Thermal Modeling of a Honeycomb Reformer including Radiative Heat Transfer

Transcription

1 Thermal Modeling of a Honeycomb Reformer including Radiaive Hea Transfer J Schöne *1, A Körnig 1, W Becer 1 and A Michaelis 1 1 Fraunhofer IKTS, Winerbergsraße 8, 0177 Dresden *Corresponding auhor: jaobschoene@isfraunhoferde Absrac: Reformer and caalyic burners are common componens in fuel cell sysems, crucial for efficien preparaion of fuel and exhaus es of he fuel cell sac In his absrac we inend o show he influence of iaion o he emperaure disribuion inside of a cylindrical ormer uni The model consiss of an axisymmeric represenaion of he inle-zone and a caalyic porous zone Fluid flow, convecive and conducive hea ransfer and simplified chemical ions for daion and orming are included as physical models Due o emperaures up o 900 C in he or iaion should be considered For he inle zone he Surface o Surface iaion model of COMSOL is used and is coupled o a 1D user defined iaion in paricipaing media model for he honeycomb which consiss of various small channels Temperaure disribuions for models wih and wihou iaion are compared 900 C and iaion heore should be included Beside of he caalys aging also he chemical equilibrium of species concenraions depends on local emperaures hence he focus of his model is on he emperaure disribuion Se Up and overning Equaions Figure 1 shows he seup up of he considered ormer geomery wih he inle pipe of 6mm cross-secion, nex o he mixing geomery (no shown here), ending in a pipe wih 1mm diameer where he honeycomb is locaed 0mm behind he cross-secion is rising The caalys paricles are locaed on a 00cpsi cordierie suppor and he cross secion of one channel is 11x11mm Keywords: iaion model coupling, orming, or model, sofc 1 Inroducion Caalyic orming is a common process in fuel cell sysems o produce synhesis from mehane Common parial daion orming ors consis of a premixing zone where mehane and air are prepared, a chamber for furher mixing and he broadening of he fluid flow for enering he caalyic honeycomb channel srucure Inside of he honeycomb, daion and orming ions ae place, generaing hydrogen from mehane and oxygen which leaves he orming uni and eners he fuel cell sac The daion of mehane leads o local high emperaures mainly responsible for caalys aging Selecive experimenal measured emperaures are ranging from 00 C up o Figure 1 Seup up of he ormer uni 1 Fluid Flow There are wo differen flow regimes denoed in Figure 1, a free-flow inle region, where an abrup rise of he cross-secion occurs and a porous flow region inside of he honeycomb For he free-flow region he well nown - urbulence model (1) is applied u u piˆ u u uiˆ Iˆ T (1)

2 0 () u u P () In he above equaions,,, p, P, and u are he densiy, he inemaic viscosiy, urbulen viscosiy, pressure, correced pressure, urbulen ineic energy, urbulen dissipaion rae and he local velociy The densiy is obained by he ideal law where M, R and T are he mean molar mass, universal consan and he emperaure The urbulen viscosiy is calculaed from The consans in equaion 1 C 1, C, C, and are he common parameers for he - urbulence model The caalyic honeycomb consiss of many small channels and for each a laminar flow can be assumed where he pressure drop can be calculaed by Darcys law Using an anisoropic permeabiliy ˆ for he whole honeycomb maes i possible o use an axis-symmeric geomery for he ormer uni model and o lower compuaional coss Pseudo Reacions u C P u : RT P C For esing purposes wo pseudo ions are included which should reproduce a fas exohermic and respecively a slower endohermic ion hea release This is achieved by using he following equaions: 1 T u u u u () (5) p M (6) C (7) ˆ u p u u (8) (9) where and are he rae consans of eiher he daion or he orming ion The variables and are fixed o a value of one a he ormer inle and he righ hand side of (9) is only differen from zero inside of he honeycomb The corresponding heaing rae is defined by: q where P P and are he oal exohermic ion power and he oal needed endohermic ion power, which are chosen so ha he oupu emperaure hes 850 C The quaniy m denoes he oal mass flow rae Hea Transpor 1 Convecion and Conducion Inside of he orming uni he convecion and conducion of hea is reaed by: ˆ T C pu T (11) T T This equaion reproduces he hea ransfer in he fuel where ˆ, C p, and T are he anisoropic hea conduciviy of he, he mean hea capaciy, he volumeric hea ransfer coefficien and he emperaure of he fuel An addiional conducive hea ransfer (1) is inroduced inside of he honeycomb ˆ Here ˆ P P (10) m T, T, q and q are he anisoropic hea ransfer coefficien of he honeycomb, he id emperaure, he ion hea source due o daion and orming processes and he iaive hea source appearing from absorpion and emission of iaion from he channel walls of he honeycomb (see nex secion) I is assumed ha he species concenraions a caalyic surface are equal o phase concenraions T T q q (1) q T I I ) (1) por ( 1

