PSI - Issue 65

Emelyanov I.G. et al. / Procedia Structural Integrity 65 (2024) 83–91 Emelyanov I.G., Puzyrev P.I. / Structural Integrity Procedia 00 (2024) 000–000

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Inside the cylindrical shell there is a hydrogen-containing gas with excess pressure p. Hydrogen penetrating into the metal wall of the shell leads to a change in the material characteristics depending on the hydrogen concentration. Therefore, it is necessary to determine the time dependence of the distribution of hydrogen concentration in the studied shell. This dependence can be determined by solving the boundary problem of heat propagation and hydrogen diffusion in solid body, Petrov, Ovchinnikov and Shikhov (1987), Olden, Thaulowand and Johnsen (2008), Rebyakov and Chernyavskij (2010), Ivanyts’kyi, Hembara and Chepil (2015),Emel'yanov and Mironov (2018). Currently, methods for solving thermal conductivity problems are well developed and verified. There are numerous computational programs ANSYS, COSMOS, COMSOL Multiphysics, for determining the temperature T in various bodies. The finite element method, which allows for the description of bodies of arbitrary geometric shape, is commonly used to determine temperature distribution. However, using commercial computing programs has disadvantages. Many commercial programs are proprietary, meaning users do not have access to the details of the algorithms and methods used within the program. Users may have limited access to solver settings within commercial programs, restricting the ability to modify numerical methods and solution parameters. However, it should be noted that commercial programs have a high level of reliability and have undergone thorough verification and validation. This makes them attractive for a wide range of engineering applications, especially when fast and accurate numerical simulations are required. If complete control over algorithms and methods is required, it is possible to develop custom solutions, but may require significant effort in development and verification. It is known that the process of heating and diffusion are driven by different physical carriers, however, in solving applied problems, it is usually hypothesized that the heat conduction equation can be used to mathematically describe the diffusion process, Lykov (1978), Vorobyov (2003), Aramanovich and Levin (1969). The cylindrical shell under study will have an axisymmetric temperature distribution. Therefore, for determining the temperature distribution T in the shell we will use the two-dimensional equation of unsteady thermal conductivity, which in the cylindrical coordinate system z, r has the form, Shevchenko, Babeshko and Piskun (1980), Emel'yanov (2019): 1 T T T r z z r r r a t                            (1) where z is axis coordinate; r is radius of an arbitrary shell point; λ(T) is thermal conductivity coefficient; a(T) is thermal diffusivity coefficient, which in general depends on temperature, and it is a heat transfer parameter and is equal to: 3. Basic equations and methods for solving heat conduction problems



a



(2)

c



t

where ct is the coefficient of specific mass heat capacity J/kgK; ρ is the density of the body. The influence of ambient temperature on the shell surface at each moment is specified by the boundary conditions. Three types or types of boundary conditions are usually used depending on the formulation of the thermal conductivity problem. The first type is temperature distribution described at each moment of time on the shell surface. The second type based on heat flow through the surface of the body is specified. For the third kind, the ambient temperature T0 and the law of heat exchange between the surface of the body and the environment are specified. For first-kind boundary conditions, it is necessary to specify the temperature on the inner surface of the cylindrical shell at each moment in time: