210 



LIMITirJG STREAMLINES 



ATTACHMENT LINE 

 SEPARATION LINE 



FIGURE 1-1. [Sasajima (1973) 



SEPARATION LINE 



FIGURE 1-2. [Hoekstra (1977)]. 



Illustrative models of stern vortices 



have the same values as they had at the point the 

 flow passed on the separation line. 



Hoekstra 's vortex model also had a conical 

 separating sheet with a cusp as shown in Figure 1-2. 

 Although the stream along the separating sheet 

 flows upward and rolls inside, it does not touch 

 the hull surface to form an attachment line. 



In addition to the study on the scale effect of 

 the stern vortices by Huse (1977) , the studies 

 based on the theory of the three-dimensional 

 boundary layer by Okuno and Himeno (1977) has made 

 it possible to discuss the detailed structure of 

 the stern vortices. However, these studies did not 

 pay much attention to the vorticity distribution. 

 The authors concluded through their study that the 

 prominent features of the stern vortices could be 

 revealed by studying diagrams of the vorticity 

 distribution. 



2. ROTOR-TYPE VORTEXMETER 



Although numerous efforts have been made to investi- 

 gate the stern vortices , the state of the art for 

 measuring the vorticity distribution in aft section 

 of a model ship remains less developed than the 

 techniques for measuring the wake distribution. 

 This is evident by the few papers in which the 

 complete data of the vorticity distribution has been 

 published. This is largely attributeible to problems 

 in developing vortexmeters for towing tank measure- 

 ments. 



In the authors' experience the problems in using 

 five-hole Pitot tubes for measuring the vorticity 

 have been in maintaining sufficient accuracy through- 

 out the measurements. The analysis of vorticity 

 distribution which includes finite difference 

 methods results in insufficient precision. Besides, 

 for one mesh point of a vorticity measurement, it is 

 necessary to use the flow velocity data from four 

 adjacent mesh points which makes it difficult to 

 perform measurements close to the hull surface as 

 well as to measure fluctuating vortex flows. 



The study of stern vortices has been greatly 

 stimulated by flow visualization developments and 

 especially noteworthy contributions have been made 

 by researchers using tuft grid observations. 

 However, flow visualization for observing the vortex 

 flow has a weak point illustrated in the following 

 discussion. 



Superimposing an arbitrary irrotational flow on 

 a vortex flow, the resulting total flow should have 

 the same vorticity as the original vortex. An 

 example is shown in Figure 2 which is a velocity 

 vector diagram of a circular vortex core super- 

 imposed on a parallel flow. Examining this figure, 

 it can safely be said that few people would be able 

 to estimate an exact geometry or locate the center 

 of the vortex from only this vector diagram of the 

 total flow (or from a photo or sketch of the tuft 

 grid observation) . 



One of the authors [Tanaka (1971)] suggested 

 adopting a rotor-type vortexmeter for towing tank 

 measurements. He applied this technique to analyze 

 the stern vortices generated by a submerged body 

 running near the free surface. The application of 

 the vortexmeter is reported in many aerodynamic 

 investigations dating back to the 50 's, and it was 

 proposed for ship research by Gadd and Hogben [1962]. 



The vital problem in adopting the rotor-type 

 vortexmeter for towing tank research lies in the 

 accurate calibration of the rotor. This is mainly 

 due to the fact that no one has succeeded in gener- 

 ating a stable vortex useful for the calibration in 

 a steady flow field. 



The rotor-type vortexmeter utilizes the principle 

 that four-unpitched vanes mounted on a rotating 

 shaft, shown in Figure 3, are not affected by any 

 parallel and shear flow and only respond to a 



(A) (B) 



parallel circular vortex 

 flow flow 



(A)+(B) 

 flow pattern on tuft grid 



FIGURE 2. Tuft grid pattern due to a circular vortex 

 and a parallel flow. 



