The empirical calibration of remote microphone probes (RMP), used to acquire wall-pressure fluctuations, can introduce spurious resonance into the sensor transfer function due to the difference in the pressure field inside the calibrator geometry over multiple calibration steps. Such spurious resonance subsequently propagates into the unsteady-pressure data at which the calibration is applied, hindering the accuracy of the measurements. Current post-processing methods for tackling these issues are often manual and strongly dependent on the operator's expertise. In this study, we propose an original semi-empirical calibration method to remove spurious resonance in a less operator-reliant manner. The approach is based on fitting an existing analytical fluid-dynamical model for the propagation of pressure waves in the probe to the empirical calibration data using Bayesian inference. The proposed method is successfully applied to three datasets, from a simple probe recessed behind a pinhole to a more complex branching RMP. For all the configurations, spurious resonance is eliminated from the transfer function with a strongly reduced impact of the operator intervention while retaining the resonant features that are characteristic of the RMP. The affected frequency bands are then replaced using the underlying physical model. In this way, the detrimental impact of spurious resonance is removed from the measured wall-pressure spectra. Furthermore, the RMP parameters retrieved by the fit can also be used as inputs to corrective models, specifically to account for averaging effects due to the probe sensing area or for the impact of grazing flow or temperature variations on the transfer function.

Unsteady surface pressures shed light on the turbulent structures of boundary-layer flows, which dictate for a large part the aerodynamic and aeroacoustic performance of bodies submersed in a flow. Remote microphone probes (RMP) provide advantages compared to flush-mounted probes because of their reduced sensing area. However, they feature a distinct transfer function (TF) that needs to be taken into account for accurate pressure measurements. The empirical calibration of the probes, e.g., using plane-wave tubes, can introduce spurious resonant frequencies into the TF due to a lack of control of the pressure field inside the calibrator over the multiple calibration steps. Current processing methods of calibration data tend to be manual and strongly related to the operator’s expertise. Depending on the processing, spurious resonance may remain in a given frequency band, or some resonance that is characteristic of the probe may wrongfully be removed. All errors in the TF inadvertently propagate to the measurements performed with the calibrated probe. In this study, a semi-empirical calibration method is proposed with the aim of removing the spurious resonance in a physics-driven manner that is less reliant on the operator. Bayesian inversion is used to fit an analytic model for the TF of the RMP to the empirical calibration data. An inviscid acoustic finite-element method (FEM) simulation serves as a benchmark dataset. As such, the semi-empirical calibration procedure can be tested in an idealized environment. The proposed method is shown to be capable of providing a highly accurate fit to the benchmark data, with much less operator intervention than current processing methods. Its application to experimental calibration data and wall-pressure measurements appears to be a feasible next step, which is bound to show the full promise and potential of the technique.