Hostname: page-component-745bb68f8f-grxwn Total loading time: 0 Render date: 2025-01-07T19:48:02.608Z Has data issue: false hasContentIssue false
  • English
  • Français

Direct numerical simulations of hypersonic boundary-layer transition for a flared cone: fundamental breakdown

Published online by Cambridge University Press:  25 April 2019

Christoph Hader Open the ORCID record for Christoph Hader [Opens in a new window]  and
Hermann F. Fasel
Christoph Hader*
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ 85721, USA
Hermann F. Fasel
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ 85721, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Direct numerical simulations (DNS) were carried out to investigate the laminar–turbulent transition for a flared cone at Mach 6 at zero angle of attack. The cone geometry of the flared cone experiments in the Boeing/AFOSR Mach 6 Quiet Tunnel (BAM6QT) at Purdue University was used for the simulations. In the linear regime, the largest integrated spatial growth rates ($N$-factors) for the primary instability were obtained for a frequency of approximately $f=300~\text{kHz}$. Low grid-resolution simulations were carried out in order to identify the azimuthal wavenumber that led to the strongest growth rates with respect to the secondary instability for a fundamental and subharmonic resonance scenario. It was found that for the BAM6QT conditions the fundamental resonance is much stronger compared to the subharmonic resonance. Subsequently, for the case which led to the strongest fundamental resonance onset, detailed investigations were carried out using high-resolution DNS. The simulation results exhibit streamwise streaks of very high skin friction and of high heat transfer at the cone surface. Streamwise ‘hot’ streaks on the flared cone surface were also observed in the experiments carried out at the BAM6QT facility using temperature sensitive paint. The presented findings provide strong evidence that the fundamental breakdown is a dominant and viable path to transition for the BAM6QT conditions.

JFM classification

Compressible Flows: Compressible boundary layers Aerodynamics: High-speed flow Instability: Transition to turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 869 , 25 June 2019 , pp. 341 - 384
Copyright
© 2019 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

Bake, S., Meyer, D. G. W. & Rist, U. 2002 Turbulence mechanism in Klebanoff transition: a quantitative comparison of experiment and direct numerical simulation. J. Fluid Mech. 459, 217–243.Google Scholar
Balakumar, P. & Chou, A.2016 Transition prediction in hypersonic boundary layers using receptivity and freestream spectra. In 54th AIAA Aerospace Sciences Meeting. AIAA 2016-0847.Google Scholar
Balakumar, P. & Kegerise, M. A.2010 Receptivity of hypersonic boundary layers over straight and flared cones. In 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition. AIAA 2010-1065.Google Scholar
Berridge, D. C., Chou, A., Ward, C. A. C., Steen, L. E., Gilber, P. L., Juliano, T. J. & Schneider, S. P.2010 Hypersonic boundary-layer transition experiments in a Mach-6 quiet tunnel. In 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition. AIAA 2010-1061.Google Scholar
Berridge, D. C., Ward, C. A. C., Luersen, R. P. K., Chou, A., Abney, A. D. & Schneider, S. P.2012 Boundary-layer instability measurements in a Mach-6 quiet tunnel. In 42nd AIAA Fluid Dynamics Conference and Exhibit. AIAA 2012-3147.Google Scholar
Blanchard, A. E., Selby, G. V. & Wilkinson, S. P.1996 A quiet tunnel investigation of hypersonic boundary-layer stability over a cooled, flared cone. NASA-CR-202200.Google Scholar
