Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-06T10:56:47.322Z Has data issue: false hasContentIssue false
  • English
  • Français

Pressure fluctuations beneath instability wavepackets and turbulent spots in a hypersonic boundary layer

Published online by Cambridge University Press:  09 September 2014

Katya M. Casper ,
Steven J. Beresh  and
Steven P. Schneider
Katya M. Casper*
Affiliation:
Sandia National Laboratories, Albuquerque, NM 87185, USA Department of Aeronautics and Astronautics, Purdue University, West Lafayette, IN 47907, USA
Steven J. Beresh
Affiliation:
Sandia National Laboratories, Albuquerque, NM 87185, USA
Steven P. Schneider
Affiliation:
Department of Aeronautics and Astronautics, Purdue University, West Lafayette, IN 47907, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

To investigate the pressure-fluctuation field beneath turbulent spots in a hypersonic boundary layer, a study was conducted on the nozzle wall of the Boeing/AFOSR Mach-6 Quiet Tunnel. Controlled disturbances were created by pulsed-glow perturbations based on the electrical breakdown of air. Under quiet-flow conditions, the nozzle-wall boundary layer remains laminar and grows very thick over the long nozzle length. This allows the development of large disturbances that can be well-resolved with high-frequency pressure transducers. A disturbance first grows into a second-mode instability wavepacket that is concentrated near its own centreline. Weaker disturbances are seen spreading from the centre. The waves grow and become nonlinear before breaking down to turbulence. The breakdown begins in the core of the packets where the wave amplitudes are largest. Second-mode waves are still evident in front of and behind the breakdown point and can be seen propagating in the spanwise direction. The turbulent core grows downstream, resulting in a spot with a classical arrowhead shape. Behind the spot, a low-pressure calmed region develops. However, the spot is not merely a localized patch of turbulence; instability waves remain an integral part. Limited measurements of naturally occurring disturbances show many similar characteristics. From the controlled disturbance measurements, the convection velocity, spanwise spreading angle, and typical pressure-fluctuation field were obtained.

JFM classification

Aerodynamics: High-speed flow Instability: Instability Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 756 , 10 October 2014 , pp. 1058 - 1091
Copyright
© Cambridge University Press 2014. This is a work of the US Government and is not subject to copyright protection in the United States. 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bane, S. P. M.2010 Spark ignition: experimental and numerical investigation with application to aviation safety. PhD thesis, California Institute of Technology, Graduate Aerospace Laboratories.Google Scholar
Beresh, S. J., Henfling, J. F., Spillers, R. W. & Pruett, B. O. M. 2011 Fluctuating wall pressures measured beneath a supersonic turbulent boundary layer. Phys. Fluids 23, 075110.CrossRefGoogle Scholar
Berridge, D. C.2010 Measurements of second-mode instability waves in hypersonic boundary layers with a high-frequency pressure transducer. Master’s thesis, Purdue University, School of Aeronautics & Astronautics.Google Scholar
Cantwell, B., Coles, D. & Dimotakis, P. 1978 Structure and entrainment in the plane of symmetry of a turbulent spot. J. Fluid Mech. 87, 641–672.CrossRefGoogle Scholar
Casper, K. M.2009 Hypersonic wind-tunnel measurements of boundary-layer pressure fluctuations. Master’s thesis, Purdue University, School of Aeronautics & Astronautics.CrossRefGoogle Scholar
