ES-DRESOR Method For Radiative Heat Transfer In One-dimensional Isotropic Scattering System

Compared with other modes of heat transfer, radiative heat transfer contains some more complex process as the emission, absorption, scattering and reflection of the radiative energy. The control equation of the radiative heat transfer is an integral differential equation. How to solve the radiative heat transfer equation (RTE) and calculate the radiative intensity is the key in the analysis of radiative heat transfer problems and practical applications. So far, many methods have been developed to solve the RTE, for example, the Discrete Ordinate method, the Monte Carlo method, the Heat Flux method, the Zone method, the Spherical Harmonics method and others. These methods do have advantages and drawbacks, and are used in different radiative heat transfer problems according to their own characteristics. In some radiative problems, the information of intensity in direction is particularly important. Based on the Monte Carlo method, the DRESOR method (Distributions of Ratio of Energy Scattered by the medium Or Reflected by the boundary surface) can get the radiative intensity with high directional resolution and has been applied to a series of radiative heat transfer problems, as the visual monitoring of the combustion temperature field in the industrial furnaces, the collimated pulse incidence, the an-isotropic scattering media and the gradient index medium and so on. The calculating of the DRESOR values is the kernel and demands the most calculating time of the program. As it is based on the MCM, the time-consuming is unavoidable and the statistical error exits, which limit the development of this method.This paper aims to improve the computational efficiency and accuracy of the DRESOR method. On the basis of the basic DRESOR method, Equation solving DRESOR method, ES-DRESOR method, is devoloped in this paper. In this method, the DRESOR values which is the kernel in the DRESOR method can be got by solving a set of linear equations instead of by the traditional ray-tracing using MCM, so as to have a great enhance on the calculation efficiency and accuracy. This study has an important significance for improving ability of DRESOR method solving radiation problems and expand its application scope. Specifically, the main work is as follows:The principles of ES-DRESOR method are given. The computing principles contain the transparent boundary surfaces and the diffuse boundary surfaces two conditions. For the former, assuming an arbitrary element emission of the system as a blackbody emission while other elements with no emission, which simplifies the intensity description given by the DRESOR. Then equation can be set up by two different calculating description of incident radiation (the standard calculating equation and the equation under the DRESOR method) equals to each other. For the latter, the calculation description of the incident intensity under the DRESOR method needs to be modified, with the contribution of the boundary surface added. The principle of establishing equations for the boundary surface elements is that the total energy reflected by boundary surface equals to the total energy scattered and/or reflected to this boundary surface. As for the spatial elements, the difference with the former one is that the contribution of boundary surface needs to be added.Numerical verification is done on this method in one-dimensional absorbing, emitting, and isotropicall scattering system. First, the reliability of this method is verified including compared with the exact solution in the literature, compared with the widely used DOM, and substituted the ES-DRESOR results into the RTE to test. Then compared the DRESOR values with the MCM, the results show a good agreement of the two method. The shaking phenomena of DRESOR values caused by the statistical error in the MCM is eliminated in the ES-DRESOR method. Compared the relative error of the radiative intensity calculated by the ES and MCM, the accuracy of the former is one order magnitude higher. What is more important is that the efficiency of the ES is two order magnitudes higher than MCM under the same discrete grids.