Application Of Single Blow Technique For Heat Transfer Measurement In Packed Bed Of Vegetables

Transcription

1 Purdue Univerity Purdue e-pub International Rerigeration and Air Conditioning Conerence School o Mechanical Engineering 2016 Application O Single Blow Technique For Heat Traner Meaurement In Packed Bed O Vegetable Dariuz Butrymowicz Bialytok Univerity o Technology, ul. Wiejka 42A, Bialytok,15-351, Poland, d.butrymowicz@pb.edu.pl Adam Lapinki Bialytok Univerity o Technology, ul. Wiejka 42A, Bialytok,15-351, Poland, a.lapinki@doktoranci.pb.edu.pl Jerzy Gagan Bialytok Univerity o Technology, ul. Wiejka 42A, Bialytok,15-351, Poland, j.gagan@pb.edu.pl Kamil Smierciew Bialytok Univerity o Technology, ul. Wiejka 42A, Bialytok,15-351, Poland, k.mierciew@pb.edu.pl Follow thi and additional work at: Butrymowicz, Dariuz; Lapinki, Adam; Gagan, Jerzy; and Smierciew, Kamil, "Application O Single Blow Technique For Heat Traner Meaurement In Packed Bed O Vegetable" (2016). International Rerigeration and Air Conditioning Conerence. Paper Thi document ha been made available through Purdue e-pub, a ervice o the Purdue Univerity Librarie. Pleae contact epub@purdue.edu or additional inormation. Complete proceeding may be acquired in print and on CD-ROM directly rom the Ray W. Herrick Laboratorie at Herrick/Event/orderlit.html

2 2669, Page 1 Application o ingle blow technique or heat traner meaurement in packed bed o vegetable Dariuz BUTRYMOWICZ*, Adam ŁAPIŃSKI, Jerzy GAGAN, Kamil ŚMIERCIEW Bialytok Univerity o Technology Wiejka 45C, Bialytok, , Poland, d.butrymowicz@pb.edu.pl * Correponding Author ABSTRACT The non-invaive meaurement o the mean heat traner coeicient or the packed bed o ruit and vegetable may be thought a till open iue. There i a clear need or the aement o heat traner condition or variou type o ruit and vegetable in order to accurately predict the thermal load that i neceary to elect rerigeration equipment or cold torage chamber. Additionally, there i igniicant development in numerical modeling o heat and ma traner procee in cold torage chamber or ruit and vegetable which require precie heat traner decription. The theoretical bai or the indirect meaurement approach o heat traner coeicient or the packed bed o vegetable that i baed on ingle blow technique i preented and dicued in the paper. The approach baed on the modiied model o Liang and Yang wa preented and dicued. The teting tand conited o a dedicated experimental tunnel along with auxiliary equipment and meaurement ytem are preented. The geometry o the teted matrice were preented. Selected experimental reult o heat traner and preure drop are preented and dicued or the packed bed o Chinee cabbage. Thee reult were preented a dimenionle relationhip. 1. INTRODUCTION The paper deal with approach o the meaurement o heat traner and low reitance in packed bed o ruit with Chinee cabbage a an exemplary cae. The knowledge on heat traner condition during cooling o vegetable and ruit i neceary or the deign o the cold torage chamber. Uually meaurement o the low reitance in packed bed o vegetable or ruit i not very diicult. However, the meaurement o the heat traner coeicient may be thought a a challenge in mot cae due to very complicated geometry o the bed element. Thi i the reaon why it i impoible to apply the implet direct method o the meaurement o the heat traner coeicient that are baed on the direct meaurement o the temperature o the vegetable, ga temperature ditribution a well a heat lux denity. Thi mean that in thi cae an indirect method mut be applied. The methodology o uch meaurement i propoed in thi paper. 2. METHODOLOGY OF HEAT TRANSFER COEFFICIENT MEASUREMENT The o-called ingle blow technique i thought to be an eicient method ued to experimentally determine the average heat traner coeicient α in the packed bed o vegetable. Heat traner coeicient i baed on the actual urace area o the bed element and take into account convective heat traner between ga and vegetable urace. In the dicued method the average heat traner coeicient α to be ound i determined by mean o the comparion o the actual temperature proile o ga (that i heated or cooled in the teted packed bed) meaured at the outlet o the teted packed bed with the predicted one on the bai o the theoretical model. The agreement between the experimental temperature proile and theoretical prediction depend on the heat traner coeicient α that i applied in the theoretical model o heat traner. Variou theoretical approache may be applied in order to predict temperature proile at the outlet or given inlet condition and the vegetable geometry. Below hort review o theoretical model which may be applied in the ingle blow method i preented. 16 th International Rerigeration and Air Conditioning Conerence at Purdue, July 11-14, 2016

