Simple Technique for Frequency-Response Enhancement of Miniature Pressure Probes

Abstract

THIS Note deals with the implementation of a simple technique to correct for the pressure measurement error produced in miniature multihole pressure probes caused by the lag in the response of the probe tubing system. As the size of the pressure probe is reduced in order to reduce flow disturbance, the probe's frequency response deteriorates. Reduced frequency response generally causes the wait times in flow-mapping experiments to increase. The wait time is the time that the probe, after it moves to a new measurement location in the flowfield, has to wait before data acquisition can be performed, in order for the pressures at the probe pressure transducers to reach steady state. Moreover, deterioration of probe frequency response limits its capability to resolve temporal information in unsteady flows. In the present work, we introduce a simple algorithm that significantly improves a probe's frequency response. Detailed work in the area was carried out by Whitmore. 1 He developed a mathematical model for a tubing system, derived from the NavierStokes and continuity equations. On the basis of this model, he then developed an algorithm to compensate for pneumatic distortion. The technique presented here is simpler and much less computationally intensive and is thus amenable to real-time implementation. The technique presented here is applicable only to critically damped or overdamped tubing systems, as discussed later. Generally, in pressure-meas uring systems such as multihole probes, the pressure at the pressure-measuring instrument (pressure transducer) can be different from the pressure at the source (i.e., the probe tip) because of the time lag and pressure attenuation in the transmission of pressures in the associated tubing. When the pressure at the pressure source is changing rapidly, the pressure at the transducer lags behind that at the source and its amplitude is attenuated because of 1) the time needed for the pressure change to propagate along the tubing (acoustic lag) and 2) the pressure drop associated with the flow though the tubing (pressure lag).2 The speed of the pressure propagation along the tubing is the speed of sound. The magnitude of the acoustic lag r thus depends on only the speed of sound a and the length of the tubing L, as expressed in r = L/a. Because the speed of sound at standard atmospheric conditions is on the order of 1100 ft/s (340 m/s), errors caused by acoustic lag are of concern only in pressure systems having very long pressure tubing. Errors associated with acoustic lag can be neglected here because the tubing lengths of interest are very short [order of 1 ft (0.3 m)]. Moreover, because of the motion of the air through the pressure tubing between the pressure source and the transducer, the