PERFORMANCE EVALUATION OF WIRE SPRING FIN FOR COMPACT PLATE-FIN HEAT EXCHANGERS

Transcription

1 Proeedings o Fith International Conerene on Enhaned, Compat and Ultra-Compat Heat Exhangers: Siene, Engineering and ehnology, Eds. R.K. Shah, M. Ishizuka,.M. Rudy, and V.V. Wadekar, Engineering Conerenes International, Hoboken, NJ, USA, September 25. CHE25 21 PERFORMANCE EVALUAION OF WIRE SPRING FIN FOR COMPAC PLAE-FIN HEA EXCHANGERS H. Iai 1, S. Kaakami 2, K. Suzuki 3, J. sujii 4 and. Abiko 5 1 Kyoto University, Kyoto, Japan, iai@meh.kyoto-u.a.jp 2 Kyoto University, Kyoto, Japan, soushi@t1kougakubu.mbox.media.kyoto-u.a.jp 3 Shibaura Institute o ehnology, Saitama, Japan, ksuzuki@si.shibaura-it.a.jp 4 Sumitomo Preision Produts Co., LD., Amagasaki, Japan, tsujii@spp.o.jp 5 Sumitomo Preision Produts Co., LD., Amagasaki, Japan, abiko-t@spp.o.jp ABSRAC Use o thin metal ire strutures as a ne type o extended heat transer surae is proposed. As one o the most basi struture o this kind, the heat transer perormane o a spring shaped in is experimentally investigated under relatively lo Reynolds number onditions (1< <1). Averaged heat transer oeiient is evaluated by modiied single-blo method hile the pressure drop is measured at a steady state lo ondition. he eets o the geometri parameters suh as ire diameter, spring pith and pith ratio ere systematially examined and the obtained data ere ompared ith that o a onventional oset in, hih is ommerially available. It as ound that the geometri parameters o the spring ins and the arrangement o spring ins in the test setion aet their perormane. Some types o sprig ins shoed better heat transer perormane than a onventional oset in, i they are evaluated in terms o the total heat transer at a onstant pumping poer. INRODUCION Development o a high temperature eetiveness ompat heat exhanger that an be used under high temperature onditions is one o the important requirement rom distributed energy systems (Suzuki et al., 23) like miro gas turbine, high temperature uel ell systems et. here are to major streams in developing suh heat exhangers, one is primary surae type and the other is plate-in type. Primary surae types have a potential to ahieve the demanding requirements at relatively lo ost as they do not need brazing proess and thereore intensive investigations are reently going on (MDonald, 2, Iai et al., 23). Plate-in types, on hih this study ouses, have been being investigated or deades and the aumulated inormation is available in handbooks and literature. For urther evolution o plate-in types, a development o eetive in geometry ould be a key. Applying porous materials, suh as ormed metals, as extended surae to ompat plate-in heat exhanger (Kim et al., 2) is one o the interesting options reently proposed. It is an attrative and probably eetive ay to enhane heat transer beause o its large surae area density. he materials o the ormed metals, hoever, are still limited today and ontrolling the detailed geometry is not an easy task. In this paper e propose a ne type o extended surae based on thin metal ire, hih may be onsidered a type o porous material. As a irst step o the study e ous on one o the most basi ire strutures, namely ire springs. Use o the ire springs as extended surae has many advantages. A large surae area density an be ahieved partiularly hen thin ires are used. Geometri parameters o ire springs suh as ire diameter, ross setional shape o ires, spring diameter, spring pith and spring length an easily be ontrolled, hih allos us to have many design options to ahieve heat transer requirements. here is a ide variety o material available too. I the ire diameter is small, spring in ill orm a lexible struture, unlike the onventional rigid ins, hih is also an advantage beause suh lexible struture ill release the thermal stress. In addition, there is no problem or mass prodution and thereore it has a potential to be ost eetive. In this study, the perormane o various ire springs as extended heat transer surae is experimentally investigated at relatively lo Reynolds number onditions. Fundamental data suh as averaged Nusselt number and rition ator o those spring ins are aumulated and their eetiveness is disussed. EXPERIMENL SEUP 154

