Numercal and Expermental Analyss of Ellptc Fnned-Tube Heat Exchangers under Msted Condtons Yuh-We Chu, Y-Xong Ln, Jn-Yuh Jang Department of Mechancal Engneerng, Natonal Cheng-Kung Unversty, Tawan Correspondng e-mal : angm@mal.ncku.edu.tw ABTRACT The numercal and expermental analyss was carred out to study the thermal-hydraulc characterstcs n ellptcal fnned-tube heat exchanger under the dry and ar/water spray cooled system. Three knds of maor/mnor axs ratos (2.5 2.8 and 3) were examned for the ellptc fnned-tube heat exchangers and the results were also compared wth the correspondng crcular fnned-tube havng the same permeter. The numercal results for the pressure and heat transfer coeffcent at varous nlet frontal veloctes (1~5 m/s) are shown and compared wth the avalable expermental data. The numercal results ndcated that the pressure drop of crcular fnned-tube heat exchanger s 3 tmes that of the ellptc fnned-tube heat exchanger, whle the heat transfer coeffcent of the crcular fnned-tube s 1.51 tmes that of the ellptc fnned-tube. The heat transfer coeffcent per unt of pressure drop for ellptc fnned-tube s 1.6-2.5 tmes of crcular fnned-tube. When the ar/water spray system s appled, the heat transfer could ncrease up to more than 30% Keywords:ellptc fnned-tube heat exchanger, mst flow, thermal-hydraulc characterstcs. INTRODUCTION Numerous desgns for ndustral heat exchangers nvolvng a bank of tubes n a flud crossflow were appled. Among many types of fnned-tube heat exchangers, those constructed of crcular and ellptc fns have been used n many ndustres. The advantage to use ellptc fnned-tube s that t can provde a lower pressure drop when the flud flows around the tube banks. But the dsadvantage s that ellptc tubes are generally restrcted to low-pressure applcatons on the tube sde. There have been a number of studes [1-5] on the characterstcs of the flow feld and heat transfer adacent to a bare ellptc tube. The dry col correlatons for a staggered crcular tube layout are the Brggs and Young [6] correlaton for heat transfer, and the Robnson and Brggs [7] correlaton for pressure drop. The convectve heat and mass transfer coeffcent and frcton factor for crcular fnned-tube heat exchanger under dry and wet condtons were reported by Idem et al. [8, 9]. For the ellptc fnned-tube heat exchanger, Brauer [10] was the frst author to study the thermal-characterstcs wth an axs rato of 1.77 under dry condton. Dunwoody [11] had dscussed the varaton of local Nusselt number wth dfferent axs rato under lamnar flow and constant wall temperature. In order to enhance the heat transfer, the dry/wet schemes were wldly used n many ndustral applcatons. MaClane-Cross and Bank [12, 13] analyzed the heat and mass transfer characterstcs n a wet surface of the heat exchangers. Fnlay and McMllan [14] obtaned the data wth the tube bank, and reported the sgnfcant effect of the water spray n heat transfer
enhancement. The formula for the desgn of mst cooled heat exchangers on the assumpton that the tubes are fully wet was proposed by Oshma et al. [15]. In ths study, the 3-D thermal hydraulc smulaton for the ellptc fnned-tube heat exchangers was developed. The effect of heat transfer and pressure drop coeffcents due to dfferent axs rato of ellptc fns was also dscussed. A water spray system was establshed for the ellptc fnned-tube heat exchanger and the spray effect on the thermal hydraulc characterstcs were also dscussed. EXPERIMENTAL