Non-gray Model Research Articles

On the compromise between accuracy and computational cost of non-gray global models for heat radiation in gas mixtures

In this study the prediction accuracy of latest versions of FSK and SLW models (Rank correlated) and WSGG model is assessed at the limit of smallest computation cost. The results of these predictions are compared with the Line-by-Line benchmark calculations. One-dimensional decoupled radiation calculation is performed on a variety of case studies in order to investigate the limit of computational cost where the accuracy of FSK and SLW model are able to surpass WSGG. The subpar performance of RC-SLW at three quadrature points is addressed by optimizing model parameters. The possibility of using an approximated mixture database is also assessed where the RC-FSK model is able to yield satisfactory results with as low as four quadrature points. Regarding the utilization of approximated curves, again the method seems to be working slightly better with RC-FSK. The outcomes of this analysis may serve as guidance regarding the efficient implementation of FSK or SLW models in CFD codes.

Are These Planets or Brown Dwarfs? Broadly Solar Compositions from High-resolution Atmospheric Retrievals of ∼10–30 M Jup Companions

Using Keck Planet Imager and Characterizer high-resolution (R ∼ 35,000) spectroscopy from 2.29 to 2.49 μm, we present uniform atmospheric retrievals for eight young substellar companions with masses of ∼10–30 M Jup, orbital separations spanning ∼50–360 au, and T eff between ∼1500 and 2600 K. We find that all companions have solar C/O ratios and metallicities to within the 1σ–2σ level, with the measurements clustered around solar composition. Stars in the same stellar associations as our systems have near-solar abundances, so these results indicate that this population of companions is consistent with formation via direct gravitational collapse. Alternatively, core accretion outside the CO snowline would be compatible with our measurements, though the high mass ratios of most systems would require rapid core assembly and gas accretion in massive disks. On a population level, our findings can be contrasted with abundance measurements for directly imaged planets with m < 10 M Jup, which show tentative atmospheric metal enrichment compared to their host stars. In addition, the atmospheric compositions of our sample of companions are distinct from those of hot Jupiters, which most likely form via core accretion. For two companions with T eff ∼ 1700–2000 K (κ And b and GSC 6214–210 b), our best-fit models prefer a nongray cloud model with >3σ significance. The cloudy models yield 2σ−3σ lower T eff for these companions, though the C/O and [C/H] still agree between cloudy and clear models at the 1σ level. Finally, we constrain 12CO/13CO for three companions with the highest signal-to-noise ratio data (GQ Lup b, HIP 79098b, and DH Tau b) and report vsini and radial velocities for all companions.

Large-scale PANDA facility – radiation experiments and CFD calculations

Abstract CFD modelling of the thermo-hydraulic phenomena in the containment during the various phases of a severe accident necessarily requires consideration of radiative heat transfer – in the presence of steam. These radiative phenomena include (i) energy transfer within the gas mixture and (ii) between the gas and surrounding structures. Preliminary calculations carried out for these types of experiments within the OECD/NEA HYMERES-2 project with the CFD code containmentFOAM using a Monte Carlo solver for thermal radiation, demonstrated that the radiative heat transfer is significant even for very small amounts of vapour in the range of ≈0.1 % to ≈2 %. For this reason, the test matrix was tailored to the two opposite extremes: either gas compositions with a low vapour/steam content, where radiative heat transfer can be neglected, or gas mixtures with higher vapour contents, so that radiative heat transfer plays a dominant role. For the selected experiments of the H2P2 series and the corresponding CFD calculations, a vessel with a diameter of 4 m and a height of 8 m was preconditioned with different air-vapour mixtures (a) at room temperature and (b) elevated temperatures. A stable helium layer was then built-up in the upper part of the vessel. The gas was then compressed by injecting helium from above which resembles with best efforts a compression with a piston in a cylinder. This results in a height-dependent and transient increase of the gas temperature. These experiments and the associated CFD calculations were developed to isolate the phenomena of thermal radiation as good as possible from convective and diffusive effects – within the always present experimental limitations. For the reference experiment with ‘dry conditions’ corresponding to the lowest experimentally possible humidity of ≈0.1 %, we show that the use of a model without radiation provides the best agreement between the experimental and numerical results. For the much higher steam content of ≈60 %, the statistical narrow band correlated-k model (SNBCK), non-gray gas model, is the best candidate for future calculations – with computationally forgivable additional effort. We also provide with the Filtered Rayleigh Scattering technique (FRS) an outlook for a possible future instrumentation approach to better meet the requirements of the CFD community.

