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

87 5

In Fig.2. the dashed lines show the temperature distribution over the wall thickness, calculated using equation (1), Emel'yanov, Mironov, and Hodak (2019). Curves 1-5 correspond to 1, 5, 10, 100, 200 seconds of heating. Solid lines show the result of numerical simulation using ANSYS Workbench Transient Thermal. The maximum error reaches 14% for curves 2 and 3. Curves 1 and 5 show good convergence.

Fig.2. Temperature distribution over the thickness of the shell wall.

If the outer surface of the shell is not thermally insulated, then we will also accept the boundary conditions on the outer surface of the shell in the form of the law of convective heat transfer. In this case, we will take the ambient temperature outside the diffusion apparatus with T = 25 ºС. Calculation shows a steady linear temperature field along the wall thickness and it shows a good agreement between the calculation results when using two different calculation algorithms.

4. Governing equations and methods for solving hydrogen diffusion problems

To solve the problem of hydrogen diffusion into the shell body, you can use methods for solving thermal conductivity problems, Vorobyov (2003), Aramanovich and Levin (1969). This significantly simplifies the solution of diffusion problems, since the methods for studying thermal conductivity problems are well developed, and the solution results can be compared with a full-scale experiment. The mathematical formalization of the problem of diffusion and boundary conditions is well studied and describes various boundary value problems, Lykov (1978), Vorobyov (2003), Bekman (2016). However, when solving applied problems, various physical constants are required, which must be obtained by experimental methods. The main problem when solving diffusion problems is the discrepancy between experimental data and results when using mathematical models. For example, in Bekman (2016)an example is given: “the diffusion coefficient of hydrogen in stainless steel at room temperature D = 10 -6 cm 2 /s . This means that after 10 hours,