CHAPTER 46 



Reference Data on Separation, Eddying, 

 and Vortex Motion 



46.1 General 133 



46.2 Separation Criteria 133 



46.3 Detection of Separation; E.xtent of the Zone . 136 



46 . 4 Predicting Apparent Flow Deflection Around 



Separation Zones 139 



46 . 5 Estimate of Separation Drag Around a Ship . 139 



46.6 Separation Phenomena Around Geometric 



and Non-Ship Forms 140 



46.7 Vortex Streets and Related Phenomena . . 141 



46.8 Vortex Streets and Vibrating Bodies . . . 141 



46 . 9 Practical AppUcations of the Strouhal Num- 



ber to Singing and Resonant Vibration . . 143 



46.10 References on Eddy Systems, Vortex Trails, 



and Singing 144 



46.1 General. Summarizing from Sees. 7.4 

 and 7.19 of Volume I, it appears that the following 

 factors are involved in a prediction of separation: 



(a) Longitudinal surface slope with reference to 

 the relative direction of motion of water and ship 

 at a distance, in both horizontal and vertical 

 planes 



(b) Rising-pressure gradient in the direction of 

 motion of the water past the body or ship surface 



(c) Nature of flow in the boundary layer ahead 

 of the separation zone, whether laminar or 

 turbulent; particularly, the magnitude of the 

 transverse velocity gradient dU/dy just forward 

 of the separation point 



(d) Roughness of the solid surface ahead of the 

 separation zone 



(e) Relative velocity of ship and water, at least 

 insofar as the size and shape of the separation 

 zone and the media which fill it (water or air or 

 both) are concerned 



(f) Hydrostatic pressure at the point or in the 

 region under consideration. It seems that atmos- 

 pheric pressure can be neglected. 



(g) Projections, recesses, and discontinuities in 

 the ship surface. 



Not too much is known quantitatively about 

 the individual effects of the items listed. However, 

 by taking the fragments of knowledge in combina- 

 tion it is possible to make estimates of probable 

 performance in ship scale and to formulate certain 

 rough design rules. 



Caution is necessary when interpreting or 

 making use of published data on separation 

 which have been derived from tests on models. 



objects, or bodies in air. Here the medium under 

 pressure surrounds the body on all sides, and the 

 undisturbed pressure is very nearly the same in 

 all directions and at all points around the body. 

 For a body operating at or near the surface of the 

 water, where the separation phenomena appear 

 to be governed largely by the hydrostatic pressure 

 and the transverse pressure gradient dp/dy, both 

 the pressure and the gradient are nominally zero 

 at the air-water interface and they increase 

 hnearly with depth. Many aspects of separation 

 appear to vary in the same way. 



46.2 Separation Criteria. Despite the numer- 

 ous factors involved, listed in Sec. 46.1, separation 

 appears to be the result, principally, of inadequate 

 lateral pressure, inadequate transverse pressure 

 gradient, and inadequate normal force to accel- 

 erate the surrounding liquid inward toward the 

 surface of a body which has a local slope greater 

 than a certain amount in any given plane. This 

 critical slope may and usually does vary with the 

 plane or stream surface in or along which the 

 flow occurs. For the transom stern shown at 1 in 

 Fig. 46.A, there is a determining slope for flow 

 along the waterline and another for flow under 

 the bottom, the latter generally paralleling the 

 buttocks. 



It is probable, although not certain, that the 

 critical slopes should be measured along stream 

 or other surfaces of equal ambient or hydrostatic 

 pressure. Knowing the position of these surfaces, 

 and the critical slopes, the naval architect might 

 then predict the locus of the points marking the 

 forward or upstream edges of a separation zone. 



Around the stern of a ship, for example, at 



133 



