Reduced combustion time model for methane in gas turbine flow fields

参Availableonlineatwww.sciencedirect.comScienceDirectINGC NATURAL GASCHEMISTRYELSEVIERJoumal of Natural Gas Chemistry 18(2009)145-155www.elsevicr.com/locate/jngcReduced combustion time model for methane in gas turbine flow fieldsMouna Lamnaouer!, Robert C. Ryder, Andreja Brankovic, Eric L. Petersen2*1. Graduate Research Assistant, Mechanical, Materials Aerospace Engineering University of Central Florida, Orlando, F4, 32816, USA;2. Associate Professor, Department of Mechanical Engineering, Texas A&M Universiry, College Station, TX, 77843, USA3. President, Engineering, Flow Parametrics, Ivoryton, CT, USA; 4. Vice President, Flow Parametrics, Ivoryton, CT, USReceived November 29, 2008; Revised January 5, 2009; Available online June 2, 2009]AbstractComputational fluid dynamics(CFD)modeling of the complex processes that occur within the bumer of a gas turbine engine has become acritical step in the design process. However, due to computer limitations, it is very difficult to completely couple the fluid mechanics solverwith the full combustion chemistry. Therefore, simplified chemistry models are required, and the topic of this research was to provide reducedchemistry models for CH,/O2 gas turbine flow fields to be integrated into CFD codes for the simulation of flow fields of natural gas-fueledburners. The reduction procedure for the CH,/O2 model utilized a response modeling technique wherein the full mechanism was solved overa range of temperatures, pressures, and mixture ratios to establish the response of a particular variable, namely the chemical reaction time. Theconditions covered were between 1000 and 2500 K for temperature, 0. I and 2 for equivalence ratio in air, and 0. I and 50 atm for pressure. Thekinetic time models in the form of ignition time correlations are given in Arrhenius-type formulas as functions of equivalence ratio, temperature,and pressure; or fuel-to-air ratio, temperature, and pressure. A single ignition time model was obtained for the entire range of conditions, andseparate models for the low-temperature and high-temperature regions as well as for fuel-lean and rich cases were also derived. Predictionsusing the reduced model were verified using results from the full mechanism and empirical correlations from experiments. The models areintended for( but not limited to)use in CFD codes for flow field simulations of gas turbine combustors in which initial conditions and degree ofmixedness of the fuel and air are key factors in achieving stable and robust combustion processes and acceptable emission levels. The chemicalme model was utilized successfully in CFD simulations of a generic gas turbine combustor with four different cases with various levels offuel-air premixingKey wordsCH4; ignition time correlations: reduced kinetic mode1. Introductionchemical kinetics models that require minimal computationaltime for combustion simulations has led to the developmentModeling the interaction between flow fields and chem- of reduced mechanismsical reactions is a complicated process due to the excessiveOne, two, and multi-step reduced mechanisms forcomputational resources required to couple the full chemistry methane oxidation were developed by Westbrook andwith a full-scale numerical flow solver. Combustion model- Dryer[1]. Similarly, Bilger developed a four-step reduceding using detailed chemistry is important to accurately pre- mechanism [2], as did Seshadri and Peters [3]. Five, six,dict certain combustion phenomena in a gas turbine design seven, and nine-step mechanisms were developed by Malphase. However, detailed chemistry contains many reactions lampalli et aL. [4]. Several other reduced mechanisms haveand species, and since the computational cost and time asso- been developed for methane [5, 6] as summarized by Smookeciated with a given reaction mechanism are directly affected [7]. The accuracy of these mechanisms has been investigatedby the number of species, the process becomes very compu- by Cao and Pope [8] and Volchkov et al. [9]. In general,tationally expensive. Hence, there is a demand for reliable the fewer-step mechanisms have been used more extensivelymodels that use less computational time yet still accurately in combustion modeling due to their simplicity. For instance,reproduce some of the important aspects of the combustion one-step methane combustion has been modeled with goodphenomena. This awareness of the importance of accurate resul中国煤化工Corresponding author. Tel: 979-845-1257: Fax: 979-845-3081: E-mail: petersen @eThe work was supported by a University Turbine Systems Research grant from theCNMHGdies, contract number 04-01Copyrighto2009, Dalian Institute of Chemical Physics, Chinese Academy of Sciences. All rights reserved.doi:0.1016s10039953(08600936Mouna Lamnaouer et al/ Joumal of Natural Gas Chemistry Vol. 18 No. 2 2009and Dryers, provide good agreement with experimental data tion method [22](CSP), and the intrinsic