Casper, K. M.2012 Pressure fluctuations beneath turbulent spots and instability wavepackets in a hypersonic boundary layer. PhD thesis, Purdue University School of Aeronautics & Astronautics.Google Scholar
Casper, K. M., Beresh, S. J. & Schneider, S. P.2011a Pressure fluctuations beneath turbulent spots and instability wavepackets in a hypersonic boundary layer. AIAA Paper 2011-372.CrossRefGoogle Scholar
Casper, K. M., Beresh, S. J. & Schneider, S. P.2011b Spanwise growth of the turbulent spot pressure-fluctuation field in a hypersonic boundary layer. AIAA Paper 2011-3873.Google Scholar
Casper, K. M., Beresh, S. J. & Schneider, S. P.2012 Characterization of controlled perturbations in a hypersonic boundary layer. AIAA Paper 2012-281.CrossRefGoogle Scholar
Chambers, F. & Thomas, A. 1983 Turbulent spots, wavepackets, and growth. Phys. Fluids 26 (5), 1160–1162.Google Scholar
Ching, C. Y. & LaGraff, J. E. 1995 Measurements of turbulent spot convection rates in a transitional boundary layer. Exp. Therm. Fluid Sci. 11, 52–60.Google Scholar
Corrsin, S. & Kistler, A. L.1955 Free-stream boundaries of turbulent flows. NACA Tech. Rep. 1244. (supersedes NACA TN 3133).Google Scholar
Dennis, D. J. C. & Nickels, T. B. 2008 On the limitations of Taylor’s hypothesis in constructing long structures in a turbulent boundary layer. J. Fluid Mech. 614, 197–206.CrossRefGoogle Scholar
Dhawan, S. & Narasimha, R. 1958 Some properties of boundary layer flow during the transition from laminar to turbulent motion. J. Fluid Mech. 3 (4), 418–435.CrossRefGoogle Scholar
Estorf, M., Radespiel, R., Schneider, S. P., Johnson, H. & Hein, S.2008 Surface-pressure measurements of second-mode instability in quiet hypersonic flow. AIAA Paper 2008-1153.Google Scholar
Fiala, A., Hillier, R., Mallinson, S. G. & Wijesinghe, H. S. 2006 Heat transfer measurement of turbulent spots in a hypersonic blunt-body boundary layer. J. Fluid Mech. 555, 81–111.Google Scholar
Fischer, M. C. 1972 Spreading of a turbulent disturbance. AIAA J. 10 (7), 957–959.CrossRefGoogle Scholar
Fujii, K. 2006 Experiment of two-dimensional roughness effect on hypersonic boundary-layer transition. J. Spacecr. Rockets 43 (4), 731–738.CrossRefGoogle Scholar
Gad-el Hak, M., Blackwelder, R. & Riley, J. 1981 On the growth of turbulent regions in laminar boundary layers. J. Fluid Mech. 110, 73–95.CrossRefGoogle Scholar
Glezer, A., Katz, Y. & Wygnanski, I. 1989 On the breakdown of the wavepacket trailing a turbulent spot in a laminar boundary layer. J. Fluid Mech. 198, 1–26.CrossRefGoogle Scholar
Gutmark, E. & Blackwelder, R. F. 1987 On the structure of a turbulent spot in a heated boundary layer. Exp. Fluids 5, 217–229.Google Scholar
Haidari, A. & Smith, D. 1994 The generation and regeneration of single hairpin vortices. J. Fluid Mech. 277, 135–162.CrossRefGoogle Scholar
Harris, J. E. & Blanchard, D. K.1982 Computer program for solving laminar, transitional, or turbulent compressible boundary-layer equations for two-dimensional and axisymmetric flow. NASA TM 83207.Google Scholar
Hedley, T. B. & Keffer, J. F. 1974 Turbulent/non-turbulent decisions in an intermittent flow. J. Fluid Mech. 64, 625–644.CrossRefGoogle Scholar
Houbolt, J. C.1966 On the estimation of pressure fluctuations in boundary layers and wakes. General Electric Report TIS 66SD296.Google Scholar
James, C. S.1958 Observations of turbulent-burst geometry and growth in supersonic flow. NACA TN 4235.Google Scholar
Johansson, A., Her, J. & Haritonidus, J. 1987 On the generation of high-amplitude wall-pressure peaks in turbulent boundary layers and spots. J. Fluid Mech. 175, 119–142.CrossRefGoogle Scholar
Johnson, C. B., Stainback, P. C., Wicker, K. C. & Boney, L. R.1972 Boundary-layer edge conditions and transition Reynolds number data for a flight test at Mach 20 (Reentry F). NASA TM X-2584.Google Scholar
