Wind Energy Handbook. Michael Barton Graham

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СКАЧАТЬ to the so‐called ‘geostrophic wind speed’, G, which is the notional wind speed driving the boundary layer as calculated from the pressure field. The geostrophic wind speed is given by

      (2.13)

      where, for neutral conditions, A = ln 6 and B = 4.5. This relationship is often referred to as the geostrophic drag law.

      The effect of surface roughness is not only to cause the wind speed to decrease closer to the ground. There is also a change in direction between the ‘free’ pressure‐driven geostrophic wind and the wind close to the ground. Although the geostrophic wind is driven by the pressure gradients in the atmosphere, Coriolis forces act to force the wind to flow at right angles to the pressure gradient, causing a characteristic circulating pattern. Thus in the northern hemisphere, wind flowing from high pressure in the south to low pressure in the north will be forced eastwards by Coriolis effects, in effect to conserve angular momentum on the rotating earth. The result is that the wind circulates anti‐clockwise around low‐pressure areas and clockwise around high‐pressure areas, or the other way round in the southern hemisphere. Close to the ground, these flow directions are modified due to the effect of surface friction. The total direction change, α, from the geostrophic to the surface wind is given by

      (2.14)

      2.6.3 Turbulence intensity

      The turbulence intensity in the neutral atmosphere clearly depends on the surface roughness. For the longitudinal component, the standard deviation σ_u is approximately constant with height, so the turbulence intensity decreases with height. More precisely, the relationship σ_u ≈ 2.5u* may be used to calculate the standard deviation, with the friction velocity u* calculated as in the previous section. More recent work (ESDU 1985) suggests a variation given by

      (2.15)

where

      (2.16)

      (2.17)

      This approximates to σ_u = 2.5u* close to the ground, but gives larger values at greater heights. The longitudinal turbulence intensity is then

      (2.18)

      The lateral (v) and vertical (w) turbulence intensities are given (ESDU 1985) by

      (2.19)

      (2.20)

      Note that specific values of turbulence intensity for use in design calculations are prescribed in some of the standards used for wind turbine design calculations, and these may not always correspond with the above expressions. For example, the now superseded Danish standard (DS 472 1992) specified

      (2.21)

      with I_v = 0.8 I_u and I_w = 0.5 I_u.

      The IEC edition 2 standard (IEC 61400‐1 1999) gives

      (2.22)

      where I₁₅ = 0.18 for ‘higher turbulence sites’ and 0.16 for ‘lower turbulence sites’, with corresponding values of a of 2 and 3, respectively. For the lateral and vertical components, a choice is allowed: either I_v = 0.8 I_u and I_w = 0.5 I_u, or an isotropic model with I_u = I_v = I_w.

      Editions 3 (IEC 61400‐1 2005) and 4 (IEC 61400‐1 2019) of the IEC standard specify

      (2.23)

      where I_ref = 0.16, 0.14, or 0.12 depending on the wind class. For lateral and vertical components, I_v must be at least 0.7I_u, and I_w at least 0.5I_u. Standard deviations are assumed constant with height, so the turbulence intensity will change with height as the mean wind speed changes due to wind shear.

      The earlier GL rules (GL 1993) simply specified 20% turbulence intensity, but the later edition (GL 2003) follows IEC edition 2.

Figure 2.4 shows example longitudinal turbulence intensities for the GL, IEC, and Danish standards. The low value for the Danish standard is for 90 m height with roughness length 0.01 m; the high value is for 30 m height with roughness length 0.3 m. The high values for IEC editions 2, 3, and 4 are the same, but the low value is significantly lower in editions 3 and 4 than in edition 2.

Figure 2.4 Turbulence intensities according to various standards

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