Gray Gas Research Articles

3D CFD simulation of a 250 MWel oxy-fuel boiler with evaluation of heat radiation calculation

The oxy-fuel process is a promising technology for capturing carbon dioxide from power plants. The fuel, in this case coal, is burned with pure oxygen instead of air in the oxy-fuel process. Since combustion with pure oxygen results in very high temperatures, flue gas must be recirculated and returned to the combustion chamber to lower and control the combustion temperature. This in turn leads to significantly higher concentrations of carbon dioxide and water vapor in the flue gas of the power plant boiler compared to the regular air-fired process, which result in increased radiant heat transfer to the evaporator tubes along the combustion chamber walls. Efficient models are available that can be applied to the numerical simulation of combustion chambers. A widely used model is the Weighted Sum of Gray Gases Model (WSGGM).In this work, the combustion chamber of an oxy-fuel power plant on a demonstration scale with an electrical output of 250 MWel was simulated to compare the results of different gas and particle radiation models. The gas radiation was modelled with the different WSGG model formulations. In addition, the influence of particle radiation was investigated. Therefore the emissivity of the particles were correlated to experimental data. The results corresponds in all cases with the output design of the power plant. The combustion exit temperature is slightly over-predicted for all models and particle properties. It has shown that the particle radiation has a strong influence on the heat wall flux in the burner region where the particle load is high.

Numerical simulation of the interaction of uranium hexafluoride with methane and oxygen in turbulent flame

Model of the uranium hexafluoride conversion in a methane-oxygen turbulent diffusion flame is presented. Model of the weighted sum of grey gases was used to calculate the absorption coefficient of mixture of uranium dioxide particles and carbon dioxide. Radiation heat transfer model was calibrated using available experimental data. A good agreement was obtained between the simulation results and experimental data.

Numerical investigation of swirl-stabilized pulverized coal flames in air and oxy-fuel atmospheres by means of large eddy simulation coupled with tabulated chemistry

This paper investigates a self-sustained swirl-stabilized pulverized coal combustion chamber, specially designed to validate numerical models under atmospheric and oxy-fuel conditions. For this purpose, a comprehensive model, which accounts for both atmospheric and oxy-fuel conditions, is developed based on Large Eddy Simulation. To describe the turbulent gas-phase chemistry, a 4D Flamelet Generated Manifold based tabulated chemistry model is coupled with the artificially thickened flame approach and implemented in an Euler–Lagrange framework. The chemistry model is able to account for finite rate chemistry, heat losses, mixing devolatilization gases and char off-gases. Radiative heat transfer is included by solving the radiative transfer equation, applying the discrete ordinate method for angular discretization and a weighted sum of gray gas model for the spectral resolution, while particles are treated as gray. The simulation results from the combustion chamber are extensively validated against the available measurement data. Operating conditions with different atmospheres are investigated to validate the models’ prediction accuracy for air and oxy-fuel atmospheres. The validation process is carried out using velocity fields, particle temperature measurements and the gas-species concentrations. Overall, the comparisons between simulations and measurements reveal a favorable agreement with only small differences near the burner opening. These results demonstrate the suitability of large-eddy simulation combined with tabulated chemistry for predicting the combustion of pulverized coal in conventional air and oxy-fuel atmospheres. Further analyses of the self-sustained coal flames are carried out; in particular, the influence of different atmospheres on the interaction of coal particles with the gas phase is studied.

Performance of banded SLW-1 in presence of non-gray walls and particles in fluidized bed combustors

