269 



90 go 1 80 



Model R„ = 1.3X 1o' 



ShipR^ =1.5X10® 



(According to Equations {1 )-(4)) 



ShipR„ =1.5X10® 



(According to Sasajima and Tanaka, 1966) 



90 



180 



FIGURE 5. Full scale circumferential velocity 

 distribution predicted by different methods. 



The experiments show that, in the vicinity of the 

 heavily-loaded blade sections which are at a dis- 

 tance from the hub, the interaction between the 

 boundary layer and the wake behind the fairing can 

 be considered insignificant; the effect of support- 

 ing vortices at the fairing junction is also negli- 

 gible or not found at all because provision is 

 usually made for a smooth transition of the fairing 

 to the shaft body. This enables simulation of each 

 component of the viscous wake VJFO(Rn) and AWp(Rn) 

 to be investigated separately with the total scale 

 effect to be determined by the method of superposi- 

 tions . Here it is expedient to make measurements 

 in the Cartesian system of coordinates as well. For 

 the model — ship correlation of the wake behind the 

 hull the method described by Boltenko et al . (1972) 

 is used. When simulating a component of the wake 

 AWp caused by the flow around appendages, use can 

 be made of the relationships of the free turbulence 

 theory (1) and (2) . According to data of the flow 

 visualization, it can be considered with an accuracy 

 sufficient for practical purposes that the stream- 

 lines on the fairing are arranged equidistant to 

 the hull surface, and that in evaluating the scale 

 effect the strip theory can be used. Then 



AW^^ = AW„ HS /c 7c 

 FS Fm = — DS Dm 



"Hm 



for 2 = — 



const 



y = ^ = const (6) 



where 



C = coefficient of the fairing resistance at 



section at a given distance £ from hull 



surface (Figure 6) ; 

 U = velocity in the hull boimdary layer at a 



given distance Z from its surface; 

 b = width of wake behind the fairing at the 



propeller. 



From the model-ship correlation data shown in Fig- 

 ure 5 it is seen that the flow nonuniformity varies 

 almost equally due to the scale effect of the hull 

 boundary layer and the wake behind the shaft fairing. 

 The mean circumferential axial wake is reduced ap- 

 proximately by one half. 



Model "c 



The discrete vortices, which develop due to separa- 

 tion from the bilge, with their axes oriented in 

 the direction of the main flow may have, in some 

 cases, especially where the flow is around the U- 

 shaped stern frames, a noticeable effect on the 

 afterbody flow pattern. Generally there are two 

 vortices arranged symmetrically in relation to the 

 center plane; however, sometimes more complex vor- 

 tical systems can be observed in the flow around 

 full ships. The development of the bilge vortices 

 leads not only to redistribution of the tangential 

 velocities at the propeller, but to the additional 

 nonuniformity of the axial wake as well due to 



a) redistribution of the velocities of the main 

 flow in the hull boundary layer and in the wake 

 behind the hull under the action of the vortex- 

 induced transverse velocities and 



b) variation of the axial velocities in the 

 vortex turbulent cores, the transverse dimensions 



Diagram 



////// 7 //////////////// 7/ / /^ / / 



Model (R„= 1.0 X lO'l 



260 







100 



Ship (R„ = 6.0 X 10^) 



260 



100 



b /c 

 m 



/C 

 DS' Dm 



(7) 



FIGURE 6. Scale effect estimates for nominal velocity 

 distribution at propeller of a twin-screw ship with 

 shafting fairings . 



