Vibrating transducers for fluid measurements - Surtees, Antony John (Energy Research Centre, 2023)
When a body vibrates in a fluid, some of the fluid is carried with it and the mass loading lowers its resonant frequency. Similarly, when compression of the fluid occurs, there is an added stiffness which by design can be made to predominate. In addition, there is an energy dissipation arising from viscous losses and acoustic radiation. The starting point of this research was a tuning fork with flat rectangular tines, designed to trap a narrow laminar of gas which is forced to pump in and out as the tines vibrate. The increase in kinetic energy, contributed by this high velocity' gas, gives the device a relatively large sensi ti vi ty as a gas density transducer. The change in frequency between vacuum and atmospheric pressure is typically a few percent, during which period the mechanical "Q" remains high enough to keep the fork sharply resonant. A high stability oscillator incorporating the transducer as the frequency controlling element was built. Small piezoelectric Cp2t) elements were used to drive the transducer and pick up the vibrations. A typical stability, equivalent to a pressure change of 0. 05 mBar was achieved. The supporting equipment re qui red for the work centred around a vacuum system with facilities for introducing a range of gases at precise rates. Computer control enabled the transducer's temperature, frequency, and "Q" factor to be measured and stored as the gas pressure was increased from vacuum. Extensive experiments were carried out on a range of tuning fork transducers, including a circular one in which a pair of disks clamped at the center acted as the tines and gave a simple radial gas displacement. Common to all these transducers is, the linearity of 1/f 2 with gas density for pressures above about 50 mBar; a departure from. linearity below this pressure; and below 10 mBar an overriding stiffness effect, where from vacuum to a few mBar the frequency paradoxically increases. The resultant calibration to this non-linear response, while exhibiting high stablility, is unattractive for general use. It has however applications over limited ranges as for example, those of a barometer or altimeter. Insight gained from experience with the double disk resonator, led to a new geometry which has resulted in an extremely viable transducer, without calibration anomalies, and capable of operating in a pressure or dehsity mode. Here, the gas is confined in two cylindrical cavities above and below a thin circular diaphragm, clamped at the periphery and again made to vibrate using p2t elements. In the fundamental mode, the alternating change in cavity volume due to compression and rarefaction of the gas, adds stiffness to the diaphragm. In the next mode, there is no net volume change, but the gas is pumped across the cavities adding inertial loading. No anomalies were experienced in the empirical calibrations obtained for each mode- the fundamental being linear with pressure Cf 2 proportional to Pl, and the first overtone linear with density (1/f 2 proportional to pl. A simple theory, which is sufficiently accurate for general design purposes, has been developed. Future work, which is of a straightforward development nature, is proposed. The high degree of stability achieved for these vibrating structures was later realised in a different geometry. In this, a long rod was excited into a torsional mode so as to produce two nodes a quarter wavelength from. either end. By securing the rod at these points and immersing the lower length in a liquid, a sensitive, robust, viscometer was produced. Driving the rod with a burst of oscillations, shears the liquid in contact with it. By removing this drive and measuring the rate of vibrational decay under the action of viscous dissipatiop, an indication of the viscosity can be obtained. The features of a pure shearing force, and the real-time, on-line nature of the device, makes it attractive for the characterisation of both thick and thin liquids and automatic process control.