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Date:
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:
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Organization (S): EDF/AMA

Handbook of Validation
V4.21 booklet: Transitory thermics of the linear structures
Document: V4.21.001

TTLL01 - Thermal Choc on an infinite wall

Summary:

· Transitory linear thermics,
· elements 2D and 3D (7 modelings),
· interests of the test:
-
test the algorithm of linear thermics transitory with change of step of time,
-
imposed temperature (with discontinuity),
-
filing of some not of time.
· The shock is modelled in 2 different ways:
-
by a linear slope: T = 100. in 10­3 second,
-
by true a discontinuity of imposed temperature.

Handbook of Validation
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1
Problem of reference

1.1 Geometry
B
With
A'
M1
M2
X
0
2L

AA = 2L = 2 m
X (M1) = 0.2 m
X (m2) = 0.8 m

1.2
Material properties

= 1 W/m °C
CP = 1 J/m3 °C

1.3
Boundary conditions and loadings

· A: T (0, T) = Tp = 100°C
for T > 0
· A': T (2L, T) = Tp = 100°C

1.4 Conditions
initial

T (X, 0) = 0°C for any X

1.5
Specified concerning modelings

Discretization in time (T):

The thermal shock requires a “fine” discretization in time nearly T = 0.

The goal of the test being to validate the various elements (various modelings), we have
chosen a single discretization in time:

10 steps
for [0.
,
1.D3] is T = 10­4 S
9
not for
[1 D3
,
1.D2]
that is to say
T = 10­3 S
9 steps
for
[1.D2
,
1.D1]
that is to say
T = 10­2 S
9
not for
[1.D1
,
1.]
that is to say
T = 10­1 S
10
not for
[1.
,
2.]
that is to say
T = 10­1 S

The shock is defined in two different ways:

· for modeling B, it is about a true shock (Tp is discontinuous):
T -

p ()
To = 0.


T +

p ()
To = 100.
· for modelings A, C, D, E, F, G, it is about a linear slope:

T

p (A) t= =
0
0.


T

p (A) t= - 3 =
10
100.
Handbook of Validation
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2
Reference solution

2.1
Method of calculation used for the reference solution

T (X, T) -

Tp
4
1
N X

N2
= sin
exp-
.
.t
0
T - T

N
L
L
C
p
N 1
2
=
2
p



X =
X-coordinate

T =
time
0
T = températur initial

E
Tp = températur imposed

E
N =
,
1,
3…
,
5

2.2
Results of reference

Temperatures at the points M1 (X = 0.2) and m2 (X = 0.8),
and at various moments (T = 0.1, 0.2, 0.7 and 2.0).

The values of reference are those given in guide VPCS.

2.3
Uncertainty on the solution

Numerical series.

2.4 References
bibliographical

[1]
J.F. SACCADURA: Initiation with the thermal transfers, Paris, Technique and documentation
(1982).

Handbook of Validation
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3 Modeling
With

3.1
Characteristics of modeling

QUAD8

One nets only half the thickness of the wall by reason of symmetry; modeling is made under
a height H = 1.0 with only one layer of elements.

L = 0.05
Limiting conditions

D
C
on [BC], [AB] and [cd.]: J = 0

H
on [AD]: Tp is imposed
With
M1
M2
B
Tp
100 °C
20 elements
0
T
10 - 3 S
points
nodes

Initial conditions
M1
N9
T = 0 °C
M2
N33
One fixes here the duration of the shock at 10 - 3 S.


3.2
Characteristics of the grid

A number of nodes: 103
A number of meshs and types: 20 QUAD8

3.3 Functionalities
tested

Commands


THER_LINEAIRE
LIST_INST

RECU_CHAMP
INST


Handbook of Validation
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4
Results of modeling A

4.1 Values
tested

Identification Reference
Aster %
difference
M1 (X = 0.2) N9



T = 0.1
65.48
65.294
­ 0.28
T = 0.2
75.58
75.814
+0.31
T = 0.7
93.01
92.867
­ 0.15
T = 2.0
99.72
99.700
­ 0.02




M2 (X = 0.8) N33



T = 0.1
8.09
8.0357
­ 0.67
T = 0.2
26.37
25.790
­ 2.20
T = 0.7
78.47
78.047
­ 0.54
T = 2.0
99.13
99.077
­ 0.05

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5 Modeling
B

5.1
Characteristics of modeling

QUAD8

One nets only half the thickness of the wall by reason of symmetry; modeling is made under
a height H = 1.0 with only one layer of elements.

