Code_Aster
®
Version
7.4
Titrate:
HSNA102 Validation of the laws of drying
Date:
16/11/04
Author (S):
S. MICHEL-PONNELLE, Y. the POPE
Key
:
V7.20.102-A
Page:
1/20
Manual of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the axisymmetric structures
HT-66/04/005/A
Organization (S):
EDF-R & D/AMA, EDF-R & D/MMC
Manual of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the structures
axisymmetric
V7.20.102 document
HSNA102 - Validation of the laws of drying on one
cylindrical concrete test-tube
Summary:
This case test is intended to not validate the calculation of the drying of the concrete, developed in the operator of thermics
linear of Code_Aster. One tests here the various laws of dissemination available in Code_Aster, namely
SECH_GRANGER
,
SECH_MENSI
,
SECH_BAZANT
and
SECH_NAPPE
. Possible dependence at the temperature of
models is however not tested.
It is about an axisymmetric case test where the water concentration is applied directly to the external wall.
The results are compared with a numerical resolution of the equations using Scilab.
Code_Aster
®
Version
7.4
Titrate:
HSNA102 Validation of the laws of drying
Date:
16/11/04
Author (S):
S. MICHEL-PONNELLE, Y. the POPE
Key
:
V7.20.102-A
Page:
2/20
Manual of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the axisymmetric structures
HT-66/04/005/A
1
Problem of reference
1.1 Geometry
One modelizes a cylindrical section of test-tube of diameter 160mm.
8 cm
1 cm
FI
FE
1.2
Material properties
Each modeling makes it possible to validate a coefficient of dissemination
D
, namely:
·
modeling a: law of Mensi
)
exp (
)
(
BC
With
C
D
=
·
modeling b: law of Granger
-
-
=
0
0
1
1
exp
)
exp (
)
,
(
T
T
R
Q
T
T
BC
With
T
C
D
S
·
modeling C: definition of D in the form of tablecloth
·
modeling D: law of Bazant
()
-
-
+
-
+
=
N
C
H
D
H
D
75
.
0
1
)
(
1
1
1
1
Code_Aster
®
Version
7.4
Titrate:
HSNA102 Validation of the laws of drying
Date:
16/11/04
Author (S):
S. MICHEL-PONNELLE, Y. the POPE
Key
:
V7.20.102-A
Page:
3/20
Manual of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the axisymmetric structures
HT-66/04/005/A
The coefficients used are those recommended by Granger in its thesis [bib1]:
SECH_MENSI
:
To = 0.74 10
- 13
m
2
/S
B = 0.05
SECH_GRANGER
To = 0.74 10
- 13
m
2
/S
B = 0.05
T
0
= 293 °K
Q
S
/R = 4700 K
- 1
SECH_NAPPE
One re-enters in the form of tablecloth the law of Mensi
Coefficient of dissemination
0
2nd-11
4th-11
6th-11
0
20
40
60
80
100
120
140
C (L/m3)
D
(
m
2/
S)
SECH_BAZANT
D1 = 3.0 10
- 10
m
2
/S
= 0.04
N = 6
2
0
0
5
.
0
1
-
-
-
=
eq
C
C
C
C
H
with
0
C
=128.8 L/m
3
and
eq
C
= 58.8 L/m
3
1.3
Boundary conditions and loadings
The calculation of drying is carried out over one 5 years duration
·
the temperature remains uniform and is worth 20 °C
·
one applies to FE C
eq
= 58.8 L/m
3
1.4 Conditions
initial
The initial conditions are consisted the initial temperature, which one takes with 20°C, and
initial water concentration, which is worth
3
0
/
8
.
128
m
L
C
=
.
Code_Aster
®
Version
7.4
Titrate:
HSNA102 Validation of the laws of drying
Date:
16/11/04
Author (S):
S. MICHEL-PONNELLE, Y. the POPE
Key
:
V7.20.102-A
Page:
4/20
Manual of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the axisymmetric structures
HT-66/04/005/A
2
Reference solution
2.1
Method of calculation used for the reference solution
The 2 reference solutions are obtained by resolution of the equation of drying by differences
finished using Scilab. The command file is given in appendix to possibly be able
to test new models.
The space discretization is the same one as for Aster with knowing of the meshs of 1 Misters the discretization
temporal is 3600 seconds for the equation of Mensi, and 60 seconds for the equation of Bazant.
