Theory of the Ducted Propeller — A Review 



The model and some of the basic mathematical ideas used at Karlsruhe 

 were also used by two other groups, working at THERM (Ordway, Ritter, Green- 

 berg, Hough, Kaskel, Lo, Sluyter, Sonnerup) and at NSRDC (Morgan, Caster, 

 Chaplin, Voigt). Though there are differences in mathematical details (e.g., 

 representation of kernel functions by elliptic or by Legendre functions, different 

 methods for a numerical solution of the integral equations, etc.), the numerical 

 results of all three groups, in so far as the same problems were treated, coin- 

 cide because a common model is used. At THERM and NSRDC the theory was 

 extended to finite-bladed propellers with tip clearance. At THERM the steady 

 part of the forces caused by nonaxial flow was also computed. 



The numerical analysis of THERM culminated in the presentation of work 

 sheets for the numerical evaluation of shroud performance for finite-bladed 

 ducted propellers in axial flow at cruise velocity (151). For specified values of 

 blade number, axial propeller position, tip clearance ( ? 0), ratio of propeller 

 radius to shroud reference radius, propeller advance ratio, the geometric pa- 

 rameters of NACA 4, 5, and 6 digit profiles and arbitrary values of propeller 

 thrust coefficient and chord line incidence, tables are presented such that the 

 shroud sectional radial force and moment coefficients and center of pressure, 

 the shroud thrust coefficient, the net shroud pressure coefficients, and the outer 

 and inner shroud surface pressure coefficients can easily be computed by hand 

 on the worksheets. Configurations other than those given by the specified pa- 

 rameter values can be handled by interpolation or extrapolation. On the propel- 

 ler blade an otpimum circulation is assumed. An addendum (156) contains 

 worksheets for the calculation of shroud-induced axial velocity. Knowing this 

 velocity, the blade geometry required to produce the assume dcirculation can be 

 determined by classical methods. The THERM tables can also be used for other 

 purposes, e.g., two-dimensional profile theory. 



The theory developed at NSRDC was condensed in a FORTRAN program for 

 the IBM-7090 high-speed computer (134). The input for the duct consists mainly 

 of the section camber and thickness ordinates, the section angle of attack, and 

 the chord-diameter ratio. There are options whereby the ideal angle of attack 

 of the duct section can be determined in the presence of the propeller. The pro- 

 peller input consists of the propeller diameter, propeller speed in revolutions 

 per second, design thrust (or propeller shaft horsepower), ship speed, number of 

 blades, inflow velocity, and circulation (or pitch distribution). If the propeller 

 is to be designed using the LERBS optimum pitch distribution, only an estimate 

 of the propeller ideal efficiency is given as input, instead of the circulation or 

 pitch distribution. The output consists of the propeller design characteristics 

 and performance, as well as the duct thrust and pressure distribution. The re- 

 sults can normally be obtained in approximately 27 minutes of computer time. 

 Consequently, features which are not included in the THERM approach include 

 the following: 



(1) Any shape can be considered for the duct. 



(2) The ducted propeller can be designed for a given thrust or horse- 

 power. 



(3) The design and predicted performances of the propeller can be 

 obtained. 



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