Unsteady Propeller Lifting-Surface Theory With Finite Number of Chordwise Modes

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Abstract
A continuing investigation at Davidson Laboratory is concerned with improvement of the mathematical model developed for the evaluation of the steady and time-dependent distributions on the blades of marine propellers operating in spatially nonuniform flow. In the present study, the surface integral equation resulting from the theory has been solved by means of the collocation method, in conjunction with the generalized lift operator, for a prescribed set of chordwise modes which reproduce the proper leading-edge singularity and fulfill the Kutta condition at the trailing edge. General programs have been developed to accommodate any geometry of propeller operating in a specified nonuniform inflow condition for a large but finite number of chordwise modes. The calculations indicate that the spanwise loading distribution and the steady and time-dependent thrust reach stable values after three to five chordwise modes, but the chordwise distribution does not converge to its final form, particularly in the neighborhood of the leading and trailing edges. A comparison of theoretical and experimental results for the vibratory thrust shows satisfactory agreement on the whole. It is believed that the principal cause of any existing discrepancies between measured and calculated results is lack of precise knowledge of the wake harmonics.

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