Señal de punto de espera en la vía de vehículos (completo)

The arrangement and size of the spires was chosen to generate conditions similar to atmospheric wind in coastal areas with regard to the mean velocity profile, tur- bulence intensity and turbulence spectrum. Characteristics of the generated undis- turbed boundary layer are shown in Figure 8.1. This is the mean of 4 profiles positioned 0.3 m apart across the test section with only spires and base plates in the tunnel. The measurements were taken about 6 m downstream of the spires. An overview of the main parameters fitted to the experimental data are listed in Table 8.1. The height denoted δ in the current study is not really the top of the boundary layer, but the maximum height level measured and which the fit is ac- ceptable for.

d0 [mm] δ [mm] U(δ) [m/s] u∗ [m/s] z0 [mm] ∆U+ Re∗

0.90 349.1 13.5 0.50 0.004 0.5 0.13

Table 8.1: Characteristics of simulated atmospheric boundary layer generated by spires. All values are at model scale.

The well-known logarithmic velocity profile was fitted to the experimental mean velocity in the lower part of the undisturbed boundary layer. The displacement

Chapter 8. Results and discussion 10−3 10−2 10−1 100 15 20 25 30 (z−d 0)/z0 U/u * b) Log law z₀=0.004mm 8 10 12 14 0 100 200 300 U 0 [m/s] z [mm] a) Power law, α=0.09 1 2 3 4 0 100 200 300 σ u,0/u* z [mm] c) 0 1 2 3 0 100 200 300 σ w,0/u* z [mm] d) 0.1 0.15 0.2 0 100 200 300 σ u,0/U0 z [mm] e) 1/ ln(z/z0) 0 1 2 3 0 100 200 300 −u0_w0_/u2 ∗ z [mm] f)

Figure 8.1: Incoming undisturbed turbulent boundary layer. The streamwise mean velocity profile is compared to the power law in a), and to the logarithmic law in b). The ’*’ in a) indicates the reference height, and ’*’ in b) indicates the outermost points of the range where the logarithmic law has been fit to the data. The index 0 shows that it is the incoming boundary layer.

8.1. Undisturbed incoming boundary layer

height d0 was found by a manual fit. It was adjusted to make the lower part of the profile as linear as possible in a plot of ln(z − d0)u∗/ν versus U/u∗. Note that the quantity d0 is mainly used in this section, where it is related to the fit of the logarithmic law. The displacement height has not been subtracted from the measurement heights in the presentation of the results in subsequent chapters, as the surface is virtually smooth. The only exception is the presentation of the results related to the rough surface in Case IXb-c. The friction velocity, u∗, was also found manually by adjusting the value until the slope of the calculated line matched the slope of the experimental data in the lower region. Adding a roughness function of ∆U+ _{= 0.5, gave a very good fit to the data below z/δ = 0.15. The value of} the roughness length z0 = 0.0044 was calculated by use of Equation 3.9. Another approach was also taken to find a roughness length representative of the measured data. The method of least squares was applied between (z −d0)/δ = 0.0060 and (z − d0)/δ = 0.1378, with the value d0 = 0.9 mm determined previously. The resulting friction velocity was u∗ = 0.49 m/s, and the roughness length z0 = 0.0040 mm, hence quite similar to the results found by a manual fit. An adjustment of z0 to fit the modified logarithmic law (Equation 3.10) to the measured inflow profile, gave a roughness length of about z0 = 0.0052 mm. The lowest part of the profile was not a straight line since d0 was not subtracted, so the fit done this way was not especially good.

A fit of the power law to the experimental data was done by the method of least squares for a given reference height. The velocity profile in the undisturbed boundary layer can be reasonably represented by a power law with an exponent α = 0.09 up to the height z = 300 mm. If the lower part of the boundary layer is excluded from the fit, an exponent of α = 0.08 − 0.09 is even better.

Converted from a model scale of 1:1000 to full-scale conditions, the roughness length in Table 8.1 corresponds to a value of z0 = 0.004 m. Typical heights of the atmospheric boundary layer was described in Section 3.1.1 and an overview of roughness categories was given in Table 3.1. Both the roughness length, the adapted α and a full-scale boundary layer height of 350 m are values typical for off sea wind in coastal areas. The mean velocity at the height corresponding to 30 m in full-scale was about 10.7 m/s.

