Theory of Unsteady Propeller Forces 



11. Yamazaki, R. and Nishiyama, S., "On the Velocity Field Near a Propeller 

 Working Steadily in Still Water," Journal of the Society of Naval Architec- 

 ture of West Japan, No. 31 (1966) 



DISCUSSION 



p. C. Pien ' • 



Naval Ship Research and Development Center 

 Washington, D.C. 



This paper is another important contribution of the author to the field of 

 propeller hydrodynamics. It is a very comprehensive paper in which the author 

 has given a complete expression of the velocity potential of a single- screw hull- 

 propeller- rudder configuration. As shown by Eqs. (25) and (26) it is written in 

 terms of the source and the vorticity distributions which are determined by sat- 

 isfying simultaneously the unsteady boundary conditions on the hull surface, 

 propeller-blade surface, and rudder surface. Once the velocity potential is ob- 

 tained, it is a relatively easy matter to compute the vibratory forces on either 

 the hull, the propeller, or the rudder. However, it seems extremely difficult to 

 calculate these time- dependent source and vorticity distributions. Would the 

 author care to suggest a practical numerical procedure to obtain these distribu- 

 tions ? 



Concerning the computation of the periodic blade loading, I would like to 

 make one remark related to the geometry of a trailing vortex sheet in the behind 

 condition. As shown in Eqs. (112) the geometry of the free- vortex sheet is a 

 function of v, which is a function of the inflow velocity as well as the blade load- 

 ing. It is convenient to make the usual assumption that the free- vortex sheet 

 lies on a helical surface with the pitch the same as the blade- face pitch. How- 

 ever, this assumption also implies that there is no circumferential inflow varia- 

 tion, otherwise the free- vortex sheet cannot possibly lie on a helical surface. 

 Hence, such an assumption may not be proper, especially when the inflow to the 

 propeller is highly nonuniform and the blade is heavily loaded. Under such cir- 

 cumstances, it may be necessary to keep the actual slip- stream geometry intact. 

 However, as shown by Eqs. (112), the problem becomes extremely difficult if no 

 simplification is made on the slip- stream geometry. A long tedious iterative 

 procedure becomes necessary. This makes one wonder whether the vortex rep- 

 resentation of a blade loading is an appropriate approach in solving an unsteady 

 propeller problem under a heavily loaded condition. I would like to know the 

 author's view on this point. 



83 



