Conditional Moment Closure for Modeling Combustion Processes and

Aug 10, 2009 - On the basis of the predicted unconditional and conditional means, detailed discussions of oxy-fuel flame characteristics, as well as t...
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Energy Fuels 2009, 23, 4370–4377 Published on Web 08/10/2009

: DOI:10.1021/ef9004829

Conditional Moment Closure for Modeling Combustion Processes and Structure of Oxy-Natural Gas Flame Gunhong Kim,† Yongmo Kim,*,† and Yong-Jin Joo‡ †

Department of Mechanical Engineering, Hanyang University, 17, Hangdang-dong, Seongdong-ku, Seoul, 133-792, Korea, and ‡ Korea Electric Power Research Institute, Munji-Dong, Yusung-Ku, Daejeon, 305-380, Korea Received May 18, 2009. Revised Manuscript Received July 2, 2009

To realistically predict the flame structure and combustion processes of oxy-fuel flames, the present study employs the conservative CMC model fully coupled with flow solver. The detailed chemistry is utilized to accurately account for thermal dissociations and nonequilibrium effects in the high-temperature combustion, as well as to properly include the convective and radiative effects on local flame structure. Numerical results indicate that the present approach is reasonably well capable of capturing the essential features and precise structure of oxy-fuel flames. On the basis of the predicted unconditional and conditional means, detailed discussions of oxy-fuel flame characteristics, as well as the capabilities and defects of the present approach, are given, along with the uncertainties of the experimental data.

mental activities include the laser Doppler technique for measuring axial velocity, the high temperature suction pyrometer for temperature, and the conventional gas sampling method for O2, CO2, UHC, CH4, H2, CO, and NOx. In addition, the project consisted of numerical calculations which were intended to predict the detailed structure and properties of oxy-natural gas flames. However, the previous numerical approach5,6 for characterizing oxy-fuel flames was based on relatively ad hoc physical models that deal with turbulent combustion processes and detailed thermo-physical properties. In general, the crucial physical processes in the turbulent oxy-fuel flames involve the chemical dissociations, turbulence-chemistry interaction, radiative heat transfer, soot formation and oxidation, thermal radiation including soot radiation and non-gray-gas properties, and turbulence-radiation interaction. Recently, to numerically simulate the oxygen-enhanced turbulent nonpremixed flame, Wang et al.7 developed the numerical model, which integrates detailed chemical kinetics, soot model, and state-of-the-art approaches for thermal radiation including soot radiation and non-gray-gas properties. However, they used the simple turbulent combustion model, such as the eddy-breakup model to account for the turbulence-chemistry interaction. Several advanced combustion models including the laminar flamelet model,8 the conditional moment closure,9 and the probability density function (pdf) transport model10 are capable

1. Introduction Recently, industries have been driven by the requirements of maintaining or improving product quality while minimizing production costs. Within these requirements, overall energy management and energy efficiency play important roles. New high-performance design technology will provide smaller, more compact furnaces offering lower capital investments. In designing or selecting high-efficiency furnaces, moreover, environmental aspects must also be taken into account. Because of the continuous development of combustion technology, current oxy-fuel and air-fuel furnaces are both able to meet existing regulations. It is generally acknowledged that oxy-fuel combustion technology has great potential to simultaneously reduce costs and achieve lower emissions.1 Compared to the air-fuel case, the design of oxy-fuel burners still relies heavily on engineering intuition and trial and error testing procedures. This is both because of the scarcity of comprehensive experimental data in semi-industrial and full-scale combustion systems and to the limited capabilities of the existing combustion models, which cannot be confidently applied to the furnace/burner design process.2 In the framework of the so-called OXYFLAM project,3,4 the development of new measuring instruments for studying oxy-fuel flames had been extensively undertaken. The OXYFLAM project was motivated to generate a detailed set of information for designing burners and validating computer codes for oxy-fuel flame calculations. The extensive experi-