3 2669, Page 2 The meaurement in the ingle blow method i to record the time variability o ga temperature proile directly at the inlet and outlet o the teted packed bed which i caued by witching the heating ection on or o i o key importance or the dicued method. The ollowing condition need to be met beore the meaurement: ga low i teady tate (contant velocity); the temperature in the meaurement ection i contant and equal in the axial and radial direction. Temperature proile hould be meaured or dierent velocitie, involving the whole range o Reynold number expected in the range o the operating condition o the packed bed. Figure 1. Energy balance or luid () and olid body () or heater exchanger element Temperature proile recorded during the ingle blow technique meaurement are ued when olving equation modelling heat exchange in the teted packed bed. The meaured temperature leap or proile at the inlet to the tet ection i the boundary condition or the model equation. The meaured temperature proile at the outlet o the tet ection hould be predicted on the bai o the model. However, the theoretical and the meaured outlet temperature proile may be compared in everal way that may be thought a equivalent. The mot baic one-dimenional model o tranient heat traner between a porou body and a luid lowing through it i the model propoed by Anzeliu (1926). Thi model became the bai or many urther modiication and i till being developed by removing the numerou impliication aumed by the author in order to obtain analytical olution o the model equation. Anzeliu (1926) model i baed on the energy balance or a olid body element (porou or perorated packing o the exchanger) in the ituation preented in Fig. 1. The ollowing aumption were made: the phyical propertie o luid are independent o temperature; ga low i teady tate ( m = cont); the olid ha a homogeneou tructure; the thermal conductivity perpendicular to the low direction i ininite (both or the luid and or the olid body); the thermal conductivity o the luid in the low direction equal to zero; the external caing o the packed bed i adiabatic; initially the temperature in the exchanger i uniorm (T = T = T i ); initially the luid temperature leap rom T i to T 1 and then it remain teady. Balance equation o the element o luid and olid body in the non-dimenional orm are a ollow: 16 th International Rerigeration and Air Conditioning Conerence at Purdue, July 11-14, 2016

4 where non-dimenional time i deined a ollow: and non-dimenional coordinate i deined a: 2669, Page 3 T T T, z (1) 2 T T NTU T T 2, z (2) A t, (3) mc x z NTU. (4) L Ater the tranormation o the above equation, two new coeicient appear in the energy balance or the olid body, namely the number o heat traner unit: A NTU, (5) mc and a parameter connected with olid body thermal conductivity k in the direction θ i parallel to the low direction: k A. (6) mc I the conductivity can be ignored, the above equation have analytical olution developed by Schumann (1929) in the orm: n ( z ) n d 1 e z J 2i z n 0, (7) d z n0 n ( z ) n d 1 e z J 2i z n 0, (8) n1 d z where i non-dimenional temperature deined a ollow: T Ti. (9) T T The ditribution o temperature obtained rom the above Schumann analytical olution can be ued to determine the heat traner coeicient i the experiment well agree with the boundary and initial condition aumed in the model. Then, comparing the meaured temperature ditribution T (t) at the packed bed (packed bed) outlet with the theoretical temperature ditribution the pot z = NTU, the bet it will be achieved i the value peciic or the teted exchanger i ued (Furna, 1932). Intead o comparing the temperature proile, their derivative can be ued, and in particular their maximum value. Locke (1950) dierentiated the olution or the outlet temperature T 2 = T (, z=ntu) at contant NTU and obtained the relationhip or the lope S o the curve decribing evolution o temperature T 2 in dimenionle coordinate. Thi make it poible to determine the derivative rom the experimental proile o outlet temperature T 2 (t) and the experimental value S max. For that value it i poible to obtain the correponding NTU value, and then ind the needed value o coeicient. Solving the model equation taking into conideration heat conductivity along the olid body i only poible with numerical method. The neceary calculation were done e.g. by Howard (1964), and hi inding in the orm o table and graph o unction NTU = (S max ) or elected value within the range o [ , ] are alo included in the paper preented by Pucci et al. (1967). The eect o the parameter on the determination o NTU i igniicant, epecially when NTU > 10. Due to the coniderable lope o the curve NTU = (S max ) thi approach o L 1 i 16 th International Rerigeration and Air Conditioning Conerence at Purdue, July 11-14, 2016

