Energy Fuels 2010, 24, 6275–6282 Published on Web 11/18/2010
: DOI:10.1021/ef101211p
New Weighted Sum of Gray Gases Model Applicable to Computational Fluid Dynamics (CFD) Modeling of Oxy-Fuel Combustion: Derivation, Validation, and Implementation Chungen Yin,* Lars C. R. Johansen, Lasse A. Rosendahl, and Søren K. Kær Department of Energy Technology, Aalborg University, 9220 Aalborg East, Denmark Received September 7, 2010. Revised Manuscript Received October 28, 2010
Radiation is the principal mode of heat transfer in furnaces. Models for gaseous radiative properties have been well-established for air combustion. However, there is uncertainty regarding their applicability to oxy-fuel conditions. In this paper, a new and complete set of weighted sum of gray gases model (WSGGM) is derived, which is applicable to computational fluid dynamics (CFD) modeling of both air-fuel and oxy-fuel combustion. First, a computer code is developed to evaluate the emissivity of any gas mixture at any condition using the exponential wide band model (EWBM), and the calculated results are validated in detail against data in the literature. Then, the validated code is used to generate emissivity databases for representative air- and oxy-firing conditions, for each of which a refined WSGGM with new parameters is derived. The practical way to implement the model to CFD simulations of combustion systems is given. Finally, as a demonstration, the new model is implemented to CFD modeling of two furnaces of very different beam lengths. The CFD results are compared to those based on the widely used WSGGM in the literature, from which some useful guidelines on oxy-fuel modeling are recommended.
lot of concerns. For instance, two approaches were identified in modeling oxy-fuel gas radiation:10 the modified weighted sum of gray gases model (WSGGM) and implementation of more detailed exponential wide band model (EWBM). The wide band correlated-κ model was used to evaluate the radiative source and wall heat flux under oxy-fuel conditions, and it was concluded that the optimized multiple gases formulation of the model using three κ levels was a good compromise concerning accuracy and efficiency.11 Different radiation models (e.g., WSGGM and spectral line-based WSGGM) were tested, in which statistical narrow band models were used as a reference. The banded WSGGM with new coefficients was recommended for CFD applications when the radiative source term had a significant influence and reasonable estimates of wall fluxes were required.12 A non-gray WSGGM was developed for three gas ratios. The results from the model with four non-gray bands were reported to be close to the spectralline-based WSGGM results for all of the cases examined.13 This paper is aimed to derive a new, complete, and accurate WSGGM applicable to all combustion conditions and to demonstrate its implementation to CFD. First, the same as the currently most widely used WSGGM derived by Smith et al.14 for air-fuel combustion, the EWBM is used as the reference model. A computer code is developed for this
1. Introduction As one of the promising CO2 capture and storage technologies, oxy-fuel combustion for heat and power generation is gaining increasing interest worldwide. However, combustion under oxy-fuel conditions is fundamentally different from air combustion, which presents new challenges. Just as reviewed in refs 1-5, some of the key research gaps have been identified and highlighted, e.g., recycle rate and oxygen concentration, burner aerodynamics and flame characterization, NOx emissions, sulfur chemistry, deposition and corrosion, radiation heat transfer, and computational fluid dynamics (CFD) modeling. Oxy-fuel conditions strongly promote radiative heat transfer, as a result of the much higher levels of CO2, H2O, and in-flame soot as well as the different CO2/H2O ratio compared to air combustion.6-9 Modeling of oxy-fuel gas radiation gains a *To whom correspondence should be addressed. Telephone: þ4530622577. Fax: þ45-98151411. E-mail:
[email protected]. (1) Buhre, B. J. P.; Elliott, L. K.; Sheng, C. D.; Gupta, R. P.; Wall, T. F. Prog. Energy Combust. Sci. 2005, 31, 283–307. (2) Tan, R.; Corragio, G.; Santos, S.; Spliethoff, H. Oxy-Coal Combustion with Flue Gas Recycle for the Power Generation Industry: A Literature Review, IFRF Doc G 23/y/1, Powerflam Project; International Flame Research Foundation (IFRF): Velsen Noord, The Netherlands, 2005. (3) Wall, T. F. Proc. Combust. Inst. 2007, 31, 31–47. (4) Figueroa, J. D.; Fout, T.; Plasynski, S.; McIlvried, H.; Srivastava, R. D. Int. J. Greenhouse Gas Control 2008, 2, 9–20. (5) Toftegaard, M. B.; Brix, J.; Jensen, P. A.; Glarborg, P.; Jensen, A. D. Prog. Energy Combust. Sci. 2010, 36, 581–625. (6) Wang, L.; Endrud, N. E.; Turns, S. R.; D’Agostini, M. D.; Slavejkov, A. G. Combust. Sci. Technol. 2002, 174, 45–72. (7) Andersson, K.; Johnsson, F. Fuel 2007, 86, 656–668. (8) Andersson, K.; Johansson, R.; Johnsson, F.; Leckner, B. Energy Fuels 2008, 22, 1535–1541. (9) Wall, T.; Liu, Y.; Spero, C.; Elliott, L.; Khare, S.; Rathnam, R.; Zeenathal, F.; Moghtaderi, B.; Buhre, B.; Sheng, C.; Gupta, R.; Yamada, T.; Makino, K.; Yu, J. Chem. Eng. Res. Des. 2009, 87, 1003–1016. r 2010 American Chemical Society
