Code_Aster ®
Version
5.0
Titrate:
TPLA01 - Infinite hollow Cylindre in thermal balance


Date:
30/08/02
Author (S):
J. Key PELLET
:
V4.01.001-C Page:
1/10

Organization (S): EDF/AMA

Handbook of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
Document: V4.01.001

TPLA01 - Infinite hollow Cylindre 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.

Handbook of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
TPLA01 - Infinite hollow Cylindre in thermal balance


Date:
30/08/02
Author (S):
J. Key PELLET
:
V4.01.001-C Page:
2/10

1
Problem of reference

1.1 Geometry

Z
IH
Re
Interior radius
IH = 0.300 m
External radius
Re = 0.35 m
Not F

R = 0.32 m
R
Z
D
C
E
F
With
B
R


1.2
Material properties

= 1 W/m °C

CP = 2. J/m3 °C (voluminal heat)

1.3
Boundary conditions and loadings

· [CD.] [AB]:
= 0 W/m2
· [EA]:
T = Ti = 100°C
· [ED]:
= I = 1729.9091 W/m2 (re-entering flow)
· [CB]: exchange
H = He = 500 W/m2 °C

T = Te = 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.
Handbook of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
TPLA01 - Infinite hollow Cylindre in thermal balance


Date:
30/08/02
Author (S):
J. Key PELLET
:
V4.01.001-C Page:
3/10

2
Reference solution

2.1
Method of calculation used for the reference solution

R
T (R) = Ti + Log
IH

T - T
T
E
I
I: temperature in skin “interns”
=
;
R
T


E
E: temperature in “external” skin
Log


IH


T

with: “radial” flows
on the walls of the cylinder are:
R


I
= +,
R

I


E
= +
.
R

E

2.2
Results of reference

Temperatures and flow at the points A, B, D, F.

2.3
Uncertainty on the solution

Analytical solution.

Handbook of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
TPLA01 - Infinite hollow Cylindre in thermal balance


Date:
30/08/02
Author (S):
J. Key PELLET
:
V4.01.001-C Page:
4/10

3 Modeling
With

3.1
Characteristics of modeling

axis (TRIA3, QUAD4)

y
L = 2.5 10-3
D
C
X y

H = 0.1
In 0.3.0.0 N1
B 0.35
0.0
N41
E
G
D
0.30 0.10 N43
E
0.30 0.05 N2
F 0.32
0.0
N17
J
0
X
I
With
F
B


3.2
Characteristics of the grid

A number of nodes: 63.

A number of meshs and types: 40 TRIA3, 20 QUAD4

3.3 Functionalities
tested

Commands



AFFE_MODELE
THERMIQUE
AXIS

THER_LINEARE
TEMP_INIT
STATIONNAIRE

EXCIT
CHARGE

AFFE_CHAR_THER
TEMP_IMPO
FLUX_REP
ECHANGE


Handbook of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
TPLA01 - Infinite hollow Cylindre in thermal balance


Date:
30/08/02
Author (S):
J. Key PELLET
:
V4.01.001-C Page:
5/10

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

Handbook of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
TPLA01 - Infinite hollow Cylindre in thermal balance


Date:
30/08/02
Author (S):
J. Key PELLET
:
V4.01.001-C Page:
6/10

5 Modeling
B

5.1
Characteristics of modeling

axis (TRIA6, QUAD8)

y
L = 2.5 10-3
D
C
X y

H = 0.1
In 0.3.0.0 N180
B 0.35
0.0
N10
E
D
0.30 0.10 N178
E
0.30 0.05 N183
F 0.32
0.0
N112
0
X
With
F
B


5.2
Characteristics of the grid

A number of nodes: 185.

A number of meshs and types: 40 TRIA6, 20 QUAD8

5.3 Functionalities
tested

Commands



AFFE_MODELE
THERMIQUE
AXIS

THER_LINEARE
TEMP_INIT
STATIONNAIRE

EXCIT
CHARGE

AFFE_CHAR_THER
TEMP_IMPO
FLUX_REP
ECHANGE


Handbook of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
TPLA01 - Infinite hollow Cylindre in thermal balance


Date:
30/08/02
Author (S):
J. Key PELLET
:
V4.01.001-C Page:
7/10

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

Handbook of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
TPLA01 - Infinite hollow Cylindre in thermal balance


Date:
30/08/02
Author (S):
J. Key PELLET
:
V4.01.001-C Page:
8/10

7 Modeling
C

7.1
Characteristics of modeling

axis (TRIA6, QUAD9)

y
L = 2.5 10-3
D
C
X y

H = 0.1
In 0.3.0.0 N199
B 0.35
0.0
N10
E
D
0.30 0.10 N197
E
0.30 0.05 N203
F 0.32
0.0
N124
0
X
With
F
B


7.2
Characteristics of the grid

A number of nodes: 205.

A number of meshs and types: 40 TRIA6, 20 QUAD9

7.3 Functionalities
tested

Commands



AFFE_MODELE
THERMIQUE
AXIS

THER_LINEARE
TEMP_INIT
STATIONNAIRE

EXCIT
CHARGE

AFFE_CHAR_THER
TEMP_IMPO
FLUX_REP
ECHANGE


Handbook of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
TPLA01 - Infinite hollow Cylindre in thermal balance


Date:
30/08/02
Author (S):
J. Key PELLET
:
V4.01.001-C Page:
9/10

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

Handbook of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
TPLA01 - Infinite hollow Cylindre in thermal balance


Date:
30/08/02
Author (S):
J. Key PELLET
:
V4.01.001-C Page:
10/10

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.
Handbook of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A

Outline document