In this chapter, the radiation exchange formulation presented the Chapter 5 is extended to partly specular surfaces, to nongray surfaces, as well as generally nondiffuse, nongray enclosures. The concept of view factor is first extended to specular surfaces. Then, exchange equations for an enclosure with partly specular, gray surfaces are derived and demonstrated through several examples, including surfaces that are curved. The electrical network analogy is revisited for partly specular surfaces, and the formulation presented in Chapter 5 for radiation shields is rederived for partly specular surfaces. A discussion of reflection and transmission through semitransparent sheets with partly specular reflection effects is also given. Next, nongray surfaces are considered, presenting the semigray approximation, as well as the band approximation. Finally, the governing equation for the intensity leaving the surface of an enclosure with arbitrary radiative properties (spectrally and directionally) is developed, from which heat transfer rates may be calculated.

At higher pressures, the spectral lines in a gas spectrum can become more broadened and shifted due to collisional effects, leading to increased spectral line mixing. In the present study, we have reviewed different line mixing models for modeling the absorption spectra for three gases of CO2, CO, and H2O and applied these models to simulate radiative spectra for pressures within approximately 5-100 bar. The simulated data were compared with the yet-published high-pressure spectral experimental data as well as experimental data published in the literature. It has been found that the empirical "pseudo-Lorentz" line shape model considering the line mixing effects shows the best performance for modeling high-pressure gas spectra for the tested conditions, which is easy to be implemented and relatively accurate, thus is recommended for high-pressure radiative heat transfer calculations in engineering applications. Based on the selected "pseudo-Lorentz" line mixing model, we have constructed a high-pressure absorption coefficients database for CO2, CO, and H2O for pressure ranging from 1 bar to 80 bar. The newly generated database considering the spectral line mixing effects was tested for radiative heat transfer calculations, and the results were compared with the ones without considering the line mixing effects. The significance of ignoring the line mixing effects on radiative heat transfer calculations under different pressures was evaluated with one-dimensional radiative heat transfer benchmark cases. The high-pressure absorption coefficients database is available from the corresponding author upon request. (c) 2023 Elsevier Ltd. All rights reserved.

In many important combustion applications, heat transfer is dominated by thermal radiation from combustion gases and soot. Thermal radiation from combustion gases is extremely complicated, and accurate and efficient predictions are only now becoming possible with the use of accurate global methods, such as full-spectrum k-distributions, and with state-of-the-art line-by-line accurate Monte Carlo methods. The coupling between turbulence and radiation can more than double the radiative loss from a flame, while making theoretical predictions vastly more complicated. This paper is an embellished version of the 2021 Max Jakob Award lecture: Radiative properties and computational methods will be briefly discussed, and several examples of turbulent reacting flows, an oxy-fuel furnace, and high-pressure fuel sprays in combustion engines will be presented. Thermal radiation can also be used as an optical diagnostic tool to determine temperature and concentration distributions, which will be briefly discussed.

In this study, we systematically compared the accuracy and computational cost of two popular solution methods for the radiative transfer equation (RTE): the spherical harmonics method (PN) and the discrete ordinates method (DOM). We first investigated convergence characteristics of different orders of PN and DOM in a series of 1D homogeneous configurations with varying optical thicknesses. Both solvers perform better for optically thicker cases. The accuracy of PN methods increases with its order, N, but the gain in accuracy reduces with the increase in N, i.e., improvement of P 7 over P 5 is less than that of P 3 over P 1 . This decreasing trend becomes more prominent as the optical thickness decreases. On the other hand, DOM's accuracy increases almost linearly with the increase in the number of ordinates (or polar angles in this study) in all cases. While comparing the directional profile of radiative intensity, both solvers per-form better when the radiative intensity is more isotropic. These solvers were then connected with a full spectrum k-distribution (FSK) spectral model and used to perform radiation-coupled simulations of a turbulent jet flame in an axi-symmetric cylindrical domain. Results obtained from P 1 to P 7 approxi-mations for PN, and 2 x 4, 4 x 4, 4 x 8, 8 x 8 finite angles for DOM are compared with that from an optically thin model, and a reference solution from line-by-line (LBL) photon Monte Carlo (PMC) method. The choice of radiation solver shows a noticeable impact on the temperature distribution of the flame. The PN solvers lead to slightly higher radiant fractions and the DOM solvers lead to slightly lower radi-ant fractions than the PMC benchmark solution. Finally, the computational costs of each of these solvers are also reported and an intermittent evaluation / time blending scheme to improve the computational efficiency of radiation solvers in radiation-coupled simulations are also demonstrated. (c) 2022 Elsevier Ltd. All rights reserved.

