TM No. 377 



through the water. The high speed runs had to be spaced at least a minute 

 apart to allow the free surface to approach equilibrium. 



Instrument Response to Off -Angle Flow. Ideally, the response of the ducted 

 meter should follow the cosine law; i.e., it should be proportional to the 

 cosine of the angle Q- between the line of fluid flow and the axis of the meter. 

 The rotating arm towing tests (OMDUM II) indicated that the cosine law was 

 only approximated by the response of the ducted meter system. The deviation 

 from the cosine law was assessed by towing each of the single meters at 

 various speeds and at various angles of & The results of this test are 

 depicted in the upper curve in figure 11-22. This plot shows R~ (defined 

 as R(0) in equation ( 11-17 )) as the ratio of the detected velocity to the 

 product of the tow velocity V and cos 0- o 



Recall that the detected velocity corresponds to the velocity-pulse 

 period calibration for zero angle. The ratio R_ would therefore be 'unity 

 if the meter response obeyed the cosine law. The numbers next to the plotted 

 points denote the number of data points obtained for each value of d. The 

 vertical bars represent the two Sigma width ( & = standard deviation). The 

 data points were obtained over a wide range of tow speeds and at a full range 

 of values for Q-. A complete listing of the experimental data is given in 

 appendix B. 



o 



Values of R for € > 80 were not obtained because (as with the OMDUM II 



calibrations) the impeller response tended to become unstable as ©■ approached 

 90°. The meter response at 90 for speeds below 175 cm sec™ 1 corresponded 

 to zero flow, indicating a certain degree of stability in the flow around the 

 cylinder. At speeds over 200 cm sec" 1 , a slight oscillation in the impeller 

 was noted. Part of this effect was probably caused by an inability to posi- 

 tion the cylinder axis closer than 2 or 3° normal to the line of flow. Thus, 

 the meter detected a slight net flow through the cylinder, which must have 

 been accompanied by vortex shedding at this angle from the flow. 



The deviation from the cosine law is indicated in figure 11-22 by the 

 increasing value of R ft with increases in 0-. The dynamics of the flow about 

 the cylinder caused it to indicate a higher rate of flow than would be 

 defined by the cosine law. Whether this was due to a higher relative 

 volume of flow or to a greater impeller sensitivity at off -angle flow is 

 not immediately obvious. 



Figure 11-22 shows that the R @ can be used as a correction factor for 

 determining the actual fluid flow at different angles of §. As demonstrated 

 later, the angle 0- can be determined uniquely from the observed outputs of 

 two orthogonally mounted meters. With a single cylinder suspended in the 

 water, one cannot, of course, determine O. However, if a single cylinder 

 is immersed in a flow environment consisting of orbital oscillations (as be- 

 neath the ocean waves), then the average error of measurement of an oscil- 

 lating velocity vector can be obtained by averaging the ratio R^ over the 

 total excursion of the motions (2 TT radians). This error value appears to 

 be about 10-12 percent except for incidence angles near 90°. 



36 



