Weighted-sum-of-gray-gases Research Articles

Study of turbulence-radiation interactions in large-eddy simulation of scaled Sandia flame D

The importance of the subgrid-scale contribution for computing the radiative source term in large-eddy simulations (LES) for the scaled Sandia flame D is studied in this work. This study is carried out by employing the flamelet generated manifolds approach as a combustion model in combination with the Eulerian stochastic field method to account for the turbulence-chemistry interaction. Furthermore, the finite volume method is employed to solve the radiative transfer equation with the non-grey weighted-sum-of-grey-gases (WSGG) model for the spectral resolution. In order to take thermal radiation into account in the LES context, the filtered radiative source term should be computed. The contribution of the resolved scales can be explicitly calculated, whereas the terms involving the subgrid-scale contributions are unclosed and require approximations. In this work, the optically thin fluctuation approximation is applied for modelling the filtered absorption term and different methods are used for computing the emission term, in which the subgrid-scales are either considered or omitted. The results show that the difference between the radiative source terms computed by accounting and by neglecting the subgrid-scale contribution is significant only in the regions where this term is small. Besides, no relevant differences are found in the profiles of mean temperature and CO2 species concentration calculated using those two different approaches. These results indicate that the subgrid-scale contribution may be neglected in the context of LES for the flame under consideration.

Evaluation of the non-gray weighted sum of gray gases models for radiative heat transfer in realistic non-isothermal and non-homogeneous flames using decoupled and coupled calculations

Radiative heat transfer plays an important role in combustion systems. Good compromise between the accuracy and computational requirements of the weighted sum of gray gases (WSGG) model makes it widely used in CFD simulations. In this paper, the accuracy of various WSGG models is assessed by the comparison with the results of radiative heat source and heat flux calculated by line by line (LBL) approach in a realistic non-isothermal and non-homogeneous flame using decoupled calculations. Then these models are implemented to CFD code to investigate the radiative heat transfer for a 600 kW furnace using coupled calculations. The experimental data from the furnace has been used to evaluate the computational applicability and reliability of WSGG models. Results show that the non-gray formulation of WSGG model is more accurate than gray modelling approach, compared with LBL results. The non-gray WSGG models of Krishnamoorthy et al. (2013), Bordbar et al. (2014) and Shan et al. (2018) provide the minimal overall errors compared with the measured temperature fields. The results demonstrate that using the non-gray approach instead of gray approach for global CFD simulation improves the simulation accuracy of thermal radiation transfer. The computing time of non-gray models is larger, approximately 3–4 times that of gray WSGG models.

APPLICATION OF THE WEIGHTED-SUM-OF-GRAY-GASES MODEL TO NON-HOMOGENEOUS H2O/CO2 MIXTURES FOR MEDIA WITH NON-GRAY WALLS

The spectral modeling of the thermal radiation in participating media is a research area that has received constant attention due to its importance in a great number of engineering problems, especially because the highly irregular spectral dependence of the absorption coefficient of a gas with the wavenumber requires the adoption of alternative methods to determine the radiative properties. This work brings a numerical study of a one-dimensional system, bounded by perfectly diffuse and non-gray walls, filled by a non-homogeneous and non-isothermal mixture of water vapor and carbon dioxide. The main objective is to estimate the magnitude of the deviations in treating surfaces that should be considered non-gray as black or gray. The spectral modeling of the problem is performed by the weighted-sum-of-gray-gases (WSGG) model and the accuracy of the solution methodology developed is evaluated by means of comparisons against the results obtained by line-by-line (LBL) integration.

