Code_Aster
®
Version
7.4
Titrate:
Note of use of model THM
Date:
06/07/04
Author (S):
S. GRANET, C. CHAVANT
Key
:
U2.04.05-A
Page
:
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Instruction manual
U2.04 booklet: Nonlinear mechanics
HT-66/04/004/A
Organization (S):
EDF-R & D/AMA
Instruction manual
U2.04 booklet: Nonlinear mechanics
Document: U2.04.05
Note of use of model THM
Summary:
One details the procedure to be followed here for the realization of a calculation THM.
Code_Aster
®
Version
7.4
Titrate:
Note of use of model THM
Date:
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Key
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Instruction manual
U2.04 booklet: Nonlinear mechanics
HT-66/04/004/A
Count
matters
Code_Aster
®
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7.4
Titrate:
Note of use of model THM
Date:
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1
The broad outline
1.1
Context of studies THM
First of all, it is advisable to define the quite precise framework of Hydro-mechanical Thermo- calculations.
Those have as an exclusive application the study of the porous environments. Knowing that, modelings THM
cover L `evolution mechanical of these mediums and the flows in their center. The latter concern
one or two fluids and is governed by the laws of Darcy (fluid darcéens). The problem of complete THM
draft thus of the flow of or the fluid (S), the mechanics of the skeleton, as well as
thermics: the resolution is entirely coupled (and not chained).
1.2 General
Calculations are based on families of laws of behavior THM for the saturated porous environments
and unsaturated. The mechanics of the porous environments gathers a very exhaustive collection of
physical phenomena concerning with the solids and the fluids. It makes the assumption of a coupling enters
mechanical evolutions of the solids and the fluids, seen like continuous mediums, with
hydraulic evolutions, which regulate the problems of dissemination of fluids within walls or of
volumes, and thermal evolutions. The formulation of hydro-mechanical Thermo modeling
(THM) in porous environment such as it is made in Code_Aster is detailed in [R7.01.11] and
[R7.01.10]. All the notations employed here thus refer to it. One recalls however some
essential notations thereafter:
Concerning the fluids, one considers (the most complete case) two phases (fluid and gas) and two
components called by convenience water and air. The following indices then are used:
W
for liquid water
AD
for the dissolved air
have
for the dry air
vp
for the water vapor
The thermodynamic variables are:
·
pressures of the components:
()
T
p
W
,
X
,
()
T
p
AD
,
X
,
()
T
p
vp
,
X
,
()
T
p
have
,
X
,
·
the temperature of the medium
()
T
T
X,
.
These various variables are not completely independent. Indeed, if only one is considered
component, thermodynamic balance between its phases imposes a relation between the pressure of
vapor and pressure of the fluid of this component. Finally, there is only one pressure
independent by component, just as there is only one conservation equation of the mass.
The number of independent pressures is thus equal to the number of independent components.
choice of these pressures varies according to laws' of behaviors.
For the case known as saturated (only one component air or water) we chose the pressure of this single
component.
For the case says unsaturated (presence of air and water), we chose like variables
independent:
·
total pressure of gas
()
have
vp
gz
p
p
T
p
+
=
,
X
,
·
capillary pressure
()
AD
W
gz
lq
gz
C
p
p
p
p
p
T
p
-
-
=
-
=
,
X
.
We will see the Aster terminology thereafter for these variables.
Code_Aster
®
Version
7.4
Titrate:
Note of use of model THM
Date:
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U2.04 booklet: Nonlinear mechanics
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1.3
Stages of calculations
For the stages necessary to the manufacture of a calculation Aster, independently of the aspects
purely THM, one will refer to the documentation of each control used.
In the whole of this document one will refer to a typical example of file of calculation given in
appendix. In any calculation Aster, several key stages must be carried out:
·
Choice of modeling
·
Data materials
·
Initialization
·
Calculation
·
Postprocessing
2
Various stages of calculation
2.1
Choice of the model
The choice is done by the use of the control
AFFE_MODELE
as in the example below:
MODELE=AFFE_MODELE (MAILLAGE=MAIL,
AFFE=_F (TOUT=' OUI',
PHENOMENE=' MECANIQUE',
MODELISATION=' AXIS_THH2MD',),);
The digital processing in THM requires a quadratic mesh since the elements are of type
P2 in displacement and P1 in pressure and temperature in order to avoid problems of oscillations.
The phenomenon
“MECHANICAL”
is obligatory whatever the selected type of modeling (with or
without mechanics).
The user must inform here in an obligatory way the key word
MODELING
. This key word allows
to define the type of affected element in a type of mesh. Modelings available in THM are them
following:
MODELING
Modeling
geometrical
Phenomena taken into account
D_PLAN_HM
plane
Mechanics, hydraulics with an unknown pressure
D_PLAN_HMD
plane
Mechanics, hydraulics with an unknown pressure (lumpé)
D_PLAN_HHM
plane
Mechanics, hydraulics with two unknown pressures
D_PLAN_HHMD
plane
Mechanics, hydraulics with two unknown pressures
(lumpé)
D_PLAN_HH2MD
plane
Mechanics, hydraulics with two unknown pressures and
two components per phase (lumpé)
D_PLAN_THH
plane
Thermics, hydraulics with two unknown pressures
D_PLAN_THHD
plane
Thermics, hydraulics with two unknown pressures
(lumpé)
D_PLAN_THH 2D
plane
Thermics, hydraulics with two unknown pressures and two
components by phase (lumpé)
D_PLAN_THM
plane
Thermics, mechanics, hydraulics with a pressure
unknown factor
D_PLAN_THVD
plane
Thermics, mechanics, hydraulics with two pressures
unknown factors (2 phases: liquid water and vapor) (lumpé)
D_PLAN_THMD
plane
Thermics, mechanics, hydraulics with a pressure
unknown factor (lumpé)
D_PLAN_THHM
plane
Thermics, mechanics, hydraulics with two pressures
unknown factors
D_PLAN_THHMD
plane
Thermics, mechanics, hydraulics with two pressures
unknown factors (lumpé)
Code_Aster
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Note of use of model THM
Date:
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D_PLAN_THH2MD
plane
Thermics, mechanics, hydraulics with two pressures
unknown factors and two components per phase (lumpé)
AXIS_HM
axisymmetric Mechanics,
hydraulics with an unknown pressure
AXIS_HMD
axisymmetric Mechanics,
hydraulics
with an unknown pressure (lumpé)
AXIS_HHM
axisymmetric Mechanics,
hydraulics with two unknown pressures
AXIS_HHMD
axisymmetric Mechanics,
hydraulics with two unknown pressures
(lumpé)
AXIS_HH2MD
axisymmetric Mechanics,
hydraulics
with two unknown pressures and
two components per phase (lumpé)
AXIS_THH
axisymmetric Thermics,
hydraulics
with two unknown pressures
AXIS_THHD
axisymmetric Thermics,
hydraulics with two unknown pressures
(lumpé)
AXIS_THH 2D
axisymmetric
Thermics, hydraulics with two unknown pressures and two
components by phase (lumpé)
AXIS_THM
axisymmetric Thermics,
mechanics, hydraulics with a pressure
unknown factor
AXIS_THMD
axisymmetric Thermics,
mechanics, hydraulics with a pressure
unknown factor (lumpé)
AXIS_THVD
axisymmetric Thermics,
mechanics,
hydraulics with two pressures
unknown factors (2 phases: liquid water and vapor) (lumpé)
AXIS_THHM
axisymmetric Thermics,
mechanics,
hydraulics with two pressures
unknown factors
AXIS_THHMD
axisymmetric Thermics,
mechanics,
hydraulics with two pressures
unknown factors (lumpé)
AXIS_THH2MD
axisymmetric Thermics,
mechanics,
hydraulics with two pressures
unknown factors and two components per phase (lumpé)
3d_HM
3D
Mechanics, hydraulics with an unknown pressure
3d_HMD
3D
Mechanics, hydraulics with an unknown pressure (lumpé)
3d_HHM
3D
Mechanics, hydraulics with two unknown pressures
3d_HHMD
3D
Mechanics, hydraulics with two unknown pressures
(lumpé)
3d_HH2MD
3D
Mechanics, hydraulics with two unknown pressures and
two components per phase (lumpé)
3d_THH
3D
Thermics, hydraulics with two unknown pressures
3d_THHD
3D
Thermics, hydraulics with two unknown pressures
(lumpé)
3d_THH 2D
3D
Thermics, hydraulics with two unknown pressures and two
components by phase (lumpé)
3d_THM
3D
Thermics, mechanics, hydraulics with a pressure
unknown factor
3d_THMD
3D
Thermics, mechanics, hydraulics with a pressure
unknown factor (lumpé)
3d_THVD
3D
Thermics, mechanics, hydraulics with two pressures
unknown factors (2 phases: liquid water and vapor) (lumpé)
3d_THHM
3D
Thermics, mechanics, hydraulics with two pressures
unknown factors
3d_THHMD
3D
Thermics, mechanics, hydraulics with two pressures
unknown factors (lumpé)
3d_THH2MD
3D
Thermics, mechanics, hydraulics with two pressures
unknown factors and two components per phase (lumpé)
The main unknown factors which are also the values of the degrees of freedom, are noted in the case of
the most complete modeling (thermal, mechanical, hydraulic 3D with two pressures
unknown factors).
Code_Aster
®
Version
7.4
Titrate:
Note of use of model THM
Date:
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{}
=
ddl
ddl
ddl
Z
y
X
ddl
T
U
U
U
U
2
PRE
1
PRE
The contents of PRE1 and PRE2 depend on the selected coupling and will be clarified in section 2.2.3.
According to modeling chosen, only some of these degrees of freedom exist. The table above
summarize the degrees of freedom used for each modeling
MODELING
X
U
y
U
Z
U
ddl
1
PRE
ddl
2
PRE
ddl
T
D_PLAN_HM
X X X
D_PLAN_HMD
X X X
D_PLAN_HHM
X X X X
D_PLAN_HHMD
X X X X
D_PLAN_HH2MD
X X X X
D_PLAN_THH
X
X
X
D_PLAN_THHD
X
X
X
D_PLAN_THH 2D
X
X
X
D_PLAN_THM
X X X X
D_PLAN_THMD
X X X X
D_PLAN_THVD
X
X
X
D_PLAN_THHM
X X X X X
D_PLAN_THHMD
X X X X X
D_PLAN_THH2MD
X X X X X
AXIS_HM
X X X
AXIS_HMD
X X X
AXIS_HHM
X X X X
AXIS_HHMD
X X X X
AXIS_HH2MD
X X X X
AXIS_THH
X
X
X
AXIS_THHD
X
X
X
AXIS_THH 2D
X
X
X
AXIS_THM
X X X X
AXIS_THMD
X X X X
AXIS_THVD
X
X
X
AXIS_THHM
X X X X X
AXIS_THHMD
X X X X X
AXIS_THH2MD
X X X X X
3d_HM
X X X X
3d_HMD
X X X X
3d_HHM
X X X X X
3d_HHMD
X X X X X
3d_HH2MD
X X X X X
3d_THH
X
X
X
3d_THHD
X
X
X
3d_THH 2D
X
X
X
3d_THM
X X X X X
3d_THMD
X X X X X
3d_THVD
X
X
X
3d_THHM
X X X X X X
Code_Aster
®
Version
7.4
Titrate:
Note of use of model THM
Date:
06/07/04
Author (S):
S. GRANET, C. CHAVANT
Key
:
U2.04.05-A
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U2.04 booklet: Nonlinear mechanics
HT-66/04/004/A
MODELING
X
U
y
U
Z
U
ddl
1
PRE
ddl
2
PRE
ddl
T
3d_THHMD
X X X X X X
3d_THH2MD
X X X X X X
The generalized stresses and the variables intern all are indicated in [§Annexe 1].
notations used are those defined in [R7.01.11].
Notice concerning the digital processing (key word ending in D):
Modelings ending in the letter D indicate that one makes an allowing processing
of diagonaliser (“lumper”) the matrix of mass in order to avoid the oscillations. For that them
points of integration are taken at the tops of the elements. One advises highly with the user
systematically to choose this type of modeling.
2.2
Definition of material
The material is defined by the control
DEFI_MATERIAU
as in the example below:
MATERBO=DEFI_MATERIAU (ELAS=_F (E=5.15000000E8,
NU=0.20,
RHO=2670.0,
ALPHA=0.,),
COMP_THM = “LIQU_AD_GAZ_VAPE”,
THM_LIQU=_F (RHO=1000.0,
UN_SUR_K=0.,
ALPHA=0.,
CP=0.0,
VISC=VISCOLIQ,
D_VISC_TEMP=DVISCOL,),
THM_GAZ=_F (MASS_MOL=0.01,
CP=0.0,
VISC=VISCOGAZ,
D_VISC_TEMP=ZERO,),
THM_VAPE_GAZ=_F (MASS_MOL=0.01,
CP=0.0,
VISC=VISCOGAZ,
D_VISC_TEMP=ZERO,),
THM_AIR_DISS=_F (
CP=0.0,
COEF_HENRY=HENRY
),
THM_INIT=_F (TEMP=300.0,
PRE1=0.0,
PRE2=1.E5,
PORO=1.,
PRES_VAPE=1000.0,
DEGR_SATU=0.4,),
THM_DIFFU=_F (R_GAZ=8.32,
RHO=2200.0,
CP=1000.0,
BIOT_COEF=1.0,
SATU_PRES=SATUBO,
D_SATU_PRES=DSATBO,
PESA_X=0.0,
PESA_Y=0.0,
PESA_Z=0.0,
PERM_IN=KINTBO,
PERM_LIQU=UNDEMI,
D_PERM_LIQU_SATU=ZERO,
PERM_GAZ=UNDEMI,
D_PERM_SATU_GAZ=ZERO,
D_PERM_PRES_GAZ=ZERO,
FICKV_T=ZERO,
FICKA_T=FICK,
LAMB_T=ZERO,
),);
Code_Aster
®
Version
7.4
Titrate:
Note of use of model THM
Date:
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2.2.1 Key word factor
ELAS
Definition of the constant linear elastic characteristics or functions of the parameter
“TEMP”
.
E
Young modulus. It is checked that
E
0
.