2 he experimental apparatus used in this study is shematially illustrated in Fig. 1. he apparatus has mainly three parts, the air dut inluding the test setion, a heater and its ontroller and the measuring devie to aumulate the time histories o luid inlet and outlet temperature at the test setion. Working luid (Air) is supplied by a ompressor. It los through a lo meter, a retiier, a heater and the test setion, and then exits into the atmosphere. Air lo rate an be ontrolled by adjusting the regulator. Figure 2 shos the test setion part o the apparatus. It is a dut having a retangular ross setion. Its height, H, idth, W and streamise length, L, are 5., 1 and 5 mm respetively. emperatures o luid at both inlet and outlet o the test setion are measured ith total 3 K-type thermoouples ith diameter o.1 mm, 15 at the inlet and the other 15 at the outlet, and their time histories are reorded at a sampling requeny o 5 Hz. Averaged heat transer oeiient o the spring ins is evaluated applying a transient Single-blo method, one o the unsteady measuring methods, hile measuring the pressure drop at the test setion under a steady state ondition. Details o the transient method are introdued in the next setion. Unit spring that is applied as extended surae in this study has a shape shon in Fig.3. he spring outer diameter is the same as the dut height (5mm), hih means that there is only one layer o the springs in the test setion. Spring length is also ixed at 5 mm throughout this study, thereore, total 2 springs are plaed inside the test setion. Spring pith, p, and the ire diameter, d, are the ontrolling parameters. he geometri parameters o the spring ins examined in this study are summarized in able 1. he symbol "3_4" in this table, or example, stands or that the diameter o the ire is.3mm and its spring pith is.4mm. Pith ratio is the ratio o pith over the ire diameter (p/d). he ire diameter and spring pith are varied in the ranges.3<d<.9 mm and.4<p<1.8mm, respetively. ε appears in the table is the porosity in the test setion that is evaluated as V in ε 1 (1) WHL V in is obtained by dividing the mass o the ins inserted in the test setion ith the density o the in material (SUS34). 4 is the surae area o the in plaed A in V d in in the test setion. It is alulated assuming that a spring is a irular ylinder o diameter d. he total heat transer area inside the test setion an be expressed as A A + WL (2) ht in 2 here point ontat beteen the spring ins and alls is assumed. Figure 1 Experimental apparatus. Figure 2 est setion. Figure 3 Spring shaped in. Case 1 Case 2 Figure 4 Spring in arrangements in test setion. 155

3 able 1 Geometri parameters o examined spring ins. mass and A in are total values o 2 springs plaed in test setion. Beause the shape o a spring is obviously inhomogeneous, eets o spring arrangements inside the test setion are expeted to be large. As typial ases, to types o spring in arrangements are employed in this study as shon in Fig.4. In Case 1, the springs are plaed as the spring axis to be parallel to the main lo diretion. In Case 2, on the other hand, spring axis is plaed ith a right angle to the main lo diretion. Charateristi length dh deined as (Manglik and Bergles, 199) 4εWHL dh (3) A ht is employed as it is oten used as a harateristis length or pin ins (Brigham and VanFossen, 1984) or sreen mesh (anaka et al. 199). Based on this harateristi length, Reynolds number, rition ator and Nusselt number are deined as ollos. EXPERIMENL PROCEDURE Single-Blo Method u dh U here u (4) ν ε P dh dh 2 2ρ u L (5) h indh Nudh λ (6) transer oeiient o the test setion is igured out. he proedure is based on the olloing theory. he heat input to the test setion is evaluated by monitoring the luid temperature at the inlet. he time response o the luid temperature at the outlet depends on the heat exhange beteen the luid and solid parts (ins and the all) in the test setion. Figure 5 shos typial time histories o the test setion inlet and outlet temperatures measured or to dierent onditions. Note that the values o temperature are normalized as, here inal is the initial temperature and inal is the inlet temperature at the end o measurement. A sharp temperature inrease is observed at the inlet immediately ater turning on the heater. he outlet temperatures ollo it but relatively in mild ays depending on the in perormane inserted in the test setion. Sloer response is a sing o a larger heat exhange beteen the orking luid and solid parts in the test setion. It shos that there is a large dierene in the outlet temperature histories even the time history proiles o the inlet temperature are quite lose as the ases shon in Fig.5. in, out 1..5 inlet temperature outlet temperature Averaged heat transer oeiient is evaluated by applying a single-blo method in this study. In this transient method, a steady lo is irst established ith the heater turned o and thereore all the system has a uniorm temperature distribution. hen the heater is suddenly turned on so that the luid temperature rises. From the dierene beteen the time history o the inlet luid temperature and that o the outlet luid temperature, the averaged heat 156 ase2 7_12ase2. 1 t [s] 2 3 Figure 5 ypial time histories o inlet and outlet normalized temperature.

