Gray Gases Model Research Articles

LES of a swirl-stabilized 40 kWth biomass flame and comparison to a coal flame

Recent advancements have introduced high-fidelity simulations in pulverized coal combustion, yet the shift toward renewable fuels like biomass raises questions about suitable modeling approaches to understand the influence of the new fuel. The current study aims to examine the variations between biomass and pulverized coal flames by employing extended high-fidelity modeling approaches integrated into a Large Eddy Simulation (LES) framework. A fully coupled solid fuel-gas phase model is developed to investigate pulverized biomass and coal flames. Models for particles that are treated in a Lagrangian manner include state-of-the-art devolatilization and char models calibrated with advanced conversion models for the conditions under investigation. Using five-dimensional tabulated flamelet manifolds, gas phase reactions are modeled by two chemical mechanisms tailored to the respective fuel properties. Radiation is considered by solving the radiative transfer equation employing the weighted sum of gray gas model. This high-fidelity simulation framework is applied to a self-sustained, swirl-stabilized 40 kWth burner that is fired with walnut shells and Rhenish lignite, respectively. Both fuels are studied under the same flow conditions and thermal output to enable a thorough analysis of the fuel effects. The results are validated with experimental particle velocities. Using advanced post-processing for particle grouping, a close link between flame shape and differences in particle trajectories is established, indicating the high significance of particle size when transitioning between fuels.

Computational assessment of soot models in ethylene/air laminar diffusion flames

To improve the accuracy of soot formation and evolution predictions, several physical and chemical models have been developed over the last decades. These models include (i) detailed chemical kinetic mechanisms describing both gas-phase chemistry related to combustion processes and reaction pathways leading to large-sized aromatic molecules, which are needed for modelling soot formation, and (ii) soot models providing a comprehensive description of soot particle dynamics and interactions with gas-phase chemical species. Accordingly, in this work, two detailed soot models, the method of moments (MOM) and the discrete sectional method (DSM), are evaluated in ethylene/air laminar diffusion flames, and their corresponding results are compared with experimental measurements. Furthermore, the NBP and KM2 chemical kinetic mechanisms are assessed and compared with each other by examining key chemical species related to soot formation and evolution. To compute gas mixture’s radiative properties, the weighted sum of grey gases model considering a grey medium is also utilised. Finally, the contributions of the soot precursors known as PAH (polycyclic aromatic hydrocarbon) to soot formation are also analysed. The main results show that the discrepancies in PAH concentrations obtained with different chemical kinetic mechanisms can be significant. In addition, compared to MOM ones, DSM results obtained here show a better agreement with experimental data. Finally, the analysis of PAH shows that those with two (A2) to four (A4) aromatic rings impact the most on soot modelling. Specifically, contributions of A4 were found to be more significant at lower heights above the burner, whereas A2 was found to be more impactful downstream as the flame develops. Maximum contributions of A2 and A4 to the soot inception rate were 66% and 85%, respectively, whereas the maximum summed contribution of PAH with five (A4R5) to seven (A7) aromatic rings accounted for only 13% of the inception rate.

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

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

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

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

Assessing the impact of wet and dry flue gas recycling on heat transfer in oxygen-fired circulating fluidized bed furnaces

Oxygen-driven circulating fluidized bed combustion (oxy-CFB) has been suggested as a potential technique for facilitating carbon capture in large-scale power generation. Precise modeling of radiative heat transfer is vital for forecasting the thermal performance of such processes. This research examines the impact of wet and dry flue gas recycling on the thermal behavior of a large-scale oxy-CFB furnace, utilizing a combined modeling strategy that merges a three-dimensional furnace process model with a thermal radiation solver. The semi-empirical furnace model operates in steady-state conditions, accounting for fluid dynamics, reactions, and heat transfer phenomena. The radiation solver, based on the zone method, employs novel correlations for radiative heat exchange between optically thick zones. The radiation solver employs a weighted sum of the gray gases model, developed specifically for oxy-combustion, and geometric optics to determine the radiative characteristics of combustion gases and particles, respectively.This research covers various process conditions and boiler loads to evaluate the influence of wet versus dry flue gas recycling on heat transfer and temperature profiles. Model results were successfully compared against small-scale oxygen-fired CFB tests and large-scale measurements in a supercritical air-fired CFB. Utilizing an external radiation solver allows for a more precise representation of radiative heat transfer and the influence of varying process conditions. The insights from this research can aid in the design of large-scale oxy-CFB facilities, and the demonstrated modeling approach can be employed for additional model development, such as integrating the external radiation solver with other modeling tools.

