Numerical Modeling of Combined Heat and Mass Transfer in an Adsorbent Bed with Rectangular Fins

Transcription

1 ICMEAT-88 Numerical Modeling of Comined Heat and Mass Transfer in an Adsorent Bed with Rectangular Fins Hoda Taleian, Hamid Niazmand, Mahdi Mahdavikhah Graduate Student, Ferdowsi university of Mashhad; Assosiate Professor, Ferdowsi university of Mashhad; Graduate Student, Ferdowsi university of Mashhad; Astract This aer investigates the erformance of an adsortion chiller working with comosite sorent SWS-L and driven y a low temerature heat source. A three-dimensional non-equilirium numerical model descriing the comined heat and mass transfer in the late finned- heat exchanger is resented. The satial variations of ressure and gas flow inside the adsorent ed along with the internal and external resistances of ed articles are considered to construct a qualified model caale of investigating nearly all the system arameters with minimum restrictions. Flow atterns and ressure distriutions throughout the ed are examined in detail for all cycle hases. It was found that the ed flow atterns are relatively comlex for the isosteric hases due to the simultaneous occurrence of adsortion and desortion rocesses. Furthermore, a detailed investigation is erformed for different fin heights and saces to identify the share of each art of the system from the inut energy during the heating hase. Keywords: adsortion chiller, finned ed, orous medium, numerical modeling, mass transfer Introduction Adsortion chillers, known as environmentally friendly technology, have een receiving much research attention in a way to ecome aroriate alternatives to the CFC-ased vaor-comression ones. As the main drawack of these systems is the weak conductivity of the adsorent ed, incororating extended surfaces is suggested to enhance the heat and mass transfer rocesses throughout the ed; however it is only recently that some studies considered the transient modeling of eds with extended surfaces, which are riefly discussed here. Zhang [] studied a D non-equilirium model, considered oth inter and intra article mass transfer resistances in an adsorer incororating axial fins. Desite the fact that the model was caale of roviding detailed information aout the heat and mass transfer rocesses through the ed very limited information is rovided. Chua et al. [] roosed a D model to study the transient and steady state ehaviors of a finned heat exchanger neglecting the details of the vaor flow through two successive fin saces. Ilis et al. [] erformed a transient two dimensional numerical study on heat and mass transfer in an annular adsorent ed assisted with axial fins. The model was fairly simlified ased on the uniform ressure aroach, which neglects the convective effects of refrigerant vaour throughout the ed. Pei-zhi [] modeled the heat and mass transfer in an adsorent ed with annular fins using a lumed arameter method to calculate temerature variations and adsorate distriution. Riffel et al. [] erformed a transient D modeling of heat and mass transfer is an adsorer with annular finned-. However, in their numerical modeling, an increment in the direction of heat/cooling containing one fin itch was considered and the convective effects of the working in the ed were ignored. Saha et al. [6] resented a dynamic modeling of adsortion ed with annular fins ased on the exerimentally confirmed adsortion isotherms and kinetic data of the sorent. The aim of the study was to analyze the erformance of a new family of comosite sorents called selective water sorents erformance (SWS) in adsortion cooling systems. Niazmand and Dazadeh [7] erformed a detailed D numerical investigation of heat and mass transfer rocesses inside an adsorent ed with annular fins. The velocity, temerature and concentration fields inside the ed are examined in detail for each rocess of the refrigeration cycle. Furthermore, the effects of fin sacing and height on the erformance of the system are discussed. However, the inut energy distriutions etween different arts of the system, which can rovide some insight aout the otimization of these systems, were not resented. Exerimental investigation for an annular finned- adsortion chiller is resented in Reference [8]. Recently, Rezk and Al- Dadah [9] resented an emirical lumed analytical simulation model for a silica gel/water adsortion chiller with rectangular fins neglecting the satial variations of the ressure and temerature throughout the ed This literature survey reveals that there is a shortage of information regarding the articulars of transfer rocesses associated with adsorent eds with extended surfaces. In this aer a detailed three dimensional numerical modeling of a SWS-L/water adsortion ed is resented. The satial variations of ressure and gas

