Unsteady Calibration of Fast-Response Pressure Probes, Part 1: Theoretical Studies

Abstract

Recent advances in miniaturization of pressure transducers, including microelectromechanical systems technology, have provided miniature, high-bandwidth pressure transducers and transducer arrays well suited for fast-response, multihole probes. The miniature size of these arrays enables a design in which the transducers are embedded in, or close to, the probe tip while maintaining a tip diameter of 1‐2 mm. Although the frequency response of such a probe is excellent, there are several unresolved issues pertaining to fluid inertia-related unsteady aerodynamic effects on probe calibration. As a result of these effects, when the probe is used in a dynamically changing flowfield a quasi-steady probe calibration can no longer be used to resolve the instantaneous velocity vector. We present theoretical analysis of these effects and formulate methods of calibrating multihole, fast-response probes for use in unsteady flows in order to accurately resolve the instantaneous velocity vector. The main objective of the theoretical analysis is to study and quantify the dependence of the probe measured pressures on the magnitude of the flow inertial effects in terms of properly formulated nondimensional parameters, as well as allow a direct comparison of theory and experiment. Among the contributions of this work, it was particularly interesting to find that proper definition of the nondimensional, flow-angle-dependent pressure coefficients renders them insensitive to unsteady effects. This has the significant ramification that the steady calibration of these coefficients can be also used in unsteady flowfields for the calculation of the flow angles. Calculation of the velocity magnitude, however, requires quantification of and correction for the fluid inertial effects.