Spectral Line-based Weighted-sum-of-gray-gases Research Articles

Application of absorption-line blackbody distribution functions for H2O-CO2 mixtures for the spectral integration of the radiative transfer equation with the SLW model

This study presents the generation and evaluation of absorption-line blackbody distribution functions for mixtures (ALBDF-M) of CO2 and H2O. These functions are employed in the spectral integration of the radiative transfer equation in the framework of the spectral line-based weighted-sum-of-gray-gases (SLW) model. The proposed approach avoids the need to model the mixture of gases when dealing with ALBDFs obtained for pure H2O and CO2 species, which is the methodology currently adopted in the SLW literature. The ALBDF-M can be used with any development of the SLW model to manage local variations of the thermodynamic state conditions. In the present study, both the rank (RC-) and the locally correlated (LC-) SLW methodologies are employed with the ALBDF-M for an uncouple solution of an axisymmetric field that is representative of the combustion of ethylene diluted with H2O. Comparisons with line-by-line (LBL) solutions show that using the ALBDF-M provides an improvement in the accuracy when compared to the standard methodology to combine the ALBDFs generated for CO2 and H2O individually.

Radiative transfer prediction in participating medium bounded with nongray walls using the SLW model

This study presents the application of the spectral line-based weighted-sum-of-gray-gases (SLW) model for the radiative transfer calculation in a participating medium bounded by two infinite, parallel and nongray walls. The proposed methodology presents a simplified approach to calculate the radiative transfer in the medium without the determination of the radiation intensity field at each wavenumber. The radiative transfer equation is modeled in a one-dimensional domain in which there is a non-isothermal homogeneous or non-homogeneous gaseous mixture of water vapor and carbon dioxide. The results are compared with the line-by-line (LBL) benchmark solution in order to quantify the magnitude of the error when using the SLW spectral model. The results show that the applied methodology provides satisfactory agreements with respect to LBL solution. In addition, it is shown that considering nongray walls leads to significant more accurate results in computation of the radiative heat transfer than the commonly applied gray wall assumption.

One-dimensional P1 method for gas radiation heat transfer in spherical geometry

Radiation heat transfer is important in spherical flame modeling, such as to determine the flame speed. It is beneficial to use one-dimensional (1D) model to solve the three-dimensional problems with spherical symmetry, while little work reports the 1D non-gray radiation heat transfer in spherical coordinates. This paper developed a 1D first order spherical harmonics (P1) model for the non-gray gas radiation in a sphere. The statistical narrow-band k-distribution (SNBCK), the weighted-sum-of-gray-gases (WSGG) and the spectral line based WSGG (SLW) are used for the non-gray radiation properties. The accuracy of the non-gray P1 method is analyzed and compared with discrete ordinates method (DOM). Results show that accuracy of the P1 method is close to DOM, except for gas mixture conditions.

Efficient SLW models for water vapor and carbon dioxide based on neural network method

Non-gray gas radiation plays an important role in combustion system, and the spectral-line-based weighted-sum-of-gray-gases (SLW) is a popular model to treat the gas radiative properties. In practical applications, the inverse calculations of the cross-sections from a specified F are time demanding. The neural network method is used here to develop inverse absorption line blackbody distribution function (ALBDF) to efficiently and accurately calculate the cross-sections from F. Results show that the neural network based SLW can predict the inverse ALBDF very well and the relative errors for the radiative heat source and heat flux for the radiation transfer are less than 2%. The computational time of the neural network based SLW is only 1/10th of the original SLW model.

Contributions of gray gases in SLW for non-gray radiation heat transfer and corresponding accuracies of FVM and P1 method

Non-gray radiation occurs in high temperature condition with participating gases, such as water vapor and carbon dioxide in combustion products. Spectral-line-based weighted-sum-of-gray-gases (SLW) method is widely used to model the non-gray radiative properties to obtain the overall radiative heat source and heat flux, while the contribution of each gray gas is usually not investigated. Knowledge of these contributions can provide information on how to optimize the SLW method or combine different radiative transfer equation solvers for different gray gases to save computational time. SLW method is used here to investigate its gray gas contribution and corresponding accuracies of the finite volume and P1 method in these gray gases. Monte Carlo method is used for each gray gas to serve as reference solution. Gray gas contributions to the total heat source and heat flux for three cases are analyzed in detail. Results show that different gray gases have completely different contributions and finite volume method and P1 method have different accuracies for the gray gases.

