Development of an integrated model of vibrating element fluid property sensors.
Author(s)
Manrique de Lara Bordoy., Maria
Type
Thesis
Abstract
Density and viscosity measurements are needed in many industrial applications. Integrated circuit techniques and micromachining allow the creation of new designs of sensors for these properties. When a structure immersed in a fluid is set in vibration, its frequency response depends on the density and viscosity of the fluid. This is the principle used in a new generation of fluid property sensors. A model that couples the structural vibration with the behaviour of the surrounding fluid is needed to optimise future sensor designs. The first part of this thesis concentrates on understanding the fluid reaction on vibrating plates of different shapes. A general expression for a thin plate of any shape is derived, with application to a rectangular plate. Numerical results are presented as a function of the dimensionless parameter beta, equal to the frequency of vibration times the characteristic length squared over the kinematic viscosity. It is shown that the pressure differential across the plate near the edge is difficult to resolve using this numerical method, especially for large values of beta which corresponds to the region of interest for the application. This is the motivation to start an asymptotic study for large values of beta. This method provides an analytical expression relating the pressure differential on the plate to the velocity of the plate. Both methods are also applied to the problem of a vibrating disc and comparisons between numerical and analytical results are given for this case. In the second part of the thesis, an integrated model for a cantilever plate sensor is presented. The analytic relation between the pressure differential across the plate and the velocity allows one to solve the equation of motion of the plate analytically. Thus the frequency response of the plate in a viscous fluid is calculated.
Version
Imperial Users only
Date Awarded
2005
Advisor
Atkinson, Professor Colin
Sponsor
Schlumberger Cambridge Research
Publisher Department
Department of Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)
Author Permission
Permission not granted