2 flow inside the ed along with the internal and external resistances of ed articles are considered. Therefore, the model can redict heat and mass transfer in eds with different article sizes and orosities. Flow atterns and ressure distriutions throughout the ed are examined in detail for all cycle hases and furthermore some considerations aout the inut energy distriution etween different arts of the ed are given. Mathematical Model As shown in Figure, the adsorent chamer consists of four asic comonents known as adsorent ed, fins, metal and thermal. Adsorent ed Metal Thermal entrance Figure : Adsorent chamer asic comonents In order to model the transort rocesses through the ed, simultaneous thermal analyses of all comonents are required ased on the following main assumtions: - The articles in the adsorent ed are all sherical with uniform size and orosity. - No heat loss is considered through the chamer wall - The adsored hase is assumed to e liquid and the refrigerant vaor is considered to e an ideal gas. - The only variale thermo hysical roerty of the adsorent ed elements is the density of adsorate gas. - The condenser and evaorator are assumed to e ideal with constant temerature during the isoaric hases. Based on aove assumtions, the governing equations of the system include the energy alance of thermal, metal and fins and couled heat and mass transfer equations of adsorent ed. They are as follows:. Thermal Fluid For simlicity and without the loss of generality only axial temerature variation is considered and the axial conduction is ignored due to the high Reynolds numers considered for this flow: C d C u T da. () h A T fins int erface. Metal Tue The transient three dimensional heat transfer equation is exressed y: C d da. () Q fin where if the control volume has an interface with the fin, otherwise is set to zero.. Fins Since fins are very thin, heat transfer is considered two dimensional in the late erendicular to the axis: fin ( C ) fin d ( fin fin ).da Q fin (). Adsorent Bed The energy alance of the adsorent ed is exressed as: gc g C wc a d () w g C gugt. da. da H d The mass alance equation of the refrigerant is given y: w gu g. da d (6) g d Where w is the adsortion rate calculated y: dw Ea * Dso ex / R ( w w) dt RuT (7) * w is the equilirium utake at temerature T and the ressure P. According to [6], the following correlation has een otained exerimentally for SWS-L: P ex * RT w.. 6 (8).78 P ex RT The refrigerant vaor suerficial velocity is determined y Darcy correlation: K a ug P (9) Where the ermeaility of an adsorent ed ( K a ) is calculated y the following equation: K a d ( ) P. Where the heat transfer coefficient is calculated from the following correlation []: Nu. 8 n n. for cooling. Re Pr n. for heating () T / M. 68 P 9. 9d T / M ()

3 Comining Darcy s law, Eq. 9, with the mass alance, Eq. 6, results in the following equation for the ressure distriution throughout the ed: g Ka w d ( g P ). da d () The equation of state is used to evaluate the density of the refrigerant vaor in desored hase: P g R T / M () The erformance of adsortion chillers is mainly evaluated ased on the coefficient of erformance (COP), and secific cooling ower (SCP), defined as: Qeva COP () Q heating Qeva SCP () m tcycle In which Q heating is the total sulied heat to the adsorent ed y the thermal during one cycle and Q eva is the roduced cooling energy in the evaorator calculated according to: Q where m L dt () eva adsortion g v L v is the latent heat, which is estimated y []: [6.9 Lv (6) ( Teva 7..)] To reduce the comutational cost and due to the symmetry, it is assumed that the section of the heat exchanger shown in Figure can e used to reasonaly redict the erformance of the whole set if aroriate oundary conditions are alied. The descried equations are numerically solved y a finite-volume technique using forward