Physical optics analysis of rotating blades in a cylinder

A relatively simple model is employed to predict the spectral level at the modulation frequency of the scattered return from a set of coplanar blades located inside an open conducting cylinder. The cylinder is assumed to be illuminated by a plane wave. Waveguide modes induced at the aperture of the cylinder are found by the field matching method whereby an S-matrix characterization of the waveguide-free space interface is obtained. Both ´horizontal´ and ´vertical´ degenerate sets of circular waveguide modes are needed for an accurate description of the scattering process. The excited modes propagate into the cylinder and illuminate a set of blades. Mode conversion occurs at this interface where modes of a given degenerate type are converted not only into modes of the same type but also into modes of the second degenerate type. This conversion process is modeled by first finding the induced currents on the blades through the physical optics principle. These currents, in turn, give rise to reflected modes which are found by the reciprocity formula The reflected modes propagate back towards the aperture where they radiate into free space. For the present investigation, the transmitted modes at the blade junction are terminated in their characteristic impedances. As the modal content at the cylinder aperture changes with the position of the blades, the resultant field pattern of the aperture modes exhibits a temporal variation. The blade modulation spectrum is obtained by Fourier transforming this time periodic signal. The adequacy of this model is tested.