Recovery of Pre-shock Acoustic Disturbances From Post-shock Pitot Pressure Fluctuations

Freestream disturbances in a supersonic/hypersonic wind tunnel pass through the bow shock of a Pitot probe before being measured by the transducer. In this study, linear interaction analysis (LIA) and iterative ensemble Kalman method are used to recover the pre-shock static pressure spectrum and wave angle from the transducer-measured Pitot-pressure timeseries. Specifically, the LIA is used as the forward model for the transfer function associated with a homogeneous field of acoustic waves passing through a nominally normal shock wave. The iterative ensemble Kalman method is then employed to infer the spectrum of upstream acoustic waves based on the post-shock Pitot pressure measured at an array of spatially sparse points. Several test cases with synthetic and real measurement data are used to demonstrate the merits of the proposed inference scheme. The study provides the basis for measuring tunnel freestream noise with intrusive probes in noisy supersonic wind tunnels.