Modeling A ============== Characteristics of modeling ----------------------------------- Volume modeling is carried out on ¼ of the tube. Thermal analysis ----------------- We test the unit heat shock :math:`(\Delta {T}_{U}=1°C)` and the "real" thermal shock :math:`\mathrm{\Delta }T=50°C` using the proposed methodology, with the "3D_ DIAG" modeling. **Unit case** :math:`(\Delta {T}_{U}=1°C)` Boundary conditions: * Extracts: :math:`{T}_{\mathit{imposée}}={T}_{\mathit{Initiale}}` * Intrados: Convection :math:`h=20000W/{m}^{2}/°C` :math:`{T}_{\mathit{EXT}}={T}_{\mathit{Fluide}}={T}_{\mathit{Initiale}}+\Delta {T}_{U}` * Zero flow at the level of the planes of symmetry Initial conditions: :math:`{T}_{\mathit{Initiale}}=20.°C={T}_{\mathit{Référence}}` **Case** :math:`\mathrm{\Delta }T=50°C` Boundary conditions: * Extracts: :math:`{T}_{\mathit{imposée}}={T}_{\mathit{Initiale}}` * Intrados: Convection :math:`h=20000W/{m}^{2}/°C` :math:`{T}_{\mathit{EXT}}={T}_{\mathit{Fluide}}={T}_{\mathit{Initiale}}+\Delta T` * Zero flow at the level of the planes of symmetry Initial conditions: :math:`{T}_{\mathit{Initiale}}=20.°C` Mechanical analysis ~~~~~~~~~~~~~~~~~~ We test the mechanical response for unit shock :math:`(\Delta {T}_{U}=1°C)` and thermal shock :math:`\mathrm{\Delta }T=50°C` using the proposed methodology, with "3D" modeling. * Boundary conditions: master plan XOY: :math:`\mathit{DZ}=0.` * Symmetry conditions: * Main Plan XOZ: :math:`\mathit{DY}=0.` * Main Plan YOZ: :math:`\mathit{DX}=0.` * Reference temperature: :math:`{T}_{\mathit{Référence}}=20.°C` * Thermal loads: :math:`\mathrm{\Delta }T=50°C` 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) Results of modeling A ------------------------------ 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. Heat shock :math:`\mathrm{\Delta }T=50°C` ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Thermal analyses ^^^^^^^^^^^^^^^^^^^^^^ +--------------------------------------+--------+--------------+------------------+-------------+ |Temperature (°C) :math:`\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| | +--------------------------------------+--------+--------------+------------------+-------------+ Mechanical analyses ^^^^^^^^^^^^^^^^^^^^^^ +---------------------------------+--------+----------+--------------+-------------------+---------+ |Stress (Pa) :math:`\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. % | +---------------------------------+--------+----------+--------------+-------------------+---------+