Numerical and asymptotic approaches to boundary-layer receptivity and transition.

Turner, M. R. (2005) Numerical and asymptotic approaches to boundary-layer receptivity and transition. PhD thesis, University of East Anglia.



We consider the interaction of a uniformly pulsating free-stream with the leading edge of a body, and consider its effect on transition. The free-stream is assumed to be incompressible, high Reynolds number flow parallel to the chord of the body, with a small, unsteady, perturbation of a single harmonic frequency. We present a method which calculates Tollmien-Schlichting (T-S) wave amplitudes downstream of the leading edge, by a combination of an asymptotic receptivity approach in the leading edge region and a numerical method which marches through the Orr-Sommerfeld region. The asymptotic receptivity analysis produces a three deck eigenmode which, in its far downstream limiting form, produces an upstream initial condition for our numerical Parabolized Stability Equation (PSE). Downstream T-S wave amplitudes are calculated for the flat plate, and good comparisons are found with the Orr-Sommerfeld asymptotics available in this region. The importance of the O(Re^{−1/2} ) term of the asymptotics is discussed, and, due to the complexity in calculating this term, we show the importance of numerical methods in the Orr-Sommerfeld region to give accurate results. We also discuss the initial transients present for certain parameter ranges, and show that their presence appears to be due to the existence of higher T-S modes in the initial upstream boundary condition. Extensions of the receptivity/PSE method to the parabola and the Rankine body are considered, and a drop in T-S wave amplitudes at lower branch is observed for both bodies, as the nose radius increases. The only exception to this trend occurs for the Rankine body at very large Reynolds numbers, which are not accessible in experiments, where a double maximum of the T-S wave amplitude at lower branch is observed. The extension of the receptivity/PSE method to experimentally realistic bodies is also considered, by using slender body theory to model the inviscid flow around a modified super ellipse to compare with numerical studies.

Item Type:Thesis (PhD)
Subjects:G000 Computing and Mathematical Sciences > G100 Mathematics
Faculties:Faculty of Science and Engineering > School of Computing, Engineering and Mathematics > Engineering and Product Design Research > Automotive Engineering
Faculty of Science and Engineering
ID Code:5351
Deposited By:Dr Matthew Turner
Deposited On:26 Nov 2009
Last Modified:08 Oct 2010 02:17

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