Code_Aster
®
Version
5.0
Titrate:
TTNL303 infinite Wall subjected to a jump of temperature
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.22.303-A
Page:
1/12
Manual of Validation
V4.22 booklet: Non-linear transitory thermics of the linear structures
HT-66/02/001/A
Organization (S):
EDF/AMA, EDF/UTO/LOCATED, Delta CAD
Manual of Validation
V4.22 booklet: Non-linear transitory thermics of the linear structures
V4.22.303 document
TTNL303 - Infinite wall subjected to a jump of
temperature 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 four modelings, two plane and two voluminal.
The functionalities tested are as follows:
·
plane thermal element,
·
voluminal thermal element,
·
variable thermal conductivity,
·
non-linear transitory thermal algorithm,
·
limiting conditions: temperature imposed with jump.
The interest of the test lies in the taking into account of variable properties in transitory analysis and the variation
temperatures imposed according to time.
Code_Aster
®
Version
5.0
Titrate:
TTNL303 infinite Wall subjected to a jump of temperature
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.22.303-A
Page:
2/12
Manual of Validation
V4.22 booklet: Non-linear transitory thermics of the linear structures
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
L = 0.2m
C
D
B
With
y
X
T (S)
T
AD
(°C)
200°
100°
10
T (S)
T
BC
(°C)
200°
100°
10
T (°C)
(W/m/°C)
200
100°
400
200°
1.2
Properties of material
= 200 + T (W/m °C)
thermal conductivity
C =
8 X 10
6
(J/m
3
°C)
voluminal heat
1.3
Boundary conditions and loadings
X = 0 | T = 200°C 0 < T
10 S
| T = 100°C T > 10 S
X = L
T = 100°C T
0 S
1.4 Conditions
initial
T (X, 0) = 100°C for any X
Code_Aster
®
Version
5.0
Titrate:
TTNL303 infinite Wall subjected to a jump of temperature
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.22.303-A
Page:
3/12
Manual of Validation
V4.22 booklet: Non-linear transitory thermics of the linear structures
HT-66/02/001/A
2
Reference solution
2.1
Method of calculation used for the reference solution
The reference solution was obtained with the computation software by finite elements “IVOHEAT” [bib2]
quoted in the reference [bib1]. This solution is based on network made up of 20 elements
isoparametric with 4 nodes of identical size, by using a method of Crank-Nicolson modified
with an accuracy of 10
- 6
.
2.2
Results of reference
Temperature with:
·
T = 10 S for x= 0.01, 0.02, 0.04, 0.06, 0.08 and 0.1,
·
T = 13 S for x= 0.01, 0.02, 0.04, 0.06, 0.08 and 0.1.
2.3 References
bibliographical
[1]
S. Orivuori, “Efficient method for solution off nonlinear heat conduction problems”, Int. J. num.
Meth. Engng, flight 14, n°10, p 1461-1476, 1979
[2]
S. Orivuori, “A finite element method applied to the solution off the transient heat conduction
problem', Licentiate Thesis, Tech. Univ., Helsinki (1977), in Finish.
Code_Aster
®
Version
5.0
Titrate:
TTNL303 infinite Wall subjected to a jump of temperature
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.22.303-A
Page:
4/12
Manual of Validation
V4.22 booklet: Non-linear transitory thermics of the linear structures
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
PLAN (TRIA6)
y
X
0.02m
With
0.2 m
D
B
Nodes
X
y
N11
0.01
0.00
N21
0.02
0.00
N41
0.04
0.00
N61
0.06
0.00
N81
0.08
0.00
N101
0.10
0.00
C
Limiting conditions:
- dimensioned AB, CD
= 0
- dimensioned AD
| T = 200°C 0 < T
10 S
| T = 100°C T > 10 S
- dimensioned BC
T = 100°C
T
0 S
3.2
Characteristics of the mesh
A number of nodes:
205
