Code_Aster ®
Version
5.0
Titrate:
TPLV100 Cylindre subjected to boundary conditions
Date:
22/12/98
Author (S):
X. DESROCHES Key
:
V4.04.100-C Page:
1/14
Organization (S): EDF/IMA/MN
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
Document: V4.04.100
TPLV100 - Cylindre 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.
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
TPLV100 Cylindre subjected to boundary conditions
Date:
22/12/98
Author (S):
X. DESROCHES Key
:
V4.04.100-C Page:
2/14
1
Problem of reference
1.1 Geometry
Z
Z
E
G
D
C
R
R
With
B
F
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 = To = 0.°C
[BC]: imposed flow
= O = 2. W/m2 °C
[CD]: exchange
h= 2. W/m2 °C
Text = 2. °C
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
TPLV100 Cylindre subjected to boundary conditions
Date:
22/12/98
Author (S):
X. DESROCHES Key
:
V4.04.100-C Page:
3/14
2
Reference solution
2.1
Method of calculation used for the reference solution
T (R, Z,) = r2 cos L
with L number of the harmonic of Fourier
- T = (l2 - 4) cos L = S
- 2r cos L
R
= -
T = 0.+ (lrsinl)
[
on AB] and [ED]
R R
0
= N = 0.
[
on BC]
0
= 2R = 2.
[
on CD]
2
NR = 2R =
(2R2 - R2) = (hText - T)
R
2
from where H
=
= 2.
R
T
2
ext.
= 2R
= 2.
Only the source term varies according to harmonic (SSL (R, Z) = l2 - 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.
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
TPLV100 Cylindre subjected to boundary conditions
Date:
22/12/98
Author (S):
X. DESROCHES Key
:
V4.04.100-C Page:
4/14
3 Modeling
With
3.1
Characteristics of modeling
AXIS-FOURIER (TRIA6)
y (Z)
R Z node
To 0. 0. N1
G
B 1. 0. N7
E
D
C 1. 0.5
N8
D 1. 1. N9
C
E 0. 1. N3
F 0.5
0. N4
X (R)
With
G 0.5
1. N6
F
B
The axes of description of the grid are X (R) and y (Z).
Mode - Fourier: 1 T (A) = 0.
S = - 3.
on all the field
[BC]:
= 2.
[CD]:
H = 2. Text = 2.
3.2 Characteristics
grid
A number of nodes: 25.
A number of meshs and types: 8 TRIA6
3.3 Functionalities
tested
Commands
Keys
THERMAL AFFE_MODELE
“AXIS_FOURIER”
TOUT
[U4.22.01]
AFFE_CHAR_THER TEMP_IMPO
NOEUD
[U4.25.02]
FLUX_REP
GROUP_MA
ECHANGE
GROUP_MA
SOURCE
TOUT
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, key word MODE_FOURIER is not
necessary in command CALC_VECT_ELEM.
The use of commands 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.
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
TPLV100 Cylindre subjected to boundary conditions
Date:
22/12/98
Author (S):
X. DESROCHES Key
:
V4.04.100-C Page:
5/14
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.
103 -
Z (F)
0. 7.
104 -
= 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
103 -
Z (F)
0. 0.12
102 -
= 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
103 -
Z (F)
0. 0.12
102 -
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
Obstruction memory:
8 megawords
Time CPU To use:
7.0 seconds
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
TPLV100 Cylindre subjected to boundary conditions
Date:
22/12/98
Author (S):
X. DESROCHES Key
:
V4.04.100-C Page:
6/14
5 Modeling
B
5.1
Characteristics of modeling
AXIS-FOURIER (QUAD8)
y (Z)
R Z node
To 0. 0. N1
G
B 1. 0. N4
E
D
C 1. 0.5
N5
D 1. 1. N6
C
E 0. 1. N3
F 0.5
0. N7
X (R)
With
G 0.5
1. N12
F
B
The axes of description of the grid are X (R) and y (Z).
Mode - Fourier: 2 T (A) = 0.
No the term source bus S L (R, Z)
=.
0 for L = 2
[BC]: = 2.
[CD]: H = 2. Text = 2.
5.2 Characteristics
grid
A number of nodes: 13.
A number of meshs and types: 2 QUAD8
5.3 Functionalities
tested
Commands
Keys
“THERMAL” AFFE_MODELE “AXIS_FOURIER”
TOUT
[U4.22.01]
AFFE_CHAR_THER TEMP_IMPO
NOEUD
[U4.25.02]
FLUX_REP
GROUP_MA
ECHANGE
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, key word MODE_FOURIER is not
necessary in command CALC_VECT_ELEM.
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
TPLV100 Cylindre subjected to boundary conditions
Date:
22/12/98
Author (S):
X. DESROCHES Key
:
V4.04.100-C Page:
7/14
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.
2.1015
0.
Z (C)
0.
1.2 1014
0.
Z (D)
0.
1.2 1013
0.
Z (F)
0.
1.4 1014
0.
Z (G)
0.
3.7 1015
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
Obstruction memory:
8 megawords
Time CPU To use:
3.8 seconds
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
TPLV100 Cylindre subjected to boundary conditions
Date:
22/12/98
Author (S):
X. DESROCHES Key
:
V4.04.100-C Page:
8/14
7 Modeling
C
7.1
Characteristics of modeling
AXIS-FOURIER (QUAD9)
y (Z)
R Z node
To 0. 0. N1
G
B 1. 0. N4
E
D
C 1. 0.5
N5
D 1. 1. N6
C
E 0. 1. N3
F 0.5
0. N7
X (R)
With
G 0.5
1. N12
F
B
The axes of description of the grid are X (R) and y (Z).
