Optically-thin Approximation Research Articles

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.

Prediction of flammable range for pure fuels and mixtures using detailed kinetics

In this work, the flammable range of several hydrocarbons was predicted using a freely-propagating flame method for pure hydrocarbons and their mixtures, investigating the effects of operating conditions, in terms of temperature, pressure, fuel/oxidizer composition. The model showed accurate agreement with a wide set of experimental data. The average deviation between the experiments and the model was reduced to ∼20% for the UFL of methanol, methane, ethane, propane, n-butane, n-heptane, ethylene, benzene and two different mixtures, methane/ethylene and methanol/benzene. Model performance was improved for the upper flammability limit by including the effect of soot radiation, modeled using an optically-thin approximation. A comprehensive kinetic mechanism was adopted, and a skeletal kinetic mechanism including a soot sectional model was used to predict soot formation in rich flames. Comparison with Calculated Adiabatic Flame Temperature (CAFT) and Le Chatelier models was also carried out, discussing the advantages of a model including the effects of chemical kinetics. Sensitivity analysis was performed to point out the major role of chemical kinetics especially at the UFL, where chemistry drives the process. This methodology showed that the chemical interaction between two different fuels at the rich limit is the reason for the deviation from the thermally controlled behavior. Finally, chemistry was found to be relevant even for the lean flammability limits predictions of lower alkanes, when pure N2O is used as oxidizer.

Soot Production and Radiative Heat Transfer in Opposed Flame Spread over a Polyethylene Insulated Wire in Microgravity

Flame spread over an insulated electrical wire is identified as a fire scenario in space vehicles. In such microgravity configurations, the contribution of thermal radiation from gaseous participating species and soot to the wire burning rate and flame spread is not fully understood and the present paper addresses this question both experimentally and numerically. A non-buoyant opposed-flow flame spread configuration over a nickel–chrome wire coated by Low Density PolyEthylene (LDPE) is considered with an O2/N2 oxidizer composed of 19% of oxygen in volume and a flow velocity of 200 mm/s. Flame spread rate, pyrolysis rate, stand-off distance, soot volume fraction, and soot temperature are experimentally determined based on optical diagnostics that capture the flame spread in parabolic flights. The numerical model uses the measured spread and pyrolysis rates as input data and solves transport equations for mass, momentum, species, energy, and soot number density and mass fraction in an axisymmetric flame-fixed coordinate system in conjunction with a simple degradation model for the LDPE and a state-of-the-art radiation model. The model considers two assumptions. First, pure ethylene results from the decomposition of LDPE and, second, an acetylene/benzene based-soot model, initially validated for C1–C3 hydrocarbons, can be extended with minor modifications to model soot production of LDPE. Comparisons between model predictions and experimental data in terms of flame structure and soot volume fraction support these assumptions. The major finding of this study is that radiation contributes negatively to the surface heat balance along the LDPE molten surface and the coating ahead of the molten front. This shows that the convective heat transfer from the flame is the main contribution to sustain the pyrolysis process and the flame spread is mainly ensured owing to the combined contribution of convection from flame and conduction inside the condensed phase. The maximum incident radiative flux along the molten ball is 17.5 kW/m2 and is reached at the molten ball trailing edge whereas the radiant fraction is about 0.25. Neglecting flame self-absorption affects these values by less than 5%, showing that the optically-thin approximation is valid for this flame. In addition, soot radiation dominates the radiative heat transfer in this flame, contributing for about two-third of the total radiation. Finally, model results show that the usually-used thermally-thin assumption throughout the LDPE coating is not strictly valid.

Modeling of large-scale under-expanded hydrogen jet fires

Large-scale hydrogen under-expanded jet flames and lab-scale H2 and CH4 jet flames are simulated by using the standard k-ε model coupled to a hybrid flamelet/transported PDF method and a narrow band correlated-k gas radiation model. The set of flames considered covers a wide range of residence times and optical thicknesses. The notional nozzle concept is adopted to determine injection conditions for the large-scale chocked flames. Model predictions in terms of flame geometry, flame structure, radiant fraction and radiative flux are consistent with the experimental data whatever the scales. Model results show that these flames do not verify the optically-thin approximation since the part of emitted radiant power re-absorbed within the flame ranges from 11% for the smallest H2 flame to about 70% for the largest H2 flame. Neglecting the turbulence-radiation interaction underestimates significantly the radiant fraction whatever the scale and these discrepancies are enhanced with increasing residence time and optical thickness. A simple analysis based on the assumption of homogenous flame is used to correlate the experimental radiant fraction as a function of τGEm(1−Q˙abs/Q˙em) where τG, Em and Q˙abs/Q˙em represent the residence time, an equivalent emission term and the part of emitted radiant power re-absorbed within the flame. Model results are used to provide a proper estimation of the equivalent emission term and self-absorption.

