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P13
The plate area A, the dielectric constant εr and the electric constant ε0 do not change as a result of the pressure. Following Eq. the capacitance increases if the distance between the plates decreases. However, the change of capacitance is not linear with respect to the deformation of the membrane. There are methods to linearize this dependency, for example, by adding a thin and compressible insulation material between the capacitor plates. This form of sensor design is referred to as ’touch mode’ [4]. Touch mode sensors can endure higher overpressures without risking the rupture of the membrane, but are also more affected by hysteresis due to increased friction with the insulation layer.
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P14
Capacitive pressure transducers can be used for a variety of applications. They are suitable for measuring static and dynamic pressures and can be designed for low- and high-pressure environments. They are not commonly found in hot sections of gas turbines. The advantages of a capacitive pressure transducer are its low power consumption and the lack of electrical noise. The disadvantages consist of its non-linearity and complex measurement circuitry.
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P15
Optical pressure measurement technologies rely on light to measure pressure. There are various established methods that use different properties of light to measure pressures. One of those methods is described below.
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Light Interferometry
P16
The main established method of optical pressure measurement is the use of interferometry. There are two common types of pressure transducers using light interferometry, the Fabry-Pérot interferometer (FPI) and fibre Bragg grating (FBG) [5]. Fibre Bragg grating does not provide the necessary temperature capabilities for dynamic pressure measurement in gas turbines, so only the Fabry-Pérot interferometer will be described here.
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P17
The Fabry-Pérot interferometer relies on the difference in travel distance of light and the resulting phase shift. In principle, a broad-band light source emits light of known wavelengths which is reflected at two different points in the sensor head. The first reflection point is at the edge between the base and the cavity seen in Fig. 2.2. This is an interface between two different materials so the light is only partially reflected. The remaining light continues to the second point of reflection, which is at the back of the diaphragm, and gets fully reflected. Both light beams then travel back through the same fiber-optic they entered. The phase delay between the two beams results in constructive or destructive interference, which can be used to measure the length of the cavity d1 seen in Figure 2.2 below. [5]
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P19
As the diaphragm deflects due to the pressure acting on it, the length d1 decreases, and the phase difference between the two light beams changes. The deflection of the diaphragm y can be assumed linear for deformations where y is much smaller than the thickness of the diaphragm t. Equation shows the pressure p depending on the diaphragm radius R, the diaphragm thickness t, the diaphragm deflection y, and Young’s modulus E and Poisson’s ratio ν of the diaphragm material. [5]
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P21
To cancel out any non-deflection induced variations in the signal, a second light source also illuminates the sensor head at a different wavelength. The two different light spectra are then cross-checked for common variations and only the deflection induced variations are shown in the output signal [5].
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P22
For dynamic pressure measurements in high-temperature areas FPI based sensors can be made with temperature resistant materials. Fiber-optic materials, such as sapphire, are used in high-temperature areas. The sensor head itself is a passive component and therefore can be used in environments where electromagnetic interferences are expected or not tolerable. The electric parts of the transducer can be mounted in a safer environment, away from the sensor head. Light only is transferred to and from the sensor head using fiber-optics. The advantages of such systems are the high-temperature capability of around 700°C for the sensor head and the possibility to include static pressure and/or temperature measurement within the dynamic pressure sensor as well [5]. The complex measurement and signal generation process is disadvantageous in comparison to other measurement technologies.
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P23
Piezoelectric transducers for dynamic pressure measurements use the piezoelectric effect to generate charge via the deformation of the piezoelectric material. This process is called the ”direct piezoelectric effect”. In principle, no external energy is needed to generate an output signal which is the reason piezoelectric transducers are called active transducers. In Figure 2.3 an exemplary cut drawing of a transverse piezoelectric transducer can be seen. The depicted parts are: 1 diaphragm, 2 preloading sleeve, 3 transfer plate, 4 piezoelectric elements, 5 spring shaped wire electrode, 6 sensor housing, 7 connector pin, and 8 sealing shoulder.
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P26
Transverse means that the charge is collected on the inner and outer surfaces of the long side of the piezoelectric elements. The transducer shown in Figure 2.3 uses a spring shaped wire as the inner electrode and the preloading sleeve in combination with the sensor housing as the outer electrode [6, p. 83].
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P27
As pressure is applied to the diaphragm, the piezoelectric elements get compressed, which results in the charging of the outer walls of the elements. The charge is collected by the electrodes and transferred to the charge amplifier via cable. At the charge amplifier, the charge output of the transducer is converted to an output signal for further use. Since the charge generated by the compression and relief of the piezoelectric elements decays over time, piezoelectric transducers can only provide dynamic pressure measurements above a certain minimum frequency which is strongly dependent on the charge amplifier used [7].
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P28
There are different materials available that show piezoelectric behavior. The most common ones are quartz (SiO2), tourmaline, crystals of the Calcium Gallium Germanium (CGG) group (Ca3Ga2Ge4O14), and gallium orthophosphate (GaPO4) [6].The latter two are commonly used for high-temperature applications due to their high temperature capabilities and lack of pyroelectric effects.
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