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Abstract: Radiative intensity with high directional resolution at boundaries can provide abundant information about the medium properties and temperature, which is very useful for inverse analysis. Monte Carlo method is a widely used method due to its flexibility for complex radiative transfer problems. In this work Distributions of Ratios of Energy Scattered Or Reflected (DRESOR) method, which is based on Monte Carlo method, is developed for radiative intensity calculation in a three-dimensional rectangular enclosure which contains an emitting, absorbing, and isotropically scattering medium. The method is validated by comparing calculated radiative intensities with those of the reverse Monte Carlo method. Then, radiative intensity for different radiative problems is examined by DRESOR method. Comparing with reverse Monte Carlo method, DRESOR method shows much better time-efficiency. DRESOR method also shows an obvious advantage if radiative intensity with high directional resolution at many different boundary positions is required. To calculate radiative intensity with high directional resolution in a system where radiative source is confined to a small volume, both standard and reverse Monte Carlo method become inefficient, the results show that DRESOR method is still an efficient tool. The results given in this study demonstrate that DRESOR method is very advantageous in situations when high directional resolution is required. [Copyright &y& Elsevier]

The distribution of ratios of energy scattered by the medium or reflected by the boundaiy surface (DRESOR) method can provide radiative intensity with high directional resolution, but also suffers the common drawbacks of the Monte Carlo method (MCM), i.e., it is time-consuming and produces unavoidable statistical errors. In order to overcome the draw-backs of the MCM, the so-called equation-solving DRESOR (ES-DRESOR) method, an equation-solving method to calculate the DRESOR values differently from the MCM used before, was proposed previously. In this method, a unit blackbody emission is supposed within a small zone around a specified point, while there is no emission elsewhere in a plane-parallel, emitting, absorbing, and isotropically scattering medium with transparent boundaries. The set of equations for the DRESOR values based on two expressions for the incident radiation was set up and solved successfully. In this paper, the ES-DRESOR method is extended to a one-dimensional system with diffusely reflecting boundaries. The principle and formulas are given. Several examples with different parameters are taken to examine the peiformance of the proposed method. The results showed that all the DRESOR values obtained using the ES-DRESOR method agree well with those got using MCM. The average relative error for the intensity obtained by the ES-DRESOR method is 9.446 x 10-6, lower by over I order of magnitude than the 2.638 x 10-4 obtained by the MCM under the same conditions. More importantly, the CPU time for computing the DRESOR values, which ranges from several hundred seconds to several thousand seconds using the MCM, is reduced to 0.167 s using the ES-DRESOR method. The computation time is shortened by about 3 orders of magnitude. The overall performance of the ES-DRESOR method is excellent. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the ES-DRESOR method, an equation-solving method to calculate the DRESOR values differently from the MCM used before, is proposed. In this method, a unit blackbody emission is supposed within a cell, while there is no emission from the remaining part of the system. This leads to the equations for the DRESOR values based on the incident radiation, and all the DRESOR values can be solved directly from the equations without the rays tracing used in the MCM. Numerical results show an excellent agreement of all DRESOR values found by ES-DRESOR method and MCM for 100 cells in 1D case with emitting, absorbing, and isotropic scattering medium and transparent boundaries. The average relative error for the intensity obtained by the ES-DRESOR method is only 3.372×10−5, lower by one order of magnitude than 4.022×10−4 obtained by the MCM under the same conditions. The CPU time for computing the DRESOR values using the MCM varies from a few hundred seconds to several thousand seconds. In contrast, it is less than 1s using the ES-DRESOR method, showing an obvious improvement in the computational efficiency. [Copyright &y& Elsevier]

Abstract: Within a graded index medium, the radiative energy rays propagate in curved paths and with a varied speed of propagation, making the solution of the transient radiative transfer complex and difficult. The DRESOR method is extended to calculate the time-resolved reflectance and transmittance from a one-dimensional, non-emitting, absorbing, anisotropically scattering medium with a linear increasing graded index exposed to a collimated truncated Gaussian pulse. Comparisons are made with the results obtained by DOM and DFEM, which indicate that the DRESOR method is accurate and effective. Compared with uniform graded index, the increase in the gradient of the refractive index significantly reduces the peak value of the reflectance and transmittance, delays the occurrence time of the transmittance and increases the duration time. The double-peak phenomenon of the time-resolved transmittance is caused by the fact that the maximum values of intensity in different directions appear at different times, which occur much later as the polar angle increases. The double-peak phenomenon of the time-resolved transmittance becomes more obvious as the increase in the graded index, the scattering albedo and the optical thickness; and the decrease in the anisotropically scattering phase function coefficient. [Copyright &y& Elsevier]

