A comparative study of gray and non-gray methods of computing gas absorption coefficients and its effect on the numberical predictions of oxy-fuel combustion

Computational Fluid Dynamics (CFD) simulations are performed to model the radiation process in natural gas fired furnaces using different gray and non-gray radiation models. Simulations of two representative furnace cases (HTAC and OXYFLAM) were performed and the computed radiative fluxes compared with measurements when available. The nearly homogeneous and isothermal conditions encountered within the furnace did not result in any significant differences in the predicted incident radiative flux profiles between the gray and non-gray models. However, differences between the gray and non-gray radiation calculations manifested itself through the temperature distributions away from the burner region.

A comparative study of gray and non-gray methods of computing gas absorption coefficients and its effect on the numerical predictions of oxy-fuel combustion Zachary Wheaton, David Stroh and Gautham Krishnamoorthy Department o f Chemical Engineering, PO Box 7101, Harrington Hall Room 323, 241 Centennial Drive, University o f North Dakota, Grand Forks, ND 58202-7101, USA Muhammad Sami ANSYS Inc., 16350 Park Ten Pl # 140,Houston, TX 77084-5159, USA Stefano Orsino ANSYS Inc., 10 Cavendish Ct., Lebanon, NH 03766, USA and Pravin Nakod ANSYS Software Pvt. Ltd.,34/2 Rajiv Gandhi Infotech Park, MIDC Hinjewadi, Pune, 411057, India ABSTRACT Computational Fluid Dynamics (CFD) simulations are performed to model the radiation process in natural gas fired furnaces using different gray and non-gray radiation models. Simulations o f two representative furnace cases (HTAC and OXYFLAM) were performed and the computed radiative fluxes compared with measurements when available. The nearly homogeneous and isothermal conditions encountered within the furnace did not result in any significant differences in the predicted incident radiative flux profiles between the gray and non-gray models. However, differences between the gray and non-gray radiation calculations manifested itself through the temperature distributions away from the burner region. 1. Introduction Oxy-fuel combustion is gaining popularity as a method to reduce the emissions o f CO2 from fossil power plants by flue gas recycling [1]. This recycling leads to high concentrations o f participating gases (CO 2 , H2 O) which, in turn, can result in significantly different gas emissivities within the boiler. This impacts the radiative transfer process and absorption of heat within the system. Several gas property calculation models have been proposed in recent years [2-4]. These are based on the weighted sum-of-gray-gases (WSGG) method where the emissivities o f gas mixtures are expressed in terms o f absorption coefficients and weighting factors. These coefficients and weight factors are obtained from a fit to total emissivity data. The WSGG method is easy to implement within the CFD framework and can be employed in either gray or non-gray radiative transfer calculations. Highly accurate non-gray calculations can be carried out employing four or five gray gases with a modest increase in computational cost particularly when the radiation calculations are performed once in several fluid iterations. These models [2-4] were suggested since the old WSGG models (eg: Smith et al. [5]) gave inaccurate results for low H2O/CO2 ratio encountered during oxy-combustion. Since, the emissivity data used for the curve fit, were generated using different radiative property models/spectroscopic databases, it is important to examine the impact o f this variation in databases on the radiation predictions in combustion simulations. Lallemant et al. [6] found that the variation in the total emissivity o f the combustion gas mixture, in a natural gas furnace, can vary significantly depending upon the property database being used. This difference may increase further in the case o f oxy-fuel combustion due to the increased levels o f CO2 and H2O. To this end, we evaluated the performance o f the proposed WSGG models in gray and non-gray radiative transfer calculations of: two natural gas furnaces, the IFRF Furnace and the HTAC Furnace. The WSGG models examined in this study are summarized in table 1. The non-gray models are denoted by the number o f gray-gases (gg) employed in their formation. Recently, a new correlation for total emissivity was developed from