Casper, K. M., Beresh, S. J., Henfling, J., Spillers, R. & Pruett, B.2013a High-speed schlieren imaging of disturbances in a transitional hypersonic boundary layer. In 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition. AIAA 2013-0376.Google Scholar
Casper, K. M., Beresh, S. J., Wagnild, R., Henfling, J., Spillers, R. & Pruett, B.2013 $b$ Simultaneous pressure measurements and high-speed schlieren imaging of disturbances in a transitional hypersonic boundary layer. In 43rd AIAA Fluid Dynamics Conference. AIAA 2013-2739.Google Scholar
Chou, A.2010 Characterization of laser-generated perturbations and instability measurements on a flared cone. Master’s thesis, Purdue University.Google Scholar
Chou, A., Ward, C. A. C., Letterman, L. E. & Luersen, R. P. K.2011 Transition research with temperature-sensitive paints in the Boeing/AFOSR Mach-6 quiet tunnel. In 41st AIAA Fluid Dynamics Conference and Exhibit. AIAA 2011-3872.Google Scholar
Chynoweth, B.2015 A New roughness array for controlling the nonlinear breakdown of second-mode waves at Mach 6. Master’s thesis, Purdue University.Google Scholar
Chynoweth, B. C., Ward, C. A. C., Greenwood, R. T., McKiernan, G. R., Fisher, R. A. & Schneider, S. P.2014 $a$ Measuring transition and instabilities in a Mach 6 hypersonic quiet wind tunnel. In 44th AIAA Fluid Dynamics Conference. AIAA 2014-2643.Google Scholar
Chynoweth, B. C., Ward, C. A. C., Henderson, R. O., Moraru, C. G., Greenwood, R. T., Abney, A. D. & Schneider, S. P.2014 $b$ Transition and instability measurements in a Mach 6 hypersonic quiet wind tunnel. In 52nd Aerospace Sciences Meeting. AIAA 2014-0074.Google Scholar
Craik, A. D. D. 1971 Non-linear resonant instability in boundary layers. J. Fluid Mech. 50 (2), 393–413.Google Scholar
Doggett, G. P., Chokani, N. D. & Wilkinson, S. P.1997 Hypersonic boundary-layer stability experiments on a flared-cone model at angle of attack in a quiet wind tunnel. In 35th Aerospace Sciences Meeting and Exhibit. AIAA 1997-0557.Google Scholar
Duan, L., Choudhari, M. M. & Zhang, C. 2016 Pressure fluctuations induced by a hypersonic turbulent boundary layer. J. Fluid Mech. 804, 578–607.Google Scholar
Fasel, H. F. 1976 Investigation of the stability of boundary layers by a finite-difference model of the Navier–Stokes equations. J. Fluid Mech. 78, 355–383.Google Scholar
Fasel, H. F., Sivasubramanian, J. & Laible, A. C. 2015 Numerical investigation of transition in a flared cone boundary layer at Mach 6. Procedia IUTAM 14, 26–35.Google Scholar
Fasel, H. F., Thumm, A. & Bestek, H. 1993 Direct numerical simulation of transition in supersonic boundary layers: oblique breakdown. In Fluids Engineering Conference, ASME.Google Scholar
Gross, A. & Fasel, H. F.2002 High-order WENO schemes based on the Roe approximate Riemann solver. In 32nd AIAA Fluid Dynamics Conference and Exhibit. AIAA 2002-2735.Google Scholar
Gross, A. & Fasel, H. F. 2008 High-order accurate numerical method for complex flows. AIAA J. 46 (1), 204–214.Google Scholar
Gross, A. & Fasel, H. F.2010 $a$ Hybrid RANS/LES simulations of turbulent channel and diffuser flows. In 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition. AIAA 2010-0919.Google Scholar
Gross, A. & Fasel, H. F. 2010b Numerical investigation of supersonic flow for axisymmetric cones. Maths Comput. Simul. 81 (1), 133–142.Google Scholar
Harten, A. 1983 High resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 49, 357–393.Google Scholar
Herbert, T. 1988 Secondary instability of boundary layers. Annu. Rev. Fluid Mech. 20, 487–526.Google Scholar
