New Trends in Combustion Simulation

Transcription

1 New Trends n Combuston Smulaton Dr. U. Schmdt 1, Dr. C.-H. Rexroth 1, Dr. Robert Scharler 2,3, Dpl.-Phys. I. Cremer 1 1 Fluent Deutschland GmbH, Brenweg 14a, D Darmstadt, Germany. 2 BIOS BIOENERGIESYSTEME GmbH, Sandgasse 47, 81 Graz, Austra 3 Insttute for Resource Effcent and Sustanable Systems, Graz Unversty of Technology, Inffeldgasse 25, 81 Graz, Austra Abstract A revew of recent developments n combuston modelng capabltes n a commercal CFD pacage s gven. The range of avalable combuston models s presented wth a partcular focus on new reacton models for fnte rate chemstry. The recently mplemented models are llustrated by two sample applcatons, le the development of a NO x postprocessor based on the Eddy Dsspaton Concept (EDC) model utlzng the ISAT algorthm. Keywords: CFD, combuston models, fnte rate chemstry, NO x 1. Introducton When early commercal CFD pacages became avalable more than 2 years ago, smulatng the complex physcs nsde combuston chambers was already one of the target applcatons. Of course, projects were often lmted by computer resources these days. Therefore n most cases reacton was taen nto account usng relatvely smple approaches such as the Eddy Dsspaton model. Today, wth ncreasng maturty of CFD technque and computng power, one focus n numercal smulaton of combuston s n the area of non-equlbrum chemstry and multphase flow. New felds of applcaton, such as the formaton of pollutants n techncal flames or the optmzaton of combuston processes, can be tacled that way. 2. Numercal Algorthm Numercal flow smulaton, or more common Computatonal Flud Dynamcs (CFD), reles on solvng conservaton or transport equatons for mass, momentum, energy and partcpatng speces. If the flow s turbulent, model equatons for specfc turbulent quanttes have to be solved n addton. Snce even wth today s super computers resolvng turbulent length scales drectly results n tremendous effort, Reynolds averaged equatons are appled to nclude the physcs of turbulence. To dscretze and solve the governng flow equatons the Fnte Volume method s employed by the majorty of commercal CFD codes. Table 1: Models for gaseous combuston avalable n FLUENT [1] Equlbrum chemstry Detaled chemstry Premxed flames Dffuson flames Partally premxed flames Zmont model (Reacton progress varable) Mxture fracton model Eddy Dsspaton model (Magnussen and Hjertager) Flamelet model Fnte Rate model Eddy-Dsspaton-Concept model PDF Transport model Zmont-/ Mxture fracton approach

2 The Reynolds averaged transport equaton for the mass fracton Y of the th speces n dfferental notaton can be wrtten as follows: Y ( ρy ) + ( ρuy ) + ( ρu" Y" ) = D + R t x x x ρ x (1) For the gaseous phase the source term R s the ey to combuston modellng. Dependng on the speed of the reactons to be modelled as well as on the current state of mxng between fuel and oxdser dfferent approaches are appled. Early combuston models have been derved on the assumpton of chemcal equlbrum. Tang nto account detaled netcs of reactons usually results n much hgher computatonal effort. Table 1 provdes an overvew of models for gaseous combuston avalable n the commercal CFD code FLUENT. 3. Combuston Models for Processes governed by Knetcs Wth ncreasng power of computers and worstatons the nterest n combuston models for detaled netcs has been growng contnuously n recent years. Wth lamnar flame processes ruled by netcs can be descrbed usng the Fnte Rate model. Le other models suted for non-equlbrum chemstry the Fnte Rate approach reles on a reacton mechansm ncludng Arrhenus parameters to defne the reactons to be smulated. Moreover, wth turbulent flames three dfferent models are avalable to do smulatons wth detaled netcs of reactons: Flamelet Model One means to combne turbulent flow and detaled netcs of reactons assurng acceptable computatonal effort s the so called Flamelet model. It taes advantage of assumng the turbulent dffuson flame to consst of a large number of sngle lamnar crosscurrent dffuson flames, so called flamelets, on a suted mcroscale. As wth the Mxture Fracton model computatonal effcency results from decouplng the soluton reacton and flow. The approach s suted to tacle moderate nonequlbrum phenomena resultng from aerodynamc stran. Eddy Dsspaton Concept Model The Eddy Dsspaton Concept (EDC) model taes advantage of assumng part of the flud to be thoroughly mxed wthn a partcular cell as well as to be the man drver for chemcal reacton. These well mxed portons of a subvolume, the so called fne scales, are regarded to resemble a constant pressure reactor. That way the governng equatons loose part of ther complexty. Usng the smplfed equatons for speces conservaton the correspondng source terms are derved from an Arrhenustype reacton mechansm. To solve for the fne scales the ISAT algorthm (n-stu adaptve tabulaton) [2] s appled to the resultng transent system of equatons. For detaled reacton mechansms made up by dozens of speces and several hundred reactons, t s hardly feasble to completely solve for netcs before enterng the flow calculaton. Therefore the ISAT algorthm employs a reference table where reacton data s collected as the flow smulaton proceeds. Each tme a new composton vector φ 1 made up from speces content, temperature and pressure has to be determned n a new tme step dt for a gven composton vector φ, the algorthm checs the reference table for entres calculated already. In case a set of values φ s found wthn acceptable tolerance, the new set s defned by just nterpolatng from exstng entres. When suted values have not been found, drect ntegraton serves to derve the new vector φ 1 also completng the table. Havng solved for speces dstrbutons and related lfe tme of fne scales, the EDC model s appled to determne source terms for the Reynolds averaged speces equatons. Usng that approach, even very slow reactons n turbulent flow, e.g. CO burnout n quenched flames and NO x reducton n SNCR systems, can be analyzed. EDC Applcaton: Smulaton of NO x formaton n a bomass grate furnace CFD was successfully appled to optmze the desgn of bomass furnaces wth respect to flue gas burnout and temperature dstrbuton by several research groups. However, the smulaton of NO x