(5) Brink, A.; Hupa, M.; Breussin, F.; Lallemant, N.; Weber, R. Modeling of Oxy-Natural Gas Combustion Chemistry. J. Propul. Power 2000, 16 (4), 609–614. (6) Breussin, F.; Lallemant, N.; Weber, R. Computing of Oxy-Natural Gas Flames using both a Global Combustion Scheme and a Chemical Equilibrium Procedure. Combust. Sci. Technol. 2000, 160, 369–391. (7) Wang, D. C.; Haworth, S. R.; Turns, M. F. Modest Interactions among Soot, Thermal Radiation, and NOx Emissions in OxygenEnriched Turbulent Nonpremixed Flames: A Computational Fluid Dynamics Modeling Study. Combust. Flame 2005, 141, 170–179. (8) Peters, N. Laminar flamelet concepts in turbulent combustion. Proc. Combust. Inst. 1986, 21, 358–374. (9) Klimenko, A. Y.; Bilger, R. W. Conditional moment closure for turbulent combustion. Prog. Energy Combust. Sci. 1999, 25, 595–687. (10) Pope, S. B. PDF methods for turbulent reactive flows. Prog. Energy Combust. Sci. 1985, 11, 119–192.

*To whom correspondence should be addressed. Telephone: þ82-22220-0428. Fax: þ82-2-2297-0339. E-mail: [email protected]. (1) Lievre, K.; Hewerson, R.; Hoke, B. Recent Developments in OxyFuel Firing for Glass Melters. Glass Ind. 2001, 82 (3), 25–31. (2) Lallemant, N.; Breussin, F.; Weber, R.; Ekman, T.; Dugue, T.; Samaniego, J. M.; Charon, O.; Van Den Hoogen, A. J.; Van Der Bemt, J.; Fufisaki, W.; Imanari, T.; Nakamura, T.; Iino, K. Heat Transfer and Pollutant Emissions Characteristics of Oxy-Natural Gas Flames in the 0.7-1 MW Thermal Input Range. J. Inst. Energy 2000, 73, 169–182. (3) Lallemant, N.; Dugue, J.; Weber, R. Analysis of The Experimental Data Collected during The OXYFLAM-1 and OXYFLAM-2 Experiments, IFRF Doc. No. F85/y/4, 1997 (4) Lallemant, N.; Dugue, J.; Weber, R. Measurement Techniques for Studying Oxy-Natural Gas Flames. J. Inst. Energy 2003, 76, 38–53. r 2009 American Chemical Society

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of accounting for turbulence-chemistry interaction. However, these state-of-the-art turbulent combustion models have been heavily applied to the air-fuel flames, while these models have not been adopted to analyze the turbulent oxy-fuel flame characteristics. In the present study, to realistically treat the turbulence-chemistry interaction encountered in the oxy-fuel flames, conditional moment closure (CMC) has been employed. The present CMC model is developed to fully interact with the flow solver. In context with this CMC aprroach, the detailed chemistry is represented by the Gri2.11 mechanism11 and the convective and radiative cooling effects on the turbulent combustion process12 are considered. To address the dominant mode of energy transfer in these high temperature combustion systems, radiative heat transfer is calculated using the finite volume method, which has been known to provide accurate results in planar, axisymmetric, and three-dimensional complex geometries with both structured and unstructured grids.13 All physical models including radiation and turbulent combustion processes have been successively implemented into our in-house flow solver based on the unstructured grid finite volume method. Moreover, the computational load of the CMC model resulting from the detailed chemistry can be handled using a parallel procedure with an automatic load-balancing algorithm. Since this study deals with the high fuel-injection velocity oxy-fuel flame which yields the relatively low soot-induced yellowish luminosity resulting from the substantial increase in turbulent mixing and oxygen entrainment, the present approach does not consider the soot formation and soot radiation. In the present work, we have chosen the measurements of the OXYFLAM project3 to validate the numerical and physical models presented.14,15 On the basis of the numerical results, the essential features of oxy-fuel combustion, as well as the capabilities and defects of the present numerical approach, are discussed.

The conservative formulation of the CMC equation has been implemented in the structured and unstructured grid finite volume methodology.14,15,19 The final transport equation for conditional averages Q is DQ FP þ divðFPÆvjηæQÞ ¼ divðFPDrQÞþ FPÆWjηæ Dt þ FPÆχjηæ

