2. Benchmark solution#
2.1. Calculation method used for the reference solution#
The reference solution is obtained by a calculation carried out using the code MOCCA (Annular Confinement Coupling Model) [bib1], [bib2]. The latter has been validated on several experimental configurations including models TAXI from CEA [bib2] and GRAPPE2 from EDF [bib3].
The modal characteristics of the non-flow structure being entered, the code MOCCA makes it possible to calculate the changes in the frequencies and the reduced damping of each mode of the structure as a function of the speed of the flow . This resolution is performed numerically by a method such as finite differences.
In the present case, the changes in the modal parameters associated with the first mode with a shell order equal to 1 constitute the reference solution.
2.2. Benchmark results#
We consider the fifth mode of the structure, first mode of order 1 in shell. The natural frequency of this non-flow mode is \(\mathrm{90,4}\mathit{Hz}\).
Average flow speed ( \(m\mathrm{/}s\) ) |
Natural frequency ( \(\mathit{Hz}\) ) |
Modal reduced damping (%) |
31.8794 |
0.0353905 |
|
31,8806 |
1,27602 |
|
31.8842 |
2.50164 |
|
31.8900 |
3,74046 |
|
31,8982 |
4,97402 |
|
31.9087 |
6.20616 |
|
31.9217 |
7.43705 |
|
31.9372 |
8.66394 |
|
31.9546 |
9.89269 |
2.3. Uncertainty about the solution#
The fluid-structure coupling model MOCCA_COQUE [bib4] resorbed in the operator CALC_FLUI_STRU was developed in the perspective of shell structures. It allows shell modes of any order to be taken into account but is limited to uniform annular sets.
For its part, code MOCCA was developed for beam-type movements, under the effect of annular flows of varying thickness. Comparisons will therefore be established for modes with a shell order equal to 1, in the presence of uniform annular flows.
The MOCCA_COQUE model is purely analytical, while the MOCCA code is based on a fluid numerical problem resolution method. Discrepancies between the reference solution and the results of the*Code_Aster* are therefore to be expected.
2.4. Bibliographical references#
PEROTIN, S. GRANGER, « A numerical model for fluid-structure coupling of a confined cylinder submitted to an axial annular flow », proceedings fifth international symposium on flow‑induced vibration and noise, Anaheim, CA, 1992, Anaheim, CA, 1992, 1992, Vol. 5, pp. 1-16.
PEROTIN, S. GRANGER, « A linearized unsteady model for computing the dynamics of cylindrical structures subjected to non-uniform annular flows at high Reynolds numbers », proceedings sixth international conference on flow-induced vibration, London, London, April 1995, London, April 1995 « Journal of Fluids and Structures » (1997) 11,183-205.
PEROTIN, S. GRANGER, « Numerical simulation of the hydroelastic behavior of the model GRAPPE2, using the code MOCCA « , HT-32/93/017/A.
PEROTIN, « Model MOCCA_COQUE concept note « , HT-32/95/021/A.