Correlated-k Method Research Articles

Estimating the Radiance in Atmosphere-Ocean Systems With Different Atmosphere Models by Discrete Spherical Harmonics Method

Abstract The radiative transfer in atmosphere-ocean systems with different atmosphere models is evaluated by the discrete spherical harmonics method. Four standard atmosphere models, namely, Tropical, Mid-Latitude Summer, Mid-Latitude Winter, and U.S. Standard (1976) limited to a height of 16 km are considered above an ocean. Two monochromatic radiations are considered according to the preponderance of the interaction they present with the participating medium, namely, λ=0.55 μm for scattering by particles and λ=16.8 μm for absorption and emission by water vapor and carbon dioxide. The absorption by the atmospheric gases considered is analyzed by the statistical narrow-band correlated-k method. The optical properties of aerosols and water clouds considered are calculated by Lorenz-Mie theory. The results obtained by the proposed discrete spherical harmonics method are in agreement with those of the literature and demonstrate the efficiency and accuracy of the developed radiative transfer code. The effects of the governing parameters of the system are investigated and show that the presence of the ocean contributes to increasing the upward radiation fluxes in the atmosphere. The presence of aerosols in the atmosphere leads to downward radiance curves at ground level that show significant peaks around the zenith angle of observation θ=0 deg. Additionally, the presence of the cloud in the atmosphere creates a discontinuity in the radiation flux curves at the height of the cloud.

Improving the modeling of spectral radiation penetration into the condensed materials with the separated full spectrum correlated-k method

The large temperature difference between the radiation source and the condensed materials in fire scenarios, makes the general form of full spectrum correlated-k method unable to accurately model both absorption and emission within the condensed phase. In this paper, a new solution form for the FSCK method is presented which accurately accounts for both. This so-called “separated” form of FSCK method solves the contributions of medium emission and boundary's incident intensity separately by implementing two different reference temperatures. The advantages of the separated FSCK method is exhibited through three case studies using the transmissivity and radiative heat source calculated by high resolution line by line calculations as the benchmark. The test cases represent a layer of six different liquid and solid hydrocarbon fuels for which the various levels of irradiation from a radiating source is introduced by the temperature of its upper wall and an effective emissivity. The case studies provide a sensitivity analysis for the magnitude and spectral form of the irradiation at the boundary. The separated form of FSCK exhibits its best performance when the incident intensity and medium emission are in the same order of magnitude. Moreover, when the peak region of the boundary's spectral irradiation is closer to the peaks of the absorption coefficient spectrum of the condensed phase, the accuracy of both separated and classical FSCK solutions decreases, though, the separated solution still provides better accuracy.

Effects of oxygen depletion on soot production, emission and radiative heat transfer in opposed-flow flame spreading over insulated wire in microgravity

The main objective of this article is to investigate experimentally and numerically the effects of reduced-oxygen contents on the soot production and emission from solid fuels in microgravity, which constitute an important issue in terms of fire safety for manned space missions. Due to its convenience for the implementation of soot-related optical diagnostics, the configuration of a flame spreading in an opposed flow over thin nickel chromium (NiCr) wires coated by low density PolyEthylene (LDPE) is considered. Experiments are conducted at a pressure of 101.3 kPa and an oxidizer velocity of 150 mm/s. The oxygen mole fraction in the oxidizer, XO2, is varied from 18% to 21% by nitrogen dilution of air. The modeling strategy lies on a surrogate fuel to mimic the combustion of LDPE by preserving its stoichiometry and the laminar smoke-point (LSP) flame height. The numerical model considers a detailed chemistry, a two-equation soot production model involving laminar smoke point (LSP)-based soot formation rates and oxidation by OH and O2, a radiation model coupling the Full-Spectrum correlated-k method with the finite volume method, and a simple degradation model for LDPE. Based on experimental evidence, the soot formation rate is scaled by the adiabatic flame temperature to account for thermal effects due to variation in XO2. The model reproduces quantitatively the increase in flame size, residence time, and soot volume fraction observed experimentally as XO2 is enhanced as well as the transition from a non-smoking to a smoking flame, which occurs for XO2 between 19% and 20%. The increase in soot volume fraction results of a combined enhancement in both residence time, owing to an increase in the fuel mass flow rate, and soot formation rate due to higher temperature in the soot formation region. The radiant fraction increases significantly with XO2 from about 17% for XO2=18% to about 36% for XO2= 21%. This increase in radiative losses is accompanied by a reduction of the temperature in the soot oxidation region. Therefore, for increasing XO2, the soot oxidation process is governed by a competition between oxygen-enhanced conditions that promote the formation of soot oxidizing species and the increase in radiative losses that dampens their formation. For the present flames, the first mechanism prevails as XO2 increases from 18% to 19% whereas the second dominates as XO2 is further increased, leading to smoking flames as actually observed for XO2=20 and 21%. The radiant fraction at the smoke-point transition and the soot oxidation freezing temperature are in line with those reported at normal gravity. Finally, model results show that, whatever XO2, the contribution of radiation to the heating process is negligible ahead of the pyrolysis front and is largely overcome by surface radiative losses along the pyrolysis region.

