Code_Aster
®
Version
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Titrate:
TPLV100 Rolls subjected to boundary conditions
Date:
22/12/98
Author (S):
X. DESROCHES
Key
:
V4.04.100-C
Page:
1/14
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/01/010/A
Organization (S):
EDF/IMA/MN
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
Document: V4.04.100
TPLV100 - Roll subjected to conditions
with the nonaxisymmetric limits
Summary:
It is about a test in stationary thermics with modeling of Fourier.
This test validates all the elements of Fourier in thermics (5 different modelings) with various types of
boundary conditions: imposed temperature, exchange, imposed flow, heat source.
The interest of the test, in addition to the validation of Fourier thermics, lies in the following points:
·
comparison between the results and an analytical solution on various harmonics of Fourier (1, 2 and
3),
·
homogeneity of the elements between them.
Code_Aster
®
Version
5.0
Titrate:
TPLV100 Rolls subjected to boundary conditions
Date:
22/12/98
Author (S):
X. DESROCHES
Key
:
V4.04.100-C
Page:
2/14
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/01/010/A
1
Problem of reference
1.1 Geometry
Z
R
Z
R
E
D
B
F
With
G
C
Radius of the cylinder R = 1 Mr.
1.2 Properties
of
materials
= 1 W/m °C
1.3
Boundary conditions and loadings
[EA]: imposed temperature
T = T
O
= 0.°C
[BC]: imposed flow
=
O
= 2. W/m
2
°C
[CD]: exchange
h= 2. W/m
2
°C
T
ext.
= 2. °C
Code_Aster
®
Version
5.0
Titrate:
TPLV100 Rolls subjected to boundary conditions
Date:
22/12/98
Author (S):
X. DESROCHES
Key
:
V4.04.100-C
Page:
3/14
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/01/010/A
2
Reference solution
2.1
Method of calculation used for the reference solution
(
)
T R Z
R
L
,
cos
=
2
with
L
number of the harmonic of Fourier
()
(
)
[] []
[]
[]
(
)
(
)
-
=
-
=
= -
=
-
+
=
=
=
=
=
=
-
=
-
=
=
=
=
T
L
L
S
T
R
L
Lr
L
N
R
N
R
R
R
R
H T
T
H
R
T
R
ext.
ext.
2
0
0
2
2
2
4
2
0
0
2
2
2
2 2
2
2
2
2
cos
cos
.
sin
.
.
.
.
R
R R
R
on AB and ED
on BC
on CD
from where
Only the source term varies according to the harmonic
()
(
)
S R Z
L
L
,
= -
2
4
.
In following modelings, one will solve the problem on harmonics 1, 2 and 3.
2.2
Results of reference
Temperatures and flow at the points B, C, D, F, G.
Code_Aster
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Version
5.0
Titrate:
TPLV100 Rolls subjected to boundary conditions
Date:
22/12/98
Author (S):
X. DESROCHES
Key
:
V4.04.100-C
Page:
4/14
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/01/010/A
3 Modeling
With
3.1
Characteristics of modeling
AXIS-FOURIER (TRIA6)
X (R)
E
D
B
F
With
G
y (Z)
C
R Z node
To 0. 0. N1
B 1. 0. N7
C 1. 0.5
N8
D 1. 1. N9
E 0. 1. N3
F 0.5
0. N4
G 0.5
1. N6
The axes of description of the mesh are X (R) and y (Z).
Mode - Fourier: 1 T (A) = 0.
S = - 3.
on all the field
[BC]:
=
2.
[CD]:
H
T
ext.
=
=
2
2
.
.
3.2 Characteristics
mesh
A number of nodes: 25.
A number of meshs and types: 8 TRIA6
3.3 Functionalities
tested
Controls
Keys
THERMAL AFFE_MODELE
“AXIS_FOURIER”
ALL
[U4.22.01]
AFFE_CHAR_THER TEMP_IMPO
NODE
[U4.25.02]
FLUX_REP
GROUP_MA
EXCHANGE
GROUP_MA
SOURCE
ALL
CALC_MATR_ELEM “RIGI_THER”
MODE_FOURIER
[U4.41.01]
CALC_VECT_ELEM “CHAR_THER”
[U4.41.02]
ASSE_MATRICE
[U4.42.02]
ASSE_VECTEUR
[U4.42.03]
FACT_LDLT
[U4.51.01]
RESO_LDLT
[U4.51.02]
CALC_CHAM_ELEM “FLUX_ELNO_TEMP”
MODE_FOURIER
[U4.61.01]
COMB_CHAM_NO COMB_FOURIER
[U4.53.02]
COMB_CHAM_ELEM COMB_FOURIER
[U4.53.03]
POST_RELEVE CHAM_GD
“EXTRACTION”
[U4.74.03]
3.4 Remarks
The number of the mode of Fourier not affecting the loading, the key word
MODE_FOURIER
is not
necessary in the control
CALC_VECT_ELEM
.