2.2
Results of reference
One is interested in the water concentration in the test-tube after 1h, 3j, 28j, 1.25 year, 3 years and 5 years.
The evolution of the profiles obtained with Scilab for the law of Mensi and the law of Bazant is visible on
[Figure 2.2-a] and [Figure 2.2-b].
Note:
The comparison between the solutions Scilab and Aster is visible in [§Annexe 2]: they are shown
concentrations obtained in the test-tube after 1h and 5 years. The maid thus is checked
correlation excluded for the solution obtained with Aster for the law of Mensi at the end of one
hour when one observes an oscillation which makes much think of a violation of the principle of
maximum observed in thermics (cf [bib2]). It would be thus interesting to be able to use them
lumpés elements when one solves the equation of drying even if the phenomenon is accentuated
here because of the boundary conditions, since one directly imposes the water concentration on
place to impose a flow [bib3].
Evolution of the water concentration in
the test-tube in the course of time
Law of Mensi
58,8
68,8
78,8
88,8
98,8
108,8
118,8
128,8
138,8
0
0,02
0,04
0,06
0,08
position X (m)
Co
N
cen
T
R
At
I
O
N
in
water
(
L
/
m
3)
1 hour
3 days
28 days
1.25 year
3 years
5 years
Appear 2.2-a: Scilab Solution - law of Mensi
Code_Aster
®
Version
7.4
Titrate:
HSNA102 Validation of the laws of drying
Date:
16/11/04
Author (S):
S. MICHEL-PONNELLE, Y. the POPE
Key
:
V7.20.102-A
Page:
5/20
Manual of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the axisymmetric structures
HT-66/04/005/A
Evolution of the water concentration in
the test-tube in the course of time
Law of Mensi
58,8
68,8
78,8
88,8
98,8
108,8
118,8
128,8
138,8
0
0,02
0,04
0,06
0,08
position X (m)
Co
N
cen
T
R
At
I
O
N
in
water
(
L
/
m
3)
1 hour
3 days
28 days
1.25 year
3 years
5 years
Appear 1.2-b: Scilab Solution - law of Bazant
TEST_RESU
are realized for the 6 characteristic moments with the X-coordinates X = 0mm, x= 40 mm
and x=60 Misters.
2.3 References
bibliographical
[1]
L. GRANGER: “Behavior differed from the concrete in the chambers of nuclear thermal power stations”
published by the Central Laboratory of the Highways Departments (1996).
[2]
S. MICHEL-PONNNELLE, A. RAZAKANAIVO: “I7-01-08 Project: Quality of the Studies in
Mechanics of the Solids Etape n°4
: study of the finite elements
”, Note EDF
:
HT-64/02/007/A, June 2002
[3]
G. DEBRUYNE, B. CIREE: “Modeling of the thermo hydration, drying and the withdrawal
concrete “, manual of Code_Aster Reference, [R7.01.12] (2001).
Code_Aster
®
Version
7.4
Titrate:
HSNA102 Validation of the laws of drying
Date:
16/11/04
Author (S):
S. MICHEL-PONNELLE, Y. the POPE
Key
:
V7.20.102-A
Page:
6/20
Manual of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the axisymmetric structures
HT-66/04/005/A
3 Modeling
With
3.1
Characteristics of modeling
One uses the law of dissemination of Mensi.
3.2
Characteristics of the mesh
The test-tube is with a grid using 80 QUAD4 regularly distributed. There is only one element in
height.
A number of nodes: 162
A number of meshs and type: 80 QUAD4
3.3
Characteristics of the temporal discretization
Initial moment (S)
Final moment (S)
Numbers of pitches of time
0 3600
10
3600 259
200
10
259 200
2.419.200
10
2.419.200
39.420.000
10
39.420.000
94.608.000
10
94.608.000
1 57.680.000
10
3.4
Functionalities tested
Controls Options
“THERMAL” AFFE_MODELE
“AXIS” “ALL”
DEFI_MATERIAU “SECH_MENSI”
THER_NON_LINE COMP_THER_NL “SECH_MENSI”
EVOL_THER_SECH
Code_Aster
®
Version
7.4
Titrate:
HSNA102 Validation of the laws of drying
Date:
16/11/04
Author (S):
S. MICHEL-PONNELLE, Y. the POPE
Key
:
V7.20.102-A
Page:
7/20
Manual of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the axisymmetric structures
HT-66/04/005/A
4
Results of modeling A
4.1 Values
tested
Water concentration at the point x=0.0:
Identification Reference Aster %
difference
after 1 a.m.
