Code_Aster
®
Version
5.0
Titrate:
TPNA300 Tubes generating heat with variable conductivity
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.41.300-A
Page:
1/12
Manual of Validation
V4.41 booklet: Nonlinear stationary thermics of axisymmetric structures HT-66/02/001/A
Organization (S):
EDF/AMA, EDF/UTO/LOCATED, Delta CAD
Manual of Validation
V4.41 booklet: Nonlinear stationary thermics of the axisymmetric structures
V4.41.300 document
TPNA300 - Tube generating heat with
variable conductivity
Summary:
This test results from the validation independent of version 3 in nonlinear stationary thermics.
It is about an axisymmetric problem 2D represented by four modelings, two axisymmetric, plane
and the voluminal last.
The functionalities tested are as follows:
·
axisymmetric thermal element,
·
plane thermal element,
·
voluminal thermal element,
·
variable properties,
·
limiting conditions (imposed temperature, heat source).
The interest of the test lies in the taking into account of variable properties and the nonlinear behavior.
Code_Aster
®
Version
5.0
Titrate:
TPNA300 Tubes generating heat with variable conductivity
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.41.300-A
Page:
2/12
Manual of Validation
V4.41 booklet: Nonlinear stationary thermics of axisymmetric structures HT-66/02/001/A
1
Problem of reference
1.1 Geometry
R
I
X
Y
T
E
T
I
R
O
(T)
Q
…
With
B
T (°C)
(W/m/°C)
40
20
50
100
0
R
I
= 6.35 X 10
- 3
m
R
E
= 25.4 X 10
- 3
m
1.2
Properties of material
= C
O
+C
1
T W/m°C
Thermal conductivity
with C
O
= 21.461 W/m °C
C
1
= 0.234 W/m °C ²
1.3
Boundary conditions and loadings
·
surface interior:
T
I
= - 17.78 °C,
·
surface external: T
E
= - 17.78 °C,
·
heat source: Q = 1.035 x10
7
W/m
3
.
1.4 Conditions
initial
Without object.
Code_Aster
®
Version
5.0
Titrate:
TPNA300 Tubes generating heat with variable conductivity
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.41.300-A
Page:
3/12
Manual of Validation
V4.41 booklet: Nonlinear stationary thermics of axisymmetric structures HT-66/02/001/A
2
Reference solution
2.1
Method of calculation used for the reference solution
The original reference solution given in the book [bib1] is based on a graphic estimate.
This reference is quoted in the manual of checking of ANSYS [bib2].
2.2
Results of reference
Temperature along AB with
R = 2.167 mm
2.3
Uncertainty on the solution
Unknown factor, it was not possible to get the original reference (delivers old, more published).
2.4 References
bibliographical
[1]
Schneider, P.J., “Conduction Heat Transfer”, Addison-Wesley Publishing Co., Inc. Reading,
Farmhouse., 2nd Printing, 1957.
[2]
ANSYS, “checking manual”, 1st edition, June 1, 1976
Code_Aster
®
Version
5.0
Titrate:
TPNA300 Tubes generating heat with variable conductivity
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.41.300-A
Page:
4/12
Manual of Validation
V4.41 booklet: Nonlinear stationary thermics of axisymmetric structures HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
AXIS (QUAD4, TRIA3)
WITH E F G H I J K L B
X (R)
y (Z)
D C
0.003
Boundary conditions:
- dimensioned AB, CD:
= 0
- dimensioned AD, BC: T=-17.78°C
Node
R
(10
- 3
m)
Z
(10
- 3
m) Points
Node
R
(10
- 3
m)
Z
(10
- 3
m)
N4
8.47
0.0
E
N6
8.47
3.0
N7
10.58
0.0
F
N9
10.58
3.0
N10
12.70
0.0
G
N12
12.70
3.0
N13
14.82
0.0
H
N15
14.82
3.0
N16
16.92
0.0
I
N18
16.92
3.0
N19
19.05
0.0
J
N21
19.05
3.0
N22
21.17
0.0
K
N24
21.17
3.0
N25
23.28
0.0
L
N27
23.28
3.0
3.2
Characteristics of the mesh
A number of nodes:
30
A number of meshs and types: 27: (9 QUAD4, 18 TRIA3)
3.3 Functionalities
tested
Controls
AFFE_MODELE
THERMICS
AXIS
ALL
DEFI_MATERIAU
THER_NL
AFFE_CHAR_THER
TEMP_IMPO
SOURCE
THER_NON_LINE
TEMP_INIT
STATIONARY
“YES”
EXCIT
CHARGE
RECU_CHAMP
INST
0.
