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Titrate:
TPLL01 - Infinite plane wall in linear thermics
Date:
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Author (S):
O. BOITEAU, J. PELLET
Key
:
V4.02.001-E
Page:
1/16
Manual of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-23/02/017/A
Organization (S):
EDF/SINETICS, AMA













Manual of Validation
V4.02 booklet: Stationary thermics of the linear structures
Document: V4.02.001



TPLL01 - Infinite plane wall in linear thermics




Summary:

This case test relates to a calculation of stationary thermics linear. It includes/understands 10 modelings which test them
elements 2D and 3D.

This case test is of several interests:
·
for modelings of A with I, it tests on almost all the elements 3D and 2D (except
2d_AXIS
,
PYRAM
and lumpés), the calculation of the basic options of linear thermics: “rigidity”, “mass”, exchange,
imposed flow, imposed temperature,
·
in modeling J, one calculates a cartography of space error via the option
ERTH_ELEM_TEMP
of
CALC_ELEM
on which will rest, in a loop PYTHON, the tool of
refinement/déraffinement LOBSTER encapsulated in
MACR_ADAP_MAIL
.
·
The orientation of the wall is unspecified compared to the axes of co-ordinates,
·
It is one of the rare case-tests to test elements TETRA10 and QUAD9 in linear thermics, with
to combine the controls
AFFE_CHAR_THER/LIAISON_DDL
, and to test
INTE_MAIL_3D
.
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Titrate:
TPLL01 - Infinite plane wall in linear thermics
Date:
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O. BOITEAU, J. PELLET
Key
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V4.02.001-E
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V4.02 booklet: Stationary thermics of the linear structures
HI-23/02/017/A
1
Problem of reference
1.1 Geometry
m
F
E
B
D
G
With
S
X
.
L
C
y
Z
The problem corresponds to an infinite wall:
and unspecified


L = 0.05 m

C = {0.03, 0.0, 0.0}
F = {0.0, 0.04, 0.0}
With = {0.015, 0.02, 0.0}
CF
OF

1.2
Material properties
= 0.75 W.m °C thermal Conduction
C
p
= 2. J.m
3
°C voluminal Heat

1.3
Boundary conditions and loadings
·
[FE] and [CD]: null flow
·
[F]: free convection (H = 30 W/m
2
°C, T
E
= 140°C)
·
[AC]: imposed temperature T
I
= 100°C
·
[ED]:density flux imposed
I
= - 1.200 W/m
2
, (outgoing flow)

1.4 Conditions
initial
To make this stationary calculation, one makes a transitory calculation (except for modelings A and G) for
which the boundary conditions are constant in time. This makes it possible to test calculations
elementary of mass intervening in the first member as well as the second member.
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Titrate:
TPLL01 - Infinite plane wall in linear thermics
Date:
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Author (S):
O. BOITEAU, J. PELLET
Key
:
V4.02.001-E
Page:
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V4.02 booklet: Stationary thermics of the linear structures
HI-23/02/017/A
2
Reference solution
2.1
Method of calculation used for the reference solution
()
(
)
T S
T
T
T
S
L
S
AM M
T
T
L
m
With
B
With
B
With
=
+
-
=
= -
-
not running
R
R

2.2
Results of reference
Temperatures and flow at the points A, B, G.

2.3
Uncertainty on the solution
Analytical solution.

2.4 References
Case test VPCS TPLL01.
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Titrate:
TPLL01 - Infinite plane wall in linear thermics
Date:
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Author (S):
O. BOITEAU, J. PELLET
Key
:
V4.02.001-E
Page:
4/16
Manual of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-23/02/017/A
3 Modeling
With
3.1
Characteristics of modeling
Plan (QUAD4, TRIA3)
One nets part of the infinite wall, such as the field is a square OF
CF
=
= L with 4 meshs TRIA3
and 2 meshs QUAD4.
F
E
B
D
With
C
G
X
0
y
N3
N1
N5
X
y
C
0.03
0
D
0.07
0.03
E
0.04
0.07
F
0
0.04
With
0.015 0.02
N5
B
0.055 0.05
N1
G
0.035 0.035 N3

3.2
Characteristics of the mesh
A number of nodes: 9
A number of meshs and types: 2 QUAD4, 4 TRIA3

3.3 Functionalities
tested
Controls
Key word factor
Single-ended spanner word
Argument
AFFE_CHAR_THER
FLUX_REP
EXCHANGE
TEMP_IMPO
LIAISON_DDL
AFFE_MODELE
PLAN
THERMICS
MACRO_MATR_ASSE
SOLVEUR
MATR_ASSE
“MULT_FRONT”
RIGI_THER
CALC_VECT_ELEM
CHAR_THER
ASSE_VECT
FACT_LDLT
RESO_LDLT
CALC_CHAM_ELEM
FLUX_ELNO_TEMP
FLUX_ELGA_TEMP