ð2Þ

where ÆW|ηæ is defined as the conditional reaction rates of species and the conditional heat transfer rates of radiation. Æχ|ηæ denotes the conditional scalar dissipation rate, and D denotes the effective turbulent diffusivity resulting from the diffusion approximation of the turbulent scalar flux, Æv00 Y00 |η æ= DrQ. The conditional velocity is generally approximated as 00 ξ00 vg ðη - e ξÞ ð3Þ Ævjηæ ¼~v þ 002 ξf 00 ξ00 is also modeled by the gradient transport assumpwhere vg tion, conventionally used in the transport equation for the mean mixture fraction ξ~. It is well-known that modeling the conditional scalar dissipation rate in CMC predictions is important, since Æχ|ηæ describes the scalar mixing of small-scale structures in turbulent flows and strongly influences reaction rates. Several models of conditional scalar dissipation rate are available and some of these models are consistent with the PDF transport equation. Among them, the model recently suggested by Mortensen16 is the most consistent one with the PDF transport equation. However, the advanced models16-18 are numerically complex and computationally expensive and they are not used here. In this study, although the flow turbulence is nonhomogeneous, the conditional scalar dissipation rate is evaluated from the model suggested by Peters8 as

Æχjηæ ¼ χst f ðηÞ ¼ χst exp½2ðerfc -1 ð2ξst ÞÞ2 - 2ðerfc -1 ð2ηÞÞ2 

2. Mathematical Formulations for Conditional Moment Closure

where

2.1. First-Order Conditional Moment Closure. The conditional average of reactive scalars for the mass fraction of all chemical species and enthalpy is Qi ðη; x, tÞ  Æψi ðx, tÞjξðx, tÞ ¼ ηæ

D2 Q þ Q divðFPÆvjηæÞ Dη2

χst ¼ χe=

Z

f ðηÞPðηÞdη

ð4Þ

ð5Þ

Here, the unconditional scalar dissipation rate χ~ can be calculated from a commonly used model such as e ε 002 e χ ¼ 2 ζf ð6Þ k~

ð1Þ

where ψ = (Y1, Y2, ..., Yn, h) and n is the number of reactive species considered. Æ.|ξ = ηæ denotes the conditional average, which is subject to the mixture fraction ξ, being set to the sample space variable η. In the following equation, the subscript i has been dropped for clarity, and all dependent variables without annotation are conditionally averaged variables.

In the case of adiabatic flame, there is no source term in the conditional enthalpy equation. When radiation and convection should be considered, however, appropriate modeling is needed to treat the conditional radiative source term and the conditional thermal boundary. Since a conditional enthalpy or temperature can strongly influence conditional reaction rates, one must solve a conditional enthalpy equation. Except for the case of weakly radiating flames, for which the optically thin assumption can be made, conditional enthalpy losses could not be easily

(11) Bowman, C. T.; Hanson, R. K.; Davidson, D. F. Gri-mech 2.11, 1995, http://www.me.berkely.edu/gri_mech/. (12) Young, K. J.; Moss, J. B. Modelling Sooting Turbulent Jet Flames Using an Extended Flamelet Technique. Combust. Sci. Technol. 1995, 105, 33–53. (13) Raithby, G. D.; Chui, E. H. A Finite-Volume Method for Predicting a Radiat Heat Transfer in Enclosures with Participating Media. J. Heat Transfer 1990, 112, 415–423. (14) Kim, G. H.; Kim, Y. M.; Bilger, R. W.; Cleary, M. J. Conditional Moment Closure and Transient Flamelet Modeling for Detailed Structure and NOx Formation Characteristics of Turbulent Nonpremixed Jet and Recirculating Flames. Combust. Theory Modell. 2007, 11 (4), 527– 552. (15) Kim, G. H.; Kang, S. M.; Kim, Y. M.; Lee, K. S. Conditional Moment Closure Modeling for a Three-Dimensional Turbulent Nonpremixed Syngas Flame with a Cooling Wall. Energy Fuels 2008, 22 (6), 3639–3648.

(16) Mortensen, M. Consistent Modeling of Scalar Mixing for Presumed, Multiple Parameter Probability Density Functions. Phys. Fluids 2005, 17 (1), 018016. (17) Vogiatzaki, K.; Cleary, M. J.; Kronenburg, A.; Kent, J. H. Modeling of Scalar Mixing in Turbulent Jet Flames by Multiple Mapping Conditioning. Phys. Fluids 2009, 21, 025105. (18) Devaud, C. B.; Bilger, R. W.; Liu, T. A New Method of Modeling the Conditional Scalar Dissipation Rate. Phys. Fluids 2004, 16 (6), 2004– 2011. (19) Cleary, M. J.; Kent, J. H. Modelling of species in hood fires by conditional moment closure. Combust. Flame 2005, 143, 357–368.

