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Receptivity and stability of hypersonic leading-edge sweep flows around a blunt body

Published online by Cambridge University Press:  06 April 2021

Youcheng Xi Open the ORCID record for Youcheng Xi [Opens in a new window] ,
Jie Ren Open the ORCID record for Jie Ren [Opens in a new window] ,
Liang Wang  and
Song Fu Open the ORCID record for Song Fu [Opens in a new window]
Youcheng Xi
Affiliation:
School of Aerospace Engineering, Tsinghua University, Beijing100084, PR China
Jie Ren
Affiliation:
Department of Mechanical Engineering, Faculty of Engineering, University of Nottingham, NottinghamNG7 2RD, UK
Liang Wang
Affiliation:
School of Aerospace Engineering, Tsinghua University, Beijing100084, PR China
Song Fu*
Affiliation:
School of Aerospace Engineering, Tsinghua University, Beijing100084, PR China
*
†Email address for correspondence: fs-dem@tsinghua.edu.cn
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Abstract

This study performs global stability/receptivity analyses of hypersonic flows over a swept blunt body with infinite span. For the first time, we obtain the characteristics of the leading attachment-line mode to the variation of sweep angles from $20^{\circ }$ to $70^{\circ }$. The global eigenfunctions exhibit the characteristics of the attachment-line instability at the leading edge. At the same time, cross-flow (at small sweep angles) or second Mack mode (at larger sweep angles) dominates further downstream. We establish an adjoint-based bi-orthogonal eigenfunction system to address the receptivity problem of such flows to any external forces and boundary perturbations. The receptivity analyses indicate that the global modes are the most responsive to external forces and surface perturbations applied in the vicinity of the attachment line, regardless of the sweep angles. It is also proven that the present global extension of the bi-orthogonal eigenfunction system can be successfully applied to complex hypersonic flows.

JFM classification

Boundary Layers: Boundary layer receptivity Boundary Layers: Boundary layer stability Compressible Flows: Compressible boundary layers
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 916 , 10 June 2021 , R2
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Bertolotti, F.P. 1999 On the connection between cross-flow vortices and attachment-line instabilities. In IUTAM Symposium on Laminar-Turbulent Transition, Laminar-Turbulent Transition (ed. H.F. Fasel & W.S. Saric), pp. 625–630. Springer.CrossRefGoogle Scholar
Choudhari, M. 1994 Theoretical Prediction of Boundary-Layer Receptivity. Fluid Dynamics and Co-located Conferences 1994-2223. American Institute of Aeronautics and Astronautics.Google Scholar
Fedorov, A.V. & Khokhlov, A.P. 2002 Receptivity of hypersonic boundary layer to wall disturbances. Theor. Comput. Fluid Dyn. 15 (4), 231–254.CrossRefGoogle Scholar
Gaillard, L., Benard, E. & Alziary de Roquefort, T. 1999 Smooth leading edge transition in hypersonic flow. Exp. Fluids 26 (1), 169–176.CrossRefGoogle Scholar
Giannetti, F. & Luchini, P. 2007 Structural sensitivity of the first instability of the cylinder wake. J. Fluid Mech. 581, 167–197.CrossRefGoogle Scholar
Giles, M.B. & Pierce, N.A. 2001 Analytic adjoint solutions for the quasi-one-dimensional Euler equations. J. Fluid Mech. 426, 327–345.CrossRefGoogle Scholar
Hill, D.C. 1995 Adjoint systems and their role in the receptivity problem for boundary-layers. J. Fluid Mech. 292, 183–204.CrossRefGoogle Scholar
Lin, R.-S. & Malik, M.R. 1996 On the stability of attachment-line boundary layers. Part 1. The incompressible swept Hiemenz flow. J. Fluid Mech. 311, 239–255.CrossRefGoogle Scholar
Mack, C.J., Schmid, P.J. & Sesterhenn, J.L. 2008 Global stability of swept flow around a parabolic body: connecting attachment-line and crossflow modes. J. Fluid Mech. 611, 205–214.CrossRefGoogle Scholar
Mack, C.J. & Schmid, P.J. 2011 Global stability of swept flow around a parabolic body: features of the global spectrum. J. Fluid Mech. 669, 375–396.CrossRefGoogle Scholar
Meneghello, G., Schmid, P.J. & Huerre, P. 2015 Receptivity and sensitivity of the leading-edge boundary layer of a swept wing. J. Fluid Mech. 775, R1.CrossRefGoogle Scholar
Obrist, D. & Schmid, P.J. 2003 On the linear stability of swept attachment-line boundary layer flow. Part 2. Non-modal effects and receptivity. J. Fluid Mech. 493, 31–58.CrossRefGoogle Scholar
Reed, H.L. & Saric, W.S. 1989 Stability of three-dimensional boundary layers. Annu. Rev. Fluid Mech. 21 (1), 235–284.CrossRefGoogle Scholar
Reshotko, E. & Beckwith, I.E. 1958 Compressible laminar boundary layer over a yawed infinite cylinder with heat transfer and arbitrary Prandtl number. NACA Tech. Rep. 1379. National Advisory Committee for Aeronautics.Google Scholar
Ruban, A.I. 1984 On the generation of Tollmien–Schlichting waves by sound. Fluid Dyn. 19 (5), 709–717.CrossRefGoogle Scholar
Saric, W.S., Reed, H.L. & White, E.B. 2003 Stability and transition of three-dimensional boundary layers. Annu. Rev. Fluid Mech. 35 (1), 413–440.CrossRefGoogle Scholar
Stewart, G. 2002 a A Krylov–Schur algorithm for large eigenproblems. SIAM J. Matrix Anal. Applics. 23 (3), 601–614.CrossRefGoogle Scholar
Stewart, G. 2002 b Addendum to ‘Krylov–Schur algorithm for large eigenproblems’. SIAM J. Matrix Anal. Applics. 24 (2), 599–601.CrossRefGoogle Scholar
Theofilis, V. 1998 On linear and nonlinear instability of the incompressible swept attachment-line boundary layer. J. Fluid Mech. 355, 193–227.CrossRefGoogle Scholar
Theofilis, V. 2011 Global linear instability. Annu. Rev. Fluid Mech. 43 (1), 319–352.CrossRefGoogle Scholar
Tumin, A. 2007 Three-dimensional spatial normal modes in compressible boundary layers. J. Fluid Mech. 586, 295–322.CrossRefGoogle Scholar
Tumin, A. 2020 LST and the eigenfunction expansion method for linearized Navier–Stokes equations – a summary. AIAA Paper 2020-0105.CrossRefGoogle Scholar
Xi, Y., Ren, J. & Fu, S. 2021 Hypersonic attachment-line instabilities with large sweep mach numbers. J. Fluid Mech. 915, A44.CrossRefGoogle Scholar
Zhong, X. 1998 High-order finite-difference schemes for numerical simulation of hypersonic boundary-layer transition. J. Comput. Phys. 144 (2), 662–709.CrossRefGoogle Scholar
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