Narrow-Duct-Streaming Calculations Using Generalized Configuration Factors Within the Discrete Ordinates Method

In calculating neutral particle transport through elongated voids with the discrete ordinates method, the problem of ray effect may occur if standard angular quadrature sets are used. To mitigate this ray effect, the configuration-factor concept developed in the theory of thermal radiation for calculating the radiation exchange among surfaces is applied here. The common configuration-factor concept is extended in such a way that the angular dependence of the radiation emitted from the surfaces can be considered. The method is applied to regular and annular cylinders with r-z geometry and incorporated into a two-dimensional discrete ordinates transport code. Calculations on a narrow-duct-streaming problem show that the ray effect is strongly reduced by this method. The new method gives results equivalent to or even better than a standard discrete ordinates calculation using a biased angular quadrature set with 166 directions at computing times for one inner iteration that are about a factor of 2 less.