HEFAT4 th Internatonal Conference on Heat Transfer, Flud Mechancs and Thermodynamcs 4 6 July 4 Orlando, Florda, UA APPLYING TAGUCHI AND GREY RELATIONAL METHOD TO A HEAT EXCHANGER WITH COIL PRING Celk N.*, Turgut E.,Yldz., Eren H. *Author for correspondence Department of Mechancal Engneerng, Frat Unversty, Elazg, 39, Turkey, E-mal: nevncelk3@gmal.com ABTRACT The goal of ths nvestgaton s to apply Taguch and Grey relatonal methods, to a concentrc heat exchanger applcaton, n order to optmze the desgn parameters. Col sprng types of the turbulators are used n the expermental study. The desgn parameters are; Reynolds number (3 Re ), outer dameter of the sprngs (D s = 7., 9.5 and mm), number of the sprngs (N s = 4, 5 and 6) and the nclne angle of the sprngs ( =, 7 and ). Nusselt number and frcton factor are the results of the study. As a result, the effects of Re,, N s, and D s on Nusselt number s found to be 79.9%, 3.%,.7% and 3.8%, respectvely. Furthermore effect of all told four parameters on frcton factor s found as 56.7%,.98%, 3.6% and.57%. INTRODUCTION A heat exchanger s a pece of equpment bult for effcent heat transfer from one medum to another. The meda may be separated by a sold wall to prevent mxng or they may be n drect contact []. Heat exchangers are wdely used n ndustry, especally n heatng, ventlaton and ar-condtonng processes as evaporator, condenser, heater, refrgerator, etc []. Turbulators are the most commonly used way to enhance heat transfer n the heat exchangers. A turbulator s a devce that turns a lamnar flow nto a turbulent flow. The heat transfer coeffcent for lquds and gases flowng through ppes n heat exchangers tends to be lmted due to a flud boundary layer close to the ppe wall that s stagnant or moves at slow speed, thus actng as an nsulatng layer. Ths boundary layer can be broken or reduced n thckness f turbulators are placed n the ppe, whch create a turbulent flow that reduces the boundarylayer thckness and thereby ncrease the heat-transfer coeffcent. Examples of turbulators for ppe flow are: twstedtape, brock, wre, sprngs, cones, etc. []. The co-author of ths study has already worked on colsprngs nserted n a concentrc tube. The expermentally found results was evaluated by means of the st [] and nd [3] Law of Thermodynamcs. The ptch of the col-wre [3-], the dameter of the col-wre [5, 6, 8, 9, ], and the length and the segmentaton of the col-sprng [] are mostly common parameters that are nvestgated by researchers. As seen from the lterature the desgn parameters may vary, and all of these varatons are done to enhance the heat transfer of course. However, enhancng the heat transfer causes wth an enhancng pressure drop meanwhle. Furthermore, to estmate the optmum number of desgn parameter s a great mportant problem. El ayed et al. [3] nvestgated the effects of heght, thckness, nter-fn spaces, number and tp-shroud clearance of fns on the heat transfer, flud flow and pressure drop. Nak et al. [4] proposed a desgn correlaton whch shows the dstrbuton of optmal rb spacng for a wde range of rb geometres and operatonal condtons. ahn et.al [5] nvestgated the effects of the longtudnal and lateral separatons of consecutvely enlarged-contracted arranged fn pars, wdths of the fns, angle of attack, heghts of fns and flow velocty on the heat and pressure drop characterstcs by usng the Taguch method. The Taguch Method s new-developed method whch nvolves desgn of experments [6]. It s developed by Gench Taguch n order to mprove the qualty of manufactured goods, and more recently also appled to engneerng botechnology marketng and advertsng [7]. A second way of parameter optmzaton s the Grey method. The Grey predcton has also been wdely used n studes of socal scences, agrculture, procreaton, power consumpton and management. In contrast to the other approaches, the Grey predcton needs as few as four data tems wthout presumng sequental dstrbuton of the lagged data. [8]. TAGUCHI AND GREY METHOD FOR OPTIMIZATION The Taguch method defnes the process objectve, or more specfcally, a target value for a performance measure of the