243 



-Q_m. 



WILLIAMS a BROWN (i937lT 

 ■LINOSEY (19381 



WARDEN 11931) 

 ZAHM, ET AL (1929) 



5x10 10° 5x10= 10° 5x10° 



REYNOLDS NUMBER (Rec) BASED ON STRUT CHORD LENGTH 



FIGURE 33. Drag coefficients of elliptical 

 section struts as a function of Reynolds 

 number based on chord length. 



ing drag coefficients are found to be 0.050 and 

 0.018 for the model and ship, respectively. Sub- 

 sitution of these drag coefficients into the above 

 formulas from Silverstein, et al. (19 38) and 

 Goldstein (1965) yields the velocity defects which 

 are shown on Figures 29 through 32. 



These computed velocity defects due to strut 

 wake are significantly greater than the velocity 

 defects which were observed at either model or full 

 scale. The cause of this over-prediction is 

 probably the fact that the formulas from Goldstein 

 are derived by assuming that the wake is being 

 calculated far enough downstream that the cross 

 flow terms in the momentum equation can be neglected. 

 This is an assumption which is undoubtedly violated 

 in the region near the struts, where the wake has 

 been predicted. 



Although the empirical method for predicting the 

 wake of the shaft struts was not successful, it 

 does at least provide some insight into how the 

 wake should vary with Reynolds number. Both the 

 width of the wake of the struts and the velocity 

 defect in the wake of the struts are proportional 

 to the square root of the drag coefficient of the 

 section. Therefore, the velocity defect and the 

 width of the wake should both decrease (like the 

 square root of the ratio of the drag coefficients) 

 as the Reynolds ntmiber increases. However, the 

 full-scale wake survey data were not collected at 

 angular increments spaced closely enough to confirm 

 this scaling law. 



The empirical method for predicting the wake 

 behind an inclined shaft is not as well defined as 

 the methods for predicting the wake behind the 

 struts. Following the methodology of Chiu and 

 Lienhard (1967) , it was assumed that the separated 

 flow behind a yawed cylinder is a function of the 

 component of the velocity normal to the cylinder. 

 Following the method of Roshko (1955) and (1958) , 

 an estimate of the velocity defect in the wake of 

 the shaft was developed based on the pressure 

 coefficient at the point of separation and the 

 Strouhal number. 



Data showing the base pressure behind a circular 



*Note: The base pressure is not necessarily the pressure at 

 the separation point because there is usually some pressure 

 variation in the separated region. 



cylinder have been collected, and are presented as 

 a function of Reynolds number in Figure 34. Based 

 on this data and the Reynolds number based on cross 

 flow velocity, the pressure coefficients for the 

 model (R = 1.63 x lo'*) and ship (R = 4.26 x 10^) 

 were found to be -1.1 and -0.2 respectively. These 

 pressure coefficients resulted in a predicted veloc- 

 ity defect, perpendicular to the shaft axis, of 

 0.25 for the model and 0.10 for the ship. However, 

 when resolved back into the direction of the flow, 

 the shaft wake is less than two percent of model 

 speed and one percent of ship speed. This is 

 significantly less than than the velocity defect 

 which is measured for either the model or the ship. 

 In fact, if the velocity defect in the direction 

 normal to the shaft were 100 percent of the forward 

 speed, the velocity defect in the wake would only 

 be seven percent, still less than the velocity 

 defect measured experimentally. 



These results are not surprising when one con- 

 siders the discussion in Chiu and Lienhard (1969) . 

 In this discussion, data are presented which point 

 out that the wake of an inclined shaft is in general 

 not parallel to the shaft. This is due to the 

 axial component of the flow along the cylinder which 

 develops a boundary layer which separates. The 

 Reynolds number for separation in the axial direc- 

 tion on the shaft is independent of the Reynolds 

 number of the flow normal to the shaft. In addition, 

 the data from Bursnall and Loftin (1952) , show that 

 as a circular cylinder is inclined further and 

 further to the flow, the transverse Reynolds number 

 at which separation takes place becomes lower and 

 lower . 



9. CONCLUSIONS 



Significant differences have been found in the 

 tangential and radial velocity component ratios 

 between the ship and the model wake surveys . In 

 particular, the full-scale tangential velocity 

 component ratio has a peak amplitude approximately 

 eight to ten percentage points higher than that at 

 model scale. Similarly, the ship radial velocity 

 component peak is higher by six to eight percentage 

 points. These differences cannot be attributed 

 to scale effects. The most likely cause seems to 