the narrow band model RADCAL that extended the range o f applicability o f the Perry (gray) model to cover lower H2O/CO2 ratios in the range 0 - 0.25 [2]. The H2O/CO2 intervals for the Perry (5 gg) model were set to cover the ranges encountered during: oxy-coal combustion with dry flue gas recycle (FGR) (0 0.3), coal combustion with air-firing/oxy-coal combustion with wet FGR (0.3 - 0.75) and natural gas combustion under air-firing (0.75 - w). Johansson et al. [3] proposed a set o f WSGG model coefficients that were optimized for H2O/CO2 ratios o f 0.125 and unity. The Smith (gray) model is the default modeling option in ANSYS FLUENT. The other gray and non-gray models were implemented as UserDefined Functions (UDFs). All calculations reported in this study were performed using the commercial computational fluid dynamic code ANSYS FLUENT (version. 12). The test cases examined in this study are described next. OXYFLAM Natural Gas Furnace In this study, a 0.8 MW oxy-flame furnace burning natural gas was simulated with the various gray and non-gray radiation models. The conditions o f the simulations were representative o f experiments conducted in the OXYFLAM project where measurements were carried out in the horizontal IFRF furnace No. 2. The OXYFLAM experiments were part o f a large project for combustors ranging from 1 MW to 2 MW, in size [6]. The refractory lined furnace was 3.44 m long with an internal diameter of 1.05 m. Natural-gas is introduced from a central tube o f diameter 16 mm and oxygen comes in from an outer annular region with outer and inner diameters o f 26 mm and 28 mm respectively. Considering the symmetry o f the furnace 1/4th o f the furnace geometry was simulated in a 3D domain employing periodic boundary conditions and 220,000 computational cells. The standard k-s model was employed for modeling the turbulent flow. The wall temperature and other boundary conditions are described elsewhere [6]. The non-adiabatic extension o f the equilibrium PDF model was employed in the calculations for modeling the turbulent chemistry. Here the instantaneous thermochemical state o f a fluid is related to its mixture fraction and its enthalpy. Under the assumption o f chemical equilibrium, all thermochemical scalars (species fractions, density, and temperature) are uniquely related to the mixture fraction(s) and the value o f each mass fraction, density and temperature were determined from calculated values o f mixture fraction, variance in mixture fraction and the enthalpy. An assumed shape probability distribution function (PDF) was employed to describe turbulence-chemistry interactions where the average value of the scalars is related to their instantaneous fluctuating values. In this study, the shape o f the PDF was described by the beta function. Figure 1 shows the wall incident radiative flux profiles predicted by the various models in the OXYFLAM furnace. There are no distinct variations in the predictions between the gray and non-gray calculations. For instance, the average relative variation in the radiative fluxes between the Perry (gray) and Perry non-gray (5 gg) model calculations were less than 1%. The differences between the gray and non-gray calculations are more pronounced in large geometries and when there are sharp gradients in the temperature. However, the relatively homogeneous and isothermal conditions encountered within the furnace as a result of the short flame length resulted in similar radiative flux profiles from the calculations. Furthermore, the variations in the radiative heat flux predictions among the various gray or non-gray models themselves are quite small in these fully coupled calculations. Figure 2 shows the radial temperature distributions at different axial burner distances in the OXYFLAM furnace. No significant variation among the profiles predicted by the various models is seen and a reasonable agreement with experimental data is observed away from the near burner zone. In the near burner zone,the agreement is not as good due to a coarser mesh employed in the calculations. However, since the focus of this study was on the comparison of the various radiative property models, the employed mesh resolution may be deemed as acceptable since we have often found that the mesh requirements for radiative transfer are less stringent than those employed for the fluid flow or the combustion processes. The variation in temperature among the gray and non-gray models are seen to increase