Without grid generated turbulence, X/D = 1

It is clear from Figure 5.27 in Section 5.5.2 (the phase averaged normal stress) that one of the tip vortices at X/D = 1 downstream the turbine, measured in the case with an incoming flow with low turbulence intensity, is located within the first 100° of each rotation at a location round z/R = 1.12. Based on this, the hot-wire measurements representing the fluctuating velocity round this location for the first 100° for each rotation were selected and studied. The positions of the hot-wire probes are specified in Table 5.9.

Table 5.9: X/D = 1, Position 1 of hot-wire probes

HW 1 HW 2 HW 3 HW 5

Distance from rotor center [m] 0.475 0.4888 0.5056 0.5264

z/R 1.056 1.086 1.124 1.170

To locate the where, or which hot-wire probe detected the tip vortex, a Matlab script was made to sort out the maximum fluctuating velocity within this selected data set for every rotation in the four time series. This location was assumed to represent the location of the tip vortex. Further, it was summed up how many maximum points each probe detected, and a probability density function of the maximum fluctuating velocity was made as a function of z/R. The distribution is given in Figure 5.33. The values are normalized by the total number of rotations, which is 1278 in these four time series.

Figure 5.33: Position 1, PDF on the location of one

tip vortex, X/D = 1 without grid turbulence Figure 5.34: Position 1, Time of which u’ maximum was measured with hot-wire probe nr. 3 in each

rotation, X/D = 1 without grid turbulence

1.050 1.1 1.15 1.2 0.2 0.4 0.6 0.8 1 z/R [-] Without grid 0 50 100 150 200 250 0 0.01 0.02 0.03 0.04 sample nr. [-] Without grid

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It is clear from Figure 5.33 that the probe located at z/R = 1.124, hot-wire probe number three, measured the highest fluctuating velocity most frequently, with 96.54 % of the times of the total number of rotations within the time series. This corresponds well to the location of the tip vortex found when presenting the phase averaged normal stress at X/D = 1 without grid generated turbulence. It was also measured at the locations of the other three probes every now and then, as can be seen in the distribution.

After locating the tip vortex, a study on the meandering of the tip vortex in the streamwise direction within each rotation could be conducted. This was done by finding when the maximum fluctuating velocity was measured within the first 100° of rotation at hot-wire probe number three for the different rotations. In one rotation it was measured round 940 samples (varied with one or two samples) which gave a total of 261 samples within the first 100° of rotation.

Figure 5.34 illustrates how the maximum fluctuating velocity measured with hot-wire probe three is distributed according to the number of sample within each rotation. The values are normalized by the total number of maximum u’ points measured with hot-wire probe number three. The sampling frequency during the measurements was, as mentioned, 20 kHz, and the free stream velocity was 10.2 m/s. This gives a distance of 5.10E-4 m variation between each sample in the streamwise direction.

The figure clearly illustrates that the location of the maximum fluctuating velocity sampled is gathered round sample number 87. It is a quite even variation around this measurement point, which gives the impression that the tip vortex meanders slightly back and forth in the streamwise direction. However, the variation is somewhat larger to the left in the figure. In other words, the tip vortex seems to appear at an earlier stage within the first 100° of the rotations more often than at a later stage. Though, the range where the maximum u’ appears most frequently seems be from sample number 60 to 90. This equals a distance of 1.53E-2 m. The total spread in the figure is 121 samples, giving a distance of 6.17E-2 m.

To be sure that this slight meandering in the streamwise direction seen in the previous section was not a contingency, the same procedure was conducted on a measurement point shifted to the right. The position of the hot-wire probes are given in Table 5.10.

Table 5.10: X/D = 1, Position 2 of hot-wire probes

HW 1 HW 2 HW 3 HW 5

Distance from rotor center [m] 0.510 0.5238 0.5406 0.5614

z/R 1.133 1.164 1.201 1.248

At this measurement point hot-wire probes 2, 3 and 5 should be placed as far to the right that hot-wire probe number 1 should measure all the maximum fluctuating velocities belonging to the tip vortex within the first 100° of rotation.

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Figure 5.35: Position 2, PDF on the location of one

tip vortex, X/D = 1 without grid turbulence Figure 5.36: Position 2, Time of which u’ maximum was measured with hot-wire probe nr. 1 in each

rotation, X/D = 1 without grid turbulence

As seen in Figure 5.35 nearly all, 99.37 % to exact, of the maximum points where located at the position of hot-wire probe number 1. The values in the figure are the normalized by the total number of rotations in the four time series, which was 1278 at this measurement point in the wake.

Conducting the same analysis as for the previous measurement point at z/R = 1.12, Figure 5.36 was obtained. Also in this figure there is a variation of when the maximum fluctuating velocity was measured when comparing the different rotations. It is a clear peak around sample number 75, and the variation is quite equal in each direction in the figure. The total spread is 100 samples, giving a distance of 5.10E-2 m, while the greatest variation lies between sample numbers 60 to 85, giving a distance of 1.28E-2 m.

Thus, is seems like the location of the tip votes is not as stable in the streamwise direction at X/D = 1 downstream the wind turbine when the turbine is placed in an incoming flow with low turbulence intensity.