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Transported PDF Modeling of Nonpremixed Turbulent CO/H2/N2 Jet FlamesXinyu Zhao a b , D. C. Haworth a b & E. David Huckabyc a National Energy Technology Laboratory-Regional University Alliance (NETL-RUA), Morgantown, West Virginia, USAb Department of Mechanical & Nuclear Engineering, The Pennsylvania State University, University Park, Pennsylvania, USAc U.S. Department of Energy-National Energy Technology Laboratory, Morgantown, West Virginia, USA

Available online: 14 May 2012

To cite this article: Xinyu Zhao, D. C. Haworth & E. David Huckaby (2012): Transported PDF Modeling of Nonpremixed Turbulent CO/H2/N2 Jet Flames, Combustion Science and Technology, 184:5, 676-693

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COMBUSTIONSCIENCEANDTECH N O LOOT

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Combust. Sci. Technol., 184: 676-693, 2012 Copyright © Taylor & Francis Group, LLC ISSN: 0010-2202 print/1563-521X online DOI: 10.1080/00102202.2012.660223

Taylor & FrancisTaylor & Francis Group

TRANSPO RTED PDF M O D ELIN G OF N O N PR EM IXED TU R B U LEN T C O /H 2/N 2 JET FLAMES

Xinyu Zhao,1’2 D. C. Haworth,1’2 and E. David Huckaby3lNational Energy Technology Laboratory-Regional University Alliance (N ETL-RU A), Morgantown, West Virginia, USA2Department o f Mechanical & Nuclear Engineering, The Pennsylvania State University, University Park, Pennsylvania, USA3 US. Department o f Energy-National Energy Technology Laboratory, Morgantown, West Virginia, USA

Turbulent COIH2IN2 ( “syngas”) flames are simulated using a transported composition probability density function (PDF) method. A consistent hybrid Lagrangian particle! Eulerian mesh algorithm is used to solve the modeled PDF transport equation. The model includes standard k-s turbulence, gradient transport for scalars, and Euclidean minimum spanning tree (EMST) mixing. Sensitivities of model results to variations in the turbulence model, the treatment of radiation heat transfer, the choice of chemical mechanism, and the PDF mixing model are explored. A baseline model reproduces the measured mean and rms temperature, major species, and minor species profiles reasonably well, and captures the scaling that is observed in the experiments. Both our results and the literature suggest that further improvements can be realized with adjustments in the turbulence model, the radiation heat transfer model, and the chemical mechanism. Although radiation effects are relatively small in these flames, consideration of radiation is important for accurate NO prediction. Chemical mechanisms that have been developed specifically for fuels with high concentrations of CO and H2 perform better than a methane mechanism that was not designed for this purpose. It is important to account explicitly for turbulence-chemistry interactions, although the details o f the mixing model do not make a large difference in the results, within reasonable limits.

Supplemental materials are available for this article. Go to the publisher’s online edition of Combustion Science and Technology to view the free supplemental file.

Keywords'. Nonpremixed turbulent flames; Probability density function method; Syngas flames

INTRODUCTION

The replacem ent o f air with pure oxygen in coal-fired systems (oxy-coal com bustion) is one option th a t is being considered for next-generation stationary power generation. The N 2-lean exhaust stream facilitates the separation o f C 0 2 from

Received 26 September 2011; revised 28 November 2011; accepted 19 January 2012.Address correspondence to Xinyu Zhao, Department of Mechanical & Nuclear Engineering, The

Pennsylvania State University, Research Building East, University Park, PA 16802, USA. E-mail: xzzl05@psu.edu

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the other com bustion products, mainly H 20 . This facilitates sequestration, thus reducing the emission o f C 0 2 into the atm osphere. A reduction in N O x (Buhre et ah, 2005) and other pollutants has also been seen in pilot-scale studies.

The therm ochem ical environm ent differs substantially from tha t o f conventional air-based com bustion because o f higher concentrations o f species including 0 2, C 0 2, and H 20 . This differing environm ent poses a challenge for the com putational models and related experim ental data that have focused on air com bustion. Also, gaseous radiation heat transfer is expected to be m ore prom inent due to the higher concentration o f H 20 and C 0 2. This should also amplify the im portance of accurate m odeling o f the turbulence-rad iation interactions, which often have been neglected in C FD calculations.

Here turbulent C O /H 2/N 2 (“ syngas” ) flames have been simulated, as a first step tow ard m odeling oxy-coal com bustion. The product com position is similar to that o f the flue gasses in coal- or biomass-fueled com bustion systems (Zahirovic et al., 2006), w ithout the com plications o f solid fuels. The gas-phase chemistry is relatively simple, while finite-rate chemistry and turbulence-chem istry interactions are im portant because o f the slow and indirect oxidation o f CO to C 0 2 (Abian et al., 2011; Barlow et al., 2000; Li et al., 2007; Zsely et al., 2005). The flame configurations are those targeted by the In ternational W orkshop on M easurem ent and C om putation o f Turbulent N onprem ixed Flam es (TN F W orkshop) (Barlow, 2011), for which detailed m easurem ents are available. Com pared to other T N F W orkshop flames (the piloted m ethane/a ir nonprem ixed turbulent jet flames, in particular), relatively few m odeling studies have been reported for the T N F syngas flames. Two difficulties from a m odeling perspective are flame stabilization and potential differential diffusion; these are discussed in subsequent sections.