This chapter focuses on coupling radiation in participating media with conduction and convection, but with the added complexity of chemical reactions occurring within the system. First, the additional challenges in coupling posed by chemical reactions are highlighted. Next, two sections are dedicated to radiation in combustion systems: one on laminar combustion and the other on turbulent combustion. A significant portion of the latter section is dedicated to the discussion of turbulence-radiation interactions (TRI) and its modeling. Several stochastic models based on assumed or transported probability distribution function (PDF) are discussed, followed by large eddy simulation (LES) and direct numerical simulation (DNS) for the treatment of both emission and absorption TRI. Multiphase combustion systems with fuel droplets and coal are also discussed, along with oxy-fuel combustion. A broad overview of the state-of-the-art in modeling radiation in turbulent combustion systems is also provided. The final section of the chapter discusses solar thermochemical reactors that utilize solar energy for chemical decomposition of fuels.

Accurate measurement of three-dimensional temperature and species mole fraction fields for combustion systems provides comprehensively detailed information for optimizing combustion process and improving combustion efficiency. The state-of-art three-dimensional combustion diagnostic techniques for temperature and species mole fraction reconstructions, either laser-based or radiation imaging-based, require solving problems of huge matrices with iterative processes based on the multiple projection measurements of flame emission or absorption. These techniques are typically computationally intensive, with limited spatial resolution and can be hardly applied to retrieve three-dimensional temperature and multiple species mole fractions simultaneously. In the present study, we extended the machine learning methodology we previously proposed (Ren et al. 2021) for the reconstruction of two-dimensional temperature and mixture species mole fraction fields to three-dimensional for a group of non-axisymmetric flames with different equivalence ratios. The developed method demonstrates its excellent capability to retrieve three-dimensional temperature with CO2, H2O, and CO mole fractions simultaneously for these targeted flames. The accuracy of the machine learning reconstructions was found to be excellent, while computational effort was reduced by at least five orders of magnitude, as opposed to conventional gradient-based optimization methods. (C) 2021 Elsevier Ltd. All rights reserved.

Both the full-spectrum k-distribution (FSK) method and the spectral line weighted-sum-of-gray-gases (SLW) method are global spectral methods, with the former based on a spectral reordering concept, while the latter uses spectral binning. Both can provide excellent accuracy with outstanding numerical efficiency to model radiative heat transfer in combustion gases. In the present paper we aim to complete the development of both methods, and to tie them together, pointing out their commonalities and differences of their nonhomogeneous media extensions, employing either the correlated or scaled absorption coefficient assumption. Results from the complete set of plausible implementations are discussed and compared in detail for several radiative heat transfer calculations carried out in both 1D slabs and a real combustion field. The results show that emission is an important criterion to examine the accuracy of global methods applied to nonhomogeneous media, i.e., those that preserve emission generally give more accurate results than those that do not. It was also found that, while proper choice of the reference temperature required by all methods is important, the recommended methods appear to be only weakly dependent on that choice. Finally, equivalent SLW schemes are generally somewhat less accurate than their FSK counterparts due to their low-order spectral integration scheme; and this may be exacerbated if full-spectrum k-distributions are determined by mixing of values from individual species, as appears to be the preferred approach by SLW users to date. (c) 2021 Elsevier Ltd. All rights reserved.

