Assessing the role of turbulence-radiation interactions in hydrogen-enriched oxy-methane flames

Statistical analysis of scalar data obtained from single-shot laser measurements in four turbulent oxy-fuel flames were carried out to develop a functional relationship for the temperature self-correlation (TSC) term for use in Turbulence Radiation Interaction (TRI) models. The developed relationship was found to be invariant with the hydrogen enrichment in the fuel, fuel jet Reynolds numbers and correlated reasonably well with the root-mean-square of temperature (T_rms). The TSC and the absorption-coefficient temperature correlation (ATC) were both modeled in terms of T_rms and employed as add-on functions in time-averaged flame simulations. Including the effects of TRI enhanced the radiant fraction by 40% and reduced outlet CO concentrations by 30% across all flames. Further, there was significant flame absorption due to the high concentrations of radiatively participating gases that would deem optically thin radiation approximations in these flames to be erroneous.     

Approximate solutions of the filtered radiative transfer equation in large eddy simulations of turbulent reactive flows

An analysis of the relevance of turbulence-radiation interaction in the numerical simulation of turbulent reactive flows is presented. A semi-causal stochastic model was used to generate a time-series of turbulent scalar fluctuations along optical paths of Sandia flame D, a widely studied piloted turbulent jet nonpremixed flame. The radiative transfer equation was integrated along these paths for every realization using a grid resolution typical of a direct numerical simulation. The correlated k-distribution method was employed to compute the radiative properties of the medium. The results were used to determine the ensemble average, as well as the extreme values, of quantities that indicate the importance of the turbulence-radiation interaction. Several approximate methods are then proposed to solve the filtered radiative transfer equation in the framework of large eddy simulations. The proposed methods are applicable along with combustion models that either assume the filtered probability density function of a conserved scalar or solve a transport equation for a joint scalar or joint scalar/velocity filtered density function. It is concluded that the errors resulting from neglecting the turbulence-radiation interaction in large eddy simulations are much lower than those found in Reynolds-averaged Navier-Stokes calculations. The optically thin fluctuation approximation may be extended to large eddy simulations yielding predictions in excellent agreement with the reference solution. If the turbulence-radiation interaction is accounted for using this approximation, the average relative error of the filtered total radiation intensity is generally below 0.3% for the studied flame.     

Analysis of the interaction between turbulent combustion and thermal radiation using unsteady coupled LES/DOM simulations

Radiation exchanges must be taken into account to improve the prediction of heat fluxes in turbulent combustion. The strong interaction with turbulence and its role on the formation of polluting species require the study of unsteady coupled calculations using Large Eddy Simulations (LESs) of the turbulent combustion process. Radiation is solved using the Discrete Ordinate Method (DOM) and a global spectral model. A detailed study of the coupling between radiative heat transfer and LES simulation involving a real laboratory flame configuration is presented. First the impact of radiation on the flame structure is discussed: when radiation is taken into account, temperature levels increase in the fresh gas and decrease in the burnt gas, with variations ranging from 100 K to 150 K thus impacting the density of the gas. Coupling DOM and LES allows to analyze radiation effects on flame stability: temperature fluctuations are increased, and a wavelet frequency analysis shows changes in the flow characteristic frequencies. The second part of the study focuses on the Turbulence Radiation Interaction (TRI) using the instantaneous radiative fields on the whole computational domain. TRI correlations are calculated and are discussed along four levels of approximation. The LES study shows that all the TRI correlations are significant and must be taken into account. These correlations are also useful to calculate the TRI correlations in the Reynolds Averaged Navier–Stokes (RANS) approach.     

Prediction of turbulence radiation interactions of CH4H2/air turbulent flames at atmospheric and elevated pressures

Predicting thermal radiation for turbulent combustion highlights the significance of turbulence radiation interactions (TRI). Thermal radiation behaviors of methane/hydrogen flames under elevated pressures are investigated numerically using the developed TRI module integrated into CFD codes. The updated non-gray weighted sum of gray gases model is used to calculate the radiative properties of participating media. TRI effects have been analyzed with 0%–50% volumetric fraction of hydrogen in the methane/hydrogen blended fuels under 1–5 atm working pressures. Employing the radiation model considering TRI achieves closer predicted consistency to the experimental data. Only thermal radiation makes the flame temperature dropped about 60–140 K, while the predicted radiative source term calculated with TRI is higher than that without TRI, which results in a colder flame (approximately 13–60 K lower). The impact of TRI on the radiation behavior is enhanced in hydrogen-enriched high-pressure flame as the predicted radiation heat flux and radiative source term are increased above 25% than that without TRI. On account of TRI effect, the net radiative heat loss increases almost 50% at elevated pressure. The strong radiation of participating media in methane/hydrogen flames under elevated pressures emphasizes the importance of TRI effect on accurate predictions of thermal radiation and NO emission.     