128.80
128.80
2.21 10
- 14
after 3 days
128.80
128.80
- 2.21 10
- 14
after 28 days
128.80
128.80
- 3.67 10
- 5
after 1.25 year
117.49
117.76
0.231
after 3 years
105.06
105.38
0.307
after 5 years
96.77
97.09
0.332
Water concentration at the point x=0.04:
Identification Reference Aster %
difference
after 1 a.m.
128.80
128.80
1.31 10
- 13
after 3 days
128.80
128.80
- 1.77 10
- 13
after 28 days
128.61
128.66
0.038
after 1.25 year
117.74
112.35
0.543
after 3 years
99.43
100.06
0.634
after 5 years
91.39
91.99
0.661
Water concentration at the point x=0.06:
Identification Reference Aster %
difference
after 1 a.m.
128.80
128.80
2.53 10
- 11
after 3 days
128.80
128.80
0.002
after 28 days
124.98
125.67
0.552
after 1.25 year
101.32
102.42
1.089
after 3 years
89.60
90.64
1.158
after 5 years
82.33
83.27
1.140
4.2 Comments
It is checked here that the made error is weak since lower than 1.5%, which is completely correct being
given the relatively coarse temporal discretization used, in particular at the end of the calculation.
Code_Aster
®
Version
7.4
Titrate:
HSNA102 Validation of the laws of drying
Date:
16/11/04
Author (S):
S. MICHEL-PONNELLE, Y. the POPE
Key
:
V7.20.102-A
Page:
8/20
Manual of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the axisymmetric structures
HT-66/04/005/A
5 Modeling
B
5.1
Characteristics of modeling
One uses the law of dissemination of Granger
5.2
Characteristics of the mesh
The test-tube is with a grid using 80 QUAD4 regularly distributed. There is only one element in
height.
A number of nodes: 162
A number of meshs and type: 80 QUAD4
5.3
Characteristics of the temporal discretization
Initial moment (S)
Final moment (S)
Numbers of pitches of time
0 3600
10
3600 259
200
10
259 200
2.419.200
10
2.419.200
39.420.000
10
39.420.000
94.608.000
10
94.608.000
1 57.680.000
10
5.4
Functionalities tested
Controls Options
“THERMAL” AFFE_MODELE
“AXIS” “ALL”
DEFI_MATERIAU “SECH_GRANGER”
THER_NON_LINE COMP_THER_NL “SECH_GRANGER”
EVOL_THER_SECH
Code_Aster
®
Version
7.4
Titrate:
HSNA102 Validation of the laws of drying
Date:
16/11/04
Author (S):
S. MICHEL-PONNELLE, Y. the POPE
Key
:
V7.20.102-A
Page:
9/20
Manual of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the axisymmetric structures
HT-66/04/005/A
6
Results of modeling B
6.1 Values
tested
Water concentration at the point x=0.0:
Identification Reference Aster %
difference
after 1 a.m.
128.80
128.80
2.21 10
- 14
after 3 days
128.80
128.80
- 2.21 10
- 14
after 28 days
128.80
128.80
- 3.67 10
- 5
after 1.25 year
117.49
117.76
0.231
after 3 years
105.06
105.38
0.307
after 5 years
96.77
97.09
0.332
Water concentration at the point x=0.04:
Identification Reference Aster %
difference
after 1 a.m.
128.80
128.80
1.31 10
- 13
after 3 days
128.80
128.80
- 1.77 10
- 13
after 28 days
128.61
128.66
0.038
after 1.25 year
117.74
112.35
0.543
after 3 years
99.43
100.06
0.634
after 5 years
91.39
91.99
0.661
Water concentration at the point x=0.06:
Identification Reference Aster %
difference
after 1 a.m.
128.80
128.80
2.53 10
- 11
after 3 days
128.80
128.80
0.002
after 28 days
124.98
125.67
0.552
after 1.25 year
101.32
102.42
1.089
after 3 years
89.60
90.64
1.158
after 5 years
82.33
83.27
1.140
6.2 Comments
One finds the same solution exactly as the law of Mensi.