low-dimension manfor flame speed results [1], they fail to reproduce some of the ifold method [23, 24](ILDM). The skeletal mechanism canimportant aspects of combustion phenomena over the range of be reduced further based on the quasi steady state approxi-operating conditions for gas turbines. This lack of accuracy mation through what is called the systematical reduction ofis primarily due to the development of reduced mechanisms the detailed mechanism to a few global steps. This methodfrom experimental results and the many unrealistic assump- was initiated by Peters [20] and Peters and Williams[21]tions made to fit the data. In cases where the reduced mecha- The computational singular perturbation method [19](CSP)nisms are accurate. they either have too many species leading through which the selection of QSSA species can be autoto an increased computational time, or fail to predict results mated, and the intrinsic low-dimensional manifold approach,for a wider range of gas turbine operating conditionsas the ILDM technique proposed by Maas and Pope [23, 24],c The purpose of this study was to derive a chemistry model result in look-up tables with coordinates associated with theat is computationally efficient when used in CFD codes, yet mixture fraction and the reaction progress variables. Theis able to predict the combustor flow fields with highin situ Adaptive Tabulation method (ISat)[25] is anotherracy. One way to achieve this is to develop a model that technique for the purpose of reducing mechanismsis derived from the full mechanism but is based on chem-ical time scales rather than solving multiple simultaneou2.1.3. Fitted kinetic modelsreactions. Arguably, the most well-known, comprehensivemethane combustion kinetics model is the gri 3. 0 mechanism[13]. However, this mechanism was tailored mostly for higherThe fitted kinetic models technique is also referred to astemperatures and lower pressures. In recent years, the authors empirical kinetic models where parameters of one-,two-,orhave utilized a methane oxidation mechanism that has been multiple-step reactions are fitted to experimental data or totuned for the higher pressures as seen in a gas turbine engidetailed kinetics simulations, The mathematical models inapplication, such as in Petersen et al. [14]. In the following most of them are given in Arrhenius-type expressions. Thesections, background information on the different processes of technique of fitting reactions to experimental data with themechanism reduction and combustion modeling are provided assumptions of quasi-global approximation and steady state isfirst. Details and predictive capabilities of the new CH4/Oz referred to as the global modeling technique. Examples of thischemical time model are presented and compared with the full technique can be found in Westbrook and Dryer[ I],Hautmanmechanism and the results of experiments.et al. [26]and the compilation edited by Peters and Rogg [5]Examples of fitting algebraic expressions to detailed kineticsimulations can be found in the works of Oran et al. [27]Clifford et aL. [28], and Molnar and Marek [ 29, 30]. They de2.1. Mechanism reduction procedureveloped a global parameterized model of the induction time asa function of pressure, species concentration, and temperatureThis technique is also referred to as IPm, or induction param-There are three different types of reduction techniques eter modeling, and the response modeling technique. This re-of a large chemical kinetics mechanism as summarized by duction method was proved to be very effective in terms ofTomlin et al. [15]:(I)mechanism reduction without time- its accuracy in predicting the induction times and heat releasescale analysis; (2 )reduction based on the investigation of time and also its simulation speed; when compared to a reducedscales; and, (3)fitted kinetics models. Each is summarized model with elementary reactions, it was 20 times faster[28]briefly as followsCombustion simulation would be much easier using suchmodels knowing that more effort could be spent on simulating2. 1.1 Mechanism reduction without time-scale analysisthe complex behavior of flow fields rather than on the chem-ical kinetics calculations(but without losing the accuracy ofThis technique is based on the identification of redun- a detailed mechanism). The response modeling technique hasdant species by analyzing the sensitivity of the reaction tobeen validated in a study done by Clifford et al. [28], whereits production rate or by inspecting sensitivities of temperathe model was used in a 2-D simulation of complex behaviorture rates. The unimportant species and reaction rates are then of a shock passing over a rectangular obstacle in a reactingeliminated, resulting in what is referred to as a skeletal mecmixture. The model reproduced all the main features of theanism or quasi-global model. Examples of this techniqueexperiments using less than 5% of the computational time ofbe found in the works of Warnatz [16], Turanyi [17], Wangthe full chemical kinetics model. Moreover the model hasand Frenklach [ 18], and Yungster and Rabinowitz 19procan, he nsed with confidence in reactive flow中国煤化工 a time-dependent CFD2. 