International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 50, Pages 3203-3216

Nonlinear unsteady flow problems by multidimensional singular integral representation analysis

E. G. Ladopoulos

Interpaper Research Organization, 56 Anagnostopoulou Street, Athens GR-106 72, Greece

Received 10 December 2001

Copyright © 2003 E. G. Ladopoulos. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A two-dimensional nonlinear aerodynamics representation analysis is proposed for the investigation of inviscid flowfields of unsteady airfoils. Such problems are reduced to the solution of a nonlinear multidimensional singular integral equation as the source and vortex strength distributions are dependent on the history of these distributions on the NACA airfoil surface. A turbulent boundary layer model is further investigated, based on the formulation of the unsteady behaviour of the momentum integral equation. An application is finally given to the determination of the velocity and pressure coefficient field around an aircraft by assuming linear vortex distribution.