Combustion Module AVL FIRE VERSION 2014

Transcription

1 Combuston Module AVL FIRE VERSION 014

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3 Combuston Module FIRE v014 AVL LIST GmbH Hans-Lst-Platz 1, A-800 Graz, Austra AST Local Support Contact: Revson Date Descrpton Document No. A 30-Jun-008 FIRE v008 - ICE Physcs & Chemstry Users Gude B 15-Apr-009 FIRE v009 - ICE Physcs & Chemstry Users Gude C 30-Sep-009 FIRE v ICE Physcs & Chemstry Users Gude D 30-Nov-010 FIRE v010 - ICE Physcs & Chemstry Users Gude E 14-Oct-011 FIRE v011 Combuston / Emsson Module F 30-Apr-01 FIRE v011.1 Combuston / Emsson Module G 8-Feb-013 FIRE v013 Combuston Module H 30-Sept-014 FIRE v014 Combuston Module Copyrght 014, AVL All rghts reserved. No part of ths publcaton may be reproduced, transmtted, transcrbed, stored n a retreval system or translated nto any language or computer language, n any form or by any means, electronc, mechancal, magnetc, optcal, chemcal, manual or otherwse, wthout pror wrtten consent of AVL. Ths document descrbes how to run the FIRE software. It does not attempt to dscuss all the concepts of computatonal flud dynamcs requred to obtan successful solutons. It s the user s responsblty to determne f he/she has suffcent knowledge and understandng of flud dynamcs to apply ths software approprately. Ths software and document are dstrbuted solely on an "as s" bass. The entre rsk as to ther qualty and performance s wth the user. Should ether the software or ths document prove defectve, the user assumes the entre cost of all necessary servcng, repar, or correcton. AVL and ts dstrbutors wll not be lable for drect, ndrect, ncdental, or consequental damages resultng from any defect n the software or ths document, even f they have been advsed of the possblty of such damage. FIRE s a regstered trademark of AVL LIST. FIRE wll be referred as FIRE n ths manual. All mentoned trademarks and regstered trademarks are owned by the correspondng owners.

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5 Combuston Module FIRE v014 Table of Contents 1. Introducton Symbols Confguratons 1-1. Overvew Spray/Combuston Interacton -.. Actvaton and Handlng of the Combuston Module - 3. Theoretcal Background Nomenclature Roman Characters Greek Characters Subscrpts Superscrpts Combuston Models Hgh Temperature Oxdaton Scheme Turbulence Controlled Combuston Model Turbulent Flame Speed Closure Combuston Model Coherent Flame Model CFM-A Model MCFM Model ECFM Model ECFM-3Z Model Probablty Densty Functon Approach PDF Transport Equaton Monte Carlo Smulaton Characterstc Tmescale Model Steady Combuston Model Mult-Speces Chemcally Reactng Flows Hydrocarbon Auto-Ignton Mechansm AnB Knock-Predcton Model Emprcal Knock Model Flame Trackng Partcle Model Basc Concept Flame Trackng Method Partcle Method Spark Ignton Modelng References Related Publcatons Combuston Input Data Control Combuston Models Eddy Breakup Model 4- AST Sept-014

6 FIRE v014 Combuston Module Model Constants Tme Scale Turbulent Flame Speed Closure Model Model Constants Coherent Flame Model Tme Scale ECFM-3Z PDF Model Rate Coeffcent Treatment Tme Scale Characterstc Tmescale Model Model Constants Tme Scale Steady Combuston Model Model Constants Flame Trackng Partcle Model Model Constants User Defned Reacton Rate Tme Dependent Actvaton of Combuston Combuston Models Auto Ignton Models Ignton Models Spark Ignton Auto Ignton Desel Desel_MIL HCCI Knock AnB Knock Emprcal Knock Model Desel Ignted Gas Engne Model D Results General Informaton Auto Ignton Models D Results General Informaton CFM Models Auto Ignton Models Optonal Output from Knock Models Knock AnB Knock 4-37 AST Sept-014

7 Combuston Module FIRE v014 Lst of Fgures Fgure 3-1: Geometrcal Defnton of the Thermal Flame Thckness Fgure 3-: AKTIM - Electrcal crcut Fgure 3-3: Spark Partcles and Flame Kernel Centers at Breakdown Tme (left) and Later (rght) Fgure 3-4: Flame Kernel Real Sze at Breakdown Tme (left) and Later (rght) Fgure 3-5: Zones n ECFM-3Z Model Fgure 3-6: Emprcal Knock Model Fgure 4-1: Combuston Parameter Tree Fgure 4-: Combuston Models Wndow Fgure 4-3: Eddy Breakup Model Wndow Fgure 4-4: Turbulent Flame Speed Closure Model Wndow Fgure 4-5: Coherent Flame Model Wndow (wthout and wth automatc parameter determnaton) Fgure 4-6: ECFM-3Z Model Wndow Fgure 4-7: ECFM-3Z Model Wndow for Gasolne Engne Applcaton Fgure 4-8: ECFM-3Z Model Wndow for Desel Auto-gnton Applcaton Fgure 4-9: PDF Model Wndow Fgure 4-10: PDF Model Wndow for User Defned Coeffcents Fgure 4-11: Characterstc Tmescale Model Wndow Fgure 4-1: Steady Combuston Model Wndow Fgure 4-13: Tme Dependent Actvaton of Combuston Models Fgure 4-14: Spark Ignton Wndow Fgure 4-15: Spark Ignton Wndow Aktm gnton model Fgure 4-16: Aktm Spark Plug Model Fgure 4-17: ISSIM Spark Plug Model Fgure 4-18: Auto Ignton Wndow for Desel Fgure 4-19: Auto Ignton Wndow for AnB Knock Fgure 4-0: Wndow for AnB Knock Fgure 4-1: D Results Wndow Fgure 4-: 3D Results Wndow AST Sept-014

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9 Combuston Module FIRE v INTRODUCTION Ths manual descrbes the usage, fles and the theoretcal background of the FIRE Combuston Module Symbols The followng symbols are used throughout ths manual. Safety warnngs must be strctly observed durng operaton and servce of the system or ts components. Cauton: Cautons descrbe condtons, practces or procedures whch could result n damage to, or destructon of data f not strctly observed or remeded. Note: Notes provde mportant supplementary nformaton. Conventon Italcs monospace MenuOpt Meanng For emphass, to ntroduce a new term. To ndcate a command, a program or a fle name, messages, nput / output on a screen, fle contents or object names. A MenuOpt font s used for the names of menu optons, submenus and screen buttons. 1.. Confguratons Software confguratons descrbed n ths manual were n effect on the publcaton date of ths manual. It s the user s responsblty to verfy the confguraton of the equpment before applyng procedures n ths manual. 30-Sept

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11 Combuston Module FIRE v014. OVERVIEW The FIRE Combuston Module enables the calculaton of speces transport/mxng phenomena and the smulaton of combuston n nternal combuston engnes and techncal combuston devces under premxed, partally premxed and/or non-premxed condtons. Chemcal knetc effects are accounted for by dfferent sngle-step and mult-step combuston models for the treatment of the hgh temperature oxdaton processes n flames. For the smulaton of the auto-gnton behavor of hydrocarbon fuels also several models are avalable whch can be combned wth the hgh temperature reacton schemes n order to form a smulaton chan for Desel auto-gnton. A knock model s avalable for the descrpton of knockng processes consderng fuel consumpton and heat formaton at the knock locatons. Ths knock model can be currently actvated only n the case of CFM combuston actvaton and s manly constructed for the ECFM but can also be used for the other CFM. A further knock model s avalable based on an emprcal approach consderng no fuel consumpton and heat formaton at knock locatons. In ths model local volumes clockwse arranged are determned gvng a knock crtera for each segment based on dfferent parameters such as temperature, fuel mass fracton, EGR, etc. Ths emprcal knock model can be used for all combuston models. The nfluence of turbulence on the mean rate of reacton may be treated by fve dfferent types of combuston models of dfferent levels of complexty. The choce depends on the applcaton case under consderaton and the purpose of the numercal smulaton. The frst model s based on the deas of the eddy dsspaton concept, whch assumes that the mean turbulent reacton rate s determned by the ntermxng of cold reactants wth hot combuston products. The second model s a turbulent flame speed closure model determnng the mean reacton rate whch s based upon an approach dependng on parameters of the turbulence such as turbulence ntensty and length scale, and of the flame structure lke flame speed and thckness, respectvely. The thrd combuston model s based on the flamelet assumpton,.e. the turbulent flame brush should be composed by an ensemble of lamnar flamelets. The length and tme scales n the reacton zone are assumed to be smaller than the characterstc turbulent length and tme scales, respectvely. Ths model conssts of several sub-models ncludng also one for the complete descrpton of the Desel auto-gnton and combuston process. The fourth model adopts the Probablty Densty Functon (PDF) approach. Ths approach fully accounts for the smultaneous effects of both fnte rate chemstry and turbulence, thus obvatng the need for any pror assumptons as to whether one or the other of the two processes determnes the mean rate of reacton. The ffth model s the Characterstc Tmescale Model whch takes nto account a lamnar and a turbulent tme scale. The lamnar tme scale consders the slower chemcal reacton rates especally at the begnnng of the combuston. The turbulent tme scale gves the nfluence of the turbulent moton to the reacton rate. A separate model s avalable for the descrpton of steady combuston processes especally n burners and furnaces. 30-Sept-014-1

12 FIRE v014 Combuston Module.1. Spray/Combuston Interacton In combnaton wth the FIRE Spray Model, the FIRE Combuston Module enables the calculaton of spray combuston processes n drect njecton engnes. Under these condtons, mxture formaton and combuston are smultaneous processes exhbtng a sgnfcant degree of nteracton and nterdependence. A successful combuston calculaton under these condtons reles very much on the accuracy of the spatal and temporal spray vapor evoluton characterstcs. The use of droplet break-up models wth sutably adjusted model parameters s hghly recommended for ths type of applcaton. At present, the WAVE breakup model s recommended for smulaton of spray combuston phenomena n Desel engnes, wth the model constants C1 and C set to 0.61 and , respectvely (for more detals please refer to the Spray Manual)... Actvaton and Handlng of the Combuston Module The characterstc features of the turbulent combuston process n a practcal devce (.e. the temporal varaton of the heat release rate, the turbulent flame speed, or the behavor of the flow-flame nteracton) strongly depend on applcaton case-specfc physcal and chemcal (fuel type) parameters. They also strongly depend on parameters such as the locaton of the gnton devce, the gnton tmng and the spark duraton. All requred nformaton s specfed n the.ssf-fle. The FIRE Combuston Module s actvated n the Solver GUI of the FIRE Workflow Manager Sept-014

13 Combuston Module FIRE v THEORETICAL BACKGROUND 3.1. Nomenclature Roman Characters q R r w heat release rate radcal pool fuel consumpton rate mean turbulent reacton rate a 1, a, a 3, a 4 A B Bl c c p c v C C 1, C, C 3 C fu, C Pr C m C n H m O l CO CO d D ds E E a f f n fu stochometrc relatons pre-exponental factor; constant; ar zone; spark stran constant; branchng agent Blnt-number reacton progress varable specfc heat capacty at constant pressure specfc heat capacty at constant volume carbon atom; correcton functon; curvature term turbulence model constants combuston model constants mxng rate constant hydrocarbon fuel carbon monoxde carbon doxde dstance current densty at electrode surface dscharge coeffcent energy actvaton energy mxture fracton mxture fracton of maxmum nucleaton fuel 30-Sept

14 FIRE v014 Combuston Module F Fc g G h H H H O I J k K Ka l l L m mn M n N N NO O O OH p P Pr Q Q h R fuel zone; functon Correcton functon resdual gas mass fracton deformaton gradent tensor; constant enthalpy; heat transfer coeffcent hydrogen atom molecular hydrogen water electrcal crcut nerts Jacoban determnant turbulence knetc energy; reacton rate flame stretch Karlovtz-number number of oxygen atoms; ntegral length scale length nductance mass; number of hydrogen atoms mnmum value of operator molecular weght; mxed zone number of carbon atoms; number of partcles ensemble of notonal partcles; atomc ntrogen ntrogen ntrogen monoxde atomc oxygen oxygen hydroxyl radcal probablty densty functon; pressure Producton term Prandtl-number ntermedate products; power; heat loss combuston heat release per fuel mass unt unversal gas constant; radus 3-30-Sept-014

15 Combuston Module FIRE v014 egr s S Sc T t u V x y Ze resdual gas chemcal reacton term stochometrc oxygen requrement; source term; surface; flame velocty; stran term Schmdt-number temperature; tracer; turbulent; transport term tme velocty volume; voltage Dstance; spark co-ordnates mass fracton Zeldovch-number Greek Characters σ n σ Pr, σ Sc Φ Γ α, β δ ε φ γ κ λ partal dervatve nucleaton varance Prandtl number, Schmdt number Increment; flter sze partcle property dffuson coeffcent; ITNFS functon turbulent flame surface densty CFM constants Kronecker delta; flame thckness dsspaton rate generalzed scalar quantty; equvalence rato Jacoban factors; functon sentropc exponent ar excess rato µ dynamc vscosty ρ densty τ υ π tme scale vscosty; stochometrc coeffcent p-number 30-Sept

16 FIRE v014 Combuston Module Ξ ω foldng factor gradent turbulent frequency; reacton rate; fuel consumpton rate ξ, η, ζ transformed coordnate system Subscrpts α a af AI arc b bd c cf crt curv CO d e eff egr evap f fr fl fu FP g gc ndex for chemcal speces; stochometrc functon maxmum annhlaton; actvaton anode fall auto-gnton spark arc burned; backward; branchng breakdown conventon; combustble; chemcal; convecton; crtcal cathode fall crtcal curvature carbon doxde dffuson electrcal effectve resdual gas evaporaton forward fresh flame fuel flame propagaton surface growth; exhaust gas gas column Sept-014

17 Combuston Module FIRE v014 H O e gn water Speces; ntermedate Inner-electrode gnton, j, l, r ndces k l lam m mean mn mn mx n N o O p pr prop r s seg spk st str S t tot u w Kolmogorov lamnar lamnar mxng mean mnmum mnmum mxed nucleaton; number of atoms ntrogen oxdaton oxygen precursor products propagaton reacton secondary segment spark stochometrc stran soot turbulent; termnaton total unburned; unversal wall flame surface densty 0 ntal 30-Sept

18 FIRE v014 Combuston Module Superscrpts 0 ntal ensemble-averaged ~ densty weghted ensemble-averaged ",' fluctuatng component [ ] concentraton; dmenson 3.. Combuston Models Ths secton descrbes the theoretcal background of the FIRE combuston module developed for the smulaton of speces transport, gnton and turbulent combuston of gaseous mxtures of hydrocarbon fuel, ar, and resdual (exhaust) gas. The determnaton of mean chemcal reacton rates represents a central problem n the numercal smulaton of chemcal knetc processes. Ths s because they appear to be hghly non-lnear functons of the local values of temperature and speces concentratons. Although t s desrable to use detaled reacton mechansms, avalable computatonal resources are nadequate to manage thousands of elementary reactons wth hundreds of partcpatng speces. Ths s due to the fact that for each speces consdered n the reacton mechansm, an addtonal conservaton equaton must be solved Hgh Temperature Oxdaton Scheme The complex oxdaton process of a hydrocarbon fuel wth ar occurrng durng the turbulent combuston process s n most cases expressed n accordance wth the current practce ([3.1]; [3.]) by a sngle step rreversble reacton of the form: 1kg { CnHmOk} + S kg { a1o + a N} ( 1+ S) kg{ a CO + a H O + ( 1 a a ) N } 3 Refer to the Speces Transport Manual for the coeffcents a 1 a 4 and S. 4 Some of the models (e.g. the ECFM) are based on more complex oxdaton schemes whch take more reacton steps and also some equlbrum reactons nto account. 3 4 (3.1) 3... Turbulence Controlled Combuston Model One of the combuston models avalable n FIRE s of the turbulent mxng controlled type, as descrbed by Magnussen and Hjertager [3.37]. Ths model assumes that n premxed turbulent flames, the reactants (fuel and oxygen) are contaned n the same eddes and are separated from eddes contanng hot combuston products. The chemcal reactons usually have tme scales that are very short compared to the characterstcs of the turbulent transport processes. Thus, t can be assumed that the rate of combuston s determned by the rate of ntermxng on a molecular scale of the eddes contanng reactants and those contanng hot products, n other words by the rate of dsspaton of these eddes. The attractve feature of ths model s that t does not call for predctons of fluctuatons of reactng speces Sept-014

19 Combuston Module FIRE v014 The mean reacton rate can thus be wrtten n accordance wth [3.37] ρr C = τ ρ mn y y, S CPr y, 1+ S fu fu fu Ox Pr (3.) R The frst two terms of the mnmum value of operator mn(...) smply determne whether fuel or oxygen s present n lmtng quantty, and the thrd term s a reacton probablty whch ensures that the flame s not spread n the absence of hot products. C fu and C pr are emprcal coeffcents and τ R s the turbulent mxng tme scale for reacton. The value of the emprcal coeffcent C fu has been shown to depend on turbulence and fuel parameters ([3.8]; [3.11]). Hence, C fu requres adjustment wth respect to the expermental combuston data for the case under nvestgaton (for engnes, the global rate of fuel mass fracton burnt) Turbulent Flame Speed Closure Combuston Model For the smulaton of homogeneously/nhomogeneously premxed combuston processes n SI engnes, a turbulent flame speed closure model (TFSCM) s avalable n FIRE. The kernel of ths model s the determnaton of the reacton rate based on an approach dependng on parameters of turbulence,.e. turbulence ntensty and turbulent length scale, and of flame structure lke the flame thckness and flame speed, respectvely. The reacton rate can be determned by two dfferent mechansms va: Auto-gnton and Flame propagaton scheme The auto-gnton scheme s descrbed by an Arrhenus approach and the flame propagaton mechansm depends manly on the turbulent flame speed. The larger reacton rate of these two mechansms s the domnant one. Hence, the fuel reacton rate ω fuel can be descrbed usng a maxmum operator va: ρ r fu = max{auto-gnton ω AI, Flame Propagaton ω FP } (3.3) The frst scheme s only constructed for ar/fuel equvalence ratos from 1.5 up to.0 and for pressure levels between 30 and 10 [bar], respectvely. The auto-gnton reacton rate ω AI can be wrtten as: ω = ρ a a3 a4 a5 a1 yfuel yo T Ta exp T AI (3.4) where a 1 to a 5 are emprcal coeffcents and T a s the actvaton temperature. The reacton rate ω FP of the flame propagaton mechansm, the second one n ths model, can be wrtten as the product of the gas densty, the turbulent burnng velocty S t and the fuel mass fracton gradent y fu va: ω = ρ S y (3.5) FP T Ths approach was ntally constructed for homogeneously premxed combuston phenomena. In order to apply ths model also for nhomogeneous charge processes, changes were made concernng the determnaton of ths reacton rate. fuel 30-Sept

20 FIRE v014 Combuston Module So n ths case, the fuel mass fracton gradent s replaced by the reacton progress varable gradent multpled by the stochometrc mxture fracton as follows: ω (3.6) FP = ρ S c Ths approach can also be used for homogeneous charge combuston and a near-wall treatment of the reacton rate s consdered addtonally. T The turbulent Karlovtz number Ka descrbes the rato of the tme scale of the lamnar flame (t F = δ l /S l ) to the Kolmogorov tme scale (t k = ), wth δ l as the lamnar flame f st υ / ε thckness, S l as lamnar flame velocty, υ as characterstc knematc vscosty and ε as dsspaton rate, respectvely. Hence, the turbulent burnng velocty S t ([3.3]; [3.33]) s determned by the followng formula dependent on the local Karlovtz number va: Ka b b 3 u' δ L = b1 S L l (3.7) t S T ( 1.0 Ka ) for 0 < Ka = SL + α u' (3.8) S T 3 4 S L α β = (3.9) S T 0.0 for Ka > 1.0 for 0.5< Ka 1.0 = (3.10) wth = b4 b b δ L SL lt.0 and b5 lt u' + β= δl α (3.11) Addtonally n these expressons, u represents the turbulence ntensty, l t the turbulent length scale and b 1 to b 7 are constants, respectvely. The lamnar burnng velocty S l, necessary for the determnaton of the turbulent burnng velocty and the flame thckness δ l can be expressed va: S L = δl 3 4 ( c + c λ + c λ + c λ + c λ ) 1 c 6 c7 + + c + p c c + c 11 9 p+ p 5 exp c 1 c13 + T c + T 14 (3.1) llustratng dentcal formulaton for both, dfferng n ther ndvdual emprcal parameters c 1 to c 14 (S l n [m/s] and δ l n [m]). Hence, the lamnar flame speed S l and flame thckness δ l, respectvely, depend on the ar excess λ, pressure p and temperature T. Fnally, the turbulent length scale l t has to be determned n order to close ths model usng the followng formulaton va: Sept-014

