Weighted Sum Of Gray Gases Model Research Articles

A numerical framework for modeling evaporation and combustion of isolated, spherically-symmetric, multi-component fuel droplets

This paper presents a comprehensive numerical framework for simulating the evaporation and combustion of isolated, spherically-symmetric, multi-component fuel droplets. The framework incorporates a detailed description of chemical reactions in the gaseous phase and is capable of modeling pure evaporation, autoignition, and hot-wire ignition scenarios.The transport equations for mass, species, and energy are solved in both the liquid (droplet) and gaseous (surrounding atmosphere) phases. Diffusion in the liquid phase is described using the Stefan-Maxwell theory, while in the gaseous phase, both molecular and thermal diffusion are considered. The model also includes the thermophoretic effect for carbonaceous particles and accounts for gas radiation through various models, ranging from optically-thin approximations to more complex methods like the P1 and discrete ordinate methods. Non-gray radiative effects are handled using the Weighted-Sum-of-Gray-Gases Model (WSGGM). Liquid/gas interface conditions are evaluated by imposing flux continuity of mass and energy, along with thermodynamic equilibrium for species. Deviations from ideal thermodynamic behavior in the liquid droplet are managed by incorporating a suitable activity coefficient or by using a proper cubic equation of state. Additionally, the presence of supporting fibers is modeled using a simplified one-dimensional approach. The transport equations are solved using the method of lines, with spatial discretization performed via the finite difference method on a body-fitted grid. The resulting system of Differential-Algebraic Equations (DAEs) is then solved using a fully-coupled approach.Thanks to its generality in terms of kinetic and thermodynamic descriptions and the reduced computational time, the proposed framework offers significant potential for advancing our understanding of the complex combustion processes of multi-component liquid fuels and for enhancing the planning and execution of experiments involving isolated fuel droplets.

Finite-rate chemistry Favre-Averaged Navier-Stokes based simulation of a non-premixed SynGas/Air flame

Abstract The present paper is devoted to the study of the influence of chemical mechanisms, turbulence models and gas radiative properties models on the characteristics of a turbulent diffusion CO/H2/N2 -air flame, i.e., the so-called syngas flame in a Favre-averaged Navier-Stokes (FANS) environment. For this purpose, a transient FANS solver for combustion is used. The simulations are carried out using three distinct turbulence models, i.e., the standard k-ε (SKE), the renormalization group (RNG) k-ε, and the Shear Stress Transport (SST) models. The turbulence-chemistry interaction is modeled using the Partially Stired Reaction (PaSR) model. The chemical mechanisms used in the present study are: (i) a compact skeletal C2 mechanism, (ii) a mechanism developped by Frassoldati-Faravelli-Ranzi (FFR) containing 14 species and 33 reactions and (iii) the optimised syngas mechanism by Varga. Radiation heat transfer is handled by the P-1 method. In addition, the performances of two gas radiative properties models, i.e., the grey mean gas and the weighted-sum-of-gray-gases (WSGG) models, are assessed in radiative heat transfer modeling of the syngas flame. The predicted results reveal that the combination of the RNG turbulence model and the C2 skeletal mechanism shows the best agreement with measurements. The WSGG model used predicts results with the same level accuracy as the grey gas model in modeling of the syngas flame.

Numerical investigation of radiative transfer during oxyfuel combustion of hydrogen and hydrogen enriched natural gas in the container glass industry