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numerical cell itself and the coding structure including the imposition of boundary conditions can be further simplified. One of the basic advantages in the unstructured grid methodology is the grid flexibility which allows to easily and accurately treat the physically or geometrically complex reacting flows. Thus, the unstructured grid approach is capable of generating the optimized and adaptively refined grid system to resolve the regions with the high gradient and the irregular boundaries while it does not considerably increase the computational time. In fact, it is well-known that, compared to the structured grid method, the unstructured grid procedure requires the slightly longer CPU time per each computational cell because it can not use the line relaxation procedure. However, the optimally refined unstructured-grid arrangement significantly reduces total cells of computational domain especially for the large-scale problems. This feature is particularly useful to numerically deal with the CMC formulation, which requires the relatively excessive CPU time, compared to the flamelet model. Since the numerical implementation of CMC is based on the operator-splitting method, parallel procedures for calculating the partitioned flame fields and the stiff ordinary differential equation (ODE) need to be devised separately. The parallel procedure for the fully coupled CMC model has attempted to parallelize the numerics associated with the partitioned flame fields, as well as the calculations of the stiff ODE, which uses the stiff ODE solver DVODE.21 For a efficient parallel implementation, the communication overhead must be minimized and the message-passing library should be compatible with all major computer architectures.

solved from the conditional heat transfer equations. If it is not possible to obtain the conditional solution of the conditional enthalpy equation, one can model an appropriate conditional enthalpy distribution, which needs to be reconciled with the overall unconditional heat transfer and enthalpy loss. An alternative approach should be chosen to calculate the conditional enthalpy profile, similarly to the treatment of Cleary and Kent,19 which determines the conditional temperature profile from the local mean temperature and pdf. In this study, we adopt the normalized enthalpy loss variable approach, which has been widely applied for the turbulent flames with convective and radiative cooling.12,15,20 The normalized enthalpy loss variable is defined as h - hmin h - hmin ð7Þ ¼ ζ ¼ had - hmin U ðξÞ Here, had is the conditional adiabatic enthalpy and hmin the conditional minimum, which is defined as the calculated enthalpy when conditional temperatures are cooled down to the surrounding temperature. The enthalpy loss variable ζ represents the local fraction of radiative or convective heat losses with respect to adiabatic states. The value of U(ξ) depends on only the mixture fraction. In the adiabatic case, this enthalpy loss variable surely remains unity. Once the Frave mean transport equation is solved to calculate the normalized enthalpy loss variable, the local nonadiabatic enthalpy profiles can be constructed directly from eq 7. In eq 7, the numerator (h - hmin) and denominator (U= had hmin) have a similar statistical correlation with the mixture fraction, and their ratio, the normalized enthalphy loss variable, is statistically independent of the mixture fraction. To derive the Favre-averaged enthalphy loss variable transport equation, the instantaneous transport equation can be obtained by substituting eq 7 of the enthalphy loss variable into the energy equation. With the Favre averaging and the neglect of the statistically noncorrelated term, the Favre-averaged enthalphy loss variable transport equation can be derived as follows:

3. Results and Discussion Conditional moment closure was applied to numerically investigate the detailed structure and combustion processes of the highly radiating oxy-fuel, non-premixed, turbulent flame. For validation of oxy-fuel flames, the case of a high-momentum, nonswirling, oxy-natural gas flame fired in the IFRF furnace 2 was chosen.2 The internal length of the furnace was 3,740 mm, and the dimension of the nearly square cross section was 1050  1050 mm. The chimney contraction diameter was 500 mm. The whole furnace was lined with refractory to maintain a very hot flame. Natural gas entered through a round pipe in the center of the burner, and the diameter of the fuel inlet was 16 mm. The oxygen stream entered through a 4-mm wide annulus. The separation distance between the oxygen stream and the natural gas stream was 6 mm, and the mass flow rates of the natural gas and oxygen were 63 kg/h and 224.5 kg/h, respectively. The thermal input of the oxy-fuel flame was 0.78 MW. Similar to previous studies, the axisymmetric description is used to simplify the modeling efforts of the full furnace.5,6 The present unstructured grid system shown in Figure 1 consisted of 10 080 triangular cells, where the larger number of cells was adaptively refined to effectively capture the characteristics of this jetlike flame with a large recirculation zone. Since the fuel compositions contained various hydrocarbon species include 86% CH4, 5.4% C2H6, 1.87% C3H8, 0.58% C4H10, 0.14% C5H12, 4.01% N2, 1.79% CO2, and 0.21% O2, the present fuel was assumed to be a mixture of 86% CH4, 7.99% C2H6, 4.01% N2, 1.79% CO2, and 0.21% O2.3 The modified k-ε model was used for predicting the flow and mixing fields, in which the model constant of Cε1 is modified from the standard