Code_Aster
®
Version
7.4
Titrate:
HSNA102 Validation of the laws of drying
Date:
16/11/04
Author (S):
S. MICHEL-PONNELLE, Y. the POPE
Key
:
V7.20.102-A
Page:
10/20
Manual of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the axisymmetric structures
HT-66/04/005/A
7 Modeling
C
7.1
Characteristics of modeling
The law of dissemination is used
SECH_NAPPE
, for which one re-enters simply the law of dissemination of
Mensi.
7.2
Characteristics of the mesh
The test-tube is with a grid using 80 QUAD4 regularly distributed. There is only one element in
height.
A number of nodes: 162
A number of meshs and type: 80 QUAD4
7.3
Characteristics of the temporal discretization
Initial moment (S)
Final moment (S)
Numbers of pitches of time
0 3600
10
3600 259
200
10
259 200
2.419.200
10
2.419.200
39.420.000
10
39.420.000
94.608.000
10
94.608.000
1 57.680.000
10
7.4
Functionalities tested
Controls Options
“THERMAL” AFFE_MODELE
“AXIS” “ALL”
DEFI_NAPPE NOM_PARA
“TSEC”
DEFI_MATERIAU “SECH_NAPPE”
THER_NON_LINE COMP_THER_NL “SECH_NAPPE”
EVOL_THER_SECH
Code_Aster
®
Version
7.4
Titrate:
HSNA102 Validation of the laws of drying
Date:
16/11/04
Author (S):
S. MICHEL-PONNELLE, Y. the POPE
Key
:
V7.20.102-A
Page:
11/20
Manual of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the axisymmetric structures
HT-66/04/005/A
8
Results of modeling C
8.1 Values
tested
Water concentration at the point x=0.0:
Identification Reference Aster %
difference
after 1 a.m.
128.80
128.80
1.32 10
- 13
after 3 days
128.80
128.80
8.83 10
- 14
after 28 days
128.80
128.80
- 4.35 10
- 5
after 1.25 year
117.49
117.51
0.012
after 3 years
105.06
105.04
- 0.021
after 5 years
96.77
96.73
- 0.037
Water concentration at the point x=0.04:
Identification Reference Aster %
difference
after 1 a.m.
128.80
128.80
1.32 10
- 13
after 3 days
128.80
128.80
- 4.41 10
- 13
after 28 days
128.61
128.65
0.029
after 1.25 year
117.74
112.11
0.328
after 3 years
99.43
99.74
0.318
after 5 years
91.39
91.68
0.319
Water concentration at the point x=0.06:
Identification Reference Aster %
difference
after 1 a.m.
128.80
128.80
2.45 10
- 11
after 3 days
128.80
128.80
0.002
after 28 days
124.98
125.57
0.471
after 1.25 year
101.32
102.18
0.856
after 3 years
89.60
90.35
0.843
after 5 years
82.33
82.99
0.798
8.2 Comments
It is seen here that the error is lower than 1%.
Code_Aster
®
Version
7.4
Titrate:
HSNA102 Validation of the laws of drying
Date:
16/11/04
Author (S):
S. MICHEL-PONNELLE, Y. the POPE
Key
:
V7.20.102-A
Page:
12/20
Manual of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the axisymmetric structures
HT-66/04/005/A
9 Modeling
D
9.1
Characteristics of modeling
One uses the law of dissemination of Bazant.
9.2
Characteristics of the mesh
The test-tube is with a grid using 80 QUAD4 regularly distributed. There is only one element in
height.
A number of nodes: 162
A number of meshs and type: 80 QUAD4
9.3
Characteristics of the temporal discretization
Initial moment (S)
Final moment (S)
Numbers of pitches of time
0 3600
10
3600 259
200 20
259 200
2.419.200
20
2.419.200
39.420.000
20
39.420.000
94.608.000
10
94.608.000
1 57.680.000
10
9.4
Functionalities tested
Controls Options
“THERMAL” AFFE_MODELE
“AXIS” “ALL”
DEFI_MATERIAU “SECH_BAZANT”
THER_NON_LINE COMP_THER_NL “SECH_BAZANT”
EVOL_THER_SECH
Code_Aster
®
Version
7.4
Titrate:
HSNA102 Validation of the laws of drying
Date:
16/11/04
Author (S):
S. MICHEL-PONNELLE, Y. the POPE
Key
:
V7.20.102-A
Page:
13/20
Manual of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the axisymmetric structures
HT-66/04/005/A
10 Results of modeling D
10.1 Values
tested
Water concentration at the point x=0.0:
Identification Reference Aster %
difference
after 1 a.m.
