Code_Aster
®
Version
5.0
Titrate:
TPLA01 - Infinite hollow roll in thermal balance
Date:
30/08/02
Author (S):
J. PELLET
Key
:
V4.01.001-C
Page:
1/10
Manual of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A
Organization (S):
EDF/AMA
Manual of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
Document: V4.01.001
TPLA01 - Infinite hollow roll in balance
thermics
Summary:
Linear stationary thermics.
Axisymmetric model; 3 modelings.
Analytical solution.
Interest of the test:
·
all axisymmetric elements: triangles and quadrangles, degrees 1 and 2,
·
boundary conditions varied: exchange, imposed temperature, imposed flow,
·
validation partial of the matrix of thermal “mass” because one makes “a false” transient.
The results are not affected by the distortion of the meshs H/L = 40.
Code_Aster
®
Version
5.0
Titrate:
TPLA01 - Infinite hollow roll in thermal balance
Date:
30/08/02
Author (S):
J. PELLET
Key
:
V4.01.001-C
Page:
2/10
Manual of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
Z
R
F
E
B
D
With
C
R
Z
R
I
R
E
Interior radius
R
I
= 0.300 m
External radius
R
E
= 0.35 m
Not F
R = 0.32 m
1.2
Material properties
= 1 W/m °C
C
p
= 2. J/m
3
°C (voluminal heat)
1.3
Boundary conditions and loadings
·
[Cd.]
[AB]:
= 0 W/m
2
·
[EA]:
T T
I
=
= 100°C
·
[ED]:
=
I
= 1729.9091 W/m
2
(re-entering flow)
·
[CB]: exchange
H H
E
=
= 500 W/m
2
°C
T T
E
=
= 17.03444 °C
1.4 Conditions
initial
To make this stationary calculation, a transitory calculation is made for which the boundary conditions are
constants in time. This makes it possible to test elementary calculations of mass intervening in
the first member as well as the second member.
Code_Aster
®
Version
5.0
Titrate:
TPLA01 - Infinite hollow roll in thermal balance
Date:
30/08/02
Author (S):
J. PELLET
Key
:
V4.01.001-C
Page:
3/10
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
()
T R
T
R
R
T
T
R
R
T
T
T
R
R
R
I
I
E
I
E
I
I
E
I
I
E
E
=
+
=
-
= +
= +
Log
:
Log
;
,
.
with
: temperature in skin “interns”
: temperature in “external” skin
“radial” flows
on the walls of the cylinder are:
2.2
Results of reference
Temperatures and flow at the points A, B, D, F.
2.3
Uncertainty on the solution
Analytical solution.
Code_Aster
®
Version
5.0
Titrate:
TPLA01 - Infinite hollow roll in thermal balance
Date:
30/08/02
Author (S):
J. PELLET
Key
:
V4.01.001-C
Page:
4/10
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 (TRIA3, QUAD4)
y
X
0
F
E
B
D
With
C
L = 2.5 10
- 3
H = 0.1
I
G
J
X y
In 0.3.0.0 N1
B 0.35
0.0
N41
D
0.30 0.10 N43
E
0.30 0.05 N2
F 0.32
0.0
N17
3.2
Characteristics of the mesh
A number of nodes: 63.
A number of meshs and types: 40 TRIA3, 20 QUAD4
3.3 Functionalities
tested
Controls
AFFE_MODELE
THERMICS
AXIS
THER_LINEARE
TEMP_INIT
STATIONARY
EXCIT
CHARGE
AFFE_CHAR_THER
TEMP_IMPO
FLUX_REP
EXCHANGE
Code_Aster
®
Version
5.0
Titrate:
TPLA01 - Infinite hollow roll in thermal balance
Date:
30/08/02
Author (S):
J. PELLET
Key
:
V4.01.001-C
Page:
5/10
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 %
difference
T (A) 100 100.000 0.00
T (B) 20 20.002 0.01
T (F) 66.506
66.507 0.00
T (D) 100 99.933 0.07
(A) 1729.91
1722.62
0.42
(B) 1482.78
1487.98
0.35
(D) 1729.91
1723.26
0.38
(F) 1621.79
1628.17
0.39
(F) 1621.79
1615.50
0.39
Code_Aster
®
Version
5.0
Titrate:
TPLA01 - Infinite hollow roll in thermal balance
Date:
30/08/02
Author (S):
J. PELLET
Key
:
V4.01.001-C
Page:
6/10
Manual of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A
5 Modeling
B
5.1
Characteristics of modeling
axis (TRIA6, QUAD8)
y
X
0
F
E
B
D
With
C
L = 2.5 10
- 3
H = 0.1
X y
In 0.3.0.0 N180
B 0.35
0.0
N10
D
0.30 0.10 N178
E
0.30 0.05 N183
F 0.32
0.0
N112
5.2
Characteristics of the mesh
A number of nodes: 185.