Analysis of large-scale fires in Makkah’s King Khaled Road tunnel using non-gray radiation models

The present study validated a fire dynamic simulation approach for reducing costs and losses in tunnel fire tests. It analyzed various radiation models, including gray, non-gray, and non-gray sooting models. The central processing unit (CPU) run time of the last model was very long, and the model is of little value in practice. The non-gray model was found to be the most accurate and efficient. This model was used to study fire behavior in the King Khaled Road tunnel in Makkah. This was done because the tunnel is small, there aren't many ways to get out, and it's hard to get firefighting teams to a place like Makkah during the Hajj season when there are a lot of people. Results showed that gas temperature, radiation, CO and CO2 concentrations, and air velocity increased with heat release rate, oxygen concentration, and soot yield. The air velocity was overpredicted during the simulations, having consequences for most of the other quantities, and this led to a cooler gas temperature, higher oxygen levels, and lower CO and CO2 concentrations. In addition, it is established that gas temperature and radiation increased when the ambient temperature increased, and oxygen concentration and air velocity were mostly unaffected by changing ambient temperature.

BICEPS: An improved characterization model for low- and intermediate-mass exoplanets

Context. The number of exoplanets with precise mass and radius measurements is constantly increasing thanks to novel ground- and space-based facilities such as HARPS, ESPRESSO, CHEOPS, and TESS. The accuracy and robustness of the planetary characterization largely depends on the quality of the data, but also requires a planetary structure model, capable of accurately modeling the interior and atmospheres of exoplanets over a large range of boundary conditions. Aims. Our goal is to provide an improved characterization model for planets with masses between 0.5 and 30 Earth masses, equilibrium temperatures below &lt;2000 K, and a wide range of planetary compositions and physical phases. Methods. In this work, we present the Bayesian Interior Characterization of ExoPlanetS (BICEPS) model, which combines an adaptive Markov chain Monte Carlo sampling method with a state-of-the-art planetary structure model. BICEPS incorporates many recently developed equations of state suited for large ranges of pressures and temperatures, a description for solid and molten planetary cores and mantles, a gaseous envelope composed of hydrogen, helium, and water (with compositional gradients), and a non-gray atmospheric model. Results. We find that the usage of updated equations of state has a significant impact on the interior structure prediction. The impact varies, depending on the planetary composition. For dense rocky planets, BICEPS predicts radii a few percent different to prior internal structure models. For volatile rich planets, we find differences of 10% or even larger. When applying BICEPS to a particular exoplanet, TOI-130 b, we inferred a 25% larger water mass fraction and a 15% smaller core than previous models. Conclusions. The presented exoplanet characterization model is a robust method applicable over a large range of planetary masses, compositions, and thermal boundary conditions. We show the importance of implementing state-of-the-art equations of state for the encountered thermodynamic conditions of exoplanets. Hence, using BICEPS improves the predictive strength of the characterization process compared to previous methods.

