Abstract
We study the receptivity and resulting global instability of boundary layers due to free-stream vortical and acoustic disturbances at moderately supersonic Mach numbers. The vortical disturbances produce an unsteady boundary layer flow that develops into oblique instability waves with a viscous triple-deck structure in the downstream region. The boundary layer fluctuations produced by the acoustic disturbances evolve into oblique normal modes in a region that lies downstream of the viscous triple-deck region but will still be fairly close to the leading edge when the phase speed of these disturbances is small compared to the free-stream velocity. We use asymptotic analysis to show that both the vortically and small phase speed acoustically-generated disturbances ultimately develop into modified Rayleigh modes that can exhibit spatial growth or decay depending on the nature of the receptivity process.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Goldstein, M.: The evolution of Tollmien-Schlichting waves near a leading edge. J. Fluid Mech. 127, 59–81 (1983)
Ricco, P., Wu, X.: Response of a compressible laminar boundary layer to free-stream vortical disturbances. J. Fluid Mech. 587, 97–138 (2007)
Goldstein, M., Ricco, P.: Non-localized instabilities resulting from leading-edge receptivity at moderate supersonic mach numbers. J. Fluid Mech. 838, 435–477 (2018)
Fedorov, A., Khokhlov, A.: Excitation of unstable modes in a supersonic boundary layer by acoustic waves. Fluid Dynamics 26(4), 531–537 (1991)
Smith, F.: On the first-mode instability in subsonic, supersonic or hypersonic boundary layers. J. Fluid Mech. 198, 127–153 (1989)
Goldstein, M., Ricco, P.: Leading edge receptivity at subsonic and moderately supersonic mach numbers. In Boundary Layer Flows-Theory. Applications and Numerical Methods, IntechOpen (2019)
Fedorov, A.: Receptivity of a high-speed boundary layer to acoustic disturbances. J. Fluid Mech. 491, 101–129 (2003)
Stewartson, K.: The theory of laminar boundary layers in compressible fluids. Claredon Press, Oxford (1964)
Gulyaev, A., Kozlov, V., Kuzenetsov, V., Mineev, B.,  Sekundov, A.: Interaction of a laminar boundary layer with external turbulence. Fluid Dynamics. Translated from Izv, Akad. Navk. SSSR Mekh. Zhid. Gaza 6, vol. 5, pp. 55-65., vol. 24, no. 5, pp. 700–710, 1989
Wu, X.: Generation of Tollmien-Schlichting waves by convecting gusts interacting with sound. J. Fluid Mech. 397, 285–316 (1999)
Acknowledgements
PR acknowledges the financial support by the Air Force Office of Scientific Research Grant FA9550-15-1-0248 with Prof. R. Cummings as Program Officer.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Ricco, P., Goldstein, M.E. (2022). Leading-Edge Receptivity of Moderately Supersonic Boundary Layers to Free-Stream Disturbances. In: Sherwin, S., Schmid, P., Wu, X. (eds) IUTAM Laminar-Turbulent Transition. IUTAM Bookseries, vol 38. Springer, Cham. https://doi.org/10.1007/978-3-030-67902-6_69
Download citation
DOI: https://doi.org/10.1007/978-3-030-67902-6_69
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-67901-9
Online ISBN: 978-3-030-67902-6
eBook Packages: EngineeringEngineering (R0)