159 



problem and which reduce respectively to body 

 radius times momentum thickness and body radius 

 times displacement thickness far from the tail 

 where boundary layer thickness is small. A con- 

 ventional momentum integral equation is derived in 

 terms of the defined parameters and this is solved 

 using an empirical relationship for skin friction 

 coefficient which assumes that wall shear-stress 

 does not change sign. Therefore the method is only 

 applicable to bodies on which the boundary layer 

 remains attached. It is also assumed that the 

 variation of static pressure across the boundary 

 layer is negligible. This latter assumption has 

 been found to be incorrect for bodies with blunt 

 tails (i.e., cone angles greater than 30°) and an 

 empirical modification has been made based on the 

 work of Patel (1974) who developed independently 

 a method which is similar to Myring's but which 

 recognises the importance of static pressure varia- 

 tion. The modification introduced in the present 

 method is that the predicted velocity distribution 

 along the body is changed empirically in the tail 

 region, the change being related to differences 

 between measured and predicted velocity distribu- 

 tions at the rear of a given body with a blunt 

 stern. It has been found that this modification 

 results in improved correlation between measured 

 and predicted boundary layer velocity profiles. 



A simple actuator disc representation of a 

 propeller has now been included in the potential 

 flow part of the calculation in order to give a 

 first approximation to the acceleration effects 

 on the flow caused by the action of the propeller. 



I-O 



DISTANCE FROM HULL 

 BODY LENGTH 



C/o) 



FIGURE 2. Measured and predicted velocities 0.96L from 

 the bow of a body of revolution with blunt stern [ Patel 

 (1973)]. 



3. RESULTS AT LOW REYNOLDS NUMBER ON AXISYMMETRIC 

 BODIES 



BODY LENGTH 



FIGURE 1. Measured and predicted velocities 0.96L from 

 the bow of a body of revolution with tail cone angle of 

 26° . 



Comparison between Predicted and Measured Results 



The main interest in the present work is in the 

 prediction of boundary layer velocity profiles in 

 the tail region of a body and the results presented 

 in this section relate to model measurements under 

 conditions giving a Reynolds number based on model 

 length from 1 x 10^ to 6 x 10^. 



The velocity measurements shown in Figure 1 were 

 made at a station 0.96 L from the bow of a body of 

 revolution of length L and having a relatively fine 

 stern (cone angle 26°) . The measurements are of 

 total velocity whereas the calculation method gives 

 values of velocity component parallel to the hull. 

 The theoretical curve in Figure 1 is obtained by 

 applying a small correction to the calculated 

 velocities to allow for the difference between 

 local flow angle and hull angle. It can be seen 

 that the resulting predicted curve gives values to 

 within 4% of the measured velocities. Detailed 

 measurements at the rear of a body of revolution 

 having a blunt stern have been reported by Patel 

 et al. (1973) and results for a station 0.96 L 

 from the bow are shown in Figure 2. The broken 

 line is the theoretical boundary layer profile 

 predicted from _Myring' s method with no allowance 

 for static pressure variation across the boundary 

 layer. This curve is significantly different from 

 the measured velocities which are more than 10% 

 less than predicted values in the inner part of 

 the boundary layer. Correlation between measured 

 and predicted results is improved when the empirical 

 modification allowing for static pressure variation 



