Weighted Sum Of Gray Gases Model Research Articles

Effects of gas and particle emissions on wall radiative heat flux in oxy-fuel combustion

Oxy-fuel combustion exhibits combustion and heat transfer characteristics different from air-fuel combustion due to high concentrations of CO2 and H2O. This study evaluated the effect of gas and particle emissions on radiative heat transfer in oxy-fuel combustion of coal. For a hexahedral furnace, prescribed gas compositions based on combustion calculation were used to simplify the combustion reactions. The values of radiative heat fluxes (qrad) were compared for different combustion modes, flue gas recirculation (FGR) methods, particle concentrations, furnace sizes and O2 concentrations in the oxidizer. The radiation was calculated by the discrete ordinate method with gaseous emission predicted by the weighted sum of gray gases models (WSGGMs). The results showed that employing an optimized WSGGM is essential for the accurate prediction of qrad in oxy-fuel combustion for gaseous fuels. The conventional WSGGM showed large errors for larger furnace volumes or under dry FGR conditions. With higher particle concentrations such as in pulverized coal combustion, however, qrad was dominated by emission of particles. The effect of gas emissivity was not critical in the furnace with a mean beam length of 8.3m. Oxy-fuel combustion with wet FGR had higher qrad than dry FGR. The O2 concentration in the oxidizer was a key parameter for oxy-fuel combustion since increasing its value linearly increased qrad.

Radiative slab heating analysis for various fuel gas compositions in an axial-fired reheating furnace

A transient radiative slab heating analysis was performed to investigate the effect of various fuel mixtures on the performance of an axial-fired reheating furnace. The various fuel mixtures tested were assumed to be attained by mixing COG (coke oven gas) and BFG (blast furnace gas), which are the two main byproduct gases found in the integrated steel mill industry. The numerical prediction of radiative heat transfer was calculated using an FVM radiation solving method, which is a well-known and efficient method for curvilinear coordinates. The WSGGM (weighted sum of gray gas model) was also adopted to calculate the radiative heat transfer in composition dependent media. The entire furnace was divided into fourteen sub-zones to calculate the radiative thermal characteristics of the furnace without flow field calculations. Each sub-zone was assumed to have homogeneous media and wall temperatures. All of the medium and wall temperatures were computed by calculating the overall heat balance using some relevant assumptions. The overall heat balance was satisfied when the net heat input equaled the three sources of heat loss in each sub-zone, wall loss, skid loss, and slab heating loss.

Analysis of Radiative Heat Flux for Nozzle Flow

— A finite volume method with non-gray gas model is applied to investigate radiative heat flux on the inside wall of nozzle. The radiative properties of non-gray gas are predicted by using weighted sum of gray gases model (WSGGM). Again, 4 gray gases and narrow band based WSGGM is used to predict total heat flux and spectral intensity on the nozzle wall. Finally, the hybrid use of 4 gray gases and narrow band based model is applied to reduce computational time preserving accuracy.

Non-gray modeling of radiative heat transfer in hydrogen combustion scenarios

SUMMARY New weighted-sum-of-gray-gases model (WSGGM) parameters for H2O vapor are derived from emissivity correlations in the open literature and presented for use in hydrogen combustion simulations. Predictions employing the new WSGGM are seen to compare favorably against the spectral-line-based WSGGM on benchmark problems as well as in media conditions representative of turbulent hydrogen diffusion flames (Sandia Flame A and a model hydrogen gas-turbine combustor). The Sandia Flame A calculations were performed in a decoupled manner employing experimental measurements of temperature and gas compositions as inputs. The measured temperature variance data were employed to model the turbulence–radiation interactions. A coupled computational fluid dynamic (CFD) calculation was performed to obtain the conditions within the gas-turbine combustor geometry. The observed accuracies of the proposed set of WSGGM parameters in conditions encompassing a wide range of H2O vapor concentrations and temperature non-homogeneities encountered in combustion media make them amenable to implementation in CFD codes. Copyright © 2011 John Wiley & Sons, Ltd.