T ransported probability density function (PD F) m ethods are one o f the best available approaches for dealing w ith complex nonlinear interactions in turbulent com bustion (Pope, 1985). P D F m ethods have been tested and applied to configurations from canonical laboratory flames to practical devices including gas-turbine com bustors and reciprocating-piston engines (H aw orth, 2010). For exploration of new com bustion regimes such as oxyfuel, P D F m ethods w ith relatively detailed chemistry offer added advantages over simpler m odels that have m ore flow- and chemistry-specific tuning param eters. To date, no transported P D F modeling studies have been reported for the T N F w orkshop syngas flames. Here, a consistent hybrid Lagrangian particle/E ulerian mesh m ethod is used to solve a modeled transport equation for the one-point, one-time jo in t P D F of species mass fractions and m ixture specific enthalpy. A comprehensive set o f physical m odels and num erical algorithm s is integrated and validated, including a spectral pho ton M onte Carlo m ethod for participating-m edium radiation. Sensitivities o f com puted results to variations in the gas-phase chemical mechanism, the radiation heat transfer model, and the P D F mixing model are explored.

The rem ainder o f the article is organized as follows. In the following section, the target flames are introduced and findings from earlier modeling studies are sum marized. Then, the physical models and num erical m ethods are described. C om parisons w ith experimental m easurem ents, including sensitivities to model variations, are reported next. In the final section, key findings are summarized and next steps are outlined.

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TNF WORKSHOP SYNGAS FLAMES

Two turbulent je t flames o f 40% CO, 30% H 2, 30% N 2 by volume issuing into coflowing air are simulated (Table 1). Flam e A has a smaller fuel-jet diam eter and higher velocity com pared to flame B, such tha t the fuel-jet-based Reynolds num bers o f the two flames are the same: Rcy = 16500. Available experim ental da ta include radial profiles o f m ean and rms axial velocity, tem perature, and species mass fractions at several distances dow nstream o f the nozzle. D etails can be found in Barlow et al. (2000) and Barlow (2011). Earlier m odeling studies for these flames have been reported in K im et al. (2001), Cuoci et al. (2007), F rassoldati et al. (2007), Zahirovic et al. (2001, 2006), and Hewson and Kerstein (2001).

K im et al. (2001) used a Reynolds-averaged form ulation w ith a k -s turbulence model. A steady flamelet model and an unsteady flamelet model based on a L agrangian approach were used to account for turbulence-chem istry interactions. Com puted profiles o f m ean velocity and m ajor species concentrations for flames A and B were shown to coincide when plotted as functions o f norm alized (by the fuel-jet-nozzle diam eter) spatial coordinates, consistent with the experimental m easurements. A n optically thin model was used for radiation. R adiation effects were shown to be small in both flames, w ith calculated radiant fractions o f approxim ately 7% and 17% for flames A and B, respectively, which are higher than the experimental values (3.4% and 7.1%, respectively).

Cuoci et al. (2007) reported Reynolds-averaged sim ulations using a k :: turbulence model and three different turbulence-chem istry interaction models. Simple chemical m echanisms were used first in coupled calculations to com pute the tem perature, m ajor species, and flow fields. Then a detailed chemical m echanism (Frassoldati et al., 2007) was used in a kinetic post-processing step to predict the form ation o f pollutants including NOx. The eddy-dissipation-concept (EDC) and steady lam inar flamelet (SLF) models showed better agreement with experiment com pared to a simpler eddy dissipation (ED) model. Discrepancies between com puted and m easured CO were found, especially far dow nstream o f the nozzle. Im proved N O x predictions were found when the tem perature fluctuations were accounted for explicitly in the post-processing. The com puted peak m ean tem perature dropped by 30-40 K w ith a discrete-ordinates radiation model, com pared to neglecting radiation.

Similar simulations were reported by Zahirovic (Zahirovic et ah, 2001, 2006), using a realizable k -s turbulence model with ED C, SLF and ED turbulence-chem istry

Table 1 Inlet specifications for syngas flames A and B (Species compositions are mass fractions)

Stream Fuel jet Coflow

T (K) 292 292CO 0.554 0H2 0.030 0N , 0.416 0.766o 2 0 0.234Diameter (mm) A: 4.58 B: 7.72 -Bulk velocity (m/s) A: 76.0 B: 45.0 0.07

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TRANSPORTED PDF MODELING OF JET FLAMES 679

interaction models. The purpose was to validate the use o f these models for biogas com bustion. Results from four different chemical mechanisms were compared: a global mechanism, a nine-species augm ented reduced mechanism, a 19-species augmented reduced mechansm, and a detailed 32-species, 153-reaction mechanism. All m echanisms except the global mechanism yielded similar results.

Hewson and Kerstein (2001) applied the one-dim ensional turbulence (ODT) m odel to these flames, and studied the evolution o f the velocity field as well as the first and second m om ents o f the reacting scalars conditioned on the m ixture fraction. R adiation was neglected. Because m olecular transport can be resolved w ith this model, the im portance o f differential diffusion could be explored. It was reported that differential diffusion is im portant close to the nozzle (to approxim ately six fuel-jet diam eters dow nstream ), where experimental data are not available. The im portance of differential diffusion also was explored in Barlow et al. (2000), by com paring the results from lam inar flame calculations w ith equal diffusivities to those w ith full differential diffusion. There it was concluded that differential diffusion plays a relatively small role in these flames, especially far dow nstream of the nozzle. In the context o f transported P D F m ethods, m olecular transport is accounted for through a mixing model. Some mixing models have been designed to consider differential diffusion (Fox, 2003; V isw anathan et al., 2011). However, these models are still at an early stage o f developm ent, and it would be better to explore differential diffusion in a configuration where the effects are less ambiguous. In the present study, differential diffusion is neglected.

A lthough no transported P D F m odeling studies have been reported for the T N F w orkshop syngas flames, several early transported P D F m odeling studies focused on similar C O /H 2/ N 2 nonprem ixed jet flames (Chen et al., 1991; Correa et al., 1985, 1988; H aw orth et al., 1988, 1989; Pope and Correa, 1987), using various chemical m echanisms and other models. The early studies were limited by the com putational power and chemical m echanisms that were available at the time. R udim entary parabolic solution algorithm s were used, and radiation heat transfer was not considered. In present study, m odern elliptic P D F solution algorithm s are used with newer chemical mechanisms, and radiation heat transfer is considered.

PHYSICAL MODELS AND NUMERICAL METHODS

A modeled transport equation for the jo in t P D F o f species m ass fractions and m ixture specific enthalpy is solved using a consistent hybrid Lagrangian particle/ Eulerian m esh (finite-volume) m ethod using a Reynolds-averaged form ulation. The physical models and num erical m ethods are introduced in subsequent subsections. F urther inform ation can be found in Sections 6 and 7 o f H aw orth (2010), and in the other cited references.

Hybrid Lagrangian Particle/Finite-Volume PDF Method

In a com position P D F m ethod, m odels are required for turbulence, turbulent scalar transport, and m olecular transport. N o further m odeling (beyond specification o f therm ochem ical and radiative properties and a chemical reaction mechanism)

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is required to account for the effects o f turbulent fluctuations in com position and tem perature on m ean chemical reaction rates or m ean radiative emission.

H ere turbulence is modeled using a standard tw o-equation k -s model, gradient transport is assumed for turbulent scalar transport, and m olecular transport is modeled using either a modified Curl (M C) (Curl, 1963; N ooren et al., 1997) or a Euclidean m inim um spanning tree (EM ST) (M asri et al., 1996; Subram aniam and Pope, 1998) mixing model. In general, EM ST is expected to be the better mixing model, as it takes into account the locality o f the mixing in com position space; in particular, EM ST has been shown to perform better at higher D am kohler numbers. D ifferential diffusion is neglected, in all cases. S tandard values have been used for all model coefficients, with two exceptions. First, the value o f the mixing model coefficient, C,h (the ratio o f a turbulence hydrodynam ic time scale to a turbulence scalar time scale), has been varied to explore its influence on model results. H ere the baseline mixing model is EM ST w ith C,,, 1.5. It should be noted that a somewhat higher value ofC^, usually has been used in PD F-based modeling studies o f turbulent jet flames using the M C mixing model (C ^re 2.0) com pared to the EM ST model (C,h 1.5). Second, the value o f Csi in the s equation has been increased from its standard value of 1.44 to 1.6 (James et al., 2001). In general, a higher value o f Csi lowers the com puted jet spreading rate. It is conventional practice in k -s modeling studies of circular je t flames to increase the value o f Csi (Jaishree and H aw orth, 2012). The influence o f a small variation in Csi on com puted m ean profiles is dem onstrated below.

The underlying finite-volume C FD solver is O penFO A M 1.5 (O penFO A M , 2011). A PISO-based, time-implicit segregated solver is used to solve the coupled m ean m om entum , pressure, energy, and k -s equations using second-order spatial discretizations. Species mass fractions and m ixture specific enthalpy are com puted on the particle side, and local m ean scalar values are estim ated as appropriately weighted averages over particle values. The principal feedback from the particle side to the finite-volume side o f the calculation is through the m ean density; this is handled using an “equivalent enthalpy”-based approach (M uradoglu et al., 1999, 2001). Particle/finite-volum e coupling and other numerical issues are discussed in detail in H aw orth (2010). Solutions are advanced in time starting from (essentially) arbitrary initial conditions until a statistically stationary state is reached. Following the recom m endation given in Jaishree and H aw orth (2012), the nom inal num ber of particles per finite-volume cell is 40.

Thermochemical Properties and Chemical Mechanisms

A 10-species, six-reaction m echanism (including NO) that was developed specifically for C O /H 2/N 2 m ixtures in the proportions o f interest here (40% /30% / 30%) (Chen, 2011) has been adopted as the baseline for this study. This relatively low -com putational-cost m echanism is well suited for perform ing param etric studies on the influences o f variations in the other physical submodels (e.g., radiation and mixing). The influence o f the chemical m echanism is also o f interest, especially for predictions o f N O and other m inor species. This has been explored by com paring results obtained using the baseline m echanism with those obtained using two other mechanisms: G R I-M ech 2.11 (Bowman et ah, 1995) (which includes NOx) and a recently updated C l m echanism (Li et ah, 2007) that does not include NOx.

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In the latter mechanism, new values o f rate constants have been recom m ended for the reactions CO + O H CO 2 + H and H C O + M ^ H + CO + M , which are im portan t in C O /H 2 systems. The m odel also has a modified heat o f form ation for the O H radical. These changes are expected to have a significant influence on the CO prediction and consequently the tem perature (Abian et al., 2011; Li et al., 2007; Zsely et al., 2005). They are also expected to have a significant influence on N O prediction in situations where prom pt N O is im portant (Dryer, 2011). T hat is not the case in the flames tha t are simulated here, but it still is o f interest to assess this m echanism, as it has been developed specifically for syngas flames.

Radiative Heat Transfer

M easured radiant fractions for flames A and B are 3.4% and 7.1%, respectively (F rank et al., 2000). Thus radiation effects are small, and radiation is neglected altogether for the baseline simulations.

Results w ithout radiation are com pared to those obtained using a gray, op tically thin model. This model considers emission from C 0 2, H 20 , and CO; the absorption coefficient is prescribed following the approach described in Smith et al. (2011).

The syngas flames simulated here have high C 0 2 concentrations com pared to hyd rocarbon /a ir flames; thus absorption in the 4.3 pm C 0 2 band is expected to be relatively high. W hile it is not anticpated tha t spectral radiation and reabsorption influence the global structure o f these flames significantly, advanced radiation trea tm ents will be required as we progress tow ard oxy-coal com bustion. Therefore, a full spectral photon M onte Carlo m ethod tha t has been used in earlier PD F-based m odeling studies (M ehta et al., 2010; W ang and M odest, 2006) also has been tested here. This model m aintains essentially line-by-line spectral accuracy, and considers emission and absorption by C 0 2 and H 20 .

