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A three-dimensional linear stability analysis is presented for two-dimensional boundary layer flows. The method of multiple scales is used to derive the amplitude and the wave number modulation equations, which take into account the nonparallelism of the basic flow. The zeroth-order eigenvalue problem is numerically integrated to calculate the quasi-parallel growth rates which are then integrated together with the nonparallel growth rates along the characteristics of the wave number modulation equations to evaluate the n-factors. The n-factors are used to determine the most dangerous frequency. The most critical frequency is defined to be the one that yields the n-factor corresponding to transition in the shortest possible distance. This definition is used to evaluate the critical frequency for the Blasius boundary layer, a wedge flow and an axisymmetric boundary layer. The effect of three-dimensional disturbances is evaluated and found to be less critical than two-dimensional disturbances regardless of the pressure gradient, the temperature distribution of the wall and the wall geometry. The effect of heating the boundary layer is evaluated for the Blasius, Falkner-Skan and axisymmetric boundary layers. In all the cases considered, heating substantially reduces the n-factors. Results are compared with those of Strazisar & Reshotko (1978) and Nayfeh & El-Hady (1980). / Ph. D.

Shear layer development over a NACA 0018 airfoil at a chord Reynolds number of 100,000 was investigated experimentally. The effects of experimental setup and analysis tools on the results were also examined. The sensitivity of linear stability predictions for measured separated shear layer velocity profiles to both the analysis approach and experimental data scatter was evaluated. Analysis approaches that are relatively insensitive to experimental data scatter were identified. Stability predictions were shown to be more sensitive to the analysis approach than to experimental data scatter, with differences in the predicted maximum disturbance growth rate and corresponding frequency of approximately 35% between approaches. A parametric study on the effects of experimental setup on low Reynolds number airfoil experiments was completed. It was found that measured lift forces and vortex shedding frequencies were affected by the end plate configuration. It was concluded that the ratio of end plate spacing to projected model height should be at least seven, consistent with the guideline for circular cylinders. Measurements before and after test section wall streamlining revealed errors in lift coefficients due to blockage as high as 9% and errors in the wake vortex shedding frequency of 3.5%. Shear layer development over the model was investigated in detail. Flow visualization images linked an observed asymmetry in wake velocity profiles to pronounced vortex roll-up below the wake centerline. Linear stability predictions based on the mean hot-wire profiles were found to agree with measured disturbance growth rates, wave numbers, and streamwise velocity fluctuation profiles. Embedded surface pressure sensors were shown to provide reasonable estimates of disturbance growth rate, wave number, and convection speed for conditions at which a separation bubble formed on the airfoil surface. Convection speeds of between 30 and 50% of the edge velocity were measured, consistent with phase speed estimates from linear stability theory.

Shear layer development over a NACA 0018 airfoil at a chord Reynolds number of 100,000 was investigated experimentally. The effects of experimental setup and analysis tools on the results were also examined. The sensitivity of linear stability predictions for measured separated shear layer velocity profiles to both the analysis approach and experimental data scatter was evaluated. Analysis approaches that are relatively insensitive to experimental data scatter were identified. Stability predictions were shown to be more sensitive to the analysis approach than to experimental data scatter, with differences in the predicted maximum disturbance growth rate and corresponding frequency of approximately 35% between approaches. A parametric study on the effects of experimental setup on low Reynolds number airfoil experiments was completed. It was found that measured lift forces and vortex shedding frequencies were affected by the end plate configuration. It was concluded that the ratio of end plate spacing to projected model height should be at least seven, consistent with the guideline for circular cylinders. Measurements before and after test section wall streamlining revealed errors in lift coefficients due to blockage as high as 9% and errors in the wake vortex shedding frequency of 3.5%. Shear layer development over the model was investigated in detail. Flow visualization images linked an observed asymmetry in wake velocity profiles to pronounced vortex roll-up below the wake centerline. Linear stability predictions based on the mean hot-wire profiles were found to agree with measured disturbance growth rates, wave numbers, and streamwise velocity fluctuation profiles. Embedded surface pressure sensors were shown to provide reasonable estimates of disturbance growth rate, wave number, and convection speed for conditions at which a separation bubble formed on the airfoil surface. Convection speeds of between 30 and 50% of the edge velocity were measured, consistent with phase speed estimates from linear stability theory.