4 I e apply an adequate heat transer model and provide the time history o inlet temperature as input data assuming an average heat transer oeiient, a predition o the time response o the luid outlet temperature beomes possible. Consequently, by mathing the predited time response o the outlet temperature to the measured one adjusting the assumed heat transer oeiient, e an estimate the averaged heat transer oeiient o the test setion. Numerial Modeling At the early stage o the development o single-blo method, muh eorts ere devoted to ahieve a step hange o inlet luid temperature hih, hoever, is not an easy task beause o the heat apaity o the heater itsel. Lian and Yang (1975) obtained an analytial solution o the outlet temperature response hen the inlet temperature hange is represented by a irst order time lag. Making use o this analytial solution ith the aid o omputers, hih is knon as a modiied single-blo method, enabled us to avoid the diiulty to ahieve a step temperature hange. Releting the development o omputer, use o single-blo based methods is reently expanding (Yagi and Mohizuki, 199, Chang et al., 1999, Luo et al., 21). he method applied in this study is similar to that used by Chen and Chang (1996) here the heat exhange beteen the luid and the side alls are inluded as ell as that beteen the luid and the ins. he major assumptions are as ollos. 1. Physial properties o the luid and solids ere onstant. 2. Flo is steady. 3. Outer side o the alls is ell insulated. 4. Loal temperatures vary only in streamise diretion (one dimensional). 5. Heat ondution is negleted 6. here is no heat exhange beteen ins and alls. he governing equations are one dimensional unsteady energy equations or orking luid, in and alls that an be expressed in non-dimensional orms as ollos: <Fluid> t <Fin> <Wall> R R + x NU in ( in ) + NU in, in NU ( in in t, NU ( t ) ) ( ) (7) (8) (9) x ερ A L L x t ε ti L ρ AU U NU R in h in A ρ A U m in NU ρ in in, in R, ερ A L h A U m ερ A L hese equations are numerially solved until a set o NUs are obtained under the initial and boundary onditions shon belo. <Initial ondition> t (, x ) (, x ) (, x <Boundary ondition> x ( t,) in A t t i ) in the boundary ondition is the normalized inlet temperature obtained in the experiment. Note that it is not neessary to be expressed as a irst order time lag beause in this study the above equations are numerially solved or every experimental run. An overall piture o the employed method is shematially illustrated in Fig.6. ime histories o both inlet and outlet temperature are experimentally aumulated. he eqs. (7-9) are numerially solved assuming NU in and NU. In the numerial proess, the measured inlet temperature is used as the boundary ondition. he numerially predited outlet temperature is ompared ith the measured outlet temperature response and i they math ell, the assumed NUs are judged to be a solution. I they do not math the values o NUs are reneed and the same proedure repeats until a onverged solution is obtained. here are several ays to evaluate i the to response urves, that are numerial one and measured one, math or not, suh as maximum slope method, ive point mathing, initial rise method et. hese methods are rather simple and easy to be applied, but use only limited part o the obtained data. In this study a method knon as a diret urve mathing is employed here the entire response urve during the measuring time interval is ompared ith the numerial ounterpart. A mean residual o the olloing orm is introdued and NUs are adjusted so that the mean residual is minimized. 2 (,.,.) meas th e (1) N.5 here, inal in in inal inal he value o residual is aeted by the measuring time interval. oo short or too long measuring time interval tends to inrease the residual. Ater a series o test experiments, the time interval as ixed at 3 seonds throughout this study. Under this measuring interval, mean residual 157

