Computing Measured Spectra from Hypersonic Pitot Probes with Flow-Parallel Freestream Disturbances

The relationship between freestream disturbances and measured pitot pressure spectra, defined as the transfer function, is investigated. Pitot probes used to characterize hypersonic facilities are considered for a variety of freestream conditions and flow-parallel disturbance types. A method to compute the transfer function using direct numerical simulation is proposed and found to have an uncertainty within 3%. Resonance due to an acoustic disturbance reflecting between the shock and pitot probe face is observed and exhibits increased amplification due to the focusing effect of shock curvature. Pitot probe geometry has the largest impact on resonant frequency, and the effect of mean freestream condition is also quantified. The transfer functions for different freestream disturbance types are found to differ by a constant factor, which is predicted by the analytic form of the transfer function in the low-frequency limit. Finally, using only the stagnation temperature and shock standoff distance, a normalization is found that collapses the results for all cases into a single curve.