Numerical simulations of microgravity ethylene/air laminar boundary layer diffusion flames

Microgravity ethylene/air laminar boundary layer diffusion flames were studied numerically. Two oxidizer velocities of 250 and 300 mm/s and three fuel injection velocities of 3, 4, and 5 mm/s were considered. A detailed gas-phase reaction mechanism, which includes aromatic chemistry up to four rings, was used. Soot kinetics was modeled by using a pyrene-based model including the mechanisms of nucleation, heterogeneous surface growth and oxidation following the hydrogen-abstraction acetylene-addition (HACA) mechanism, polycyclic aromatic hydrocarbon (PAH) surface condensation and soot particle coagulation. Radiative heat transfer from CO, CO2, H2O and soot was calculated using the discrete ordinate method (DOM) coupled to a wide-band correlated-k model. Model predictions are in quantitative agreement with the available experimental data. Model results show that H and OH radicals, responsible for the dehydrogenation of sites in the HACA process, and pyrene, responsible for soot nucleation and PAH condensation, are located in a thin region that follows the stand-off distance. Soot is produced in this region and, then, is transported inside the boundary layer by convection and thermophoresis. The combustion efficiency is significantly lower than 1 and is reduced as the flow residence time increasing, confirming that these sooting micro-gravity diffusion flames are characterized by radiative quenching at the flame trailing edge. In particular, this quenching phenomenon explains the increase in flame length with the oxidizer velocity observed in previous experimental studies. The effects of using approximate radiative-property models, namely the optically-thin approximation and gray approximations for soot and combustion gases, were assessed. It was found that the re-absorption and the spectral dependence of combustion gases and soot must be taken into account to predict accurately temperature, soot volume fraction, flame geometry and flame quenching.

Simulations of sooting turbulent jet flames using a hybrid flamelet/stochastic Eulerian field method

The stochastic Eulerian field method is applied to simulate 12 turbulent C1−C3 hydrocarbon jet diffusion flames covering a wide range of Reynolds numbers and fuel sooting propensities. The joint scalar probability density function (PDF) is a function of the mixture fraction, enthalpy defect, scalar dissipation rate and representative soot properties. Soot production is modelled by a semi-empirical acetylene/benzene-based soot model. Spectral gas and soot radiation is modelled using a wide-band correlated-k model. Emission turbulent radiation interactions (TRIs) are taken into account by means of the PDF method, whereas absorption TRIs are modelled using the optically thin fluctuation approximation. Model predictions are found to be in reasonable agreement with experimental data in terms of flame structure, soot quantities and radiative loss. Mean soot volume fractions are predicted within a factor of two of the experiments whereas radiant fractions and peaks of wall radiative fluxes are within 20%. The study also aims to assess approximate radiative models, namely the optically thin approximation (OTA) and grey medium approximation. These approximations affect significantly the radiative loss and should be avoided if accurate predictions of the radiative flux are desired. At atmospheric pressure, the relative errors that they produced on the peaks of temperature and soot volume fraction are within both experimental and model uncertainties. However, these discrepancies are found to increase with pressure, suggesting that spectral models describing properly the self-absorption should be considered at over-atmospheric pressure.