5 hange o NUs, in the ases here the atual NUs take large values. Figure 7 is an example omparing the numerially predited outlet temperature proile to that is obtained in experiment. Solid line shos the onverged predition and NUs used in this alulation ere employed as the inal results. o broken lines in the igure sho numerial results obtained by setting the NU in to be 2 perent lager or smaller than the solid line ase. heir deviation rom the experimental data an learly be onirmed. Larger NU leads a sloer time response o the outlet temperature. RESULS AND DISCUSSIONS Figure 6 Flohart o Single Blo Method. o assess the experimental proedure, an oset in, ommerially available, is inserted in the test setion and both heat transer and pressure drop measurements ere onduted. he obtained results ere ompared ith the empirial ormula proposed by Manglik and Bergles (199). Figure 8 shos j ator and rition ator or the oset in. In the igure, it seems the agreement o the present j ator ith the empirial ormula is good enough to disuss the heat transer perormane. he rition ator obtained shos an even better agreement ith that o the empirial ormula as shon in the igure. hese omparisons validate a disussion based on the experimental data obtained in this study. he obtained data o oset in is used as a reerene in the latter igures to evaluate the perormane o spring ins % ase1.1 Manglik and Bergles (empirial) ransient method.2 +2% j.1, exp., theo., theo. (NU in +2%). 1 t [s] 2 Figure 7 Comparison o predited outlet temperature ith experimentally obtained data present Manglik and Bergles (empirial eq.) typially takes a value around.1 degree, and the inrease o the inlet temperature is typially 1 degrees depending on the lo rate. In addition to the evaluation by the residual, there is one more limiter employed in this study that is the normalized outlet temperature at the end o measuring time interval. I it is less than.3, the experimental data as not onsidered valid. his is to avoid the inlusion o less reliable data to disussion, beause the too small temperature inrease at the outlet should be suering the problem o temperature measurement auray. he outlet temperature predition also beomes less sensitive to the dh Figure 8 j-ator and rition ator o oset in experimentally obtained. 158

6 Nu dh (a-1) Case 1 3_4 3_9 3_ dh (b-1) Case _4 3_9 3_ (-2) Case 2 3_4 3_9 3_ Nu dh (a-2) Case 2 3_4 3_9 3_ dh (b-2) Case 2 3_4 3_9 3_ (-2) Case 2 3_4 3_9 3_18 Figure 9 Spring in perormane evaluation (Constant ire diameter, d.3 mm) Figure 9 ompares (a) Nusselt number, (b) rition ator and () heat transer rate per unit volume, Q, in terms o the pumping poer, P, or spring ins having ire diameter o.3 mm. (a-1) to (-1) are or Case 1 arrangement hile (a-2) to (-2) or Case 2. P and Q in igure () are deined as ollos. 