3 Fgure 1: Calculated mole fracton profles of NH 3 and NO n a 44 W plot-scale bomass grate furnace (left hand pcture profle of mole fracton X NH3 [-] n the vertcal symmetry plane of the furnace; rght hand pcture profle of mole fracton X NO [-] n the vertcal symmetry plane of the furnace) formaton was lmted by the necessty to nclude far more complex chemstry than for combuston smulaton whch leads to computaton tmes that are by far too long for engneerng applcatons. BIOS BIOENERGIESYSTEME GmbH n cooperaton wth the Insttute for Resource Effcent and Sustanable Systems, Graz Unversty of Technology, developed a CFD NO x formaton model for bomass grate furnaces whch covers the release of NO x precursors from the fuel bed and the subsequent CFD smulaton of NO x formaton wth detaled chemstry n the combuston chamber [3]. An own-developed emprcal model was used for the combuston of sold bomass on the grate. Ths model supples veloctes, speces concentratons (CH 4, CO, CO 2, H 2, H 2 O, O 2, NO, NH 3, HCN) and temperatures of flue gas above the surface of the fuel layer as boundary condtons for subsequent CFD smulaton of turbulent reactve flow n the furnace. Under the assumpton that NO x formaton reactons do not sgnfcantly nfluence the flow pattern n the furnace, a tme savng 2-step approach was appled for CFD smulatons. The Realzable -ε turbulence model, the Eddy Dsspaton / Fnte Rates Knetcs combuston model n combnaton wth a global methane 3-step mechansm (CH 4, CO, CO 2, H 2, H 2 O) and the Dscrete Ordnates radaton model where used for basc gas phase combuston smulaton n the present case. The models were valdated for combuston smulaton n bomass furnaces wth lab-scale test cases as well as FT-IR n-stu measurements of speces concentratons (CH 4, CO, CO 2, H 2 O) and temperature measurements at a plot-scale 44 W th bomass grate furnace wth ar stagng technology [4,5,6]. The CFD smulaton of gas phase fuel NO x formaton n a postprocessor mode was performed wth the Eddy Dsspaton Concept n combnaton wth a detaled reacton mechansm wth 5 speces and 253 reactons (Klpnen 92) whch was developed under consderaton of NO x netcs n bomass combuston systems. Ths method allows for a detaled consderaton of both flow and chemstry. Frst 3D CFD smulatons were performed for the above mentoned furnace under dfferent operatng condtons. Fbre board was used as fuel wth a hgh ntrogen content. Fg. 1 shows calculated mole fracton profles of NH 3 and NO n the vertcal symmetry plane of the furnace. Consderng all uncertantes n comparng measurements wth smulatons of grate fred furnaces whch underle fluctuatons n operatng condtons and flow, the qualtatve and quanttatve agreement wth experments and netc smulatons was good. Prevous calculatons wth varous NO x postprocessors whch could not even gve qualtatvely correct results, were outperformed. No HCN emssons where calculated at the furnace outlet whch s n accordance wth lterature and experence. The average converson rate of NH 3 (whch showed to be the predomnant NO x precursor) n the furnace was n qualtatve agreement wth detaled netc nvestgatons wth an deal reactor networ. Furthermore, the NH 3 conversons rates could be verfed wth FT-IR n-stu measurements near the secondary ar nozzles whch showed NH 3 concentratons below the detecton lmt. The calculated NO emssons at the furnace outlet where about an order of magntude hgher as the correspondng NO 2 emssons, whch s n complance wth lterature data and measurements (conventonal flue gas analyss). For all test cases the smulated NO x emssons (NO and NO 2 ) where about 1% hgher than the measured ones at the boler outlet. The developed CFD NO x postprocessor n combnaton wth detaled reacton netcs could be successfully tested for 3D furnaces smulatons. More tests and comparsons wth measurements at

