The non-viscous swirling flow of an incompressible fluid in a circular pipe with arbitrary form of meridian section is analyzed. When the deformation of the pipe from a circular cylinder is sufficiently small, perturbations of the flow can be assumed to be small comparing with the basic swirling flow. In the present analysis the more practical profiles of the basic flow containing exponential functions are chosen than the previous works, in which the basic flow with the constant axial velocity and the constant angular velocity was used. Applying the perturbation theory to solve the equations, the first order solution is obtained analytically. Numerical calculations show that the phenomena of blocking which diverge the solutions can also occur in this case.
There are few papers for nonuniform in-plane motions of wings, practical applications of which may concern lead-lag motion of helicopter blades and motions of horizontal stabilizer in T-Tail flutter. In the present formulation Fouriertransform is used, which makes development of the theory straighttorward, universal, and routine. Drag problems (on zero-lift symmetric wings) and lift problems (on zero-thickness wings) are treated for both two-and three-dimensional cases. Drag problems show a drag due to the instant acceleration, while lift problems yield and upwash dependent on the whole history of th wing motions.
The measurements of the aerodynamic forces acting on an oscillating two-dimensional NACA 0012 wing section were performed with a 120 mmφ Mach-Zehnder interferometer for the range 0.0 to 0.025 of the reduced frequencies. The slopes and the sizes of the loops of the normal force and the pitching moment coefficients were found to be appreciably smaller than the theoretical ones by Theodorsen's theory of an oscillating flat plate. The effect of the boundary layer along the wing surface to these discrepancies is discussed based on Theodorsen's theory applied to an oscillating flat plate with aileron, the amplitudes of which were estimated from Schlieren photographs of the boundary layers of two-dimensional 12% and 16.7% elliptic airfoil sections.