Luces de extremo de pista (véase la Figura 8-15)

Time series were measured with hot-wire to see if the experimental data were in agreement with atmospheric turbulence spectra and length scales. The measure- ments were taken in the centre of the tunnel 6 meters downstream of the spires at the four heights 10 mm, 30 mm, 100 mm and 300 mm. The sampling frequency used to acquire the four time series was 13.158 kHz, so the highest frequency in the spectra was 13158/2 = 6579 Hz. The sampling time was close to 45 seconds.

The integral length scales at these four measurement heights were calculated from the velocity time series using Equation 3.29, and are listed in Table 8.2. The same values are plotted in Figure 8.3 with the recommended values by Counihan (1975) and ESDU (Freris, 1990) calculated from Equation 3.30 and 3.31 respectively. The experimental integral length scale increases with height. According to Counihan, the integral length scale in the atmospheric boundary layer increases with height up to 200-300 m. The calculated integral length scale at the highest level is smaller than the ESDU value at this height. The integral length scale at the height 30 m given by Counihan for a roughness length of z0 = 0.004 m gives a full-scale value of 271 m, while the corresponding result recommended by ESDU is 116 m. Both these values are of the same order as the integral length scale found from the time series, which at full-scale is 164 m at the height 30 m. The results are consequently in agreement with a model scale of 1:1000. This is also confirmed by the length scale in Harris‘ spectrum model. The recommended value for atmospheric conditions

is LHarris = 1800 (Counihan, 1975), and the value LHarris = 1800/1000 = 1.8

employed in the model results in good agreement with the measured data (not shown here). All this implies that the energy distribution in the generated boundary layer is similar to the one in the full-scale atmosphere.

Height [mm] x_L u [mm] 10 144.1 30 164.2 100 189.8 300 204.9

Table 8.2: Calculated integral length scales at four different heights in the incoming flow.

The power density spectrum was calculated from the time series using Fast Fourier Transform. The number of samples in each FFT window was 214

, so the total number of windows used was 36. The size of the FFT windows was chosen so that it was low enough to give a clear spectrum at the high frequency end, and at the same time high enough to close the spectrum at the lowest frequencies (as seen when plotting fΦuu). The results were also smoothed. In Figure 8.4, fΦuu is plotted as a function of the normalized frequency X = fx_L

u/U on a semi-log axes, while the same is plotted on log-log axes in Figure 8.5. The experimental turbulence spectra are compared to von Karmans and Kaimals models for power density spec- tra in both figures. The length scales LKarman used at the different heights in von

Chapter 8. Results and discussion 0 100 200 300 0 50 100 150 200 250 300 350 x_L u [m] z [m] ESDU Counihan Calculated

Figure 8.3: Integral length scales calculated from the experimental data. Recom- mended values given by Counihan (1975) and ESDU (Freris, 1990) are also plotted. All values are in full-scale, and the roughness length is z0 = 0.004 m.

Karman’s model was the calculated integral length scales (x_L

u) which are listed in Table 8.2, hence not a length scale found by adjusting the model to the data. The length scale used in Kaimal’s model is LKaimal = 2.329LKarman.

It can be shown that both models used for comparison will approximate to a straight line with slope −5/3 in the high frequency range when plotted on a log-log axes (Φuu ∼ f−5/3). The positioning of this line depends on the mean velocity, the integral length scale and the standard deviation. It is seen from Figure 8.5 that the measured data have an identical slope. This is known as the inertial subrange, where energy is neither produced nor dissipated but handed down to smaller and smaller scales. The dissipation of turbulent kinetic energy into heat by viscous effects occurs at the highest frequencies. The area in between this, where the calculated values are higher than what the model predicts, is known as the pre-dissipative bump (Coantic and Lasserre, 1999). The pre-dissipative bump is less visible as the height increases, while the inertial subrange becomes broader.

Values higher than the model values can be seen at the top of the curves fΦuu in Figure 8.4 at the three highest of the four measured elevations. This top occurs where the physical frequency is about 7 Hz. The explanation for these high values might be that the measurement device was oscillating at this frequency. Since this is not the case at the lowest height, a more probable explanation is that the top is due to the way the boundary layer is set up.

The experimental data agrees very well with the von Karman power spectrum, and to some less extent with the Kaimal power spectrum. This could be expected, as the von Karman model is known to fit well with wind tunnel turbulence. The measured values are in least accordance with the models in the regions with the pre- dissipative bump and for the maximum experimental values of fΦuu as commented on above.

8.2. Flow above model - an overview