The substitution of natural gas with hydrogen is one way to eliminate direct CO2 emissions. However, oxyfuel combustion of hydrogen or hydrogen enriched natural gas leads to different exhaust gas properties due to a changed composition compared to conventional combustion. In combustion simulation, the emissivity of a gas mixture is usually approximated using a Weighted Sum of Gray Gases (WSGG) model. Most of the existing WSGG models have been validated for natural gas combustion with air or oxyfuel and are therefore not applicable to hydrogen-oxyfuel combustion. CFD simulations showed, that none of the investigated WSGG models is able to predict the radiative heat transfer for all considered combustion scenarios with appropriate accuracy. In addition, in container glass manufacturing more than 95% of the heat flux to the glass surface is transferred by radiation because of the high process temperatures. Due to the changed gray gas emissivity, the high content of water vapor leads to a different emission spectrum of the exhaust gas. The influence of the changed emission spectrum on radiative heat transfer and the penetration depth of radiation in the glass melt is investigated using a simulation model of a pilot plant and non-gray modelling of the radiation transport. The CFD simulations show slightly enhanced radiative heat transfer to the glass and a slightly deeper penetration depth especially for wavelength below 2.2 μm for hydrogen-oxyfuel combustion.

New gas radiation model of high accuracy based on the principle of weighted sum of gray gases

The standard WSGG (Weighted Sum of Gray Gases) model is very fast and simple but can lead to relatively high discrepancies in the computation of the radiative heat transfer. A new model of high accuracy relying on the principle of the WSGG model is proposed. Contrary to the standard WSGG model, the pressure absorption coefficient depends here weakly on the temperature while the weighting factor is not predefined by a mathematical function. Mathematical properties on the model parameters are obtained and we show that all the model parameters can be determined from only one of them. This last is reconstructed with an efficient inverse algorithm from the total radiative heat source data computed with the LBL method using HITEMP 2010. We propose an efficient method to find good initial guesses (of the model parameters) leading to the best accuracy of the model. It is shown, on 17 selected 1D cases representative of the combustion of CO2H2O mixtures, that the maximum relative errors on the radiative heat source for the new model (based on 6 gray gases) does not exceed 3.5% (for these 17 cases) whereas for the standard WSGG model, these errors vary up to 14.5% (five cases have errors higher than 10.0% and nine cases have errors between 5.0% and 10.0%). The accuracy of the total radiative heat flux is also greatly enhanced with the new model. We also show that the present model is robust and can be used in 3D geometry.

CFD analyses of large-scale tests highlighting the effects of thermal radiation in steam-containing atmospheres

In simulations of heat transfer in large gaseous volumes under moderate temperatures, thermal radiation is traditionally neglected to simplify the computations. In recent years however, some small as well as large-scale experiments have demonstrated that thermal radiation may have a strong effect on the temperature field if the atmosphere contains an infrared absorbing gas such as vapor, even in small concentrations. This has in particular been shown in the H2P2 series of tests performed in the large-scale PANDA facility at the Paul Scherrer Institute. For these tests an air-helium-steam mixture was compressed with a helium injection, which caused the formation of a hot bubble. The initial vapor volume fraction varied between 0.1 % and 60%. In this paper, we report the results of CFD simulations conducted for the five H2P2 tests. The turbulence model k-ω SST was used, while thermal radiation was considered using the simple P1 model as a default, in conjunction with the Weighted Sum of Gray Gases Model (WSGGM) to specify steam absorptivity. For comparison purposes we also made use of the more advanced Monte-Carlo model for selected experiments. CFD Best Practice Guidelines were employed, in particular through preliminary grid and time-step sensitivity studies.The temperature and helium concentration fields matched the experimental data quite accurately, except for the test with very low vapor content (H2P2_1_2, 0.1% vol. steam), where the temperature was somewhat over-estimated. This may be due to the inadequacy of the radiation models at these extreme conditions. Two major conclusions can be drawn from this study: 1) ignoring thermal radiation can lead to large over-predictions of temperature, even when the steam content is low (order of 1%) and 2) the simple P1 model provides sufficient accuracy. Use of the more sophisticated Monte-Carlo model yielded similar and slightly more accurate results, albeit at a considerably larger CPU expenditure (5–7 times).

