On modeling two-mode vibration sensors for combined density and viscosity measurements

Abstract

Torsional and bending mode vibrations of a hollow cylinder shall be used for combined measurement of density and viscosity of a fluid. The employment of two different vibration modes has the advantage that modes with good sensitivity for either density or viscosity measurements can be used. For a detailed discussion of the dependencies of the sensitivity, a description of the fluid forces and a model of the sensor are required. Analytical solutions for the fluid forces acting on an oscillating cylindrical structure usually consider a two-dimensional situation. FEM simulations are performed in order to investigate the suitability of such solutions in order to describe fluid forces in a three-dimensional situation and for different bending modes. For the case at hand, an analytical relationship between the resonance frequency and the density of the liquid can be formulated. This analytical relationship forms a valuable basis for further investigations.

Simultaneous phase control of multiple frequencies of multi-degree-of-freedom systems

“…This offers numerous possibilities for the improvement and enhancement of resonance based sensor principles, e.g. to measure both viscosity and density (Heinisch et al., 2014; Wattinger, 2014) or for rheological measurements (Brack and Dual, 2013).…”