Code_Aster
®
Version
5.0
Titrate:
TPLA301 Distribution of temperature in a short cylinder
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.01.301-A
Page:
1/6
Manual of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A
Organization (S):
EDF/AMA, EDF/UTO/LOCATED, Delta CAD
Manual of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
V4.01.301 document
TPLA301 - Distribution of temperature in
a cylinder runs
Summary:
This test results from the validation independent of version 3 in linear stationary thermics.
The axisymmetric problem 2D aims to validate the axisymmetric thermal elements under
temperature imposed in the case of a cylinder court on radial and axial behavior.
It comprises only one modeling (axisymmetric).
The results are compared with a solution based on a graphic estimate.
Code_Aster
®
Version
5.0
Titrate:
TPLA301 Distribution of temperature in a short cylinder
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.01.301-A
Page:
2/6
Manual of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
T
sup
X
Z
T
inf
T
cyl
R
1
Y
L
R
1
= L = 0.1524 m
R
Z
E
D
C
B
With
J
I
H
G
F
L
I
H
G
K
Points
(r=0)
Z
(x10
- 3
)
Points
(r=r
1
/2)
Z
(x10
- 3
)
With
0.0
F
0.0
B
38.1
G
38.1
C
76.2
H
76.2
D
114.3
I
114.3
E
152.4
J
152.4
1.2
Properties of material
= 1.7307 W/m.°C thermal Conductivity
1.3
Boundary conditions and loadings
Imposed temperatures:
·
T
inf
= T
cyl
= 17.778°C,
·
T
sup
= 4.444°C.
1.4 Conditions
initial
Without object.
Code_Aster
®
Version
5.0
Titrate:
TPLA301 Distribution of temperature in a short cylinder
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.01.301-A
Page:
3/6
Manual of Validation
V4.01 booklet: Stationary thermics of the 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 at points A B C D E F G H I J
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”, 1
St
edition, June 1, 1976
Code_Aster
®
Version
5.0
Titrate:
TPLA301 Distribution of temperature in a short cylinder
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.01.301-A
Page:
4/6
Manual of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
AXIS (QUAD4)
Limiting conditions:
- dimensioned AE
= 0. W/m
2
- dimensioned AK, KL T =-17.778°C
- dimensioned IT
T = 4.444°C
n1 (A)
n5 (E)
n4 (D)
n3 (C)
N2 (B)
n11 (F)
n15 (J)
n14 (I)
n13 (H)
n12 (G)
y (Z)
X (R)
n21 (K)
n25 (L)
Not
X
y
Node
With
0.000 0.000
N1
B
0.000 0.381
N2
C
0.000 0.762
N3
D
0.000 1.143
N4
E
0.000 1.524
N5
F
0.762 0.000
N11
G
0.762 0.381
N12
H
0.762 0.762
N13
I
0.762 1.143
N14
J
0.762 1.524
N15
3.2
Characteristics of the mesh
A number of nodes:
25
A number of meshs and types: 16 QUAD4
3.3 Functionalities
tested
Controls
AFFE_MODELE
THERMICS
AXIS
ALL
AFFE_CHAR_THER
TEMP_IMPO
THER_LINEAIRE
EXCIT
CHARGE
RECU_CHAMP
NUME_ORDRE
3.4 Remarks
Voluminal heat
C
p
does not intervene in this test, but must obligatorily be declared. One
takes
C
p
= 2.0 J/m
3
°C.
The limiting condition
= 0. are implicit on the free edges.
Limiting conditions, T =
-
17.778°C on KL, and T = 4.444 on, are incompatible at the point L
(node n25).
Code_Aster applies a “law of overload” which, in this case, consists in taking into account
last condition limits entered. The command of assignment of the imposed temperatures thus has large
influence on the results obtained.
In the case treated, the temperature on the higher face (IT) is affected after that on the blank of
roll (KL).
Code_Aster
®
Version
5.0
Titrate:
TPLA301 Distribution of temperature in a short cylinder
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.01.301-A
Page:
5/6
Manual of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A
4
Results of modeling A
4.1 Values
tested
Identification Reference Aster
Front KL
% difference
Front KL
NISA
Temperature (°C)
Nodes
n1 T (A)
-
17.778
-
17.778
0.00% * 17.778
N2 T (B)
-
14.000
-
13.79
-
1.50%
13.953
n3 T (C)
-
9.111
-
8.908
-
2.27%
9.151
N4 T (D)
-
2.889
-
2.713
-
6.10%
2.892
N5 T (E)
4.444
4.444
0.00% *
4.444
N11 T (F)
-
17.778
-
17.778
0.00% * 17.778
N12 T (G)
-
14.889
-
14.999
0.74% 15.179
N13 T (H)
-
10.667
-
11.005
3.16% 11.499
N14 T (I)
-
4.444
-
4.412
-
0.72%
4.854
N15 T (J)
4.444
4.444
0.00% *
4.444
(*: Imposed temperature)
4.2 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
8 megawords
Time CPU To use: 2.06 seconds
Code_Aster
®
Version
5.0
Titrate:
TPLA301 Distribution of temperature in a short cylinder
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.01.301-A
Page:
6/6
Manual of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A
5
Summary of the results
Modeling gives results whose value (on 10) exceeds the tolerance fixed initially
(5%). The maximum change obtained is of
-
6.10%, it is located on the smallest value of reference.
In this test, Code_Aster applies a “law of overload” which in this case consists in taking in
count the last condition limits entered. The command of assignment of the imposed temperatures, thus has
a great influence on the results obtained.
Calculations were carried out in °C. Determination of the variation, by considering the temperatures in °F,
give a maximum value very different from that obtained in °C.
A calculation carried out with software NISA gives identical results has those of Aster (checked in
case where the temperature imposed on the point L is of 4.44°C).
The quality of the results could be improved by carrying out a finer mesh, the problem of
overload would be always present, but the area of influence of the temperature imposed on the point L would be
weaker. The results are regarded as acceptable taking into account modeling
carried out (mesh and system of unit, law of overload).