Code_Aster
®
Version
4.0
Titrate:
SDND110 Lācher of a system masses specific
Date:
12/01/98
Author (S):
G. JACQUART
Key:
V5.01.110-A
Page:
1/6
Manual of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HP-51/96/032 - Ind A
Organization (S):
EDF/EP/AMV
Manual of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
V5.01.110 document
SDND110 - To release of a system masses specific
with fluid force of blade
Summary:
This test implements a specific mass having a speed initial and subjected to a force of blade
fluid which slows down it. The fluid non-linearity of blade as well as the algorithm of point fixes which is associated are for them
thus tested. The reference solution is obtained in an analytical way for the uniform profile and by integration
numerical direct out of
Code_Aster
for the parabolic profile, with a pitch of very small time to ensure itself
convergence of the solution.
Code_Aster
®
Version
4.0
Titrate:
SDND110 Lācher of a system masses specific
Date:
12/01/98
Author (S):
G. JACQUART
Key:
V5.01.110-A
Page:
2/6
Manual of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HP-51/96/032 - Ind A
1
Problem of reference
1.1 Geometry
Z
X
X
X
·
F
O
2L
M
1.2
Material properties
specific mass:
m = 1000 kg
width:
2L = 100 mm
density of the fluid:
F = 1000 kg/m
3
viscosity:
= 1.E6
·
with a parabolic profile of flow in the fluid blade:
= -
=
= -
=
-
0 0833
0 19992
0 9996 10
0
6
.
,
.
,
.
.
,
·
with a uniform profile of flow in the fluid blade:
= -
=
=
=
0 0833
0 1666
0
0
.
,
.
,
,
1.3
Boundary conditions and loadings
The mass is plunged in an incompressible fluid, and an indeformable obstacle is present in X = 0
and displacements only for X > 0 authorize.
1.4 Conditions
initial
Initial distance from the mass to the obstacle:
6 mm
Initial speed:
0.1 m/s
X
X
0
0
=
= -
Code_Aster
®
Version
4.0
Titrate:
SDND110 Lācher of a system masses specific
Date:
12/01/98
Author (S):
G. JACQUART
Key:
V5.01.110-A
Page:
3/6
Manual of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HP-51/96/032 - Ind A
2
Reference solution
2.1
Method of calculation used for the reference solution
Analytical resolution for the uniform mode
For the uniform mode, the differential equation governing the movement of stop of the mass is written
the following way:
MX
X
X
X
X
= +
2
By integrating once the differential equation, one obtains an expression the speed of the projectile in
function of its position:
X
X
X
X
X
X
M
= -
+
+
=
0
0
0
2
2
where
While integrating once again compared to time this differential equation it comes:
T
X
X
X
X
X
Log XX
X
X
=
+
- +
+
-
1
2
1
1
0
0
0
2
0
0
2
0
.
Numerical resolution for the streamline flow
The dynamic equation to which this system is subjected is as follows:
MX
X
X
X
X
X
X
= + +
2
3
This equation cannot be solved in an analytical way, one uses a resolution by a diagram
of integration temporal of the dynamic problem. One can rewrite the system in the form:
M
X
X
X
X
X
X
T
T
T
T
T
T
-
= +
2
3
One uses the diagram of Euler modified to integrate this equation in time.
X X
0
0
,
given to T
0
,
To repeat:
X
X
X
X
X
M
X
T
T
dt
X
X
dt X
X
X
dt X
I
I
I
I
I
I
I
I
I
I
I
I
I
I
=
+
-
= +
=
+
=
+
+
+
+
+
2
3
1
1
1
1
as long as
T
T
I
end
+
<
1
.
2.2
Uncertainty on the solution
Analytical solution for the uniform profile, approximate for the other.