3.4 Remarks
To test the key word factor LIAISON_DDL, the linear relation was introduced (checked by the solution):
T (G) - T (B) = 40.
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Titrate:
TPLL01 - Infinite plane wall in linear thermics
Date:
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Key
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V4.02.001-E
Page:
5/16
Manual of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-23/02/017/A
4
Results of modeling A
4.1 Values
tested
Identification Reference
Aster %
difference
T (A)°C 100.
100.00
0.00
T (B)°C 20.
20.00
0.00
T (G) °C 60.
60.00
0.00
() ()
2
/
.
m
W
m
I
m
R
R
960. 960.00
0.00
() ()
2
/
.
m
W
m
J
m
R
R
720. 720.00
0.00
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Titrate:
TPLL01 - Infinite plane wall in linear thermics
Date:
13/09/02
Author (S):
O. BOITEAU, J. PELLET
Key
:
V4.02.001-E
Page:
6/16
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V4.02 booklet: Stationary thermics of the linear structures
HI-23/02/017/A
5 Modeling
B
5.1
Characteristics of modeling
Plan (QUAD8, TRIA6)
F
E
B
D
With
C
G
X
0
y
N13
N6
N22
X y

C 0.03
0
D 0.07
0.03
E 0.04
0.07
F 0 0.04
To 0.015
0.02
N22
B 0.055
0.05
N6
G
0.035 0.035 N13
5.2
Characteristics of the mesh
A number of nodes: 23
A number of meshs and types: 4 TRIA6, 2 QUAD8
5.3 Functionalities
tested
Controls
Key word factor
Simple key word
Argument
AFFE_CHAR_THER_F
FLUX_REP
LIAISON_DDL
EXCHANGE
TEMP_IMPO
AFFE_MODELE
PLAN
THERMICS
THER_LINEAIRE
CALC_CHAM_ELEM
FLUX_ELNO_TEMP
FLUX_ELGA_TEMP
5.4 Notice
To test the key word factor LIAISON_DDL, the linear relation was introduced (checked by the solution)
T (G) ­ T (B) = 40.

6
Results of modeling B
6.1 Values
tested
Identification Reference
Aster %
difference
T (A)°C 100.
100.00
0.00
T (B)°C 20.
20.00
0.00
T (G) °C 60.
60.00
0.00
() ()
2
/
.
m
W
m
I
m
R
R
960. 960.00
0.00
() ()
2
/
.
m
W
m
J
m
R
R
720. 720.00
0.00
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Titrate:
TPLL01 - Infinite plane wall in linear thermics
Date:
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V4.02.001-E
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V4.02 booklet: Stationary thermics of the linear structures
HI-23/02/017/A
7 Modeling
C
7.1
Characteristics of modeling
Plan (QUAD8, TRIA6)
F
E
B
D
With
C
G
X
0
y
N14
N6
N24
X
y
C
0.03
0
D
0.07
0.03
E
0.04
0.07
F
0
0.04
With
0.015 0.02
N24
B
0.055 0.05
N6
G
0.035 0.035 N14
7.2
Characteristics of the mesh
A number of nodes: 25
A number of meshs and types: 4 TRIA6, 2 QUAD9
7.3 Functionalities
tested
Controls
Key word factor
Simple key word
Argument
AFFE_CHAR_THER_F
FLUX_REP
EXCHANGE
TEMP_IMPO
AFFE_MODELE
PLAN
THERMICS
THER_LINEAIRE
CALC_CHAM_ELEM
FLUX_ELNO_TEMP
FLUX_ELGA_TEMP


8
Results of modeling C
8.1 Values
tested
Identification Reference
Aster %
difference
T (A) °C
100.
100.00
0.00
T (B) °C
20.
20.00
0.00
T (G) °C
60.
60.00
0.00
() ()
2
/
.
m
W
m
I
m
R
R
960. 960.00
0.00
() ()
2
/
.
m
W
m
J
m
R
R
720. 720.00
0.00
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Code_Aster
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Version
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Titrate:
TPLL01 - Infinite plane wall in linear thermics
Date:
13/09/02
Author (S):
O. BOITEAU, J. PELLET
Key
:
V4.02.001-E
Page:
8/16
Manual of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-23/02/017/A
9 Modeling
D
9.1
Characteristics of modeling
Voluminal (HEXA8)
F
E
B
D
With
C
G
X
0
y
N16
N6
N20
X y Z