Hofferth, J. W. & Saric, W. S.2012 Boundary-layer transition on a flared cone in the Texas A&M Mach 6 quiet tunnel. In 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition. AIAA 2012-0923.Google Scholar
Horvath, T. J., Berry, S. A., Hollis, B. R., Chang, C. L. & Singer, B. A.2002 Boundary layer transition on slender cones in conventional and low disturbance Mach 6 wind tunnels. In 32nd AIAA Fluid Dynamics Conference and Exhibit. AIAA 2002-2743.Google Scholar
van Ingen, J. L.2008 The $e^{N}$ method for transition prediction. Historical review of work at TU Delft. In 38th Fluid Dynamics Conference and Exhibit. AIAA 2008-3830.Google Scholar
Johnson, H. & Candler, G.2005 Hypersonic boundary layer stability analysis using PSE-Chem. In 35th AIAA Fluid Dynamics Conference and Exhibit. AIAA 2005-5023.Google Scholar
Kachanov, Y. S. 1994 Physical mechanisms of laminar-boundary-layer transition. Annu. Rev. Fluid Mech. 26 (1), 411–482.Google Scholar
Kachanov, Y. S. & Levchenko, V. Y. 1984 The resonant interaction of disturbances at laminar–turbulent transition in a boundary layer. J. Fluid Mech. 138, 209–247.Google Scholar
Kimmel, R. L., Poggie, J. & Schmisseur, J.2000 Effect of pressure gradients on axisymmetric hypersonic boundary layer stability. In 38th Aerospace Sciences Meeting and Exhibit. AIAA 2000-0538.Google Scholar
Kimmel, R. L.1993 The effect of pressure gradients on transition zone length in hypersonic boundary layers. Tech. Rep. Wright Lab Wright-Patterson AFB OH.Google Scholar
Klebanoff, P. S., Tidstrom, K. D. & Sargent, L. M. 1962 The three-dimensional nature of boundary-layer instability. J. Fluid Mech. 12 (1), 1–34.Google Scholar
Lachowicz, T. J., Chokani, N. & Wilkinson, S. P. 1996a Boundary-layer stability measurements in a hypersonic quiet tunnel. AIAA J. 34 (12), 2496–2500.Google Scholar
Lachowicz, T. J., Chokani, N. & Wilkinson, S. P.1996 $b$ Hypersonic boundary layer stability over a flared cone in a quiet tunnel. In 34th Aerospace Sciences Meeting and Exhibit. AIAA 1996-0782.Google Scholar
Laible, A. & Fasel, H. F.2011 Numerical investigation of hypersonic transition for a flared and a straight cone at Mach 6. In 41st AIAA Fluid Dynamics Conference and Exhibit. AIAA 2011-3565.Google Scholar
Laible, A. C.2011 Numerical investigation of boundary layer transition for cones at Mach 3.5 and 6.0. PhD thesis, The University of Arizona.Google Scholar
Laible, A. C., Mayer, C. S. J. & Fasel, H. F.2008 Numerical investigation of supersonic transition for a circular cone at Mach 3.5. In 38th Fluid Dynamics Conference and Exhibit. AIAA 2008-4397.Google Scholar
Laible, A. C., Mayer, C. S. J. & Fasel, H. F.2009 Numerical investigation of transition for a cone at Mach 3.5: oblique breakdown. In 39th AIAA Fluid Dynamics Conference. AIAA 2009-3557.Google Scholar
Laurence, S. J., Wagner, A., Ozawa, H. & Hannemann, K.2014 Visualization of hypersonic boundary-layer transition on a slender cone. In 19th AIAA International Space Planes and Hypersonic Systems and Technologies Conference. AIAA 2014-3110.Google Scholar
van Leer, B. 1982 Flux-vector splitting for the Euler equations. Intl Conf. Numer. Methods Fluid Dyn. 170, 507–512.Google Scholar
Li, F., Choudhari, M., Chang, C. L. & White, J.2010 $a$ Analysis of instabilities in non-axisymmetric hypersonic boundary layers over cones. In 10th AIAA/ASME Joint Thermophysics and Heat Transfer Conference. AIAA 2010-4643.Google Scholar
Li, F., Choudhari, M. M., Chang, C. L. & White, J.2012 Secondary instability of second mode disturbances in hypersonic boundary layers. NASA Tech. Rep. NF1676L-13407.Google Scholar
