Code_Aster ®
Version
3
Titrate:
WTNV107 saturated porous Surface subjected to a shock thermo hydraulic Date:
03/12/96
Author (S):
J.M. PROIX, J. WABINSKI Key
:
V7.31.107-A Page:
1/6

Organization (S): EDF/IMA/MN

Handbook 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 diffusion 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).
Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HI-75/96/063/A

Code_Aster ®
Version
3
Titrate:
WTNV107 saturated porous Surface subjected to a shock thermo hydraulic Date:
03/12/96
Author (S):
J.M. PROIX, J. WABINSKI Key
:
V7.31.107-A Page:
2/6


1
Problem of reference

1.1
Surface geometry: quarter of cylinder of axis Z, radius R = 6 m, of
height H = 10 m

Z
Co-ordinates of the points:

With
6 ­ 6
5
R = 6 m
10 m
B
3,7
­ 5,5
5
C
1,76
­ 4,24
5
D
4,57
­ 2,3
5
y
X


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 “joint”.
orders of magnitude of the loadings are not realistic. The other thermal characteristics are
presumedly null.

Hydraulic thermics Coupling
heat
modulate of Biot

voluminal
M
m

(MPa)
(K-1)
C


0
(

J.m3)
3.3 10-10 3.
109 4.
10­11

Density Entropie
Porosity
Conductivity Conductivity
hydraulic thermics
fluid
mass

T
H
(kg m3)
fluid Sm
0
(W.m1K1)
(m2.Pa1 s1)
J.kg1

103
10.0.5 3. 10­8 3.
10­8

Thermal characteristics
decrease 0
(s1)
0

1.3
Boundary conditions and loadings

· Left edge: pressure of the fluid = 10 Pa temperature 10°K
· Other edges: heat flux and hydraulics null

1.4 Conditions
initial

The fields of displacement, pressure, temperature are initially all null.
Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HI-75/96/063/A

Code_Aster ®
Version
3
Titrate:
WTNV107 saturated porous Surface subjected to a shock thermo hydraulic Date:
03/12/96
Author (S):
J.M. PROIX, J. WABINSKI Key
:
V7.31.107-A Page:
3/6


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


C0 T


P
T T =
- 3
R

T

m
T
T

· hydraulic equation of evolution

1 P


T
H P =
- 3

M
m
T
T

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:

C

0
T
T
3
T
=
-
Tr
m T
P = T and


1
C
with
and
0
T = H
=

M
Tr

It is an equation of the diffusion type of the heat defined on a surface.
One chose a cylindrical surface, the problem depends only on the angle (unidimensional problem
of diffusion).

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
PRES
9.76
C 20
TEMP
9.81
D 20
PRES
9.89

Uncertainty on the solution: analytical solution
Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HI-75/96/063/A

Code_Aster ®
Version
3
Titrate:
WTNV107 saturated porous Surface subjected to a shock thermo hydraulic Date:
03/12/96
Author (S):
J.M. PROIX, J. WABINSKI Key
:
V7.31.107-A Page:
4/6


3 Modeling
With

3.1
Characteristics of modeling

Elements: meshs QUAD8 and TRIA6 of modeling 3d_JOINT_CT

Z
y
X

Modeling 3d_JOINT_CT

Discretization in time: calculation with 20s in a step. Implicit scheme (= 1).

Boundary conditions:

DDL_IMPO
(GROUP_NO:l1
PRES: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 grid

4 meshs TRIA6, 2 meshs QUAD8
1 in height, 6 in length.
10 meshs SEG3

3.3 Functionalities
tested

Commands

Keys
AFFE_MODELE 3d_JOINT_CT

[U4.22.01]
DEFI_MATERIAU PORO_JOINT
[U4.23.01]
AFFE_CHAR_MECA DDL_IMPO
NEAR, TEMP
[U4.25.02]
FLUX_THM_REP
FLUN, FLUN_HYDRO
STAT_NON_LINE PARM_THETA
[U4.32.01]
Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HI-75/96/063/A

Code_Aster ®
Version
3
Titrate:
WTNV107 saturated porous Surface subjected to a shock thermo hydraulic Date:
03/12/96
Author (S):
J.M. PROIX, J. WABINSKI Key
:
V7.31.107-A Page:
5/6


4
Results of modeling A

4.1 Values
tested

(node/not) Instant
Component
Reference Aster %
difference
N18 A
20
TEMP
9.74 9.74804 < 0.082
N8 B
20
PRES
9.76 9.76372 < 0.038
N7 C
20
TEMP
9.81 9.81803 < 0.008
N6 D
20
PRES
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



Obstruction memory:
8 MW
Time CPU To use:
3.7 seconds

Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HI-75/96/063/A

Code_Aster ®
Version
3
Titrate:
WTNV107 saturated porous Surface subjected to a shock thermo hydraulic Date:
03/12/96
Author (S):
J.M. PROIX, J. WABINSKI Key
:
V7.31.107-A Page:
6/6


5
Summary of the results

These results validate modeling 3d_JOINT_CT.
Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HI-75/96/063/A

Outline document