THEORY OF THE DUCTED PROPELLER- 



A REVIEW 



Johannes Weissinger and Dieter Maass 

 Institut fur Angewandte Mathematik 

 " Universitdt Karlsruhe ■■ ■ ■■ 

 Karlsruhe, Germany 



■'■ '' '" ■"■■■■ ABSTRACT — •-• " ■■■- '•■■ >^-...:- 



This review is concerned mainly with the theory of ducted propellers 

 in incompressible, nonviscous, steady flow. Emphasis is laid on theo- 

 ries which try to determine the complete flow field and which have 

 been developed in the last IZ years. A brief survey of the development 

 before 1955, which was covered in a review presented by Sacks and 

 Burnell in 1959, is given. 



The main part starts with the theory of the duct alone (ring airfoil) in 

 axial and nonaxial flow. The numerical methods which form the basis 

 for the theory of the ducted propeller are outlined briefly, and some of 

 the basic assumptions are considered critically. The effects of cam- 

 ber (including taper) and thickness of the profile and of a central body 

 are treated. 



This theory is easily extended to a theory of the ducted actuator disk of 

 constant load without tip clearance in axial flow. Some linear terms 

 usually neglected in linear theories are shown to have a considerable 

 influence. 



The theory of the actuator disk with tip clearance treated next builds 

 the link to the theory of the ducted propeller with a finite number of 

 blades. The main problem is the determination of the velocity induced 

 by the free vortices shed from the propeller blades. This can be solved 

 only by a priori assumptions on the form of the vortex surface. These 

 can be checked and improved to some extent by iteration. In nonaxial 

 flow, the propeller produces an unsteady field, which, so far, can be 

 treated only by very rough methods. In this case, the duct experiences 

 not only a lift, but also a side force. 



The emphasis of the review is on analysis, not on design. The under- 

 lying models (vortex configurations, etc.), the numerical methods, and 

 the numerical results are the main subject. 



1. INTRODUCTION 



1.1 A Brief Historical Survey 



By choosing the proper type of duct, the velocity at a propeller can be in- 

 creased ("Kort nozzle") or decreased ("pump-jet"). The Kort nozzle is used 

 for increasing the efficiency of heavily loaded propellers, e.g., in S/VTOL 



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