Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-29T21:03:16.608Z Has data issue: false hasContentIssue false
  • English
  • Français

Breakdown mechanisms and heat transfer overshoot in hypersonic zero pressure gradient boundary layers

Published online by Cambridge University Press:  01 August 2013

Kenneth J. Franko  and
Sanjiva K. Lele
Kenneth J. Franko
Affiliation:
Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305, USA
Sanjiva K. Lele
Affiliation:
Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

A laminar Mach 6 flat plate boundary layer is perturbed using three different types of disturbances introduced through blowing and suction. The linear and nonlinear development and eventual breakdown to turbulence are investigated using direct numerical simulation. The three different transition mechanisms compared are first mode oblique breakdown, second mode oblique breakdown and second mode fundamental resonance. The focus of the present work is to compare the nonlinear development and breakdown to turbulence for the different transition mechanisms and explain the heat transfer overshoot observed in experiments. First mode oblique breakdown leads to the shortest transition length and a clear peak in wall heat transfer in the transitional region. For all three transition mechanisms, the development of streamwise streaks precedes the breakdown to fully turbulent flow. The modal linear and nonlinear development are analysed including the breakdown of the streaks. The effect of wall cooling is investigated for second mode fundamental resonance and no qualitative differences in the nonlinear processes are observed. Finally, the development towards fully turbulent flow including mean flow, turbulent spectra, and turbulent fluctuations is shown and the first mode oblique breakdown simulation shows the furthest development towards a fully turbulent flow.

JFM classification

Compressible Flows: Compressible boundary layers Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulent transition
Type
Papers
Information
Journal of Fluid Mechanics , Volume 730 , 10 September 2013 , pp. 491 - 532
Copyright
©2013 Cambridge University Press 

