the radial velocity is on the hub condition. Thus, the hub boundary condition is 

 needed not only to find the hub effect on the pitch distribution but also to make 

 the solution stable. 



The specified boundary conditions are well satisfied in general, although when 

 the boundary condition on the hub is included, the cavity conditions are slightly 

 less accurate, as shown in Figures 11 and 12. The differences in the radial veloc- 

 ities occurring for the case with and the case without the hub boundary condition 

 (see Figures 13 and 14) indicate an instability. The radial velocity satisfying the 

 hub boundary condition in Figure 13 is the stable solution. In Figure 15 the pitch- 

 diameter ratio is shown for Model 4717C with hub images. In Figure 16 the camber 

 correction factors are shown for Model 4717C with and without hub images. When the 

 computed results obtained without consideration of the hub boundary condition 

 happened to have radial velocities with small values, the results were very close to 

 the solutions obtained when the hub boundary condition was considered. The numerical 

 results reported in the following discussion were obtained without satisfying the 

 hub boundary condition. In the cases given, the instability phenomenon was not 

 noticed. 



NUMERICAL EXAMPLES FOR PROPELLER DESIGN AND DISCUSSIONS 



Many supercavitating propellers have been designed and tested in the past; of 



2 

 that number, two propellers, DTNSRDC Models 3770 and 3870 were chosen to determine 



if this design program is reasonable. The former propeller has three blades and a 

 low advance coefficient, and the latter has four blades and a high advance coeffi- 

 cient. Experiments showed that both propellers had smooth cavities. The experi- 



2 

 mental results and the previous design calculations are available. 



The design and performance characteristics of the two propellers are shown in 

 Table 2. 



It is extremely difficult to compare the present numerical results to the 

 experimental results for propellers that were designed using an entirely different 

 method. The present program is intended for design, not prediction. The present 

 program does not produce data on leading-edge cavity thicknesses, input that is 

 essential to the design of propellers similar to Models 3770 and 3870. To check 

 the reasonableness of the present program we guessed at the leading-edge cavity 

 thicknesses for Models 3770 and 3870; this is presented in Figure 17. Because the 



27 