Results obtained using three different levels o f radiation treatm ent are com pared in the results section: N o radiation (baseline), gray optically thin radiation, and spectral radiation w ith reabsorption.

Flame Stabilization

A practical issue in sim ulating these syngas je t flames is flame stabilization. In the laboratory , the flame is anchored to the lip o f the fuel-jet tube by a small recirculation zone just dow nstream o f the nozzle wall (thickness 0.88 mm) (Barlow et ah, 2000; Cuoci et al., 2007; Giacomazzi et ah, 2008); no pilot was required and no lift-off was observed in the experiments. This anchoring m echanism was confirmed by Giacomazzi et al. (2006), who perform ed high-spatial resolution (10 5m). large- eddy sim ulation for a 25 m m by 15 m m area near the nozzle wall.

Resolving the recirculation zone in a full-flame sim ulation with detailed chemistry would be com putationally prohibitive. It is expedient to use a coarser mesh and to introduce an artificial anchoring m echanism, and that is the approach tha t has been taken in m ost o f the earlier m odeling studies. The extent to which artificial stabilization is necessary depends on the chemical m echanism that is used. Cuoci et al. (2007) stabilized the flame by including a short upstream section o f the fuel tube in their com putational dom ain; the com putational cost was kept down through

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the use of small chemical mechanisms, with the use o f detailed chemistry limited to a post-processing step. In the sim ulations o f Zahirovic et al. (2006), a small high- tem perature zone was introduced at a location just dow nstream o f the nozzle to act as an artificial pilot.

F o r the com putational meshes and chemical mechanisms that are used in this study, the simulated flames blow out in the absence o f an artificial anchoring m echanism. Therefore, a small zone near the nozzle is designated as the ignition zone. In the ignition zone, a local equilibrium calculation is perform ed for any com putational particle whose m ixture fraction is w ithin 2% o f the stoichiometric value. This corresponds to approxim ately 6 x 10 fi% (by mass) o f the to tal fluid in the com putational dom ain. A sensitivity study has been done to minimize the extent of the ignition zone, and to confirm that it has negligible influence on com puted m ean and rms tem perature and m ajor species profiles. On the other hand, N O chemistry (dom inated by therm al N O here) is slow, and local equilibrium m ay lead to unrealistically high local N O levels. To m itigate this, particle N O values in the ignition zone are set to zero.

Computational Mesh, Initial and Boundary Conditions

The computational domain is a 10-degree wedge with a single finite-volume cell in the azimuthal direction, corresponding to axisymmetric simulations. The inlet is at the plane of the fuel-jet nozzle exit, and the domain extends 80d in the axial direction and 15d in the radial direction, where cl is the fuel-jet diameter. A nonuniform mesh o f2700 finite-volume cells is used, with finer resolution close to the fuel nozzle and mixing zone.

In earlier PDF-based modeling studies for nonpremixed turbulent jet flames, little difference has been found between results obtained using a top-hat inlet m ean velocity profile and measured inlet m ean velocity profiles (where available). Here, top-hat p rofiles are specified for m ean velocity, composition, and tem perature at the inlet using the values given in Table 1. Inlet values of turbulence kinetic energy (k) are specified to be the experimental values. Inlet values of dissipation rate of turbulence kinetic energy (s) are specified to correspond to a turbulence integral length scale of lT 0.03 cl: here s = C°'75/-rL5/ / r , where C,, = 0.09 is a standard k -s model constant. A t the outlet, a fixed pressure o f one atmosphere is specified and zero-gradient conditions are used for all other quantities. Zero gradient conditions are applied at the outer radial boundary, and symmetry conditions are applied on the azimuthal faces.

Initial conditions in the com putational dom ain correspond to am bient air. The sim ulations are advanced in time with a com putational time step o f 5 ps for flame A and 10 ps for flame B (corresponding to a m axim um m aterial C ourant num ber of approxim ately 0.5), until a statistically stationary state is reached (approxim ately 2 s, or 200 flow-through times based on the fuel-jet m ean velocity). Results then are time-averaged for approxim ately 0.5 s (50 flow-through times) to reduce statistical noise in the reported m ean and rms profiles.

Computational Acceleration

The sim ulations have been run on small m ultiprocessor systems using up to eight cores. Simple dom ain decom positions have been perform ed in the axial direction, and in some cases an additional level o f parallelization has been implemented

TRANSPORTED PDF MODELING OF JET FLAMES 683

for the particle chemistry calculations (H aw orth, 2010; Jaishree and H aw orth, 2012). In m ost cases, in situ adaptive tabulation (ISAT) (Lu and Pope, 2009) has been used to accelerate the com putation o f the chemical source terms. Verification that results obtained using ISA T are essentially the same as those obtained by direct integration o f the chemical source term s is provided in the following section.

RESULTS AND DISCUSSION

The calculation o f chemical source term s dom inates the com putational effort, and it is desirable to reduce this cost using ISAT. The accuracy and efficacy o f using ISA T is verified first. Then results obtained using the baseline models (with ISAT) are presented. This is followed by discussions o f the influences o f variations in four aspects o f the physical modeling: the turbulence m odel (C6i), radiation, the chemical m echanism, and the P D F mixing model. All m ean and rms profiles correspond to mass- (Favre-) averaged quantities. The figures tha t are included in the article represent a subset o f the available results. A m ore complete set of figures is provided in the Supplem entary M aterial tha t is available online.