2. Reduction based on the investigation of time-scalesofCNMHGredict burning velocityand swirl-stabilizedreacting flow in a representative turbine engine fuel nozzleThis technique includes the quasi steady state approxima- They used a combustion chemistry approach developed attion [1, 20, 21](QSSA), the computational singular perturba-NASA Glenn Research Center by Molnar and Marek [30].Joumal of Natural Gas Chemistry Wol. 18 No. 2 2009147The chemistry model is based on the response modeling ap- conjunction with one-two, or multiple-step reactions can beproach. The time accuracy of the model was confirmed found in the works of Brankovic et al. [ 31, 34] and Lee andthrough accurate prediction of flame speed for a methane-air Yeh[351reactant mixture [31For the case of infinitely fast chemistry with a hetero-In the present study, a fitted kinetic/response modeling geneous mixture, the conserved scalar equilibrium approachtechnique was adopted. Ignition delay times were utilized as is considered. When finite- rate chemistry is assumed, thehe selection criteria for a wide range of input parameters: flamelet based on G-equation [34], the coherent flame, or thetemperatures between 1000 and 2500 K, pressures between flame surface density model is used for homogeneous mix0. 1 and 50 atm, and equivalence ratios )between 0. I and tures. In the case of heterogeneous mixtures, the flamelet2. As is shown below, the ignition delay time is an excellent based on conserved scalar[36]or the conditional moment clo-indicator of the chemical reaction time, based on the deple sure(CMC) model is considered [37]tion of the fuel, for the practical conditions of interest hereinAlthough reduced mechanisms through traditional reduction 3. Approachtechniques, such as the ones listed above for hydrocarbons(specifically methane)widely exist, the response modeling 3. 1. Chemistry modeltechnique to the authors knowledge has only been developedfor Hydrogen based on shock-tube studies with high argonThe combustion model used to model the chemical kidilutions[27] and for ethylene oxidation([28]with the excep- netics herein is the Eddy Dissipation(ED)Model.Whention of a recent study done by Molnar and Marek (29, 30] formethane and Jet-A fuelsinfinitely fast chemistry is assumed, the eddy DissipationModel of Magnussen and Hjertager [ 33] is used as shown inEquation(2). The model takes the minimum of three rates:2.2. Reacting flow modelingthe mean fuel mass fraction, the mean oxidizer mass fraction,and the product mass fraction, in order to calculate the chem-When a chemistry model is coupled with the goveming ical source term. Combustion would be described by a singquations for viscous flows, a reacting flow model results. step global reactionThe means of modeling the combustion process are chosenbased on the combustion conditions. When infinitely fastCH4+aIr- CO2+ 2H20+7.52Nchemistry and a premixed homogeneous mixture are assumed,limited i eddy dissipation model assumes that the reaction isthe Bray-Moss-Libby, turbulent flame speed, or Eddy Break- limited by micro-mixing, meaning that the chemical kineticup models are used. The Eddy Break-up model is the typical times are fast compared to the mixing times. However, whenexample of a"mixed is burnt"combustion model and is pop- the chemical time Te becomes greater than the mixing timeular for its simplicity, steady convergence, and implementa- Tmix, then the reaction is limited by chemical kinetics. In thistion. The first attempt to develop the model is due to Spald- case, chemical kinetics becomes more important, and finite-ing[32], whose idea was to replace the chemical time scale rate chemistry should be assumedof a one-step reaction by the turbulent time scale, eliminatingSeveral attempts have been made for finite-rate chemistrythe influence of chemical kinetics. the model was then im- correction of the ed combustion model [38, 39], and nowproved by Magnussen and Hjertager[33], who called it the the eddy dissipation model is used in a form that allows foreddy-dissipation model. It simply relates the rate of combus- finite-rate chemistry. This new form of the ED model hastion to the rate of dissipation of eddies and expresses the rate been used in combustion simulations with encouraging resultsof reaction by the mean concentration of a reacting species, [30,39-41]. The chemical source term is given bythe turbulent kinetic energy, and the rate of dissipation of thisAE oxygenenergy. Combustion could then be described by a single-stepglobal reactionwhere y is the mass fraction and r is the overall reaction sto-F+vO→(1+uP1) ichiometric coefficient on a mass basis. The subscript i in-In which, F stands for fuel, O for oxidizer, P for prod- dicates the number of the reaction considered. In this form,ucts of the reaction, and v is the stoichiometric