128.80
128.80
0.
after 3 days
128.80
128.80
- 3.70 10
- 7
after 28 days
118.42
118.63
0.175
after 1.25 year
70.36
70.51
2.227
after 3 years
63.63
63.76
0.210
after 5 years
60.67
60.73
0.102
Water concentration at the point x=0.04:
Identification Reference Aster %
difference
after 1 a.m.
128.80
128.80
- 2.21 10
- 14
after 3 days
128.66
128.70
0.031
after 28 days
105.89
106.80
0.853
after 1.25 year
68.25
68.53
0.415
after 3 years
62.24
62.40
0.259
after 5 years
60.06
60.13
0.119
Water concentration at the point x=0.06:
Identification Reference Aster %
difference
after 1 a.m.
128.80
128.80
- 1.18 10
- 11
after 3 days
120.99
122.47
1.225
after 28 days
92.11
93.21
1.192
after 1.25 year
65.16
64.80
0.563
after 3 years
60.62
60.76
0.234
after 5 years
59.43
59.49
0.097
10.2 Comments
It is checked here that the made error is weak since lower than 1.5%.
Code_Aster
®
Version
7.4
Titrate:
HSNA102 Validation of the laws of drying
Date:
16/11/04
Author (S):
S. MICHEL-PONNELLE, Y. the POPE
Key
:
V7.20.102-A
Page:
14/20
Manual of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the axisymmetric structures
HT-66/04/005/A
11 Summary of the results
For the whole of modelings, one obtains a difference between solution SCILAB and the solution
Code_Aster lower than 1.5% what makes it possible to validate the establishment of the various laws of drying
in the code. Let us note simply that one observes a violation of the principle of the maximum at the beginning of
simulation with Aster for the law of Mensi. This can be explained (by analogy with thermics) by
the “hydrous shock” important due the made-to-order to impose the boundary conditions (water concentration
imposed). This problem should be able to be solved by the use of the lumpés elements of same
way that in thermics.
Code_Aster
®
Version
7.4
Titrate:
HSNA102 Validation of the laws of drying
Date:
16/11/04
Author (S):
S. MICHEL-PONNELLE, Y. the POPE
Key
:
V7.20.102-A
Page:
15/20
Manual of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the axisymmetric structures
HT-66/04/005/A
Appendix 1 Command file Scilab
Main.sci:
getf (“/home/xxxx/librairie.sci”);
//PARAMETERS OF THE DIGITAL SIMULATION
//
//discretization of the width
x0 = 0.08;
X = [- 0.080:0.001:+0.080]; [n1 N2] = size (X);
//water content initial
Cinit = 128.8;
Ci = Cinit * ones (1, N2);
//boundary conditions with 50%HR
CL = [58.8 58.8];.
