Code_Aster ®
Version
5.0
Titrate:
TTNL302 infinite Mur subjected to a constant flow with variable properties
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.22.302-A Page:
1/14
Organization (S): EDF/AMA, EDF/UTO/LOCATED, Delta CAD
Handbook of Validation
V4.22 booklet: Non-linear transitory thermics of the linear structures
V4.22.302 document
TTNL302 - Infinite Mur subjected to a constant flow
with variable properties
Summary:
This test results from the validation independent of version 3 in nonlinear transitory thermics.
It is about a linear problem 1D represented by five modelings, one planes, four the other voluminal ones.
The functionalities tested are as follows:
· element of plane thermics,
· voluminal element of thermics,
· algorithm of transitory thermics non-linear,
· variable properties,
· limiting condition: imposed flow.
The interest of the test lies in the taking into account of properties variable (thermal conductivity and heat
voluminal).
The results are compared with an analytical solution.
Handbook of Validation
V4.22 booklet: Non-linear transitory thermics of the linear structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
TTNL302 infinite Mur subjected to a constant flow with variable properties
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.22.302-A Page:
2/14
1
Problem of reference
1.1 Geometry
y
D
C
Q
E
X
With
B
L
Q (W/m ²)
, C
L = 2 m
1,5
AE=EB= 1m
1
1
T (S)
T (°C)
1
1.2
Properties of material
= 1.0 + 0.5 T W/m.°C
Thermal conductivity
C = 1.0 + 0.5 T J/m3.°C Chaleur
voluminal
1.3
Boundary conditions and loadings
· dimensioned [AD]: flow imposed Q = 1 W/m ² for T > 0,
· dimensioned [AB], [BC], [CD] = O.
1.4 Conditions
initial
T (X, 0) = 0°C for any X
Handbook of Validation
V4.22 booklet: Non-linear transitory thermics of the linear structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
TTNL302 infinite Mur subjected to a constant flow with variable properties
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.22.302-A Page:
3/14
2
Reference solution
2.1
Method of calculation used for the reference solution
Semi-analytical solution utilizing functions of error:
x2
X
T (X, T) = 2 1+ 2 (T/) exp-
+ x.erfc -
1
-
4t
2 T
2
2
with er (
FC X)
and
=
dt
X
where X = X-coordinate
T = time
This formula is valid only for (T) = C (T) = 1. + 0.5T
2.2
Results of reference
Temperature at points A (X = 0) and E (X = 1) at the moment T following: T = 0.1, 0.3, 0.5, 0.7 and 1s
2.3
Uncertainty on the solution
Unknown factor, due to the evaluation of the functions of error.
2.4 References
bibliographical
[1]
Segal, NR. Praagman, “A fast implementation off explicit time stepping algorithms with the finite
element method for has class off nonlinear evolution problems ", Int. J. num. Meth. Engng, flight 23,
p 155-168, 1986.
Handbook of Validation
V4.22 booklet: Non-linear transitory thermics of the linear structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
TTNL302 infinite Mur subjected to a constant flow with variable properties
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.22.302-A Page:
4/14
3 Modeling
With
3.1
Characteristics of modeling
PLAN (QUAD9)
y
D
C
F
0.1 m
m20
m11 m10
m1
X
With
E
B
1. m
2.m
Limiting conditions:
Not
X
y
Node
With
0.0
0.0
N1
- dimensioned AB, BC, CD = 0
D
0.0
0.1
N3
- dimensioned AD
Q = 1 W/m ² °C
E
1.0
0.0
N61
F
1.0
0.1
N63
3.2
Characteristics of the grid
A number of nodes:
123
A number of meshs and types: 20 QUAD9
3.3 Functionalities
tested
Commands
AFFE_MODELE
THERMIQUE
PLAN
TOUT
DEFI_MATERIAU
THER_NL
AFFE_CHAR_THER
FLUX_REP
THER_NON_LINE
TEMP_INIT
VALE
INCREMENT
LIST_INST
RECU_CHAMP
INST
3.4 Remarks