Importance, influence and limits of CFD radiation modeling for containment atmosphere simulations

In the appearance of steam, the CFD modeling of thermal-hydraulic phenomena in reactor containments during various phases of an accident necessarily requires consideration of radiative heat transfer. These radiation phenomena involve (i) energy transfer within the gas mixture and (ii) between the gas and the surrounding structures which have a much higher thermal inertia. Preliminary calculations performed for the present experiments in the OECD/NEA HYMERES-2 project with the CFD code containmentFoam using a Monte Carlo thermal radiation solver with non-gray gas modeling of steam absorption, showed that radiant heat transfer is important even with a very low amount of steam (≈ 2%). Therefore, the test matrix was tailored to the two opposite extremes: Either gas compositions with low steam content, where radiative heat transfer can be neglected, or gas mixtures containing larger amounts of steam, so that radiative heat transfer plays a dominant role. For the two selected experiments within the H2P2 series and the corresponding CFD calculations, a vessel with a diameter of 4 m and a height of 8 m was preconditioned with different mixtures of air/steam at room and elevated temperatures. This was followed by the build-up of a stable helium stratification in the upper part of the vessel. Helium was then injected from the top at a higher mass flow rate, which (a) compresses the gas atmosphere, (b) resembles piston compression and (c) leads to a height-dependent and transient increase in gas temperature below this helium stratification, influenced by thermal radiation effects — or their absence. These experiments and the associated CFD calculations were developed to isolate the thermal radiation phenomena as much as possible from convective and diffusive effects. They are the first of their kind to be conducted in a large-scale thermal-hydraulic facility. It is demonstrated (a) that neglecting thermal radiation for the high steam content case, the temperature rise is significantly over-predicted by a factor of two compared to the application of the suggested Monte Carlo thermal radiation solver with non-gray gas modeling, (b) the computational effort considering CFD and non-gray gas radiation is feasible with the suggested tailored Monte Carlo solver and (c) that the suggested radiation model outperforms the widespread used P1 radiation model.

Modeling Thermal Radiation in Combustion Environments: Progress and Challenges

Modeling thermal radiation in combustion environments can be extremely challenging for two main reasons. First, the radiative transfer equation (RTE), which is the cornerstone of modeling radiation in such environments, is a five-dimensional integro-differential equation. Second, the absorption and scattering coefficients of molecular gases and particulates prevalent in combustion environments oscillate strongly with the wavenumber (or wavelength), i.e., the medium is strongly nongray, requiring the solution of the RTE for a large number of wavenumbers. This article reviews the progress that has been made in this area to date with an emphasis on the work performed over the past three decades. Progress in both deterministic and stochastic (Monte Carlo) solutions of the RTE is reviewed, in addition to the review of the treatment of the spectral properties of gases, soot, and fuel droplets that dominate combustion environments, i.e., spectral or nongray models. The application of the various state-of-the-art nongray models and RTE solution methods to flames (particularly turbulent), fires, combustors, and other combustion systems are summarized along with a critical discussion of the pros and cons of the models and methods. Finally, the challenges that remain in modeling thermal radiation in combustion systems are highlighted and future outlooks are shared.

Performance analysis of a concentrated direct absorption solar collector (DASC) with nanofluids using computational fluid dynamics and discrete ordinates radiation modelling (CFD-DORM)

This study utilises computational modelling to investigate the application of thermal nanofluids in direct absorption solar collectors (DASC), including the effect of optical and thermal properties on the prediction of thermal energy production. A single-phase, computational fluid dynamics (CFD) model has been used to understand the hydrothermal behaviour of nanofluids operated at high temperature. A non-gray discrete ordinate radiation model (DORM) was coupled to the CFD to capture the dependence of optical parameters on the bulk temperature variation. In order to increase the robustness of the numerical modelling approach, the extinction coefficient of the solar participating media, including the reflective and transmissive behaviour of the semitransparent wall, were taken into consideration. Results show that the exergy efficiency is lower when using fully diffusive conditions at the semitransparent wall as opposed to fully specular conditions. Overall, exergy efficiency decreases with the Nusselt number, Nu, (until Nu=10∼12), although it increases with non-dimensional irradiation. When modelling with temperature-dependent as opposed to temperature-independent properties of the working fluid, the Carnot efficiency was found to vary by 0.67% to 3.30%. Additionally, a correlation between the hydraulic entrance length and Reynolds number, Re, (in the range Re<1,000) has been established and this can be applied for the further hydrothermal analysis. This study serves as a basis for future numerical modelling of any volumetric solar receiver that takes into account the various key system performance indicators of the solar participating media.

