A Geometrically Consistent Linearization Method for an Elliptic Strut,
BRITISH COLUMBIA UNIV VANCOUVER DEPT OF MECHANICAL ENGINEERING
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Study of irrotational, incompressible flows about thin geometries can be carried out using the well-known perturbation procedures. In two-dimensional flows exact solutions based on mappings can be used to compare the accuracy of first-order solutions is not sufficiently accurate in representing the pressure and velocity distribution, especially about the leading edge. For three-dimensional flows exact solutions are rare and, for more complex problems such as ship wave resistance formulations, an exact solution does not exist but are very difficult to calculate. Therefore, it would appear advantageous to improve first-order calculations. To this end a perturbation method that incorporates the geometric properties of the disturber is studied. This method is first applied to a symmetric Joukowski airfoil, to an ellipse and an elliptic strut. This method, here called the geometrically-consistent linearization method, predicts the leading edge pressure variations correctly for the two foils studied and appears to be superior to the classical first-order solutions. An iterative solution following this procedure further improves the calculation. The method discussed and the following iteration procedure seem to form an efficient numerical solution to airfoil flow problems. The method is then applied to a elliptic strut wave-resistant calculation.