A number of meshs and types: 80 TRIA6
3.3 Functionalities
tested
Controls
AFFE_MODELE
THERMICS
PLAN
ALL
DEFI_MATERIAU
THER_NL
AFFE_CHAR_THER_F
TEMP_IMPO
THER_NON_LINE
TEMP_INIT
VALE
INCREMENT
LIST_INST
RECU_CHAMP
INST
3.4 Remarks
The discretization in pitch of time is as follows:
10 pitches for [0. , 1.D-3] is
T = 1.D-4
9 pitches for [1.D-3, 1.D-2] are
T = 1.D-3
9 pitches for [1.D-2, 1.D-1] are
T = 1.D-2
9 pitches for [1.D-1, 1.D0] are
T = 1.D-1
9 pitches for [1.D0, 10.D0] are
T = 1.D0
3 pitches for [10.D0, 13.D0] are
T = 1.D0
Code_Aster
®
Version
5.0
Titrate:
TTNL303 infinite Wall subjected to a jump of temperature
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.22.303-A
Page:
5/12
Manual of Validation
V4.22 booklet: Non-linear transitory thermics of the linear structures
HT-66/02/001/A
4
Results of modeling A
4.1 Values
tested
Identification Reference
Aster %
difference
tolerance
Temperature (°C) with t=10 S
N11 176.165
174.954
-
0.687
2%
N21 153.213
151.049
-
1.412
2%
N41 118.600
116.576
-
1.707
2%
N61 103.715
103.195
-
0.502
2%
N81 100.368
100.417
0.049
2%
N101 100.014
100.088
0.074
2%
Temperature (°C) with t=13 S
N11 128.125
128.377
0.197
2%
N21 139.970
139.846
-
0.089
2%
N41 124.719
122.209
-
2.013
2%
N61 107.182
106.279
-
0.842
2%
N81 101.290
101.186
-
0.103
2%
N101 100.134
100.203
0.067
2%
4.2 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
8 megawords
Time CPU To use: 10.26 seconds
Code_Aster
®
Version
5.0
Titrate:
TTNL303 infinite Wall subjected to a jump of temperature
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.22.303-A
Page:
6/12
Manual of Validation
V4.22 booklet: Non-linear transitory thermics of the linear structures
HT-66/02/001/A
5 Modeling
B
5.1
Characteristics of modeling
3D (PENTA6)
Z
y
X
Limiting conditions:
- face X = 0.0
| T = 200°C 0 < T
10 S
| T = 100°C T > 10 S
- face X = 0.2
T = 100°C
T
0 S
- others faces
= 0
0.02m
0.02m
N55
N10
N37
N19
N91
N73
N63
N17
N45
N26
N98
N81
0.2 m
5.2
Characteristics of the mesh
A number of nodes:
189
A number of meshs and types: 160 PENTA6
5.3 Functionalities
tested
Controls
AFFE_MODELE
THERMICS
3D
ALL
DEFI_MATERIAU
THER_NL
AFFE_CHAR_THER_F
TEMP_IMPO
THER_NON_LINE
TEMP_INIT
VALE
INCREMENT
LIST_INST
RECU_CHAMP
INST
5.4 Remarks
The discretization in pitch of time is as follows:
10 pitches for [0. , 1.D-3] is
T = 1.D-4
9 pitches for [1.D-3, 1.D-2] are
T = 1.D-3
9 pitches for [1.D-2, 1.D-1] are
T = 1.D-2
9 pitches for [1.D-1, 1.D0] are
T = 1.D-1
9 pitches for [1.D0, 10.D0] are
T = 1.D0
3 pitches for [10.D0, 13.D0] are
T = 1.D0
Code_Aster
®
Version
5.0
Titrate:
TTNL303 infinite Wall subjected to a jump of temperature
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.22.303-A
Page:
7/12
Manual of Validation
V4.22 booklet: Non-linear transitory thermics of the linear structures
HT-66/02/001/A
6
Results of modeling B
6.1 Values
tested
Identification Reference
Aster %
difference
tolerance
Temperature (°C) with t=10 S
N10 176.165
175.087
-
0.612
2%
N17 176.165
174.910
-
0.713
2%
N19 153.213
151.182
-
1.326
2%
N26 153.213
151.020
-
1.431
2%
N37 118.600
116.314
-
1.928
2%
N45 118.600
116.379
-
1.872
2%
N55 103.715
102.759
-
0.921
2%
N63 103.715
102.892
-
0.793
2%
N73 100.368
100.239
-
0.129
2%
N81 100.368
100.285
-
0.083
2%
N91 100.014
100.060
0.046
2%
N98 100.014
100.066
0.052
2%
Temperature (°C) with t=13 S
N10 128.125
129.395
0.991
2%
N17 128.125
128.291
0.130
2%
N19 139.970
139.819
-
0.108
2%
N26 139.970
140.209
0.171
2%
N37 124.719
122.986
-
1.390
2%
N45 124.719