New coefficients of the weighted-sum-of-gray-gases model for gas radiation characteristics of hydrogen/natural gas blends combustion

To achieve carbon neutrality, hydrogen/natural gas blends are gaining momentum as a clean low-carbon fuel for the future. In order to accurately carry out the CFD numerical simulation of hydrogen/natural gas blends combustion, it is imperative to establish a precise model for gas radiation characteristics. The existing weighted-sum-of-gray-gases model (WSGGM) is not suitable for high hydrogen content fuels, such as hydrogen/natural gas blends. Hence, new coefficients of WSGGM is formulated specifically for the combustion of hydrogen/natural gas blends, drawing upon the groundwork established by the statistical narrow-band model (SNB model). This model is specifically designed to be applicable within the ambient pressures, encompassing the temperature regime of 400–2500 K, a path-length range of 0.001–60 m, and a hydrogen blending ratio of 20%–70%. The radiative heat transfer characteristics of the sum of the molar fraction of H2O and CO2 at 0.9, 0.6, and 0.3 were studied according to application conditions. The WSGGM is implemented to compute the radiative heat transfer in non-isothermal and non-homogeneous gas mixtures. When compared to the benchmark model, the deviation of the wall heat flux does not surpass 5.20%. The results demonstrate the excellent adaptability of the WSGG coefficients in simulating the radiative heat transfer during hydrogen/natural gas blends combustion.

Applications of weighted-sum-of-gray-gas model with soot to an experimental aero-engine combustion chamber

Due to the importance of radiation during combustion in the aero-engine, the weighted-sum-of-gray-gas (WSGG) model considering both gas and soot is applied to the combustion modelling for an experimental aero-engine in this work. Five gray gases are chosen to resolve the absorption coefficients of CO2-H2O mixture, with which the Planck-mean absorption coefficients of soot are used for the spectral consideration of gas-soot mixture. Together with the discrete ordinate method, the radiation effects using WSGG model on the combustion are presented. Comparisons are made between full-scale combustion simulations without radiation and those with radiation from gas only or gas-soot mixture. Results show that radiation from either gas or gas-soot mixture leads to no more than 3% differences in temperature and 5% differences in species concentrations. However, the temperature of combustor liner walls in the primary zone (i.e., the main combustion region) is significantly altered with an average of 100 K rise when considering radiation from gas only and a maximum of 500 K rise when considering radiation from gas-soot mixture. Results also show that the temperature of combustor liner walls with radiation from gas-soot mixture becomes more well-distributed than that either without radiation or with radiation from gas only.

New gas radiation model based on the principle of weighted sum of gray gases. Application to CO2–H2O mixtures at high temperature

A new gas radiation model based on the principle of weighted-sum-of-gray-gases (WSGG) is proposed. It is shown that expressing the weighting factors as linear functions of the temperature is more suitable than the fourth-order polynomial dependence to the temperature that is commonly adopted in the WSGG model. Using an efficient inverse algorithm, it was estimated a set of twelve spatially nonconstant parameters of the new model based on four gray gases, namely the coefficients of the linear functions and the pressure absorption coefficients. The inverse algorithm is based on the adjoint state of the radiative transfer equation (RTE) using as data the total radiative heat source instead of the total gas emissivity data. The parameters are fitted using data generated with line-by-line (LBL) simulations based on HITEMP2010. In the present work, the proposed gas radiation model is applied to determine the parameters of H2O–CO2 mixtures at atmospheric pressure with partial pressure ratio equal to 2, within the range of temperature between 400 K and 1800 K and for thicknesses of the gas layer up to 3.0 m. By applying the inverse algorithm to a given case, the present gas radiation model has the level of accuracy of the LBL method. The application of the same parameters to other test cases does not lead to the same level of accuracy, since the parameters obtained are spatially dependent. However, averaging these parameters in the inverse algorithm results in a gas radiation model with spatially constant parameters. When applied to several (1-D and 3-D) test cases in the conditions for which the parameters were obtained, this led to a significant reduction in the normalized errors on the radiative heat source and, for many of these cases, on the radiative heat flux compared to that obtained with the standard WSGG model.

