Figure 2 shows a typical example of the measured tubing transfer function for a tubing length used in the measurement of unsteady pressures in an oscillating cascade. In this case a slight amplification can be seen over the frequency range of interest, indicating a resonant peak at a higher frequency. The phase distortion is more significant due to the importance of the relative phase of surface pressure flictuations and the vibration of the blade.
Figure 2. Transfer Function of the measurement system for the blade flitter case (brass tube, 180mm x 1mm Portex tubing and connector)

Figure 3 shows the transfer function for a single tube of a 5hole probe used to make measurements in the wake of a bluff body exhibiting vortex shedding. Small tube diameters near the probe head and a longer tubing length results in a system in which viscous attenuation dominates over any resonant effects.
Figure 3. Transfer Function of the measurement system for the vortex shedding case (5 hole probe, 0.75mm Portex tubing and connector)

Figure 4 shows the effectiveness of the transfer function correction method in reconstructing an original reference signal from a distorted one. The tubing system of Fig. 3 was subjected to a 100Hz saw waveform using the transfer function measurement apparatus. Significant phase lag and attenuation relative to the reference signal is clearly apparent in the uncorrected signal and the increased attenuation of higher harmonics alters the waveform shape. The previously measured transfer function was then used to infer the original signal and this is labeled “corrected” in Fig. 4. This can be seen to closely match the original reference signal.
Figure 4. Effect of transfer function correction with single hole of a 5hole probe (100Hz saw wave)

The requirement for miniaturization of pneumatic probes makes the use of offboard transducers particularly attractive, however, traditionally this has been assumed to limit the probe to steadystate measurements only. By using transfer function correction, it is possible to use a conventional pneumatic probe to make timeaccurate measurements. To validate the use of transfer function correction for probe measurements, the 5hole probe used above was mounted adjacent to a single element hotwire probe in the wake of a bluff body exhibiting vortex shedding at frequency of 58 Hz. The agreement between the hotwire and pneumatic probe with transfer function correction was similar to the level of agreement between two hotwire probes at the same spacing in the same fbw. Further details can be found in SimsWilliams and Dominy (1998b).
Because probes are generally used to make measurements at different locations in the ft>wfield sequentially, some form of synchronization is required in order to obtain instantaneous ft>wfield data. In cases where the unsteadiness is imposed externally (eg: forced vibration), or where it is coupled with some mechanical oscillation (eg: aeroelasticity), this may be accomplished using triggered sampling from the mechanical motion. For cases of selfexcited aerodynamic unsteadiness, this is more difficult. The unsteady reconstruction technique of SimsWilliams and Dominy (2000) uses a signal from a stationary reference probe, and a complex convolution in the frequency domain, to effectively synchronize probe measurements made sequentially. This provides a more robust determination of relative phase than simply using triggered sampling, and this makes the technique appropriate even for weakly periodic fbw – fields. Figure 5 shows the instantaneous vorticity field in the wake of a ‘Gurney Flap” high lift device on the trailing edge of an inverted airfoil. By producing a series of these images vortex shedding can be clearly observed.
Figure 5. Instantaneous nondimensional vorticity in the wake of a Gurney Flap

Unlike other methods of unsteady ft>wfield measurement, the use of a pressure probe allows the observation of static and stagnation pressure, as well as velocity. Figure 6 illustrates the instantaneous stagnation pressure field corresponding to Fig. 5. An issue of interest regarding the understand – ing/interpretation of unsteady results is the decoupling between stagnation pressure (the measure of loss for steady flow only) and entropy (the measure of loss in general). This has been observed computationally for a LP turbine cascade subject to incoming unsteady wakes (He, 1992, 1996) and has been observed computationally and experimentally adjacent to the wake of bluff bodies exhibiting vortex shedding (SimsWilliams and Dominy 1998b). In Fig. 6, packets of stagnation pressure deficit corresponding to the shed vortices can be observed, but importantly, it is also possible to see regions where the stagnation pressure coefficient is greater than unity. As discussed above, in an unsteady flow, instantaneous stagnation pressure and entropy become uncoupled. The frequency of the shedding in this case was approximately 300Hz. Further details of this work on Gurney flap vortex shedding may be found in SimsWilliams et al. (1999) and SimsWilliams (2001).
The upper limit on the frequency response, which can be obtained for multihole probes using transferfunction correction, is restricted both by the level of correction required (which results in a deterioration in signal to noise ratio), and by time required for the flow around the head of the probe to develop (since the assumed sensitivity of the probe is based on a steadystate calibration).
Figure 6. Instantaneous stagnation pressure coefficient in the wake of a Gurney Flap

For typical multihole probes used in lowspeed applications, these two factors both suggest a similar upper limit in the region of 1000Hz.
References
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