Code_Aster
®
Version
5.0
Titrate:
TPNA300 Tubes generating heat with variable conductivity
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.41.300-A
Page:
5/12
Manual of Validation
V4.41 booklet: Nonlinear stationary thermics of axisymmetric structures HT-66/02/001/A
4
Results of modeling A
4.1 Values
tested
Identification Reference
Aster %
difference
tolerance
Temperature (°C)
N4
-
5.00
-
4.92
-
1.70
5%
N7 2.22
2.06
-
7.35
5%
N10 5.56
5.57
0.10
5%
N13 6.67
6.60
-
1.07
5%
N16 5.56
5.60
0.76
5%
N19 2.78
2.76
-
0.71
5%
N22
-
1.67
-
1.93
15.30
5%
N25
-
8.89
-
8.63
-
2.90
5%
N6
-
5.00
-
4.96
-
0.87
5%
N9 2.22
2.04
-
8.18
5%
N12 5.56
5.56
0.04
5%
N15 6.67
6.60
-
1.02
5%
N18 5.56
5.61
0.91
5%
N21 2.78
2.77
-
0.26
5%
N24
-
1.67
-
1.91
14.24
5%
N27
-
8.89
-
8.61
-
3.17
5%
4.2 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
8 megawords
Time CPU To use: 2.24 seconds
Code_Aster
®
Version
5.0
Titrate:
TPNA300 Tubes generating heat with variable conductivity
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.41.300-A
Page:
6/12
Manual of Validation
V4.41 booklet: Nonlinear stationary thermics of axisymmetric structures HT-66/02/001/A
5 Modeling
B
5.1
Characteristics of modeling
PLAN (QUAD8, TRIA6)
X
y
Boundary conditions:
- dimensioned AB, CD:
= 0
- dimensioned AD, BC: T=-17.78°C
D
30°
C
IN N60 N46 N33 N21 N13 N7 N2 N5 B
N134
N214
N184
N160
N245
N294
N285
N268
N103 N117
N149 N121N168
N181
N211 N204
5.2
Characteristics of the mesh
A number of nodes:
300
A number of meshs and types: 95 (73 QUAD8, 22 TRIA6)
5.3 Functionalities
tested
Controls
AFFE_MODELE
THERMICS
PLAN
ALL
DEFI_MATERIAU
THER_NL
AFFE_CHAR_THER
TEMP_IMPO
SOURCE
THER_NON_LINE
TEMP_INIT
STATIONARY
“YES”
EXCIT
CHARGE
RECU_CHAMP
INST
0.