NAKED
Poisson's ratio. It is checked that
- 1.
naked
0.5
.
ALPHA
Isotropic thermal expansion factor of the grains.
2.2.2 Single-ended spanner word
COMP_THM
Allows to select as of the definition of material the mixing rate THM. The possible laws are
COMP_THM =/`LIQU_SATU `,
/`LIQU_GAZ `,
/`GAS `,
/`LIQU_GAZ_ATM `,
/`LIQU_VAPE_GAZ `,
/`LIQU_AD_GAZ_VAPE `,
/`LIQU_VAPE `,
/“GAS”
Law of reaction of a perfect gas i.e. checking the relation
P
RT Mv
/
/
=
where P is
pressure,
density,
Mv
molar mass, R the constant of perfect gases and T
temperature (cf [R7.01.11] for more details). For an only saturated medium. Data
necessary of the field material are provided in the operator
DEFI_MATERIAU
, under the word
key
THM_GAZ
.
/“LIQU_SATU”
Law of behavior for porous environments saturated by only one fluid (cf [R7.01.11] for more
details). The data necessary of the field material are provided in the operator
DEFI_MATERIAU
, under the key word
THM_LIQ
.
/“LIQU_GAZ_ATM”
Law of behavior for a porous environment unsaturated with a fluid and gas with pressure
atmospheric (cf [R7.01.11] for more details). Data necessary of the field material
are provided in the operator
DEFI_MATERIAU,
under the key words
THM_LIQ
and
THM_GAZ
.
/“LIQU_VAPE_GAZ”
Law of behavior for a porous environment unsaturated water/vapor/dry air with change with
phase (cf [R7.01.11] for more details). The data necessary of the field material are
provided in the operator
DEFI_MATERIAU
, under the key words
THM_LIQ
,
THM_VAPE
and
THM_GAZ
.
/“LIQU_AD_GAZ_VAPE”
Law of behavior for a porous environment unsaturated water/vapor/dry air/air dissolved with
phase shift (cf [R7.01.11] for more details). Data necessary of the field
material are provided in the operator
DEFI_MATERIAU
, under the key words
THM_LIQ
,
THM_VAPE
,
THM_GAZ
and
THM_AIR_DISS
.
Code_Aster
®
Version
7.4
Titrate:
Note of use of model THM
Date:
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Author (S):
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/“LIQU_VAPE”
Law of behavior for porous environments saturated by a component present in liquid form
or vapor. with phase shift (cf [R7.01.11] for more details). Data
necessary of the field material are provided in the operator
DEFI_MATERIAU
, under the words
keys
THM_LIQ
and
THM_VAPE
. This law is valid only for modelings of the type THVD.
/“LIQU_GAZ”
Law of behavior for a porous environment unsaturated fluid/gas without phase shift
(Cf [R7.01.11] for more details). The data necessary of the field material are provided
in the operator
DEFI_MATERIAU,
under the key words
THM_LIQ
and
THM_GAZ
.
The table below specifies the obligatory key words for under following controls in
function of the selected mixing rate.
Legends:
O: Obligatory key word
T: Obligatory key word in Thermics
: Useless key word for this type of mixing rate
LIQU_SATU
LIQU_GAZ
GAS
LIQU_GAZ_AT
M
LIQU_VAPE_GAZ LIQU_AD_GAZ_VAPE LIQU_VAPE
THM_INIT
O
O
O
O
O
O
O
PRE1 O
O
O
O
O
O
O
PRE2
O
O
O
PORO O
O
O
O
O
O
O
TEMP T
O
O
T
O
O
O
PRES_VAPE
O
O
O
THM_DIFFU
O
O
O
O
O
O
O
R_GAZ
O
O
O
O
O
RHO O
O
O
O
O
O
O
BIOT_COEF O
O
O
O O
O O
PESA_X O
O
O
O
O O
O
PESA_Y O
O
O
O
O O
O
PESA_Z O
O
O
O
O O
O
SATU_PRES
O
I
O
O
O
O
D_SATU_PRES
O
I
O
O
O
O
PERM_LIQU
I
O
I
O
O
O
O
D_PERM_LIQU_SATU
O
O
O
O
O
PERM_GAZ
O
O
O
O
D_PERM_SATU_GAZ
O
O
O
O
D_PERM_PRES_GAZ
O
O
O
O
FICKV_T
O
O
FICKV_PV
FICKV_PG
FICKV_S
D_FV_T
D_FV_PG
FICKA_T
O
FICKA_PA
FICKA_PL
FICKA_S
D_FA_T
CP T
T
T
T
T
T
T
PERM_IN/PERM_END O
O O
O
O
O
O
LAMB_T T
T
T
T
T T
T
LAMB_S
LAMB_PHI
LAMB_CT
D_LB_T
D_LB_S
D_LB_PHI
THM_LIQU
O
O
O
O
O
O
RHO O
O
O
O
O
O
UN_SUR_K O
O
O O
O O
VISC O
O
O
O
O
O
D_VISC_TEMP O
O
O
O
O
O
ALPHA T
T
T
T
T
T
CP T
T
T
T
T
T
THM_GAZ
O
O
O
O
O
MASS_MOL
O
O
O O O
Code_Aster
®
Version
7.4
Titrate:
Note of use of model THM
Date:
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Author (S):
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Key
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VISC
O
O
O
O
O
D_VISC_TEMP
O
O
O O
O
CP
T
T
T
T
T
THM_VAPE_GAZ
O
O
O
MASS_MOL
O O O
CP
O
O
O
VISC
O
O
O
D_VISC_TEMP
O
O
O
THM_AIR_DISS
O
CP
O
COEF_HENRY
O
2.2.3 Key word factor
THM_INIT
For all the Hydro-mechanical Thermo behaviors, it makes it possible to describe a state of reference of
the structure (cf [R7.01.11] and [R7.01.14]). Its syntax is as follows:
THM_INIT = _F (
TEMP =
temp
,
[R]
PRE1
=
pre1
,
[R]
PRE2 =
pre2
,
[R]
PORO =
poro
,
[R]
PRES_VAPE
=
pvap
, [R]
)
For including/understanding these data well, it is necessary to distinguish the unknown factors with the nodes, which we call
{}
U
ddl
and values defined under the key word
THM_INIT
that we call
p
ref.
and
T
ref.
{}
=
ddl
ddl
ddl
Z
y
X
ddl
T
U
U
U
U
2
PRE
1
PRE
Significance of the unknown factors
PRE1
and
PRE2
vary according to the models. While noting
W
p
pressure
of water,
AD
p
pressure of dissolved air,
lq
p
pressure of fluid
AD
W
lq
p
p
p
+
=
,
have
p
,
vp
p
pressure
of vapor,
have
p
pressure of dry air and
vp
have
G
p
p
p
+
=
total gas pressure and
lq
G
C
p
p
p
-
=
capillary pressure (also called suction), one has the following significances of the unknown factors
PRE1
and
PRE2
Behavior
KIT
LIQU_SATU
LIQU_GAZ_ATM GAS LIQU_VAPE_GAZ
PRE1
lq
p
lq
p
-
p
G
lq
G
C
p
p
p
-
=
PRE2
p
G
Behavior
KIT
LIQU_GAZ LIQU_VAPE
LIQU_AD_GAZ_VAPE
PRE1
lq
G
C
p
p
p
-
=
lq
p
lq
G
C
p
p
p
-
=
PRE2
p
G
p
G
Table 2.2.3-1: contents of PRE1 and PRE2
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One will be able to refer to [§3.3.2.3] documentation of the control
STAT_NON_LINE
[U4.51.03].
One then defines the “total” pressures and the temperature by:
p
p
p
T
T
T
ddl
ref.
ddl
ref.
=
+
=
+
;
All values in input or exit (boundary conditions or result of
IMPR_RESU
) are
nodal unknown factors
ddl
ddl
T
p
and
.
On the other hand in fact the pressures and the total air temperature are used in the laws of
behavior
p
R
MR. T
=
for perfect gases,
D
dp
K
dT
L
L
L
L
L
=
-
3
for the fluid and in
relation capillary saturation/pressure.
Let us note that the nodal values can be initialized by the key word
ETAT_INIT
control
STAT_NON_LINE
(cf 2.3).
The user must be very careful in the definition of the values of
THM_INIT
: indeed, the definition of
several materials with values different from the quantities defined under
THM_INIT
conduit with
discontinuous values initial of the pressure and the temperature, which is not in fact not compatible
with the general processing which is made of these quantities. We thus advise with the user
following step:
·
if there is initially a uniform field of pressure or temperature, it is informed
directly by the key word
THM_INIT
,
·
if there is a nonuniform field, one defines for example a reference by the key word
THM_INIT
control
DEFI_MATERIAU
, and initial values compared to this
reference by the key word
ETAT_INIT
control
STAT_NON_LINE
(cf 2.3).
TEMP
Temperature of reference
ref.
T
.
The value of the temperature of reference entered behind the key word
TEMP_REF
order
AFFE_MATERIAU
is ignored.
PRE1
As seen in table 1:
For the behaviors:
LIQU_SATU
, and
LIQU_VAPE
pressure of fluid of reference.
For the behavior:
GAS
standard gas pressure.
For the behavior:
LIQU_GAZ_ATM
pressure of fluid of changed reference of sign.
For the behaviors:
LIQU_VAPE_GAZ
,
LIQU_AD_GAZ_VAPE
and
LIQU_GAZ
pressure
thin cable of reference.
PRE2
For the behaviors:
LIQU_VAPE_GAZ
,
LIQU_AD_GAZ_VAPE
and
LIQU_GAZ
and pressure of
standard gas.
Important remark:
One never should take a value of
PRE2
equalize to zero under penalty of problems
numerical.
PORO
Initial porosity.
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PRES_VAPE
Initial steam pressure for the behaviors:
LIQU_VAPE_GAZ
,
LIQU_AD_GAZ_VAPE
,
LIQU_VAPE
and
LIQU_GAZ
.
Note:
The initial vapor pressure must be taken in coherence with the other data.
Very often, one leaves the knowledge of an initial state of hygroscopy. The degree
hygrometrical is the relationship between the steam pressure and the steam pressure
saturating at the temperature considered. One then uses the law of Kelvin which gives
pressure of the fluid according to the steam pressure, of the temperature and of
saturating steam pressure:
=
-
)
(
ln
0
T
p
p
T
M
R
p
p
sat
vp
vp
ol
vp
W
W
W
. This relation is not
valid that for isothermal evolutions. For evolutions with variation of
temperature, knowing a law giving the steam pressure saturating to
temperature
0
T
, for example:
(
)
-
+
-
+
=
5
.
273
1354
.
559
.
31
5
.
273
7858
.
2
0
0
0
10
)
(
T
T
sat
vp
T
p
, and a degree
of hygroscopy
HR
, one deduces the steam pressure from it thanks to
)
(
)
(
0
0
T
p
HR
T
p
sat
vp
vp
=
.
Moreover, one never should take a value of
PRES_VAPE
equalize to zero.
2.2.4 Key word factor
THM_LIQU
This key word relates to all behaviors THM utilizing a fluid (cf [R7.01.11]). Its
syntax is as follows:
THM_LIQU = _F (
RHO
=
rho
,
[R]
UN_SUR_K
=
usk
,
[R]
ALPHA
=
alp
,
[R]
CP
=
CP,
[R]
VISC =
VI,
[function
**]
D_VISC_TEMP =
dvi
, [function
**]
)
RHO
Density of the fluid for the pressure defined under the key word
PRE1
key word factor
THM_INIT
.
UN_SUR_K
Opposite of the compressibility of the fluid:
K
L
.
ALPHA
Expansion factor of the fluid
L
If
p
L
indicate the pressure of the fluid,
L
its density and
T
the temperature, it
behavior of the fluid is:
D
dp
K
dT
L
L
L
L
L
=
-
3
CP
Specific heat with constant pressure of the fluid.
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VISC
[function **]
Viscosity of the fluid. Function of the temperature.
D_VISC_TEMP
[function **]
Derived from the viscosity of the fluid compared to the temperature. Function of the temperature.
The user must ensure coherence with the function associated with
VISC
.
2.2.5 Key word factor
THM_GAZ
This key word factor relates to all behaviors THM utilizing a gas (cf [R7.01.11]).
For the behaviors utilizing at the same time a fluid and a gas, and when one takes into account
the evaporation of the fluid, the coefficients indicated here relate to dry gas. Properties of
vapor are indicated under the key word
THM_VAPE_GAZ
. Its syntax is as follows:
THM_GAZ = _F (
MASS_MOL
=
Mgs
,
[R]
CP
=
CP,
[R]
VISC =
VI,
[function
**]
D_VISC_TEMP =
dvi
,
[function
**]
)
MASS_MOL
Mass molar dry gas.
M
gs
If
p
gs
indicate the pressure of dry gas,
gs
its density,
R
the constant of gases
perfect and
T
the temperature, the reaction of dry gas is:
p
RT
M
gs
gs
gs
=
.
CP
Specific heat with constant pressure of dry gas.
VISC
[function **]
Viscosity of dry gas. Function of the temperature.
D_VISC_TEMP
[function **]
Derived compared to the temperature from viscosity from dry gas. Function of the temperature.
The user must ensure coherence with the function associated with
VISC
.
2.2.6 Key word factor
THM_VAPE_GAZ
This key word factor relates to all behaviors THM utilizing at the same time a fluid and one
gas, and fascinating of account the evaporation of the fluid (cf [R7.01.11]). Coefficients indicated here
relate to the vapor. Syntax is as follows:
THM_VAPE_GAZ = _F
(
MASS_MOL =
m
,
[R]
CP
=
CP,
[R]
VISC =
VI,
[function
**]
D_VISC_TEMP =
dvi
, [function
**]
)
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MASS_MOL
Mass molar vapor.
M
vp
CP
Specific heat with constant pressure of the vapor.
VISC
[function **]
Viscosity of the vapor. Function of the temperature.
D_VISC_TEMP
[function **]
Derived compared to the temperature from viscosity from the vapor. Function of the temperature.
The user must ensure coherence with the function associated with
VISC
.
