Theory of the Ducted Propeller — A Review 



In a further simplification, it is assumed that r(r) is constant: r(r) = r^v^). 

 Then vp< is produced by concentrated helical vortices trailing from each of the 

 N blade tips and can be expressed by integrals of Legendre functions over an in- 

 finite interval in a way similar to that in the previous section. 



Three typical distributions of F/a and G a are shown in Fig. 22. Since 

 their importance is determined by their magnitude relative to unity, we see that 

 the duct-propeller coupling is, in fact, large enough to account for a significant 

 improvement over the simple superposition model but not large enough to dis- 

 credit the superposition model as a reasonable first approximation. A typical 

 pressure distribution is shown in Fig. 23. — 



0.0 

 -0.2 



Prop*U*r 



0.0 

 G/« 

 -0.2 



Fig. 22 - (See (157)) Camber 

 functions for ducted propeller 

 at angle of attack (n = 3, y.- 0.95, 

 d/R„= 0.2, x„/c = -0.25) 



(a) \ = 0.5, 



(b) X = 0.5. 



(c) X = L.O, 



= 0.5 

 = 0.25 

 = 0.5 



7. FINAL REMARKS 



The theory of ducted propellers as presented in this review has reached a 

 first goal. Based on linearizations which have been successfully used for a long 

 time in propeller and airfoil theory, a consistent and complete theory has been 

 developed for axial, nonviscous, incompressible flow. To some extent, the basic 

 linear assumptions have been checked by nonlinear theories; the linearization 

 does not affect the relevant results gravely. Insofar as the effects of viscosity, 

 compressibility, and cavitation can be determined separately, the theory should 

 now afford a reliable tool for predicting design and performance. 



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