3 3 U A µ dhredh Aht P P (11) 2 3 V 2ρ d V h A ht in in + ha h A Q (12) V V In eah igure, results o oset in () are inluded as a reerene. As the ire diameter is onstant, larger spring pith orresponds to a larger porosity and less in surae area. It is shon that the spring arrangement strongly aets the perormane o spring ins. In Case 1, larger spring pith results in larger Nu dh and dh, that is ompletely opposite in Case 2. Nu dh in Case 1 shos lear dependeny on but it is not signiiant in Case 2 taking almost onstant values. he values o Nu dh and dh in Case 1 are generally omparable or less than hile they take muh higher values in Case 2 at any studied. Fig.9(-1) and (-2) sho that heat transer perormane is alays better than that obtained ith Case 1 arrangement, hen it is evaluated in terms o pumping poer. In Case 2 arrangement, on the other hand, there are ases hih ahieve larger heat transer rate than at a onstant pumping poer. In Fig.9 (a-2) Nu dh shos small h Case 1 5_12 7_12 9_ Case 2 5_12 7_12 9_ Figure 1 Spring in perormane evaluation (Constant pith, p1.2 mm)

7 Nu dh (a-1) Case 1 5_1 7_14 9_ dh (b-1) Case _1 7_14 9_18 (-1) Case _1 7_14 9_ Nu dh (a-2) Case 2 5_1 7_14 9_ dh (b-2) Case 2 5_1 7_14 9_ (-2) Case 2 5_1 7_14 9_18 Figure 11 Spring in perormane evaluation (Constant pith ratio, p/d 2.) dependeny on the spring pith. Q dependeny on spring pith in Fig.9(-2) is mainly due to the dierene in in surae area. Similar perormane evaluations are shon in Figs.1 and 11. Figure 1 ompares spring ins having same spring pith, p1.2 mm. In this ase pith ratio and porosity beome smaller as the ire diameter inreases. Figure 11 ompares spring ins having same spring pith ratio, p/d2.. Porosity takes smaller value or springs ith larger ire diameter. Nu dh and dh or onstant pith ases are omitted or spae limitation. Above disussion or Fig.9 is generally valid or these igures. None o the spring in having Case 1 arrangement reahes to the perormane. hough the pressure loss penalty is relatively mild in Case 1 arrangement, heat transer oeiient is also lo and thereore in surae area is not eetively used. A urther investigation or details o lo and thermal ields is needed to disuss the reason or these eatures o spring ins, but one possibility is that the spring ire is overed by the thermal boundary developed upstream part o the spring itsel in Case 1 arrangement. It seems that the pith ratio is an important parameter in Case 2. In Fig.11(-2), all data points losely all in one line. Furthermore, the spring ins hih sho better perormane than in Fig.9(-2), Fig.1 Case 2 and Fig.11(-2), have pith ratio less than 2. Spring ins having smaller pith ratio tend to sho preerable perormane. 16 CONCLUSIONS Use o thin metal ire strutures as o extended heat transer surae is proposed. he perormane o various ire springs is experimentally investigated at relatively lo Reynolds number onditions. Averaged heat transer oeiient is evaluated by Modiied-Single Blo method hile the pressure drop is measured at a steady state. he major onlusions are as ollos. 1. he arrangement o spring ins in the test setion has a large impat on their perormane and an totally hange its heat transer harateristis even the same springs are used. Case 2 arrangement generally shoed preerable perormane ompared ith Case he geometri parameters o the spring ins suh as ire diameter, spring pith, spring pith ratio aet its perormane as extended surae. In Case 2 arrangement, pith ratio seems to be an important parameter governing its perormane. 3. here are some spring ins hih sho better heat transer perormane than a onventional oset in hen they are evaluated in terms o the total heat transer at a onstant pumping poer. NOMENCLAURE