C 0.03
0 0
D
0.07 0.03 0
E
0.04 0.07 0
F 0 0.04
0
To 0.015
0.02
0 N20
B 0.055
0.05
0 N6
G
0.035 0.035 0
N16
Z
9.2
Characteristics of the mesh
A number of nodes: 21
A number of meshs and types: 4 HEXA8 + 20 QUAD4
9.3 Functionalities
tested
Controls
Key word factor
Simple key word
Argument
AFFE_CHAR_THER_F
FLUX_REP
EXCHANGE
TEMP_IMPO
AFFE_MODELE
3D
THERMICS
THER_LINEAIRE
CALC_CHAM_ELEM
FLUX_ELNO_TEMP
FLUX_ELGA_TEMP
INTE_MAIL_3D
POSt_RELEVE


10 Results of modeling D
10.1 Values
tested
Identification Reference
Aster %
difference
T (A) °C
100.
100.00
0.00
T (B) °C
20.
20.00
0.00
T (G) °C
60.
60.00
0.00
() ()
2
/
.
m
W
m
I
m
R
R
960. 960.00
0.00
() ()
2
/
.
m
W
m
J
m
R
R
720. 720.00
0.00
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Code_Aster
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Version
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Titrate:
TPLL01 - Infinite plane wall in linear thermics
Date:
13/09/02
Author (S):
O. BOITEAU, J. PELLET
Key
:
V4.02.001-E
Page:
9/16
Manual of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-23/02/017/A
11 Modeling
E
11.1 Characteristics of modeling
Voluminal (PENTA6)
F
E
B
D
With
C
G
X
0
y
N11
N10
N12
X y Z

C 0.03
0 0
D
0.07 0.03 0
E
0.04 0.07 0
F 0 0.04
0
To 0.015
0.02
0 N12
B 0.055
0.05
0 N10
G
0.035 0.035 0
N11
Z
11.2 Characteristics of the mesh
A number of nodes: 21
A number of meshs and types: 8 PENTA6 + 8 TRIA3 + 16 QUAD4
11.3 Functionalities
tested
Controls
Key word factor
Simple key word
Argument
AFFE_CHAR_THER_F
FLUX_REP
EXCHANGE
TEMP_IMPO
AFFE_MODELE
3D
THERMICS
THER_LINEAIRE
CALC_CHAM_ELEM
FLUX_ELNO_TEMP
FLUX_ELGA_TEMP


12 Results of modeling E
12.1 Values
tested
Identification Reference
Aster %
difference
T (A) °C
100.
100.00
0.00
T (B) °C
20.
20.00
0.00
T (G) °C
60.
60.00
0.00
() ()
2
/
.
m
W
m
I
m
R
R
960. 960.00
0.00
() ()
2
/
.
m
W
m
J
m
R
R
720. 720.00
0.00
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Code_Aster
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Titrate:
TPLL01 - Infinite plane wall in linear thermics
Date:
13/09/02
Author (S):
O. BOITEAU, J. PELLET
Key
:
V4.02.001-E
Page:
10/16
Manual of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-23/02/017/A
13 Modeling
F
13.1 Characteristics of modeling
Voluminal (HEXA20)
F
E
B
D
With
C
G
X
0
y
N45
N16
N57
X
y
Z
C
0.03
0
0
D
0.07
0.03
0
E
0.04
0.07
0
F
0
0.04
0
With
0.015 0.02
0
N57
B
0.055 0.05
0
N16
G
0.035 0.035 0
N45
Z
13.2 Characteristics of the mesh
A number of nodes: 59
A number of meshs and types: 4 HEXA20 + 20 QUAD8
13.3 Functionalities
tested
Controls
Key word factor
Simple key word
Argument
AFFE_CHAR_THER_F
FLUX_REP
EXCHANGE
TEMP_IMPO
AFFE_MODELE
PLAN
THERMICS
THER_LINEAIRE
CALC_CHAM_ELEM
FLUX_ELNO_TEMP
FLUX_ELGA_TEMP


14 Results of modeling F
14.1 Values
tested
Identification Reference
Aster %
difference
T (A) °C
100.
100.00
0.00
T (B) °C
20.
20.00
0.00
T (G) °C
60.
60.00
0.00
() ()
2
/
.
m
W
m
I
m
R
R
960. 960.00
0.00
() ()
2
/
.
m
W
m
J
m
R
R
720. 720.00
0.00
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Code_Aster
®
Version
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Titrate:
TPLL01 - Infinite plane wall in linear thermics
Date:
13/09/02
Author (S):
O. BOITEAU, J. PELLET
Key
:
V4.02.001-E
Page:
11/16
Manual of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-23/02/017/A
15 Modeling
G
15.1 Characteristics of modeling
Voluminal (PENTA15)
F
E
B
D
With
C
G
X
0
y
N52
N28
N61
X y Z