WSGG correlations based on HITEMP2010 for gas mixtures of H2O and CO2 in high total pressure conditions

This study presents weighted-sum-of-gray-gases (WSGG) model coefficients for mixtures of H2O and CO2 with fixed mole ratio of 2/1 for high total pressure conditions. The mole ratio represents typical products of stoichiometric combustion of methane in air, which has received significant attention for high pressure applications. The coefficients are based on HITEMP2010 database, and are valid for path-lengths ranging from 0.01 to 30 m, temperatures varying from 400 to 2500 K, and total pressures of 1.0, 2.0, 5.0, 10, 20, and 40 atm. As a first validation of the WSGG model, a comparison with benchmark line-by-line (LBL) total emittance is presented, showing accurate results. Total emittance is shown to have significant pressure dependence, which emphasizes the importance of generating WSGG coefficients fitted to high pressure emittance values. To better assess the model accuracy, calculations for radiative heat flux and volumetric source are performed for two one-dimensional test cases, considering nonisothermal, homogeneous and non-homogeneous conditions. Results show acceptable deviations from the LBL solution for the homogeneous case, with even lower deviations for the non-homogeneous case, as long as the ratio between the species is fixed at 2/1. The effect of pressure is also significant on both radiative heat flux and volumetric source, while its behavior shows that interpolation is a good alternative to obtain WSGG solutions for intermediate pressures.

Evaluation of the WSGG model against line-by-line calculation of thermal radiation in a non-gray sooting medium representing an axisymmetric laminar jet flame

This paper presents an evaluation of the weighted-sum-of-gray-gases (WSGG) model in the computation of the radiative heat transfer in an axisymmetric gas system composed of H2O, CO2 and soot by comparison with line-by-line (LBL) integration. The test cases consider temperature and species concentrations fields that are representative of a laminar diffusion jet flame of ethylene diluted with H2O. Different approaches are considered in the application of the WSGG model, including the use of WSGG coefficients obtained for different ratios between the mole concentrations of H2O and CO2, and the superposition between the coefficients of H2O/CO2 and soot. The WSGG coefficients for H2O and CO2 are based on HITEMP2010 database, while for soot they are based on the consideration of linear spectral dependence of its absorption coefficient. The spatial integration of the radiative transfer equation is carried out with the discrete ordinates method. The results in the paper show that, although the ratio between the mole concentrations of H2O and CO2 varies locally in the flame, using WSGG coefficients for a constant ratio, but equivalent to the global average ratio in the flame, can provide satisfactory solutions in comparison to the LBL integration. Moreover, the superposition method between the WSGG coefficients of combined H2O/CO2 and of soot proved accurate considering both moderate and high concentrations of soot. The paper provides algebraic relations for the temperature and concentration fields, which can be used for the evaluation of other gas models in future studies.

New pressurized WSGG model and the effect of pressure on the radiation heat transfer of H2O/CO2 gas mixtures

In this study, a new pressurized weighted-sum-of-gray-gases (WSGG) model of a H2O/CO2 gas mixture under pressurized conditions was proposed to calculate the radiation heat transfer of various pressurized combustion equipment. The new WSGG model and its parameters, which are suitable for a pressure range of 1–30 bar, was developed based on the statistical narrowband (SNB) model of EM2C laboratory. Moreover, its temperature range is 500–2500 K, path-length range is 0.001–60 m, and the range of the molar ratio for H2O/CO2 is 0.125–4. Therefore, the new WSGG model is suitable for many fuels under pressurized conditions. The one-dimensional case results demonstrate that the new WSGG model can well predict the radiation heat transfer of the gas mixture under pressurized conditions compared with the benchmark model. In addition, the new model was used to study the effect of pressure on the radiation heat transfer of the gas mixture. The results show that increasing the pressure within a certain range could enhance the radiation heat transfer of the gas mixture, and this effect was also associated with the temperature, the molar ratio and the path-length. In conclusion, the new WSGG model can be applied to the calculation and research of radiation heat transfer in pressurized combustion chambers, such as pressurized boilers, gas turbines, internal combustion engines and aircraft engines.

Application of the WSGG Model to Solve the Radiative Transfer in Gaseous Systems With Nongray Boundaries

This paper presents a methodology for the application of the weighted-sum-of-gray-gases (WSGG) model to systems where the medium is bounded by nongray surfaces. The method relies on the assumption that each gray gas absorption coefficient is randomly spread across the entire wavenumber spectrum. It follows that, in the spectral integration of the radiative transfer equation (RTE), the local emission term can be computed by the joint probability of emission from the subsections of the spectrum related to each gray gas coefficient and from each wall emissivity band. One advantage of the proposed methodology is that it allows the use without any modification of WSGG correlations that are available in the literature. The study presents a few test cases considering a one-dimensional (1D), nonuniform medium slab composed of H2O and CO2, bounded by nongray surfaces. The accuracy of the methodology is assessed by direct comparison with line-by-line (LBL) calculations.

