Sevik 



flow which are deterministic and periodic in nature. However numerous cases 

 exist in which the blades of turbomachines are subjected to random fluctuations 

 of a flow field. A common example is the fan of a household air conditioner op- 

 erating behind an ornamental grill. Another example is a marine propeller 

 immersed in the turbulent boundary layer of a ship. 



In this paper a theoretical analysis of the response of a propulsor to random 

 velocity fluctuations is given. As a special example the theory has been used to 

 predict the force fluctuations on a propeller of low solidity with blades of rela- 

 tively high aspect ratio operating in a homogeneous, isotropic turbulence field. 

 It is reasonable to expect that the response of the propeller will depend on two 

 parameters, namely, the ratio of propeller diameter and the ratio of blade chord 

 to a characteristic turbulent eddy size. It is shown that the power spectrum 

 peaks at the origin and drops off rapidly with increasing frequency. 



THEORETICAL CONSIDERATIONS 



The statistical properties of the force fluctuations experienced by a propul- 

 sor operating in a turbulent flow can readily be related to those of the random 

 velocity fluctuations, if the response of the propulsor is linear. Imagine the 

 propulsor to be subdivided into an arbitrarily large number of small surface 

 elements, and consider one such element located at y^ (Fig. 1). Steady and un- 

 steady fluid velocities are measured with respect to a Cartesian coordinate sys- 

 tem a' (a' = l',2',3') which is fixed in space. An unprimed system a(a = 1, 2,3) 

 rotates with the propeller and is oriented so that one of its axes coincides with 

 the axis of symmetry of the propeller. 



AXIS OF ROTATION 

 OF PROPULSOR 





LOCATION OF i'^ SURFACE 

 ELEMENT OF PROPULSOR 



FREE-STREAM 

 VELOCITY 



U 



Fig. I - Coordinate systems. The primed 

 coordinate system is fixed in space, and 

 the unprimed coordinate system rotates 

 with the propulsor. 



292 