~ ξξ e χ ðe ζ - 1Þ cλP U DFe ζ e þ1 þ r 3 ðF ~ve -S ζÞ ¼ -r 3 ½FDrζ ð8Þ Dt 2 U rad where Uξξ denotes the second derivative of U to the mixture fraction and Srad is the source term from the radiative heat transfer, normalized with the denominator U(ξ) of eq 7. The radiative heat loss can be obtained from the finite volume method using various radiation models. The second term in the rhs of eq 8 is originated from the term containing the square of the mixture fraction gradient in the instantaneous enthal loss variable transport equation. The Favre-averaged modeling of term is quite similar to the procedure to derive the mixture fraction variance equation.20 2.2. Multidimensional CMC Model Fully Coupled with Flow Solver. In the present fully coupled CMC approach,14,15 some unavoidable numerical difficulties arise. One of these numerical difficulties is the requirement of excessive array-size for the conditional means, Q, which is related to spatial grids and numerical bins of the conserved scalar space for the various reactive scalars. Recently the parallel algorithm has emerged as a promising tool to improve the numerical efficiency and robustness of the CMC approach for large array sizes associated with conditional means and stiff ODE calculations.15 In the discretized formulation of the present unstructured grid finite volume approach, the cell-centered collocated scheme is employed because the control volume is represented by a (20) Louis, J. J. J.; Kok, J. B. W.; Klein, S. A. Modeling and Measurements of a 16-kW Turbulent Nonadiabatic Syngas Diffusion Flame in a Cooled Cylindrical Combustion Chamber. Combust. Flame 2001, 125, 10125–1031.

(21) Brown, P. N.; Byrne, G. D.; Hindmarsh, A. C. A VariableCoefficient ODE Solver SIAM. J. Sci. Stat. Comput. 1989, 10, 1038– 1051.

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Figure 1. Unstructured-grid arrangement for the oxy-fuel combustor.

value (1.44) to 1.50 to improve the quality of the flow and mixing fields. This oxy-fuel flame is characterized by the strong radiation due to the higher temperature and abundant radiative species. In calculating oxy-combustions, therefore, special caution must be given to the modeling of thermal boundary conditions and radiative properties of the mixture. In our calculation, a gas absorption coefficient is obtained for the transport equation of radiative intensity. This was done using the total absorption coefficient applicable for high-temperature flames of 2000-3000 K, in which total emissivity of CO2-H2O mixtures was computed from the Edwards exponential wide-band mode.22 The wall emissivity of the oxy-fuel combustor was selected in the same way as those of a previous work; the emissivity of the furnace wall was set to 0.6 and that of the chimney to 0.4.22 The detailed thermal boundary conditions were previously given in reference.23 In this study, the wall boundary condition was imposed by using the measured wall temperature, which is actually close to the near-wall temperature of the recirculated flue gas. In the previous work6 of Breussin et al., the temperature measured at the exit of the oxy-fuel furnace was 1958 K, and the hot zone of strong recirculation generated by the highmomentum jet had a temperature of around 1850-1900 K. In our calculations, the predicted temperature of the recirculation zone was about 1800-2000 K and the predicted temperature of the exhaust gas, 1,990 K, was slightly higher than the actual temperature measured. This implies that the thermal boundary conditions are appropriate for the present model. Before we discuss this combustion characteristic of oxy-fuel flames, it is worthwhile to analyze the adiabatic flamelet structure for the air-fuel and oxy-fuel flames at the relatively low scalar dissipation rate, χst = 0.1 s-1. Figure 2 shows the temperature, mass fraction of major species in the mixture fraction space for air-fuel and oxy-fuel diffusion flamelets. As shown in Figure 2(a), compared to the air-fuel flame, the oxyfuel flame yields a much broader hot-flame zone especially in the lean side of the mixture fraction space. This indicates that the chemical reaction of the oxy-fuel flame occurs within a much broader zone of the mixture fraction space. To numerically analyze the oxy-fuel flame field, it is quite important to check the heat loss effects on the conditional flame structure. As displayed in Figure 3, the cooling effects on the structure of the present oxy-fuel flame are taken into account, in terms of the conditional temperature and the conditional CO and CO2 mole fractions. By decreasing the normalized enthalpy loss variable, the conditional temperature decreases and the CO and CO2 mole fractions are sensitively changed through the thermal dissocia-