Code_Aster
®
Version
5.0
Titrate:
TPNA300 Tubes generating heat with variable conductivity
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.41.300-A
Page:
7/12
Manual of Validation
V4.41 booklet: Nonlinear stationary thermics of axisymmetric structures HT-66/02/001/A
6
Results of modeling B
6.1 Values
tested
Identification Reference
Aster %
difference
tolerance
Temperature (°C)
N60
-
5.00
-
4.84
-
3.194
5%
N46 2.22
2.14
-
3.491
5%
N33 5.56
5.65
1.544
5%
N21 6.67
6.66
-
0.082
5%
N13 5.56
5.65
1.694
5%
N7 2.78
2.80
0.665
5%
N2
-
1.67
-
1.90
13.788
5%
N5
-
8.89
-
8.62
-
3.089
5%
N134
-
5.00
-
4.84
-
3.194
5%
N160 2.22
2.14
-
3.491
5%
N184 5.56
5.65
1.543
5%
N214 6.67
6.66
-
0.082
5%
N245 5.56
5.65
1.694
5%
N268 2.78
2.80
0.665
5%
N285
-
1.67
-
1.90
13.737
5%
N294
-
8.89
-
8.62
-
3.089
5%
N103
-
5.00
-
4.84
-
3.141
5%
N117 2.22
2.15
-
3.365
5%
N149 5.56
5.65
1.557
5%
N121 6.67
6.66
-
0.078
5%
N168 5.56
5.65
1.694
5%
N181 2.78
2.80
0.650
5%
N211
-
1.67
-
1.90
13.777
5%
N204
-
8.89
-
8.62
-
3.075
5%
6.2 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
8 megawords
Time CPU To use: 2.83 seconds
Code_Aster
®
Version
5.0
Titrate:
TPNA300 Tubes generating heat with variable conductivity
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.41.300-A
Page:
8/12
Manual of Validation
V4.41 booklet: Nonlinear stationary thermics of axisymmetric structures HT-66/02/001/A
7 Modeling
C
7.1
Characteristics of modeling
3D (HEXA8, PENTA6)
X
y
Z
.001
30°
Boundary conditions:
- internal and external face
T=-17.78°C
- others
= 0
N14
N30
N51
N68
N90
N114
N134
N151
N22
N43
N67
N102
N150
N208
N251
N291
N11
N307
N3
N171
N7
N19 N37 N61 N85N124
N177
N220
N255
N266
7.2
Characteristics of the mesh
A number of nodes:
309
A number of meshs and types: 190 (144 HEXA8, 46 PENTA6)
7.3 Functionalities
tested
Controls
AFFE_MODELE
THERMICS
3D
ALL
DEFI_MATERIAU
THER_NL
AFFE_CHAR_THER
TEMP_IMPO
SOURCE
THER_NON_LINE
TEMP_INIT
STATIONARY
“YES”
EXCIT
CHARGE
RECU_CHAMP
INST
0.
Code_Aster
®
Version
5.0
Titrate:
TPNA300 Tubes generating heat with variable conductivity
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.41.300-A
Page:
9/12
Manual of Validation
V4.41 booklet: Nonlinear stationary thermics of axisymmetric structures HT-66/02/001/A
8
Results of modeling C
8.1 Values
tested
Identification Reference
Aster %
difference
tolerance
Temperature (°C)
N22
-
5.00
-
4.90
-
1.909
5%
N43 2.22
2.09
-
5.933
5%
N67 5.56
5.58
0.408
5%
N102 6.67
6.63
-
0.561
5%
N150 5.56
5.62
0.993
5%
N208 2.78
2.77
-
0.217
5%
N251
-
1.67
-
1.92
15.047
5%
N291
-
8.89
-
8.63
-
2.960
5%
N14
-
5.00
-
4.90
-
1.908
5%
N30 2.22
2.09
-
5.933
5%
N51 5.56
5.58
0.408
5%
N68 6.67
6.63
-
0.561
5%
N90 5.56
5.62
0.993
5%
N114 2.78
2.77
-
0.217
5%
N134
-
1.67
-
1.92
15.047
5%
N151
-
8.89
-
8.63
-
2.960
5%
N19
-
5.00
-
4.93
-
1.440
5%
N37 2.22
2.16
-
2.596
5%
N61 5.56
5.54
-
0.274
5%
N85 6.67
6.65
-
0.260
5%
N124 5.56
5.60
0.705
5%
N177 2.78
2.82
1.536
5%
N220
-
1.67
-
1.90
13.946
5%
N255
-
8.89
-
8.58
-
3.474
2%
8.2 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
8 megawords
Time CPU To use: 2.81 seconds
Code_Aster
®
Version
5.0
Titrate:
TPNA300 Tubes generating heat with variable conductivity
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.41.300-A
Page:
10/12
Manual of Validation
V4.41 booklet: Nonlinear stationary thermics of axisymmetric structures HT-66/02/001/A
9 Modeling
D
9.1
Characteristics of modeling
AXIS (QUAD9)
X (R)
y (Z)
Boundary conditions:
- dimensioned AB, CD:
= 0
- dimensioned AD, BC: T=-17.78°C
Node
R
(10
- 3
m)
Z
(10
- 3
m) Points
Node
R
(10
- 3
m)
Z
(10
- 3
m)
N11
8.47
2.5
E
N15
8.47
5.5
N21
10.58
2.5
F
N25
10.58
5.5
N31
12.70
2.5
G
N35
12.70
5.5
N41
14.82
2.5
H
N45
14.82
5.5
N51
16.92
2.5
I
N55
16.92
5.5
N61
19.05
2.5
J
N65
19.05
5.5
N71
21.17
2.5
K
N75
21.17
5.5
N81
23.28
2.5
L
N85
23.28
5.5
WITH E F G H I J K L B
D C
0.003
0.0025
9.2
Characteristics of the mesh
A number of nodes:
95
A number of meshs and types: 18 QUAD9
9.3 Functionalities
tested
Controls
AFFE_MODELE
THERMICS
3D
ALL
DEFI_MATERIAU
THER_NL
AFFE_CHAR_THER
TEMP_IMPO
SOURCE
THER_NON_LINE
TEMP_INIT
STATIONARY
“YES”
EXCIT
CHARGE
RECU_CHAMP
INST
0.
