Code_Aster
®
Version
5.0
Titrate:
TPLP303 Distribution of the temperature in the section of a conduit
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.05.303-A
Page:
1/8
Manual of Validation
V4.05 booklet: Stationary thermics of the plane structures
HT-66/02/001/A
Organization (S):
EDF/AMA, EDF/UTO/LOCATED, Delta CAD
Manual of Validation
V4.05 booklet: Stationary thermics of the plane structures
V4.05.303 document
TPLP303 - Distribution of the temperature in
section of a conduit of chimney
Summary:
This test results from the validation independent of version 3 in linear stationary thermics.
It is about a problem plane 2D represented by seven modelings mixing each one several types
elements.
The functionalities tested are as follows:
·
plane thermal element,
·
voluminal thermal element,
·
limiting condition: convection.
The interest of the test lies in the mixture of different elements.
The results are compared with an analytical solution.
Code_Aster
®
Version
5.0
Titrate:
TPLP303 Distribution of the temperature in the section of a conduit
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.05.303-A
Page:
2/8
Manual of Validation
V4.05 booklet: Stationary thermics of the plane structures
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
X
Z
Y
has
has
H
I
T
I
H
E
T
E
= 1.2192 m have
B = 0.3048 m
B
B
1
2
3
4
5
6
7
8
9
10
11
12
With
B
C
D
1.2
Properties of material
=
1.7307 W/m °C Conductivity thermal
1.3
Boundary conditions and loadings
·
Interior surface: H
I
= 68.135 W/m ² °C; T
I
= 37.78 °C,
·
External surface: H
E
= 17.034 W/m ² °C; T
E
= - 17.78 °C.
1.4 Conditions
initial
Without object.
Code_Aster
®
Version
5.0
Titrate:
TPLP303 Distribution of the temperature in the section of a conduit
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.05.303-A
Page:
3/8
Manual of Validation
V4.05 booklet: Stationary thermics of the plane 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 method of relieving
numerical. This reference is quoted in the manual of checking of ANSYS [bib2].
2.2
Results of reference
Temperature at the points n°1 to 11.
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”, 1
St
edition, June 1, 1976
Code_Aster
®
Version
5.0
Titrate:
TPLP303 Distribution of the temperature in the section of a conduit
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.05.303-A
Page:
4/8
Manual of Validation
V4.05 booklet: Stationary thermics of the plane structures
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
PLAN (TRIA3, QUAD4)
Boundary conditions:
- dimensioned AD: T
ext.
= 37.778 °C
H = 68.135 W/m ² °C
- dimensioned BC: T
ext.
= - 17.778 °C
H = 17.034 W/m ² °C
- dimensioned AB, CD
= 0
With
D
C
X
y
N1
N3
N2
N4
N6
N5
N7
N9
N8
N10
N12
N11
0.3
B
45°
3.2
Characteristics of the mesh
A number of nodes:
12
A number of meshs and types: 6 (5 QUAD4, 1 TRIA3)
3.3 Functionalities
tested
Controls
AFFE_MODELE
THERMICS
PLAN
ALL
AFFE_CHAR_THER
EXCHANGE
THER_LINEAIRE
EXCIT
CHARGE
RECU_CHAMP
NUME_ORDRE
Code_Aster
®
Version
5.0
Titrate:
TPLP303 Distribution of the temperature in the section of a conduit
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.05.303-A
Page:
5/8
Manual of Validation
V4.05 booklet: Stationary thermics of the plane structures
HT-66/02/001/A
4
Results of modeling A
4.1 Values
tested
Relative variation %
Absolute deviation
Identification Reference
Aster difference
tolerance
difference tolerance
Temperature (°C)
Points
N1 30.889
29.795
-
3.541
2%
-
1.09
0.5
N2
-
1.333
-
2.528
89.632
2%
-
1.19
0.5
N3
-
15.167
-
16.036
5.729
2%
-
0.869
0.5
N4 34.000
34.718
2.111
2% 0.718 0.5
N5 8.611
8.566
-
0.518
2%
-
0.045
0.5
N6
-
11.278
-
10.810
- 4.152
2%
-
4.152
0.5
N7 34.278
34.114
-
0.480
2%
-
0.164
0.5
N8 12.556
12.716
1.274
2%
0.160
0.5
N9
-
7.611
-
8.152
7.111
2%
-
0.541
0.5
N10 13.500
13.973
3.506
2% 0.473 0.5
N11
-
5.889
-
5.909
0.336 2%
-
0.02
0.5
N12
-
5.444
-
5.377
-
1.229
2% 0.067 0.5
4.2 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
8 megawords
Time CPU To use: 2.36 seconds
Code_Aster
®
Version
5.0
Titrate:
TPLP303 Distribution of the temperature in the section of a conduit
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.05.303-A
Page:
6/8
Manual of Validation
V4.05 booklet: Stationary thermics of the plane structures
HT-66/02/001/A
5
Complementary modelings B, C, D, E, F and G
Modeling b:
·
Mesh identical to that described in the card of modeling, on 1/8 of the structure, but
with quadratic elements,
·
System of unit (°C, W, m, S).
