Transport Equations in Axisymmetric Toroidal Coordinates

This paper presents a derivation of the conservation-law form of the single energy group transport equation in an axisymmetric toroidal coordinate system formed by rotating a nest of smooth, simply closed, plane curves of arbitrary parametric description about an axis that does not intersect the nest. This general equation can be used for generating equations specific to particular cross-section geometries or as the basis of a finite difference equation for the general case. The effect of both the toroidal and poloidal curvatures of the system are investigated, and criteria for the validity of cylindrical and planar approximations are established. The diffusion equation for this geometry is derived, and it is shown to be formally homologous to the “r-θ” cylindrical diffusion equation if the coordinate system is orthogonal and if the azimuthal coordinate, , can be ignored.