Code_Aster
®
Version
5.0
Titrate:
TPNA300 Tubes generating heat with variable conductivity
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.41.300-A
Page:
11/12
Manual of Validation
V4.41 booklet: Nonlinear stationary thermics of axisymmetric 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)
N11
-
5.00
-
4.83
-
3.333
5% 0.167 0.3
N21 2.22
2.15
-
3.347
5%
-
0.074
0.3
N31 5.56
5.65
1.551
5%
0.086
0.3
N41 6.67
6.66
-
0.078
5%
-
0.005
0.3
N51 5.56
5.65
1.694
5%
0.094
0.3
N61 2.78
2.80
0.663
5%
0.018
0.3
N71
-
1.67
-
1.90
13.741
5%
-
0.229
0.3
N81
-
8.89
-
8.62
-
3.088
5% 0.275 0.3
N15
-
5.00
-
4.83
-
3.333
5% 0.167 0.3
N25 2.22
2.15
-
3.347
5%
-
0.074
0.3
N35 5.56
5.65
1.551
5%
0.082
0.3
N45 6.67
6.66
-
0.078
5%
-
0.005
0.3
N55 5.56
5.65
1.694
5%
0.094
0.3
N65 2.78
2.80
0.663
5%
0.018
0.3
N75
-
1.67
-
1.90
13.741
5%
-
0.229
0.3
N85
-
8.89
-
8.62
-
3.088
5% 0.275 0.3
10.2 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
8 megawords
Time CPU To use: 2.44 seconds
Code_Aster
®
Version
5.0
Titrate:
TPNA300 Tubes generating heat with variable conductivity
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.41.300-A
Page:
12/12
Manual of Validation
V4.41 booklet: Nonlinear stationary thermics of axisymmetric structures HT-66/02/001/A
11 Summary of the results
Four modelings give results whose certain values exceed the fixed tolerance
initially (5%):
·
for modeling A (AXIS: QUAD4, TRIA3), the maximum change is 15,3% and 4 values on
16 exceed the tolerance,
·
for modeling B (PLANE: QUAD8, TRIA6), the maximum change is 13,8% and 3 values
on 24 exceed the tolerance,
·
for modeling C (3D: HEXA8, PENTA6), the maximum change is 15% and 5 values on
24 exceed the tolerance,
·
for modeling D (AXIS: QUAD9), the maximum change is 13,7% and 4 values out of 16
exceed the tolerance.
These goings beyond of tolerance are observed for values close to 0.
Calculations were carried out in °C. Determination of the variation, by considering the temperatures in °F
(as in the reference solution), a maximum change very different from that obtained in °C gives
(3% instead of 15%).
Moreover, it was not possible to get the original reference (delivers of Kreith), quoted in
manual of checking of ANSYS. Method of acquisition the reference solution (estimate
graph) and its uncertainty are thus not known.
The results are regarded as acceptable taking into account the points evoked above.
This test made it possible to test the taking into account a variable thermal conductivity within several
modelings. The main controls tested are as follows:
·
DEFI_MATERIAU
associated the key word
THER_NL
,
allowing to define the characteristics of one
material whose characteristics vary according to the temperature,
·
THER_NON_LINE
order allowing the resolution of a thermal nonlinear problem
stationary or not.