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Inclined slow acoustic waves incident to stagnation point probes in supersonic flow

Published online by Cambridge University Press:  13 March 2019

Thomas Schilden Open the ORCID record for Thomas Schilden [Opens in a new window]  and
Wolfgang Schröder
Thomas Schilden*
Affiliation:
Institute of Aerodynamics, RWTH Aachen University, 52062 Aachen, Germany
Wolfgang Schröder
Affiliation:
Institute of Aerodynamics, RWTH Aachen University, 52062 Aachen, Germany Forschungszentrum Jülich, 52425 Jülich, JARA High-Performance Computing, Germany
*
†Email address for correspondence: t.schilden@aia.rwth-aachen.de
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Abstract

Tunnel noise in supersonic testing facilities is known to be a decisive factor in boundary layer transition experiments. It defines initial conditions for the growth of modal instabilities by the receptivity mechanism. That is, to interpret experimental results, the determination of tunnel noise is of crucial importance. It is common to use stagnation point probes equipped with pressure transducers in supersonic flows, but since tunnel noise undergoes modulation during the measurement, the probes must be calibrated. The predominant component of tunnel noise is caused by the nozzle boundary layer which radiates highly inclined slow acoustic waves. Therefore, the calibration of stagnation point probes for these disturbances is essential. For quasi-steady deviations from the free stream, an analytic reduced-order method holds. A corresponding conflicting model derived by Stainback & Wagner (1972, AIAA Paper 72-1003) is revised and corrected. Inclined slow acoustic waves generate higher pressure perturbations at the probe than non-inclined waves. In general, costly three-dimensional direct numerical simulations can be used for calibration. In this study, however, new axisymmetric boundary conditions are proposed to reduce the problem to two dimensions to efficiently investigate the detection of incident inclined slow acoustic waves by stagnation point probes. A cylindrical probe with a rounded edge is investigated in supersonic flow at a Mach number $Ma=5.9$. For the inclination angle of radiated slow acoustic waves, stagnation point pressure fluctuations abruptly decay with increasing Strouhal number and a similar behaviour can be seen at constant Strouhal number with increasing inclination angle. Two simple criteria for the onset of decay based on the radial wavenumber are deduced. Furthermore, stagnation point pressure fluctuations were decomposed into an initial pulse impact and resonant amplification to separately investigate the effects. The initial pulse determines the overall pressure signal. At high inclination angles, a new mechanism for resonance caused by a surface pressure wave travelling at the phase speed of the incident wave was found to supersede resonance caused by oscillating acoustic waves prevailing at low inclination angles.

JFM classification

Compressible Flows: Gas dynamics Aerodynamics: High-speed flow Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 866 , 10 May 2019 , pp. 567 - 597
Copyright
© 2019 Cambridge University Press 