(10) Becher, V.; Spliethoff, H. Spectral radiation measurements on oxy-fuel natural gas flames and flue gases: Comparison of air and oxy-fuel radiation. Proceedings of 1st Oxy-Fuel Combustion Conference; Cottbus, Germany, 2009. (11) Str€ ohle, J.; Epple, B. Spectral modeling of radiative heat transfer in oxy-coal combustion. Proceedings of 1st Oxy-Fuel Combustion Conference; Cottbus, Germany, 2009. (12) Johansson, R.; Andersson, K.; Leckner, B.; Thunman, H. Int. J. Heat Mass Transfer 2010, 53, 220–230. (13) Krishnamoorthy, G.; Sami, M.; Orsino, S.; Perera, A.; Shahnam, M.; Huckaby, E. D. Int. J. Comput. Fluid Dyn. 2010, 24, 69–82. (14) Smith, T. F.; Shen, Z. F.; Friedman, J. N. J. Heat Transfer 1982, 104, 602–608.
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reference model, and the calculation results are validated in detail against data in the literature. Then, the code is used to generate the emissivity databases for a number of representative air-fuel and oxy-fuel conditions, for each of which a refined WSGGM with new parameters is derived. The new WSGGM is compared to the Smith et al. WSGGM in terms of the evaluated emissivity and absorption coefficient under oxy-fuel conditions. The two WSGGMs are found to make a remarkable difference when the beam lengths are large, while the difference is negligible when the beam lengths are small. From this, one could expect that the new WSGGM will make a noticeable difference from the Smith et al. WSGGM in CFD results when applied to large-scale oxyfuel combustion modeling, because radiation heat transfer (one of the most important sources in the energy equation) is proportional to the absorption coefficient. One may also expect that the two WSGGMs will produce very similar CFD results when applied to small-scale oxy-fuel combustion modeling. Finally, the implementation of the new WSGGM is demonstrated. One is CFD modeling of a 0.8 MW oxy-natural gas flame furnace, and the other is CFD evaluation of oxy-fuel firing with dry flue gas recycle in a 609 MW utility boiler. The CFD results are compared to those based on the Smith et al. WSGGM, which verifies the above expectations.
Figure 1. Band shapes for the EWBM.
of Ri,j, ωi,j, and βi,j as a function of the temperature. The analytical expressions for Ri,j, ωi,j, and βi,j, the detailed wide band model correlation parameters for various participating gases, and the special bands for different gases can be found in refs 16-18. 8 > ð1Þ with an upper limit head at ηU, i, j : > (R > > i, j - ðηU, i, j - ηÞ=ωi, j > e for η < ηU, i, j > > > ¼ ðS=dÞ ω i, j > η, i, j > > 0 for η > ηU, i, j > > > < ð2Þ symmetrical band with center at ηC, i, j : Ri, j - 2jη - ηC, i, j j=ωi, j ð3Þ ðS=dÞη, i, j ¼ e > > ωi , j > > > > ð3Þ with an lower limit head at η > L, i, j : > (R > i, j - ðη - ηL, i, j Þ=ωi, j > > e for η > ηL, i, j > > > ðS=dÞη, i, j ¼ ωi, j : 0 for η < ηL, i, j
2. New WSGGM: Derivation and Validation 2.1. EWBM: Calculation Procedure and Code Validation. A computer code is developed to calculate the total emissivity of any gas mixture at any condition using the EWBM. The required input parameters are gas temperature (Tg) total gas pressure (PT) mean beam length or path length (L) and molar fraction of different species in the gas mixture (xi). In the EWBM,15,16 eq 1 is used to calculate the spectral absorptivity of a homogeneous gas path of length L for species i and band j. In this equation, (S/d)i,j denotes the mean line intensity to line spacing ratio, Fi is the density of gas species i, βi,j represents π times the mean line width to spacing ratio at 1 atm total pressure, and Pe,i is the dimensionless equivalent broadening pressure for species i. 0 1 B B - ðS=dÞ F L C C B C i, j i Rη, i, j ¼ 1 - expBsffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiC B C ðS=dÞ F L i, j i A @ 1þ βi, j Pe, i
