The Dynamic Calibration Uncertainty of Fast Response Pressure Probes

While standards like the GUM ‘Guide to the Uncertainty in Measurement’ and the ASME ‘Test Uncertainty’ provide clear guidelines for the computation of the uncertainty of steady measurements, uncertainty evaluation methods of dynamic data (measurements of time-dependent quantities), have not been equally addressed. Dynamic measurements require the correction of the data for the instrument’s bandwidth limitations. The application of an experimental transfer function is often used at such extend, whose contribution to the final uncertainty is rarely considered.

In the turbomachinery field, time-resolved flow measurements are employed for the characterization of broad-band unsteady phenomena, directly impacting the performance of the components (i.e. wakes, secondary flows, tip clearance flows, stator-rotor interactions). In particular, fast response pressure probes are a well-established and widely-used measurement technique for turbomachinery flows. They usually feature piezoresistive sensors recessed in the probe’s body and connected to the flow through a pneumatic line-cavity system. The dynamic response of the probe, which is defined by the line-cavity system’s characteristics, can be experimentally characterized through shock tube tests and its transfer function can be computed.

The aim of the present work is to perform an uncertainty analysis of the dynamic calibration of pressure probes in shock tubes and an evaluation of its propagation in the measurement results through the transfer function. Experimental data from dynamic calibrations performed at the shock tube of the von Karman Institute for Fluid Dynamics (VKI), literature data and analytical models are employed in the analysis. Error sources considered are related to the quality of the calibration input signal, the post-processing of the dynamic calibration data and the method used to identify the transfer function model parameters. The analysis is focused in the particular case of low-pressure shock tubes (pressure ratio at the order of ~1.1 - 1.3), commonly used for the calibration of fast response pressure probes. A Monte Carlo method is used for the propagation of uncertainties to the sensor’s output signal and to the parameters of the transfer function. Finally, an application of the method is presented, where the uncertainty of a dynamic calibration of a pressure probe is computed and its propagation to a measurement case is performed.