2.2.7 Key word factor
THM_AIR_DISS
This key word factor relates to behavior THM
THM_AD_GAZ_VAPE
taking into account
dissolution of the air in the fluid (cf [R7.01.11]). The coefficients indicated here relate to the air
dissolved. Syntax is as follows:
THM_AD_GAZ_VAPE = _F (
CP
=
CP,
[R]
COEF_HENRY
= KH
,
[function **]
)
CP
Specific heat with constant pressure of the dissolved air.
COEF_HENRY
Constant of Henry
H
K
, allowing to connect the molar concentration of dissolved air
ol
AD
C
(moles/m3) with the pressure of dry air:
H
have
ol
AD
K
p
C
=
Note:
The constant of Henry that we use here expresses in Pa.m
3
.mol
- 1
. In the literature it
exist various manners of writing the law of Henry. For example in the formulation of the book
loads of the platform Alliances [bib2]. The law of Henry is given
by
W
W
ol
have
have
has
L
M
M
H
P
=
with the concentration of air in water that have it can bring back to one
density such as
AD
has
L
=
. H is a coefficient which is expressed out of AP. It will be necessary in
these cases to write equivalence
W
W
H
M
H
K
=
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2.2.8 Key word factor
THM_DIFFU
Obligatory for all behaviors THM (cf [R7.01.11]). The user must ensure himself of
coherence of the functions and their derivative. Syntax is as follows:
THM_DIFFU = _F
(
R_GAZ
=
rgaz
,
[R]
RHO
=
rho
,
[R]
CP
=
CP,
[R]
BIOT_COEF
=
bio
,
[R]
SATU_PRES
=
sp,
[function]
D_SATU_PRES =
dsp
,
[function]
PESA_X
=
px,
[R]
PESA_Y
=
py,
[R]
PESA_Z
=
pz,
[R]
PERM_IN =
perm
,
[function]
PERM_LIQU
=
perml,
[function]
D_PERM_LIQU_SATU
=
dperm,
[function]
PERM_GAZ
=
permg,
[function]
D_PERM_SATU_GAZ
=
dpsg
,
[function]
D_PERM_PRES_GAZ
=
dppg
,
[function]
FICKV_T =
fvt
,
[function]
FICKV_PV =/
fvpv, [function]
/1
,
[DEFECT]
FICKV_PG =/fvpg, [function]
/1
,
[DEFECT]
FICKV_S =
/
fvs
,
[function]
/1
,
[DEFECT]
D_FV_T
=
/
dfvt,
[function]
/0
,
[DEFECT]
D_FV_PG =/dfvgp, [function]
/0
,
[DEFECT]
FICKA_T =
conceited person
,
[function]
FICKA_PA =/fapv, [function]
/1
,
[DEFECT]
FICKA_PL =/fapg, [function]
/1
,
[DEFECT]
FICKA_S =
/
fas
,
[function]
/1
,
[DEFECT]
D_FA_T
=
/
dfat,
[function]
/0
,
[DEFECT]
LAMB_T
=
/
lambt
,
[function]
/0
[DEFECT]
LAMB_S
=
/
lambs
,
[function]
/1
,
[DEFECT]
LAMB_PHI =/lambp, [function]
/1
,
[DEFECT]
LAMB_CT =/lambct
, [function]
/0
,
[DEFECT]
D_LB_S
=
/
dlambs
,
[function]
/0
,
[DEFECT]
D_LB_T
=
/
dlambt
,
[function]
/0
,
[DEFECT]
D_LB_PHI =/dlambp
, [function]
/0
,
[DEFECT]
SIGMA_T =
St,
[function]
D_SIGMA_T
=
dst
,
[function]
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PERM_G_INTR =
pgi
,
[function]
CHAL_VAPO
=
cv,
[function
**]
EMMAG
=
EM,
[R]
)
R_GAZ
Constant of perfect gases.
RHO
For the hydraulic behaviors initial homogenized density [R7.01.11].
CP
For the thermal behaviors, specific heat with constant stress of the solid alone (of
grains).
Note:
Attention it acts here of the specific heat only and not of “
p
C
”, as it is
fact for other thermal controls. The density of the grains is calculated in
the code starting from the homogenized density [R7.01.11].
BIOT_COEF
Coefficient of Biot.
SATU_PRES [function **]
For the unsaturated material behaviors (
LIQU_VAPE_GAZ
,
LIQU_GAZ
,
LIQU_GAZ_ATM)
, isotherm of saturation function of the capillary pressure.
Note:
For numerical reasons, it should be prevented that saturation reaches value 1. Also it is
very strongly recommended to multiply the capillary function (generally lain between 0
and 1) by 0,999.comme indicated on the command file given in example in appendix.
D_SATU_PRES
[function **]
For the unsaturated material behaviors (
LIQU_VAPE_GAZ
,
LIQU_GAZ
,
LIQU_GAZ_ATM)
, derived from saturation compared to the pressure.
PESA_X
Gravity according to X, used only if the modeling chosen in
AFFE_MODELE
1 or 2 includes
variables of pressure.
Note:
Gravity defined here is that used in the equation of Darcy only. When there is
mechanical calculations, gravity is also defined in
AFFE_CHAR_MECA
.Cette
notice applies of course for the three components of gravity.
PESA_Y
Gravity according to y, used only if the modeling chosen in
AFFE_MODELE
1 or 2 includes
variables of pressure.
PESA_Z
Gravity according to Z, used only if the modeling chosen in
AFFE_MODELE
1 or 2 includes
variables of pressure.
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PERM_IN
[function **]
Intrinsic permeability: function of porosity.
The permeability to the conventional direction
K
, whose dimension is that a speed is calculated
following way:
K
K K
G
rel
L
=
int
µ
where
K
int
is the intrinsic permeability,
K
rel
the relative permeability,
µ
viscosity,
L
density of the fluid and
G
the acceleration of gravity.
PERM_LIQ
[function **]
Permeability relating to the fluid: function of saturation.
D_PERM_LIQ_SATU
[function **]
Derived from the Permeability relating to the fluid compared to saturation: function of saturation.
PERM_GAZ
[function **]
Permeability relating to gas: function of the saturation and the gas pressure.
D_PERM_SATU_GAZ
[function **]
Derived from the permeability to gas compared to saturation: function of the saturation and of
gas pressure.
D_PERM_PRES_GAZ
[function **]
Derived from the permeability to gas compared to the gas pressure: function of the saturation and of
gas pressure.
FICKV_T
[function **]
For the behaviors
LIQU_VAPE_GAZ
and
LIQU_AD_GAZ_VAPE
, multiplicative part of
coefficient of Fick function of the temperature for the dissemination of the vapor in the mixture
gas. The coefficient of Fick which can be a function of saturation, the temperature, pressure
gas and the steam pressure, one defines it as a product of 4 functions:
FICKV_T
,
FICKV_S
,
FICKV_PG
,
FICKV_VP
. Only
FICKV_T
is obligatory for the behaviors
LIQU_VAPE_GAZ
and
LIQU_AD_GAZ_VAPE
.
FICKV_S
[function **]
For the behaviors
LIQU_VAPE_GAZ
and
LIQU_AD_GAZ_VAPE
, multiplicative part of
coefficient of Fick function of saturation for the dissemination of the vapor in the gas mixture.
If this function is used, one recommends to take
FICKV_S (1) = 0
.
FICKV_PG
[function **]
For the behaviors
LIQU_VAPE_GAZ
and
LIQU_AD_GAZ_VAPE,
multiplicative part of
coefficient of Fick function of the gas pressure for the dissemination of the vapor in the mixture
gas.
FICKV_PV
[function **]
For the behaviors
LIQU_VAPE_GAZ
and
LIQU_AD_GAZ_VAPE
, multiplicative part of
coefficient of Fick function of the steam pressure for the dissemination of the vapor in
gas mixture.
D_FV_T
[function **]
For the behaviors
LIQU_VAPE_GAZ
and
LIQU_AD_GAZ_VAPE
, derived from the coefficient
FICKV_T
compared to the temperature.
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D_FV_PG
[function **]
For the behaviors
LIQU_VAPE_GAZ
and
LIQU_AD_GAZ_VAPE
, derived from the coefficient
FICKV_PG
compared to the gas pressure.
FICKA_T
[function **]
For the behavior
LIQU_AD_GAZ_VAPE,
multiplicative part of the coefficient of Fick function
temperature for the dissemination of the air dissolved in the liquid mixture. The coefficient of Fick
being able to be a function of saturation, the temperature, pressure of dissolved air and pressure of
fluid, one defines it as a product of 4 functions:
FICKA_T
,
FICKA_S
,
FICKV_PA
,
FICKV_PL
. In the case of
LIQU_AD_GAZ_VAPE
, only
FICKA_T
is obligatory.
FICKA_S
[function **]
For the behavior
LIQU_AD_GAZ_VAPE,
multiplicative part of the coefficient of Fick function
saturation for the dissemination of the air dissolved in the liquid mixture.
FICKA_PA
[function **]
For the behavior
LIQU_AD_GAZ_VAPE,
multiplicative part of the coefficient of Fick function
pressure of air dissolved for the dissemination of the air dissolved in the liquid mixture.
FICKA_PL
[function **]
For the behavior
LIQU_AD_GAZ_VAPE,
multiplicative part of the coefficient of Fick function
pressure of fluid for the dissemination of the air dissolved in the liquid mixture.
D_FA_T
[function **]
For the behavior
LIQU_AD_GAZ_VAPE,
derived from the coefficient
FICKA_T
compared to
temperature.
LAMB_T
[function **]
Multiplicative part of the thermal conductivity of the mixture depend on the temperature
(cf [§2.2.9]). This operand is obligatory in the thermal case.
LAMB_S
[function **]
Multiplicative part (equalizes to 1 per defect) of the thermal conductivity of the mixture dependant on
saturation (cf [§2.2.9]).
LAMB_PHI
[function **]
Multiplicative part (equalizes to 1 per defect) of the thermal conductivity of the mixture dependant on
porosity (cf [§2.2.9]).
LAMB_CT
[function **]
Part of the thermal of the constant mixture and additive conductivity (cf [§2.2.9]). This constant
is equal to zero per defect.
D_LB_T
[function **]
Derived from the part of thermal conductivity of the mixture depend on the temperature by
report/ratio at the temperature.
D_LB_S
[function **]
Derived from the part of thermal conductivity of the mixture depend on saturation.
D_LB_PHI
[function **]
Derived from the part of thermal conductivity of the mixture depend on porosity.
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EMMAG
[function **]
Coefficient of storage. This coefficient is taken into account only in the cases of
modelings without mechanics.
2.2.9 Recapitulation of the functions of couplings and their dependence
The tables below points out the various functions and their possible dependences and
obligation.
Key word factor
THM_LIQU
RHO
0
lq
UN_SUR_K
lq
K
1
ALPHA
lq
CP
p
lq
C
VISC
()
T
lq
µ
D_VISC_TEMP
()
T
T
lq
µ
Key word factor
THM_GAZ
MASS_MOL
ol
have
M
CP
p
have
C
VISC
()
T
have
µ
D_VISC_TEMP
()
T
T
have
µ
Key word factor
THM_VAPE_GAZ
MASS_MOL
ol
VP
M
CP
p
vp
C
VISC
()
T
vp
µ
D_VISC_TEMP
()
T
T
vp
µ
Key word factor
THM_AIR_DISS
CP
p
AD
C
COEF_HENRY
H
K
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Key word factor
THM_INIT
TEMP
T
init
PRE1
1
P
init
PRE2
2
P
init
PORO
0
NEAR
_
VAPE
0
vp
p
2.2.9.1 Key word factor
THM_DIFFU
R_GAZ
R
RHO
0
R
CP
S
C
BIOT_COEF
B
SATU_PRES
()
C
lq
p
S
D_SATU_PRES
()
C
C
lq
p
p
S
PESA_X
m
X
F
PESA_Y
m
y
F
PESA_Z
m
Z
F
PERM_IN
()
int
K
PERM_LIQU
()
lq
rel
lq
S
K
D_PERM_LIQU_SATU
()
lq
lq
rel
lq
S
S
K
PERM_GAZ
(
)
gz
lq
rel
gz
p
S
K
,
D_PERM_SATU_GAZ
(
)
lq
gz
lq
rel
gz
S
p
S
K
,
D_PERM_PRES_GAZ
(
)
gz
gz
lq
rel
gz
p
p
S
K
,
FICKV_T
)
(
T
F
T
vp
FICKV_S
)
(
S
F
S
vp
FICKV_PG
)
(
G
gz
vp
P
F
FICKV_PV
)
(
vp
vp
vp
P
F
D_FV_T
T
T
F
T
vp
)
(
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D_FV_PG
gz
gz
gz
vp
P
P
F
)
(
FICKA_T
)
(T
F
T
AD
FICKA_S
)
(S
F
S
AD
FICKA_PA
)
(
AD
AD
AD
P
F
FICKA_PL
)
(
lq
lq
AD
P
F
D_FA_T
T
T
F
T
AD
)
(
LAMB_T
)
(T
T
T
D_LB_T
T
T
T
T
)
(
LAMB_PHI
)
(
T
D_LB_PHI
)
(
T
LAMB_S
)
(S
T
S
D_LB_S
S
S
T
S
)
(
LAMB_CT
T
CT
Note:
If there is thermics:
T
is a function of porosity, saturation and temperature and is given under
form product of three functions:
T
cte
T
T
lq
T
S
T
T
T
S
+
=
)
(
).
(
).
(
with
)
(T
T
T
(a.c. D
LAMB_T
) obligatory and others
functions by defect taken equal to one, except
0
=
T
cte
.
For the coefficient of Fick of the gas mixture, in the case
LIQU_VAPE_GAZ
and
LIQU_AD_GAZ_VAPE
)
(
).
(
).
(
).
(
)
,
,
,
(
S
F
T
F
P
F
P
F
S
T
P
P
F
S
vp
T
vp
gz
gz
vp
vp
vp
vp
gz
vp
vp
=
with
)
(T
F
T
vp
obligatory, other functions being taken by defect equal to one, and the derivative
equal to zero. one will neglect the derivative compared to steam pressure and saturation.
In the case
LIQU_VAPE_GAZ_AD
, the coefficient of Fick of the liquid mixture will be under
form:
)
(
).
(
).
(
).