Here, only the stepwise procedure using the EWBM to evaluate the total emissivity is given. (1) For each gas i, calculate the mass-path length product, χi = FiL. (2) For band j of gas i, calculate the parameters Pe,i,j, Ri,j, ωi,j, and βi,j. (3) R For band j of gas i, calculate the total band absorptance, Ai,j ηL,i,jηU,i,jRη,i,jdη. (4) For band j of gas i, calculate the band transmissivity, τi,j, and evaluate the upper and lower limits of each band, ηU,i,j and ηL,i,j. (5) When all of the band limits are calculated, sort in blocks and arrange in increasing order, with the lower limit of block k þ 1 being the same as the upper limit of block k. (6) Comparing whether the limits of a given block belongs to none, one, or several absorption bands, compute the block transmissivity as the product of the band transmissivity to which the block belongs by τb = τ1 τ2 etc. (7) Multiply each block emissivity (1 - τb) by the fraction of blackbody radiation in the block limits and sum over all of the blocks. The result of this summation gives the total emissivity, ε. A computer code in Cþþ is developed to evaluate the emissivity of any gas mixture at any condition using the EWBM. In this study, the computer code is validated against the example given in ref 19. Different from our work, the calculation in ref 19 was based on simplified or approximate expressions, which were also well-documented in ref 20 and were reported to “produce surprisingly accurate results”. The validation shows that almost all of the mid-results are precisely the same, and the total emissivity is 0.167 257 in our study versus 0.167 253 in ref 19 for a given gas mixture. The gas mixture and step-by-step calculation results of the EWBM computer code are given in detail in Table S1 in the Supporting Information.
ð1Þ
For overlapping bands, the transmissivity τη = 1 - Rη is nearly the product of the transmissivities of each band. Rη, mix ¼ 1 -
M Y N Y
ð1 - Rη, i, j Þ
ð2Þ
i¼1 j ¼1
The product is over all bands j of all species i. Because it is known from quantum mechanics that the line strength decreases exponentially in the band wings far away from the band center, a wide band model may then be used to prescribe how (S/d)i,j and βi,j vary with wavenumber η. In the EWBM, three crude band shapes are allowed, as sketched in Figure 1. For the three shapes, (S/d)i,j can be evaluated by eq 3, where Ri,j and ωi,j are the integrated band intensity and bandwidth parameter, respectively. Then, the EWBM is simply a prescription
(17) Siegel, R.; Howell, J. Thermal Radiation Heat Transfer, 4th ed.; Taylor and Francis Group: Abingdon, U.K., 2002. (18) Modest, M. F. Radiative Heat Transfer, 2nd ed.; Academic Press: New York, 2003. (19) Lallemant, N.; Weber, R. Radiative Property Models for Computing Non-sooty Natural Gas Flames, IFRF Doc G 08/y/2; International Flame Research Foundation (IFRF): Velsen Noord, The Netherlands, December 1993. (20) Lallemant, N.; Weber, R. Int. J. Heat Mass Transfer 1996, 39, 3273–3286.
(15) Edwards, D. K.; Menard, W. A. Appl. Opt. 1964, 3, 621–625. (16) Edwards, D. K.; Balakrishnan, A. Int. J. Heat Mass Transfer 1973, 16, 25–40.
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condition), the emissivity plots evaluated by the two WSGGMs show the most remarkable difference. The relative error, 100(εnew-εSmith)/εSmith, is over 50% for a beam length of 0.8 m and over 100% for a beam length of 25 m. Here, εnew and εSmith denote the total emissivity evaluated by the new and Smith et al. WSGGMs, respectively. When Pw/Pc equals 1 (i.e., the wet flue gas recycling condition) or 2 (i.e., without recycling), the two WSGGMs show remarkable difference only for large beam lengths (beyond about 5-10 m, depending upon the gas composition). Figure 3 shows the evaluated emissivity as a function of the gas temperature for different oxy-fuel conditions: Pw/Pc = 0.125, 1, and 2. In all of these cases, the total pressure is 1 atm, the partial pressures of H2O and CO2 sum up to 1 atm, and the domain-based beam length equals L = 3.6(Vdomain/Adomain) = 40 m. The mean relative error, 100(εnew - εSmith)/εSmith, is 129, 22, and 20% over the temperature range of 500-3000 K for the three ratios Pw/Pc = 0.125, 1, and 2, respectively. In summary, in terms of the evaluated emissivity (and also absorption coefficient), the new WSGGM shows the most remarkable difference from the Smith et al. WSGGM for oxy-fuel combustion with dry flue gas recycling; a significant difference can be observed even at small beam lengths. For other oxy-fuel conditions, the two WSGGMs show a significant difference only when the beam lengths are over a few meters. As a result, one could expect that the implementation of the new WSGGM in CFD modeling of lab-scale oxy-fuel test rigs may not show a clear difference from the Smith et al. WSGGM. However, when the new WSGGM is implemented to CFD modeling of large-scale oxy-fuel combustion, it is expected to produce a noticeable difference from the Smith et al. WSGGM. 