It is noted that the quadratic interpolation improves the results, the maximum change is 49.16% for
the value of reference nearest to 0.
Modeling C:
·
Finer mesh (22 QUAD8 + 4 TRIA6), on 1/8 of the structure,
·
System of unit (°C, W, m, S).
It is noted that compared to modeling B, the maximum change does not decrease but increases
(54.58%).
Modeling D:
·
Mesh identical to that described in the card of modeling, on 1/8 of the structure,
·
System of English unit (°F, Btu, feet, hr).
It is noted that the maximum relative variation decreases in an important way ( 33.29%), this variation is not more
located at the same place. On the other hand it is always located on the value of reference nearest to 0.
Modeling E:
·
Mesh identical to that described in the card of modeling, on 1/8 of the structure, but
with quadratic elements,
·
System of English unit (°F, Btu, feet, hr).
It is noted that the quadratic elements improve the results by with a linear modeling
(maximum change of 6.5%).
Modeling F:
·
cutting identical to that described in the card of modeling (12 QUAD4) but on 1/4 of
the structure,
·
System of English unit (°F, Btu, feet, hr).
It is noted that this mesh with linear elements (without TRIA3) is much more precise,
the maximum change is of 5.27%.
Modeling G:
·
Cutting identical to that described in the card of modeling, but on 1/4 of the structure
and with quadratic elements,
·
System of English unit (°F, Btu, feet, hr).
It is noted that this mesh (without TRIA3) is much less precise than at the time of modeling F,
the maximum change is of 6.26%.
Code_Aster
®
Version
5.0
Titrate:
TPLP303 Distribution of the temperature in the section of a conduit
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.05.303-A
Page:
7/8
Manual of Validation
V4.05 booklet: Stationary thermics of the plane structures
HT-66/02/001/A
6
Results of modelings B, C, D, E, F and G
On the figure below we present the points of observation (for more details to see the card of
test corresponding).
1
2
3
4
5
6
7
8
9
10
11
12
With
B
C
D
In the tables presented below we give for each modeling the results
obtained with Code_Aster, like for modeling has the results obtained with code NISA
(calculations carried out by Mr. CLERK EDF/DER/ADE). We grayed the upper deviations than
tolerance (2%).
