Code_Aster
®
Version
5.0
Titrate:
TPLV305 Heat gradient in a cylinder (Fourier)
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.04.305-A
Page:
1/8
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A
Organization (S):
EDF/AMA, EDF/UTO/LOCATED, Delta CAD
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
V4.04.305 document
TPLV305 - Heat gradient in a cylinder
(Fourier)
Summary:
This test results from the validation independent of version 3 in linear stationary thermics.
It validates the thermal axis_fourier and voluminal elements with for boundary conditions of the temperatures
imposed according to a harmonic function (mode 1).
It comprises two modelings, one 3D and the other using of the thermal elements axis_fourier.
The interest of this test is the validation of the thermal elements axis_fourier and the control
COMB_CHAM_NO.
Code_Aster
®
Version
5.0
Titrate:
TPLV305 Heat gradient in a cylinder (Fourier)
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.04.305-A
Page:
2/8
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
R
O
O
Z
R
0
= 6.096 m
With
E
F
G
B
D
J
I
H
C
y
Z
1.524
y
1.2
Properties of material
= 1.7307 W/m.°C
Thermal conductivity
1.3
Boundary conditions and loadings
The limiting condition is applied to the external surface of the cylinder, it breaks up into:
·
a symmetrical limiting condition of revolution associated with harmonic 0:
CL1: T
0
=
-
17.778°C
·
a symmetrical limiting condition compared to
associated harmonic 1:
CL2: T
1
cos
= 44.444 cos
(°
C
)
T
0
T
1
cos
O
O
T
0
- T
1
T
1
X
y
X
y
1.4 Conditions
initial
Without object.
Code_Aster
®
Version
5.0
Titrate:
TPLV305 Heat gradient in a cylinder (Fourier)
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.04.305-A
Page:
3/8
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal 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 an analytical approach.
This reference is quoted in the manual of checking of ANSYS [bib2]
2.2
Results of reference
·
Temperature at the points A, E, F, G, B for mode 0 (CL1),
·
Temperature at the points A, E, F, G, B mode 0 and mode 1 recombined (CL1+CL2) for
= 0°,
45°, 90° and 180°.
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]
Kreith, F., “Principles off heat transfer”, International Textbook Co., Scranton, Pennsylvania,
2nd Printing, 1959.
[2]
ANSYS: “Checking manual”, 1
St
edition, June 1, 1976
Code_Aster
®
Version
5.0
Titrate:
TPLV305 Heat gradient in a cylinder (Fourier)
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.04.305-A
Page:
4/8
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
AXIS_FOURIER (QUAD4)
Points
X
nodes
With
0.000
N1, N2
E
1.524
N3, N4
F
3.048
N5, N6
G
4.572
N7, N8
B
6.096
N9, N10
Limiting conditions:
- dimensioned AB, CD
= 0
- dimensioned BC
. mode 0 T = - 17.778
. mode (0 +1)
T = - 17.778 +44.444 cos
With
E
F
G
B
D
J
I
H
C
X (R)
y (Z)
1.5
3.2
Characteristics of the mesh
A number of nodes:
10
A number of meshs and types: 4 QUAD4
3.3 Functionalities
tested
Controls
AFFE_MODELE
THERMICS
AXIS_FOURIER
ALL
AFFE_CHAR_THER
TEMP_IMPO
CALC_MATR_ELEM
RIGI_THER
MODE_FOURIER
CALC_VECT_ELEM
CHAR_THER
NUME_DDL
RENUM
“RCMK”
ASSE_MATRICE
MATR_ELEM
NUME_DDL
ASSE_VECTEUR
VECT_ELEM
NUME_DDL
FACT_LDLT
MATR_ASSE
RESO_LDLT
MATR_FACT
CHAM_NO
COMB_CHAM_NO
COMB_FOURIER
NUME_MODE
TYPE_MODE
ENG
COMB_R
Code_Aster
®
Version
5.0
Titrate:
TPLV305 Heat gradient in a cylinder (Fourier)
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.04.305-A
Page:
5/8
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A
4
Results of modeling A
4.1 Values
tested
Relative variation %
Absolute deviation
Identification Reference
Aster difference tolerance difference tolerance
Temperature
(°C)
CL1 (mode = 0)
N1, N2
-
17.778
-
17.778
0.000 1%
-
1.14e-12
0.01
N3, N4
-
17.778
-
17.778
0.000 1%
-
9.09e-13
0.01
N5, N6
-
17.778
-
17.778
0.000 1%
-
6.82e-13
0.01
N7, N8
-
17.778
-
17.778
0.000 1%
-
3.41e-13
0.01
N9, N10
*
-
17.778
-
17.778
0.000 1%
0.000e+0
0.01
CL1+CL2 (mode 0 and 1)
= 0° N1, N2
-
17.778
-
17.778
0.000 1%
-
1.14e-12
0.01
N3, N4