21 Combuston Module FIRE v k ε t = C µ l (3.13) Wthn the TFSC model the evaluaton of the fresh gas propertes, such as pressure and temperature, are requred for the determnaton of the lamnar burnng velocty S l. The same procedure s used for ts determnaton as for the CFM Coherent Flame Model A turbulent premxed combuston regme can be specfed usng dfferent propertes such as chemcal tme scale, ntegral length scale and turbulence ntensty. Due to the assumpton that n many combuston devces (e.g. recprocatng nternal combuston engnes) the chemcal tme scales are much smaller n comparson to the turbulent ones, an addtonal combuston concept can be appled: the Coherent Flame Model or CFM. The CFM s applcable to both premxed and non-premxed condtons on the bass of a lamnar flamelet concept, whose velocty S l and thckness δ l are mean values, ntegrated along the flame front, only dependent on the pressure, the temperature and the rchness n fresh gases. Such a model s attractve snce a decoupled treatment of chemstry and turbulence s consdered. All flamelet models assume that reacton takes place wthn relatvely thn layers that separate the fresh unburned gas from the fully burnt gas. Usng ths assumpton the mean turbulent reacton rate s computed as the product of the flame surface densty Σ and the lamnar burnng velocty S l va: wth ρ r (3.14) fu = ω L Σ ω L as the mean lamnar fuel consumpton rate per unt surface along the flame front. For lean combuston: ω = ρ S ρ = ρ y (3.15) L fu,fr L wth In ths equaton ρ fu,fr s the partal fuel densty of the fresh gas, ρ fr the densty of the fresh gas and y fu,fr s the fuel mass fracton n the fresh gas. When combuston starts new terms are computed, source terms and two quanttes n order to use equaton (3.14): Σ and S l. Currently, three dfferent CFM s are avalable whch are descrbed n ncreasng complexty n the followng chapters. Frst the standard CFM s descrbed, than the MCFM for applcaton under very fuel rch or lean condtons and fnally the ECFM whch s coupled to the spray module n order to descrbe DI-SI engne combuston phenomena. fu,fr fr fu,fr CFM-A Model The CFM-A s applcable for homogeneous and nhomogeneous premxed combuston examples where the determnaton of the lamnar flame speed s only vald wthn a specfc range of the equvalence rato dependent on the appled fuel. Outsde of ths equvalence rato range the flame speed s zero resultng n no fuel consumpton. 30-Sept

22 FIRE v014 Combuston Module Evoluton of Turbulent Flame Surface Densty The followng equaton s solved for the flame surface densty Σ ([3.10];[3.15]): Σ + t x j t ( u ) ν Σ j Σ = S Σ= S g S a + S LAM x j σ Σ x j (3.16) wth Σ as the turbulent flame surface densty (the flame area per unt volume), σ Σ s the turbulent Schmdt number, ν t s the turbulent knematc vscosty, S g s the producton of the flame surface by turbulent rate of stran and S a s the annhlaton of flame surface due to reactants consumpton: wth S ρ fu,fr L g = α K eff Σ and Sa =β Σ (3.17) ρfu S where K eff s the mean stretch rate of the flame, S a s wrtten for the case of lean combuston but equvalent equaton s obtaned for rch condtons by replacng the fuel mass fracton by the oxdant mass fracton. S LAM s the contrbuton of lamnar combuston to the generaton of flame surface densty. The term consders three dfferent effects: S LAM P + C + S = (3.18) showng the contrbuton of propagaton, curvature and stranng to the flame propagaton as descrbed later Stretchng and Quenchng of Flamelets Stretchng and quenchng of flame surface densty n term S Σ of equaton (3.16) s treated through the Intermttent Turbulence Net Flame Stretch- or ITNFS-model [3.39] descrbng the nteracton between one vortex and a flame front through drect smulaton [3.4]. By extendng t to a complete turbulent flow, t s assumed that the total effect of all turbulent fluctuatons can be deduced from the behavor of each scale. The producton of flame surface densty comes essentally from the turbulent net flame stretch. The flame stretch s wrtten as the large scale characterstc stran ε/k corrected by a functon C t, whch accounts for the sze of turbulence scales, vscous and transent effects [3.40]. C t s a functon of turbulence parameters and lamnar flame characterstcs. Hence, the turbulent flame stretch K t s dependent upon the turbulent to lamnar flame velocty and length ratos: C t = f(u /S l, l t /δ l ). u s the RMS turbulence velocty, l t the ntegral turbulent length scale and δ l the lamnar flame thckness. K eff = K t = ε C k K (3.19) K t s a very mportant property snce t nfluences the source term for the flame surface and therefore the mean turbulent reacton rate. α and β are arbtrary tunng constants used n CFM Sept-014

23 Combuston Module FIRE v Lamnar Flame Speed The lamnar flame speed s supposed to depend only upon the local pressure, the fresh gas temperature T fr from equaton (3.5) and the local unburned fuel/ar equvalence rato φ fr. If the correlaton of Metghalch and Keck [3.41] s chosen n the GUI, the followng emprcal relatons (vald for premxed combuston at hgh pressure and temperature) are appled: S L a1 a T fr p = SL0 ( 1.1yEGR ) T (3.0) ref pref T ref and p ref are the reference values of the standard state. a 1 and a are fuel dependent parameters. To account for the effect of exhaust gas rates the lamnar burnng velocty S l n the above relaton s decreased by the factor (1.0.1 y egr ). It s evdent that ths formulaton fals for y egr (=exhaust gas mass fracton) values larger than 0.5 snce the lamnar flame speed becomes negatve. For the lamnar flame speeds also tabulated values are avalable. These are consdered to be more accurate than the emprcal relatons above. The tables have been created by determnng the lamnar flame speeds from detaled reacton mechansms. They are avalable for the followng fuels: CH 4, C H 6, C 3 H 8, CNG, C 7 H 16 and H. For fuels whch are not on ths lst, FIRE automatcally chooses the most relevant table Lamnar Flame Thckness The lamnar flame thckness δ l s defned from the temperature profle along the normal drecton of the flame front (refer to Fgure 3-1): L ( T max T mn )/ ( dt / d x) max δ = (3.1) Fgure 3-1: Geometrcal Defnton of the Thermal Flame Thckness Blnt [3.3] proposed a correlaton ndependent from the flame studed. Ths correlaton takes the form of the Blnt number: Bl δ ( µ / Pr) / ( ρ S ) L = wth δb = b fr L (3.) δb 30-Sept

24 FIRE v014 Combuston Module where µ b s the lamnar dynamc vscosty evaluated for the burned gases and s calculated wth a temperature T b specfc to the burned gases. Ths temperature s evaluated as follows: b fr ( Qh / cp ) yfu, fr T = T + (3.3) So the lamnar flame thckness δ l from Blnt s correlaton s dependent on T fr, S l, the combuston heat release per fuel mass unt Q h (defned from enthalpy of formaton), c p and the vscosty of ar. Fnally, t s also dependent on the fuel mass fracton y fu,fr n the fresh gases. The temperature of the fresh gases s obtaned by an sentropc transformaton (see below) from gnton pressure/temperature condtons (p 0,T 0 ) to local state (p,t fr ) Fuel Reacton Rate If Σ s the volumetrc flame surface densty and f the mean lamnar fuel consumpton rate s supposed to be equal to S l, the mean fuel reacton rate may be wrtten as: ρr = ρ y S Σ (3.4) fu fr fu,fr L Isentropc Transformaton Wthn the CFM, the evaluaton s requred for the propertes (densty and fuel mass fracton) of the fresh gases (Duclos, et al.). These fresh gases are defned as follows: f (p 0,T 0 ) s the ntal pressure-temperature state before combuston starts and f p s the actual pressure, the fresh gases are n the (p,t) state usng the sentropc temperature T fr and densty ρ fr computed usng an sentropc transformaton as: 1 κ p0 κ T fr = T0, ρfr = p p R 0 T fr (3.5) where R 0 s the ntal gas constant and κ = c P /c V at local condtons. Snce the specfc heats are not constant, the relaton (3.5) s supposed to be a good approxmaton of the sentropc transformaton MCFM Model The MCFM s based on the same concept as the CFM-A but extensons are avalable n order to use t for a broader applcaton range. The dfferences to the standard CFM-A model are the determnaton of the lamnar flame speed and addtonal consderatons for the flame stretchng corrected by the chemcal tme as descrbed n the followng chapters Extended Lamnar Flame Speed For the model n the prevous secton (CFM-A) the descrpton for the determnaton of the lamnar flame speed and thckness were lmted to equvalence rato levels φ between ~ 0.6 to ~ 1.7 (fuel type dependent). In order to use these determnatons also for very fuel lean and rch condtons, extensons for ther determnatons are performed for equvalence rato levels lower than 0.5 and hgher than.0. For equvalence ratos outsde of the normal range, correlatons (lnear decrease) are made n order to have fuel consumpton also n very fuel lean or rch regons Sept-014

25 Combuston Module FIRE v014 The extenson for the flame speed determnaton has been mplemented especally for drect njected gasolne engnes n case of hghly stratfed charge dstrbuton Extended Stretchng of Flamelets Two man contrbutons are consdered n the stretch term K whch s used for the producton of the flame surface densty: turbulence and the combned effects of curvature and thermal expanson. Ths stretch can be modeled usng the assumpton of local sotropy of the flame surface densty dstrbuton va: 1 c K = α K t + a 3 SL Σ (3.6) c where K lam represents the lamnar stretch, K t s the mean turbulent stretch of the flame known from CFM-A usng the ITNFS-model [3.39] and a 3 s a constant. In the above formula c represents the progress varable whch s defned va: K lam c ρ y ρ y fu = 1 (3.7) fr fu,fr Correcton of Chemcal Tme The characterstc tmes for the ncrease of the flame surface densty are of the same order as the chemcal tmes, especally n the case of fast pston veloctes n recprocatng engnes, otherwse ths correcton s neglgble. For those engne-lke runnng condtons a correcton s essental and s made as follows: If K s the rate of the lnear ncrease of the flame surface densty (= sum of the lamnar and turbulent contrbuton), the rate of lnear ncrease K eff can be deduced from: K eff K 1+ K τ = (3.8) C wth τ C as chemcal tme calculated from the characterstc tme of the lamnar flame usng the Zeldovch number Ze va: C = a 4 δl S Ze τ (3.9) L wth S L as lamnar flame speed, δ L as ts flame thckness and a 4 as constant. The Zeldovch number Ze s calculated usng the actvaton temperature T of the fuel oxdaton. Hence, Ze T ( T T ) a a b fr = (3.30) Tb wth T b and T fr as the temperatures of the burnt and fresh gas phases, respectvely. 30-Sept

26 FIRE v014 Combuston Module ECFM Model The ECFM (E stands for extended) has been manly developed n order to descrbe combuston n DI-SI engnes. Ths model s fully coupled to the spray model and enables stratfed combuston modelng ncludng EGR effects and NO formaton. The model reles on a condtonal unburned/burnt descrpton of the thermochemcal propertes of the gas. The ECFM contans all the features of the CFM and the mprovements of the MCFM. Dfferences to the prevous coherent flame models are descrbed n the followng chapters. Up to now the ECFM-3Z combuston model (see next chapter) was only applcable for autognton cases, although the code s prepared to handle both gnton procedures, autognton and spark gnton. Now the gasolne engne ECFM combuston model can also be actvated va the ECFM-3Z mode usng all the attractve features such as the general speces treatment or separate CO/CO oxdaton reacton mechansm. So all standard engne applcatons can be done now wth only one dentcal combuston model Chemcal Knetc Reactons For turbulent combuston phenomena, the ECFM model leads to the calculaton of the mean fuel reacton rate. Hence, ths model uses a -step chemstry mechansm for the fuel converson lke: m k m Cn HmOk n + O n CO + HO 4 + (3.31) n k C nhmok O n CO + m + (3.3) n order to consder CO and H formaton n near stochometrc and fuel rch condtons, whle for fuel lean condtons ther formaton s neglected. In the above formula n, m and l represent the number of carbon, hydrogen and oxygen atoms of the consdered fuel. The reacton rate for reacton (3.31) s calculated by: H ωfu = ω γ (3.33),1 wth γ as a functon dependng on the equvalence rato φ, number of carbon and hydrogen atoms, respectvely, and for the second fuel consumpton reacton (3.3): L ( 1. γ) ωfu, = ωl 0 (3.34) wth ω l as the mean lamnar fuel consumpton rate descrbed earler. The ndvdual reacton rates of each speces partcpatng n the -step reacton mechansm can be expressed by: ω = υ ω,r fu,r (3.35) r = 1 wth υ,r as the stochometrc coeffcents of speces n the reacton r, whle for the reactants these coeffcents are negatve and for the products postve, respectvely Sept-014

27 Combuston Module FIRE v Fuel Reacton Rate The mean turbulent fuel reacton rate s computed as the product of the flame surface densty Σ and the lamnar burnng velocty S L va: γ for fuelreacton1 ρr fu = Σ υ,rωfu,r = ˆ ΣωL (3.36) r = 1 ( 1.0 γ) for fuelreacton Thermodynamc Quanttes From the prevous sectons t s obvous that the extended CFM can be closed f the local propertes of the burnt and unburned gases are known. Hence, n each computatonal cell two concentratons have to be calculated: a concentraton n the unburned gases and a concentraton n the burnt gases, respectvely. Hence two addtonal transport equatons have to be ntroduced, one for the unburned fuel mass fracton and one for the unburned oxygen mass fracton. In case of spray applcatons a source term S evap for the unburned fuel mass fracton has to be added. Usng these two addtonal equatons and the hypothess of local homogenety and sotropy each mass fracton can be determned. Below the two transport equatons are gven: t t x eff fu,fr ( ρ yfu,fr ) + ( ρ U j yfu,fr ) = Sevap j x j µ σ y x eff O,fr ( y ) ( U y ) µ ρ + ρ 0 j y x O,fr j O =,fr x j x j σ j (3.37) (3.38) Addtonally, a transport equaton for the unburned gas enthalpy s also ntroduced as shown below: t x eff fr ( ρ h fr ) + ( ρ U j h fr ) = ρ ε + + h evap j x j µ σ h x j ρ ρ fr p t (3.39) wth a source term h evap n case of evaporaton of the lqud fuel. Usng the unburned enthalpy and unburned gas composton, the local unburned gas temperature can be calculated. It s supposed that the unburned gas phase conssts of 5 man unburned speces, namely fuel, oxygen, molecular ntrogen, carbon doxde and water, whle for the burnt gas phase t s assumed that no fuel remans any more snce due to the hgh temperature regon the fuel molecules decompose. The burnt gas s composed of 11 speces, such as the atomc and molecular oxygen, ntrogen and hydrogen (O, O, N, N, H, H ), carbon monoxde and doxde, water, OH and NO. Usng y fu,fr and y O,fr as mass fractons of the fresh fuel and oxygen tracer, the rchness φ fr of the fresh gas can be mmedately obtaned as the rato of those propertes lke: where y fu,fr φ fr = αfu (3.40) yo,fr αfu s a constant stochometrc functon of the consdered fuel. 30-Sept

28 FIRE v014 Combuston Module The fresh gas ntrogen mass fracton can be easly obtaned as sum of all ntrogen contanng mass fractons. In case of resdual gas consderaton, the remanng gas n the fresh gas phase s consdered to be CO and H O, respectvely. The CO mass fracton n the unburned gas phase s obtaned as functon of all carbon contanng speces whle the fresh gas H O mass fracton depends on all hydrogen contanng speces and the fuel mass fractons, respectvely. The remanng quantty to be determned s the composton of the burnt gas phase. Due to the assumpton that no fuel exsts any more n the burnt phase, the knowledge of the mass fractons n the unburned phase leads drectly to the mass fractons of the burnt gas. Hence, the composton of the burnt gas can be re-constructed usng the Favre-averaged progress varable c as descrbed prevously. If y s the mean Favre-averaged mass fracton of speces, the burnt mass fracton (ndex b) s calculated va: y y ( 1 c) c y,fr,b = (3.41) Pollutant Modelng Complex chemcal schemes are strongly dependent on the local temperature, pressure and gas composton and the knowledge of these propertes allows an accurate determnaton of the pollutants. In spte of ths, for savng computng tme mostly schemes wth lmted steps and speces are consdered for smulaton. For the ECFM t s supposed that no fuel exsts n the burnt gas phase, but chemcal reacton may occur. Two dfferent knds of chemcal mechansms are consdered. The reactons n the burnt gas are assumed to be bulk reactons, whch means that no local reacton zone s taken nto account. These reactons are computed usng the propertes of the burnt gas phase, snce only reactons n hgh temperature regon are effectvely computed. In unburned regons the reacton rates are assumed to be neglgble. For the frst chemcal scheme t s assumed that the reactons are very fast and the partcpatng speces are n equlbrum. The followng reactons are consdered usng the Mentjes/Morgan [3.38] mechansm for computaton at the burnt gas temperature: O O O N O H + H N O H OH + CO CO + H O 4OH (3.4) Ths equlbrum mechansm solves molar concentratons of the partcpatng speces. Addtonally, four equatons are requred n order to solve these ten concentratons and these equatons are the element conservaton relatons for C, H, O and N. Frst the equlbrum constants K C are calculated by the formula: r C ( A lnt + B / T + C + D T E T ) K = exp + (3.43) r wth T A = T/1000 [K] and A r to E r are constants for each reacton r. A r A r r A r A Sept-014

29 Combuston Module FIRE v014 Then the element conservaton equatons nvolvng ntrogen, whch s decoupled from the remander of the system, are solved for the molecular and atomc ntrogen. The eght remanng equatons are then algebracally combned n order to obtan two cubc equatons wth two unknowns whch represent the scaled concentratons of atomc hydrogen and carbon monoxde. The smultaneous cubc equatons are solved usng a Newton-Raphson teraton loop wth scaled concentratons from the prevous tme step as ntal values. The second mechansm calculates the NO formaton usng the classcal extended Zeldovch scheme as follows: N N + O k1f + O NO + N k1b kf NO + O kb k3f N + OH NO + H k3b (3.44) wth the reacton rates ω NO, for each reacton r consderng both formaton and destructon of NO, respectvely. The reacton rate ω of each partcpatng speces n the reacton r usng the stochometrc coeffcents υ,r can be wrtten as: 3 ω = υ ω (3.45) r = 1, r These two mechansms are solved n a sequental way for computatonal effectveness. It s assumed that speces wth low concentratons are n statonary state and that ther mass fractons reman at ther equlbrum values durng the knetc phase. The above sub-model s appled f the Extended Zeldovch NO model s chosen n the Emsson models GUI. For more nformaton about the pollutant formaton models refer to the Emsson Manual. NO Ignton Model Fve dfferent gnton models are avalable for the CFM combuston models. Two models of ncreasng complexty are avalable for the ntaton of combuston by a spark plug when usng ECFM: the sphercal delay model and AKTIM. The ISSIM gnton model s only applcable wth the ECFM-3Z combuston model. Sphercal Model Ths gnton model can be used for all CFM models (manly recommended). In ths model a sphercal flame kernel s released usng the spark poston, gnton tme, flame kernel radus and spark duraton wth the flame surface densty specfed n the FIRE Workflow Manager. The flame surface densty s kept constant n all gnton cells wthn the flame kernel radus over the spark duraton. After end of gnton the flame surface densty must be self-sustanng for a propagatng combuston. 30-Sept

30 FIRE v014 Combuston Module Sphercal Delay Model The sphercal-delay model does not try to smulate all the effects takng place n front of the spark plug durng the tme of ntalzaton. Instead, a phenomenologcal representaton s used whch assumes that the tme of flame ntalzaton s a functon of the chemcal tme and of the mass fractons of the reactve gases. Usng ths hypothess a crteron s ntroduced as follows: C ( t) n t ρ d t = a 5 (3.46) 0 ρ0 τfl wth a 5 and n as constants, τ fl as the flame tme and ρ o s the ar densty at standard state. Ths crteron s ntegrated from the start of gnton and the deposton of the flame takes place f ths crtera C reaches a value larger than unty. The flame deposton s made usng a determned flame kernel radus R 1 whch s assumed to be the product of the thermal expanson rate and the lamnar flame thckness wth a 6 as constant va: Tb R1 = a 6 δl (3.47) T The flame tme s assumed to be the rato of the lamnar flame thckness to ts speed usng the prevalng temperature, pressure and gas composton at the spark plug as: δ fr L τ Fl = (3.48) SL Durng the tme t 1 (= tme at whch the flame kernel s released dependng on the deposton crteron) the flame radus s R 1. The poston of the flame kernel s not fxed and fluctuates from one tme step to the other dependng on the local turbulence condton. Consderng the fluctuatons, the flame s deposted wth respect to a spatal functon whch s chosen to be central to the spark plug. The spatal dstrbuton of the assumed flame surface densty follows a Gaussan functon and s descrbed va: d( x ) R1 l dst Σ = Ae (3.49) ( x) wth d(x) as dstance from a pont n the computatonal doman to the spark plug center and A as a constant wth: A = Σ( x) dv = 4πR (3.50) V l dst n the prevous formulaton s a representatve fluctuaton length at the spark poston and s assumed to be: dst l + u t l 0 1 = (3.51) where u s the turbulence ntensty, t the actual tme and l 0 s a constant representng the fluctuaton of the electrcal arc. For ths gnton model only the flame surface densty s ntalzed and the combuston whch takes place between t (start of gnton) and t 1 (flame surface densty deposton) s neglected Sept-014

