Recent Theoretical and Experimental 

 Developments in the Prediction 

 of Propeller Induced Vibration 

 Forces on Nearby Boundaries 



Bruce D. Cox and Edwin P. Rood 



David W. Taylor Naval Ship Research and Development Center 



Bethesda, Maryland 



William S. Vorus 

 University of Michigan 

 Ann Arbor, Michigan 



John P. Breslin 



Stevens Institute of Technology 



Hoboken , New Jersey 



ABSTRACT 



This paper concerns recent advances in the theory 

 and numerical solution of propeller induced pressure 

 forces acting on ship hull surfaces. The analysis 

 is formulated in terms of the diffracted potential 

 flow about general three-dimensional hull boundaries 

 in the presence of a free surface. The influence 

 of the propeller is derived from lifting-surface 

 theory, explicitly accounting for finite blade 

 number, blade thickness and skew, and radial and 

 chordwise loading (steady and unsteady, but sub- 

 cavitating) . Two methods have been developed to 

 calculate the periodic forces. In the direct 

 approach, time-dependent source singularities are 

 distributed over the body surface with the strengths 

 determined for a prescribed propeller onset flow. 

 The force is then found by applying the extended 

 Lagally theorem. In the second approach, based on 

 a special application of Green's theorem, the force 

 is obtained by finding the velocity potential at 

 the propeller generated by the boundary executing 

 simple oscillatory motions. 



A towing tank experiment is described in which 

 blade frequency forces were measured on a body of 

 revolution adjacent to a propeller operating in 

 virtually uniform flow. The simplifications of 

 body shape and propeller loading provided a physical 

 model which could be treated in a reasonably exact 

 fashion by the theory. The body consisted of two 

 parts. A heavy afterbody, attached to the towing 

 strut, acted as a seismic mass at all but very low 

 frequencies. The forces were measured on a light, 

 rigid forebody supported from the afterbody by a 

 specially designed strain-gaged flexure assembly. 

 Tests with two propellers differing only in blade 

 thickness revealed the separate contributions of 

 blade loading and thickness and the results obtained 

 agree favorably with the analytical predictions. 



1 . INTRODUCTION 



Propeller induced ship hull virbration continues to 

 be a major source of uncertainty and, indeed, 

 frustration to the naval architect. Today we witness 

 a trend toward larger and faster ships with higher 

 power being delivered to the propeller. These 

 designs are inherently more susceptible to propeller 

 related vibration problems, as has been learned 

 from bitter and usually costly experience and this 

 situation has focused renewed attention on the need 

 for improved methods to predict propeller exciting 

 forces - methods which are both reliable and practi- 

 cal for application during the design process. 



Two distinct, but related types of propeller 

 exciting forces (and moments) produce hull vibration. 

 Unsteady blade loads developed by the propeller 

 operating in the nonuniform ship wake and trans- 

 mitted to the hull directly through the propeller 

 shafting are termed bearing forces. Periodic 

 pressure forces acting on the surface of the 

 hull , arising from the propeller unsteady veloc- 

 ity and pressure fields, are called surface forces. 

 Various approaches have been developed to predict 

 these forces from model tests. For example, bearing 

 forces are measured on a model propeller in a water 

 tunnel using wake screens to simulate the flow at 

 the ship stern. Surface pressures can be obtained 

 from measurements of transducers distributed over 

 the surface of the model hull afterbody. Alterna- 

 tively, the entire hull afterbody can be cantilevered 

 on a flexure assembly instrumented to measure the 

 total surface force [separated stern technique, 

 Stuntz et al. (1960) ] . 



The foregoing experimental techniques, and 

 others [most notably Lewis (1969)], have proven to 

 be costly and difficult to carry out in practice. 

 Moreover, a large number of experiments would be 

 required to examine all the pertinent physical 

 parameters, including hull form, propeller clearances. 



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