ISAT

A key ISA T param eter is the global error tolerance, sisat- Smaller values of S i s a t correspond to higher accuracy and higher com putational cost. In m ost P D F modeling studies, values between 1CT4 and 1CT3 have been used, and s is a t = 10~3 has been shown to be satisfactory for m ost purposes (Jaishree and H aw orth, 2012; James et al., 2001). Here, results obtained using ISAT w ith S isat = 10~4 and with s i s a t = 10~3 have been com pared w ith results obtained using direct integration of the chemical source terms. The largest differences are in m inor species profiles. An example (mean and rm s radial O H profiles at x /c l= 40 for flame A) is shown in Figure 1. W ith Sisat = 10 3. m ean tem perature and m ajor species profiles are within approxim ately 5%, and rms tem perature and m inor species profiles are within approximately 10% o f those obtained w ith direct integration. On a single processor, the overall sim ulation time for ISAT w ith Sisat = 10 is approxim ately 3% o f that for direct

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r /d

(a) (b)

Figure 1 Comparisons between direct integration and ISAT with different tolerances at x /i/= 40. (a) Mean temperature; (b) mean OH gas fraction. (Figure is provided in color online.)

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integration. W ith S isat = 10~4, m ean tem perature and m ajor species profiles are within approxim ately 2% o f those obtained with direct integration, while the differences in rms tem perature and m inor species profiles rem ain approxim ately 10%. The overall sim ulation time for ISAT w ith S isat = 10 4 is approxim ately 5% o f that for direct integration. All subsequent results have been obtained using ISA T with £i s a t = 10 3.

Baseline Model Results

Results for the baseline m odels ( Csi = 1.6, no radiation, 10-species chemistry, EM ST mixing w ith C,,, 1.5) are presented next. The predicted flame length basedon the m ean stoichiometric m ixture fraction value (cv/ 0.295) is 49.5 d and 50 d for flames A and B, respectively. This is slightly higher than the m easured value o f 47d, and can be im proved with a small decrease in Csi (discussed below).

C om parisons o f com puted and m easured radial profiles o f m ean and rms tem perature, m ajor species and m inor species at x /c l= 20 and at x / d 40 for flames A and B are shown in Figures 2 and 3. As can be seen in the figures, scaling by the jet diam eter essentially collapses the profiles for the tem perature and m ajor species (C 0 2, H 20 , CO), consistent w ith the experimental findings. M inor species profiles (OH and N O ) do not scale simply w ith nozzle diam eter, because o f their stronger dependence on local scalar dissipation rate and convective residence time, and the model captures these trends as well (e.g., higher N O for flame B com pared to flame A). For all quantities, the level o f quantitative agreement between model and experim ents is at least as good as any tha t has been reported in the literature to date, if not better. It is particularly notew orthy tha t the com puted fluctuation levels are in reasonably good agreement w ith the experiments for all quantitities.

The principal discrepancies between m odel and experiment are in the m ean H 20 (underpredicted close to the centerline at the m ore upstream location), the m ean CO (overpredicted, especially at the m ore dow nstream location), and m ean NO. The discrepancy in H 20 m ight be a consequence o f neglecting differential diffusion. As discussed earlier, there is evidence that differential species diffusion plays a role in these flames on the fuel-rich side, close to the nozzle (Barlow et al., 2000; Hewson and Kerstein, 2001), because o f the high diffusivity o f H 2. The com puted m ean CO is very sensitive to the jet spreading rate, as will be shown in the next subsection. The experimental uncertainty for CO is also high (10%) com pared to other m ajor species (e.g., 3% for H 2). Predicted N O levels depend strongly on the chemical m echanism and the local tem perature (hence, radiation). A t upstream locations, NO levels m ay also be influenced by the treatm ent that has been used to anchor the flame, as discussed earlier. The reported experim ental uncertainty for N O is 10% to 15%. The influences o f radiation and the chemical m echanism are discussed below.

Effects of CEi

It is custom ary practice in k ;; m odeling studies o f turbulent jet flames to treat C£i as an adjustable param eter tha t can be tuned to control the spreading rate. The effects o f reducing

TRANSPORTED PDF MODELING OF JET FLAMES 685

(a)

\

(b)

(g)

(d) (e) (f)

(h) (0

Ci)

Figure 2 Computed and measured mean and RMS radial profiles of flames A and B, scaled on nozzle diameter, at x /d = 20. (a) Mean temperature; (b) rms temperature; (c) mean NO mass fraction; (d) rms NO mass fraction; (e) mean CO mass fraction; (f) tms CO mass fraction; (g) mean OH mass fraction; (h) rms OH mass fraction; (i) mean C 0 2 mass fraction; (j) mean H20 mass fraction. (Figure is provided in color online.)

com puted m ean CO profile is especially pronounced. The relatively high sensitivity o f CO m ight be a consequence o f the relatively slow CO chemistry; its chemical time scale is o f the same order as the flow time scale (Barlow et al., 2000).

Effects of Radiation

As discussed earlier, radiation is relatively weak in these flames. Nevertheless, its effects are discernable. They are m ost evident at dow nstream locations for species that are particularly sensitive to small variations in tem perature: CO and NO. Therm al N O is dom inant for these flames (F rank et ah, 2000).

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(b)

(0(e)

(g) (i)

(j)

Figure 3 Computed and measured mean and RMS radial profiles of flames A and B, scaled on nozzle diameter at x /d = 40. (a) Mean temperature; (b) rms temperature; (c) mean NO mass fraction; (d) rms NO mass fraction; (e) mean CO mass fraction; (f) tms CO mass fraction; (g) mean OH mass fraction; (h) rms OH mass fraction; (i) mean C 0 2 mass fraction; (j) mean H20 mass fraction. (Figure is provided in color online.)

Figure 5 shows computed m ean tem perature, CO, and N O profiles at x / d = 40 for flames A and B with three radiation models. As expected, the com puted m ean tem perature is highest when radiation is neglected altogether and is lowest when a gray, optically thin model is used; results from the spectral model with reabsorption are between these two extremes. The maxim um drop in the com puted m ean tem perature from the no-radiation model to the optically thin model is approximately 40 K for flame A and 100 K for flame B. Lower tem peratures result in lower CO and N O , and bring the computed m ean CO and N O profiles into closer agreement with experiment.

