Improvement of the numerical framework for selective catalytic reduction applications

Transcription

1 Improvement of the numercal framework for selectve catalytc reducton applcatons J. Baleta,1, M. Vuanovć 1, N. Duć 1, K. Pachler, D. Schellander 1 Faculty of Mechancal Engneerng and Naval Archtecture, Unversty of Zagreb, Zagreb, Croata Advanced Smulaton Technologes, AVL Lst GmbH, Graz, Austra Abstract The focus of ths work s mprovement and valdaton of the mathematcal framework of commercal computatonal flud dynamcs code Fre for descrbng selectve catalytc reducton processes. Frst step was further development of exstng model for heat conducton nsde the sold by enablng multlayer smulatons, n order to have more accurate temperature profle and therefore more accurate heat transfer. Valdaton was carred out on the wellestablshed expermental results from PhD thess of Felx Brkhold. Furthermore, 3D numercal smulatons of UWS necton n hot flue gases was conducted wth the am of determnaton of new set of parameters for urea thermolyss reacton rate. Introducton Varous envronmental regulatons put ever strngent requrements on the automotve ndustry as a part of soluton to the problem of global warmng and clmate change. The urea-water soluton (UWS) based selectve catalytc reducton (SCR) s a promsng method for meetng the NOx emsson lmtatons of the current EURO 6 standard for road vehcles propelled by the desel engne. In prncple, the UWS spray s nected nto a hot exhaust gas stream precedng the SCR catalyst and ammona s generated through seres of chemcal reactons. Then, the generated ammona acts n varous denox reactons as a reductant. Spatally unform dstrbuton of the reducng agent that precedes the SCR catalyst s a crucal factor for the converson of NOx. The unformty of dstrbuton and the degree of processng of the reducng agent upstream of the SCR catalyst can be, besdes the evaporaton and decomposton, nfluenced also by the spray/wall nteracton. Due to ncreasng prce of expermental equpment and wth ncrease of both the computatonal power and ts affordablty durng the last two decades, numercal smulatons are becomng a valuable desgn tool n the feld of nternal combuston engnes. Usage of CFD smulatons to nvestgate and mprove thermochemcal processes s becomng ncreasngly mportant [1]. Obectve of the current work s further mprovement of exstng framework by upgradng thn wall module whch s used for the calculaton of heat transfer nsde solds and optmzaton of urea thermolyss model parameters. These mprovements should result n a more accurate representaton of SCR processes and thus provde support to ever ncreasng ndustry demands for relable desgn tools. Mathematcal models In ths study, as n the most engneerng applcatons today, the Euleran-Lagrangan method for solvng the multphase flow phenomena s used. In ths approach, the spray droplets are represented by fnte numbers of droplet groups called parcels. It s assumed that all the droplets wthn one parcel are smlar n sze and have the same physcal propertes. The moton and the transport of the parcels are tracked through the flow feld usng a Lagrangan formulaton, whle the gas phase s descrbed by solvng conservaton equatons usng an Euleran formulaton. The couplng between the lqud and the gaseous phase s taken nto account by ntroducng approprate source terms for nterfacal mass, momentum, and energy exchange []. Equatons of contnuum mechancs are based on the conservaton laws for mass, momentum and energy. The general form of the tme averaged conservaton equaton for any dependent varable φ of the contnuous phase n the dfferental form s: ( ) ( u ) ( ) S (1) t In the above equaton denotes the densty, u Cartesan velocty, dffuson coeffcent, and S represents the source term of the dependent varable. The frst term s an unsteady term, the second term s convecton, the thrd term s dffuson and the last term s source or snk. The source term S s used for the couplng of the lqud and the gaseous phases. In order to nclude all relevant phenomena appearng the UWS necton nto confned space of moble SCR systems sutable mathematcal descrpton of the followng processes s needed: momentum nteracton between gas phase and droplets; evaporaton and thermolyss of droplets; heat transfer between wall and droplets; spray/wall nteracton; Correspondng author: akov.baleta@fsb.hr Proceedngs of the European Combuston Meetng 015

