Numerical analysis of high speed wind tunnel flow disturbance measurements using stagnation point probes

Since supersonic test facilities have tunnel noise that strongly influences boundary layer transition experiments, the determination of tunnel noise is of great significance to properly evaluate and interpret experimental results. The composition of tunnel noise, which consists of acoustic, entropy and vorticity modes, highly influences the boundary layer receptivity. The measurement of the separate modes is a major goal of ongoing research. In this study, the properties of stagnation point probes for a newly developed modal decomposition method for tunnel noise are investigated by direct numerical simulation. Pressure and heat flux responses of a stagnation point probe to various entropy and acoustic mode input functions are analysed to investigate how tunnel noise is perceived by corresponding sensor types. The interaction of the incident mode and the shock wave upstream of the probe is analysed and the resulting wave pattern in the subsonic region between shock wave and probe is evidenced. It is found that pure incident acoustic or entropy modes cause acoustic and entropy waves downstream of the shock wave whose strengths differ depending on the incident mode. The resulting wave pattern downstream of the shock wave is determined by postshock acoustic waves propagating bidirectionally between shock wave and probe. Formulating a model equation linking pressure and heat flux fluctuations to the initially caused postshock acoustic and entropy wave, a criterion for the applicability of stagnation point probes measuring pressure and heat flux fluctuations in the new modal decomposition method can be deduced: to distinguish between the incident mode types based on their pressure and heat flux signal the perception of initially generated entropy waves downstream of the shock wave by the heat flux sensor is crucial. The transfer function between entropy waves and heat flux is shown to have low pass filter characteristics and the cutoff Strouhal number could be estimated by control theory. The analysis of the frequency response to continuous incident waves corroborated this cutoff Strouhal number.

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