L = 0.05
Limiting conditions

D
C
on [BC], [AB] and [cd.]: = 0

H
on [AD]: Tp is imposed Tp = 100°C
With
M1
M2
B
Tp
100 °C
20 elements
0
T
points
nodes

Initial conditions
M1
N9
One affects the temperature directly of
M2
N33
100°C at moment 0.


5.2
Characteristics of the grid

A number of nodes: 103
A number of meshs and types: 20 QUAD8

5.3 Functionalities
tested


Commands


THER_LINEAIRE
TEMP_INIT
CHAM_NO

RECU_CHAMP
INST

AFFE_CHAM_NO


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6
Results of modeling B

6.1 Values
tested

Identification Reference
Aster %
difference
M1 (X = 0.2) N9



T = 0.1
65.48
65.369
­ 0.17
T = 0.2
75.58
75.841
0.35
T = 0.7
93.01
92.875
­ 0.14
T = 2.0
99.72
99.700
­ 0.02




M2 (X = 0.8) N33



T = 0.1
8.09
8.113
0.28
T = 0.2
26.37
25.872
­ 1.89
T = 0.7
78.47
78.071
­ 0.51
T = 2.0
99.13
99.078
­ 0.05

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7 Modeling
C

7.1
Characteristics of modeling

HEXA8

One nets only half the thickness of the wall by reason of symmetry; modeling is made under
a height and a thickness H = 1.0 with only one layer of elements.

L = 0.05
Limiting conditions

D
C
on [BC], [AB] and [cd.]: = 0

H
on [AD]: Tp is imposed
With
M1
M2
B H
Tp
100 °C
20 elements HEXA8
0
T
10­3 S
points
nodes

Initial conditions
M1

N21 with N24
T = 0°C
M2

N69 with N72
One fixes here the duration of the shock at 10­3 S.


7.2
Characteristics of the grid

A number of nodes: 84
A number of meshs and types: 20 HEXA8

7.3 Functionalities
tested


Commands


THER_LINEAIRE
LIST_INST

RECU_CHAMP
INST


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8
Results of modeling C

8.1 Values
tested

Identification Reference
Aster %
difference
M1 (X = 0.2) N21



T = 0.1
65.48
65.31
­ 0.26
T = 0.2
75.58
75.81
+0.31
T = 0.7
93.01
92.87
­ 0.15
T = 2.0
99.72
99.70
­ 0.02




M2 (X = 0.8) N69



T = 0.1
8.09
7.98
­ 1.31
T = 0.2
26.37
25.76
­ 2.30
T = 0.7
78.47
78.05
­ 0.53
T = 2.0
99.13
99.08
­ 0.05

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9 Modeling
D

9.1
Characteristics of modeling

HEXA20

One nets only half the thickness of the wall by reason of symmetry; modeling is made under
a height and a thickness H = 1.0 with only one layer of elements.

L = 0.05
Limiting conditions

D
C
on [BC], [AB] and [cd.]: = 0

H
on [AD]: Tp is imposed
With
M1
M2
B H
Tp
100 °C
20 elements HEXA20
0
T
10­3 S
points
nodes

Initial conditions
M1

N57 with N64
T = 0°C
M2

N201 with N208
One fixes here the duration of the shock at 10­3 S.