oxygen-to-fuel it is possible to take multi-step reaction kinetics into account.mass ratio. Alternatively, a multi-step scheme can be used, At equilibrium conditions, the model automatically reduces towhere each reaction has its own mean reaction rate. The mean the Magnussen- Hjertager model [33]. The rate expression inreaction rate, wF, is given byEquation(4)can be rewritten in terms of the times, such that,kWF= AEB-min CF,,BEBTmir and中国煤化工where CR, Co, and Cp are the mean concentration of fueloxidizer, and products, respectively. A and B are model conCN Go Fuelstants, k is the kinetic energy, v is the dissipation of the kineticTmix T Tmix Tcenergy, and EB stands for Eddy Breakup. Examples of simu- where fuel/Tmix is the mixing rate, and Wuel/Te is the chemi-lations that employed the eddy break up/dissipation model in cal rateMouna Lamnaouer et al/ Joumal of Natural Gas Chemistry VoL. 18 No. 2 2009The chemical source term d is then determined by taking at 0.37[CH4]o, where [CHalo is the initial methane concenthe minimum of the chemical kinetic rate and the mixing as trationshown in Equation(7)To elaborate, this expression is achieved from the wellknown solution of the first-order equation, Equation (9),rmix' refuel T’Based on this approach, chemical kinetic time models are gen-CH4]=[CHaoexp(-t/Te)erated for incorporation into Equation(7)By definition, the characteristic time in Equation (9)It is now crucial to come up with a definition of the ki- equal to the ignition delay time whennetic times. First, it is important to understand howCHa-[CHaCH40-CH=63%(12)model works in terms of the limiting times. Let us assume alinear approximation of the arrhenius reaction with three timeFigure 2 shows the methane fuel concentration(moleregions;non-mixed,mixed, and reactive/mixed. Figure I il- fraction)as a function of time for a methane/air mixture withlustrates the process. This approach is similar to the PaSr =0.8 at 1800 K and 1 atm as calculated by the detailed kimodel(Partially Stirred Reactor)[38]. The rate of fuel con- netics model described in more detail below. The ignition desumption is then determined from Figure 1lay time is 189 us for this result. Also shown in Figure 2is the result of Equation(11)(plotted in terms of mole frac-tion rather than[ CHaD)assuming the 63% time constant, Te, isMixed regionReactioequal to the ignition delay time of 189 us. The general shapeof the CHa mole fraction time history agrees qualitatively withthe assumption of first-order fuel depletion[CHJ from MechanismCH]=[ CHJ, exp(-t/89μ)CLinear approximation0.37[CHl1000Time(us)Figure 1. CH4 mole fraction(or concentration) change over time, showinglimiting times as utilized in Equation(8)for =0.8, 1800 K, and 1 atmdcH」CC-C1C1-CTime(us)Figure 2. Determination of the kinetic time from the well- known first orderIf T, is the chemical time and T2 is the mixing time, then theory in comparison to the definition utilized herein and the fuel concen-the reaction is mixing-controlled and the chemical source term tration time history for =0.8.1800K, and I atmis determined from the mixing rate. However, when finitechemistry is more important, the kinetic time becomes the 3.2. Kinetic time def initionslimiting time, and the reaction is chemically controlled. In thiscase, Te >Tmix, where Tmix =n+T2 and Tc=n+T2+T3. TheThe methane-based chemical kinetics mechanism utilizedrate of fuel consumption becomesby Petersen et al.[14, 42] was employed for the kinetic timed CHa [ CH4(9) computations. It is based on the modeling work at NUI Gal-way and was built from the ground up(i. e, starting with CH4),The chemical time is defined by the time it takes for the taking into account lower temperatures and higher pressuresfuel to react or ignite, so therefore the kinetic time could be from ignition experiments, making the mechanism a goodmodeled as the ignition delay time such thatcandidate for this study. Further details behind the develop-(10) ment of thel kinetics mechanism can be found in pe-Another method to determine the kinetic time is based on tersen中国煤化工 scription of the shockthe assumption of an exponential decay in[CH4], from first- tubeorder response theory, which turns out to be a good approx- dationCNMHG31. Numerical simula-imation for ignition delay time determination for methane- tions were conducted using the CHEMKIN SHOCK applicaair mixtures as is shown in Figure 2. The chemical time tion found in the Chemkin collection software package [44]from first-order theory is therefore given by: Tc= time that predicts the chemical changes occurring after reactiveJoumal of Natural Gas Chemistry VoL. 18 No. 2 2009149gas mixture shock heating. For the calculations herein, con-stant pressures and enthalpies were assumed as this is the casemost representative of gas turbine combustion. For modelinga premixed fuel and oxidizer at constant-enthalpy, constantpressure conditions, the solution from the SHOCK module for80×10—xcHo)an initial temperature corresponding to the