Michael F. Modest

The Weighted-Sum-of-Gray-Gases Model for Arbitrary Solution Methods in Radiative Transfer

The weighted-sum-of-gray-gases approach for radiative transfer in nongray participating media, first developed by Hottel in the context of the zonal method, has been shown to be applicable to the general radiative equation of transfer. Within the limits of the weighted-sum-of-gray-gases model (nonscattering media within a black-walled enclosure), any nongray radiation problem can be solved by any desired solution method after replacing the medium by an equivalent small number of gray media with constant absorption coefficients. Some examples are presented for isothermal media and media at radiative equilibrium, using the exact integral equations as well as the popular P-1 approximation for the equivalent gray media solutions. The results demonstrate the equivalency of the method with the quadrature of spectral results, as well as the tremendous computer times savings (by a minimum of 95 percent) that are achieved.

The Full-Spectrum Correlated-k Distribution for Thermal Radiation From Molecular Gas-Particulate Mixtures

A new Full-Spectrum Correlated-κ Distribution has been developed, which provides an efficient means for accurate radiative transfer calculations in absorbing/emitting molecular gases. The Full-Spectrum Correlated-κ Distribution can be used together with any desired solution method to solve the radiative transfer equation for a small number of spectral absorption coefficients, followed by numerical quadrature. It is shown that the Weighted-Sum-of-Gray-Gases model is effectively only a crude implementation of the Full-Spectrum Correlated-κ Distribution approach. Within the limits of the Full-Spectrum Correlated-κ Distribution model (i.e., an absorption coefficient obeying the so-called scaling approximation), the method is exact. This is demonstrated by comparison with line-by-line calculations for a one-dimensional CO 2 -N 2 gas mixture as well as a two-dimensional CO 2 -H 2 O-N 2 gas mixture with varying temperature and mole fraction fields

Narrow-band and full-spectrum k-distributions for radiative heat transfer—correlated-k vs. scaling approximation

The correlated-k and scaled-k distribution methods for radiative heat transfer in molecular gases are developed based on precise mathematical principles, for both narrow band and full spectrum models. Their differences and commonalities are high-lighted and discussed. Applications to narrow spectral bands of nonhomogeneous gases show both methods to be about equally accurate. For full-spectrum calculations, on the other hand, the scaled-k distribution consistently outperforms the correlated-k model.

Backward Monte Carlo Simulations in Radiative Heat Transfer

Standard Monte Carlo methods trace photon bundles in a forward direction, and may become extremely inefficient when radiation onto a small spot and/or onto a small direction cone is desired. Backward tracing of photon bundles is known to alleviate this problem if the source of radiation is large, but may also fail if the radiation source is collimated and/or very small. Various implementations of the backward Monte Carlo method are discussed, allowing efficient Monte Carlo simulations for problems with arbitrary radiation sources, including small collimated beams, point sources, etc., in media of arbitrary optical thickness

Heat Conduction in a Moving Semi-infinite Solid Subjected to Pulsed Laser Irradiation

Heat conduction in a moving semi-infinite body subject to laser irradiation is considered. The body of knowledge of exact analytical solutions for Gaussian laser irradiation is expanded to include pulsed lasers, and laser beams that penetrate into the body with exponential decay. For applications with complicated geometries (laser melting and evaporation), a simple integral method, based on one-dimensional diffusion is presented and its range of validity determined.

Application of composition PDF methods in the investigation of turbulence–radiation interactions

Abstract The composition probability density function (PDF) method is used to study radiating reactive flows. The method is able to treat turbulence–radiation interactions (TRI) in a rigorous way: many unclosed terms due to TRI in the traditional Reynolds-averaging process can be calculated exactly and all others can be accurately modeled by using the optically thin eddy approximation. The application of the method is demonstrated by considering a simplified methane/air diffusion flame, which shows enhancement of the radiative fluxes as a result of TRI. The importance of considering different TRI terms is investigated, indicating that the absorption coefficient–Plank function correlation is the most important.

Importance of Turbulence-Radiation Interactions in Turbulent Diffusion Jet Flames

Traditional modeling of radiative transfer in reacting flows has ignored turbulence-radiation interactions (TRI). Radiative fluxes, flux divergences and radiative properties have been based on mean temperature and concentration fields. However, both experimental and theoretical work have suggested that mean radiative quantities may differ significantly from those predictions based on the mean parameters because of their strongly nonlinear dependence on the temperature and concentration fields. The composition PDF method is able to consider many nonlinear interactions rigorously, and the method is used here to study turbulence-radiation interactions. This paper tries to answer two basic questions: (1) whether turbulence-radiation interactions are important in turbulent flames or not; and (2) if they are important, then what correlations need to be considered in the simulation to capture them. After conducting many flame simulations, it was observed that, on average, TRI effects account for about 1/3 of the total drop in flame peak temperature caused by radiative heat losses. In addition, this study shows that consideration of the temperature self correlation alone is not sufficient to capture TRI, but that the complete absorption coefficient-Planck function correlation must be considered.

A probability density function approach to modeling turbulence-radiation interactions in nonluminous flames

Abstract The interactions between turbulence and radiation, although acknowledged and qualitatively understood over the last several decades, are extremely difficult to model. Traditional Eulerian turbulence models are incapable of addressing the closure problem for any realistic reactive flow situation, on account of the large number of unknown turbulent moments. A novel approach, based on the velocity-composition joint probability density function (PDF) method, has been used to attain closure. The ability of this method to accurately determine any one-point scalar correlation makes it a suitable candidate for modeling turbulence–radiation interactions (TRI) . Results presented for a bluff-body-stabilized methane–air diffusion flame demonstrate the importance of turbulence–radiation interactions in flame calculations.

A multi-scale full-spectrum correlated-k distribution for radiative heat transfer in inhomogeneous gas mixtures

A multi-scale full-spectrum correlated-k distribution model has been developed and tested for radiative transfer calculations in absorbing/emitting molecular gases. The gas or gas mixture is broken up into different groups by separating different absorbing species and, for each specie, by collecting them into spectral groups according to the lower level energy of their spectral lines. Like all k-distribution methods as well as the full-spectrum correlated-k (FSCK) model, the new model may be used with any arbitrary radiative transfer equation solver. Results for one- and two-dimensional inhomogeneous gas mixtures with varying temperature and mole fraction fields are presented and compared with line-by-line benchmarks and the FSCK model, showing very good accuracy in situations with severe temperature gradients and/or sharp mole fraction ratio changes.

Medium resolution transmission measurements of CO2 at high temperature

Abstract Medium resolution transmissivities of CO2 were measured at temperatures between 300 and 1550 K for the 4.3, 2.7 and 2.0 μm bands. Measurements were made with a new drop tube design, which guarantees a truly isothermal high-temperature gas column. Data were collected with an FTIR-spectrometer, allowing for much better spectral resolution than most previous high-temperature measurements. The measured data were compared with two line-by-line and two narrow band databases. The data show some discrepancies with high-resolution databases at higher temperatures, indicating missing and/or incorrectly extrapolated spectral lines.