Code_Aster
®
Version
8.2
Titrate:
WTNV127 Désaturation of a porous environment without air (3D)
Date:
04/05/06
Author (S):
S. GRANET
Key
:
V7.31.127-B
Page:
1/8
Manual of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-62/06/005/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
Document: V7.31.127
WTNV127 Désaturation of a porous environment without
air (modeling 3d_THV)
Summary:
One heats a porous environment whose pores are filled with a mixture of water and water vapor. Saturation
initial in fluid is 50%, the loading is a uniform heat flux on the edges of the field.
modeling made by only one cubic element corresponds to the modeling of a homogeneous problem in
space.
The reference solution is an approximate analytical solution.
Code_Aster
®
Version
8.2
Titrate:
WTNV127 Désaturation of a porous environment without air (3D)
Date:
04/05/06
Author (S):
S. GRANET
Key
:
V7.31.127-B
Page:
2/8
Manual of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-62/06/005/A
1
Problem of reference
1.1 Geometry
Co-ordinates of the points (m):
With
0
0
100
E
0
0
0
B 100
0.100 F 100
0 0
C 100.100.100 G 100.100 0
D
0.100.100 H
0.100 0
1.2
Properties of material
One gives here only the properties whose solution depends, knowing that the command file
contains other data of material (thermal conductivity, moduli of elasticity…) who finally
do not play any part in the solution of the dealt with problem.
Liquid water
Density (kg.m
- 3
)
Heat with constant pressure (J.K
- 1
)
thermal expansion factor of the fluid (K
- 1
)
10
3
4180
0.
Vapor
Heat-storage capacity (J.K
- 1
)
Initial enthalpy (latent heat of vaporization)
Mass molar (kg.mol
- 1
)
1900
2,5E6.
0,018
Skeleton
Heat-storage capacity with constant stress (J.K
- 1
) 1050
Initial State
Porosity
Temperature (K)
Pressure of fluid (AP)
Steam pressure (AP)
Initial saturation in fluid
0,3
300
1E5
3700
0,5
Constants
Constant of perfect gases
8,315
Coefficients
homogenized
Homogenized density (kg.m
- 3
)
Isotherm of sorption
2200
()
(
)
0
0
12
10
5
.
0
C
vp
C
C
P
P
P
P
S
-
-
-
=
-
With
3700
0
=
vp
P
5
0
10
-
=
C
P
D
C
WITH B
H
G
F
E
Code_Aster
®
Version
8.2
Titrate:
WTNV127 Désaturation of a porous environment without air (3D)
Date:
04/05/06
Author (S):
S. GRANET
Key
:
V7.31.127-B
Page:
3/8
Manual of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-62/06/005/A
1.3
Boundary conditions and loadings
On all the faces:
Heat flux
6
10
.
=
N
Q
ext.
Hydraulic flow no one
2
Reference solution
2.1
Method of calculation
2.1.1 Calculation of the steam pressure starting from the temperature
We suppose the linear curve of saturation. It is thus written:
C
P
S
S
S
+
=
0
éq
2.1.1-1
[R7.01.11] equation [éq 3.2.1-2] give then:
(
)
(
)
C
vp
vp
vp
vp
lq
lq
C
lq
lq
P
S
S
m
S
P
S
m
-
-
-
=
-
=
0
0
0
0
0
0
0
0
1
éq
2.1.1-2
It is written that the total water mass is preserved (because there is no water flow at the edge) and one obtains:
(
)
(
)
(
)
0
1
0
0
0
=
-
-
+
-
=
+
S
P
S
m
m
vp
vp
C
vp
lq
vp
lq
éq
2.1.1-3
[R7.01.11] equation [éq 4.4-1] gives in addition
(
)
(
)
-
+
-
+
-
-
+
=
1
ln
1
1
1
ln
0
0
0
0
0
0
T
T
T
T
C
C
R
M
T
T
H
H
R
M
P
RT
M
p
p
p
lq
p
vp
ol
vp
lq
vp
ol
vp
lq
ol
vp
vp
vp
lq
éq
2.1.1-4
Coupling of the equations [éq 2.1.1-3] and [éq 2.1.1-4], for which it is necessary to add the equation of perfect gases
for the vapor, is a strongly nonlinear system which we will solve in small disturbance, it
who allows to linearize it.
Code_Aster
®
Version
8.2
Titrate:
WTNV127 Désaturation of a porous environment without air (3D)
Date:
04/05/06
Author (S):
S. GRANET
Key
:
V7.31.127-B
Page:
4/8
Manual of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-62/06/005/A
All made calculations, one obtains:
(
)
(
)
(
)
(
)
(
)
-
=
-
-
=
-
-
-
+
-
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
T
T
H
H
R
M
P
RT
M
p
P
T
T
R
M
p
S
P
S
RT
M
S
S
P
lq
vp
ol
vp
lq
lq
ol
vp
vp
vp
ol
vp
vp
lq
vp
lq
ol
vp
vp
lq
vp
éq 2.1.1-5
2.1.2 Calculation of the temperature
[R7.01.11] equation [éq 3.2.4.3-1] gives:
T
C
p
T
Q
vp
m
gz
+
-
=
0
3
éq
2.1.2-1
(since the other expansion factors are null).
Equation [éq 3.2.4.3-2] gives:
(
)
T
S
lq
m
gz
3
1
-
=
éq
2.1.2-2
One thus obtains:
(
)
T
C
p
S
Q
vp
lq
+
-
-
=
0
1
éq
2.1.2-3
In this problem,
Q
is anything else only the heat brought per unit of volume.