The large- and small-scale Ca II K structure of the Milky Way from observations of Galactic and Magellanic sightlines

Aims: By utilising spectra of early-type stellar probes of known distances in the same region of the sky, the large and small-scale (pc) structure of the Galactic ISM can be investigated. This paper determines the variation in line strength of CaII at 3933.661 A, as a function of probe separation for a sample of stars, including many sightlines in the Magellanic Clouds. Methods: FLAMES-GIRAFFE data taken with the VLT towards early-type stars in 3 Galactic & 4 Magellanic open clusters in CaII are used to obtain the velocity, EW, column density and line width of IS Galactic Ca for a total of 657 stars, of which 443 are Magellanic sightlines. In each cluster there are 43-110 stars observed. Additionally, FEROS and UVES CaII & NaI spectra of 21 Galactic & 154 Magellanic early-type stars are presented and combined with data from the literature to study the Ca column density/parallax relationship. Results: For the four Magellanic clusters studied with FLAMES, the strength of the Galactic IS CaII K EW over transverse scales from 0.05-9 pc is found to vary by factors of 1.8-3.0, corresponding to column density variations of 0.3-0.5 dex in the optically-thin approximation. Using FLAMES, FEROS and UVES archive spectra, the min and max reduced EW for MW gas is found to lie in the range 35-125 mA & 30-160 mA for CaII K and NaI D, respectively. The range is consistent with a simple model of the ISM published by van Loon et al. (2009) consisting of spherical cloudlets of filling factor 0.3, although other geometries are not ruled out. Finally, the derived functional form for parallax and CaII column density is found to be pi(mas)=1/(2.39e-13 x N(CaII)(cm-2)+0.11). Our derived parallax is 25 per cent lower than predicted by Megier et al. (2009) at a distance of 100 pc and 15% lower at a distance of 200 pc, reflecting inhomogeneity in the CaII distribution in the different sightlines studied.

Influence of thermal radiation on soot production in Laminar axisymmetric diffusion flames

The aim of this paper is to study the effect of radiative heat transfer on soot production in laminar axisymmetric diffusion flames. Twenty-four C1–C3 hydrocarbon–air flames, consisting of normal (NDF) and inverse (IDF) diffusion flames at both normal gravity (1g) and microgravity (0g), and covering a wide range of conditions affecting radiative heat transfer, were simulated. The numerical model is based on the Steady Laminar Flamelet (SLF) model, a semi-empirical two-equation acetylene/benzene based soot model and the Statistical Narrow Band Correlated K (SNBCK) model coupled to the Finite Volume Method (FVM) to compute thermal radiation. Predictions relative to velocity, temperature, soot volume fraction and radiative losses are on the whole in good agreement with the available experimental data. Model results show that, for all the flames considered, thermal radiation is a crucial process with a view to providing accurate predictions for temperatures and soot concentrations. It becomes increasingly significant from IDFs to NDFs and its influence is much greater as gravity is reduced. The radiative contribution of gas prevails in the weakly-sooting IDFs and in the methane and ethane NDFs, whereas soot radiation dominates in the other flames. However, both contributions are significant in all cases, with the exception of the 1g IDFs investigated where soot radiation can be ignored. The optically-thin approximation (OTA) was also tested and found to be applicable as long as the optical thickness, based on flame radius and Planck mean absorption coefficient, is less than 0.05. The OTA is reasonable for the IDFs and for most of the 1g NDFs, but it fails to predict the radiative heat transfer for the 0g NDFs. The accuracy of radiative-property models was then assessed in the latter cases. Simulations show that the gray approximation can be applied to soot but not to combustion gases. Both the non-gray and gray soot versions of the Full Spectrum Correlated k (FSCK) model can be then substituted for the SNBCK with a reduction in CPU time by a factor of about 20 in the latter case.

Influence of radiative property models on soot production in laminar coflow ethylene diffusion flames

Two axisymmetric laminar coflow non-smoking and smoking ethylene diffusion flames are studied numerically in order to assess the influence of different radiative property models on the soot formation and oxidation processes. Simulations are carried out by considering the Steady Laminar Flamelet (SLF) concept and a modified two-equation acetylene-based model to describe the soot nucleation, surface growth and oxidation processes. Several radiative property models are considered: the simple Optically Thin Approximation (OTA), the Weighted-Sum of Grey-Gases (WSGG), the Grey-Wide-Band model (GWB), the Statistical Narrow Band Correlated-k model (SNBCK) and the Full Spectrum Correlated-k model (FSCK). Comparisons between calculations carried out with the SNBCK model and experimental data show a reasonable agreement. Model results show that the choice of the radiative property models influence largely the soot prediction, especially in the upper part of the flame where oxidation occurs. Simulations show that the reabsorption of spectral gas and soot is an important feature and thus the commonly used OTA or grey models introduce large discrepancies. The GWB model leads to improved solutions, but it should be avoided if accurate predictions are desired. The FSCK provides equivalent results as compared to the SNBCK model with a substantial gain in CPU time.