Numerical study on oxy-fuel combustion characteristics of industrial furnace firing coking dry gas

One of the most promising methods for clean utilization of hydrocarbon fuels and CO2 capture is oxy-fuel combustion. However, report on oxy-fuel burning of industrial gas is still limited. In the study, numerical simulation was conducted to explore the oxy-fuel combustion performance of a coking dry gas fired industrial furnace. A modified weighted sum gray gas (WSGG) model with a four-gray body and fourth-degree temperature polynomial was proposed for both air and oxy-fuel combustion with the introduction of the fourth graybody. The impacts of oxygen content, excess oxygen ratio, oxygen purity, and dehydration efficiency on combustion and heat transfer were mainly investigated. The maximum furnace temperature increases significantly, and the high temperature region inside the furnace shrinks and moves downward as the oxygen content rises. The H2O content increases from ∼20% to ∼37%, and the CO2 content decreases from ∼77% to ∼60%. The furnace temperature is up to 1835 K under air conditions, while the furnace temperature is reduced by 195 K under oxy-fuel condition of 21% O2 content. The composition of flue gas barely changes as the excess oxygen ratio increases from 1.02 to 1.20. Although the CO2 enrichment in flue gas and the improvement of oxy-fuel combustion performance benefit from an increase in oxygen purity, the combustion performance further advances little when it is raised to over 98%. Additionally, when dehydration efficiency grows, radiant heat transfer decreases and the flue gas temperature at the furnace outlet rises. The content of O2 and N2 has little relationship with dehydration efficiency. This study aids in understanding the actual oxy-fuel combustion process of an industrial gas-fired boiler and offers a possible theoretical basis for clean burning of petrochemical combustible gas and carbon capture.

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

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

Effects of Radiation Model on Soot Modeling in Laminar Coflow Diffusion Flames at Elevated Pressure

ABSTRACT Detailed numerical simulations of C2H4/Air coflow laminar sooting flames at atmospheric and elevated pressures are performed with fully coupled flow, gas-phase reactions, soot dynamics, and nongray radiative heat transfer. The soot dynamics is modeled using a hybrid method of moments combined with a polycyclic aromatic hydrocarbon (PAH) mechanism. Nongray radiative heat transfer by CO2, H2O, and soot is calculated using different methods to study the effect of radiation model on the predictions. The discrete ordinates radiation model (DOM) and P1 radiation model are compared. Three radiative property models with different accuracy and efficiency are included: a) full-spectrum correlated- distribution (FSCK) model, b) weighted sum of gray gas model with original parameters (WSGG-Smith), and c) WSGG model with optimized parameters for variable mole ratios and elevated pressure (WSGG-SK). The optically thin approximation (OTA) model is also compared to a simple baseline case. The results show that the temperature and soot volume fraction predicted by the DOM combined with the WSGG-SK model are consistent with the FSCK model, with errors less than 2%. When the pressure increases to 8 bar, errors of P1 and OTA models increase significantly, the maximum temperatures predicted by the P1 and OTA models have errors of 36 K and 63 K, and the relative errors of the peak soot volume fraction are 18% and 24%, respectively.

A two-zone subgrid flame model for predicting radiant emission from fires

A simple two-zone subgrid temperature distribution is developed to model turbulence-radiation interaction in the Fire Dynamics Simulator. The new approach enforces consistency between the subgrid flame distribution and the heat release rate from the eddy dissipation model. To investigate the performance of the new model, we simulate the University of Maryland turbulent line burner and compare global radiative fraction as a function of coflow oxygen dilution. The results suggest that the model can improve grid resolution dependence in prediction of radiative emissions. Sensitivity of the model predictions to the assumed fuel carbon to CO fraction (a parameter of the two-step fast chemistry scheme) was found to be significant, which is not surprising since this parameter essentially controls the in-flame soot concentration and generally has a first-order effect on resolved emission. Four different model variations were tested, corresponding to varying degrees of complexity in modeling the subgrid correlations for the absorption coefficient. Differences in results between model implementations were on par with the variation in results obtained with different path lengths applied to the gray gas model for the absorption coefficient.