differencing scheme for unsteady terms and central differencing scheme for oth of the diffusion and convective ones. The resulting discretized equations are solved using an alternating direction imlicit (ADI) method and the tri-diagonal solver algorithm. direction, 6 control volumes in y direction, 8 grids etween fins and grids in redial direction of the, roduces reasonaly grid indeendent results for the ase case(fin sacing of 6 mm and height of 8 mm). Two different time stes are emloyed for the isosteric and isoaric hases due to the relatively raid variations of the arameters in isosteric hases. It can e shown that adoting. second for isosteric hases and. second for isoaric ones rovides reasonale time accurate results. It must e emhasized that the duration of isoaric heating and cooling hases are determined ased on the occurrence of a certain level of the average adsored amount. The values of w max and w min are chosen according to the % of the maximum and minimum ossile ed asored amount at the ressure of evaorator and condenser and at the temerature of cooling and heating thermal, resectively. Moreover, two cycles are required for the cyclically steady state conditions to e estalished. For validation of the numerical scheme, a comarison has een made with the exerimental data of Restuccia et al. []. A ack of finned stainless steel s is used as the heat exchanger with comosite sorent SWS-L and water as the working air similar to what is used in the resent study. The exeriments were carried out at the standard conditions of a sortion air conditioner at the low desortion temerature of aout 9 ºC. All relevant secifications of the exerimental set u can e found in Restuccia et al. []. In Figure the time variations of the mean ed temerature in the exerimental set u has een comared with its corresonding temerature in the numerical counterart. Reasonale agreement etween the results is an indication of the roer mathematical modeling and the accuracy of the numerical scheme desite the fact that heat exchanger geometry is different from that of resent study ecause the governing equations, mathematical modeling, and numerical rocedure are asically identical. Y FS Z X Present modeling Exerimental data FH/ T(C) 8 Y(m) 6 Cooling/heating fliud Metal z(m) Bed Fins Figure : A magnified view of the control volumes in all different domains Numerous grid indeendency tests have een erformed in search for the otimum numer of grid oints. In this study, emloying 6 control volumes in x time(sec) Figure : Comarison etween numerical and exerimental time variations of the ed mean temerature All related ed secifications and chamer working conditions are listed in Tale.

4 Tale : Parameters value and modeling conditions Parameter Symol Unit Value Inlet cold water temerature Inlet hot water temerature Evaorator temerature Condenser temerature Adsorent mean density Secific heat of adsorent Adsorent thermal conductivity Heat of adsortion Inner diameter of the Outer diameter of the Tcooling K. Theating K 8. Tcond K. Teva K 8. - m C H Jkg kg 6 K - - K 9 Wm. - 6 Jkg.76 Di mm.9 Do mm.7 Fin thickness FT mm. Particle diameter Porosity of the article Porosity of the ed d mm..6.6 Results and Discussion Adsortion chillers go through isosteric and isoaric heating and cooling rocesses in their thermodynamic cycle. In the isosteric heating hase hot water asses through the metal and a strong desortion occurs secially around the, which leads to the formation of local high ressure region and the generation of a radial vaor flow through the ed as shown in Figure. In contrast, adsortion rocess still occurs in the uright corner art of the ed, which can e attriuted to the simultaneous effects of following factors: () it takes longer time for heat to defuse to this region, which is farthest from the heated surfaces, () this region has adsored much less adsorate gas in the revious hase and () the chamer ressure rises due to the vaor accumulation which acts in favor of adsortion in this region. Adsortion around the uright corner of the ed also creates a local region of low ressure, which causes the flow of vaor from disroing areas of the ed and also from the chamer to this region. Fins enhance the heat and mass transfer through the ed consideraly as indicated in Figure (). Relatively strong desortion occurs in the regions close to the fin surfaces as comared to the core region. It is notale that no adsortion haens around this region of the ed and the desored vaor inters the chamer increasing its ressure (m/s) Pa. (m/s) () Figure : Velocity vectors and ressure contours in the x-y lane in the midoint of the two successive fins in isosteric heating hase () x-z lane located at y = in isosteric heating hase Pa.