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Several aspects of the subharmonic instability of boundary layers are studied. First, the subharmonic instability of incompressible flows over a flat plate is investigated using the resonant triad model and the Floquet model. The primary wave is taken in the form of a two-dimensional (2-0) Tollmien-Schlichting (T-S) wave. The subharmonic wave is taken in the form of a three-dimensional (3-D) wave. Results from both models are presented and compared with the experimental data and numerical simulation. It is found that the results of the Floquet model are in good agreement with the experimental data and numerical simulation, whereas the results of the resonant triad model agree only qualitatively with the experimental data. Second, the subharmonic instability of incompressible flows over a 2-0 hump is studied using the Floquet model. The mean flow over the hump is calculated by using interacting boundary layers, thereby accounting for viscid/inviscid interactions. The results show that increasing the hump height results in an increase in the amplification factors of the primary and subharmonic waves. When the hump causes separation, the growth rates of both the primary and subharmonic waves are considerably larger than those obtained in the case of no separation. Third, the subharmonic instability of compressible boundary layers over a flat plate is studied using the Floquet model. Results are presented for adiabatic wall boundary conditions and subsonic, transonic, and supersonic flows. For supersonic flows results are presented for first- and second-mode primary waves. The effect of Mach number, spanwise wavenumber, primary-wave amplitude, Reynolds number, and frequency are studied. Fourth, results for the effect of heat transfer on the subharmonic instability of a two-dimensional compressible boundary layer over a flat plate are presented for different Mach numbers. For supersonic flows results are presented for first- and second-mode waves. The effect of different levels of heat transfer on changing the features of the subharmonic compressible instability is evaluated. Fifth, results for the effect of suction on the subharmonic instability of a two-dimensional compressible boundary layer over a flat plate are presented. It is found that when the primary wave is a first-mode merging with a second-mode, the subharmonic wave is strongly destabilized by suction. Sixth, the effect of a bulge on the subharmonic instability of compressible boundary layers is studied. It is found that the effect of compressibility on reducing the growth rate of the disturbances weakens as the hump height increases. / Ph. D.

An experiment has been conducted to examine the generation and subsequent evolution of boundary-layer disturbances on a two-dimensional airfoil up through transition to turbulent flow. The experiment was conducted at the NASA Langley Research Center "2 ft by 3 ft Low Speed Wind Tunnel Facility." The primary objective of the experiment was to generate a comprehensive database that includes the effect of the external disturbance environment on the transition process and can be used as a benchmark for future transition prediction tools. The airfoil used for this experiment was custom designed. The model was a 6% thick, 4-ft chord unswept symmetric wing. A description of the design procedure, along with the theoretical stability characteristics of the airfoil will be presented in this paper. The experiment consisted of establishing the mean flow conditions, forcing two-dimensional Tollmien-Schlichting (T-S) waves in the boundary layer using modulated acoustic bursts in the free-stream, and acquiring the mean boundary-layer data and fluctuating disturbance data using hot-wire probes. The acoustic receptivity due to surface roughness near Branch I has been examined. The surface roughness consisted of two-dimensional strips of tape applied at and symmetrically spaced about Branch I. Repeated roughness elements were spaced one wavelength apart based upon the wavelength of the primary forcing frequency as determined by linear-stability theory. The test conditions consisted of mean flow velocities of 15 and 20 m/s, which correspond to chord Reynolds numbers of 1.25 and 1.68 million, respectively. Boundary-layer disturbance profiles and constant boundary-layer height chordwise traverses were acquired and examined at individual frequencies and in total energy amplitude / broadband forms. The experimental results match well with linear stability theory and linear parabolized stability equations, indicating breakdown of disturbances between N-factors of 7 and 11 with surface roughness on the model. It was observed that when the flow physics change, differences between linear-stability theory and experiment are strongly apparent. An amplitude-based breakdown criterion was defined for the developing boundary-layer responses, which were burst-type packets like the acoustic forcing signal. A criterion was defined for the breakdown of both maxima of the T-S-like disturbance profile. Overall, the effects of surface roughness and free-stream acoustic forcing on boundary-layer receptivity and stability were examined in a well-documented disturbance environment. These results will be used to validate and refine non-linear flow theories as well as help to provide an improved understanding and improved methods to control flow transition. / Ph. D.

Boundary layer characteristics at the trailing edge of a tiltrotor blade model were measured using a flattened pitot probe and a single hot wire. The blade was mounted in Virginia Tech Stability Wind tunnel stationary on a turntable on the wind tunnel's upper wall with the tip pointing down. The measurement point was located at 1 mm behind the trailing edge to make it possible to measure the flow near the blade surface and measure the boundary layer on both sides of the trailing edge in a same run. Mean velocity profiles were measured for a variety of Reynolds numbers and angles of attack. Turbulence intensity and spectral measurements were performed using a single hot wire at the highest Reynolds number. Conclusion was reached that both of the flattened pitot probe and single hot wire are good for boundary layer thickness measurements. Displacement thickness, which is important in trailing edge noise prediction, was calculated from the profile data and fit using an algebra expression against the tip angle of attack. Once the relationship between tip angle of attack and local effective angle of attack is obtained by lifting line theory, the results can be used in the trailing edge noise prediction code. / Master of Science