4 varous bomass furnaces (plot-scale and ndustral scale) are necessary and ongong n order to valdate the CFD model. Frst calculatons needed about 2 wees on a sngle PC processor for a grd sze of 275, cells, but a consderable speed up can be acheved wth parallel processng. The newly developed NO x postprocessor allows to nvestgate n detal NO x reducton measures n bomass grate furnaces and, therefore, s a powerful tool for the optmsaton of furnace desgns and process control. However, a reduced NO x reacton mechansm s currently beng developed n order to allow for a reducton of calculaton tme and to mae ths tme-consumng method more attractve for ndustral applcatons. Furthermore, a coupled smulaton of both combuston and NO x formaton reactons wth the EDC and ths reduced mechansm s planned n order to overcome weanesses of basc combuston smulaton wth the EDM and global combuston chemstry. PDF Transport Model Compared to alternatve methods le the concept of Presumed PDFs, solvng PDF transport equatons s the most general means to determne a probablty densty functon P. Transport equatons descrbng the evoluton of PDFs n tme and space can be derved from the Naver-Stoes equatons. The PDF transport equaton solved n FLUENT reads as follows: ( ρp) ( ρv P) + t x = x J ( ρu ψ P) " ρ 1 + ψ P + ( ρ S P), ψ ρ x ψ The probablty densty functon may be nterpreted as the probablty for a flud porton to be of a certan composton, temperature and pressure. Wth ths type of PDF, a so called composton PDF, some standard turbulence model s needed n addton. The man advantage of ths approach les n the fact that the hghly non-lnear source term s well defned and does not call for addtonal modelng of turbulent fluctuatons of speces and temperature. In contrast turbulent convecton and molecular dffuson (frst terms on the rght hand sde of eq. (2)) need to be modeled. As common a gradent dffuson approach serves to account for turbulent convecton. For turbulent dffuson of speces and energy the Modfed Curl model [7] or the IEM [8] model can be chosen. Snce the PDF s hgh dmensonal, the transport equaton s solved by a stochastc method, the Monte-Carlo algorthm. Ths method approxmates the probablty densty functon by many dscrete values referred to as stochastc partcles each representng a sngle state of the reactng flow. PDF Transport Applcaton: Flame D The well documented flame D serves to valdate the PDF transport model. Due to dfferences n flow velocty and speces concentraton ths partally premxed flame resembles to a dffuson flame. For numercal analyss standard -ε turbulence model and seletal reacton mechansm have been appled on an axsymmetrc mesh made up from 2352 cells. A comparson of measured and computed results for the mass fracton of CO along the normalzed radus of the flame shows good agreement (Fg.2). (2) r/d (at x/d=1) 1 2 r/d (at x/d=2) Fgure 2: Mass fracton of CO along normalzed radus of flame ( measured, Modfed Curl and IEM) 1 2 r/d (at x/d=3)

5 4. Summary Tang a loo at combuston modellng n commercal CFD codes has shown a clear tendency towards more complex approaches accountng for detaled netcs of reactons. In ths context the mplementaton of the PDF transport model and the ISAT algorthm deserves specal attenton. At the moment the PDF transport model s the most general approach to solve the closure problem arsng from turbulence-speces nteracton. As a consequence of the usage of the ISAT technology the EDC model has evolved to a valuable fnte rate model for ndustral scale applcatons. The most recent class of new combuston models just now allows for analyzng complex phenomena le formaton and destructon of pollutants n modern combustors. 5. References [1] FLUENT 6.1 User s Gude Volume 2, Fluent In., February 23. [2] POPE, S. B., Computatonally effcent mplementaton of combuston chemstry usng n-stu adaptve tabulaton, Combuston Theory and Modelng, 1:41-63, [3] OBERNBERGER, I., WIDMANN, E., SCHARLER, R., Entwclung enes Abbrandmodells und enes NOx-Postprozessors zur Verbesserung der CFD-Smulaton von Bomasse- Festbettfeuerungen, Endbercht des glechnamgen Forschungsprojetes des Bundesmnsterums für Verehr, Innovaton und Technologe (GZ /2-V/3/21), Insttute for Ressource Effcent and Sustanable Systems (ed.), Graz Unversty of Technology, 23. [4] SCHARLER R., Entwclung und Optmerung von Bomasse-Rostfeuerungen durch CFD- Analyse, Dssertaton, Technsche Unverstät Graz, Austra, 21. [5] SCHARLER, R., FLECKL, T., OBERNBERGER, I., Modfaton der Magnussen-Parameter für Bomasse-Rostfeuerungen mttels Heßgas n-stu FT-IR Absorptonsspetrosope, n: Tagungsband der Konferenz 2. Deutscher Flammentag, September 21, Essen, VDI-GET (Ed.), VDI Berchte Nr. 1629, pp , ISBN X, 21. [6] SCHARLER, R., FLECKL, T., OBERNBERGER, I., Modfcaton of a Magnussen Constant of the Eddy Dsspaton Model for bomass grate furnaces by means of hot gas n-stu FT-IR absorpton spectroscopy, Progress n Computatonal Flud Dynamcs, Vol. 3, Nos. 2-4, pp , 23. [7] JANICKA, J., KOLBE, W., KOLLMANN, W J., Closure of the transport equaton for the pdf of turbulent scalar felds, Journal Non-Equlbrum Thermodynamcs, 4:47, [8] DOPAZO, C., O BRIEN, E. E., Functonal formulaton of nonsothermal turbulent reactve flows, Phys. Fluds, 17:1968, 1975.