31 Combuston Module FIRE v014 Convecton at the Spark Plug The convecton velocty at the spark has a strong nfluence onto the flame development and can be hardly neglected. Snce ths phenomenon at the spark s very complex, a smplfed model for the convecton at the spark plug s used where the convecton effect onto the flame kernel sze for ts deposton and quenchng s calculated. The flow convecton effect on the flame development depends on the gnton duraton. The approach uses a local source term representng a flame surface densty flux whch s proportonal to the mean flow veloctes at the spark. Ths flux starts after the deposton of the flame surface and contnues durng the electrc dscharge. The source term for the flame surface s estmated va: S ( ) = CC πr1 UC Σ (3.5) wth C C as constant functon of the drag effect of the electrodes, R 1 as the radus durng the flame deposton and u C s the local unburned gas convecton velocty computed by the relaton: U C ρ ρ wth u as the mean local velocty at the spark. Ellpsodal Model fr U = (3.53) Ths gnton model s manly developed for CFM-A and MCFM where a flame kernel can be specfed whch wll be "deformed" due to the level of turbulence and flow condtons at the spark plug resultng n an ellpsodal form (consderng an ntal sphercal form durng lamnar phase to the ellpsodal form durng turbulent phase). Prncpally the rad and gnton delay tme (deposton tme for the flame kernel) s calculated automatcally whch s currently not mplemented (therefore not recommended, needs experence for the ntalzaton of the requred parameters). AKTIM - Arc and Kernel Trackng Ignton Model The prevous model may perform accurately n some smple homogeneous engnes, but t clearly shows a lack n terms of predcton when engne parameter varatons on spark gnton are performed. The need to nclude phenomena lke charge stratfcaton, avalable electrcal energy, heat losses to the spark plug and the nfluence of turbulence on the early flame kernel lead to the development of the Arc and Kernel Trackng gnton Model, or AKTIM ([3.1]; [3.1]). AKTIM s based on three sub-models whch descrbe realstcally the dfferent parts of the spark plug ntaton: - the secondary electrcal nductve system. - the spark, represented by a set of Lagrangan partcles. - the flame kernels, descrbed as well by Lagrangan markers, that can be seen as the ntal flame development of dfferent engne cycles. 30-Sept

32 FIRE v014 Combuston Module Electrcal Crcut Fgure 3- shows a scheme of a classcal nductve gnton system. When the swtch s opened (at the prescrbed tme of gnton) electrcal energy s stored n the prmary nductance and only 60% of ths energy s avalable at the secondary crcut. AKTIM contans a model of the secondary crcut only; thus at gnton tme the ntal electrcal energy n secondary crcut E s (0) the resstance R s and the nductance L s are gven as nput parameters. After a few µs the voltage reaches the breakdown voltage V bd - whch depends on the gas densty around the spark plug and the nter-electrode dstance d e - and a spark s formed. Durng the next few µs an amount of electrcal energy E bd s transmtted to the gas (to the flame kernels n the current model) gven by: Fgure 3-: AKTIM - Electrcal crcut where G and C bd are constant. V E bd = G. (3.54) C bd bdde Then the man spark phase (glow phase) lasts a few ms, correspondng to the vsble spark observed n experments. The avalable energy E s and the ntensty decrease at the secondary electrcal s crcut are gven by: de dt s s ( t) ( t) = R ( t) V ( t). ( t) = Es L ( t) s s s e s (3.55) The nter-electrode voltage V e s gven by the relaton V V e gc ( t) = V = C gc cf.l + V spk. af p. + V ds s gc (3.56) where V cf and V af are the cathode and anode voltage falls (constant), V gc s the voltage n the gas column along the spark length l spk, p s the gas pressure n the vcnty of the spark, C gc s a constant and ds s the dscharge coeffcent, by default equals to Sept-014

33 Combuston Module FIRE v014 Durng the glow phase the nter-electrode voltage V e may reach the breakdown voltage agan. A new breakdown then occurs: the prevous spark vanshes and a new one s created. The glow phase lasts as long as electrcal energy remans. Spark Model At the nstant of breakdown a spark s ntated between the electrodes. In AKTIM t s represented by a set of Lagrangan partcles orgnally equally spaced between the electrodes. These partcles are transported by the mean flow except the ones at the spark extremtes (at the cathode and the anode). An arc curvature effect s ncluded, dependng on the gas dynamcs vscosty (Fgure 3-3). The dstance between adjacent spark partcles s mantaned nsde a gven range so that partcles are added or removed permanently. The spark length l spk appearng n the calculaton of the gas column voltage (3.56) s the sum of the dstances between adjacent spark partcles l mean multpled by a turbulent foldng factor. The producton of turbulent foldng can be splt nto a mean and turbulent Ξ arc component: lspk = Ξarc.l mean 1 dξarc 1 = Ξarc dt ( a + A ) T T (3.57) In the case of strong convecton at the spark plug, the spark length can be many tmes larger than the nter-electrode dstance d e, nvolvng a drect ncrease of the gas column voltage V gc that can lead to a new breakdown. In ths case, the spark partcles are suppressed and a new set of partcles correspondng to a new spark s ntated. Fgure 3-3: Spark Partcles and Flame Kernel Centers at Breakdown Tme (left) and Later (rght) 30-Sept

34 FIRE v014 Combuston Module Flame Kernel Model The flame kernel model draws ts nspraton from the Dscrete Partcle Ignton Kernel (DPIK) model of Fan et al [3.4]. At nstants of breakdown, a set of around N K =4000 Lagrangan flame kernels are ntated along the spark (Fgure 3-3). Each of them represents the gravty center of a possble flame kernel, havng a statstcal weght 1/N K. Each flame kernel s ntally a sphere of mposed radus 0.005mm contanng the fresh gas mass m fr that wll be burned durng the combuston ntaton phase: m = ρ πr d (3.58) fr fr where R eff = mm, and an excess of energy equals to 0.6E bd provded by the electrcal crcut. eff The flame kernels are then transported by the mean gas flow and a turbulent dsperson effect smlar to the one of O'Rourke (refer to the Spray Manual) for the fuel spray s added. Durng the glow phase, the kernels receve the electrcal power Q e from the spark: e Q e d = e exp 0.5.Vgc. s (3.59) l spk When the crtcal energy E crt s reached the kernel gnton occurs and a fracton of the fresh gas mass m fr s used to ntalze the kernel burnt gas mass m b. The crtcal energy s gven by: E γ = πδl (3.60) γ 1 crt lspk.p. 4 where p s the local gas pressure and δ l the local flame thckness. In car engne applcatons the crtcal energy s reached nstantaneously. After the gnton, the evoluton of each flame kernel s determned by the evoluton of ts excess of energy E and ts burnt gas mass m : where b dmb = ρfrseff U dt de = Q e QW dt Leff ρfr s the fresh gas densty as calculated by the ECFM model, kernel surface, U Leff s ts lamnar flame speed and Seff s the effectve Q W s the wall heat loss. The flame kernel combuston s accompaned by a fuel consumpton n the gas phase, n cells ncluded nto the flame kernel volume. (3.61) 3-30-Sept-014

35 Combuston Module FIRE v014 Fgure 3-4: Flame Kernel Real Sze at Breakdown Tme (left) and Later (rght) The effectve kernel surface s gven by: Seff = fw. Ξ.4π 1/ 3 3m b r = 4πρb ( r ) (3.6) wth r the kernel radus - ncreasng wth tme as proportonal to the burnt mass fracton ρ b the burnt gas densty nsde the kernel (see eq. 3.75), Ξ the turbulent (Fgure 3-4) - foldng of the surface and f w a wall factor. The turbulent foldng factor Ξ models the stretchng and quenchng of the kernel surface. Its evoluton s treated by the ITNFS model [3.39]. The wall factor f w measures the part of the kernel surface whch s n contact wth the spark plug walls and therefore s nactve as far as the kernel combuston s concerned. If there s no overlappng, the factor s equal to 1. The effectve lamnar flame speed U Leff n relaton (3.61) s gven by: ULeff = 0.5.U δl ζ = r. 1 ζ + L ( ζ 1) Tb T + ζ b (3.63) where T b s the burnt gas nsde the th kernel. The kernel burnt gas temperature and densty are related by: Tb ρb = T = ρ b b E + m Cp T T b b b. b (3.64) Fnally, the wall heat loss term Q W n equaton (3.61) s calculated as: Q W W ( T T ) = h.s. (3.65) b SP 30-Sept

36 FIRE v014 Combuston Module where h s a gven heat transfer coeffcent equal to 000 W/m K, SW s the contact surface between the flame kernel and the spark plug and T s the spark plug temperature. When usng AKTIM, t s recommended to mesh the spark plug n order to correctly capture the flow dynamcs and wall heat transfer. In partcular the kernel-wall contact surface and the spark plug temperature are then accurately computed. However f the spark plug s not meshed, the wall heat loss relaton (3.65) stll apples usng T spk = 600K and a rough evaluaton of the contact surface based on the dstance between the flame kernel center and the cathode/anode locatons. When the combuston of a flame kernel ends, ts surface s deposted as flame surface densty randomly n a cell contaned nto the kernel volume, thus ntalzng the ECFM model. ISSIM - Imposed Stretch Spark Ignton Model Ths new Euleran mult-spark gnton model (ISSIM) s based on the electrcal crcut model of AKTIM as descrbed n the prevous chapter whch provdes the spark length and duraton and estmate the energy transferred to the gas and the amount of burnt gas mass deposted at the spark. At gnton tmng an ntal burned gas profle s created. Then, the reacton rate s drectly controlled by the flame surface densty (FSD) equaton whose source terms are modfed to correctly represent flame surface growth durng gnton. As long as a spark exsts, a spark source term s added to the ECFM n order to ensure the flame holder effect at the spark. The usage of the FSD equaton naturally allows multspark descrpton (.e. modelng more than one spark plug at a tme or multple frngs of a sngle spark, or combnatons of both). The ISSIM model can only be appled wth the ECFM-3Z combuston model and not wth the ECFM. The ISSIM model has a much smpler structure than the former Lagrangan AKTIM model and presents some clear advantages that should mprove the smulaton of SI engnes: Both the early gnton and turbulent propagaton phases are consstently modeled snce the flame surface densty equaton s transported from the very begnnng of spark gnton; The model provdes the amount of burnt gas mass deposted n the vcnty of the spark, the spark source term n the ECFM equaton and the correspondng fuel consumpton rate; Durng gnton, the flame growth s not controlled by a 0D model, but drectly by the ECFM equaton usng local evaluatons of the Euleran felds. Ths has two advantages: 1. It approprately accounts for the effect of mxture stratfcaton n the vcnty of the spark whch s not the case wth AKTIM;. It accounts for the aerodynamc effects resultng from the mean flow and turbulence at the spark and the resultng spark and flame stretch; It accounts for the flame holder effect and provdes means to ntegrate a blow-off n the case of excessve convecton at the spark; SP Sept-014

37 Combuston Module FIRE v014 Electrcal Crcut The electrcal system model s descrbed n the prevous chapter and s based on the electrcal crcut model of the Lagrangan AKTIM (classcal nductve gnton system) usng the same formulas and equatons. Spark Model At breakdown the spark length s equal to the spark gap d e. Then, the spark s stretched ( l mean ) by mean convecton and turbulent moton of the flow. The total length of the spark s lspk as gven n the same equaton (3.57) as for AKTIM. The model for the spark wrnklng by the turbulent flow Ξ arc s gven by the spark wrnklng evoluton equaton whch has the same form as for AKTIM (see equaton (3.57)) where a T and A T are the spark stran by the turbulent and the mean flow, respectvely. a T corresponds to the effect of the turbulent eddes greater than the arc thckness l c and lower than the half length of the spark l M. l c s estmated as follows: l c πd s = (3.66) s where D S s the current densty at the electrode surface, whch s of the order of 100 A/cm durng glow mode. l M s smply wrtten: 1 l M = l spk (3.67) The computaton of the stran a T s smlar to the ITNFS functon n the equaton of the flame surface densty equaton: a T u Γ l = (3.68) t where l t s the ntegral length scale of turbulence and u s the correspondng fluctuaton velocty. Γ = 0.8 ln() 3 lt max 3 ( l, η) max( l, l ) c l t M t 3 (3.69) The mean stran A T s the contrbuton of the mean flow and t s expressed as follows: A T u l = (3.70) M The mean spark length l mean can be affected by the flow convecton assumng a rectangular shape for the spark, so that the equaton for l mean reads: dl dt mean u ~ ( x, t) = (3.71) spk 30-Sept

38 FIRE v014 Combuston Module ~ s the resolved velocty feld at the spark plug. where u ( x spk, t) Spark and Flame Kernel Couplng Durng the arc and glow phases, only a fracton of the spark energy s released to the gas. The energy released n a thn regon near the electrodes s essentally lost by fall voltage. The energy loss to the electrodes durng the glow phase s about 70-80%. The potental dfference between both electrodes, also called spark voltage s wrtten: where V = V + V + V (3.7) spk V cf s the cathode fall voltage, cf af gc V af s the anode fall voltage and V gc s the gas column voltage. The anode fall voltage s smlar for the arc and glow modes and equal to V for Inconel (an alloy based on Nckel, Chrome and ron). The cathode fall voltage s 7.6 V durng arc phase and 5 V durng glow phase for Inconel. The gas column voltage s approxmately equvalent: V gc Cd p n a = e (3.73) where C s a constant (6.31 durng arc phase and durng glow phase), s the crcut ntensty through the gas column (n A), n s a constant (0.75 durng arc phase and 0.3 durng glow phase), d e s the spark gap, p the pressure, a s a constant equal to The voltage on the gas column depends on the spark length. The expresson (3.73) s avalable only for non-convectve and non-turbulent flows. The descrpton of the breakdown and arc phases s very complex: extremely short duraton, presence of a plasma channel, very hgh temperatures and unsteady behavor. The modelng of these modes s therefore a complex ssue whch s not computed but the ntal condtons are set for the spark dscharge n terms of energy deposton. The energy deposted after these phases s expressed as a functon of the spark gap and of the breakdown voltage: where C bd J E C = d bd e Vbd K =. K s also a constant (for ar m bd (3.74) K 1. 5 kv = ). mm The energy transferred to the gas s: The breakdown voltage s wrtten: gn ( tgn ) = 0, Ebd E 6 (3.75) V bd = F 1 c ρ K d ρ0 e (3.76) where ρ 0 s the densty at standard condtons (300K, 1bar) and functon. At the frst breakdown: F c s a correcton Sept-014

39 Combuston Module FIRE v014 c max 16, ρ ρ0 = max 0.1, ρ ρ0 In the case of restrke (by convecton), F = 1. In practce F (3.77) c V bd can be affected by unsteady effects. Moreover, t does not nclude the effect of the electrode geometry and materal. It may be notced that contrary to the gas column voltage, the breakdown voltage s controlled by the gas densty (and not the pressure) near the electrode surface. Before the spark s created, the voltage between the electrodes V spk ncreases wth the rse rate of 1 kv/ms. When the breakdown voltage s reached a spark s formed and an amount of energy (Eq. (3.75)) s deposted to the gas. After that, the energy provded to the gas durng the glow phase s computed. Durng the glow phase, the voltage fall s localzed n the vcnty of the electrodes. Therefore t s assumed that the energy released wthn these regons s lost to the electrodes. Fnally, the energy transferred to the gas s deduced from the gas column voltage and the ntensty as follows: degn dt ( t) where the gas column voltage s wrtten: V gc ( t) ( t) = (3.78) s V gc = 40.46l spks p (3.79) To ncorporate the effect of the electrode dameter (d el ) on the spark effcency, a correcton functon s added to the gas column voltage resultng n the followng formula: V gc del lspk = 40.46l spks p e (3.80) Ths energy E gn s used to determne f gnton s successful or not. The crtcal gnton energy s retaned: E c γ = lspk 4πpδ L (3.81) γ 1 Whle Egn ( t) < Ec( t), the flame kernel s not created. On the contrary, f E ( t) Ec ( t) gn >, a flame kernel s formed around the spark and gnton starts. In that case, an amount of burnt gas mass s deposted at the spark whch corresponds to a cylnder wth radus and heght l spk : δ L m gn b = ρ l 4πδ (3.8) u spk L spkplg 30-Sept

40 FIRE v014 Combuston Module ISSIM-LES (Large Eddy Smulaton) Spark Ignton Model ISSIM-LES descrbes the early flame kernel development n a way that s requred by the LES framework allowng the followng gnton features lke: mult-gnton n tme and space, re-gnton and flame holder effect under strong convecton condton around the flame kernel. The ISSIM-LES approach used n FIRE s based on the descrpton gven by Coln and Truffn [3.16], where the modfed transport equaton for the flame surface densty (FSD) (see chapter for more nformaton) can be expressed as: Σ t = T res + T sgs + αs res + S sgs + αc res + αc sgs gn ( αs NΣ) + ( 1 α ) ( 1+ τ ) ΞS Σ + ω d P r b l Σ where α remans close to zero durng gnton and equal unty when gnton s over. Therefore S res + Cres ( S d NΣ) s suppressed durng gnton and replaced by the term r b ( 1 τ ) ΞS Σ + l flame kernel radus and as: Σ Ξ = c Σ = P. In the above equatons Ξ represents the turbulent wrnklng factor, rb the ω Σ gn ( c c ) c s the FSD gnton source term. These terms can be defned ~ N wth Σ (( c c ) N ) c ~ c = Σ + ω gn Σ Σgn Σc 3 3 max,0 c = wth Σgn = and rb = 4 c dt rb π gn dv 1 3 c gn represents a Gaussan profle of the ntal volume fracton and s defned as (c 0 s a constant and x spark s the spark plug poston): c gn = c e 0 x x spark 0.6 ˆ Note: The ISSIM-LES approach can only be used wth the ECFM-3Z combuston model n combnaton of actvated lamnar terms and one of the turbulence models, LES or LES-CSM, respectvely Sept-014

41 Combuston Module FIRE v Lamnar Terms for the Flame Surface Densty Equaton The addtonal source term for the flame surface densty equaton, whch consders the contrbuton of lamnar reactons conssts of three terms: P consders the propagaton of the flame: ρ P = S ΣN L ρ fr (3.83) C consders the creaton and destructon of flame surface by the curvature: C ρ = S ( N )Σ ρ fr L (3.84) S consders the stranng of the flame by all structures of turbulence: ~ (3.85) S = ( u NN : u~ )Σ wth: N = c c Large Eddy Smulaton (LES) Terms for the ECFM / ECFM-3Z combuston model The followng chapter descrbes the modfcatons, whch are necessary for the FSD transport equaton and source terms n the framework of LES. The CFMLES method was frst ntroduced by Rchard et al. n 007 [3.53] where modfcatons of the dffuson and source terms were ntroduced n order to keep the flame brush thckness equal to ˆ = n x flt wth n flt as model parameter (5 to 10). Scale ˆ represents a combuston flter sze whch s n flt tmes larger than the LES grd scale x. Therefore nstantaneous quanttes can have now 3 dfferent mathematcal formalsms as gven n the followng: φ ~ φ ˆ φ cell average value Favre fltered value thckened flteredlength scale The ntroducton of the combuston flter sze s done snce eddes smaller than the flame thckness are not able to wrnkle the flame front [3.15]. The flame brush thckness should be equal to the combuston flter sze ˆ whch s controlled by the controllng δ cn factor F. The controllng factor should ensure the equalty [3.53]: Fδ = = ˆ cn n res x (3.86) The dervaton of the controllng parameter s based on the natural flame brush thckness, grd spatal resoluton and correspondng equlbrum wrnklng factor used as an estmator for SGS (sub-grd scale) turbulence level nsde the cell. 30-Sept

42 FIRE v014 Combuston Module The FSD equaton, as a part of the CFMLES combuston approach, s derved accordng to [3.53] fltered to the combuston flter and splt nto resolved and unresolved parts: Σ t = Tres + Tsgs + S res + S sgs + Cres + Csgs + P (3.87) where T res, S res, C res and P are the transport, stran, curvature and propagaton terms due to resolved flow motons (see chapter ) and T sgs, S sgs and C sgs are the unresolved transport, stran and curvature terms, respectvely, wth: Σ t = t ( u~~ ˆ υ Σ) + σ Σ + ( u~ NN : u~ ) c c L,0 d c(1 c) P * * lam ( N ) Σ + β S ( Σ Σ ) Σ ( S NΣ) S d Cres Tres c Sc t Tsgs Csgs Γ uˆ ˆ uˆ Σ + Σ +, σ S c S l l res δ ˆ Dsplacement speed s calculated from the conservaton of mass through the flame front: Sl ρ S d ρ Sl ρ fr S d = ρ fr Ssgs (3.88) = (3.89) and the normal to the flame front N s calculated as above (see chapter ) as normalzed gradent of the reacton progress varable feld. The Gamma functon n the above FSD equaton s derved n [1001] and adopted for the CFMLES n [999]. It represents the effectve stran of the flame by turbulence at all relevant scales smaller than ˆ. The fluctuaton velocty s obtaned from dmensonal relatons and smple Smagornskylke model (C s = 0.1): ~ t uˆ' = µ ρ C s X (3.90) δ L s the flame thckness from Bnt s correlaton descrbed above. Inputs for C sgs are lamnar FSD and Bray-Moss-Lbby expresson [999] as: Σ lam = ~ ~ ~ ρ + ρ + ( c c ) N and c = c ( τ 1) c (3.91) fr Fnally the controllng parameter F can be defned as: Sept-014

43 Combuston Module FIRE v Sept ) (1 ˆ ˆ ˆ, ˆ ˆ 8 ˆ ˆ ˆ, ˆ 1 K u S u Sc Sc K u S u n F l l c t t c c l l c x res Γ + Γ = ρ δ σ υ σ υ σ δ σ (3.9) Model parameters K 1 and K are obtaned from the thermal expanson rate 1 = b ρ fr ρ τ as: ( ) = * * 1 τ τ τ τ τ β c K (3.93) τ β + = 1 1 * * c K (3.94) wth 5 = res n, 3 4 * = β and 5 * = 0. c. c σ s a correcton factor n the expressons of the dffusvty and SGS stran and can be expressed as: ( ) ( ) Γ Ξ = = ˆ ˆ ˆ, ˆ * * u S u c S wth n l l eq l cn cn x res c δ τ τ τ τ τ β δ δ σ (3.95) and eq Ξ s the equlbrum wrnklng factor gven by: = + Γ + = Ξ ˆ ˆ ˆ 1 1 ˆ ˆ ˆ, ˆ ˆ 1 * u C and c u S u S s t l l t l eq υ τ β δ υ (3.96) Note: The LES approach usng the unresolved source terms for the FSD can only be used wth the ECFM and ECFM-3Z combuston model n combnaton wth actvated lamnar terms and one of the turbulence models, LES or LES-CSM, respectvely.

