Development of the algorithm for calculating the optimal molding modes of the BeO slurry using various rheological models

Abstract

This paper presents the results of calculating a mathematical model of the flow and heat transfer of thermoplastic beryllium oxide in a round channel of a molding installation. An algorithm for calculating the system of equations based on the Herschel-Bulkley rheological model has been developed. The finite-difference analogue of the equations system of motion, continuity, and energy is solved numerically using the CrankNicholson difference scheme. The three-parameter equation is used to test the consistency of experimental, data, and how adequately the physical features of the non-isothermal flow of the slurry convey comparing to the Shvedov-Bingham model. The calculation results illustrate that the proposed model reflects the most important features of the thixotropic flow character of the slurry and is in better agreement with the experimental data of viscoplastic fluids. It provides the calculations of speed of viscous-plastic flow of the slurry based on Shvedov-Bingham and Herschel Bulkley’s two rheological models considering the peculiarities of coagulation structure formation and flow mechanism with boundary conditions. As a result of calculations, the fields of velocity, temperature, and density were obtained, which describe the regularities of the flow and heat transfer of a thermoplastic slurry. The change in the Nusselt criterion along the length of the shaping cavity is shown, which coincides with the analytical solution of Nusselt under first kind boundary conditions. The optimal conditions for the process of ceramics molding by hot casting method have been found, allowing to obtain a hardened product with a homogeneous structure of beryllium ceramics at the outlet.