NUMERICAL SCHEMES AND COMPUTER PROGRAM 



There are several computer programs for lifting-surface design of subcavitating 

 propellers. Supercavitating propellers are similar to wide- and thick-bladed sub- 

 cavitating propellers when the cavity thickness is known; therefore, it would seem 

 reasonable to use an existing computer program for subcavitating propellers rather 

 than to start the entire complicated program from scratch. Among the available 

 programs, the recent program by Kerwin was chosen for two reasons: (1) it included 

 the effect of sources and vortices, and (2) it could include the effects of rake and 

 skew with variable X. 



The main differences between the programs for supercavitating and subcavitating 

 propellers are as follows. The strengths of source distributions are not known in 

 the supercavitating case because the cavity shape is not known while the blade thick- 

 ness is assumed to be known for the subcavitating case. Therefore, the program for 

 solving the cavity-source distribution is written according to the present theory 

 explained in the previous section and becomes the main frame of the present program. 

 Routines in the Kerwin program are used as much as possible. The source is distrib- 

 uted not only on the blade but also in the cavity wake according to Equations (31) 

 and (34). Therefore, the number of meshes for supercavitating propellers is almost 

 as much as two and a half times the number for the subcavitating case. The chord- 

 wise load distribution is taken from the supercavitating cascade theory of pre- 

 liminary design rather than from airfoil theory. The forces on the blade are ob- 

 tained from Equations (41) and (45). 



Figure 4 gives the outline of the flow charts of the lifting-surface program. 



Attention should also be drawn to the following points, which differ from the 

 existing program for subcavitating propellers. 



Because of the singular behavior of the kernels of integrals appearing in the 

 induced velocity expressions in Equations (17) and (18), all the integrations related 

 to bound and trailing vorticity, and the source distribution are integrated analyt- 

 ically in a small interval of the radial direction on the blade and cavity where the 

 collocation points are located; using Equation (35). 



Because of the singularity along the leading edge, both for source and load 

 distribution, the interval that includes the leading edge is treated separately. 

 That is, the leading-edge load is the integrated load obtained when the remaining 

 load distribution is subtracted from the total load. The leading-edge source 



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