2 two-component wall flm ncludng nteracton wth gas phase and exhaust tube; secondary break-up of spray. Boundary layer assumptons [3] lead to the mplementaton of the wall flm model as a D fnte volume method on the ar flow wall boundares. Flm thckness equaton s the basc governng equaton for the wall flm flow. It represents a slghtly modfed formulaton of the contnuty equaton where, nstead of mass, the wall flm thckness s conserved property. The Cartesan formulaton of the flm thckness equaton s: u u 1 1 ( S md S mv ) () t 1 A Flm thckness s represented by δ, ρ s the flm densty, u 1 and u are flm velocty components, S md and S mv are source terms and A s the surface of the flm. If we assume that the source terms are provded, equaton () can be solved explctly f the velocty components are known. Flm momentum equaton descrbes dynamcs of lqud flm nteracton wth ts envronment - wall, ar stream above flm, mpngng droplets, etc. Equaton (3) gves mathematcal formulaton of wall flm momentum conservaton law: dm u u V n dl p n dl mg S M dt ( ) ˆ ˆ L (3) Flm momentum s denoted wth M, ρ s the flm densty, u s the flm velocty, V s wall velocty, nˆ s normal to the face cell facng outwards, L s length of the face cell boundary, δ s the flm thckness, p s flm pressure, m s flm mass, g s gravty vector, Γ s the term that takes nto account all shear stresses and S M presents varous source and snk terms such as flm entranment, spray droplets mpngement and flm evaporaton. Heat transfer has a maor mpact on the water evaporaton and urea thermolyss so ts accurate descrpton s desrable. Current approach n Fre for heat conducton calculaton nsde the sold employs the so called thn wall module where sold s represented as a monolayer of a gven thckness and lnear temperature change s assumed. The mean sold temperature s used for heat transfer calculaton on both sdes of the sold. Ths approach has obvous drawbacks, especally n the case of thck or mult-materal solds or n solds wth pronounced temperature gradents. In order to overcome those dffcultes we developed the mproved model whch enables multlayer sold dscretzaton, ether unform or non-unform and mult-materal propertes defnton. The 1D heat conducton modelng can be consdered as accurate when the followng assumptons are satsfed [4] : the sold s thn compared wth the proportons of the computatonal volume; L the sold s a stackng of homogeneous layers,.e. wth constant propertes; lateral heat conducton s neglgble wth regard to normal heat conducton. In ether steady or transent calculatons, the followng equatons are solved wthn a thn wall: T T 0 (4) t c t p T T (5) In the above expressons stands for the thermal conductvty, T s temperature, s densty and c s specfc heat. The 1D heat conducton s solved wthn the thn wall thckness, and s coupled wth the flud energy equaton. The wall thckness can now be dscretzed n multple layers and the number of nodes per layer could be specfed. Hence, there s a constant space step per layer. Ths enables more accurate calculatons of heat transfer wth small computatonal tme trade off. Thermolyss of urea s modeled wth Arrhenus equaton whch contans actvaton energy and frequency factor whch have maor nfluence on chemcal knetcs. It s also am of ths work to obtan optmzed set of ths parameters and use t to predct some expermental cases. Brkhold plate case - settngs Well establshed case of the plate coolng from PhD thess of Felx Brkhold [5] s used for valdaton of multlayer thn module. Detals of settngs are gven n [5], whle only bref descrpton s gven here. Thn metal plate ( mm) was placed nsde the mddle of rectangular channel wth dmensons of 94x10x400 mm as can be seen on the Fgure 1. Unform ar flow passes both above and below the plate wth velocty of 30 m/s. Urea water spray s nected nto the ar stream above the plate and, dependng on the local condtons there wll or won t be wall flm formaton on the plate. Thermocouples are used to measure change n the plate temperature. We wll note further on cases where there s flm formaton as cold and where there s no wall flm as hot. Fgure 1. Mesh representaton of computatonal doman Durng the grd dependency smulatons t was found that the unform computatonal mesh consstng of 08 p