The use of the controls
COMB_CHAM_NO
and
COMB_CHAM_ELEM
key word
COMB_R
is not one
recombination of Fourier but a simple validation of this key word.
Code_Aster
®
Version
5.0
Titrate:
TPLV100 Rolls subjected to boundary conditions
Date:
22/12/98
Author (S):
X. DESROCHES
Key
:
V4.04.100-C
Page:
5/14
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/01/010/A
4
Results of modeling A
4.1 Values
tested
Identification
Reference
Aster %
difference
= 0
T (B)
1.
0.9981
0.19
T
(F)
0.25
0.2484
0.66
R
(B)
2 1.993
0.36
R
(F)
1. 0.9924
0.76
(B)
1. 0.9996
0.04
(F)
0.5 0.4982
0.37
Z
(B)
0. 5.
10
3
-
Z
(F)
0. 7.
10
4
-
= 45
T (B)
0.7071
0.7057
0.192
T
(F)
0.177
0.1756
0.65
R
(B)
1.414 1.4018
0.87
R
(F)
0.7071 0.6848 3.15
(B)
0.707 0.7069 0.027
(F)
0.3535 0.3512 0.65
Z
(B)
0. 0.36
10
3
-
Z
(F)
0. 0.12
10
2
-
= 135
T (B)
0.707
0.7057
0.19
T
(F)
0.177
0.1756
0.65
R
(B)
1.414 1.4018
0.87
R
(F)
0.707 0.685
3.15
(B)
0.707 0.7069 0.027
(F)
0.3535 0.3533 0.06
Z
(B)
0. 0.36
10
3
-
Z
(F)
0. 0.12
10
2
-
4.2 Remarks
The values of flows to the nodes are realized on the elements containing this node.
It is noticed that the exact solution is not found. This is with the fact that numerical integration
thermal matrix of rigidity is approximate (formula at 3 points of GAUSS). If one were used
formulate at 6 points, one would find the solution exactly.
4.3 Parameters
of execution
Version: 4.00.02
Machine: CRAY C90
System UNICOS:
8.04
Overall dimension memory:
8 megawords
Time CPU To use:
7.0 seconds
Code_Aster
®
Version
5.0
Titrate:
TPLV100 Rolls subjected to boundary conditions
Date:
22/12/98
Author (S):
X. DESROCHES
Key
:
V4.04.100-C
Page:
6/14
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/01/010/A
5 Modeling
B
5.1
Characteristics of modeling
AXIS-FOURIER (QUAD8)
X (R)
E
D
B
F
With
G
y (Z)
C
R Z node
To 0. 0. N1
B 1. 0. N4
C 1. 0.5
N5
D 1. 1. N6
E 0. 1. N3
F 0.5
0. N7
G 0.5
1. N12
The axes of description of the mesh are X (R) and y (Z).
Mode - Fourier: 2 T (A) = 0.
No the term bus source
()
S R Z
L
.
=
0
for
L
= 2
[BC]:
=
2.
[CD]:
H
T
ext.
=
=
2
2
.
.
5.2 Characteristics
mesh
A number of nodes: 13.
A number of meshs and types: 2 QUAD8
5.3 Functionalities
tested
Controls
Keys
“THERMAL” AFFE_MODELE “AXIS_FOURIER”
ALL
[U4.22.01]
AFFE_CHAR_THER TEMP_IMPO
NODE
[U4.25.02]
FLUX_REP
GROUP_MA
EXCHANGE
GROUP_MA
CALC_MATR_ELEM “RIGI_THER”
MODE_FOURIER
[U4.41.01]
CALC_VECT_ELEM “CHAR_THER”
[U4.41.02]
ASSE_MATRICE
[U4.42.02]
ASSE_VECTEUR
[U4.42.03]
FACT_LDLT
[U4.51.01]
RESO_LDLT
[U4.51.02]
CALC_CHAM_ELEM “FLUX_ELNO_TEMP”
MODE_FOURIER
[U4.61.01]
5.4 Remarks
The number of the mode of Fourier not affecting the loading, the key word
MODE_FOURIER
is not
necessary in the control
CALC_VECT_ELEM
.
