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Description
Background
The state of the boundary layer has a large role in the investigation of high-speed flow fields for aerospace applications. A turbulent boundary layer causes heat flux on the surface of a hypersonic vehicle to dramatically increase when compared to the laminar case. Performance is also impacted by boundary layer turbulence due to increased skin friction drag, and fluid-structure interactions may impose harsher structural and environmental constraints than those in the laminar flow.
Experimental data on high-speed boundary layer transition and turbulence obtained in shock tubes or shock tunnels is fundamental to advance the current understanding of the underlying phenomena. Many of the widely used low-order computational models have been developed and calibrated for low-speed flows, requiring correction approaches to be expanded into the high-speed domain. Higher-fidelity computations, such as Large Eddy Simulation (LES), still require turbulence models to emulate the flow field at its smallest scales, and Direct Numerical Simulation (DNS) of complex, three-dimensional flow fields is still computationally challenging.
However, when collecting the experimental data for such application, the effects of free stream disturbances inevitably produced by a conventional shock tunnel itself must not be neglected. These disturbances include, for example, acoustic fluctuations radiated from the turbulent boundary layer of the nozzle [1]. Disturbances of acoustic nature are known to be amplified in the boundary layer on the test model and cause transition to occur much earlier than in flight, even though the exact governing mechanisms are still not fully understood.
In order to enable the best use of experimental observations conducted in conventional shock tubes or shock tunnels and support the interpretation of data obtained in different facilities, it is therefore important to quantify the free stream environment, in terms of inherent acoustic disturbances. Among the most widely used techniques to that end are hot-wire anemometry (HWA) and pitot probes. However, HWA faces many challenges for application in short-time impulse facilities, such as a limited bandwidth, excessive total temperature, and environmental conditions that may be compromising for the delicate hot wires. Pitot probes require accounting for damping effects of protective cavities and possible effects of the probe geometry, which is not standardized [2].
In the present work, free stream disturbance measurements in a shock tunnel are presented using the alternative technique of Focused Laser Differential Interferometry (FLDI). FLDI is a non-intrusive technique capable of detecting density fluctuations up to remarkably small scales at high frequency in high-speed flow fields.
Methodology
The experiments are conducted in the High Enthalpy Shock Tunnel Göttingen (HEG) of the German Aerospace Center (DLR). HEG is a free-piston shock tunnel, capable of generating a range of hot free stream conditions equivalent to atmospheric flight at multiple altitudes [3]. Free stream density disturbances are obtained in the present work for free stream unit Reynolds numbers of approximately 1.5e6, 2.2e6, and 2.4e6 1/m, and total enthalpies of 11.9, 9.8, and 3.5 MJ/kg, respectively.
The FLDI setup uses an Oxxius LCX-532S DPSS, 532 nm continuous wavelength laser, expanded to approximately 45 mm diameter and focused on a plane 1920 mm away from the field lens. Sanderson prisms are used to produce the differentiation pair, which are separated by 175 μm. The probing pair is multiplied into a 6-by-1 multi-foci array, by means of a diffractive optical element (DOE). The DOE is positioned in the optical setup such that all 6 FLDI probes maintain parallelism between each other across the test section. Both the differentiation axis and the axis containing the multiple independent probes are oriented in the streamwise direction and coincident to the center axis of the nozzle. Detection is performed by means of Thorlabs DET36A2 photodetectors at 25 MHz, using 25x amplification provided by SRS SR445A DC-350 MHz preamplifiers.
The FLDI data is post-processed to account for the wavelength-dependent sensitivity length, assuming a uniform flow field in the nozzle core region. Density fluctuations are transformed into pressure fluctuations assuming isentropic conditions.
Results
Free stream fluctuations in terms of FLDI phase shift spectra will be shown. In this data, the lower and upper frequency bounds of the FLDI instrument are identified. Convection velocities are calculated by cross-correlating the time signals from the streamwise FLDI probes, which are separated by a known distance. Using the obtained convection velocities, the frequency bounds are converted into the smaller and larger detected disturbance wavelengths.
RMS values of density and pressure fluctuations will be calculated from the post-processed FLDI data within the identified frequency bounds. The RMS of pressure fluctuation will be compared with measurements performed in a previous work using pressure transducers in a wedge probe in HEG [2], for the free stream unit Reynolds number 2.4e6 1/m case. The spectra of the pressure fluctuations for all cases will also be shown, and the effect of Reynolds number and total enthalpy will be analyzed.
Conclusion
This work presents measurements of free stream acoustic disturbances using a multi-foci Focused Laser Differential Interferometer (FLDI) in the free-piston shock tunnel HEG of the German Aerospace Center (DLR).
The ease of implementation of FLDI and its clean view of the disturbance spectrum make it a promising candidate technique for the standardization of free stream disturbance measurements, aiming at improving the interpretation and comparison of boundary layer data across different facilities.
References
[1] L. Duan et al. “Characterization of Freestream Disturbances in Conventional Hypersonic Wind Tunnels”. Journal of Spacecraft and Rockets 56.2 (Mar. 2019), pp. 357–368. DOI: 10.2514/1.a34290.
[2] A. Wagner et al. “Combined free-stream disturbance measurements and receptivity studies in hypersonic wind tunnels by means of a slender wedge probe and direct numerical simulation”. Journal of Fluid Mechanics 842 (Mar. 2018), pp. 495–531. DOI: 10.1017/jfm.2018.132.
[3] Deutsches Zentrum für Luft- und Raumfahrt (DLR). “The High Enthalpy Shock Tunnel Göttingen of the German Aerospace Center (DLR)”. Journal of large-scale research facilities 4, A133 (Oct. 2018). DOI: 10.17815/jlsrf-4-168.
Summary
In the present work, free stream disturbance measurements in a shock tunnel are presented using the technique of Focused Laser Differential Interferometry (FLDI). The measurements are aimed at quantifying the free stream environment in terms of inherent acoustic disturbances. The experiments are conducted in the High Enthalpy Shock Tunnel Göttingen (HEG) of the German Aerospace Center (DLR) under free stream unit Reynolds numbers of approximately 1.5e6, 2.2e6, and 2.4e6 1/m, and total enthalpies of 11.9, 9.8, and 3.5 MJ/kg, respectively. The FLDI is a 6-by-1 multi-foci setup, distributed in the streamwise direction. The measurements are compared to previous data obtained in HEG using pressure transducers in a wedge probe, and the effect of Reynolds number and total enthalpy are analyzed.