2.3 References
bibliographical
[1]
G.JACQUART “Modeling of the forces of fluid blade” - HP-61/94/159/A
Code_Aster
®
Version
4.0
Titrate:
SDND110 Lācher of a system masses specific
Date:
12/01/98
Author (S):
G. JACQUART
Key:
V5.01.110-A
Page:
4/6
Manual of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HP-51/96/032 - Ind A
3 Modeling
With
3.1
Characteristics of modeling
For modeling, one uses two nodes NO1 and separate NO2 of a distance L = 1m, to which are
affected two discrete elements of type POI1.
Node NO1 represents the mass, node NO2 represents the rigid plan. One is thus applied
condition of embedding to node NO2.
An obstacle of the type
BI_PLAN_Z
(two parallel plans separated by a play) is used to simulate
connection through the fluid.
One chooses to take OZ for generator of this plan is
NORM_OBST
: (0., 0., 1.).
Normal stiffness
RIGI_NOR
is assigned to an arbitrary value, because the contact takes place through
fluid.
It remains to define the parameters
DIST_1
and
DIST_2
who give the half-spacing between the plans in
contact. One takes
DIST_1
=
DIST_2
=
(
L-play
)
/2 = 0.497 Misters.
NB:
These distances are fictitious and do not correspond to physical dimensions of the objects.
3.2
Characteristics of the mesh
A number of nodes: 2
A number of meshs and types: 2
3.3 Functionalities
tested
Controls
Keys
AFFE_CHAM_NO
SIZE
DEPL_R
[U4.26.01]
PROJ_VECT_BASE
VECT_ASSE
[U4.55.02]
PROJ_MATR_BASE
MATR_ASSE
[U4.55.01]
DEFI_OBSTACLE
TYPE
BI_PLAN_Y
[U4.21.07]
DYNA_TRAN_MODAL
VITE_INIT_GENE
[U4.54.03]
DYNA_TRAN_MODAL
SHOCK
NOEU_2
[U4.54.03]
DYNA_TRAN_MODAL
SHOCK
LAME_FLUIDE
[U4.54.03]
DYNA_TRAN_MODAL
SHOCK
ALPHA
[U4.54.03]
DYNA_TRAN_MODAL
SHOCK
BETA
[U4.54.03]
DYNA_TRAN_MODAL
SHOCK
CHI
[U4.54.03]
DYNA_TRAN_MODAL
SHOCK
DELTA
[U4.54.03]
Code_Aster
®
Version
4.0
Titrate:
SDND110 Lācher of a system masses specific
Date:
12/01/98
Author (S):
G. JACQUART
Key:
V5.01.110-A
Page:
5/6
Manual of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HP-51/96/032 - Ind A
4
Results of modeling A
4.1 Values
tested
Identification
Reference
(m)
Aster
(m)
% Difference
For the parabolic profile:
Ux (t=0.02)
1.98583e3
1.98582e3
0.005
Ux (t=0.04)
3.91819e3
3.91819e3
0.000
Ux (t=0.06)
5.61048e3
5.61068e3
0.004
Ux (t=0.2)
5.90398e3
5.90347e3
0.004
For the uniform profile:
Ux (t=0.02)
1.98828e3
1.98878e3
0.000
Ux (t=0.04)
3.93216e3
3.93216e3
0.000
Ux (t=0.06)
5.66658e3
5.6669e3
0.006
Ux (t=0.2)
5.99946e3
5.99914e3
0.005
4.2 Remarks
One observes in this case a very good precision in the reproduction by the calculation of displacement
structure (less than 0.006% of difference with the analytical solution), and a good prediction of
the position of stop of the system.
4.3 Parameters
of execution
Version: 3.05
Machine: CRAY C90
System:
UNICOS 8.0
Overall dimension memory:
8 megawords
Time CPU To use:
100 seconds
Code_Aster
®
Version
4.0
Titrate:
SDND110 Lācher of a system masses specific
Date:
12/01/98
Author (S):
G. JACQUART
Key:
V5.01.110-A
Page:
6/6
Manual of Validation
V5.01 booklet: Nonlinear dynamics of the discrete systems
HP-51/96/032 - Ind A
5
Summary of the results
Good agreement between the results obtained and the values of reference.