9.2
Characteristics of the grid

A number of nodes: 248
A number of meshs and types: 20 HEXA20

9.3 Functionalities
tested


Commands


THER_LINEAIRE
LIST_INST

RECU_CHAMP
INST


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10 Results of modeling D

10.1 Values
tested

Identification Reference
Aster %
difference
M1 (X = 0.2) N57



T = 0.1
65.48
65.29
­ 0.28
T = 0.2
75.58
75.81
+0.31
T = 0.7
93.01
92.87
­ 0.15
T = 2.0
99.72
99.70
­ 0.02




M2 (X = 0.8) N201



T = 0.1
8.09
8.04
­ 0.67
T = 0.2
26.37
25.79
­ 2.20
T = 0.7
78.47
78.05
­ 0.54
T = 2.0
99.13
99.08
­ 0.05

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11 Modeling
E

11.1 Characteristics of modeling

PENTA6

One nets only half the thickness of the wall by reason of symmetry; modeling is made under
a height and a thickness H = 1.0 with only one layer of elements. Each cube is cut out
in 2 pentahedrons.

L = 0.05
Limiting conditions

D
C
on [BC], [AB] and [cd.]: = 0

H
on [AD]: Tp is imposed
With
M1
M2
B H
Tp
100 °C
20 elements PENTA6
0
T
10­3 S
points
nodes

Initial conditions
M1

N21 with N24
T = 0°C
M2

N69 with N72
One fixes here the duration of the shock at 10­3 S.


11.2 Characteristics of the grid

A number of nodes: 84
A number of meshs and types: 40 PENTA6

11.3 Functionalities
tested


Commands


THER_LINEAIRE
LIST_INST

RECU_CHAMP
INST


Handbook of Validation
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12 Results of modeling E

12.1 Values
tested

Identification Reference
Aster %
difference
M1 (X = 0.2) N21



T = 0.1
65.48
65.31
­ 0.26
T = 0.2
75.58
75.81
+0.31
T = 0.7
93.01
92.87
­ 0.15
T = 2.0
99.72
99.70
­ 0.02




M2 (X = 0.8) N69



T = 0.1
8.09
7.98
­ 1.31
T = 0.2
26.37
25.76
­ 2.30
T = 0.7
78.47
78.05
­ 0.53
T = 2.0
99.13
99.08
­ 0.05

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13 Modeling
F

13.1 Characteristics of modeling

PENTA15

One nets only half the thickness of the wall by reason of symmetry; modeling is made under
a height and a thickness H = 1.0 with only one layer of elements. Each cube is cut out
in 2 pentahedrons.

L = 0.05
Limiting conditions

D
C
on [BC], [AB] and [cd.]: = 0

H
on [AD]: Tp is imposed
With
M1
M2
B H
Tp
100 °C
20 elements PENTA15
0
T
10­3 S
points
nodes

Initial conditions
M1

N62 with N70
T = 0°C
M2

N218 with N226
One fixes here the duration of the shock at 10­3 S.


13.2 Characteristics of the grid

A number of nodes: 269
A number of meshs and types: 40 PENTA15

13.3 Functionalities tested
Commands


THER_LINEAIRE
LIST_INST

RECU_CHAMP
INST


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14 Results of modeling F

14.1 Values
tested

Identification Reference
Aster %
difference
M1 (X = 0.2) N62



T = 0.1
65.48
65.29
­ 0.28
T = 0.2
75.58
75.81
+0.31
T = 0.7
93.01
92.87
­ 0.15
T = 2.0
99.72
99.70
­ 0.02




M2 (X = 0.8) N218



T = 0.1
8.09
8.04
­ 0.67
T = 0.2
26.37
25.79
­ 2.20
T = 0.7
78.47
78.05
­ 0.54
T = 2.0
99.13
99.08
­ 0.05

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15 Modeling
G

15.1 Characteristics of modeling

TETRA4

One nets only half the thickness of the wall by reason of symmetry; modeling is made under
a height and a thickness H = 1.0 with only one layer of elements. Each cube is cut out
in 5 tetrahedrons.

L = 0.05
Limiting conditions

D
C
on [BC], [AB] and [cd.]: = 0

H
on [AD]: Tp is imposed
With
M1
M2
B H
Tp
100 °C
20 elements TETRA4
0
T
10­3 S
points
nodes

Initial conditions
M1
N12,
N17
T = 0°C
M2
N48,
N53
One fixes here the duration of the shock at 10­3 S.


