This paper deals with a new approach to lifting line theory in which the presence of a hub and/or duct is taken into account by introducing the generalized induction factors. The proposed mathematical model is built on the assumption that the hub and/or duct are simulated with infinite cylinders. The circulation distribution function is represented in the form of a series of orthogonal Jacobi polynomials that covers all cases that can occur in practical propeller design, including both zero and nonzero gap conditions. The integral equation of the lifting line theory is solved numerically by applying the highest accuracy quadrature formula for singular integrals. Propellers with optimum and arbitrary circulation distribution are considered. The proposed theory is intended to improve design of the near hub and duct blade sections, cavitation control, and integral propeller characteristics. Numerical results are presented for the purpose of comparison with different methods and to illustrate the developed approach.

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