4. B modeling#
4.1. Characteristics of modeling#
Modeling B is identical to modeling A (see paragraph [§3.1]), but this time a simplified representation of the beam is used.
A group of elements corresponding to one of the tubes is designated, which defines the only equivalence class for all the tubes in the bundle. The geometry of the beam is defined by giving the coordinates of the centers of the tubes in the plane orthogonal to the beam. It is then assumed, in resolving the fluid-structure coupling, that all the tubes have the same modal deformation, which is that of the tube defining the equivalence class. In fact, the mode studied corresponds to an overall movement of the tubes in the bundle.
The changes in the frequency and the reduced damping of the first two modes of flexure of the beam are calculated for average flow velocities varying from \(0\) to \(\mathrm{10 }m/s\) in steps of \(\mathrm{1 }m/s\). An initial reduced amortization of 12.3% is taken into account.
Given the nature of the mode studied (beam set mode), modeling B must lead to results that are very similar to those of modeling A.
4.2. Characteristics of the mesh#
The characteristics of the mesh in this second modeling are the same as those of modeling A, i.e.:
459 knots used and 470 SEG2 stitches.
The mesh file is in ASTER format.
4.3. Calculation steps#
The functionalities that we want to validate are the same as those listed for modeling A (see paragraph [§3.3]), but this time using a simplified representation of the beam.
The definition of the parameters taking into account the fluid-elastic coupling of a simplified representation of the beam is carried out with the operator DEFI_FLUI_STRU, keyword factor FAISCEAU_AXIAL.
The calculation of the changes in frequencies and reduced modal damping as a function of the average flow speed, by implementing the model MEFISTEAU based on a simplified representation of the beam, is performed by the operator CALC_FLUI_STRU.
4.4. Tested values#
The tests focus on the reduced frequencies and damping of the first two modes of flexure of the beam, at the average flow speed of \(\mathrm{4 }m/s\). The experimental measurements concern only the characteristics of the first mode of vibrating flexure along the longest side of the chamber. This mode is the first one determined by calculation. Two types of tests are carried out:
a comparison test with the experimental values on the first mode,
a test on the first two modes in order to guarantee the non-regression of the code.
4.4.1. Frequencies of the first two modes of beam bending#
Comparison test with the experience on the first mode:
The tolerance for relative deviation from the experimental value is equal to 10%.
Mode number |
Experimental value |
Calculated value |
Relative deviation |
1 |
4.47 \(\mathrm{Hz}\) |
4.735 \(\mathrm{Hz}\) |
|
4.4.2. Reduced damping of the first two modes of beam bending#
Comparison test with the experience on the first mode:
The tolerance for relative deviation from the experimental value is 20%.
Mode number |
Experimental value |
Calculated value |
Relative deviation |
1 |
19% |
22.6474% |
|