3.2. Demonstrations. As mentioned earlier, oxy-fuel combustion is fundamentally different from air-fuel combustion. As a result, a reliable CFD simulation of oxy-fuel combustion has to properly account for the different combustion chemistry, heat transfer, and mixing under oxy-fuel conditions, besides all of those that need to be taken care of in traditional air-fuel combustion modeling. Some useful efforts have been successfully made to CFD analyses of oxy-fuel processes,13,21-24 which focus on different aspects, e.g., gas-phase combustion mechanism and mixing. In this paper, the purpose of the CFD simulations is mainly to demonstrate the implementation of the new WSGGM in oxy-fuel combustion modeling and partly to verify the expectations derived from the comparison in the evaluated emissivity plots. In this study, two furnaces are modeled. One is a real 0.8 MW oxy-natural gas flame furnace. The other is a 609 MW air-fuel utility boiler but assumed to be operating under oxy-fuel conditions with dry flue gas recycling. The former has a domainbased beam length of about 0.8 m, while the latter has a beam length of about 10.6 m. For the comparison to make sense, one has to be aware of two key issues here. One is that modeling of radiation heat transfer in combustion systems is very complicated. There are two key issues, i.e., how to calculate radiation intensity at different locations along different directions from RTEs and how to evaluate radiation properties at different locations. For the first issue,
2.2. New WSGGM and Its Implementation to CFD. The validated EWBM code is used to generate the emissivity databases for representative air-fuel and oxy-fuel conditions (i.e., different partial pressures of CO2 and H2O, Pc and Pw), in all of which the beam length (L) and temperature (Tg) are in the range of 0.001-60 m and 500-3000 K, respectively. The partial-pressure ratio, beam length, and temperature cover the entire range of combustion systems in power industries. For each of the representative conditions, the emissivity database is a 146 101 matrix: 146 values for (Pw þ Pc)L times 101 data points for Tg. Then, optimization techniques are used to derive new parameters for the refined WSGGM (eq 4). In the refined model, the gas temperature is normalized by a reference temperature (1200 K), which largely simplifies the optimization procedure and greatly improves the accuracy of the model parameters. It has to be mentioned that the i, j, I, and J in eq 4 are just data-fitting parameters and have nothing to do with the jth band of ith species in the EWBM. Table 1 only lists the new WSGGM parameters (ki and bε,i,j) for the representative oxy-fuel conditions. ε ¼
I X
aε, i ðTg Þð1 - e- ki PL Þ
ð4Þ
i¼0
8 J X > Tg j - 1 > > bε, i, j i ¼ 1, :::, I aε, i > 0 > aε, i ðTÞ ¼ > Tref > > j¼1 < I ¼ 4, J ¼ 4, Tref ¼ 1200 ðin units of kelvinÞ for a better estimate I X > > > k0 ¼ 0 : represents windows in the spectrum; aε, 0 ¼ 1 aε, i > 0 > > > > i¼1 : P : sum of the partial pressures of all of the participating gases ðatmÞ
Because the new WSGGM consists of a number of different conditions and Pw, Pc, and Pw/Pc are never constant throughout any real combustion system, how to implement the new model to CFD modeling might be a practical problem. Table 2 shows the way used in this paper to implement the new WSGGM to CFD modeling of oxy-fuel combustion. Implementing the new model in a non-gray calculation by solving one set of radiative transfer equations (RTEs) for each of the four gray gases or bands is expected to improve CFD results of oxy-fuel combustion. The air-fuel counterpart of the new model, whose parameters are not completely given here, can be implemented to CFD in a similar way.
3. Results and Discussion 3.1. Comparison in the Emissivity Evaluated by Different Models under Oxy-Fuel Conditions. The following different models are compared when they are used to evaluate gaseous radiative properties under typical oxy-fuel conditions: (1) the Smith et al. WSGGM (three gray gases plus one clear gas) originally proposed for air-fuel combustion,14 which has been very widely and successfully used in CFD, (2) the EWBM, i.e., the reference model used in both ref 14 and this work (As a test, this model has been implemented directly to CFD in this study. It is found to significantly slow CFD simulations. Meanwhile, it makes no difference in CFD results compared to the new WSGGM), and (3) the new WSGGM (four gray gases plus one clear gas), i.e., eq 4 with parameters listed in Table 1 (Here, it has to be mentioned that the new WSGGM is a general model applicable to all firing conditions. The air-fuel counterpart of the new model is not completely given here). Figure 2 shows the emissivity plots as a function of the beam length at different oxy-fuel conditions (i.e., Pw/Pc = 0.125, 1, and 2). In the three cases, the total pressure is 1 atm, the partial pressures of H2O and CO2 sum up to 1 atm, and the gas temperature is 1750 K. Overall, a significant difference can be observed in the emissivity plots evaluated by the two WSGGMs, and the difference increases with the beam length. When Pw/Pc equals 0.125 (i.e., the dry flue gas recycling
(21) Chui, E. H.; Douglas, M. A.; Tan, Y. Fuel 2003, 82, 1201–1210. (22) Andersen, J.; Rasmussen, C. L.; Giselsson, T.; Glarborg, P. Energy Fuels 2009, 23, 1379–1389. (23) Kim, G.; Kim, Y.; Joo, Y. J. Energy Fuels 2009, 23, 4370–4377. (24) Cao, H.; Sun, S.; Liu, Y.; Wall, T. F. Energy Fuels 2010, 24, 131–135.
