4. B modeling

4.1. Characteristics of modeling

The characteristics of modeling B are identical to those of modeling A, except for the damping in fluid at rest and the coefficient of added mass to which, in accordance with the results of the second series of tests, the respective values of 1.1% and the added mass of 2.01188 were assigned.

4.2. Characteristics of the mesh

Identical to those of modeling A.

4.3. Calculation steps

Identical to those of modeling A.

4.4. Tested features

Identical to those of modeling A.

4.5. Tested values

The second series of tests differs from the first essentially in the value of the damping of the dynamic system coupled with fluid at rest; the latter is no longer 1.1% but 1.3%. [Figure 6.1-a] shows the calculation/test comparison for this new configuration. The vibratory instability of the tube results in a sudden and strong increase in the calculated displacement RMS. The rate at which this increase occurs is the speed of system instability. The calculation makes it possible to estimate this speed at \(1.85m/s\) while the experimental observation is closer to \(\mathrm{1,95 }m/s\). The calculation/measurement difference for this essential result is therefore of the order of 5% for this other configuration.

Figure 6.1-a: Displacement RMS ****as a function of the flow intertube speed, ****expressed at point E as a percentage of the outside diameter of the tube. **

4.6. notes

The modal deformations under flow are assumed to remain unchanged compared to those calculated as fluid at rest.

4.7. Non-regression tests

To ensure the non-regression of the code, the operators TEST_FONCTION and TEST_TABLE are used in the command file. These two operators make it possible to test respectively, on the one hand, the values of natural frequencies and reduced damping, and on the other hand, the displacement RMS. The tolerance is set at 1E—03%.