process. Ths may be a flow rate, temperature, etc. The target of a process may also be a mnmum or maxmum; for example, the goal may be to maxmze the output flow rate. The devaton n the performance characterstc from the target value s used to defne the loss functon for the process. The method, determnes the desgn parameters affectng the process. Parameters are varables wthn the process that affect the performance measure such as temperatures, pressures, etc. that can be easly controlled. The number of levels that the parameters should be vared at must be specfed. By Taguch method, orthogonal arrays can be created for the parameter desgn ndcatng the number of and condtons for each experment. The selecton of orthogonal arrays s based on the number of parameters and the levels of varaton 45
for each parameter, and wll be expounded below. Fnally, the method conducts the experments ndcated n the completed array to collect data on the effect on the performance measure, and t completes data analyss to determne the effect of the dfferent parameters on the performance measure. In Taguch method, a loss functon s used to calculate the devaton between the expermental value and the desred value. Ths loss functon s further transformed nto a sgnal-to-nose (/N) rato [9]. everal /N ratos are avalable dependng on the type of characterstcs; lower s better (LB), nomnal s best (NB), or hgher s better (HB). The /N ratos whch condenses the multple data ponts wthn a tral, depends on the type of characterstcs beng evaluated. In ths study hgher Nusselt number wth lower frcton factor s the ndcaton of better performance. Therefore, HB for the Nu number and LB for the frcton factor are selected for obtanng optmum performance characterstcs: L HB L LB n n y n y n where y expresses the resultng value and n ndcates the number of experments run under such expermental condtons. The /N rato η j for the th performance characterstc n the j th experment can be expressed as: j log( L j ) (3) An analyss of varance ANOVA s performed to determne whch parameters are statstcally sgnfcant. The /N rato and ANOVA analyses allow the predcton of the optmal combnaton of process parameters []. A confrmaton experment s then conducted to verfy the optmal process parameters determned from the parameter desgn. ANOVA and F test are used to analyse the expermental data as [6]: n m J T m (4) n A A N m, E T A (5) A V V, F A A f Ao V A E (6) where T s the sum of squares due to the total varaton, m s the sum of squares due to the means, A s the sum of squares due to parameter A (n present study A represents Reynolds number), E s the sum of squares due to error, j s the value of each experment, J s the number of experments n orthogonal array, A s the sum of the th level of parameter A, () () N s repeatng number of each level of parameter A, f A s the degree of freedom of parameter A, and V A s the varance of parameter A. Grey relatonal analyss, whch s based on the grey system theory, can be used to determne the complcated nterrelatonshps between multple performance characterstcs. The grey relatonal coeffcent s found as follows []: r x k, x k mn mn x k x k x k max max x k x k k x k max max x k x k where x (k) s the normalzed value of the k th performance characterstc n the th experment and s the dstngushng coeffcent (, ). The value of can be adjusted n accordance wth actual system requrements. The grey relatonal grade s a weghtng-sum of the grey relatonal coeffcent. It s defned as follows []: r p x, x rr k, x k p k where p s the number of performance characterstcs. For grey relatonal analyss, the expermental results for Nu number and frcton factor are frst normalzed n the range between and, whch s termed, grey relatonal generaton. Usng the grey relatonal analyss and the statstcal analyss of varance, the optmal combnaton of parameters can be predcted. EXPERIMENTAL PROCEDURE Fgure presents the schematc vew of the whole set up. Detaled nformaton about the expermental procedure s already gven n an artcle of co-authors []. Reynolds number (3<Re<) base on the flowrate of the ar flow and dameter of nner ppe, nclne angle (poston of the sprng n the nner tube) of the sprngs ( =, 7 and ), number of the sprngs (N s = 4, 5 and 6), and outer dameter of the sprngs (D s = 7., 9.5, mm) are the ndependent desgn parameters that affect the heat transfer and pressure drop. Nusselt numbers (Nu) and frcton factor (f) are the non-dmensonal dependent parameters that are amed to be obtaned as the results. Table Factors and levels used n the experments Parameter Re N s D s Par. Code A B C D 3399 4 7. 