Study of the Heat Transfer of a Large-Scale Tunnel Furnace Based on Numerical Modeling

The aim of this work is to perform a thermal analysis of the operational conditions of a large-scale roller conveyor furnace in a ceramic factory. The entire furnace was divided into three subzones according to the combustion conditions, and the temperature and gas (CO2, H2O vapor, and O2) distributions of each subzone were evaluated. The computational fluid dynamics (CFD) approach was employed to simulate the flow, temperature profile, and heat transfer. The realizable k–ε model was applied for turbulence simulation of the fluid flow coming from the burners. The discrete ordinates method (DOM) and weighted sum of gray gases (WSGG) model were used for simulation of the radiative heat transfer of the furnace. The high accuracy of the simulation methods was validated with the temperature data of the furnace measured by an infrared thermal camera. From the comparisons between the furnace's operating conditions and the numerical simulations, it was concluded that the simulation methods yielded successful results, and relative deviations of up to 22% were observed in the side wall.

A full spectrum k-distribution based non-gray radiative property model for fly ash particles

Particle radiation characteristics have a strong wavelength-dependence. However, the gray particle assumption is widely used for coal combustion simulations, which cannot reflect the non-gray radiative property of the particles. In this study, based on the measured complex index of refraction from literatures (Gupta and Wall, 1985, Goodwin and Mitchner, 1989, and Lohi et al., 1992), a new non-gray particle radiative property model for fly ash is proposed by combining the features of full-spectrum k-distribution (FSK) model with the weighted sum of gray gases (WSGG) model. Four gray particles with different absorption and scattering efficiencies are used to replace the non-gray particles, for which absorption efficiency, scattering efficiency and weighting factor are directly obtained from the k-distribution, with model parameters obtained based on rational polynomials. Simultaneously, a gray particle model based on the Planck’s law is also obtained for comparison. The new model is systematically validated by comparing the radiative source terms and radiative heat fluxes, with those predicted by the line-by-line (LBL) integration of Mie-data in a one-dimensional plane-parallel slab system. The maximum relative error of radiative source term is 8% for the new non-gray radiative property model, 13% for Planck mean coefficients, 14% for modified Johansson model (Johansson, 2017), and 18% for empirical-constant model in non-isothermal inhomogeneous particle media, respectively. Combining the new non-gray radiative property model with the non-gray formulation of WSGG-SK model (Guo et al., 2015), the prediction accuracy is further validated by LBL solutions in the gas and particle mixture. Moreover, the contribution of gases and particles to radiative heat transfer is discussed at different path lengths, which shows the accuracy of the particle radiative property model determines the prediction accuracy of the radiative heat transfer in large-scale furnace.

Prediction of the radiative heat transfer in small and large scale oxy-coal furnaces

Predicting thermal radiation for oxy-coal combustion highlights the importance of the radiation models for the spectral properties of gases and particles. This study numerically investigates radiation behaviours in small and large scale furnaces through refined radiative property models, using the full-spectrum correlated k (FSCK) model and Mie theory based data, compared with the conventional use of the weighted sum of grey gases (WSGG) model and the constant values of the particle radiation properties. Both oxy-coal combustion and air-fired combustion have been investigated numerically and compared with combustion plant experimental data. Reasonable agreements are obtained between the predicted results and the measured data. Employing the refined radiative property models achieves closer predicted heat transfer properties to the measured data from both furnaces. The gas-phase component of the radiation energy source term obtained from the FSCK property model is higher within the flame region than the values obtained by using the conventional methods. The impact of using non-grey radiation behaviour of gases through the FSCK is enhanced in the large scale furnace as the predicted gas radiation source term is approximately 2–3 times that obtained when using the WSGG, while the same term is in much closer agreement between the FSCK and the WSGG for the pilot-scale furnace. The predicted total radiation source term (from both gases and particles) is lower in the flame region after using the refined models, which results in a hotter flame (approximately 50–150 K higher in this study) compared with results obtained from conventional methods. In addition, the predicted surface incident radiation reduces by using the refined radiative property models for both furnaces, in which the difference is relevant with the difference in the predicted radiation properties between the two modelling techniques. Numerical uncertainties resulting from the influences of combustion model, turbulent particle dispersion and turbulence modelling on the radiation behaviours are discussed.