Pressure effects on the soot production and radiative heat transfer of non-buoyant laminar diffusion flames spreading in opposed flow over insulated wires

Abstract This paper investigates experimentally and numerically pressure effects on soot production and radiative heat transfer in non-buoyant opposed-flow flames spreading over wires coated by Low Density PolyEthylene (LDPE). Experiments, conducted in parabolic flights, consider pressure levels ranging from 50.7 kPa to 121.6 kPa and an oxidizer flowing parallel to the wire's axis at a velocity of 150 mm/s and composed of 20% O2/80% N2 in volume. The numerical model includes a detailed chemistry, a two-equation smoke-point based soot production model, a radiation model coupling the Full-Spectrum correlated-k method with the finite volume method and a simple degradation model for LDPE. An analysis of the experimental data shows that the spread rate, the pyrolysis mass flow rate, and the residence time for soot formation are independent of pressure whereas the soot formation rate is third-order in pressure. The model reproduces quantitatively the effects of pressure on soot production and captures the transition from non-smoking to smoking flames. The radiant fraction increases with pressure because of an enhancement in soot radiation whereas the contribution of radiating gases remains approximately constant over the range of pressures considered. In addition, gas radiation dominates at pressure lower than 75 kPa whereas soot radiation prevails at higher-pressure levels. Consistently with the data obtained at normal gravity, the smoke-point transition is found to occur for a radiant fraction of about 0.3 and the soot oxidation freezing temperature is estimated in the range 1350–1450 K. Eventually, whatever the pressure considered, the surface re-radiation from the wire is higher than the incident radiative flux from the flame to the surface along the entire wire. This shows that radiative heat transfer contributes negatively to the heating of the unburnt LDPE and to the heat balance along the pyrolysing surface.

Study of turbulence-radiation interactions in a heated jet using direct numerical simulation coupled to a non-gray Monte-Carlo solver

Direct Numerical Simulations of a strongly heated jet of water vapor discharging into a low-speed coflow of cold water vapor is fully coupled with a reciprocal Monte-Carlo method to account for radiative heat transfer. The spectral dependency of the radiative properties is modeled using the Correlated-k method. Such a numerical and modeling setup allows for studying accurately the turbulent jet development submitted to radiative heat transfer. Contrary to the previous study by Armengol et al. [International Journal of Heat and Mass Transfer 139 (2019), pp. 456–474], the present conditions show a direct effect of thermal radiation in the jet developed zone located downstream the jet potential core. Results are analyzed to identify the effects of thermal radiation on turbulence properties of the temperature field, and reciprocally. The analysis reveals a complex coupling between the mean temperature field and the mean radiative power as well as between their fluctuations. This is studied in various profiles of average and root-mean-square properties, and completed by considering budgets of enthalpy variance and turbulence spectra.

PLATON II: New Capabilities and a Comprehensive Retrieval on HD 189733b Transit and Eclipse Data