In this study, banded one gas spectral line-based weighted sum of gray gases (banded SLW-1) model is coupled with a 3-D radiation code based on method of lines (MOL) solution of discrete ordinates method (DOM) for freeboard of METU 0.3 MWt atmospheric bubbling fluidized bed combustion (ABFBC) test rig containing non-gray gas, non-gray particle mixture bounded by non-gray walls. Spectral parameters of banded SLW-1 are estimated by the approach based on two emissivities calculated at two different path lengths L1 and L2. The predictive accuracy of banded SLW-1 model is tested by comparing its incident wall heat flux and source term predictions with measurements and predictions of banded SLW. The results indicate that band-wise selection of L1 and L2 based on spectrally averaged mean beam length provides the most accurate radiative heat transfer predictions. Furthermore, based on a sensitivity analysis on the test rig under consideration, utilization of path lengths L1 and L2 which are 0.10 and 1.10 times of the spectrally dependent mean beam length is found to yield the best radiative heat transfer predictions in terms of accuracy. Incident heat flux and source term predictions of banded SLW-1 are found to be in reasonable agreement with those of banded SLW under both air and oxy-fired conditions. Furthermore, CPU time requirement of banded SLW-1 is about 20–25 times lower than that of banded SLW. With the introduction of fly ash recycling, particle load increases an order of magnitude leading to further improvement in the accuracy of banded SLW-1. On the other hand, gray wall assumption leads to accurate radiative heat flux predictions whereas this assumption leads to considerable inaccuracies in the source term predictions in the upper region of freeboard. However, those inaccuracies become insignificant with the introduction of fly ash recycling. Application of the model to different wall conditions common in the industry indicates that discrepancies between the source term predictions of gray and non-gray cold water wall and those of gray and non-gray cold slag covered water wall are insignificant for the combustion test rig under consideration which is attributed to the combined effects of low wall temperatures and similar gray and non-gray wall emissivities.

Effects of ladle lid or online preheating on heat preservation of ladle linings and temperature drop of molten steel

Two usual ways used in steel plants to preserve the heat of the ladle lining are online preheating and ladle capping. In this study, the finite volume method (FVM) was adopted to build a combustion and fluid-solid heat transfer 3D model for online preheating, and a fluid-solid heat transfer 3D model for the process of ladle capping and the heavy ladle. The numerical computational analysis was conducted by the Fluent software. Through the weighted sum of grey gases model (WSGGM), variable emissivity and absorptivity of the flue gas during the preheating process were taken into account and added into the energy conservation equation of the flue gas in the form of a source item via the radiation transfer equation. This paper analyzed the influence of the two heat-preserving measures, namely ladle capping and online preheating by means of regenerative combustion, on the heat preservation effect of the ladle lining, and further compared and analyzed their effects on the temperature drop of molten steel. As suggested by the results, capping during the empty ladle process had better effect on the molten steel’s temperature drop than during the heavy ladle process. Full-process capping can reduce the molten steel’s temperature drop rate by 0.11 K min−1 than when no capping was added at all. When 10–30 min of online preheating was applied during empty ladle process, the average temperature of the working lining of the ladle can be raised by about 72.5–130.3 K. The rate of heat increase on the lining decelerates as the online preheating was prolonged. As for the effect on the temperature drop of molten steel in heavy ladle process, 30 min of online preheating had almost the same effect as the full-process capping.

Systematic study of the impact of chemistry and radiation on extinction and carbon monoxide formation at low scalar dissipation rates

In fire flames scalar dissipation rates in the reaction zone are low and radiation becomes important for extinction. The chemistry mechanism also strongly affects extinction and CO formation. The present study applies the unsteady laminar flamelet approach (or, equivalently, the conditional moment closure (CMC) method in mixture fraction domain, without transport in physical space). Six chemistry mechanisms are analyzed. In addition to adiabatic conditions, three radiation models are considered: RADCAL-based gray gas; weighted sum of gray gases (WSGG); and prescribed radiative fraction model. The oxygen mass fraction values for extinction are discussed, diluting the oxidizer by adding nitrogen. Carbon monoxide profiles are reported as well. The radiative fraction model is not capable of predicting the strong radiative effects at low scalar dissipation rates, while the RADCAL-based and the WSGG model are able to do so. The analysis of extinction and CO reveals strong sensitivity to the mesh in mixture fraction space, as well as to the shape of the conditional scalar dissipation rate profile. Results with the ARM2 mechanism and GRI3 are in very close agreement, so that significant time savings are possible, using ARM2.