post-shock condi-tions is the same as treating the mixture as if it were in anadiabatic, constant-pressure, well-stirmed reactor at the sameinitial temperature.It can be shown that modeling the kinetic times based onan isothermal process(as in Molnar and Marek [29, 30))doesnot affect the results appreciably. An example is provided in2.0x10Figure 3, where CO and No concentrations are plotted againstHCH)=533 Hstime for the two processes, the first process being that of con-OH)=527stant enthalpy and pressure, and the second process being thatof constant temperature. The latter calculation was achieved50060070through simulation with the senKiN application that eTime (us)be found in the Chemkin software package [44]. ItIgure 4. The ignition delay time(Tgn) is defined as the sudden rise in CH"shown from Figure 3 that by assuming either one ofor OH" concentrations compared to the fuel time history for a stoichiometriccesses, the times corresponding to the maximum concentra-methane-air mixture at l atm, 1600 K and eltion levels are nearly the same in both cases, which are rep-resentative of the real fuel-air mixtures of interest herein. A 3.3. Methodologysimilar conclusion can be drawn by comparing ignition timesbetween the two process assumptions.Since the goal of the present effort was to develop chemical time expressions at temperatures and pressures of interestto gas turbines, a matrix of conditions was formulated. Table I shows the different CHa/Air mixtures used in this studyng mole fractions and(o), which ranged from 0. 1 to 2.0. Table 2 shows the range ofconditions over which the kinetic times were computed withChemkin using the full kinetics mechanism [42 ]. These con-ditions included temperatures from 1000 to 2500 K and pres-sures from 0. 1 to 50 atm. Over 900 computer runs were per-formed, and thefor NO. cO. andH2O were recorded for each, although the focus of the presentConstant Tstudy is on the overall chemical, or ignition delay time--- Constant h and pTable 1. Experimental mixtures and mole fractionsMixture NoMole fraction of mixtures(%)Equivalence ratioTime(us)Figure 3. Predicted CCmole fractions using both the constant-Tand constant enthalssumptions for a lean(o=0.8)methane-air40420.2075.80ixture at I atm and Ieling the reaction as an isothermal process5.9019.8074.30kinetic times, although there is an effect77019307280695019017150For the calculations in the present paper, the ignition de11.2018.70lay time is defined as the sudden increase in Ch'( Figure 4)128018.30680246since CH' chemiluminescence has been shown to be a good144018006760representation of hydrocarbon ignition in shock-tube experi159017701740ments[45]. Ignition times can also be determined from OHconcentration rise as is shown in Figure 4. Both species yield中国煤化工similar ignition times. In fact, for the real fuel-air mixturesof interest herein(i e, undiluted ), there is little difference be-CNMHGhull mechanismEquivalence ratiotween ignition delay times defined using OH", CH", theirground state counterparts(OH and CH), 0.37 [CH)o, or evenl000-2500the abrupt change in temperature or other key species.Increment≈10Mouna Lamnaouer et al Joumal of Natural Gas Chemistry Vol. 18 No. 2 20094. Kinetic time modelespectively. It can be observed that at about a temperature be-low 1400 K, the model starts showing non-linearity on a logversus IT plot, and the slope of the ignition delay curve startsOnce the kinetic times were generated for the conditions decreasing. In addition to the effect temperature has on theiven in Tables I and 2, analytical fits were performed for the shape of the curve, the mixture equivalence ratio contributesbehavior of the ignition time as a function of the pressure, tem- to the shift of the data vertically. Mixtures with the highestperature, and equivalence ratio. The generated kinetic times equivalence ratios resulted in the shortest ignition delay times,were plotted on Arrhenius-type plots, and their behavior was although as seen in Figure 5, the effect of equivalence ratio ismonitored as the different parameters changed. The results are relatively minor as compared to the effect of temperature andshownin Figure 5 for pressures of o1, 1. 5, 20, and 50 atm, pressure1.2#06#-1s|°中0.8·中20.8一=210T/《K")l0//(K)10//(K2)1,4中=1.6中16中=0810/T/《KFigure 5. Results for CHa/Air mixture ignition delay times as a function of temperature and equivalence ratio(CH/Air, 0. 