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 DISTANCE FROM HUB (°/c.) 

 BODY LENGTH 



FIGURE 4. Velocity profiles immediately ahead of the 

 propeller DTNSRDC body 5225-1 [Kuang (1976)]. 



associated with the wakes from the four struts 

 which each produce a 'trough' in the measured flow 

 field. The high harmonic amplitudes at high har- 

 monic numbers implies a possible inaccuracy in 

 results from a Fourier analysis based on the finite 

 number of measured points. This was investigated 

 theoretically by assuming an idealised wake defect 

 giving a triangular waveform as indicated in 

 Figure 6. The number of wake defects and wake 

 width could be varied and for each assumed flow 

 field an exact Fourier analysis was obtained ana- 

 lytically and the results were compared with similar 

 analyses determined numerically with the waveform 

 described at discrete points as specified in the 

 measurements. Figure 7 shows results obtained with 

 4 narrow wake defects and 120 points specifying the 

 velocity profile. Two wake widths are considered; 

 when maximum wake width is 9° harmonics above 20 

 are in reasonable agreement with the exact solution 

 although harmonics below 20 are too low; when wake 

 width is reduced to 4*5° the amplitude of harmonics 

 from the exact solution falls slowly with increas- 

 ing harmonic number whereas the amplitudes deter- 

 mined numerically show no reduction in amplitude. 

 In this case, where points are specified every 3° 

 and the width of each wake defect is only 455° , 

 'aliasing' in the numerical results is not un- 

 expected. Such pitfalls in numerical analysis are 

 well known and Manley (1945) shows that erroneous 

 values in analyses of the type described above 

 might be expected at harmonic numbers given by 

 (N-jK) where N is the number of specified points, 

 K the number of wake defects and j is an integer. 

 A parametric study for triangular waveforms in 



obtained. This information is relevant to the 

 estimation of unsteady forces generated by a pro- 

 peller. Some tests have been made in a wind tunnel 

 to assess the reliability of model measurements at 

 a typical propeller position on a three dimensional 

 body. Inflow non-uniformity was introduced by 

 fitting four struts to the body and the velocity 

 field was measured by a single traversable pitot- 

 static prove with head 1.5 mm in diameter. Measure- 

 ments at a given radius were made on different runs 

 with incremental steps of 1°, 2°, and 3° in the 

 circumferential position of the probe and 10 repeat 

 runs were made with 3° incremental steps. A Fourier 

 analysis of each set of results was made and the 

 harmonic spectra are summarised in Figure 5. It 

 can be seen that the standard deviations in the 

 magnitudes of wake harmonics are quite small show- 

 ing that misleading information concerning the 

 relative magnitudes of different wake harmonics 

 would not be obtained on any one run. The differ- 

 ences in magnitudes from the runs with 1°, 2°, and 3^ 

 steps in probe position are also quite small in 

 general although a few wake harmonics, such as 11, 

 do show significant changes. No consistent trend 

 is observed in comparing amplitudes at low harmonic 

 number but at harmonic numbers greater than 25 the 

 amplitudes obtained from the run with 1° steps tend 

 to be higher than those from other runs , the impli- 

 cation being that choosing a coarser step size has 

 resulted in a small loss in accuracy. 



The amplitudes of wake harmonics at harmonic 

 numbers greater than 20 are small (less than 0.005 

 times tunnel speed) except for harmonic numbers 

 which are multiples of 4. These higher values are 



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I STEPS (I run) 

 B 2° STEPS RUN) 

 D 3° STEPS (MEAN OF II RUNS) 



STANDARD DEVIATION 



HARMONIC NUMBER 



FIGURE 5. Harmonic analysis of different measurements 

 of a non-uniform flow field. 