(
)
,
,
,
(
S
F
T
F
P
F
P
F
S
T
P
P
F
S
AD
T
AD
lq
lq
AD
AD
AD
AD
lq
AD
AD
=
, with
)
(T
F
T
AD
obligatory,
other functions being taken by defect equal to one, and the derivative equalizes to zero. One
consider that the derivative compared to the temperature (the others are in any case taken
equal to zero).
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2.3
Initialization of calculation
To define an initial state, it is necessary to define a state of stresses (with the elements), unknown factors
nodal. and of the internal variables.
·
In the key word
THM_INIT
of
DEFI_MATERIAU
, one defines values of reference for
nodal unknown factors.
·
By the key word
DEPL
key word factor
ETAT_INIT
control
STAT_NON_LINE
, one
affect the fields of initialization of the nodal unknown factors.
·
By the key word
SIGM
key word factor
ETAT_INIT
. control
STAT_NON_LINE
,
the fields of initialization of the stresses are affected.
·
By the key word
VARI
key word factor
ETAT_INIT
(possibly) it is affected
fields of initialization of the internal variables.
In order to specify the things, one recalls to which category of variables belong each
physical size (these physical sizes existing or not according to selected modeling):
Unknown factors
nodal
Z
y
X
lq
G
C
U
U
U
T
p
p
p
,
,
,
,
,
,
Stresses
at the points
of Gauss
,
,
,
,
,
,
,
p
yz
xz
xy
zz
yy
xx
Z
y
X
m
AD
m
have
m
vp
m
W
Z
AD
y
AD
X
AD
AD
Z
have
y
have
X
have
have
Z
vp
y
vp
X
vp
vp
Z
W
y
W
X
W
W
Q
Q
Q
Q
H
H
H
H
m
m
m
m
,
,
,
,
,
,
,
,
M
M
,
M
,
,
M
M
,
M
,
,
M
M
,
M
,
,
M
M
,
M
,
Variables
interns
lq
vp
lq
S
p,
,
,
The correspondence between name of component Aster and physical size is clarified in
[§Annexe 1].
The initialization of the nodal unknown factors as well as the difference between initial state and state of reference have
summer described and detailed in [§2.2.3]. It is reminded the meeting nevertheless that
ref.
ddl
p
p
p
+
=
for the pressures
PRE1
and
PRE2
and
ref.
ddl
T
T
T
+
=
for the temperatures, where
ref.
p
and
ref.
T
are defined under the key word
THM_INIT
control
DEFI_MATERIAU
.
The key word
DEPL
key word factor
ETAT_INIT
control
STAT_NON_LINE
defines the values
initial of
{}
ddl
U
. The initial values of the densities of the vapor and the dry air are
defined starting from the initial values of the vapor and gas pressures (values read under the key word
THM_INIT
control
DEFI_MATERIAU
). It is noticed that, for displacements,
decomposition
ref.
ddl
U
U
U
+
=
is not made: the key word
THM_INIT
control
DEFI_MATERIAU
thus does not allow to define initial displacements. The only way of initializing displacements
is thus to give them an initial value by the key word factor
ETAT_INIT
control
STAT_NON_LINE
.
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Concerning the stresses, the fields to be informed are the stresses indicated in appendix I
according to selected modeling.
Initial values of the enthali, which belong to the generalized stresses are defined in
to leave the key word
SIGM
key word factor
ETAT_INIT
control
STAT_NON_LINE
. The introduction
initial conditions is very important, for the enthali. In practice, one can reason in
considering that one has three states for the fluids:
·
the state running,
·
the state of reference: it is that of the fluids in a free state. In this state of reference, one can
to consider that the enthali are null,
·
the initial state: it must be in thermodynamic balance. For the enthali of water and
vapor one will have to take:
0
0
)
(
=
=
=
=
-
=
-
=
m
AD
init
m
have
init
init
m
vp
init
W
atm
init
W
W
ref.
L
init
W
m
W
init
H
H
T
L
H
p
p
p
p
H
one
vaporisati
of
latent
heat
and with
()
(
)
Kg
J
T
T
L
/
15
.
273
2443
2500800
-
-
=
Note:
The initial vapor pressure will have to be taken in coherence with these choices (cf [§2.2.3]).
Concerning the mechanical stresses, the partition of the stresses in stresses total and effective
is written:
1
p
+
=
'
where
is the total stress, a.c. D that which checks:
()
0
=
+
m
R
F
Div
is the effective stress. For the laws of effective stresses, it checks
:
(
)
0
,
dT
D
F
D
-
=
, where
(
)
U
U
+
=
T
2
1
and
represent the internal variables.
p
is calculated according to the water pressures. The adopted writing is incremental and, if one
wants that the value of
p
that is to say coherent with the value
ref.
p
(
PRE1
) definite under the key word
THM_INIT
, it is necessary to initialize
p
by the key word
SIGM
key word factor
ETAT_INIT
control
STAT_NON_LINE
.
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Warning:
In the case of fields of pressures or temperatures heterogeneous, it is necessary to ensure “manually
continuity “enters the fields. That Ci is not for the moment not taken into account automatically.
In the current state, the degrees of freedom (ddl) to the nodes located at the interface between two meshs
take the value of the ddl material initialized in the last as on the figure. Consequently it
materials affected in first is found with heterogeneous values of displacements. To ensure
continuity, it is necessary to impose on the nodes medium (in grayed on [Figure 2.3-a]) an average value enters
two materials. This processing necessary in is seen of a correct postprocessing but does not have
of impact on calculation in him even.
Appear 2.3-a: Management of discontinuities between two meshs
If one refers to the example presented in [§Annexe 3], the fields of displacements initialized in
ETAT_INIT
are then defined for example in the following way:
CHAMNO=CREA_CHAMP (MAILLAGE=MAIL,
OPERATION=' AFFE',
TYPE_CHAM=' NOEU_DEPL_R',
AFFE= (_F (TOUT=' OUI',
NOM_CMP=' TEMP',
VALE=0.0,),
_F (GROUP_NO=' SURFBO',
NOM_CMP=' PRE1',
VALE=7.E7,),
_F (GROUP_NO=' SURFBG',
NOM_CMP=' PRE1',
VALE=3.E7,),
_F (NOEUD= (“NO300”, “NO296”),
NOM_CMP=' PRE1',
VALE=5.E7,),
_F (GROUP_NO=' SURFBO',
NOM_CMP=' PRE2',
VALE=0.0,),
_F (GROUP_NO=' SURFBG',
NOM_CMP=' PRE2',
VALE=0.0,),),);
And stress fields in the following way:
SIGINIT=CREA_CHAMP (MAILLAGE=MAIL,
OPERATION=' AFFE',
TYPE_CHAM=' CART_SIEF_R',
AFFE= (_F (GROUP_MA=' BO',
NOM_CMP=
(“SIXX”, “SIYY”, “SIZZ”, “SIXY”, “SIXZ”,
“SIYZ”, “SIP”, “M11”, “FH11X”, “FH11Y”, “ENT11”,
“M12”, “FH12X”, “FH12Y”, “ENT12”,
“QPRIM”, “FHTX”, “FHTY”, “M21”,
“FH21X”, “FH21Y”, “ENT21”,
“M22”, “FH22X”, “FH22Y”, “ENT22”,),
VALE=
(0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 2500000.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0., 0., 0., 0.),),),);
M1
M2
Value with the node of the ddl re-entered for the mesh
M2 (affected as a second)
Value to be modified (average between M1 etM2)
Value with the node of the ddl re-entered for the mesh
M1 (affected in first)
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2.4
Loadings and boundary conditions
All the boundary conditions or loading are affected via the control
AFFE_CHAR_MECA
[U4.44.01]. The loadings are then activated by the key word factor
EXCIT
control
STAT_NON_LINE
.
In a conventional way, two types of boundary conditions are possible:
·
Conditions of the Dirichlet type which consist in imposing on part of border of
values fixed for main unknown factors belonging to
{}
ddl
U
(and not
init
ddl
U
U
U
+
=
)
for that one uses key word factor
DDL_IMPO
of
AFFE_CHAR_MECA
.
·
Conditions of the Neuman type which consist in imposing values on the “quantities
dual “, either by not saying anything (null flows), or in their giving a value via the key words
FLUN
,
FLUN_HYDR1
and
FLUN_HYDR2
key word factor
FLUX_THM_REP
control
AFFE_CHAR_MECA
. This flow is then multiplied by a function of time (by defect equalizes with
1) in under the word key one
EXCIT
control
STAT_NON_LINE
. Mechanical conditions
in total stresses
.n
are they given via
PRES_REP
control
AFFE_CHAR_MECA
. One will refer to the documentation of this control to know some
possibilities.
From a syntactic point of view the conditions of Dirichlet thus apply as to the example
according to
DIRI=AFFE_CHAR_MECA (MODELE=MODELE,
DDL_IMPO= (_F (GROUP_NO=' GAUCHE',
TEMP=0.0,),
_F (TOUT=' OUI',
PRE2=0.0,),
_F (GROUP_NO=' GAUCHE',
PRE1=0.0,),
_F (TOUT=' OUI',
DX=0.0,),
_F (TOUT=' OUI',
DY=0.0,),
_F (TOUT=' OUI',
DZ=0.0,),
),)
For the conditions of Neuman, syntax will be then as on the following example:
NEU1=AFFE_CHAR_MECA (MODELE=MODELE,
FLUX_THM_REP=_F (GROUP_MA=' DROIT',
FLUN=200.,
FLUN_HYDR1=0.0,
FLUN_HYDR2=0.0),);
NEU2=AFFE_CHAR_MECA (MODELE=MODELE,
PRES_REP=_F (GROUP_MA=' DROIT',
PRES=2.,),);
One defines then the multiplicative function which one wants to apply, for example with NEU1:
FLUX=DEFI_FONCTION (NOM_PARA=' INST',
VALE=
(0.0, 386.0,
315360000.0, 312.0,
9460800000.0, 12.6),);
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The loadings are then activated in
STAT_NON_LINE
via the key word
EXCIT
in the manner
following:
EXCIT= (
_F (CHARGE=DIRI,),
_F (CHARGE=NEU2,),
_F (CHARGE=NEU1,
FONC_MULT=FLUX,),
),
FLUN
corresponds to the value of the heat transfer rate.
FLUN_HYDR1
and
FLUN_HYDR2
correspond to
values of the hydraulic flows associated the pressures
PRE1
and
PRE2
. If there is no ambiguity for
thermics or mechanics, on the other hand hydraulic main unknown factors
PRE1
and
PRE2
change according to the selected coupling. As it below is pointed out
Behavior
LIQU_SATU
LIQU_VAPE LIQU_GAZ_ATM
GAS
LIQU_VAPE_GAZ
LIQU_GAZ
LIQU_AD_GAZ_VA
EP
PRE1
lq
p
lq
p
lq
p
-
p
G
lq
G
C
p
p
p
-
=
PRE2
p
G
Associated flows are:
For
PRE1
,
FLUN_HYDR1
:
(
)
ext.
vp
ext.
W
vp
W
M
M
+
=
+
N
M
M
.
For
PRE2
,
FLUN_HYDR2
:
(
)
ext.
have
ext.
AD
have
AD
M
M
+
=
+
N
M
M
.
We thus will summarize the various possibilities by distinguishing the case where one imposes values on
PRE1
and/or
PRE2
and that where one works on combinations of the 2. It is announced that one can of course
to have various types of boundary conditions according to the pieces of border (groups of nodes
or of meshs) which one treats. For a more complete and more detailed outline in the way in which are
treated the boundary conditions in the case unsaturated, one will refer to the note reproduced in
appendix 2.
·
Case of the boundary conditions utilizing main unknown factors
PRE1
and
PRE2
One summarizes here the usual case where one imposes value on
PRE1
and/or
PRE2
.
-
Dirichlet on
PRE1
and Dirichlet on
PRE2
The user imposes a value on
PRE1
and
PRE2
; flows are results of
calculation.
-
Dirichlet on
PRE1
and Neuman on
PRE2
The user imposes a value on
PRE1
and a value with flow associated with
PRE2
in
saying anything on
PRE2
or by giving a value to
FLUN_HYDR2
.
-
Dirichlet on
PRE2
and Neuman on
PRE1
The user imposes a value on
PRE2
and a value with flow associated with
PRE1
in
saying anything on
PRE1
or by giving a value to
FLUN_HYDR1
.
-
Neuman on
PRE2
and Neuman on
PRE1
Two flows are imposed either by not saying anything on
PRE1
and/or
PRE2
(null flows)
maybe by giving a value to
FLUN_HYDR1
.et/ou
FLUN_HYDR2
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·
Case of the boundary conditions utilizing a linear relation between
main unknown factors
PRE1
and
PRE2
It is also possible to handle linear combinations of
PRE1
and
PRE2
. It is necessary
however to handle that with precaution so as to start from a correctly posed problem.
The syntax of this operator is detailed in the documentation of
AFFE_CHAR_MECA
,
the example below into famous this type of condition:
P_DDL=AFFE_CHAR_MECA (MODELE=MODELE,
LIAISON_GROUP= (_F (
GROUP_NO_1= “EDGES”,
GROUP_NO_2= “EDGES”,
DDL_1=' PRE1',
DDL_2=' PRE2',
COEF_MULT_1 = X,
COEF_MULT_2 = Y.,
COEF_IMPO =z,),),
);
This control means that on the border defined by the group of nodes “EDGES”, them
pressures
PRE1
and
PRE2
are connected by the linear relation
X
PRE1 + y PRE2 = Z
Note:
Flows imposed are scalar quantities which can apply to a line
or a surface interns with the modelized solid. In this case, these boundary conditions
correspond to a source.