downstream of the furnace at higher axial distances, with a maximum variation of 50 K observed between the Chalmers (5 gg) model and the gray models at an axial distance o f 1.42 m. At the outlet the mass weighted average temperatures in the Perry (gray) and the Perry (5 gg) calculations were determined to be 1996 K and 1958 K respectively. Figure 3 shows the radial variations in the axial velocities at various axial distances. Here no significant variation among the profiles predicted by the various models is seen at all axial distances with a reasonable agreement observed against the experimental data. With the highly radiatively participating media encountered within the furnace (the volume averaged concentrations within the furnace were determined to be: 63% H2O and 34% CO2 respectively) one may expect non-gray WSGG method to be more accurate but in this particular furnace where temperature gradients are not large and the length scales are small, the temperature distributions are nearly homogeneous and this homogeneity results in small differences between the gray and non-gray models. The H2 O/CO2 ratio is about 2 which is also within the range o f applicability o f the default Smith et al. [5] model. High Temperature Air Combustion (HTAC) Natural Gas Furnace In the H TAC technology, the fuel is oxidized in an environment that contains a large amount o f inert/flue gas. This results in temperature and species fields that are fairly hom ogeneous within the furnace. In the IFRF HTAC experiments, this w as achieved by operating the furnace with a large amount o f hot flue gas recirculation. Several papers have been published on the HTAC IFRF case and the reader is referred to these here [8, 9]. The current study focuses on investigating the effect o f using non gray radiation m odel on the temperature and incident radiative flux profiles in the furnace. The H TAC IFRF experiments were carried out in a refractory lined furnace with a 2 m square cross-section and a length o f 6.25 m. The furnace w as equipped with a 0.58 M W th burner w hich w as operated under steady state conditions. The burner consisted o f a central oxidizer jet and tw o natural gas injectors positioned 28cm away from the central jet. The com position (wet basis) o f the central oxidizer jet w as 19.5% O2, 59.1% N 2, 15% H 2O, 6.4% CO2, and it was supplied at a temperature o f 1573 K. Detailed description o f the experimental set up and measured data can be found in [7]. The numerical study em ployed a 500K computational grid to calculate flow field and temperature in one quarter o f the furnace. Similar to the O XYFLAM case above, the reactive flow w as computed using the equilibrium non premixed com bustion model. Turbulence was m odeled using the realizable k-epsilon truculence model. The radiation w as m odeled using the D iscrete Ordinates model using four different options: Perry gray m odel, Smith gray model (default option in FLUENT), Perry non-gray (5 gases) and Chalmers non-gray (5 gases). The four cases were run to com plete convergence and mass and energy balances were satisfied to a close tolerance. The temperature and species predictions are nearly identical for the 4 cases mentioned above. Figure 4 show s the incident radiation on the side wall o f the furnace. All the four m odeling option perform reasonably w ell capturing the flat incident radiation on the w alls which w as measured between 300 and 350 kW. The differences among the four m odels are very small. This is expected considering that in this case the media is fairly hom ogeneous and the ratio o f H2 O/CO2 is between 1 and 2. Figure 5 shows the molar H2 O/CO2 ratios within the furnace in the calculations performed em ploying the Perry (5 gg) model. Please note that other m odels predicted a similar profile and hence are not shown here. It is clear from the plot that m ost o f the furnace is at a ratio o f around 2 w hich is also covered by the default Smith (gray) m odeling option in A N SY S FLUENT. Figure 6 show s the temperature contours on the periodic planes inside the furnace for the Perry non gray m odel. Again, one can see that the majority o f the furnace volum e is at a uniform temperature with peak value only about 100 K above the uniform value o f around 1800 K. Similar temperature plots are obtained for the other three cases. The outlet temperature predictions were also found to be very similar am ong the various gray and non-gray m odels with a maximum difference