1. Reference problem#
1.1. Geometry#
The structure studied is a slice of a cylinder, modelled axisymmetrically, (cf HPLA100)
1.2. Material properties#
The material is homogeneous, isotropic, and linear thermoelastic. The mechanical coefficients are
\(E\mathrm{=}{2.10}^{5}M\mathrm{/}{\mathit{mm}}^{2}\); \(\nu \mathrm{=}0.3\)
The expansion coefficient is a function of temperature:
\(\alpha \mathrm{=}{10}^{\mathrm{-}5}°{C}^{\mathrm{-}1}\) for \(T\mathrm{=}100°C\), \(\alpha \mathrm{=}{10}^{\mathrm{-}4}°{C}^{\mathrm{-}1}\) for \(T\mathrm{=}0°C\)
The reference temperature is \(0°C\). The thermal coefficients are equal to:
\(\lambda \mathrm{=}1W\mathrm{/}mK\), \(\rho {C}_{p}\mathrm{=}1000\mathit{MJ}\mathrm{/}{m}^{3}K\)
1.3. Boundary conditions and thermal calculation loads#
On its inner edge, the cylinder is subjected to an exchange with a fluid that changes abruptly from \(100°C\) to \(0°C\):
zero flow at the edges \(\mathit{AB}\), \(\mathit{BC}\), \(\mathit{CD}\)
on edge \(\mathit{AD}\), convective exchange condition, with:
\(H\mathrm{=}100W\mathrm{/}{\mathit{mm}}^{2}\mathrm{/}°C\)
\(\mathit{Text}\mathrm{=}100°C\) to \(t\mathrm{=}\mathrm{0s}\), then \(0°C\) to \(t\mathrm{=}\mathrm{0.01s}\), and then kept constant.
1.4. Boundary conditions and loads for mechanical calculation#
Symmetry conditions
Unrestrained case: zero displacement following \(\mathit{Oy}\) along side \(\mathit{AB}\).
Blocked case: zero displacement following \(\mathit{Oy}\) along sides AB and \(\mathit{CD}\).
Loading: thermal expansion.