Abstract Recently, we introduced PLanetary Atmospheric Tool for Observer Noobs (PLATON), a Python package that calculates model transmission spectra for exoplanets and retrieves atmospheric characteristics based on observed spectra. We now expand its capabilities to include the ability to compute secondary eclipse depths. We have also added the option to calculate models using the correlated-k method for radiative transfer, which improves accuracy without sacrificing speed. Additionally, we update the opacities in PLATON—many of which were generated using old or proprietary line lists—using the most recent and complete public line lists. These opacities are made available at R = 1000 and R = 10,000 over the 0.3–30 μm range, and at R = 375,000 in select near-IR bands, making it possible to utilize PLATON for ground-based high-resolution cross-correlation studies. To demonstrate PLATON’s new capabilities, we perform a retrieval on published Hubble Space Telescope (HST) and Spitzer transmission and emission spectra of the archetypal hot Jupiter HD 189733b. This is the first joint transit and secondary eclipse retrieval for this planet in the literature, as well as the most comprehensive set of both transit and eclipse data assembled for a retrieval to date. We find that these high signal-to-noise data are well matched by atmosphere models with a C/O ratio of and a metallicity of times solar where the terminator is dominated by extended nanometer-sized haze particles at optical wavelengths. These are among the smallest uncertainties reported to date for an exoplanet, demonstrating both the power and the limitations of HST and Spitzer exoplanet observations.

A Maximum Entropy-Inspired Interpolative Closure for the Prediction of Radiative Heat Transfer in Laminar Co-Flow Diffusion Flames

ABSTRACT An interpolative-based first-order maximum entropy (M1) moment closure for providing approximate solutions to the equation of radiative transfer in non-gray participating media is proposed and described. This newly developed non-gray moment closure technique results in significant computational savings compared to an approach that makes use of the direct numerical solution of the optimization problem for entropy maximization. Its predictive capabilities are also assessed by comparing its solutions to those of the more commonly adopted first-order spherical harmonics (P1) moment closure technique, as well as the popular discrete ordinates method (DOM), which is used as a benchmark for the model comparisons. The evaluations are performed for sooting co-flow laminar diffusion flames for blends of ethanol and methane fuels at atmospheric as well as at elevated pressures and include comparisons to available experimental data for soot volume fraction and flame temperature. The strong spectral dependence exhibited by the absorption coefficient of real gases is treated herein using the statistical narrow-band correlated-k method, and the chemical kinetics of the underlying species are modeled using a reduced mechanism for methane and ethanol fuels. Theoretical details of the proposed interpolative M1, along with a description of the proposed Godunov-type finite-volume scheme developed for the numerical solution of the resulting system of hyperbolic moment equations are briefly discussed. The finite-volume method makes use of limited second-order solution reconstruction, multi-block body-fitted quadrilateral meshes with anisotropic adaptive mesh refinement (AMR), and an efficient Newton–Krylov–Schwarz (NKS) iterative method for solution of the resulting nonlinear algebraic equations arising from the finite-volume discretization procedure. The numerical results for laminar co-flow flames show that the flame solutions and predictions of soot formation of the non-gray M1 maximum-entropy moment closure are very promising and in very good agreement with those of both the DOM and P1 spherical harmonics model, while offering a substantial reduction in the number of dependent solution variables, compared to the DOM.

PetitRADTRANS

We present the easy-to-use, publicly available, Python package petitRADTRANS, built for the spectral characterization of exoplanet atmospheres. The code is fast, accurate, and versatile; it can calculate both transmission and emission spectra within a few seconds at low resolution (λ/Δλ = 1000; correlated-k method) and high resolution (λ/Δλ = 106; line-by-line method), using only a few lines of input instruction. The somewhat slower, correlated-k method is used at low resolution because it is more accurate than methods such as opacity sampling. Clouds can be included and treated using wavelength-dependent power law opacities, or by using optical constants of real condensates, specifying either the cloud particle size, or the atmospheric mixing and particle settling strength. Opacities of amorphous or crystalline, spherical or irregularly-shaped cloud particles are available. The line opacity database spans temperatures between 80 and 3000 K, allowing to model fluxes of objects such as terrestrial planets, super-Earths, Neptunes, or hot Jupiters, if their atmospheres are hydrogen-dominated. Higher temperature points and species will be added in the future, allowing to also model the class of ultra hot-Jupiters, with equilibrium temperatures Teq ≳ 2000 K. Radiative transfer results were tested by cross-verifying the low- and high-resolution implementation of petitRADTRANS, and benchmarked with the petitCODE, which itself is also benchmarked to the ATMO and Exo-REM codes. We successfully carried out test retrievals of synthetic JWST emission and transmission spectra (for the hot Jupiter TrES-4b, which has a Teq of ∼1800 K).