Code_Aster
®
Version
5.0
Titrate:
TPLV100 Rolls subjected to boundary conditions
Date:
22/12/98
Author (S):
X. DESROCHES
Key
:
V4.04.100-C
Page:
7/14
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/01/010/A
6
Results of modeling B
6.1 Values
tested
Identification Reference
Aster %
difference
T (B) 1. 1.
0.
T (C) 1. 1.
0.
T (D) 1. 1.
0.
T (F) 0.25 0.25
0.
T (G) 0.25 0.25
0.
R
(B)
2. 2.
0.
R
(C)
2. 2.
0.
R
(D)
2. 2.
0.
R
(F)
1. 1.
0.
R
(G)
1. 1.
0.
(B)
2. 2.
0.
(C)
2. 2.
0.
(D)
2. 2.
0.
(F)
1. 1.
0.
(G)
1. 1.
0.
Z
(B)
0.
2.10
15
0.
Z
(C)
0.
1.2 10
14
0.
Z
(D)
0.
1.2 10
13
0.
Z
(F)
0.
1.4 10
14
0.
Z
(G)
0.
3.7 10
15
0.
6.2 Remarks
The analytical solution is found exactly.
6.3 Parameters
of execution
Version: 4.00.02
Machine: CRAY C90
System UNICOS:
8.04
Overall dimension memory:
8 megawords
Time CPU To use:
3.8 seconds
Code_Aster
®
Version
5.0
Titrate:
TPLV100 Rolls subjected to boundary conditions
Date:
22/12/98
Author (S):
X. DESROCHES
Key
:
V4.04.100-C
Page:
8/14
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/01/010/A
7 Modeling
C
7.1
Characteristics of modeling
AXIS-FOURIER (QUAD9)
X (R)
E
D
B
F
With
G
y (Z)
C
R Z node
To 0. 0. N1
B 1. 0. N4
C 1. 0.5
N5
D 1. 1. N6
E 0. 1. N3
F 0.5
0. N7
G 0.5
1. N12
The axes of description of the mesh are X (R) and y (Z).
Mode - Fourier: 3 T (A) = 0.
S = 5.
on all the field
[BC]:
=
2.
[CD]:
H
T
ext.
=
=
2
2
.
.
7.2 Characteristics
mesh
A number of nodes: 15.
A number of meshs and types: 2 QUAD9
7.3 Functionalities
tested
Controls
Keys
“THERMAL” AFFE_MODELE “AXIS_FOURIER”
ALL
[U4.22.01]
AFFE_CHAR_THER TEMP_IMPO
NODE
[U4.25.02]
FLUX_REP
GROUP_MA
EXCHANGE
GROUP_MA
SOURCE
ALL
CALC_MATR_ELEM “RIGI_THER”
MODE_FOURIER
[U4.41.01]
CALC_VECT_ELEM “CHAR_THER”
[U4.41.02]
ASSE_MATRICE
[U4.42.02]
ASSE_VECTEUR
[U4.42.03]
FACT_LDLT
[U4.51.01]
RESO_LDLT
[U4.51.02]
CALC_CHAM_ELEM “FLUX_ELNO_TEMP”
MODE_FOURIER
[U4.61.01]
7.4 Remarks
The number of the mode of Fourier not affecting the loading, the key word
MODE_FOURIER
is not
necessary in the control
CALC_VECT_ELEM
.
Code_Aster
®
Version
5.0
Titrate:
TPLV100 Rolls subjected to boundary conditions
Date:
22/12/98
Author (S):
X. DESROCHES
Key
:
V4.04.100-C
Page:
9/14
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/01/010/A
8
Results of modeling C
8.1 Values
tested
Identification Reference
Aster %
difference
T (B) 1. 1.
0.
T (C) 1. 1.
0.
T (D) 1. 1.
0.
T (F) 0.25 0.25 0.
T (G) 0.25 0.25
0.
R
(B)
2. 2.
0.
