Each concept has been evaluated in the cavitation tunnel and includes measurements 

 of both tip vortex cavitation inception and performance — lift, drag, and roll moment. 

 These measurements were made at a Reyonlds number R of approximately 5 x 10 . 



REPRESENTATION OF THE TIP-VORTEX ROLLUP PROCESS 

 The importance of tip vortices in fluid mechanics is demonstrated by the wealth 

 of literature dealing with the subject. In the past, an accurate mathematical rep- 

 resentation of the tip-vortex rollup phenomenon has been limited by the difficulties 

 in handling the complicated three-dimensional aspects of the tip crossflows and the 

 turbulent vortex. Today, as more detailed experimental data become available and 

 numerical techniques become more sophisticated, the ability of the analytical models 



to predict the observed tip vortices is being improved. 



2 

 The first generation of models to represent the vortex rollup phenomenon con- 

 sisted of a simplified semi-two-dimensional theory, where a vortex sheet emanates 

 from the trailing edge of a wing and rolls up into a concentrated vortex under the 

 action of its self-induced velocity field. The strength of the vortex is determined 

 by the spanwise load distribution of the wing. This simplified model failed to 

 correctly predict the size and stength of observed vortices. 



As more experimental data emerged, the later models became more realistic and 



3 

 elaborate; for example velocity surveys of tip vortices indicated a tangential 



velocity distribution (as shown in Figure 2) . These data identified an inner core 



with a rotational vortex structure which is surrounded by an irrotational vortex 



region. Incorporation of this observed vortex structure gave rise to a second 



generation vortex model. However, this model also failed to predict the observed 



vortices, due in part to an inability to predict the core radius. Continued experi- 



4 

 mental work led to the hypothesis that the tip vortex core radius was a function of 



the boundary layer on the wing tip surface. Later work substantiated this hypothe- 

 sis. The effects of the tip boundary layer characteristics on both the tip vortex 

 tangential velocity and core radius are illustrated in Figure 3. Here, a comparsion 

 is made between a laminar boundary layer tip flow — untripped — and a turbulent bound- 

 ary layer tip flow — tripped. The data indicate that the thicker turbulent boundai y 

 layer on the pressure side of the wing tip results in an increased tip vortex core 

 radius and a decrease in the tip vortex maximum tangential velocity as compared to 



