Code_Aster ®
Version
5.0
Titrate:
Thermal TPLV305 Gradient in a cylinder (Fourier)

Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.04.305-A Page:
1/8

Organization (S): EDF/AMA, EDF/UTO/LOCATED, Delta CAD
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
V4.04.305 document

TPLV305 - Thermal 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 command
COMB_CHAM_NO.
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Thermal TPLV305 Gradient in a cylinder (Fourier)

Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.04.305-A Page:
2/8

1
Problem of reference

1.1 Geometry
Z
D
J
I
H
C
ro
y
O
1.524
With
E
F
G
B
y
Z
r0 = 6.096 m


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: T0 = - 17.778°C
· a symmetrical limiting condition compared to associated harmonic 1:
CL2: T1 cos = 44.444 cos (°C)

T0
y
O
y
- T1
O

T1
X
X
T0 T1 cos


1.4 Conditions
initial

Without object.

Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Thermal TPLV305 Gradient in a cylinder (Fourier)

Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.04.305-A Page:
3/8

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 handbook 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”, 1st edition, June 1, 1976
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Thermal TPLV305 Gradient in a cylinder (Fourier)

Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.04.305-A Page:
4/8

3 Modeling
With

3.1
Characteristics of modeling

AXIS_FOURIER (QUAD4)

y (Z)
D
J
I
H
C
1.5
X (R)
With
E
F
G
B
Limiting conditions:
Points
X
nodes
With
0.000
N1, N2
- dimensioned AB, CD = 0
E
1.524
N3, N4
- dimensioned BC
F
3.048
N5, N6
. mode 0 T = - 17.778
G
4.572
N7, N8
. mode (0 +1) T = - 17.778 +44.444 cos
B
6.096
N9, N10


3.2
Characteristics of the grid

A number of nodes:
10
A number of meshs and types: 4 QUAD4

3.3 Functionalities
tested

Commands




AFFE_MODELE
THERMIQUE
AXIS_FOURIER
TOUT

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

ANGL

COMB_R


Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Thermal TPLV305 Gradient in a cylinder (Fourier)

Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.04.305-A Page:
5/8

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

Obstruction memory:
8 megawords
Time CPU To use: 3.12 seconds

Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Thermal TPLV305 Gradient in a cylinder (Fourier)

Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.04.305-A Page:
6/8

5 Modeling
B

5.1
Characteristics of modeling

3D (PENTA6, HEXA8)

Z
=180°
N155
=90°
N273
N145
N265
N139
N274
N243
N133
N197
N266
N244
N123
N69
N49
N57
N65
N198
N53
=45°
X
N124
N17
N54
N5
N3
N18

z=0
z=1.524
N6
N70
N69
y
N4
45°
N50
N49
Limiting conditions:
N58
N57
N66
N65
- external face (N8, N155, N273)
N134
N133
T = - 17.778 + 44.444 cos
90°
N140
N139

- face interns (N8, N123, N273)
N146
N145

N155
N154
= 0


5.2
Characteristics of the grid

A number of nodes:
274
A number of meshs and types: 128 (16 PENTA6, 112 HEXA8)

5.3 Functionalities
tested

Commands




AFFE_MODELE
AFFE
THERMIQUE
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
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Thermal TPLV305 Gradient in a cylinder (Fourier)

Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.04.305-A Page:
7/8

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

Obstruction memory:
8 megawords
Time CPU To use: 2.19 seconds
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Thermal TPLV305 Gradient in a cylinder (Fourier)

Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.04.305-A Page:
8/8

7
Summary of the results

Two modelings carried out (AXIS_FOURIER and 3D) give excellent results, the variation
maximum is of - 0.006% for two modelings

This test made it possible to test in AXIS_FOURIER command 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.

Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A

Outline document