R
(C)
2. 2.
0.
R
(D)
2. 2.
0.
R
(F)
1. 1.
0.
R
(G)
1. 1.
0.
(B)
3. 3.
0.
(C)
3. 3.
0.
(D)
3. 3.
0.
(F)
1.5 1.5
0.
(G)
1.5 1.5
0.
Z
(B)
0.
1.2 10
14
0.
Z
(C)
0.
5.5 10
14
0.
Z
(D)
0.
4.6 10
15
0.
Z
(F)
0.
1.1 10
15
0.
Z
(G)
0.
1.8 10
14
0.
8.2 Remarks
The analytical solution is found exactly.
8.3 Parameters
of execution
Version: 4.00.02
Machine: CRAY C90
System UNICOS:
8.04
Overall dimension memory:
8 megawords
Time CPU To use:
3.9 seconds
Code_Aster
®
Version
5.0
Titrate:
TPLV100 Rolls subjected to boundary conditions
Date:
22/12/98
Author (S):
X. DESROCHES
Key
:
V4.04.100-C
Page:
10/14
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/01/010/A
9 Modeling
D
9.1
Characteristics of modeling
AXIS-FOURIER (QUAD4)
E
G
D
C
B
F
With
50 subdivisions in R
y (Z)
X (R)
R Z node
To 0. 0. N1
B 1. 0. N151
C 1. 0.5
N152
D 1. 1. N153
E 0. 1. N3
F 0.5
0. N76
G 0.5
1. N78
The axes of description of the mesh are X (R) and y (Z).
Mode - Fourier: 2 T (A) = 0.
S = 0.
on all the field
[BC]:
=
2.
[CD]:
H
T
ext.
=
=
2
2
.
.
9.2 Characteristics
mesh
A number of nodes: 153
A number of meshs and types: 100 QUAD4
9.3 Functionalities
tested
Controls
Keys
“THERMAL” AFFE_MODELE “AXIS_FOURIER”
ALL
[U4.22.01]
AFFE_CHAR_THER TEMP_IMPO
NODE
[U4.25.02]
FLUX_REP
GROUP_MA
EXCHANGE
GROUP_MA
SOURCE
ALL
CALC_MATR_ELEM “RIGI_THER”
MODE_FOURIER
[U4.41.01]
CALC_VECT_ELEM “CHAR_THER”
[U4.41.02]
ASSE_MATRICE
[U4.42.02]
ASSE_VECTEUR
[U4.42.03]
FACT_LDLT
[U4.51.01]
RESO_LDLT
[U4.51.02]
CALC_CHAM_ELEM “FLUX_ELNO_TEMP”
MODE_FOURIER
[U4.61.01]
9.4 Remarks
The number of the mode of Fourier not affecting the loading, the key word
MODE_FOURIER
is not
necessary in the control
CALC_VECT_ELEM
.
Code_Aster
®
Version
5.0
Titrate:
TPLV100 Rolls subjected to boundary conditions
Date:
22/12/98
Author (S):
X. DESROCHES
Key
:
V4.04.100-C
Page:
11/14
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/01/010/A
10 Results of modeling D
10.1 Values
tested
Identification Reference
Aster %
difference
T (B) 1. 0.9998
2.10
3
T (C) 1. 0.9998
2.10
3
T (D) 1. 0.9998
2.10
3
T (F) 0.25
0.2498
0.02
T (G) 0.25
0.2498
0.02
R
(B)
2. 1.9800 1.
R
(C)
2. 1.9800 1.
R
(D)
2. 1.9801 1.
R
(F)
1. 1.0000 4. 10
3
R
(G)
1. 1.0000 4. 10
3
(B)
2. 2.0000 4. 10
3
(C)
2. 2.0000 4. 10
3
(D)
2. 2.0001 5. 10
3
(F)
1. 1.0000 4. 10
3
(G)
1. 1.0000 4. 10
3
Z
(B)
0.
2.10
5
-
Z
(C)
0.
2.10
5
-
Z
(D)
0.
2.10
5
-
Z
(F)
0.
2.10
8
-
Z
(G)
0.
2.10
8
-
10.2 Remarks
Bad precision recorded on
R
(B),
R
(C),
R
(D) is explained by the fact that B, C and D are
nodes of the edge, therefore flows are not realized on adjacent elements in the direction
variation in temperature (direction R).
