Linearized inverse method for the design of two-element ducted propellers

The linear inverse method for ducted propellers or annular airfoils is applied to the design of the two ducts of a two-element ducted propeller. The calculated inviscid duct thrusts are corrected for viscous drag. In a parametric study, the relative lengths of the two elements were varied within a fixed total length of the installation. Also the location of the propeller in the aft duct was varied. The objective was to maximize the sum of the thrusts of the elements. As is the case with multi-element airfoils, the sum of the thrust increases compared with the single-element reference duct, provided suitable pressure distributions for both the forward and aft ducts are prescribed. The theoretically predicted increase in thrust is of about the same magnitude as the increase in the lift of two-element airfoils in comparison with the corresponding single-element airfoil. Hydrodynamically efficient short forward ducts are thin and have a sharp leading edge, which is likely to cause flow separation in the uneven wake of a ship. The minimum acceptable ratio of the forward length to the aft length may be about 1 : 3. For a forward duct of this length, a pressure distribution with a rather long roof-top is found to be advantageous, producing a well rounded leading edge.