168 



B. At model self-propulsion conditions these 

 differences are up to 5 percent for vehicle A but 

 60 percent for vehicle B. The secondary flow pre- 

 diction for the full-scale conditions on body A 

 given in Figure 16 can again be seen to be higher 

 than the measured values but only by up to 4 percent 

 at the two radii considered. In this case the use 

 of a smaller scaling effect would lead to higher 

 predicted values such that the differences between 

 these and the measured values would increase to the 

 order of 6 percent. 



The above results show that the agreement between 

 the measured and predicted data has been limited and 

 further work is required before the proposed scaling 

 method can be regarded as satisfactory. The princi- 

 pal requirement is for further high Reynolds number 

 data and it is proposed to obtain this by additional 

 full-scale trials, together with experiments on 

 models in a compressed air wind tunnel. 



6. CONCLUSIONS 



An integral boundary-layer calculation method for 

 bodies of revolution is shown to give a good pre- 

 diction of boundary layer velocity profile for 

 attached flows in the tail region of a body. 



Inclusion of a simple actuator disc representa- 

 tion of a propeller in the calculation method gives 

 a reasonable first approximation to the effect of a 

 propeller on the flow. 



Comparison between results from Fourier analyses 

 of measurements from runs repeated a number of 

 times and of measurements made with different 

 incremental steps in probe position indicates that 

 wake harmonics can be determined reliably. from 

 measurements at model scale. 



Fourier analyses of idealised velocity profiles 

 representing wake defects in an otherwise uniform 

 flow field have been obtained analytically. Com- 

 parison between these results and numerical harmonic 

 analyses of the same profile specified at a dis- 

 crete number of points shows no significant differ- 

 ences in the amplitudes of wake harmonics at high 

 harmonic number provided that the width of the wake 

 is not too small. 



The measurements presented herein indicate that 

 the velocity defect produced behind a control sur- 

 face is only slightly affected by either the 

 presence of a propeller aft of the control surface, 

 or by the change in Reynolds number from model to 

 full-scale. 



Near the hull, where the flow is influenced by 

 secondary flow effects, the velocity defect behind 

 a control surface is much smaller than predicted 

 from two-dimensional data. For positions outside 

 the influence of the secondary flow the velocity 

 defect approaches the two-dimensional value. 



The velocity defect is of a similar order of 

 magnitude for the two bodies examined. However, the 

 secondary flow effects are significantly larger 

 for the vehicle with the blunter stern. 



The secondary flow produced by the interaction 

 of a control surface with the hull boundary layer 

 is reduced significantly by the presence of a 

 propeller aft of the control surface, and from 

 model to full-scale conditions. This reduction 



increases with increasing propeller diffusion ratio. 



By using the unpowered model measurements as 

 datum it has been possible to predict the model 

 powered mean circumferential velocities to within 

 4 percent for radial positions from the hull greater 

 than 12.5 percent of the propeller radius. At this 

 radius itself, the predictions are within 7 percent 

 for the finer stern model and 14 percent for the 

 fuller stern; however, the latter may be due to 

 separation effects which are not taken into account 

 in the prediction method. 



Predictions of the mean circumferential velocity 

 at the full-scale conditions for the vehicle with 

 the finer stern are high by up to 15 percent. If 

 the ship prediction is made at a reduced Reynolds 

 number suggested by speed trial results the pre- 

 dictions come within 2 percent. Predictions of the 

 powered velocity defect are wit in 6 percent for 

 model conditions and 2 percent for ship conditions, 

 the latter figure applying to either the true or 

 reduced full-scale Reynolds number. Predictions of 

 the model powered secondary flow are within 5 per- 

 cent for the body with the finer stern, but up to 

 60 percent for the fuller form. However, for the 

 full-scale conditions obtained on the finer stern 

 the predictions are within 4 percent at the true 

 Reynolds number, and 6 percent at the reduced value. 



A practical method of estimating propeller in- 

 duction and wake scaling effects has been proposed 

 and demonstrated to give limited agreement with 

 model and full-scale data. Further experimental 

 data are required to refine the method and to this 

 end high Reynolds number model experiments are 

 planned to be carried out in a compressed air wind 

 tunnel, and further full-scale trials scheduled. 



REFERENCES 



Head, M. R. (1960) . Entrainment in the turbulent 

 boundary layer. British ARC, R S M 3152. 



Huang, T. T. , S. Santelli, H. T. Wang, and N. C. 

 Groves. (1976) . Propeller/stern/boundary-layer 

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Luxton, R. E., and A. D. Young. (1962). Generalised 

 methods for the calculation of the laminar com- 

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 heat transfer and non-uniform pressure distri- 

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Manley, R. G. (1945) . Waveform analysis. Chapman 

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Myring, D. F. (1973) . The profile drag of bodies 

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Patel, V. C. (1974) . A simple integral method for 

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Patel, V. C, A. Nakayama, and R. Damian. (1973). 

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Raj, R. , and B. Lakshminarayana. (1973). Charac- 



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