10.98). The correlation re- Similarly, the oxygen concentration also slows down ignitionsults expressed in the fuel-to-air ratio form are summarized in at lean conditions but speeds up ignition at rich conditions,Table 4. Note that increasing f/a always has a retarding effect although to a larger degree than seen in the CHa exponent.on ignition(i.e, longer ignition delay times), particularly forTable 5. CH4/Air mixture ignition delay time correlations expressedthe fuel-rich casesas functions of the fuel-lean and -rich cases in the molefraction form. T is in seconds, P is in atm,T and (E/R)are in KTign=AXx. x xo, x P xexpIE/RT]zER(K)产2Lean227×10-80.1551434-0901205360990Rch413×10-1-0.187-2099-0.931200060985Overall 2.37x I00.1040030-0915202640987To investigate the validity and accuracy of the modelsesented herein, comparison to previous efforts would bebeneficial. Petersen et al. [46] presented a comprehensive correlation of ignition delay time data for similar con-ditions studied herein: temperatures(1400 to 2050 K), pres-sures(I to 480 atm), o(0.5 to 2.0); and concentrations up toCH4]=36×10-5 molem3,[O2]=3.6×10-5 mol/cm3,and[M]=3.6x10>molcm. The correlation is given by the folowing expression:Tigm=4.05e-5ICH4J033[O2]-1.05exp( 51.8/RT]Where Tign is the ignition delay time in seconds, the activationenergy(51.8 kcal/mol) is in kcal/ mol, and R is the universalo Fuel lean correlationgas constant. The overall pressure dependence is P-o.72.ThePetersen et al. [46] correlation was based on shock-tubeture ignition data. Figure 9 presents this studys overall corre-102101010310210lation in comparison to the Petersen et al. [46] correlationFigure 8. Fuel rich and fuel lean methane ignition delay time correlations(a)fuel rich,(b)fuel leano High-Tregion corelation nTable 4. CH,/Air mixture ignition delay time correlationsexpressed in the fuel-to-air ratio form. T is in seconds,P is in atm, T and (E/R)are in KAx(f/a)x P*xexpIE/RTIER(K0900205350104.19×10-90.238093119899Overall230×10900960915202640.987Additional correlations for methane ignition delay times中国煤化工are given in Table 5 as a function of mole fraction, temperature, and pressure for fuel-lean and-rich cases as in molnarCNMHG 1010 10and Marek [29, 30]. When this correlation is applied the re-F.(Petersen co. )(us)sults achieved are similar to the results obtained from the cor- Figure 9. This study's high-temperature region comelation in comparisonrelations in Table 4. It is for the user to decide which of thewith Petersen et al. correlation [46]Natural Gas Chemistry VoL 18 NoNote that the Petersen et al. correlation is only valid for and is configured with a small-diameter, central exit port totemperatures between 1400 and 2050 K, so the comparison eliminate or minimize combustion oscillations. The area ratiois performed over that range only. The agreement between of the pre-mixer to dump zone is 20: 1. The(overall)ignitionthe two correlations is quite good, leading to the conclusion delay equation used in the flow simulation is that shown inthat the model developed herein is able to accurately predict Table 5. The baseline chemistry model utilized is that develreal experimental data such as shock-tube experimental data. oped by Molnar and Marek [29, 301, as previously investigatedThis result is not unexpected since the detailed mechanism by Brankovic et al. [311 for model problems featuring time.and its inherent kinetics rates were validated rather thoroughly dependent flame phenomenaover similar ranges of temperature, pressure, and stoichiome-try with shock tube(and other)data5. Computational fluid dynamics modelingThe validation and accuracy investigations of the kinetictime models presented above have led to improved corre- Figure 10. Schematic of pre-mixer section of the computational domainlations for ignition delay time that enable prediction of the used in CFD simulations for improved kinetic time modelcombustion of fuel-air mixtures using computational fluid dnamics(CfD)design tools. These tools combine full three-Four test cases have been simulated using CFD; each atdimensional, time-dependent Navier-Stokes representation of o=0.5 which is representative of the overall combustor equivthe flow aerodynamics and time-dependent chemical reaction alence ratio for low-NO power generation gas turbines. Themodels for the incoming reactants. In application to practical specific test cases are as follows: Case 1: Co-annular,aircombustion systems, the simulations capture complete details swirled at 45 fuel non-swirled at 300 K Case 2: Co-annularof boundary layers, recirculation zones, and turbulent mixing shear-layer mixing with air(non-swirled), fuel non-swirled atprocesses between fuel and air. The simulations are there- 300 K Case 3: Co-annular, non-swirling perfect pre-mix offore especially capable of predicting non-uniformities in the fuel and air at 800 K. Case 4: Co-annular, non-swirling unfuel-air profile entering the combustor of a typical gas tur- mixed of fuel and air at 800 K In Cases l and 2, iterative studbine engine, which can lead to combustion instabilities and ies of the cold flow mixing were performed to ensure that avoperational problems in practical systems. Careful applica- erage(or fully mixed)temperature at the pre-mixer exit planetion of the tool, together with accurate modeling of the igni- was 800 K. The four conditions investigated, therefore, covertion delay and heat release, can potentially enable the predic- a range of mixing and temperature effects common in naturaltion of important design factors such as combustion instabil- gas-fueled combustion