Figure 2. Adiabatic flamelet structure of oxy-fuel and air-fuel flame at χst = 0.1 s-1.

tion reaction. As shown in the precalculated nonadiabatic flamelet data, the nonadiabatic calculations together with the detailed chemistry are essential to predict the temperature and gas compositions in high-temperature, strongly radiating flames. Figure 4 shows the predicted streamlines, contours of axial velocity, and temperature in the oxy-fuel flame field. As would be expected, the jet-like flame field with the large recirculated zone is created in this oxy-fuel combustor. The volume of the chamber is shown to be mostly filled with the hot flue gas, which is largely cooled down by radiative and convective heat transfers in the recirculated zone. It is also expected that the temperature field in the upstream hot flame zone could be considerably influenced by the entrainment of the recirculated cooled product gas. There exists the low temperature gradient at the furnace wall, and these tendencies were also observed in experiment. In Figure 5, quantitative comparison of predictions with measurements has been made for the radial profiles of axial velocity at three axial locations. In the upstream region

(22) Coppalle, A.; Vervisch, P. the Total Emissivities of High-Temperature Flames. Combust. Flame 1983, 49, 101–108. (23) Bollettini, U.; Breussin, F.; Lallemant, N.; Weber, R. Mathematical Modelling of Oxy-Natural Gas Flames, IFRF Doc. No. F 85/y/6, 1997.

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(x= 0.22 m), the predicted profile of axial velocity has a good conformity with the measured one. However, at the downstream locations, the spreading rate of the fuel jet was somewhat underestimated. This discrepancy may be attributed mainly to defects of the modified k-ε model and also to the inlet boundary conditions.

In Figure 6, the predicted profiles of temperature are compared with the measured ones at three axial locations. Numerical results indicate that the overall qualitative agreement between predictions and measurements are reasonably good. However, the significant qualitative and quantitative discrepancies exist in the upstream flame field. Around at the radial location (4.0 cm < r < 8.5 cm) in the upstream lean-mixture region (x = 0.22 m), the temperature field is substantially overestimated and the high-temperature zone exists. These discrepancies could be mainly attributed to the shortcomings of the modified k-ε turbulence model, as well as experimental errors. There is a tendency that the k-ε turbulence model usually underestimates the strength of flow reversal in the recirculation zone, as well as the entrainment of the cooled product gas to the upstream high-temperature zone. Thus, in the upstream hot zone, the overestimated temperature in the upstream hot zone could be partly caused by the underestimated entrainment of the cooled product gas. It is also possible that the temperature overestimation could be influenced partly by the uncertainties of the thermal boundary condition at furnace wall as well as marginally by the neglect of turbulence-radiation interaction in the present approach. It is also necessary to note that, compared to the air-fuel flame, the laminar oxy-fuel flame yields a much higher and broader high-temperature zone especially in the lean side of the mixture fraction space. Thus, at the upstream region with the high scalar dissipation rate, it is quite possible that the turbulent oxy-fuel flame creates a much broader hightemperature zone especially in the lean side of the mixture fraction space. In this regard, we think that experimental errors could be partially responsible for these discrepancies. Moreover, the temperature profiles for this oxy-flame field was measured by using the intrusive technique.17 To assess the reliability of the measured temperature distribution, Lallemant et al. made equilibrium calculations to estimate gas temperature in the external recirculation zone using measured H2 concentrations.3 In their analytical work, the estimated temperature distribution indicated the existence of a slightly higher temperature zone, similar to our results. This implies that experimental errors could be involved in the temperature measurements especially in the upstream hot flame zone.

Figure 3. Nonadiabatic flamelet data for oxy-fuel flame at χst = 0.1 s-1.

Figure 4. Predicted streamlines, contours of axial velocity and temperature field in a high-momentum oxy-natural gas flame.

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Figure 5. Comparison between measured (symbols) and predicted (solid lines) velocity.

Figure 6. Comparison between measured (symbols) and predicted (solid lines) temperature.

Figure 7. Comparison between measured (symbols) and predicted (dashed and solid lines) CO and CO2 volume fraction at four axial locations.