Li, F., Choudhari, M., Chang, C. L., Wu, M. & Greene, P. T.2010 $b$ Development and breakdown of Görtler vortices in high speed boundary layers. In 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition. AIAA 2010-0705.Google Scholar
Luersen, R. P. K.2012 Techniques for application of roughness for manipulation of second-mode waves on a flared cone at Mach 6. Master’s thesis, Purdue University.Google Scholar
Mack, L. M.1969 Boundary-layer stability theory. Jet Propulsion Laboratory.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
McKiernan, G. R., Chynoweth, B. C. & Schneider, S. P.2015 Instability and transition experiments in the Boeing/AFOSR Mach 6 quiet tunnel. In 45th AIAA Thermophysics Conference. AIAA 2015-2317.Google Scholar
Meersman, J. A., Hader, C. & Fasel, H. F.2018 Hypersonic boundary-layer transition: comparison of the fundamental resonance breakdown for a flared and straight cone at Mach 6. In 2018 Fluid Dynamics Conference. AIAA 2018-3851.Google Scholar
Morkovin, M. V. 1969 On the many faces of transition. In Viscous Drag Reduction (ed. Wells, C. S.), pp. 1–31. Springer.Google Scholar
Pruett, C. D. & Chang, C. L. 1998 Direct numerical simulation of hypersonic boundary-layer flow on a flared cone. Theor. Comput. Fluid Dyn. 11 (1), 49–67.Google Scholar
Pruett, C. D. & Chang, C.-L. 1995 Spatial direct numerical simulation of high-speed boundary-layer flows. Part II: Transition on a cone in Mach 8 flow. Theor. Comput. Fluid Dyn. 7 (5), 397–424.Google Scholar
Schneider, S. P. 2015 Developing mechinism-based methods for estimating hypersonic boundary-layer transition in flight: the role of quiet tunnels. Prog. Aerosp. Sci. 72, 17–29.Google Scholar
Shope, F.1991 Aerodynamic design of a hypersonic body with a constant adverse pressure gradient. In 9th Applied Aerodynamics Conference. AIAA 1991-3319.Google Scholar
Sivasubramanian, J. & Fasel, H. F. 2015 Direct numerical simulation of transition in a sharp cone boundary layer at Mach 6: fundamental breakdown. J. Fluid Mech. 768, 175–218.Google Scholar
Terwilliger, N.2011 Numerical investigation of boundary layer instability modes on a compression cone at Mach 6. Master’s thesis, The University of Arizona.Google Scholar
Ward, C. A. C., Wheaton, B. M., Chou, A., Berridge, C. D., Letterman, L. E., Luersen, R. P. K. & Schneider, S. P.2012 Hypersonic boundary-layer transition experiments in the Boeing/AFOSR Mach-6 quiet tunnel. In 50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition. AIAA 2012-0282.Google Scholar
Ward, C. A. C., Wheaton, B. M., Chou, A., Gilbert, P. L., Steen, L. E. & Schneider, S. P.2010 Boundary-layer transition measurements in a Mach-6 quiet tunnel. In 40th Fluid Dynamics Conference and Exhibit. AIAA 2010-4721.Google Scholar
Ward, C. A. C.2010 Hypersonic crossflow instability and transition on a circular cone at angle of attack. Master’s thesis, Purdue University.Google Scholar
Weinert, H. L. 2009 A fast compact algorithm for cubic spline smoothing. Comput. Statistics and Data Anal. 53 (4), 932–940.Google Scholar
Wheaton, B. M., Juliano, T. J., Berridge, D. C., Chou, A., Gilbert, P. L., Casper, K. M., Steen, L. E. & Schneider, S. P.2009 Instability and transition measurements in the Mach-6 quiet tunnel. In 39th AIAA Fluid Dynamics Conference. AIAA 2009-3559.Google Scholar
White, F. M. 2006 Viscous Fluid Flow, International Edition. McGraw-Hill.Google Scholar
Wu, J.-Z., Ma, H.-Y. & Zhou, M.-D. 2007 Vorticity and Vortex Dynamics. Springer.Google Scholar
Zhong, X. 1998 High-order finite-difference schemes for numerical simulation of hypersonic boundary-layer transition. J. Comput. Phys. 114 (1), 662–709.Google Scholar