241 



o 



< 



5x10° 10 5«I0' 10° 



REYNOLDS NUMBER (ReJ BASED ON SHIP LENGTH 



FIGURE 27. Longitudinal velocity component 

 ratio at 0-degree position of 0.533 radius 

 as a function of Reynolds number based on 

 hull length. 



inclined a total of 

 The effect of resolv- 



dealt with primarily by potential flow techniques, 

 combined with calculations of the boundary layer 

 displacement thickness. It was also assumed that 

 the viscous flow about the appendages could be 

 dealt with empirically. 



The velocity in the propeller disk, expressed in 

 shaft coordinates, was decomposed as follows: 



Velocity = Uniform Stream 



+ Perturbation due to Hull 



+ Perturbation due to Boundary Layer 



+ Viscous Wake of Struts 



+ Viscous Wake of Shafting. 



The principal factor contributing to the radial and 

 tangential components of the velocity in the pro- 

 peller plane is the inclination of the shaft to the 

 free stream. The shafting of the ATHENA makes an 

 angle of 8.9° with the baseline. In addition, at 

 15 knots (Fjj = 0.36) , the ATHENA takes a bow-up 

 trim of 0.3° as indicated by model experiments. 

 Thus, the propeller shaft is 

 9.2° to the incident stream, 

 ing the incident stream into shaft coordinates is 

 shown on Figure 28 . 



The effects of perturbing the incident stream by 

 the presence of the hull were obtained by means of 

 potential flow calculations. For the purposes of 

 this study, the free surface was represented by the 

 zero Froude number condition, and the calculations 

 were made for a double model in an infinite fluid. 

 The hull was reflected about the mean waterline at 

 15 knots, and flow about the resulting body was 

 computed using the DTNSRDC potential flow program 

 [Dawson and Dean (1972) ] . The results of this 

 computation are also shown on Figure 28. As can 

 be seen, the effects due to the perturbation of the 

 incident flow by the hull are small, on the order 

 of two percent of the ship speed. 



The effects of the displacement thickness of the 

 boundary layer were considered next. The intention 

 was to increase the thickness of the hull by the 

 displacement thickness of the boundary layer, and to 

 repeat the potential flow calculations . However , 

 at its thickest point, the model scale boundary 

 layer determined from the equivalent body of 

 revolution calculations, would only have increased 



the thickness of the hull by 1 percent of the beam. 

 The full-scale boundary layer would have increased 

 the thickness even less. Since the complete hull 

 potential flow had only a two percent effect, the 

 revised potential flow was not computed for such a 

 small change in effective hull shape. The error 

 due to neglecting the displacement thickness of the 

 boundary layer is probably much less than the error 

 incurred by making the zero Froude number approxi- 

 mation for the potential flow calculations. There- 

 fore, the velocity component ratios based on only 

 the first potential flow calculations are presented 

 in Figures 29 through 32. 



The velocity defect caused by the struts was 

 predicted using an empirical scheme based on data 

 from aerodynamics. The velocity defect was com- 

 puted using the following formula from page 584 of 

 Goldstein (1965) . 



r/R = 633 



I 2 



I 1 - 



I I _ 

 C 

 91 VO 



-J I I I 1 1 V 



GO ° 



_ _0 dB"^"- - - 



-1 — I — I — I — r 



3-D POTENTIAL FLOW 



UNIFORM FLOW 



O MEASURED VALUES 



120 160 200 240 



ANGLE IN DEGREES 



Velocity Component Ratios Predicted and Measured Full-Scale 

 Trial 2, Vg = 7 87m/s 



FIGURE 28. Effect of shaft inclination and hull po- 

 tential flow on velocity component ratios for R/V 

 ATHENA at 0.633 radius. 



