Numerical Solution of Two-Dimensional Axisymmetric Free Convection within Isotope Separating Thermal Diffusion Column

Abstract

A numerical method for integrating the equations of change without the Boussinesque approximation is presented for axisymmetric free convection within thermal diffusion column. A finite difference analogue of equations of change in terms of primitive variables (density, radial and axial velocities, and temperature) is solved by a modified Newton method. Errors in a finite difference approximation of derivatives for temperature and density are reduced by introduction of a perturbation or deviation from an analytically obtainable base temperature distribution. Roundoff errors in a Gaussian elimination procedure are also reduced with the adoption of “scaling” and a partial pivoting strategy of the Jacobian matrix. A relation for total mass conservation is used to prevent the density from converging to a trivial solution, i.e. zero. The method has been applied to a total reflux flow of Ar gas within the 1,000 mm height thermal diffusion column with an inner hot radius of 0.2 mm and an outer cold radius of 5 mm, between which the temperature differs by 50∼400K. The “end effect” appears within 15 mm portion from the top and bottom plates.