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

Abstract

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.

Characterization of Freestream Disturbances in Conventional Hypersonic Wind Tunnels

“…A new modal decomposition method was proposed to decompose hot-wire and pitot-probe measurements of freestream disturbances into the three Kovasznay modes (i.e., acoustic, entropy, and vorticity modes). By replacing the pitot-probe transfer function by Stainback and Wagner [33] with the DNS-predicted pitot-probe transfer function by Schilden and Schröder [40], the new combined modal decomposition method can yield rms values of modal amplitudes within a selected frequency band. In all, the joint effort of the specialists group has resulted in a significantly improved knowledge base pertaining to the nature and spectral contents of windtunnel freestream disturbances, with the purpose of quantifying the stochastic input to the receptivity process in a broadband disturbance environment of conventional, cold-flow hypersonic wind tunnels.…”

“…This modal decomposition method was based on total pressure and stagnation point heat flux fluctuations to decompose freestream disturbances via a sensitivity matrix containing transfer functions between the measured quantities and acoustic and entropy mode computed in DNS. Schilden and Schröder [40] showed that the proposed method is limited to a very low Strouhal number of the incident disturbances (i.e., the heat flux probe has to be very small to perceive essential postshock entropy modes). At this point, the hot wire is a promising alternative to the rather large SPP because it is basically a very small heat flux probe.…”

“…At this point, the hot wire is a promising alternative to the rather large SPP because it is basically a very small heat flux probe. On the other hand, the transfer functions of Schilden and Schröder [40] or Chaudhry and Candler [34] relating postshock total pressure to preshock acoustic and entropy disturbances could be used to replace the transfer function of Stainback and Wagner [33] in the hot-wire method. Therefore, the hot-wire and SPP modal decomposition methods can be merged.…”

Numerical Investigation of Roughness Effects on Transition on Spherical Capsules

“…For supersonic flows, the code has been employed and validated for the flow past a cone and around a blunt stagnation point probe. 36,37 The DNS by the Technical University of Munich (TUM) are performed using the Navier Stokes Multi Block solver (NSMB). NSMB is an MPI-parallelized, finite-volume code for structured grids with a wide variety of numerical schemes and it has been extensively tested in studies of hypersonic flows.…”

Characterization of Freestream Disturbances in Conventional Hypersonic Wind Tunnels

“…This modal decomposition method was based on total pressure and stagnation point heat flux fluctuations to decompose freestream disturbances via a sensitivity matrix containing transfer functions between the measured quantities and acoustic and entropy mode computed in DNS. Schilden and Schröder [40] showed that the proposed method is limited to very low Strouhal number of the incident disturbances, i.e., the heat flux probe has to be very small to perceive essential postshock entropy modes. At this point the hot-wire is a promising alternative to the rather large SPP since it is basically a very small heat flux probe.…”