Study of the non-gray-TRI effect on the turbulent methane combustion under O2/CO2 atmosphere

The radiative heat transfer dominates the major part of total heat transfer of turbulent methane combustion under O2/CO2 atmosphere, and accurate description of it is difficult but essential for improving the combustion simulation accuracy. Considering the large amount of participating media under O2/CO2 atmosphere and the remarkable turbulence-radiation interaction (TRI) effect, the weighted-sum-of-gray-gases (WSGG) model is adopted to calculate radiative properties of flue gas and the TRI effect is modeled (referred to as non-gray-TRI model). Based on the above model verified by experiment results of the relevant literature, the turbulent methane combustion under O2/CO2 atmosphere is simulated, and the accuracy of ignoring radiation or calculating by gray model, gray-TRI model and WSGG model are analyzed respectively. The results indicate that ignoring the radiation or using the gray model will produce substantial errors, and the TRI effect is not obvious when using the gray model. However, the TRI effect reduces the overall temperature of the combustion chamber when using the WSGG model. Therefore, the non-gray-TRI model is necessary to improve the simulation accuracy of turbulent methane combustion under O2/CO2 atmosphere.

New weighted-sum-of-gray-gases model for typical pressurized oxy-fuel conditions

Pressurized oxy-fuel combustion technology has received considerable attention due to its ability to improve the overall system efficiency and to control CO2 emissions. The characteristics of radiation heat transfer are significant for pressurized oxy-fuel gas mixture and different from those under atmospheric conditions. Therefore, to calculate the radiation characteristics of pressurized oxy-fuel gas mixture quickly and accurately, new weighted-sum-of-gray-gases (WSGG) model for pressurized oxy-fuel conditions was first presented in this paper, which was applied in 3 typical high pressure conditions: 5, 10, and 15 bar. The new WSGG model correlations were suitable for pressurized conditions with a molar ratio range of 0.125-2, temperature range of 400-2500 K, and path length range of 0.1-20 m. Calculations for a variety of typical pressurized oxy-fuel combustion cases showed that the new WSGG model can accurately predict the radiation characteristics and heat transfer characteristics of the gas mixtures compared with the SNB model benchmark. In addition, the application of the previous atmospheric WSGG models yielded non-ideal results under pressurized conditions. Consequently, the new model can provide efficient and accurate radiation heat transfer results for pressurized oxy-fuel conditions and can be used to design pressurized oxy-fuel combustion furnaces or boilers.

Assessment of several gas radiation models for radiative heat transfer calculations in a three-dimensional oxy-fuel furnace under coal-fired conditions

Oxy-fuel coal combustion is a promising Carbon Capture and Storage technology that allows retro-fitting of existing power plants. Due to high concentrations of CO2 and H2O and the strong and irregular spectral variation of their absorption coefficients, prediction of radiative heat transfer in oxy-fuel combustion systems requires a non-grey gas radiation model. Several models, including narrow-band correlated-k (NBCK), wide-band correlated-k (WBCK), full-spectrum correlated-k (FSCK), and weighted-sum-of-grey-gases (WSGG) models, were used to predict radiative heat transfer by CO2 and H2O in a three-dimensional real-size virtual coal-fired furnace under air- and oxy-fuel (dry and wet flue-gas recycle) conditions. The best agreement with the benchmark solution calculated by the NBCK model with the updated EM2C parameters is achieved by the FSCK model. The WBCK model is less accurate. The WSGG parameter sets of Kangwanpongpan et al. (2012) and Bordbar et al. (2014) are most suited for oxy-fuel combustion among the six sets considered. The FSCK model offers the best performance in terms of both accuracy and computational efficiency among the considered gas radiation models and is recommended for CFD simulations of real-sized oxy-coal systems.