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I

(a) (b) (c)

(d) (e) (0

Figure 4 Comparisons of results obtained using two different values of CEl (CEl = 1.6 and CEl = 1.56) at x /d = 40 for flame B. (a) Mean axial velocity; (b) mean mixture fraction; (c) mean temperature; (d) mean CO; (e) mean C 0 2; (f) mean OH. (Figure is provided in color online.)

8

(a) (b)

optically-I

8 3E 05

IE-05

r/d r/d

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Figure 5 Comparisons of results obtained using three radiation models at x /d = 40. (a) Mean CO, flame A; (b) mean NO, flame A; (c) mean CO, flame B; (d) mean NO; flame B. (Figure is provided in color online.)

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Effects of Chemical Mechanism

M ean and rms tem perature, C 0 2, H 20 , and O H profiles are similar for the three m echanisms that have been tested. The effects o f changes in the chemical m echanism are m ost evident in com puted CO, H 2, and N O levels; these are shown at x /c l= 40 in Figures 6 and 7 for flame A. The C l m echanism does not include NO. Large differences can be seen in com puted N O levels between G R I-M ech 2.11 and the 10-species m echanism, in particular. G R I-M ech 2.11 overpredicts the CO, H 2, and N O levels for bo th flames, com pared to the two m echanisms that have been developed specifically for syngas.

As pointed out by F rank et al. (2000), only therm al N O should exist in the syngas flames. The additional N O paths in the GRI-2.11 m echanism could lead to the overprediction o f NO levels. To assess this assum ption, all N O pathw ays have been removed from the GRI-2.11 mechanism, except the three-step extended Zeldovich mechanism. Figure 7 shows that N O prediction is greatly im proved when nonther- mal N O is removed, and the results are nearly identical to those obtained using the 10-species mechanism. The im provem ent seen here supports the conclusion that only therm al N O exists in the syngas flames.

Effects of the Mixing Model

In a P D F m ethod, the mixing model plays a central role, especially in situations where finite-rate chemistry and turbulence-chem istry interactions are im portant. T hat is the case in these syngas flames, because o f the slow CO chemistry. The D am kohler num ber is estim ated to be unity at x / d 20 for flame B (Barlow et ah, 2000), and decreases w ith dow nstream distance. Therefore, these syngas flames tend to have broad reaction zones (Chen et ah, 1991), and finite-rate chemistry plays an im portant role.

Results obtained using two different mixing m odels (M C and EM ST) were com pared first for the same value o f C,h (C,h = 1.5), and only m inor differences were found (not shown). Then results obtained using EM ST were com pared for different values o f C f 1.0, 1.5, 2.0, and 8.0. Increasing C^ increases the mixing rate; in the

0.06

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Figure 6 Comparisons of results obtained using three different chemical mechanisms at x / d — 40 for flame A. (a) Mean CO; (b) mean H2. (Figure is provided in color online.)

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2E-05

r /d

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Figure 7 Comparisions between full GRI-2.11 NOx chemistry and GRI-2.11 with extended Zeldovich thermal NO only for flame A. (a) Mean NO mass fraction, x /d = 20; (b) mean NO mass fraction, x /d = 40. (Figure is provided in color online.)

limit —> oo, local fluctuations go to zero, and the model essentially reduces to awell-stirred reactor model. W hile = 8.0 is high com pared to values tha t norm ally are used in PD F-based m odeling studies, it serves to illustrate the trends and the

gF

(a) (b) (c)

(d)

Figure 8 Comparisons of results obtained using different values of C for flame B. (a) Mean temperature, x /d = 20; (b) rms temperature, x /d = 20; (c) mean NO mass fraction, x /d = 20; (d) rms NO mass fraction, x /d = 20; (e) mean temperature, x /d = 40; (f) rms temperature, x /d = 40; (g) mean NO, x /d = 40; (h) rms NO, v/i/=40. (Figure is provided in color online.)

690 X. ZHAO ET AL.

im portance o f turbulent fluctuations. Examples are shown in Figure 8. The changes in com puted m ean and rms profiles for values o f between 1.0 and 2.0 are relatively small, but they are dram atic w ith = 8.0. F o r = 8.0, local com position and tem perature fluctuations are dam ped significantly, and the com puted peak m ean tem perature increases by over 200 K. This underscores the im portance of accounting properly for turbulence-chem istry interactions in these flames.

Flame Structure in Mixture Fraction Space

C onditional m ean tem perature and O H mass fractions obtained using two mixing models (M C and EM ST with C ^ = 1.5, all other values correspond to the baseline model) are com pared w ith m easurem ents in Figure 9 for flame B. The definition o f the m ixture fraction and the m ixture fraction bin w idth are consistent with those reported in the experiments (Barlow et al., 2000). The two mixing models give similar profiles, although the M C results show m ore fluctuations. The conditional m ean tem perature profiles show good agreement w ith experiment at x / d = 20 and on the fuel-lean side at x /c l= 50. However, the conditional m ean O H mass fractions are overpredicted at bo th locations w ith bo th mixing models. W ith consideration of radiation, the peak m ean tem peratures would drop by as m uch as 100 K. The prediction o f m inor species on the fuel-rich side is expected to improve w ith better chemical mechanisms. Hewson and Kerstein (2001) also showed conditional m ean tem perature

2000

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Mixture fractionfraction Mixture fraction

(a) (b)

2000

1500

10000.001

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0.3 0.4 0.5 0.2Mixture fraction

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Figure 9 Comparisons of conditional mean profiles obtained using different mixing models for flame B. (a) Conditional mean temperature, x /d = 20; (b) conditional mean OH mass fraction, x /d = 20; (c) conditional mean temperature, x /d = 50; (d) conditional mean OH mass fraction, x /d = 50. (Figure is provided in color online.)

