Code_Aster
®
Version
6.4
Titrate:
TPLV102 - Transport of heat by convection
Date:
03/06/03
Author (S):
J.P. LEFEBVRE, G. BERTRAND
Key
:
V4.04.102-B
Page:
1/6
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/03/008/A
Organization (S):
EDF-R & D/AMA, CS IF
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
Document: V4.04.102
TPLV102 - Transport of heat by convection
in a parallelepiped
Summary:
This functionality was developed in the code in order to be able to test the nonsymmetrical matrices.
Stationary thermal calculation is carried out on elements of the quadrangle type to 4 nodes.
Code_Aster
®
Version
6.4
Titrate:
TPLV102 - Transport of heat by convection
Date:
03/06/03
Author (S):
J.P. LEFEBVRE, G. BERTRAND
Key
:
V4.04.102-B
Page:
2/6
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/03/008/A
1
Problem of reference
1.1 Geometry
One considers the plane thermal problem of a square cavity (on side equal to 1) where heat
propagate:
·
by convection (i.e the particles constituting the medium of the cavity move at a speed
U
supposed here constant); speed
U
is supposed to form an angle of 67.5° with the axis
X
,
·
by conduction.
1.2
Material properties
One takes
=
CP 1
10
6
=
-
from where a diffusivity
=
=
-
CP 10
6
and as one takes
U
U
=
=
=
+
1
10
6
,
.
one has the Peclet number
EP
L
(
L
is the length
characteristic, here
L
=
1
.).
1.3
Boundary conditions and loadings
On segments AB and BC, one imposes a temperature T = 1.
On segment AE, one imposes a temperature T = 0.
On the 2 other sides, one in the condition by defect, namely, one is with null flow.
Code_Aster
®
Version
6.4
Titrate:
TPLV102 - Transport of heat by convection
Date:
03/06/03
Author (S):
J.P. LEFEBVRE, G. BERTRAND
Key
:
V4.04.102-B
Page:
3/6
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/03/008/A
2
Reference solution
2.1
Method of calculation used for the reference solution
The reference solution is that recommended by Hughes and Brooks in their article referred to
bibliographical [bib1].
One can take as exact solution the field of temperature of the border projected upstream on
the border downstream according to the direction speed.
2.2
Results of reference
One tests the temperatures on the border between points E and D.
2.3
Uncertainty on the solution
Analytical solution.
2.4 References
bibliographical
[1]
T.J.R. HUGHES, A. BROOKS “A multidimensional design with No crosswind dissemination” -
T.J.R. HUGHES ED., Finite Element Methods for convection doninated flows, AMD vol. 34
(ASME, New York (1979)).
Code_Aster
®
Version
6.4
Titrate:
TPLV102 - Transport of heat by convection
Date:
03/06/03
Author (S):
J.P. LEFEBVRE, G. BERTRAND
Key
:
V4.04.102-B
Page:
4/6
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/03/008/A
3 Modeling
With
3.1
Characteristics of modeling
Modeling is plane: the mesh consists of 100 square elements QUAD4 of equal sizes,
and 50 elements SEG2 on the borders.
·
the temperature of 0.0 is imposed on
GROUP_NO
d2,
·
the temperature equalizes to 1.0 is imposed on
GROUP_NO
C1 and C4.
3.2
Characteristics of the mesh
50 SEG2, 100 QUA4
3.3 Functionalities
tested
Controls
AFFE_MODELE AFFE
MODELING “PLAN”
AFFE_CHAM_NO
SIZE
“DEPL_R”
AFFE_CHAR_THER CONVECTION SPEED
(AFFE_CHAM_NO)
MACRO_MATR_ASS MATR_ASS
OPTION
“RIGI_THER_CONV_D'
CALC_VECT_ELEM
OPTION
“CHAR_THER”
Code_Aster
®
Version
6.4
Titrate:
TPLV102 - Transport of heat by convection
Date:
03/06/03
Author (S):
J.P. LEFEBVRE, G. BERTRAND
Key
:
V4.04.102-B
Page:
5/6
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/03/008/A
4
Results of modeling A
4.1 Values
tested
Identification Reference
Aster %
difference
T (N31) x=1.0
1.
1.0009
0.0009
T (N29) x=0.8
1.
0.9920
0.008
T (N27) x=0.6
1. 1.0495 0.0495
T (N25) x=0.4
1. 0.845 0.155
T (N23) x=0.2
0. 0.055 0.155
T (N1) x=0.
0. 0.
0.155
Code_Aster
®
Version
6.4
Titrate:
TPLV102 - Transport of heat by convection
Date:
03/06/03
Author (S):
J.P. LEFEBVRE, G. BERTRAND
Key
:
V4.04.102-B
Page:
6/6
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/03/008/A
5
Summary of the results
Good nonsymmetrical matrix installation of for a plane thermal problem.