A new WSGG radiation model of CO/CO2 mixed gas for solar-driven coal/biomass fuel gasification

Gasification driven by solar energy with CO2 is an ideal way of low-carbon resource utilization. However, there is a lack of research on the radiation heat transfer process which is important in gasification simulation. In this study, we developed a new the weighted-sum-of-gray-gases (WSGG) model to calculate the radiation heat transfer properties of CO and CO2 mixtures in solar-driven coal/biomass fuel gasification. Benchmarked against the statistical narrow-band model (SNB) of the EM2C laboratory, the WSGG model is suitable for the temperature range of 400–2500 K and the path length range of 0.001–60 m. This study also explored the effect of the CO/CO2 molar ratio on the overall emissivity of the mixture. Furthermore, the model introduces a pressure term into the emissivity calculation process and broadens the pressure range (1 bar, 5 bar, 45 bar). For the first time, the WSGG model is applied to the case where the H/C element ratio is 0, and the fluctuating temperature distribution case (1000 – 2000 K) is analyzed, which is suitable for coal/biomass fuel gasification. In addition, this study calculated the one-dimensional radiation transfer equation. The results show that the average radiation source term difference between the new WSGG and the benchmark SNB model is within 5 % in common solar gasification engineering conditions (5 bar, 5 m). Meanwhile, this study also clarified the effect of pressure on the radiation heat transfer with different temperatures.

A wide-band based weighted-sum-of-gray-gases model for participating media: Application to [formula omitted]-[formula omitted] mixtures with or without soot

The presence of participating gases and soot in combustion processes often makes the thermal radiation the main mechanism of heat transfer due to the elevated temperatures involved. The accurate solution of the radiative transfer equation (RTE) through the line-by-line (LBL) integration in engineering applications is in general still impracticable due to the high computational effort required to account for the millions of spectral lines that characterize the absorption coefficient of a gas. Global spectral models, such as the weighted-sum-of-gray-gases (WSGG) model, are attempts to replace the LBL integration with low computational cost and satisfactory accuracy. In the present study, an improvement of the WSGG model through a partition of the spectrum is proposed. The spectrum is divided into a set of ranges in which the standard methodology of the WSGG model is applied to determine the gray gases coefficients in these bands. This is the central aspect of what is named here a wide-band based WSGG (WBW) model, which consists firstly of determining the emittance of each band from the HITEMP 2010 database, then obtaining the pressure-absorption coefficients and the temperature-dependent coefficients. The total radiative heat flux and radiative heat source are obtained by the summation of the contribution of each band individually. For soot, a gray gas approach is considered for each band via Planck-mean absorption coefficients. A set of 1D problems consisting of two infinite parallel black walls, filled with a non-isothermal and non-homogeneous gaseous mixture of water vapor, carbon dioxide and soot, is solved. The results show that, especially in cases where the thermal radiation of soot is dominant, the maximum deviations obtained with the proposed method in relation to the LBL solution reduce by almost three times compared to other global WSGG models in the literature, in addition to decreasing by 40% the number of equations that need to be solved.

Influence of operating pressure on combustion and heat transfer in pressurized oxy-fuel combustion evaluated by numerical modeling

Pressurized oxy-fuel combustion (POFC) is an advanced-generation energy plant system that is used to capture and store carbon and can realize a high-efficiency generation cycle with increased heat transfer and minimized efficiency penalty. In this study, we conducted a numerical investigation to characterize the heat transfer, combustion reaction, and NOx emissions of a 0.1 MWth POFC system. In addition, the weighted-sum-of-gray-gases (WSGG) model was applied in the POFC conditions to precisely evaluate the radiative heat transfer based on a comparative analysis of various WSGG models. Both the measured and calculated results revealed that the temperature, including its peak value, decreased with the increasing pressure. Moreover, the average total heat recovery rate increased by approximately 0.2% upon increasing the pressure by 2 bar, and the proportion of the radiative heat transfer rate increased. Furthermore, the combustion reactions containing the O, H, and OH radicals were promoted with the increasing operating pressure, exhibiting a high peak value in a wide area. Consequently, the net reaction rates of the reactions involving HO2 and H2O2 increased with the pressure. Overall, NO was produced in the initial section of the oxy-flame, beyond which the oxidation reaction of NO with HO2 occurred to yield NO2, and the increasing pressure further promoted these reactions.

