Code_Aster ®
Version
7.4
Titrate:
HSNA102 ­ Validation of the laws of drying


Date:
16/11/04
Author (S):
S. MICHEL-PONNELLE, Y. the Key POPE
:
V7.20.102-A Page:
1/20
Organization (S): EDF-R & D/AMA, EDF-R & D/MMC
Handbook 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 diffusion 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.
Handbook of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the axisymmetric structures
HT-66/04/005/A

Code_Aster ®
Version
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Titrate:
HSNA102 ­ Validation of the laws of drying


Date:
16/11/04
Author (S):
S. MICHEL-PONNELLE, Y. the Key POPE
:
V7.20.102-A Page:
2/20

1
Problem of reference

1.1 Geometry

One models a cylindrical section of test-tube of diameter 160mm.
1 cm
FI
FE
8 cm


1.2
Material properties

Each modeling makes it possible to validate a coefficient of diffusion D, namely:

· modeling a: law of Mensi D (C) = Aexp (BC)
T
Q
S
1
1
· modeling b: law of Granger D (C, T) = Aexp (BC)
exp-

-


0
T

R T
0
T
· modeling C: definition of D in the form of tablecloth





1

· modeling D: law of Bazant D (H) = D1 +


1 - H () N
C


1+


1 - 75
.
0

Handbook of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the axisymmetric structures
HT-66/04/005/A

Code_Aster ®
Version
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Titrate:
HSNA102 ­ Validation of the laws of drying


Date:
16/11/04
Author (S):
S. MICHEL-PONNELLE, Y. the Key POPE
:
V7.20.102-A Page:
3/20


The coefficients used are those recommended by Granger in its thesis [bib1]:

SECH_MENSI:
With = 0.74 10-13 m2/S
B = 0.05

SECH_GRANGER
With = 0.74 10-13 m2/S
B = 0.05
T0 = 293 °K
Qs/R = 4700 K-1

SECH_NAPPE
One re-enters in the form of tablecloth the law of Mensi
Coefficient of diffusion
6th-11
4th-11
S)
2/
m
(
D 2nd-11
0
0
20
40
60
80
100
120
140
C (L/m3)

SECH_BAZANT
D1 = 3.0 10-10 m2/S
= 0.04
N = 6
2
C C

- 0
H = 1 - 5
.
0


with C =128.8 L/m3 and C = 58.8 L/m3
C
C

0
eq
0 - eq


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 Ceq = 58.8 L/m3

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
C0 =
8
.
128 L/Mr.
Handbook of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the axisymmetric structures
HT-66/04/005/A

Code_Aster ®
Version
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Titrate:
HSNA102 ­ Validation of the laws of drying


Date:
16/11/04
Author (S):
S. MICHEL-PONNELLE, Y. the Key POPE
:
V7.20.102-A Page:
4/20

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
138,8
128,8
3)
L
/
m 118,8
(
1 hour
108,8
water
3 days
in
28 days
N
98,8
I
O
1.25 year
88,8
T
R
At
3 years
cen
78,8
5 years
N
Co
68,8
58,8
0
0,02
0,04
0,06
0,08
position X (m)

Appear 2.2-a: Solution Scilab - law of Mensi
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Code_Aster ®
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Titrate:
HSNA102 ­ Validation of the laws of drying


Date:
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Author (S):
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:
V7.20.102-A Page:
5/20

Evolution of the water concentration in
the test-tube in the course of time
Law of Mensi
138,8
128,8
3)
L
/
m 118,8
(
1 hour
108,8
water
3 days
in
28 days
N
98,8
I
O
1.25 year
88,8
T
R
At
3 years
cen
78,8
5 years
N
Co
68,8
58,8
0
0,02
0,04
0,06
0,08
position X (m)

Appear 1.2-b: Solution Scilab - law of Bazant

The TEST_RESU are carried out 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 enclosures of nuclear thermal power stations”
published by Laboratoire Central of Ponts and Chaussées (1996).
[2]
S. MICHEL-PONNNELLE, A. RAZAKANAIVO: “I7-01-08 Project: Quality of Etudes in
Mechanics of Solides ­ 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 “, handbook of Référence Code_Aster, [R7.01.12] (2001).

