4. B modeling#
4.1. Characteristics of modeling#
The axisymmetric modeling is carried out on a slice of the tube.
4.1.1. Thermal analysis#
We test the unit heat shock \((\Delta {T}_{U}=1°C)\) and the thermal shock \(\mathrm{\Delta }T=50°C\) using the proposed methodology, with the « AXIS_DIAG » modeling.
Unit case \((\Delta {T}_{U}=1°C)\)
Boundary conditions:
Extracts: \({T}_{\mathit{imposée}}={T}_{\mathit{Initiale}}\)
Intrados: Convection \(h=20000W/{m}^{2}/°C\) \({T}_{\mathit{EXT}}={T}_{\mathit{Fluide}}={T}_{\mathit{Initiale}}+\Delta {T}_{U}\)
Initial conditions: \({T}_{\mathit{Initiale}}=0.°C\)
Case \((\Delta T=50°C;\Delta T=100°C;\Delta T=200°C)\)
Boundary conditions:
Extracts: \({T}_{\mathit{imposée}}={T}_{\mathit{Initiale}}\)
Intrados: Convection \(h=20000W/{m}^{2}/°C\) \({T}_{\mathit{EXT}}={T}_{\mathit{Fluide}}={T}_{\mathit{Initiale}}+\Delta T\)
Initial conditions: \({T}_{\mathit{Initiale}}=20.°C\)
4.1.2. Mechanical analysis#
We test the mechanical response for unit shock \((\Delta {T}_{U}=1°C)\) and thermal shock \(\mathrm{\Delta }T=50°C\) using the proposed methodology, with the « AXIS » modeling.
Boundary conditions: EF rating: \(\mathit{DY}=0.\)
Reference temperature: \({T}_{\mathit{Référence}}=0.°C\)
Thermal loads: \(\mathrm{\Delta }T=50°C\)
4.2. Characteristics of the mesh#
To properly take into account the thermal shock on the inner wall of the tube, refinement has been imposed.
For mechanical modeling, the same mesh is used but with quadratic cells.
Number of nodes: 504 linear
Number of meshes and types: 460 QUAD4 (thermal analysis)
Number of meshes and types: 460 QUAD8 (mechanical analysis)
4.3. B modeling results#
4.3.1. Unitary case#
Only a non-regression test is used on this calculation, which does not use the CALC_THERMECA_MULT macro command.
4.3.2. Heat shock \(\mathrm{\Delta }T=50°C\)#
These results were obtained with CALC_THERMECA_MULT and the following coefficients:
\({T(x,t)}_{\Delta T}=\beta \mathrm{.}{\stackrel{̃}{T}}_{\Delta {T}_{U}}(x,t)+{T}_{\mathit{initiale}}\)
Thermal shock |
\(\beta\) |
|
\(\Delta T=50°C\) |
Temperature (°C) \(\Delta T=50°C\) |
||||
Time |
Location |
Reference type |
Reference |
Tolerance (%) |
0.1 sec |
Intrados |
“AUTRE_ASTER” |
39.60439148764347 |
|
A |
“AUTRE_ASTER” |
26.057424514530002 |
||
B |
“AUTRE_ASTER” |
22.127310880200298 |
||
C |
“AUTRE_ASTER” |
20.072931376414274 |
||
D |
“AUTRE_ASTER” |
20.000074233637914 |
||
3.0 s |
Intrados |
“AUTRE_ASTER” |
62.791991296545994 |
|
A |
“AUTRE_ASTER” |
57.91447605545711 |
||
B |
“AUTRE_ASTER” |
54.26645281787711 |
||
C |
“AUTRE_ASTER” |
45.020909667984306 |
||
D |
“AUTRE_ASTER” |
31.02483220030017 |
||
4.3.3. Mechanical analyses#
Stress (Pa) \(\Delta T=50°C\) |
|||||
Time |
Location |
Constraint |
Reference type |
Reference |
Tolerance |
0.1 sec |
Intrados |
SIXX |
“AUTRE_ASTER” |
-2223.323126038972 |
|
SIYY |
“AUTRE_ASTER” |
-78755606.54685567 |
|
||
SIZZ |
“AUTRE_ASTER” |
-78753557.89057745 |
|
||
VMIS |
“AUTRE_ASTER” |
78752358.91557704 |
|
||
A |
SIXX |
“AUTRE_ASTER” |
-1225712.1785479188 |
|
|
SIYY |
“AUTRE_ASTER” |
-22196222.627284177 |
|
||
SIZZ |
“AUTRE_ASTER” |
-20970978.954915553 |
|
||
VMIS |
“AUTRE_ASTER” |
20385606.92198515 |
|
||
B |
SIXX |
“AUTRE_ASTER” |
-1428428.090007163 |
|
|
SIYY |
“AUTRE_ASTER” |
-2329006.724762771 |
|
||
SIZZ |
“AUTRE_ASTER” |
-900846.4000951699 |
|
||
VMIS |
“AUTRE_ASTER” |
1247569.5007786928 |
|
||
C |
SIXX |
“AUTRE_ASTER” |
-1152140.4888492671 |
|
|
SIYY |
“AUTRE_ASTER” |
4900600.802635529 |
|
||
SIZZ |
“AUTRE_ASTER” |
6052925.081161121 |
|
||
VMIS |
“AUTRE_ASTER” |
6703597.4346061945 |
|
||
D |
SIXX |
“AUTRE_ASTER” |
-499617.21189450816 |
|
|
SIYY |
“AUTRE_ASTER” |
5263164.8315241365 |
|
||
SIZZ |
“AUTRE_ASTER” |
5763009.107557128 |
|
||
VMIS |
“AUTRE_ASTER” |
6028267.390181367 |
|
||
Extrados |
SIXX |
“AUTRE_ASTER” |
1437.4754262985766 |
||
SIYY |
“AUTRE_ASTER” |
5263716.868909629 |
|
||
SIZZ |
“AUTRE_ASTER” |
5262478.893439884 |
|
||
VMIS |
“AUTRE_ASTER” |
5261660.514976556 |
|
||
4.4. notes#
For modeling B, if we take a zero temperature for the unit case, we notice larger relative differences for the unit case (Max 10%). This difference is much smaller for 50° C. The origin of these values is mainly due to the presence of the non-zero initial temperature for 50° C. or for the current version of the unit calculation.
Example: Given two values T1= 1 and T2=1.1, the relative error is:
by 10% with an initial temperature of 0°C
by 0.47% with an initial temperature of 20°C