Flame characterisation of gas-assisted pulverised coal combustion using FPV-LES

A multiphase flamelet/progress variable (FPV) model for the large eddy simulation (LES) of gas-assisted pulverised coal combustion (PCC) is developed. The target of the simulation is the Darmstadt turbulent gas-assisted swirling solid fuel combustion chamber. The coal particles are treated as Lagrangian point particles, the position, momentum and energy of which are tracked. The gas phase is described by the low-Mach Navier-Stokes equations alongside the Eulerian transport equations of the governing variables for the FPV model. The set of chemical states of the PCC flame is pre-tabulated in a six-dimensional flamelet table and determined by the mixing of the primary fuel stream, volatiles and char off-gases with the oxidising air, the progress of chemical reactions, the interphase heat transfer, as well as sub-grid scale variations. A presumed β-PDF approach for the total mixture fraction is applied to capture sub-grid scale effects. The discrete ordinate method (DOM) with the weighted sum of grey gases model (WSGGM) is employed to model radiation. The FPV-LES results are validated against the experimental evidence and a good agreement of the predicted mean and RMS velocities, as well as the mean gas temperature between experiments and simulations is obtained. The contributions of the pilot, volatile and char off-gas fuel streams to the coal flame are analysed. It is found that most regions of the furnace are dominated by either pilot or volatile combustion, while char conversion only occurs in the far downstream and outer furnace regions. The pilot gas dominates the near-wall region inside the quarl, whereas the volatile gas mainly released from small particles dominates a first volatile combustion zone in the interior of the internal recirculation zone. Larger particles heat up more slowly and release their volatile content further downstream, leading to a secondary volatile combustion zone.

A Compact WSGG Formulation to Account for Inhomogeneity of H2O–CO2 Mixtures in Combustion Systems

Abstract An alternative weighted-sum-of-gray-gases (WSGG) model is proposed with a single set of constant pressure-based absorption coefficients that accounts for different mole fraction ratios (MRs) of H2O–CO2. The method requires no further interpolation, which in turn brings not only less uncertainty into the model but also simplifies its use. The hitemp2010 spectral database along with the line-by-line (LBL) integration is employed to generate a set of accurate total emissivities from which the WSGG coefficients are fitted. The fitting procedure employs a novel formulation to account for the MR dependence, leading to a more compact set of WSGG correlations when compared to the alternatives available in the literature. The new formulation takes advantage of the weak interdependence of temperature and molar fraction ratio in the weight factors and therefore separates their effects by two independent correlations. As oxy-fired combustion usually occurs in two distinct scenarios, dry- and wet-flue gas recirculation (FGR), the paper also proposes two other sets of coefficients intended to support the MR ranges corresponding to these specific conditions. Comparisons made against the benchmark LBL integration and other WSGG models, for one- and three-dimensional calculations, show the satisfactory level of accuracy of the proposed sets of correlations. In particular, the three-dimensional test case illustrates that the new model is also applicable to conditions observed in air–fuel combustion.

A hybrid non-gray gas radiation heat transfer solver based on OpenFOAM

Radiation heat transfer is important in many combustion conditions. Efficient and accurate predictions of the radiation energy is essential for numerical simulation of combustion. A hybrid non-gray gas radiation solver is developed based on the open-source OpenFOAM framework. The weighted-sum-of-gray-gases (WSGG) model is used for the non-gray gas radiative properties. The discrete ordinates method (DOM) and first order spherical harmonics (P1) method are adopted to solve the different gray gas RTEs in the WSGG model. The performance of the hybrid solver is analyzed in detail for three cases. Results show that the accuracy of the hybrid solver decreases with increasing the number of gray gases solved by the P1 method, while the computational time increases. The advantage of the hybrid solver is more obvious in isotherm and homogenous cases, in which the relative mean errors in terms of radiative heat flux and heat source can be less than 5% while reducing half of the computational time.

