Modelling of scattering and absorption coefficients for a polydispersion

An adequate treatment of the thermal radiation heat transfer mechanism is e ssential to a mathematical model of the combustion process or to design a c ombustion device. Predictive tools using flux models, such as the discrete transfer method, the discrete ordinates method and the spherical harmonics method, that solve the radiative heat transfer equation, require as input t he values of the absorption and scattering coefficients of the participatin g media. Such coefficients must be evaluated in an expedite fashion since c omputational fluid dynamics and radiative flux models are extremely time de manding by themselves. In this work, a curve fitting approach to the Mie th eory is used to evaluate the above-mentioned coefficients for intermediate and large particles, ensuring a compromise between accuracy and computation al economy. The same coefficients for small particles are calculated using power series to represent the Mie coefficients accurately and economically. Predictions with the present models were performed for soot, carbon partic les and fly ash and are presented herein. The results have proved that the models proposed in this work are computationally much faster than the prohi bitive Mie theory calculations: reductions in computing times as high as th ree-hundred fold. Additionally, the referred models allow for the achieveme nt of very accurate results: a relative error between approximated values a nd the corresponding Mie exact solution almost always below 5%. (C) 1999 El sevier Science Ltd. All rights reserved.