The discretization in step of time is as follows:
10 steps for [0. , 5.D-2] is T = 5.D-3
19 step for [5.D-2, 1.D0] is T = 5.D-2
Handbook of Validation
V4.22 booklet: Non-linear transitory thermics of the linear structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
TTNL302 infinite Mur subjected to a constant flow with variable properties
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.22.302-A Page:
5/14
4
Results of modeling A
4.1 Values
tested
Identification Reference
Aster %
difference
tolerance
Temperature (°C)
Node N1 T = 0.1s
0.330
0.329
- 0.204%
1%
““T = 0.3s
0.544
0.544
- 0.048%
1%
““T = 0.5s
0.682
0.681
- 0.075%
1%
““T = 0.7s
0.789
0.789
- 0.036%
1%
““T = 1.0s
0.918
0.920
0.254%
1%
Node N3 T = 0.1s
0.330
0.329
- 0.204%
1%
““T = 0.3s
0.544
0.544
- 0.048%
1%
““T = 0.5s
0.682
0.681
- 0.075%
1%
““T = 0.7s
0.789
0.789
- 0.036%
1%
““T = 1.0s
0.918
0.920
0.254%
1%
Node N61 T = 0.1s
0.004
0.004
1.161%
1%
““T = 0.3s
0.071
0.071
- 0.377%
1%
““T = 0.5s
0.160
0.161
0.573%
1%
““T = 0.7s
0.247
0.251
1.616%
1%
““T = 1.0s
0.366
0.380
3.951%
1%
Node N63 T = 0.1s
0.004
0.004
1.161%
1%
““T = 0.3s
0.071
0.071
- 0.377%
1%
““T = 0.5s
0.160
0.161
0.573%
1%
““T = 0.7s
0.247
0.251
1.616%
1%
““T = 1.0s
0.366
0.380
3.951%
1%
4.2 Remarks
The relative error is to the maximum of 3.9%.
4.3 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Obstruction memory:
8 megawords
Time CPU To use: 19.44 seconds
Handbook of Validation
V4.22 booklet: Non-linear transitory thermics of the linear structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
TTNL302 infinite Mur subjected to a constant flow with variable properties
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.22.302-A Page:
6/14
5 Modeling
B
5.1
Characteristics of modeling
3D (HEXA20)
Z
y
Nodes
H
Nodes
N121
0.1 m 0.1 m
N126
G
N1
D
C
N8
E
X
F
With
B
1 m
Limiting conditions:
Nodes
X
y
Z
- faces ABCD, ABFE = 0
N1
0.0
0.0
0.05
- faces EFGH, DCGH
N8
0.0
0.1
- 0.05
= 0
- face BFGC
N121
1.0
0.0
- 0.05
= 0
- face AEHD
Q
N126
1.0
0.1
0.05
= 1 W/m ²
5.2
Characteristics of the grid
A number of nodes:
248
A number of meshs and types: 20 HEXA20
5.3 Functionalities
tested
Commands
AFFE_MODELE
THERMIQUE
3D
TOUT
DEFI_MATERIAU
THER_NL
AFFE_CHAR_THER
FLUX_REP
THER_NON_LINE
TEMP_INIT
VALE
INCREMENT
LIST_INST
RECU_CHAMP
INST
5.4 Remarks
The discretization in step of time is as follows:
10 steps for [0. , 5.D-2] is T = 5.D-3
19 step for [5.D-2, 1.D0] is T = 5.D-2
Handbook of Validation
V4.22 booklet: Non-linear transitory thermics of the linear structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
TTNL302 infinite Mur subjected to a constant flow with variable properties
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.22.302-A Page:
7/14
6
Results of modeling B
6.1 Values
tested
Identification Reference
Aster %
difference
tolerance
Temperature (°C)
Node N1 T = 0.1s
0.330
0.330
- 0.129
1%
““T = 0.3s
0.544
0.543
- 0.149
1%
““T = 0.5s
0.682
0.681
- 0.154
1%
““T = 0.7s
0.789
0.788
- 0.092
1%
““T = 1.0s
0.918
0.920
0.222
1%
Node N8 T = 0.1s
0.330
0.330
- 0.129
1%
““T = 0.3s
0.544
0.543
- 0.149
1%
““T = 0.5s
0.682
0.681
- 0.154
1%
““T = 0.7s
0.789
0.788
- 0.092
1%
““T = 1.0s
0.918
0.920
0.222
1%
Node N121 T = 0.1s
0.004
0.004
10.931
1%
““T = 0.3s
0.071
0.071
- 0.242
1%
““T = 0.5s
0.160
0.161
0.587
1%
““T = 0.7s
0.247
0.251
1.619
1%
““T = 1.0s
0.366
0.380
3.95
1%
Node N126 T = 0.1s
0.004
0.004
10.931
1%
““T = 0.3s
0.071
0.071
- 0.242
1%
““T = 0.5s
0.160
0.161
0.587
1%
““T = 0.7s
0.247
0.251
1.619
1%
““T = 1.0s
0.366
0.380
3.95
1%
6.2 Remarks
The relative error is to the maximum of 3.95%, except for X = 1 at the moment T = 0.1s the error is 11%.