While calling
Flight
the total volume of the part and
Surfing
its side surface and
T
the time of application
flows:
N
Q.
ext.
Flight
Surfing
T
Q
=
éq
2.1.2-4
2.1.3 System to be solved
(
)
(
)
(
)
(
)
(
)
(
)
=
-
-
-
-
-
-
-
-
-
-
+
-
N
Q.
0
0
1
0
1
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
ext.
lq
vp
lq
lq
vp
ol
vp
lq
ol
vp
vp
ol
vp
vp
vp
lq
ol
vp
vp
lq
Flight
Surfing
T
T
P
P
C
S
T
H
H
R
M
RT
M
p
RT
M
p
S
S
RT
M
S
S
éq 2.1.2-5
Code_Aster
®
Version
8.2
Titrate:
WTNV127 Désaturation of a porous environment without air (3D)
Date:
04/05/06
Author (S):
S. GRANET
Key
:
V7.31.127-B
Page:
5/8
Manual of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-62/06/005/A
2.2
Results of reference
One gives the value of the temperature, the pressure of fluid and the steam pressure, solution
system (10) with the data summarized in the paragraph [§1.2] and pointed out Ci below. For
calculation of the heat-storage capacities, one uses the following relations:
(
)
(
)
0
0
0
0
0
0
0
0
1
1
vp
L
L
lq
S
S
S
R
-
-
-
=
-
(
)
(
)
p
vp
vp
L
p
lq
L
lq
S
S
C
S
C
S
C
C
-
+
+
-
=
1
1
0
0
0
= C
C
, this last relation being true because the expansion factor of the grains is null.
0
S
S
0
T
0
vp
p
0
vp
H
0
vp
(calculated)
lq
5,00E-01 - 1,00E-12 3,00E+02
3,70E+03
2,50E+06
2,67E-02 1,00E+03
0
R
0
S
(calculated)
S
C
p
lq
C
L
p
vp
C
0
C
(calculated)
2,20E+03 3,00E-01 2,93E+03
1,05E+03
4,18E+03
1,90E+03 2,78E+06
N
Q
.
ext.
T
Surfing
Flight
1,00E+06 100
6,00E+04
1,00E+06
After resolution, one obtains the following results:
vp
P
425
lq
P
L
- 1,4E+06
T
2e+00
2.3 Uncertainties
Uncertainties are rather large because the analytical solution is an approximate solution of
fact of the linearization of the equations.
Code_Aster
®
Version
8.2
Titrate:
WTNV127 Désaturation of a porous environment without air (3D)
Date:
04/05/06
Author (S):
S. GRANET
Key
:
V7.31.127-B
Page:
6/8
Manual of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-62/06/005/A
3 Modeling
With
3.1
Characteristics of modeling A
Modeling in plane deformations. A Q8 element.
3.2 Functionalities
tested
Order Option
AFFE_MODELE
3d_THVD
DEFI_MATERIAU
THM_LIQU
THM_DIFFU
THM_INIT
ELAS
AFFE_CHAR_MECA DDL_IMPO PRE1
TEMP
STAT_NON_LINE COMP_INCR
RELATION KIT_THV
RELATION_KIT
LIQU_VAPE
HYDR_UTIL
Discretization in time: only one pitch of time: 10
2
S.
3.3 Values
tested
Node
Type of value
Moment (S)
Reference
(analytical)
Aster Difference
(%)
NO1
DEPL/TEMP
10
2
2 2,15 8%
NO1
DEPL/PRE1
10
2
- 1,4
10
6
- 1,46
10
6
4%
NO1
VARI_ELNO_ELGA/V3
10
2
425 460
8%
One thus finds results relatively close to the analytical results. Uncertainty remaining
enough broad because of linearization equations.
Code_Aster
®
Version
8.2
Titrate:
WTNV127 Désaturation of a porous environment without air (3D)
Date:
04/05/06
Author (S):
S. GRANET
Key
:
V7.31.127-B
Page:
7/8
Manual of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-62/06/005/A
4 Modeling
B
Even modeling but into selective.
4.1
Characteristics of modeling B
Modeling in plane deformations. A Q8 element
4.2 Functionalities
tested
Order
Option
AFFE_MODELE
3d_THVS
DEFI_MATERIAU
THM_LIQU
THM_DIFFU
THM_INIT
ELAS
AFFE_CHAR_MECA DDL_IMPO PRE1
TEMP
STAT_NON_LINE COMP_INCR
RELATION KIT_THV
RELATION_KIT
LIQU_VAPE
HYDR_UTIL
Discretization in time: only one pitch of time: 10
2
S.
4.3 Values
tested
Node
Type of value
Moment (S)
Reference
(analytical)
Aster Difference
(%)
NO1
DEPL/TEMP
10
2
2
2,15 8%
NO1
DEPL/PRE1
10
2
- 1,4
10
6
- 1,46
10
6
4%
NO1
VARI_ELNO_ELGA/V3
10
2
425
460
8%
One thus finds results relatively close to the analytical results. Uncertainty remaining
enough broad because of linearization equations.
Code_Aster
®
Version
8.2
Titrate:
WTNV127 Désaturation of a porous environment without air (3D)
Date:
04/05/06
Author (S):
S. GRANET
Key
:
V7.31.127-B
Page:
8/8
Manual of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-62/06/005/A
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