Wave interactions in three-dimensional boundary layers
Vonderwell, Mark Phillip
This item is only available for download by members of the University of Illinois community. Students, faculty, and staff at the U of I may log in with your NetID and password to view the item. If you are trying to access an Illinois-restricted dissertation or thesis, you can request a copy through your library's Inter-Library Loan office or purchase a copy directly from ProQuest.
Permalink
https://hdl.handle.net/2142/21780
Description
Title
Wave interactions in three-dimensional boundary layers
Author(s)
Vonderwell, Mark Phillip
Issue Date
1995
Doctoral Committee Chair(s)
Riahi, Daniel N.
Department of Study
Mechanical Science and Engineering
Discipline
Theoretical and Applied Mechanics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Applied Mechanics
Engineering, Aerospace
Language
eng
Abstract
The roles of weakly nonlinear triad interactions and the self-interaction of primary instabilities in the transition-to-turbulence process in three-dimensional boundary layers are investigated. Resonant triad interactions are studied in the boundary layer on the leading edge of a swept wing under typical commercial jet cruise conditions. Both compressible and incompressible models are developed using the method of multiple scales and a spectral collocation numerical method. Detuning parameters for the wavenumbers and frequencies and the effects of the growth of the boundary layer are included in the modeling. The spatial and temporal growth of numerous triads consisting of different combinations of crossflow (CF) and Tollmein-Schlichting (TS) modes are studied for a specific laminar flow control wing.
Calculations using the model indicate that the spatial evolution of the triad amplitudes is strongly dependent upon the initial spectrum of amplitudes and phases. Specific predictions are impossible without this information, but general conclusions regarding interaction strength are possible. Calculations indicate that triads consisting of three crossflow modes are abundant, but the interaction between the modes is relatively weak. Triads with two TS modes and one CF mode are also numerous and the interaction may strongly affect the CF mode.
Comparison of results from the compressible and incompressible theories show significant differences in some cases. Compressibility is stabilizing to individual modes and usually weakens the interactions among them as well. Nonparallel effects are usually destabilizing according to both models and may significantly affect the evolution of the triad amplitudes.
The self-interaction of disturbances is investigated in the three-dimensional boundary layer over a rotating disk. The method of multiple scales is used to model the weakly nonlinear growth of the critical stationary crossflow mode. The Landau constant is evaluated using a spectral collocation numerical method. Results indicate that nonlinearity is destabilizing, so subcritical instability and super-exponential growth is possible.
Use this login method if you
don't
have an
@illinois.edu
email address.
(Oops, I do have one)
IDEALS migrated to a new platform on June 23, 2022. If you created
your account prior to this date, you will have to reset your password
using the forgot-password link below.