Modelling of MILD combustion in a lab-scale furnace with an extended FGM model including turbulence–radiation interaction

The flamelet generated manifold (FGM) model is suitable for moderate or intense low oxygen dilution (MILD) combustion provided the flamelets underlying the manifold include the effects of strong dilution by products of the fuel/oxidizer mixture. Here we propose such an extended model based on the use of non-premixed flamelets diluted at the airside and develop its application to non-adiabatic combustion in a lab-scale furnace. The extended model is referred to as diluted air FGM (DA-FGM) model. In the DA-FGM model in addition to mixture fraction, progress variable and scaled enthalpy loss, one additional controlling parameter named air dilution level, is introduced leading to a four-dimensional lookup table for laminar flames. For turbulent flames also variances of mixture fraction and progress variable are taken into account as independent variables leading to a six-dimensional table. Using a RANS approach implemented in OpenFOAM-2.3.1, the DA-FGM model has been applied to MILD combustion of Dutch natural gas in a lab-scale furnace operated at a thermal power 9 kW and at equivalence ratio 0.8. Radiation is described using a weighted-sum-of-gray-gases (WSGG) model. The validation study is mainly done using a grey WSGG model with TRI taken into account. The relative importance of including turbulence radiation interaction (TRI) and spectral treatment of radiative transfer is also studied. The predicted velocity and temperature statistics are in good agreement with the experimental LDA and CARS data provided not only the mixture fraction fluctuations but also the progress variable fluctuations are taken into account.

New WSGG model for gas mixtures of H2O, CO2, and CO in typical coal gasifier conditions

This study develops a new weighted-sum-of-gray-gases (WSGG) model for the radiative characteristics of CO, H2O, and CO2 mixtures in pulverized coal gasification plants under a typical high pressure (45 atm). This is significant for prediction of radiative heat transfer in computational fluid dynamic (CFD) calculation. The new high-pressure WSGG model and its parameters are based on the statistical narrow band (SNB) model of EM2C Laboratory. The new model applies to the temperature range of 500–3000 K and the path length range of 0.1–20 m. Moreover, the model can calculate the radiation characteristics of gas mixtures under different partial pressures of three gases. Therefore, the new model can be applied to the radiation transfer in pulverized coal gasification under specific high pressure. The results of one-dimensional cases show that the new model can well predict the radiative heat transfer process of gas mixtures. The error of radiation heat flux is less than 5.38%, and the radiation source term error is less than 0.67%, while the accuracy of the traditional WSGG model is very low under gasification conditions, and the error is more than 25% compared with the benchmark. When the new model is embedded into the CFD simulation of a high-pressure gasifier, the maximum temperature difference between the new and traditional models is up to 300 K, while the calculated absorption coefficient and radiation source term of gas mixtures are noticeably different. In conclusion, compared with the traditional model, the new WSGG model has higher accuracy for calculating gas radiation heat transfer under the condition of coal gasification. This paper also provides the parameters of the new model, which can be used in the CFD engineering simulation of coal gasification plants.

Assessment of weighted-sum-of-gray-gases models for gas-soot mixture in jet diffusion flames

The global radiative property models are widely used in combustion simulation due to its high computational efficiency. This study assesses the weighted sum of gray gases (WSGG) models for gas-soot mixture in the simulations of turbulent jet diffusion flame at atmospheric pressure with fully coupled combustion and radiation heat transfer. Non-adiabatic tabulated chemistry approach and the method of moments were employed for combustion modeling and soot particle dynamics. The radiative transfer equations are solved by the discrete ordinate model. Two kinds of WSGG model based on mixture modeling (MM) and superposition method (SM), and their combination with the gray and non-gray soot radiative property models are involved in the comparison. First, the radiative property models are evaluated on the one-dimensional parallel plate system using line-by-line model as the benchmark, and then the WSGG models are evaluated on the basis of the FSCK model in the combustion simulation. The results show that MM and SM provide similar prediction accuracy, while MM has much lower computational cost. The MM combined with the non-gray soot radiative property model (MMNS) provides the best accuracy for gas-soot mixture. Moreover, the relative error of MM combined with gray soot radiative property model (MMGS) is less than 10% for radiation source term, which is acceptable in engineering simulation. The gray implementation of WSGG model has low accuracy, which indicates that it is necessary to use the non-gray implementation of WSGG model in CFD simulations.