Radiation heat transfer analysis of the monolith type solid oxide fuel cell

In this study, a modeling framework for heat and mass transport is established for a unit monolith type SOFC, with emphasis on quantifying the radiation heat transfer effects. The Schuster–Schwartzchild two-flux approximation is used for treating thermal radiation transport in the optically thin yttria-stabilized-zirconia (YSZ) electrolyte, and the Rosseland radiative thermal conductivity is used to account for radiation effects in the optically thick Ni–YSZ and LSM electrodes. The thermal radiation heat transfer is coupled to the overall energy conservation equations through the divergence of the local radiative flux. Commercially available FLUENT™ CFD software was used as a platform for the global thermal-fluid modeling of the SOFC and the radiation models were implemented through the user-defined functions. Results from sample calculations show significant changes in the operating temperatures and parameters of the SOFC with the inclusion of radiation effects.     

The role of turbulent fluctuations on radiative emission in hydrogen and hydrogen-enriched methane flames

A theoretical analysis is reported in the present work to quantify the increase of radiative emission due to turbulence for hydrogen and hydrogen-enriched methane diffusion flames burning in air. The instantaneous thermochemical state of the reactive mixture is described by a flamelet model along with a detailed chemical mechanism. The shape of the probability density function (pdf) of mixture fraction is assumed. The results show that turbulent fluctuations generally contribute to reduce the Planck mean absorption coefficient of the medium, in contrast with the blackbody emissive power, which is significantly increased by turbulence. If the turbulence level is relatively small, the influence of turbulence on the absorption coefficient is marginal. Otherwise, fluctuations of the absorption coefficient of the medium should be taken into account. The scalar dissipation rate and the fraction of radiative heat loss have a much lower importance than the turbulence intensity on the mean radiative emission.     

Statistical modeling of thermal radiation transfer in buoyant turbulent diffusion flames

A statistical (Monte Carlo) method for radiative heat transfer has been incorporated in CFD modeling of buoyant turbulent diffusion flames in stagnant air and in a cross-wind. The model and the computational tool have been developed and applied to simulate both burner flames with controlled fuel supply rate and in self-sustained pool fires with burning rates coupled with flame radiation. The gas–soot mixture was treated either as gray (using the effective absorption coefficient derived from total emissivity data or the Planck mean absorption coefficient) or as non-gray (using the weighed sum of gray gases model). The comparison of predicted radiative heat fluxes indicates applicability of the gray media assumption in modeling of thermal radiation in case of high soot content. The effect of turbulence-radiation interaction is approximately taken into account in calculation of radiation emission, which is corrected to allow for temperature self-correlation and absorption-temperature correlation. In modeling buoyant propane flames in still air above 0.3 m diameter burner, extensive comparison is presented of the predictions with the measurements of gas species concentrations, temperature, velocity and their turbulent fluctuations, and radiative heat fluxes obtained in flames with different heat release rates. Similar to previously published experimental data, the predicted burning rate of flames above the acetone pools exposed to flame radiation increases with the pool diameter and approaches a constant level for large pool sizes. The magnitude of predicted burning rates is shown to be in agreement with the reported measurements. Augmentation of burning rate of the pool fire in a cross-wind because of increased net radiative heat flux received by the fuel surface and non-monotonic dependence of burning rate on cross-wind velocity, subject to the pool diameter, is predicted. The statistical treatment of thermal radiation transfer has been found to be robust and computationally efficient.     