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and species mass fraction profiles. In their results, the conditional m ean tem peratures at bo th location were overpredicted, while the conditional m ean O H predictions showed good agreement w ith the experiment.

Scatter plots o f tem perature vesus m ixture fraction for flame B obtained using the EM ST mixing model with = 1.5 can be found in the Supplem entary M aterial online. Local extinction was reported by H ewson and Kerstein (2001) at x / d = 6 , where no experim ental da ta are available. Here, no local extinction is found at x / d = 6, x / d = 20 and x / d = 50, which is consistent w ith the experimental observations.

CONCLUSION

A consistent hybrid Lagrangian particle/E ulerian mesh com position PD F m ethod has been used to simulate two turbulent syngas flames. Key elements of the baseline model include the use o f a standard k ;; turbulence m odel, gradient transport for scalars, and the EM ST mixing model. The baseline model reproduces the m easured m ean and rms tem perature, m ajor species, and m inor species profiles reasonaly well, and captures the scaling tha t is observed in the experiments. F urther im provem ents can be realized w ith adjustm ents in the current turbulence m odel or using an alternative model, consideration o f radiation heat transfer, and improved chemical mechanisms. A lthough radiation effects are relatively small in these flames, consideration o f radiation is im portant for accurate N O predictions. In the oxyfuel context, N O is m ore o f an issue for potential corrosion in the C 0 2 pipelines (via acid form ation), ra ther than as an air pollutant. Chemical mechanisms that have been developed specifically for syngas (high concentrations o f fuel CO and H 2) perform better than a benchm ark m echanism (G R I-M ech 2.11) that was not designed for this purpose. It is im portant to account explicitly for turbulence-chem istry interactions, although the details o f the mixing m odel do not m ake a large difference, within reasonable limits. Rem aining disrepancies between model and experiment may, in part, be attributed to the neglect o f differential diffusion.

In future work, we will move tow ard environm ents tha t are m ore representative o f the target oxy-coal application. Accurate treatm ent o f radiation heat transfer will be m ore im portant, and the spectral radiation m odel will be extended to include CO.

ACKNOWLEDGMENTS

As part o f the N ational Energy Technology L abora to ry ’s Regional University Alliance (N ETL-R U A ), a collaborative initiative o f the N ETL, this technical effort was perform ed under the RES contract DE-FE0004000. This w ork was supported in part through instrum entation funded by the N ational Science F oundation through grant OCI-0821527. The authors also thank Professor F. L. D ryer o f Princeton for providing the C l chemical m echanism and for helpful discussions.

REFERENCES

Abian, M., Gimenez-Ldpez, J., Bilbao, R., and Alzueta, M.U. 2011. Effect of different concentration levels of C 0 2 and H 2G on the oxidation of CO: Experiments and modeling. Proc. Combust. Inst., 33, 317-323.

Dow

nloa

ded

by [P

enns

ylva

nia

State

U

nive

rsity

] at

13:1

1 22

May

20

12

692 X. ZHAO ET AL.

Barlow, R.S. 2011. Intern’]. Workshop on Measurement and Computation o f Turbulent Non-premixed Flames, Combustion Research Facility, Sandia National Laboratories, Livermore, CA; http://www.ca.sandia.gov/TNF/

Barlow, R.S., Fiechtner, G.J., Carter, C.D., and Chen, J.Y. 2000. Experiments on the scalar structure of turbulent C O /H 2/N 2jet flames. Combust. Flame, 120, 549-569.

Bowman, C.T., Flanson, R.K., Davidson, D .F., Gardiner, W.C., Lissianski, V., Smith, G.P., Golden, D.M ., Frenklach, M., and Goldenberg, M. 1995. GRI-Mech 2.IF, Available at http://www.nie.berkeley.edu/gri_mech

Buhre, B.J.P., Elliott, L.K., Sheng, C.D., Gupta, R.P., and Wall, T.F. 2005. Oxy-fuel combustion technology for coal-fired power generation. Prog. Energy Combust. Sci., 31, 283-307.

Chen, J.Y. 2011. http://ww w.sandia.gov/TNF/chem istry.htm lChen, J.Y., Dibble, W., and Bilger, R.W. 1991. PD F modeling of turbulent nonpremixed C O /

H2/N 2 jet flames with reduced mechanism. Proc. Combust. Inst., 23, 775-780.Correa, S.M., Drake, M.C., Pitz, R.W., and Shyy, W. 1985. Prediction and measurement of a

non-equilibrium turbulent diffusion flame. Proc. Combust. Inst., 20, 337-343.Correa, S.M., Gulati, A., and Pope, S.B. 1988. Assessment of a partial-equilibrium/M onte

Carlo model for turbulent syngas flames. Combust. Flame, 72, 159-173.Cuoci, A., Frassoldati, A., Ferraris, G.B., Faravelli, T., and Ranzi, E. 2007. The ignition,

combustion and flame structure of carbon monoxide/hydrogen mixtures, Note 2: Fluid dynamics and kinetic aspects of syngas combustion. Int. J. Hydrogen Energy, 32, 3486- 3500.

Curl, R.L. 1963. Dispersed phase mixing: I. Theory and effects in simple reactors. AIC hE J., 9, 175-181.

Dryer, F.L. 2011. Princeton University, Personnal communication.Fox, R.O. 2003. Computational Models for Turbulent Reacting Flows, Cambridge University

Press, Cambridge, UK.Frank, J.H., Barlow, R.S., and Lundquist, C. 2000. Radiation and nitric oxide formation in

turbulent non-premixed jet flames. Proc. Combust. Inst., 28, 447-454.Frassoldati, A., Faravelli, T., and Ranzi, E. 2007. The ignition, combustion and flame

structure of carbon monoxide/hydrogen mixtures, Note 1: Detailed kinetic modeling of syngas combustion also in presence of nitrogen compounds. Int. J. Hydrogen Energy, 32, 3471-3485.