15.2 Characteristics of the grid

A number of nodes: 84
A number of meshs and types: 100 TETRA4

15.3 Functionalities
tested


Commands


THER_LINEAIRE
TEMP_INIT
STATIONNAIRE

IMPR_RESU
NUMERO_ORDRE

AFFE_CHAR_THER_F
TEMP_IMPO


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16 Results of modeling G

16.1 Values
tested

Identification Reference
Aster %
difference
M1 (X = 0.2)



T = 0.1 N12
65.48
65.37
­ 0.17
N17
65.49
65.27
­ 0.33
T = 0.2 N12
75.58
75.84
+0.34
N17
75.58
75.80
+0.29
T = 0.7 N12
93.01
92.88
­ 0.14
N17
93.01
92.86
­ 0.16
T = 2.0 N12
99.72
99.70
­ 0.02
N17
99.72
99.70
­ 0.02




M2 (X = 0.8)



T = 0.1 N48
8.09
8.08
­ 0.11
N53
8.09
7.97
­ 1.43
T = 0.2 N48
26.37
25.85
­ 1.96
N53
26.37
25.74
­ 2.39
T = 0.7 N48
78.47
78.07
­ 0.51
N53
78.47
78.04
­ 0.55
T = 2.0 N48
99.13
99.08
­ 0.05
N53
99.13
99.08
­ 0.05

16.2 Remarks

At the beginning of transient, one observes slightly different values between the nodes located in
a plan X = constant (< 3 per 1000). This anomaly seems to be due to modeling in tetrahedrons
with 4 nodes. The results remain nevertheless correct compared to the other elements 3D.

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17 Modeling
J

17.1 Characteristics of modeling

TETRA4_D

One nets only half the thickness of the wall by reason of symmetry; modeling is made under
a height and a thickness H = 1.0 with only one layer of elements. Each cube is cut out
in 5 tetrahedrons.

One uses modeling “3d_DIAG” applied to TETRA4, which corresponds to the lumpage of
stamp of thermal mass.

L = 0.05
Limiting conditions

D
C
on [BC], [AB] and [cd.]: = 0

H
on [AD]: Tp is imposed
With
M1
M2
B H
Tp
100 °C
20 elements TETRA4_D
0
T
10­3 S
points
nodes

Initial conditions
M1
N12,
N17
T = 0°C
M2
N48,
N53
One fixes here the duration of the shock at 10­3 S.


17.2 Characteristics of the grid

A number of nodes: 84
A number of meshs and types: 100 TETRA4

17.3 Functionalities
tested


Commands


THER_LINEAIRE
TEMP_INIT
STATIONNAIRE

IMPR_RESU
NUMERO_ORDRE

AFFE_CHAR_THER_F
TEMP_IMPO


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18 Results of modeling J

18.1 Values
tested

Identification Reference
Aster %
difference
M1 (X = 0.2)



T = 0.1 N12
65.48
65.34
­ 0.21
N17
65.49
65.24
­ 0.36
T = 0.2 N12
75.58
75.84
+0.34
N17
75.58
75.80
+0.29
T = 0.7 N12
93.01
92.87
­ 0.15
N17
93.01
92.86
­ 0.16
T = 2.0 N12
99.72
99.70
­ 0.02
N17
99.72
99.70
­ 0.02




M2 (X = 0.8)



T = 0.1 N48
8.09
8.18
+1.16
N53
8.09
8.08
­ 0.15
T = 0.2 N48
26.37
25.90
­ 1.77
N53
26.37
25.79
­ 2.20
T = 0.7 N48
78.47
78.06
­ 0.52
N53
78.47
78.02
­ 0.57
T = 2.0 N48
99.13
99.07
­ 0.05
N53
99.13
99.07
­ 0.05

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19 Modeling
K

19.1 Characteristics of modeling

PENTA6_D

One nets only half the thickness of the wall by reason of symmetry; modeling is made under
a height and a thickness H = 1.0 with only one layer of elements. Each cube is cut out
in 2 pentahedrons.

One uses modeling “3d_DIAG” applied to PENTA6, which corresponds to the lumpage of
stamp of thermal mass.

