Recovery of freestream disturbance spectrum from stagnation pressure spectrum for hypersonic pitot probes

An investigation of the transfer function of freestream disturbances to measured transducer pressure spectrum is presented. We simulate flow around a variety of probe geometries corresponding to instruments used by hypersonic experimental facilities. The stagnation pressure spectrum measured by the simulated pressure transducer is compared to the forced freestream disturbances to yield the transfer function. Freestream fast acoustic, slow acoustic, and entropy disturbances are each considered. Calculating the transfer function in this way is novel, and we particular attention to validation. The transfer function is found to be a strong function of probe geometry, and a primary resonance related to the shock standoff distance is found. The effect of freestream Reynolds number, stagnation temperature, and Mach number are investigated. A derivation of the Reynolds-decomposed Rayleigh Pitot-tube equation is also presented, which is shown to yield the transfer function in the low-frequency limit and describe the effect of disturbance type. Finally, we present a normalization using only the freestream conditions and shock standff distance which collapses the transfer functions of all pitot probe cases into a single curve.