Joksch, A. & Kleiser, L. 2008 Growth of turbulent spots in high-speed boundary layers on a flat plate. Intl J. Heat Fluid Flow 29, 1543–1557.Google Scholar
Juliano, T., Segura, R., Borg, M., Casper, K., Hannon, M., Wheaton, B. & Schneider, S.2008 Starting issues and forward-facing cavity resonance in a hypersonic quiet tunnel. AIAA Paper 2008-3735.Google Scholar
Katz, Y., Seifert, A. & Wygnanski, I. 1990 On the evolution of the turbulent spot in a laminar boundary layer with a favourable pressure gradient. J. Fluid Mech. 221, 1–22.CrossRefGoogle Scholar
Keyes, F. G. 1951 A summary of viscosity and heat-conduction data for He, A, $\mathrm{H}_2, \mathrm{O}_2, \mathrm{N}_2$ , CO, $\mathrm{CO}_2, \mathrm{H}_2 \mathrm{O}$ , and air. Trans. ASME 73, 589–596.Google Scholar
Kimmel, R. L., Demetriades, A. & Donaldson, J.1995 Space–time correlation measurements in a hypersonic transitional boundary layer. AIAA Paper 95-2292.Google Scholar
Kimmel, R. L. & Kendall, J. M.1991 Nonlinear disturbances in a hypersonic laminar boundary layer. AIAA Paper 1991-0320.CrossRefGoogle Scholar
Krishnan, L. & Sandham, N. D. 2006a Effect of Mach number on the structure of turbulent spots. J. Fluid Mech. 566, 225–234.CrossRefGoogle Scholar
Krishnan, L. & Sandham, N. D. 2006b On the merging of turbulent spots in a supersonic boundary layer flow. Intl J. Heat Fluid Flow 27, 542–550.Google Scholar
Ladoon, D. W.1998 Wavepackets generated by a surface glow discharge on a cone at Mach 4. PhD thesis, Purdue University, School of Aeronautics & Astronautics.Google Scholar
Lagraff, J. E. & Jones, T. V.1995 Turbulent spot growth rates and generation in a compressible boundary layer. AFOSR TR 96-0070 (citation ADA304396 in DTIC).Google Scholar
Mack, L. M.1984 Boundary layer linear stability theory. In Report 709, Special Course on Stability and Transition of Laminar Flow, pp. 1–81. AGARD.Google Scholar
Makita, H. & Nishizawa, A. 2001 Characteristics of internal vortical structures in a merged turbulent spot. J. Turbul. 2 (12), 1–14.CrossRefGoogle Scholar
Mautner, T. S.1983 Investigation of the wall pressure, wall shear stress and velocity fields associated with a turbulent spot in a laminar boundary layer. PhD thesis, University of California, San Diego.CrossRefGoogle Scholar
Mautner, T. S.1988 Comparison of the wall pressure fluctuations in artificially generated turbulent spots, natural transition and turbulent boundary layers. AIAA Paper 1988-0409.Google Scholar
Mautner, T. S. & Van Atta, C. W. 1982 An experimental study of the wall-pressure field associated with a turbulent spot in a laminar boundary layer. J. Fluid Mech. 118, 59–77.CrossRefGoogle Scholar
Mee, D. J. 2002 Boundary-layer transition measurements in hypervelocity flows in a shock tunnel. AIAA J. 40 (8), 1542–1548.Google Scholar
Mee, D. J. & Goyne, C. P. 1996 Turbulent spots in boundary layers in a free-piston shock-tunnel flow. In Shock Waves, vol. 6, pp. 337–343. Springer.Google Scholar
Narasimha, R. 1985 The laminar-turbulent transition zone in the boundary layer. Prog. Aerosp. Sci. 22, 29–80.CrossRefGoogle Scholar
Park, S. & Lauchle, G. 2009 Wall pressure fluctuation spectra due to boundary-layer transition. J. Sound Vib. 319, 1067–1082.Google Scholar
Pate, S. R. & Brown, M. D.1969 Acoustic measurements in supersonic transitional boundary layers. AEDC TR 69-182.Google Scholar
Raman, K. R.1974 A study of surface pressure fluctuations in hypersonic turbulent boundary layers. NASA Contractor Rep. 2386.CrossRefGoogle Scholar
Redford, J. A., Sandham, N. D. & Roberts, G. T. 2012 Numerical simulations of turbulent spots in supersonic boundary layers: effects of Mach number and wall temperature. Prog. Aerosp. Sci. 52, 67–79.CrossRefGoogle Scholar
