Open AccessTransport equations in axisymmetric toroidal coordinates
Author(s) -
S.L. Gralnick
Publication year - 1975
Language(s) - English
Resource type - Reports
DOI - 10.2172/4076521
Subject(s) - rotational symmetry , cylindrical coordinate system , coordinate system , orthogonal coordinates , toroid , physics , basis (linear algebra) , parametric equation , planar , spherical coordinate system , mathematical analysis , plane (geometry) , elliptic coordinate system , geometry , diffusion equation , mathematics , convection–diffusion equation , classical mechanics , plasma , quantum mechanics , computer graphics (images) , economy , economics , service (business) , computer science
A derivation is presented 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 which does not intersect the nest. This general equation may 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-theta'' cylindrical diffusion equation if the coordinate system is orthogonal and if the azimuthal coordinate, phi, is ignorable. (auth