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Version
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Titrate:
TPLL01 - Infinite plane Mur in linear thermics


Date:
13/09/02
Author (S):
O. BOITEAU, J. Key PELLET
:
V4.02.001-E Page:
1/16

Organization (S): EDF/SINETICS, AMA

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

TPLL01 - Infinite plane Mur 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,
Lumpés PYRAM and), 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 option ERTH_ELEM_TEMP
CALC_ELEM on which will rest, in a loop PYTHON, the tool of
refinement/déraffinement HOMARD 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 commands AFFE_CHAR_THER/LIAISON_DDL, and to test INTE_MAIL_3D.
Handbook of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-23/02/017/A

Code_Aster ®
Version
6.0
Titrate:
TPLL01 - Infinite plane Mur in linear thermics


Date:
13/09/02
Author (S):
O. BOITEAU, J. Key PELLET
:
V4.02.001-E Page:
2/16

1
Problem of reference

1.1 Geometry

E
S
B
The problem corresponds to an infinite wall:
and unspecified
CF
OF
D
G

F
L = 0.05 m
m

C = {0.03, 0.0, 0.0}
y
With
F = {0.0, 0.04, 0.0}
L
With = {0.015, 0.02, 0.0}
.
X
C
Z


1.2
Material properties

= 0.75 W.m °C thermal Conduction

CP = 2. Voluminal J.m3 °C Chaleur

1.3
Boundary conditions and loadings

· [FE] and [CD]: null flow
· [F]: free convection (H = 30 W/m2 °C, Te= 140°C)
· [AC]: imposed temperature Ti = 100°C
· [ED]:density flux imposed i= - 1.200 W/m2, (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.
Handbook of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-23/02/017/A

Code_Aster ®
Version
6.0
Titrate:
TPLL01 - Infinite plane Mur in linear thermics


Date:
13/09/02
Author (S):
O. BOITEAU, J. Key PELLET
:
V4.02.001-E Page:
3/16

2
Reference solution

2.1
Method of calculation used for the reference solution

S
T (S) = MT + (T - T
B
With)
S = AM M not running
L

T
R
- T
B
With
= -
Mr.


L

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.
Handbook of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-23/02/017/A

Code_Aster ®
Version
6.0
Titrate:
TPLL01 - Infinite plane Mur in linear thermics


Date:
13/09/02
Author (S):
O. BOITEAU, J. Key PELLET
:
V4.02.001-E Page:
4/16

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.

E
B
X
y
y
N1
C
0.03
0
D
0.07
0.03
G
F
D
E
0.04
0.07
N3
F
0
0.04
With
0.015 0.02
N5
B
0.055 0.05
N1
With
G
0.035 0.035 N3
N5
C
X
0


3.2
Characteristics of the grid

A number of nodes: 9

A number of meshs and types: 2 QUAD4, 4 TRIA3

3.3 Functionalities
tested

Commands
Key word factor
Single-ended spanner word
Argument

AFFE_CHAR_THER
FLUX_REP
ECHANGE
TEMP_IMPO

LIAISON_DDL

AFFE_MODELE
PLAN
THERMIQUE

MACRO_MATR_ASSE
SOLVEUR
“MULT_FRONT”

MATR_ASSE
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.
Handbook of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-23/02/017/A

Code_Aster ®
Version
6.0
Titrate:
TPLL01 - Infinite plane Mur in linear thermics


Date:
13/09/02
Author (S):
O. BOITEAU, J. Key PELLET
:
V4.02.001-E Page:
5/16

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
R (R
m) .i (m
)
2
W/m
960. 960.00
0.00
R (R
m). J (m
)
2
W/m
720. 720.00
0.00


Handbook of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-23/02/017/A

Code_Aster ®
Version
6.0
Titrate:
TPLL01 - Infinite plane Mur in linear thermics


Date:
13/09/02
Author (S):
O. BOITEAU, J. Key PELLET
:
V4.02.001-E Page:
6/16

5 Modeling
B

5.1
Characteristics of modeling

Plan (QUAD8, TRIA6)