Effect of moisture release on radiation behavior of burning coal bed between enclosed confined surfaces

In this study, a numerical analysis was performed to predict the radiation characteristics of burning coal layers heated on confined surfaces in an enclosed chamber. The one-dimensional (1D) unsteady energy balance equation and radiative transfer equation (RTE) were solved simultaneously using the semi-implicit Runge–Kutta method (SIRK) and discrete ordinate method (DOM). In addition to the 1D analysis, a commercial software was used to analyze the two-dimensional (2D) radiation behavior of the burning coal layers using the DOM.The heat generation rate (relevant to the combustion rate) and particle absorption coefficient were independently determined using combustion and thermal emission experiments. The gas absorption coefficient was calculated from gray gas models to account for the change of H2O vapor along coal and gas mixture with high moisture content. The dimensionless radiative heat flux and temperature distribution were determined for the three calculation cases. Two different predictions based on 1D and 2D geometries were validated against measured heat flux and temperature data. The effect of the moisture release inside the particle layer was particularly examined. The result indicates that the condensation of H2O is probably more responsible than the absorption of H2O vapor for a reduced heat flux observed in the combustion condition of high moisture coal burning at high pressure.

Effects of Hydrogen/Methane on the Thermal Environment of Heavy-Duty Gas Turbine Combustor

Hydrogen is the most promising fuel for reducing carbon emissions, but hydrogen combustion produces higher temperature compared to hydrocarbon fuel. In this paper, a three-dimensional compressible combustion–flow–heat transfer model of combustor was established, and a dry-low-emission combustor was examined by using the realizable model, transported probability density function, and discrete ordinates model combining weighted sum of gray gas model, analyzing the effects of hydrogen/methane blended fuel and thermal boundaries on the combustor thermal environment. The results show that when the fuel hydrogen volume percentage increases from 0 to 75%, the maximum gas temperature and concentration on the central axis of the combustor increase by about 160.8 and 662.9%, respectively; the maximum incident radiant heat flux of the combustor wall increases by about 150%; and the local maximum ratio of the radiant heat transfer to the total heat transfer through the wall increases from about 34 to about 49%. The effect of the boundary conditions varies depending on the hydrogen percentage. At the hydrogen percentage of 75%, the maximum wall-incident radiant heat flux under the adiabatic condition is nearly 180.3 and 77.4% higher than the values at 1370 and 1920 K isothermal boundaries, respectively.

Numerical investigation to evaluate the effects of gravity and pressure on flame structure and soot formation of turbulent non-premixed methane-air flame

In this study, a turbulent non-premixed (diffusion) methane-air flame has been investigated computationally to analyze the influences of pressure and gravity on flame structure and sooting characteristics between 1 and 10 atm. The simulation has been conducted in a 2-D axisymmetric computational domain using the finite volume-based computational fluid dynamics (CFD) code. The interaction of turbulence and chemistry is modeled by considering the steady laminar flamelet model (SLFM) and the GRI Mech 3.0 chemical mechanism. The radiative heat transfer calculation is carried out by considering the discrete ordinate (DO) method and the weighted sum grey gas model (WSGGM). The semi-empirical Moss-Brookes model is considered to calculate soot. The impact of gravity on flame and sooting characteristics are evaluated by comparing the normal-gravity flames with the zero-gravity flames. The effect of soot and radiation on flame temperature is also examined. The results show a close agreement with the measurement when both soot and radiation are included in the numerical modeling. The rates of soot formation, surface growth, and oxidation increase with increased operating pressure, regardless of gravity. Zero-gravity flames have a higher soot volume fraction, a wider soot-containing zone, a higher CO mass fraction, and a lower flame temperature than normal-gravity flames while maintaining constant pressure. In normal-gravity flames, the CO mass fraction decreases with pressure, whereas it increases with pressure rise in flames of zero gravity. Flames of zero gravity appear taller and broader compared to the flames of normal-gravity for a fixed pressure. An increase in pressure significantly reduces the flame length and width in normal-gravity flames. However, the pressure elevation has little effect on the shape of a zero-gravity flame. The outcomes of the present study will assist in fully understanding the combustion and sooting characteristics of turbulent diffusion flames that will help design and develop high-efficiency, pollutant-free combustion devices and fire suppression systems for space application.