Experimental and computational infrared imaging of bluff body stabilized laminar diffusion flames

The concept of comparing measured and computed images is extended to the mid-infrared spectrum to provide a non-intrusive technique for studying flames. Narrowband radiation intensity measurements of steady and unsteady bluff body stabilized laminar ethylene diffusion flames are acquired using an infrared camera. Computational infrared images are rendered by solving the radiative transfer equation for parallel lines-of-sight through the flame and using a narrowband radiation model with computed scalar values. Qualitative and quantitative comparisons of the measured and computed infrared images provide insights into the flame stabilization region and beyond. The unique shapes and sizes of the flames observed in the measured and computed infrared images are similar with a few exceptions which are shown to be educational. The important differences occur in the flame stabilization region suggesting improvements in thermal control of the experiment and soot formation and heat loss models.     

Application of the full spectrum correlated-k distribution approach to modeling non-gray radiation in combustion gases

The treatment of radiative transport through combustion gases is rendered extremely difficult by the strong spectral variation of the absorption coefficients of molecular gases. In the full spectrum correlated-k distribution (FSCK) approach, a transformation is invoked, whereby the radiative transfer equation (RTE) is transformed from wavenumber to non-dimensional Planck-weighted wavenumber space after reordering of the spectrum. The reordering results in a relatively smooth spectrum, allowing accurate spectral integration with very few quadrature points. The numerical procedures, required to use the FSCK model for full-scale combustion applications, have been outlined in this article. The FSCK model was first coupled with the Discrete Ordinates Method (DOM) for solution of the transformed RTE. The accuracy of the model was then examined for a variety of cases ranging from homogeneous one-dimensional media to inhomogeneous multi-dimensional media with simultaneous variations in both temperature and concentrations. Comparison with line-by-line calculations shows that the FSCK model is exact for homogeneous media, and that its accuracy in inhomogeneous media is limited by the accuracy of the scaling approximation. Several approaches for effective scaling of the absorption coefficient are examined. The model is finally used for radiation calculations in a full-scale combustor, with full coupling to fluid flow, heat transfer and multi-species chemistry. The computational savings resulting from use of the FSCK model is found to be more than four orders of magnitude when compared with line-by-line calculations.     

Effect of dilatation on scalar dissipation in turbulent premixed flames

The scalar dissipation rate signifies the local mixing rate and thus plays a vital role in the modeling of reaction rate in turbulent flames. The local mixing rate is influenced by the turbulence, the chemical, and the molecular diffusion processes which are strongly coupled in turbulent premixed flames. Thus, a model for the mean scalar dissipation rate, and hence the mean reaction rate, should include the contributions of these processes. Earlier models for the scalar dissipation rate include only a turbulence time scale. In this study, we derive exact transport equations for the instantaneous and the mean scalar dissipation rates. Using these equations, a simple algebraic model for the mean scalar dissipation rate is obtained. This model includes a chemical as well as a turbulence time scale and its prediction compares well with direct numerical simulation results. Reynolds-averaged Navier-Stokes calculations of a test flame using the model obtained here show that the contribution of dilatation to local turbulent mixing rate is important to predict the propagation phenomenon.     

Radiative transfer within non Beerian porous media with semitransparent and opaque phases in non equilibrium: Application to reflooding of a nuclear reactor

A local radiative transfer model is developed for strongly anisotropic porous media with an opaque phase and a mixture of two semitransparent phases. At the optically thick limit, the homogenized phase associated with the opaque interfaces is characterized by generalized extinction and scattering coefficients at equilibrium, a phase function and an effective refraction index, by following the model of Taine et al. [1] for non Beerian media. The radiative transfer model is based on a Radiative Transfer Equation (RTE) with three source terms, which are associated with the temperature fields of the opaque interfaces and the two semitransparent phases. This RTE has been solved by a perturbation technique, which allows radiative interfacial fluxes and radiative powers per unit volume, that are exchanged between phases, to be computed at local scale. The main contributions are obtained at zeroth order perturbation. Corrective contributions at first order perturbation are also determined: Radiative fluxes and powers are then expressed from coupled Fourier’s laws, which are characterized by radiative conductivity tensors associated with each phase.Illustrative results are given for the radiative modeling of reflooding of a damaged nuclear reactor core. Pragmatic conclusions on the cooling efficiency by steam and water droplets are finally given.     