E
B
X y
y

N6
C 0.03
0
G
D 0.07
0.03
F
D
E 0.04
0.07
N13
F 0 0.04
To 0.015
0.02
N22
With
B 0.055
0.05
N6
N22
G
0.035 0.035 N13
C
X
0


5.2
Characteristics of the grid

A number of nodes: 23

A number of meshs and types: 4 TRIA6, 2 QUAD8

5.3 Functionalities
tested

Commands
Key word factor
Simple key word
Argument
AFFE_CHAR_THER_F
FLUX_REP
ECHANGE
TEMP_IMPO
LIAISON_DDL
AFFE_MODELE
PLAN
THERMIQUE
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
R (R
m) .i (m
)
2
W/m
960. 960.00
0.00
R (R
m). J (m
)
2
W/m
720. 720.00
0.00

Handbook of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-23/02/017/A

Code_Aster ®
Version
6.0
Titrate:
TPLL01 - Infinite plane Mur in linear thermics


Date:
13/09/02
Author (S):
O. BOITEAU, J. Key PELLET
:
V4.02.001-E Page:
7/16

7 Modeling
C

7.1
Characteristics of modeling

Plan (QUAD8, TRIA6)

E
X
y
B
y
C
0.03
0
N6
D
0.07
0.03
G
E
0.04
0.07
F
D
F
0
0.04
N14
With
0.015 0.02
N24
B
0.055 0.05
N6
With
G
0.035 0.035 N14
N24
C
X
0


7.2
Characteristics of the grid

A number of nodes: 25

A number of meshs and types: 4 TRIA6, 2 QUAD9

7.3 Functionalities
tested

Commands
Key word factor
Simple key word
Argument
AFFE_CHAR_THER_F
FLUX_REP
ECHANGE
TEMP_IMPO
AFFE_MODELE
PLAN
THERMIQUE
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
R (R
m) .i (m
)
2
W/m
960. 960.00
0.00
R (R
m). J (m
)
2
W/m
720. 720.00
0.00

Handbook of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-23/02/017/A

Code_Aster ®
Version
6.0
Titrate:
TPLL01 - Infinite plane Mur in linear thermics


Date:
13/09/02
Author (S):
O. BOITEAU, J. Key PELLET
:
V4.02.001-E Page:
8/16

9 Modeling
D

9.1
Characteristics of modeling

Voluminal (HEXA8)

E
X y Z
N6

y
B
C 0.03
0 0
D
0.07 0.03 0
E
0.04 0.07 0
F
G
N16
D
F 0 0.04
0
To 0.015
0.02
0 N20
B 0.055
0.05
0 N6
N20
With
G
0.035 0.035 0
N16
C
X
Z 0


9.2
Characteristics of the grid

A number of nodes: 21

A number of meshs and types: 4 HEXA8 + 20 QUAD4

9.3 Functionalities
tested

Commands
Key word factor
Simple key word
Argument
AFFE_CHAR_THER_F
FLUX_REP
ECHANGE
TEMP_IMPO
AFFE_MODELE
3D
THERMIQUE
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
R (R
m) .i (m
)
2
W/m
960. 960.00
0.00
R (R
m). J (m
)
2
W/m
720. 720.00
0.00

Handbook of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-23/02/017/A

Code_Aster ®
Version
6.0
Titrate:
TPLL01 - Infinite plane Mur in linear thermics


Date:
13/09/02
Author (S):
O. BOITEAU, J. Key PELLET
:
V4.02.001-E Page:
9/16

11 Modeling
E

11.1 Characteristics of modeling
Voluminal (PENTA6)

E
X y Z
N10

y
B
C 0.03
0 0
D
0.07 0.03 0
E
0.04 0.07 0
F
G
N11
D
F 0 0.04
0
To 0.015
0.02
0 N12
B 0.055
0.05
0 N10
N12
With
G
0.035 0.035 0
N11
C
X
Z 0