A number of meshs and types: 40 TRIA6, 20 QUAD8
5.3 Functionalities
tested
Controls
AFFE_MODELE
THERMICS
AXIS
THER_LINEARE
TEMP_INIT
STATIONARY
EXCIT
CHARGE
AFFE_CHAR_THER
TEMP_IMPO
FLUX_REP
EXCHANGE
Code_Aster
®
Version
5.0
Titrate:
TPLA01 - Infinite hollow roll in thermal balance
Date:
30/08/02
Author (S):
J. PELLET
Key
:
V4.01.001-C
Page:
7/10
Manual of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A
6
Results of modeling B
6.1 Values
tested
Identification Reference
Aster %
difference
T (A) 100 100.00
0.00
T (B) 20 20.00 0.00
T (F) 66.506
66.506 0.00
T (D) 100 100.00
0.00
(A) 1729.91 1729.89
0.00
(B) 1482.78 1482.77
0.00
(D) 1729.91 1729.88
0.00
(F) 1621.79 1621.77
0.00
(F) 1621.79 1621.78
0.00
Code_Aster
®
Version
5.0
Titrate:
TPLA01 - Infinite hollow roll in thermal balance
Date:
30/08/02
Author (S):
J. PELLET
Key
:
V4.01.001-C
Page:
8/10
Manual of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A
7 Modeling
C
7.1
Characteristics of modeling
axis (TRIA6, QUAD9)
y
X
0
F
E
B
D
With
C
L = 2.5 10
- 3
H = 0.1
X y
In 0.3.0.0 N199
B 0.35
0.0
N10
D
0.30 0.10 N197
E
0.30 0.05 N203
F 0.32
0.0
N124
7.2
Characteristics of the mesh
A number of nodes: 205.
A number of meshs and types: 40 TRIA6, 20 QUAD9
7.3 Functionalities
tested
Controls
AFFE_MODELE
THERMICS
AXIS
THER_LINEARE
TEMP_INIT
STATIONARY
EXCIT
CHARGE
AFFE_CHAR_THER
TEMP_IMPO
FLUX_REP
EXCHANGE
Code_Aster
®
Version
5.0
Titrate:
TPLA01 - Infinite hollow roll in thermal balance
Date:
30/08/02
Author (S):
J. PELLET
Key
:
V4.01.001-C
Page:
9/10
Manual of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A
8
Results of modeling C
8.1 Values
tested
Identification Reference
Aster %
difference
T (A) 100 100.00
0.00
T (B) 20 20.00 0.00
T (F) 66.506
66.506 0.00
T (D) 100 100.00
0.00
(A) 1729.91
1729.89
0.00
(B) 1482.78
1482.77
0.00
(D) 1729.91
1729.88
0.00
(F) 1621.79
1621.77
0.00
(F) 1621.79
1621.77
0.00
Code_Aster
®
Version
5.0
Titrate:
TPLA01 - Infinite hollow roll in thermal balance
Date:
30/08/02
Author (S):
J. PELLET
Key
:
V4.01.001-C
Page:
10/10
Manual of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A
9
Summary of the results
This problem is correctly solved:
·
with the various types of elements whatever the degree of interpolation,
·
is not affected by the shape of the elements H/L = 40.