Space-angle discontinuous Galerkin method for radiative transfer between concentric cylinders

The integro-differential radiative transfer equation (RTE) for concentric cylinders problem involving scattering, absorption and emission is solved using the discontinuous Galerkin (DG) finite element method (FEM). The space-angle DG method directly solves the cylindrically-symmetric RTE as a three-dimensional problem, where a 1D spatially domain in radial distance r is twice extruded in the cosine of polar angle (μ) and the difference in azimuthal angle (φ˜) directions. Thus, the method has a higher accuracy than hybrid FEM-Discrete Ordinate (SN) and FEM-Spherical Harmonic (PN) methods. This is reflected by numerically verified convergence rate of p+1 for smooth problems and space-angle polynomial interpolation order of p. The axisymmetric RTE formulation is more complicated than the plane-parallel formulation, for having two independent angle directions (μ and φ˜) and an extra derivative term with respect to φ˜ in the differential equation. This results in a complex characteristic structure in r−φ˜ plane with strong discontinuity lines in radiation intensity I. A method of characteristics is formulated and implemented to verify the DG formulation and demonstrate its accuracy when such strong discontinuities persist in the solution, specifically when there are no scattering and absorption terms. The relaxation of inter-element continuity constraint of continuous FEMs by this DG method implies its superiority in numerically capturing such discontinuities. Finally, a benchmark problem pertained to heat radiation in a gray gas and another one with nonzero phase function demonstrate the effectiveness of the method in modeling black-body and scattering angular integration terms.

Large eddy simulations of the UMD line burner with the conditional moment closure method

The conditional moment closure (CMC) method is applied in combination with large eddy simulations (LES-CMC) to the UMD line burner configuration. This corresponds to a low-strain, buoyant diffusion flame. The low strain rate conditions are representative of fire conditions and the aim of the study is to evaluate LES-CMC results, including radiative effects. Only conditions far from extinction are studied. The weighted sum of grey gases model (WSGGM) for radiation is applied in mixture fraction space. Results are compared to what is obtained when radiation is taken into account as a local loss term in the conditional heat release rate, with prescribed radiative fraction. It is shown that the conditional scalar dissipation rate (CSDR) profile in mixture fraction space and the spatial terms in the transport equations for the conditional quantities have a major impact with the non-local WSGGM approach, while this is not the case in adiabatic simulations, nor in the radiative fraction approach. In the latter, only the value of the CSDR at stoichiometric is important, making this approach less sensitive. However, the latter are not well suited for extinction simulations.

New formulae for gray gas absorptivities of H2O, CO2, and CO

In our previous publications we have presented revised and extended versions of Hottel’s total emissivity charts for water vapor, carbon dioxide, carbon monoxide and their mixtures. In applications, not only emissivity but also absorptivity is required. In 1935, Hottel and Mangelsdorf produced formulae for calculating total absorptivity using total emissivity for carbon dioxide and water vapor. In 1959, Penner proposed another formula. In this paper we determine accuracy of these approximate formulae using the most advanced line-by-line model based on HITEMP-2010. The accuracy has been determined over 400–3000 K range for both absorbing gas temperatures and source temperatures, for total pressure range from 0.5 bar to 80 bar, and mole fractions (in mixtures with nitrogen) from 0.1 to 1.0 for carbon dioxide, water vapor and carbon monoxide. The path-length range examined is from 0.01 to 3000 bar cm. Furthermore, new formulae have been derived and they provide more accurate predictions.

Numerical assessment of radiative heat transfer impact on pollutant formation processes in a compression ignition engine