122.569
-
1.724
2%
N55 107.182
105.967
-
1.134
2%
N63 107.182
106.050
-
1.056
2%
N73 101.290
100.945
-
0.341
2%
N81 101.290
101.005
-
0.282
2%
N91 100.134
100.126
-
0.008
2%
N98 100.134
100.142
0.008
2%
6.2 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
8 megawords
Time CPU To use: 11.30 seconds
Code_Aster
®
Version
5.0
Titrate:
TTNL303 infinite Wall subjected to a jump of temperature
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.22.303-A
Page:
8/12
Manual of Validation
V4.22 booklet: Non-linear transitory thermics of the linear structures
HT-66/02/001/A
7 Modeling
C
7.1
Characteristics of modeling
3D (HEXA8)
0.03
X
Y
0.05
=40°
Z
Y
Z
X
Y
X
origin of axis X
N80 N112
N160 N224
N288
N352
N17
N36 N122
N193 N257
N321
Limiting conditions:
- face x=0 | T = 200°C 0 < T
10 S
| T = 100°C T > 10 S
- face x=0.2 T = 100°C T
0 S
- others faces
= 0
Nodes
X
N80, N17
0.01
N112, N36
0.02
N160, N122 0.04
N224, N193 0.06
N288, N257 0.08
N352, N321 0.10
Sight plan X0Y
Sight plan YOZ
O
O
0.02
0.02
7.2
Characteristics of the mesh
A number of nodes:
588
A number of meshs and types: 360 HEXA8
7.3 Functionalities
tested
Controls
AFFE_MODELE
THERMICS
3D
ALL
DEFI_MATERIAU
THER_NL
AFFE_CHAR_THER_F
TEMP_IMPO
THER_NON_LINE
TEMP_INIT
VALE
INCREMENT
LIST_INST
RECU_CHAMP
INST
7.4 Remarks
The discretization in pitch of time is as follows:
10 pitches for [0. , 1.D-3] is
T = 1.D-4
9 pitches for [1.D-3, 1.D-2] are
T = 1.D-3
9 pitches for [1.D-2, 1.D-1] are
T = 1.D-2
9 pitches for [1.D-1, 1.D0] are
T = 1.D-1
9 pitches for [1.D0, 10.D0] are
T = 1.D0
3 pitches for [10.D0, 13.D0] are
T = 1.D0
Code_Aster
®
Version
5.0
Titrate:
TTNL303 infinite Wall subjected to a jump of temperature
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.22.303-A
Page:
9/12
Manual of Validation
V4.22 booklet: Non-linear transitory thermics of the linear structures
HT-66/02/001/A
8
Results of modeling C
8.1 Values
tested
Relative variation %
Absolute deviation
Identification Reference Aster difference
tolerance difference tolerance
Temperature (°C)
T = 10 S
N80 176.165
174.992
-
0.666
2%
-
1.17
3.0
N17 176.165
174.992
-
0.666
2%
-
1.17
3.0
N112 153.213
151.092
-
1.384
2%
-
2.12
3.0
N36 153.213
151.092
-
1.384
2%
-
2.12
3.0
N160 118.600
116.331
-
1.913
2%
-
2.27
3.0
N122 118.600
116.331
-
1.913
2%
-
2.27
3.0
N224 103.715
102.817
-
0.866
2%
-
0.898
3.0
N193 103.715
102.817
-
0.866
2%
-
0.898
3.0
N288 100.368
100.265
-
0.102
2%
-
0.103
3.0
N257 100.368
100.265
-
0.102
2%
-
0.103
3.0
N352 100.014
100.066
0.052
2%
0.052
3.0
N321 100.014
100.066
0.052
2%
0.052
3.0
T = 13 S
N80 128.125
128.829
0.550
2%
0.704
3.0
N17 128.125
128.829
0.550
2%
0.704
3.0
N112 139.970
139.893
-
0.055
2%
-
0.077
3.0
N36 139.970
139.893
-
0.055
2%
-
0.077
3.0
N160 124.719
122.718
-
1.605
2%
-
2.00
3.0
N122 124.719
122.718
-
1.605
2%
-
2.00
3.0
N224 107.182
105.988
-
1.114
2%
-
1.19
3.0
N193 107.182
105.988
-
1.114
2%
-
1.19
3.0
N288 101.290
100.974
-
0.312
2%
-
0.316
3.0
N257 101.290
100.974
-
0.312
2%
-
0.316
3.0
N352 100.134
100.136
0.002
2%
0.002
3.0
N321 100.134
100.136
0.002
2%
0.002
3.0
8.2 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
8 megawords
Time CPU To use: 16.56 seconds
Code_Aster
®
Version
5.0
Titrate:
TTNL303 infinite Wall subjected to a jump of temperature
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.22.303-A
Page:
10/12
Manual of Validation
V4.22 booklet: Non-linear transitory thermics of the linear structures
HT-66/02/001/A
9 Modeling
D
9.1
Characteristics of modeling
