USE OF A TORSIONAL WAVE SENSOR TO MEASURE THE LEVEL OF A COMPRESSIBLE FLUID

In nuclear pressurized water reactors, information about fluid masses or fluid 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 fluid. Yet, in case 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. ssumptions have been made: the transverse dimensions of the waveguide are small compared to its length and the wavelengths in the fluid. 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 fluid 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 fluid-loaded waveguide motion. Finally, some simulations are made, highlighting the influence of the compressibility.