4676 7 5 9.5 3 597 6 4 777 -- -- -- 5 8564 -- -- -- 6 989 -- -- -- Varyng Reynolds number from 3 to means turbulent flow s consdered as flow regon. As prevously mentoned, the ndependent parameters are coded as A, B, C, D k k (7) (8) 46
for readng faclty. The control factors and ther levels are lsted n Table. Accordng to Taguch qualty desgn concept, a L 8 orthogonal array wth 8 rows (correspondng to the number of experments) s set and presented n Table. Regardless of category of the performance characterstcs, a greater η value corresponds to a better performance. Therefore, the optmal level of the desgn parameters s the level wth the greatest η value. By applyng Eqs. () () and (3), the η values for each experment of L 8 array (Table ) are calculated. The results for Nusselt number are exhbted n Table 3 and the results for frcton factor are gven n Table 4. Fgure chematc vew of expermental setup [] Table /N ratos for Nusselt number and frcton factor Control factors /N rato (η) /N rato (η) Exp.no A B C D Nu f 5.89438.77767 8.3363836 3.96798 3 3 3 3 3.996334 7.97649 4 8.3577373.88798 5 3 3.56745 3.5545 6 3 3 3.5783 3.967 7 3 3.89767.58993 8 3 3 33.446.98876 9 3 3 3 34.99.4665 4 3 3 34.9953445.837 4 3.59669.9499 4 3 33.8364769.574 3 5 3 35.7496779.6984 4 5 3 34.447489.3786 5 5 3 34.7688.3 6 6 3 35.668787.463796 7 6 3 37.47597.555 8 6 3 35.597.99 Accordng to Table 3, t s seen that, based on the analyss of /N rato, the effects of the optmal Reynolds number, nclne angle, sprng numbers, sprngs dameter, and are found to be 36.3 ( 6-A6), 33.3 ( 3-B3), 33. ( 3 C3) and 34. ( 3-D3), respectvely. It s to say that; f we consder the levels A6B3C3D3, we can obtan the optmal Nusselt number. Table 3 Average /N ratos for Nusselt number Control factors 3 4 5 6 A 8. 3.5 3.7 33.7 34.9 36.3 * B 3.9 3.99 33.3 * -- -- -- C 3.3 3.77 33. * -- -- -- D 3.5 3.3 34. * -- -- -- * Optmum level, Overall mean = 3.68 db Table 4 Average /N ratos for frcton factor Control factors 3 4 5 6 A -.65-8.6-4.75-3.34 -. * -.3 B -4.36 * -5.49-6.49 -- -- -- C -3.48 * -5.8-7.67 -- -- -- D -.9 * -5.9-8.34 -- -- -- * Optmum level, Overall mean = -5.45 db 47
A smlar concluson can be made about the frcton factor by consderng Table 4. From the table we see that, the effects of the optmal Reynolds number, nclne angle, sprng numbers, sprngs dameter are found to be -. ( 5-A5), -4.36 ( -B), -3.48 ( C) and -.9 ( -D), respectvely. It means; f we consder the levels A5BCD, we can obtan the optmal frcton factor. Fg represents these results n graph form for Nusselt number, and Fg 3 does t for frcton factor. Fgure /N ratos for Nusselt number Fgure 3 /N ratos for frcton factor A better feel for the relatve effect of the dfferent expermental parameters on Nusselt number and frcton factor are obtaned by decomposton of varance, whch s called analyss of varance. The magntude of the effects of the expermental parameters on Nusselt number and frcton factor are amed to be determned by means of varance analyss method ANOVA []. The ANOVA evaluates the expermental errors and test of sgnfcance to understand the effect of varous factors. The method and equaton of the ANOVA are n Table 5 and Table 6, respectvely for Nusselt number and frcton factor. Table 5 Results of the analyss of varance for Nusselt number degree of freedom (df) sum of square () vara nce (V) F test F.5 contrbuton % A 5 3.5 6. 98.5 * 4.38 79.9 B 5.36.65. * 5.4 3. C 3.3.5.49 * 5.4.7 D.86.4 86.83 * 5.4 3.88 error 6.788.3 -- --.38 sum -- 6.46 -- -- -- * gnfcant at least 95% confdence level Table 6 Results of the analyss of varance for frcton factor degree of freedom (df) sum of square () vara nce (V) F test F.5 Contrbuton % A 5 5.75 45. 