44 FIRE v014 Combuston Module ECFM-3Z Model The exstng ECFM model s devoted to gasolne combuston. The ECFM-3Z model was developed by the GSM consortum (Groupement Scentfque Moteurs) specfcally for Desel combuston. Ths s a combuston model based on a flame surface densty transport equaton and a mxng model that can descrbe nhomogeneous turbulent premxed and dffuson combuston. The model reles on the ECFM combuston model, prevously descrbed and mplemented n FIRE and on a three areas mxng descrpton. Further t s coupled wth an mproved burnt gas chemstry descrpton compared to ECFM. Up to now the ECFM-3Z combuston model was only applcable for auto-gnton cases, although the code s prepared to handle for both gnton procedures, auto-gnton and spark gnton,. Now the gasolne engne ECFM combuston model can also be actvated va the ECFM-3Z mode usng all the attractve features such as the general speces treatment or separate CO/CO oxdaton reacton mechansm. So all standard engne applcatons can be done now wth only one dentcal combuston model. Fgure 3-5: Zones n ECFM-3Z Model Mult-Component Capabltes for the ECFM-3Z Model When usng the ECFM-3Z model t s possble to defne the fuel as consstng of more than one chemcal speces. The fuel can be prescrbed as a mxture of several components. In prncpal an arbtrary number of fuel components s possble, but t s recommended to use a mxture of up to 6 or 8 hydrocarbons. By usng ths number of components each group of hydrocarbons can be represented. Ths descrpton s avalable for all types of combuston. The provded soluton enables a connecton to the mult-component spray capabltes. If n the spray module the fuel s defned as consstng of several components, then the same components can be chosen n the gas phase set-up (refer to the Speces Transport Manual). Snce the Lagrangan and the gas phase have to be connected, t s mportant to prescrbe the same ndex for each fuel component n the spray module and the gas phase ntal condtons set-up Sept-014

45 Combuston Module FIRE v014 The ECFM-3Z combuston model uses the fuel components to combne them temporarly to a fuel mxture durng the calculaton. Ths means that effects lke auto-gnton and flame propagaton are handled for ths combned fuel wthn the combuston model. The rate of reacton for each fuel component s fnally splt up. By dong ths t s possble to calculate the consumpton of each component separately. The development of the combuston products s based on the consumpton of the sngle components The Global Speces Equatons Compared to the standard ECFM model, the ECFM-3Z model takes nto account: three new tracers for NO, CO and H n order to know the mass fractons n the unburned gases, two speces descrbng the mxng, quanttes) F ρ Fu and and an ntermedate speces for auto-gnton y~ I. Thus sx more scalars are taken nto account. A ρ O (only used to rebuld mxng In the ECFM-3Z model, the transport equatons are solved for the averaged quanttes of chemcal speces O, N, CO, CO, H, H O, O, H, N, OH and NO. Here, averaged means these quanttes are the global quanttes for the three mxng zones (that s n the whole cell). Therefore, the term "burnt gases" ncludes the real burnt gases n the mxed zone b b (zone M n Fgure 3-5) plus a part of the unmxed fuel (zone F n Fgure 3-5) and ar b (zone A n Fgure 3-5). Ths equaton s classcally modeled as: ρy~ t X ρu~ y~ + x X x µ µ t y~ X + Sc Sc t x = ω (3.97) X u m = m where α. ω X s the combuston source term and The fuel s dvded n two parts: the fuel present n the fresh gases, present n the burnt gases, u u mfu / V ρ = = m / V ρ u y~ Fu y~ ~ Fu + y b y~ Fu b m = m b b mfu / V ρ = = m / V ρ y~ X s the averaged mass fracton of speces u y~ Fu and the fuel u Fu Fu b Fu Fu y~ Fu and Fu (3.98) ρy~ t wth b Fu y~ = as the mean fuel mass fracton n the computatonal cell. u m Fu (resp. b m Fu ) s the mass of the fuel contaned n fresh gases (resp. burnt gases). A transport u equaton s used to compute y~ Fu : u u u Fu ρ Fu t Fu u µ µ + = ρ ~ S Fu x x + Sc Sc t x where u~ y~ y~ (3.99) + ω u S Fu s the source term quantfyng the fuel evaporaton n fresh gases. u Fu u ω Fu s a source term takng auto-gnton, premxed flame and mxng between mxed unburned and mxed burnt areas nto account. 30-Sept

46 FIRE v014 Combuston Module The Mxng Model The amount of mxng s computed wth a characterstc tme scale based on the k-ε model. Durng evaporaton, t s necessary to specfy the amount of fuel gong nto the mxed zone (from zone F to M=M u +M b ) and the amount gong nto the "pure fuel" zone (nto zone F=F u +F b ). For a desel spray, the fuel droplets are very close to each other and are located n a regon essentally made of fuel. After the evaporaton of the fuel, an adequate tme s needed for the mxng from the nearly pure fuel regon wth the ambent ar (mxng from zone F and A to M). In ths case, the mxng of fuel wth ar s modeled by ntally placng the fuel nto the pure fuel zone. So, the fuel whch evaporates from a droplet s released n the pure fuel zone F=F u +F b ). In order to descrbe the three mxng zones, two new quanttes are ntroduced: the F F u,f b,f unmxed fuel y~ Fu ( ~ A u,a b,a y~ Fu = y~ Fu + y Fu ) and the unmxed oxygen y~ ( y~ = y~ O + O ). The equatons for these unmxed speces are: A O O y ~ ρy~ t ρy~ t ρu~ y~ µ y~ F F F Fu Fu Fu F + SFu x x Sc x = ρ A A A O ρu~ y~ O y~ O µ A M + = ρe O x x Sc x ~ + ρe F M Fu (3.100) The mxng model s descrbed by the source terms and F M E Fu n the unmxed fuel A M E O and unmxed oxygen equatons. The amount of mxng s computed wth a characterstc tme scale based on the k-epslon model: E E F M Fu A M O 1 = τ m 1 = τ m y~ y~ F Fu A O F 1 y~ y~ 1 y~ Fu A O O ρ ρm u ρ u u ρm u M M Fu M M ar + EGR (3.101) M M s the mean molar mass of the gases n the mxed area, M Fu s In equaton (3.101), the molar mass of fuel, M O s the molar mass of O, M ar + EGR s the mean molar mass of u the unmxed ar+egr gases, ρ s mean densty, ρ s the densty of the unburned gases (the densty of fresh gases that would be obtaned f combuston had not occurred), y~ O s the oxygen mass fracton defned by equaton (3.103) and τ m s the mxng tme defned as: u 1 ε τ m =βm (3.10) k m β s a constant wth the default value 1. The oxygen mass fracton n the unmxed ar s computed as follows: Sept-014

47 Combuston Module FIRE v014 y~ y~ TO O = 1 y~ TFu (3.103) where y~ TO and y~ TFu are the oxygen and fuel tracer respectvely Condtonal Compostons Mxed Zone In order to reconstruct the mxed and unmxed parts, as mentoned above, two speces have been ntroduced, unmxed fuel and unmxed oxygen ( y~ and y~ ). Knowng these two quanttes, the mxed quanttes can be constructed. The man assumpton s that the unburned gas composton of ar+egr s the same n the mxed and unmxed areas. Thus f the total amount of oxygen (the oxygen n the mean/total cell) and the unmxed oxygen ( y~ ) s known, then the mass rato of ar + EGR mxed over A O total ar + EGR (n the total cell) s known. The mass of fuel tracer n the mxed area s obtaned drectly from the dfference between the fuel tracer and the unmxed fuel, as for the oxygen speces: F Fu A O ρ ρ M TFu = ρ TFu ρ F Fu M A TO = ρto ρ O (3.104) For the unburned and burnt fuel mass fractons the unmxed part must be subtracted from the unmxed fuel zone: ρ ρ u,m Fu b,m Fu = ρ = ρ u Fu b Fu ( 1 ~ c) ρ ~ cρ F Fu F Fu (3.105) wth the Favre averaged progress varable: ~ c u m y~ 1 = 1 m y~ For the other speces α we defne a coeffcent the oxygen tracer. u Fu = (3.106) c y~ A A O O = y~ TO TFu A co whch s the rato of the unmxed O to y~ y~ A X = (3.107) where y~ TX s the mass fracton of the tracer of the X speces: for speces O, CO, NO, Soot and H, a transport equaton s drectly solved for these tracers as shown n the prevous secton. For speces N, CO and H O, the tracers are reconstructed from the N, C and H atom balance equatons. TX 30-Sept

48 FIRE v014 Combuston Module Fresh and Burnt Gases There are two ways to obtan the burnt gas propertes dependng on the value of the progress varable c. When the value of c exceeds 0.05, these propertes are deduced from the mean and the unburned gas quanttes usng the classcal relatonshp between the mean value, the unburned one, the burnt one and c. When the value of c s too low, we obtan these quanttes assumng they are the result of a complete combuston (+ equlbrum) under the local thermo-chemcal condtons. Prevously t was descrbed how to defne the equvalent quanttes n the mxed zone, startng from the mean speces mass fractons and enthalpes. Now, the mxed zone tself wll be dvded nto fresh and burnt gas zones. In all CFM models, the flame front s descrbed as an nfntely thn nterface that separates fresh and burnt gases. In order to correctly compute the lamnar flame speed n the fresh mxture and the pollutant formaton n the burnt gases, the speces mass fractons must be known precsely n these two regons, y~ and u,m X u,m y~ (These quanttes are evaluated f: c>0.05, and f the mass fracton occuped by the mxed zone s ρ A + F < These mass fractons are defned as: where by: u,m m (resp. b,m X b,m u,m u,m mx y~ X = (3.108) u,m u,m m b,m b,m mx y~ X = (3.109) b,m b,m m b,m m ) s the unburned (resp. burnt) mass n the mxed zone defned ρ m m u,m b,m = ( 1 ~ c) m ~ M = cm M (3.110) where M m s the total mass n the mxed zone of the cell The Auto-gnton Model The gnton delay s computed ether through a correlaton or through an nterpolaton from tabulated values. An ntermedate speces ntegrates the advance n the auto-gnton process. When the delay tme s reached, the mxed fuel s oxdzed wth a chemcal characterstc tme. The Auto-gnton Delay The auto-gnton of the unburned mxture s computed over the unburned mxed gases. The gnton delay s obtaned by dfferent means, dependng on the parameter specfed by the user n the GUI: The correlaton used for desel combuston s: τ d = u,m 0.53 u,m 0.05 u 0.13 u T ( NO ) ( N Fu ) ( ) e ρ u,m u,m 5914 (3.111) Sept-014

49 Combuston Module FIRE v014 where molar concentratons are gven n mole per cubc meter, the temperature n K, the u densty ρ n kg/m 3. The tabulaton of n-heptane auto-gnton delay s done over a specfc range of pressures, temperatures, equvalence rato and EGR rates. Two versons of accessng the tabulated values are avalable. The frst one s calculatng the gnton delay tme accordng to a onestep gnton behavor. The second approach s treatng the gnton delay as a two-step event whch ncludes also the cool flame burnng under lean and low temperature condtons. The Intermedate Speces The ntermedate speces ρ has the same evoluton equaton as the fuel tracer I ρ TFu wthout the source term due to spray evaporaton. Assumng the mass of ntermedate speces n zones F and A s zero and that ts molar mass s equal to the fuel molar mass, therefore the condtoned molar concentraton reads: N ρ C M I M V I = (3.11) M M Fu The ntermedate speces ncreases n tme wth the followng source term: N M I M t = N M TFu M F ( τ ) d (3.113) where F s a functon of the delay tme τ d : M N I M B τd + 4( 1 Bτd ) M N TFu M F( τ d ) = (3.114) τ d where B s a constant set to 1s. The F functon was chosen to avod tme step dependency for auto-gnton. Oxdaton of the Fuel The auto-gnton delay s reached when the molar concentraton of ntermedate exceeds M M the molar concentraton of the fuel tracer I M 1 N > N. The mxed fuel s oxdzed wth TFu M a chemcal characterstc tme. The fuel molar concentraton evoluton s: N u,m Fu M t N = τ u,m Fu M c (3.115) The chemcal characterstc tme τ c s defned by: where c 0 c Ta b T τ = τ e (3.116) T a s an actvaton temperature set to 6000 K, and the constant 0 τ c s equal to 5 x 10-5 s. 30-Sept

50 FIRE v014 Combuston Module Oxdaton Knetcs of the Fuel The premxed flame and the auto-gnton n the fresh gases lead to a snk term of fuel n the unburned mxed zone. Ths fuel s then oxdzed by the model presented n ths secton. Ths oxdaton leads to the formaton of CO and CO n the burned gases. For the ECFM-3Z, a dfferent fuel converson mechansm (-step chemstry mechansm) s used compared to the ECFM. Due to the ntroducton of CO/CO knetcs the fuel oxdaton model has been modfed. The same model s used for auto-gnton and premxed flame consumpton. In the Unburnt Gases As prevously mentoned, the model s enrched by new unburned gases speces. It s assumed that the unburned gas composton ncludes fuel, O, N, CO, CO, H O, H, NO. Thus compared to the standard ECFM model, three more tracers need to be ntroduced, CO tracer, H tracer and NO tracer. These tracers should be ntroduced n the balance equatons when the condtoned burnt gas concentratons are computed. The oxdaton of the fuel s decomposed n two phases: A frst partal oxdaton of fuel s realzed whch leads to the formaton of a great amount of CO, and a few CO, n the burnt gases of the mxed zone. In the burnt gases of the mxed zone, the CO prevously generated s oxdzed to CO. Ths new oxdaton mechansm provdes a more accurate descrpton of the formaton of CO n the case of lean mxtures. Assumng the mean fuel composton s C x H y O z, where coeffcents m, n and l were prevously defned for a mono or mult-component fuel, a functon of the local mean equvalence rato φ s then defned as: f φ < φ1 α = 1 y z x + 4 x φ f φ1 < φ < φ α = x + y f φ < φ α = 0 (3.117) where φ = and φ =0. 9φcrt, wth φ crt the crtcal equvalence rato above whch there s not enough oxygen to complete the oxdaton of fuel nto CO: If φ < φ, a part of the unburned fuel φ y z = x + x 4 crt (3.118) u,m Fu nto the burnt gases as a source of burnt gas fuel burnt gas fuel s gven by: y~ cannot be oxdzed and s transferred nstead M y~ n the mxed zone. The source of b,m Fu M Sept-014

51 Combuston Module FIRE v014 u b u Fu = dn Fu u We have d[ C H O ].9 d[ C H O ] n m φ φ crt dn (3.119) u φ crt l = eff n m l AI + ECFM 0 when > φ as the effectve snk term for unburned fuel and [ ] u n m l AI ECFM to auto-gnton and premxed flame. For O, CO, H O, CO and H the source terms are: φ φ wth d [ C ] u nh mol eff d C H O as the snk term due + dn dn dn dn dn u O u CO u HO u CO u H = dn u Fu = dn = dn = dn = dn x u Fu u Fu u Fu u Fu ( 1+ α( 1 r )) α α ( 1 r ) y CO [ 1 α( 1 r )] y ( 1 α) x CO CO x + y 4 α (3.10) In the Burnt Gases Due to very rch premxed flames or the dffuson of unmxed fuel n the burnt mxed regon, t s possble to fnd fuel n the burnt gases. It s assumed that the combuston s controlled by chemstry n the mxed zone, the mxng process beng descrbed by the mxng between zones. Therefore, the model already used for the oxdaton by auto-gnton s the frst smple model to be adopted. N b,m Fu M t where τ c s gven by equaton (3.116). N = τ b,m Fu M c (3.11) The Regresson Model In order to compute mult-njecton or local extncton, a smplfed regresson model has been ntroduced. Ths model transfers burnt gas quanttes nto unburned gas quanttes when the local burnt gas temperature s too low. Frst the coeffcent ~ c y~ I I = s defned, whch defnes the state of the auto-gnton F y~ TFu y~ Fu process. The regresson model s used f auto-gnton s swtched on: ~ f ci < 1, the auto-gnton delay has not been reached yet, there s no combuston by auto-gnton n the fresh gases. ~ f ci = 1, the auto-gnton delay has been reached, the combuston by autognton n the fresh gases s under way. 30-Sept

52 FIRE v014 Combuston Module ~ In every cell where ci > (local condton and local modfcaton of varables), t s consdered that the auto-gnton combuston process s fnshed, the auto-gnton delay ~ calculaton can be restarted by mposng c = 0, that s: ~I y = 0. A temperature I T deav s defned, whch represents the mnmum temperature allowed n the b burnt gases. If the burnt gas temperature T s lower than T T deav + 00K (wth = T 100K n practce), t s consdered that the reactons n burnt gases are deav cut = progressvely stopped. In ths case the burnt gases have to be transferred to the unburned zone Post Flame Chemstry As the condtonal quanttes are known, t s possble to compute chemstry n a condtonal way. Thus all the auto-gnton chemstry s computed usng the unburned gas propertes and all the pollutant, post oxdaton and equlbrum chemstry s computed usng the burnt gas propertes. Thus the mean gas propertes are updated through burnt gas propertes modfcaton. In the ECFM-3Z model, the approach s the same as for ECFM model. Knowng the burnt gases composton and burnt gas temperature, the procedure starts wth calculatng the post flame chemstry. Ths operaton s an teratve process, whch modfes the burnt gases composton and the burnt gas temperature. The new burnt gas composton s used to update the mean mass fractons and the new burnt gas temperature s used to update the mean enthalpy. After the calculaton of y~ by the burnt gas combuston model, an equlbrum b,m X b,m computaton and a pollutant formaton are performed to correct the burnt gas state and temperature. The post-flame chemstry of the model s an mproved verson of the ECFM model. The major change s the ntroducton of a knetc oxdaton of the CO. Thus, the CO/CO equlbrum s no longer consdered n the equlbrum package. An equlbrum resoluton of the remanng set of equatons was rewrtten. The consdered equlbrum reactons are: N O H N O H OH O H O O + H + H (3.1) The N /N reacton can be treated separately as n the ECFM. The other set of equatons can be reduced n one polynomal equaton (6 th degree). Ths equaton s then solved usng a Newton method, whch s straghtforward wth a polynomal expresson. The consdered knetc oxdaton of CO s: Sept-014

53 Combuston Module FIRE v014 + (3.13) CO OH CO + H Ths system s solved based on the burnt gas composton and temperature, whch allows the estmaton of the speces mass fractons y~ gven by the turbulent combuston b,m X model to be corrected. Fnally, these new estmates of averaged mass fractons y~ X Probablty Densty Functon Approach b,m y~ are consdered n the The PDF combuston model, avalable n FIRE, takes nto account the smultaneous effects of both fnte rate chemstry and turbulence, and thus obvates the need for any pror assumptons as to whether one of the two processes s lmtng the mean rate of reacton. Addtonally, benefts of the PDF approach le n the fact that t provdes a complete statstcal descrpton of the scalar quanttes under consderaton. Thus, t allows frst (mean values), second (varance), and even hgher (skewness) order moments to be easly extracted, and that the term expressng the rate of chemcal reacton appears n closed form;.e. requres no modelng. In ths method, the thermochemstry of the reactve mxture s expressed n terms of a reacton progress varable c (whch s algebracally related to y fu ), the mxture fracton f, and the enthalpy n order to account for non-adabatc bulk compresson effects on temperature. The reacton progress varable c s defned as: = y b,m X b,m Pr c (3.14) ypr, where y Pr, s the maxmum product mass fracton to occur, such that ether all the fuel or all the oxdant s depleted (or both for stochometrc mxtures). The varable c s bounded by the values of zero and unty, correspondng to fully unburned and burnt states, regardless of equvalence rato. The current method solves a transport equaton for the jont probablty densty functon p ( ψ) of the mxture fracton f, the reacton progress varable c, and the enthalpy h by means of a Monte Carlo Smulaton technque. Ths enables accurate determnaton of the chemcal sources n terms of the nstantaneous thermochemcal quanttes of the reactve system PDF Transport Equaton The sngle-pont PDF equaton for the Favre averaged jont probablty p( ψ) wrtten ([3.51]; [3.5]) as: ~ can be 30-Sept