(m/s).. 69.(m/s).. () Figure : Velocity vectors and ressure contours in the x-y lane in the midoint of the two successive fins in isoaric heating hase () x-z lane located at y = in isoaric heating hase When the chamer ressure reaches to the condenser ressure, the condenser valve is oened and the isoaric heating hase egins. The heat transfer to the ed continues and the desored vaor leaves the chamer 7

5 867 9 toward the condenser to kee the chamer ressure constant. Tyical vaor velocity filed and its ressure contours are lotted in Figure. There is a continuous flow of the desored vaor towards the chamer during this hase. Similarly, the region etween the two fins in the x-z lane as shown in Figure () indicates an almost arallel flow with uniform velocity rofile. After reaching a given level of desortion, the isosteric cooling hase egins. In this hase all connecting valves are closed and due to the adsortion rocess, the chamer ressure reduces until reaching the evaorator ressure. The velocity field and ressure contours are lotted in Figure 6 for the same ed cross section as revious figure. In isosteric hase, the adsorent close to the solid walls cools down y the cooling flow and the adsortion rocess starts, which in turn generates local low ressure regions and causing a strong vaor flow towards the metal surface. A local high ressure region around the uright corner is detected where the vaor flows toward the chamer indicating that desortion rocess still continues there. This flow attern can e attriuted to the relatively low heat transfer rate to this area resulting in a lower desortion level in the revious hase and also the reduction of the chamer ressure as the result of strong adsortion in regions close to the metal. In Figure 6() the effect of fins are more considerale in the adsortion rocess. The strong adsortion close to the fin surfaces reduces the ressure along these surfaces as comared to the central section, where the velocity field is also weaker. The final hase is the isoaric cooling hase, where the chamer valve to evaorator is oened and the refrigerant vaor is adsored y the ed. As shown in Figure 7, due to the cooling effects, a rather strong rate of adsortion occurs throughout the ed and mostly in regions where cooling is stronger. Adsortion also forms a relatively strong ressure gradient that facilitates the flow of the refrigerant vaor to the farthest region from the chamer in the left side of the ed. At the end of this hase, the amount of adsored water in the uer right art of the ed is less than the other arts due to its higher temerature, which in turn makes this region to adsor refrigerant in the susequent isosteric heating hase as mentioned earlier. Figure 7() shows that adsortion occurs uniformly as the vaor flows from the chamer towards the metal in the assage formed y the fins. Continuous reduction in the length of the velocity vectors is an indication of the continuous adsortion through this section of the ed. Similar flow atterns can e oserved at other times during this hase (m/s) (m/s).(m/s) (m/s) 6.. () Figure 6: Velocity vectors and ressure contours in the x-y lane in the midoint of the two successive fins in isosteric cooling hase () x-z lane located at y = in isosteric cooling hase.. () Figure 7: Velocity vectors and ressure contours in the x-y lane in the midoint of the two successive fins in isoaric cooling hase () x-z lane located at y = in isoaric cooling hase One of the imortant arameters in the design of the heat exchangers for the adsortion cooling systems is the geometric secifications including fins dimensions and sacing, which directly affects the erformance of the system. COP variations with fin height and sacing can e comrehended easily using the energy sharing etween different arts of the system. Figure 8 demonstrates the distriution of the sulied thermal energy etween the adsorent ed, fins, metal and thermal, and the required desortion heat for different fin height and sacing. Oviously, excet for the desortion heat, the transferred energy to all other