An imposed solution in the development process of compression ignition engines is the use of numerical research employing Computational Fluid Dynamics (CFD). At the high operating temperatures in compression ignition engines, the radiative heat transfer influences the overall temperature profile and heat transfer, which also affects the formation processes of pollutants. For the radiative transfer calculation in this work, method of discrete ordinates (DOM) employing Finite Volume Method (FVM) is implemented with user functions into the AVL FIRE™ CFD code. The absorptivity and emissivity are described with the implemented Weighted Sum of Grey Gases Model (WSGGM) based on non-isothermal and nonhomogeneous absorption coefficient correlations for carbon dioxide, water vapour and soot. The implemented procedure is extended to work with moving meshes, parallel computing and rezoning procedure, which are needed to account the radiative heat transport in internal combustion engines. Additionally, the focus of this work is on the performed validation of calculated mean temperature, pressure, rate of heat release and emission results against the compression ignition engine experimental measurements. Results with the implemented radiation model showed lower peak temperatures for approximately 10 K, which resulted in around 18% lower nitrogen oxides concentrations, and up to 20% higher soot concentrations at the end of engine operating cycle. The most dominant impact of the radiative heat transfer on soot formation is visible at the crank angles, where peak temperatures occur. The performed parameter study of the piston and head wall emissivity values showed a reduction in mean in-cylinder pressure and NO mass fraction for a less reflective surface. From the conducted parameter analysis of ordinates number, the sufficient accuracy is achieved for simulations with eight ordinates, which resulted in approximately 50% increased computational time. Finally, it may be concluded that the combination of implemented models is useful to predict the heat transfer of internal combustion engine focussing on the radiative heat transport, which can be an important factor for the development of forthcoming internal combustion engines.

Thermal radiation characteristics in dilute phase region of the oxy-fuel combustion pressurized fluidized bed

The thermal radiation transfer was complex due to high pressure, complicated flue gas components and abundant particles in the dilute phase region of oxy-fuel combustion pressurized fluidized bed. To carry out the radiation heat transfer, numerical simulations were done based on weighted sum of gray gases model (WSGG) and Mie theory. The Radiation Transfer Equations (RTE) of bubbling fluidized bed and circulating fluidized bed was solved by discrete ordinate method (DOM). The radiation heat transfer of fluidized bed under air combustion was verified and then the simulations were accomplished under pressurized oxy-fuel combustion hypothesis. The results revealed that the particle radiation was still dominant under pressurized oxy-fuel combustion. The change of total pressure and gas composition had slight effects on the radiation heat transfer in the fluidized bed. The gas radiation described by the new pressurized WSGG model and RTE solving by body-fitted coordinate system were much accurate to simulate radiation heat transfer. All the results were significant to provide theoretical basis of designing and building an oxy-fuel combustion pressurized fluidized bed.

Application of a new grey prediction model and grey average weakening buffer operator to forecast China’s shale gas output

Scientifically and accurately forecasting of future shale gas output tends is very important in making energy policies, especially for China whose historical data of shale gas output is very limited. The existing grey shale gas output prediction model does not perform well in prediction due to its defects. To overcome these shortcoming, this paper, based on the principle of “new information priority”, combined with the contradiction between model prediction results and qualitative data analysis conclusions, designs a grey prediction model combining new initial conditions and original data reprocessing. Then the new model’s accumulative order is optimized by fraction accumulation generation operation and its properties is discussed. Finally, the new model is used to simulate and forecast shale gas output in China from 2012 to 2018 and compared it with the existing shale gas prediction model. The comparison results show that the new model reduces by 84.34%, 68.96% and 75.60% of the mean relative simulation percentage error (MRSPE), mean relative prediction percentage error (MRPPE) and comprehensive mean relative percentage error (CMPPE) respectively. This paper not only has theoretical innovations but also provides a good mathematical method for predicting shale gas output.

Radiative transfer calculations in fire simulations: An assessment of different gray gas models using the software FDS

The accuracy of the gray gas (GG) assumption for modeling the radiative transfer in fire simulations is studied for a closed compartment, an open environment, and a compartment with an opening. The liquid fuels used for each case are ethanol, heptane and methanol, respectively. Three different GG formulations, implemented on the solver Fire Dynamics Simulator (FDS), are tested and compared to experimental data. Transient, large eddy simulations (LES) are carried out in FDS, where the radiative transfer is solved coupled to the fluid flow and combustion processes. For each fire configuration, the GG formulations are compared to each other and to experimental data. The mean radiative heat flux computed in the simulations showed a good correspondence to measurements, especially for the ethanol and heptane flames, with average deviations ranging between 7% and 21%, which indicates that the GG assumption is adequate even for these weakly-sooting fuels. Among the GG models tested, the default formulation employed by FDS and the one based on a weighted-sum-of-gray-gases estimation of the medium emittance performed similarly, both providing in general more accurate results than the approach using the Planck-mean absorption coefficient.

