Code_Aster
®
Version
5.0
Titrate:
TTLP301 Transfer of heat in a perforated plate
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.23.301-A
Page:
1/8
Manual of Validation
V4.23 booklet: Transitory thermics of the plane systems
HT-66/02/001/A
Organization (S):
EDF/AMA, EDF/UTO/LOCATED, Delta CAD
Manual of Validation
V4.23 booklet: Transitory thermics of the plane systems
V4.23.301 document
TTLP301 - Transfer of heat in a plate
perforated
Summary:
This test, industrialist, result from the validation independent of version 3 in linear transitory thermics.
It is about a problem plane 2D represented by two modelings, one planes, the other voluminal one.
The functionalities tested are as follows:
·
plane thermal element,
·
voluminal thermal element,
·
transitory algorithm of thermics,
·
boundary conditions of exchange and flow.
Code_Aster
®
Version
5.0
Titrate:
TTLP301 Transfer of heat in a perforated plate
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.23.301-A
Page:
2/8
Manual of Validation
V4.23 booklet: Transitory thermics of the plane systems
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
Coolant
Graphite
Fuel
Ø 15.87
Ø 12.7
Ø 18.79
E
D
C
B
With
1.2
Properties of material
=
0.1 W/cm °C
Thermal conductivity
C
p
=
1.0 J/cm
3
°C
Voluminal heat
1.3
Boundary conditions and loadings
·
[ED] Convection coefficient H = 1 W/cm
2
°C T
ext.
= 0°C,
·
[AC] Density flux Q = 1 W/cm
2
,
·
[AB], [BE], [CD.]
= 0.
1.4 Conditions
initial
T (T = 0) = 0
Code_Aster
®
Version
5.0
Titrate:
TTLP301 Transfer of heat in a perforated plate
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.23.301-A
Page:
3/8
Manual of Validation
V4.23 booklet: Transitory thermics of the plane systems
HT-66/02/001/A
2
Reference solution
2.1
Method of calculation used for the reference solution
The reference solution is a numerical solution obtained by the finite element method. This
solution is based on a linear triangular network presented below. Calculations were
carried out by considering an increment of time
T = 0.01 S.
2.2
Results of reference
Temperature at the point C for t=0.1, 0.2,…, 0.9, 1.0, 1.1, 1.2 S
2.3 References
bibliographical
[1]
J. Donea, “One the accuracy off finite element solutions to the transient heat-conduction
equation ", Int. J. num. Meth. Engng, flight 8, n°1, p 103-110, 1974
Code_Aster
®
Version
5.0
Titrate:
TTLP301 Transfer of heat in a perforated plate
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.23.301-A
Page:
4/8
Manual of Validation
V4.23 booklet: Transitory thermics of the plane systems
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
PLAN (TRIA6)
E
D
C
B
With
Limiting conditions:
- dimensioned AC
Q
= 1 W/cm ²
- dimensioned ED
H
= 1 W/cm ² °C
T
ext.
= 0°C
- dimensioned AB, BE, cd.
= 0
y
X
N1
3.2
Characteristics of the mesh
A number of nodes:
718
A number of meshs and types: TRIA6: 335 (SEG3: 22)
3.3
Functionalities tested
Controls
AFFE_MODELE
THERMICS
PLAN
ALL
AFFE_CHAR_THER
FLUX_REP
EXCHANGE
THER_LINEAIRE
TEMP_INIT
VALE
INCREMENT
LIST_INST
RECU_CHAMP
INST
3.4 Remarks
Limiting condition, Flow
= 0., not modelized (implicit).
