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Nonlinear transition mechanism on a blunt cone at Mach 6: oblique breakdown

Published online by Cambridge University Press:  15 March 2021

Andrew B. Hartman Open the ORCID record for Andrew B. Hartman [Opens in a new window] ,
Christoph Hader Open the ORCID record for Christoph Hader [Opens in a new window]  and
Hermann F. Fasel
Andrew B. Hartman*
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ85721, USA
Christoph Hader
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ85721, USA
Hermann F. Fasel
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ85721, USA
*
†Email address for correspondence: andrewmach1@arizona.edu
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Abstract

Direct numerical simulations (DNS) were carried out to investigate laminar-turbulent transition for a blunt (right) cone ($7^\circ$ half-angle) at Mach 5.9 and zero angle of attack. First, (linear) stability calculations were carried out by employing a high-order Navier–Stokes solver and using very small disturbance amplitudes in order to capture the linear disturbance development. Contrary to standard linear stability theory (LST) results, these investigations revealed a strong ‘linear’ instability in the entropy-layer region for a very short downstream distance for oblique disturbance waves with spatial growth rates far exceeding those of second-mode disturbances. This linear instability behaviour was not captured with conventional LST and/or the parabolized stability equations (PSE). Secondly, a nonlinear breakdown simulation was performed using high-fidelity DNS. The DNS results showed that linearly unstable oblique disturbance waves, when excited with large enough amplitudes, lead to a rapid breakdown and complete laminar-turbulent transition in the entropy layer just upstream of the second-mode instability region.

JFM classification

Aerodynamics: High-speed flow Boundary Layers: Boundary layer stability Instability: Transition to turbulence
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , R2
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Berlin, S., Lundbladh, A. & Henningson, D. 1994 Spatial simulations of oblique transition in a boundary layer. Phys. Fluids 6 (6), 1949–1951.CrossRefGoogle Scholar
Chakravarthy, S., Peroomian, O., Goldberg, U. & Palaniswamy, S. 1998 The CFD++ computational fluid dynamics software suite. AIAA and SAE 1998 World Aviation Conference. AIAA 1998–5564.CrossRefGoogle Scholar
Chang, C.-L. & Malik, M.R 1994 Oblique-mode breakdown and secondary instability in supersonic boundary layers. J. Fluid Mech. 273, 323–360.CrossRefGoogle Scholar
Dietz, G & Hein, S 1999 Entropy-layer instabilities over a blunted flat plate in supersonic flow. Phys. Fluids 11 (1), 7–9.CrossRefGoogle Scholar
Fasel, H.F., Thumm, A. & Bestek, H. 1993 Direct numerical simulation of transition in supersonic boundary layers: oblique breakdown. In Transitional and Turbulent Compressible Flows, pp. 77–92. ASME-FED 151.Google Scholar
Gross, A. & Fasel, H.F. 2008 High-order accurate numerical method for complex flows. AIAA J. 46 (1), 204–214.CrossRefGoogle Scholar
Haas, A.P. 2020 Private communication.Google Scholar
Hader, C. & Fasel, H.F. 2019 Direct numerical simulations of hypersonic boundary-layer transition for a flared cone: fundamental breakdown. J. Fluid Mech. 869, 341–384.CrossRefGoogle Scholar
Husmeier, F. & Fasel, H.F. 2007 Numerical investigations of hypersonic boundary layer transition for circular cones. 18th AIAA Computational Fluid Dynamics Conference. AIAA 2007–3843.CrossRefGoogle Scholar
Jewell, J.S., Kennedy, R.E., Laurence, S.J. & Kimmel, R.L. 2018 Transition on a variable bluntness 7-degree cone at high Reynolds number. 2018 AIAA Aerospace Sciences Meeting. AIAA 2018–1822.CrossRefGoogle Scholar
Jewell, J.S. & Kimmel, R.L. 2016 Boundary-layer stability analysis for Stetson's mach 6 blunt-cone experiments. J. Spacecr. Rockets, 258–265.Google Scholar
Kennedy, R.E., Jagde, E.K., Laurence, S.J., Jewell, J.S. & Kimmel, R.L. 2019 Visualizations of hypersonic boundary-layer transition on a variable bluntness cone. In AIAA Aviation 2019 Forum. AIAA 2019–3079.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle Scholar
Lei, J. & Zhong, X. 2012 Linear stability analysis of nose bluntness effcts on hypersonic boundary layer transition. J. Spacecr. Rockets, 24–37.CrossRefGoogle Scholar
Mack, L.M. 1969 Boundary-layer stability theory. Jet Propulsion Laboratory, NASA CR-131501.Google Scholar
Marineau, E.C., Moraru, G.C., Lewis, D.R., Norris, J.D., Lafferty, J.F., Wagnild, R.M. & Smith, J.A. 2014 Mach 10 boundary layer transition experiments on sharp and blunted cones. 19th AIAA International Space Planes and Hypersonic Systems and Technologies Conference. AIAA 2014–3108.CrossRefGoogle Scholar
Mayer, C.S.J., Von Terzi, D.A. & Fasel, H.F. 2011 a Direct numerical simulation of complete transition to turbulence via oblique breakdown at Mach 3. J. Fluid Mech. 674, 5–42.CrossRefGoogle Scholar
Mayer, C.S.J., Wernz, S. & Fasel, H.F. 2011 b Numerical investigation of the nonlinear transition regime in a Mach 2 boundary layer. J. Fluid Mech. 668, 113–149.CrossRefGoogle Scholar
Paredes, P., Choudhari, M.M. & Li, F. 2019 a Laminar-turbulent transition upstream of the entropy-layer swallowing location in hypersonic boundary layers. AIAA Aviation 2019 Forum. AIAA 2019–3215.CrossRefGoogle Scholar
Paredes, P., Choudhari, M.M., Li, F., Jewell, J.S. & Kimmel, R.L. 2019 b Nonmodal growth of traveling waves on blunt cones at hypersonic speeds. AIAA Journal 57 (11), 4738–4749.CrossRefGoogle Scholar
Rosenboom, I., Hein, S. & Dallmann, U. 2013 Influence of nose bluntness on boundary-layer instabilities in hypersonic cone flows. 30th Fluid Dynamics Conference. AIAA 2013-3591.Google Scholar
Schubauer, G.B. & Skramstad, H.K. 1948 Laminar boundary layer oscillations and transition on a flat plate. NASA Rep. 909.CrossRefGoogle Scholar
Stetson, K. 1979 Effect of bluntness and angle of attack on boundary layer transition on cones and biconic configurations. In 17th Aerospace Sciences Meeting. AIAA 1979–0269.CrossRefGoogle Scholar
Stetson, K. 1983 Nosetip bluntness effects on cone frustum boundary layer transition in hypersonic flow. 16th Fluid and Plasmadynamics Conference. AIAA 1983-1763.CrossRefGoogle Scholar
White, F.M. 2006 Viscous Fluid Flow, International edn. McGraw-Hill.Google Scholar