2.5
Nonlinear calculation
Calculation is carried out by the control
STAT_NON_LINE
as in the example below:
U0=STAT_NON_LINE (MODELE=MODELE,
CHAM_MATER=CHMAT0,
EXCIT= (
_F (CHARGE=T_IMP,),
_F (CHARGE=CALINT,
FONC_MULT=FLUX,),),
COMP_INCR=_F (RELATION=' KIT_THHM',
RELATION_KIT= (“ELAS”, “LIQU_GAZ”
, “HYDR_UTIL”),),
RECH_LINEAIRE =_F (RESI_LINE_RELA = 1.E-3,
RHO_MIN = 0.1,
RHO_MAX = 0.2,
ITER_LINE_MAXI = 3,),
ETAT_INIT=_F (DEPL=CHAMNO,
SIGM=SIGINIT),
INCREMENT=_F (LIST_INST=INST1,),
NEWTON=_F (MATRICE=' TANGENTE', REAC_ITER=10,),
CONVERGENCE=_F (RESI_GLOB_MAXI=1.0000000000000001E-05,
ITER_GLOB_MAXI=150,
ARRET=' NON',
ITER_INTE_MAXI=5,),
ARCHIVAGE=_F (PAS_ARCH=1,),);
To this control one assigns the model (key word
MODEL
), it/the materials (key word
CHAM_MATER
),
/the loadings (key word
EXCIT
) and the initial state (key word
ETAT_INIT
) that one defined by all
controls described previously.
For general information concerning this control and his syntax, one will refer to its
documentation. It is specified just that the method of calculation is a method of Newton.
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Caution:
Under the key word factor NEWTON, one must put a matrix of the type
“TANGENT”
and not
“ELASTIC”
.
One speaks here only about what is specific to calculations THM with knowing the key words factors
RELATION
and
RELATION_KIT
key word
COMP_INCR
who are closely dependant.
RELATION
is informed by relations of the types
who allow to solve
at the same time from two to four equilibrium equations. The equations considered depend on
suffix
with the following rule:
M
indicate the mechanical equilibrium equation,
T
indicate the thermal equilibrium equation,
H
indicate a hydraulic equilibrium equation.
V
indicate the presence of a phase in form vapor (in addition to the fluid
)
Only one letter
H
mean that the porous environment is saturated (only one variable of pressure p), by
example either of gas, or of fluid, or of a liquid mixture/gas (of which the pressure of gas is
constant).
Two letters
H
mean that the porous environment is not saturated (two variables of pressure p), by
example a liquid mixture/vapor/gas.
The presence of two letters HV means that the porous environment is saturated by a component (with
practical of water), but that this component can be in liquid form or vapor. There is not whereas one
conservation equation of this component, therefore only one degree of freedom pressure, but there is a flow
fluid and a flow vapor. The possible relations are then the following ones:
/“KIT_HM”
/“KIT_THM”
/“KIT_HHM”
/“KIT_THH”
/“KIT_THV”
/“KIT_THHM”
The table below summarizes to which kit each modeling corresponds:
KIT_HM
D_PLAN_HM, D_PLAN_HMD, AXIS_HM, AXIS_HMD, 3D_HM, 3D_HMD
KIT_THM
D_PLAN_THM, D_PLAN_THMD, AXIS_THM, AXIS_THMD, 3D_THM, 3D_THMD
KIT_HHM
D_PLAN_HHM, D_PLAN_HHMD, AXIS_HHM, AXIS_HHMD, 3D_HHM, 3D_HHMD,
D_PLAN_HH2MD, AXIS_HH2MD, 3d_HH2MD
KIT_THH
D_PLAN_THH, D_PLAN_THHD, AXIS_THH, AXIS_THHD, 3D_THH, 3D_THHD,
D_PLAN_THH 2D, AXIS_THH 2D, 3D_THH 2D
KIT_THV
D_PLAN_THVD, AXIS_THVD, 3D_THVD
KIT_THHM
D_PLAN_THHM, D_PLAN_THHMD, AXIS_THHM, AXIS_THHMD, 3D_THHM,
3d_THHMD, D_PLAN_THH2MD, AXIS_THH2MD, 3d_THH2MD
For each modelized phenomenon (thermal and/or mechanical and/or hydraulic), one must specify
in
RELATION_KIT
:
·
The mechanical model of behavior of the skeleton if there is mechanical modeling (
M
),
/'ELAS
'
/“CJS”
/“LAIGLE”
/“ELAS_THM”
/“CAM_CLAY”
/“DRUCKER_PRAGER”
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·
The behavior of the fluids/gas, (the same one as that indicated in
COMP_THM
under
DEFI_MATERIAU
, cf [§2.2.2])
/'LIQU_SATU
'
/'LIQU_GAZ
'
/“GAS”
/“LIQU_GAZ_ATM”
/“LIQU_VAPE_GAZ”
/“LIQU_AD_GAZ_VAPE”
/“LIQU_VAPE”
·
Moreover in all the cases, one must imperatively inform:
HYDR_UTIL
under
RELATION_KIT
(this key word makes it possible to inform the curve of saturation and its derivative in
function of the capillary pressure as well as the relative permeability and its derivative according to
saturation).
If one mentions the example above, one deals with in a coupled way a hydro-mechanical thermo problem
for a porous environment unsaturated with
LIQU_GAZ
like behavior of the fluid, and a law
rubber band like mechanical behavior.
Caution:
According to
chosen, all the behaviors are not licit (for example if one
chosen porous environments unsaturated, one cannot affect a behavior of the gas type
perfect). all the possible combinations are summarized below
For relation
KIT_HM
:
(“ELAS” “GAS”
“HYDR_UTIL”)
(“CJS”
“GAS”
“HYDR_UTIL”)
(“LAIGLE”
“GAS”
“HYDR_UTIL”)
(“CAM_CLAY” “GAS”
“HYDR_UTIL”)
(“ELAS” “LIQU_SATU” “HYDR_UTIL”)
(“CJS”
“LIQU_SATU” “HYDR_UTIL”)
(“LAIGLE”
“LIQU_SATU” “HYDR_UTIL”)
(“CAM_CLAY” “LIQU_SATU” “HYDR_UTIL”)
(“ELAS” “LIQU_GAZ_ATM” “HYDR_UTIL”)
(“CJS”
“LIQU_GAZ_ATM” “HYDR_UTIL”)
(“LAIGLE”
“LIQU_GAZ_ATM” “HYDR_UTIL”)
(“CAM_CLAY” “LIQU_GAZ_ATM” “HYDR_UTIL”)
For relation
KIT_THM
:
(“ELAS” “GAS”
“HYDR_UTIL”)
(“CJS”
“GAS”
“HYDR_UTIL”)
(“LAIGLE”
“GAS”
“HYDR_UTIL”)
(“CAM_CLAY”
“GAS”
“HYDR_UTIL”)
(“ELAS”
“LIQU_SATU”
“HYDR_UTIL”)
(“CJS”
“LIQU_SATU”
“HYDR_UTIL”)
(“LAIGLE”
“LIQU_SATU”
“HYDR_UTIL”)
(“CAM_CLAY”
“LIQU_SATU”
“HYDR_UTIL”)
(“ELAS” “LIQU_GAZ_ATM” “HYDR_UTIL”)
(“CJS”
“LIQU_GAZ_ATM” “HYDR_UTIL”)
(“LAIGLE”
“LIQU_GAZ_ATM”
“HYDR_UTIL”)
(“CAM_CLAY”
“LIQU_GAZ_ATM”
“HYDR_UTIL”)
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For relation
KIT_HHM
:
(“ELAS” “LIQU_GAZ”
“HYDR_UTIL”)
(“CJS”
“LIQU_GAZ”
“HYDR_UTIL”)
(“LAIGLE”
“LIQU_GAZ”
“HYDR_UTIL”)
(“CAM_CLAY” “LIQU_GAZ”
“HYDR_UTIL”)
(“ELAS” “LIQU_VAPE_GAZ”
“HYDR_UTIL”)
(“CJS”
“LIQU_VAPE_GAZ”
“HYDR_UTIL”)
(“LAIGLE”
“LIQU_VAPE_GAZ”
“HYDR_UTIL”)
(“CAM_CLAY” “LIQU_VAPE_GAZ”
“HYDR_UTIL”)
(“ELAS” “LIQU_AD_GAZ_VAPE”
“HYDR_UTIL”)
(“CJS”
“LIQU_AD_GAZ_VAPE”
“HYDR_UTIL”)
(“LAIGLE”
“LIQU_AD_GAZ_VAPE”
“HYDR_UTIL”)
(“CAM_CLAY” “LIQU_AD_GAZ_VAPE”
“HYDR_UTIL”)
For relation
KIT_THH
:
(“LIQU_GAZ” “HYDR_UTIL”)
(“LIQU_VAPE_GAZ”
“HYDR_UTIL”)
(“LIQU_AD_GAZ_VAPE” “HYDR_UTIL”)
For relation
KIT_THV
:
(“LIQU_VAPE”
“HYDR_UTIL”)
For relation
KIT_THHM
:
(“ELAS” “LIQU_GAZ”
“HYDR_UTIL”)
(“CJS”
“LIQU_GAZ”
“HYDR_UTIL”)
(“LAIGLE”
“LIQU_GAZ”
“HYDR_UTIL”)
(“CAM_CLAY”
“LIQU_GAZ” “HYDR_UTIL”)
(“ELAS” “LIQU_VAPE_GAZ”
“HYDR_UTIL”)
(
“CJS”
“LIQU_VAPE_GAZ” “HYDR_UTIL”
)
(
“LAIGLE”
“LIQU_VAPE_GAZ”
“HYDR_UTIL”
)
(
“CAM_CLAY”
“LIQU_VAPE_GAZ” “HYDR_UTIL”
)
(“ELAS” “LIQU_AD_GAZ_VAPE”
“HYDR_UTIL”)
(
“CJS”
“LIQU_AD_GAZ_VAPE” “HYDR_UTIL”
)
(
“LAIGLE”
“LIQU_AD_GAZ_VAPE” “HYDR_UTIL”
)
(
“CAM_CLAY”
“LIQU_AD_GAZ_VAPE” “HYDR_UTIL”
)
Note:
In the event of problem of convergence it can be very useful to activate linear search
as indicated in the example given at the head of this section. Linear search
do not improve however systematically convergence, it is thus to handle with
precaution.
2.6
postprocessing
The post processing data in THM does not vary a post usual Aster processing. One recalls
just that for any impression of the values which are not the nodal unknown factors, it is necessary
to calculate these values by the control
CALC_ELEM
whose one gives an example hereafter.
For the stresses:
U0=CALC_ELEM (reuse =U0,
MODELE=MODELE,
CHAM_MATER=CHMAT0,
TOUT_ORDRE=' OUI',
OPTION= (“SIEF_ELNO_ELGA”),
RESULTAT=U0,);
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For the internal variables:
U0=CALC_ELEM (reuse =U0,
MODELE=MODELE,
CHAM_MATER=CHMAT0,
TOUT_ORDRE=' OUI',
OPTION= (“VARI_ELNO_ELGA”),
RESULTAT=U0,);
It should however be recalled that all the values of displacements at exits correspond to
ddl
U
and
not
ref.
ddl
U
U
U
+
=
.
It is also important to know the name of the stresses and the numbers of the internal variables.
All that is consigned in appendix I.
Thus the following example makes it possible to print the liquid water mass on the HIGH group of nodes to all
moments.
TAB1=POST_RELEVE_T (ACTION=_F (INTITULE=' CONT',
GROUP_NO= (“HIGH”),
RESULTAT=U0,
NOM_CHAM=' SIEF_ELNO_ELGA',
TOUT_ORDRE=' OUI',
NOM_CMP= (“M11”),
OPERATION=' EXTRACTION',),);
IMPR_TABLE (TABLE=TAB1,
FICHIER=' RESULTAT',
FORMAT=' AGRAF',
PAGINATION=' INST',
NOM_PARA= (“INST”, “COOR_X”, “M11”),);
The following example makes it possible to print the values of porosity to node 1 and the first moment.
TAB2=POST_RELEVE_T (ACTION=_F (INTITULE=' DEPL',
NOEUD=' NO1',
RESULTAT=U0,
NOM_CHAM=' VARI_ELNO_ELGA',
NUME_ORDRE=1,
NOM_CMP= (“V2”),
OPERATION=' EXTRACTION',),);
IMPR_TABLE (TABLE=TAB2,
FICHIER=' RESULTAT',
FORMAT=' AGRAF',
PAGINATION=' INST',
NOM_PARA= (“INST”, “COOR_X”, “V2”),);
Concerning the layout of isovaleurs IDEAS as GIBI are the two tools used.
2.6.1 Isovaleurs with Gibi
A file .cast readable by controls GIBI east creates via the control
IMPR_RESU
as on
the example below:
IMPR_RESU (RESU=_F (FORMAT=' CASTEM',
RESULTAT=U0,
MAILLAGE=MAIL,
NUME_ORDRE=1,),),
The file obtained is then read by a file of processing. An example of files gibi of processing
data is in [§Annexe 4].
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2.6.2 Isovaleurs with IDEAS
A file .unv readable by IDEAS is created via the control
IMPR_RESU
with format IDEAS as on
the example below:
IMPR_RESU (RESU=_F (FORMAT=' IDEAS',
RESULTAT=U0,
MAILLAGE=MAIL,
NUME_ORDRE=1,),),
3 Bibliography
[1]
Catsius Clay project. Calculation and testing off behavior off unsaturated clay have barrier in
radioactive waste repositories.
[2]
Card-index of model of thermal reference Couplage hydraulic ANDRA-CNT ACSS 02-006
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Internal appendix 1 generalized Stresses and variables
Stresses:
Number
Name of component Aster
Contents Modelings
1
SIXX
xx
So mechanical (.
M
…)
2
SIYY
yy
So mechanical (.
M
…)
3
SIZZ
zz
So mechanical (.
M
…)
4
SIXY
xy
So mechanical (.
M
…)
5
SIXZ
xz
So mechanical (.
M
…)
6
SIYZ
yz
So mechanical (.
M
…)
7
SIP
p
So mechanical (.
M
…)
8
M11
W
m
In all the cases
9
FH11X
X
W
M
In all the cases
10
FH11Y
y
W
M
In all the cases
11
FH11Z
Z
W
M
In all the cases
12
ENT11
m
W
H
In all the cases
13
M12
vp
m
If 2 unknown pressures (.
HH
…)
14
FH12X
X
vp
M
If 2 unknown pressures (.
HH
…)
15
FH12Y
y
vp
M
If 2 unknown pressures (.
HH
…)
16
FH12Z
Z
vp
M
If 2 unknown pressures (.
HH
…)
17
ENT12
m
vp
H
If 2 unknown pressures (.
