Singularity method applied to the classical Helmholtz flow coupling procedure with boundary layer calculation

A free streamline wake model based on singularity distribution is proposed in order to treat the flow past an arbitrary curved obstacle with Helmholtz's wake. The slipping condition gives the vortex distribution on the obstacle and the steady evolution condition is written on the first part of the free streamlines in order to find their locations, the geometry of the second part being fixed by an asymptotic study. The validity of the method is judged by comparing results with those obtained by a formulation, to be used as a standard, which encloses conformal mapping and is an adaptation of Levi-Civita's method. Good agreement leads us to envisage extending the method to multi-element systems. Correlatively, we show a coupling procedure with a boundary layer calculation. Applied to the circular cylinder, it allows to bring out the existence of sub-and supercritical ranges. Although the latter is well predicted for the separation angle and the drag coefficient, the former is only approximately approached, with an overestimate of the critical Reynolds number as an immediate consequence.