An investigation of liquid velocity measurement using PZT cylinders

Abstract

A novel ultrasonic velocimeter was developed in this study using a single element PZT cylinder encapsulated within an isothermal cavity. The rig was designed to hold a small sample volume of test liquid (typically less than 0.2ml), as a prerequisite for biological application. An admittance spectrum for the liquid filled cavity displayed sharp piezoelectric modes indicating strong coupling between the cylinder and liquid. This coupling was further improved by using liquid soap as a coupling agent. The phase velocity was measured, using the change in frequency associated with change in acoustic mode number. Early results indicated a change in frequency, with mode number decrease over the superimposed piezoelectric resonance providing a skewed value for phase velocity. This problem is evidenced in the literature precluding continuous wave interferometry as a realisable means of measuring phase velocity. This study examines the common problem of frequency pulling and resonant interaction between acoustic and piezoelectric modes. For the first time an alternative is shown to traditional "electro-acoustic" models, utilising an extension of Mason's transmission line model with the addition of a "mechanical-acoustic" transformer to represent energy coupling between the piezoelectric and surrounding liquid. It was found the transformer coupling coefficient could be described as the inner surface area of the cylinder. In an attempt to quantify the behaviour of this model it has been simplified into an "electro-acoustic" equivalent lumped circuit elements. Each liquid mode is represented as a series tuned LeR circuit. The solution to the frequency pulling was unravelled by implementing a stochastic optimiser (adaptive mutation breeder algorithm) to predict the coupling coefficient between mechanical and acoustic modes. It also predicts acoustic equivalent circuit parameters and further utilise it to extract the velocity of sound from the test liquid. Three test liquids were evaluated including water, FC43 and FC75 at a constant temperature of 30 °C±O.Ol "C. Initial results indicate a strong correlation between the model and experiment with accumulative admittance errors falling below 5%. Subsequently it was possible to achieve phase velocity measurements with a "worst case" standard deviation of less than 3.74. It has been the hypothesis of this study to show, in concept, that inline tube velocimeter is plausible using continuous wave cylindrical interferometry.