5 2669, Page 4 determination o with the ue o maximum lope S max involve coniderable error or certain combination o parameter S max and. The accuracy o determining o heat traner coeicient uing the ingle blow method can be improved by extending the Anzeliu model, providing that: the leap o the inlet temperature o the luid occur not immediately; heat conductivity in the olid body occur not only in the axial direction but alo in the radial direction; the external wall o the packed bed (packed bed) i not adiabatic; conequently there i a radial temperature gradient in the packed bed; preure drop o the luid lowing through the packed bed (packed bed) caue change o it temperature due to Joule-Thomon eect; the ditribution o luid velocity in the axial direction i heterogeneou due to diturbance o ga low occurring at the element o the packed bed (packed bed). The modiication o the initial condition o Schumann olution propoed by Liang and Yang (1975) minimize the problem connected with experimental realiation o the non-immediate temperature leap at the teted exchanger inlet. Liang and Yang model wa urther extended by Cai et al. (1984) by taking into conideration alo the conductivity o the olid body in the axial direction. The olution o thi model could be obtained by numerical procedure, however. In thi cae the temperature proile at the exchanger inlet can be any unction o time. Chen and Chang (1996) added to the model an equation decribing the heat traner between luid and the caing. They alo took into account the Joule-Thomon eect (Chen and Chang, 1997), and inally alo radial conductivity (Chang et al., 1999). Luo et al., 2001, highlighted the impact o diturbance o luid low caued by the element o exchanger packing (o-called axial diperion). Taking into conideration that the uually the meaurement cover large number o tet run then the mot ueul will be the analytical olution o the temperature proile at the outlet o the teted packed bed, however. One o the ource o inaccuracy o the heat traner coeicient determined by mean o the ingle blow method i the diiculty o the realiation o the immediate temperature leap at the exchanger inlet. Due to the thermal capacity o the heater any temperature change alway occur at a certain time pan. Liang and Yang (1975) propoed the dimenionle inlet temperature proile obtained in the dicued tet method ater witching the heater on or o a the exponential unction: / *,0 1 e, (10) where * i an experimentally determined dimenionle contant. The above temperature proile a the boundary condition or modiied Anzeliu model equation (Liang and Yang, 1975). In the equation or luid energy balance it thermal capacity wa taken into conideration o the equation or ga energy balance wa obtained a ollow: b1 b2, (11) z and in the olid body the thermal conductivity wa ignored o that Eq. (2) wa ued. In the dimenionle orm thi equation can be preented a ollow:. (12) The coeicient b 1 and b 2 in Eq. (11) are contant and deined a ollow: v mc b1 b, b 2 2 A mc, (13),min where v i the volume o luid inide the packed bed per length in the low direction, and A,min i the mallet croection urace area o the packed bed available or the lowing luid. It mut be remembered that temperature T 1, neceary to calculate hould be the value ettled at the inlet ater a uiciently long time ater witching the heater on or o. Equation (11) and (12) with boundary condition Eq. (10) and the ollowing initial condition: (0, z) = (0, z) = 0, (14) were olved (Liang and Yang, 1975) with the ue o the Laplace tranorm which gave a et o equation: 16 th International Rerigeration and Air Conditioning Conerence at Purdue, July 11-14, 2016