HH
…)
18
M21
have
m
If 2 unknown pressures (.
HH
…)
19
FH21X
X
have
M
If 2 unknown pressures (.
HH
…)
20
FH21Y
y
have
M
If 2 unknown pressures (.
HH
…)
21
FH21Z
Z
have
M
If 2 unknown pressures (.
HH
…)
22
ENT21
m
have
H
If 2 unknown pressures (.
HH
…)
18
M22
AD
m
If modeling of the dissolved air (… HH2…)
19
FH22X
X
AD
M
If modeling of the dissolved air (… HH2…)
20
FH22Y
y
AD
M
If modeling of the dissolved air (… HH2…)
21
FH22Z
Z
AD
M
If modeling of the dissolved air (… HH2…)
22
ENT22
m
AD
H
If modeling of the dissolved air (… HH2…)
23
QPRIM
'
Q
So thermal
24
FHTX
X
Q
So thermal
25
FHTY
y
Q
So thermal
26
FHTZ
Z
Q
So thermal
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In the case without mechanics, the variables internal:
Number
Name component Aster
Contents
1 V1
0
lq
lq
-
2 V2
0
-
3 V3
0
vp
vp
p
p
-
4 V4
lq
S
In the case with mechanics the first numbers will be those corresponding to mechanics (V1 in
elastic case, V1 and following for plastic models). The number of the variables intern above will have
then to be incremented of as much.
Appendix 2 Example I of command file
# EXAMPLE OF CALCULATION AXIS_THH2MD
BEGINNING ();
PRE_GIBI ();
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # #
INST1=DEFI_LIST_REEL (DEBUT=0.0,
INTERVALLE= (
_F (JUSQU_A=500000000., NOMBRE=50,),
_F (JUSQU_A=2000000000., NOMBRE=20,),
),);
MAIL=LIRE_MAILLAGE ();
MAIL=DEFI_GROUP (reuse =MAIL,
MAILLAGE=MAIL,
CREA_GROUP_NO= (_F (GROUP_MA=' BAS',),
_F (GROUP_MA=' HAUT',),
_F (GROUP_MA=' GAUCHE',),
_F (GROUP_MA=' DROIT',),
_F (GROUP_MA=' BO',),
),);
MODELE=AFFE_MODELE (MAILLAGE=MAIL,
AFFE=_F (TOUT=' OUI',
PHENOMENE=' MECANIQUE',
MODELISATION=' AXIS_THH2MD',),);
#
#
UN=DEFI_CONSTANTE (VALE=1.0,);
UNDEMI=DEFI_CONSTANTE (VALE=0.5,);
ZERO=DEFI_CONSTANTE (VALE=0.0,);
VISCOLIQ=DEFI_CONSTANTE (VALE=1.E-3,);
VISCOGAZ=DEFI_CONSTANTE (VALE=1.E-03,);
DVISCOL=DEFI_CONSTANTE (VALE=0.0,);
DVISCOG=DEFI_CONSTANTE (VALE=0.0,);
LI2=DEFI_LIST_REEL (DEBUT=-1.E9,
INTERVALLE= (
_F (JUSQU_A=1.E9,
NOMBRE=500,),),);
LI1=DEFI_LIST_REEL (DEBUT=0.10000000000000001,
INTERVALLE=_F (JUSQU_A=0.98999999999999999,
PAS=1.E-2,),);
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# LIMITATION OF SATURATION MAX (<1)
# CONSTBO = DEFI_CONSTANTE (VALE: 0.99);
#
SLO = FORMULA (REAL = ''' (REAL:PCAP) =
0.4 ''');
SATUBO=CALC_FONC_INTERP (FONCTION=SLO,
LIST_PARA=LI2,
NOM_PARA=' PCAP',
PROL_GAUCHE=' LINEAIRE',
PROL_DROITE=' LINEAIRE',
INFO=2,);
DSATBO=DEFI_CONSTANTE (VALE=0.,);
#
#
# COEFF. FICK
#
FICK=DEFI_CONSTANTE (VALE=3.E-10,);
KINTBO=DEFI_CONSTANTE (VALE=9.9999999999999995E-19,);
HENRY=DEFI_CONSTANTE (VALE=50000.,);
MATERBO=DEFI_MATERIAU (ELAS=_F (E=5.15000000E8,
NU=0.20000000000000001,
RHO=2670.0,
ALPHA=0.,),
COMP_THM = “LIQU_AD_GAZ_VAPE”,
THM_LIQU=_F (RHO=1000.0,
UN_SUR_K=0.,
ALPHA=0.,
CP=0.0,
VISC=VISCOLIQ,
D_VISC_TEMP=DVISCOL,),
THM_GAZ=_F (MASS_MOL=0.01,
CP=0.0,
VISC=VISCOGAZ,
D_VISC_TEMP=ZERO,),
THM_VAPE_GAZ=_F (MASS_MOL=0.01,
CP=0.0,
VISC=VISCOGAZ,
D_VISC_TEMP=ZERO,),
THM_AIR_DISS=_F (
CP=0.0,
COEF_HENRY=HENRY
),
THM_INIT=_F (TEMP=300.0,
PRE1=0.0,
PRE2=1.E5,
PORO=1.,
PRES_VAPE=1000.0,
DEGR_SATU=0.4,),
THM_DIFFU=_F (R_GAZ=8.32,
RHO=2200.0,
CP=1000.0,
BIOT_COEF=1.0,
SATU_PRES=SATUBO,
D_SATU_PRES=DSATBO,
PESA_X=0.0,
PESA_Y=0.0,
PESA_Z=0.0,
PERM_IN=KINTBO,
PERM_LIQU=UNDEMI,
D_PERM_LIQU_SATU=ZERO,
PERM_GAZ=UNDEMI,
D_PERM_SATU_GAZ=ZERO,
D_PERM_PRES_GAZ=ZERO,
FICKV_T=ZERO,
FICKA_T=FICK,
LAMB_T=ZERO,
),);
CHMAT0=AFFE_MATERIAU (MAILLAGE=MAIL,
AFFE= (_F (GROUP_MA=' BO',
MATER=MATERBO,),
),);
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CHAMNO=CREA_CHAMP (MAILLAGE=MAIL,
OPERATION=' AFFE',
TYPE_CHAM=' NOEU_DEPL_R',
AFFE= (_F (TOUT=' OUI',
NOM_CMP=' TEMP',
VALE=0.0,),
_F (TOUT=' OUI',
NOM_CMP=' PRE2',
VALE=1000.0,),
_F (TOUT=' OUI',
NOM_CMP=' PRE1',
VALE=1.E6,),
),);
TIMP=AFFE_CHAR_MECA (MODELE=MODELE,
DDL_IMPO= (_F (TOUT=' OUI',
TEMP=0.0,),
_F (GROUP_NO= (“HIGH”, “LOW”, “LEFT”, “RIGHT”),
DX=0.0,),
_F (GROUP_NO= (“HIGH”, “LOW”, “LEFT”, “RIGHT”),
DY=0.0,),
_F (GROUP_MA=' GAUCHE',
PRE2=15000.,),
_F (GROUP_MA=' GAUCHE',
PRE1=1.E6,),
),
);
SIGINIT=CREA_CHAMP (MAILLAGE=MAIL,
OPERATION=' AFFE',
TYPE_CHAM=' CART_SIEF_R',
AFFE= (_F (GROUP_MA=' BO',
NOM_CMP=
(“SIXX”, “SIYY”, “SIZZ”, “SIXY”, “SIXZ”,
“SIYZ”, “SIP”, “M11”, “FH11X”, “FH11Y”, “ENT11”,
“M12”, “FH12X”, “FH12Y”, “ENT12”,
“QPRIM”, “FHTX”, “FHTY”, “M21”,
“FH21X”, “FH21Y”, “ENT21”,
“M22”, “FH22X”, “FH22Y”, “ENT22”,),
VALE=
(0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 2500000.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0., 0., 0., 0.),),
),);
U0=STAT_NON_LINE (MODELE=MODELE,
CHAM_MATER=CHMAT0,
EXCIT= (
_F (CHARGE=TIMP,),),
COMP_INCR=_F (RELATION=' KIT_THHM',
RELATION_KIT= (“ELAS”, “LIQU_AD_GAZ_VAPE”, “THER_POLY”, “HYDR_UTIL”),),
ETAT_INIT=_F (DEPL=CHAMNO,
SIGM=SIGINIT,),
INCREMENT=_F (LIST_INST=INST1,
),
NEWTON=_F (MATRICE=' TANGENTE',
REAC_ITER=1,),
RECH_LINEAIRE=_F (RESI_LINE_RELA=0.10000000000000001,
ITER_LINE_MAXI=3,),
CONVERGENCE=_F (
RESI_GLOB_RELA=1.E-6,
ITER_GLOB_MAXI=80,
),
PARM_THETA=0.8,
SOLVEUR=_F (METHODE=' MULT_FRONT',
STOP_SINGULIER=' NON',),
);
END ();
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Appendix 3 Example 2 of command files
# EXAMPLE OF CALCULATION AXIS_THHMD FOR A BI-MATERIAUX (BARRIER OUVRAGEE AND
# BARRIER GEOLOGICAL)
BEGINNING (CODE=_F (NOM=' WTNA100A', NIV_PUB_WEB=' INTERNET'),);
MAIL=LIRE_MAILLAGE ();
#
# LISTS MOMENTS OF CALCULATION
#
INST1=DEFI_LIST_REEL (DEBUT=0.0,
INTERVALLE= (_F (JUSQU_A=1.E7, NOMBRE=10,),
_F (JUSQU_A=1.E8, NOMBRE=1,),
_F (JUSQU_A=1.E9, NOMBRE=9,),),);
MAIL=DEFI_GROUP (reuse =MAIL,
MAILLAGE=MAIL,
CREA_GROUP_NO= (_F (GROUP_MA=' LBABG',),
_F (GROUP_MA=' LBABO',),
_F (GROUP_MA=' LINTBO',),
_F (GROUP_MA=' LINTBG',),
_F (GROUP_MA=' SURFBO',),
_F (GROUP_MA=' SURFBG',),
_F (GROUP_MA=' SURF',),),);
MODELE=AFFE_MODELE (MAILLAGE=MAIL,
AFFE=_F (TOUT=' OUI',
PHENOMENE=' MECANIQUE',
MODELISATION=' AXIS_THHMD',),);
#
#
UN=DEFI_CONSTANTE (VALE=1.0,);
ZERO=DEFI_CONSTANTE (VALE=0.0,);
VISCOLIQ=DEFI_CONSTANTE (VALE=1.E-3,);
VISCOGAZ=DEFI_CONSTANTE (VALE=1.8E-05,);
DVISCOL=DEFI_CONSTANTE (VALE=0.0,);
DVISCOG=DEFI_CONSTANTE (VALE=0.0,);
LI2=DEFI_LIST_REEL (DEBUT=0.0,
INTERVALLE=_F (JUSQU_A=1.E9, PAS=1.E6,),);
LI1=DEFI_LIST_REEL (DEBUT=1.E-5,
INTERVALLE=_F (JUSQU_A=1.0, PAS=0.099999,),);
#
# PROPERTIES OF BARRIER OUVRAGEE
#
LTBO=DEFI_CONSTANTE (VALE=0.59999999999999998,);
LSO = FORMULA (REAL = ''' (REAL:SAT) = (0.35 * SAT) ''');
LSBO=CALC_FONC_INTERP (FONCTION=LSO,
LIST_PARA=LI1,
NOM_PARA=' SAT',
PROL_GAUCHE=' LINEAIRE',
PROL_DROITE=' LINEAIRE',
INFO=2,);
DLSBO=DEFI_CONSTANTE (VALE=0.35,);
SSL = FORMULA (REAL = ''' (REAL:PCAP) = 0.99 * (1.- PCAP * 6.E-9) ''');
SATUBO=CALC_FONC_INTERP (FONCTION=SL,
LIST_PARA=LI2,
NOM_PARA=' PCAP',
PROL_DROITE=' CONSTANT',
PROL_GAUCHE=' CONSTANT',
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INFO=2,);
DSL = FORMULA (REAL = ''' (REAL:PCAP) = - 6.E-9 * 0.99 ''');
DSATBO=CALC_FONC_INTERP (FONCTION=DSL,
LIST_PARA=LI2,
NOM_PARA=' PCAP',
PROL_DROITE=' CONSTANT',
PROL_GAUCHE=' CONSTANT',
INFO=2,);
PERM = FORMULA (REAL = ''' (REAL:SAT) = SAT ''');
PERM11BO=CALC_FONC_INTERP (FONCTION=PERM,
LIST_PARA=LI1,
NOM_PARA=' SAT',
PROL_DROITE=' CONSTANT',
PROL_GAUCHE=' CONSTANT',
INFO=2,);
DPERMBO = FORMULA (REAL = ''' (REAL:SAT) = 1.''');
DPR11BO=CALC_FONC_INTERP (FONCTION=DPERMBO,
LIST_PARA=LI1,
NOM_PARA=' SAT',
PROL_DROITE=' CONSTANT',
PROL_GAUCHE=' CONSTANT',
INFO=2,);
PERM2BO = FORMULA (REAL = ''' (REAL:SAT) = 1.- SAT ''');
PERM21BO=CALC_FONC_INTERP (FONCTION=PERM2BO,
LIST_PARA=LI1,
NOM_PARA=' SAT',
PROL_DROITE=' CONSTANT',
PROL_GAUCHE=' CONSTANT',
INFO=2,);
DPERM2BO = FORMULA (REAL = ''' (REAL:SAT) = - 1.''');
DPR21BO=CALC_FONC_INTERP (FONCTION=DPERM2BO,
LIST_PARA=LI1,
NOM_PARA=' SAT',
PROL_DROITE=' CONSTANT',
PROL_GAUCHE=' CONSTANT',
INFO=2,);
#
# CONDUCTIVITY THERMAL OF THE BO
#
DM8=DEFI_CONSTANTE (VALE=9.9999999999999995E-08,);
KINTBO=DEFI_CONSTANTE (VALE=9.9999999999999995E-21,);
MATERBO=DEFI_MATERIAU (ELAS=_F (E=1.9E+20,
NU=0.20000000000000001,
RHO=2670.0,
ALPHA=0.,),
COMP_THM = “LIQU_GAZ”,
THM_LIQU=_F (RHO=1000.0,
UN_SUR_K=5.0000000000000003E-10,
ALPHA=1.E-4,
CP=4180.0,
VISC=VISCOLIQ,
D_VISC_TEMP=DVISCOL,),
THM_GAZ=_F (MASS_MOL=0.02896,
CP=1000.0,
VISC=VISCOGAZ,
D_VISC_TEMP=ZERO,),
THM_VAPE_GAZ=_F (MASS_MOL=0.017999999999999999,
CP=1870.0,
VISC=VISCOGAZ,
D_VISC_TEMP=ZERO,),
THM_INIT=_F (TEMP=293.0,
PRE1=0.0,
PRE2=1.E5,
PORO=0.34999999999999998,
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PRES_VAPE=2320.0,
DEGR_SATU=0.57420000000000004,),
THM_DIFFU=_F (R_GAZ=8.3149999999999995,
RHO=2670.0,
CP=482.0,
BIOT_COEF=1.0,
SATU_PRES=SATUBO,
D_SATU_PRES=DSATBO,
PESA_X=0.0,
PESA_Y=0.0,
PESA_Z=0.0,
PERM_IN=KINTBO,
PERM_LIQU=PERM11BO,
D_PERM_LIQU_SATU=DPR11BO,
PERM_GAZ=PERM21BO,
D_PERM_SATU_GAZ=DPR21BO,
D_PERM_PRES_GAZ=ZERO,
LAMB_T=LTBO,
LAMB_S=LSBO,
D_LB_S=DLSBO,
LAMB_CT=0.728),);
#
# PROPERTIES OF THE GEOLOGICAL BARRIER
#
KINTBG=DEFI_CONSTANTE (VALE=9.9999999999999998E-20,);
LTBG=DEFI_CONSTANTE (VALE=0.59999999999999998,);