Scaling of heated plane jets with moderate radiative heat transfer in coupled DNS

The effects of thermal radiation in a heated jet of water vapor are studied with a direct numerical simulation coupled to a Monte-Carlo solver. The adequacy of the numerical setup is first demonstrated in the uncoupled isothermal and heated turbulent plane jets with comparisons to experimental and numerical data. Radiative energy transfer is then accounted for with spectral dependency of the radiative properties described by the Correlated-k (ck) method. Between the direct impact through modification of the temperature field by the additional radiative transfer and the indirect one where the varied flow density changes the turbulent mixing, the present study is able to clearly identify the second one in the jet developed region by considering conditions where effects of thermal radiation are moderate.When using standard jet scaling laws, the different studied cases without radiation and with small-to-moderate radiative heat transfer yield different profiles even when thermal radiation becomes locally negligible. By deriving another scaling law for the decay of the temperature profile, self-similarity is obtained for the different turbulent jets. The results of the study allow for distinguishing whether thermal radiation modifies the nature of heat transfer mechanisms in the jet developed region or not while removing the indirect effects of modified density.

Planetary Spectrum Generator: An accurate online radiative transfer suite for atmospheres, comets, small bodies and exoplanets

We have developed an online radiative-transfer suite (https://psg.gsfc.nasa.gov) applicable to a broad range of planetary objects (e.g., planets, moons, comets, asteroids, TNOs, KBOs, exoplanets). The Planetary Spectrum Generator (PSG) can synthesize planetary spectra (atmospheres and surfaces) for a broad range of wavelengths (UV/Vis/near-IR/IR/far-IR/THz/sub-mm/Radio) from any observatory (e.g., JWST, ALMA, Keck, SOFIA), any orbiter (e.g., ExoMars, Juno), or any lander (e.g., MSL). This is achieved by combining several state-of-the-art radiative transfer models, spectroscopic databases and planetary databases (i.e., climatological and orbital). PSG has a 3D (three-dimensional) orbital calculator for most bodies in the solar system, and all confirmed exoplanets, while the radiative-transfer models can ingest billions of spectral signatures for hundreds of species from several spectroscopic repositories. It integrates the latest radiative-transfer and scattering methods in order to compute high resolution spectra via line-by-line calculations, and utilizes the efficient correlated-k method at moderate resolutions, while for computing cometary spectra, PSG handles non-LTE and LTE excitation processes. PSG includes a realistic noise calculator that integrates several telescope/instrument configurations (e.g., interferometry, coronagraphs) and detector technologies (e.g., CCD, heterodyne detectors, bolometers). Such an integration of advanced spectroscopic methods into an online tool can greatly serve the planetary community, ultimately enabling the retrieval of planetary parameters from remote sensing data, efficient mission planning strategies, interpretation of current and future planetary data, calibration of spectroscopic data, and development of new instrument/spacecraft concepts.

Treatment of overlapping gaseous absorption with the correlated-kmethod in hot Jupiter and brown dwarf atmosphere models

The correlated-k method is frequently used to speed up radiation calculations in both one-dimensional and three-dimensional atmosphere models. An inherent difficulty with this method is how to treat overlapping absorption, i.e. absorption by more than one gas in a given spectral region. We have evaluated the applicability of three different methods in hot Jupiter and brown dwarf atmosphere models, all of which have been previously applied within models in the literature: (i) Random overlap, both with and without resorting and rebinning, (ii) equivalent extinction and (iii) pre-mixing of opacities, where (i) and (ii) combine k-coefficients for different gases to obtain k-coefficients for a mixture of gases, while (iii) calculates k-coefficients for a given mixture from the corresponding mixed line-by-line opacities. We find that the random overlap method is the most accurate and flexible of these treatments, and is fast enough to be used in one-dimensional models with resorting and rebinning. In three-dimensional models such as GCMs it is too slow, however, and equivalent extinction can provide a speed-up of at least a factor of three with only a minor loss of accuracy while at the same time retaining the flexibility gained by combining k-coefficients computed for each gas individually. Pre-mixed opacities are significantly less flexible, and we also find that particular care must be taken when using this method in order to to adequately resolve steep variations in composition at important chemical equilibrium boundaries. We use the random overlap method with resorting and rebinning in our one-dimensional atmosphere model and equivalent extinction in our GCM, which allows us to e.g. consistently treat the feedback of non-equilibrium chemistry on the total opacity and therefore the calculated P-T profiles in our models.