Advances in non-gray radiation calculation in combusting environments using a modified reference approach

The radiative heat transfer should be calculated very accurately in many combustion domains. This work uses the spectral-line based weighted-sum-of-gray-gases (SLW) model to calculate the radiation heat transfer in a model furnace representing a combustion field with high temperature gradient variations. The past researchers have commonly implemented the reference approach in the SLW model. However, the reference approach produces error because of enforcing a reference temperature to perform the non-gray radiation heat transfer calculations in non-isothermal domains. In this work, we implement a modified reference approach, which reduces such errors in non-gray gas calculations. We show that the SLW model results in more accurate radiation source term and radiative heat transfer calculations if it is incorporated with the current modified reference approach instead of coupling with the past common reference approach.

Modelling of flameless oxy-fuel combustion with emphasis on radiative heat transfer for low calorific value blast furnace gas

Using low calorific value (LCV) gases such as blast furnace gas (BFG) issued from steelmaking industry in steelmaking heating process itself has a very positive impact on the environment and the energy saving. A burner of 325kW using flameless oxy-fuel combustion technology combining with central BFG preheating has been designed for efficient utilization of BFG and less pollutant emissions. In view of industrial application, such technology is one of the potential candidates due to easy furnaces retrofitting, carbon capture potential, low NOx emissions and limited capital expenditures. Modelling such flameless oxy-fuel LCV BFG combustion is still very challenging because finite rate chemistry should be taken into account and radiative heat transfer from fumes issued from BFG combustion should be described properly. If we focus on the latter challenge, most efforts in the literature were spent on developing gaseous radiative properties for high calorific value (HCV) gases such as natural gas, and very few studies were reported on radiation of LCV gases. However, in industrial combustion systems, radiative heat transfer represents more than 80% of the total heat transfer transmitted into charge. Therefore, calculating radiation with accuracy in industrial combustion systems firing on LCV gases is crucial. Along this purpose, the study was devoted to the application of a new gaseous radiative properties model called Spectral Line-based Weighted-Sum-of-Gray-Gases (SLWSGG) adapted for BFG combustion. Full coupling combustion radiation CFD with this newly adapted radiative properties model implemented into Ansys Fluent® was performed for a semi-industrial furnace incorporating the aforementioned oxy-fuel BFG burner. CFD results were compared to the experimental data such as temperature and species concentrations. It was seen that flameless characteristics homogeneous temperature field and maximum temperature of 1400°C were reproduced by numerical simulation. At some measurement points located on the transverse temperature profiles, it was noted that CFD results obtained with the newly adapted SLWSGG model were closer to the pyrometer measurements as compared to the CFD results obtained with the standard WSGG model available in Ansys Fluent®. This can be explained by the fact that the new radiation model evaluated the BFG-air combustion products radiative properties with lower emissivity compared to the higher emissivity of the rich gas like natural gas and that the standard radiation model's coefficients in Fluent® were a priori fitted for radiative properties of rich gas combustion. It can be concluded that newly adapted radiation model should be used to calculate the radiative heat transfer with more accuracy in industrial furnaces for LCV BFG.

