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Title:Wave interactions in three-dimensional boundary layers
Author(s):Vonderwell, Mark Phillip
Doctoral Committee Chair(s):Riahi, Daniel N.
Department / Program:Mechanical Science and Engineering
Discipline:Theoretical and Applied Mechanics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Applied Mechanics
Engineering, Aerospace
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.
Issue Date:1995
Rights Information:Copyright 1995 Vonderwell, Mark Phillip
Date Available in IDEALS:2011-05-07
Identifier in Online Catalog:AAI9543758
OCLC Identifier:(UMI)AAI9543758

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