The importance of accurately modelling soot and radiation coupling in laminar and laboratory-scale turbulent diffusion flames

Ultrafine and highly light absorbing soot particles have been known to be harmful to human health and a major climate forcer. Understanding the mechanisms of soot formation and developing reliable and robust soot models are essential to design efficient and clean combustion systems. Thermal radiation is often the dominant heat transfer mode in both turbulent and laminar flames and affects soot formation through its influence on temperature. Significant progress has been made in modelling soot formation, thermal radiation transfer, and turbulence radiation interaction in hydrocarbon flames over the last three decades. However, the optically thin approximation has still been used to simplify thermal radiation transfer modelling and turbulence radiation interaction has often been neglected in soot formation modelling without proper justification. In this paper, soot models developed for laminar and laboratory scale turbulent jet diffusion flames, non-gray radiative heat transfer models, and turbulence radiation interaction models are reviewed. The aim of this review is to highlight the importance of thermal radiation heat transfer in both laminar and turbulent diffusion flames and turbulence radiation interaction in turbulent jet diffusion flames. Use of the optically thin approximation is often not justified even in laminar diffusion flames. This is particularly true in diffusion flames at elevated pressures or microgravity. Although the prediction of soot in both laminar and turbulent flames is primarily influenced by soot kinetic model, it is also significantly affected by aerosol dynamic model, thermal radiation heat transfer model, and turbulence radiation interaction model. It is important to accurately model soot aerosol dynamics and non-gray thermal radiation transfer in laminar diffusion flames and additionally to adequately model turbulence radiation interaction in turbulent flames for the purpose of validating reaction mechanisms and soot kinetic models.

Non-gray gas and particle radiation in a pulverized coal jet flame

In pulverized coal combustion, the participating radiative media includes gas, soot, and coal/char particles; a fundamental understanding of their radiation behavior is essential for the prediction of radiation heat transfer and control of radiation in the furnace. In this study, the individual contributions of gas, soot, and coal particles to the total radiation were examined based on the large eddy simulation of the CRIEPI pulverized coal jet flame. The radiation transfer equation was solved using the discrete ordinate method with state-of-the-art non-gray radiative property models of multi-phase media. The full spectrum correlated k-distributions (FSCK) model was used to calculate the radiative property of the gas-soot mixture. A burnout-based particle radiative property model was applied for coal/char particles. The results showed that the predicted spatial distributions of coal particles, tar, and soot were in good agreement with the experimental data. The gray gas radiation model predicted temperatures approximately 50 K lower in this flame, and the peak soot volume fraction was predicted at approximately 22% lower. For the laboratory scale burner under examination, the individual radiative contributions of gas, soot, and coal/char were found to be 35%, 40%, and 25%, respectively, so that it was necessary to consider all components for accurate prediction. Moreover, these contribution ratios varied with the flame position. Because of the high particle concentration, the individual contribution of coal/char particles accounted for up to 65% in the devolatilization region. Soot radiation played an important role in the pulverized coal flame. In the region where the ensemble-averaged soot volume fraction reached the maximum of 2.7 ppm, the individual contribution of soot was 50% of the total radiation, which accounted for 70% of the total particles (soot and char) radiation.

Exploring the deep atmospheres of HD 209458b and WASP-43b using a non-gray general circulation model

