Hostname: page-component-848d4c4894-r5zm4 Total loading time: 0 Render date: 2024-06-21T22:31:02.819Z Has data issue: false hasContentIssue false
  • English
  • Français

Global receptivity analysis: physically realizable input–output analysis

Published online by Cambridge University Press:  03 February 2023

Omar Kamal Open the ORCID record for Omar Kamal [Opens in a new window] ,
Matthew T. Lakebrink  and
Tim Colonius
Omar Kamal*
Affiliation:
Department of Mechanical and Civil Engineering, California Institute of Technology, Pasadena, CA 91125, USA
Matthew T. Lakebrink
Affiliation:
The Boeing Company, Hazelwood, MO 63042, USA
Tim Colonius
Affiliation:
Department of Mechanical and Civil Engineering, California Institute of Technology, Pasadena, CA 91125, USA
*
†Email address for correspondence: okamal@caltech.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

In the context of transition analysis, linear input–output analysis determines the worst-case disturbances to a laminar base flow based on a generic right-hand-side volumetric/boundary forcing term. The worst-case forcing is not physically realizable, and, to our knowledge, a generic framework for posing physically realizable worst-case disturbance problems is lacking. In natural receptivity analysis, disturbances are forced by matching (typically local) solutions within the boundary layer to outer solutions consisting of free-stream vortical, entropic and acoustic disturbances. We pose a scattering formalism to restrict the input forcing to a set of realizable disturbances associated with plane-wave solutions of the outer problem. The formulation is validated by comparing with direct numerical simulations of a Mach 4.5 flat-plate boundary layer. We show that the method provides insight into transition mechanisms by identifying those linear combinations of plane-wave disturbances that maximize energy amplification over a range of frequencies. We also discuss how the framework can be extended to accommodate scattering from shocks and in shock layers for supersonic flow.

JFM classification

Aerodynamics: High-speed flow Boundary Layers: Boundary layer receptivity Boundary Layers: Boundary layer stability
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 956 , 10 February 2023 , R5
Check for updates
Copyright
© The Author(s), 2023. Published by 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