This error was obtained for the smallest value of the temperature (T = 0.004°C). This variation
be explained by the fact that the function of error in this point is 0.025347 and that uncertainty on
calculation of the function of error is unknown.
6.3 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Obstruction memory:
8 megawords
Time CPU To use: 8.30 seconds
Handbook of Validation
V4.22 booklet: Non-linear transitory thermics of the linear structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
TTNL302 infinite Mur subjected to a constant flow with variable properties
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.22.302-A Page:
8/14
7 Modeling
C
7.1
Characteristics of modeling
3D (TETRA4)
X
G
C
Longitudinal axis X following the trisecting one (X=Y=Z)
Limiting conditions:
B
- faces ABCD, ABFE
= 0
0.2 m
- faces EFGH, DCGH
= 0
- face BFGC
= 0
Z
- face AEHD
Q = 1 W/m ²
0.2 m
Z
Z
Y
X = 1.
N1
N6
N8
N103
N106
D
H
N105
N3
N4
N9
N108
N2
N5
N7
N104
N107
X
Y X
Y
H
D
With
E
X
Section X = 0.
Section X = 1.
E
With
7.2
Characteristics of the grid
A number of nodes:
224
A number of meshs and types: 692 TETRA4 (and 8 TRIA3)
7.3 Functionalities
tested
Commands
AFFE_MODELE
AFFE
THERMIQUE
3D
DEFI_MATERIAU
THER_NL
AFFE_CHAR_THER
FLUX_REP
THER_NON_LINE
TEMP_INIT
VALE
INCREMENT
LIST_INST
RECU_CHAMP
INST
7.4 Remarks
The discretization in step of time is as follows:
10 steps for [0. , 5.D-2] is T = 5.D-3
19 step for [5.D-2, 1.D0] is T = 5.D-2
Handbook of Validation
V4.22 booklet: Non-linear transitory thermics of the linear structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
TTNL302 infinite Mur subjected to a constant flow with variable properties
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.22.302-A Page:
9/14
8
Results of modeling C
8.1 Values
tested
Identification Reference
Aster
Relative variation (%)
Absolute deviation (°C)
difference
tolerance
difference
tolerance
Temperatures in °C:
Face
X = 0.m
N7 node
T = 0.1s
0.330
0.3295
- 0.162%
1.%
- 0.000536
0.005
““
T = 0.3s
0.544
0.5425
- 0.273%
1.%
- 0.00149
0.005
““
T = 0.5s
0.682
0.6796
- 0.351%
1.%
- 0.00239
0.005
““
T = 0.7s
0.789
0.7861
- 0.362%
1.%
- 0.00285
0.005
““
T = 1.0s
0.918
0.9165
- 0.159%
1.%
- 0.00146
0.005
N5 node
T = 0.1s
0.330
0.3279
- 0.627%
1.%
- 0.00207
0.005
““
T = 0.3s
0.544
0.5418
- 0.406%
1.%
- 0.00221
0.005
““
T = 0.5s
0.682
0.6791
- 0.422%
1.%
- 0.00288
0.005
““
T = 0.7s
0.789
0.7858
- 0.409%
1.%
- 0.00323
0.005
““
T = 1.0s
0.918
0.9162
- 0.192%
1.%
- 0.00176
0.005
Section
X = 1.m
Node N107 T = 0.1s
0.00394
0.004140
5.085%
1.% 0.000200 0.005
““
T = 0.3s
0.0706
0.07013
- 0.665%
1.%
- 0.000470
0.005
““
T = 0.5s
0.160
0.1596
- 0.228%
1.%
- 0.000364
0.005
““
T = 0.7s
0.247
0.2488
0.730%
1.%
0.00180
0.005
““
T = 1.0s
0.366
0.3766
2.889%
1.%
0.0106
0.005
Node N108 T = 0.1s
0.00394
0.004002
1.577%
1.%
- 0.0000621
0.005
““
T = 0.3s
0.0706
0.06937
- 1.742%
1.%
- 0.00123
0.005
““
T = 0.5s
0.160
0.1586
- 0.895%
1.%
- 0.00143
0.005
““
T = 0.7s
0.247
0.2476
0.238%
1.%
0.000587
0.005
““
T = 1.0s
0.366
0.3753
2.534%
1.%
0.00928
0.005
8.2 Remarks
The selected nodes correspond to the extreme results on the same section.
