1: Schematic drawing of a turbine flow meter with A) flow straightener and B) rotor. C) shows the position of the mechanical counter 

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... r u i n M r u o u t , x = u i n > u r e l > Figure 1.4: Steady flow entering and leaving the rotor for an ideal frictionless rotor with infinitesimally thin helical rotor blades with blade angle ...

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... spurious count behaviour of a turbine meter can be explained by considering the forces acting on an aerofoil in an oscillating flow. The blades of the turbine rotor most commonly used in gas transport systems have a rounded leading edge and a sharp trailing edge (see figure 4.1). This difference in edge shape causes the spurious ...

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... velocity fluctuations, u ′ 1 , have also been measured using a hot wire anemome- ter (Dantec type 55P11 wire diameter 5 µm with 55H20 support) placed 11.9 cm from the top wall in the middle of the left duct. The hot wire measurements of the velocity fluctuations agree within 25% with pressure fluctuation measurements when using equation 4.12. During other measurements the hot wire was removed. The amplitude of the velocity fluctuations, u ac = |u ′ |, are made dimensionless by means of the Strouhal number, Sr t blade = f t blade /u ac , with f the frequency and t blade the thickness of the blade. The time scale is related to the pressure in the reservoir V 1 , assuming it has a cos (2πf t) time dependence for sin (2πf t) pressure fluctuations. From the Schlieren visualizations, it is also observed that depending on the initial conditions the flow can display two different modes (figure 4.15). In the first mode the first vortex is created above the slanted side of the edge model starting at t/T = 0. A second vortex with a circulation of opposite sign is created when the flow changes direction at t/T = 0.5. Both vortices move as a vortex pair away from the edge ( figure 4.15(a)). We will refer to this mode as "mode 1". In the second mode the first vortex is created starting at t/T = 0.5 next to the edge model. A second vortex of opposite sign is created starting at t/T = 0 above the slated side of the edge. They move away from the edge as a vortex pair over the slanted side ( figure 4.15(b)). This mode will be referred to as "mode 2". While it is possible to force the flow in mode 2 (figure 4.15(b)), in most experiments mode 1 ( figure 4.15(a)) is dominant. At Sr t blade = 1.6 the vortices that are created are small and it is no longer possible to sustain mode 2 behaviour during a measurement. At even higher Strouhal number, Sr t blade = 3.2, the mode of vortex shedding changed spontaneously during the measurement from one mode to the other and back. These measurements are not included in this ...

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... velocity fluctuations, u ′ 1 , have also been measured using a hot wire anemome- ter (Dantec type 55P11 wire diameter 5 µm with 55H20 support) placed 11.9 cm from the top wall in the middle of the left duct. The hot wire measurements of the velocity fluctuations agree within 25% with pressure fluctuation measurements when using equation 4.12. During other measurements the hot wire was removed. The amplitude of the velocity fluctuations, u ac = |u ′ |, are made dimensionless by means of the Strouhal number, Sr t blade = f t blade /u ac , with f the frequency and t blade the thickness of the blade. The time scale is related to the pressure in the reservoir V 1 , assuming it has a cos (2πf t) time dependence for sin (2πf t) pressure fluctuations. From the Schlieren visualizations, it is also observed that depending on the initial conditions the flow can display two different modes (figure 4.15). In the first mode the first vortex is created above the slanted side of the edge model starting at t/T = 0. A second vortex with a circulation of opposite sign is created when the flow changes direction at t/T = 0.5. Both vortices move as a vortex pair away from the edge ( figure 4.15(a)). We will refer to this mode as "mode 1". In the second mode the first vortex is created starting at t/T = 0.5 next to the edge model. A second vortex of opposite sign is created starting at t/T = 0 above the slated side of the edge. They move away from the edge as a vortex pair over the slanted side ( figure 4.15(b)). This mode will be referred to as "mode 2". While it is possible to force the flow in mode 2 (figure 4.15(b)), in most experiments mode 1 ( figure 4.15(a)) is dominant. At Sr t blade = 1.6 the vortices that are created are small and it is no longer possible to sustain mode 2 behaviour during a measurement. At even higher Strouhal number, Sr t blade = 3.2, the mode of vortex shedding changed spontaneously during the measurement from one mode to the other and back. These measurements are not included in this ...

