226 



Reynolds number. Therefore, while treating a much 

 more difficult problem, the results of the tanker 

 experiments are not applicable to the scaling of 

 the wakes of high-speed hull forms. 



The full-scale velocity component ratios which 

 are presented here were obtained at a speed of 15 

 knots; the corresponding Froude and Reynolds numbers 

 were 0.36 and 4.10 x 10^ respectively. The model 

 wake survey was conducted in a towing tank at the 

 full-scale Froude number. This resulted in a 

 model speed of 5.22 knots, and a Reynolds number of 

 1.56 X 10 . The full-scale boundary layer measure- 

 ments were conducted at four speeds between 6 . 2 and 

 16.5 knots. These speeds correspond to Reynolds 

 numbers between 1.7 x 10^ and 4.5 x 10^ respec- 

 tively. The model-scale boundary layer measure- 

 ments were obtained on a doiible model in a wind 

 tunnel at a Reynolds number of 1.68 x IQ^. 



Significant differences are observed between the 

 model and full-scale velocity components, particu- 

 larly in the magnitudes of the radial and tangen- 

 tial velocity components. These differences are 

 in the regions away from the ship's hull and 

 appendages; therefore, these differences do not 

 seem to be due to Reynolds number effects. A more 

 likely explanation is a lack of ship-model simi- 

 larity, possibly due to unexplained differences in 

 hull form or initial trim. 



In order to obtain an understanding of the com- 

 ponents which contribute most significantly to the 

 deviation of the wake from uniform axial flow, an 

 attempt has been made to predict the velocity com- 

 ponents as seen by the propeller. To make this 

 prediction, the velocity field (in shaft coordinates) 

 was decomposed into its major components as follows: 



Velocity = Uniform Stream 



+ Perturbation due to Hull 



+ Perturbation due to Hull Boundary 



Layer 

 + Viscous Wake of Struts 

 + Viscous Wake of Shafting 



The results of this decomposition show that the 

 inclination of the propeller shaft to the free 

 stream is the most significant factor contributing 

 to the deviation of the velocity from a purely 

 axial uniform flow. In particular, approximately 70 

 percent of the measured radial and tangential flow 

 is contributed by the inclination of the shaft to 

 the uniform stream. The boundary layer of the hull 

 is found to contribute insignificantly to the per- 

 turbation of the free stream. Although the viscous 

 wake of the shafts and struts makes a significant 

 contribution to the nonuniformity of the flow, the 

 empirical technique proposed herein overpredicts 

 the wake of the struts and underpredicts the wake 

 of the shafting. 



2. BACKGROUND 



During the last ten to fifteen years there has been 

 a marked increase in the installed horsepower per 

 shaft on high-speed commercial and naval vessels. 

 This increase in power has led to increased steady 

 and unsteady forces on propellers , and increased 

 loads on the hull surface . If adequate structural 

 designs are to be developed for the propeller, its 

 shafting, and the shaft supports; then the un- 

 steady forces and moments on the propeller must be 



known accurately. Similarly, if the hull is to be 

 habitable and to have minimal vibration, the 

 structural design must adequately account for the 

 propeller-induced surface forces. The propeller 

 forces and surface loads can in turn only be ac- 

 curate if they are determined using the full-scale 

 flow into the propeller. 



Several theories exist for predicting the un- 

 steady forces and moments acting on a propeller in 

 a nonuniform flow, and the hull-surface forces 

 induced by a propeller. Tsakona et al. (1974) and 

 Frydenlund and Kerwin (1977) report on two of the 

 theories for the unsteady forces on a propeller; 

 Vorus (1974) reports on a theory for predicting 

 the hull-surface forces. In these theories, the 

 flow into the propeller is used in conjunction 

 with an unsteady lifting-surface theory to predict 

 the unsteady forces on the propeller and hull as 

 the propeller rotates through the nonuniform flow. 



Typically, a propeller is wake adapted, that is, 

 designed to the radial distribution of the circum- 

 ferential mean velocity. The alternating forces 

 are determined by considering the propeller in a 

 nonuniform flow circumferentially . The variations 

 of the forces and moments in the nonuniform stream 

 from those in the uniform stream are then con- 

 sidered to be the unsteady forces and moments on the 

 propeller. 



The longitudinal component of the velocity in 

 the propeller disk is the principal component of 

 the velocity on a transom stern ship with inclined 

 shafts. Typically the radial and tangential com- 

 ponents vary sinusoidally around the propeller 

 disk, and have peaks which are 20 to 25 percent of 

 the longitudinal velocity component. However, in 

 the process of determining the circumferential 

 average of the radial and tangential velocity com- 

 ponents , these components are reduced to 1 or 2 

 percent of the longitudinal velocity component. 

 Because of this, the tangential velocity component 

 contributes very little to the angle of attack on 

 a propeller blade as computed for the propeller 

 design. However, in unsteady force calculations, 

 the longitudinal velocity component varies from 

 its mean by 10 to 15 percent while the radial and 

 tangential components vary by 1000 percent from 

 their means. Thus the variation in the tangential 

 velocity component contributes significantly to 

 the changes in the angle of attack on a propeller 

 blade as it rotates through the wake. These 

 changes in angle of attack in turn result in the 

 unsteady forces and moments on the propeller. 



Experiments by Boswell [Boswell et al. 1976) ] , 

 show that the maximum unsteady loads on the 

 propeller occur in the area where the tangential 

 flow velocities in the propeller disk are at their 

 maximum. As will be seen later, it is the tangen- 

 tial velocity components that are in least agree- 

 ment between model and full scale. It is this 

 fact that makes the issue of wake scaling important 

 to the accurate determination of the unsteady 

 forces on a full-scale propeller. 



3. TRIAL VESSEL AND INSTRUMENTATION 



A number of criteria went into the selection of 

 the ship on which the full-scale measurements would 

 be made. The hull form and appendage arrangement 

 of the ship had to correspond to that which is 

 typical of high-speed twin-screw commercial and 