Simulations with a 3D general circulation model (GCM) suggest that one potential driver behind the observed radius inflation in hot Jupiters may be the downward advection of energy from the highly irradiated photosphere into the deeper layers. Here, we compare dynamical heat transport within the non-inflated hot Jupiter WASP-43b and the canonical inflated hot Jupiter HD 209458b, with similar effective temperatures. We investigate to what extent the radiatively driven heating and cooling in the photosphere (at pressures smaller than 1 bar) influence the deeper temperature profile (at pressures between 1 to 700 bar). Our simulations with the new non-gray 3D radiation-hydrodynamical model expeRT/MITgcm show that the deep temperature profile of WASP-43b is associated with a relatively cold adiabat. The deep layers of HD 209458b, however, do not converge and remain nearly unchanged regardless of whether a cold or a hot initial state is used. Furthermore, we show that different flow structures in the deep atmospheric layers arise. There, we find that WASP-43b exhibits a deep equatorial jet, driven by the relatively fast tidally locked rotation of this planet (0.81 days), as compared to HD 209458b (3.47 days). However, by comparing simulations with different rotation periods, we find that the resulting flow structures only marginally influence the temperature evolution in the deep atmosphere, which is almost completely dominated by radiative heating and cooling. Furthermore, we find that the evolution of deeper layers can influence the 3D temperature structure in the photosphere of WASP-43b. Thus, dayside emission spectra of WASP-43b may shed more light onto the dynamical processes occurring at greater depths.

Retrieval Study of Brown Dwarfs across the L-T Sequence

A large suite of 228 atmospheric retrievals is performed on a curated sample of 19 brown dwarfs spanning the L0–T8 spectral types using the open-source Helios-r2 retrieval code, which implements the method of short characteristics for radiative transfer and a finite-element description of the temperature–pressure profile. Surprisingly, we find that cloud-free and cloudy (both gray and nongray) models are equally consistent with the archival SpeX data from the perspective of Bayesian model comparison. Only upper limits for cloud properties are inferred if log-uniform priors are assumed, but the cloud optical depth becomes constrained if a uniform prior is used. Water is detected in all 19 objects, and methane is detected in all of the T dwarfs, but no obvious trend exists across effective temperature. As carbon monoxide is only detected in a handful of objects, the inferred carbon-to-oxygen ratios are unreliable. The retrieved radius generally decreases with effective temperature, but the values inferred for some T dwarfs are implausibly low and may indicate missing physics or chemistry in the models. For the early L dwarfs, the retrieved surface gravity depends on whether the gray-cloud or non-gray-cloud model is preferred. Future data are necessary for constraining cloud properties and the vertical variation of chemical abundances, the latter of which is needed for distinguishing between the chemical instability and traditional cloud interpretation of the L-T transition.

Optimized Phonon Band Discretization Scheme for Efficiently Solving the Nongray Boltzmann Transport Equation

Abstract The phonon Boltzmann transport equation (BTE) is an important tool for studying the nanoscale thermal transport. Because phonons have a large spread in their properties, the nongray (i.e., considering different phonon bands) phonon BTE is needed to accurately capture the nanoscale transport phenomena. However, BTE solvers generally require large computational cost. Nongray modeling imposes significant additional complexity on the numerical simulations, which hinders the large-scale modeling of real nanoscale systems. In this work, we address this issue by a systematic investigation on the phonon band discretization scheme using real material properties of four representative materials, including silicon, gallium arsenide, diamond, and lead telluride. We find that the schemes used in previous studies require at least a few tens of bands to ensure the accuracy, which requires large computational costs. We then propose an improved band discretization scheme, in which we divide the mean free path domain into two subdomains, one on either side of the inflection point of the mean free path accumulated thermal conductivity, and adopt the Gauss–Legendre quadrature for each subdomain. With this scheme, the solution of the phonon BTE converges (error &amp;lt; 1%) with less than ten phonon bands for all these materials. The proposed scheme allows significantly reducing the time and memory consumption of the numerical BTE solver, which is an important step toward large-scale phonon BTE simulations for real materials.

