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Growth mechanisms of second-mode instability in hypersonic boundary layers

Published online by Cambridge University Press:  15 December 2020

Xudong Tian Open the ORCID record for Xudong Tian [Opens in a new window]  and
Chihyung Wen Open the ORCID record for Chihyung Wen [Opens in a new window]
Xudong Tian
Affiliation:
Department of Mechanical Engineering and Interdisciplinary Division of Aeronautical and Aviation Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong SAR, China
Chihyung Wen*
Affiliation:
Department of Mechanical Engineering and Interdisciplinary Division of Aeronautical and Aviation Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong SAR, China
*
†Email address for correspondence: [email protected]
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Abstract

Stability analyses based on the rates of change of perturbations were performed to study the growth mechanisms of second-mode instability in hypersonic boundary layers. The results show that the streamwise velocity perturbation is strengthened by the concurrence of the momentum transfer due to the wall-normal velocity fluctuation and the streamwise gradient of the pressure perturbation near the wall, while the wall-normal velocity perturbation is dominated by the wall-normal gradient of the pressure perturbation. Meanwhile, the change of fluctuating internal energy is sustained by the advection of perturbed thermal energy in the vicinity of the critical layer and by the dilatation fluctuation near the wall. The energy transport by the wall-normal velocity fluctuation accounts for the growth of second-mode instability, and the growth rate depends on the relative phase of the energy transport by the wall-normal velocity fluctuation to the total time rate of change of fluctuating internal energy in the vicinity of the critical layer. Moreover, this relative phase is associated with the mutual interaction between the critical-layer fluctuation and the near-wall fluctuation. Porous walls recast this mutual interaction by delaying the phase of the wall-normal energy transport near the wall, resulting in the stabilization of the second mode.

JFM classification

Boundary Layers: Boundary layer stability Instability: Transition to turbulence Boundary Layers: Boundary layer control
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 908 , 10 February 2021 , R4
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

REFERENCES

Anderson, J.D. Jr. 2006 Hypersonic and High-Temperature Gas Dynamics. American Institute of Aeronautics and Astronautics.CrossRefGoogle Scholar
Brès, G.A., Inkman, M., Colonius, T. & Fedorov, A.V. 2013 Second-mode attenuation and cancellation by porous coatings in a high-speed boundary layer. J. Fluid Mech. 726, 312–337.CrossRefGoogle Scholar
Chang, C.-L., Malik, M., Erlebacher, G. & Hussaini, M. 1991 Compressible stability of growing boundary layers using parabolized stability equations. In 22nd Fluid Dynamics, Plasma Dynamics and Lasers Conference. AIAA Paper 91-1636.Google Scholar
Doak, P.E. 1989 Momentum potential theory of energy flux carried by momentum fluctuations. J. Sound Vib. 131 (1), 67–90.CrossRefGoogle Scholar
El-Hady, N.M. 1980 Nonparallel Stability of Three-Dimensional Compressible Boundary Layers. Part 1: Stability Analysis. National Aeronautics and Space Administration.Google Scholar
Fedorov, A. 2011 Transition and stability of high-speed boundary layers. Annu. Rev. Fluid Mech. 43, 79–95.CrossRefGoogle Scholar
Fedorov, A., Shiplyuk, A., Maslov, A., Burov, E. & Malmuth, N. 2003 Stabilization of a hypersonic boundary layer using an ultrasonically absorptive coating. J. Fluid Mech. 479, 99–124.CrossRefGoogle Scholar
Fedorov, A.V., Malmuth, N.D., Rasheed, A. & Hornung, H.G. 2001 Stabilization of hypersonic boundary layers by porous coatings. AIAA J. 39 (4), 605–610.CrossRefGoogle Scholar
Kendall, J.M. 1975 Wind tunnel experiments relating to supersonic and hypersonic boundary-layer transition. AIAA J. 13 (3), 290–299.CrossRefGoogle Scholar
Kozlov, V.F., Fedorov, A.V. & Malmuth, N.D. 2005 Acoustic properties of rarefied gases inside pores of simple geometries. J. Acoust. Soc. Am. 117 (6), 3402–3411.CrossRefGoogle ScholarPubMed
Kuehl, J.J. 2018 Thermoacoustic interpretation of second-mode instability. AIAA J. 56 (9), 3585–3592.CrossRefGoogle Scholar
Li, F. & Malik, M.R. 1996 On the nature of PSE approximation. Theor. Comput. Fluid Dyn. 8 (4), 253–273.CrossRefGoogle Scholar
Mack, L.M. 1975 Linear stability theory and the problem of supersonic boundary-layer transition. AIAA J. 13 (3), 278–289.CrossRefGoogle Scholar
Mack, L.M. 1984 Boundary-layer stability theory. In Special Course on Stability and Transition of Laminar Flow (ed. Michel, R.), AGARD Rep. 709, pp. 3-1–3-81.Google Scholar
Malik, M.R. 1990 Numerical methods for hypersonic boundary layer stability. J. Comput. Phys. 86 (2), 376–413.CrossRefGoogle Scholar
Malmuth, N., Fedorov, A., Shalaev, V., Cole, J., Hites, M., Williams, D. & Khokhlov, A. 1998 Problems in high speed flow prediction relevant to control. In 2nd AIAA, Theoretical Fluid Mechanics Meeting. AIAA Paper 98-2695.CrossRefGoogle Scholar
Morkovin, M.V. 1994 Transition in open flow systems-a reassessment. Bull. Am. Phys. Soc. 39 (9), 1–31.Google Scholar
Rasheed, A., Hornung, H.G., Fedorov, A.V. & Malmuth, N.D. 2002 Experiments on passive hypervelocity boundary-layer control using an ultrasonically absorptive surface. AIAA J. 40 (3), 481–489.CrossRefGoogle Scholar
Rayleigh, Lord 1945 The Theory of Sound. Dover.Google Scholar
Stetson, K., Thompson, E., Donaldson, J. & Siler, L. 1983 Laminar boundary layer stability experiments on a cone at Mach 8. I - Sharp cone. In 16th Fluid and Plasmadynamics Conference. AIAA Paper 83-1761.CrossRefGoogle Scholar
Tumin, A. 2007 Three-dimensional spatial normal modes in compressible boundary layers. J. Fluid Mech. 586, 295–322.CrossRefGoogle Scholar
Unnikrishnan, S. & Gaitonde, D.V. 2019 Interactions between vortical, acoustic and thermal components during hypersonic transition. J. Fluid Mech. 868, 611–647.CrossRefGoogle Scholar
Van Ingen, J. 2008 The eN method for transition prediction. Historical review of work at TU Delft. In 38th Fluid Dynamics Conference and Exhibit. AIAA Paper 2008-3830.CrossRefGoogle Scholar
Wagner, A., Kuhn, M., Schramm, J.M. & Hannemann, K. 2013 Experiments on passive hypersonic boundary layer control using ultrasonically absorptive carbon–carbon material with random microstructure. Exp. Fluids 54 (10), 1606.CrossRefGoogle Scholar
Zhao, R., Liu, T., Wen, C.Y., Zhu, J. & Cheng, L. 2018 Theoretical modeling and optimization of porous coating for hypersonic laminar flow control. AIAA J. 56 (8), 2942–2946.CrossRefGoogle Scholar
Zhu, Y., Chen, X., Wu, J., Chen, S., Lee, C. & Gad-el Hak, M. 2018 Aerodynamic heating in transitional hypersonic boundary layers: role of second-mode instability. Phys. Fluids 30 (1), 011701.CrossRefGoogle Scholar