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... velocity fluctuations, u ′ 1 , have also been measured using a hot wire anemome- ter (Dantec type 55P11 wire diameter 5 µm with 55H20 support) placed 11.9 cm from the top wall in the middle of the left duct. The hot wire measurements of the velocity fluctuations agree within 25% with pressure fluctuation measurements when using equation 4.12. During other measurements the hot wire was removed. The amplitude of the velocity fluctuations, u ac = |u ′ |, are made dimensionless by means of the Strouhal number, Sr t blade = f t blade /u ac , with f the frequency and t blade the thickness of the blade. The time scale is related to the pressure in the reservoir V 1 , assuming it has a cos (2πf t) time dependence for sin (2πf t) pressure fluctuations. From the Schlieren visualizations, it is also observed that depending on the initial conditions the flow can display two different modes (figure 4.15). In the first mode the first vortex is created above the slanted side of the edge model starting at t/T = 0. A second vortex with a circulation of opposite sign is created when the flow changes direction at t/T = 0.5. Both vortices move as a vortex pair away from the edge ( figure 4.15(a)). We will refer to this mode as "mode 1". In the second mode the first vortex is created starting at t/T = 0.5 next to the edge model. A second vortex of opposite sign is created starting at t/T = 0 above the slated side of the edge. They move away from the edge as a vortex pair over the slanted side ( figure 4.15(b)). This mode will be referred to as "mode 2". While it is possible to force the flow in mode 2 (figure 4.15(b)), in most experiments mode 1 ( figure 4.15(a)) is dominant. At Sr t blade = 1.6 the vortices that are created are small and it is no longer possible to sustain mode 2 behaviour during a measurement. At even higher Strouhal number, Sr t blade = 3.2, the mode of vortex shedding changed spontaneously during the measurement from one mode to the other and back. These measurements are not included in this ...

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... we find some similarities in the variation with time, the effect of the vortex pair travelling away from the edge has a large effect on the calculations in mode 2. From the prediction of vorticity distribution using the vortex blob method, we can see that while the vortex pair moves away a part of the vortex remains close to the edge. However, the visualisations do not show this vortex left behind. The same effect takes place for mode 1 behaviour ( figure 4.18(c,d,g,h and k)). This vortex has less effect on the edge pressure, because it is not close to the edge as in the case of mode ...

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... order to verify that the difference in shape of the edges of the blades of the rotor causes the ghost counts, the rotor in the turbine meter was replaced with a rotor with a blade profile with a chamfered leading edge ( figure ...

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... considered the boundary layer along a semi-infinite flat plate (Schlichting, 1979) (see figure B.1). The flow has a constant, steady, velocity, U , parallel to the x-axis and there is no pressure gradient. The boundary layer equations B.1 reduce ...

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... experiments in this thesis are performed on gas turbine flow meters of Elster- Instromet. The dynamical response measurements have been carried out at the Eind- hoven University of Technology with the gas turbine meter type SM-RI-X G250, see figure 1.3. This meter has an internal pipe diameter of 100 mm. The accuracy of the flow measurement is 0.1% for volume flows in the range from 20 to 400 m 3 /h. The meter is designed for pressures ranging from atmospheric pressure up to 20 bar (this type of meter is also available for work pressures up to 100 bar). The rotor is made of aluminium and has helical shaped blades (see figure 1.2). We will refer to this me- ter as turbine meter 1. Additional steady flow experiments have been performed by Elster-Instromet with simplified prototypes which we refer to as turbine meter 2, 3, 4 and 5. Additional experiments with oscillatory flow have been performed by Gasunie with a larger version of the SM-RI-X G250, the SM-RI-X G2500 with a internal pipe diameter of 300 ...

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... experiments in this thesis are performed on gas turbine flow meters of Elster- Instromet. The dynamical response measurements have been carried out at the Eind- hoven University of Technology with the gas turbine meter type SM-RI-X G250, see figure 1.3. This meter has an internal pipe diameter of 100 mm. The accuracy of the flow measurement is 0.1% for volume flows in the range from 20 to 400 m 3 /h. The meter is designed for pressures ranging from atmospheric pressure up to 20 bar (this type of meter is also available for work pressures up to 100 bar). The rotor is made of aluminium and has helical shaped blades (see figure 1.2). We will refer to this me- ter as turbine meter 1. Additional steady flow experiments have been performed by Elster-Instromet with simplified prototypes which we refer to as turbine meter 2, 3, 4 and 5. Additional experiments with oscillatory flow have been performed by Gasunie with a larger version of the SM-RI-X G250, the SM-RI-X G2500 with a internal pipe diameter of 300 ...

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... influence of the shape of the blade was investigated by replacing the standard rotor with a rotor a with different blade shape. The original rotor has blades with a rounded upstream leading edge and a chamfered trailing edge. The rotor was replaced by a rotor with chamfered leading edges similar to the trailing edges ( figure 3.18). To determine the behaviour of the rotor with chamfered leading edges in pulsating flow some of the measurements carried out with the standard rotor are repeated using the new rotor. Figure 3.19 shows the results of the measurements carried out at a pulsation frequency of 164 Hz and mainstream velocities of u 0 = 1, 5 and 15 m/s, compared to the measurement data obtained for the standard rotor. Within the accuracy of the measurement no difference was found. To verify this further a quadratic fit as explained in section 3.6.1 was made and this parameter was plotted against Strouhal number, Sr L blade for low frequencies (f = 24, 69, 117 and 164 Hz) ( figure 3.20). Again, we see that within the accuracy level of the measurements there is no difference between the deviation of the volume flow measurement for the rotor with blades with rounded leading edges and the rotor with blades with chamfered leading edges. ...