Modelling and optimisation of the Microflown

In this thesis a particular thermal flow sensor, the Microflown, is studied. By virtue of its property to be sensitive to particle velocity, the physical quantity associated with sound, the sensor is especially used for sound intensity measurements. It is endeavoured to physically understand the behaviour of the Microflown and to give an adequate description of its sensitivity. The purpose of the presented analytic model is to deduce an explicit expression for the temperature difference between the two heated wires of the sensor due to an imposed particle velocity, to which the output signal is proportional. This is achieved by finding first the temperature distribution around the heated wires from the heat diffusion equation. This stationary temperature profile is altered slightly, asymmetrically, due to the forced convection of an acoustic wave. It is shown that this particle velocity can be described by a small perturbation term added to the heat equation to obtain an expression for the resulting temperature difference of the wires. The thus obtained sensitivity function is seen to be well characterised by two important characteristic frequencies, a ‘thermal’ frequency, and a second corner frequency related to the heat capacity of the wires. Another important property of this function is its value at zero frequency. An explicit expression for this low frequency sensitivity is found, allowing a good description and consequently optimisation of the sensor for the measurement of steady flows. The model is verified by acoustic measurements on many sensors of varying geometries and a satisfying correspondence between theory and measurement is found. Since the Microflown is mainly used for sound intensity measurements, an overview of the different principles that can be applied to measure sound intensity is given, methods based on particle velocity sensors, pressure microphones or a combination of them. The measurement principle that seems to be most favourable makes use of one pressure microphone and one particle velocity sensor. The advantage of this principle is that no pressure gradients or spatial derivatives of the particle velocity are involved. This so-called p-u probe is an affordable and practical measuring device for measuring several acoustic parameters and can easily be extended to a three-dimensional probe. The calibration method of the sensor that is most common, the standing wave tube, is described next. It considers particularly the limits of validity of this method by analysing the effects of the viscous and thermal properties of the gas in the tube. These viscothermal effects on the calibration are shown to be small. Nevertheless, they should be considered in the design of a standing wave tube; by proper design the viscothermal effects can be made negligible. Then it is shown that the sensor’s sensitivity and frequency behaviour can be determined electronically as well, and an electronic method for determination of the device output response, which is more convenient, is therefore presented. The previous approach, the introduction of a small perturbation to the heat diffusion equation, is applied to the electronic case: the small additional electrical heating of one of the two wires can be described by a perturbation term. Using a specific property of Green’s functions, the electrical response of the other wire can be translated to the acoustic response. The principle is shown to be geometry independent, it can be applied for a wide range of thermal flow sensors, even for those consisting of more than two wires. The method is not only less complicated, it also makes it possible to cover easily the entire acoustic frequency spectral range. The theory is experimentally verified for various thermal flow sensors of different geometries. The model developed in the second chapter is the basis for further optimisation. Since the theory is now implemented into a numeric program, several assumptions and restrictions for the deduction of the analytic model can be dropped. The implementation of the numeric model into a software program allows for an investigation of the influence of varying sensor dimensions on the sensitivity. Thus, improved devices could be fabricated, among which Microflowns with a new geometry consisting of three, instead of two, wires of which the central wire is most heated. These three-wire sensors have a significantly improved signal-tonoise ratio and a larger frequency bandwidth. The last two chapters deal with the noise that is present in the output signal. First a method to reduce the noise level of the particle velocity sensor is described. This method is based on the utilisation of cross-correlation spectra instead of auto correlation spectra of two of these sensors. The underlying principle is that the time averaged cross correlation signal of two uncorrelated noise sources is theoretically zero. The larger the measuring time and therefore the number of data points stored, the smaller the variance of the noise power in the cross spectrum. Finally, the characteristics and origins of the noise are investigated in detail. Especially the low-frequency noise is analysed and it is observed that the voltage fluctuations exhibit a spectral density that for low frequencies behaves as 1/f α with 1 < α < 3. The approach of introducing a perturbation that has shown to be useful in the former chapters, is applied to analyse the influence of small fluctuations of external physical quantities on the fluctuations of the wire temperature and consequently on the spectral density of the output voltage. Besides, the dependence of the low-frequency noise on wire temperature and on the dissipated power are investigated experimentally. It is found that the electrical power dissipation and the related self-heating of the wire play an important role in the observed noise behaviour, although this phenomenon is not well understood yet. A difference in the power dependence of this noise between the sensor wires and a common metal film resistor is observed. We propose different possible explanations for this noise behaviour