New optical exchange gap concept to calculate self-irradiance direct exchange areas in cylindrical industrial furnaces

A direct integration scheme based on the trapezoidal integration method associated with Romberg's acceleration algorithm is proposed to calculate numerically with the desired accuracy, direct exchange areas (DEAs) within an axisymmetric enclosure confining non-isothermal and inhomogeneous non-grey gaseous combustion products with soot. A three-dimensional integral needs to be evaluated, but axisymmetry and reciprocity of DEAs bring a notable processing time reduction. The integration process poses difficulties pertinent to singular DEAs of self-irradiance. Evaluating self-irradiance of gas volume zones is the concern of this investigation, in which we introduce a new concept that we call the optical exchange gap (OEG). It has been established that the OEG width associated with a volume zone, optimized with extreme care to meet Erkku's data, decreases with the radial position and radial optical thickness. A correlation, deduced to derive the OEG width for a given situation, has been shown to be more efficient, simple and accurate than a proper center-to-center distance technique. The effectiveness of the developed procedure was demonstrated by comparison of model predictions, using the zonal method in conjunction with the weighted-sum of grey gases (WSGG) model, with highly accurate reference data and by carrying out an error analysis.