Giacomazzi, E., Picchia, F.R., Arcidiacono, N., and Cecere, D. 2006. Numerical simulation of turbulent combustion on CRESCO platform. Final Workshop of Grid Projects, “PON RICERCA 2000-2006, AV VISO 1575.”

Giacomazzi, E., Picchia, F.R., Cecere, D., and Arcidiacono, N. 2008. Unsteady simulation of a C O /H 2/N 2 air turbulent non-premixed flame. Combust. Theor. Model., 12, 1125- 1152.

Haworth, D.C. 2010. Progress in probability density function methods for turbulent reacting flows. Prog. Energy Combust. Sci., 36, 168-259.

Haworth, D.C., Drake, M.C., and Blint, R.J. 1988. Stretched laminar flamelet modeling of a turbulent jet diffusion flame. Combust. Sci. Technol., 60, 287-318.

Haworth, D.C., Drake, M.C., Pope, S.B., and Blint, R.J. 1989. The importance of time- dependent flame structures in stretched laminar flamelet models for turbulent jet diffusion flames. Proc. Combust. Inst., 22, 589-597.

Hewson, J.C., and Kerstein, A.R. 2001. Stochastic simulation of transport and chemical kinetics in turbulent C O /H 2/N 2 flames. Combust. Theor. Model., 5, 669-697.

Jaishree, J., and Haworth, D.C. 2012. Comparisons of Lagrangian and Eulerian PD F methods in simulations of nonpremixed turbulent jet flames with moderate-to-strong turbulence-chemistry interactions. Combust. Theor. Model., 16(3), 435-463.

Dow

nloa

ded

by [P

enns

ylva

nia

State

U

nive

rsity

] at

13:1

1 22

May

20

12

TRANSPORTED PDF MODELING OF JET FLAMES 693

James, S., Anand, M.S., Razdan, M.K., and Pope, S.B. 2001. In situ detailed chemistry calculations in combustor flow analyses. J. Eng. Gas Turbines Power, 123, 747-756.

Kim, S.K., Kang, S.M., and Kim, Y.M. 2001. Flamelet modeling for combustion processes and NOx formation in the turbulent nonpremixed C O /H 2/N 2 jet flames. Combust. Sci. Techno!., 168, 47-83.

Li, J., Zhao, Z., Kazakov, A., Chaos, M., Dryer, F.L., and Scire, J.J. 2007. A comprehensive kinetic mechanism for CO, CH20 , CH3OH combustion. Int. J. Client. Kinet., 39, 109-136.

Lu, L., and Pope, S.B. 2009. An improved algorithm for in situ adaptive tabulation. J. Comput. Phys., 228, 361-386.

Masri, A.R., Subramaniam, S., and Pope, S.B. 1996. A mixing model to improve the PDF simulation of turbulent diffusion flames. Proc. Combust. Inst., 26, 49-57.

Mehta, R.S., Haworth, D.C., and Modest, M.F. 2010. Composition PD F /photon Monte Carlo modeling of moderately sooting turbulent jet flames. Combust. Flame, 157, 982-994.

Muradoglu, M., Jenny, P., Pope, S.B., and Caughey, D.A. 1999. A consistent hybrid finite volume/particle method for the PD F equations of turbulent reactive flows. J. Comput. Phys., 154, 342-371.

Muradoglu, M., Pope, S.B., and Caughey, D.A. 2001. The hybrid method for the PDF equations of turbulent reactive flows: Consistency conditions and correction algorithms. J. Comput. Phys., 172, 841-878.

Nooren, P.A., Wouters, H.A., Peeters, T.W.J., Roekaerts, D., Maas, U., and Schmidt, D. 1997. Monte Carlo PD F modeling of a turbulent natural-gas diffusion flame. Combust. Theor. Model. 1, 79-96.

OpenFOAM. 2011. http://www.openfoam .comPope, S.B. 1985. PD F methods for turbulent reactive flows. Prog. Energy Combust. Sci., 11,

119-192.Pope, S.B., and Correa, S.M. 1987. Joint PD F calculation of a non-equilibrium turbulent

diffusion flame. Proc. Combust. Inst., 21, 1341-1348.Smith, N., Gore, J., Kim, J., and Tang, Q. 2011. Intern I. Workshop on Measurement and

Computation o f Turbulent Nonpremixed Flames: Radiation models. Combustion Research Facility, Sandia National Laboratories, Livermore, CA; http://www.ca.sandia.gov/TNF/ radiation.html

Subramaniam, S., and Pope, S.B. 1998. A mixing model for turbulent reactive flows based on Euclidean minimum spanning trees. Combust. Flame, 115, 487-514.

Viswanathan, S., Wang, H., and Pope, S.B. 2011. Numerical implementation of mixing and molecular transport in LES/PD F studies of turbulent reacting flows. J. Comput. Phys., 230, 6916-6957.

Wang, A., and Modest, M.F. 2006. Photon Monte Carlo simulation for radiative transfer in gaseous media represented by discrete particle fields. J. Heat Transfer, 128, 1041- 1049.

Zahirovic, S., Scharler, R., Kilpinen, P., and Obernberger, I. 2001. Validation of flow simulation and gas combustion sub-models for the CFD-based prediction of NOx formation in biomass grate furnaces. Combust. Theor. Model., 5, 669-697.

Zahirovic, S., Scharler, R., and Obernberger, I. 2006. Advanced gas phase combustion m odels: Validation for biogases by means of LES and experiments as well as application to biomass furnaces. Presented at the 7th European Conference on Industrial Furnaces and Boilers, April 18-21, Porto, Portugal.

Zsely, I.G., Zador, J., and Turanyi, T. 2005. Uncertainty analysis of updated hydrogen and carbon monoxide mechanisms. Proc. Combust. Inst. 30, 1273-1281.