270 



of which can be rather large as shown in Figure 2 . 

 Thus the whole flow field containing bilge vor- 

 tices can be divided into three parts: 



1) the region of turbulent core, 



2) the region of vortex effect on the hull bound- 

 ary layer and 



3) the region of nondisturbed flow in the bound- 

 ary layer or in the wake (Figure 7) . 



The laws for changing the relative velocities in 

 each of these regions are different in model-ship 

 correlation. 



Evaluating the scale effect of disturbances in 

 the boundary layer is rather a complicated task 

 partly due to the difficulty of distinguishing these 

 disturbances in the nonuniform three-dimensional 

 boundary layer of the hull. Therefore, at the ini- 

 tial stages of investigation the principal attention 

 was paid to the specific features of such kind of 

 flow in simplified conditions, i.e., under the as- 

 sumption that artificial vortex systems were pro- 

 duced by means of profiles of small aspect ratio 

 at the boiondary layer of a flat surface [Poostoshniy 

 (1975)]. For such simpler flows one can use the 

 approximate methods of evaluating the scale effect 

 of axial velocities in the region where influence 

 of the vortex is observed. These methods will be 

 based on a combination of experiment and theory or 

 approximate semiempirical schemes, which is most 

 important for having a general idea of the phe- 

 nomenon . 



Extra losses of axial velocities in the vortex 

 cores are rather high for some ship models (reach- 



// i /////////// I /, , ///////// ^ // / Z 



U = constant 



Region of Vortex Influence 

 on the Boundary Layer 



Vortex Core 



Undisturbed Flow Region ^ 



Velocity Distribution 

 in the Core 



AU = 



Theory 



Circulation Distribution in the Bilge Vortex 

 'Core of Tanl<er Model (A = 60000 t), r„ = 1 .1 m /s 



2.0 r 



Eii) 

 r(7,i 



1.0 



^Y^Distribution of Circulation in a Vortex 

 ^■^ Core of Free Flow. rQ=0.07m^/s 



1.0 



lg(r/r,) + 1 



2.0 



FIGURE 7. Velocity field in the boundary layer with 

 longitudinal discrete vortices. 



ing 20-30% of the mean wake value) ; these losses 

 are also to be studied in detail. 



As shown by the experiments (Figure 6) the 

 circulation distribution law for the cores of bilge 

 vortices is similar to that for the vortex cores in 

 the free flow. So, in order to evaluate the scale 

 effect of a relative defect of the axial velocity 

 in the core, i.e., the core allowance, use can be 

 made of the theoretical relationships derived for 

 linear turbulent vortices. 



Calculated results which are based upon rather 

 a small amount of data on the variation in eddy 

 viscosity coefficients with Rn obtained during model 

 tank tests and fall-scale hydrodynamic experiments 

 lead to the conclusion that a model-ship correlation 

 involves relative decrease of the core size. How- 

 ever, far from decreasing, the wake allowance, unlike 

 that for the boundary layer, may even be markedly 

 growing. Some additional variation in the distribu- 

 tion of axial velocities in the core caused by an 

 increase in Rn may also be due to an increase in the 

 longitudinal pressure gradient at the stern owing 

 to the reverse effect of the hull boundary layer on 

 the external potential flow both on model and ship. 



It is impossible at present to develop a flow 

 model of this complexity, define the component ve- 

 locities changing under different model-ship corre- 

 lation laws and, finally, determine these laws; in 

 other words it is impossible to develop a well- 

 founded method for simulation of a three-dimensional 

 wake flow with discrete vortices. The results of 

 the above-mentioned preliminary studies are of 

 qualitative character and need experimental verifi- 

 cation. A series of comparative model and full-scale 

 tests carried out mainly by Japanese researchers 

 [Namimatsu and Muroaka (1973) , Taniguchi and Fujita 

 (1959) ] confirm the existence of bilge vortices in 

 full-scale conditions as well, though the data re- 

 ported in the above papers are inadequate to judge 

 the quantitative aspect of the phenomenon. We can 

 only observe that the disturbances induced by the 

 vortices in the flow around a ship are less notice- 

 able, i.e., the flow is cleaned up. Therefore the 

 attempt to use a more generalized model (model "a") 

 seems to be justified also in this case, i.e., in 

 the presence of developed bilge vortices, or at 

 least an attempt to establish limits for the appli- 

 cation of this' flow model should be made. Compara- 

 tive data obtained from model and full-scale tests 

 are a decisive factor here. 



Unfortunately no data of nominal wake distribu- 

 tion at the propeller are available. For an indirect 

 evaluation of the scale effect of nominal wake we 

 shall make use of the test data obtained in Japan 

 for a 36000 t (displacement) tanker and its 1/37- 

 and 1/20-scale models [Taniguchi and Fujita (1969)]. 

 The measurements were taken in the boundary layer 

 near the sternpost at a distance of I.ID from the 

 propeller disk. In laboratory conditions the ve- 

 locity field was measured both during the towing 

 tests and self-propelled tests. The tests performed 

 with the model (A = 1:20) allow the propeller effect 

 at the measurement plane to be considered as negli- 

 gible (-0.05 V) and practically constant within the 

 region equivalent to the propeller disk area. The 

 comparison between the velocity distribution in the 

 wake transverse section for 2 = Bp (where Zp = 

 propeller axis level) and the circumferential dis- 

 tribution of the axial velocities (Figures 8 and 9) 

 for this tanker and those for a "Krym"-type tanker 

 shows that the simplified method of model-ship cor- 