The Improved Direct Collocation Meshless Approach for Radiative Heat Transfer in Participating Media

The moving least-squares (MLS) direct collocation meshless method (DCM) is an effective numerical scheme for solving the radiative heat transfer in participating media. In this method the trial function is constructed by a MLS approximation and the radiative transfer equation (RTE) is discretized directly at nodes by collocation. The main drawback of this method is that, like most of the other numerical methods, the solution to the RTE by the DCM also suffers much from nonphysical oscillations in some cases caused by the convection-dominated property of the RTE. To overcome the numerical oscillations, special stabilization techniques are usually adopted, which increases the complexity and computation time of problem. In the present work a new scheme based on the outflow-boundary intensity interpolation correction is proposed that can easily ensure a large reduction in numerical oscillations of results without any complex stabilization technique. Adaptive support domain technique is also adopted, and the size of the support domain of each evaluated point changes with the density of nodes with irregular distribution. Five cases are studied to illustrate the numerical performance of these improvements. The numerical results compare well with the benchmark approximate solutions, and it is shown that the improved moving least-square direct collocation meshless method (iDCM) is easily implemented, efficient, of high accuracy, and excellent stability, to solve radiative heat transfer in homogeneous participating media.     

辐射对CO／H2／N2燃料反向对撞扩散火焰结构的作用

考虑和不考虑辐射作用,在宽广的拉伸率条件下,计算研究了组分CO、H2和N2摩尔分数分别为40%、30%和30%的燃料与空气(79%N2和21%O2)的详细层流对撞火焰结构.使用固有流形分析技术,考虑Leeds氮化学等,对Liu和Rogg发展的38步机理进行了修改.为研究辐射自吸收的作用,采用光细辐射模型(OTM)和窄带辐射模型(NBM),模型计算结果与Drake等的测量结果吻合良好.     

Application of the lattice Boltzmann method for solving the energy equation of a 2-D transient conduction-radiation problem

A lattice Boltzmann method (LBM) is used to solve the energy equation in a test problem involving thermal radiation and to thus investigate the suitability of scalar diffusion LBM for a new class of problems. The problem chosen is transient conductive and radiative heat transfer in a 2-D rectangular enclosure filled with an optically absorbing, emitting and scattering medium. The energy equation of the problem is solved alternatively with a previously used finite volume method (FVM) and with the LBM, while the radiative transfer equation is solved in both cases using the collapsed dimension method. In a parametric study on the effects of the conduction-radiation parameter, extinction coefficient, scattering albedo, and enclosure aspect ratio, FVM and LBM are compared in each case. It is found that, for given level of accuracy, LBM converges in fewer iterations to the steady-state solution, independent of the influence of radiation. On the other hand, the computational cost per iteration is higher for LBM than for the FVM for a simple grid. For coupled radiation-diffusion, the LBM is faster than the FVM because the radiative transfer computation is more time-consuming than that of diffusion.     

Second-order-accurate discrete ordinates solutions of transient radiative transfer in a scattering slab with variable refractive index

The discrete ordinates method (DOM) with a second-order upwind interpolation scheme is applied to solve transient radiative transfer in a graded index slab suddenly exposed to a diffuse strong irradiation at one of its boundaries. The planar medium is absorbing and anisotropically scattering. From the comparison of the results obtained by the first-order DOM, the second-order DOM, the modified DOM and the Monte Carlo method, it can be seen that the numerical diffusion in the transient solutions obtained by the second-order DOM is less than that in the solutions obtained by the first-order DOM, but the numerical diffusion is still noticeable, especially for optically thin and moderate cases. By contrast, for optically thick cases the numerical diffusion due to the finite difference of the advection term of the transient radiative transfer equation is minor. In general, it is still necessary to adopt a DOM with a higher order scheme to capture the wave front of transient radiative transfer accurately. Besides, the influence of numerical diffusion is a little less noticeable for the case with a larger gradient of refractive index, and the distribution of direction-integrated intensity around the irradiation boundary decreases and that around the other boundary increases with the increase of the anisotropically scattering coefficient.     

Radiative heat transfer to flow of a combustible mixture in a vertical channel

The paper studies the flow of a combustible mixture in a vertical channel in the presence of radiative heat transfer as a model for biomass moving bed gasifiers operating in the temperature range 750–1500 K. The simplistic binary reaction A → B is assumed, and both the optically thick (high density gas) and the optically thin (low density gas) situations are considered for the radiative heat transfer. Analytical and numerical solutions are obtained and discussed quantitatively.     

