A Hybrid Solution Methodology for Efficient Solving of Radiative Heat Transfer in Non Gray Medium Using WSSG Model

Abstract

The weighted sum of gray gases (WSGG) method has been used extensively for radiation modeling of non gray medium gases. The radiative transfer equation (RTE) for each gray gas can be solved using the Discrete Ordinate (DO) model, which is sufficiently accurate over wide range of optical thickness, but it is computationally expensive. The P1 approximation is an efficient alternative to solve the RTE, but applicable to optically thick medium only. In the present work, a hybrid solution methodology to solve RTE in a non gray medium using WSGG model is proposed. Results for the case of four gray gases are presented. The philosophy is to achieve the optimum performance using combination of the P1 and DO model with respect to the optical thickness of the gray gases being solved with minimal loss in accuracy. In this approach, the transparent and/or optically thin gases are solved using the DO model while the P1 approximation is used for the optically thick gases. This combination reduces the total number of radiation intensity equation to be solved very significantly. A study of accuracy and computational cost for the hybrid solution methodology has been done for a variety of test cases in order of increasing complexity. It has been found that the hybrid solution methodology, in which RTE for two gray gases are solved by DO model and the remaining two gray gases by P1 approximation, provided similar accuracy with significant speedup compared to the conventional approach in which RTE for all gray gases are solved with DO model. Another variant of the hybrid approach, in which DO model is used only for the transparent gas, is also considered and found to be sufficiently accurate for most of the cases.