SETUP AND DATA REDUCTION Three types of fnned-tube confguratons, as shown n Fgure 1, were tested n the present study. The physcal model and the confguraton were shown n Fgure2 and Fgure 3. Ther detal geometrc parameters are tabulated n Table 1. The experments were conducted n an nduced open wnd tunnel as shown n Fgure 4. Ths setup was based on the ASHRAE 41.2 standard [16]. The ar flow was drven by a 3.73-kW (5-hp) centrfugal fan wth an nverter to provde varous nlet veloctes. An ar-straghtened equalzer and a mxer were provded to mnmze the effect of flow maldstrbuton. The ar temperatures at the nlet and the ext zones across the test secton were measured by K-type thermocouples the accuracy of whch was approxmately 0.2 %. The pressure of the test col was detected by a precson YOKOGAWA dfferental pressure transducer, readng to 0.1Pa. The workng flud on the tube sde was hot water and the temperature of the water was controlled by a thermostat reservor. The hot water nlet temperature was controlled at 75 ; for the spray condton, the chlled water was controlled at 20. Both the nlet and outlet temperature of the workng flud (water) were measured by two precalbrated RTDs (pt100). Ther accuracy was wthn ±0.05. The water volumetrc flow rate was measured by a magnetc volume flow meter wth 0.002 L/s resoluton. A data acquston system (hybrd recorder) was used to collect and convert the entre data sgnals and then transmt the converted sgnals through a GPIB nterface to the host computer for further operaton. The energy balance between the ar and tube sde was ±5% for dry condton and ±7% for spray condton. For spray condton, water was sprayed nto the stream of ar. The so-called steady state method was employed n determnng the heat transfer performance of the core. The water spray water system whch ncludes water pump, ar - compressor and 3 spray nozzles was ntroduced nto the ar tunnel about 0.5 m upstream of the heat-exchanger. The spray nozzles used were IKEUCHI two-flud fan-shaped (type BIMV 8002) for small flow rate. The permtted spray rate was 1.0 to 10.2 L/hr dependng on the pressure of ar and water at the back of the nozzles, as shown n table 1. To obtan the average heat transfer coeffcents h from the measured expermental data, theε-ntu (effectveness-number of transfer unt) method [17] under the cross overall counterflow wth both fluds unmxed was appled. THREE-DIMENSIONAL MATHEMATICAL ANALYSIS Fgure 3 desgnates the computatonal doman, and the coordnate system s also llustrated n the fgure. The dmensonless equatons for contnuty, momentum, and energy may be express n tensor form as u = 0 ( 1 )
p u u ρ( u u ) = + [ μeff ( + ) ρu ' u '] p p' T ρc p ( u T ) = u + u ' + ( k ρc p u ' T' ) In ths study, the k-ε turbulent model was ntroduced to smulate the flow feld more accurately. The k-ε turbulent s shown as below μeff k ( ρu k) = ( ) + ρ( Pr ε ) ( 4 ) σ k μeff ε ε Pr ( ρu ε ) = ( ) + ρ [( c + c P c ε] P r σ ε k 1 3 ε ) r 2 μt u 2 u u 2 2 = [2( ) + ( + ) 2 ( u ) ] ( 6 ) ρ 3 Because the governng equatons are ellptc n spatal coordnates, boundary condtons are requred for all boundares of the computaton doman. At the up-stream boundary, located the dstance as tube outsde dameter from the frst row tube, unform flow velocty u n and temperaturet n are assumed. At the down-stream end of the computatonal doman, the Neumann boundary condton was appled. At the sold surface, no-slp condtons and constant temperature T tube are specfed. At the symmetry plane, normal velocty and the temperature varaton along the normal drecton s set to be zero. The local heat transfer coeffcent could be expressed n dmensonless form by the Nusselt number Nu, defne as T ( ) " h H q H Tb Nu = = = ( ) wall ( 9 ) k k ( Tw Tb ) n Where k s the thermal conductvty of the flud. To represent the pressure drop, the frcton factor f was ntroduced as below p n p H f = 1 ( 10 ) ρ u 2 4 L where p n s the pressure at the nlet plane. 2 n In ths study, a body-ftted coordnate system along wth a multblock system was used to generate a general curvlnear coordnates system numercally by solvng Laplace equatons wth proper control of grd denstes. A control-volume-based fnte-dfference formulaton was used to solve the governng equatons. The system of fnte-dfference equatons were solved teratvely usng the SIMPLER algorthm [18]. A grd system, as shown as Fgure 5, for the ellptc fnned-tube bank was adopted n the computaton doman. To ensure the accuracy and valdty of the numercal results, three dfferent grd systems, 158 12 8, 190 15 10, and 228 18 12 for the ellptc fnned-tube bank were tested. It was found that the relatve error for the total amount of heat transfer was less than 1.2%. Iteratve computatons were performed on a computer wth Pentum 4 1.8G CPU. Typcal CPU tme was 3-4 hours for each case. ( 2 ) ( 3 ) ( 5 )
RESULT AND DISCUSSION Expermental and numercal smulatons of thermal-hydraulc characterstcs of three types of ellptc fnned-tube heat exchangers wth dfferent fn axs rato (3.1, 2.8, and 2.5) were presented. The pressure drop and average heat transfer coeffcent of crcular fnned-tube heat exchanger were also beng compared wth the expermental and numercal results of ellptc fnned-tube heat exchangers. The pressure drops of the three dfferent axs ratos of ellptc fnned-tube heat exchangers for dfferent values of nlet frontal velocty are shown n Fgure 6. As shown n Fgure 6, the value of the pressure drop ncreased as a parabolc curve wth an ncrease of the frontal velocty. In general, the expermental results are 18-23% hgher than the numercal results. The pressure drop of the crcular fnned-tube heat exchanger s 2.4 tmes the value of ellptc fnned-tube heat exchanger wth axs rato 2.5; 2.9 tmes the value of ellptc fnned-tube heat exchanger wth axs rato 2.8; and 3.2 tmes the value of ellptc fnned-tube heat exchanger wth axs rato 3.1. Fgure 7 presents the varatons of the average heat transfer coeffcent h wth the frontal velocty for the three types of fnned-tube heat exchangers, respectvely. Also shown n the fgure for comparson s the crcular fnned-tube heat exchanger data. It s shown that the numercal results are 32-45% hgher than the expermental results. Ths s probably due to the fact that the actual boundary condtons for the tube surfaces n the experment do not occur under constant wall temperature. As shown n the fgure, the average heat transfer coeffcent h of the crcular fnned-tube s about 49% hgher than the value of the ellptc fnned-tube heat exchanger wth axs rato 2.5; 52% hgher than the value of ellptc fnned-tube heat exchanger wth axs rato 2.8; and 56% hgher than the value of ellptc fnned-tube heat exchanger wth axs rato 3.1. The numercal and expermental results for the heat transfer coeffcent per unt pressure drop h / ΔP versus the nlet frontal velocty are shown n Fgure 8. Both the expermental and numercal predctons ndcate that the