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Table 1. New Parameters for the WSGGM, Applicable to Oxy-Fuel Flames band i
ki
1 2 3 4
0.009422 0.415646 11.617018 319.911168
Pw f 0 atm; Pc f 0 atm 0.778969 -1.342848 -0.011449 0.343754 -0.007627 0.242233 0.080082 -0.049280
0.964858 -0.234886 -0.173738 0.001861
-0.195747 0.044008 0.033868 0.002232
1 2 3 4
0.256738 3.108033 52.585782 440.845718
Pw = 0.1 atm; Pc = 0.1 atm 0.492304 -0.433789 0.082686 0.486294 0.144385 -0.083662 0.079515 -0.110361
0.279329 -0.369752 0.002003 0.051379
-0.057770 0.070509 0.003902 -0.007983
1 2 3 4
0.132242 14.660767 1.750654 165.763926
Pw = 0.3 atm; Pc = 0.1 atm 0.478371 -0.608643 0.101065 0.204118 0.185155 0.299794 0.191665 -0.277448
0.475098 -0.202202 -0.240346 0.133514
-0.109044 0.042771 0.046968 -0.021280
1 2 3 4
0.051237 0.688383 13.763205 289.841885
1 2 3 4
0.052694 0.752776 11.543306 252.938841
Pw/Pc = 1:4; Pw þ Pc = 1 atm 0.486247 -0.644137 0.213959 0.306543 0.181991 -0.020460 0.106180 -0.096088
0.485654 -0.264417 -0.053791 0.028114
-0.107808 0.051889 0.015058 -0.002443
1 2 3 4
0.052378 0.712283 8.067637 195.892573
Pw/Pc = 1:2; Pw þ Pc = 1 atm 0.383225 -0.510937 0.251481 0.161562 0.208239 0.070697 0.147259 -0.156339
0.442201 -0.150405 -0.135668 0.057698
-0.106398 0.028982 0.032090 -0.007266
1 2 3 4
0.051639 0.617739 6.051770 150.875915
Pw/Pc = 3:4; Pw þ Pc = 1 atm 0.255953 -0.276222 0.340392 -0.126902 0.160253 0.289548 0.201452 -0.233937
0.311285 0.051357 -0.284144 0.095159
-0.084903 -0.010259 0.060344 -0.013302
1 2 3 4
0.051487 0.571797 5.398936 130.622859
Pw/Pc = 1:1; Pw þ Pc = 1 atm (corresponding to wet flue gas recycling) 0.164048 -0.087793 0.195253 0.412652 -0.339810 0.197886 0.112364 0.450929 -0.388486 0.238339 -0.288619 0.121962
-0.063573 -0.038963 0.079862 -0.017651
1 2 3 4
0.054480 0.555304 5.040174 100.372663
1 2 3 4
0.060800 5.608831 0.676040 84.540632
bε,i,1
bε,i,2
bε,i,3
Pw/Pc = 1:8; Pw þ Pc = 1 atm (corresponding to dry flue gas recycling) 0.515415 -0.618162 0.430921 0.199807 0.298581 -0.265758 0.138767 -0.001851 -0.049353 0.087511 -0.067295 0.013489
Pw/Pc = 2:1; Pw þ Pc = 1 atm -0.002188 0.286129 0.546857 -0.714799 -0.001911 0.764177 0.317219 -0.415470
bε,i,4
-0.092082 0.052910 0.013012 -5.54 10-6
-0.048594 0.452812 -0.581819 0.186570
-0.016243 -0.088841 0.115069 -0.028335
Pw/Pc = 4:1; Pw þ Pc = 1 atm -0.053999 0.434975 -0.152413 -0.094953 0.952010 -0.696161 0.606525 -0.853216 0.545562 0.369661 -0.517493 0.244011 PT = 1 atm; 0.001 e L e 60 m; 0.001 e PL e 60 atm m; 500 e Tg e 3000 K
0.005094 0.136316 -0.107328 -0.038451
there are a few original works/models, e.g., the discrete transfer model25 and the discrete ordinates model.26 Combustion environments, e.g., air-fuel versus oxy-fuel, make no difference in either the RTEs themselves or the way to solve them; they will only affect the gaseous radiative properties. One needs to stick to the same radiation model when comparing different WSGGMs to reliably examine their effect. The other is the way employed in Fluent for radiation modeling because this commercial package is used in the
CFD demonstrations. When the Smith et al. WSGGM (three gray gases plus one clear gas) is used in Fluent, the combustion gas mixture is still treated as one gray medium. Therefore, instead of solving one set of RTEs for each of the gray gases, only one set of RTEs is actually solved for the gray medium. The total emissivity, ε, is evaluated using the Smith et al. WSGGM, from which the effective absorption coefficient, ka, is calculated as ka ¼ - 1=L lnð1 - εÞ ðm- 1 Þ
(25) Lockwood, F. C.; Rizvi, S. M. A.; Shah, N. G. Proc. Inst. Mech. Eng., Part C 1986, 200, 79–87. (26) Raithby, G. D.; Chui, E. H. J. Heat Transfer 1990, 112, 415–423.
