Mathematical Model of One and Two-Step Methods Calculation of Thermal Fields and Stress-Strain State of Multilayer Cylindrical Constructions

Abstract

Two-step and one-step methods for calculating thermal fields and stress-strain state of multilayer cylindrical constructions (parts of vessel bodies or reactors) have been developed to ensure their functioning under the conditions of high internal pressure and temperature. The efficiency of this algorithms by a simple example of the contact interaction of two cylinders of equal rigidity (α = 0,5) and thermal conductivity in two cylinders in contact heat exchange with thermal conductivity of similar value (α = 0,5) are shown. Two-step method implements the alternate solution step by step of applying kinematic and force tasks for solving the problem of static contact and the tasks of heat transfer and heat field for solving the thermal problem. One-step method realizes the solution of either the power problem on basis of the determined the error resulting from the addressing the kinematic problem, as it is determined in the previous step, or the kinematic problem on the basis of the specified error stemming from the addressing the force problem, which is also defined in the previous step for solve the static contact problem. Also, one-step method realizes the solution applied to the heat transfer problem based on the specified value of the error deriving from the initial addressing the said problem which is determined in the previous step.