systemsity, flashback, and flame holding, which can then be addressedComputational results in the form of graphic contours ofby more detailed design applications of the toolxial velocity and static temperature are shown in Figures 11or In this study, attention has been directed to the prediction 12 and 13. The pre-mixer and upstream component of thenew f T separate flows to investigate the performance of the combustor are shown in Figure Il, where axial velocity connew kinetic time model for the case of methane-air combus- tours display little variation across the four types of inlet contion, at operating conditions representative of power genera- ditions. Early mixing of the two streams(i.e, before the dumption gas turbine combustors. Incoming flow into power gener- plane of the combustor) leads to relatively similar velocity andation turbine combustors can fall into a wide range of operat- temperature contours within the combustor. Closer inspectioning conditions, depending on the output power level and type of the flows, as shown in Figures 12 and 13, indicates thatof machine. Mass flow rates of air for the largest machines the new kinetic time ignition delay model results in only mirange up to several hundred kg/s at the fan inlet. Typical nor differences in the thermal field when temperature scalesues for the air at the fan inlet are static pressure 20 atm reflect the local values better This result is because the par-static temperature=800 K, with various levels of ticular ignition time delay in this model, using typical inputurbulence and swirl imparted to theas it enters values for the inlet of the premixer, suggests ignitthe combustortimes of approximately 9.5 seconds. Based on theA representative cylindrical, annular dump combustor, and inlet velocities of the fuel-air stream. the 9.5-seccwith a long pre-mixer section is used here to investigate the dence time occurs well within the dump combustor, and theredifferent flame shapes and temperature contours determined fore, peak burning temperatures occur only far downstreamusing a combination of inlet mixing conditions and fuel/air into the combustor That is no reartion is seen within thetemperatures. The computational domain used here is shown prer中国煤化工 ences between the fourin Figure 10. The length L of the pre-mixer was selected to casesbe 1.6m, so that residence times using typical fuel and air lengthCNMHGPlane via the differenticates that the ignitiongas velocities would be approximately 40 ms. Following the time delay model is producing expected results, but also thatpre-mixer is a cylindrical dump combustor featuring a central, the model requires anchoring to flames that are characteristiclindrical bluff body. The dump combustor is 2.0 m long, of practical combustor154Mouna Lamnaouer et al/ Joumal of Natural Gas Chemistry Vol. 18 No. 2 20096. ConclusionsU(ms)-25-51535557595A reduced mechanism for methane oxidation kinetictimes has been developed, The models presented herein arevalid over a wide range of gas turbine conditions. The temper-Case 3atures ranged from 1000 to 2500 K, and pressures were variedCase 4from 0. 1 to 50 atm, respectively. The mixture compositionscovered fuel-to-air equivalence ratios between 0.1 and 2.Ki-netic times for methane were obtained from a detailed mech-anism used in earlier studies by the primary authors. The dataFigure 11. Axial velocity contours, with emphasis on flow in the pre-mixer were fitted into reduced models as functions of temperature,and near-field of the dump combustor. CFD simulation results for four test pressure and mixture composition. an overall model for igni-cases. X is the axial coordinate. Case 1: Co-annular, air swirled at 450fuel non-swirled at 300 K; Case 2: Co-annular shear-layer mixing with air tion delay times was also provided. Since ignition delay times(non-swirled), fuel non-swirled at 300 K Case 3: Co-annular, non-swirling vary strongly with temperature, pressure, and the mixture conperfect pre-mix of fuel and air at 800 K: Case 4: Co-annular, non-swirling, centration, multiple models were developed for low-and highun-mixed fuel and air at 800 Kas well as fuel rich and leanmodels showed good agreement when compared to the exper-CFD simulations based on combustion chemistry that do imental results as summarized in the Petersen et al.