Calculations carried out out of W, m, °C
MOD
*
has
MOD
*
B MOD
*
C MOD
*
has
Points ref. ASTER
Variation
%
ASTER
Variation % ASTER
Variation %
NISA
Variation %
1 34.278 34.114
0.480
34.141
0.401 34.181 0.283 34.114 0.480
2 13.500 13.973 3.506
13.277
1.653 13.277 1.649 13.973
3.506
3 5.444 5.377
1.229
5.685
4.421 5.681 4.357 5.377 1.229
4 34.000 34.718 2.111
33.715
0.840 33.847 0.450 34.718
2.111
5 12.556 12.716 1.274
12.140
3.314 12.056 3.982 12.716
1.274
6 5.889 5.909 0.336
6.258
6.258 6.283 6.694 5.909 0.336
7 30.889 29.795
3.541
29.440
4.690 29.290 5.177 29.795 3.541
8 8.611 8.566
0.518
7.057
18.049
7.012 18.566 8.566 0.518
9 7.611 8.152 7.111
8.283
8.693 8.300 9.049 8.152 7.111
10 1.333 2.528 89.632
1.988
49.164 2.061 54.578 2.528 89.632
11 11.278 10.810 4.152
11.571 2.597 11.579 2.671 10.810 4.152
12 15.167 16.036 5.729 15.273 0.701 15.287 0.791 16.036 5.729
* Modeling
Code_Aster
®
Version
5.0
Titrate:
TPLP303 Distribution of the temperature in the section of a conduit
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.05.303-A
Page:
8/8
Manual of Validation
V4.05 booklet: Stationary thermics of the plane structures
HT-66/02/001/A
Calculations carried out in Btu, feet, °F
MOD D
MOD E
MOD F
MOD G
Points ref. ASTER Variation %
ASTER
Variation %
ASTER
Variation % ASTER Variation
%
1 93.7
93.404 0.316 93.453 0.264 93.454 0.262
93.450
0.267
2 56.3
57.152 1.513 55.898 0.713 56.872 1.017
55.884
0.739
3 22.2
22.321 0.545 21.767 1.948 22.220 0.090
21.761
1.975
4 93.2
94.492 1.386 92.686 0.552 94.149 1.018
92.688
0.549
5 54.6
54.889 0.529 53.852 1.370 54.568 0.590
53.821
1.427
6 21.4
21.364 0.168 20.736 3.101 20.936 2.167
20.725
3.155
7 87.6
85.631 2.247 84.992 2.977 96.572 1.173
85.064
2.894
8 47.5
47.419 0.169 44.702 5.890 45.003 5.257
44.523
6.268
9 18.3
17.326 5.323 17.091 6.507 17.335 5.273
17.237
5.807
10 29.6 27.450 7.264 28.421 3.983 29.899 1.010
27.978
5.480
11 11.7 12.542 7.201 11.172 4.509 11.560 1.194
11.272
3.659
12.4.7 3.135 33.285 4.509 4.089 4.824 2.633
4.452
4.932
From these 7 analyzes, we can make the following observations:
·
the mesh suggested in the test probe (5 QUAD4 + 2 TRIA3) is not adapted. For
to bring closer the reference solution there are two possibilities:
-
to use the quadratic mesh on 1/8 of the structure,
-
to use a linear mesh without triangle on ¼ of the structure,
·
the choice of the system of unit to important considerable in the calculation of the relative variation,
·
for same modeling (A) the results between Code_Aster and NISA are identical.
7
Summary of the results
The modeling carried out on 1/8 of the structure gives results of which many values
exceed the tolerance fixed initially (2%). The maximum change obtained is 89%, it is on
smaller value of reference. The analysis of the isotherms shows that those are not
perpendiculars with straight line cd., the condition of symmetry is not observed.
To find an explanation to these important differences, several complementary modelings
(cf were carried out annexes B). The conclusions are as follows:
·
the change of the system of units (°C - >°F) makes it possible to decrease the maximum change with one
value of 33%,
·
modeling with quadratic elements (and in °F) improves the results, the variation
maximum is 6.8%,
·
the modeling of one 1/4 of the structure with only of the QUAD4 (and in °F) improves them
results, the maximum change is of 5.27%,
·
the modeling A, carried out with software NISA, gives results identical to those of
Code_Aster.
Moreover, it was not possible to get the original reference (delivers of Kreith) quoted in
manual of checking of ANSYS. Method of acquisition of the reference solution and its uncertainty
are thus not known.
The results are regarded as acceptable taking into account the points evoked above.
However it will be necessary to seek complementary elements on the reference solution.