162 



2n 



FIGURE 6. Theoretical representation of wake defects 

 in the flow field. 



which N, K, and wake width were varied showed that, 

 in general, errors did not become significant until 

 wake width was less than twice the angular spacing 

 of the specified points, i.e., 720°/N. 



4. USE OF THE PREDICTION METHOD IN PROPELLER DESIGN 



A knowledge of the flow in the region of a propeller 

 is required first, in order to design it, and 

 second, to estimate its performance characteristics. 

 The former requires an estimate of the unpowered 

 mean velocity through the propeller position to- 

 gether with the radial variation of mean circum- 

 ferential velocity. Of the latter, the' prediction 

 of iinsteady propeller forces in particular also 

 requires the detail wake structure at the propeller 

 position in the powered condition. 



The theoretical boundary layer prediction method 

 outlined in Section 2 cannot be used directly to 

 predict the above wake information for practical 

 vehicle configurations because of limitations such 

 as its restriction to unappended bodies of revolu- 

 tion. However, it can be employed indirectly by 

 using the method to predict the changes from model 

 testing conditions to full-scale vehicle conditions 

 and then applying these scale effects to available 

 model data. 



The procedure adopted for the predictions dis- 

 cussed in the following section was to replace the 

 non symmetric, appended vehicle by an equivalent 

 body of revolution. Powered and unpowered boundary 

 layer predictions were then carried out and, by 

 assuming a simple power law for the boundary layer 

 velocity profile, the mean circumferential veloci- 

 ties were determined for the equivalent model and 

 full-scale bodies. In this way it was possible to 

 estimate at any position the scale effect upon the 

 unpowered wakes, the propeller induction effects, 

 and any combination of the two. These effects were 

 then applied to all the measured unpowered model 

 data to give predictions of both model and full- 

 scale powered wakes for comparison with measured 

 data. 



5. COMPARISON BETWEEN PREDICTED AND MEASURED RESULTS 

 ON NON-SYMMETRIC BODIES 



As part of a programme to investigate the effects 

 of scaling and prope,Ller induction on wakes, experi- 



ments have been carried out on two practical vehicle 



forms covering a range of Reynolds numbers , based 



on body length, from approximately 1 x 10 to 



ft 

 6 X 10 . The two vehicles concerned were propelled 



by a single centre line propeller and were fitted 



with a set of cruciform after-control surfaces just 



ahead of the propeller. The afterbody form was 



axisymmetric in both cases, one vehicle having a 



fine stern (vehicle A) and the other a blunt stern 



(vehicle B) . 



The low Reynolds number data were obtained in the 

 ship tanks at AMTE (Haslar) using small conventional 

 pitot static tubes. For body A, measurements were 

 made at a position 25 percent of the local control 

 surface chord aft of the control surface trailing 

 edge. This corresponded to 28 percent of the 

 propeller diameter forward of the propeller. The 

 measurements were made at 2° intervals over an angle 

 of approximately 90° centred on one control surface, 

 and at radial distances from the body surface of 

 12.5 percent and 25 percent of the propeller radius. 

 For body B, data were obtained 24 percent of the 

 local control surface chord aft of the control 

 surface trailing edge, corresponding to 22 percent 

 of the propeller diameter forward of the propeller. 

 In this case 6 pitot static tubes were used cover- 

 ing a range of radial distances from the hull of 

 12.5 percent to 65 percent of the propeller radius. 



The high Reynolds number data were obtained from 

 trials carried out at sea on vehicle A using 5 con- 



fd) M=I20, K-4, WAKE WIDTH 9. 



■lO 



X NUMERICAL 

 I EXACT 



u 



4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 

 HARMONIC NUMftER 



Cb) N-I20, K-4, WAKE WIDTH 4 '2 . 



■10. 



3-051. 

 a. 



< 



:i;::::iiiixxxxxxxx 



8 12 



16 20 24 28 32 36 40 44 48 52 56 60 64 

 HARMONIC NUMBER 



FIGURE 7. Comparison between an exact Fourier analysis 

 of the theoretical velocity profile and a numerical 

 analysis of the same profile specified at a discrete 

 number of points. 