11.2 Characteristics of the grid

A number of nodes: 21

A number of meshs and types: 8 PENTA6 + 8 TRIA3 + 16 QUAD4

11.3 Functionalities
tested

Commands
Key word factor
Simple key word
Argument

AFFE_CHAR_THER_F
FLUX_REP
ECHANGE
TEMP_IMPO

AFFE_MODELE
3D
THERMIQUE

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
R (R
m) .i (m
)
2
W/m
960. 960.00
0.00
R (R
m). J (m
)
2
W/m
720. 720.00
0.00

Handbook of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-23/02/017/A

Code_Aster ®
Version
6.0
Titrate:
TPLL01 - Infinite plane Mur in linear thermics


Date:
13/09/02
Author (S):
O. BOITEAU, J. Key PELLET
:
V4.02.001-E Page:
10/16

13 Modeling
F

13.1 Characteristics of modeling
Voluminal (HEXA20)

E
X
y
Z
N16
y
B
C
0.03
0
0
N45
D
0.07
0.03
0
E
0.04
0.07
0
F
G
D
F
0
0.04
0
With
0.015 0.02
0
N57
N57
B
0.055 0.05
0
N16
With
G
0.035 0.035 0
N45
C
X
Z 0


13.2 Characteristics of the grid

A number of nodes: 59

A number of meshs and types: 4 HEXA20 + 20 QUAD8

13.3 Functionalities
tested

Commands
Key word factor
Simple key word
Argument

AFFE_CHAR_THER_F
FLUX_REP
ECHANGE
TEMP_IMPO

AFFE_MODELE
PLAN
THERMIQUE

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
R (R
m) .i (m
)
2
W/m
960. 960.00
0.00
R (R
m). J (m
)
2
W/m
720. 720.00
0.00

Handbook of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-23/02/017/A

Code_Aster ®
Version
6.0
Titrate:
TPLL01 - Infinite plane Mur in linear thermics


Date:
13/09/02
Author (S):
O. BOITEAU, J. Key PELLET
:
V4.02.001-E Page:
11/16

15 Modeling
G

15.1 Characteristics of modeling
Voluminal (PENTA15)

E
X y Z
N28

y
B
C 0.03
0 0
D
0.07 0.03 0
E
0.04 0.07 0
F
G
N52
D
F 0 0.04
0
To 0.015
0.02
0 N61
B 0.055
0.05
0 N28
N61
With
G
0.035 0.035 0
N52
C
X
Z 0


15.2 Characteristics of the grid

A number of nodes: 65

A number of meshs and types: 8 PENTA15 + 8 TRIA6 + 16 QUAD8

15.3 Functionalities
tested

Commands
Key word factor
Simple key word
Argument
AFFE_CHAR_THER
FLUX_REP
ECHANGE
TEMP_IMPO
AFFE_MODELE
3D
THERMIQUE
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
R (R
m) .i (m
)
2
W/m
960. 960.00
0.00
R (R
m). J (m
)
2
W/m
720. 720.00
0.00

Handbook of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-23/02/017/A

Code_Aster ®
Version
6.0
Titrate:
TPLL01 - Infinite plane Mur in linear thermics


Date:
13/09/02
Author (S):
O. BOITEAU, J. Key PELLET
:
V4.02.001-E Page:
12/16

17 Modeling
H

17.1 Characteristics of modeling
Voluminal (TETRA4)

E
X y Z
N2

y
B
C 0.03
0 0
D
0.07 0.03 0
E
0.04 0.07 0
F
G
N13
D
F 0 0.04
0
To 0.015
0.02
0 N7
B 0.055
0.05
0 N2
N7
With
G
0.035 0.035 0
N13
C
X
Z 0


17.2 Characteristics of the grid

A number of nodes: 18

A number of meshs and types: 20 TETRA4 + 6 TRIA3 + 16 QUAD8

17.3 Functionalities
tested

Commands
Key word factor
Simple key word
Argument
AFFE_CHAR_THER_F
FLUX_REP
ECHANGE
TEMP_IMPO
AFFE_MODELE
3D
THERMIQUE
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
R (R
m) .i (m
)
2
W/m
960. 960.00 0.00
R (R
m). J (m
)
2
W/m
720. 720.00 0.00