Spherical and cylindrical shocks in a non-ideal dusty gas with magnetic field under the action of heat conduction and radiation heat flux

In this article, the propagation of spherical or cylindrical shock waves in a mixture of small solid particles of microsize and a non-ideal gas with conductive as well as radiative heat fluxes are studied under the influence of an azimuthal or axial magnetic field. The solid particles are uniformly distributed in the mixture, and the shock wave is assumed to be driven by a piston. It is assumed that the equilibrium flow conditions are maintained and the moving piston continuously supplies the variable energy input. The density of the undisturbed medium is assumed to be constant in order to obtain the self-similar solutions. Heat conduction is expressed in terms of Fourier’s law, and the radiation is considered to be of diffusion type for an optically thick gray gas model. The thermal conductivity and the absorption coefficient are assumed to vary with temperature and density. Numerical calculations have been performed to obtain the flow profiles of variables. The effects of different values of the non-idealness parameter, the strength of the magnetic field, the mass concentration, the ratio of the density of solid particles to the initial density of the gas, the piston velocity index, and the adiabatic index are shown in detail. It is interesting to note that in the presence of an azimuthal magnetic field, the pressure and density vanish at the piston, and hence, a vacuum is formed at the center of symmetry, which is in excellent agreement with the laboratory condition to produce the shock wave. The author of the article agrees to the retraction of the article effective AUGUST 20, 2021.

Assessments on SGG and WSGG spectral models in high-ash coal combustion

In radiation process, a variety of models can be used to represent the spectral radiative properties of combustion gases. In coal combustion, the high level of soot concentration brings higher complexity to the formulation. Several pieces of research are found, comparing different radiation models usually applied to idealized laboratory situations. Only a few works explore the behavior of such models in real scale applications, such as coal-fired furnaces. Comparisons among different arrangements of the SGG and WSGG models were carried out by means of CFD simulations, applied to a boiler of a real 160 MW coal-fired power plant. Five different cases were simulated. The most simple case was set with a fixed absorption coefficient SGG model, while the most detailed case was achieved by employing a WSGG model with gas and soot absorption coefficients overlay. Temperature fields were well represented by all cases, with maximum deviations of 6%. Predictions on radiative heat flux for the SGG models were significantly lower than the WSGG simulations, with relative deviations up to 16.46%. Even though deviations on radiative heat flux are significant, results suggest the suitability of simple gray gas models in fast assessments of industrial applications such as coal-fired furnaces.

Numerical study of an unsteady confined thermal plume under the influence of gas radiation

Influence of gas radiation on a thermal plume initiated by a linear heat source in a confined cavity is investigated through numerical simulations. A 2D pure convection case is first considered to validate the numerical code by comparing the critical Rayleigh number against literature results. Then, simulations are extended to 3D configurations for three different values of the Rayleigh number: 106, 1.2×106and 1.2×107. The evolution of the plume is analyzed and shows that the transition to unsteadiness appears much earlier for 3D case. Periodic solutions in time exhibit a stationary plane wave which is further broken in the chaotic regime. Finally, gas radiation is introduced at Ra=1.2×107by considering different gaseous media: on one hand, a gray gas model with various optical thicknesses, and on the other hand, a real gas model for humid air (air - H2O mixture). Results show a strong influence of the radiative transfer on flow regimes. By increasing the optical thickness, radiation tends to stabilize the plume and delays the onset of unsteadiness. Comparison of the time-averaged temperature and velocity distributions for the considered gas models indicates that gas radiation reduces the spatial spreading of the plume but has little effects on the kinetic field.

