274 



Application of this procedure can be illustrated 

 on a medium size tanker model (Model 1) . 



Experimental studies of the velocity field for 

 the operating propeller were performed during free- 

 running model tests with the operational relative 

 speed, Fn = V/i'gLii = 0.22. Wake characteristics 

 ahead of and behind the propeller were measured at 

 equal distances from the propeller centre with a 

 6-point probe [devised at our model tank, Otlesnov 

 (1969) ] , which enables simultaneous measurements of 

 total head pressure, (H) , static pressure, (P) , and 

 flow angles in the horizontal and vertical planes 

 in the immediate vicinity of the propeller. VBien 

 processing the measured data and analysing the nom- 

 inal wake, use was made of calibration relationships 

 which took into account the interference of flow 

 angles in the vertical and horizontal planes with 

 the readings of .the probe. Figures 10 and 11 il- 

 lustrate the initial data and the calculated induced 

 velocities for the starboard-side of the propeller 

 disk (right-hand rotation) in the region where 

 sections experience maximum loading. 



Comparison (Figure 12) of the nominal velocity 

 field with the effective velocity field calculated 

 from Eqs. (11)-{12) and (13)-(18) shows the pro- 

 nounced effect the propeller has on the wake at the 

 lower part of the propeller disk and the minor ef- 

 fect at the upper part of the same . This may be 

 accounted for by a better possibility for momentum 

 exchange between the external flow and the viscous 

 wake under the action of radial induced velocities 

 in a relatively thin wake at the lower part of the 

 propeller disk, and a worse possibility at the upper 

 part where the thickness of the viscous wake is much 

 greater (see isotachs in Figure 1) . 



Nominal Field 



Effective Field (Titov and Otlesnov, 1975) 

 Effective Field (Proposed Method) 

 Effective Field (Hoekstra, 1977) 



X 0.6 - 



I 



90 



180 



180 



FIGURE 11. Circumferential distribution of velocity 

 components in way of propeller (r = 0.756). 



FIGURE 12. Influence of propeller operation on 

 velocity distributions. 



The above two methods for defining effective 

 field axial velocities yield results which, as a 

 whole, show satisfactory agreement. However there 

 are some systematic discrepancies in the regions 

 of 6 " 0° and 6 ~ 80-160°, and additional analysis 

 is required to explain these. 



Besides, the velocity distribution data obtained 

 on the basis of measurements ahead of and behind 

 the propeller in operation make it possible to find 

 the thrust distribution (load coefficient of pro- 

 peller, Crpjj,) over the propeller disk area 



W^ + U 2 



c^(ce) = (— ) - 1 



xe 



(19) 



Figure 13 and the equivalent system of singularities 



Q(ce) 



w /u 

 a xe 



(20) 



In its turn, the knowledge of this system of singu- 

 larities allows one to calculate the induced ve- 

 locities over the total wake region ahead of the 

 propeller, and perform a more detailed analysis of 

 the effect the nonuniformity of load distribution 

 over the disk has on thrust deduction. 



The following conclusions can be drawn from the 

 comparison of Fourier transform coefficients for 

 the circumferential distribution of axial velocities 

 of the nominal field obtained for the model and ship 