8.3 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Obstruction memory:
8 megawords
Time CPU To use: 13.08 seconds
Handbook of Validation
V4.22 booklet: Non-linear transitory thermics of the linear structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
TTNL302 infinite Mur subjected to a constant flow with variable properties
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.22.302-A Page:
10/14
9 Modeling
D
9.1
Characteristics of modeling
3D (TETRA10)
Z
Longitudinal axis X following the trisecting one (X=Y=Z)
N4
N7
N12 N16 N25
Limiting conditions:
X
D
H
G
C
N1
N9
N15 N17 N23
- faces ABCD, ABFE
= 0
N2
N10 N13 N20 N22
- faces EFGH, DCGH
= 0
- face BFGC
B
= 0
N3
N6
N14 N18 N21
- face AEHD
Q = 1 W/m ²
X
N5
N8
N11 N19 N24
Y
With
E
Z
0.2 m
Section X = 0.
Z
N601
N605
N611
Y
0.2 m
N602
X = 1.
N603
N599
N606
N610
N607
N608
H
D
X
X
Y
N600
N604
N609
Section X = 1
E
With
9.2
Characteristics of the grid
A number of nodes:
1310
A number of meshs and types: 697 TETRA10 (and 8 TRIA6)
9.3 Functionalities
tested
Commands
AFFE_MODELE
AFFE
THERMIQUE
3D
DEFI_MATERIAU
THER_NL
AFFE_CHAR_THER
FLUX_REP
THER_NON_LINE
TEMP_INIT
VALE
INCREMENT
LIST_INST
RECU_CHAMP
INST
9.4 Remarks
The discretization in step of time is as follows:
10 steps for [0. , 5.D-2] is T = 5.D-3
19 step for [5.D-2, 1.D0] is T = 5.D-2
Handbook of Validation
V4.22 booklet: Non-linear transitory thermics of the linear structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
TTNL302 infinite Mur subjected to a constant flow with variable properties
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.22.302-A Page:
11/14
10 Results of modeling D
10.1 Values
tested
Identification Reference
Aster
Relative variation (%)
Absolute deviation (°C)
difference
tolerance
difference
tolerance
Temperatures in °C:
Face
X = 0.m
N4 node
T = 0.1s
0.330
0.3291
- 0.281%
1.%
- 0.000926
0.005
““
T = 0.3s
0.544
0.5423
- 0.318%
1.%
- 0.00173
0.005
““
T = 0.5s
0.682
0.6794
- 0.383%
1.%
- 0.00261
0.005
““
T = 0.7s
0.789
0.7860
- 0.384%
1.%
- 0.00303
0.005
““
T = 1.0s
0.918
0.9164
- 0.180%
1.%
- 0.00165
0.005
N25 node
T = 0.1s
0.330
0.3292
- 0.255%
1.%
- 0.000843
0.005
““
T = 0.3s
0.544
0.5423
- 0.314%
1.%
- 0.00171
0.005
““
T = 0.5s
0.682
0.6794
- 0.382%
1.%
- 0.00261
0.005
““
T = 0.7s
0.789
0.7860
- 0.383%
1.%
- 0.00303
0.005
““
T = 1.0s
0.918
0.9163
- 0.180%
1.%
- 0.00165
0.005
Section
X = 1.m
Node N606 T = 0.1s
0.00394
0.004331
9.913%
1.% 0.000391 0.005
““
T = 0.3s
0.0706
0.07021
- 0.551%
1.%
- 0.000389
0.005
““
T = 0.5s
0.160
0.1596
- 0.251%
1.%
- 0.000402
0.005
““
T = 0.7s
0.247
0.2488
0.710%
1.%
0.00175
0.005
““
T = 1.0s
0.366
0.3764
2.855%
1.%
0.0104
0.005
Node N611 T = 0.1s
0.00394
0.004332
9.944%
1.% 0.000392 0.005
““
T = 0.3s
0.0706
0.07021
- 0.550%
1.%
- 0.000388
0.005
““
T = 0.5s
0.160
0.1596
- 0.251%
1.%
- 0.000402
0.005
““
T = 0.7s
0.247
0.2488
0.710%
1.%
0.00175
0.005
““
T = 1.0s
0.366
0.3764
2.855%
1.%
0.0104
0.005
10.2 Remarks
The calculated results are almost identical on the nodes of the same section.
