Comparison of Theory and Experiment on Ducted Propellers 



In addition to these studies, some work has been done on the ducted propel- 

 ler system at an angle of incidence, Kriebel (24) and Greenberg et al. (26). In 

 both these approaches, the mathematical model is similar to the linearized the- 

 ory discussed previously. As a first approximation, both Kriebel and Greenberg 

 et al. showed that the ducted propeller may be regarded as a superposition of the 

 ducted propeller at zero incidence plus a cylindrical duct at a given incidence. 

 This approximation, however, does not account for the side forces and moments 

 which occur on a propeller at an angle of attack (27). Greenberg et al. refined 

 the approximation by taking into account the cyclic variation of the blade loading 

 and these additional forces appear in the solution. 



Some theoretical work has been done on the effect of blade tip clearance on 

 performance. Both Kopeyetskiy (28) and Tachmindji (29) have considered the 

 case of a finite-bladed propeller in an infinite cylinder. Lifting-line theory was 

 utilized by both and the theories are essentially the same although different nu- 

 mercial solutions are utilized. Turbal carried out a theoretical and experimen- 

 tal investigation utilizing the previous theories (30), while English (31) and 

 Gearhart (32) have utilized one -dimensional analysis to obtain the effect of blade 

 tip clearance. Gearhart and Turbal considered the viscosity of the fluid in their 

 analyses. 



In the next section, comparisons will be made between pertinent theoretical 

 and experimental results. 



THEORETICAL AND EXPERIMENTAL COMPARISONS 



Criteria for Comparison 



Determination of whether a theory is adequate for predicting experimental 

 performance is highly subjective. To offset this problem to some extent, cri- 

 teria for the adequacy of the comparisons will be established on the basis of the 

 use of the data. Two types of measurements will be analyzed in the following 

 sections; pressure or velocity distributions and forces and moments. The pres- 

 sure or velocity distributions will be both those on the annular airfoil surface 

 and those within the flow field of the airfoil. Knowledge of the pressure distri- 

 bution on the airfoil, or duct, is necessary: [1] for estimation of the critical 

 Mach number in air or the critical cavitation number in water, [2] for estima- 

 tion of the probable boundary -layer characteristics such as separation, and 

 [3] for making structural analyses. Satisfactory prediction will be taken to 

 mean that the predicted pressure distribution is generally within experimental 

 accuracy and that the pressure distribution is adequate for determining the 

 foregoing items. Unsatisfactory prediction will be taken to mean that the pre- 

 dicted pressure distribution is not adequate for determining these items. For 

 many comparisons the prediction will be marginal, in that the pressure distri- 

 bution is adequate for determining only some of these items. 



Knowledge of the velocity field of the annular airfoil, or duct, is necessary: 

 [1] for design of the propeller, stator and guide vanes (if used), [2] for predict- 

 ing improvement in cavitation performance of the propeller, and [3] for deter- 

 mining the interaction of the duct with a centerbody (hub) or other bodies in the 



1315 



