An analytic benchmark solution to the linear, time-dependent isothermal laminar flow fission-product plateout problem

Abstract

The time-dependent convective-diffusion equation with radioactive decay is solved analytically in axisymmetric cylindrical geometry for laminar and slug velocity profiles under isothermal conditions. Concentration-dependent diffusion is neglected. The laminar flow solution is derived using the method of separation of variables and Frobenius' technique for constructing a series expansion about a regular singular point. These solutions, which describe the transport of fission products in a flowing stream, are then used to determine the pointwise and integrated concentrations of radioactive material deposited on a conduit wall using a standard mass-transfer model. Extensive parametric investigations have been conducted by varying the wall mass-transfer coefficient, diffusion coefficient, flow velocity, pipe radius and species half-life in the deposition models. The computational results indicate that the plateout estimates for the slug flow model are typically 5–100% greater than for the laminar model. The effect of axial diffusion is necessarily negligible for Péclet numbers greater than 100. Little increased plateout is observed for Péclet numbers less than 100; an additional 8% is predicted for a Péclet number of 20 if axial diffusion is included. Characteristic stream, wall and integrated deposition profiles are shown. Representative results from the analysis of fission-product deposition measurements for diffusion tubes in the Fort St Vrain high-temperature gas-cooled reactor plateout probe are presented. Using single-region slug and laminar models, the wall mass-transfer coefficients, diffusion coefficients and inlet concentrations are determined using least-squares analysis. The diffusion coefficients and inlet concentrations are consistent between tubes. The computed diffusion coefficients and wall mass-transfer coefficients are in agreement with known literature values. The analysis indicates that little difference can be discerned between computed laminar and slub flow-model parameters unless accurate data is obtained under strictly regulated conditions.