3. Modeling A#

3.1. Characteristics of modeling#

Volume modeling is carried out on ¼ of the tube.

3.2. Thermal analysis#

We test the unit heat shock \((\Delta {T}_{U}=1°C)\) and the « real » thermal shock \(\mathrm{\Delta }T=50°C\) using the proposed methodology, with the « 3D_ DIAG » modeling.

Unit case \((\Delta {T}_{U}=1°C)\)

Boundary conditions:

  • Extracts: \({T}_{\mathit{imposée}}={T}_{\mathit{Initiale}}\)

  • Intrados: Convection \(h=20000W/{m}^{2}/°C\) \({T}_{\mathit{EXT}}={T}_{\mathit{Fluide}}={T}_{\mathit{Initiale}}+\Delta {T}_{U}\)

  • Zero flow at the level of the planes of symmetry

Initial conditions: \({T}_{\mathit{Initiale}}=20.°C={T}_{\mathit{Référence}}\)

Case \(\mathrm{\Delta }T=50°C\)

Boundary conditions:

  • Extracts: \({T}_{\mathit{imposée}}={T}_{\mathit{Initiale}}\)

  • Intrados: Convection \(h=20000W/{m}^{2}/°C\) \({T}_{\mathit{EXT}}={T}_{\mathit{Fluide}}={T}_{\mathit{Initiale}}+\Delta T\)

  • Zero flow at the level of the planes of symmetry

Initial conditions: \({T}_{\mathit{Initiale}}=20.°C\)

3.2.1. 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 « 3D » modeling.

  • Boundary conditions: master plan XOY: \(\mathit{DZ}=0.\)

  • Symmetry conditions:

    • Main Plan XOZ: \(\mathit{DY}=0.\)

    • Main Plan YOZ: \(\mathit{DX}=0.\)

  • Reference temperature: \({T}_{\mathit{Référence}}=20.°C\)

  • Thermal loads: \(\mathrm{\Delta }T=50°C\)

3.3. 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: 2520 linear

  • Number of meshes and types: 1840 HEXA8 (thermal analysis)

  • Number of meshes and types: 1840 HEXA20 (mechanical analysis)

3.4. Results of modeling A#

3.4.1. Unitary case#

Only a non-regression test is performed on these thermal and mechanical calculations which do not use the CALC_THERMECA_MULT macro command.

3.4.2. Heat shock \(\mathrm{\Delta }T=50°C\)#

3.4.2.1. Thermal analyses#

Temperature (°C) \(\Delta T=50°C\)

Time

Location

Reference type

Reference

Tolerance (%)

0.1 sec

Intrados

“AUTRE_ASTER”

42.22934518732506

A

“AUTRE_ASTER”

26.01122459885759

B

“AUTRE_ASTER”

21.870849415508467

C

“AUTRE_ASTER”

20.0473226322084

D

“AUTRE_ASTER”

20.000032488497183

3.0 s

Intrados

“AUTRE_ASTER”

66.47322145431414

A

“AUTRE_ASTER”

61.29797584453274

B

“AUTRE_ASTER”

57.358943368182715

C

“AUTRE_ASTER”

47.16496697879001

D

“AUTRE_ASTER”

31.506146137279625

3.4.2.2. Mechanical analyses#

Stress (Pa) \(\Delta T=50°C\)

Time

Location

Constraint

Reference type

Reference

Tolerance

0.1 sec

Intrados

SIXX

“AUTRE_ASTER”

37489.29855405912

200

SIYY

“AUTRE_ASTER”

-90763742.58663052

  1. %

SIZZ

“AUTRE_ASTER”

-89835467.18538839

  1. %

VMIS

“AUTRE_ASTER”

90353481.53295466

  1. %

A

SIXX

“AUTRE_ASTER”

-1373909.820313106

  1. %

SIYY

“AUTRE_ASTER”

-21611891.279474393

  1. %

SIZZ

“AUTRE_ASTER”

-22078479.83997749

  1. %

VMIS

“AUTRE_ASTER”

20478467.497951064

  1. %

B

SIXX

“AUTRE_ASTER”

-1514515.7112189943

  1. %

SIYY

“AUTRE_ASTER”

-521744.0661440513

  1. %

SIZZ

“AUTRE_ASTER”

-1231398.7126009488

  1. %

VMIS

“AUTRE_ASTER”

1058986.1070860107

  1. %

C

SIXX

“AUTRE_ASTER”

-1162145.1699433196

  1. %

SIYY

“AUTRE_ASTER”

5599015.596422898

  1. %

SIZZ

“AUTRE_ASTER”

5110992.015038196

  1. %

VMIS

“AUTRE_ASTER”

6537321.490726789

  1. %

D

SIXX

“AUTRE_ASTER”

-492556.42792592593

  1. %

SIYY

“AUTRE_ASTER”

5280378.736995371

  1. %

SIZZ

“AUTRE_ASTER”

5401344.682695183

  1. %

VMIS

“AUTRE_ASTER”

5835328.274520403

  1. %

Extrados

SIXX

“AUTRE_ASTER”

-18026.486515487028

SIYY

“AUTRE_ASTER”

4861145.702066543

  1. %

SIZZ

“AUTRE_ASTER”

5535035.500733721

  1. %

VMIS

“AUTRE_ASTER”

5248692.688594596

  1. %