3 Radiaive Hea Transfer Due o he high emperaures one should accoun for iaive hea ransfer Beween he walls of he free-flow region and he honeycomb enrance, surface-o-surface iaion can be assumed because opical hicness is hin in respec o disances inside of he orming uni Theore one can use he COMSOL module Surface-o-Surface Radiaion as i is Inside he honeycomb a paricipaing media approach for he homogenized channel srucure is needed bu he build-in COMSOL module includes only isoropic absorpion So an anisoropic 1d paricipaing media approach is inroduced by including he following PDEs: di1 T I1 (1) dz di T I (15) dz Inensiy I 1 is saring from he honeycomb inle and inensiy I is saring from he oule of he honeycomb Boh inensiies are coupled via he local id emperaure The absorpion coefficien was deermined from a separae d channel model and he consan denoe he Sefan-Bolzmann consan honeycomb: iaion in anisoropic, ransparen media modified iosiy J mod iriaion z I I 1 J mod r J J iaive inensiy I 1 iaive inensiy I inle zone: surface o surface iaion iosiy J Figure Domains and boundaries wih surface-osurface iaion and iaion in paricipaing media approach Use of COMSOL Muliphysics All equaions are realized wihin COMSOL Muliphysics a To ve equaions (1) o (5) he Fluid Flow Single Phase Flow Turbulen Flow - COMSOL module is used All boundaries are se o no-slip boundary condiion excep inle where mass-flow inle is chosen and oule where pressure is se o zero Wihin he honeycomb he pressure drop is represened by an addiional volume force source erm in form of Darcys law (8) so he channel srucure is reaed as porous media The appearing anisoropic permeabiliy is deermined by analyzing a d cross secion of one channel bu is no shown here The componens of ˆ perpendicular o he channel direcion are se one order of magniude lower han in channel direcion because hey can no be se o zero for numerical reasons For he pseudo ion equaion (9) he Mahemaics PDE Inerfaces Coefficien Form PDE COMSOL module is used where he source erm f is se o zero excep inside he honeycomb The hea ransfer is inroduced by eiher using he Hea Transfer Hea Transfer in Fluids COMSOL module for emperaure and he Hea Transfer Hea Transfer in Solids COMSOL module for he honeycomb These modules are coupled by a hea exchange source T T For all presened erm resuls adiabaic behavior is assumed hus all boundaries are insulaed and only inle is se o a fixed emperaure and he oule is se o convecive ouflow condiion For he iaive hea ransfer in he free-flow region he Hea Transfer Radiaion Surface-o-Surface Radiaion COMSOL module and inside he honeycomb he Mahemaics Classical PDEs Convecion-Diffusion COMSOL module is used In Figure all surfaces ha are in surface-o-surface iaion exchange are shown A he honeycomb enrance he surface-o-surface iaion model is coupled o he 1d iaion in paricipaing media and he Hea Transfer in Solids model This is achieved by inroducing a Prescribed Radiosiy

