Code_Aster
®
Version
6.4
Titrate:
TTNL03 - Thermo hydration. Simulation of an adiabatic test
Date:
01/07/03
Author (S):
G. DEBRUYNE
Key
:
V4.22.003-A
Page:
1/8
Manual of Validation
V4.22 booklet: Nonlinear thermics of the linear structures
HT-66/03/008/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V4.22 booklet: Non-linear transitory thermics of the linear structures
Document: V4.22.003
TTNL03 - Thermo hydration.
Simulation of an adiabatic test
Summary:
The purpose of this test is to validate the thermo behavior hydrating
THER_HYDR
, by simulating a test
adiabat:
a freshly-mixed concrete sample is plunged in a calorimeter, the catch being carried out with release of heat,
it is a question of finding the field of temperature and hydration in the course of time.
The temperature and the degree of hydration are uniform in the sample. The temperature measured in
calorimeter will be thus the reference solution, the hydration being determined by analytical integration of the law
of evolution.
2 modelings are proposed: three-dimensional and axisymmetric.
Code_Aster
®
Version
6.4
Titrate:
TTNL03 - Thermo hydration. Simulation of an adiabatic test
Date:
01/07/03
Author (S):
G. DEBRUYNE
Key
:
V4.22.003-A
Page:
2/8
Manual of Validation
V4.22 booklet: Nonlinear thermics of the linear structures
HT-66/03/008/A
1
Problem of reference
1.1 Geometry
y
X
4
3
1
2
1 m
1 m
Concrete
q.n = 0
1.2
Material properties
The material has the following thermal characteristics:
Thermal conductivity: K
S
= 6 kJ/H/m/°K
voluminal variation of enthalpy:
H = 2.4 10
5
kJ/m
3
,
and characteristics relating to the behavior hydrating following:
Heat per degree of hydration: Q
0
= 1.490410
5
kJ/m
3
Constant of Arrhenius: Ar = 4000/°K.
Note:
The constant of Arrhenius is always expressed in Kelvin degree. The temperatures are
expressed in °C.
Affinity function of the hydration:
Degree of hydration H
Affinity A (H) (1/H)
0 6510
0.008 6360
0.016 2485
0.019 2460
0.038 9520
0.047 21800
0.08 37600
0.138 51600
0.232 51400
0.351 28200
0.44 16100
0.5 11700
0.63 5570
0.73 4240
0.81 1780
0.88 302
0.97 50
1.00 0
Code_Aster
®
Version
6.4
Titrate:
TTNL03 - Thermo hydration. Simulation of an adiabatic test
Date:
01/07/03
Author (S):
G. DEBRUYNE
Key
:
V4.22.003-A
Page:
3/8
Manual of Validation
V4.22 booklet: Nonlinear thermics of the linear structures
HT-66/03/008/A
1.3
Boundary conditions and loadings
One imposes a heat flux no one on all the faces of the solid. The loading is only initiated
by a heat source depending on the hydration
Q = Q
0
h.
1.4 Conditions
initial
The initial temperature is of 20.9°C
Code_Aster
®
Version
6.4
Titrate:
TTNL03 - Thermo hydration. Simulation of an adiabatic test
Date:
01/07/03
Author (S):
G. DEBRUYNE
Key
:
V4.22.003-A
Page:
4/8
Manual of Validation
V4.22 booklet: Nonlinear thermics of the linear structures
HT-66/03/008/A
2
Reference solution
2.1
Method of calculation used for the reference solution
The reference solution in temperature is given by the at every moment measured temperatures
during the adiabatic test.
The reference solution for the degree of hydration is calculated analytically according to
temperatures measured by integrating the law of evolution of the degree of hydration
hy
:
hy A H E
T
Ar
T
=
- +
()
(
.
273 6)
T being expressed in °C
2.2
Results of Reference
The results relate to the first 60 hours of the test.
T (out of H)
T (in °C)
hy (in %)
0 20.9 0
1 21.4 0.8
2 21.9 1.6
3 22.1 1.9
4 22.3 2.2
5 22.5 2.58
10 35.3 23.2
15 57.8 59.4
20 68.3 76
30 75.8 88
45 77.9 92
60 79.1 94
2.3
Uncertainty on the solution
Measure temperatures during the test. Integration of the law of evolution of
hy
on pitches of time
varying between 1h and 5h.