The UK Met Office global circulation model with a sophisticated radiation scheme applied to the hot Jupiter HD 209458b

To study the complexity of hot Jupiter atmospheres revealed by observations of increasing quality, we have adapted the UK Met Office global circulation model (GCM), the Unified Model (UM), to these exoplanets. The UM solves the full 3D Navier-Stokes equations with a height-varying gravity, avoiding the simplifications used in most GCMs currently applied to exoplanets. In this work we present the coupling of the UM dynamical core to an accurate radiation scheme based on the two-stream approximation and correlated-k method with state-of-the-art opacities from ExoMol. Our first application of this model is devoted to the extensively studied hot Jupiter HD 209458b. We have derived synthetic emission spectra and phase curves, and compare them to both previous models also based on state-of-the-art radiative transfer, and to observations. We find a reasonable a agreement between observations and both our day side emission and hot spot offset, however, our night side emission is too large. Overall our results are qualitatively similar to those found by Showman et al. (2009) with the SPARC/MITgcm, however, we note several quantitative differences: Our simulations show significant variation in the position of the hottest part of the atmosphere with pressure, as expected from simple timescale arguments, and in contrast to the "vertical coherency" found by Showman et al. (2009). We also see significant quantitative differences in calculated synthetic observations. Our comparisons strengthen the need for detailed intercomparisons of dynamical cores, radiation schemes and post-processing tools to understand these differences. This effort is necessary in order to make robust conclusions about these atmospheres based on GCM results.

Markov chain formalism for generalized radiative transfer in a plane-parallel medium, accounting for polarization

A Markov chain formalism is developed for computing the transport of polarized radiation according to Generalized Radiative Transfer (GRT) theory, which was developed recently to account for unresolved random fluctuations of scattering particle density and can also be applied to unresolved spectral variability of gaseous absorption as an improvement over the standard correlated-k method. Using Gamma distribution to describe the probability density function of the extinction or absorption coefficient, a shape parameter a that quantifies the variability is introduced, defined as the mean extinction or absorption coefficient squared divided by its variance. It controls the decay rate of a power-law transmission that replaces the usual exponential Beer-Lambert-Bouguer law. Exponential transmission, hence classic RT, is recovered when a→∞. The new approach is verified to high accuracy against numerical benchmark results obtained with a custom Monte Carlo method. For a<∞, angular reciprocity is violated to a degree that increases with the spatial variability, as observed for finite portions of real-world cloudy scenes. While the degree of linear polarization in liquid water cloudbows, supernumerary bows, and glories is affected by spatial heterogeneity, the positions in scattering angle of these features are relatively unchanged. As a result, a single-scattering model based on the assumption of subpixel homogeneity can still be used to derive droplet size distributions from polarimetric measurements of extended stratocumulus clouds.

Transported scalar PDF modeling of oxygen-enriched turbulent jet diffusion flames: Soot production and radiative heat transfer

Turbulent jet flames fueled either by propane or a methane/ethylene blend and burning under different oxygen indexes (OI) in the range from 21% (air) to 100% (pure oxygen), studied experimentally by Wang et al. (2002), were simulated by using an hybrid flamelet/Stochastic Eulerian Field (SEF) method, an acetylene/benzene-based two-equation soot model, and a wide-band correlated-k (WBCK) method to model the spectral dependence of the absorption coefficient of the gaseous radiatively participating species and soot. Emission Turbulent Radiation Interactions (TRIs) are taken into account by means of the PDF method, whereas absorption TRIs are modeled using the optically-thin fluctuation approximation (OTFA). Model predictions in terms of soot volume fraction, radiant heat flux distribution along the wall of the combustion chamber, and radiant fraction are compared with the experimental data of Wang et al. (2002), showing a reasonable agreement. The non-monotonic evolution of the soot production with the OI, increasing sharply when the OI is enhanced from 21% to about 40% and then being significantly reduced as the OI is further increased, and the effects of the fuel sooting propensity, with the propane flames producing much more soot than the methane/ethylene blend flames, are well reproduced by the numerical model. The non-monotonic influence of the OI on soot production can be explained by several competing mechanisms. The soot production tends to be enhanced owing to, on the one hand, the increase in temperature and, on the other hand, a positive feedback between surface growth process and soot surface area observed for moderate level of oxygen enrichment. Oppositely, the soot production tends to be reduced due to a decrease in residence time and an enhancement in the oxidation of both soot precursors and soot particles.

Accuracy tests of radiation schemes used in hot Jupiter global circulation models

The treatment of radiation transport in global circulation models (GCMs) is crucial to correctly describe Earth and exoplanet atmospheric dynamics processes. The two-stream approximation and correlated-k method are currently state-of-the-art approximations applied in both Earth and hot Jupiter GCM radiation schemes to facilitate rapid calculation of fluxes and heating rates. Their accuracy have been tested extensively for Earth-like conditions, but verification of the methods' applicability to hot Jupiter-like conditions is lacking in the literature. We are adapting the UK Met Office GCM, the Unified Model (UM), for the study of hot Jupiters, and present in this work the adaptation of the Edwards-Slingo radiation scheme based on the two-stream approximation and the correlated-k method. We discuss the calculation of absorption coefficients from high temperature line lists and highlight the large uncertainty in the pressure-broadened line widths. We compare fluxes and heating rates obtained with our adapted scheme to more accurate discrete ordinate (DO) line-by-line (LbL) calculations ignoring scattering effects. We find that, in most cases, errors stay below 10 % for both heating rates and fluxes using ~ 10 k-coefficients in each band and a diffusivity factor D = 1.66. The two-stream approximation and the correlated-k method both contribute non-negligibly to the total error. We also find that using band-averaged absorption coefficients, which have previously been used in radiative-hydrodynamical simulations of a hot Jupiter, may yield errors of ~ 100 %, and should thus be used with caution.

Simulation of Radiative Transfer in Nonequilibrium Plasmas Containing N and O Species Based on the Approximate Collision-Radiative Method

An approximate collision-radiative method is developed to calculate energy level populations of atoms and applied to simulate radiative transfer in a shock layer. Considering nonequilibrium plasmas with the electronic temperature below 20000 K, we introduce correction factors to the Saha—Boltzmann equation and simplify the master equation of the full collision-radiative model. Based on the method, the error of heat flux is smaller than 5% in a two-cell problem and smaller than 7% in the Stardust re-entry flow field compared with the correlated-k method. Furthermore, almost a factor of 2 is obtained in the improvement of computational efficiency compared with the nonequilibrium air radiation (NEQAIR) code. The results show that the present method is reliable and efficient.

Influence of turbulence–radiation interactions in laboratory-scale methane pool fires

The objective of this study is to assess the effects of Turbulence–Radiation Interactions (TRI) on the structure of small-scale pool fires and on the radiative fluxes transferred to surrounding surfaces. Fire-induced flow is modeled by using a buoyancy-modified k-ε model and the Steady Laminar Flamelet (SLF) model coupled with a presumed Probability Density Function (pdf) approach. A 34-kW methane pool fire produced by burner with a diameter of 0.38 m is simulated by neglecting radiation, by considering radiation without TRIs, and by considering radiation with TRIs. Computations carried out with radiation are based on the Full Spectrum Correlated-k (FSCK) method. TRIs are taken into account by considering the Optically-Thin Fluctuation Approximation (OTFA). The mean radiative source term and the mean RTE are then closed by using a presumed pdf of the mixture fraction, scalar dissipation rate, and enthalpy defect. When TRIs are considered predicted flame structure, radiant fraction and radiative fluxes are found in quantitative agreement with the available experimental data. Simulations reveal that TRIs significantly enhance radiative losses and substantially contribute to the drop in temperature due to radiation. TRIs also contribute to reduce turbulence levels and the root mean square (rms) values of temperature fluctuations. In addition radiative heat fluxes on remote targets are found to be considerably higher than those obtained from radiative calculations based on mean properties. Finally different levels of closure for the TRI-related terms are assessed. Model results show that the complete absorption coefficient-Planck function correlation should be considered in order to properly take into account the influence of TRIs on the emission term whereas the effect of absorption coefficient self-correlation on the absorption term is a reduction by about 12% of the radiant fraction.