Natural element method for NON-GRAY radiation heat transfer problems

A radiation code based on the meshless Natural Element Method (NEM) for spatial discretization and on the Discrete Ordinates Method (DOM) for angular discretization of radiative transfer equation was developed for realistic calculation of the radiative heat transfer in two-dimensional complex geometries containing real gases with non-gray behavior (namely mixtures of H2O, CO2 and N2). The spectral line-based weighted-sum-of-gray-gases (SLW) model was used to calculate the radiative properties of the medium. The boundaries are assumed to be opaque, diffuse and gray. The shape functions in the NEM are constructed by interpolations from the natural neighbors, and the essential boundary conditions can be imposed directly. The predictive accuracy of the proposed method is assessed by applying it to five test problems and comparing its predictions with other numerical solutions reported in the literature. The predictions are also compared with those of the gray gas model. A good agreement was observed between the results of the NEM/DOM/SLW method and other numerical methods, and it is shown that the natural element method has good accuracy, and can be used for the solution of radiative heat transfer problems in irregular enclosures containing non-gray media.

Relationship between the spectral line based weighted-sum-of-gray-gases model and the full spectrum k-distribution model

The relationship between the spectral line based weighted-sum-of-gray-gases (SLW) model and the full-spectrum k-distribution (FSK) model in isothermal and homogeneous media is investigated in this paper. The SLW transfer equation can be derived from the FSK transfer equation expressed in the k-distribution function without approximation. It confirms that the SLW model is equivalent to the FSK model in the k-distribution function form. The numerical implementation of the SLW relies on a somewhat arbitrary discretization of the absorption cross section whereas the FSK model finds the spectrally integrated intensity by integration over the smoothly varying cumulative-k distribution function using a Gaussian quadrature scheme. The latter is therefore in general more efficient as a fewer number of gray gases is required to achieve a prescribed accuracy. Sample numerical calculations were conducted to demonstrate the different efficiency of these two methods. The FSK model is found more accurate than the SLW model in radiation transfer in H2O; however, the SLW model is more accurate in media containing CO2 as the only radiating gas due to its explicit treatment of ‘clear gas.’

Application of the Spectral Line-based Weighted-Sum-of-Gray-Gases model (SLWSGG) to the calculation of radiative heat transfer in steel reheating furnaces firing on low heating value gases

The Spectral Line-based Weighted-Sum-of-Gray-Gases (SLWSGG) model is applied to calculate the gaseous radiative properties of the aero- or oxy-combustion products of low heating value gases issued from steel making process such as Blast Furnace Gas (BFG) as well as of high heating value gases such as Coke Oven Gas (COG) and conventional Natural Gas (NG). The comparison of total emissivities shows that the 3-gray-gases SLWSGG model is in very good agreement with the Hottel and Sarofim's database. The 3-gray-gases SLWSGG model is then integrated into AnsysFluent® Discrete Ordinates method under User Defined Function and CFD simulations are performed using these combined models. The simulations are done, with full combustion-radiation coupling, for steel reheating furnaces firing on three types of gases: BFG, COG and NG. The results are compared with the simulations realized with the 1-gray-gas WSGG model available in AnsysFluent®. The comparison shows that the 1-gray-gas WSGG model highly overestimates the steel discharging temperature as compared to the 3-gray-gases SLWSGG model. Significant temperature differences are observed between the two radiative models, i.e. 116°C, 55°C and 67°C for the BFG, COG and NG cases, respectively. It can be concluded that the 3-gray-gases SLWSGG model should be used to calculate the radiation heat transfer in large industrial furnaces with more accuracy not only for low heating value gases such as BFG but also for high heating value gases such as COG and NG.