2.4 References
bibiographic
[1]
CESAR-LCPC 3.2. Manual of examples. Modeling of the concrete at the youth. January 1996
[2]
Gilles DEBRUYNE: Analyze models of behavior of the concrete in CESAR:
transferability of model TEXO-MEXO in Code_Aster. CR MN 97-193. 24/12/97
Code_Aster
®
Version
6.4
Titrate:
TTNL03 - Thermo hydration. Simulation of an adiabatic test
Date:
01/07/03
Author (S):
G. DEBRUYNE
Key
:
V4.22.003-A
Page:
5/8
Manual of Validation
V4.22 booklet: Nonlinear thermics of the linear structures
HT-66/03/008/A
3 Modeling
With
3.1
Characteristics of modeling
Modeling
AXIS
3.2
Characteristics of the mesh
A number of nodes: 4
A number of meshs and types: 1 QUAD4
3.3 Functionalities
tested
Controls
DEFI_FONCTION HYDR
DEFI_MATERIAU THER_HYDR AFFINITY
CHALHYDR
QSR_K
THER_NON_LINE COMP_THER_NL
RELATION
THER_HYDR
4
Results of modeling A
4.1 Values
tested
Identification Moments Reference
Aster %
difference
T node 1
5
22.5 22.47
0.139
T node 1
15
57.8 56.82
1.696
T node 1
60
79.1 76.67
3.066
hy Pt of Gauss 1
5
2.58D-2 2.52D-2
2.101
hy Pt of Gauss 1
15
5.94D-1 5.97D-1
0.53
hy Pt of Gauss 1
60
9.4D-1 9.32D-1
0.871
Code_Aster
®
Version
6.4
Titrate:
TTNL03 - Thermo hydration. Simulation of an adiabatic test
Date:
01/07/03
Author (S):
G. DEBRUYNE
Key
:
V4.22.003-A
Page:
6/8
Manual of Validation
V4.22 booklet: Nonlinear thermics of the linear structures
HT-66/03/008/A
5 Modeling
B
5.1
Characteristics of modeling
Z
X
y
N07
N05
N06
N08
N03
N01
N02
N04
5.2
Characteristics of the mesh
A number of nodes: 8
A number of meshs and types: 1 HEXA8 + 4 QUAD4 (faces)
5.3 Functionalities
tested
Controls
DEFI_FONCTION HYDR
DEFI_MATERIAU THER_HYDR AFFINITY
CHALHYDR
QSR_K
THER_NON_LINE COMP_THER_NL
RELATION THER_HYDR
6
Results of modeling B
6.1 Values
tested
Identification Moments Reference
Aster %
difference
T node 1
5
22.5 22.47
0.139
T node 1
15
57.8 56.82
1.696
T node 1
60
79.1 76.67
3.066
hy Pt of Gauss 1
5
2.58D-2 2.52D-2
2.101
hy Pt of Gauss 1
15
5.94D-1 5.97D-1
0.53
hy Pt of Gauss 1
60
9.4D-1 9.32D-1
0.871
Code_Aster
®
Version
6.4
Titrate:
TTNL03 - Thermo hydration. Simulation of an adiabatic test
Date:
01/07/03
Author (S):
G. DEBRUYNE
Key
:
V4.22.003-A
Page:
7/8
Manual of Validation
V4.22 booklet: Nonlinear thermics of the linear structures
HT-66/03/008/A
7
Summary of the results
The error obtained compared to the reference solution is about 1% with regard to
temperature and the hydration. Let us announce that the problem was dealt with with pitches of time of the command
from 15 minutes what is relatively small for the phenomenon of hydration which lasts several
tens of hours.
Code_Aster
®
Version
6.4
Titrate:
TTNL03 - Thermo hydration. Simulation of an adiabatic test
Date:
01/07/03
Author (S):
G. DEBRUYNE
Key
:
V4.22.003-A
Page:
8/8
Manual of Validation
V4.22 booklet: Nonlinear thermics of the linear structures
HT-66/03/008/A
Intentionally white left page.