Analytic solutions to linear, time-dependent fission product deposition models for isothermal laminar, slug, or multiregion flow conditions

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. The slug flow multiregion solution is obtained using the method of separation of variables. The Davidon Variable Metric Minimization algorithm is used to compute the coupling coefficients. These solutions, which describe the transport of fission products in a flowing stream, are then used to determine the concentration of radioactive material deposited on a conduit wall using a standard mass transfer model. Extensive single and multiregion parametric investigations are conducted by varying the wall mass transfer coefficient, diffusion coefficient, flow velocity, pipe radius, and species half-life. Single region results indicate that the plateout estimates for the slug flow model are typically 5 to 100% greater than for the laminar model. The effect of axial diffusion is negligible for Peclet numbers greater than 100. Increased plateout is observed for Peclet numbers less than 100; an additional 8% is predicted for a Peclet number of 20 when axial diffusion is included. Graphical presentation is used to depict concentration profile results for the various flow studies in single and multiregion conditions. Fission product deposition measurements for five diffusion tubes in a Fort St. Vrain High-Temperature Gas-Cooled reactor plateout probe are analyzed. 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 derived diffusion coefficients and wall mass transfer coefficients are in relative agreement with known literature values.