Account for variations in the H 2O to CO 2 molar ratio when modelling gaseous radiative heat transfer with the weighted-sum-of-grey-gases model

This work focuses on models suitable for taking into account the spectral properties of combustion gases in computationally demanding applications, such as computational fluid dynamics. One such model, which is often applied in combustion modelling, is the weighted-sum-of-grey-gases (WSGG) model. The standard formulation of this model uses parameters fitted to a wide range of temperatures, but only for specific ratios of H 2O to CO 2. Then, the model is limited to gases from fuels with a given composition of hydrogen and carbon, unless several sets of fitted parameters are used. Here, the WSGG model is modified to account for various ratios of H 2O to CO 2 concentrations. The range of molar ratios covers both oxy-fuel combustion of coal, with dry- or wet flue gas recycling, as well as combustion of natural gas. The non-grey formulation of the modified WSGG model is tested by comparing predictions of the radiative source term and wall fluxes in a gaseous domain between two infinite plates with predictions by a statistical narrow-band model. Two grey approximations are also included in the comparison, since such models are frequently used for calculation of gas radiation in comprehensive combustion computations. It is shown that the modified WSGG model significantly improves the estimation of the radiative source term compared to the grey models, while the accuracy of wall fluxes is similar to that of the grey models or better.

New Weighted Sum of Gray Gases Model Applicable to Computational Fluid Dynamics (CFD) Modeling of Oxy−Fuel Combustion: Derivation, Validation, and Implementation

Radiation is the principal mode of heat transfer in furnaces. Models for gaseous radiative properties have been well-established for air combustion. However, there is uncertainty regarding their applicability to oxy−fuel conditions. In this paper, a new and complete set of weighted sum of gray gases model (WSGGM) is derived, which is applicable to computational fluid dynamics (CFD) modeling of both air−fuel and oxy−fuel combustion. First, a computer code is developed to evaluate the emissivity of any gas mixture at any condition using the exponential wide band model (EWBM), and the calculated results are validated in detail against data in the literature. Then, the validated code is used to generate emissivity databases for representative air- and oxy-firing conditions, for each of which a refined WSGGM with new parameters is derived. The practical way to implement the model to CFD simulations of combustion systems is given. Finally, as a demonstration, the new model is implemented to CFD modeling of two ...

A new weighted-sum-of-gray-gases model for CO 2–H 2O gas mixtures

Decoupled radiative transfer calculations of Sandia Flame D are performed employing experimental measurements of temperature and gas compositions and the discrete ordinates method. Turbulence radiation interactions are accounted for employing temperature variance measurements. The spatial variations in the mean H 2O/CO 2 ratios within the flame are seen to vary widely and sometimes fall outside the range of the weighted-sum-of-gray-gases model (WSGGM) parameters reported in the literature. Therefore, parameters for a new WSGGM are computed from total emissivity correlations encompassing the range of the H 2O/CO 2 ratios encountered within the flame. Predictions from the new model compare favorably against the spectral-line-based WSGGM and existing benchmarks.

Study on the radiative transfer through non-gray gas mixtures within an irregular 3-D enclosure by using the modified weighted sum of gray gas method

In this study the modified weighted sum of gray gases model (WSGGM) using the gray gas regrouping technique and the discrete or- dinates interpolation method (DOIM) are applied to analyze the radiative transfer within an irregular 3-D enclosure filled with non-gray gas mixture of CO2, H2O and N2. The computer code developed in this study is successfully applied for solving the non-gray gas radia- tion within a 3-D rectangular enclosure and the gray gas radiation within an irregular 3-D enclosure by showing fairly good agreements with the existing results. In this paper the radiative transfer within an irregular 3-D enclosure filled with non-isothermal non-gray gases with uniform mixtures of CO2, H2O and N2 is studied to demonstrate the applicability of the modified sum of gray gases model for ir- regular systems and to examine the effect of the concentrations of CO2 and H2O on the radiative transfer within modern combustors. Results show that the wall heat fluxes and the radiative heat source terms are increased as the concentrations of CO2 and H2O are in- creased. Results also show that the radiative fluxes caused by the mixture gases with high concentrations CO2 and H2O which can be observed in oxy-fuel combustion systems can reach up to nearly twice of those found in ordinary air-fuel combustion systems.