Assessment of Radiative Heating for Hypersonic Earth Reentry Using Nongray Step Models

Accurate prediction of the aerothermal environment is of great significance to space exploration and return missions. The canonical Fire II trajectory points are simulated to investigate the radiative transfer in the shock layer for Earth reentry at hypervelocity above 10 km/s using a developed radiation–flowfield uncoupling method. The thermochemical nonequilibrium flow is solved by an in-house PHAROS Navier–Stokes code, while the nongray radiation is integrated by the tangent slab approximation, respectively, combined with the two-, five-, and eight-step models. For the convective heating, the present results agree well with the data of Anderson’s relation. For the radiative heating, the two-step model predicts the closest values with the results of Tauber and Sutton’s relationship, while the five- and eight-step models predict far greater. The three-step models all present the same order of magnitude of radiative heating of 1 MW/m2 and show a consistent tendency with the engineering estimation. The Planck-mean absorption coefficient is calculated to show the radiative transfer significantly occurs in the shock layer. By performing the steady simulation at each flight trajectory point, the present algorithm using a nongray step model with moderate efficiency and reasonable accuracy is promising to solve the real-time problem in engineering for predicting both convective and radiative heating to the atmospheric reentry vehicle in the future.

Monte Carlo method with SNBCK nongray gas model for thermal radiation in containment flows

During a postulated severe accident in light water reactors, containment flows are characterized by relatively low velocities and modest temperature differences after depressurization of the reactor cooling system. Owing to the low gas temperature level and small temperature differences, gas radiation heat transfer was neglected in CFD simulations of hydrogen transport and mixing in containment flows. During the natural mixing and dilution processes, thermal radiation can affect the fluid temperatures and thereby influence the buoyancy forces in the presence of large amounts of steam. In order to quantify the effect of thermal radiation, an efficient Monte Carlo method with statistical narrow band correlated-k (SNBCK) nongray gas model has been implemented to solve the radiative transfer equation within the framework of containmentFOAM. The tailored Monte Carlo solver is validated against the OECD/NEA SETH-2 PANDA ST1 experiments, and it is proven that gas radiation has a significant effect on the gas temperature field and the helium-steam mixing process. The results clearly indicate that gas radiation cannot be neglected in containment flows even at modest temperature differences (ΔT<50K).

Thermal transport in beta-gallium oxide thin-films using non-gray Boltzmann transport equation

Phonon transport in β-Ga2O3 thin films and metal-oxide field effect transistors (MESFETs) are investigated using non-gray Boltzmann transport equations (BTEs) to decipher the effect of ballistic-diffusive phonon transport. The effects of domain size, and energy dissipation to various phonon modes and subsequent phonon–phonon energy exchange on the thermal transport and temperature distribution is investigated using non-gray BTE. Our analysis deciphered that domain size plays a major role in thermal transport in β-Ga2O3 but energy dissipation to various phonon modes and subsequent phonon–phonon energy exchange does not affect the temperature field significantly. Phonon transport in β-Ga2O3 MESFETs on diamond substrate is investigated using coupled non-gray BTE and Fourier model. It is established that the ballistic effects need to be considered for devices with β-Ga2O3 layer thickness less than 1 μm. A non-gray phonon BTE model should be used near hotspot in the thin β-Ga2O3 layer as the Fourier model may not give accurate temperature distribution. The results from this work will help in understanding the mechanism of phonon transport in the β-Ga2O3 thin films and energy efficient design of its FETs.

Assessment of weighted-sum-of-gray-gases models for gas-soot mixture in jet diffusion flames

The global radiative property models are widely used in combustion simulation due to its high computational efficiency. This study assesses the weighted sum of gray gases (WSGG) models for gas-soot mixture in the simulations of turbulent jet diffusion flame at atmospheric pressure with fully coupled combustion and radiation heat transfer. Non-adiabatic tabulated chemistry approach and the method of moments were employed for combustion modeling and soot particle dynamics. The radiative transfer equations are solved by the discrete ordinate model. Two kinds of WSGG model based on mixture modeling (MM) and superposition method (SM), and their combination with the gray and non-gray soot radiative property models are involved in the comparison. First, the radiative property models are evaluated on the one-dimensional parallel plate system using line-by-line model as the benchmark, and then the WSGG models are evaluated on the basis of the FSCK model in the combustion simulation. The results show that MM and SM provide similar prediction accuracy, while MM has much lower computational cost. The MM combined with the non-gray soot radiative property model (MMNS) provides the best accuracy for gas-soot mixture. Moreover, the relative error of MM combined with gray soot radiative property model (MMGS) is less than 10% for radiation source term, which is acceptable in engineering simulation. The gray implementation of WSGG model has low accuracy, which indicates that it is necessary to use the non-gray implementation of WSGG model in CFD simulations.