43. * 4.38 56.7 B 3.685 6.84 6.53 * 5.4.98 C 53.44 6.6 5.4 * 5.4 3.6 D 89.838 44.9 4.9 * 5.4.57 error 6 6.78.4 4.57 sum 338.796 * gnfcant at least 95% confdence level The F test s used to make a decson about the quantty of the effects, n other words; the magntude of the found analyses results s evaluated by means of F test. The calculated F values are compared to approprate standard confdence tables whch are presented by Ross s textbook []. In the case of any F value turns out as a result of the mentoned comparson to be hgher than such F value on the table, t s concluded that the analyss s at the assumed confdence level. Accordng to ths analyss, the most effectve parameters wth respect to Nusselt number s the Reynolds number (43.45) and then dameter of the sprng, nclne angle and number of the sprngs n order. On the other hand, the effect of 48
Re number s the hghest on frcton factor and the dameter of the sprngs, number of the sprngs and nclned angle comes orderly. Table 7 and Table 8 show the confrmaton for the analyss. It s seen here that, the estmated Nusselt number by the analyss s 84.64, and t s found 86.88 by the experments. When the frcton factor s handled t s observed that the predcted f s.66, but the expermentally found one s.68. Table 7 Results of the confrmaton experment for Nusselt number Intal Optmum parameters parameters Predcton Experment A6B3CD A6B3C3D3 A6B3C3D3 Nu 59.66 84.64 86.88 /N rato (db) 35.5 38.55 38.78 * Improvement of /N rato for Nusselt number = 3.7 db Table 8 Results of the confrmaton experment for frcton factor Intal Optmum parameters parameters Predcton Experment A6B3CD A5BCD A5BCD f.65.66.68 /N rato (db) -.54 3.59 3.35 * Improvement of /N rato for Nusselt number = 3.7 db Now the attenton s turned to the grey relatonal analyss. The results of the analyss are presented n Table 9 and Table. Accordng to the performed experment desgn, t s clearly observed from Table 9 and Fg 4 that, experment 7 has the hghest grey relatonal grade. It means the hghest Nu number and lowest frcton factor that s obtaned at the same tme can be reached at experment 7. o t s the optmal value. Table 9 Grey relaton coeffcent and grey relatonal grade values Exp. no Control factor Grey Relatonal coeff. Grey relatonal Order A B C D Nu f grade.333.89.57 4.36.538.45 7 3 3 3 3.395.333.364 8 4.363.789.576 3 5 3.46.64.533 5 6 3 3.43.68.55 6 7 3.4.94.676 9 8 3 3.48.77.66 9 3 3 3.54.73.635 4 3 3.598.73.665 4.45..75 7 4 3.59.86.69 8 3 5 3.673.84.757 5 4 5 3.544.93.737 6 5 5 3.575.975.775 3 6 6 3.664.87.767 4 7 6 3..858.99 8 6 3.6.986.84 The grey relatonal grade values for each level of the turbulator parameters are calculated by usng the same method. The grey relatonal grade values are shown n Table. nce the grey relatonal grade represents the level of correlaton between the reference sequence and the comparablty of sequence, the greater value of the grey relatonal grade means that the compatblty sequence has a stronger correlaton, to the reference sequence. Fgure 4 Grey relatonal grades Fgure 5 Effect of desgn parameters on mult performance characterstcs 49
Table The response table for grey relatonal grade Control factor 3 4 5 6 Max- Mn A.46.538.646.694.756.833*.37 B.669*.667.69 -- -- --.4 C.7*.65.6 -- -- --.9 D.67*.648.647 -- -- --.3 * overal mean = 65 Based on the grey relatonal grade values gven n Table, the optmal desgn parameter was obtaned for Re number at 6, (A6), nclne angle (B), number of the sprngs, (C), and dameter of the sprngs (D). Effect of desgn parameters on the mult-performance s also gven n Fg 5 for better understandng. These results mprove that the for maxmum Nusselt number, mnmum frcton factor the optmal case can be reached wth the experment A6BCD. CONCLUION In ths study, an expermental work on the energy analyss of a concentrc tube heat exchanger wth col sprng turbulators was handled. The optmzaton of the desgn parameters were performed by use of two methods, namely Taguch and Grey methods. The effect of desgn parameters, such as Re number, nclne angle of the sprngs n the tube, dameter of the sprng nsert the tube and number of the sprngs, on the Nusselt number and frcton factor were amed to be determned. As a result, the effects of desgn parameters Re,, N s, and D s on Nusselt number was found as 79.9%, 3.