Experimental and Numerical Study of the Flow Field and Temperature Field for a Large-Scale Radiant Syngas Cooler

Experimental and numerical studies on the gas-particle flow field and temperature field in the industrial-scale radiant syngas cooler (RSC) have been carried out. The bench-scale cold model experiment was presented for measuring the gas flow field in the RSC. The accuracy and performance of four turbulent flow models were evaluated according to the comparison of predicted results with experimental results. The ash particle trajectories were predicted by the stochastic Lagrangian model and the interaction between the gas and particle phase was also considered by two-way coupling method. A discrete ordinate model (DOM) was used for solving the radiative heat transfer equation when the radiative properties were calculated by weighted-sum-of-gray-gases model (WSGGM). The Ranz−Marshall correlation for the Nusselt number was used to account for convection heat-transfer between the gas phase and the particle phase. The ash particle radiative heat transfer was also considered. The physical properties of gas mixtu...

Radiation modelling in oxy-fuel combustion scenarios

Coal combustion was simulated in a lab-scale furnace and a full scale utility boiler at air-burn, oxy-combustion with dry- and wet-flue gas recycles. Good agreement was obtained between the numerical predictions and experimental measurements. The study confirmed that certain dry and wet recycle ratios imitate the temperature and heat transfer characteristics found in air combustion. The performances of five grey models to predict the radiative properties of gases in the simulations were examined. Emissivity correlations developed for purely CO2 media were not found to be suitable to predict the property at low H2O/CO2 ratios encountered during dry-recycle. Therefore, a new total emissivity correlation and a weighted-sum-of-grey-gases (WSGG) model were formulated to address the shortcomings and inaccuracies in existing grey gas models under oxy-firing. The new WSGG model with 4 band intervals was found to perform well in test cases that were representative of air- and oxy-firing conditions in boilers.

Modeling of Multiphase Flow and Heat Transfer in Radiant Syngas Cooler of an Entrained-Flow Coal Gasification

A comprehensive model has been developed to analyze the multiphase flow and heat transfer in the radiant syngas cooler (RSC) of an industrial-scale entrained-flow coal gasification. The three-dimensional multiphase flow field and temperature field were reconstructed. The realizable k−ϵ turbulence model is applied to calculate the gas flow field, while the discrete random walk model is applied to trace the particles, and the interaction between the gas and the particle is considered using a two-way coupling model. The radiative properties of syngas mixture are calculated by weighted-sum-of-gray-gases model (WSGGM). The Ranz−Marshall correlation for the Nusselt number is used to account for convection heat transfer between the gas phase and the particles. The discrete ordinate model is applied to model the radiative heat transfer, and the effect of ash/slag particles on radiative heat transfer is considered. The model was successfully validated by comparison with the industrial plant measurement data, which...

Transient radiative heating characteristics of slabs in a walking beam type reheating furnace

Transient radiative heating characteristics of slabs in a walking beam type reheating furnace is predicted by the finite-volume method (FVM) for radiation. The FVM can calculate the radiative intensity absorbed and emitted by hot gas as well as emitted by the wall with curvilinear geometry. The non-gray weighted sum of gray gas model (WSGGM) which is more realistic than the gray gas model is used for better accurate prediction of gas radiation. The block-off procedure is applied to the treatment of the slabs inside which intensity has no meaning. Entire domain is divided into eight sub-zones to specify temperature distribution, and each sub-zone has different temperatures and the same species composition. Temperature field of a slab is acquired by solving the transient 3D heat conduction equation. Incident radiation flux into a slab is used for the boundary condition of the heat conduction equation governing the slab temperature. The movement of the slabs is taken into account and calculation is performed during the residence time of a slab in the furnace. The slab heating characteristics is also investigated for the various slab residence times. Main interest of this study is the transient variation of the average temperature and temperature non-uniformity of the slabs.

