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Stability of supersonic boundary layer over an unswept wing with a parabolic airfoil

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Abstract

Under the low-noise Mach 3 flight conditions for a supersonic passenger aircraft having unswept wings with a thin parabolic airfoil, laminar-turbulent transition is due to amplification of the first mode. Stability of a local self-similar boundary layer over such a wing is investigated both using the \(e^{N}\) method in the framework of linear stability theory and direct numerical simulation (DNS). It is found that the instability amplitude should reach a maximum over the entire spectral range above the profiles of 2.5% and thicker. The locus of maximum appears at the trailing edge and moves to the leading edge as the profile becomes thicker, while the maximum amplitude decreases. The theoretical findings are supported by DNS of the linear wave packets propagating in the boundary layer. Significance of these results to the design of laminar supersonic wings is discussed.

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References

  1. Klochkov, V.V., Rozhdestvenskaya, S.M.: Analysis of prerequisites for the formation of supersonic passenger air transport and aircraft markets. Innovations 250(8), 60–66 (2019)

    Google Scholar 

  2. Joslin, R.D.: Aircraft laminar flow control. Annu. Rev. Fluid Mech. (1998). https://doi.org/10.1146/annurev.fluid.30.1.1

    Article  Google Scholar 

  3. Sturdza, P.: Extensive Supersonic Natural Laminar Flow on the Aerion Business Jet. In: 45th AIAA Aerospace Sciences Meeting and Exhibit (2007). https://doi.org/10.2514/6.2007-685

  4. Morkovin, M.V., Reshotko, E., Herbert, T.: Transition in open flow systems: a reassessment. Bull. Am. Phys. Soc. 39(9), 1–31 (1994)

    Google Scholar 

  5. Zurigat, Y.H., Nayfeh, A.H., Masad, J.A.: Effect of pressure gradient on the stability of compressible boundary layers. AIAA J. (1992). https://doi.org/10.2514/3.11206

    Article  Google Scholar 

  6. Masad, J.A., Zurigat, Y.H.: Effect of pressure gradient on first mode of instability in compressible boundary layers. Phys. Fluids (1994). https://doi.org/10.1063/1.868384

    Article  Google Scholar 

  7. Ren, J., Fu. S.: Effect of pressure gradient on the stability of hypersonic boundary layer flows. In: AIAA, p. 2134 (2017). https://doi.org/10.2514/6.2017-2134

  8. Chuvakhov, P.V., Egorov, I.V., Ilyukhin, I.M., Obraz, A.O., Fedorov, A.V.: Boundary-layer instabilities in supersonic expansion corner flows. AIAA J. (2021). https://doi.org/10.2514/1.J060145

    Article  Google Scholar 

  9. Chuvakhov, P.V., Egorov, I.V.: Numerical simulation of disturbance evolution in the supersonic boundary layer over an expansion corner. Fluid Dyn. (2021). https://doi.org/10.1134/s0015462821050025

    Article  MathSciNet  Google Scholar 

  10. Liebhardt, B., Lütjens, K., Tracy, R.R., Haas, A.O.: Exploring the prospect of small supersonic airliners—a case study based on the Aerion AS2 Jet. In: 17th AIAA Aviation Technology, Integration, and Operations Conference (2017). https://doi.org/10.2514/6.2017-3588

  11. Chuvakhov, P.V., Fedorov, A.V., Obraz, A.O., Ilyukhin, I.M.: Disturbance evolution over an upswept wing in a Mach 3 flow. In: AIP Conference Proceedings (2021). https://doi.org/10.1063/5.0051730

  12. Malik, M., Zang, T., Bushnell, D.: Boundary layer transition in hypersonic flows. In: AIAA Paper (1990). https://doi.org/10.2514/6.1990-5232

  13. Masson, C., Boivin, S., Langlois, M., Paraschivoiu, I.: Curvature and nonparallel effects in 3-D compressible transition analysis. In: 35th Aerospace Sciences Meeting and Exhibit (1997). https://doi.org/10.2514/6.1997-824

  14. Egorov, I.V., Novikov, A.V.: Direct numerical simulation of boundary layer flow over a flat plate at hypersonic flow speeds. Comput. Math. Math. Phys. (2016). https://doi.org/10.1134/S0965542516060129

    Article  Google Scholar 

  15. Jiang, G.-S., Shu, C.-W.: Efficient implementation of weighted ENO schemes. J. Comput. Phys. (1996). https://doi.org/10.1006/jcph.1996.0130

    Article  MathSciNet  Google Scholar 

  16. Sychev, V.V., Ruban, A.I., Sychev, V.V., Korolev, G.L., Goldstein, M.E.: Asymptotic Theory of Separated Flows. Cambridge University Press, Cambridge (1998). https://doi.org/10.1017/CBO9780511983764

    Book  Google Scholar 

  17. Ashley, H., Landahl, M.: Aerodynamics of Wings and Bodies. Reading, Massachusettes (1965)

    Google Scholar 

  18. Lagerstrom, P.A.: Laminar Flow Theory. Princeton University Press, Princeton (1996)

    Book  Google Scholar 

  19. Ginoux, J.J.: Laminar Boundary Layers, Course Note 104. von Karman Institute for Fluid Dynamics, Rhode-Saint-Genèse (1978)

    Google Scholar 

  20. Mack, L.M.: Boundary Layer Stability Theory. Jet Propulsion Laboratory, Pasadena (1969)

    Google Scholar 

  21. Obraz, A.O., Fedorov, A.V.: The high-speed flow stability (HSFS) software package for stability analysis of compressible boundary layers. TsAGI Sci. J. (2017). https://doi.org/10.1615/TsAGISciJ.2017022797

    Article  Google Scholar 

  22. Fischer, M.C.: Spreading of a turbulent disturbance. AIAA J. (1972). https://doi.org/10.2514/3.50265

    Article  Google Scholar 

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Acknowledgements

The authors are grateful to Anton Obraz (senior researcher of TsAGI and MIPT) for stability calculations using the boundary layer profiles extracted from DNS solution.

Funding

The work has been carried out at MIPT under the support of Russian Science Foundation (Project No. 19-79-10132).

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Authors and Affiliations

  1. Central Aerohydrodynamic Institute (TsAGI), Zhukovsky, Russia

    P. V. Chuvakhov & I. M. Ilyukhin

  2. Moscow Institute of Physics and Technology (MIPT), Dolgoprudny, Russia

    P. V. Chuvakhov, I. M. Ilyukhin & A. V. Fedorov

Authors
  1. P. V. Chuvakhov
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  2. I. M. Ilyukhin
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  3. A. V. Fedorov
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The authors contributions to the manuscript preparation are nearly equal.

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Correspondence to I. M. Ilyukhin.

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Communicated by Jean-Christophe ROBINET.

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Chuvakhov, P.V., Ilyukhin, I.M. & Fedorov, A.V. Stability of supersonic boundary layer over an unswept wing with a parabolic airfoil. Theor. Comput. Fluid Dyn. 38, 1–13 (2024). https://doi.org/10.1007/s00162-023-00680-z

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  • DOI: https://doi.org/10.1007/s00162-023-00680-z

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