The discretization in pitch of time is as follows:
10 pitches for [0. , 0.2D+0] is
T = 2.D-2
10 pitches for [0.2D+0, 1.2D+1] are
T = 1.D-1
Code_Aster
®
Version
5.0
Titrate:
TTLP301 Transfer of heat in a perforated plate
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.23.301-A
Page:
5/8
Manual of Validation
V4.23 booklet: Transitory thermics of the plane systems
HT-66/02/001/A
4
Results of modeling A
4.1 Values
tested
Identification Reference
Aster
% difference
Tolerance
Node Time (S)
T (°C)
T (°C)
n1 0.1
1.045
1.0664
2.05%
2%
“0.2
1.447
1.4515
0.31%
2%
“0.3
1.742
1.7480
0.35%
2%
“0.4
1.982
1.9847
0.14%
2%
“0.5
2.189
2.1929
0.18%
2%
“0.6
2.373
2.3757
0.11%
2%
“0.7
2.541
2.5451
0.16%
2%
“0.8
2.698
2.7010
0.11%
2%
“0.9
2.846
2.8491
0.11%
2%
“1.0
2.986
2.9889
0.10%
2%
“1.1
3.120
3.1232
0.10%
2%
“1.2
3.248
3.2517
0.11%
2%
4.2 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
8 megawords
Time CPU To use: 3.89 seconds
Code_Aster
®
Version
5.0
Titrate:
TTLP301 Transfer of heat in a perforated plate
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.23.301-A
Page:
6/8
Manual of Validation
V4.23 booklet: Transitory thermics of the plane systems
HT-66/02/001/A
5 Modeling
B
5.1
Characteristics of modeling
3D (PENTA15)
E
D
C
B
With
Limiting conditions:
- dimensioned AC
Q
= 1 W/cm ²
- dimensioned ED
H
= 1 W/cm ² °C
T
ext.
= 0°C
- dimensioned AB, BE, cd.
= 0
y
X
n1
n719
n911
n1629
n1821
n1
5.2
Characteristics of the mesh
A number of nodes:
2538
A number of meshs and types: PENTA15: 670 (QUAD8: 44)
5.3 Functionalities
tested
Controls
AFFE_MODELE
THERMICS
3D
ALL
AFFE_CHAR_THER
FLUX_REP
EXCHANGE
THER_LINEAIRE
TEMP_INIT
VALE
INCREMENT
LIST_INST
RECU_CHAMP
INST
5.4 Remarks
Limiting condition
= 0. implicit: not modelized.
The discretization in pitch of time is as follows:
10 pitches for [0. , 0.2D+0] is
T = 2.D-2
10 pitches for [0.2D+0, 1.2D+1] are
T = 1.D-1
Code_Aster
®
Version
5.0
Titrate:
TTLP301 Transfer of heat in a perforated plate
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.23.301-A
Page:
7/8
Manual of Validation
V4.23 booklet: Transitory thermics of the plane systems
HT-66/02/001/A
6
Results of modeling B
6.1 Values
tested
Identification Reference
Aster
% difference
Tolerance
Node Time (S)
T (°C)
T (°C)
n1 0.1
1.045
1.0665
2.05%
2%
“0.2
1.447
1.4514
0.30%
2%
“0.3
1.742
1.7480
0.35%
2%
“0.4
1.982
1.9847
0.14%
2%
“0.5
2.189
2.1929
0.18%
2%
“0.6
2.373
2.3757
0.11%
2%
“0.7
2.541
2.5451
0.16%
2%
“0.8
2.698
2.7010
0.11%
2%
“0.9
2.846
2.8491
0.11%
2%
“1.0
2.986
2.9889
0.10%
2%
“1.1
3.120
3.1232
0.10%
2%
“1.2
3.248
3.2517
0.11%
2%
6.2 Remarks
Difference between the values with the nodes n1, n719, n911, n1629, n1821 about 1.e-8.
6.3 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
8 megawords
Time CPU To use: 7.74 seconds
Code_Aster
®
Version
5.0
Titrate:
TTLP301 Transfer of heat in a perforated plate
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.23.301-A
Page:
8/8
Manual of Validation
V4.23 booklet: Transitory thermics of the plane systems
HT-66/02/001/A
7
Summary of the results
Two modelings give results whose only one value exceeds the fixed tolerance
initially. The maximum change is equal to 2.05%, and is thus not very higher than the fixed tolerance (2%). it
is located on the smallest value of temperature and for the weakest moment the T (starting of
problem).
Two modelings, PLAN (TRIA6) and 3D (PENTA15) gives the same results, which is
normal since the mesh and the degree of interpolation are identical.
A finer mesh in the area of the N1 node should improve quality of the results which are
regarded as acceptable taking into account modelings carried out.