266 



propeller is normally defined in the idealized con- 

 ditions of the towing tank, it is absolutely neces- 

 sary to evaluate and take account of the effect of 

 operating conditions, i.e. , the effect that increas- 

 ing the roughness of the hull surface as well as the 

 ship motions and drift have on the extent of flow 

 nonuniformity at the afterbody. There are also 

 some additional tasks, such as improvement of the 

 method used for definition of the ducted propeller 

 velocity field, estimation of a possible change in 

 the wake flow over the propeller axial length, and 

 thinking over the practicability of the m.ethods of 

 disturbing action upon the flow pattern with preset 

 requirements. The methods of experimental defini- 

 tion of the flow velocities in the vicinity of the 

 hull model are no less important. It is impossible 

 to cover the results of all the above studies in a 

 short report like this, so we shall restrict our- 

 selves to the following traditional problems : the 

 scale effect of the velocity field and the propeller 

 effect on the flow formation at the stern. 



2. SCALE EFFECT OF THE NOMINAL VELOCITY FIELD 



The decrease of the mean wake in a model--ship 

 correlation with sufficient accuracy can be at- 

 tributed to variation in total frictional losses. 

 The problem of simulating the local wake is far 

 more complicated. The flow in way of the propeller 

 is a combination of two three-dimensional flows: 

 the boundary layer in the upper part of the after- 

 body with intensive secondary flows characteristic 

 of this region and the initial part of the wake de- 

 veloping behind the hull which may contain discrete 

 vortices resulting from the boundary layer separa- 

 tion in way of the bilge where the flow' lines from 

 under the bottom are extending to hull side sur- 

 face (Figure 1 and 2). As shown by experiments, 

 the contribution of each of these factors depends 

 on afterbody fullness, stern frame form, buttock 

 angles, and some other parameters. 



The distributions of the relative axial veloci- 

 ties Ux/Y|5 (y/(5;Rn) are different for the boundary 

 layer, the wake, and the vortex effect region, and 

 largely depend on the afterbody lines and the 

 history of the flow. The solution of the scale 

 effect problem by a purely experimental way is not 

 practicable, so when the general laws of variation 

 in the flow characteristics are established for 



model - ship correlation, the approximate methods 

 of the semiempirical theory of turbulent boundary 

 layer and of the free turbulence theory are of 

 great importance; also important are comprehensive 

 physical investigations of the afterbody flow which 

 are necessary for the refinement of the flow model 

 and formulation of the simplifying assumptions. 

 Such investigations should cover the whole of the 

 viscous wake region (Figure 1 and 2) and not be 

 limited to the disk propeller area as is usually 

 done in practice. 



The phenomenon being too complicated, a general 

 approach to simulating the flow seems to be unat- 

 tainable at present. Therefore, it is expedient 

 to discuss some particular models of the flow. Some 

 of the flows may be considered as the most common 

 types which can easily be investigated. These are: 



a) the velocity field of a single-screw ship of 

 moderate fullness with V-shaped or U-shaped frames 

 where the contribution of bilge vortices is not 

 significant; 



b) the velocity field of high-speed, twin-screw 

 container ships; 



a more complex pattern and more complex scaling laws 

 are characteristic for 



c) the velocity field of full ships (6 > 0.8) 

 with U-shaped frames where the intensive bilge 

 vortices are formed; 



d) the velocity field of the very full ships with 

 the boundary layer separation at the afterbody. 



Model "a" 



The calculation data obtained for a three-dimensional 

 boundary layer lead to the conclusion that with moder- 

 ate transverse flows the variation in characteristics 

 of the main flow accounting to Rn does not differ 

 markedly from those obtained for a two-dimensional 

 boundary layer. Hence, for practical estimation of 

 the axial velocity field in the upper part of the 

 afterbody (Figure 1) we can use, without introduc- 

 ing large errors , the boundary layer correlation 

 schemes developed to fit the two-dimensional flow 

 on the basis of the logarithmic law and the velocity 

 defect law. For simulating the wake flow use can be 

 made, with some assumptions, of the known Prandtl 

 asymptotic solution for a two-dimensional flow 

 which was obtained on the assumption that the flow 

 is barotropic and that the velocity defect, Au, is 



FIGURE 1. Nominal velocity 

 field in the propeller plane 

 for a model of tanker with 

 moderate block coefficient, 



B 



0.73 (model 1) . 



