3. Modeling A#
3.1. Characteristics of modeling#
The model consists of Timoshenko’s straight beam elements: POU_D_T.
Divided into 199 elements uniformly distributed throughout the tube:
Section \([\mathrm{AB}]\): |
99 elements |
Section \([\mathrm{BC}]\): |
1 element |
Section \([\mathrm{CD}]\): |
99 elements |
Nodes \(A\) and \(D\) are blocked in the following directions:
\(X\), \(Y\) and \(Z\) in translation |
\(Y\) in rotation |
3.2. Characteristics of the mesh#
The total number of nodes used for this mesh is 200.
The meshes (type SEG2) are 199 in number.
The mesh file is in ASTER format.
3.3. Calculation steps#
The fluid flow velocity profile and the parameters taking into account fluid-structure coupling are defined by operators DEFI_FONC_FLUI and DEFI_FLUI_STRU.
We then calculate the modal parameters of our structure taking into account fluid-elastic forces with CALC_FLUI_SRU.
The definition of the multiple excitation zones is carried out by a call to the operator DEFI_SPEC_TURB, which makes it possible to establish the link between interspectral matrix and shape functions. The excitations are then projected onto the modal basis using the operator PROJ_SPEC_BASE and the modal response interspectra are calculated by the operator DYNA_SPEC_MODAL.
Finally, the autospectra of constraints at the nodes are deduced by a call to REST_SPEC_PHYS.
We can only calculate the spectral response for one flow speed at a time, so these last three steps (PROJ_SPEC_BASE, DYNA_SPEC_MODAL, REST_SPEC_PHYS) are carried out in a loop, in the command file, where we go through the list of flow velocities.
3.4. Tested values#
Identification |
Reference 1 area |
Calculation 2 excitement areas |
% difference |
|
Frequency Mode 2 Fluid—elastic coupling (speed \(\mathrm{1,5}m/s\)) Uniform speed profile (\(1m/s\)) Viscache coefficients 1 |
32.28018 Hz |
32.28018 Hz |
0.0 |
|
Reduced dampening Mode 2 Fluid—elastic coupling (speed \(\mathrm{1,5}m/s\)) Uniform speed profile (\(1m/s\)) Viscache coefficients 1 |
8.960594E—01% |
8.960594E—01% |
0.0 |
|
Frequency Mode 2 Fluid—elastic coupling (speed \(\mathrm{1,5}m/s\)) Stair speed profile (\(\mathrm{0,5}\) and \(1m/s\)) Viscache coefficients 1 |
31.39222 Hz |
31.39222 Hz |
0.0 |
|
Reduced dampening Mode 2 Fluid—elastic coupling (speed \(\mathrm{1,5}m/s\)) Stair speed profile (\(\mathrm{0,5}\) and \(1m/s\)) Viscache coefficients 1 |
9,170868E—01% |
9,170842E—01% |
0.0 |
|
Frequency Mode 2 Fluid—elastic coupling (speed \(\mathrm{1,5}m/s\)) Stair speed profile (\(\mathrm{0,5}\) and \(1m/s\)) Uniform Coefficient |
32.19244 Hz |
32.19244 Hz |
0.0 |
|
Reduced dampening Mode 2 Fluid—elastic coupling (speed \(\mathrm{1,5}m/s\)) Stair speed profile (\(\mathrm{0,5}\) and \(1m/s\)) Uniform Coefficient |
5.947656E—0.1% |
5.947633E—0.1% |
0.0 |
|
Frequency Mode 2 Fluid—elastic coupling (speed \(\mathrm{1,5}m/s\)) Uniform speed profile (\(\mathrm{0,5}m/s\)) Uniform Coefficient |
32.28018 Hz |
32.28018 Hz |
0.0 |
|
Reduced dampening Mode 2 Fluid—elastic coupling (speed \(\mathrm{1,5}m/s\)) Uniform speed profile (\(\mathrm{0,5}m/s\)) Uniform Coefficient |
6.071243E—01% |
6.071211E—01% |
0.0 |
|
Value of the RMS of movement for flow speed \(\mathrm{0,7}m/s\) Uniform speed profile (\(\mathrm{0,5}m/s\)) Uniform Coefficient |
1.20960E—06 m |
1.20960E—06 m |
1.20953E—06 m |
—0.005 |
Value of the RMS of movement for flow speed \(\mathrm{1,1}m/s\) Uniform speed profile (\(\mathrm{0,5}m/s\)) Uniform Coefficient |
8.46330E—06 m |
8.46290E—06 m |
—0.005 |
|
Value of the RMS of movement for flow speed \(\mathrm{1,5}m/s\) Uniform speed profile (\(\mathrm{0,5}m/s\)) Uniform Coefficient |
3.91328E—05 m |
3.91308E—05 m |
—0.005 |
|
Value of the RMS of movement for flow speed \(\mathrm{0,7}m/s\) Uniform speed profile (\(\mathrm{1,0}m/s\)) Viscache coefficients 1 |
2.83236E—06 m |
2.83221E—06 m |
—0.005 |
|
Value of the RMS of movement for flow speed \(\mathrm{1,1}m/s\) Uniform speed profile (\(\mathrm{1,0}m/s\)) Viscache coefficients 1 |
1.36880E—05 m |
1.36783E—05 m |
—0.005 |
|
Value of the RMS of movement for flow speed \(\mathrm{1,5}m/s\) Uniform speed profile (\(\mathrm{1,0}m/s\)) Viscache coefficients 1 |
3.24409E—05 m |
3.24393E—05 m |
—0.005 |