A flow model for a Joukowsky airfoil with an inclined spoiler or split flap is constructed based on the early work by Parkinson and Jandali. No restriction is imposed on the airfoil camber, the inclination and length of the spoiler or split flap, and the angle of incidence. The flow is assumed to be steady, two-dimensional, inviscid and incompressible. A sequence of conformal transformations is developed to deform the contour of the airfoil and the spoiler (split flap) onto the circumference of the unit circle over which the flow problem is solved. The partially separated flow region behind these bluff bodies is simulated by superimposing suitable singularities in the transform plane. The trailing edge, the tip of the spoiler (flap) are made critical points in the mappings so that Kutta conditions are satisfied there. The pressures at these critical points are matched to the pressure inside the wake, the only empirical input to the model. Some studies of an additional boundary condition for solving the flow problem were carried out with considerable success. The chordwise pressure distributions and the overall lift force variations are compared with experiments. Good agreement in general is achieved. The model can be extended readily to airfoils of arbitrary profile with the application of the Theodorsen transformation. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

The thesis deals with some new applications of the wake source model, a two-dimensional incompressible potential flow model used for bodies experiencing flow separation. The body contour is conformally mapped to a circle, for which the flow problem is solved using source singularities to create free streamlines simulating the separating shear layers. In common with other inviscid theories, it generally requires the pressure in the separated flow region, and the location of separation if boundary-layer controlled. Different mapping sequences and flow models have been constructed for the following five problems, 1. the trailing-edge stall for single element airfoils, 2. flat plates with separation bubbles, 3. separation bubbles upstream of spoilers with downstream wakes, 4. spoiler/slotted flap combinations, at which the spoiler inclination is arbitrary, and 5. two-element airfoils near (trailing-edge) stall. Predictions of pressure distribution are compared with wind tunnel measurements, and good agreement is found in cases 1 and 5. The initial shape of the separation streamlines also appears to be satisfactory. Results in cases 2 and 3 are promising although more work is needed to improve the bubble shapes and their pressure distributions. Partial success has been achieved on spoiler/ slotted flap configurations, depending on the spoiler inclination. For strong wake effect on the flap (e. g. δ = 90° ), the model predicts a very high suction peak over it. Whereas the experimental data resemble a stalled distribution even though flow visualization indicates the flap to be unstalled. This may be related to a limitation of the method, also noted in the separation-bubble problems, that it cannot specify a complete boundary condition on a free streamline. This discrepancy diminishes as the spoiler angle becomes smaller (e. g. δ = 30° ) in the cases of higher incidences so that the wake boundary tugs away from the flap sooner. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

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The boundary-layer behavior over an airplane's wings is of great importance in take-off and landing of the airplane. If its angle of attack is increased past a critical value, the flow separates from the lifting surface, resulting in a drastic loss of lift and a major increase in drag. In response to this phenomenon, many mechanisms have been studied to control the boundary-layer. First neglected because of implementation difficulties of its application, moving wall boundary-layer control methods have mainly relied on experimental research. The moving wall concept is principally applied as a rotating cylinder protruding into the airfoil. The purpose of this thesis is to provide a computational base to these experiments and to use mathematical tools of computational fluid dynamics and optimization to predict the optimum rotating speed of the cylinder, placed at the leading edge of the airfoil. For the sake of simplicity, we replace the airfoil by a flat plate with a wedge trailing edge. To model the incompressible viscous two-dimensional Navier-Stokes equations, the finite element method is applied on an unstructured two-dimensional mesh. An adaptive remeshing strategy utilized in conjunction with an error estimator controls the solution's accuracy. The aerodynamic forces acting on the total surface are computed from the finite element approximation. The ratio of the lift and the power required to move the flat plateairfoil and to rotate the cylinder forms the objective function to be optimized. A graph of the objective function versus the angle of attack is first constructed for several rotational speeds to provide a rough visual estimate of the optimum value for every angle of attack. Ultimately, an automatic optimization process provides the final solution. This results in the ideal rotational speed to be applied as the angle of attack varies. / Master of Science