WSGG Model Correlations to Compute Nongray Radiation From Carbon Monoxide in Combustion Applications

This paper presents correlations for the weighted-sum-of-gray-gases (WSGG) model for carbon monoxide based on HITEMP2010. The correlations are valid for pressure path lengths from 0.0001 atm·m up to 10 atm·m, total pressure in the order of 1.0 atm, and for temperatures ranging from 400 K up to 2500 K. Some test cases embodying nonhomogeneous, nonisothermal conditions are presented, and the results for the WSGG model are compared with the line-by-line (LBL) solutions for CO.

Um estudo numérico da influência da radiação sobre a turbulência em uma chama turbulenta 2D axissimétrica

This paper presents a study of the influence of thermal radiation on turbulence in the simulation of a turbulent, non-premixed methane-air flame. In such a problem, two aspects need to be considered for a precise evaluation of the thermal radiation: the turbulence-radiation interactions (TRI), and the radiative properties of the participating species, which are treated here with the weighted-sum-of-gray-gases (WSGG) model based on recently obtained correlations from HITEMP2010 database. The chemical reactions rates were considered as the minimum values between the Arrhenius and Eddy Break-Up rates. A twostep global reaction mechanism was employed, while the turbulence modeling was considered via standard k–e model. The source terms of the energy equation consisted of the heat generated in the chemical reaction rates as well as in the radiation exchanges. The discrete ordinates method (DOM) was employed to solve the radiative transfer equation (RTE), including the TRI. Comparisons of simulations with/without radiation demonstrated that radiation influenced turbulent-properties (root mean square of velocity and temperature fluctuations, and turbulent kinetic energy of the velocity fluctuations). Radiation smoothed turbulent-properties fields. The influence of radiation was more important on the temperature fluctuations than on the velocity fluctuations. Keywords: thermal radiation, turbulence, TRI, CFD, non-premixed flame.

Radiative modelling by the zonal method and WSGG model in inhomogeneous axisymmetric cylindrical enclosure

Nongray radiation calculations are carried out for a case problem available in the literature. The problem is a non-isothermal and inhomogeneous CO2-H2O- N2 gas mixture confined within an axisymmetric cylindrical furnace. The numerical procedure is based on the zonal method associated with the weighted sum of gray gases (WSGG) model. The effect of the wall emissivity on the heat flux losses is discussed. It is shown that this property affects strongly the furnace efficiency and that the most important heat fluxes are those leaving through the circumferential boundary. The numerical procedure adopted in this work is found to be effective and may be relied on to simulate coupled turbulent combustion-radiation in fired furnaces.

An assessment of some non-gray global radiation models in enclosures

The accuracy of several non-gray global gas/soot radiation models, namely the Wide-Band Correlated-K (WBCK) model, the Spectral Line Weighted-sum-of-gray-gases model with one optimized gray gas (SLW-1), the (non-gray) Weighted-Sum-of-Gray-Gases (WSGG) model with different sets of coefficients (Smith et al., Soufiani and Djavdan, Taylor and Foster) was assessed on several test cases from the literature. Non-isothermal (or isothermal) participating media containing non-homogeneous (or homogeneous) mixtures of water vapor, carbon dioxide and soot in one-dimensional planar enclosures and multi-dimensional rectangular enclosures were investigated. For all the considered test cases, a benchmark solution (LBL or SNB) was used in order to compute the relative error of each model on the predicted radiative source term and the wall net radiative heat flux.