Ci (1) = CL (1); Ci ($) = CL (2);
Ci_bazant = Ci;
//not of time
dt = 60; //[S]
//coefficients of the law of Bazant
D1 = 3.0E-10; //[m2/S]
= 0.04 have;
N = 6;
TMAX = 5; //years
//______________________________________________________________________
//
//DIGITAL SIMULATION
//
J = 0;
u=file (“open”, “resultat_g”, “unknown”);
for year = 0:TMAX,
year
for day = 0:364,
for hour = 0:23,
minute = 0;
for minute = 0:59,
D_bazant
=
diffusion_bazant (D1, has, N, Cinit, 58.8, Ci_bazant, 293,293 * ones (Ci), 4700);
Ci_bazant = linear_drying (D_bazant, Ci_bazant, CL, dt, X, “whodunnit”);
yew ((year == 0 & day == 0 & hour == 1 & minute == 0) | …
(year == 0 & day == 3 & hour == 0 & minute == 0) | …
(year == 0 & day == 28 & hour == 0 & minute == 0) | …
(year == 1 & day == 91 & hour == 0 & minute == 0) | …
(year == 3 & day == 0 & hour == 0 & minute == 0) | …
(year == 5 & day == 0 & hour == 0 & minute == 0)) then,
year, day, hour
t=81:1:161;
for tk=t,
fprintf (U, “% 6.3f % 6.3f”, X (tk), Ci_bazant (tk)) ;
end,
end,//yew
end,//for minute
end,//for hour
end,//for day
end,//for year
slip by (“closed”, U);
Code_Aster
®
Version
7.4
Titrate:
HSNA102 Validation of the laws of drying
Date:
16/11/04
Author (S):
S. MICHEL-PONNELLE, Y. the POPE
Key
:
V7.20.102-A
Page:
16/20
Manual of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the axisymmetric structures
HT-66/04/005/A
Librairie.sci:
________________________________________________________________
//
//NONLINEAR COEFFICIENT OF DISSEMINATION FOR THE DRYING OF THE CONCRETE
//LAW OF MENSI D (C) = A. exp (b.C)
//THERMIC ACTION D (C, T) = D (C, T0).(T/T0) .EXP [- Q/R * (1/T-1/T0)]
//
//coefficient of the law of Mensi has
//B coefficient of the law of Mensi
//C vector of the water contents [-]
//T0 temperature of reference [K]
//T vector of the temperatures [K]
//Q_R Q/R (being worth 4700 K)
function D = diffusion_mensi (has, B, C, T0, T, Q_R),
D = has * ones (C).* exp (B * C);
D = D. * (T./(T0 * ones (T))) ;
D = D. * exp (Q_R * ((ones (T)./T0) - (ones (T)./T))) ;
endfunction,
//
//________________________________________________________________
//
//NONLINEAR COEFFICIENT OF DISSEMINATION FOR THE DRYING OF THE CONCRETE
//LAW OF BAZANT
//THERMIC ACTION D (C, T) = D (C, T0).(T/T0) .EXP [- Q/R * (1/T-1/T0)]
//
//D1 coefficient of the law of Bazant
//has coefficient of the law of Bazant (alpha)
//N coefficient of the law of Bazant
//C0 water content with 100%HR
//Cext water content of the surrounding medium
//C vector of the water contents [-]
//T0 temperature of reference [K]
//T vector of the temperatures [K]
//Q_R Q/R (being worth 4700 K-1)
function D = diffusion_bazant (D1, has, N, C0, Cext, C, T0, T, Q_R),
H = ones (C)-0.5 * ((C-C0 * ones (C))/(Cext-C0))** 2;
D = (((1-a) * ones (C)./(ones (C)+ (4 ** N) * (ones (C)-h) ** N))+a * ones (C)) * D1;
D = D. * (T./(T0 * ones (T))) ;
D = D. * exp (Q_R * ((ones (T)./T0) - (ones (T)./T))) ;
endfunction,
//________________________________________________________________
//
//DISSEMINATION
//Resolution by the method the finite differences
//
//D vector of the coefficients of dissemination
//Ci vector of the water contents at the moment J [-]
//CL boundary condition in xmin and xmax of the type Dirichlet (C=C0)
//dt not of time [S]
//X vector of the X-coordinates [m]
//mode_ polar/Cartesian
function cf = linear_drying (D, Ci, CL, dt, X, mode_),
[n1, N2] = size (Ci);