ð5Þ
In the same way, the new WSGGM is implemented in Fluent via a user-defined function. 6278
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Table 2. Way To Implement the Oxy-Fuel Part of the New Model to CFD if (Pw þ Pc e 0.1) else if (Pw þ Pc e 0.3) else if (Pw þ Pc e 0.5) else if (Pw e 0.2Pc)
use data set for use data set for use data set for
Pw þ Pc = 0:0 Pw/Pc = 0.1:0.1 Pw/Pc = 0.3:0.1
use data set for
else if (Pw e 0.4Pc) else if (Pw e 0.6Pc) else if (Pw e 0.9Pc) else if (Pw e 1.1Pc)
use data set for use data set for use data set for use data set for
else if (Pw e 2.5Pc) else
use data set for use data set for
Pw/Pc = 0.125 (dry flue gas recycling) Pw/Pc = 0.25 Pw/Pc = 0.50 Pw/Pc = 0.75 Pw/Pc = 1 (wet flue gas recycling) Pw/Pc = 2 Pw/Pc = 4
Figure 3. Emissivity versus the gas temperature at Pw/Pc = 0.125, 1, and 2 for a constant beam length of 40 m.
plotted for reference. The purpose is not to validate the CFD results with the experiments. Instead, it is mainly to show whether or not the two WSGGMs will make a noticeable difference in the CFD results when applied to the modeling of this small-scale oxy-fuel furnace. Moreover, one needs to be aware of the accuracy of the experimental data when trying to compare the CFD results to the experimental data. For instance, the temperatures were measured by a watercooled suction pyrometer, which was then calibrated with coherent anti-Stokes Raman spectroscopy temperature measurements. However, extrapolating the calibration curve for Figure 2. Emissivity versus the beam length at Pw/Pc = 0.125, 1, and 2 for a constant temperature of 1750 K.
(27) Lallemant, N.; Breussin, F.; Weber, R.; Ekman, T.; Dugue, J.; Samaniego, J. M.; Charon, O.; van den Hoogen, A. J.; van der Bemt, J.; Fujisaki, W.; Imanari, T.; Nakamura, T.; Iino, K. J. Energy Inst. 2000, 73, 169–182. (28) Breussin, F.; Lallemant, N.; Weber, R. Combust. Sci. Technol. 2000, 160, 369–397. (29) Lallemant, N.; Dugue, J.; Weber, R. Analysis of the Experimental Data Collected during the OXYFLAM-1 and OXYFLAM-2 Experiments (Phase 1: 1995-1996), IFRF Doc F 85/y/4; International Flame Research Foundation (IFRF): Velsen Noord, The Netherlands, May 1997.