C 0.03
0 0
D
0.07 0.03 0
E
0.04 0.07 0
F 0 0.04
0
To 0.015
0.02
0 N61
B 0.055
0.05
0 N28
G
0.035 0.035 0
N52
Z
15.2 Characteristics of the mesh
A number of nodes: 65
A number of meshs and types: 8 PENTA15 + 8 TRIA6 + 16 QUAD8
15.3 Functionalities
tested
Controls
Key word factor
Simple key word
Argument
AFFE_CHAR_THER
FLUX_REP
EXCHANGE
TEMP_IMPO
AFFE_MODELE
3D
THERMICS
CALC_MATR_ELEM
OPTION
“RIGI_THER”
NUME_DDl
ASSE_MATRICE
CALC_VECT_ELEM
OPTION
“CHAR_THER”
ASSE_VECTEUR
FACT_LDLT
RESO_LDLT
PRE_GIBI
CALC_CHAM_ELEM
FLUX_ELNO_TEMP
FLUX_ELGA_TEMP

16 Results of modeling G
16.1 Values
tested
Identification Reference
Aster %
difference
T (A) °C
100.
100.00
0.00
T (B) °C
20.
20.00
0.00
T (G) °C
60.
60.00
0.00
() ()
2
/
.
m
W
m
I
m
R
R
960. 960.00
0.00
() ()
2
/
.
m
W
m
J
m
R
R
720. 720.00
0.00
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Code_Aster
®
Version
6.0
Titrate:
TPLL01 - Infinite plane wall in linear thermics
Date:
13/09/02
Author (S):
O. BOITEAU, J. PELLET
Key
:
V4.02.001-E
Page:
12/16
Manual of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-23/02/017/A
17 Modeling
H
17.1 Characteristics of modeling
Voluminal (TETRA4)
F
E
B
D
With
C
G
X
0
y
N13
N2
N7
X y Z

C 0.03
0 0
D
0.07 0.03 0
E
0.04 0.07 0
F 0 0.04
0
To 0.015
0.02
0 N7
B 0.055
0.05
0 N2
G
0.035 0.035 0
N13
Z
17.2 Characteristics of the mesh
A number of nodes: 18
A number of meshs and types: 20 TETRA4 + 6 TRIA3 + 16 QUAD8
17.3 Functionalities
tested
Controls
Key word factor
Simple key word
Argument
AFFE_CHAR_THER_F
FLUX_REP
EXCHANGE
TEMP_IMPO
AFFE_MODELE
3D
THERMICS
THER_LINEAIRE
PARM_THETA
1
CALC_CHAM_ELEM
FLUX_ELNO_TEMP
FLUX_ELGA_TEMP


18 Results of modeling H
18.1 Values
tested
Identification Reference
Aster %
difference
T (A) °C
100.
100.00
0.00
T (B) °C
20.
20.00
0.00
T (G) °C
60.
60.00
0.00
() ()
2
/
.
m
W
m
I
m
R
R
960. 960.00 0.00
() ()
2
/
.
m
W
m
J
m
R
R
720. 720.00 0.00
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Code_Aster
®
Version
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Titrate:
TPLL01 - Infinite plane wall in linear thermics
Date:
13/09/02
Author (S):
O. BOITEAU, J. PELLET
Key
:
V4.02.001-E
Page:
13/16
Manual of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-23/02/017/A
19 Modeling
I
19.1 Characteristics of modeling
Voluminal (TETRA10)
F
E
B
D
With
C
G
X
0
y
N04
N09
N01
X
y
C
0.03
0
D
0.07
0.03
E
0.04
0.07
F
0
0.04
With
0.015 0.02
N01
B
0.055 0.05
N09
G
0.035 0.035 N04
19.2 Characteristics of the mesh
A number of nodes: 125
A number of meshs and types: 48 TETRA10 + 16 TRIA6
19.3 Functionalities
tested
Controls
Key word factor
Simple key word
Argument
AFFE_CHAR_THER_F
FLUX_REP
EXCHANGE
TEMP_IMPO
AFFE_MODELE
3D
THERMICS
THER_LINEAIRE
PARM_THETA
1.0
CALC_CHAM_ELEM
FLUX_ELNO_TEMP
FLUX_ELGA_TEMP