New optical exchange gap concept to calculate self-irradiance direct exchange areas in cylindrical industrial furnaces

A direct integration scheme based on the trapezoidal integration method associated with Romberg's acceleration algorithm is proposed to calculate numerically with the desired accuracy, direct exchange areas (DEAs) within an axisymmetric enclosure confining non-isothermal and inhomogeneous non-grey gaseous combustion products with soot. A three-dimensional integral needs to be evaluated, but axisymmetry and reciprocity of DEAs bring a notable processing time reduction. The integration process poses difficulties pertinent to singular DEAs of self-irradiance. Evaluating self-irradiance of gas volume zones is the concern of this investigation, in which we introduce a new concept that we call the optical exchange gap (OEG). It has been established that the OEG width associated with a volume zone, optimized with extreme care to meet Erkku's data, decreases with the radial position and radial optical thickness. A correlation, deduced to derive the OEG width for a given situation, has been shown to be more efficient, simple and accurate than a proper center-to-center distance technique. The effectiveness of the developed procedure was demonstrated by comparison of model predictions, using the zonal method in conjunction with the weighted-sum of grey gases (WSGG) model, with highly accurate reference data and by carrying out an error analysis.

Application of the WSGG model for the calculation of gas–soot radiation in a turbulent non-premixed methane–air flame inside a cylindrical combustion chamber

This paper presents a study of the effect of soot on the radiative heat transfer in a turbulent, non-premixed methane–air flame inside a combustion chamber. In this problem, an important aspect to be considered is the steep variation of the radiative properties of the medium, which is treated with the weighted-sum-of-gray-gases (WSGG) model based on the superposition of correlations recently obtained for water vapor, carbon dioxide mixtures and soot. The discrete ordinates method (DOM) is employed for the angular integration of the radiative transfer equation (RTE), taking into account turbulence–radiation interactions (TRI). Calculations indicate that the global contribution of soot to the radiative heat transfer in the chamber was of 8%, which is compatible with methane flames. However, in the region with the highest concentration of soot, it was observed a local increase of 30% in the radiative volumetric source in the medium, and of 25% in the radiative heat flux on the wall. In the second part of the paper, the WSGG model is compared with the line-by-line (LBL) integration using the final temperature and concentrations fields obtained from the global flame calculation, leading to average and maximum normalized errors of 1.2% and 4.8%, respectively, and requiring only 1/7000 of the computation effort of the LBL integration. This result indicates that the WSGG model, in spite of its relative simplicity, can provide accurate results for the spectral integration of the radiative properties of gas–soot mixtures in combustion processes.

A comprehensive evaluation of different radiation models in a gas turbine combustor under conditions of oxy-fuel combustion with dry recycle

The oxy-fuel combustion is a promising CO2 capture technology from combustion systems. This process is characterized by much higher CO2 concentrations in the combustion system compared to that of the conventional air-fuel combustion. To accurately predict the enhanced thermal radiation in oxy-fuel combustion, it is essential to take into account the non-gray nature of gas radiation. In this study, radiation heat transfer in a 3D model gas turbine combustor under two test cases at 20atm total pressure was calculated by various non-gray gas radiation models, including the statistical narrow-band (SNB) model, the statistical narrow-band correlated-k (SNBCK) model, the wide-band correlated-k (WBCK) model, the full spectrum correlated-k (FSCK) model, and several weighted sum of gray gases (WSGG) models. Calculations of SNB, SNBCK, and FSCK were conducted using the updated EM2C SNB model parameters. Results of the SNB model are considered as the benchmark solution to evaluate the accuracy of the other models considered. Results of SNBCK and FSCK are in good agreement with the benchmark solution. The WBCK model is less accurate than SNBCK or FSCK. Considering the three formulations of the WBCK model, the multiple gases formulation is the best choice regarding the accuracy and computational cost. The WSGG model with the parameters of Bordbar et al. (2014) [20] is the most accurate of the three investigated WSGG models. Use of the gray WSSG formulation leads to significant deviations from the benchmark data and should not be applied to predict radiation heat transfer in oxy-fuel combustion systems. A best practice to incorporate the state-of-the-art gas radiation models for high accuracy of radiation heat transfer calculations at minimal increase in computational cost in CFD simulation of oxy-fuel combustion systems for pressure path lengths up to about 10barm is suggested.