Examples

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 5-hole 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 5-hole probe (100Hz saw wave)

The requirement for miniaturization of pneumatic probes makes the use of off-board transducers particularly attractive, however, traditionally this has been assumed to limit the probe to steady-state measurements only. By us­ing transfer function correction, it is possible to use a conventional pneumatic probe to make time-accurate measurements. To validate the use of transfer function correction for probe measurements, the 5-hole probe used above was mounted adjacent to a single element hot-wire probe in the wake of a bluff body exhibiting vortex shedding at frequency of 58 Hz. The agreement be­tween the hot-wire and pneumatic probe with transfer function correction was similar to the level of agreement between two hot-wire probes at the same spacing in the same fbw. Further details can be found in Sims-Williams and Dominy (1998b).

Because probes are generally used to make measurements at different loca­tions in the ft>w-field sequentially, some form of synchronization is required in order to obtain instantaneous ft>w-field 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 self-excited aerodynamic unsteadiness, this is more difficult. The unsteady reconstruction technique of Sims-Williams 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 non-dimensional vorticity in the wake of a Gurney Flap

Unlike other methods of unsteady ft>w-field 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 (Sims-Williams 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 Sims-Williams et al. (1999) and Sims-Williams (2001).

The upper limit on the frequency response, which can be obtained for multi­hole probes using transfer-function 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 steady-state calibration).

Figure 6. Instantaneous stagnation pressure coefficient in the wake of a Gurney Flap

For typical multi-hole probes used in low-speed applications, these two factors both suggest a similar upper limit in the region of 1000Hz.

References

Bell, D. L. and He, L., 2000, Three-Dimensional Unsteady Flow for an Oscillating Turbine Blade and the Infhence of Tip Leakage, Journal of Turbomachinery, Vol. 122, pp. 93-101.

Buffum, D. H. and Fleeter, S., 1993, Wind Tunnel Wall Effects in a Linear Oscillating Cascade, Journal of Turbomachinery, Vol. 115, pp. 147-156.

Bolcs, A. and Korbacher, H., 1993, Periodicity and Repetitivity of Unsteady Measurements of an Annular Turbine Cascade at off design Flow Conditions, ASME 93-GT-107.

Carta, F. O. and St. Hilaire, A. O., 1978, Experimentally Determined Stability Parameters of a Subsonic Cascade Oscillating Near Stall, Journal of Engineering for Power, Vol. 100,

pp. 111-120.

Fleeter, S., Novick, A. S., Riffel, R. E. and Caruthers, J. E., 1977, An Experimental Deter­mination of the Unsteady Aerodynamics in a Controlled Oscillating Cascade, Journal of Engineering for Power, Vol. 99, pp. 88-96.

Fransson, T. H., 1990, Analysis of Experimental Time-Dependent Blade Surface Pressures from an Oscillating Turbine Cascade with the Inflience-Coefficient Technique, ASME 90- GT-225.

Frey, K. K. and Fleeter, S., 2001, Oscillating Airfoil Aerodynamics of a Rotating Compres­sor Blade Row, Journal of Propulsion and Power, Vol. 17, pp. 232-239.

He, L., 1992, Stagnation Pressure-Entropy Decoupling on a High Load LP Turbine Cas­cade, Unpublished work, Whittle Laboratory, Cambridge University.

He, L., 1996, Time-marching Calculations of Unsteady Flows, Blade Row Interaction and Flutter, Unsteady Flows in Turbomachines, Lecture Series 1996-05, von Karman Institute for Fluid Dynamics, Brussels, Belgium.

He, L. and Denton, J. D., 1991, An Experiment on Unsteady Flow Over an Oscillating Airfoil, ASME paper 91-GT-181.

Hooper, J. D. and Musgrove, A. R., 1991, Multi-Hole Pressure Probes for the Determina­tion of the Total Velocity Vector in Turbulent Single-Phase Flow, 4th International Sym­posium Transport Phenomena in Heat and Mass Transfer, The University of New South Wales, Sydney, Australia, ed. JA Reizes, July, 1991.

Irwin, H. P.A. H., Cooper, K. R. and Girard, R., 1979, Correction of Distortion Effects Caused by Tubing Systems in Measurements of Fluctuating Pressures, Journal of Indus­trial Aerodynamics, Vol. 5, pp. 93-107.

Manwaring, S. R., Rabe, D. C., Lorence C. B. and Wadia, A. R., 1997, Inlet Distortion Gen­erated Forced Response of a Low-Aspect-Ratio Transonic Fan, Journal of Turbomachin­ery, Vol. 119, pp. 665-676.

Minkierwicz, G. and Russler, P., 1998, Unsteady Aerodynamics in Transonic Compressor Rotor Blade Passages, AIAA 98-3897.

Sims-Williams, D. B., 2001, Self-Excited Aerodynamic Unsteadiness Associated with Pas­senger Cars, PhD Thesis, School of Engineering, University of Durham, Durham.

Sims-Williams, D. B. and Dominy, R. G., 1998a, Experimental Investigation into Unsteadi­ness and Instability in Passenger Car Aerodynamics, SAE Paper 980391 in Developments in Vehicle Aerodynamics (SAE SP-1318), 1998.

Sims-Williams, D. B. and Dominy, R. G., 1998b, The Validation and Application of a 5 Hole Pressure Probe with Tubing Transfer Correction for Time-Accurate Measurements in Unsteady Flows, Second MIRA International Conference on Vehicle Aerodynamics, Coventry, 20-21 October, 1998.

Sims-Williams, D. B. and Dominy, R. G. 2000, The Reconstruction of Periodic Pressure Fields from Point Measurements, SAE Paper 1999-01-0809 in SAE Transactions 2000.

Sims-Williams, D. B., White, A. J. and Dominy, R. G., 1999, Gurney Flap Aerodynamic Unsteadiness, Sports Engineering, (1999) 2, pp. 221-233.