3 000 orthogonal cells wth sze of 1 mm produces suffcently accurate results. For the smulaton advanced k-zeta-f turbulence model was used [6]. Implct tme dscretzaton scheme was used wth tme step sze of s. s solved for the normal heat conducton, that way makng valuable tme and CPU savngs. Brkhold plate case - results Fgure. shows results of hot cases wthout thn wall module modfcatons. As t can be seen, prevous approach s perfectly capable of descrbng the gradual coolng of the thn plate solely by convecton. Fgure 4: ACCI vs. new thn wall module Fnally, Fgure 5 presents comparson of the new approach wth expermental data from Brkhold whch s now accurately descrbng plate coolng. Fgure : Plate coolng hot cases The same cannot be stated for the cold case n whch wall flm formaton was observed. Lqud formed on the plate surface acts as generous heat snk and mono layer thn wall module s not capable to descrbe heat transfer properly whch can be clearly seen as dscrepancy from expermental measurements n the Fgure. Fgure 5: Plate coolng usng new approach - cold case Km case settngs and results Km measured urea soluton evaporaton n hot exhaust gas to get values for NH 3 converson rates [7]. Fgure 6 shows scheme of expermental secton wth locatons of samplng probes. Dfferent dstances from nozzle locatons are used to calculate NH 3 converson effcency when quas-steady state s reached. Fgure 3: Plate coolng cold case One way to overcome ths ssue s usng AVL Code Couplng Interface (ACCI) whch enables smultaneous smulaton of two domans whch are connected through the common nterface. After each tme step, nformaton s exchanged at the nterface. Ths approach demands addtonal computatonal power and tme for the nformaton exchange and s therefore not sutable. Fgure 4 shows doman decomposton usng developed multlayered thn wall module. It can be seen that we don t need two meshes as was the case wth ACCI approach. Instead, we ust make surface selecton and defne t as a thn wall. That way, only one equaton Fgure 6: Schematc vew of the expermental secton from Km In Fre, an evaporaton model for spray wth parameters s gven. The parameters E4 actvaton energy and E5 frequency factor are steerng thermolyss model for the droplet mass transfer whth respect NH 3 converson rate. Fgure 7 shows computatonal doman consstng of hexahedral elements. Smulaton settngs regardng turbulence modellng and tme

4 dscretzaton reman the same and reader can refer to prevous secton for detals. Fgure 7: Km case doman dscretzaton On the followng fgures there can be seen comparson between the old parameters, new parameters and expermental measurements from Km. New parameters show better agreement wth experment n all cases compared to the old ones. Fgure 8: Comparson of results - Cases 1-3 Set of parameters, namely actvaton energy and frequency factor of Arrhenus equaton, whch was obtaned by comparson of smulated results wth expermental ones, yelded good agreement and was used for other cases n whch exhaust gas mass flow and temperature were vared. Fgure 9: Comparson of results - Cases 4-6 Fgure 10: Comparson of results - Cases 6-9 Smulaton of these cases predcted NH3 converson effcency wth satsfactory matchng wth measured data. It can be concluded that new parameter show good results n range of u = 9 m/s of gas velocty. Conclusons After general ntroducton and presented detals of mathematcal models, ncludng mprovements n modelng of heat conducton and optmzaton of thermolyss parameters, two dfferent smulaton settngs have been presented and descrbed. Comparson wth relevant expermental data yelded satsfactory agreement. Improved thn wall module now enables consderable savngs n computatonal resources and/or tme. Obtaned optmzed set of evaporaton model constants favorable agreement wth expermental results and gves confdence for commercal applcaton of mplemented CFD wall flm module The contnuaton of ths work ncludes mplementaton of many new models n order to descrbe mportant phenomena such as: multcomponent evaporaton of wall flm, mechansm of urea deposts formaton, nteracton of spray wth porous wall and catalyst nlet Fnally, ths study concludes that mathematcal models regardng spray/wall nteractons and wall flm formaton ntegrated n Fre CFD code can be used as a valuable tool for the desgn and optmzaton of real moble SCR systems. Acknowledgements The authors wsh to thank the AVL Lst GmbH, Graz, Austra for the fnancng and opportunty to work on the research proect. Authors would also wsh to thank the CFD development group at AVL-AST, Graz, Austra, for ther support and techncal dscussons durng the model development. References [1] J.J. Klemeš, P.S. Varbanov, S. Perucc, D. Husngh, Mnmsng emssons and energy wastage by mproved ndustral processes and ntegraton of renewable energy, J. Clean. Prod. 18 (010)

5 [] H. Mkulčć, E. von Berg, M. Vuanovć, P. Preschng, R. Tatschl, N. Duć, Numercal analyss of cement calcner fuel effcency and pollutant emssons, Clean Technol. Envron. Polcy. 15 (013) d [3] H. Schlchtng, K. Gersten, K. Gersten, Boundary-Layer Theory, 000. [4] AVL, FIRE VERSION 013. manual, 013. [5] F. Brkhold, Selektve katalytsche Redukton von Stckoxden n Kraftfahrzeugen : Untersuchung der Ensprtzung von Harnstoffwasserlosung, Das Karlsruher Insttut für Technologe (KIT), 007. [6] K. Hanalć, M. Popovac, M. Hadžabdć, A robust near-wall ellptc-relaxaton eddyvscosty turbulence model for CFD, Int. J. Heat Flud Flow. 5 (004) [7] J.Y. Km, S.H. Ryu, J.S. Ha, Numercal Predcton on the Characterstcs of Spray- Induced Mxng and Thermal Decomposton of Urea Soluton n SCR System, n: ASME 004 Intern. Combust. Engne Dv. Fall Tech. Conf., ASME, 004: pp