Redshift-space distortion of the 21-cm background from the epoch of reionization - I. Methodology re-examined

The peculiar velocity of the intergalactic gas responsible for the cosmic 21cm background from the epoch of reionization and beyond introduces an anisotropy in the three-dimensional power spectrum of brightness temperature fluctuations. Measurement of this anisotropy by future 21cm surveys is a promising tool for separating cosmology from 21cm astrophysics. However, previous attempts to model the signal have often neglected peculiar velocity or only approximated it crudely. This paper re-examines the effects of peculiar velocity on the 21cm signal in detail, improving upon past treatment and addressing several issues for the first time. (1) We show that properly accounting for finite optical depth eliminates the unphysical divergence of 21cm brightness temperature in overdense regions of the IGM found by previous work that employed the usual optically-thin approximation. (2) The approximation made previously to circumvent the diverging brightness temperature problem by capping velocity gradient can misestimate the power spectrum on all scales. (3) The observed power spectrum in redshift-space remains finite even in the optically-thin approximation if one properly accounts for the redshift-space distortion. However, results that take full account of finite optical depth show that this approximation is only accurate in the limit of high spin temperature. (4) The linear theory for redshift-space distortion results in ~30% error in the observationally relevant wavenumber range, at the 50% ionized epoch. (5) We describe and test two numerical schemes to calculate the 21cm signal from reionization simulations to incorporate peculiar velocity effects in the optically-thin approximation accurately. One is particle-based, the other grid-based, and while the former is most accurate, we demonstrate that the latter is computationally more efficient and can achieve sufficient accuracy. [Abridged]

On the efficiency of production of the Fe Kα emission line in neutral matter

The absolute luminosity of the Fe Kalpha emission line from matter illuminated by X-rays in astrophysical sources is nontrivial to calculate except when the line-emitting medium is optically-thin to absorption and scattering. We characterize the Fe Kalpha line flux using a dimensionless efficiency, defined as the fraction of continuum photons above the Fe K shell absorption edge threshold energy that appear in the line. The optically-thin approximation begins to break down even for column densities as small as 2 x 10^22 cm^-2. We show how to obtain reliable estimates of the Fe Kalpha line efficiency in the case of cold, neutral matter, even for the Compton-thick regime. We find that, regardless of geometry and covering factor, the largest Fe Kalpha line efficiency is attained well before the medium becomes Compton-thick. For cosmic elemental abundances it is difficult to achieve an efficiency higher than a few percent under the most favorable conditions and lines of sight. For a given geometry, Compton-thick lines-of-sight may have Fe Kalpha line efficiencies that are orders of magnitude less than the maximum possible for that geometry. Configurations that allow unobscured views of a Compton-thick reflecting surface are capable of yielding the highest efficiencies. Our results can be used to estimate the predicted flux of the narrow Fe Kalpha line at ~6.4 keV from absorption models in AGN. In particular we show that contrary to a recent claim in the literature, absorption dominated models for the relativistic Fe Kalpha emission line in MCG -6-30-15 do not over-predict the narrow Fe Kalpha line for any column density or covering factor.

A reexamination of the greenhouse effect due to CFC-11 and CFC-12

Employing the most recent laboratory absorption-coefficient data 1 on the thermal infrared (i.r.) bands of CFC-11 (CFCl 3) and CFC-12 (CF 2Cl 2), which were measured at several temperatures relevant to the troposphere and the stratosphere, the greenhouse effect produced by these two CFCs has been reexamined. The effect upon the atmospheric radiative fluxes due to the temperature dependence of the absorption coefficient, especially in the many hot bands present in this spectral region, has been studied. The validity of the often used optically-thin approximation has been scrutinized in view of the observed enhancement in the absorption by the CFCs at low temperatures. The influence of absorption by water vapor on the radiative transfer through columns of CFC-11 and CFC-12 has also been considered. It has been shown that, even though each of these individual refinements may modify the previously estimated effect due to the CFCs by a small amount only, the collective effect may be a non-negligible 35% change in the surface-troposphere heating for every ppbv of CFC-11 and CFC-12 each introduced into a model atmosphere.