Application of the model of a porous solid to thermal-hydraulic calculations of reactors and heat exchangers

A system of equations is derived for the averaged motion of liquid in the heterogeneously anisotropic rod zone of a nuclear reactor (by analogy with a porous solid), due allowance being made for the three-dimensional forces of nonlinear friction, inertial forces, and the forces of viscous interaction between neighboring cells. For calculating the averaged temperature field in the heterogeneously anisotropic zone of the reactor an energy equation is derived in which the effective thermal diffusivity is regarded as a scalar quantity. In order to illustrate the applicability of this approach to the macroscopic calculation of the velocity and temperature fields in the rod zones, the results of a numerical integration of the system of equation are presented for the case in which nonuniformities of the velocity distribution exist at the entrance and outlet of the zone or fuel-element cassette. An approximate equation is also obtained for estimating the relaxation length of the hydraulic perturbation at the entrance into the zone.