The latest hyperspectral measurements of combustion flames by Rhoby et al. (2014) provided extensive spatially and spectrally resolved information of flame radiation, which has been explored to retrieve two-dimensional, multi-scalar values of these flames with the conventional gradient-based optimization method. The drawback of that method is that the inverse radiation problem was solved through iterations with computationally intensive radiative heat transfer calculations and high-resolution wide-spectrum modeling, making the retrieving process very time-consuming. In the present study, we propose a machine learning based efficient inverse radiation model to retrieve two-dimensional temperature, CO2, H2O, and CO mole fractions of laminar flames from hyperspectral measurements. The model is trained with synthetic numerical data and is tested against previously made OH-laser absorption measurements and chemical equilibrium calculations for ethylene laminar flames with different equivalence ratios. The training data generation process, machine learning model architecture, model training, and validations are discussed in detail. Results have shown that the proposed machine learning based inverse radiation model is both accurate and efficient. (C) 2021 Elsevier Ltd. All rights reserved.

Numerical modeling of radiative transfer in nongray reacting media is a challenging problem in computational science and engineering. The choice of radiation models is important for accurate and efficient high-fidelity combustion simulations. Different applications usually involve different degrees of complexity, so there is yet no consensus in the community. In this paper, the performance of different radiative transfer equation (RTE) solvers and spectral models for a turbulent piloted methane/air jet flame are studied. The flame is scaled from the Sandia Flame D with a Reynolds number of 22,400. Three classes of RTE solvers, namely the discrete ordinates method, spherical harmonics method, and Monte Carlo method, are examined. The spectral models include the Planck-mean model, the full-spectrum k-distribution (FSK) method, and the line-by-line (LBL) calculation. The performances of different radiation models in terms of accuracy and computational cost are benchmarked. The results have shown that both RTE solvers and spectral models are critical in the prediction of radiative heat source terms for this jet flame. The trade-offs between the accuracy, the computational cost, and the implementation difficulty are discussed in detail. The results can be used as a reference for radiation model selection in combustor simulations.

•An inverse radiation model is developed based on the machine learning approach.•Scalar profiles can be accurately retrieved for mixture of CO2, H2O and CO.•Comprehensive tests and experimental measurements were conducted.

The full-spectrum correlated-k-distribution (FSCK) look-up table previously developed by the authors Wang et al. (2018) provides an efficient means for accurate calculations of radiative properties of gas soot mixtures. Except for those of soot, radiative properties of particles are impossible to tabulate in FSCK look-up tables since particles of different compositions and sizes may have different local temperatures. In order to combine the radiative properties of particles with those of gas-soot mixtures from the FSCK look-up table, two schemes named gas FSK-particle FSK (FSK-FSK) and gas FSK-particle Gray (FSK-Gray) schemes, are proposed. The FSK-FSK scheme employs the correlation principle to obtain the radiative properties of gas-particle mixtures in FSCK form on-the-fly while the FSK-Gray scheme uses the Planck-mean absorption coefficient to represent particle spectral behavior. Several radiative heat transfer calculations across a 1D slab are carried out to test the accuracy of the two schemes. Furthermore, radiative heat transfer in a realistic coal flame and a scaled version of it are determined to validate the performance of the developed scheme. Results show that use of either scheme gives results of excellent accuracy with extremely low computational cost compared to benchmark line-by-line results. (C) 2019 Elsevier Ltd. All rights reserved.