dx_ = zeros (1, N2-2); dx_ (1:$) = (X (3:$) - X (1:$-2))* 0.5;
//Cf_ = (D * dt * (ones (dx_)./(dx_ ** 2)).* (Ci (3:$) - 2 * Ci (2:$-1) +Ci (1:$-2)))+Ci (2:$-1);
dx3 = ((…
(X (2:$-1) - X (1:$-2)).*…
(X (3:$) - X (1:$-2)) …
).*…
(X (3:$) - X (2:$-1)) …
);
d2C_dx2 = 2 * (Ci (3:$).* (X (2:$-1) - X (1:$-2))…
here (2:$-1).* (X (3:$) - X (1:$-2))…
+Ci (1:$-2).* (X (3:$) - X (2:$-1)));
Code_Aster
®
Version
7.4
Titrate:
HSNA102 Validation of the laws of drying
Date:
16/11/04
Author (S):
S. MICHEL-PONNELLE, Y. the POPE
Key
:
V7.20.102-A
Page:
17/20
Manual of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the axisymmetric structures
HT-66/04/005/A
d2C_dx2 = d2C_dx2./dx3;
yew (mode_ == “whodunnit”) then,
dC_dx = (Ci (3:$).* (X (2:$-1) - X (1:$-2)) ** 2…
here (1:$-2).* (X (3:$) - X (2:$-1)) ** 2);
//here (2:$-1).* ((X (2:$-1) - X (1:$-2)) ** 2 - (X (3:$) - X (2:$-1))** 2)…
dD_dx = (D (3:$).* (X (2:$-1) - X (1:$-2)) ** 2…
- D (1:$-2).* (X (3:$) - X (2:$-1)) ** 2);
//- D (2:$-1).* ((X (2:$-1) - X (1:$-2)) ** 2 - (X (3:$) - X (2:$-1))** 2)…
dC_dx = dC_dx./dx3;
dD_dx = dD_dx./dx3;
I = find (x==0); [k1 k2] = size (I);
yew (~ (k1==0)) then, X (I) = X (i+1)/10, end,
//printf (“1st command % S; 2nd command % S”, string (min (dC_dx)), string (min (d2C_dx2)));
d2C_dx2 = d2C_dx2 + dC_dx./X (2:$-1);
end,
Cf_ = Ci (2:$-1) +dt * (D (2:$-1).* d2C_dx2);
yew (mode_ == “whodunnit”) then,
Cf_ = Cf_ +dt * (dD_dx.* dC_dx);
end,
Cf = zeros (1, N2); Cf (2:$-1) = Cf_; Cf (1) = CL (1); Cf ($) = CL (2);
endfunction,
//
//________________________________________________________________
//
Code_Aster
®
Version
7.4
Titrate:
HSNA102 Validation of the laws of drying
Date:
16/11/04
Author (S):
S. MICHEL-PONNELLE, Y. the POPE
Key
:
V7.20.102-A
Page:
18/20
Manual of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the axisymmetric structures
HT-66/04/005/A
Appendix 2 Comparison Aster/Scilab
A2.1
SECH_MENSI
/
SECH_GRANGER
/
SECH_NAPPE
Water concentration in the test-tube after 1h
(zoom)
58,8
68,8
78,8
88,8
98,8
108,8
118,8
128,8
138,8
148,8
0,06
0,065
0,07
0,075
0,08
position X (m)
C
onc
E
N
T
R
has
T
I
one E
N
E
has
U
(L/m
3
)
Scilab
SECH_GRANGER
SECH_MENSI
SECH_NAPPE
Water concentration in the test-tube after 5ans
58,8
63,8
68,8
73,8
78,8
83,8
88,8
93,8
98,8
103,8
0
0,02
0,04
0,06
0,08
position X (m)
C
onc
E
N
T
R
has
T
I
one E
N
E
has
U (
L
/
m
3
)
Scilab
SECH_GRANGER
SECH_MENSI
SECH_NAPPE
Code_Aster
®
Version
7.4
Titrate:
HSNA102 Validation of the laws of drying
Date:
16/11/04
Author (S):
S. MICHEL-PONNELLE, Y. the POPE
Key
:
V7.20.102-A
Page:
19/20
Manual of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the axisymmetric structures
HT-66/04/005/A
A2.2
SECH_BAZANT
Water concentration in the test-tube after 1h
(zoom)
5,88E+01
6,88E+01
7,88E+01
8,88E+01
9,88E+01
1,09E+02
1,19E+02
1,29E+02
1,39E+02
0,06
0,065
0,07
0,075
0,08
position X (m)
C
O
N
cen
T
R
At
I
O
N
in
water
(
L
/
m
3)
SECH_BAZANT
SCILAB
Water concentration in the test-tube after 5 years
5,88E+01
5,93E+01
5,98E+01
6,03E+01
6,08E+01
6,13E+01
0
0,02
0,04
0,06
0,08
position X (m)
C
O
N
cen
T
R
At
I
O
N
in
water
(
L
/
m
3)
SECH_BAZANT
SCILAB
Code_Aster
®
Version
7.4
Titrate:
HSNA102 Validation of the laws of drying
Date:
16/11/04
Author (S):
S. MICHEL-PONNELLE, Y. the POPE
Key
:
V7.20.102-A
Page:
20/20
Manual of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the axisymmetric structures
HT-66/04/005/A
Intentionally white left page.