At the downstream locations (x=0.82 and 1.42 m), temperatures were somewhat overestimated, especially for the central high-temperature regions, while those predicted for the flue gas agreed relatively well with those measured at all axial locations. The overestimated temperature at these two downstream locations could be partly caused by the underestimated entrainment of the cooled product gas to the central high-temperature zone. It is also feasible that the temperature overestimation could be affected partly by the uncertainties of the thermal boundary condition as well as marginally by the neglect of turbulence-radiation interaction in the present comprehensive model.

In Figures 7-9, the quantitative comparison of prediction with measurement is shown for the radial profiles of H2, O2, CO, CO2, N2, and CH4 at four axial locations. In terms of the CO2 volume fraction, the predicted profile qualitatively reproduces the measured profile well at all locations. However, especially in the central high-temperature region of all axial stations, the CO2 volume fraction is underestimated mainly because of the underestimated entrainment of the cooled product gas to the hot flame zone, as well as partly because of the enhanced chemical dissociation corresponding to the overestimated temperature field. Evidently, the underpredictions of CO2 concentration are closely tied with the overprediction of temperature at these axial locations. 4375

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Figure 8. Comparison between measured (symbols) and predicted (dashed and solid lines) H2 and O2 volume fraction at four axial locations.

Figure 9. Comparison between measured (symbols) and predicted (dashed and solid lines) N2 and CH4 volume fraction at four axial locations.

Especially in the central region of three locations (x = 0.22, 0.82, and 1.42 m), while the volume fraction of intermediate species including H2 and CO are overestimated due to the enhanced chemical dissociation, as well as the underestimated entrainment of the cooled product gas. In terms of the O2

volume fraction, the predicted profile qualitatively reproduces the measured profile well at all locations. However, especially around at the radial location (4.0 cm < r < 8.5 cm) in the upstream lean-mixture region (x = 0.22 m), the O2 volume fraction is overestimated mainly due to the underestimated 4376

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Figure 10. Conditional means of temperature, CO, CO2, and pdf shapes at different radial positions of an axial station (x=0.22 m).

entrainment of the cooled product gas to the hot flame zone, as well as partly because of the enhanced chemical dissociation. In terms of the N2 volume fraction, the predicted radial profiles reproduce the corresponding measurements relatively well at all locations. In order to investigate the overestimated temperature zone around at the upstream lean-mixture location (x=0.22 m), the conditional means for temperature CO and CO2 volume fractions are illustrated in Figure 10, for three different radial positions (r=2.5, 5.3, and 20 cm) of the same axial location, x=0.22 m. The presumed pdfs of the mixture fraction are also displayed to show the mixing states at respective radial positions. Three radial positions represent three characteristic reaction zones: the main reaction zone between fresh fuel and oxygen stream, the lean-mixture high-temperature zone between recirculated hot-flue gas and fresh oxygen stream, and the recirculating postflame zone. The mixing characteristics of the three distinct reaction zones are clearly distinguished by the pdf shapes in Figure 10. From the pdf profile in the main reaction zone (r=2.5 cm), intensive mixing exists between the fresh fuel stream and the fresh oxygen stream. At this location, the conditional profiles of temperature, CO and CO2 species show the conventional flame structure of oxy-fuel combustion. With regard to the hot-flue gas recirculation zone (r=20 cm), the mixing state is almost approaching the stoichiometric condition that corresponds to the overall mixture fraction determined by inlet conditions. Because of the convective and strongly radiative heat transfers, the conditional temperature profiles are drastically cooled down. The conditional CO and CO2 profiles show the almost terminated dissociation processes in this relatively low-temperature zone (around 1840 K). As previously discussed, the lean-mixture hightemperature zone could be explained using the conditional profiles in more detail. First, the pdf shape at r = 5.3 cm confirms the existence of mixing between the entrained cooled products (ξ~P = 0.2, TP = 1,840 K) and the lean mixture stream. This mixing process in the turbulent nonpremixed flame field can surely create the high-temperature zone at the upstream lean-mixture location (x=0.22 m).

(2) In the upstream region (x = 0.22 m), the predicted profile of axial velocity has a good conformity with the measured one. However, at the downstream locations, the spreading rate of the fuel jet was somewhat underestimated. This discrepancy may be attributed mainly to defects of the modified k-ε model and also to the inlet boundary conditions. (3) In terms of the temperature distribution, the overall qualitative agreement between predictions and measurements are reasonably good. However, around at the radial location (4.0 cm