Handbook of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the axisymmetric structures
HT-66/04/005/A

Code_Aster ®
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Titrate:
HSNA102 ­ Validation of the laws of drying


Date:
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Author (S):
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:
V7.20.102-A Page:
6/20

3 Modeling
With

3.1
Characteristics of modeling

One uses the law of diffusion of Mensi.

3.2
Characteristics of the grid

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

Moment Initial (S)
Moment Final (S)
Numbers of steps 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

Commands Options


“THERMAL” AFFE_MODELE
“AXIS” “ALL”

DEFI_MATERIAU “SECH_MENSI”


THER_NON_LINE COMP_THER_NL “SECH_MENSI”


EVOL_THER_SECH




Handbook of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the axisymmetric structures
HT-66/04/005/A

Code_Aster ®
Version
7.4
Titrate:
HSNA102 ­ Validation of the laws of drying


Date:
16/11/04
Author (S):
S. MICHEL-PONNELLE, Y. the Key POPE
:
V7.20.102-A Page:
7/20

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.
Handbook of Validation
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HT-66/04/005/A

Code_Aster ®
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Titrate:
HSNA102 ­ Validation of the laws of drying


Date:
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:
V7.20.102-A Page:
8/20

5 Modeling
B

5.1
Characteristics of modeling

One uses the law of diffusion of Granger

5.2
Characteristics of the grid

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

Moment Initial (S)
Moment Final (S)
Numbers of steps 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

Commands Options


“THERMAL” AFFE_MODELE
“AXIS” “ALL”

DEFI_MATERIAU “SECH_GRANGER”



THER_NON_LINE COMP_THER_NL “SECH_GRANGER”


EVOL_THER_SECH




Handbook of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the axisymmetric structures
HT-66/04/005/A

Code_Aster ®
Version
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Titrate:
HSNA102 ­ Validation of the laws of drying


Date:
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Author (S):
S. MICHEL-PONNELLE, Y. the Key POPE
:
V7.20.102-A Page:
9/20

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.
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Code_Aster ®
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HSNA102 ­ Validation of the laws of drying


Date:
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:
V7.20.102-A Page:
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7 Modeling
C

7.1
Characteristics of modeling

One uses the law of diffusion SECH_NAPPE, for which one re-enters simply the law of diffusion of
Mensi.

7.2
Characteristics of the grid

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

Moment Initial (S)
Moment Final (S)
Numbers of steps 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

Commands 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




Handbook of Validation
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HT-66/04/005/A

Code_Aster ®
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Titrate:
HSNA102 ­ Validation of the laws of drying


Date:
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:
V7.20.102-A Page:
11/20

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%.
Handbook of Validation
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Code_Aster ®
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Titrate:
HSNA102 ­ Validation of the laws of drying


Date:
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:
V7.20.102-A Page:
12/20

9 Modeling
D

9.1
Characteristics of modeling

One uses the law of diffusion of Bazant.

9.2
Characteristics of the grid

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

Moment Initial (S)
Moment Final (S)
Numbers of steps 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

Commands Options


“THERMAL” AFFE_MODELE
“AXIS” “ALL”

DEFI_MATERIAU “SECH_BAZANT”



THER_NON_LINE COMP_THER_NL “SECH_BAZANT”


EVOL_THER_SECH




Handbook of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the axisymmetric structures
HT-66/04/005/A

Code_Aster ®
Version
7.4
Titrate:
HSNA102 ­ Validation of the laws of drying


Date:
16/11/04
Author (S):
S. MICHEL-PONNELLE, Y. the Key POPE
:
V7.20.102-A Page:
13/20

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%.
Handbook of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the axisymmetric structures
HT-66/04/005/A

Code_Aster ®
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Titrate:
HSNA102 ­ Validation of the laws of drying


Date:
16/11/04
Author (S):
S. MICHEL-PONNELLE, Y. the Key POPE
:
V7.20.102-A Page:
14/20

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.

