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Radiative Transfer Modeling of a Large Pool Fire by Discrete Ordinates, Discrete Transfer, Ray Tracing, Monte Carlo and Moment Methods

Five computational methods for solution of the radiative transfer equation in an absorbing-emitting and non-scattering gray medium were compared on a 2 m JP-8 pool fire. The temperature and absorption coefficient fields were taken from a synthetic fire due to the lack of a complete set of experimental data for fires of this size. These quantities were generated by a code that has been shown to agree well with the limited quantity of relevant data in the literature. Reference solutions to the governing equation were determined using the Monte Carlo method and a ray tracing scheme with high angular resolution. Solutions using the discrete transfer method, the discrete ordinate method (DOM) with both S(sub 4) and LC(sub 11) quadratures, and moment model using the M(sub 1) closure were compared to the reference solutions in both isotropic and anisotropic regions of the computational domain. DOM LC(sub 11) is shown to be the more accurate than the commonly used S(sub 4) quadrature technique, especially in anisotropic regions of the fire domain. This represents the first study where the M(sub 1) method was applied to a combustion problem occurring in a complex three-dimensional geometry. The M(sub 1) results agree well with other solution techniques, which is encouraging for future applications to similar problems since it is computationally the least expensive solution technique. Moreover, M(sub 1) results are comparable to DOM S(sub 4).

Jensen, K. A.

Discrete-ordinates finite-element method for atmospheric radiative transfer and remote sensing

The principal features of the discrete-ordinates finite-element method are reviewed, and the applicability of general-purpose discrete-ordinates codes to atmospheric radiative transfer and remote sensing problems is demonstrated. In particular, numerical results for typical problems arising in meteorology, climatology, and remote sensing are shown to be in good agreement with results from other methods and measurements. A sample two-dimensional calculation demonstrates that specific capabilities available in the discrete-ordinates code TWOTRAN can produce new results that are valuable in the characterization of atmospheric effects on remote sensing (e.g., the adjacency effect). The intrinsic limitations of the method are also considered, and it is concluded that the strengths of the discrete-ordinates finite-element method outweigh its weaknesses.

Gerstl, S. A. W.

Low-energy electron transport with the method of discrete ordinates

The one-dimensional discrete ordinates code ANISN was adapted to transport low energy (a few MeV) electrons. Calculated results obtained with ANISN were compared with experimental data for transmitted electron energy and angular distribution data for electrons normally incident on aluminum slabs of various thicknesses. The calculated and experimental results are in good agreement for a thin slab (0.2 of the electron range), but not for the thicker slabs (0.6 of the electron range). Calculated results obtained with ANISN were also compared with results obtained using Monte Carlo methods.

Bartine, D. E.

Spectral Spherical Harmonics Discrete Ordinate Method

A new method for modeling the radiative transfer in inhomogeneous three-dimensional media illuminated by a Gaussian beam is described. This approach, called the Spectral Spherical Harmonics Discrete Ordinate Method (SSHDOM), uses the Fourier expansion method to transform the three-dimensional radiative transfer into an one-dimensional equation in the spectral domain, and the Spherical Harmonics Discrete Ordinate Method (SHDOM) for its solution. Specifically, (i) the source function is represented in the spectral domain through a spherical harmonic expansion, (ii) the spectral one-dimensional radiative transfer equation is integrated along discrete ordinates through a spatial grid, and (iii) the solution method is based on the Picard iteration. Both SSHDOM and SHDOM algorithms are implemented in a common computer code.

Gaussian beam

Nongray radiative gas analyses using the S-N discrete ordinates method

The S-N discrete ordinates method is applied to analyze radiative heat transfer in nongray gases. Spectral correlation between the terms in the equation of transfer is considered for black or nearly nonreflecting walls. Formulations to apply the S-N method using a narrow-band or the exponential wide-band model are presented. The net radiative wall heat fluxes and the radiative source distributions are obtained for uniform, parabolic, and boundary layer-type temperature profiles, as well as for a parabolic concentration profile. The narrow- and wide-band nongray solutions are compared with gray-band approximations using the same band models. The computational speed of the gray-band approximation is obtained at the expense of accuracy in the internal fluxes and radiative source distributions. The wall radiative flux predictions by the gray-band approximation are satisfactory.