3.2.1. Modeling of the 0.8 MW Oxy-Natural Gas Flame Furnace. This oxy-fuel furnace is used for the demonstration mainly because all of the details (e.g., geometrical, operational, and experimental data) are available, which can be seen in refs 27 and 28. The experimental data will also be 6279
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Table 3. Summary of the Settings of the Four Computational Cases sub-models in common
chemistry
gaseous radiative properties
case 1-1 JL four-step (refined) case 1-2 standard k-ε for turbulence, discrete ordinates for radiation, EDC for turbulence-chemistry interaction, domain-based beam length of 0.8 m, case 2-1 WD two-step (refined) a mesh having 608864 hexahedral cells of high quality case 2-2
WSGGM of Smith et al.14 new WSGGM (Table 1) WSGGM of Smith et al.14 new WSGGM (Table 1)
Table 4. Refined Multi-step CH4 Global Combustion Mechanisms (Kinetic Rate Data in Units of m, s, kmol, J, and K) number
reactions
rate equations (kmol m-3 s-1)
A
1 2 3
Refined WD Two-Step Combustion Mechanism under Oxy-Fuel Conditions (Revised WD) (d[CH4]/dt) = ATbe-E/(RT)[CH4]0.7[O2]0.8 5.03 1011 CH4 þ 1.5O2 f CO þ 2H2O CO þ 0.5O2 f CO2 (d[CO]/dt) = ATbe-E/(RT)[CO][O2]0.25[H2O]0.5 2.24 106 CO2 f CO þ 0.5O2 (d[CO2]/dt) = ATbe-E/(RT)[CO2][H2O]0.5[O2]-0.25 1.10 1013
1 2 3 4
CH4 þ 0.5O2 f CO þ 2H2 CH4 þ H2O f CO þ 3H2 H2 þ 0.5O2 T H2O CO þ H2O T CO2 þ H2
Refined JL Four-Step Combustion Mechanism (Revised JL) (d[CH4]/dt) = ATbe-E/(RT)[CH4]0.5[O2]1.25 (d[CH4]/dt) = ATbe-E/(RT)[CH4][H2O] (d[H2]/dt) = ATbe-E/(RT)[H2][O2]0.5 (forward) (d[CO]/dt) = ATbe-E/(RT)[CO][H2O] (forward)
4.4 1011 3.0 108 5.69 1011 2.75 109
b
E
0 0 -0.97
2.00 108 4.18 107 3.28 108
0 0 0 0
1.26 108 1.26 108 1.465 108 8.36 107
Figure 4. Absorption coefficient and radiation source term at 142 cm downstream of the burner.
computational cost, the use of the different WSGGMs does not make a remarkable difference based on the mesh of 608 864 cells. The CFD results are compared to the available experimental data at different axial distances, which shows consistently, relatively good agreement with the experimental data. Here, only the results at 142 cm downstream of the burner are plotted, because the radiation effects are believed to be progressively apparent in the far downstream locations. Figure 4 plots the radial profiles of absorption coefficients and the radiation source term, -3qBrad(rB) kBa(rB)(G(rB) 4σTg4(rB)), where G(rB) and σ represent the incident radiation at the current location and the Stefan-Boltzmann constant. Overall, the absorption coefficients calculated using the new WSGGM are about ∼5% higher than those evaluated by the Smith et al. WSGGM. This can also be expected from the emissivity-beam length plots for Pw/Pc = 2 (see Figure 2). The radiation source term shows a similar trend as the absorption coefficient. The new WSGGM makes little difference from the Smith et al. WSGGM in the calculated radiation source. As a result, one may expect that the CFD results based on the different WSGGMs will be close to each other for this 0.8 MW oxy-natural gas flame furnace. The predicted gas temperature and species at the same axial location downstream of the burner are plotted in Figure 5, in which the experimental data are also plotted. Figure 5 verifies very well the expectation that the two WSGGMs make negligible difference in the CFD results for this
use at higher temperatures (over 2200 K) likely introduced errors in the temperature.29,30 The measured H2 concentrations were also believed to a few percentages to overestimate their actual values because of the recombination reactions occurring in the quenching section of the gas-sampling probe.29,30 With these experimental data as reference, the mixing and chemistry may be thoroughly examined in CFD simulations of this oxy-flame. Table 3 summarizes the sub-models used in the four simulations whose results are presented in this paper. Besides the two different WSGGMs, two different combustion mechanisms are also used. One is the two-step mechanism of Westbrook and Dryer (WD),31 refined for use in CFD modeling under oxy-fuel conditions by Andersen et al.22 The other is the four-step mechanism of Jones and Lindstedt (JL),32 refined by Kim et al.33 using the original H2 oxidation model.34 The refined schemes are given in details in Table 4. In terms of the (30) Bollettini, U.; Breussin, F.; Lallemant, N.; Weber, R. Mathematical Modeling of Oxy-Natural Gas Flames, IFRF Doc F 85/y/6; International Flame Research Foundation (IFRF): Velsen Noord, The Netherlands, May 1997. (31) Westbrook, C. K.; Dryer, F. L. Combust. Sci. Technol. 1981, 27, 31–43. (32) Jones, W. P.; Lindstedt, R. P. Combust. Flame 1988, 73, 233–249. (33) Kim, J. P.; Schnell, U.; Scheffknecht, G. Combust. Sci. Technol. 2008, 180, 565–92. (34) Marinov, N. M.; Westbrook, C. K.; Pitz, W. J. Detailed and global chemical kinetics model for hydrogen. In Transport Phenomena in Combustion; Chan, S. H., Ed.; Taylor and Francis Group: Abingdon, U.K., 1996.
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Figure 5. CFD-predicted gas temperature and species versus the measured data at 142 cm downstream of the burner.
oxy-fuel flame furnace, whose domain-based beam length is about 0.8 m. Another finding from Figure 5 is that both the refined WD two-step and JL four-step mechanisms predict the gas temperature and species concentrations quite well and the refined JL four-step mechanism also reasonably predicts the H2 level. Comparatively, the original WD two-step combined with the eddy dissipation model, whose results are not given here, largely underpredicts the CO level and overpredicts the flame peak temperatures. The temperature peak in this furnace is found to be a little higher than 3000 K, i.e., the temperature upper limit of the emissivity databases from which the new WSGGM is derived. This has no influence at all on either the conclusions of this study or the applicability of the new WSGGM. First, the two WSGGMs do not really make a noticeable difference in the CFD results of this oxy-fuel test rig, which can be observed from the CFD results. Actually, a constant gas absorption coefficient throughout the whole combustion chamber, 0.3 m-1, was used in the simulation of this flame in ref 28. Second, in large-scale oxy-fuel furnaces with flue gas recycling, the temperature peaks are certainly below 3000 K. Therefore, the new WSGGM would be completely applicable to industrial oxy-fuel furnaces, without compromising the data-fitting accuracy by extending the emissivity databases to unnecessarily higher temperatures. 3.2.2. Modeling of the 609 MW Utility Boiler. The tangentially fired 609 MW utility boiler, as sketched in Figure 6, is a conventional air-fuel boiler in operation. The details about this boiler can be found in refs 35 and 36. In this demonstration,
the fuel to this boiler is changed to natural gas of equivalent heat input and the combustion air is changed to a mixture of O2 and CO2 (27 wt % O2 and 73 wt % CO2). This boiler is selected here mainly to demonstrate whether or not the new WSGGM will make a noticeable difference with the Smith et al. WSGGM in CFD results when applied to large-scale oxy-fuel combustion modeling. Two simulations are carried out. The only difference between them is that the new WSGGM is used in one case and the Smith et al. WSGGM is used in another. In both cases, the refined WD global combustion mechanism is used. All of the other settings (e.g., mesh and sub-models) are the same as the works in refs 35 and 36. Figure 6 plots the predicted absorption coefficient, radiation source term, and gas temperature along the vertical furnace centerline (as indicated in the boiler), using the different WSGGMs for gaseous radiative properties. The two WSGGMs are found to result in a difference of about 120% in the absorption coefficient, which will produce a 120% difference in the gaseous radiative source term (using the total property models here) if all of the other parameters remain the same. If about 15% of the total heat released during oxy-natural gas combustion were to be associated with radiation, then the different WSGGMs would result in a temperature difference of about 18%. In Figure 6, a maximum temperature difference of about 200 K is observed along the vertical centerline, which is located in the far downstream locations of the main combustion zone. The temperature difference predicted in this 609 MW boiler is much more noticeable than the 0.8 MW furnace (as shown by the first demonstration), just as expected. The noticeable temperature difference in the primary combustion and burnout zones, although not as remarkable as the difference in the
(35) Yin, C.; Caillat, S.; Harion, J. L.; Baudoin, B.; Perez, E. Fuel 2002, 81, 997–1006. (36) Yin, C.; Rosendahl, L.; Condra, T. J. Fuel 2003, 82, 1127–1137.
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Figure 6. Comparison of the CFD-predicted gas temperature and species using the different WSGGMs.
far downstream locations, will certainly influence the combustion characteristics and pollutant formation. The large temperature difference in the far downstream locations will greatly affect the heat-transfer characteristics further downstream. As a result, the use of this new, complete, and accurate WSGGM would be recommended for large-scale oxy-fuel combustion modeling, which would be more beneficial if this new model is applied with non-gray calculation.
the difference may be negligible when they are applied to small-scale oxy-fuel modeling. The implementation of the new WSGGM to CFD is demonstrated via modeling of a real 0.8 MW oxy-natural gas flame furnace and a 609 MW utility boiler, assumed to be operating under oxy-fuel conditions. The demonstration results well-verify the expectations. As a byproduct of the CFD demonstration, both the refined JL four-step and refined WD two-step combustion mechanisms combined with the eddy dissipation concept are found to largely outperform the original WD two-step mechanism combined with the eddy dissipation model for oxy-fuel combustion modeling.
4. Conclusions A new, complete, and accurate WSGGM, applicable to both air-fuel and oxy-fuel combustion modeling and applicable to both gray and non-gray calculation, has been successfully derived. Equation 4 and Tables 1 and 2 show the oxy-fuel part of the new model. When used to evaluate gas emissivity under oxy-fuel conditions, the new model shows a significant difference from the currently most widely used WSGGM, in particular at large beam lengths. As a result, one may expect a noticeable difference in the predicted flow, temperature, and species fields when the two WSGGMs are implemented to CFD modeling of large-scale oxy-fuel combustion, while
Acknowledgment. This work was financially supported by Grant ForskEL 2009-1-0256, “Advanced Modeling of Oxy-Fuel Combustion of Natural Gas”. Supporting Information Available: Detailed step-by-step calculation results for a given gas mixture, using the EWBM computer code developed for this paper (Table S1). This material is available free of charge via the Internet at http:// pubs.acs.org.
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