Analytical and Experimental Investigations for Modelling the Fluid-Structure-Interaction in Annular Gaps

Modelling the mechanical vibrations of pressurized water reactor internals the fluid-structure-interaction is to be taken into account. Especially at VVER-440 reactors there is a strong influence of the fluid due to the specific geometry. The intention of the presentation is to provide a solution of the continuity and the Navier-Stokes equations for the special case of a narrow annular gap geometry considering the fluid friction.
To obtain an analytical solution for these coupled 3D partial differential equations further assumptions and simplifications must be made:

• the width of the annular gap is small compared with the diameter,
• displacements of the mechanical structure are small compared with the gap width
• the fluid flow velocity components are independent on the radius.

Keeping these assumptions in mind one can reduce the dimension of the continuity equation from 3D to 2D by averaging over the gap width.
Two elementary types of motion of the cylinder are considered: parallel displacement and pendular motion. By superimposing these elementary types even more general motions can be described.
In practice the application could be meaningful for core barrel motion at LWRs in general and for flow induced vibrations of control elements at VVER-440 reactors.
The analytical results are compared with experimental ones from a cylindrical pendulum setup. The criteria of comparison are the eigenfrequency and the damping of the pendulum in the static and flowing fluid. There is a good agreement between analytical and experimental results. Especially the strong influence of the chosen boundary condition upon the pressure equations can be shown.