272 



wake, both in our practice and in the practice of 

 other model tanks , use has been made in recent 

 years of engineering procedures based on the results 

 of nominal velocity field measurements and propeller 

 theory relationships [Hoekstra (1977) , Raestad 

 (1972), Nagamatsu and Sasajima (1975)]. 



If we assume that the propeller effects are 

 mainly due to the factors mentioned above , the 

 propeller can be thought of as having a large diam- 

 eter when evaluating the mean wake field. 



This assumption will result in a decrease of the 

 wake coefficient. The decrease of the frictional- 

 resisted wake due to the propeller effect can be 

 taken as inversely proportional to the square root 

 of the diameter. Then, 



Fe 



= "f/'^ 



+ „^/2V^) 



(8) 



where 



w /V 

 a A 



/r 



+ C 



Th 



Th (pV2/2)F 



To define the potential component Wpg it is 

 reasonable to apply the known propeller theory 

 relationship 



W = W ^ + (tn/2) X (w /V) 

 pe pN z 



> + - I*^^^- ^ 



(9) 



where 



pN 



= experimentally defined potential component 

 of the nominal wake field, 

 tg = thrust deduction at zero velocity of 

 model . 

 Allowing for the smallness of the 2nd term in (9) , 

 the thrust deduction fraction undergoing only minor 

 changes can be assumed for single-screw ships to be 

 to = 0.07-0.10 (the last figure relating to fuller 

 hull shapes) . 



The final expression for the mean effective wake 

 field (taking into account the scale effect) has 

 the form, 



W ^ (Rn ) 

 pN m 



+ tn/2(/l + C 



Th 



D] 



FN 



/l/2(/l + C^h + ^' ' "^FO^^m' 



the effective wake, and in the main they correctly 

 reflect the variation trends of the flow at the 

 stern while the propeller is in operation. However, 

 they do not permit: taking into account and evalu- 

 ating some qualitative changes in the hull boundary 

 layer, which may take place due to propeller opera- 

 tion, such as variation in circulation of bilge 

 vortices and their positions in relation to the 

 ship hull; the possibility of preventing or reduc- 

 ing the separation about the stern zone with the 

 propeller in operation; and, on the other hand, 

 the possibility of the boundary layer separation in 

 the vicinity of the stern above the propeller. 

 Therefore, when performing a quantitative analysis 

 of the effect the propeller has on the wake and the 

 harmonic spectrum of the velocity field, these 

 methods, in spite of their relative simplicity and 

 convenience, should be applied rather carefully, as 

 for most tentative estimates. 



At the present stage of the wake problem in- 

 vestigation the development of experimental methods 

 is of decisive importance. 



Both for the improvement of the general knowledge 

 of propeller effects on the flow pattern at the 

 stern and for the solution of problems associated 

 with ship form design, the accumulation of data 

 on the effective velocity fields for ships of 

 various types and the improvement of model test 

 methods is of great importance, especially those 

 taking account propeller induced velocities or 

 eliminating the same from measurement data. 



A practical method for estimating the effective 

 velocity field, Ux, by way of flow velocity mea- 

 surements at some distance ahead of the propeller 

 in "open water" and behind the hull, was given in 

 Titov and Otlesnov (1975) . For measured data 

 analysis the quasi-steady theory was accepted. 



When the hydrodynamic flow angle, Bi, of a 

 propeller blade section for the propeller operating 

 in "open water" is equal to that behind the hull. 



tgBi 



where 



(V^ + W^)/aiT 



(U + 

 xe 



W")/(UT - U„ ) 



a ye 



(11) 



W and W" 

 a a 



axial induced velocities ahead 

 of the propeller in "open water' 

 and behind the hull 



U = circumferential component of the effective 

 velocity field 



The axial component of the effective velocity field 

 ahead of the propeller is determined from the 

 relation 



(10) 



where 



C = frictional resistance coefficient in two- 

 dimensional flow. 



TABLE 1. Comparison of the Mean Effective Wake 

 Calculated by Approximate Methods With 

 That Obtained from Self-Propelled Tests 

 (Model No. 1) 



Relationship (10) displays good agreement with 

 the model test data (see Table 1) and W^ values 

 close to those obtained from the full-scale test 

 analysis. 



As can be seen from the Table, all known approxi- 

 mate methods yield practically the same results. 



By making some additional assumptions, similar 

 methods can also be applied for an approximate 

 estimation of the circumferential distribution of 



Titov - Poostoshniy method 

 Nagamatsu - Sasajima method (1975) 

 Roestad method (1972) 

 Self-propulsion test data 

 Nominal wake 



0.345 

 0.340 

 0.355 

 0.350 

 0.390 