Combustion diagnostics have reached high levels of refinement, but it remains difficult to simultaneously reconstruct the three-dimensional (3-D) temperature and species concentration fields. Tomographic reconstructions for high dimensional diagnostics are typically conducted with prevailing iterative methods. Due to the high data throughput, they are usually inefficient and computationally formidable. In this study, we present an inverse radiation model based on the machine learning approach to reconstruct 3-D temperature and mixture species concentrations fields from infrared emission spectral measurements for a laminar flame. Flame emission was detected with an imaging Fourier-transform spectrometer, obtaining a 2-D array of hyperspectral data. A machine learning model was trained with synthetic spectral emission for gas mixtures of CO2, H2O, and CO. The developed method demonstrates its excellent capability of solving nonlinear inverse problems, providing an efficient and global inverse radiation model, and is able to retrieve 3-D temperature and mixture species concentrations simultaneously.

In recent years, the importance of radiative heat transfer in combustion has been increasingly recognized. Detailed models have become available that accurately represent the complex spectral radiative properties of reacting gas mixtures and soot particles, and new methods have been developed to solve the radiative transfer equation (RTE). At the same time, the trends toward higher operating pressures and higher levels of exhaust-gas recirculation in compression-ignition engines, together with the demand for higher quantitative accuracy from in-cylinder CFD models, has led to renewed interest in radiative transfer in engines. Here an in-depth investigation of radiative heat transfer is performed for a heavy-duty diesel truck engine over a range of operating conditions. Results from 10 different combinations of turbulent combustion models, spectral radiation property models, and RTE solvers are compared to provide insight into the global influences of radiation on energy redistribution in the combustion chamber, heat losses, and engine-out pollutant emissions (NO and soot). Also, the relative importance of the individual contributions of molecular gas versus soot radiation, the spectral model, the RTE solver, and unresolved turbulent fluctuations in composition and temperature (turbulence-radiation interactions - TRI) are investigated. Local instantaneous temperatures change by as much as 100 K with consideration of radiation, but the global influences of radiation on heat losses and engine-out emissions are relatively small (in the 5-10% range). Molecular gas radiation dominates over soot radiation, consideration of spectral properties is essential for accurate predictions of reabsorption, a simple RTE solver (a first-order spherical harmonics - P1 - method) is sufficient for the conditions investigated, and TRI effects are small (less than 10%). While the global influences of radiation are relatively small, it is nevertheless desirable to explicitly account for radiation in in-cylinder CFD. To that end, a simplified CFD radiation model has been proposed, based on the findings reported here. (C) 2018 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

With today's computational capabilities, it has become possible to conduct line-by-line (LBL) accurate radiative heat transfer calculations in spectrally highly nongray combustion systems using the Monte Carlo method. In these calculations, wavenumbers carried by photon bundles must be determined in a statistically meaningful way. The wavenumbers for the emitting photons are found from a database, which tabulates wavenumber–random number relations for each species. In order to cover most conditions found in industrial practices, a database tabulating these relations for CO2, H2O, CO, CH4, C2H4, and soot is constructed to determine emission wavenumbers and absorption coefficients for mixtures at temperatures up to 3000 K and total pressures up to 80 bar. The accuracy of the database is tested by reconstructing absorption coefficient spectra from the tabulated database. One-dimensional test cases are used to validate the database against analytical LBL solutions. Sample calculations are also conducted for a luminous flame and a gas turbine combustion burner. The database is available from the author's website upon request.

In turbulent combustion, the turbulent fluctuations of temperature and species concentrations have strong effects on chemical and radiative heat sources. Turbulence-chemistry interactions (TCI) and turbulence-radiation interactions (TRI) create a set of "closure" problems when the governing partial differential equations are averaged. The presumed probability distribution function (presumed-PDF) method assumes a form of probability distribution function to close the chemical source term. The emphasis of this work is developing a high-fidelity radiation model that works in tandem with combustion models that use the presumed-PDF method to close the turbulent source terms. A finite volume based photon Monte Carlo method with a line-by-line spectral model is applied with the presumed-PDFs of mixture fraction, scalar dissipation rate and enthalpy defect to account for TRI effects. An efficient wavenumber selection scheme is proposed for the line-by-line photon Monte Carlo method considering TRI. The model is validated with one-dimensional exact line-by-line solutions for different TRI treatments and with a coupled combustion simulation for an open jet flame. (C) 2018 Published by Elsevier Ltd.