6 p d 2669, Page 5 b1 b2, (15) dz p, (16) 1 p,0 * 1, (17) p p * where denote the tranorm, and p i it argument. The olution to the et o Eq. (15) (17) in relation to i a ollow (Liang and Yang, 1975): p b 2 exp 1 z b1 1 p. (18) * 1 p p * Finding the invere Laplace tranorm or Eq. (18) at z = NTU, the ollowing relationhip decribing the proile o dimenionle temperature at the packed bed outlet are obtained: a) i < t* (i.e.: t < L/w ): (, NTU) = 0 (19) b) when t* (i.e.: t L/w ): t* 1 / * b2t* t* * * *, NTU e e I02 b2t t e I02 b2t d d. (20) * t* 0 In the above relationhip the ymbol t* denote dimenionle time deined a ollow: NTU t*, (21) b1 and w i the mean velocity o luid in the packed bed. Provided the relatively high numerical cot connected with the application o more complex mathematical model o heat traner in regenerator, the author decided that the ue the above modiied Liang and Yang model (Liang and Yang, 1975). The key element in thi model i the conideration o the exponential character o the inlet temperature proile which allow to avoid a coniderable error reulting rom the impoibility to execute an immediate leap o temperature at the inlet o the teted packed bed. It i recognized that the accuracy o thi model hould be atiactory or indirect meaurement o the heat traner coeicient. 3. TEST APPARATUS The experimental part o the ingle blow method i carried out in a wind tunnel. Temperature and preure meaurement point are placed at the inlet and outlet o the teted packed bed. Static preure dierence i meaured in order to determine the rictional low reitance. In addition, the velocity o ga low through the packed bed hould be alo meaured. It may be uggeted that the temperature o ga lowing through the packed bed hould be raied above the ambient temperature by approximately K. An electrical heating coil made o reitance wire may be applied or thi purpoe. Due to the required velocity homogeneity, the heating coil hould diturb the low a little a poible. The tructure o the coil alo aect the ga temperature proile obtained ater witching it on or o which i important rom the point o view o the theoretical model applied to draw up the reult o the meaurement. The implet model oer the analytical olution or which an immediate temperature leap at the meaurement ection inlet i aumed. Some o the theoretical model aume the inlet temperature proile that i decribed by an exponential unction achieved in the experiment. In more complicated numerical model there i no limitation concerning the proile o inlet temperature o the retriction concerning the heating ection (mainly it length in the direction o ga low) are le important. Due to the homogeneity o velocity proile required in the 16 th International Rerigeration and Air Conditioning Conerence at Purdue, July 11-14, 2016

7 2669, Page 6 cae o the theoretical model, it i recommended to place a low traightener (in the orm o a honeycomb packed bed) beore the tet ection. In order to eliminate the inluence o diturbance generated at the tunnel outlet geometry, a imilar low traightener hould be alo placed at the outlet o the tet ection. Reduction o the channel hydraulic diameter between the tunnel inlet and the tet ection i required in order to reduce turbulence level in the low. The tet tunnel conit o three ection a it i how in Fig. 2. Air low rate in the tunnel wa controlled by mean o change o the centriugal exhaut an rotational peed. The electric heater capacity wa alo controlled. The tet tand conit o three part: the inlet ection with an electrical heater; the meaurement ection with the teted packed bed o vegetable; an exhaut an with a diuer. Section Section Section Figure 2. Schematic diagram o the tet tunnel: 1 low rectiier; 2 air low rate and temperature enor; 3 - electric air heater; 4 conuor/diuer; 5 thermocouple net at the teted bed inlet; 6 moiture enor; 7 preure gauge; 8 teted packed bed o vegetable; 9 thermocouple net at the teted bed outlet; 10 exhaut an Figure 3. Schematic o the tet ection: 1- teted packed bed; 2- thermocouple net at the bed inlet; 3 - thermocouple net at the bed outlet; 4- preure gauge; 5- air moiture enor The chematic o the tet ection i how in Fig. 3. The temperature ditribution at the inlet and outlet to the tet ection were meaured by mean o the thermocouple net. Baed on thee meaurement the average temperature o air at the inlet and outlet were obtained under tranient operating condition. The ollowing baic parameter are meaured on the tet tand: air temperature at the tunnel inlet; 16 th International Rerigeration and Air Conditioning Conerence at Purdue, July 11-14, 2016