REFERENCES

Bae, H.J., Dawson, S.T.M. & McKeon, B.J. 2020 Resolvent-based study of compressibility effects on supersonic turbulent boundary layers. J. Fluid Mech. 883, A29.CrossRefGoogle Scholar
Balakumar, P. 2015 Receptivity of hypersonic boundary layers to acoustic and vortical disturbances (Invited). AIAA Paper 2015-2473.CrossRefGoogle Scholar
Bugeat, B., Chassaing, J.-C., Robinet, J.-C. & Sagaut, P. 2019 3D global optimal forcing and response of the supersonic boundary layer. J. Comput. Phys. 398, 108888.CrossRefGoogle Scholar
Chu, B.-T. 1965 On the energy transfer to small disturbances in fluid flow (Part I). Acta Mechanica 1 (3), 215–234.CrossRefGoogle Scholar
Cook, D.A., Knutson, A., Nichols, J.W. & Candler, G.V. 2020 Matrix methods for input–output analysis of 2D and 3D hypersonic flows. AIAA Paper 2020-1820.CrossRefGoogle Scholar
Cook, D.A. & Nichols, J.W. 2022 Free-stream receptivity of a hypersonic blunt cone using input–output analysis and a shock-kinematic boundary condition. Theor. Comput. Fluid Dyn. 36 (1), 155–180.CrossRefGoogle Scholar
Crouch, J.D. 1992 Non-localized receptivity of boundary layers. J. Fluid Mech. 244, 567–581.CrossRefGoogle Scholar
Duck, P.W., Ruban, A.I. & Zhikharev, C.N. 1996 The generation of Tollmien–Schlichting waves by free-stream turbulence. J. Fluid Mech. 312, 341–371.CrossRefGoogle Scholar
Fedorov, A.V. 2003 Receptivity of a high-speed boundary layer to acoustic disturbances. J. Fluid Mech. 491, 101–129.CrossRefGoogle Scholar
Fedorov, A.V. & Khokhlov, A.P. 2001 Prehistory of instability in a hypersonic boundary layer. Theor. Comput. Fluid Dyn. 14 (6), 359–375.CrossRefGoogle Scholar
Goldstein, M.E. 1983 The evolution of Tollmien–Sclichting waves near a leading edge. J. Fluid Mech. 127, 59–81.CrossRefGoogle Scholar
Jeun, J., Nichols, J.W. & Jovanović, M.R. 2016 Input–output analysis of high-speed axisymmetric isothermal jet noise. Phys. Fluids 28 (4), 047101.CrossRefGoogle Scholar
Kamal, O., Rigas, G., Lakebrink, M.T. & Colonius, T. 2021 Input/output analysis of hypersonic boundary layers using the One-Way Navier–Stokes (OWNS) equations. AIAA Paper 2021-2827.CrossRefGoogle Scholar
Lugrin, M., Beneddine, S., Leclercq, C., Garnier, E. & Bur, R. 2021 Transition scenario in hypersonic axisymmetrical compression ramp flow. J. Fluid Mech. 907, A6.CrossRefGoogle Scholar
Ma, Y. & Zhong, X. 2003 a Receptivity of a supersonic boundary layer over a flat plate. Part 1. Wave structures and interactions. J. Fluid Mech. 488, 31–78.CrossRefGoogle Scholar
Ma, Y. & Zhong, X. 2003 b Receptivity of a supersonic boundary layer over a flat plate. Part 2. Receptivity to free-stream sound. J. Fluid Mech. 488, 79–121.CrossRefGoogle Scholar
Ma, Y. & Zhong, X. 2005 Receptivity of a supersonic boundary layer over a flat plate. Part 3. Effects of different types of free-stream disturbances. J. Fluid Mech. 532, 63–109.CrossRefGoogle Scholar
Malik, M.R. 1990 Numerical methods for hypersonic boundary layer stability. J. Comput. Phys. 86 (2), 376–413.CrossRefGoogle Scholar
McKenzie, J.F. & Westphal, K.O. 1968 Interaction of linear waves with oblique shock waves. Phys. Fluids 11 (11), 2350–2362.CrossRefGoogle Scholar
Monokrousos, A., Åkervik, E., Brandt, L. & Henningson, D.S. 2010 Global three-dimensional optimal disturbances in the Blasius boundary-layer flow using time-steppers. J. Fluid Mech. 650, 181–214.CrossRefGoogle Scholar
Nichols, J.W. & Candler, G.V. 2019 Input–output analysis of complex hypersonic boundary layers. AIAA Paper 2019-1383.CrossRefGoogle Scholar
Nichols, J.W. & Lele, S.K. 2011 Global modes and transient response of a cold supersonic jet. J. Fluid Mech. 669, 225–241.CrossRefGoogle Scholar
Qin, F. & Wu, X. 2016 Response and receptivity of the hypersonic boundary layer past a wedge to free-stream acoustic, vortical and entropy disturbances. J. Fluid Mech. 797, 874–915.CrossRefGoogle Scholar
Ruban, A.I., Keshari, S.K. & Kravtsova, M.A. 2021 On boundary-layer receptivity to entropy waves. J. Fluid Mech. 929, A17.CrossRefGoogle Scholar
Schmidt, O.T., Towne, A., Rigas, G., Colonius, T. & Brès, G.A. 2018 Spectral analysis of jet turbulence. J. Fluid Mech. 855, 953–982.CrossRefGoogle Scholar
Schrader, L.-U., Brandt, L. & Henningson, D.S. 2009 Receptivity mechanisms in three-dimensional boundary-layer flows. J. Fluid Mech. 618, 209–241.CrossRefGoogle Scholar
Skene, C.S., Yeh, C.-A., Schmid, P.J. & Taira, K. 2022 Sparsifying the resolvent forcing mode via gradient-based optimisation. J. Fluid Mech. 944, A52.CrossRefGoogle Scholar
Thompson, K.W. 1987 Time dependent boundary conditions for hyperbolic systems. J. Comput. Phys. 68 (1), 1–24.CrossRefGoogle Scholar
Towne, A., Rigas, G., Kamal, O., Pickering, E. & Colonius, T. 2022 Efficient global resolvent analysis via the one-way Navier–Stokes equations. J. Fluid Mech. 948, A9.CrossRefGoogle Scholar
Trefethen, L.N., Trefethen, A.E., Reddy, S.C. & Driscoll, T.A. 1993 Hydrodynamic stability without eigenvalues. Science 261 (5121), 578–584.CrossRefGoogle ScholarPubMed