Improvement of Accuracy of Radiative Heat Transfer Differential Approximation Method for Multi Dimensional Systems by Means of Auto-Adaptable Boundary Conditions

Abstract

Differential approximation is derived from radiation transfer equation by averaging over the solid angle. It is one of the more effective methods for engineering calculations of radiative heat transfer in complex three-dimensional thermal power systems with selective and scattering media. The new method for improvement of accuracy of the differential approximation based on using of auto-adaptable boundary conditions is introduced in the paper. The efficiency of the named method is proved for the test 2D-systems. Self-consistent auto-adaptable boundary conditions taking into consideration the nonorthogonal component of the incident to the boundary radiation flux are formulated. It is demonstrated that taking in-to consideration of the non-orthogonal incident flux in multidimensional systems, such as furnaces, boilers, combustion chambers improves the accuracy of the radiant flux simulations and to more extend in the zones adjacent to the edges of the chamber. Test simulations utilizing the differential approximation method with traditional boundary conditions, new self-consistent boundary conditions and “precise” discrete ordinates method were performed. The mean square errors of the resulting radiative fluxes calculated along the boundary of rectangular and triangular test areas were decreased 1.5–2 times by using auto-adaptable boundary conditions. Radiation flux gaps in the corner points of non-symmetric systems are revealed by using auto-adaptable boundary conditions which can not be obtained by using the conventional boundary conditions.