(46]cornot include ignition delay models explicitly, e.g, thoserelation. The accuracy and high predictive capability of theSpalding [32], and Magnussen and Hjertager[33], typically model makes it an excellent candidate to be incorporated inproduce results with little variation in these 4 cases. Compar- CFD codes for gas turbine flow field simulations, and someson of CFD results with experimental data for simple comrepresentative CFD calculations using the new model with anbustos is in progress, in an effort to validate the ignition de- eddy dissipation routine were provided. The ignition correla-lay models using performance data such as combustion flame tions herein can also be used for ignition calculations in lieshape,combustor exit temperature, and emissions values for of running the complete kinetics mechanism and in comparingto and corelative effects of reactant concentration, pressure, and stoiAcknowledgementsT(K)1000This work was supported through a University Turbine SystemsResearch grant from the South Carolina Institute for Energy Stud-Case 2ies, contract number 04-01-SRll4, with Dr. Richard Wenglartz asReferences[I] Westbrook C K, Dryer FL Combustion Science and Technol-Figure 12, Static temperature contours, witasis on flow in the pre-ogy,1981,27:31mixer and near-field of the dump combustor. Resuits are presented for the [2] Bilger R W, Starmer H, Kee RJ. Combustion and Flame, 1990.80:135[3] Seshadri K, Peters N. Combustion and Flame, 1988, 73: 23[4] Mallampalli H, Fletcher T H, Chen J Y. Journal of EngineeringT(K)1000l60for Gas Turbines and Power, 1998, 120: 703Case I[5] Peters N. Rogg B. Reduced Kinetic Mechanisms for Apptions in Combustion Systems. Berlin-Heidelberg: SprinVerlag, 1993[6] Rogg B. Technical Report CUED/A-THERMOTR57, Cam-bridge University, Engineering Department, September 1992[7 Smooke M D. Lecture Notes in Physics 384, Springer-Verlag,19918]cR Camhuetinn and Flame, 2005, 143(4): 450中国煤化工 -pecho L n. Combustion,CNMHG4): 390ion Science and technol-ogy,1996,120:357Figure 13. Temperature contours at expanded temperature scale. Results [lI] Bruel P Rogg B, Bray KnC. Proceedings of the Combustionare presented for the four test casesInstitute, 1990. 23: 759Journal of Natural Gas Chemistry Vol. 18 No. 2 2009[12] Westbrook C K, Dryer FL. Progress in Energy Combustion Sci- [32] Spalding D B. 16th Symposium on Combustion, Combustionence,1986:10nst, Pittsburg, PA, 1976, 1657[13] Smith G P, Golden D M, Frenklach M, Moriarty N w, Eite- [33] Magnussen B F, Hjertager B H. Proceedings of the Combustionneer B, Goldenberg M. Bowman C T, Hanson R K, Song S,Institute, 1976. 16: 719GardinerWC,Lissianskivv,qinZgri-MecH3.0,http[34]EggenspielerG,MenonS.JOurnalofPropulsionandPower2004,20(6):1076[14] Petersen E L, Hall J M, Smith S D, De Vries J, Amadio A, [35] Lee D, Yeh C L. Journal of Propulsion and Power, 1993, 9(2)Crofton M. Journal of Engineering for Gas Trubines and Power2007,129:937[15] Tomlin A S, Turanyi T, Pilling M J. In: Pilling MJ ed. Compre[36] Blanquart G, Pitsch H. Proceedings of the Combustion Institute,hensive Chemical Kinetics, Low-Temperature Combustion and2005,30:2745Autoignition, 1997, 35: 4[37] Bilger R W. Physics of Fluids A, 1993. 5(2): 436[16] Warnatz J Joumal of Physical Chemistry, 1983, 87: 1008[38] Golovitchev V I, Chomiak J. Scandinavian-Nordic Section of[17] Turanyi T, Beres T, Vajda S International Joumal Chemical Ki-the Combustion Institute, September 10-ll, Trondheim, Nor-[18] Wang H, Frenklach M. Combustion and Flame, 1991, 87(3, 4): [39] Peters A A F, Weber R. Combustion Science and Technology.1995,110:67[19] Yungster S, Rabinowitz M J Joumal of Propulsion and Power, [40] Magel H C, Schneider R, Risio B, Schnell U, Hein K RG.8thIntemational Symposium on Transport Phenomena in Combus-[20] Peters N. In: Numerical Simulation of Combustion Phenomena,tion, San fransisco, CA, 1995Golwinski R et al, Eds, Lecture Notes in Physics, 1985, 90[41] Brink A, Mueller C, Kilpinen P, Hupa M. Combustion and[21] Peters N, williams F A. Combustion and Flame, 1987, 68: 185Flame,2000,123:1275[22] Lam S H, Goussis D A Intemational Joumal of Chemical Ki-[42] Petersen E L, Kalitan D M, Simmons S L, Bourque G, Curran HgenIc,1994,26:46J, Simmie J M. Proceedings of the Combustion Institute, 2007,[23] Maas U, Pope S B. Combustion and Flame, 1992. 88: 239[24] Maas U, Pope S B. Proceedings of the Combustion Institute,1992,24:103[43] Petersen EL, Rickard M J A, Crofton M w, Abbey E D, Traum[25] Pope S B Combustion Theory and Modeling, 1997, 1: 41MJ, Kalitan D M. Measurement Science and Technology, 2005[26] Hautman D J, Dryer F L, Schug K P, Glassman I. Combustion16:1716Science and Technology, 1981, 25(5, 6): 219[44] Kee rJ, Rupley FM, Miller J A, Coltrin M E, Grcar JF, Meeks[27] Oran E S, Boris J P, Young TR, Flanigan M, Picone M. ProE, Moffat H K, Lutz A E, Dixon-Lewis G, Smooke M D, Wareedings of the Combustion institute, 1981, 18: 1641nate J, Evans G H, Larson R S, Mitchell R E, Petzold L R,[28] Clifford L J, Milne A M, Murray B A. Combustion and Flame,Reynolds w C, Caracotsios M. Stewart WE, Glarborg P, Wang1996,1043):311C, Adigun O. Chemkin Collection, Release 3. 6, Reaction De-[29] Molnar M, Marek C J. NASA TM-212702, 2003sign, Inc, San Diego, CA, 2000[30]Molnar M, Marek CJ. AlAA Paper 2005-0549, 43rd Aerospace [45] Hall J M, Rickard MJ A, Petersen E L Combustion Science andSciences Meeting and Exhibit, January 2005Technology, 2005: 455[31]Brankovic A, Ryder R C, Petersen E L ALAA Paper 2006-806 [46] Petersen E L, Rohrig M, Davidson D F, Hanson R K, Bowman44th Aerospace Sciences Meeting and Exhibit, January 2006CT. Proceedings of the Combustion Institute, 1996, 26: 799中国煤化工CNMHG