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References

Ali, S. R. C., Zárate Cárdenas, R., Radespiel, R., Schilden, T. & Schröder, W. 2018 Stagnation point probes in hypersonic flow. In New Results in Numerical and Experimental Fluid Mechanics XI, Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol. 136, pp. 117–127. Springer.Google Scholar
Bouslog, S. A., An, M. Y., Hartmann, L. N. & Derry, S. M.1991 Review of boundary layer transition flight data on the space shuttle orbiter. AIAA Paper 91-0741.Google Scholar
Chaudhry, R. S. & Candler, G. V. 2017 Computing measured spectra from hypersonic pitot probes with flow-parallel freestream disturbances. AIAA J. 55 (12), 4155–4166.Google Scholar
Duan, L. & Choudhari, M. M.2013 Numerical study of pressure fluctuations due to a mach 6 turbulent boundary layer. AIAA Paper 2013-0532.Google Scholar
Duan, L., Choudhari, M. M., Chou, A., Muñoz, F., Ali, S. R. C., Radespiel, R., Schilden, T., Schröder, W., Marineau, E. C., Casper, K. M. et al. 2018 Characterization of freestream disturbances in conventional hypersonic wind tunnels. AIAA Paper 2018-0347.Google Scholar
Duan, L., Choudhari, M. M. & Wu, M. 2014 Numerical study of acoustic radiation due to a supersonic turbulent boundary layer. J. Fluid Mech. 746, 165–192.Google Scholar
Fedorov, A. V. 2003 Receptivity of a high-speed boundary layer to acoustic disturbances. J. Fluid Mech. 491, 101–129.Google Scholar
Fedorov, A. V. 2011 Transition and stability of high-speed boundary layers. Annu. Rev. Fluid. Mech. 43, 79–95.Google Scholar
Fedorov, A. V., Ryzhov, A. A., Soudakov, V. G. & Utyuzhnikov, S. V. 2013 Receptivity of a high-speed boundary layer to temperature spottiness. J. Fluid Mech. 722, 533–553.Google Scholar
Hartmann, D., Meinke, M. & Schröder, W. 2008 An adaptive multilevel multigrid formulation for cartesian hierarchical grid methods. Comput. Fluids 37, 1103–1125.Google Scholar
Hein, S., Theiss, A., Di Giovanni, A., Schilden, T., Schröder, W., Paredes, P., Choudhari, M. M., Li, F. & Reshotko, E.2018 Numerical investigation of roughness effects on transition on spherical capsules. AIAA Paper 2018-0058.Google Scholar
Huang, J., Zhang, C., Duan, L. & Choudhari, M. M.2017 Direct numerical simulation of hypersonic turbulent boundary layers inside an axisymmetric nozzle. AIAA Paper 2017-0067.Google Scholar
Khan, M. M. S. & Reshotko, E. 1980 Stability of the laminar boundary layer on a blunted plate in supersonic flow. In Laminar-Turbulent Transition (ed. Eppler, R. & Fasel, H.), pp. 186–200. Springer.Google Scholar
Kovasznay, L. S. G.1953 Turbulence in supersonic flow. AIAA Paper 53-682.Google Scholar
Laufer, J. 1961 Aerodynamic noise in supersonic wind tunnels. J. Aero. Sci. 28 (9), 658–692.Google Scholar
Laufer, J. 1964 Some statistical properties of the pressure field radiated by a turbulent boundary layer. Phys. Fluids 7, 1191–1197.Google Scholar
Lin, T. C., Grabowsky, W. R. & Yelmgren, K. E. 1984 The search for optimum configurations for re-entry vehicles. J. Spacecr. Rockets 21 (2), 142–149.Google Scholar
Lintermann, A., Schlimpert, S., Grimmen, J. H., Günther, C., Meinke, M. & Schröder, W. 2014 Massively parallel grid generation on HPC systems. Comput. Meth. Appl. Mech. Engng 277, 131–153.Google Scholar
Logan, P.1988 Modal analysis of hot-wire measurements in supersonic turbulence. AIAA Paper 88-0423.Google Scholar
Ma, Y. & Zhong, X. 2003a Receptivity of a supersonic boundary layer over a flat plate. Part 1. Wave structures and interactions. J. Fluid Mech. 488, 31–78.Google Scholar
Ma, Y. & Zhong, X. 2003b Receptivity of a supersonic boundary layer over a flat plate. Part 2. Receptivity to free-stream sound. J. Fluid Mech. 488, 79–121.Google Scholar
Ma, Y. & Zhong, X. 2005 Receptivity of a supersonic boundary layer over a flat plate. Part 3. Effects of different type of free-stream disturbances. J. Fluid Mech. 532, 63–109.Google Scholar
McKenzie, J. F. & Westphal, K. O. 1968 Interaction of linear waves with oblique shock waves. Phys. Fluids 11, 2350–2362.Google Scholar
Moore, F. K.1954 Unsteady oblique interaction of a shock wave with a plane disturbance. NACA Report No. 1165.Google Scholar
Morkovin, M. V. 1960 Note on the assesment of flow disturbances at a blunt body traveling at supersonic speeds owing to flow disturbances in free stream. J. Appl. Mech. 27 (2), 223–229.Google Scholar
Pate, S. R.1977 Dominance of radiated aerodynamic noise on boundary-layer transition in supersonic-hypersonic wind tunnels. PhD thesis, Tennessee University.Google Scholar
Pogorelov, A., Meinke, M. & Schröder, W. 2015 Cut-cell method based large-eddy simulation of tip-leakage flow. Phys. Fluids 27, 075106.Google Scholar
Reshotko, E.1994 Boundary layer instability, transition and control. AIAA Paper 94-0001.Google Scholar
Robinet, J.-Ch. & Casalis, G. 2001 Critical interaction of a shock wave with an acoustic wave. Phys. Fluids 13, 1047–1059.Google Scholar
Schilden, T. & Schröder, W. 2017 Numerical analysis of high speed wind tunnel flow disturbance measurements using stagnation point probes. J. Fluid Mech. 833, 247–273.Google Scholar
Schilden, T., Schröder, W., Ali, S. R. C., Wu, J., Schreyer, A.-M. & Radespiel, R. 2016 Analysis of acoustic and entropy disturbances in a hypersonic wind tunnel. Phys. Fluids 28, 056104.Google Scholar
Schneider, S. P. 2001 Effects of high-speed tunnel noise on laminar-turbulent transition. J. Spacecr. Rockets 38 (3), 323–333.Google Scholar
Schneider, S. P. 2008a Effects of roughness on hypersonic bounday-layer transition. J. Spacecr. Rockets 45, 193–209.Google Scholar
Schneider, S. P. 2008b Summary of hypersonic boundary-layer transition experiments on blunt bodies with roughness. J. Spacecr. Rockets 6, 1090–1105.Google Scholar
Schneiders, L., Günther, C., Meinke, M. & Schröder, W. 2016 An efficient conservative cut-cell method for rigid bodies interacting with viscous compressible flows. J. Comput. Phys. 311, 62–86.Google Scholar
Stainback, P. C. & Wagner, R. D.1972 A comparison of disturbance levels measured in hypersonic tunnels using a hot-wire anemometer and a pitot pressure probe. AIAA Paper 72-1003.Google Scholar
Wurster, K. E.1981 An assessment of the impact of transition on advanced winged entry vehicle thermal protection system mass. AIAA Paper 81-1090.Google Scholar
Zhang, C. & Duan, L.2015 Acoustic radiation from high-speed turbulent boundary layers in a tunnel-like environment. AIAA Paper 2015-0839.Google Scholar
Zhong, X. & Wang, X. 2012 Direct numerical simulation on the receptivity, instability, and transition of hypersonic boundary layers. Annu. Rev. Fluid. Mech. 44, 527–561.Google Scholar