Impact of wall temperature difference on heat and mass transfers in gray and non-gray gas mixtures

This study deals with the numerical investigation of the effect of wall temperature difference ( on heat and mass transfers in a differentially heated square cavity, filled with gas mixtures (air-CO2 or air-H2O) at a fixed average concentration of pollutant (15% CO2 or H2O). The governing equations are solved by a finite-difference method and the prediction of radiative transfer in molecular gases is taken into account by the SLW model of Denison and Webb. The results are graphically displayed and discussed for two values of (5 °C and 50 °C), when the concentration and temperature gradient generate opposing motions. The results obtained with a non-gray gas are also related to those of a gray gas model, in order to investigate if this assumption is appropriate to be used instead of non-gray calculations.

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

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

Using a flamelet generated manifold method in transported probability density function modeling of soot formation and thermal radiation

The simple semi-empirical precursor soot model of Brookes and Moss based on the soot number density and soot mass concentration is adopted in a transported probability density function (PDF) method for turbulent diffusion flames. The gas phase chemistry is described by a flamelet generated manifold (FGM) based on the mixture fraction, progress variable and enthalpy loss. The accuracy of the FGM method is validated by using flamelet solutions that are not included in the generating set of the FGM. To account for the radiative heat transfer in the flames, we use a non-gray weighted sum of gray gases model for the gas radiation and a gray soot radiation model. Turbulence–radiation interaction is closed at the level of the optically thin fluctuation approximation and the Reynolds averaged radiative transfer equation is solved by means of a discrete transfer method. The proposed modeling approach is applied in simulations of two turbulent non-premixed methane–air flames at one bar and three bar pressure, respectively. Predictions of the mean temperature and mean soot volume fraction are in good agreement with the measurements in the one bar flame. In the higher pressure flame the mean soot volume fraction is over predicted. For this flame, simulation results using the semi-empirical model of Lindstedt provided better agreement with the measurements. The main difference between the Brookes and Moss model and the Lindstedt model is the nine-times increased soot particle agglomeration rate of the latter. When using the same increased agglomeration rate parameter in the Brookes and Moss model the results become virtually identical. The negligible molecular diffusion of the soot was accounted for by neglecting mean molecular diffusion of the soot variables and by greatly reducing their micro-mixing. The effect of this differential soot diffusion on the mean soot volume fraction is found to be small, but it is significant for the variance of the soot volume fraction.

Numerical study of thermal radiation heat transfer using lattice Boltzmann method

In this work, we present an extension of the lattice Boltzmann method for solving radiative transfer equation (RTE) in emitting, absorbing, and non-scattering gaseous mixtures produced by combustion. A numerical procedure based on LBM is first developed for a single absorption coefficient avoiding spectral effect (gray gas model). Therefore, an infrared radiative global model is associated with the LBM to assess the radiative heat exchanges in molecular gaseous mixtures. A global model based on absorption distribution function (ADF) and a D2Q16 scheme are implemented to solve the 2D RTE. Results are presented in terms of temperature, radiative heat flux, and volumetric radiative power. Effects of radiative behavior and spectral structure of gaseous mixtures are put in evidence. The application of the LBM-ADF8 to gaseous mixture produced by combustion emphasizes the importance of taking into account its spectral structures. The error induced by the gray media approximation is put in evidence.

RadLib: A radiative property model library for CFD

RadLib is a C++ library of radiation property models that can be applied to variety of systems involving radiative heat transfer, including CFD simulations. RadLib includes three major radiation property models—Planck Mean (PM) absorption coefficients, the weighted sum of gray gases (WSGG) model, and the rank-correlation spectral line weighted-sum-of-gray-gases (RCSLW) model. RadLib includes C++, Python, and Fortran interfaces and can be expanded to include additional models. Several example cases illustrate use of the models with an included ray-tracing solver, compare their accuracy relative to line-by-line (LBL) solutions, and examine their computational costs. Additionally, an integrated CFD example of an ethylene burner configuration using Fire Dynamics Simulator (FDS) is provided. RadLib provides researchers with convenient access to validated radiation property models and a framework for further development. Program summaryProgram Title: RadLibCPC Library link to program files:https://doi.org/10.17632/rs5kvnr86r.1Developer's repository link:https://github.com/BYUignite/radlibCode Ocean capsule:https://codeocean.com/capsule/0997975/treeLicensing provisions: MITProgramming language: C++, Fortran, PythonNature of problem: Radiative heat transfer in combustion CFD problems is typically neglected or oversimplified, resulting in significant error and inaccuracy in combustion simulations. Radiation modeling, however, often requires a high degree of specialization due to its complexity and the challenges associated with implementation in existing CFD codes, which presents a substantial obstacle to researchers who wish to address the inaccuracies introduced by insufficient radiative heat transfer modeling in combustion simulations.Solution method: We present RadLib, an open-source C++ library of validated radiation property models that can be applied alongside various RTE solution methods to ease some of the obstacles associated with radiation modeling for combustion CFD. The package includes C++, Fortran, and Python interfaces, several illustrative examples with a provided ray-tracing solver and an integrated example using Fire Dynamics Simulator (FDS). RadLib can also be expanded to include additional radiation property models and interfaces.Additional comments including restrictions and unusual features: The library is intended to be used in Linux-like terminal applications.