Riley, J. J. & Gad-el Hak, M. 1984 The dynamics of turbulent spots. In Frontiers in Fluid Mechanics (ed. Davis, S. H. & Lumley, J. L.), pp. 123–155. Springer.Google Scholar
Sankaran, R. & Antonia, R. A. 1988 Influence of a favorable pressure gradient on the growth of a turbulent spot. AIAA J. 26 (7), 885–887.CrossRefGoogle Scholar
Sankaran, R., Sokolov, M. & Antonia, R. 1988 Substructures in a turbulent spot. J. Fluid Mech. 197, 389–414.CrossRefGoogle Scholar
Savas, O.1979 Some measurements in synthetic turbulent boundary layers. PhD thesis, California Institute of Technology, Graduate Aeronautical Laboratories.Google Scholar
Schneider, S. P.1998 Design of a Mach-6 quiet-flow wind-tunnel nozzle using the $\mathrm{e}^{**}\mathrm{N}$ method for transition estimation. AIAA Paper 98-0547.Google Scholar
Schneider, S. 2000 Laminar-flow design for a Mach-6 quiet-flow wind tunnel nozzle. Curr. Sci. 79 (6), 790–799.Google Scholar
Schneider, S. P. 2008 The development of hypersonic quiet tunnels. J. Spacecr. Rockets 45 (4), 641–664.Google Scholar
Schubauer, G. B. & Klebanoff, P. S.1955 Contributions on the mechanics of boundary-layer transition. NACA Rep. 1289.Google Scholar
Seifert, A. & Wygnanski, I. 1995 On turbulent spots in a laminar boundary layer subjected to a self-similar adverse pressure gradient. J. Fluid Mech. 296, 185–209.CrossRefGoogle Scholar
Seifert, A., Zilberman, M. & Wygnanski, I. 1994 On the simultaneous measurements of two velocity components in the turbulent spot. J. Engng Maths 28, 43–54.Google Scholar
Singer, B. 1996 Characteristics of a young turbulent spot. Phys. Fluids 8 (2), 509–521.Google Scholar
Sivasubramanian, J. & Fasel, H. F.2010a Direct numerical simulation of a turbulent spot in a cone boundary layer at Mach 6. AIAA Paper 2010-4599.Google Scholar
Sivasubramanian, J. & Fasel, H. F.2010b Numerical investigation of boundary-layer transition initiated by a wavepacket for a cone at Mach 6. AIAA Paper 2010-900.Google Scholar
Sivasubramanian, J. & Fasel, H. F.2011 Transition initiated by a localized disturbance in a hypersonic flat-plate boundary layer. AIAA Paper 2011-374.CrossRefGoogle Scholar
Steen, L. E.2010 Characterization and development of nozzles for a hypersonic quiet wind tunnel. Master’s thesis, Purdue University, School of Aeronautics & Astronautics.Google Scholar
Taylor, G. I. 1938 The spectrum of turbulence. Proc. R. Soc. Lond. A 164, 476–490.CrossRefGoogle Scholar
Vinod, N. 2007 The signature of laminar instabilities in the zone of transition to turbulence. J. Turbul. 8 (2).Google Scholar
Wadhams, T. P., Mundy, E., MacLean, M. G. & Holden, M. S. 2008 Ground test studies of the HIFIRE-1 transition experiment part 1: experimental results. J. Spacecr. Rockets 45 (6), 1134–1148.Google Scholar
Wheaton, B.2009 Roughness-induced instability in a laminar boundary layer at Mach 6. Master’s thesis, Purdue University, School of Aeronautics & Astronautics.Google Scholar
Wygnanski, I., Sokolov, M. & Friedman, D. 1976 On a turbulent ‘spot’ in a laminar boundary layer. J. Fluid Mech. 78, 785–819.Google Scholar
Wygnanski, I., Zilberman, M. & Haritonidis, J. 1982 On the spreading of a turbulent spot in the absence of a pressure gradient. J. Fluid Mech. 123, 69–90.Google Scholar
Zanchetta, M.1996 Kinetic heating and transition studies at hypersonic speeds. PhD thesis, Imperial College of Science, Technology, and Medicine.Google Scholar
Zharov, V. A., Htun, H. & Khlopkov, Y. I. 2009 Statistical modeling of the turbulent transition in the boundary layer. J. Appl. Mech. Tech. Phys. 50 (5), 742–746.CrossRefGoogle Scholar
Zilberman, M., Wygnanski, I. & Kaplan, R. E. 1977 Transitional boundary layer spot in a fully turbulent environment. Phys. Fluids 20, S258–S271.Google Scholar