Mode - Fourier: 3 T (A) = 0.
S = 5.
on all the field
[BC]:
= 2.
[CD]:
H = 2. Text = 2.
7.2 Characteristics
grid
A number of nodes: 15.
A number of meshs and types: 2 QUAD9
7.3 Functionalities
tested
Commands
Keys
“THERMAL” AFFE_MODELE “AXIS_FOURIER”
TOUT
[U4.22.01]
AFFE_CHAR_THER TEMP_IMPO
NOEUD
[U4.25.02]
FLUX_REP
GROUP_MA
ECHANGE
GROUP_MA
SOURCE
TOUT
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, key word MODE_FOURIER is not
necessary in command CALC_VECT_ELEM.
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
TPLV100 Cylindre subjected to boundary conditions
Date:
22/12/98
Author (S):
X. DESROCHES Key
:
V4.04.100-C Page:
9/14
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 1014
0.
Z (C)
0.
5.5 1014
0.
Z (D)
0.
4.6 1015
0.
Z (F)
0.
1.1 1015
0.
Z (G)
0.
1.8 1014
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
Obstruction memory:
8 megawords
Time CPU To use:
3.9 seconds
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
TPLV100 Cylindre subjected to boundary conditions
Date:
22/12/98
Author (S):
X. DESROCHES Key
:
V4.04.100-C Page:
10/14
9 Modeling
D
9.1
Characteristics of modeling
AXIS-FOURIER (QUAD4)
y (Z)
50 subdivisions in R
R Z node
To 0. 0. N1
G
D
B 1. 0. N151
E
C 1. 0.5
N152
D 1. 1. N153
C
E 0. 1. N3
F 0.5
0. N76
X (R)
G 0.5
1. N78
With
F
B
The axes of description of the grid are X (R) and y (Z).
Mode - Fourier: 2 T (A) = 0.
S = 0.
on all the field
[BC]:
= 2.
[CD]:
H = 2. Text = 2.
9.2 Characteristics
grid
A number of nodes: 153
A number of meshs and types: 100 QUAD4
9.3 Functionalities
tested
Commands
Keys
“THERMAL” AFFE_MODELE “AXIS_FOURIER”
TOUT
[U4.22.01]
AFFE_CHAR_THER TEMP_IMPO
NOEUD
[U4.25.02]
FLUX_REP
GROUP_MA
ECHANGE
GROUP_MA
SOURCE
TOUT
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, key word MODE_FOURIER is not
necessary in command CALC_VECT_ELEM.
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
TPLV100 Cylindre subjected to boundary conditions
Date:
22/12/98
Author (S):
X. DESROCHES Key
:
V4.04.100-C Page:
11/14
10 Results of modeling D
10.1 Values
tested
Identification Reference
Aster %
difference
T (B) 1. 0.9998
2.103
T (C) 1. 0.9998
2.103
T (D) 1. 0.9998
2.103
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. 103
R (G)
1. 1.0000 4. 103
(B)
2. 2.0000 4. 103
(C)
2. 2.0000 4. 103
(D)
2. 2.0001 5. 103
(F)
1. 1.0000 4. 103
(G)
1. 1.0000 4. 103
Z (B)
0.
2.105
-
Z (C)
0.
2.105
-
Z (D)
0.
2.105
-
Z (F)
0.
2.108
-
Z (G)
0.
2.108
-
10.2 Remarks
The bad precision recorded on R (B), R (C), R (D) is explained by the fact why 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
Obstruction memory:
8 megawords
Time CPU To use:
5.8 seconds
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
TPLV100 Cylindre subjected to boundary conditions
Date:
22/12/98
Author (S):
X. DESROCHES Key
:
V4.04.100-C Page:
12/14
11 Modeling
E
11.1 Characteristics of modeling
AXIS-FOURIER (TRIA3)
y (Z)
50 subdivisions in R
R Z node
To 0. 0. N1
G
D
B 1. 0. N151
E
C 1. 0.5
N152
D 1. 1. N153
C
E 0. 1. N3
F 0.5
0. N76
X (R)
G 0.5
1. N78
With
F
B
The axes of description of the grid are X (R) and y (Z).
Mode - Fourier: 2 T (A) = 0.
S = 0.
on all the field
[BC]:
= 2.
[CD]:
H = 2. Text = 2.
11.2 Characteristics
grid
A number of nodes: 153
A number of meshs and types: 200 TRIA3
11.3 Functionalities
tested
Commands
Keys
“THERMAL” AFFE_MODELE “AXIS_FOURIER”
TOUT
[U4.22.01]
AFFE_CHAR_THER TEMP_IMPO
NOEUD
[U4.25.02]
FLUX_REP
GROUP_MA
ECHANGE
GROUP_MA
SOURCE
TOUT
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, key word MODE_FOURIER is not
necessary in command CALC_VECT_ELEM.
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
TPLV100 Cylindre subjected to boundary conditions
Date:
22/12/98
Author (S):
X. DESROCHES Key
:
V4.04.100-C Page:
13/14
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 7.103
T (D) 1. 1.0003 0.033
T (F) 0.25
0.2500 9.103
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.
4.103
Z (C)
0.
4.103
Z (D)
0.
4.103
Z (F)
0.
1.103
Z (G)
0.
1.103
12.2 Remarks
The bad precision recorded on R (B), R (C), R (D) is explained by the fact why 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
Obstruction memory:
8 megawords
Time CPU To use:
6.1 seconds
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
TPLV100 Cylindre subjected to boundary conditions
Date:
22/12/98
Author (S):
X. DESROCHES Key
:
V4.04.100-C Page:
14/14
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).
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/01/010/A
Outline document