-
6.667
-
6.667
0.000 1%
1.820e-8
0.01
N5, N6
4.444
4.444
0.000
1%
3.650e-8
0.01
N7, N8
15.556
15.555
-
0.006
1%
-
1.000e-3
0.01
N9, N10
*
26.667 26.666
-
0.004
1%
-
1.000e-3
0.01
= 45° N1, N2
-
17.778
-
17.778
0.000 1%
-
1.14e-12
0.01
N3, N4
-
9.921
-
9.921
0.003 1%
-
3.370e-4
0.01
N5, N6
-
2.064
-
2.065
0.033 1%
-
6.730e-4
0.01
N7, N8
5.792
5.792
0.000
1%
-
1.040e-5
0.01
N9, N10
13.649
13.649
-
0.003
1%
-
3.460e-4
0.01
= 90° N1, N2
-
17.778
-
17.778
0.000 1%
-
1.14e-12
0.01
N3, N4
-
17.778
-
17.778
0.000 1%
-
9.09e-13
0.01
N5, N6
-
17.778
-
17.778
0.000 1%
-
5.68e-13
0.01
N7, N8
-
17.778
-
17.778
0.000 1%
-
2.27e-13
0.01
N9, N10
-
17.778
-
17.778
0.000 1%
2.27e-13
0.01
= 180° N1, N2
-
17.778
-
17.778
0.000 1%
-
1.14e-12
0.01
N3, N4
-
28.889
-
28.889
0.000 1%
-
1.820e-8
0.01
N5, N6
-
40.000
-
40.000
0.000 1%
-
3.650e-8
0.01
N7, N8
-
51.111
-
51.111
0.000 1%
1.040e-6
0.01
N9, N10
-
62.222
-
62.222
0.000 1%
2.27e-13
0.01
* imposed temperatures
4.2 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
8 megawords
Time CPU To use: 3.12 seconds
Code_Aster
®
Version
5.0
Titrate:
TPLV305 Heat gradient in a cylinder (Fourier)
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.04.305-A
Page:
6/8
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A
5 Modeling
B
5.1
Characteristics of modeling
3D (PENTA6, HEXA8)
Limiting conditions:
- external face (N8, N155, N273)
T = - 17.778 + 44.444 cos
- face interns (N8, N123, N273)
= 0
X
Z
y
N123
N3
N5
N17
N53
N124
N4
N6
N18
N54
N65
N57
N49
N69
N155
N145
N139
N133
=45°
=90°
N197
N243
N265
N273
N198
N244
N266
N274
=180°
z=0
z=1.524
45°
N70
N50
N58
N66
N69
N49
N57
N65
90°
N134
N140
N146
N155
N133
N139
N145
N154
5.2
Characteristics of the mesh
A number of nodes:
274
A number of meshs and types: 128 (16 PENTA6, 112 HEXA8)
5.3 Functionalities
tested
Controls
AFFE_MODELE
AFFE
THERMICS
3D
AFFE_CHAR_THER
TEMP_IMPO
THER_LINEAIRE
EXCIT
CHARGE
RECU_CHAMP
NUME_ORDRE
5.4 Remarks
Calculations were carried out by considering complete loading CL1+CL2:
Timp =
-
17.778 + 44.444 cos
Code_Aster
®
Version
5.0
Titrate:
TPLV305 Heat gradient in a cylinder (Fourier)
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.04.305-A
Page:
7/8
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A
6
Results of modeling B
6.1 Values
tested
Relative variation %
Absolute deviation
Identification Reference
Aster difference tolerance difference tolerance
CL1+CL2
Temperature
(°C)
= 0 N123, N124
-
17.778
-
17.778
0.000 1%
-
3.330e-5
0.01
N53, N54
-
6.667
-
6.667
0.000 1%
1.330e-7
0.01
N17, N18
4.444
4.444
0.001
1%
2.840e-5
0.01
N5, N6
15.556
15.555
-
0.006
1%
-
9.730e-4
0.01
N3, N4
*
26.667
26.666
-
0.004
1%
-
1.000e-3
0.01
= 45 N69, N70
-
9.921
-
9.921
0.003 1%
-
3.460e-4
0.01
N49, N50
-
2.064
-
2.065
0.031 1%
-
6.480e-4
0.01
N57, N58
5.792
5.792
0.001
1%
8.240e-5
0.01
N65, N66
*
13.649
13.649 0.000 1%
-
5.68e-13
0.01
= 90 N133, N134
-
17.778
-
17.778
0.000 1%
-
3.750e-5
0.01
N139, N140
-
17.778
-
17.778
0.000 1%
-
5.030e-5
0.01
N145, N146
-
17.778
-
17.778
0.000 1%
-
6.990e-5
0.01
N155, N156
*
-
17.778
-
17.778
0.000 1%
9.09e-13
0.01
= 180 N197, N198
-
2.889
-
2.889
0.000 1%
-
6.440e-5
0.01
N243, N244
-
40.000
-
40.000
0.000 1%
-
7.680e-5
0.01
N265, N266
-
5.1111
-
5.1111
0.000 1%
-
5.210e-5
0.01
N273, N274
*
-
62.222
-
62.222
0.000 1%
+6.82e-13
0.01
* imposed temperatures
6.2 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
8 megawords
Time CPU To use: 2.19 seconds
Code_Aster
®
Version
5.0
Titrate:
TPLV305 Heat gradient in a cylinder (Fourier)
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.04.305-A
Page:
8/8
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A
7
Summary of the results
Two modelings carried out (
AXIS_FOURIER
and
3D
) excellent results, the variation give
maximum is of
-
0.006% for two modelings
This test made it possible to test in AXIS_FOURIER the control
COMB_CHAM_NO
with the operands
following:
·
COMB_FOURIER
to calculate the temperature in an angle given,
·
COMB_R
to carry out a linear combination of modes 0 and 1.