10.3 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Obstruction memory:
8 megawords
Time CPU To use: 25.88 seconds
Handbook of Validation
V4.22 booklet: Non-linear transitory thermics of the linear structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
TTNL302 infinite Mur subjected to a constant flow with variable properties
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.22.302-A Page:
12/14
11 Modeling
E
11.1 Characteristics of modeling
3D (HEXA27)
Longitudinal axis X following the trisecting one (X=Y=Z)
X
G C
Limiting conditions:
B
- faces ABCD, ABFE
= 0
- faces EFGH, DCGH
= 0
0.1 m
- face BFGC
= 0
- face AEHD
Q = 1 W/m ²
Z
0.1 m
Z
Z
X = 1.
Y
N3
N85
N2
N43 N165 N42
D
H
N86 N249 N88
N166 N308 N168
N4
N87
N1
N44 N167 N41
X
Y X
Y
With
E
H
D
X
Section X = 0.
Section X = 1.
E
With
11.2 Characteristics of the grid
A number of nodes:
369
A number of meshs and types: 20 HEXA27 (and 1 QUAD9)
11.3 Functionalities
tested
Commands
AFFE_MODELE
AFFE
THERMIQUE
3D
DEFI_MATERIAU
THER_NL
AFFE_CHAR_THER
FLUX_REP
THER_NON_LINE
TEMP_INIT
VALE
INCREMENT
LIST_INST
RECU_CHAMP
INST
11.4 Remarks
The discretization in step of time is as follows:
10 steps for [0. , 5.D-2] is T = 5.D-3
19 step for [5.D-2, 1.D0] is T = 5.D-2
Handbook of Validation
V4.22 booklet: Non-linear transitory thermics of the linear structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
TTNL302 infinite Mur subjected to a constant flow with variable properties
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.22.302-A Page:
13/14
12 Results of modeling E
12.1 Values
tested
Identification Reference
Aster
Relative variation (%)
Absolute deviation (°C)
difference
tolerance
difference
tolerance
Temperatures in °C:
Face
X = 0.m
Node N249 T = 0.1s
0.330
0.3291
- 0.283%
1.%
- 0.000933
0.005
““
T = 0.3s
0.544
0.5423
- 0.317%
1.%
- 0.00173
0.005
““
T = 0.5s
0.682
0.6794
- 0.376%
1.%
- 0.00256
0.005
““
T = 0.7s
0.789
0.7860
- 0.378%
1.%
- 0.00298
0.005
““
T = 1.0s
0.918
0.9165
- 0.168%
1.%
- 0.00154
0.005
Section
X = 1.m
Node N308 T = 0.1s
0.00394
0.004331
9.926%
1.% 0.000391
0.005
““
T = 0.3s
0.0706
0.07021
- 0.554%
1.%
- 0.000391
0.005
““
T = 0.5s
0.160
0.1596
- 0.227%
1.%
- 0.000363
0.005
““
T = 0.7s
0.247
0.2488
0.726%
1.%
0.00179
0.005
““
T = 1.0s
0.366
0.3766
2.886%
1.%
0.0106
0.005
12.2 Remarks
The calculated results are identical (except for 107) on the nodes of the same section.
12.3 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Obstruction memory:
8 megawords
Time CPU To use: 9.68 seconds
Handbook of Validation
V4.22 booklet: Non-linear transitory thermics of the linear structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
TTNL302 infinite Mur subjected to a constant flow with variable properties
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.22.302-A Page:
14/14
13 Summary of the results
Five modelings carried out, have same cutting in the direction of propagation of
temperature, they are different only by their type of meshs.
Five modelings give results whose certain values exceed the fixed tolerance
initially (1%). The maximum change is 9.9%. It appears for the smallest value of reference
located in the middle of the wall and at the beginning of the transient.
A grid finer associate with a finer temporal discretization should improve quality of
results.
Moreover, the reference solution utilizes a function of error whose precision is unknown.
The results are regarded as acceptable taking into account the points evoked above.
This test made it possible to test hexahedral and tetrahedral meshs in non-linear thermics
transient as well as the principal following thermal commands:
· DEFI_MATERIAU associated with key word THER_NL, allowing to define the characteristics of one
material whose characteristics vary according to the temperature (conductivity and
enthalpy),
· THER_NON_LINE orders allowing the resolution of a thermal nonlinear problem
stationary or not.
Handbook of Validation
V4.22 booklet: Non-linear transitory thermics of the linear structures
HT-66/02/001/A
Outline document