54 FIRE v014 Combuston Module ~ wth p( ψ) range ~ p ρ t x ( Ψ) p( Ψ) k I + ρu ~ k { ω ( Ψ) p( Ψ) } { ~ N " J, u p( )} ~ k α ρ φ = Ψ Ψ + φ = Ψ p( Ψ) IV x II k N + ρ α= 1 α= 1 Ψ α Ψ α beng the probablty that at locaton x and tme t, a quantty φ s wthn the ψ < φ < ψ + d ψ. The quantty ψ s related to the mean densty ρ va the followng expresson: ( Ψ) ( Ψ) α 1 1 ~ III x ~ V = (3.15) p ρ = dψ (3.16) ρ 0 The terms II and IV n equaton (3.15) descrbe the transport of probablty n physcal space. Turbulent convecton s modeled usng a gradent-dffuson approxmaton [3.51]. x k µ ~ " { ( )} ( Ψ) t p ρ u k φ = Ψ ~ p Ψ = x k σ t x k (3.17) Term III of equaton (3.15) that expresses the effect of chemcal reacton on the probablty densty functon p( ψ) ~ appears n closed form and s modeled here as [3.10] Yp ( x, t) ( x, t) = Yp ( x, ) ( x, t) ωp ( x, t) = dt ρ( x, t) Y ( x, ) c dc ω p = A C x y [ H ] [ O ] exp a n m p E RT (3.18) Term V of equaton (3.15) represents turbulent mxng between reactants, products, and ntermedate states. It s modeled by means of a stochastc mxng model [3.18], expressed as: α = 1 β= 1 C τ K N m N ~ p Ψ Ψ α β ( Ψ) Cm ( Ψ) + ~ p( Ψ ) ~ α p( Ψβ ) K ( Ψ, Ψα, Ψβ ) τ µ φα φ Sc x x 1 1 ( Ψ, Ψα, Ψβ ) = A( α) f Ψ ( 1 α) Ψα α( Ψα + Ψβ ) dα 0 k β k φ = Ψ ~ p = dψ dψ α β (3.19) wth the characterstc mxng tme scale τ and the modelng constant C m Sept-014

55 Combuston Module FIRE v014 Based upon the values of the relevant physcal quanttes at tme t, a Monte Carlo smulaton advances the soluton of the ntegro dfferental equaton (PDF transport equaton) to tme level t+ t. Ths s done n order to obtan the new feld values for the mxture fracton, the reacton progress varable c and for the enthalpy, and hence densty. Usng these values, the pressure and velocty felds are updated teratvely by means of the SIMPLE algorthm untl convergence s acheved Monte Carlo Smulaton In order to solve the PDF transport equaton, the contnuous probablty densty functon ~ p( ψ) of the jont scalars such as mxture fracton f, reacton progress varable c, and enthalpy h are assumed to be represented by an ensemble of N notonal partcles [3.50]. At tme t, the n th partcle at locaton x has the propertes: The ensemble-average of any functon Q(Φ)s then defned by: ( n ) ( n ) Φ ( x,t ) = Ψ( x,t ) (3.130) n= 1 Fluctuatng components can be obtaned va: ( ) N 1 ( n ) Q ~ ( x,t ) = Q Φ ( x,t ) (3.131) N N { Q ~ } Q ( x,t ) = ( x,t ) Q ( n ) (3.13) 1 N n = 1 ( ) Φ ( x,t ) In order to advance the PDF from tme t to t+ t, the notonal partcles are moved across physcal space, smultaneously changng ther values n a prescrbed manner accordng to equatons (3.18) and (3.19). The probablty densty functon ~ p( ψ) s shown to change n tme due to four dstnct processes, namely convecton and dffuson n physcal space, and reacton and mxng n composton space. In the Monte Carlo method, these processes are smulated sequentally, based on an explct operator splttng method, to advance tme from t to t+ t. For the ensemble of notonal partcles at locaton x, the mathematcal operatons are as follows: Convecton The convectve term n the PDF transport equaton s smulated by replacement of n c elements. These are randomly selected at x by n c elements selected from the upstream ensemble, wth n c determned from: n c t x = N ( x,t ) (3.133) u~ 30-Sept

56 FIRE v014 Combuston Module Dffuson Smulaton of dffuson n physcal space s effected by random selecton of n d+ and n d- partcles from ensembles at x +1 and x -1, respectvely. These are then used to replace n d+ and n d- partcles randomly selected from the ensemble at x. The numbers n d+ and n d- are: t x 1 ρ n d+ / N Γ ± = t( 1,t ) (3.134) Molecular Mxng In order to smulate mxng, the followng operaton s repeated n m tmes: n m 1 = tnω( x,t ) (3.135) where ω s the turbulent frequency, obtaned from ε/k. Two partcles, denoted by n and m, ( n ) ( m) are selected randomly. Ther propertes Φ (,t ) and Φ (,t ) are then replaced by ther averaged value Chemcal Reacton x x { } mx ( n ) ( m) Φ ( x,t ) = Φ( x,t ) + Φ( x,t ) (3.136) 1 The effect of chemcal reacton, whch corresponds to convectve transport n composton space usng PDF formulaton, s obtaned through ntegraton of equaton: dφ dt ( n ) = S n = 1,,... ( n ( ) ) N Φ for each element for the tme nterval t, startng from the ntal condton: (3.137) ( n ) Φ = Φ( x,t ) (3.138) to produce the new value: ( n ) Φ = Φ (,t+ t ) (3.139) x Fully Dynamc Monte Carlo Partcle Number Densty Control In order to reduce the memory requrement of the Monte Carlo smulaton method for soluton of the jont-scalar probablty densty functon transport equaton, a fully dynamc partcle number densty control algorthm s mplemented. Here, the local Monte Carlo partcle number densty s adjusted each tme step accordng to the local varance of the reacton progress varable or of the mxture fracton varance, dependng on whether combuston/mxng s already actve or not. Hence, the total number of Monte Carlo partcles requred for soluton of the PDF transport equaton s reduced by about 50[%], smultaneously mantanng a maxmum number of partcles n the reacton/mxng zones. Numercal accuracy of the mxng/combuston smulaton s thus mantaned by the hgh number of partcles n the regons of prmary nterest, smultaneously reducng overall memory requrements Sept-014

57 Combuston Module FIRE v Characterstc Tmescale Model In desel engnes a sgnfcant part of combuston s thought to be mxng-controlled. Hence, nteractons between turbulence and chemcal reactons have to be consdered. The model descrbed n ths secton combnes a lamnar and a turbulent tme scale to an overall reacton rate. The tme rate of change of a speces m due to ths tme scale can be wrtten as follows: dy dt m Y Y * τ m m = (3.140) c where y α s the mass fracton of the speces α and y * α * s the local nstantaneous thermodynamc equlbrum value of the mass fracton. τ c s the characterstc tme for the achevement of such equlbrum. It s suffcent to consder the seven speces fuel, O, N, CO, CO, H, H O to predct thermodynamc equlbrum temperature accurately enough. The characterstc tme τ c of a lamnar and a turbulent tme scale can be descrbed by: τ = τ + f τ (3.141) c l t The lamnar tme scale s derved from an Arrhenus type reacton rate: τ = A Ea [ C H ] [ O ] exp 1 l x y (3.14) RT The turbulent tme scale s proportonal to the eddy break-up tme: k τ t = C (3.143) ε The delay coeffcent f smulates the ncreasng nfluence of turbulence on combuston after gnton and can be calculated from the reacton progress r: f r ( 1 e )/ = (3.144) r Y CO + Y H O 1 Y + Y N CO + Y H = (3.145) Ths whole approach s conceptually consstent wth the model of Magnussen. The ntaton of combuston reles on lamnar chemstry. Turbulence starts to have an nfluence after combuston events have already been observed. The combuston wll be domnated by turbulent mxng effects n regons of τ l << τ t. The lamnar tme scale s not neglgble n regons near the njector where hgh veloctes cause a very small turbulent tme scale. 30-Sept

58 FIRE v014 Combuston Module Auto gnton s calculated by the Shell Model whch s ntegrated n the specfc model descrpton. The gnton model s appled where ever T < 1000 [K]. The ntegrated model descrpton also ncludes smulaton of NO and soot. The formaton of NO s descrbed by the extended Zeldovch mechansm. The soot formaton and oxdaton s descrbed by a combnaton of the models of Hroyasu and Nagle/Strckland-Constable. All pollutant models are shown n more detal n the Emsson Manual Steady Combuston Model The Steady Combuston Model was developed [3.5] for the purpose of modelng combuston n ol-fred utlty furnaces, when one s not partcularly nterested n the detals of combuston, but when the flame dynamcs s of crucal mportance to the heat transfer n the furnace. It uses emprcal knowledge n order to nclude the nfluences of evaporaton, nducton, knetcs and coke combuston n an Arrhenus type expresson. The model s well suted for the whole range of typcal ol flames, startng from partally pre-mxed to flames governed by several dfferent streams of fuel and ar. In order to gve physcal results for the model, the fuel must be consdered pre-mxed wth the prmary stream of ar, snce the model already takes the mxng tme mplctly nto account. The model s mplemented through the reacton rate, whch can be wrtten as follows: r Y t ν fu fu O = ρ = ρ k Y fu Y O (3.146) ν where ρ s the densty, k the reacton rate constant, y fu the fuel mass fracton, y O the oxygen mass fracton and ν fu and ν O are the exponents that determne the reacton order. Therefore, the reacton rate always depends on fuel mass fracton, but t s only senstve to oxygen mass fracton when t s low, delmted n the model by 3%: ν fu = 1 ν O = 1 for Y O < 0.03 ν O = 0 for Y O > 0.03 Constant k, whch could be characterzed as a combuston velocty, wll be wrtten n the followng manner: k b k = (3.147) where b k s the combuston velocty coeffcent and the total tme of combuston τ k, conssts of three dfferent parts: tme of evaporaton and nducton τ e tme of oxdaton τ ox tme of coke combuston τ cc For each tme mentoned, there s an expresson ganed by the experment. For the tme of evaporaton and nducton t s: e 5 10 RT τ k τ = A e d (3.148) o Sept-014

59 Combuston Module FIRE v014 wth T as local temperature, R as the unversal gas constant and d 0 as ntal droplet dameter. The tme of oxdaton s descrbed as: and the tme of coke combuston as: ox d o τ (3.149) = (T 73.15) 1.79 cc = χ ( τ + τ ) ox where χ 0.75 s a constant for small droplet dameters. τ (3.150) The combuston velocty coeffcent b k, used here for the purpose of swtchng on the nfluence of oxygen dffuson, has the followng values dependng on the oxygen mass fracton: b k = 100/3 for y O < 0.03 b k = 1 for y O > 0.03 Ths model gves a good coverage of a knetc combuston,.e., of the combuston when there s always suffcent oxygen for the combuston of evaporated fuel n the zone surroundng the droplet. But, f there s lack of oxygen, the whole combuston wll be governed by the process of the oxygen dffuson n the zone of droplet. In ths model ths s solved by adjustng the values of b k and ν O to dfferent values when oxygen concentratons are small, makng the reacton rate dependent on the avalablty of oxygen. That modfcaton was made to the orgnal model [3.6], n order to cover the flames wth secondary ar, lke the one of Ijmuden expermental furnace Mult-Speces Chemcally Reactng Flows Hydrocarbon Auto-Ignton Mechansm The chemstry of gnton has been the subject of numerous studes ([3.17]; [3.30]; [3.34]; [3.35]). There s now a general, although not precse, understandng of the hydrocarbon oxdaton mechansm at pressure and temperature condtons relevant to compresson gnton of desel fuels. The reacton mechansm used n FIRE for the smulaton of homogeneous charge compresson gnton, Desel fuel self-gnton and knock onset has been developed along the lnes of the reacton scheme orgnally proposed for the study of auto-gnton phenomena n gasolne engnes ([3.34]; [3.35]). In ths reacton scheme, speces that play a smlar role n the gnton chemstry are combned and treated as a sngle entty. The auto-gnton model makes use of the followng generc molecules: e 30-Sept

60 FIRE v014 Combuston Module fu O R B Q pr I hydrocarbon fuel of the structure C n H m O l oxygen total radcal pool branchng agent ntermedate speces products nactve (nert) speces These take part n the followng generalzed reactons: Intaton: ω Fu + Ox R (I) Propagaton: ω p R R + P 1 R ω R + B ω 4 R R + Q ω R + Q R + B (II) (III) (IV) (V) Branchng: B b R ω (VI) Lnear Termnaton: 3 R ω I (VII) Quadratc Termnaton: t ω R I (VIII) The reacton rates ω of the above knetc scheme are rather complex expressons and are not outlned n detal here. For more nformaton refer to [3.35]. The ndvdual rate coeffcents appearng n ω take the common Arrhenus form k Ea, /( RT) = A e (3.151) or, as n reacton II, a form composed from three separate rates: k p 1 = (3.15) kp 1 [ Ox] kp kp [ Fu] Sept-014

61 Combuston Module FIRE v014 where [ ] denotes molecular concentraton n, for example, [kmol/m³], and kp 1, kp, and kp 3 are the rate coeffcents for the propagaton steps. In order to use the reacton mechansm wthn the framework of a multdmensonal computaton, reactons II to V have been mass-balanced due to Schäpertöns and Lee [3.54]. The adaptaton of the knetc rate parameters to enable applcaton of the model to study self-gnton of desel fuel follows the lnes of Theobald and Cheng [3.57] AnB Knock-Predcton Model The development of an auto-gnton model that s suffcently realstc to be predctve s a central problem snce the computer tme assocated wth a realstc model based on the resoluton of several chemcal equlbra s stll too long for the smulaton of knock n combuston chambers. Therefore a knock model based on a so-called AnB model usng equatons s used whch s currently coupled to the CFM combuston model (especally constructed for the ECFM, but can also be used for the other CFM) descrbed n ths chapter. These two equatons are used n order to descrbe the growth of a precursor representng the auto-gnton delay. The model s based on the knowledge of the autognton delay. Frst, the appearance of a pseudo precursor [3.4] s calculated and f the precursor quantty s suffcent (equal to the unburned fuel mass fracton) the chemcal oxdaton reacton of the fuel s trggered. Hence the fuel consumpton due to auto-gnton becomes: y t fu = y fu c 1 e Ta Tgb (3.153) where c 1 s a constant, T a the actvaton temperature and T gb the local temperature of the burnt gas phase. In the case of auto-gnton crtera actvaton, the characterstc oxdaton tme of the fuel s consdered to be constant. As a startng pont for the formulaton of the precursor the reacton adapted for reference fuels (PRF fuels) s used lke: c RON n B / Tfr θ = A p e (3.154) 100 The gnton delay θ s calculated wth RON as the fuel octane number [3.], c s a constant, p s the pressure n bar and T fr s the local temperature of the fresh gas phase n Kelvn. A, n and B are varables of the AnB model and have to be tuned dependng on the calculaton confguraton. These parameters can be changed n the GUI where reference values are gven. The knetcs of the precursor formaton from the delay s calculated usng an exponental functon where the precursor concentraton y s calculated pror to the auto-gnton lke: p 30-Sept

62 FIRE v014 Combuston Module y p t = y fu,fr F( θ) wth ( θ) = θ + c θ 3 y y p fu,fr F (3.155) where y fu, fr s the fuel mass fracton of the unburned gas phase. In order to avod artfcal extncton due to drops n precursor concentraton caused by dffuson or convecton for example after reachng the auto-gnton crteron, the precursor contnues to be produced. Hence, after auto-gnton the change n the precursor s smply calculated by : y p t = c 4 y fu,fr e c5 / Tgb ρ ρ fr y y fu fu,fr (3.156) where c 3, c 4 and c5 are constants and ρ fr s the densty n the fresh gas. In order to consder effects of the fuel/ar rato of the fuel mxture the delay calculaton functon s corrected usng the equvalence rato φ as : RON eff c 6 ( φ 1) c = 7 (3.157) RONe Ths correcton ndcates that the mnmum delay of the mxture s obtaned at stochometrc ar/fuel condtons ( c 6 and c 7 are constants). Fnally, the pressure s corrected due to the assumpton that the presence of resdual gas tends to decrease the partal pressure of the components. Hence the pressure term n the delay calculaton formula s replaced by : p eff p 1+ y = (3.158) res where y res represents the mass fracton of the resdual gas. The problem n couplng the auto-gnton model wth the CFM les n the estmaton of the flame surface densty generaton by the burnt gases produced by auto-gnton. Hence, a farly smple couplng s used assumng that the so-created flame surface s vrtually lamnar and the reacton zone nfntely thn durng the flame establshment whch can be descrbed by: Σ = c (3.159) where c represents the reacton progress varable. Snce ths reacton can be ntated n regons where the flame surface already exsts, the followng equaton s smplfed to these regons by : Σ =, ( Σ c ) max (3.160) wth Σ as the flame surface densty representng the local area of the flame per unt volume Sept-014

63 Combuston Module FIRE v014 Usng the AnB knock model t s recommended to use small tme-step ncrements durng the combuston phase (~1.e-6 sec) n order to get good modelng of the acoustc wave propagaton caused by auto-gnton. Addtonally, local pressure hstores for ponts near the auto-gnton poston (user dependent selecton) should be wrtten by the user to an output fle usng user-functons such as useout.f n order to get a good representaton of the spatal locaton of knock poston Emprcal Knock Model Ths knock model s based on an emprcal approach (EKM) dentfyng the possblty that knock can occur wthn specfed regons dependng on dfferent parameters. Dependng on TCA measurements sutable parameters were found n order to descrbe a knock behavor and to gve the locaton of knockng areas or predctons, respectvely. The most mportant nfluence propertes for the knock probablty were detected to be the amount of EGR, the temperature T, the progress varable c, the mxture mass fracton y f and the volume of each segment, respectvely. The most sutable knock crteron compared to TCA measurement was dentfed to be: c crt ( 1 c ) y vol f,sum seg = y EGR,segTseg seg (3.161) y f,seg volsum where propertes wth an overbar and ndex seg (.e. segment) are mass averaged over all cells contaned n each segment whle propertes wth ndex sum are the mass averaged propertes of all cells contaned n 1 angular arranged segments. As today s combuston applcatons are very complex (e.g. engne smulaton wth combuston chamber, valves, ntake/exhaust ports etc.) a cell-selecton has to be defned by the user for the most mportant part (e.g. for engnes the combuston chamber snce the ntake for example can be neglected). The defned cell-selecton by the user has to be named by knock_detecton otherwse no knock s calculated. As shown n Fgure 3-6, for the frst approach the axs of the combuston chamber should be the z-axs and 1 angular segments normal to the z-axs are defned n the same way as a clock wth an angular control lmt of 0 degree (ragl). The radal control volume lmt (rlm) s currently fxed by a factor: 7 bore r lm = (3.16) 8 The nformaton for the knock crteron s wrtten automatcally nto an output-fle named emprcal_knock_crterum.out startng wth the tme or crank-angle (run mode dependent) n the frst row and then mean hstores of the knock crterons of all 1 segments are wrtten clockwse startng wth the 1 o clock poston. 30-Sept

64 FIRE v014 Combuston Module z-axs as Combuston Chamber Axs Segment Dstrbuton Geometry Fgure 3-6: Emprcal Knock Model Flame Trackng Partcle Model Basc Concept The Flame-Trackng-Partcle Model (FTPM) s a numercal algorthm to smulate the knetcs of the premxed flame represented by a surface. The method s based on a wellbalanced combnaton between Lagrangan and Euleran approach. From the Lagrangan formulaton, t takes an advantage of obtanng the detaled evoluton of surface movement based on flame speed and local flow velocty. From the Euleran approach, heurstc numercal stablty s acheved and t s possble to compute a smooth surface normal vector feld from Lagrangan partcles, whch s crucal n order to nclude the effect of turbulent combuston as accurate as possble Flame Trackng Method The FT method deals wth the sub-grd model of lamnar/turbulent combuston. The essence of the model can be readly explaned on the example of lamnar flame propagaton. In the FT method, the flame surface shape and area are found based on the Huygens prncple. In other words, the front of a propagatng flame surface at any nstant s formed by the envelope of spheres emanatng from every pont on the flame surface at the pror nstant due to burnng of the fresh mxture at local velocty u n (normal to the flame surface) and due to convectve moton of the mxture at local velocty V. The local nstantaneous flame velocty u n s taken from look-up tables ncludng n general the effects of mxture dluton wth combuston products, flame stretchng and flammablty lmts. The local nstantaneous flow velocty V s calculated usng a hgh-order nterpolaton technque. In D flow approxmaton, the flame surface s represented by straght lne segments, whereas n 3D calculatons, the flame surface s represented by set of notonal ponts Sept-014