Handbook of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-23/02/017/A

Code_Aster ®
Version
6.0
Titrate:
TPLL01 - Infinite plane Mur in linear thermics


Date:
13/09/02
Author (S):
O. BOITEAU, J. Key PELLET
:
V4.02.001-E Page:
13/16

19 Modeling
I

19.1 Characteristics of modeling
Voluminal (TETRA10)

E
B
X
y
y
N09
C
0.03
0
D
0.07
0.03
G
F
D
E
0.04
0.07
N04
F
0
0.04
With
0.015 0.02
N01
B
0.055 0.05
N09
With
G
0.035 0.035 N04
N01
C
X
0


19.2 Characteristics of the grid

A number of nodes: 125

A number of meshs and types: 48 TETRA10 + 16 TRIA6

19.3 Functionalities
tested

Commands
Key word factor
Simple key word
Argument
AFFE_CHAR_THER_F
FLUX_REP
ECHANGE
TEMP_IMPO
AFFE_MODELE
3D
THERMIQUE
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
R (R
m) .i (m
)
2
W/m
960. 960.00
0.00
R (R
m). J (m
)
2
W/m
720. 720.00
0.00

Handbook of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-23/02/017/A

Code_Aster ®
Version
6.0
Titrate:
TPLL01 - Infinite plane Mur in linear thermics


Date:
13/09/02
Author (S):
O. BOITEAU, J. Key PELLET
:
V4.02.001-E Page:
14/16

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 HOMARD
encapsulated in MACR_ADAP_MAIL (cf [U7.03.01]).
The calculation of this card of indicator of error is carried out, via option “ERTH_ELEM_TEMP” of the operator
of postprocessing CALC_ELEM, on a EVOL_THER (provides to key word RESULTAT) 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 option “FLUX_ELNO_TEMP” of CALC_ELEM which 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 which 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 option “ERTH_ELNO_ELEM” (afterwards
the call to “ERTH_ELEM_TEMP”) makes it possible 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 grid”, that a case test
of not-regression of options “ERTH_ELEM_TEMP” and “ERTH_ELNO_ELEM” and of their adherence
with the process of mending of meshes.
This case test takes again the characteristics of modeling I and its grid (TETRA10 + TRIA6)
associated.

21.2 Functionalities
tested

Commands




AFFE_CHAR_THER_F
FLUX_REP
ECHANGE
TEMP_IMPO

AFFE_MODELE
3D
THERMIQUE

THER_LINEAIRE

CALC_ELEM
FLUX_ELNO_TEMP
ERTH_ELEM_TEMP
ERTH_ELNO_ELEM

MACR_ADAP_MAIL
RAFFINEMENT


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 software HOMARD. The relative tolerance is thus severe: 5.10­ 6%.

Identification
Aster
Tolerance
Value of ERTREL on mesh MA1
4.15918735 10­5 5.10­8
before mending of meshes
Value of ERTREL on node NO4
4.15918735 10­5 5.10­8
before mending of meshes
Value of ERTREL on the M1 mesh
5.48408914 10­6 5.10­7
after mending of meshes
Handbook of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-23/02/017/A

Code_Aster ®
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6.0
Titrate:
TPLL01 - Infinite plane Mur in linear thermics


Date:
13/09/02
Author (S):
O. BOITEAU, J. Key PELLET
:
V4.02.001-E Page:
15/16

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.

Handbook of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-23/02/017/A

Code_Aster ®
Version
6.0
Titrate:
TPLL01 - Infinite plane Mur in linear thermics


Date:
13/09/02
Author (S):
O. BOITEAU, J. Key PELLET
:
V4.02.001-E Page:
16/16

Intentionally white left page.

Handbook of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-23/02/017/A

Outline document