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

Adams, N. A. & Kleiser, L. 1996 Subharmonic transition to turbulence in a flat plate boundary layer at Mach number 4.5. J. Fluid Mech. 317, 301–335.CrossRefGoogle Scholar
Alba, C. R., Casper, K. M., Beresh, S. J. & Schneider, S. P. 2010 Comparison of experimentally measured and computed second-mode disturbances in hypersonic boundary-layers. AIAA Paper 2010-897.Google Scholar
Andersson, P., Brandt, L., Bottaro, A. & Henningson, D. S. 2001 On the breakdown of boundary layer streaks. J. Fluid Mech. 428, 29–60.CrossRefGoogle Scholar
Beam, R. M. & Warming, R. F. 1978 An implicit factored scheme for compressible Navier–Stokes equations. AIAA J. 16, 393–402.CrossRefGoogle Scholar
Bhaskaran, R. 2010 Large eddy simulation of high pressure turbine cascade. PhD thesis, Stanford University, Stanford, CA.Google Scholar
Bradshaw, P. 1977 Compressible turbulent shear layers. Annu. Rev. Fluid Mech. 9, 33–54.Google Scholar
Brandt, L. & Henningson, D. S. 2002 Transition of streamwise streaks in zero-pressure-gradient boundary layers. J. Fluid Mech. 472, 229–261.CrossRefGoogle Scholar
Chou, A., Ward, C. A. C., Letterman, L. E., Luersen, R. P. K., Borg, M. P. & Schneider, S. P. 2011 Transition research with temperature-sensitive paints and in the Boeing/AFOSR Mach-6 quiet tunnel. AIAA Paper 2011-3872.CrossRefGoogle Scholar
Collis, S. S. 1997 A computational investigation of receptivity in high-speed flow near a swept leading-edge. PhD thesis, Stanford University.Google Scholar
Cook, A. W. & Cabot, W. H. 2004 A high-wavenumber viscosity for high-resolution numerical methods. J. Comput. Phys. 195, 594–601.Google Scholar
Cook, A. W. & Cabot, W. H. 2005 Hyperviscosity for shock–turbulence interactions. J. Comput. Phys. 203, 379–385.Google Scholar
Cossu, C., Brandt, L., Bagheri, S. & Henningson, D. S. 2011 Secondary threshold amplitudes for sinuous streak breakdown. Phys. Fluids 23, 074103.CrossRefGoogle Scholar
Dhawan, S. & Narasimha, R. 1958 Some properties of boundary layer flow during transition from laminar to turbulent motion. J. Fluid Mech. 3, 418–436.Google Scholar
Duan, L., Beekman, I. & Martin, M. P. 2010 Direct numerical simulation of hypersonic turbulent boundary layers with varying free stream Mach number. AIAA Paper 2010-353.CrossRefGoogle Scholar
Duan, L., Beekman, I. & Martin, M. P. 2011 Direct numerical simulation of hypersonic turbulent boundary layers. Part 3. Effect of Mach number. J. Fluid Mech. 672, 245–267.CrossRefGoogle Scholar
Fedorov, A. V. 2003 Receptivity of a high-speed boundary layer to acoustic disturbances. J. Fluid Mech. 491, 101–129.CrossRefGoogle Scholar
Fedorov, A. V. 2011 Transition and stability of high-speed boundary layers. Annu. Rev. Fluid Mech. 43, 79–95.CrossRefGoogle Scholar
Fernholz, H. H. & Finley, P. J. 1996 The incompressible zero pressure gradient boundary layer: an assessment of the data. Prog. Aerosp. Sci. 32, 245–311.Google Scholar
Franko, K. 2011 Linear and nonlinear processes in hypersonic boundary layer transition to turbulence. PhD thesis, Stanford University.Google Scholar
Franko, K., Bhaskaran, R. & Lele, S. 2011 Direct numerical simulation of transition and heat-transfer overshoot in a Mach 6 flat plate boundary layer. AIAA Paper 2011-3874.Google Scholar
Guarini, S. E., Moser, R. D., Shariff, K. & Wray, A. 2000 Direct numerical simulation of a supersonic turbulent boundary layer at Mach 2.5. J. Fluid Mech. 414, 1–33.CrossRefGoogle Scholar
Hœpffner, J., Brandt, L. & Henningson, D. S. 2005 Transient growth on boundary layer streaks. J. Fluid Mech. 537, 91–100.Google Scholar
Holden, M. S. 1972 An experimental investigation of turbulent boundary layers at high Mach number. NASA Contractor Rep. 111242.Google Scholar
Hopkins, E. J. & Inouye, M. 1971 An evaluation of theories for predicting turbulent skin friction and heat transfer on flat plates at supersonic and hypersonic Mach numbers. AIAA J. 9, 993–1003.Google Scholar
Horvath, T. J., Berry, S. A. & Hollis, B. R. 2002 Boundary layer transition on slender cones in conventional and low disturbance Mach 6 wind tunnels. AIAA Paper 2002-2743.Google Scholar
Husmeier, F. & Fasel, H. 2007 Numerical investigations of hypersonic boundary layer transition for circular cones. AIAA Paper 2007-3843.CrossRefGoogle Scholar
Jiang, L., Choudhari, M., Chang, C.-L. & Liu, C. 2006 Numerical simulations of laminar–turbulent transition in supersonic boundary layer. AIAA Paper 2006-3224.Google Scholar
Johnsen, E., Larsson, J., Bhagatwala, A. V., Cabot, W. H., Moin, P., Olson, B. J., Rawat, P. S., Shankar, S. K., Sjögreen, B., Yee, H. C., Zhong, X. & Lele, S. K. 2010 Assessment of high-resolution methods for numerical simulations of compressible turbulence with shock waves. J. Comput. Phys. 229, 1213–1237.Google Scholar
Kachanov, Y. S. 1994 Physical mechanisms of laminar-boundary-layer transition. Annu. Rev. Fluid Mech. 26, 411–482.CrossRefGoogle Scholar