New H 2 O weighted sum of gray gases model for natural convection flows within large cavities

Radiation heat transfer plays a significant role in buoyancy driven flows for large scale facilities. In the analysis of nuclear containment safety during severe accidents, it has been found that the thermal radiation particularly affects the temperature distribution and containment pressurization due to the humidity environment. In order to model thermal radiation, one of the main challenges is the description of nongray gas property for the steam-air mixtures. The weighted sum of gray gases model (WSGG) is a reasonable method in engineering applications because of its computational efficiency. There are many WSGG models available for combustion applications, but none of them is dedicated for low temperature applications. Furthermore, most of the existing WSGG models only provide the fixed partial pressure ratios (e.g., p H 2 O = 2p CO 2 for methane). To overcome this limitation, a tailored WSGG model is derived by the Line-by-Line model for a gas mixture composed of arbitrary concentrations of H 2 O. This tailored WSGG model is valid for the pressure path length ranging from 0.0001 to 10 atm · m, and for the temperature from 300 to 1200 K. The WSGG correlations are verified against the Line-by-Line benchmark solutions with isothermal/non-isothermal temperatures and homogeneous/non-homogeneous concentrations. The results demonstrate the ability and efficiency of the new tailored WSGG formulation.

Exponential shock wave in perfectly conducting self-gravitating rotational axi-symmetric dusty gas with magnetic field, radiative and conductive heat fluxes

In the present paper, we study the exponential shock propagation in a self-gravitating rotational axisymmetric perfectly conducting mixture of van der Waal gas and solid particles with magnetic field either axial or azimuthal and radiative and conductive heat fluxes. In our model, the solid particles are distributed continuously in the mixture and are chemically inert, and the equilibrium conditions for flow are preserved in the entire region of flow field behind shock wave. In a thick gray gas model case, the radiation is assumed to be of diffusion type. The Fourier's heat conduction law is used to express the heat conduction. The effects of the problem parameters variations are discussed. It is shown that the density of micro size solid particles to the gas initial density ratio or the gravitational parameter or the rotational parameter or the gas adiabatic index has effects to enhance the shock wave strength. Also, it is derived that an increase in the nonidealness of the gas, Alfvén Mach number, and the mass concentration of solid particles in the mixture have decaying effects on the strength of shock wave. It is shown that the shock wave is stronger when magnetic field is axial and weaker for azimuthal magnetic field.

Radiative property model for non-gray particle based on dependent scattering

The radiative heat transfer of the particles has been investigated based on the gray body and the independent scattering. However, the radiative properties of the particles are strongly wavelength dependent and interact with each other with the increase of particle concentration. In order to indicate the radiative heat transfer under the high particle volume fraction, the radiation heat transfer model of non-gray particle is developed in this paper, which is based on the ideology of the weighted sum of gray gases (WSGG) model and the full-spectrum correlated k-distribution (FSCK) model, and the dependent scattering of particles is considered. For a one-dimensional plane-parallel slab system, the WSCK (the Weighted Sum of Gray Particles based on the full-Spectrum Correlated k-distribution) model is verified. Compared with the modified LBL model based on Mie theory and dependent scattering theory, the maximum errors of the dependent scattering WSCK (WSCKD) model are about 3.3% for the radiative heat flux and 11.5% for the radiative source term under non-isothermal and inhomogeneous conditions. The radiative heat flux and radiative source term by the WSCKD model and the independent scattering WSCK (WSCKI) model are almost identical for the low particle volume fraction and the calculation accuracy is higher by the WSCKD model on the industrial scale. For the high particle volume fraction, the WSCKD model is more accurate, especially for particle systems with a large percentage of small particles or a relatively high-volume fraction. In addition, the radiative heat transfers of gases, particles and gas-particle mixtures at different one-dimensional scales are examined, highlighting the crucial role of particle radiative property model in large furnaces.