LSG = FORMULA (REAL = ''' (REAL:SAT) =
(0.05 * SAT) ''');
LSBG=CALC_FONC_INTERP (FONCTION=LSG,
LIST_PARA=LI1,
NOM_PARA=' SAT',
PROL_GAUCHE=' LINEAIRE',
PROL_DROITE=' LINEAIRE',
INFO=2,);
DLSBG=DEFI_CONSTANTE (VALE=0.05,);
MATERBG=DEFI_MATERIAU (ELAS=_F (E=1.9E+20,
NU=0.20000000000000001,
RHO=2670.0,
ALPHA=0.0,),
COMP_THM = “LIQU_GAZ”,
THM_LIQU=_F (RHO=1000.0,
UN_SUR_K=5.0000000000000003E-10,
ALPHA=1.E-4,
CP=4180.0,
VISC=VISCOLIQ,
D_VISC_TEMP=DVISCOL,),
THM_GAZ=_F (MASS_MOL=0.02896,
CP=1000.0,
VISC=VISCOGAZ,
D_VISC_TEMP=ZERO,),
THM_VAPE_GAZ=_F (MASS_MOL=0.017999999999999999,
CP=1870.0,
VISC=UN,
D_VISC_TEMP=ZERO,),
THM_INIT=_F (TEMP=293.0,
PRE1=0.0,
PRE2=1.E5,
PORO=0.050000000000000003,
PRES_VAPE=2320.0,
DEGR_SATU=0.81179999999999997,),
THM_DIFFU=_F (R_GAZ=8.3149999999999995,
RHO=2670.0,
CP=706.0,
BIOT_COEF=1.0,
SATU_PRES=SATUBO,
D_SATU_PRES=DSATBO,
PESA_X=0.0,
PESA_Y=0.0,
PESA_Z=0.0,
PERM_IN=KINTBG,
PERM_LIQU=PERM11BO,
D_PERM_LIQU_SATU=DPR11BO,
PERM_GAZ=PERM21BO,
D_PERM_SATU_GAZ=DPR21BO,
D_PERM_PRES_GAZ=ZERO,
LAMB_T=LTBG,
LAMB_S=LSBG,
Code_Aster
®
Version
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Titrate:
Note of use of model THM
Date:
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D_LB_S=DLSBG,
LAMB_CT=1.539),);
CHMAT0=AFFE_MATERIAU (MAILLAGE=MAIL,
AFFE= (_F (GROUP_MA=' SURFBO',
MATER=MATERBO,),
_F (GROUP_MA=' SURFBG',
MATER=MATERBG,),),);
#
# ASSIGNMENT OF L INITIAL STATE
#
CHAMNO=CREA_CHAMP (MAILLAGE=MAIL,
OPERATION=' AFFE',
TYPE_CHAM=' NOEU_DEPL_R',
AFFE= (_F (TOUT=' OUI',
NOM_CMP=' TEMP',
VALE=0.0,),
_F (GROUP_NO=' SURFBO',
NOM_CMP=' PRE1',
VALE=7.E7,),
_F (GROUP_NO=' SURFBG',
NOM_CMP=' PRE1',
VALE=3.E7,),
_F (NOEUD= (“NO300”, “NO296”),
NOM_CMP=' PRE1',
VALE=5.E7,),
_F (GROUP_NO=' SURFBO',
NOM_CMP=' PRE2',
VALE=0.0,),
_F (GROUP_NO=' SURFBG',
NOM_CMP=' PRE2',
VALE=0.0,),),);
# EVOLUTIONARY FLOW IMPOSES IN INTERNAL P.
#
FLUX=DEFI_FONCTION (NOM_PARA=' INST',
VALE=
(0.0, 386.0,
315360000.0, 312.0,
9460800000.0, 12.6),);
CALEXT=AFFE_CHAR_MECA (MODELE=MODELE,
DDL_IMPO= (_F (TOUT=' OUI',
TEMP=0.0,),
_F (TOUT=' OUI',
PRE2=0.0,),
_F (TOUT=' OUI',
DX=0.0,),
_F (TOUT=' OUI',
DY=0.0,),),);
CALINT=AFFE_CHAR_MECA (MODELE=MODELE,
FLUX_THM_REP=_F (GROUP_MA=' LINTBO',
FLUN=1.0,
FLUN_HYDR1=0.0,
FLUN_HYDR2=0.0,),);
SIGINIT=CREA_CHAMP (MAILLAGE=MAIL,
OPERATION=' AFFE',
TYPE_CHAM=' CART_SIEF_R',
AFFE= (_F (GROUP_MA=' SURFBO',
NOM_CMP=
(“SIXX”, “SIYY”, “SIZZ”, “SIXY”, “SIXZ”, “SIYZ”, “SIP”, “M11”, “FH11X”,
“FH11Y”, “ENT11”, “M12”, “FH12X”, “FH12Y”, “ENT12”, “M21”, “FH21X”, “FH21Y”, “ENT21”, “QPRIM”,
“FHTX”, “FHTY”),
VALE=
(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, - 70000.0, 0.0, 0.0, 0.0,
2450000.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0),),
_F (GROUP_MA=' SURFBG',
NOM_CMP=
(“SIXX”, “SIYY”, “SIZZ”, “SIXY”, “SIXZ”, “SIYZ”, “SIP”, “M11”, “FH11X”,
“FH11Y”, “ENT11”, “M12”, “FH12X”, “FH12Y”, “ENT12”, “M21”, “FH21X”, “FH21Y”, “ENT21”, “QPRIM”,
“FHTX”, “FHTY”),
VALE=
(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, - 29900.0, 0.0, 0.0, 0.0,
2450000.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0),),),);
U0=STAT_NON_LINE (MODELE=MODELE,
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CHAM_MATER=CHMAT0,
EXCIT= (
_F (CHARGE=CALEXT,),
_F (CHARGE=CALINT,
FONC_MULT=FLUX,),
),
COMP_INCR=_F (RELATION=' KIT_THHM',
RELATION_KIT= (“ELAS”, “LIQU_GAZ”, “THER_POLY”, “HYDR_UTIL”),),
ETAT_INIT=_F (DEPL=CHAMNO,
SIGM=SIGINIT),
INCREMENT=_F (LIST_INST=INST1,),
NEWTON=_F (MATRICE=' TANGENTE',
REAC_ITER=10,),
CONVERGENCE=_F (RESI_GLOB_MAXI=1.0000000000000001E-05,
ITER_GLOB_MAXI=150,
ARRET=' NON',
ITER_INTE_MAXI=5,),
PARM_THETA=0.56999999999999995,
ARCHIVAGE=_F (PAS_ARCH=1,),);
U0=CALC_ELEM (reuse =U0,
MODELE=MODELE,
CHAM_MATER=CHMAT0,
TOUT_ORDRE=' OUI',
OPTION= (“SIEF_ELNO_ELGA”, “VARI_ELNO_ELGA”),
RESULTAT=U0,);
TRB=POST_RELEVE_T (ACTION=_F (INTITULE=' DEPL',
GROUP_NO= (“LBABG”, “LBABO”),
RESULTAT=U0,
NOM_CHAM=' DEPL',
NUME_ORDRE= (1,10,11,20),
NOM_CMP= (“PRE1”),
OPERATION=' EXTRACTION',),);
TRB2=POST_RELEVE_T (ACTION=_F (INTITULE=' CONT',
GROUP_NO= (“LBABG”, “LBABO”),
RESULTAT=U0,
NOM_CHAM=' SIEF_ELNO_ELGA',
TOUT_ORDRE=' OUI',
NOM_CMP= (“M11”, “FH11X”, “FH11Y”),
OPERATION=' EXTRACTION',),);
ZTRB3=POST_RELEVE_T (ACTION=_F (INTITULE=' DEPL',
NOEUD= (“NO294”, “NO295”, “NO299”, “NO300”, “NO304”, “NO305”, “NO309”),
RESULTAT=U0,
NOM_CHAM=' VARI_ELNO_ELGA',
TOUT_ORDRE=' OUI',
NOM_CMP= (“V2”),
OPERATION=' EXTRACTION',),);
IMPR_TABLE (TABLE=TRB,
FICHIER=' RESULTAT',
FORMAT=' AGRAF',
PAGINATION=' INST',
NOM_PARA= (“INST”, “COOR_X”, “PRE1”),);
IMPR_TABLE (TABLE=ZTRB,
FICHIER=' RESULTAT',
FORMAT=' AGRAF',
PAGINATION=' INST',
NOM_PARA= (“INST”, “COOR_X”, “PRE1”),);
#
# V2 density of the fluid
#
IMPR_TABLE (TABLE=ZTRB3,
FICHIER=' RESULTAT',
FORMAT=' AGRAF',
PAGINATION=' INST',
NOM_PARA= (“INST”, “COOR_X”, “V2”),);
END ();
Code_Aster
®
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Titrate:
Note of use of model THM
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Appendix 4 Post processing GIBI
* FILE DESIGN CONTAINING THE RESULTS
* ---------------------------------------------
OPTI REST FORM “VISUTHMTBTCAS3-1.CAST”;
REST FORM;
* OPTI TRAC PSC;
* trace of the mesh
trac ALL;
* Creation of contours (to be able to trace the isovaleurs
* without the elements: necessary if very fine mesh)
contout = contour all;
trac contout;
* list of the moments has to strip
lis0 = lect 0 1 2 3 4 5 6 7 8 9 10;
* model selection
moc = (MALL ELEM QUA8);
* and (MALL ELEM SEG3);
*
Mandelevium = moc MODE MECHANICAL RUBBER BAND;
* Looping over the moments
* --------
N = dime lis0;
to repeat loop1 N;
I = (extr lis0 &loop1) + 1;
p = U0. I. inst;
* Deformation
depla = U0. I. DEPL;
titrate “TBT cas3-1: Deformation Time = ' p' seconds”;
def1 = DEFORMS ALL depla 5. red;
init1 = DEFORMS ALL depla 0. blue;
TRAC (def1 and init1);
TRAC def1;
def1s = DEFORMS red SAND depla 1.;
init1s = DEFORMS SAND depla 0. blue;
titrate “TBT cas3-1: Deformation Sands Time = ' p' seconds”;
TRAC (def1s and init1s);
titrate “TBT cas3-1: Deformation BO Temps = ' p' seconds”;
def1bo = DEFORMS (BO1 and BO2) depla 5. red;
init1bo = DEFORMS (BO1 and BO2) depla 0. blue;
TRAC (def1bo and init1bo);
* (the chpoint depla is transf in chamelem for the temperatures)
cham2 = CHAN CHAM depla Mandelevium NODE;
* Visualization of the temperatures with THM
chtemp = EXCO TEMP cham2;
titrate “TBT cas3-1: Temperature Time = ' p' seconds”;
* trac chtemp Mandelevium 14 WHOLE;
trac chtemp Mandelevium 14 contout;
* Visualization of the pressure of pores
chpre1 = EXCO PRE1 cham2;
titrate “TBT cas3-1: Pressure of pores Time = ' p' seconds”;
* trac chpre1 Mandelevium 14 WHOLE;
* Visualization of the increase in gas pressure
chpre2 = EXCO PRE2 cham2;
titrate “TBT cas3-1: Increase in Pgz Time = ' p' seconds”;
trac chpre2 Mandelevium 14 contout;
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* Stresses
sig = U0. I. SIEF;
sigxx = EXCO SMXX sig;
sigyy = EXCO SMYY sig;
sigzz = EXCO SMZZ sig;
sigp = EXCO SIP sig;
* Calculation forced Total
sixxt = sigxx + sigp;
siyyt = sigyy + sigp;
sizzt = sigzz + sigp;
TITRATE “TBT CAS3-1: Stress Sxx Time = ' p' seconds”;
* trac sigxx Mandelevium 14 WHOLE;
trac sigxx Mandelevium 14 contout;
* TITRATE “TBT CAS3-1: Cont. total Sxx Time = ' p' seconds”;
* trac sixxt Mandelevium 14 contout;
TITRATE “TBT CAS3-1: Stress Syy Time = ' p' seconds”;
* trac sigyy Mandelevium 14 WHOLE;
trac sigyy Mandelevium 14 contout;
* TITRATE “TBT CAS3-1: Cont. total Syy Time = ' p' seconds”;
* trac siyyt Mandelevium 14 contout;
TITRATE “TBT CAS3-1: Stress Szz Time = ' p' seconds”;
* trac sigzz Mandelevium 14 WHOLE;
trac sigzz Mandelevium 14 contout;
* TITRATE “TBT CAS3-1: Cont. total Szz Time = ' p' seconds”;
* trac sizzt Mandelevium 14 contout;
TITRATE “TBT CAS3-1: Pressure SIP Time = ' p' seconds”;
trac sigp Mandelevium 14 contout;
* variable internal
VAr = U0. I. VARI;
var1 = EXCO V1 VAr;
var2 = EXCO V2 VAr;
var3 = EXCO V3 VAr;
var4 = EXCO V4 VAr;
TITRATE “TBT CAS3-1: Increase porosity has T = ' p' seconds”;
* trac var1 Mandelevium 14 WHOLE;
trac var1 Mandelevium 14 contout;
TITRATE “TBT CAS3-1: Accroissement RhoLiq has T = ' p' seconds”;
* trac var2 Mandelevium 14 WHOLE;
trac var2 Mandelevium 14 contout;
TITRATE “TBT CAS3-1: Accroissement Pvp has T = ' p' seconds”;
* trac var3 Mandelevium 14 WHOLE;
trac var3 Mandelevium 14 contout;
TITRATE “TBT CAS3-1: Saturation has T = ' p' seconds”;
* trac var4 Mandelevium 14 WHOLE;
trac var4 Mandelevium 14 contout;
* One reduces to sand
* sigb=REDU sig sand;
* sigxx = EXCO SMXX sigb;
* TITRATE “TBT CAS3-1:SiXX SANDS t=' p' seconds”;
* trac sigxx Mandelevium 14 SANDS;
end loop1;
opti gift 5;
end;
Code_Aster
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Appendix 5 additional Elements on the conditions with
limits in THM
In what follows one does not take into account the dissolved air (the index lq corresponds then to that of water W) and one
stick to the case unsaturated.