Abstract: Radiation heat transfer in a two-dimensional rectangular enclosure containing CO2/H2O/N2 mixtures was calculated using the line-by-line and the statistical narrow-band correlated-k models. The radiative transfer equation was solved using the discrete ordinates method along with the T7 quadrature scheme. The updated HITEMP spectroscopic database, HITEMP2010, was employed in line-by-line calculations to obtain the most accurate line-by-line results. The statistical narrow-band model parameters of Sourfiani and Taine [IJHMT 40, 987–991, 1997] were used to obtain the statistical narrow-band correlated-k model results. Calculations were carried out for five test cases involving isothermal/non-isothermal and homogeneous/inhomogeneous CO2/N2, H2O/N2, and CO2/H2O/N2 mixtures. The present line-by-line results can serve as benchmark results for the purpose of validating other approximate models in gas radiation heat transfer calculations in two-dimensional enclosures. Results of the statistical narrow-band correlated-k model are in good agreement with those of the line-by-line method in all the test cases. The statistical narrow-band correlated-k model was found sufficiently accurate to generate benchmark solutions in multi-dimensional gas radiation transfer problems where line-by-line calculations are infeasible due to excessively long computing time. [Copyright &y& Elsevier]

Abstract: Thermal radiation transfer in one-dimensional enclosure between two parallel plates filled with real gases, namely CO2, H2O, or their mixtures, was calculated using the line-by-line approach and the statistical narrow-band model. Line-by-line calculations were carried out using the HITEMP1995, HITRAN2004, HITRAN2008, HITEMP2010, and updated CDSD-1000 databases. This study demonstrates the importance of spectral database to the accuracy of line-by-line calculations through a systematic comparison of line-by-line results using different databases. Calculations of the statistical narrow-band model were conducted using the EM2C narrow-band database. The strong dependence of line-by-line results on the spectral database was demonstrated through several gas radiation transfer problems in planar-plate enclosure containing real gases of both isothermal or non-isothermal and uniform or non-uniform concentrations at 1atm. Fairly significant differences were found between the line-by-line results using the HITEMP2010 database and those using older databases. Very good agreement in both the wall heat flux and the radiative source term was observed between the line-by-line results using the HITEMP2010 database and the results of the statistical narrow-band model in all the cases tested, confirming the EM2C narrow-band parameters for both H2O and CO2 are accurate. For cases involving CO2 the line-by-line results using the HITEMP2010 database are in excellent agreement with those using the updated CDSD-1000 databases. The line-by-line results based on the HITEMP2010 database should be used as benchmark solutions to evaluate the accuracy of other approximate models. [Copyright &y& Elsevier]

A SNBCK/DRESOR combined method is presented in order to predict the radiative heat transfer of gas and soot mixtures at different temperature configurations. The mixtures of the combustion gases (H 2 O, CO 2 , CO) and the different soot loadings were analyzed to explore the influence of the soot on the non-gray radiation. The radiative source and the intensities with high directional resolution calculated by the DRESOR method were investigated at different temperature configurations. The accuracy of the SNBCK/DRESOR model was also analyzed and compared to the LBL/DOM approach, where the relative errors were less than 4%. The results indicate that the SNBCK/DRESOR method has a better efficiency than the SNBCK/DOM method. [ABSTRACT FROM AUTHOR]

Abstract: This paper extends the DRESOR (Distribution of Ratios of Energy Scattered by the medium Or Reflected by the boundary surface) method to radiative transfer in a variable refractive index medium. In this method, the intensity is obtained from the source term along the curved integration paths determined only by the variable refractive index, and the DRESOR values are calculated by the Monte Carlo method in which the propagation of the energy bundles are affected by Snell''s law. With given temperatures on the black boundaries of a one-dimensional medium, the temperature distribution inside the medium with a variable scattering property is calculated under the condition of radiative equilibrium. It is shown that the DRESOR method has a good accuracy in the cases studied. For an isotropic-scattering medium with the same optical thickness, the scattering albedo has no effect on the temperature distribution, which can be obtained from the general equations and can be seen as an extension of what exists for a constant refractive index; however, the different refractive index causes obvious changes in the temperatures inside the medium. The effect of anisotropic scattering on the temperature distribution cannot be ignored, although it is still weaker than the effect caused by variation in the refractive index. [Copyright &y& Elsevier]

• The calculation error is not markedly affected by the change in scattering albedo. • The minimum error increases with an increase in surface emissivity when MOTE<0.1. • Minimum NEBs are given for a desirable error level of 1.0%. • The maximum MOTE for different surface emissivity increases linearly with an increase in NEB. A method for directly and quantitatively evaluating the computational accuracy of the Monte Carlo method (MCM) simulation of radiative transfer has been proposed in previous research. In this note, the effects of surface emissivity and scattering albedo on the computational accuracy of MCM are evaluated in this study. The results indicate that scattering albedo exerts no significant effect on the accuracy of MCM. When the mean optical thickness per element (MOTE) is less than 0.1, an increase in surface emissivity from 0.1 to 0.9 leads to an increase in minimum calculation error by about 3 to 4 times, which is not closely associated with the change in MOTE. If the desired accuracy is set at 1.0% with an acceptable cost, as surface emissivity increases from 0.001 to 0.9999, the minimum number of energy bundles (NEB) required for surface elements increases from 6 to 6000, and the corresponding maximum MOTE increases from 0.0002 to 0.26. For space elements with an increase in surface emissivity from 0.001 to 0.9999, the minimum NEB for the desired accuracy of 1.0% increases from 2 to 1980. For the desired accuracy, the maximum MOTE for different surface emissivity increases linearly with an increase in NEB. [ABSTRACT FROM AUTHOR]