Theory of the Ducted Propeller — A Review 



a) 



0.12 



0.06 



0.50 



0.25 



Fig. 18 - (See (153) ) Uniformly loaded ducted 

 propeller with infinite blade number at zero 

 incidence. Cylindrical duct, X = 0.5, x^^ = 0, 

 ^ = 0.9, J - 0, Cjp = 0.1. (a) Radial velocity 

 induced by the propeller slipstream on the 

 duct; (b) ring vortex distribution on the duct. 

 Suffix (0) refers to constant pitch of helical 

 vortices, (1) to pitch improved by one itera- 

 tion. 



equation (4.10), from which an improved duct 

 distribution y^i^ is then determined. This pro- 

 cedure can be iterated. Because the pitch j (x) 

 varies, the induced velocities, e.g., Vy'\^^ , must 

 be calculated by numerical integration (over an 

 infinite interval) which makes the computations 

 much more cumbersome. For the example 

 discussed above, the effect of axial pitch varia- 

 tion is shown in Fig. 18. Qualitatively, the ef- 

 fect is a shift of the "effective" propeller plane 

 rearward by approximately 2% of the chord 

 length. The corresponding duct thrust coeffi- 

 cients differ also by 2%. From this example it 

 may be concluded that the small differences in 

 the final results do not justify the additional 

 computational effect of the iteration procedure. 



5. THE FINITE-BLADED DUCTED 

 PROPELLER IN AXIAL FLOW 



Fig. 19 - (See (153)) 

 Duct vortex distri- 

 bution for two pro- 

 peller locations and 

 other parameters as 

 in Fig. 18 



If a propeller -fixed system of cylinder co- 

 ordinates (x,r,0) is introduced, the flow that is 



unsteady is shroud-fixed coordinates will be steady and periodic in 4> with a pe- 

 riod Itj/H. Because of the rotational symmetry of the duct, no additional normal 

 velocity is introduced on the duct surface by the rotation. 



1237 



