In nuclear pressurized water reactors, information about #uid masses or #uid levels is required, especially in the reactor vessel, where the core of the reactor must be immersed, to avoid damage or accidents. To reinforce the existing instrumentation, the possibilities of an immersed torsional wave sensor (that is, an elastic solid waveguide) have already been looked into and modelled, considering an incompressible surrounding #uid. Yet, in case of depressurization, the #uid can turn into a two-phase #uid. This is the reason why a way to extend the existing model has been investigated. As a "rst step, in this paper, the compressibility of the surrounding #uid has been taken into account.
Some assumptions have been made: the transverse dimensions of the waveguide are small compared to its length and the wavelengths in the #uid. The focus is on a cylindrical waveguide, with an elliptic cross-section. Use is made of elliptic co-ordinates and Mathieu functions. The analysis starts with the elasticity equations for the waveguide. Then, from the exact expression of the pressure exerted by the #uid on the waveguide boundary, a long-wavelength approximation is obtained. In the end, the principle of energy conservation is applied, leading to an approximate equation governing the #uid-loaded waveguide motion. Finally, some simulations are made, highlighting the in#uence of the compressibility.