v8.21.200 FDLL200 - Embedded and free piping by fluid-structure beam

Summary:

The objective is to calculate the low-frequency behavior of a pipe filled with water. The pipe has a circular cross section; it is embedded at one end and free on the other side.

We use the elasto-acoustic beam elements available in Code_Aster that take into account the fluid structure interaction (PHENOMENE = “MECANIQUE”, MODELISATION = “FLUI_STRU”).

The boundary conditions are mechanical to simulate the embedment of the structure, and acoustic to simulate the fluid reservoir condition at this point (boundary conditions of zero pressure and zero fluid displacement potential).

The fluid under consideration is a heavy fluid in order to highlight the phenomenon of coupling between the fluid column and the constituent structure of the pipe. The properties of the fluid and of the material of the structure are chosen so that the speed of a wave propagating in the fluid is the same as the speed of a mechanical wave propagating in the pipe. Under these conditions, the first mode of the structure resonates at the same frequency as the fluid column.

Modeling A is based on a constant section and an exact analytical solution then exists which provides the first natural frequency. Its comparison with the results produced by Code_Aster (search for eigenvalues) makes it possible to validate the consideration of fluid structural coupling in the longitudinal direction, as transversal effects are non-existent in this model. The stiffness matrix and the mass matrix are thus partially tested.

The B and C models are used to validate the case of variable circular sections. In the first, the section is declared of variable type (VARI_SECT =” HOMOTHETIQUE “in AFFE_CARA_ELEM) but the parameters define a constant section. The solution is therefore the same as for modeling A. In the last modeling, the section is really variable and we only perform a non-regression test.

• 1. Reference problem
  • 1.1. Geometry
  • 1.2. Material properties
  • 1.3. Boundary conditions and loading
• 2. Benchmark solution
  • 2.1. Calculation method used for the reference solution
  • 2.2. Benchmark results
  • 2.3. Uncertainty of the solution
  • 2.4. Bibliographical references
• 3. Modeling A
  • 3.1. Characteristics of modeling
  • 3.2. Characteristics of the mesh
  • 3.3. Calculus
  • 3.4. Tested values
  • 3.5. note
• 4. B modeling
  • 4.1. Characteristics of modeling
  • 4.2. Tested values
  • 4.3. note
• 5. C modeling
  • 5.1. Characteristics of modeling
  • 5.2. Tested values
• 6. Summary of results