L = 0.05
Limiting conditions

D
C
on [BC], [AB] and [cd.]: = 0

H
on [AD]: Tp is imposed
With
M1
M2
B H
Tp
100 °C
20 elements PENTA6_D
0
T
10­3 S
points
nodes

Initial conditions
M1
N21
with
N24
T = 0°C
M2
N69
with
N72
One fixes here the duration of the shock at 10­3 S.


19.2 Characteristics of the grid

A number of nodes: 84
A number of meshs and types: 40 PENTA6

19.3 Functionalities
tested


Commands


THER_LINEAIRE
LIST_INST

RECU_CHAMP
INST


Handbook of Validation
V4.21 booklet: Transitory thermics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
TTLL01 - Thermal Choc on an infinite wall


Date:
30/08/02
Author (S):
J. Key PELLET
:
V4.21.001-F Page:
21/24

20 Results of modeling K

20.1 Values
tested

Identification Reference
Aster %
difference
M1 (X = 0.2)



T = 0.1
65.48
65.28
­ 0.30
T = 0.2
75.58
75.81
+0.31
T = 0.7
93.01
92.87
­ 0.15
T = 2.0
99.72
99.70
­ 0.02




M2 (X = 0.8)



T = 0.1
8.09
8.087
­ 0.03
T = 0.2
26.37
25.81
­ 2.14
T = 0.7
78.47
78.04
­ 0.55
T = 2.0
99.13
99.08
­ 0.05

Handbook of Validation
V4.21 booklet: Transitory thermics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
TTLL01 - Thermal Choc on an infinite wall


Date:
30/08/02
Author (S):
J. Key PELLET
:
V4.21.001-F Page:
22/24

21 Modeling
L

21.1 Characteristics of modeling

HEXA8_D

One nets only half the thickness of the wall by reason of symmetry; modeling is made under
a height and a thickness H = 1.0 with only one layer of elements.

One uses modeling “3d_DIAG” applied to HEXA8, which corresponds to the lumpage of
stamp of thermal mass.

L = 0.05
Limiting conditions

D
C
on [BC], [AB] and [cd.]: = 0

H
on [AD]: Tp is imposed
With
M1
M2
B H
Tp
100 °C
20 elements HEXA8_D
0
T
10­3 S
points
nodes

Initial conditions
M1
N21
with
N24
T = 0°C
M2
N69
with
N72
One fixes here the duration of the shock at 10­3 S.


21.2 Characteristics of the grid

A number of nodes: 84
A number of meshs and types: 20 HEXA8

21.3 Functionalities tested
Commands


THER_LINEAIRE
LIST_INST

RECU_CHAMP
INST


Handbook of Validation
V4.21 booklet: Transitory thermics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
TTLL01 - Thermal Choc on an infinite wall


Date:
30/08/02
Author (S):
J. Key PELLET
:
V4.21.001-F Page:
23/24

22 Results of modeling L

22.1 Values
tested

Identification Reference
Aster %
difference
M1 (X = 0.2)



T = 0.1
65.48
65.28
­ 0.30
T = 0.2
75.58
75.81
+0.31
T = 0.7
93.01
92.87
­ 0.15
T = 2.0
99.72
99.70
­ 0.02




M2 (X = 0.8)



T = 0.1
8.09
8.087
­ 0.03
T = 0.2
26.37
25.81
­ 2.10
T = 0.7
78.47
78.04
­ 0.55
T = 2.0
99.13
99.08
­ 0.05

Handbook of Validation
V4.21 booklet: Transitory thermics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
TTLL01 - Thermal Choc on an infinite wall


Date:
30/08/02
Author (S):
J. Key PELLET
:
V4.21.001-F Page:
24/24

23 Summary of the results

At the end of 0.7 S the error is definitely lower than 1% for the various thermal elements 2D
(QUAD8) and 3D (HEXA8 - HEXA20 - PENTA6 - PENTA15 - TETRA4) used.

It does not seem that the lumpage improves the numerical result.

It would be advisable to test the elements lumpés with a true jump as in modeling B.

Handbook of Validation
V4.21 booklet: Transitory thermics of the linear structures
HT-66/02/001/A

Outline document