Abstract

In preparation for determining material properties such as Sieverts’ constant (solubility) and diffusivity (transport rate) we give a detailed discussion on a model describing some gas release experiment. Aiming to simulate the time-dependent hydrogen fluxes and concentration profiles efficiently, we provide an analytical solution for the diffusion equations on a cylindrical specimen and a cylindrical container for three boundary conditions (B.C.). These (B.C.) occur in three phases – loading phase, evacuation phase and gas release phase. In the loading phase the specimen is charged with hydrogen assuring a constant partial pressure of hydrogen. The gas will be quickly removed in the second phase, in the third phase, the hydrogen is released from the specimen to the gaseous phase. The diffusion equation in each phase is a simple homogeneous equation. Due to the complex time-dependent (B.C.), we transform the homogeneous equations to the non-homogeneous ones with a zero Dirichlet (B.C.). Compared with the time consuming numerical methods our analytical approach has an advantage that the flux of desorbed hydrogen can be explicitly given and therefore can be evaluated efficiently. Our analytical solution also assures that the (B.C.) are exactly satisfied. The interaction between specimen and container is taken into account.

摘要

在准备确定诸如Sieverts常数（溶解度）和扩散率（传输速率）之类的材料特性时，我们对描述某些气体释放实验的模型进行了详细讨论。为了有效地模拟随时间变化的氢通量和浓度分布，我们为三个边界条件（BC）的圆柱试样和圆柱容器上的扩散方程提供了解析解。这些（BC）分为三个阶段-加载阶段，疏散阶段和气体释放阶段。在加载阶段，样品中充有氢气，以确保氢气的恒定分压。气体将在第二相中快速去除，在第三相中，氢从样品释放到气相中。各相中的扩散方程是简单的齐次方程。由于时间相关的复杂（BC），我们将齐次方程转换为Dirichlet（BC）为零的非齐次方程。与费时的数值方法相比，我们的分析方法具有以下优点：可以明确给出脱附氢的通量，因此可以有效地进行评估。我们的分析解决方案还确保（BC）完全满足。考虑到样品和容器之间的相互作用。与费时的数值方法相比，我们的分析方法具有以下优点：可以明确给出脱附氢的通量，因此可以有效地进行评估。我们的分析解决方案还确保（BC）完全满足。考虑到样品和容器之间的相互作用。与费时的数值方法相比，我们的分析方法具有以下优点：可以明确给出脱附氢的通量，因此可以有效地进行评估。我们的分析解决方案还确保（BC）完全满足。考虑到样品和容器之间的相互作用。