%,.7% and 3.8%, respectvely. As t s expected, ncreasng heat transfer causes ncreasng frcton factor. By these methods, the effect of four desgn parameters on frcton factor was found as 56.7%,.98%, 3.6% and.57%. It s concluded that the optmal case was obtaned wth the experment A6BCD, whch ndcates maxmum Nusselt number, mnmum frcton factor. REFERENCE [] Incropera F.P., and dewtt, D.P., Fundementals of Heat and Mass Transfer, nd ed., 98, Wley, New York. [] Eren H., Celk N., Yldz. and Durmus, A., Heat transfer and frcton factor of col sprngs nserted n the horzontal concentrc tubes, Transactons of AME, Journal of Heat Transfer,, 3 (), pp.-. [3] Naphon, P., Effect of col-wre nsert on heat transfer enhancement and pressure drop of the horzontal concentrc tubes, Internatonal Communcatons n Heat and Mass Transfer, 6, 33, pp. 753 763 [4] Yakut, K., and ahn, B., The effects of vortex characterstcs on performance of coled wre turbulators used for heat transfer augmentaton, Appled Thermal Engneerng, 4, 4, pp. 47 438 [5] Promvonge, P., Thermal performance n crcular tube ftted wth coled square wres, Energy Converson and Management, 8, 49, pp. 98 987 [6] Promvonge, P., Thermal enhancement n a round tube wth snal entry and coled-wre nserts, Internatonal Communcatons n Heat and Mass Transfer, 8, 35, pp.63 69 [7] Promvonge, P., Thermal augmentaton n crcular tube wth twsted Tape and wre col turbulators, Energy Converson and Management, 8, 49, pp. 949 955 [8] Prasad, R. C., Performance evaluaton usng exergy analyss applcaton to wre-col nserts n forced convecton heat transfer, Internatonal Journal of Heat and Mass Transfer, 3, 37,994, pp. 97 [9] Garca A., Vcente P. G., and Vedma A., Expermental study of heat transfer enhancement wth wre col nserts n lamnartranston-turbulent regmes at dfferent prandtl numbers, Internatonal Journal of Heat and Mass Transfer, 5, 48, pp. 464 465 [] Agrawal K. N., Kumar A., Behabad M. A. A., and Varma H. K., Heat transfer augmentaton by coled wre nserts durng forced convecton condensaton of R- nsde horzontal tubes, Internatonal Journal of Multphase, 998, 4, pp. 635 65 [] Ozceyhan V., Conjugate heat transfer and thermal stress analyss of wre col nserted tubes that are heated externally wth unform heat flux, Energy Converson and Management, 5, 46, pp. 543 559 [] hoj Y., ato K., and Olver D. R., Heat transfer enhancement n round tube usng coled wre: Influence of length and segmentaton, Heat Transfer - Asan Research., 3, 3, pp. 99 7 [3] El-ayed.A., Mohamed M.., Abdel-latf A.M., and Abouda A.E., Investgaton of turbulent heat transfer and flud flow n longtudnal rectangular-fn arrays of dfferent geometres and shrouded fn array, Expermental Thermal and Flud cence, Vol. 6,, pp.879 9 [4] Nak, Probert.D., and Bryden I.G., Heat transfer characterstcs of shrouded longtudnal rbs n turbulent forced convecton, Internatonal Journal of Heat and Flud Flow, 999,, pp. 374 84 [5] ahn B., Yakut K., Kotcoglu I., and Celk C., Optmum desgn parameters of a heat exchanger, Appled Energy, 5, 8, pp. 9 6 [6] Taguch G., Introducton to qualty engneerng. Asan Productvty Organzaton, Tokyo, 99. [7] elden P., ales H., Process Engneerng: A personal workshop. Mlwaukee, Wsconsn: AQ Qualty Press. pp. 37, 997. [8] Deng J.L., Introducton to grey theory, Journal of Grey ystem, 989,, pp. 4. [9] Hsu C.Y., and Tsang C.H., Effects of ZnO buffer layer on the optoelectronc performances of GZO flms. olar Energy Materals and olar Cells, 8, 9, pp.53 536 [] Chen D.Y., and Hsu C.Y., Growth of Ga-doped ZnO flms wth ZnO buffer layer by sputterng at room temperature, uperlattces and Mcrostructure, 8, 44, pp. 74 753 [] Deng J.L., Introducton to grey system. Journal of Grey ystem, 989,, pp. 4 [] Ross, P.J., Taguch Technques for Qualty Engneerng, nd edton, 996, McGraw Hll Co. New York. 5