The full-spectrum correlated-k-distribution (FSCK) look-up table previously developed by the authors Wang et al. (2018) provides an efficient means for accurate calculations of radiative properties in nonhomogeneous media in conjunction with conventional radiative transfer equation (RTE) solvers. However, the current FSCK look-up table cannot be combined with statistical RTE solvers. A random-number relation was derived using the new implementation proposed in Wang et al. (2018) for the use of FSCK tables together with photon Monte Carlo (PMC) RTE solvers, and a corresponding random-number database including CO2, H2O, CO and soot has been constructed. Radiative heat transfer for two realistic scaled flames is studied to test the performance of the FSCK/PMC method using both FSCK look-up table and random-number database. Results show that the FSCK/PMC method can achieve almost the same accuracy but at cheaper computational cost and much lower memory requirement compared to the benchmark line-by-line solutions. (C) 2018 Published by Elsevier Ltd.

To improve the efficiency of full-spectrum k-distribution look-up tables a new scheme has been devised to store correlated k-values. Unlike the previous look-up table developed by the authors [9,10], from which full-spectrum k-distributions must be determined with multi-step interpolations, the new table stores correlated values, which can be directly retrieved from the new table avoiding several calculations and interpolations, thus saving considerable CPU time during radiative calculations. The same species as in the previous table, i.e., CO2, H2O, CO and soot, are included in the new table, for which the construction details are illustrated. Previous and new tables as well as their implementations are compared in this work. Calculations of radiative heat sources for two scaled flames are employed to validate the new table. Results show that the new table gives results of similar accuracy but at considerably cheaper computational cost than the previous table for both gas mixtures and gas-soot mixtures. (C) 2018 Published by Elsevier Ltd.

Computational studies of the effects of radiative transfer in combustion have been hindered for a long time by the lack of relatively accurate and computationally affordable radiation models. The Photon Monte Carlo (PMC) method with line-by-line (LBL) database is very accurate but can be quite expensive if a large number of photon bundles are to be traced. One possible alternative is to use high-order spherical harmonics (PN) methods for solutions of the Radiative Transfer Equation (RTE) combined with the full-spectrum k-distribution (FSK) method for the spectral model. In this study, high-order spherical harmonics (PN) methods up to the order of P7 together with an FSK look-up table have been applied to study nongray radiative transfer in the combustion simulation of an artificial turbulent jet flame, Sandia Flame D×4, which is scaled up from the well-studied Sandia Flame D. Comparing the results of the PMC+LBL and P1+FSK in a coupled simulation, it is found that the scalar fields predicted by high-order PN methods are only marginally better than that from the P1+FSK results and are still different from the PMC+LBL result. Following the coupled simulation, a snapshot study based on a frozen field of Sandia Flame D×4 is carried out to further investigate the potential and limitation of high-order PN method for this specific type of flame.

In this study, a previously developed inverse radiation model for a single gas species is extended to mixtures of the combustion gas species CO2, H2O and CO. Time-averaged transmissivities and their root mean -square (rms) values are successfully related to time-averaged temperatures, species concentrations and their rms values by considering interactions between turbulence and radiation (TRI). The sensitivity of the rms transmissivity spectra to all the parameters to be retrieved are examined and optimal wavenumber ranges for retrieving turbulent scalars of the gas mixtures are discussed. To validate the models, measured spectra are synthesized for different combinations of species concentrations, temperatures, turbulent intensities, pressure path length and turbulent length scales. Results show that mean and rms temperature and species concentrations and other turbulent scalars can be retrieved accurately from turbulent transmissivity measurements as long as the turbulent intensity is below 15% and the pressure path length for the gas mixture is less than 60 bar.cm. (C) 2016 Elsevier Ltd. All rights reserved.