65 Combuston Module FIRE v014 Turbulent Velocty Modelng In the turbulent flow feld, the mean energy release rate n the cell, Q, s composed of two terms: energy release due to frontal combuston, combuston, Q v. Q f, and energy release due to volumetrc Q f = ρ QΣS u, (3.163) fr n T where ρ fr s the fresh mxture densty, Q s the combuston heat, and summaton s made over all flame segments n the cell,.e. ndex relates to the -th flame surface segment. The second term Q v s calculated by usng the partcle method as descrbed below. In the turbulent flow feld, a pulsatng velocty vector dstorts the mean reactve (flame) surface by wrnklng t. The local nstantaneous flame wrnklng can be taken nto account by proper ncreasng the normal flame velocty, or n other words, by ntroducng a concept of local turbulent flame velocty u T. The local turbulent flame velocty s defned as u T = uns / Sn, (3.164) where S s the surface area of the wrnkled flame at a gven segment and area of the equvalent planar flame. S n s the surface In the theory of turbulent combuston, there are many correlatons between u T and E.g. one of the classcal correlatons has been found by Damköhler [3.19]: u n. u ut un 1 + (3.165) un where u s the local turbulence ntensty, related to the turbulent knetc energy or to pulsatng velocty correlatons. Instead of equaton (3.165) one can use any other avalable correlaton for the turbulent flame velocty. In detaled nvestgatons t was found that for calculatons n engne combuston chambers e.g. the formulaton by Guelder [3.33] delvers good physcal results: u u u un 1 unl v T n (3.166) One can apply the Huygens prncple to model only the mean shape of the turbulent flame: each elementary porton of flame surface dsplaces n tme due to burnng of the fresh mxture at local velocty u T (normal to the flame surface) and due to convectve moton of the mxture at local velocty V. It stands to reason that the turbulent combuston model s also vald for the lamnar combuston as a lmtng case. Ths s one of the model advantages. Usng the same model ths feature allows to calculate the ntal lamnar flame kernel growth from the spark gnton wth contnuous transton to turbulent combuston Sept

66 FIRE v014 Combuston Module Surface Evoluton Numercal methods for surface evoluton are dvded nto two categores: front trackng methods based on Lagrangan frame and front capturng methods based on Euleran frame. The algorthm used n FTPM method has an advantage of both Euleran and Lagrangan approaches. Method can stably compute geometrcal propertes and easly handle topologcal changes, but numercal schemes suffer from numercal dffuson and oscllatons along the surface movement. FTM s manly based on the Lagrangan partcle method n order to track characterstc nformaton and t s well-balanced wth the Euleran method to obtan a surface normal vector feld and reduce numercal nstablty caused by explct partcle movement. In an evoluton of the surface from a gven velocty and an ntal partcle locaton, the method conssts of four steps: Computaton of volume fracton, Computaton of surface normal vectors, Re-seedng of partcles, Movement of partcles. Step 1: Computaton of volume fracton The volume fracton s an averaged nformaton of representng the surface and t s used to compute the effect of the surface locaton caused by turbulent models n compressble Naver-Stokes equatons. The computaton of the volume fracton from gven partcles can be easly done by obtanng an averaged plane surface n each cell. Step : Computaton of surface normal vectors A normal vector feld from the averaged surface does not have good qualty to correctly present the surface geometry. Ths s because the contnuty of the normal vector feld s not guaranteed and the dscontnuty s obvously caused by gnorng neghbor nformaton and averagng locatons of partcles per cell. In order to avod such a local dsturbance, a reconstructon of a contnuous global surface s proposed by an teratve scheme. The method quckly converges under the crteron of globally obtanng the surface close to prevous partcles. The surface normal vector feld from the reconstructed surface s crucally used to apply dfferent types of velocty feld on each partcle to evolve a surface n a turbulent combuston feld. The reconstructon of a global surface structure based on partcle locatons corresponds to an Euleran approach. Step 3: Re-seedng of partcles There are two typcal drawbacks of usng a partcle-based method to evolve a surface n a gven velocty feld: 1. To obtan a vscosty soluton under an effect of shock and rarefacton and. to follow topologcal changes (breakng and mergng). Man dffcultes are caused by the hyperbolc nature of Lagrangan partcle movement and the lack of explct surface representaton. It s rather smple to solve the frst problem from re-seedng partcles. But, t s not easy to decde where partcles should be reseeded n the computatonal doman. Interestngly, a soluton of the frst problem s related to the second ssue. In order to resolve such problems, t s well-known that the Euleran approach s hghly potental and t s already done n Step wth a proposed algorthm Sept-014

67 Combuston Module FIRE v014 However, even though the globally reconstructed surface n Step gves a good qualty of the normal vector feld, t may lose the qualty of surface locaton tracked by partcles along the characterstcs because the algorthm works based on a global crteron and t s not dffcult to recognze that the global crteron averages out the local property. Now, before re-seedng of partcles, the globally reconstructed surface n Step s locally moved n order to preserve the qualty of characterstc nformaton whle surface normal vectors are preserved. Therefore, the valuable characterstc nformaton from the Lagrangan approach s not deterorated and the smooth surface normal from the Euleran approach to present geometrcal nformaton n Step can be stll used. Step 4: Movement of partcles From Step 1 to Step 3, partcles are re-seeded and the surface normal vector feld s computed. In ths step, partcles are smply moved along an obtaned velocty feld whch s a combnaton of flame velocty and turbulent flud velocty Partcle Method Pre-flame reactons The partcle method PM allows contnuous montorng of pre-flame reactons. Wthn the method, a certan number of Lagrangan partcles move n the pre-flame zone accordng to the local velocty vector. In each partcle, the pre-flame reactons proceed at the rates determned by ts nstantaneous temperature and speces concentratons. For determnng the tme and locaton of pre-flame auto-gnton a certan crteron s adopted. Such a crteron s usually based on the fxed rate of temperature rse n the partcle, e.g., 10 7 or 10 8 K/s. When the auto-gnton crteron s met n one or several partcles n the computatonal cell, all amount of fuel n ths cell are burnt durng one tme step. Ths process corresponds to the fast reactons and volumetrc combuston/exploson n pre-flame zone. The number of partcles n the pre-flame zone can be less than the number of computatonal cells. For keepng the number densty of partcles at a reasonable level, consstent procedures of partcle clonng and clusterng have been developed. The pre-flame partcles are traced untl the entre geometry s traversed by the frontal or volumetrc combuston. Post-flame reactons For montorng pollutants (NOx, soot, etc.), the PM s also appled to the combuston products. When the flame passes a computatonal cell, ths cell s automatcally flled wth n partcles. For stochometrc and fuel-rch mxtures, the new partcles are assgned wth the temperature, as well as fuel, ntrogen, water vapor, and carbon doxde concentratons taken from the cell center, whereas the concentraton of molecular oxygen, soot, CO and prompt NO are taken from look-up tables n the FT method. For fuel-lean mxtures, the new partcles are assgned wth the temperature from the cell center, whereas fuel, oxygen, ntrogen, water vapor, and carbon doxde concentratons are calculated from the stochometrc relatonshp assumng complete combuston, and the concentraton of soot, CO and prompt NO s taken from look-up tables n the FT method. The mean values of pollutant mass fractons are then obtaned by statstcal averagng over all partcles currently located n a gven cell. In general, the PM mples the exstence of both pre-flame and post-flame partcles, whch dffer by a sngle ndex denotng ther status. Dependng on ths ndex, a dfferent set of knetc equatons s solved. 30-Sept

68 FIRE v014 Combuston Module Knetc database The coupled FTPM algorthm s supplemented wth the database of tabulated lamnar flame veloctes, prompt NO, flame soot and free oxygen, as well as flame CO for a gven fuel ar mxture n the wde range of ntal temperature, pressure, exhaust gas recrculaton, as well as the reacton knetcs of pre-flame fuel oxdaton. The detaled, reduced, and overall knetc mechansms of hydrocarbon (pre-flame) auto-gnton at ICE condtons for methane, ethanol, propane, n-heptane, so-octane, n-decane, n-tetradecane, and n-heptane so-octane blends (PRF) have been developed and valdated and the correspondng database has been constructed. Also, the knetc database for (post-flame) pollutant formaton (soot, thermal NO) at ICE condtons has been developed for these ndvdual hydrocarbons and fuel blends. In combnaton wth the flame velocty database for the FT method, these knetc databases consttute a unque tool for advanced combuston smulaton Spark Ignton Modelng The FT gnton model s based on dfferences n physcs of flame propagaton mmedately after gnton and at a fnte tme after gnton. At the gnton stage the flame s known to develop from the small-sze dscharge channel through the phase of mxture gnton and flame formaton. Combuston at ths stage (from now on called ntal stage) s mostly governed by local physco-chemcal propertes of the reactve mxture and by small-scale turbulence. In the fully developed turbulent flame (regular stage properly treated n the FT model), combuston s to a large extent governed by large-scale turbulence. Of course, there s a need n proper talorng the ntal and regular stages of flame propagaton. Physcally, the turbulent flame n IC engne condtons s the hghly wrnkled lamnar flame. Therefore, one can use the classcal expresson for the turbulent flame velocty at such condtons: vt u t = un 1 + (3.167) v where u n s the lamnar flame velocty, ν t the turbulent (eddy) vscosty, ν m and the molecular vscosty. At the ntal stage of flame propagaton ncludng gnton stage, when the flame kernel s small, the flame front can be wrnkled only by the low-energy flow velocty pulsatons wth the length scale less than the characterstc sze (dameter) of flame kernel. In ths case, all velocty pulsatons of the larger scale play a role of the mean convectve flow dsplacng the flame kernel as a whole. Snce at the ntal stage the flame sze n URANS smulatons s on the order of grd spacng, t appears that m u u and l u are n general the unresolved pulsatng velocty and length scale (ths s the reason for the subscrpt u whch means unresolved ). Thus at the ntal stage of flame propagaton (at tme t>t gn, t gn s the tme of gnton trggerng), the turbulent (eddy) vscosty n equaton (3.167) should be estmated based on the tme dependent unresolved pulsatng velocty of scale lower than the nstantaneous equvalent flame kernel dameter,.e., vt ( t) ~ uu ( t) lu ( t) at lu ( t) d f ( t). (3.168) Sept-014

69 Combuston Module FIRE v014 Wthout loss of generalty, one can assume that l d u f and rewrte equaton (3.168) as v t ~ uud f (3.169) To estmate u u, one can use the approach suggested n [3.31], whch ntroduces the rato of unresolved-to-total turbulent knetc energes fk = ku / k, where k u ( 3/ ) uu s the unresolved turbulent knetc energy and k = ( 3/ ) u s the resolved turbulent knetc energy, whereas u u and u are the unresolved and resolved pulsatng veloctes, respectvely. Accordng to [3.31], the rato of unresolved-to-total turbulent knetc energes depends upon the characterstc grd spacng as /3 1 f k ~, (3.170) Λ C µ where 3 / Λ = k / ε (3.171) s the ntegral length scale of turbulence (ε s the turbulence dsspaton rate), and C µ = 0.09 s the constant n the k ε model of turbulence. Accordng to [3.3], relatonshp (3.170) can be appled to tme dependent condtons once the tme scale of f changes n k s smaller than that of turbulence quanttes. Because we are nterested n d the unresolved turbulence on scale f rather than of scale one can rewrte equaton (3.170) of [3.31] as f k ~ 1 d f Cµ Λ /3 (3.17) C = 0.09 Now, takng nto account that µ and usng equatons (3.169) and (3.171), one u fnally obtans for the turbulent flame velocty at the ntal stage t, n of equaton (3.156) the followng relatonshp: u 1/ 3 4 / 3 vt, n ε d f t, n = un 1+ ~ un (3.173) vm vm Physcally, when the ntal stage of turbulent flame propagaton comes to an end, the flame velocty should be determned by the correlaton avalable n the FT model for the regular stage of flame propagaton, e.g., by the Guelder expresson. Ths transton takes place at the tme when u t,n becomes larger than u t. 30-Sept

70 FIRE v014 Combuston Module 3.3. References [3.1] Ahmad-Befru, B., Gosman, A. D., Lockwood, R.C. and Watkns, A. P. "Multdmensonal Calculaton of Combuston n an Idealzed Homogeneous Charge Engne: A Progress Report." Socety of Automotve Engneers (SAE) , [3.] Ahmad-Befru, B. and Kratochwll, H. "Multdmensonal Calculaton of Combuston n a Loop-scavenged Two-stroke Cycle Engne." Proc. of the Internatonal Symposum on Dagnostcs and Modelng of Combuston n Internal Combuston Engnes. The Japanese Socety of Mechancal Engneers. Tokyo, 1990: [3.3] Basara, B., Krajnovc, S., Grmaj, S. and Pavlovc, Z. Near-wall formulaton of the Partally Averaged Naver-Stokes turbulence model, AIAA Journal, Vol. 49, pp [3.4] Blnt, R.J. "The Relatonshp of the Lamnar Flame Wdth to Flame speed." Combuston Sc. and Tech. 49 (1986): [3.5] Bogdan, Ž. and Duć, N. The Mathematcal Model of the Steam Generator Combuston Chamber, Proc 4th Symposum KoREMA, Zagreb, pg. 77, 199. [3.6] Bogdan, Ž., Duć, N. and Schneder, D.R. Three-dmensonal Smulaton of the Performance of an Ol-fred Combuston Chamber, Proc. of the nd European Thermal Scences & 14th UIT Natonal Heat Transfer Conference, Rome, ,1996. [3.7] Bogensperger, M. "A Comparatve Study of Dfferent Calculaton Approaches for the Numercal Smulaton of Thermal NO Formaton." Dss. U. Graz, [3.8] Boe, W. "Vom Brennstoff zum Rauchgas. Feuerungstechnsches Rechnen mt Brennstoffkenngrößen und sene Verenfachung mt Mtteln der Statstk." Lepzg: Teubner, [3.9] Borgh, R., Delamare, L. and Gonzales, M. "The Modelng and Calculaton of a Turbulent Flame Propagaton n a Closed Vessel." CORIA - URA, No. 30 CNRS - Faculte des Scences de Rouen. [3.10] Brandstätter, W. and Johns, R.J.R. "The Applcaton of a Probablty Method to Engne Combuston Modelng." IMechE C58/83, [3.11] Candel, S. and Ponsot, T. "Flame Stretch and the Balance Equaton for the Flame Area." Combust. Sc. and Tech. 70 (1990): [3.1] Cant, R. S. and Bray, K.N.C. "Straned Lamnar Flamelet Calculaton of Premxed Turbulent Combuston n a Closed Vessel." nd Internatonal Symposum on Combuston. Pttsburgh: The Combuston Insttute, [3.13] Charlette F., Meneveau C. and Veynante D., A power-law flame wrnklng model for LES of premxed turbulent combuston PART I: non-dynamc formulaton and ntal tests, Combuston and Flame, Vol. 131, No. 1-, pp , 00 [3.14] Coln, O., Benkenda, A. and Angelberger, C. "3D Modelng of Mxng, Ignton and Combuston Phenomena n Hghly Stratfed Gasolne Engnes", Ol & Gas Scence and Technology - Rev IFP, 58(1), 47-6 (003) Sept-014

71 Combuston Module FIRE v014 [3.15] Coln O., Duclos F., Veynante D. and Ponsot T., A thckened flame model for large eddy smulatons of turbulent premxed combuston, Phys. Fluds, Vol. 1, No. 7, pp , 000 [3.16] Coln O. and Truffn, K., "A spark gnton model for large eddy smulaton based on an FSD transport equaton (ISSIM-LES)," Proceedng of the Combuston Insttute, vol. 33, pp , 011. [3.17] Cox, R. and Cole, J. "Chemcal Aspects of the Autognton of Hydrocarbon-Ar Mxtures." Combuston Flame 60 (1985): [3.18] Curl, R.L. "Dspersed phase mxng: 1. Theory and Effects n Smple Reactors." AICHE Journal 9 (1963): [3.19] Damkoehler G. Der Enfuss der Turbulenz auf de Flammen-geschwndgket n Gasgemschen. Zs Electrocheme 1940; 6: [3.0] Delhaye, B. and Cousyn, B. "Computaton of Flow and Combuston n Spark Ignton Engne and Comparson wth Experment." SAE , [3.1] Deuflhard, P. and Nowak, U. "Extrapolaton Integrators for Quaslnear Implct ODEs," In: Deuflhard, P., Engqust, B. (eds.): Large Scale Scentfc Computng, Brkhaeuser, Prog. Sc. Comp. 7, (1987): [3.] Douaud, A.M. and Eyzat, P. Four Octane Number Method for Predctng the Ant- Knock Behavor of Fuels and Engnes, SAE ,1978 [3.3] Duclos, J.M., Veynante, D. and Ponsot, T. "A Comparson of Flamelet Models for Premxed Turbulent Combuston." Combuston and Flame 95 (1993): [3.4] Duclos, J. M., Zolver, M. and Bartaud, T. "3D Modelng of Combuston for DI-SI Engnes, Ol & Gas Scence and Technology". -Rev. IFP, Vol. 54 (1999), No., pp [3.5] Duclos, J. M., Zolver, M. and Bartaud, T. "3D Modelng of Combuston for DI-SI Engnes", Ol & Gas Scence and Technology -Rev. IFP, 54(), (1999) [3.6] Duclos, J.M. and Coln, O. "Arc and Kernel Trackng Ignton Model for 3D Spark- Ignton Engne Calculatons", COMODIA, (001) [3.7] Ehrg, R., Nowak, U., Oeverdeck, L. and Deuflhard, P. "Advanced Extrapolaton Methods for Large Scale Dfferental Algebrac Problems." In: Hgh Performance Scentfc and Engneerng Computng, Bungartz, H. J., Durst, F. and Zenger Chr. (eds.), Lecture Notes n Computatonal Scence and Engneerng, Sprnger Vol 8, (1999): [3.8] el Tahry, S.H. "A Turbulent Combuston Model for Homogeneous Charge Engnes." Combuston Flame 79 (1990): [3.9] Fan, L., L, G., Han, Z. and Retz, R.D. "Modelng fuel preparaton and stratfed combuston n a gasolne drect njecton engne", SAE , [3.30] Fsch, A., Read, A., Affleck, W. and Haskell, W. "The Controllng Role of Cool Flames n Two-Stage Ignton." Combuston Flame 13 (1969): Sept

72 FIRE v014 Combuston Module [3.31] Grmaj, S. Srnvasan, R. and Jeong, E. PANS turbulence models for seamless transton between RANS and LES; fxed pont analyss and prelmnary results. ASME paper FEDSM45336, 003. [3.3] Görner, K. Technsche Verbrennungssysteme, Grundlagen, Modelbldung, Smulaton. Sprnger Verlag Berln Hedelberg, [3.33] Guelder O.L. Turbulent premxed flame propagaton models for dfferent combuston regmes Symposum (Internatonal) on Combuston, Volume 3, Issue 1, 1991, Pages [3.34] Halstead, M., Krsch, L., Prothero, A. and Qunn, O. "A Mathematcal Model for Hydrocarbon Auto-Ignton at Hgh Pressures." Proc. Royal Socety of London, A46, 1975: [3.35] Halstead, M., Krsch, L. and Qunn, C. "The Autognton of Hydrocarbon Fueld at Hgh Temperatures and Pressures - Fttng of a Mathematcal Model." Combuston Flame 30 (1977): [3.36] Heywood, J. B. Internal Combuston Engne Fundamentals. McGrawHll Book Company, Second Seres, [3.37] Hoyasu, H., and Nshda, K. Smplfed Three Dmensonal Modelng of Mxture Formaton and Combuston n a DI Desel Engne. SAE 89069, [3.38] Jones, W.P. and Lndstedt, R.P. "Global Reacton Schemes for Hydrocarbon Combuston." Combuston and Flame 73 (1988): [3.39] Kdo, H., Nakahara, M. and Hashmoto, J. "A Turbulent Burnng Velocty Model Takng Account of the Preferental Dffuson Effect". The Fourth Internatonal Symposum COMODIA 98, [3.40] Kobayash, H., Kawabata, Y., Maruta, K. "Expermental Study on General Correlaton of Turbulent Burnng Velocty at Hgh Pressure." 7 th Internatonal Symposum on Combuston. Pttsburgh: The Combuston Insttute, 1998: [3.41] Kong, S.C., Han, Z. and Retz, R.D. The Development and Applcaton of a Desel Ignton and Combuston Model for Multdmensonal Engne Smulaton. SAE 95078, [3.4] Lafossas, F.A., Castagne, M., Dumas, J.P. and Henrot, S. Development and Valdaton of a Knock Model n Spark Ignton Engnes Usng a CFD code, SAE , 00. [3.43] Maas, U. and Pope, S. B. "Smplfyng Chemcal Knetcs; Intrnsc low-dmensonal Manfolds n Composton Space." Combuston and Flame 88 (199): [3.44] Magnussen, B.F. and Hjertager, B.H. "On mathematcal modelng of turbulent combuston wth specal emphass on soot formaton and combuston." Sxteenth Internatonal Symposum on Combuston. Pttsburgh: The Combuston Insttute, [3.45] Mentjes, K. and Morgan, A.P. "Element Varables and the Soluton of Complex Chemcal Equlbrum Problems," GMR-587, General Motors Research Laboratores, Mchgan, [3.46] Meneveau, C. and Ponsot, T. "Stretchng and Quenchng of Flamelets n Premxed Turbulent Combuston." Combuston Flame 86 (1991): Sept-014

