268 



medium displacement are shown in Figure 3 as an 

 illustration. Isotaches (lines U = const) plotted 

 in Figure 1 show that the upper part of the propel- 

 ler disk is in the hull boundary layer region and 

 here the flow contraction will take place almost 

 normal to the constant velocity lines rather than 

 to the longitudinal center plane. In this connec- 

 tion an attempt was made to evaluate the variation 

 of the flow velocities in the upper part of the 

 propeller disk using the approximate method re- 

 ported at the 13th ITTC, which provides quite a 

 good agreement with the full-scale test data, and 

 those obtained by calculation of the three- 

 dimensional boundary layer [Boltenko et al. (1972)]. 

 The results of the refined model — ship correlation 

 for this model within the propeller disk practically 

 coincide. Velocity deviations of 3-4% V are ob- 

 served only in the vicinity of the viscous wake 

 boundary in its upper sections (outside the propel- 

 ler disk). Figure 3. However, in some cases (e.g., 

 with pronoionced V-shaped afterbody frames) the hull 

 boundary layer can play a more significant role in 

 the formation of the wake flow, and in that case 

 its effect should additionally be taken into con- 

 sideration. Similar practical methods based on more 

 general assumptions with respect to regularities 

 in the variations of the axial velocities were given 

 by the towing tanks of Europe and Japan [Sasajima 

 and Tanaka (1966), Hoekstra (1977), Dyne (1974)]. 

 For comparison Figure 4 shows the model — ship cor- 

 relation results obtained by the Japanese method* 

 for some specific profiles of the wake of the model 

 under consideration. As is seen, this method leads 

 to a greater contraction of the wake in model — ship 

 correlation and does not take into account the varia- 

 tions of the velocity defect in the centerline plane. 

 However, apart from some limited regions in the 

 vicinity of 9 = 0° and 180° the circumferential dis- 

 tribution of axial velocities V^(c,Q) calculated by 

 both methods differs slightly (Figure 5) . For the 

 above reasons substantial discrepancies in the 

 vicinity of 6 = 0° and 9 = 180° can give rise to an 

 appreciable change in the harmonic spectrum of the 

 field especially in the amplitudes of the even har- 

 monics . 



At present it is difficult to find an acceptable 

 practical method of simulating the transverse ve- 

 locities, though the semiempirical theory indicates 

 the possibility of a noticeable scale effect of the 

 secondary flow velocities in the three-dimensional 

 boundary layer of the ship. 



Model "b" 



The flow nonuniformity in way of the propeller of 

 the twin-screw ship is mainly due to the hull bound- 

 ary layer and the additional loss of velocity in the 

 wake behind appendages 



V - U 



V 



U, 



U, 



u. 



H 



U, 



V 



u 



= W + W + Aw 

 P FO F 



(5) 



(Y/L) X 10'' 



LWL 



ooo Model, Experiment 



13 



-According to 

 Equations (1)-(4I 



-According to 

 Sasajima and 

 Tanaka, 1966 



(Y/L) X 10^ 



(Y/L) X 10^ 



FIGURE 4. Full scale wake predicted by different 

 methods . 



where 



W 

 P 



FO 



AW 

 F 



U 

 U, 



= potential component of the wake ; 



= viscous wake due to the effect of the hull 



boundary layer; 

 = additional losses of velocity in the wake 



behind the appendages ; 

 = horizontal local velocity 

 = horizontal local velocity in the "bare" 



hull boundary layer. 



*The method of Japanese researches was used as described by 

 Dyen (1974). 



The investigation of the wake scale effect for a 

 twin-screw ship, with a probable interaction between 

 the wake components, involves a number of complex 

 hydrodynamic problems. They include that of the 

 hull three-dimensional boundary layer, also the wake 

 behind the propeller shaft fairing placed at an 

 angle of attack to the flow inside the boundary 

 layer, in which case not only is the mean velocity 

 Vjj(y) changed but also the extent and the scale of 

 the "outside" flow turbulence. Then there is also 

 the wake — boundary layer interaction problem and, 

 finally, oblique flow around the circular cylinder 

 (shaft) placed in the turbulent boundary layer. 

 Many of the above problems are concerned with some 

 insufficiently known aspects of hydrodynamics of 

 viscous fluid and, therefore, cannot be completely 

 solved for the present. As with the previous case, 

 approximation schemes can be used for practical 

 estimations. By way of illustration let us con- 

 sider the model — ship correlation data for a twin- 

 screw ship equipped with propeller-shaft fairings. 