Numerical analysis of methane–air combustion considering radiation effect

Turbulent premixed methane–air combustion in a cylindrical chamber is numerically simulated considering radiation effect. Reaction rates are considered as minimum rates between Arrhenius rates and eddy break up rates. A five step reduced mechanism is used. Turbulent modeling is done via standard k- ε model imposed by empirical inlet boundary conditions. Source terms of energy equation consist of reaction rates and radiation effects. The discrete ordinate method (DOM) is employed to solve the radiative transfer equation (RTE) and the weighted sum of gray gas model (WSGGM) is imposed to consider radiation effect of non-gray gases. The results indicate that in the case of turbulent combusting flows, the effect of radiation of gases can affect the temperature and species concentrations. The numerical results obtained considering radiation effect are closer to the experimental data than that of the case without radiation effect.

Radiative heat transfer between two concentric spheres separated by a two-phase mixture of non-gray gas and particles using the modified discrete-ordinates method

The radiative heat transfer between two concentric spheres separated by a two-phase mixture of non-gray gas and a cloud of particles is investigated by using the combined finite-volume and discrete-ordinates method, named modified discrete-ordinates method (MDOM), which integrates the radiative transfer equation (RTE) over a control volume and a control angle simultaneously like in the finite-volume method (FVM) and treats the angular derivative terms due to spherical geometry as the conventional discrete-ordinates method (DOM). The radiative properties involving non-gray gas and particle behavior are modeled by using the extended weighted sum of gray gases model (WSGGM) with particles. Mathematical formulation and final discretization equations for the RTE are introduced by considering the behavior of a two-phase mixture of non-gray gas and particles in a spherically symmetric concentric enclosure. The present approach is validated by comparing with the results of previous works including gray and non-gray radiative heat transfer. Finally, a detailed investigation of the radiative heat transfer with non-gray gases and/or a two-phase mixture is conducted to examine the dependence of the radiative heat transfer upon temperature ratio between inner and outer spherical enclosure, particle concentration, and particle temperature.

Multiscale modeling of turbulent combustion and NOx emission in steam crackers

AbstractA 3D RANS simulation of lean premixed turbulent combustion in an industrial scale steam cracking furnace is performed. Turbulence is represented by a renormalization group (RNG) k − ε model, while combustion is modeled with a skeletal mechanism. The eddy dissipation concept (EDC) model is used to account for turbulence/combustion interaction. The turbulent combustion regime is identified as a “thin flame regime with pockets” or a “corrugated flamelet regime”. A weighted sum of gray gases model (WSGGM) is used to account for the gas radiative properties. The radiative transfer equation is solved using the P‐1 and discrete ordinates method in the conservative finite volume formulation. NOx calculations are performed as a postprocessing step, with the flow field, temperature, and species concentrations fixed. The formation of NO through thermal, prompt, and N2O intermediate mechanisms is considered. The in situ adaptive tabulation technique is used to decrease the computational time required to treat the combustion chemistry. The effect of radiation models on the predicted furnace wall, tube skin, and flue gas temperature profiles and heat fluxes toward the reactor tubes, as well as on the predicted species and NO concentration profiles and structure of the furnace flames under normal firing conditions, is discussed. © 2007 American Institute of Chemical Engineers AIChE J, 2007

Impact of radiation models in CFD simulations of steam cracking furnaces

The endothermic thermal cracking process of hydrocarbons takes place in tubular reactor coils suspended in large gas-fired pyrolysis furnaces. Heat transfer to the reactor tubes is mostly due to radiation from the furnace refractory walls and the flue gas. A three-dimensional (3-D) simulation of the flow in an industrial scale steam cracking furnace is performed. The renormalization group (RNG) k − ɛ turbulence model is used. The combustion kinetics is modeled by a three-step reaction mechanism, while turbulence–chemistry interaction is taken into account through the Finite Rate/Eddy-Dissipation model. The Discrete Ordinates model (DOM), the P-1 and the Rosseland Radiation model are used for modeling of the radiative heat transfer. The results of using the different radiation models are compared mutually with adiabatic simulation results. The absorption coefficient of the gas mixture is calculated by means of a Weighted-Sum-of-Gray-Gas model (WSGGM). The effect is discussed of the use of different radiation models on the predicted wall, tube skin and flue gas temperature profiles and heat fluxes towards the reactor tubes, as well as on the predicted species concentration profiles and structure of the furnace flames under normal firing conditions.