A comparison of the turbulence intensity of the measured data and a theoretical expression (Equation 3.25) is shown in Figure 8.1e). The turbulence intensity does not decrease as much as expected with height. The slightly high values for the turbulence intensity profile is mostly due to the fact that the normal stress in the streamwise direction (σu,0) does not decrease with height as it should. It decreases up to 50 mm, is constant in the range 50 mm to 100 mm, and then increases to values similar to those close to the ground at the top of the boundary layer. It is worth noticing that these variations are in the range around 1.3 - 1.4 m/s, so σu,0can be considered approximately constant throughout the boundary layer. According to Equation 3.24 the turbulence intensity at the height corresponding to 30 m and the power law coefficient (α) should be equal. The latter was found to be 0.08-0.1 dependent on the heights utilized in the power law fit. A full-scale roughness length of z0 = 0.004 m results in α = 0.1 from Equation 3.24. The measured turbulence

Chapter 8. Results and discussion

intensity at this height is 0.12-0.13, which is a bit high.

According to Gong and Ibbetson (1989) a lack of a constant stress layer near the surface is common in wind tunnel experiments. It often decreases almost lin- early with height instead. This is not the case in the current study, where the shear stress u0

w0

is approximately constant up to 0.1δ, with a mean value in this region of u0

w0

= −0.278 m2 /s2

. The calculated friction velocity is u∗ = p

−u0 w0

= 0.53 m/s, hence corresponding satisfactory with the values of friction velocity found by the manual fit and the method of least squares to the logarithmic law. The differences are within typical uncertainties of the friction velocity, as implied by for instance Krogstad et al. (1992). In contrast to theory u0_w0 _{does increase with height above} 0.1δ (see Figure 8.1f). Some measurements were also taken at heights above the outermost measurement point shown in Figure 8.1, and it was then confirmed that the trend is reversed. The Reynolds stresses decreases at heights above 350 mm. This unexpected tendency can be explained by the spires which generate the incom- ing boundary layer in the lower part of the wind tunnel. The height of 350 mm taken as the top of the boundary layer in this study is not really the height where the longitudinally velocity become constant, it actually increases even more further up.

The ratios of standard deviations to friction velocity near the surface in the streamwise and vertical directions are σu/u∗ = 2.8 and σw/u∗ = 1.2 respectively with u∗ = 0.5 m/s. If the friction velocity calculated from the shear stress is used instead, the ratios decreases to σu/u∗ = 2.64 and σ_w/u∗ = 1.13. Cao and Tamura (2007) reported values of σu/u∗ = 2.35 and σw/u∗ = 1.1 for flow above a smooth surface similar to the surface in the current study. The mean values derived from all the field data reviewed by Counihan (1975) were σu/u∗ = 2.5 and σ_w/u∗ = 1.25. Mochizuki and Nieuwstadt (1996) studied the maximum in the streamwise velocity fluctuations in wall turbulence and its dependence on Reynolds number. Data was collected from both numerical and experimental studies. They found that the most probable peak value for σu/u∗ in a turbulent boundary layer under zero pressure gradient was 2.71 ± 0.14, and that it within statistical errors was independent of Reynolds number. Also, they did not find any significant difference in the magnitude of this peak value above rough and smooth surfaces. These data were obtained for walls which could be considered as smooth, but at lower Reynolds numbers than the current study. Mochizuki and Nieuwstadt stressed the fact that the accuracy in the method used to find the friction velocity is of great importance in this context. A choice has to be made for the constants when the logarithmic velocity profile is used to find u∗, which introduces significant errors to the friction velocity. Mochizuki and Nieuwstadt commented that an experiment in the atmospheric boundary layer could be a candidate for studying the near-wall turbulent flow at very large Reynolds numbers. Data for the atmospheric boundary layer has for instance been given by Panofsky and Dutton (1984), with a near surface value of σu/u∗ = 2.39. As mentioned by Mochizuki and Nieuwstadt most atmospheric measurements are done at heights which are at least 10 meters above the surface. This could explain why the near surface values of normalized streamwise velocity fluctuations reported by for instance Panofsky and Dutton, and Counihan are lower than the results found

8.1. Undisturbed incoming boundary layer

by Mochizuki and Nieuwstadt. Hutchins and Marusic (2007) stated that since the year 2000 it has been well-known that the inner-scaled peak in σu/u∗ rises with Reynolds number. They gave a formula found by a curve fit to experimental and numerical data  σ2 u u2 ∗  peak = 1.036 + 0.965 ln δu∗ ν