20 Results of modeling I
20.1 Values
tested
Identification Reference
Aster %
difference
T (A) °C
100.
100.00
0.00
T (B) °C
20.
20.00
0.00
T (G) °C
60.
60.00
0.00
() ()
2
/
.
m
W
m
I
m
R
R
960. 960.00
0.00
() ()
2
/
.
m
W
m
J
m
R
R
720. 720.00
0.00
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Code_Aster
®
Version
6.0
Titrate:
TPLL01 - Infinite plane wall in linear thermics
Date:
13/09/02
Author (S):
O. BOITEAU, J. PELLET
Key
:
V4.02.001-E
Page:
14/16
Manual of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-23/02/017/A
21 Modeling
J
21.1 Characteristics of modeling
It is about a case functional test and of data-processing not-regression of the calculation of the indicator of error has
established posteriori in thermics (cf [R4.10.03]). It exhumes a cartography of space error on
which will rest, in a loop PYTHON, the tool of refinement/déraffinement LOBSTER
encapsulated in
MACR_ADAP_MAIL
(cf [U7.03.01]).
The calculation of this card of indicator of error is carried out, via the option `
ERTH_ELEM_TEMP
'of the operator
of postprocessing
CALC_ELEM,
on one
EVOL_THER
(provides to the key word
RESULT)
coming from one
former thermal calculation (linear or not, transient or stationary, isotropic or orthotropic, via
THER_LINEAIRE
or
THER_NON_LINE,
cf environment necessary, parameter setting and perimeter
of use [R4.10.03] §6.2/4).
This calculation requires as a preliminary the recourse to the option `
FLUX_ELNO_TEMP
'of
CALC_ELEM
who determines
values of the vector heat flux to the nodes (cf example of use [R4.10.03] §6.5).
The indicator consists of fifteen components per element and for a given moment. In this case
test, one calculates the fifteen components but the procedure of refinement/déraffinement does not rest
that on the component
ERTABS
who represents the absolute total space error (cf [R4.10.03] §6.3).
In order to be able post-to treat via
POST_RELEVE
or GIBI, one needs to extrapolate fields by
element in fields with the nodes by element. The addition of the option `
ERTH_ELNO_ELEM
'(afterwards
the call to `
ERTH_ELEM_TEMP'
) allows to carry out this purely data-processing transformation. For one
moment and a given finite element, it does nothing but duplicate the fifteen components of the indicator on
each node of the element.
This modeling thus constitutes as much an example of use, in a loop PYTHON,
possible couplings “calculation of indicator”/“refinement/déraffinement of mesh”, that a case test
of not-regression of the options `
ERTH_ELEM_TEMP
'and `
ERTH_ELNO_ELEM'
and their adherence
with the process of mending of meshes.
This case test takes again the characteristics of modeling I and its mesh (
TETRA10
+
TRIA6
)
associated.
21.2 Functionalities
tested
Controls
AFFE_CHAR_THER_F
FLUX_REP
EXCHANGE
TEMP_IMPO
AFFE_MODELE
3D
THERMICS
THER_LINEAIRE
CALC_ELEM
FLUX_ELNO_TEMP
ERTH_ELEM_TEMP
ERTH_ELNO_ELEM
MACR_ADAP_MAIL
REFINEMENT

22 Results of modeling J
22.1 Values
tested
One tests the data-processing not-regression of component ERTREL (relative total space error) of
the indicator of error compared to the V6.2.1 versions of platforms SGI and SUN of Code_Aster and of
the V4.3 version of the software LOBSTER. The relative tolerance is thus severe: 5.10
­ 6
%.
Identification
Aster
Tolerance
Value of
ERTREL
on the mesh
MA1
before mending of meshes
4.15918735 10
­ 5
5.10
­ 8
Value of
ERTREL
on the node
NO4
before mending of meshes
4.15918735 10
­ 5
5.10
­ 8
Value of
ERTREL
on the mesh
M1
after mending of meshes
5.48408914 10
­ 6
5.10
­ 7
background image
Code_Aster
®
Version
6.0
Titrate:
TPLL01 - Infinite plane wall in linear thermics
Date:
13/09/02
Author (S):
O. BOITEAU, J. PELLET
Key
:
V4.02.001-E
Page:
15/16
Manual of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-23/02/017/A
23 Summary of the results
The field solution (linear) belongs to the space of interpolation of all the elements tested.
results are thus naturally excellent.
background image
Code_Aster
®
Version
6.0
Titrate:
TPLL01 - Infinite plane wall in linear thermics
Date:
13/09/02
Author (S):
O. BOITEAU, J. PELLET
Key
:
V4.02.001-E
Page:
16/16
Manual of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-23/02/017/A


























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