Determination des efforts exerces par le vent sur un brise-vent

Summary

When it is planned to erect artificial windbreaks, it is necessary to estimate the stress that will be exerted by the wind in order to calculate the mechanical characteristics of the supports. To that end, this paper proposes simple fomulas to calculate the drag coefficients of artificial windbreaks, based on their geometrical characteristics.

The drag force exerted by the wind on a windbreak having an height H can be written:

$$D = \tfrac{1}{2}C_{dh} \rho u^2 \left( H \right) \cdot H$$

for unit length and taking the reference wind speed u(H) at H level. The drag coefficient C _dh is calculated by integrating elementary drag forces between ground level and H level, which can be written as:

$${\text{d}}D = \tfrac{1}{2}C_d \rho u^2 \left( z \right){\text{d}}z$$

C _d being the drag coefficient of a grid element as determined in an uniform flow.

Considering the logarithmic wind profile u(z)= u ^*/k ln z/z ₀ and integrating between z ₀ and H leads to the following relation between C _dh and C _d:

$$\frac{{C_{dh} }}{{C_d }} = 1 - \frac{2}{{\ln H/z_0 }} + \frac{2}{{\left( {\ln H/z_0 } \right)^2 }}$$

which is illustrated by Figure 2.

The drag coefficient C _d may be determined as a function of windbreak porosity φ following the works of Valensi and Rebont (1959) and Castro (1971).

Valensi and Rebont propose:

$$C_d = 2.\frac{{1 - m^2 \phi ^2 }}{{1 + m^2 \phi ^2 }}$$

with m = 0.95 for a metal web and 0.9 < m < 0.95 for a perforated plate (Figure 1).

From Castro's work, lower C _d values may be derived by adjusting his experimental values to a fourth-degree polynomial:

$$C_d = 1.85 - 1.74\phi - 0.85\phi ^2 + 1.73\phi ^3 - \phi ^4$$

.

Using these relationships, it is possible to calculate C _dh knowing φ and H/z ₀. The results of computations for H/z ₀ = 200 are compared with the experimental results of Tani (1958), Hagen and Skidmore (1971), Seginer (1975) and de Bray (1971) in Figure 3.

While C _dh estimations based on C _d values derived from Valensi and Rebont (1969) are in good agreement with experimental values of Tani, Hagen and Skidmore and Seginer, calculations derived from Castro's data agree well with de Bray's results.

It is not possible at the present time to decide which is the more suitable relationship, but it seems preferable for structure computations to adopt C _d values based on the work of Valensi and Rebont.

The determination of the application point of the drag force leads to the relation

$$\frac{{z_1 }}{H} = \frac{1}{2}\frac{{\left( {\ln H/z_0 } \right)^2 - \ln H/z_0 + \tfrac{1}{2}}}{{\left( {\ln H/z_0 } \right)^2 - 2\ln H/z_0 + 2}}$$

giving the z ₁ level of this point. The variation of z ₁/H as a function of H/z ₀ is given in Figure 4.