h / ΔP rato decreases wth the ncrease of the frontal velocty, and ths rato for ellptc fned tube s about 55-150% hgher than for the crcular fnned tube. Fgure 9 shows the heat enhancement whle applyng the ar/water spray system under dfferent ar/water ratos. As shown n the fgure, when the ar/water rato are 0.15% and 0.3%, the amounts of heat transfer are 16% and 33%, respectvely, hgher than the dry condton for the ellptc fnned tube wth axs rato 2.5; 18% and 34%, respectvely, hgher than the dry condton for the ellptc fnned tube wth axs rato 2.8; 25% and 38%, respectvely, hgher than the dry condton for the ellptc fnned tube wth axs rato 3.1. CONCLUSION Expermental and numercal predctons of the thermal-hydraulc characterstcs of ellptc fnned-tube heat exchangers are presented. For the dry condtons, the pressure drop of crcular fnned-tube heat exchanger are respectvely 2.4, 2.9 and 3.2 tmes the values of ellptc fnned-tube heat exchanger wth axs rato 2.5, 2.8 and 3.1. The average heat transfer coeffcent h of crcular fnned-tube are respectvely about 49%, 52% and 56% hgher than the values of ellptc fnned-tube heat exchangers wth axs ratos 2.5, 2.8 and 3.1. The heat transfer coeffcent per unt pressure drop h / ΔP for ellptc fned tube s about 55-150% hgher than for the crcular fnned tube. The heat transfer could be enhanced whle applyng the ar/water spray system. When the ar/water rato are
0.15% and 0.3%, the amounts of heat transfer are 16% and 33%, respectvely, hgher than the dry condton for the ellptc fnned tube wth axs rato 2.5; 18% and 34%, respectvely, hgher than the dry condton for the ellptc fnned tube wth axs rato 2.8; 25% and 38%, respectvely, hgher than the dry condton for the ellptc fnned tube wth axs rato 3.1. ACKNOWLEDGEMENTS Fnancal support for ths work was provded by the Natonal Scence Councl of Tawan, under contract NSC 94-2212-E-006-014. REFERENCES 1. Seban, R., and Drake, R., 1953. Local Heat-Transfer Coeffcents on the Surface of an Ellptc Cylnder n a Hgh Speed Ar Stream. Trans. Am. Soc. Mech. Eng., vol. 75, pp. 235-240 2. Drake, R., Seban, R., 1953. Doughty D., and Ln S., Local Heat Transfer Coeffcents on Surface of an Ellptc Cylnder. Axs Rato 1:3, n a Hgh Speed Ar Stream, Trans. Am. Soc. Mech. Eng., vol. 75, pp. 1291-1302 3. Ota, T., Aba, S., Tsuruta, T., and Kaga, M., 1983. Forced Convecton Heat Transfer form an Ellptc Cylnder of Axs rato 1:2. Bull. Jpn. Soc. Mech. Eng., vol. 26, pp. 262-267 4. Ota, T., Nshyama, H., and Taoka, Y., 1984. Heat Transfer and Flow around an Ellptc Cylnder, Int. J. Heat Mass Transfer. vol. 27, pp. 1771-1779 5. Nshyama, H., Ota, T., and Matsumo, T., 1988. Heat Transfer and Flow around an Ellptc Cylnders n Tandem Arrangement. Jpn. Soc. Mech. Eng. Int. J. Ser. II, vol. 31, pp. 410-419 6. Brggs, D. E. and Young, E. H., 1963. Convecton heat transfer and pressure drop of ar flowng across trangular ptch banks of fnned tubes. Chem. Eng. Prog. Symp. Ser., vol.59, no.41, pp. 1-10, 7. Robnson, K. K. and Brggs, D. E., 1966. Pressure Drop of Ar Flowng Across Trangular Ptch Banks of Fnned Tubes, Chem. Eng. Prog. Symp. Ser. vol.62, no. 64, pp. 177-184 8. Idem, S. A. and Jacob, A.M. and Goldchmdt, V. W., Heat Transfer Characterzaton of a Fnned-Tube Heat Exchanger (wth and wthout Condensaton). Transacton of the ASME, vol. 112, pp. 64-70, 1990. 