We point out here the choice of the unknown factors of pressure.
Behavior
LIQU_GAZ
and
LIQU_VAPE_GAZ
PRE1
Capillary pressure:
lq
gz
C
p
p
p
-
=
PRE2
Gas pressure
have
vp
gz
p
p
p
+
=
A5.1 variational Formulation of the conservation equations
One refers here to [R7.01.11]. These equations are
(
)
0
=
+
+
+
vp
lq
vp
lq
Div
m
m
M
M
&
&
éq A5.1-1
(
)
0
=
+
have
have
Div
m
M
&
éq A5.1-2
The deduced variational formulation is given by
(
)
(
)
(
)
AD
ext.
vp
ext.
lq
vp
lq
vp
lq
P
D
D
D
m
m
1
1
1
1
1
.
.
+
=
+
+
+
-
M
M
M
M
&
&
éq
A5.1-3
AD
ext.
have
have
have
P
D
D
D
m
2
2
2
2
2
.
.
=
+
-
M
M
&
éq A5.1-4
The capillary pressures and of gas are related to the pressure of water, vapor and dry air by the relations:
lq
gz
C
p
p
p
-
=
éq A5.1-5
have
vp
gz
p
p
p
+
=
éq A5.1-6
Code_Aster
®
Version
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Titrate:
Note of use of model THM
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The steam pressure is not an independent variable. It is connected to the pressure of fluid
lq
p
by
relations
(
)
T
dT
H
H
dp
dp
m
lq
m
vp
lq
lq
vp
vp
-
+
=
éq A5.1-7
(
)
lq
lq
lq
p
lq
m
lq
dp
T
dT
C
dh
-
+
=
3
1
éq A5.1-8
dT
C
dh
p
vp
m
vp
=
éq A5.1-9
These relations show that the steam pressure is given completion not the knowledge of
lq
p
(and of its evolution). Often, these relations are used to establish the law of Kelvin,
=
-
)
(
ln
0
T
p
p
T
M
R
p
p
sat
vp
vp
ol
vp
lq
lq
lq
,
but this law is not used directly in Aster.
The reference documents Aster do not say anything on what are the variables
1
and
2
. But two elements
can put to us on the runway:
·
On the one hand,
AD
P
1
1
and
AD
P
2
2
whereas
AD
P
1
and
AD
P
2
are spaces of membership of PRE1
and PRE2 (thus including their boundary conditions).
·
In addition, in chapter 7. of [R7.01.10], one sees that the virtual deformation
()
(
)
=
,
,
,
,
,
,
,
2
2
1
1
*
v
v
E
el
G
is related to the vector of virtual displacement nodal
(
)
,
,
,
2
1
*
v
U
=
el
by the same operator
el
G
Q
that that which connects between them the deformation
()
(
)
T
T
p
p
p
p
el
G
=
,
,
,
,
,
,
,
2
2
1
1
U
U
E
and nodal displacement
(
)
T
p
p
el
,
,
,
2
1
U
U
=
:
-
el
el
G
el
G
*
*
U
Q
E
=
-
el
el
G
el
G
U
Q
E
=
It is then clear that
1
and
2
are virtual variations of
1
p
and
2
p
From where the table:
*
1
1
C
p
p
p
p
C
C
=
=
=
*
1
1
lq
p
p
p
p
lq
lq
=
=
=
*
2
2
gz
p
p
p
p
gz
gz
=
=
=
Code_Aster
®
Version
7.4
Titrate:
Note of use of model THM
Date:
06/07/04
Author (S):
S. GRANET, C. CHAVANT
Key
:
U2.04.05-A
Page
:
46/50
Instruction manual
U2.04 booklet: Nonlinear mechanics
HT-66/04/004/A
A5.2 Case of boundary conditions utilizing unknown factors
main
What we say in this paragraph and the following relates to part of the border
D
on which
conditions are prescribed: nothing prevents of course that these conditions are not the same ones on
parts of different borders. We treat in this chapter the usual case where one imposes conditions on
PRE1 and/or PRE2, in opposition to the following chapter where we will speak about linear relations between unknown factors.
imp
lq
gz
C
C
p
p
p
p
=
-
=
imp
vp
have
gz
gz
p
p
p
p
=
+
=
Flows are then computation results by [éq A5.1-3] and [éq A5.1-4]
·
Dirichlet PRE1, neuman PRE2
It is the case where one imposes a value on PRE1 and a value with flow associated with PRE2, by not saying anything on PRE2
or by giving a value to
FLUN_HYDR2
of
FLUX_THM_REP
in
AFFE_CHAR_MECA
. Let us call
ext.
2
M
this
imposed quantity, which will be worth
0
if nothing is known as relative with PRE2. We will note
imp
p
p
1
1
=
the condition
imposed on PRE1
This corresponds to:
imp
imp
imp
lq
gz
C
C
C
p
p
p
p
p
p
=
=
-
=
1
To make the demonstration within the nonhomogeneous framework, it would be necessary to introduce a raising of the condition
imp
p
p
1
1
=
(c.à.d a particular field checking this condition). That weighs down the writings and does not bring anything, one
thus places itself within the homogeneous framework
0
1
=
imp
p
In [éq A5.1-3] and [éq A5.1-4], one can thus take and
2
unspecified and
1
checking
0
1
=
on
D
One
then start to take
0
1
=
and
0
2
=
on all the edge
and one obtains [éq A5.1-1] and [éq A5.1-2] with
feel distributions. One multiplies then [éq A5.1-1] by
1
such as
0
1
=
on
D
one multiplies [éq A5.1-2]
by
2
unspecified, one integrates by part, one takes account of [éq A5.1-3] and [éq A5.1-4] and one obtains, in
indicating by
N
the normal at the edge:
2
2
2
2
.
.
=
=
D
D
D
D
ext.
have
M
N
M
Code_Aster
®
Version
7.4
Titrate:
Note of use of model THM
Date:
06/07/04
Author (S):
S. GRANET, C. CHAVANT
Key
:
U2.04.05-A
Page
:
47/50
Instruction manual
U2.04 booklet: Nonlinear mechanics
HT-66/04/004/A
One deduces some
D
ext.
have
=
on
.
2
M
N
M
·
Dirichlet PRE2, neuman PRE1
It is the case where one imposes a value on PRE2 and a value with flow associated with PRE1, by not saying anything on PRE1
or by giving a value to
FLUN_HYDR1
of
FLUX_THM_REP
in
AFFE_CHAR_MECA
. Let us call
ext.
1
M
this
imposed quantity, which will be worth
0
if nothing is known as relative with PRE2. We will note
imp
p
p
2
2
=
the condition
imposed on PRE2
This corresponds to:
imp
imp
imp
vp
have
gz
gz
gz
p
p
p
p
p
p
=
=
+
=
2
The demonstration is the same one as in the preceding paragraph and leads to:
(
)
D
ext.
vp
lq
=
+
on
.
1
M
N
M
M
A5.3 Case of boundary conditions utilizing relations
linear between main unknown factors
Code_Aster makes it possible to introduce like boundary conditions of the relations between degrees of freedom, carried
by the same node or different nodes. This possibility is reached via the key word
LIAISON_DDL
of
the control
AFFE_CHAR_MECA
.
That is to say
imp
lq
p
the value which one wants to impose on the pressure of fluid on
D
. Taking into account [éq A5.1-5], and
choice of the main unknown factors for this behavior, one writes:
imp
lq
C
gz
p
p
p
p
p
=
-
=
-
1
2
éq A5.3-1
The linear relations are treated in Aster by introduction of multipliers of Lagrange. This corresponds
in the species with the following formulation:
To find
µ
,
2
1
, p
p
such as:
(
)
(
)
(
)
(
)
*
2
1
1
2
1
2
*
2
2
1
1
,
,
.
.
µ
µ
µ
-
-
+
-
-
+
+
+
-
+
+
+
-
D
imp
lq
D
imp
lq
have
have
vp
lq
vp
lq
D
p
D
p
p
p
D
D
m
D
D
m
m
M
M
M
&
&
&
éq
A5.3-2
To make the demonstration within the nonhomogeneous framework, it would be necessary to introduce a raising of the condition
0
1
2
=
-
-
imp
lq
p
p
p
(a.c. D of the particular fields checking this condition). That weighs down the writings and
do not bring anything, one thus places itself within the homogeneous framework
0
=
imp
lq
p
Code_Aster
®
Version
7.4
Titrate:
Note of use of model THM
Date:
06/07/04
Author (S):
S. GRANET, C. CHAVANT
Key
:
U2.04.05-A
Page
:
48/50
Instruction manual
U2.04 booklet: Nonlinear mechanics
HT-66/04/004/A
One then starts to take
0
1
=
and
0
2
=
on all the edge
and one obtains [éq A5.1-1] and [éq A5.1-2] with
feel distributions. One multiplies then [éq A5.1-1] by
1
unspecified one multiplies [éq A5.1-2] by
2
unspecified, one integrates by part, one carries the results found in [éq A5.3-2] and one obtains:
(
)
(
)
(
)
*
2
1
1
2
1
2
*
2
1
,
,
0
.
.
.
.
µ
µ
µ
=
-
+
-
+
+
+
D
D
D
have
D
vp
lq
D
D
p
p
D
D
N
M
N
M
M
éq
A5.3-3
It is clear that [éq A5.3-3] gives again well
0
1
2
=
=
-
imp
lq
p
p
p
While taking moreover
0
1
2
=
-
, one finds:
(
)
1
1
0
.
.
=
+
+
D
have
vp
lq
D
N
M
M
M
From where one deduces:
(
)
D
have
vp
lq
=
+
+
on
0
.
N
M
M
M
éq A5.3-4
A5.4 nonlinear cases
We do not make here that to tackle more difficult questions consisting in imposing either the steam pressure or
pressure of dry air. Taking into account the relations [éq A5.1-7], [éq A5.1-8] and [éq A5.1-9] to impose a value on
steam pressure amounts imposing a nonlinear relation on the pressure of fluid. In the same way to impose one
pressure of dry air.
As example, we approach the case of a pressure of dry air imposed for a behavior
LIQU_VAPE_GAZ
, and we suppose that we can write the nonlinear relation connecting the pressure of
vapor and pressure of fluid.
The relation to be imposed is thus:
imp
have
vp
vp
gz
have
p
p
p
p
p
p
=
-
=
-
=
2
éq A5.4-1
By differentiating this relation, one will find a condition on the virtual variations of pressures:
(
)
C
gz
lq
vp
gz
lq
lq
vp
gz
have
dp
dp
p
p
dp
dp
p
p
dp
dp
-
-
=
-
=
That is to say still
(
)
2
1
1
2
2
1
dp
p
p
dp
p
p
dp
dp
p
p
dp
dp
lq
vp
lq
vp
lq
vp
have
-
+
=
-
-
=
The variational formulation would be then:
(
)
(
)
(
)
*
2
1
2
1
2
*
2
2
1
1
,
,
1
.
.
µ
µ
µ
-
+
+
-
-
+
+
+
-
+
+
+
-
D
lq
vp
lq
vp
D
imp
have
vp
have
have
vp
lq
vp
lq
D
p
p
p
p
D
p
p
p
D
D
m
D
D
m
m
M
M
M
&
&
&
Code_Aster
®
Version
7.4
Titrate:
Note of use of model THM
Date:
06/07/04
Author (S):
S. GRANET, C. CHAVANT
Key
:
U2.04.05-A
Page
:
49/50
Instruction manual
U2.04 booklet: Nonlinear mechanics
HT-66/04/004/A
And one would find:
(
)
2
1
2
1
2
1
,
0
1
.
.
.
.
µ
=
-
+
+
+
+
D
lq
vp
lq
vp
D
have
D
vp
lq
D
p
p
p
p
D
D
N
M
N
M
M
While taking
0
1
2
1
=
-
+
lq
vp
lq
vp
p
p
p
p
one would find:
(
)
0
.
.
1
=
-
+
-
N
M
N
M
M
have
lq
vp
vp
lq
lq
vp
p
p
p
p
éq A5.4-2
Code_Aster
®
Version
7.4
Titrate:
Note of use of model THM
Date:
06/07/04
Author (S):
S. GRANET, C. CHAVANT
Key
:
U2.04.05-A
Page
:
50/50
Instruction manual
U2.04 booklet: Nonlinear mechanics
HT-66/04/004/A
Intentionally white left page.