Sec. 46.9 



DATA ON SEPARATION, EDDYING, AND VORTEXES 



143 



approximating this figure, resonant vibration 

 will ensue, with a magnification of vibration 

 amplitude and possible damage to the rod. 



The use of deflectors or longitudinal-vortex 

 generators, to serve as an auxiliary transfer 

 mechanism to get fast-moving water from the 

 outer portions of the boundary layers into the 

 inner portions and thus to provide the kinetic 

 energy in the inner portion necessary to defer 

 separation, is discussed in Sec. 36.27 of Volume I. 

 However, the necessary quantitative data for 

 calculating the effect of these generators are not 

 available at the present time (1955). 



46.9 Practical Applications of the Strouhal 

 Number to Singing and Resonant Vibration. As 

 an illustration of the application of the knowledge 

 presently available (1955) to the prediction of 

 possible singing of a propeller blade, take the case 

 of the propeller designed for the transom-stern 

 ABC ship in Sees. 70.21 through 70.38 of Part 4. 



Assume that this propeller, originally manu- 

 factured with the relatively fine trailing edges 

 depicted in Fig. 70. 0, has had its edges damaged 

 by curling and nicking so that, as a temporary 

 measure, the trailing edge from about O.bORu^^ 

 to 0.78/?Ma>t has been chipped away and rounded 

 off as shown by the broken line of diagram 1 of 

 Fig. 70. P. It is estimated that the effective 

 thickness t at this edge is about 0.75 in or 0.0625 

 ft; see the discussion of this matter in Sec. 70.46. 

 In other words, the vortex trail expected to be 

 shed by the trailing edge corresponds to that 

 which would be shed by a non-vibrating 2-diml 

 circular-section rod 0.0625 ft in diameter, moving 

 through the water at the same speed and occupy- 

 ing the same position as the trimmed-off trailing 

 edge of the damaged blade. 



The basic data, for a designed ship speed of 

 20.5 kt, are, from Sec. 70.26: 



Diameter, maximum, of propeller, 20 ft 



Speed of advance V a , 27.87 ft per sec 



Speed of rotation of propeller, 1.62 rps 



Kinematic viscosity of salt water, 1.2817(10"'^) ft" 



per sec 



Mass density of salt water, 1.9905 slugs per ft^. 



The rotational speed of the propeller at the 0.64 

 radius, halfway between 0.50 and 0.78i2Max , is 

 27r(20/2) (0.64) 1.62 = 65.15 ft per sec. The blade- 

 section speed at that radius is the combination of 

 the rotational speed and the speed of advance, or 

 TBiade= [(65.15)' + (27.87)T' = 70.86 ft per sec. 

 The d- or diameter Reynolds number R^ for 



the effective diameter of the damaged trailing 

 edge is (FB,„d»)(0/'' = (70.86) (0.0625) (10^)/ 

 1.2817 = 0.3455 million. From the left-hand 

 diagram of Fig. 46.G the corresponding Strouhal 

 number (S„ is about 0.21. Then since S„ = JD/U^ 

 or, in this case, {J){t)/V^u^i« , the predicted fre- 

 quency is / = S„(FB,ado)// = 0.21 (70.86) /0.0625 

 = 238 hertz or 238 cycles per sec. This is well 

 above the low hmit of 10 cycles per sec and well 

 below the upper limit of 700 cycles per sec for 

 audible singing, given in Sec. 70.46. Singing on 

 the damaged (and temporarily repaired) blade 

 of the ABC ship is liable to occur unless a chisel 

 edge is left when the damaged parts are chipped 

 away, as diagrammed in Fig. 70.P. 



Two illustrative examples of the method of 

 calculating the eddy frequency for 2-diml circular- 

 section rods that may be subject to resonant 

 vibration are worked out in Sees. 41.6 and 46.8, 

 respectively. As an indication of the range of 

 frequencies which may be encountered on high- 

 speed vessels where these hydroelastic interactions 

 are liable to pose troublesome problems, take the 

 case of the very wide strut arms, with a chord 

 length of 3.75 ft, mentioned by P. Mandel 

 [SNAME, 1953, p. 514]. 



Assume that the proposed strut section is used 

 on a large ship, with a thickness-chord ratio of 

 4.35. As indicated in Fig. 3 on page 408 of the 

 reference, the effective t (or D) along the trailing 

 edge is 2.5 in or 0.21 ft. Assume further a ship 

 speed of 25 kt, equivalent to 42.22 ft per sec, 

 since at higher speeds the vortex trail might be 

 replaced by a vapor cavity. As in Sec. 46.8, the 

 kinematic viscosity is taken as 1.2817(10"'') ft' 

 per sec and the mass density as 1.9905 slugs per ft''. 



The (^-Reynolds number is then VD/v or 

 (42.22)0.21(10')/1.2817 = 0.6917 million. From 

 the graph of Fig. 46. G the Strouhal number S„ 

 is 0.292. Then / = S,y/D = (42.22)0.292/0.21 = 

 58.7 hertz or 58.7 cycles per sec. 



In practice the strut problem is further compli- 

 cated by the fact that the strut-arm section may 

 not lie with its meanline exactly in the line of flow. 

 Or if properly aligned for straight-ahead running, 

 even taking account of the twist in the inflow jet 

 which is induced ahead of the propeller position, 

 the strut-arm section may run at an appreciable 

 yaw angle when the ship makes a turn. It is 

 probable that, if the yaw angle becomes large 

 enough so that the separation point on that side 

 of the trailing edge which is yawed outward 

 moves aft and becomes essentially fixed at the 



