Solution Method of Inverse Problems to estimate the Profile of Absorption Coefficient in Two-dimensional Radiative Heat Transfer Systems

A method to solve inverse radiative property value problems is developed to obtain two-dimensional distribution of absorption coefficient in combustion chambers or furnaces from the profiles of the temperature and the radiative flux of the surrounding walls and of the gas temperature. In the analysis, initial guess of the absorption coefficients of each gas element are given at first, and by solving the forward problem, the wall radiative flux distribution corresponding to the given wall and gas temperature distributions is obtained. The initial guess of the absorption coefficients is corrected so as that the difference between the calculated and the given values of the wall radiative flux becomes small by using the successive linearlization method. The exchange factors required to solve the forward problem are obtained by the Monte Carlo method. In the present study, an algorithm is proposed to push the time-consuming Monte Calro process out of the convergence loop in which the values of the absorption coefficients are estimated and the Monte Carlo procedure is carried out only one time before the convergence process begins.