A comprehensive evaluation of the WSGG model for air- and oxy-fuel combustion conditions through three-dimensional calculations

This paper reports an assessment of the accuracy of most formulations of the weighted-sum-of-gray-gases (WSGG) model proposed in the last decade for the treatment of mixtures of water vapor and carbon dioxide. The analysis is based on non-coupled, three-dimensional radiative transfer calculations of cases representative of air- and oxy-fuel combustion at fixed or varying H2O–CO2 mole fraction ratios (MR). The reference solution is computed by line-by-line (LBL) integration. The WSGG model is shown as capable to provide accurate results for all cases under study, with existing correlations for the model displaying maximum errors below 4%. Formulations developed considering MR variations can in general be safely used even for cases where MR is constant; likewise, fixed-MR correlations can be applied for varying-MR scenarios, as long as the regions of most importance for the radiative transfer have a MR value close to the one for which the correlations were generated. The superposition WSGG model is tested as well, and it yields consistently accurate results for all test cases, although at a significantly larger processing cost than the standard WSGG model. An alternative approach for treating media with varying mole ratio, consisting of interpolating fixed-MR correlations, is also found to be promising.

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This paper reports an assessment of the accuracy of most formulations of the weighted-sum-of-gray-gases (WSGG) model proposed in the last decade for the treatment of mixtures of water vapor and carbon dioxide. The analysis is based on non-coupled, three-dimensional radiative transfer calculations of cases representative of air- and oxy-fuel combustion at fixed or varying H2O–CO2 mole fraction ratios (MR). The reference solution is computed by line-by-line (LBL) integration. The WSGG model is shown as capable to provide accurate results for all cases under study, with existing correlations for the model displaying maximum errors below 4%. Formulations developed considering MR variations can in general be safely used even for cases where MR is constant; likewise, fixed-MR correlations can be applied for varying-MR scenarios, as long as the regions of most importance for the radiative transfer have a MR value close to the one for which the correlations were generated. The superposition WSGG model is tested as well, and it yields consistently accurate results for all test cases, although at a significantly larger processing cost than the standard WSGG model. An alternative approach for treating media with varying mole ratio, consisting of interpolating fixed-MR correlations, is also found to be promising.

Numerical solutions of radiative heat transfer in combustion systems using a parallel modified discrete ordinates method and several recent formulations of WSGG model

The aim of the paper is to perform 3D radiative transfer calculations in combustion gas mixtures. For this purpose, a parallel modified Discrete Ordinates Method with a cell-vertex formulation on unstructured tetrahedral grid is proposed for solving the Radiative Transfer Equation (RTE) in realistic geometries. Several recent formulations of the weighted-sum-of-gray-gases (WSGG) model are implemented. To reduce the false scattering, the cell-vertex formulation is combined with an Exponential scheme and is compared to the Step scheme. The results are then compared with published results on non-isothermal and non-homogeneous gas mixtures. The use of non-gray WSGG models shows a very good level of accuracy for the evaluation of wall heat transfer and radiative heat source. The Exponential scheme is more accurate than the Step scheme. The summation over the wavenumber spectrum of the radiative model is usually carried out after having computed the radiative quantities for each discrete angular direction. By summing first over the wavenumber spectrum, a reduction in the computation time is significantly obtained, up to a factor of 16 on a case study. Also, additionnal significant speedup is obtained with an efficient distributed and multi-threaded parallel algorithm. When the Step scheme is used, the computation time increases very slightly with the number of gray gases. The procedure to speed up the calculations can be applied to any arbitrary numerical method for solving the spectral RTE.