2. Benchmark solution#
2.1. Calculation method used for the reference solution#
Comparison with the numerical results of a volume modeling with Samcef V7.0 with 50 time steps (module THERNL for calculating the transient temperature field and repeated with module MECANL for non-linear mechanical calculation).
An implicit schema is used to integrate the heat equation.
The non-linear mechanical calculation was performed with SAMCEF using axisymmetric modeling with 5 time steps (geometric nonlinear modeling) and volume modeling (a quarter cylinder) with 5 time steps (geometric nonlinear modeling).
2.2. Benchmark results#
Evolution of the temperature field according to the thickness on the lower side of the cylinder
Axisymmetric calculation with 50 time steps |
|
Time = 0.5 sec |
Time = 25 sec |
1.25355E+01 |
8.64267E+01 |
5.71233E+00 |
7.65695E+01 |
2.44526E+00 |
6.77355E+01 |
1.12189E+00 |
5.98610E+01 |
4.83644E-01 |
5.28476E+01 |
2.22443E-01 |
4.66462E+01 |
9.62036E-02 |
4.11801E+01 |
4.43444E-02 |
3.64106E+01 |
1.92310E-02 |
3.22765E+01 |
8.87973E-03 |
2.87468E+01 |
3.85960E-03 |
2.57723E+01 |
1.78524E-03 |
2.33283E+01 |
7.78650E-04 |
2.13761E+01 |
3.63114E-04 |
1.98963E+01 |
1.64448E-04 |
1.88596E+01 |
8.80577E-05 |
1.82514E+01 |
6.54904E-05 |
1.80507E+01 |
Volume calculation with 50 time steps |
|
Time = 0.5 sec |
Time = 25 sec |
1.26658E+01 |
8.64175E+01 |
5.64556E+00 |
7.65753E+01 |
2.50690E+00 |
6.77332E+01 |
1.10448E+00 |
5.98571E+01 |
5.06396E-01 |
5.28510E+01 |
2.23330E-01 |
4.66453E+01 |
9.98984E-02 |
4.11819E+01 |
4.41255E-02 |
3.64095E+01 |
2.02976E-02 |
3.22781E+01 |
8.97177E-03 |
2.87460E+01 |
4.05352E-03 |
2.57736E+01 |
1.79338E-03 |
2.33275E+01 |
8.25938E-04 |
2.13766E+01 |
3.68531E-04 |
1.98979E+01 |
1.74367E-04 |
1.88647E+01 |
8.91805E-05 |
1.82450E+01 |
6.98548E-05 |
1.80607E+01 |
Evolution of the longitudinal stress \({\sigma }_{T}\)
Cases where the pressure is not following
Geometric nonlinear volume calculation with 5 time steps |
|||
\(t(s)\) |
\(\sigma\) |
Point \(A\) |
Point \(B\) |
15.0 |
\({\sigma }_{T}\) |
1.21692E8 |
1.67285E8 |
20.0 |
\({\sigma }_{T}\) |
1.39804E8 |
1.65266E8 |
25.0 |
\({\sigma }_{T}\) |
1.28967E8 |
1.57980E8 |
Geometric nonlinear axisymmetric calculation with 5 time steps |
|||
\(t(s)\) |
\(\sigma\) |
Point \(A\) |
Point \(B\) |
15.0 |
\({\sigma }_{T}\) |
1.20472E8 |
1.66917E8 |
20.0 |
\({\sigma }_{T}\) |
1.39164E8 |
1.70412E8 |
25.0 |
\({\sigma }_{T}\) |
1.28421E8 |
1.63168E8 |
Cases where the pressure is follow
Geometric nonlinear volume calculation with 5 time steps |
|||
\(t(s)\) |
\(\sigma\) |
Point \(A\) |
Point \(B\) |
15.0 |
\({\sigma }_{T}\) |
1.21692E8 |
1.67285E8 |
20.0 |
\({\sigma }_{T}\) |
1.39894E8 |
1.65313E8 |
25.0 |
\({\sigma }_{T}\) |
1.29032E8 |
1.58007E8 |
Geometric nonlinear axisymmetric calculation with 5 time steps |
|||
\(t(s)\) |
\(\sigma\) |
Point \(A\) |
Point \(B\) |
15.0 |
\({\sigma }_{T}\) |
1.20472E8 |
1.65934E8 |
20.0 |
\({\sigma }_{T}\) |
1.39252E8 |
1.64075E8 |
25.0 |
\({\sigma }_{T}\) |
1.28485E8 |
1.56886E8 |
2.3. Uncertainty about the solution#
Uncertainty less than \(\text{1 \%}\) for thermal calculation, uncertainty less than \(\text{0.5 \%}\) for mechanical calculation.