o f about 5 -1 0 K. Conclusions Two natural gas fired furnaces are simulated using gray and non-gray models for radiation predictions. The furnace configurations were specifically chosen for the very high concentrations o f radiatively participating gases present in both them. In both furnaces, the gray and non-gray models employed in this study, resulted in identical wall radiative heat flux and exit gas temperature profiles as a result o f the nearly homogeneous and isothermal conditions within the furnaces. This indicates that high concentrations o f radiatively participating gases by themselves are not necessary to warrant the use o f non-gray radiative property models. The temperature gradients and the geometric length scale of the combustor also need to be taken into account. Furthermore, the predictions from the default model for computing the radiative properties in ANSYS FLUENT (Smith (gray)) were identical to other recently proposed models for oxy-combustion scenarios. This is expected since H2 O/CO2 ratios are within the range o f applicability o f Smith (gray) model. References [1] Buhre BJP, Elliott LK, Sheng CD, Gupta RP, Wall TF. Oxy-fuel combustion technology for coal-fired power generation. Prog Energy Combust Sci 2005; 31:283-307. [2] Krishnamoorthy G, Sami M, Orsino S, Perera A, Shahnam M, Huckaby ED. Radiation modeling in oxy-fuel combustion scenarios. Int J Comput Fluid Dyn 2010; 24:69-82. [3] Johansson R, Andersson K, Leckner B, Thunman H. Models for gaseous radiative heat transfer applied to oxy-fuel conditions in boilers. Int J Heat Mass Transf 2010; 53:220-30. [4] Yin C, Johansen LCR, Rosendahl LA, K$r SK. New weighted sum o f gray gases model applicable to computational fluid dynamics (CFD) modeling o f oxy-fuel combustion: Derivation, validation, and implementation. Energy Fuels 2010; 24:6275-82. [5] Smith TF, Shen ZF, Friedman JN. Evaluation o f coefficients for the weighted sum o f gray gases model. J Heat Transf - Trans ASME 1982; 104:602-8. [6] Lallemant, N, Sayre A, Weber R. Evaluation o f emissivity correlations for H 2 O-CO2 -N 2 /air mixture and coupling with solution methods o f the radiative transfer equation. Prog Energy Combust Sci 1996; 22:543-574. [7] Weber, R., Orsino, S., Lallemant, N. and Verlaan, AD, "Combustion o f natural gas with high temperature air and large quantities o f flue gas", Proceedings o f the Combustion Institute, Vol. 28, pp. 1315-1321, 2000. [8] Orsino, S., Weber, R. and Bollettini, U., "Numerical simulation o f com bustion o f natural gas with high-temperature air", Com bustion Science and Technology, Vol. 170, pp. 1-34, 2001. [9] Mancini, M., Weber, R. and Bollettini, U., "Predicting NO x emissions o f a burner operated in flameless oxidation mode", Proceedings o f the Combustion Institute, Vol. 28, pp.1155-1163, 2002 [10] Hottel HC, Noble JJ, Sarofim AF. Heat and mass transfer. Chapter 5. In: D.W. Green and R.H. Perry, eds. Perry's chemical engineers' handbook. 8th ed. New York: McGraw-Hill, 2007. [11] Krishnamoorthy G. A new weighted-sum-of-gray gases model for CO2-H 2O gas mixtures. Int. Comm. Heat and Mass Transfer 2010; 37:1182-1186. [12] Johansson R, Andersson K, Leckner B, Thunman H. Models for gaseous radiative heat transfer applied to oxy-fuel conditions in boilers. Int J Heat Mass Transf 2010; 53:220-30. Table 1: Summary of WSGG models examined in this study. H2O/CO2 intervals Source Model notation Radiative property employed within the database models 0 - 0.25, 0.25 - 0.67, Hottel et al. [10], Hottel charts and SNB 0.67 - 1.5, 1.5 - 2.33, Perry (gray) RADCAL [8, 9] 2.33-4,4-oo Perry non-gray Hottel charts and SNB 0 - 0.3, 0.3 - 0.75, Krishnamoorthy [110] (5 gg) RADCAL [8, 9] 0. 75-oo Johansson et al. [12] Chalmers (5 gg) EM2C SNB [11] 0 -0.125, 0.125 - oo Smith et al [5] Smith (gray) EWBM [12] 0.5 - 1.5, 1.5 - 2.5 Krishnamoorthy et al. [211] Incident radiative flux, W/m2 Axial distance, m Figure 1: The wall incident radiative flux profiles predicted by the various models in the OXYFLAM furnace. Figure 2: Radial temperature variations at different axial burner distances in the OXYFLAM furnace. Figure 3: Radial axial velocity variations at different axial burner distances in the OXYFLAM furnace. Incident radiaiton (kW/m2) Axial distance [m] Figure 4. Incident radiation flux profile along the axial direction. Figure 5. H2O/CO2 ratio on tw o periodic planes o f the furnace using Perry (5gg) model. Figure 6. Temperature contours on the periodic planes.