Modelling thermal radiation from one-meter diameter methane pool fires

The first objective of this article is to implement a comprehensive radiation model in order to predict the radiant fractions and radiative fluxes on remote surfaces in large-scale methane pool fires. The second aim is to quantify the importance of Turbulence-Radiation Interactions (TRIs) in such buoyant flames. The fire-induced flow is modelled by using a buoyancy-modified k-ε model and the Steady Laminar Flamelet (SLF) model coupled with a presumed probability density function (pdf) approach. Spectral radiation is modelled by using the Full-Spectrum Correlated-k (FSCK) method. TRIs are taken into account by considering the Optically-Thin Fluctuation Approximation (OTFA). The emission term and the mean absorption coefficient are closed by using a presumed pdf of the mixture fraction, scalar dissipation rate and enthalpy defect. Two 1m-diameter fires with Heat Release Rates (HRR) of 49 kW and 162 kW were simulated. Predicted radiant fractions and radiative heat fluxes are found in reasonable agreement with experimental data. The importance of TRIs is evidenced, computed radiant fractions and radiative heat fluxes being considerably higher than those obtained from calculations based on mean properties. Finally, model results show that the complete absorption coefficient-Planck function correlation should be considered in order to properly take into account the influence of TRIs on the emission term, whereas the absorption coefficient self-correlation in the absorption term reduces significantly the radiant fractions.

Modelling thermal radiation in buoyant turbulent diffusion flames

This work focuses on the numerical modelling of radiative heat transfer in laboratory-scale buoyant turbulent diffusion flames. Spectral gas and soot radiation is modelled by using the Full-Spectrum Correlated-k (FSCK) method. Turbulence-Radiation Interactions (TRI) are taken into account by considering the Optically-Thin Fluctuation Approximation (OTFA), the resulting time-averaged Radiative Transfer Equation (RTE) being solved by the Finite Volume Method (FVM). Emission TRIs and the mean absorption coefficient are then closed by using a presumed probability density function (pdf) of the mixture fraction. The mean gas flow field is modelled by the Favre-averaged Navier–Stokes (FANS) equation set closed by a buoyancy-modified k-ϵ model with algebraic stress/flux models (ASM/AFM), the Steady Laminar Flamelet (SLF) model coupled with a presumed pdf approach to account for Turbulence-Chemistry Interactions, and an acetylene-based semi-empirical two-equation soot model. Two sets of experimental pool fire data are used for validation: propane pool fires 0.3 m in diameter with Heat Release Rates (HRR) of 15, 22 and 37 kW and methane pool fires 0.38 m in diameter with HRRs of 34 and 176 kW. Predicted flame structures, radiant fractions, and radiative heat fluxes on surrounding surfaces are found in satisfactory agreement with available experimental data across all the flames. In addition further computations indicate that, for the present flames, the gray approximation can be applied for soot with a minor influence on the results, resulting in a substantial gain in Computer Processing Unit (CPU) time when the FSCK is used to treat gas radiation.

A computational framework for predicting laminar reactive flows with soot formation

Numerical modeling is an attractive option for cost-effective development of new high-efficiency, soot-free combustion devices. However, the inherent complexities of hydrocarbon combustion require that combustion models rely heavily on engineering approximations to remain computationally tractable. More efficient numerical algorithms for reacting flows are needed so that more realistic physics models can be used to provide quantitative soot predictions. A new, highly-scalable combustion modeling tool has been developed specifically for use on large multiprocessor computer architectures. The tool is capable of capturing complex processes such as detailed chemistry, molecular transport, radiation, and soot formation/destruction in laminar diffusion flames. The proposed algorithm represents the current state of the art in combustion modeling, making use of a second-order accurate finite-volume scheme and a parallel adaptive mesh refinement (AMR) algorithm on body-fitted, multiblock meshes. Radiation is modeled using the discrete ordinates method (DOM) to solve the radiative transfer equation and the statistical narrow-band correlated-k (SNBCK) method to quantify gas band absorption. At present, a semi-empirical model is used to predict the nucleation, growth, and oxidation of soot particles. The framework is applied to two laminar coflow diffusion flames which were previously studied numerically and experimentally. Both a weakly-sooting methane–air flame and a heavily-sooting ethylene–air flame are considered for validation purposes. Numerical predictions for these flames are verified with published experimental results and the parallel performance of the algorithm analyzed. The effects of grid resolution and gas-phase reaction mechanism on the overall flame solutions were also assessed. Reasonable agreement with experimental measurements was obtained for both flames for predictions of flame height, temperature and soot volume fraction. Overall, the algorithm displayed excellent strong scaling performance by achieving a parallel efficiency of 70% on 384 processors. The proposed algorithm proved to be a robust, highly-scalable solution method for sooting laminar flames.