This phenomenon is not found on
, because
is balanced by 1/R.
10.3 Parameters
of execution
Version: 4.00.02
Machine: CRAY C90
System UNICOS:
8.04
Overall dimension memory:
8 megawords
Time CPU To use:
5.8 seconds
Code_Aster
®
Version
5.0
Titrate:
TPLV100 Rolls subjected to boundary conditions
Date:
22/12/98
Author (S):
X. DESROCHES
Key
:
V4.04.100-C
Page:
12/14
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/01/010/A
11 Modeling
E
11.1 Characteristics of modeling
AXIS-FOURIER (TRIA3)
E
G
D
C
B
F
With
50 subdivisions in R
y (Z)
X (R)
R Z node
To 0. 0. N1
B 1. 0. N151
C 1. 0.5
N152
D 1. 1. N153
E 0. 1. N3
F 0.5
0. N76
G 0.5
1. N78
The axes of description of the mesh are X (R) and y (Z).
Mode - Fourier: 2 T (A) = 0.
S = 0.
on all the field
[BC]:
=
2.
[CD]:
H
T
ext.
=
=
2
2
.
.
11.2 Characteristics
mesh
A number of nodes: 153
A number of meshs and types: 200 TRIA3
11.3 Functionalities
tested
Controls
Keys
“THERMAL” AFFE_MODELE “AXIS_FOURIER”
ALL
[U4.22.01]
AFFE_CHAR_THER TEMP_IMPO
NODE
[U4.25.02]
FLUX_REP
GROUP_MA
EXCHANGE
GROUP_MA
SOURCE
ALL
CALC_MATR_ELEM “RIGI_THER”
MODE_FOURIER
[U4.41.01]
CALC_VECT_ELEM “CHAR_THER”
[U4.41.02]
ASSE_MATRICE
[U4.42.02]
ASSE_VECTEUR
[U4.42.03]
FACT_LDLT
[U4.51.01]
RESO_LDLT
[U4.51.02]
CALC_CHAM_ELEM “FLUX_ELNO_TEMP”
MODE_FOURIER
[U4.61.01]
11.4 Remarks
The number of the mode of Fourier not affecting the loading, the key word
MODE_FOURIER
is not
necessary in the control
CALC_VECT_ELEM
.
Code_Aster
®
Version
5.0
Titrate:
TPLV100 Rolls subjected to boundary conditions
Date:
22/12/98
Author (S):
X. DESROCHES
Key
:
V4.04.100-C
Page:
13/14
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/01/010/A
12 Results of modeling E
12.1 Values
tested
Identification Reference
Aster %
difference
T (B) 1. 0.9995 0.049
T (C) 1. 0.9999 7.10
3
T (D) 1. 1.0003 0.033
T (F) 0.25
0.2500 9.10
3
T (G) 0.25
0.2498 0.077
R
(B)
2. 1.977
1.14
R
(C)
2. 1.9819
0.90
R
(D)
2. 1.9856
0.72
R
(F)
1. 0.993
0.68
R
(G)
1. 1.007
0.68
(B)
2. 1.9992 0.04
(C)
2. 2.0000 -
(D)
2. 2.0008 0.04
(F)
1. 1.0004 0.04
(G)
1. 0.9995 0.05
Z
(B)
0.
4.10
3
Z
(C)
0.
4.10
3
Z
(D)
0.
4.10
3
Z
(F)
0.
1.10
3
Z
(G)
0.
1.10
3
12.2 Remarks
Bad precision recorded on
R
(B),
R
(C),
R
(D) is explained by the fact that B, C and D are
nodes of the edge, therefore flows are not realized on adjacent elements in the direction
variation in temperature (direction R).
This phenomenon is not found on
, because
is balanced by 1/R.
12.3 Parameters
of execution
Version: 4.00.02
Machine: CRAY C90
System UNICOS:
8.04
Overall dimension memory:
8 megawords
Time CPU To use:
6.1 seconds
Code_Aster
®
Version
5.0
Titrate:
TPLV100 Rolls subjected to boundary conditions
Date:
22/12/98
Author (S):
X. DESROCHES
Key
:
V4.04.100-C
Page:
14/14
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/01/010/A
13 Summary of the results
This problem is correctly solved:
·
whatever the number of harmonic of Fourier,
·
by the various types of elements (degree 1 or 2).