Contactless liquid detection in a partly filled tube by resonance

Contactless fluid level detection in process equipment is an important challenge for the process automation industry, especially under high-pressure conditions. In this study, a method is presented, which permits the contactless measurement of liquid levels in thin opaque capillaries at high pressures. The method is based on the mass dependence of the flexural resonance frequencies of a finite section of a tube. These resonance frequencies are determined from the complex electrical impedance of a slitted toroid coil exciting a magnet attached to the tube. The system has been theoretically described using a set of two Bernoulli-Euler beams, resulting in an analytical solution for the equation of motion. To validate the model, experiments have been performed on a thick-walled stainless steel capillary partly filled with mercury. The model is in good agreement with the experimental data. Moreover, the sensitivity of the method appears to be adequate as a fluid level indicator for control purposes in industrial applications.