Bavin, Vashkevich, and Miniovich 



ratio on the fluctuating pressure amplitude; their influence turned out to be 

 rather small. Experiments carried out in the Soviet Union confirmed the afore- 

 mentioned conclusion about good agreement of experimental and theoretical val- 

 ues of pressures generated by a propeller in a uniform flow. 



The effect of nonuniform inflow conditions on the propeller-induced pres- 

 sure was first taken into account by Babaev (3). However, later experiments 

 showed his equation to overestimate the nonuniformity contribution, due to some 

 shortcomings in the underlying assumptions. A more general expression for 

 the pressure generated by a propeller operating in a nonuniform flow is given 

 in Ref. 5. It is based on the quasi-steady assumption; i.e., at a given circula- 

 tion value the pressure induced by a propeller blade in a nonuniform flow is 

 considered to be the same as in the case of a uniform flow. In 1963 Tsakonas, 

 Breslin, and Jen concluded from their study (6) that the effect of a nonuniform 

 inflow on the vibratory pressure is negligible at the propeller location and in- 

 creases with distance from the propeller. The unsteady blade loading distribu- 

 tion was determined in this work approximately by applying results of unsteady 

 two-dimensional airfoil theory. 



In the present report the relation between fluctuating pressure and nonsta- 

 tionary circulation around the blade of a propeller operating in a nonuniform 

 flow will be obtained. It will be shown that within linearized theory this relation 

 remains the same as in the case of a uniform flow. Thus the above mentioned 

 assumption made in Ref. 5 is proved to be valid. Equations will be given which 

 make it possible to compute the amplitudes of the blade -frequency pressure 

 harmonics for the propeller operating in a wake, provided the circulation on the 

 blade is known. 



Calculations performed by the authors indicate that maximum pressure val- 

 ues in a nonuniform inflow may increase to 1.6 times those in a uniform flow. 

 The results of the blade -frequency pressure measurements are available. 



PRESSURE FIELD AROUND A PROPELLER OPERATING 

 IN A WAKE 



Let us consider a z-bladed propeller advancing in the positive direction of 

 the X axis and rotating at constant angular velocity around the x axis in a non- 

 uniform flow (Fig. 1). The relative inflow velocity at the propeller location is 

 equal to (-Vp • i + Av), where Vp is the mean axial velocity and ^\ is the per- 

 turbation velocity induced by a ship hull. The perturbation velocity Av is as- 

 sumed to be a function of position only (i.e., independent of time) and small 

 compared to Vp. 



Nonuniform flow at the propeller leads to variation of the relative velocity 

 and the angle of incidence of a blade section during propeller rotation. Hence, 

 both constituents of the pressures produced by a propeller in nonuniform flow 

 should differ from those attending propeller operation in uniform flow. How- 

 ever, it is evident from the equations for the blade -thickness constituents of the 

 propeller- induced pressures (e.g., see Ref. 1) that for such thin bodies as pro- 

 peller blades the effect of the nonuniform inflow conditions on the pressure 