6 arts of the system are essentially considered as a waste, since, in the cooling hases, the added heat to these arts must e removed without any direct contriutions to the desortion rocess and the resulting cooling ower. Figure shows that as the fin height increases at a fixed fin sacing, the share of inut energy for the desortion rocess increases significantly, which means the wasted energy in the cycle reduces and therefore, the COP increases consideraly. Figure 8 also indicates that fin sacing variations at a given fin height slightly affect the useful share of the desortion heat, which also reflects in the slight variations of the COP with the fin sacing. List of Symols E Activation energy ( Jkg ) a FH FS R M Pr D so P Fin Height (m) Fin sace (m) Gas constant( Jkg - K ) Molar mass( kgmol ) Prandtl numer Pre-exonent constant of surface diffusivity( m s ) Pressure (Pa) - Re Reynolds numer FS= mm FH= mm FS= mm FH= mm t Time(s) R u u Velocity ( ms ) Universal gas constant( Jmol - K ) - FS=6 mm FH= mm FS=6 mm FH= mm Figure 8: Distriution of the sulied thermal energy etween different arts of the system including the: adsorent ed (); fins (); metal (); thermal (); and desortion heat () during heating hases Greek symols Ω σ Collision integral Collision diameter for Lennard- Jones otential(a) Viscosity (Pa.s) Conclusions In this aer, a three-dimensional model has een develoed for redicting the dynamic erformance of an intermittent adsortion cycle working with the comosite sorent SWS-L and water. In articular, the model includes the extended surfaces to enhance the transfer characteristi of the adsortion ed known for the relatively low thermal conductivity. Taking into account oth the internal and the external mass transfer resistance among the adsorent articles the vaor flow atterns and ressure distriutions throughout the ed are examined for all cycle hases. It was found that the ed flow atterns are relatively comlex for the isosteric hases due to the simultaneous occurrence of adsortion and desortion rocesses. Furthermore, a detailed investigation of the share of each art of the system from the inut energy during the heating hase is resented for different fins height and sacing. It was found that COP increases as the ed height increases, while it is less sensitive to the fins sacing. - Thermal conductivity ( Wm - K ) Suscrits a g Adsorate Adsorent Vaor References [] Zhang, L.Z.,. A three-dimensional nonequilirium model for an intermittent adsortion cooling system. Solar Energy, 69 (),.7. [] Chua, H.T., Ng, K.C., Wang, W., Ya, C., Wang, X.L.,. Transient modeling of a two-ed silica gelwater adsortion chiller. Int. J. Heat Mass Transf, 7(), Feruary, [] Ilis, G.G., Moedi, M., Ülkü, S.,. A dimensionless analysis of heat and mass transort in an adsorer with thin fins; uniform ressure aroach. Int Comm Heat Mass Transf, 8(6), July, [] Yong, P.Z., 9. Heat and mass transfer in adsorent ed with consideration of non-equilirium 6

7 adsortion. Al. Therm. Eng, 9 (-), Octoer,. 98. [] Riffel, D.B., Wittstadt, U., Schmidt, F.P., Núñez, T., Belo, F.A., Leite, A.P.F., Ziegler, F.,. Transient modeling of an adsorer using finned- heat exchanger. Int. J. Heat Mass Transf, (7-8), March, [6] Saha, B.B., Chakraorty, A., Koyama, S., Aristov, Y.I., 9. A new generation cooling device emloying CaCl-in-silica gel-water system. Int. J. Heat Mass Transf, (-), January,. 6. [7] Niazmand, H., Dazadeh, I.,. Numerical simulation of heat and mass transfer in adsorent eds with annular fins. Int. J. Refrigeration, (), May, [8] Restuccia, G., Freni, A., Russo, F., Vasta, S.,. Exerimental investigation of a solid adsortion chiller ased on a heat exchanger coated with hydrohoic zeolite. Al. Therm. Eng, (), July, [9] Rezk, A.R.M., Al-Dadah, R.K.,. Physical and oerating conditions effects on silica gel/water adsortion chiller erformance. Al. Energy,. 89(), January, -9. [] San, J., Hsu, H., 9. Performance of a multi-ed adsortion heat um using SWS-L comosite adsorent and water as the working air. Al Therm Eng, 9(8-9), June, [] Restuccia, G., Freni, A., Vasta, S., Aristov, Y.,. Selective water sorent for solid sortion chiller: exerimental results and modeling. Int. J. Refrigeration,7(), May,