Kim, T. K.

Discrete ordinates solutions of nongray radiative transfer with diffusely reflecting walls

Nongray gas radiation in a plane parallel slab bounded by gray, diffusely reflecting walls is studied using the discrete ordinates method. The spectral equation of transfer is averaged over a narrow wavenumber interval preserving the spectral correlation effect. The governing equations are derived by considering the history of multiple reflections between two reflecting wails. A closure approximation is applied so that only a finite number of reflections have to be explicitly included. The closure solutions express the physics of the problem to a very high degree and show relatively little error. Numerical solutions are obtained by applying a statistical narrow-band model for gas properties and a discrete ordinates code. The net radiative wail heat fluxes and the radiative source distributions are obtained for different temperature profiles. A zeroth-degree formulation, where no wall reflection is handled explicitly, is sufficient to predict the radiative transfer accurately for most cases considered, when compared with increasingly accurate solutions based on explicitly tracing a larger number of wail reflections without any closure approximation applied.

Menart, J. A.

Radiation heat transfer calculations using a control-angle, control-volume-based discrete ordinates method

A control-angle, control-volume-based discrete ordinates method (CA - CV DOM) is presented in this paper. A detailed formulation of the discretization equation is presented in two-dimensional Cartesian coordinate system. The procedure can be extended to curvilinear coordinate system with minor modifications. The step and modified-exponential schemes are used in this study. Present results converged to the grid independent solutions quickly and compared favorably against other published results for six test problems.

Chai, John C.

Comparisons of cylindrical and rectangular media radiative transfer solutions using the S-N discrete ordinates method

The application of the S-N discrete ordinates method is compared for r-z and x-y problems with similar boundary conditions. The complexities of the r-z solution come from the additional angular derivative, which makes this into a virtual three-dimensional problem. Effects of spatial differencing schemes, phase functions, and grid spacing are considered and compared for these x-y and r-z problems.

Jendoubi, Slah

Modifications Of Discrete Ordinate Method For Computations With High Scattering Anisotropy: Comparative Analysis

A numerical accuracy analysis of the radiative transfer equation (RTE) solution based on separation of the diffuse light field into anisotropic and smooth parts is presented. The analysis uses three different algorithms based on the discrete ordinate method (DOM). Two methods, DOMAS and DOM2+, that do not use the truncation of the phase function, are compared against the TMS-method. DOMAS and DOM2+ use the Small-Angle Modification of RTE and the single scattering term, respectively, as an anisotropic part. The TMS method uses Delta-M method for truncation of the phase function along with the single scattering correction. For reference, a standard discrete ordinate method, DOM, is also included in analysis. The obtained results for cases with high scattering anisotropy show that at low number of streams (16, 32) only DOMAS provides an accurate solution in the aureole area. Outside of the aureole, the convergence and accuracy of DOMAS, and TMS is found to be approximately similar: DOMAS was found more accurate in cases with coarse aerosol and liquid water cloud models, except low optical depth, while the TMS showed better results in case of ice cloud.

Korkin, Sergey V.

Discrete ordinate theory of radiative transfer. 2: Scattering from maritime haze

Discrete ordinate theory was used to calculate the reflected and transmitted radiance of photons which have interacted with plane parallel maritime haze layers. The results are presented for three solar zenith angles, three values of the surface albedo, and a range of optical thicknesses from very thin to very thick. The diffuse flux at the lower boundary and the cloud albedo were tabulated. The forward peak and other features in the single scattered phase function caused the radiance in many cases to be very different from that for Rayleigh scattering. The variation of the radiance with both the zenith or nadir angle and the azimuthal angle is more marked, and the relative limb darkening under very thick layers is greater, for haze than for Rayleigh scattering. The downward diffuse flux at the lower boundary for A = O is always greater and the cloud albedo is always less for haze than for Rayleigh layers.

Kattawar, G. W.