Additives Injected Into the Boundary Layer of an Underwater Body 



TURBULENCE STUDIES OF THE WAKE 



To obtain more detailed information on the effect of the injection of a poly- 

 mer solution on the drag, a study of the turbulence in the wake was made using 

 two concentrations of POLYOX WSR-301, 100 ppm, and 500 ppm. A tunnel ve- 

 locity of 400 cm/sec and an injection flow rate of 30 ml/sec through the 0.25 

 mm nose slot were used for all the runs. 



A hot-film probe was used to measure the turbulence and the average ve- 

 locity in the wake. The sensitive element is a thin platinum film, mounted near 

 the tip of the conical nose of the probe, which is maintained at a constant tem- 

 perature by appropriate electronics (Evans, 1963). This type of probe essen- 

 tially responds to the turbulence fluctuations in the direction of the mean veloc- 

 ity in the tunnel (Ling, 1955). The probe was mounted in the same holder as 

 used for the dye work, with the platinum film 7 cm behind the tail of the model. 

 This is the same position as used for the dye runs. The frequency response of 

 the probe is reasonably flat to about 1000 cps, and the average velocity output 

 of the equipment was adjusted so that it had a linear response over the velocity 

 range encountered in the wake. 



The procedure in each set of runs was to record the turbulence signal for 

 about a minute starting at the centre of the wake without a polymer solution in 

 the boundary layer. The polymer solution was then injected, and the turbulence 

 again recorded for about a minute. The average velocity at that position in the 

 wake was read from a meter, and any changes in the velocity when the polymer 

 solution was injected were recorded. After each run the probe was moved up 

 0.5 cm and the procedure repeated until the probe was out of the wake. 



The recorded turbulence signal was passed through a digitizer with a sam- 

 pling rate of 2500 samples/sec, and the resulting digital tape was processed on 

 our Packard-Bell PB-250 computer to obtain the mean square of the turbulence 

 velocities, and the power spectrum of the turbulence at the probe positions in 

 the wake. 



Figures 18 and 19 show the average velocity profiles and the mean square 

 of the turbulence velocities for the wake with no fluid injection, and with 100 

 ppm, and 500 ppm solutions of POLYOX WSR-301 injected at 30 ml/sec. The 

 tunnel velocity for these runs was about 400 cm/sec. Two effects of the poly- 

 mer solution injection are shown. For the 100 ppm solution the mean velocity 

 increased and the turbulence level decreased; for the 500 ppm solution, the 

 mean velocity increased markedly, but the turbulence level also increased. 

 There is a reading error of about plus or minus 2 cm/sec in the average veloc- 

 ity curves. The significance of the differences shown in Fig. 19 for the probe 

 positions between 2 cm and 3 cm above the wake centre-line is not known. 



Figure 20 shows a set of spectrum of the turbulence taken 0.5 cm above the 

 wake centre-line for the 100 ppm solution. Figure 21 shows three sets of spec- 

 tra for the 500 ppm solution taken at the centre-line of the wake, 1.5 cm above 

 the centre-line, and 3 cm above the centre-line. These curves are plots of log * 

 vs log k where 4- is the mean square of the turbulence velocity per unit wave 

 number k, and k = 277 (frequency of the turbulence signal) divided by the average 

 velocity passed the probe. 



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