275 



90 SB 



FIGURE 13. Load distribution over the propeller disk 

 (based on effective velocity field measurements). 



(model-ship correlation) , as well as of the velocity 

 field in model tests taking account of propeller 

 effects. "Hhe amplitudes of harmonics deteririning 

 the nonstationary hydrodynamic forces and moments 

 (Figures 14 and 15) may vary several times under the 

 influence of the above factors. 



It should be mentioned that no definite regular- 

 ity could be observed here. With some relative 

 radii the amplitudes increase, with others they 

 decrease. 



As the variation in harmonic spectrum of the 

 velocity field is of rather a complicated nature 

 let us illustrate the effect the variation of axial 

 velocities due to scale effect and propeller opera- 

 tion has on the constant component of the hydro- 

 dynamic bending moment in the vertical plane which 

 is mainly defined by the first decomposition har- 

 monic [Voitkunskiy (1973) ] ; 



■ VO 



20 



yO 



where 



"ho " JCj/4/_ /T[ai+(1//T) (J+2K^Cj)a JdT 



TO 



Pyg = -JC2/-Q:f/T[bi+(l//T)(J+2Kg/C^)b^g]dT 



(21) 



(22) 



(23) 



J = V /nD 



Tg = relative radius of propeller hub 

 K .K = thrust and torque coefficients at 



design speed 

 a^ibj = Fourier transform coefficients for 



the cosines and sines of the first 



harmonic of axial velocity on a given 



radius 



3,Q»ti,n = Fourier transform coefficients for 

 I y 1 u 



the cosine and sine of the first 



harmonic of tangential velocity on a 



given radius 

 Ci,C2 = coefficients 



/ = coefficient depending on radius 



e = distance between the design propeller 



shaft section and the propeller disk 



The distributions of transverse relative ve- 

 locities Ue = Ug/V were taken as equal. 



Table 2 shows the design estimates of relative 

 values of the constant component, Hyg/KQ, as based 

 on various initial data. 



As can be seen, the calculated results based on 

 the nominal velocity field data may differ (even 

 qualitatively) from those obtained with considera- 

 tion for the scale effect or the effect of operat- 

 ing propeller. Although the local variations of 

 the nominal field due to the scale effect or pro- 

 peller operation are quantities of the same order 

 (see Figures 5 and 12) , the constant component 

 values of the bending moment in the vertical plane 

 determined from the effective field prove to be 

 4-5 times as large. Physically this may be due to 

 the fact that, in contrast to the scale effect, 

 the propeller effect on the viscous flow in the 

 upper parts of the propeller disk differs from that 

 in the lower part. In the upper part of the disk 

 (6 = 0- 90°) the effective field distribution of 

 velocities in way of the heavier loaded blade sec- 

 tions differs only slightly from the nominal field 

 distribution, while in its lower part (6 = 90-180°) 

 the effective field velocities are much in excess 

 of the nominal field velocities (by a factor of 

 1.5-2). This increases the asymmetry of circum- 

 ferential distribution of the effective field axial 



-0.2 



Ship, Nominal Field (Correlation Based 

 on Equations (l)-(4)) 



Model, Nominal Field 



Model, Effective Field 

 (Proposed Method) 



Model, Effective Field (According 

 to Titov and Otiesnov, 1975} 



FIGURE 14. Influence of scale effect and propeller 

 operation on harmonic spectrum. 