Study the thermal radiation effects in gas-solid flows with gray and non-gray P1 models implemented in MFiX

Thermal radiation is a dominant mode of heat transfer in combustion/gasification, packed/circulating bed reactors, and energy storage/conversion devices. In hydrocarbon fuel combustion, the high absorption and emission of product gases like CO2 and H2O significantly affect the heat transfer characteristics. It is essential to understand the radiative energy propagation in such applications. In the present study, we developed a framework to implement the P-1 radiation model in MFiX for Eulerian-Eulerian (Two fluid-TFM) and Eulerian-Lagrangian (Discrete element-DEM and Particle in cell-PIC) models. The P-1 is a simplification of the spherical harmonics method. The framework has been verified on various flue gas conditions. The verified solver results are validated against the benchmark results available in the literature. The verified and validated gray and non-gray weighted sum of gray gas models is evaluated for dry and wet flue gas conditions. They are also used to study gas-solid flows in a fluidized bed/riser.

Numerical solutions of radiative heat transfer in combustion systems using a parallel modified discrete ordinates method and several recent formulations of WSGG model

The aim of the paper is to perform 3D radiative transfer calculations in combustion gas mixtures. For this purpose, a parallel modified Discrete Ordinates Method with a cell-vertex formulation on unstructured tetrahedral grid is proposed for solving the Radiative Transfer Equation (RTE) in realistic geometries. Several recent formulations of the weighted-sum-of-gray-gases (WSGG) model are implemented. To reduce the false scattering, the cell-vertex formulation is combined with an Exponential scheme and is compared to the Step scheme. The results are then compared with published results on non-isothermal and non-homogeneous gas mixtures. The use of non-gray WSGG models shows a very good level of accuracy for the evaluation of wall heat transfer and radiative heat source. The Exponential scheme is more accurate than the Step scheme. The summation over the wavenumber spectrum of the radiative model is usually carried out after having computed the radiative quantities for each discrete angular direction. By summing first over the wavenumber spectrum, a reduction in the computation time is significantly obtained, up to a factor of 16 on a case study. Also, additionnal significant speedup is obtained with an efficient distributed and multi-threaded parallel algorithm. When the Step scheme is used, the computation time increases very slightly with the number of gray gases. The procedure to speed up the calculations can be applied to any arbitrary numerical method for solving the spectral RTE.

Analysis of the Heat Transfer Within Combustor Liners Using a Combined Monte Carlo and Two-Flux Method

Abstract One consequence of increasing efficiency of gas turbine combustors is higher temperatures within the combustor. Management of larger heat load has been advanced to protect the combustor wall and turbines, and among those are thermal barrier coatings (TBCs). Historically, both the flame and TBCs have received a simplified radiation treatment using effective absorptivities and emissivities. In this study, non-gray radiation is compared with gray and black radiation by combining three-dimensional Monte Carlo Ray Tracing solution of non-gray flames in a model gas turbine combustor to one-dimensional energy balance within combustor liners. A recent large eddy simulation of a gas turbine combustor is analyzed, where both gray and non-gray models are exercised. A two-band spectral model is employed for the TBC, where a translucent band and an opaque band are identified. A line-by-line treatment for gas-phase radiation is adopted, and the incident radiative energy on the combustor wall is collected using the MCRT solver, where the fraction of radiative energy within the translucent band is collected and compared with those obtained from the blackbody assumption. The temperature along the multilayered combustor wall is computed, and parametric comparison is conducted. The effects of the nongray flame radiation are more prominent at elevated pressures than at atmospheric pressure. The gray model is found to over-predict the TBC temperature, which leads to a difference of approximately 150 K in the prediction of peak temperature on the hot side of the TBC.