Use of a torsional wave sensor to measure the level of a compressible fluid

In nuclear pressurized water reactors, information about fluid masses or fl 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 t he existing instrumentation, the possibilities of an immersed torsional wav e sensor (that is, an elastic solid waveguide) have already been looked int o and modelled, considering an incompressible surrounding fluid. Yet, in ca se of depressurization, the fluid can turn into a two-phase fluid. This is the reason why a way to extend the existing model has been investigated. As a first step, in this paper, the compressibility of the surrounding fluid 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 fluid. The foc us is on a cylindrical waveguide, with an elliptic cross-section. Use is ma de of elliptic co-ordinates and Mathieu functions. The analysis starts with the elasticity equations for the waveguide. Then, from the exact expressio n of the pressure exerted by the fluid on the waveguide boundary, a long-wa velength approximation is obtained. In the end, the principle of energy con servation is applied, leading to an approximate equation governing the flui d-loaded waveguide motion. Finally, some simulations are made, highlighting the influence of the compressibility. (C) 2000 Academic Press.