Code_Aster
®
Version
3
Titrate:
WTNV107 Surfaces porous saturated subjected to a hydraulic thermo shock
Date:
03/12/96
Author (S):
J.M. PROIX, J. WABINSKI
Key
:
V7.31.107-A
Page:
1/6
Manual of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HI-75/96/063/A
Organization (S):
EDF/IMA/MN
Manual of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
V7.31.107 document
WTNV107 - Subjected saturated porous surface
with a hydraulic thermo shock
Summary:
One considers a surface problem (in 3D) of behavior of a saturated porous environment subjected to one
hydraulic thermo loading.
One studies a transient state, for the problems of coupled dissemination the thermo hydraulic (however part
mechanics does not intervene, indeformable porous surface).
The model is 3D surface, with a thermo behavior hydraulic linear for modeling
3d_JOINT_CT
.
The test validates in particular the taking into account of the curvature of surface (portion of cylinder).
Code_Aster
®
Version
3
Titrate:
WTNV107 Surfaces porous saturated subjected to a hydraulic thermo shock
Date:
03/12/96
Author (S):
J.M. PROIX, J. WABINSKI
Key
:
V7.31.107-A
Page:
2/6
Manual of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HI-75/96/063/A
1
Problem of reference
1.1
Surface geometry: quarter of cylinder of axis Z, radius R = 6 m, of
height H = 10 m
Co-ordinates of the points:
With
6 6
5
B
3,7
5,5
5
C
1,76
4,24
5
D
4,57
2,3
5
X
y
Z
10 m
R =
6 m
1.2
Material properties
The values chosen for the characteristics of materials are not representative of the properties of
usual continuous porous materials (clay), more than of the characteristics of rock “gasket”.
orders of magnitude of the loadings are not realistic. The other thermal characteristics are
presumedly null.
Hydraulic thermics Coupling
heat
voluminal
modulate of Biot
M
(MPa)
()
m
K
-
1
(
)
C
J m
0
3
.
3.3 10
10
3.
10
9
4.
10
11
Density Entropy
Porosity
Conductivity
thermics
Conductivity
hydraulics
fluid
(kg m
3
)
mass
fluid
S
m
0
J.kg
1
T
(W.m
1
K
1
)
H
(m
2
.Pa
1
S
1
)
10
3
10.0.5 3. 10
8
3.
10
8
Thermal characteristics
decrease
0
(S
1
)
0
1.3
Boundary conditions and loadings
·
Left edge: pressure of the fluid = 10 AP temperature 10°K
·
Other edges: heat flux and hydraulics null
1.4 Conditions
initial
The fields of displacement, pressure, temperature are initially all null.
Code_Aster
®
Version
3
Titrate:
WTNV107 Surfaces porous saturated subjected to a hydraulic thermo shock
Date:
03/12/96
Author (S):
J.M. PROIX, J. WABINSKI
Key
:
V7.31.107-A
Page:
3/6
Manual of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HI-75/96/063/A
2
Reference solution
2.1
Method of calculation used for the reference solution
In the absence of voluminal forces, the hydrothermal system of coupled equations is written (for one
nonheating material) (
being the surface Laplacian):
·
thermal equation of evolution
T
R
m
T
C
T
T
T
P
T
=
-
0
3
·
hydraulic equation of evolution
H
m
P
M
P
T
T
T
=
-
1
3
By choosing the boundary conditions identical for the two problems, and of the coefficients such
that the equations are identical one brings back to the solution of only one equation:
P T
T
C
T
T
T
M
C
T
T
R
m
T
H
R
=
=
-
=
=
and
with
and
0
0
3
1
It is an equation of the dissemination type of the heat defined on a surface.
One chose a cylindrical surface, the problem depends only on the angle (unidimensional problem
of dissemination).
One can seek solutions by separating the variables (space and time), which gives a solution
in product the exponential ones of the time and cosine of the variable of space.
To check the initial conditions, one obtains a development in series (resolution semi-analytical
problem).
2.2
Results of reference
Value of components of the temperature and the pressure for certain nodes and the moment of
calculation T = 20s.
Not Urgent
component
Reference
To 20
TEMP
9.74
B 20
NEAR
9.76
C 20
TEMP
9.81
D 20
NEAR
9.89
Uncertainty on the solution: analytical solution
Code_Aster
®
Version
3
Titrate:
WTNV107 Surfaces porous saturated subjected to a hydraulic thermo shock
Date:
03/12/96
Author (S):
J.M. PROIX, J. WABINSKI
Key
:
V7.31.107-A
Page:
4/6
Manual of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HI-75/96/063/A
3 Modeling
With
3.1
Characteristics of modeling
Elements: meshs
QUAD8
and
TRIA6
modeling
3d_JOINT_CT
X
y
Z
Modeling 3d_JOINT_CT
Discretization in time: calculation with 20s in a pitch. Implicit scheme (
= 1).
Boundary conditions:
DDL_IMPO
(GROUP_NO:l1
NEAR:10 TEMP:10
)
FLUX_THM_REP
(GROUP_MA:l2
FLUN:0. FLUN_HYDRO:0)
(GROUP_MA:high FLUN:0. FLUN_HYDRO:0)
(GROUP_MA:low
FLUN:0. FLUN_HYDRO:0)
3.2
Characteristics of the mesh
4 meshs TRIA6, 2 meshs QUAD8
1 in height, 6 in length.
10 meshs SEG3
3.3 Functionalities
tested
Controls
Keys
AFFE_MODELE 3d_JOINT_CT
[U4.22.01]
DEFI_MATERIAU PORO_JOINT
[U4.23.01]
AFFE_CHAR_MECA DDL_IMPO
FLUX_THM_REP
NEAR, TEMP
FLUN, FLUN_HYDRO
[U4.25.02]
STAT_NON_LINE PARM_THETA
[U4.32.01]
Code_Aster
®
Version
3
Titrate:
WTNV107 Surfaces porous saturated subjected to a hydraulic thermo shock
Date:
03/12/96
Author (S):
J.M. PROIX, J. WABINSKI
Key
:
V7.31.107-A
Page:
5/6
Manual of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HI-75/96/063/A
4
Results of modeling A
4.1 Values
tested
(node/not) Urgent
Component
Reference Aster %
difference
N18 A
20
TEMP
9.74 9.74804 < 0.082
N8 B
20
NEAR
9.76 9.76372 < 0.038
N7 C
20
TEMP
9.81 9.81803 < 0.008
N6 D
20
NEAR
9.89 9.8895 < 0.005
4.2 Remarks
The calculated solution is close to the reference solution, the curvature of surface is well taken in
count.
4.3 Parameters
of execution
Version: 3.06.13
Machine: CRAY C90
Overall dimension memory:
8 MW
Time CPU To use:
3.7 seconds
Code_Aster
®
Version
3
Titrate:
WTNV107 Surfaces porous saturated subjected to a hydraulic thermo shock
Date:
03/12/96
Author (S):
J.M. PROIX, J. WABINSKI
Key
:
V7.31.107-A
Page:
6/6
Manual of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HI-75/96/063/A
5
Summary of the results
These results validate modeling
3d_JOINT_CT
.