8 A in : Fin surae area [m 2 ] A : Wall surae area [m 2 ] A : Cross setional area o test setion [m 2 ] A ht : otal surae area [m 2 ] : Heat apaity [J/(kg K)] dh : Hydrauli diameter [m] d : Wire diameter [m] dh : Frition ator H : Channel height o test setion [m] h : Mean heat transer oeiient [W/(m 2 K)] j : j ator Nu/(RePr 1/3 ) L : Streamise length o test setion [m] m : Mass lo rate [kg/s] m in : Mass o in [kg] m : Mass o all [kg] NU : Number o transer unit o in Nu dh : Averaged Nusselt number P : Pressure drop [Pa] P : Pumping poer per volume [W/m 3 ] Pr : Prandtl number p : Spring pith [m] : Reynolds number based on dh, u dh/ν : Initial luid temperature [K] inal : Fluid inlet temperature at the end o measurement [K] : emperature [K] in : Fluid temperature at test setion inlet [K] out : Fluid temperature at test setion outlet [K] t : ime [s] u : Fluid mean veloity in test setion U /ε U : Fluid mean veloity at test setion inlet [m/s] V : Volume o test setion WHL W : Width o test setion [m] ε : Porosity in test setion λ : hermal ondutivity o luid [W/(m K)] µ : Visosity o luid [Pa s] ν : Kineti visosity o luid [m 2 /s] ρ : Density [kg/ m 3 ] subsript : Fluid in : Fin : Wall supersript : Non dimensional value Aknoledgement his study is partially supported by Japan Siene and ehnology Ageny (JS) as a researh in CRES projet Miro Gas urbine and Solid Oxide Fuel Cell Hybrid Cyle or Distributed Energy System, and by the Ministry o Eduation, Siene, Sports and Culture, Grant-in-Aid No REFERENCES Brigham, B.A., and VanFossen, G.J., 1984, Length to Diameter Ratio and Ro Number Eets in Short Pin Fin Heat ranser, J. Engineering or Gas urbines and Poer, Vol. 16, pp Chang, Z.C., Hung, M.S., Ding, P.P., and Chen, P.H., 1999, Experimental evaluation o thermal perormane o Giord-MMahon regenerator using an improved singleblo model ith radial ondution, Int. J. Heat Mass ranser, Vol.42, pp Chen, P.H., and Chang, Z.C., 1996, An improved model or the single-blo measurement inluding the nonadiabati side all eet, Int. Comm. Heat Mass ranser, Vol. 23, No. 1, pp Chen, P.H., Chang, Z.C., and Huang, B.J., 1996, Eet o oversize in ire-sreen matrix to the matrix-holding tube on regenerator thermal perormane, J. Cryogenis, Vol. 36, pp Iai, H., Watanabe, H., atsumi, K., and Suzuki, K., 23, Conjugate heat transer or a minimal unit model o ounter lo type orrugated primary surae heat exhangers, International Journal o Heat Exhangers, Vol.4 No.1, pp Kim, S.Y., Paek, J.W., and Kang, B.H., 2, Flo and Heat transer orrelations or porous in in a plate-in heat exhanger, ASME J. Heat ranser, Vol. 122, pp Lian, C.Y., and Yang, W.J., 1975, Modiied Single- Blo ehnique or Perormane Evaluation on Heat ranser Suraes, J. Heat ranser. Ser.C,97, pp Luo, X., Roetzel, W., and Ludersen, U., 21, he single-blo transient testing tehnique onsidering longitudinal ore ondution and luid dispersion, Int. J. Heat Mass ranser, Vol. 44, pp Manglik, R.M., and Bergles, A.E., 199, he thermalhydrauli design o the retangular oset-strip-in ompat heat exhanger. Comapt Heat Exhangers (Edited by R.K.Shah, A.D.Kraus and D. Metzger), Hemisphere, pp MDonald, C.F., 2, Lo-ost ompat primary surae reuperator onept or miroturbines, Applied hemal Engineering, Vol. 2, pp Suzuki, K., and Iai, H., 23, High Perormane Ruperators or the Solid Oxide Fuel Cell-Miro Gas urbine Hybrid System, Pro. o 4th International Conerene on Compat Heat Exhangers and Enhanement ehnology or the Proess Industries, pp anaka, M., Yamashita, I., and Chisaka, F., 199, Flo and Heat ranser Charateristis o the Stirling Regenerator in an Osillating Flo, JSME International Journal, Series II, Vol. 33, pp Yagi, Y., and Mohizuki, S., 199, Development o a Modiied Single-Blo Method (An Appliation to Parallel Plate Heat ranser Suraes), JSME, B, Vol.56, No.529, pp , (in Japanese). 161