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Theory of Tubing Transfer Function Approach
The tubing transfer function approach presented in this paper is based on a technique originally employed for wall pressure measurements in wind engineering by Irwin et al. (1979). This technique was subsequently applied for multi-hole probe measurements by Sims-Williams and Dominy (1998a) and by Hooper and Musgrove (1991).
The unsteady pressure signal propagates from the pressure tapping to the off-board pressure transducer via the tubing between them. The signal can be amplified by resonance effects at particular frequencies and will be attenuated by viscous effects at higher frequencies. There will also be a time-lag for the pressure signal to reach the transducer which will result in an increasing phase
offset at higher frequencies. This frequency-dependent tubing response can be characterized by a transfer function. Once the transfer function of a given tubing system is known, then it is possible to correct for the tubing distortion. This technique requires that the system obeys the principal of linear superposition so that an unsteady signal can be decomposed into multiple frequency components, and this has been confirmed.
To utilize this approach, the tubing transfer function of the pressure measuring system must be known in advance, and this can be obtained experimentally. A test unsteady pressure signal including a range of frequencies is recorded by a reference pressure transducer directly and by another pressure transducer via a tubing length used for actual unsteady pressure measurements. Fast Fourier Transforms (FFTs) of both the undistorted and distorted signals are computed. The complex tubing system transfer function TF(f) is expressed as:
ТПЛ = Щ (1)
The corrected coefficients A (f) are then transformed back to the time domain using an inverse FFT in order to obtain a corrected pressure signal with the effect of tubing distortion eliminated. Both amplitude and phase distortions are removed, the latter being essential if multiple simultaneous signals are to be compared.