Handbook of Validation
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Titrate:
HSNA102 ­ Validation of the laws of drying


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:
V7.20.102-A Page:
15/20

Appendix 1 Fichier of Scilab command

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);
Handbook of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the axisymmetric structures
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Code_Aster ®
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Titrate:
HSNA102 ­ Validation of the laws of drying


Date:
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Author (S):
S. MICHEL-PONNELLE, Y. the Key POPE
:
V7.20.102-A Page:
16/20

Librairie.sci:
________________________________________________________________
//
//NONLINEAR COEFFICIENT OF DIFFUSION FOR THE DRYING OF THE CONCRETE
//LOI 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 DIFFUSION 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,
//________________________________________________________________
//
//DIFFUSION
//Resolution by the method the finite differences
//
//D vector of the coefficients of diffusion
//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)));
Handbook of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the axisymmetric structures
HT-66/04/005/A

Code_Aster ®
Version
7.4
Titrate:
HSNA102 ­ Validation of the laws of drying


Date:
16/11/04
Author (S):
S. MICHEL-PONNELLE, Y. the Key POPE
:
V7.20.102-A Page:
17/20

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,
//
//________________________________________________________________
//
Handbook of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the axisymmetric structures
HT-66/04/005/A

Code_Aster ®
Version
7.4
Titrate:
HSNA102 ­ Validation of the laws of drying


Date:
16/11/04
Author (S):
S. MICHEL-PONNELLE, Y. the Key POPE
:
V7.20.102-A Page:
18/20

Appendix 2 Comparison Aster/Scilab

A2.1 SECH_MENSI/SECH_GRANGER/SECH_NAPPE
Water concentration in the test-tube after 1h
(zoom)
148,8
U
138,8
has
E
128,8
N
118,8
)
3108,8
T
I
one E
Scilab
(L/m 98,8
T
R
has
SECH_GRANGER
N
E
88,8
SECH_MENSI
78,8
onc
SECH_NAPPE
C
68,8
58,8
0,06
0,065
0,07
0,075
0,08
position X (m)


Water concentration in the test-tube after 5ans
)
3 103,8
L
/
m
98,8
U (
93,8
has
E
88,8
N
83,8
Scilab
78,8
T
I
one E
SECH_GRANGER
73,8
T
R
has
SECH_MENSI
N
68,8
E
SECH_NAPPE
63,8
onc
C
58,8
0
0,02
0,04
0,06
0,08
position X (m)


Handbook of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the axisymmetric structures
HT-66/04/005/A

Code_Aster ®
Version
7.4
Titrate:
HSNA102 ­ Validation of the laws of drying


Date:
16/11/04
Author (S):
S. MICHEL-PONNELLE, Y. the Key POPE
:
V7.20.102-A Page:
19/20

A2.2 SECH_BAZANT
Water concentration in the test-tube after 1h
(zoom)
1,39E+02
3) 1,29E+02
L
/
m
(1,19E+02
water 1,09E+02
in
N 9,88E+01
I
O
SECH_BAZANT
8,88E+01
T
R
At
SCILAB
7,88E+01
cen
N 6,88E+01
O
C 5,88E+01
0,06
0,065
0,07
0,075
0,08
position X (m)


Water concentration in the test-tube after 5 years
6,13E+01
3)
L
/
m
(6,08E+01
water 6,03E+01
in
N
I
O 5,98E+01
SECH_BAZANT
T
R
At
SCILAB
5,93E+01
cen
N
O
C 5,88E+01
0
0,02
0,04
0,06
0,08
position X (m)

Handbook of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the axisymmetric structures
HT-66/04/005/A

Code_Aster ®
Version
7.4
Titrate:
HSNA102 ­ Validation of the laws of drying


Date:
16/11/04
Author (S):
S. MICHEL-PONNELLE, Y. the Key POPE
:
V7.20.102-A Page:
20/20

Intentionally white left page.
Handbook of Validation
V7.20 booklet: Thermomechanical nonlinear statics of the axisymmetric structures
HT-66/04/005/A

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