Assessment of radiative property models in non-gray sooting media

The radiative transfer equation (RTE) is solved by the Finite Volume Method (FVM) in 1D and 2D axisymmetric configurations containing mixtures of water vapor, carbon dioxide and soot. Several radiative property models, namely simple gray models, the Statistical Narrow Band Correlated- k (SNBCK) model, the Weighted-Sum-of-Gray-Gases (WSGG) model, the Full-Spectrum Correlated- k (FSCK) model, the Spectral-Line-Based Weighted-Sum-of-Gray-Gases (SLW) model, a Gray-Narrow-Band (GNB) model and a Gray-Wide-Band (GWB) model, are assessed by comparison with reference calculations based on the Ray Tracing (RT) method coupled with the Statistical Narrow Band (SNB) model. Different treatments of overlapping bands are implemented with the SNBCK model, namely the correlated approach, the uncorrelated approach, and the mixing schemes of Modest and Riazzi (J. Quant. Spectros. Rad. Trans. 90 (2005) 169–189) and of Solovjov and Webb (J. Quant. Spectros. Rad. Trans. 65 (2000) 655–672) (Superposition and Multiplication). The Full Spectrum (FS) k-distributions required to run both FSCK and SLW are assembled from the same narrow band (NB) database as for the SNB and the SNBCK models using either the mixing model of Modest and Riazzi or the Multiplication scheme. The correlated SNBCK is the most accurate model but is too time consuming for engineering applications. The computational efficiency of the SNBCK can be considerably improved without altering the quality of the solutions by using the gas mixing scheme of Modest and Riazzi. Numerical results show that, in this case, good accuracy for spectrally-integrated quantities is obtained by considering only a 2-point Gauss–Legendre quadrature scheme. The FSCK and the SLW, using FS k-distributions assembled with the Modest and Riazzi scheme, are found to be the best compromise in terms of accuracy and computational requirements. It is found that FSCK predictions remain satisfactory by reducing the number of quadrature points of the Gauss–Legendre scheme up to seven.

A Monte Carlo implementation to solve radiation heat transfer in non-uniform media with spectrally dependent properties

This paper presents the application of the Monte Carlo method to solve the radiative heat exchange in non-homogeneous, non-isothermal gases with spectrally dependent properties. Among others models, the absorption-line blackbody (ALB) distribution function, originally defined and derived for the spectral line-based weighted-sum-of-gray-gases (SLW) model, allows an immediate, simple implementation of the Monte Carlo method to account the spectral dependence of the radiative properties. This work shows how the Monte Carlo method can be combined to the ALB distribution function, and provides results for heat transfer in a mixture of water vapor, carbon dioxide and nitrogen that have satisfactory agreement with the SLW method and with line-by-line integration. Finally, the solution technique is employed to solve two examples aiming at demonstrating the effect of the absorbing species concentration on the thermal radiative exchanges. The method is of great interest for the computation of radiative transfer in combustion systems where the chemical species concentration and the temperature are not uniform.

Numerical simulation of radiative heat transfer from non-gray gases in three-dimensional enclosures

The discrete ordinates and the discrete transfer methods are applied to the numerical simulation of radiative heat transfer from non-gray gases in three-dimensional enclosures. Several gas radiative property models are used, namely the correlated k-distribution (CK), the spectral line-based weighted-sum-of-gray-gases (SLW) and the weighted-sum-of-gray-gases (WSGG) methods. The results are compared with recently published accurate calculations based on the statistical narrow band model. The WSGG model is computationally efficient, but often yields relatively large errors. It should be used only if moderate accuracy is sufficient. The SLW model is the best alternative regarding the compromise between accuracy and numerical efficiency. However, an optimization of the coefficients of the model is essential to reduce the computational requirements, especially in the case of gas mixtures. The CK model is the most accurate of the methods evaluated here, but too time consuming for engineering applications, although recent developments may partly overcome this shortcoming.

The Spectral-Line Weighted-Sum-of-Gray-Gases Model for H2O/CO2 Mixtures

The weighted-sum-of-gray-gases model, first introduced by Hottel and Sarofim for expressing total gas emissivities and in the context of the zone method, has recently been extended to the general form of the radiative transfer equation (RTE). The fundamental radiative property of the model is the locally defined absorption coefficient, which permits the use of arbitrary solution methods of the RTE. Denison and Webb developed a spectral line-based weighted-sum-of-gray-gases (SLW) model by constructing a histogram representation of the high-resolution spectra of H{sub 2}O. Subsequently, a novel absorption-line black body distribution function was developed that easily allows the black body weights a{sub j} of any desired number of gray gases to be determined by simple differencing rather than accessing detailed spectral line information. The distribution function also provides the means of incorporating a spatial dependence of the gray gas absorption cross sections on temperature, pressure, and species mole in nonisothermal, nonhomogeneous problems. 15 refs., 3 figs.