Code_Aster ®
Version
8.2
Titrate:
WTNV127 ­ Désaturation of a porous environment without air (3D)

Date:
04/05/06
Author (S):
Key S. GRANET
:
V7.31.127-B Page:
1/8

Organization (S): EDF-R & D/AMA

Handbook 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 steam. Saturation
initial in liquid 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.
Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-62/06/005/A

Code_Aster ®
Version
8.2
Titrate:
WTNV127 ­ Désaturation of a porous environment without air (3D)

Date:
04/05/06
Author (S):
Key S. GRANET
:
V7.31.127-B Page:
2/8

1
Problem of reference

1.1 Geometry

H
G

D
C

E
F

WITH B

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)
103
Heat with constant pressure (J.K-1)
4180
thermal dilation coefficient of the liquid (K-1) 0.
Vapor
Heat-storage capacity (J.K-1)
1900
Initial enthalpy (latent heat of vaporization) 2,5E6.
Mass molar (kg.mol-1)
0,018
Skeleton
Heat-storage capacity with constant constraint (J.K-1) 1050
Initial State
Porosity
0,3
Temperature (K)
300
Pressure of liquid (Pa)
1E5
Steam pressure (Pa)
3700
Initial saturation in liquid
0,5
Constants
Constant of perfect gases
8,315
Coefficients
Homogenized density (kg.m-3)
2200
homogenized Isotherme of sorption
S (
=
- -
-
-
C
P)
12
0 5
.
10
(
0
0
C
P
vp
P
C
P)
With 0 = 3700
vp
P

0
5
= 10
-
C
P

Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-62/06/005/A

Code_Aster ®
Version
8.2
Titrate:
WTNV127 ­ Désaturation of a porous environment without air (3D)

Date:
04/05/06
Author (S):
Key S. GRANET
:
V7.31.127-B Page:
3/8

1.3
Boundary conditions and loadings

On all the faces:

Heat flux
6
Q .n = 10
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:

S = S + S
0
CP
éq
2.1.1-1

[R7.01.11] equation [éq 3.2.1-2] give then:

m

=
- 0 0 0
lq
lq S
C
P
lq
Slq

éq
2.1.1-2
m

= - 0 0 1
-
0
0 0
vp
(vp vp) (S) S vp
C
P

It is written that the total water mass is preserved (because there is no water flow at the edge) and one obtains:

m + m = 0

lq
vp
(
éq
2.1.1-3
-
lq
vp) S
P +
C
(
0
-
vp
vp) (1 - S0) = 0

[R7.01.11] equation [éq 4.4-1] gives in addition

p
ol
vp M
=
vp
1
ln
P +
0
p
RT
lq
vp
lq
éq
2.1.1-4
M ol
vp (
ol
0
M
0
H - 0
H
vp
lq) 1
1
vp
p
p
T
T

- +
(C - C
vp
lq)



0

ln
+
-
0


1
R
T
T
R
T T


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.
Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-62/06/005/A

Code_Aster ®
Version
8.2
Titrate:
WTNV127 ­ Désaturation of a porous environment without air (3D)

Date:
04/05/06
Author (S):
Key S. GRANET
:
V7.31.127-B Page:
4/8

All made calculations, one obtains:


ol
ol

1 S M
M
Pvp (- 0
lq
vp)
(- 0)

vp
S +
- (- 0
lq
vp)

S
vp
T
P
1 S p
0

=
lq
(
0) 0

-



vp
2

RT

R
0
T



éq 2.1.1-5
P
M ol
M ol
vp -
vp
P =
vp
lq
(0h - 0h
vp
lq) T

0
0
2

p
RT
R
0
vp
lq
T



2.1.2 Calculation of the temperature

[R7.01.11] equation [éq 3.2.4.3-1] gives:
Q
m
= - T p

+ C0
3
T

gz
vp


éq
2.1.2-1
(since the other dilation coefficients are null).
Equation [éq 3.2.4.3-2] gives:
1
m
(Slq)
=
gz

éq
2.1.2-2
T
3
One thus obtains:
Q
= - (
- S
+ 0
1

lq) p
C T
vp


éq
2.1.2-3

In this problem, Q
is anything else only the heat brought per unit of volume.
By calling Vol the total volume of the part and Surf its side surface and T
the time of application
flows:
Surfing
Q
= T

Q
N
.
ext.
éq
2.1.2-4
Flight

2.1.3 System to be solved


1
ol
S M
ol
M
(- 0
lq
vp)
(
0)
vp
S +
- (- 0
lq
vp)

vp
S
S p
0
- (1 - 0) 0



vp
2
0
RT
RT



P
0
ol
ol
0
0
vp

1
M vp
M vp (H -
vp
lq
H)








-
-
lq
P =
0



0
0
2
p
RT
R
0


vp
lq
T

Surfing


T
T
Q
N
.

0
- (
1 - S
C
Flight
lq)

0

ext.











éq 2.1.2-5
Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-62/06/005/A

Code_Aster ®
Version
8.2
Titrate:
WTNV127 ­ Désaturation of a porous environment without air (3D)

Date:
04/05/06
Author (S):
Key S. GRANET
:
V7.31.127-B Page:
5/8

2.2
Results of reference

One gives the value of the temperature, the pressure of liquid 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
1 -)
0
0 0
=
-
- -

S
0
R

lq SSL
(0
1 SSL) 0 0vp
C 0 =

(1 -)
S
p

+

+ 1

Sc
lq SSL C
S
C
lq
(
L)
p
vp
vp
0
0
C = C, this last relation being true because the dilation coefficient of the grains is null.

S

0
S
0
T
0
p


vp
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
C
C
C
lq L
p
vp
0
(calculated)
2,20E+03 3,00E-01 2,93E+03
1,05E+03
4,18E+03
1,90E+03 2,78E+06



Q
N
.
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.
Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-62/06/005/A

Code_Aster ®
Version
8.2
Titrate:
WTNV127 ­ Désaturation of a porous environment without air (3D)

Date:
04/05/06
Author (S):
Key S. GRANET
:
V7.31.127-B Page:
6/8

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 step of time: 102 S.

3.3 Values
tested

Node
Type of value
Moment (S)
Reference
Aster Difference
(%)
(analytical)
NO1
DEPL/TEMP
102 2 2,15 8%

NO1
DEPL/PRE1
102 - 1,4
106 - 1,46
106 4%

NO1
VARI_ELNO_ELGA/V3
102.425.460
8%

One thus finds results relatively close to the analytical results. Uncertainty remaining
enough broad because of linearization equations.

Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-62/06/005/A

Code_Aster ®
Version
8.2
Titrate:
WTNV127 ­ Désaturation of a porous environment without air (3D)

Date:
04/05/06
Author (S):
Key S. GRANET
:
V7.31.127-B Page:
7/8

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 step of time: 102 S.

4.3 Values
tested

Node
Type of value
Moment (S)
Reference
Aster Difference
(analytical)
(%)
NO1
DEPL/TEMP
102 2
2,15 8%

NO1
DEPL/PRE1
102 - 1,4
106 - 1,46
106 4%

NO1
VARI_ELNO_ELGA/V3
102 425
460
8%

One thus finds results relatively close to the analytical results. Uncertainty remaining
enough broad because of linearization equations.

Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-62/06/005/A

Code_Aster ®
Version
8.2
Titrate:
WTNV127 ­ Désaturation of a porous environment without air (3D)

Date:
04/05/06
Author (S):
Key S. GRANET
:
V7.31.127-B Page:
8/8

Intentionally white left page.
Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-62/06/005/A