) show the function of optial ass flow rate for Water and Air side respectively. As it is clear fro these Figures the optial ass flow rate will increase with growing hydraulic diaeter draatically. However, in tube side this increase is ore. In tube side, soe factors such as Louver angle, Louver spacing and Louver gap are also deterinant. Using equation of (4) the optial ass flow rate for Water and Air are 0.7 and 1.45 kg/s respectively. After doing echanical and theral designing process heat exchanger efficiency increased 5% and entropy generation decreased about 1.5% and 1 % for tube and fin side respectively. Fi gure 6. Optial ass flow rate for Water based on entropy iniizat ion

9 118 Masoud Asadi et al.: Entropy Generation in a Plate-Fin Copact Heat Exchanger with Louvered Fins Fi gure 7. Optial ass flow rate for Air based on entropy iniization REFERENCES [1] Beauvais, F.N. (1965), An Aerodynaic Look at Autootive Radiators, SAE Paper No [] Davenport, C. J. (198) Correlation for Heat Transfer and Flow Friction Characteristics of Louvered Fin, AIChESyp. Ser. 79, [] DeJong, N. C., and Jacobi, A.M. (1997) An experiental Study of Flow and Heate Transfer in Parallel-Plate Arrays: Local, Row-by-row and Surface Averaged Behavior, International Journal of Heat and Mass Transfer, Vol. 40, No. 6, pp [4] Kurosaki, Y., Kashiwagi, T., Kobayashi, H., Uzuhashi, H., and Tang, S. (1988) Experiental Study on Heat Transfer fro Parallel Louvered Fins by Laser Holographic Interferoetry, Experiental Theral and Fluid Science, Vol. 1 pp [5] Springer, M. E., and Thole, K. A. (1998b) Experiental Design for Flowfield Studies of Louvered Fins, Experiental Theral and Fluid Science, Vol. 18, pp [6] Zhang, L. W., Balachandar, S., Tafti, D. K., Najjar, F. M. (1997) Heat Transfer Enhanceent echaniss in Inline and Staggered Parallel-Plate in Heat Exchangers, InternationalJournal of Heat and Mass Transfer, Vol. 40, No. 10, pp