This paper analyzes and tests the ability of the surface source singularity method to calculate flow about two-dimensional lifting airfoils using the relatively small element numbers typical of three-dimensional cases. The aim is to discover improved calculation techniques for both two and three dimensions. The body of the paper presents a series of test airfoils about which the flow has been calculated by various refinements of the method. Conclusions are drawn from the results. The original form of the method, which uses flat surface elements, piecewise constant source density, and a constant surface vorticity distribution, is found to be satisfactory for 'ordinary' simple airfoils with finite trailing edges. For airfoils with very thin and/or highly loaded aft portions the original form of the method experiences difficulty, generally due to the fact that a singularity of the source density is required at the trailing edge. By using a parabolic surface vorticity the difficulty is largely alleviated, and satisfactory results are obtained. This modification is very easy to implement numerically. Further refinements consisting of curved surface elements, piecewise-parabolic source density, and the Kutta condition extrapolated to the trailing edge improve the solution still further and produce extremely accurate pressure distribution on rather extreme airfoils with surprisingly small element numbers
The use of higher-order surface singularity distributions to obtain improved potential flow solutions for two-dimensional lifting airfoils
Die Anwendung von Oberflaechensingularitaetsverteilungen hoeherer Ordnung zur Gewinnung verbesserter Potentialstroemungsloesungen fuer zweidimensionale Tragflaechen
Computer Methods in Applied Mechanics and Engineering ; 5 , 1 ; 11-35
1975
, 7 Quellen
Article (Journal)
English