PLAN (TRIA3, QUAD4)
Y
X
0.1
=50°
N12 N19
N33
N47
N61
N75
C
B
D
With
0.06
Limiting conditions:
- dimensioned AB, CD
= 0
- dimensioned AD | T = 200°C 0 < T
10 S
| T = 100°C T > 10 S
- dimensioned BC T = 100°C T
0 S
Nodes
X
y
N8
0.01
0.00
N15
0.02
0.00
N29
0.04
0.00
N43
0.06
0.00
N57
0.08
0.00
N71
0.10
0.00
X
y
N8 N15
N29
N43
N57
N71
9.2
Characteristics of the mesh
A number of nodes:
147
A number of meshs and types: 200 (40 QUAD4, 160 TRIA3)
9.3 Functionalities
tested
Controls
AFFE_MODELE
THERMICS
PLAN
ALL
DEFI_MATERIAU
THER_NL
AFFE_CHAR_THER_F
TEMP_IMPO
THER_NON_LINE
TEMP_INIT
VALE
INCREMENT
LIST_INST
RECU_CHAMP
INST
9.4 Remarks
The discretization in pitch of time is as follows:
10 pitches for [0. , 1.D-3] is
T = 1.D-4
9 pitches for [1.D-3, 1.D-2] are
T = 1.D-3
9 pitches for [1.D-2, 1.D-1] are
T = 1.D-2
9 pitches for [1.D-1, 1.D0] are
T = 1.D-1
9 pitches for [1.D0, 10.D0] are
T = 1.D0
3 pitches for [10.D0, 13.D0] are
T = 1.D0
Code_Aster
®
Version
5.0
Titrate:
TTNL303 infinite Wall subjected to a jump of temperature
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.22.303-A
Page:
11/12
Manual of Validation
V4.22 booklet: Non-linear transitory thermics of the linear structures
HT-66/02/001/A
10 Results of modeling D
10.1 Values
tested
Relative variation %
Absolute deviation
Identification Reference Aster difference
tolerance difference tolerance
Temperature (°C)
T = 10 S
N8 176.165
174.997
-
0.663
2%
-
1.17
3.0
N12 176.165
175.154
-
0.574
2%
-
1.01
3.0
N15 153.213
151.117
-
1.368
2%
-
2.10
3.0
N19 153.213
151.246
-
1.284
2%
-
1.97
3.0
N29 118.600
116.416
-
1.842
2%
-
2.18
3.0
N33 118.600
116.246
-
1.985
2%
-
2.35
3.0
N43 103.715
102.884
-
0.801
2%
-
0.831
3.0
N47 103.715
102.664
-
1.014
2%
-
1.05
3.0
N57 100.368
100.283
-
0.084
2%
-
0.085
3.0
N61 100.368
100.208
-
0.159
2%
-
0.160
3.0
N71 100.014
100.067
0.053
2%
0.053
3.0
N75 100.014
100.057
0.043
2%
0.044
3.0
T = 13 S
N8 128.125
128.512
0.302
2%
0.387
3.0
N12 128.125
129.103
0.764
2%
0.978
3.0
N15 139.970
139.689
-
0.201
2%
-
0.281
3.0
N19 139.970
140.233
0.188
2%
0.263
3.0
N29 124.719
122.723
-
1.601
2%
-
2.00
3.0
N33 124.719
123.198
-
1.220
2%
-
1.52
3.0
N43 107.182
106.051
-
1.055
2%
-
1.13
3.0
N47 107.182
105.887
-
1.209
2%
-
1.30
3.0
N57 101.290
101.004
-
0.282
2%
-
0.286
3.0
N61 101.290
100.902
-
0.383
2%
-
0.388
3.0
N71 100.134
100.143
0.009
2%
0.009
3.0
N75 100.134
100.116
-
0.018
2% 0.018 3.0
10.2 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
8 megawords
Time CPU To use: 11.06 seconds
Code_Aster
®
Version
5.0
Titrate:
TTNL303 infinite Wall subjected to a jump of temperature
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.22.303-A
Page:
12/12
Manual of Validation
V4.22 booklet: Non-linear transitory thermics of the linear structures
HT-66/02/001/A
11 Summary of the results
A modeling among four modelings carried out give results of which a value
exceed little the tolerance fixed initially (2%). The maximum change is of:
·
2.013% for modeling PLAN (TRIA6),
·
1.928% for modeling 3D (PENTA6),
·
1.913% for modeling 3D (HEXA8),
·
1.985% for modeling PLAN (TRIA3, QUAD4).
It is noted that this variation is whatever the modeling close to 2%, all modelings
carried out, have same cutting in the direction of propagation of the temperature.
The results obtained are regarded as acceptable for the whole of modelings
This test made it possible to test the taking into account of a variable thermal conductivity with a condition
limit varying in the course of time.