73 Combuston Module FIRE v014 [3.47] Meneveau, C. and Sreenvasan, K.R. "The Multfractal Nature of Turbulent Energy Dsspaton." Journal of Flud Mechancs 4 (1991): [3.48] Metghalch, M. and Keck, J.C. "Burnng Veloctes of Mxtures of Ar wth Methanol, Isooctane and Indolene at Hgh Pressure and Temperature." Combuston and Flame 48 (198): [3.49] Ponsot, T., Veynante, D. and Candel, S. "Quenchng Processes and Premxed Turbulent Combuston Dagrams." Journal of Flud Mechancs 8 (1991): [3.50] Pope, S.B. "A Monte Carlo Method for the PDF Equatons of Turbulent Flow." MIT-EL [3.51] Pope, S.B. "PDF Methods for Turbulent Reactve Flows." Prog. Energy Combuston Scence 11 (1985). [3.5] Pope, S. B. and Cheng, W. K. "The Stochastc Flamelet Model of Turbulent Premxed Combuston." nd Internatonal Symposum on Combuston. Pttsburgh: The Combuston Insttute, [3.53] Rchard S., Coln O., Vermorel O., Benkenda A., Angelberger C. and Veynante D., Towards large eddy smulaton of combuston n spark gnton engnes, Proceedngs of the Combuston Insttute, Vol. 31, No. 1, pp , 007 [3.54] Schäpertöns, H. and Lee, W. "Multdmensonal Modelng of Knockng Combuston n SI Engnes." SAE 85050, [3.55] Spaldng, D. B. Combuston and Mass Transfer. Oxford: Pergamon Press, [3.56] Tatschl, R., Pachler, K., Fuchs, H., and Almer, W. "Multdmensonal Smulaton of Desel Engne Combuston - Modelng and Expermental Verfcaton." Proceedngs of the Ffth Conference 'The Workng Process of the Internal Combuston Engne'. Graz, Austra, [3.57] Theobald, M. and Cheng, W. "A Numercal Study of Desel Ignton." ASME 87-FE-, [3.58] Zeldovch, Y. B., Sadovnkov, P. Y. and Frank-Kamenetsk, D. A. Oxdaton of Ntrogen n Combuston. Translaton by M. Shelef, Academy of Scences of USSR, Insttute of Chemcal Physcs, Moscow-Lenngrad, Related Publcatons [3.59] Brandstätter, W., Ptcher, G., Tatschl, R. and Wnklhofer, E. "Modelng of Homogeneous-Charge Combuston n SI Engnes." MTZ Worldwde - Motortechnsche Zetschrft 58:(1997). [3.60] Carteller, W., Chmela, F., Kapus, P. and Tatschl, R. "Mechansms Leadng to Stable and Effcent Combuston n Lean Burn Gas Engnes." Proceedngs Internatonal Symposum COMODIA 94, The Japan Socety of Mechancal Engneers, 1994: [3.61] Frolov, S.M., Suffa, M., Tatschl, R. and Wolansk, P. "3D Modelng of Pulsed Jet Combuston." Zel'Dovch Memoral "Int. Conf. on Combuston", Moscow, Russa, Sept

74 FIRE v014 Combuston Module [3.6] Pachler, K., Tatschl, R., Fuchs, H. and Schwarz, W. "A Three-Dmensonal Smulaton of Desel Combuston Modelng and Expermental Valdaton." Internatonal Congress " Le moteur desel Evolutons et mutatons", Lyon, France, [3.63] Preschng, P., Wanker, R., Carteller, P. and Tatschl, R. CFD Modelng of HCCI Engne Combuston Valdaton and Applcaton, ICE 003 Conference, Naples 003. [3.64] Preschng, P. Ramusch G., Ruetz J. and Tatschl, R. 3D-CFD Modelng of Conventonal and Alternatve Desel Combuston and Pollutant Formaton A Valdaton Study, JSAE F&L 007, JSAE , SAE [3.65] Preschng, P. and Poredos, A. Premxed IC Engne Combuston Smulaton Applyng a Novel Type of Flame Trackng Approach, Internatonal Multdmensonal Engne Modelng User s Group Meetng at the SAE Congress, 014 [3.66] Tatschl, R. and Brandstätter, W. "Multdmensonal Calculaton of Spark Flame Intaton by Adoptng a Generc Hydrocarbon Knetc Scheme." Computatonal Methods n Appled Scences. Ch. Hrsch (Ed.) Elsever Publshers B.V., 199: [3.67] Tatschl, R. "A Mult-Scalar PDF Method for SI Engne Combuston Smulaton." Proceedngs of the 11th Symposum on Turbulent Shear Flows. Grenoble, [3.68] Tatschl, R., Bogensperger, M. and Redger, H. "Current Status and Future Developments of FIRE Combuston Models." Proceedngs of the 3rd Internatonal FIRE User Meetng. Graz, Austra, [3.69] Tatschl, R., Bogensperger, M. and Redger, H. "Modelng Spray Combuston n Desel Engnes." nd CIMAC Internatonal Congress on Combuston Engnes, Copenhagen, [3.70] Tatschl, R., Fuchs, H. and Brandstätter, W. "Expermentally Valdated Mult- Dmensonal Smulaton of Mxture Formaton and Combuston n Gasolne Engnes." IMechE C499/050, [3.71] Tatschl, R., Gabrel, H.P. and Preschng, P. "FIRE A Generc CFD Platform for DI Desel Engne Mxture Formaton and Combuston Smulaton." Internatonal Multdmensonal Modelng User's Group Meetng at the SAE Congress. Detrot, U.S.A., 001. [3.7] Tatschl, R., v. Künsberg Sarre, Ch., Pachler, K., Schneder, J. and Wnklhofer, E. "Multdmensonal Smulaton of Gasolne Drect Injecton Engnes." Socety of Automotve Engneers of Japan, , [3.73] Tatschl, R., v. Künsberg Sarre, Ch., Preschng, P. and Putz, N. "A Comprehensve CFD Workflow for the Modelng of Gasolne DI Engnes." The 1 st Natonal Congress on Fluds Engneerng. Muju Resort, Korea, 000. [3.74] Tatschl, R., Pachler, K. and Wnklhofer, E. "A Comprehensve DI Desel Combuston Model for Multdmensonal Engne Smulaton." Proceedngs Internatonal Symposum COMODIA 98, The Japan Socety of Mechancal Engneers, 1998: [3.75] Tatschl, R. and Redger, H. "PDF Modelng of Stratfed Charge SI Engne Combuston." SAE , Sept-014

75 Combuston Module FIRE v014 [3.76] Tatschl, R., Redger, H. and Bogensperger, M. "Multdmensonal Smulaton of Spray Combuston and Pollutant Formaton n a Medum Speed Marne Desel Engne." FISITA World Automotve Congress. Pars, 1998: [3.77] Tatschl, R., Redger, H. and Fuchs, H. "A Mult-Scalar PDF Method for Inhomogeneous-Charge SI Engne Combuston Smulaton." Advanced Computaton & Analyss of Combuston. G.D. Roy, S.M. Frolov, P. Gv (Edtors). Moscow: ENAS Publshers (1997). [3.78] Tatschl, R., Redger, H., v. Künsberg Sarre, Ch., Putz, N. and Kcknger, F. "Rapd Meshng and Advanced Physcal Modelng for Gasolne DI Engne Applcaton." Internatonal Multdmensonal Engne Modelng User's Group Meetng at the SAE Congress. Detrot, U.S.A., 000. [3.79] Tatschl, R., Redger, H., v. Künsberg Sarre, Ch., Putz, N. and Kcknger, F. "Fast Grd Generaton and Advanced Physcal Modelng Keys to Successful Applcaton of CFD to Gasolne DI Engne Analyss." ImechE. London, U.K [3.80] Tatschl, R., Weser, K. and Retbauer, R. "Multdmensonal Smulaton of Flow Evoluton, Mxture Preparaton and Combuston n a 4-Valve SI Engne." Proceedngs Internatonal Symposum COMODIA 94, The Japan Socety of Mechancal Engneers, 1994: [3.81] Tatschl, R., Wesler, B., Alajbegovc, A. and v. Künsberg Sarre, Ch. "Advanced 3D Flud Dynamc Smulaton for Desel Engnes." Thesel 000. Valenca, Span, 000. [3.8] Weser, K., Versaevel, P. and Motte, P. "A New 3D Model for Vaporzng Desel Sprays Based on Mxng-Lmted Vaporzaton." SAE , 000. [3.83] Wnklhofer, E., Fradl, G.K. and Tatschl, R. "Flame Vsualzaton n Gasolne Engnes - New Tools n Engne Development." IPC-8 Techncal Paper No , Socety of Automotve Engneers of Japan, Inc., Sept

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77 Combuston Module FIRE v COMBUSTION INPUT DATA Ths secton explans how the combuston nput data can be generated wthn the FIRE Workflow Manager and descrbes the data n the Solver Steerng Fle for the FIRE Combuston Module. In general f certan features are actvated, whch are not requred, the optons wll be grayed out. Select Module actvaton at the top of the parameter tree to access the Combuston toggle swtch and turn on the toggle swtch to actvate the module. The Combuston parameter tree s dsplayed n the Modules folder as follows: 4.1. Control Fgure 4-1: Combuston Parameter Tree Select Control n the parameter tree and then actvate/deactvate the followng: Default Extended output Addtonal output nformaton (mass-averaged data) for the flow, combuston and spray module wll be prnted after each tme step n case of ts actvaton. Off 4.. Combuston Models Select Combuston models n the parameter tree to access the followng models: Fgure 4-: Combuston Models Wndow 30-Sept

78 FIRE v014 Combuston Module Refer to secton for detals on Tme dependent actvaton Eddy Breakup Model Select Eddy Breakup Model and On to dsplay the followng optons: Off On Fgure 4-3: Eddy Breakup Model Wndow Deactvates the turbulence controlled combuston model (Magnussen formulaton). Actvates the turbulence controlled combuston model (Magnussen formulaton). Default Actve 4-30-Sept-014

79 Combuston Module FIRE v Model Constants Specfcaton of the model constants A and B. Constant A Constant B The exact value for the constant A s problem specfc and depends on the fuel and the detaled structure of the turbulent flow feld. Thus t requres adjustment accordng to avalable expermental data. Common values for engne applcatons are between 3 and 5. An ncrease n A leads to an ntensfcaton of the turbulent reacton rate. Ths s constant C fu used n equaton (3.). A value of about has been found to be vald for B over a broad range of applcatons and should not be changed arbtrarly. Recommended value for SI engne smulaton: 0.5 Recommended value for CI (compresson gnton) engne smulaton: 1.0 Ths s constant C Pr used n equaton (3.). Default Tme Scale Specfes the reacton tme scale n the Magnussen combuston model. The optons are descrbed below: SI engne combuston smulaton s recommended to be performed usng the global tme scale opton; spray combuston smulaton should be performed usng the local tme scale defnton. Default Local Global Stretch The depleton rate of the combustble mxture s taken to be proportonal to the reacton tme scale τ R determned by the local value of the rato of the turbulence knetc energy k and ts dsspaton rate ε. The depleton rate of the combustble mxture s taken to be proportonal to the reacton tme scale τ R determned by the global value of the rato of the turbulence knetc energy k and ts dsspaton rate ε The depleton rate of the combuston mxture s determned by the local value of the rato of k/ε corrected by a functon consderng the flame characterstcs (thckness, velocty) and turbulence parameters (ITNFS model, refer to chapter 3..4.) Actve 30-Sept

80 FIRE v014 Combuston Module Lmt An addtonal feature for the tme scale determnaton s the local turbulent tme scale lmt. The local turbulent tme scale s lmted to a certan level accordng to the followng formula: ε ε 1 ε Γ = max, 0 k k C1 k wth ε dsspaton rate [m /s 3 ] k turbulence knetc energy [m /s ] constant (default value 1.0E+05) C 1 User Actvates Lmt: If the user wants to change the value of constant C 1, a new value must be wrtten for t nto the Lmt nput feld. The rate of converson of the fuel ar mxture s calculated accordng to the mean reacton rate wth a predefned value for the reacton tme scale τ R. Actvates Tme scale [s] 4... Turbulent Flame Speed Closure Model The turbulent flame speed closure model has been developed and tested for both homogeneous and nhomogeneous charge combuston n SI engnes. Select Turbulent Flame Speed Closure Model to access the followng optons: Fgure 4-4: Turbulent Flame Speed Closure Model Wndow Sept-014

81 Combuston Module FIRE v014 Off TFSCA TFSCB Deactvates the turbulent flame speed closure combuston model. Actvaton usng TFSCA s manly constructed for homogeneous charge combuston. Actvaton usng TFSCB s for both homogeneous and nhomogeneous charge combuston, respectvely. For the later actvaton a specal near-wall treatment of the reacton rate s consdered, addtonally. Default Actve Model Constants Specfcaton of the model constants CAI and CFP. Constant CAI Constant CFP The CAI constant nfluences the reacton rate determned by usng an auto-gnton reacton mechansm and should be kept constant at zero for all applcatons. No valdaton has been made up to now usng ths auto-gnton mechansm. An ncreased value n CAI leads to a much faster combuston start (auto-gnton mechansm). Refer to equaton (3.15). The CFP model constant nfluences the flame propagaton reacton rate and should be used only. The exact value for ths model constant CFP s problem specfc and depends on detaled structure of the turbulent flow feld and flame, respectvely. An ncrease n CFP results n an ntensfcaton of the reacton rate (value > 0.0). Refer to equaton (3.16). Default Sept

82 FIRE v014 Combuston Module Coherent Flame Model The FIRE Coherent Flame Model (ECFM) has been mplemented and tested for homogeneously premxed turbulent combuston n SI engnes and can also be used for nonpremxed combuston applcatons. Select Coherent Flame Model to dsplay the one of the followng wndows: Fgure 4-5: Coherent Flame Model Wndow Default Off Deactvates the coherent flame model. Actve CFM-A MCFM ECFM Ths can be used for homogeneous and nhomogeneous charges. The man dfference between the CFM-A and MCFM models s the determnaton of the lamnar flame speed. Ths can be used for homogeneous and nhomogeneous charges. For very fuel rch and fuel lean regons the lamnar flame speed n MCFM s modfed accordng to the local fuel/ar equvalence rato. Addtonally, a lamnar stretch term s consdered. Ths can be used for homogeneous and nhomogeneous charges wth features of the MCFM. The man feature of ths model s that t can be used n combnaton wth the Spray Module (manly developed for GDI applcaton). It s recommended to use ths model for all types (premxed and non-premxed) of gasolne and gas engne applcatons Sept-014

83 Combuston Module FIRE v014 ECFM-3Z The ECFM-3Z model can be used for both gasolne and desel auto-gnton applcatons. Ths s the recommended choce. If CFM-A, MCFM or ECFM s selected, the followng optons are avalable: Automatc model parameters Intal flame surface densty Stretch factor Consumpton factor Automatc specfcaton of the ntal flame surface densty, stretch and consumpton factor can be selected for full (Correlatons_FL) and part (Correlatons_PL) load engne condtons. If ths button s actvated the followng 3 parameters are automatcally determned and cannot be changed by the user (grayed out). If ths opton s used only the Sphercal gnton model s used. Note: These correlatons are derved for the ECFM usng the Database correlatons (tabulated flame speeds) for the lamnar flame speed (to be set n the Intal Condtons) and are not recommended for other CFM models. The two optons Correlatons_FL and Correlatons_PL can only be accessed f the Database opton s actvated for the lamnar flame speed n the ntal condtons part of the GUI. Specfcaton of the ntal flame surface densty wthn the gnton cells. Ths s a problem specfc model constant (recommended value [1/m]). Ths value nfluences the gnton delay. The hgher the ntal value the shorter the gnton delay. Note: If ECFM and Aktm/ISSIM (Intal flame kernel shape, see below) are selected ths opton s meanngless and does not appear. If Automatc model parameters s actvated, ths opton s meanngless and s grayed out (automatc determnaton). Ths s a problem specfc model constant (recommended value ). An ncrease of the stretch factor leads to an ntensfcaton of the producton of the flame surface densty and hence n a shorter and faster combuston phase. Note: If Automatc model parameters s actvated, ths opton s meanngless and s grayed out (automatc determnaton). Model constant (recommended value 1.0) whch should not be changed. Note: If Automatc model parameters s actvated, ths opton s meanngless and s grayed out (default value s used). Off 300 [1/m] Sept

84 FIRE v014 Combuston Module Combuston chamber cell selecton If Automatc model parameters s actvated ths button s vsble where a cell selecton for the combuston chamber can be selected. Not vsble Note: If ths selecton s not avalable a default value for the stretch factor of 1.6 s used. Intal flame kernel shape Prncpally each gnton model can be used for each CFM model (see recommendaton n the descrpton of each model) Sphercal: Ths gnton model can be used for all CFM models (manly recommended). In ths model a sphercal flame kernel s released usng the gnton tme, flame kernel radus and spark duraton wth the flame surface densty specfed n the FIRE Workflow Manager. The flame surface densty s kept constant n the gnton cells over the spark duraton. Sphercal Note: If Automatc model parameters s actvated, ths opton s meanngless and s grayed out (default model s used). Sphercal_Delay: Ths gnton model s manly developed for the ECFM model (however AKTIM n connecton wth ECFM should be preferred, see below) and should not be used for the other CFM models. A specfc tme for the deposton of the flame kernel after spark tmng s calculated. Addtonally, the sphercal flame radus and the flame surface densty n the gnton cells are automatcally determned. The only specfcaton n the FIRE Workflow Manager s the gnton tme and the actvaton of Sphercal_Delay. Ths model can also be actvated for the other CFM models (not recommended) but can lead to no flame kernel deposton (no gnton). The "Ellpsodal" s smlar to the "Sphercal_Delay" model but n the latter model a sphercal flame kernel s consdered. Ignton reference radus parameter: The user can modfy the flame kernel radus to actual requrements Sept-014

85 Combuston Module FIRE v014 Ellpsodal: Ths gnton model s manly developed for CFM-A and MCFM where a flame kernel can be specfed whch wll be "deformed" due to the level of turbulence and flow condtons at the spark plug resultng n an ellpsodal form (consderng an ntal sphercal form durng lamnar phase to the ellpsodal form durng turbulent phase). Prncpally the rad and gnton delay tme (deposton tme for the flame kernel) s calculated automatcally whch s currently not mplemented (therefore not recommended, needs experence for the ntalzaton of the requred parameters). Intal radus of ellpsod 1 Frst radus. Intal radus of ellpsod Second radus. Ignton delay tme Specfes the gnton delay tme. Aktm: The Arc and Kernel Ignton Model can be used wth the ECFM and ECFM-3Z combuston models only. It s an accurate and physcally-based spark gnton model, takng the spark plug electrcal crcut, spark moton and flame kernel dynamcs and combuston nto account. The flame surface densty deposton s the result of ths complex modelng. Actvaton of Aktm expert mode Electrcal dscharge law exponent Dscharge coeffcent ds used n equaton (3.56) for the calculaton of the gas column voltage. Intal flame kernel dameter Intal dameter of the flame kernels generated after a spark breakdown. Maxmum number of flame kernels per breakdown Maxmum number of flame kernels that can be created durng a breakdown. Kernel enthalpy deposton factor Blendng factor appled on the enthalpy source term comng from burnt kernel deposton. A value of 1 can lead to a dvergence of the calculaton. 1.0 [-] [m] [m] [s] [m] Sept

86 FIRE v014 Combuston Module Lamnar terms ISSIM: The Imposed Stretch Spark Ignton Model can be used wth the ECFM-3Z combuston model only. It s currently the most accurate and physcally-based spark gnton model where the spark plug electrcal crcut, spark moton and flame kernel dynamcs and combuston are taken nto account. The flame surface densty deposton s the result of a complex modelng. If LES or LES CSM turbulence model s actvated n combnaton wth ECFM or ECFM-3Z, the lamnar term swtch has to be actvated, otherwse unresolved source terms of the FSD are not consdered/solved. Ths swtch actvates or deactvates the lamnar terms for the flame surface densty transport equaton. If LES or LES CSM turbulence model s actvated n combnaton of ECFM or ECFM-3Z, the lamnar term swtch has to be actvated, otherwse unresolved source terms of the FSD are not consdered/solved. Off Tme Scale Specfcaton of the average stretch tme scale n the Coherent Flame Model. The optons avalable are as follows: Default Local Global User The stretch of the flame s taken to be proportonal to the stretchng tme scale determned by the local value of the rato of the turbulence knetc energy k and ts dsspaton rate ε. The stretch of the flame s taken to be proportonal to the stretchng tme scale determned by the global value of the rato of the turbulence knetc energy k and ts dsspaton rate ε. The rate of stretch of the flame s calculated wth a predefned value for the stretchng tme scale. Actvates Tme scale. Actve [s] Sept-014

