Boundary-layer flows near leading edges of generally curved obstacles have been studied for a long time. Apart from having many practical applications, the theory and approaches prevailing in this area stimulate development of a variety of computational tools and form a ground for testing them. The specific aim of this work is to study two-dimensional laminar boundary layer flows near the leading edges of airfoils and other elongated bodies, and to explore geometries for which boundary layer separation can be avoided. This class of problems is relevant to optimal design of wings, aircraft and projectile noses, laminar flow control methods and adaptive wing technology. One of the findings of this work suggests that local modifications to parabolic wing noses can yield up to 11% increase in the unseparated angle of attack. Another result obtained here is the set of shortest possible generalised elliptic noses of long symmetric bodies which allow unseparated flow. Methods adopted in this work are based on the combined use of numerically solved Prandtl equations written in Gortler variables, and inviscid solutions obtained semi-analytically by the conformal mapping method. The resulting technique being reliable, fast and computationally inexpensive, can complement or test the results obtained using a comprehensive CFD approach. / Thesis (Ph.D.)--School of Mathematical Sciences, 2002.

A new turbulence model designed for two-dimensional, steady and unsteady boundary layers in strong adverse pressure gradients is described. The model is developed in a rational way based on an understanding of the flow physics obtained from recent experimental observations. The turbulent shear stress is given by a mixing length model, but the variation of the mixing length in the outer region is not constant; it varies according to an integral form of the turbulence kinetic-energy equation. This approach allows for the history effects of the turbulence to be taken into account in an approximate but rational way. The form of the near-wall mixing length model is derived based on the rigorous distribution of the shear stress near the wall, and it takes into account the pressure and convection terms which become important in strong adverse pressure gradients. Since the significance of the normal stresses in turbulent kinetic-energy production is increasing as separation is approached, a model accounting for this contribution is incorporated. The model is calibrated using available experimental data. These data also indicate a change in turbulence structure near and through separation. Such a change can be significant and is accounted for here using an empirical function. The complete model was tested against steady and unsteady, two-dimensional experimental cases with adverse pressure gradient up to separation. Improved predictions compared to those obtained with other turbulence models were demonstrated. The general and rational approach that led to the derivation of the model allows the straightforward extension of the model in the region of separation. The further extension to steady and unsteady, three-dimensional cases is indicated. / Ph. D.

The boundary-layer receptivity resulting from acoustic forcing over a flat plate with a surface irregularity is investigated. The unsteady free-stream disturbances couple with the steady perturbations resulting from the surface irregularity to form a traveling-wave mode. The resonance condition necessary for receptivity requires a forcing at a wave number equal to that of the Tollmien-Schlichting (TS) eigenmode and a frequency equal to that of the free-stream acoustic disturbance. The basic (mean) flow is calculated using an interacting boundary layer (IBL) scheme that accounts for viscous/inviscid interactions. Then, the method of multiple scales is used to find the total amplitude of the generated wave. Results of this study show how the transition process is significantly stimulated. Also, the dependence of the receptivity on the geometry of the roughness element as well as on the amplitude and frequency of the acoustic disturbance is studied. Application of suction is shown to reduce the receptivity resulting from the roughness element. / Master of Science