4 T/ x [K/m] Temperaure [ C] boundary condiion in he Surface-o-Surface iaion mode and he value for iosiy is calculaed by: J I 1 1 T (16) por por The inensiy I is se equal o he iriaion 1 obained from he surface-o-surface iaion module and he hermal boundary condiion for he honeycomb enrance is given by: ˆ T (1 ) T n (17) por A he ormer oule he inensiy I is se o T 5 Resuls and Discussion 51 Esimaing he adsorpion coefficien Comparing he emperaure of a deailed d model, represening one single honeycomb channel including hea ransfer by conducion and surface-o-surface iaion, wih a 1d model, ruled by equaions (1), (1) and (15) where he righ hand side of equaion (1) only conains he iaion source erm, leads o an esimaion for he absorpion coefficien Figure shows he configuraion of he d and 1d model wih boundary condiions D honeycomb channel (hermal conducion including surface o surface iaion) Surfaces in iaion exchange o each oher and o T amb I1 Tamb n ( (1 por 1D honeycomb channel (hermal conducion including iaive hea ransfer in ransparen media) x n ( T ) 0 bul T amb 850C T 750C x I T ) bult ) (1 por) ( Tamb T ) I1 ( T I ) 1 x I ( T I ) x ( 1 por) bul T ( T I1 I) por x Figure Configuraion and boundary condiions for a deailed d hea convecion model wih surface-osurface iaion and he corresponding homogenized 1d hea conducion model including a iaion in paricipaing media approach Figure and Figure 5 show curves of he mean id emperaure along he channel and is spaial derivaive for he d model in comparison wih calculaed curves from he 1d model wih varying values of he absorpion coefficien The bes agreemen for he used configuraion is obained for 100m deailed d wih SS 1d wih =500m -1 1d wih =100m -1 1d wihou Figure Comparison of emperaures along channel direcion for d surface-o-surface iaion and he 1d iaion in paricipaing media model for several absorpion coefficiens deailed d wih SS 1d wih =500m -1 1d wih =100m -1 1d wihou Figure 5 Comparison of emperaure giens along channel direcion for d surface-o-surface iaion and 1d iaion in paricipaing media model for several absorpion coefficiens 5 Reforming Uni Model The main focus of his wor is he emperaure disribuion of he id honeycomb comparing he cases for hea ranspor wih and wihou iaion In Figure 6 he conour plos of hese emperaures are shown The surface-o-surface iaion ends o equilibrae he emperaures beween he paricipaing surfaces which resuls in increasing emperaures along all boundaries excep he honeycomb inle where he emperaure is decreasing In hose regions where he emperaure is increasing he fuel is pre-

5 Temperaure [ C] Temperaure [ C] heaed because of he ne hea flow from boundaries o he free-flow domain Inside of he honeycomb he emperaure disribuions are differen from each oher bu in he same range emperaure T g id emperaure T s no iaion wih iaion no iaion wih iaion [ C] T mean T mean 00 T a r=0mm T a r=0mm 00 T a r=15mm 00 T a r=15mm Figure 8 Mean id and emperaure along he main flow direcion in comparison wih axial lines a differen ial posiions 6 Conclusion and Ouloo Figure 6 Solid and emperaure disribuion of he ormer uni model wih and wihou iaion The conours of he id emperaure are more ineresing and of pracical relevance In case of iaion, id emperaures are nearly everywhere lower han in he pure hea conducion and convecion case The oal decrease of he maximal emperaure of around 100K is beer depiced in Figure 7 where he cross secion averaged emperaures for and id are ploed Radial emperaure variaions are shown in Figure 8 where for axial lines a r 0mm and r 15mm he id and emperaures are ploed Wihin his wor an axis symmeric ormer uni model was developed including mass ranspor in free-flow and porous regions, mos simplified chemical ions and hea ranspor including convecion, conducion and iaion The caalyic honeycomb was considered as a porous media wih anisoropic properies allowing an axisymmeric implemenaion A developed 1d sub model for iaion in paricipaing media along a channel srucure showed good agreemen wih a deailed d surface-o-surface iaion channel model The derived ormer uni model showed a significan influence of he emperaure disribuion on hea ransfer by iaion as expeced The presened model only considers only consan maerial properies bu emperaure dependen ones are in progress The very simple ion approach will be exchanged by more convenien ones and phase chemisry should also be included in furher wor wihou id wihou 00 wih id wih Figure 7 Mean id and emperaure along he main flow direcion wih and wihou iaion