87 Combuston Module FIRE v ECFM-3Z Select the ECFM-3Z model to dsplay the followng optons (gasolne and desel autognton mode): Fgure 4-6: ECFM-3Z Model Wndow Fgure 4-7: ECFM-3Z Model Wndow for Gasolne Engne Applcaton The parameters, factors and sub-models are the same as for ECFM and are descrbed n the ECFM actvaton chapter Sept

88 FIRE v014 Combuston Module Fgure 4-8: ECFM-3Z Model Wndow for Desel Auto-gnton Applcaton Default Spark gnton model Mxng model parameter Auto gnton model No: Spark-gnton off. The other models for spark gnton are descrbed n chapter Ths parameter nfluences the transfer of fuel from the pure fuel zone to the mxed zone. No: Auto-gnton off. Formula: Auto-gnton delay tme s calculated from Arrhenus emprcal approach (not recommended). Table: Auto-gnton delay tme s nterpolated from tabulaton. User: For later use. Two-Stage: Auto-gnton delay tme for cool flame gnton and man gnton s nterpolated from tabulated values. Ths s the recommended choce, whch takes nto account databases for dfferent fuel types. The followng databases are avalable: methane, -octane, n-heptane, ethanol, dme. If the fuel whch was selected at the ntal condtons does not match exactly, the nearest database s chosen automatcally. No 1.0 Table Sept-014

89 Combuston Module FIRE v014 Autognton model parameter Chemcal reacton tme Extncton temperature Ths only works wth the optons Table and Twostage for the Auto-gnton model. The nverse of ths value s multpled wth the gnton delay tme from the databases. Ths means that values larger than 1 are acceleratng the gnton and vce versa. Ths value nfluences the rate of reacton of the fuel durng premxed combuston and durng autognton. Temperature lmt below whch the fuel s transformed back from burnt status to unburned status. When multple njectons are calculated, the recommended value s 1500 K or hgher e Sept

90 FIRE v014 Combuston Module PDF Model The mult-scalar PDF model has been developed and tested for fuel/ar mxng processes and homogeneous/nhomogeneous charge combuston n SI engnes, ncludng gasolne DI combuston. Select the PDF Model to dsplay the followng optons: Fgure 4-9: PDF Model Wndow Default Off On Deactvates the mult-scalar PDF speces transport, mxng and combuston model. Actvates the mult-scalar PDF model for all SI flame types usng fully dynamc Monte Carlo partcle number densty adjustment (hgher accuracy and less memory requrement). Actve Sept-014

91 Combuston Module FIRE v Rate Coeffcent Treatment Specfcaton of the Arrhenus reacton coeffcents ether by the user or automatcally. Default Auto The coeffcents are set automatcally based on data of Westbrook and Dyer dependng on the used fuel type. Mxng rate constant: Specfes the value of the mxng rate constant n the PDF transport equaton. Recommended value for engne applcatons Changng the value weakly affects the gnton delay tme but exhbts sgnfcant nfluence on the man combuston phase. Increasng the value reduces the duraton of the man combuston phase. User Specfes the pre-exponental factor and the actvaton energy of the chemcal reacton rate expresson n the PDF transport equaton n addton to the mxng rate constant (Fgure 4-10). Mxng rate constant Specfes the value of the mxng rate constant n the PDF transport equaton. Recommended value for engne applcatons Changng the value weakly affects the gnton delay tme but exhbts sgnfcant nfluence on the man combuston phase. Increasng the value reduces the duraton of the man combuston phase. Preexponental factor 1e+11 Recommended value: 1.0E11. An ncrease of the value leads to a faster chemcal reacton and hence (n the case of SI engne combuston) to a shortenng of the gnton delay (.e. tme untl [%] mass fracton burnt). Dependng on the ratos of the physcal and chemcal tme scales, the value may also slghtly affect the duraton of the man combuston phase. Actvaton energy Recommended value: 1.8E08. A small decrease of the value results n a dramatc augmentaton of the flame propagaton velocty n premxed SI engne combuston, and hence, to a shortenng of the gnton delay and the man combuston duraton. 1.8e Sept

92 FIRE v014 Combuston Module Note: The Preexponental factor and Actvaton energy quanttes represent chemcal knetc data that may vary n lterature, dependng on ther determnaton. They always stay consstent therefore they should not be changed arbtrarly. If they are set to zero ther values are automatcally determned from lterature data as a functon of fuel type (Methane Hexadecane). Fgure 4-10: PDF Model Wndow for User Defned Coeffcents Tme Scale The value for the mxng tme scale τ n the PDF transport equaton s specfed n ths secton. Default Local Global User The mxng processes n the flame are taken to be proportonal to the tme scale τ. Ths s determned by the local value of the rato of the turbulence knetc energy k and ts dsspaton rate ε. The turbulent mxng s taken to be proportonal to the mxng tme scale τ. Ths s determned by the global value of the rato of the turbulence knetc energy k and ts dsspaton rate ε. Stratfed charge combuston and flame propagaton n premxed charge showed good agreement wth expermental data for adopton of the global tme scale opton. Turbulent mxng n the flame s calculated accordng to a predefned value for the mxng tme scale τ. Actvates Tme scale Actve [s] Sept-014

93 Combuston Module FIRE v Characterstc Tmescale Model Select the Characterstc Tmescale Model to dsplay the followng wndow: Fgure 4-11: Characterstc Tmescale Model Wndow Default Off Deactvates the Characterstc Tmescale Model. Actve On Actvates the Characterstc Tmescale Model. 30-Sept

94 FIRE v014 Combuston Module Model Constants Auto gnton constant Premxed combuston constant Turbulent combuston constant Ths constant nfluences the auto gnton of the fuel. The larger the value, the faster the reacton (shorter gnton delay). Ths constant s used n equaton IV of the SHELL model (secton ). Ths constant nfluences the lamnar part of the combned reacton rate. The larger the value, the faster the reacton. Ths s constant A used n equaton (3.14). Ths constant nfluences the turbulent part of the combned reacton rule. The smaller the value, the faster the reacton. Ths s constant C used n equaton (3.116). Default e e Tme Scale Specfcaton of the reacton tme scale n the Characterstc Tmescale Model. The optons are descrbed as follows: Default Local Global User The mxng processes n the flame are taken to be proportonal to the tme scale τ. Ths s determned by the local value of the rato of the turbulence knetc energy k and ts dsspaton rate ε. The turbulent mxng s taken to be proportonal to the mxng tme scale τ. Ths s determned by the global value of the rato of the turbulence knetc energy k and ts dsspaton rate ε. Turbulent mxng n the flame s calculated accordng to a predefned value for the mxng tme scale τ. Actvates Tme scale. Actve [s] Sept-014

95 Combuston Module FIRE v Steady Combuston Model Select Steady Combuston Model to dsplay the followng wndow: Fgure 4-1: Steady Combuston Model Wndow Model Constants Preexponental factor Actvaton energy Droplet dameter Ths constant nfluences the reacton rate. The larger the value the slower the reacton. Ths constant nfluences the reacton rate. The larger the value the faster the reacton. Ths constant descrbes the ntal average dameter of a fuel droplet and nfluences the reacton rate. The smaller the value, the faster the combuston. Default 9.434e e Sept

96 FIRE v014 Combuston Module Flame Trackng Partcle Model Select Steady Combuston Model to dsplay the followng wndow: Fgure 4-13: Steady Combuston Model Wndow Sept-014

97 Combuston Module FIRE v Model Constants Combuston parameter Ignton parameter Symmetry factor Partcle method Ths constant nfluences the man reacton rate. The larger the value the faster the reacton. Usual range s between 0.5 and 1.8. Ths constant nfluences the spark gnton delay. The larger the value the longer the gnton delay. Usually no modfcaton of ths value s necessary. Ths constant s necessary to prescrbe a correct gnton behavor for splt combuston geometres. For a full geometry the factor has to be equal to 1. For a half model the factor has to be equal to, and so on. Ths pull-down menu allows choosng between the optons for the partcle method. Optons are: Off partcle method off Pre-flame calculate pre-flame chemstry Post-flame calculate only postflame chemstry Both calculate pre- and post-flame chemstry Default Off If the opton Pre-flame or Both s chosen for the Partcle Method three addtonal ASCII output fles are wrtten to the Case drectory: knock_output.dat: the four columns of the fle contan: crank angle, mass of cells wth auto-gnton progress > 1%, mass of cells wth auto-gnton progress > 3%, mass of cells wth auto-gnton progress > 5% knock_output_mean.dat: the two columns contan: crank angle, mean auto-gnton progress varable (over the pre-flame zone) knock_output_dstr.dat: Ths output fle s organzed n blocks. The crank angle postons, s headng each block. The two columns of each block contan the auto-gnton progress (between 0% and 10%) and the mass dstrbuton for ths range of auto-gnton progress respectvely. 30-Sept

98 FIRE v014 Combuston Module User Defned Reacton Rate The user can mplement hs own combuston model nto a subroutne wth the name "use_cctrat.f". Select the User Defned Reacton Rate to access the followng optons: Default Off Deactvates the user defned reacton rate. Actve Explct Implct The subroutne s called before the SIMPLE loop. The subroutne s called at each teraton wthn the SIMPLE loop Tme Dependent Actvaton of Combuston Combuston Models Select the Tme dependent actvaton toggle swtch and clck on Table to show the followng: Fgure 4-14: Tme Dependent Actvaton of Combuston Models 4-30-Sept-014

99 Combuston Module FIRE v014 Wthn the upper table, the combuston models can be actvated only for a certan tme durng the whole calculaton. The combuston model constants are the same as descrbed n the prevous sectons. To adjust the model constants clck on the number on the left sde to hghlght the lne wthn the table. When the lne s hghlghted (as shown above), clck on Open model to get an addtonal wndow, whch contan the model nformaton Auto Ignton Models For some applcatons t s useful to only actvate the auto gnton procedure durng certan tme ntervals. In the Auto gnton wndows, select the Tme dependent actvaton toggle swtch to access the actvaton and deactvaton tme/crank angle nput felds, whch can be defned by the user Ignton Models Select Ignton models n the parameter tree to dsplay the two optons Spark Ignton and Auto Ignton Spark Ignton Select On to dsplay the followng wndow (except when Aktm/ISSIM gnton model s actvated): Fgure 4-15: Spark Ignton Wndow The followng optons are avalable: Default Off Deactvates the spark gnton model. Actve On Number of spark locatons Spark locatons Actvates the spark gnton model. Specfes the number of spark locatons. 1 Clck to access an nput table wth x, y, and z coordnates of spark locatons. Spark tmng Specfes the gnton spark tme as a constant value or nput a table (as descrbed below) correspondng to all spark locatons Sept

100 FIRE v014 Combuston Module Flame kernel sze [m] Ignton duraton [s] Specfes the flame kernel radus as a constant value or nput a table (as descrbed below) correspondng to all spark locatons. Note: Ths value s meanngless f Aktm, ISSIM, Sphercal_Delay or Ellpsodal s selected as Intal flame kernel shape of the ECFM combuston model. Specfes the gnton duraton as a constant value or nput a table (as descrbed below) correspondng to all spark locatons. Note: Ths value s meanngless f Aktm, ISSIM, Sphercal_Delay or Ellpsodal s selected as Intal flame kernel shape of the ECFM combuston model ndcates that the user can nput values n a table relatng to the number of spark locatons. The followng optons are avalable: 1. Constant Ths s the default settng and specfes that the parameter value entered n the feld wll reman constant for the entre smulaton and for all spark locatons.. Tmng for Spark Tmng Iteraton. Radus for Flame Kernel Sze. Duraton for Ignton Duraton. The parameter nput feld s replaced by the relevant button mentoned above. Select t to open an nput table where parameter values can be entered for each spark locaton. When the Aktm gnton model s actvated (ECFM Intal flame kernel shape) the wndow s dsplayed as shown. The optons are descrbed above. Fgure 4-16: Spark Ignton Wndow Aktm gnton model The wndow for the Aktm spark plug model looks lke the followng: Sept-014

101 Combuston Module FIRE v014 Fgure 4-17: Aktm Spark Plug Model The followng optons are avalable Face selecton Cathode locaton Anode locaton Electrode dameter Specfcaton of the spark plug boundary face selecton on the mesh. It wll be nvolved n the calculaton of the flame kernels heat losses. If the spark plug s not meshed, use the default NoSelecton. Locaton of the cathode on the mesh. x-coordnate y-coordnate z-coordnate Locaton of the anode on the mesh. x-coordnate y-coordnate z-coordnate Specfcaton of the electrode dameter (assumed dentcal on cathode and anode sde). NoSelecton 0 [m] 0 [m] 0 [m] 0 [m] 0 [m] [m] [m] Cathode voltage Specfcaton of the cathode voltage. 5 [V] Anode voltage Specfcaton of the anode voltage [V] Inductance Resstance Intal energy Specfcaton of the nductance n the spark plug secondary electrcal crcut. Specfcaton of the resstance n the spark plug secondary electrcal crcut. Specfcaton of the electrcal energy ntally avalable n the spark plug secondary electrcal crcut. 0 [H] 0000 [Ω] 0.04 [J] 30-Sept

102 FIRE v014 Combuston Module When the ISSIM gnton model s actvated (only wth the ECFM-3Z combuston model) the wndow for the spark plug model s dsplayed as shown. Fgure 4-18: ISSIM Spark Plug Model The followng optons are avalable Spark locaton Locaton of the spark (centre between cathode and anode). x-coordnate y-coordnate z-coordnate 0 [m] 0 [m] 0 [m] Spark gap Specfcaton of the dstance between electrodes [m] Electrode dameter Specfcaton of the electrode dameter [m] Cathode voltage Specfcaton of the cathode voltage. 5 [V] Anode voltage Specfcaton of the anode voltage [V] Inductance Resstance Specfcaton of the nductance n the spark plug secondary electrcal crcut. Specfcaton of the resstance n the spark plug secondary electrcal crcut. 0 [H] 0000 [Ω] Sept-014

103 Combuston Module FIRE v014 Intal energy Symmetry factor Specfcaton of the electrcal energy ntally avalable n the spark plug secondary electrcal crcut. Specfcaton of the symmetry factor. For symmetry the factor s, for a sphere t s 1, for an eghth of a sphere t s [J] Auto Ignton Fgure 4-19: Auto Ignton Wndow for Desel Default Off Deactvates the auto gnton model. Actve Desel Select Desel to dsplay the avalable optons shown n Fgure 4-19: Desel Actvates the spray auto gnton model for desel engne applcatons. Actvates Reacton coeffcent. Reacton coeffcent: Specfes the reacton rate coeffcent for the formaton of ntermedate products n the Desel self-gnton model (e.g. Dodecane: 1.e+07). Increasng/decreasng the value for the ntermedate formaton coeffcent by one order of magntude reduces/ncreases the gnton delay by approxmately [ms], respectvely, dependng on the detals of the applcaton case under consderaton. 1e+07 Tme dependent actvaton: Refer to secton Sept

104 FIRE v014 Combuston Module Desel_MIL Select Desel_MIL to access the avalable optons: Desel_MIL Actvates the Multple Ignton Locaton Model. Actvates Reacton coeffcent. Desel_MIL allows that the auto gnton may happen at dfferent locatons and at dfferent tmes. Ths s managed by checkng the gnton crteron for each cell ndvdually. Note: For Desel opton the gnton process s stopped f any cell has reached the gnton crteron. Reacton coeffcent: The Reacton Coeffcent nput s the same as for Desel. 1e+07 Tme dependent actvaton: Refer to secton HCCI Select HCCI to access the avalable optons: HCCI Actvates the auto-gnton model for Homogeneous Charge Compresson Ignton engne smulatons (SHELL model). Actvates Reacton coeffcents: Reacton rate coeffcents of the Shell model [3.35]. Parameter AQ: Only nfluences the gnton delay - the larger the value the shorter the delay. Parameter AB: Influences the cool flame - the smaller the value the smaller the cool flame part. Parameter A0F1: The larger the value the shorter the gnton delay and the more ntensve the prereactons (cool flame). Parameter A0F4: The larger the value the shorter the gnton delay. Tme dependent actvaton: Refer to secton e+1 4.4e e e Sept-014

105 Combuston Module FIRE v Knock Select Knock to access the avalable optons: Knock (Shell Model) Knock (Shell Model wth temperature couplng) Actvates the auto-gnton model to be used to descrbe the development of radcals and reacton heat n the case of knockng combuston events. Ths feature s only vald for SI combuston (homogeneous and GDI) and n combnaton wth the Magnussen Model, the Turbulent Flame Speed Closure Model (TFSCM) and the Coherent Flame Model (CFM). Actvates Reacton coeffcent: The default value s 1.88E+04 for the reacton rate coeffcent n the case of knockng combuston. Note: Only n the case of knockng combuston the spark gnton and auto gnton models are actvated at the same tme. Tme dependent actvaton: Refer to secton Ths opton actvates the Shell auto-gnton model but a temperature on the unburnt sde of the mxture s calculated, whch s then used to determne the reacton rate for knockng. 1.88e e AnB Knock Select AnB Knock and On for Spark Ignton to dsplay the avalable optons n the followng wndow: Fgure 4-0: Auto Ignton Wndow for AnB Knock Default 30-Sept

106 FIRE v014 Combuston Module AnB Knock Actvates the auto-gnton model used to descrbe the fuel consumpton and heat release n the case of knockng combuston events n order to model the acoustc wave propagaton. Ths feature s only vald for SI combuston (homogeneous and GDI) currently only n combnaton wth the Coherent Flame Model (CFM, especally constructed for the ECFM). Parameter A: Pre-exponental factor n the gnton delay expresson due to auto-gnton (Arrhenus approach). Parameter n: Pressure exponent n the gnton delay expresson. Parameter B: Actvaton temperature n the gnton delay expresson. Parameter RON: Fuel octane number, lmted up to 140, used n the gnton delay expresson Emprcal Knock Model Note: Only n the case of knockng combuston the spark gnton and auto gnton models are actvated at the same tme. For a better acoustc wave propagaton modelng the user should use small tme step ncrements durng the combuston phase and for local pressure hstores the user should defne ponts near auto-gnton postons (user dependent selectons) and wrte the nformaton nto an outputfle (user-functon). Tme dependent actvaton: Refer to secton Select Emprcal Knock Model to access the avalable optons: Emprcal Knock Model Actvates the emprcal auto-gnton model used to descrbe the possblty that knock can occur wthn specfed regons. A crteron s calculated determned wthn dfferent segments and data s wrtten to emprcal_knock_crterum.out output-fle. Ths feature s only vald for SI combuston (homogeneous and GDI) and n combnaton wth the Magnussen Model, the Turbulent Flame Speed Closure Model (TFSCM) and the Coherent Flame Model (CFM). Note: Only n the case of knockng combuston the spark gnton and auto gnton models are actvated at the same tme. The output-fle s only wrtten f the user defnes a cell-selecton named knock_detecton, otherwse no knock s calculated Sept-014

107 Combuston Module FIRE v Desel Ignted Gas Engne Model The Desel gnted gas engne model combnes homogeneous premxed gas combuston wth Desel gnton. It s possble to use the Eddy Breakup combuston model or the ECFM combuston model for the man burnng phase. The auto-gnton model s chosen automatcally. Auto-gnton s calculated n regons whch are rcher than the homogeneous mxture. Select Desel gnted gas engne to access the followng avalable optons: Fgure 4-1: Wndow for AnB Knock Default Off Automatc Manual Ths opton calculates the mean fuel mass fracton n the whole doman and uses ths value as a lmt for cells wth auto-gnton. Note: Ths opton s recommended. Wth ths opton the user can specfy the lmtng mass fracton value by hand. Fuel mass fracton lmt Actve 0 30-Sept

108 FIRE v014 Combuston Module 4.4. D Results To add a D output regon to the project, clck on D results n the parameter tree wth the rght mouse button and choose D: Insert from the submenu. To delete a D output regon from the project, clck on the name (.e. D[1]) wth the rght mouse button and choose Remove from the submenu. Select the name of the D output regon n the parameter tree to dsplay the followng wndow. Fgure 4-: D Results Wndow Default Sel. for D output Name of D output Ths pull-down menu ncludes the names of cell selectons defned for the volume mesh. Select the approprate Cell Selecton that corresponds to the desred boundary. The name selected n Sel. for D output s automatcally entered here. Enter a name for the output regon. Ths name wll also appear n the parameter tree. NoName The averaged quanttes are wrtten to the.fla-fle and.fl-fle. For a short descrpton of the quanttes refer to secton General Informaton 1. Rate of heat release. Accumulated heat release 3. Mean mxture fracton 4. Mean burnt fuel mass fracton Sept-014

109 Combuston Module FIRE v Mean products mass fracton 6. Mean resdual gas mass fracton 7. Mean equvalence rato 8. Mean unburned equvalence rato 9. Mean reacton progress varable 10. Mean reacton rate 11. Mean turbulent reacton rate 1. Mean knetc reacton rate Auto Ignton Models 1. Mean radcal R mass fracton. Mean radcal R rate 3. Mean agent B mass fracton 4. Mean agent B rate 5. Mean ntermedate Q mass fracton 6. Mean ntermedate Q rate D Results Select 3D results n the parameter tree to dsplay the followng wndow: Fgure 4-3: 3D Results Wndow 30-Sept