Kawai, S., Shankar, S. K. & Lele, S. K. 2010 Assessment of localized artificial diffusivity scheme for large-eddy simulation of compressible turbulent flows. J. Comput. Phys. 229, 1739–1762.Google Scholar
Kimmel, R. L. 1993 Experimental transition zone lengths in pressure gradient in hypersonic flow. In Transitional and Turbulent Compressible Flows (ed. Kral, L. D. & Zang, T. A.). ASME.Google Scholar
Kloker, M. 2002 DNS of transitional boundary-layer flows at sub- and hypersonic speeds. In DGLR Paper JT2002-017, DGLR-Jahrestagung, Stuttgart, Sept. 2002.Google Scholar
Koevary, C., Laible, A., Mayer, C. & Fasel, H. 2010 Numerical simulations of controlled transition for a sharp circular cone at Mach 8. AIAA Paper 2010-4598.Google Scholar
Krishnan, L. & Sandham, N. D. 2006 Effect of Mach number on the structure of turbulent spots. J. Fluid Mech. 566, 225–234.Google Scholar
Lele, S. K. 1992 Compact finite-difference schemes with spectral-like resolution. J. Comput. Phys. 103, 16–42.CrossRefGoogle Scholar
Ma, Y. & Zhong, X. 2003a Receptivity of a supersonic boundary layer over a flat plate. Part 1. Wave structures and interaction. 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 types of free stream disturbances. J. Fluid Mech. 532, 63–109.Google Scholar
Mack, L. M. 1969 Boundary layer stability theory. Jet Propulsion Laboratory document 900-277 (Rev A).Google Scholar
Malik, M. R., Spall, R. E. & Chang, C. L. 1990 Effects of nose bluntness on boundary layer stability and transition. AIAA Paper 1990-0112.Google Scholar
Martin, M. P. 2007 Direct numerical simulation of hypersonic turbulent boundary layers. Part 1. Initialization and comparison with experiments. J. Fluid Mech. 570, 347–364.Google Scholar
Masad, J. A. 1993 Relationship between transition and modes of instability in supersonic boundary layers. NASA Contractor Rep. 4562.Google Scholar
Maslov, A. A., Shiplyuk, A. N., Sidorenko, A. A. & Arnal, D. 2001 Leading-edge receptivity of a hypersonic boundary layer on a flat plate. J. Fluid Mech. 426, 73–94.Google Scholar
Mayer, C. S. J., von Terzi, D. A. & Fasel, H. F. 2011 Direct numerical simulation of complete transition to turbulence via oblique breakdown at Mach 3. J. Fluid Mech. 674, 5–42.Google Scholar
Nagarajan, S. 2004 Leading edge effects in bypass transition. PhD thesis, Stanford University.Google Scholar
Nagarajan, S., Lele, S. K. & Ferziger, J. H. 2003 A robust high-order compact method for large eddy simulation. J. Comput. Phys. 191, 392–419.Google Scholar
Narasimha, R. 1985 The laminar–turbulent transition zone in the boundary layer. Prog. Aerosp. Sci. 22, 29–80.CrossRefGoogle Scholar
Pirozzoli, S., Grasso, F. & Gatski, T. B. 2004 Direct numerical simulation and analysis of a spatially evolving supersonic turbulent boundary layer at $M= 2. 25$ . Phys. Fluids 16, 530–545.Google Scholar
Pruett, C. D. & Chang, C.-L. 1995 Spatial direct numerical simulation of high-speed boundary layer flows. Part 2. Transition on a cone in Mach 8 flow. Theor. Comput. Fluid Dyn. 7, 397–424.CrossRefGoogle Scholar
Roy, C. J. & Blottner, F. G. 2006 Review and assessment of turbulence models for hypersonic flows: 2D/axisymmetric cases. AIAA Paper 2006-713.Google Scholar
Schlatter, P., Brandt, L., de Lange, H. C. & Henningson, D. S. 2008 On streak breakdown in bypass transition. Phys. Fluids 20, 101505.Google Scholar
Schneider, S. P. 2001 Effects of high-speed tunnel noise on laminar–turbulent transition. J. Spacecr. Rockets 38, 323–333.Google Scholar
Sivasubramanian, J. & Fasel, H. F. 2010 Numerical investigation of boundary layer transition initiated by a wave packet for a cone at Mach 6. AIAA Paper 2010-900.CrossRefGoogle Scholar
Stetson, K. F. & Kimmel, R. L. 1992 On hypersonic boundary-layer stability. AIAA Paper 1992-0737.Google Scholar
Stetson, K. F. & Kimmel, R. L. 1993 On the breakdown of a hypersonic laminar boundary layer. AIAA Paper 1993-0896.Google Scholar
Thumm, A., Wolz, W. & Fasel, H. 1990 Numerical simulation of spatially growing three-dimensional disturbance waves in compressible boundary layers. In IUTAM Symposium on Laminar–Turbulent Transition (ed. Arnal, D. & Michel, R.), pp. 303–308. Springer.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, 1134–1148.Google Scholar
Walz, A. 1969 Boundary Layers of Flow and Temperature. MIT.Google Scholar
Wang, M., Lele, S. K. & Moin, P. 1996 Sound radiation during local laminar breakdown in a low-Mach-number boundary layer. J. Fluid Mech. 319, 197–218.Google Scholar
White, F. M. 2006 Viscous Fluid Flow. McGraw-Hill.Google Scholar
Wilkinson, S. P. 1997 A review of hypersonic boundary layer stability experiments in a quiet Mach 6 wind tunnel. AIAA Paper 1997-1819.Google Scholar
Xiong, Z. & Lele, S. K. 2004 Distortion of upstream disturbances in a Hiemenz boundary layer. J. Fluid Mech. 519, 201–232.CrossRefGoogle Scholar