8 2669, Page 7 air temperature at the teted bed inlet ; air temperature at the teted bed outlet; tatic preure drop at the teted bed; dynamic preure at the tunnel inlet; air humidity at the channel inlet and outlet; electric heater on/o ignal. Thermocouple o the type o TP201 J o the diameter 0.5 mm were applied. The thermocouple o the open junction type were applied which enabled low thermal inertia. The thermocouple were calibrated or three temperature level with ue o the calibration Pt100 enor. The maximum dierence between calibration enor reading and thermocouple reading were not exceed ±0.15 K. The reported meaurement were carried out or the cae o Chinee cabbage. The prepared packed bed o Chinee cabbage beore inertion in the tet tunnel were how in Fig. 4. The teted cabbage wa inerted in the gauze container. Figure 4. The packed Bed o Chinee cabbage prepared or inertion to the tet channel The dimenion o the prepared packed bed were a ollow: width m; height m; length m; number o cabbage 12. The detailed parameter o the teted bed were preented in Table 1. packed bed ma [kg] Table 1.Parameter o the teted bed o Chinee cabbage total volume [dm 3 ] volume occupied by vegetable [dm 3 ] volume o ree pace [dm 3 ] poroity outer urace area o vegetable [m 2 ] denity [kg/m 3 ] m m V V m V p A p I II III average The average ma o the teted bed wa kg; the average ma o the ingle cabbage wa 1.35 kg; average heat traner urace area o the ingle cabbage m 2. The average hydraulic diameter o the packed bed d h may be aeed on the bai o poroity: 16 th International Rerigeration and Air Conditioning Conerence at Purdue, July 11-14, 2016

9 d h 2669, Page 8 4Ap Vp 4 4, (22) U A a p where: A p urace area o ree pace; V p volume o ree pace; U p perimeter o ree pace; V - total volume o ree pace; - poroity (V p /V); a peciic urace area (A p /V). p 4. TEST RESULTS The obtained reult baed on the application o the decribed ingle blow technique or the packed bed o Chinee cabbage were preented in Table 2. It hould be noted that Reynold number Re wa baed on low parameter in the equivalent channel inide the packed bed and w i velocity at the teted bed inlet. On the bai o the obtained experimental reult the ollowing correlation decribing heat traner in packed bed o Chinee cabbage may be propoed: Nu Re Pr. (23) Table 2. Reult o heat traner meaurement w [m/] Δp [Pa] Re α [W/m 2 K] Nu Pr j D Figure 5. Comparion o meaured Nuelt number Nu with propoed correlation eq. (23) The comparion o the meaurement reult with propoed dimenionle relationhip eq. (23) i preented in Fig. 5. It i worth to note that relatively high heat traner coeicient were achieved in the reported tet. Thi may be 16 th International Rerigeration and Air Conditioning Conerence at Purdue, July 11-14, 2016

10 2669, Page 9 attributed to the high heat traner urace area enhancement o the teted cabbage ince the average outer urace area wa taken into account in the meaurement procedure. 5. SUMMARY Thi paper preent the methodology o the meaurement o heat traner coeicient or packed bed compoed o the vegetable. The reported meaurement were carried out or the cae o Chinee cabbage. It i neceary to emphaize the neceity to develop an indirect method o meaurement o the heat traner coeicient by mean o ingle blow technique. The current reult involve the modiication o thi method propoed by Liang and Yang (Liang and Yang, 1975). The author believe that the propoed methodology proved to be ueul and produced reliable value o coeicient given by relationhip eq. (23) or the teted packed bed o Chinee cabbage. Further development o the propoed methodology may be propoed or the cae o the other vegetable. NOMENCLATURE A heat traner area, m 2 A cro ection, m 2 b 1,b 2 coeicient (contant) c peciic heat at contant preure, J/(kg K) d h average hydraulic diameter o the packed bed, m Fanning low reitance actor Darcy low reitance actor D G ma lux denity, kg/(m 2 ) I 0 modiied Beel unction o the irt kind o zero order j Colburn coeicient J 0, J 1 Beel unction o the irt kind o zero and irt order, repectively, k heat conduction, W/(m K) L length o the packed bed, m m ma, kg m ma low rate, kg/ Nu Nuelt number NTU number o thermal unit p argument Pr Prandtl number Re Reynold number S max maximum lope t time, t* dimenionle time T temperature, C, K w mean velocity o luid, m/ x ditance between inlet and outlet o the packed bed, m z, y dimenionle ditance to the packed bed inlet heat traner coeicient, W/(m 2 K) η variable integration dimenionle temperature dimenionle axial conduction parameter ξ variable integration denity, kg/m 3 dimenionle time ν volume o luid inide the packed bed per length, m 3 /m 16 th International Rerigeration and Air Conditioning Conerence at Purdue, July 11-14, 2016

