Several panel methods are developed to model subsonic aerodynamics. The vorticity panel method for two-dimensional problems is capable of handling general unsteady, potential, lifting flows. The lifting surface is modelled with a vortex sheet and the wakes by discrete vortices. As an imitation of the conditions at the trailing edge, stagnation conditions on both surfaces are used. The over-determined system is solved by an optimization scheme. The present predictions are in good agreement with experimental data and other computations. Moreover the present approach provides an attractive alternative to those developed earlier. Two panel methods for three-dimensional nonlifting problems are developed. One uses source distributions over curved elements and the other vorticity distributions over flat elements. For the source formulation, the effect of weakly nonlinear geometry on the numerical results is shown to accelerate the convergence of numerical values in general. In addition, the extensive comparisons between two formulations reveal that the voticity panel method is even more stable and accurate than the curved source panel method. Another vorticity panel method is developed to study the lifting l flows past three-dimensional bodies with sharp edges. The body is modelled by single vortex sheet for thin bodies and two vortex sheets for thick bodies while the wakes are modelled with a number of strings of discrete vortices. The flows are assumed to separate along the the sharp edges. The combination of continuous vorticity on the lifting surface and discrete vortices in the wakes yields excellent versatility and the capability of handling the tightly rolled wakes and predicting continuous pressure distributions on the lifting surface. The method is applied to thin and thick low-aspect-ratio delta wings and rectangular wings. The computed aerodynamic forces and wake shapes are in quantitative agreement with experimental data and other computational results. / Ph. D.

A general nonlinear, nonplanar unsteady vortex panel method for potential-flow is developed. The surface is modeled as a collection of triangular elements on which the vorticity vector is piecewise linearly varying. The wake emanates from the sides and trailing edges of the thin lilting surfaces and is modeled as a progressively formed collection of vortex filaments. This model provides a continuous pressure distribution on the surface while allowing the wake to roll up as tightly as needed. The wake position is determined as part of the solution and no prior knowledge of the position or strength is assumed. An adaptive grid technique is used to redistribute the circulation of the vortex filaments of the wake as the wake sheet spreads. The aerodynamic model is coupled with dynamic equations of motion. Forced oscillation tests are conducted on flat rectangular and delta wings. Dynamic tests are performed to predict wing rock of a slender delta wing restricted to one degree of freedom in roll. The aerodynamic/dynamic model is coupled with control laws that govern the motion of flaperons so that a prescribed pitch motion is executed and wing rock is suppressed. ( 300 pages, 107 figures ) / Ph. D.

An engineering model designed for the analysis of high angle-of-attack flight characteristics is developed and applied to the problem of aircraft poststall departure. The model consists of an aerodynamics package used interactively with a six-degree-of-freedom flight simulator. The aerodynamics are computed via a nonlinear lifting line theory with unsteady wake effects due to a discrete, nonplanar vortex system. A fully configured aircraft (main wing, horizontal tail and vertical fin) is mathematically constructed by modeling all lifting surfaces with bound, discrete vortex segments and associated control points; vehicle geometric influence on high angle-of-attack flight characteristics is included through complete variability in the relative locations, orientations and sizes of the flight surfaces. This aircraft model is “flown” through prescribed maneuvers by integrating the equations of motion. Selected results of trajectory simulations presented for a typical general aviation aircraft provide the following insights to wing-drop departure subsequent to stall. The abruptness of poststall roll-off depends on the presence of flight asymmetries at the stall break and the rate of stall penetration. Such out-of-trim flight conditions induce asymmetric wing panel unstall subsequent to deep stall penetration resulting in large wing-drop-producing roll moments. However, the abrupt departure from symmetric flight conditions is also found to be mathematically possible. This is a consequence of multiple lifting line solutions which exist for bound vortex systems assigned the lift properties of airfoils having stall discontinuities. The dynamic model is well suited to the prediction of departure resistance benefits realized through passive aerodynamic modifications, for example, drooped leading edge outboard wing panels. The model can also be applied to the generation of dynamic stability derivatives by analytically simulating forced oscillation test procedures. / Ph. D.