Numerical investigation of combustion with non-gray thermal radiation and soot formation effect in a liquid rocket engine

A numerical analysis was carried out in order to investigate the combustion and heat transfer characteristics in a liquid rocket engine in terms of non-gray thermal radiation and soot formation. Governing gas and droplet phase equations with PSIC model, turbulent combustion model with liquid kerosene fuel, soot formation, and non-gray thermal radiative equations are introduced. A radiation model was implemented in a compressible flow solver in order to investigate the effects of thermal radiation. The finite-volume method (FVM) was employed to solve the radiative transfer equation, and the weighted-sum-of-gray-gases model (WSGGM) was applied to model the radiation effect by a mixture of non-gray gases and gray soot particulates. After confirming the two-phase combustion behavior with soot distribution, the effects of the O/F ratio, wall temperature, and wall emissivity on the wall heat flux were investigated. It was found that the effects of soot formation and radiation are significant; as the O/F ratio increases, the wall temperature decreases. In addition, as the wall emissivity increases, the radiative heat flux on the wall increases.

회색가스재조합을 이용한 회색가스가중합법 개발 및 3차원 복사열전달에의 적용

The narrow band-averaged transmissivity of CO₂-H₂O mixtures is expressed by multiplying the transmissivities of CO₂ and H₂O. Applying the multiplication property of narrow band transmissivities for gas mixtures of CO₂-H₂O of the narrow band based WSGGM (weighted sum of gray gases model), the number of gray gases, required for accurate representation of the absorption characteristics by using the narrow band based WSGGM, is significantly increased. To reduce the computational loads by reducing the number of gray gases, we propose a gray gas regrouping process where the gray gases used for the WSGGM are regrouped into a specified number of groups according to the magnitudes of absorption coefficients. To evaluate the proposed WSGGM for gas mixtures, the radiative transfer problems through 3-dimensional gas media are considered. The radiative source terms and the radiative heat fluxes obtained by using the proposed method are fairly well compared to previous results obtained by using the SNB model and other models. The regrouping technique results in an excellent computational efficiency with minor loss of accuracy.

Assessments of Spectral Narrow Band and Weighted-Sum-of-Gray-Gases Models for Computational Fluid Dynamics Simulations of Pool Fires

The statistical narrow band (SNB), correlated-k (CK), and weighted-sum-of-gray-gases (WSGG) models have been incorporated into a computational fluid dynamics (CFD) code. Their accuracy and computing times are evaluated for three pool fires scenarios. CFD_CK and CFD_SNB yield similar predictions, and the former is three times more CPU demanding than the latter. CFD_CK is unrealistic for practical fire applications. Temperature and velocity predictions with CFD_WSGG and CFD_SNB agree better in the persistent and plume regions, but significant discrepancies are found in the intermittent region. The overall predictions of the two approaches show reasonable agreement. The WSGG model should not be discarded for CFD fire simulations.

Effect Of Radiation Models On Cfd Simulations Of Upward Flame Spread

In combustion applications, the weighted-sum-of-grey-gases (WSGG) model is widely used because it is computationally efficient, but it often yields relatively large errors. The objective of this study is to examine the effect of radiation models on CFD predictions of flame spread. To this end, a statistical narrow band (SNB) model and the WSGG model are employed for the simulation of two upward flame spread scenarios, one being a largescale flame spread over a vertical PMMA wall while the other representing flame spread along vertical corner walls. The entire flame spread model also consists of a four equation turbulence model, an eddy-break-up (EBU) combustion model, a discrete transfer (DT) radiation model, a simple soot model and a non-charring pyrolysis model. Quantitative comparison is made between the prediction results obtained with the SNB model and the WSGG model as well as the experimental data. Results clearly show that the SNB model yields more accurate results than the WSGG approach. However, the SNB model is about four to five times more time consuming than the WSGG model. Therefore, for simulations of complex engineering applications a compromise between accuracy and numerical efficiency should be taken into account.