Kinetic and radiative extinctions of spherical burner-stabilized diffusion flames

Extinction of steady, spherical diffusion flames stabilized by a spherical porous burner was investigated by activation energy asymptotics. An optically-thin radiation model was employed to study the effect of radiation on flame extinction. Four model flames with the same adiabatic flame temperature and fuel consumption rate but different stoichiometric mixture fraction and flow direction, namely the flames with fuel issuing into air, diluted fuel issuing into oxygen, air issuing into fuel, and oxygen issuing into diluted fuel, were adopted to understand the relative importance of residence time and radiation intensity. Results show that for a specified flow rate emerging from the burner, only the kinetic extinction limit at low Damköhler numbers (low residence times) exists. In the presence of radiative heat loss, extinction is promoted so that it occurs at a larger Damköhler number. By keeping the radiation intensity constant while varying the flow rate, both the kinetic and radiative extinction limits, representing the smallest and largest flow rates, between which steady burning is possible, are exhibited. For flames with low radiation intensity, extinction is primarily dominated by residence time such that the high-flow rate flames are easier to be extinguished. The opposite is found for flames suffering strong radiative heat loss. The kinetic extinction limit might occur at mass flow rates lower than what is needed to keep the flame outside of the burner and not observable. An extinction state on the radiative extinction branch can be either kinetic or radiative depending on the process.     

Modeling the 3-D radiation of anisotropically scattering media by two different numerical methods

An original model and code for 3-D radiation of anisotropically scattering gray media is developed where radiative transfer equation (RTE) is solved by finite volume method (FVM) and scattering phase function (SPF) is defined by Mie Equations (ME). To the authors’ best knowledge this methodology was not developed before. Missing the benchmark, another new 3-D model and code, which solve the same problems, based on a combination of zone method (ZM) and Monte Carlo method (MC), as a solution of RTE, is developed. Here SPF is also calculated by Mie Equations. The conception ZM + MC is numerically expensive and is used and recommended only as a benchmark. The 3-D rectangular enclosure and the spherical geometry of particles are considered. The both models are applied: (i) to an isotropic and to four anisotropic scattering cases previously used in literature for 2-D cases and (ii) to solid particles of several various coals and of a fly ash. The agreement between the predictions obtained by these two different numerical methods for coals and ash is very good. The effects of scattering albedo and of wall reflectivity on the radiative heat flux are presented. It was found that the developed 3-D model, where FVM was coupled with ME, is reliable and accurate. The methodology is also suitable for extension towards: (i) mixture of non-gray gases with particles and (ii) incorporation in computational fluid dynamics.     

Generalized radiative transfer equation for porous medium upscaling: Application to the radiative Fourier law

Many porous media cannot be homogenized as Beerian semi-transparent media. Effective extinction, absorption and scattering coefficients can indeed have no physical meaning for small or intermediate optical thicknesses. A generalized radiative transfer equation (GRTE), directly based on the extinction cumulative distribution function, the absorption and scattering cumulative probabilities and the scattering phase function is established for this optical thickness range. It can be solved by a statistical Monte Carlo approach. For a phase of a porous medium that is optically thick at local scale, the GRTE degenerates into a classical Beerian RTE. In these conditions, a radiative conductivity tensor is directly obtained, by a perturbation method, and expressed with the radiative coefficients of this RTE and temperature. As illustrations, exhaustive radiative conductivity results are given for a set of overlapping transparent spheres within an opaque phase and for opaque rod bundles.     

Discontinuous Galerkin finite element method for radiative heat transfer in two-dimensional media with inner obstacles

A discontinuous Galerkin finite element method (DGFEM) with unstructured meshes is presented to solve the radiative transfer equation (RTE) in two-dimensional media with inner obstacles. The computation domain is discretized into a tessellation of unstructured elements and the elements are assumed to be discontinuous on the inner-element boundaries. The shape functions are constructed on each element and the continuity of the computation domain is maintained by modeling an up-winding numerical flux across the inner boundaries, which makes the DGFEM suitable and numerical stable for radiative transfer problems involved with strong non-uniformity and discontinuity induced by ray effects. The DGFEM discretization for RTE is presented and the accuracy of DGFEM is verified. Radiative transfer problems in square and irregular media with inner obstacles are investigated, the influence of medium parameters and the obstacle shielding effects are discussed.