9. Idem, S. A., and Goldchmdt, V. M., 1993. Sensble and Latent Heat Transfer to a Baffled Fnned-Tube Heat Exchanger. Heat Transfer Eng., vol. 14, no. 3, pp. 26-35 10. Brauer, H., 1964. Compact Heat Exchangers, Chem. Process Engneerng, London. vol. 45, no. 8, pp. 451-460 11. Dunwoody, N.T., 1962. Thermal Results for Forced Heat Convecton through Ellptcal Ducts. J. of Appled Mech., vol. 29, pp. l65-170 12. Maclane-Cross, I. L., and Banks, P. J., 1972. Coupled Heat and Mass Transfer n Regenerators-predcton Usng an Analogy wth Heat Transfer. J. of Heat Transfer, vol. 15, pp. 1225-1242 13. Maclane-Cross, I. L., and Banks, P. J., 1981. A General Theory of Wet Surface Heat Exchangers and ts Applcaton to Regeneratve Evaporatve Coolng. J. of Heat Transfer, vol. 109, pp. 784-787 14. Fnlay, I. C. and McMllan, T., 1970. Pressure drop, heat and mass transfer durng ar/water mst flow across a bank of tubes. Natonal Engneerng Laboratory, NEL-Report, No. 474 15. Oshma, T., Iuch, S., Yoshda, A., and Tkamatsu, K., 1972. Desgn Calculaton Method of Ar-Cooled Heat Exchangers wth Water Spray. Heat Transfer Jap. Res. 1, pp. 47-55 16. ASHRAE Standard 41.2-1987, Standard Method for Laboratory Ar-Flow Measurement. Amercan Socety of Heatng, Refrgeratng and Ar-Condtonng Engneers. Atlanta, GA 17. Shah, R. K., 1983. Heat Exchanger Basc Desgn Method. n S. Kakac, R. K. Shah, and A. E. Bergles (eds.), Low Reynolds Number Flow Heat Exchangers, pp. 21-72, Hemsphere, New York 18. Pantakers, S. V., 1981. A Calculaton Procedure for Two-Dmensonal Ellptc Problem. Numer. Heat Transfer, vol. 4, pp. 409-426
Table 1. Geometrc Parameters of the Test Sectons Crcular Fnned-Tube H.X. Ellptc Fnned-Tube H. X. Axs Rato 1.0 2.5 2.8 3.1 Tube Outsde Dameter ( mm ) 27 36.8 14.6 37.6 13.2 38 12 Wdth of Heat Exchanger ( mm ) 266 226 226 226 Fn Thckness ( mm ) 0.5 0.5 0.5 0.5 Fn Heght ( mm ) 7 7 7 7 Fn Ptch (fns/n) 8 8 8 8 Transverse Tube Spacng (mm) 42 34 34 34 Longtudnal Tube Spacng (mm) 37 50 50 50 Tube numbers 24 32 32 32 Pass numbers 4 4 4 4 Hydraulc Dameter Re Dh (mm) 6.72 7.63 8.33 8.83 a b a Ar = b = 2.5,2.8,3.1 Fgure 1. Test Secton Fgure 2. Ellptc Fnned-Tube Confguraton Fgure 3. Computatonal Doman
17 16 1 18 9 11 進 2 3 4 5 6 7 19 8 10 12 13 14 15 20 19 21 11. ar sde nlet temperature measurng staton 12. nlet area 13. ar straghtener 14. pressure tap (nlet) 15. test secton 16. pressure tap (outlet) 17. ar mxer 18. ar straghtener 19. ar sde outlet temperature measurng staton 20. nozzle pressure tap (nlet) 21. multple nozzles plate 1. nozzle pressure tap (outlet) 2. ar straghtener 3. flexble duct 4. varable exhaust fan system 5. dscharge 6. thermostat reservor 7. volumetrc flow meter 8. dfferental pressure transducer 9. data acquston system 10. workng computer Fgure 4. Schematc Dagram of the Expermental Setup Fgure 5. Computaton Grd System for Ellptc Fnned-Tube Banks
300 ΔP( pa) 200 Numerc Expermental h( W / m 2 K) 100 80 60 Numerc 100 40 20 Expermental 0 0 2 4 6 Frontal Velocty (m/s) Fgure 6. Pressure drops for dfferent values of frontal velocty 0 0 2 4 6 Frontal Velocty (m/s) Fgure 7. Heat transfer coeffcent for dfferent values of frontal velocty h ΔP 5 4 3 2 Numerc Q wet/qdry 1.6 1.5 1.4 1.3 spray water to ar mass rato (Ar=2.5) 0.3% (Ar=2.5) 0.15% (Ar=2.8) 0.3% (Ar=2.8) 0.15% (Ar=3.1) 0.3% (Ar=3.1) 0.15% 1 1.2 0 0 2 4 6 Frontal Velocty (m/s) 1.1 2 3 4 5 6 Frontal Velocty(m/s) Fgure 8. Heat transfer coeffcent per unt pressure drop for dfferent values of frontal velocty Fgure 9. Heat enhancement by dfferent axs ratos and spray ratos vares wth frontal velocty