11 2669, Page 10 ubcript: luid i initial value olid (packed bed) w wall o exchanger 1, 2 packed bed inlet and outlet, repectively REFERENCES Achenbach E. (1995). Heat and low characteritic o packed bed. Experimental Thermal and Fluid Science 10, ANSYS FLUENT Theory Guide, April ASHRAE Handbook Rerigeration (2006). Alvarez G., Bournet P.-E., Flick D. (2003). Two-dimenional imulation o turbulent low and traner through tacked phere. International Journal o Heat and Ma Traner 46, Anzeliu A. (1926). Über Erwärmung vermittel durchtrömender Medien. Zeitchrit ür Angewandte Mathematik und Mechanik 6, No 4, Becker B.R., Fricke B.A. (2004). Heat traner coeicient or orced-air cooling and reezing o elected ood. International Journal o Rerigeration 27, Ben Amara S., Laguerre O., Flick D. (2004). Experimental tudy o convective heat traner during cooling with low air velocity in a tack o object. International Journal o Thermal Science 43, Cai Z.H., Li M.L., Wu Y.W., Ren H.S. (1984). A modiied elected point matching technique or teting compact packed bed urace. International Journal o Heat and Ma Traner 27, Iue 7, Chen P.-H., Chang Z.-Ch. (1996) An improved model or the ingle-blow meaurement including the non-adiabatic ide wall eect. International Communication in Heat and Ma Traner 23, No. 1, Chen P.-H., Chang Z.-Ch. (1997). Meaurement o thermal perormance o cryocooler regenerator uing an improved ingle-blow method. International Journal o Heat and Ma Traner 40, No. 10, Chang Z.-Ch., Hung M.-Sh., Ding P.-P., Chen P.-H. (1999). Experimental evaluation o thermal perormance o Giord McMahon regenerator uing an improved ingle-blow model with radial conduction. International Journal o Heat and Ma Traner 42, Deraeye T., Blocken B., Derome D., Nicolai B., Carmeliet J. (2012). Convective heat and ma traner modelling at air-porou material interace: Overview o exiting method and relevance. Chemical Engineering Science 74, Howard C.P. (1964). The ingle blow problem including the eect o longitudinal conduction. ASME Paper No. 64-GTP-11, preented at Ga Turbine Conerence and Product Show, Houton TX, USA. Kay W.M., London A.L. (1997). Compact packed bed. McGraw-Hill. Kondjoyan A. (2006). A review on urace heat and ma traner coeicient during air chilling and torage o ood product, International Journal o Rerigeration 29, Liang C.Y., Yang. W.-J. (1975). Modiied ingle-blow technique or perormance evaluation on heat traner urace. Tranaction o the ASME Serie C: Journal o Heat Traner 97, Locke G.L. (1950). Heat traner and low riction characteritic o porou olid. Technical Report No. 10, Department o Mechanical Engineering, Stanord Univerity, Stanord CA, USA. Luo X., Roetzel W., Lüderen U. (2001). The ingle-blow tranient teting technique conidering longitudinal core conduction and luid diperion. International Journal o Heat and Ma Traner 44, Pucci P.F., Howard C.P., Pierall C.H. Jr. (1967). The ingle-blow tranient teting technique or compact packed bed urace. Tran. ASME: Journal o Engineering or Power 89, Schumann T.E.W. (1929). Heat traner: a liquid lowing through porou prim. J. Franklin Int. 208, No 3, th International Rerigeration and Air Conditioning Conerence at Purdue, July 11-14, 2016

12 2669, Page 11 Verboven P., Datta A.K., Anh N.T., Scheerlinck N., Nikolai B.M. (2003). Computation o airlow eect on heat and ma traner in a microwave oven, Journal o Food Engineering 59, ACKNOWLEDGEMENT The work wa completed within the tatutory activitie S/WM/2/ th International Rerigeration and Air Conditioning Conerence at Purdue, July 11-14, 2016