Numerical study on forced convection in the exhaust problem using the spectral line-based weighted sum of gray gases model

In this work, influences of thermal radiation on forced convection in the Exhaust problem are effectively simulated by application of the spectral line-based weighted sum of gray gases (SLW) model. The Exhaust problem includes an abrupt contraction in a horizontal channel. The working fluid of this problem is an air mixture with 10% CO2 and 20% H2O mole fractions. This mixture is regarded as an emitting, absorbing and non-scattering medium. In addition, the gray model is utilized to simulate the radiative medium based on total emissivity. Then, the findings of this model are compared with the results of SLW model as the main case to attain the error rate of gray model in simulating the Exhaust problem. The results clearly show the differences between the gray and SLW models to simulate the thermal behaviors are strongly dependent on the radiation-conduction parameter (25 ≤ RC ≤ 50) and wall emissivity (0 ≤ ɛw ≤ 1). In this regards, the gray model is unable predict the real results in many cases.

Numerical study of hydrogen/methane buoyant fires using FireFoam

Hydrogen/methane buoyant fires with various hydrogen volume fractions ranging from 0% to 20% were numerically studied in this paper. The modified eddy dissipation concept combustion model for multi-fuels in the large eddy simulation (LES) framework was employed for combustion, and especially the infinitely fast rate based on “global” concept was improved. Combined with the weighted sum of gray gas model for emission/absorption coefficient, the finite volume discrete ordinates model was used to compute the radiative heat transfer. The predicted centerline temperature, velocity, and flame height are in good consistence with the measured data. Furthermore, the detailed analysis was conducted on the dependency of the parameters such as centerline temperature and velocity, flame height, and soot volume fraction on hydrogen volume concentration.

Effect of oxygen enrichment in spectral thermal radiation in an unconfined turbulent bluff-body flame

Oxy-fuel combustion is a modern carbon capture and storage (CCS) technique that improves the combustion process and reduces the environmental penalty of many combustion systems. Evidently, the accurate radiative calculation of oxy-fuel combustion is very important to obtain more improved combustion system designs with less environmental drawbacks. In the present study, a small scale unconfined turbulent bluff-body flame is numerically simulated to calculate the gas radiative properties using three different approaches of ignoring radiation, applying a modified version of the weighted sum of gray gases (WSGG) model, and employing the spectral line based weighted sum of gray gases (SLW) model. First, the selected bluff-body flame is validated against experimental data. The early outcome is that the simulation results of three chosen approaches are very close if there is no oxygen enrichment. Next, the effect of oxygen enrichment is carefully investigated imposing the aforementioned spectral radiation approaches. The achieved results indicate that the predicted gas temperature becomes more sensitive to the implemented radiative approach as the oxygen concentration in the oxidizer increases. In very high oxygen enrichment condition, the gas temperature predicted by SLW model shows up to 155 K differences with that of ignoring radiation approach. The simulation results also show that the oxygen enrichment would raise the CO2 and H2O volume fractions in the flame zone. Therefore, the non-grayness of gases becomes more significant in such conditions and the accurate radiative calculation becomes more essential. This is investigated carefully in this study.

Combined convection–radiation heat transfer from n-octane combusted gas passing through different geometrical ducts

The combined radiation–convection heat transfer occurs in many industrial devices; in many occasions, the significant role of radiation is neglected in engineering modeling. The current study is an attempt to address the importance of radiation heat transfer involvement in numerical computations. The investigation takes place in two heat transfer modes of with radiation (case_rad) and without radiation consideration (case_norad) for different duct geometries of base cylinder, small cylinder, divergent frustum cone, and convergent frustum cone. To account the radiation effect in the ducts, discrete transfer radiation method is applied, while a weighted sum of gray gases model for absorption coefficient modeling in non-homogenous participating media is appropriate for combustion of n-octane gas in ducts. The convergent duct structure shows the most radiative flux of − 1514.4 W m−2, whereas small cylinder demonstrates the lowest radiative flux of − 1033.14 W m−2. The overall heat flux of convergent configuration outperforms due to homogenous distribution of O2 and high oxygen mass fraction for combustion, while increasing the surface area in the flow direction aids the heat transfer improvement. The small cylinder is characterized with better flow dynamics (Vmax = 25.72 m s−1, TKEmax = 9.45 m2 s−2); however, its deficiency in heat transfer leads to high temperature along the duct (Tmax = 710 K).