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A Natural Formulation for the Solution of 2d or Axisymmetric Inverse Problems
No full textINTERNATIONAL JOURNAL NUMERICAL METHODS IN ENGINEERIN
Vortex equilibrium in flows past bluff bodies
No full textThe equilibrium conditions of a point vortex in the separated flow past a locally deformed wall is studied in the framework of the two-dimensional potential flow. Equilibrium locations are represented as fixed points of the vortex Hamiltonian contour line map. Their pattern is ascribable to the Poincaré-Birkhoff fixed-point theorem. An ‘equilibrium manifold', representing the generalization of the Föppl curve for circular cylinders, is defined for arbitrary bodies. The property ∂ω/∂ψ ˜ =0 holds on it, with ψ ˜ being the stream function and ω the streamline slope of the pure potential flow. A ‘Kutta manifold' is defined as the locus of vortices in flows that separate at a prescribed point (Kutta condition). The existence of standing vortices that satisfy the Kutta condition is discussed for symmetric bodies. On the basis of an asymptotic expansion of the equilibrium manifold, Kutta manifold and body geometry, it is shown that different classes of symmetric bodies exist which are ranked by the number of allowable standing vortices that satisfy the Kutta conditio
On the Circulation Manifold for Two Adjacent Lifting Sections
Full text linkThe circulation functional relative to the potential flow past two adjacent lifting sections is studied for two cases. In the first case we consider two adjacent circles. The circulation is computed as a function of the displacement of the secondary circle along the axis joining the two centers and of the angle of attack of the secondary circle. The gradient of such functional is computed by deriving a set of elliptic functions with respect both to their argument and to their period. In the second case studied, we considered a wing-flap configuration. The circulation is computed by some implicit mappings, whose differentials with respect to the variation of the geometrical configuration in the physical space are found by divided differences. Configurations giving rise to local maxima and minima in the circulation manifold are presented
On the formulation of an inverse problem and an optimization method for turbomachinery design,
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