The atmospheric influence on the flow downstream wind turbines

The interest in producing non-fossil fuel energy has increased during the last years due to the believed effects of carbon dioxide. One alternative energy source that has been used more and more is the wind. The wind turbines installed today are of the order of 1 MW and the trend is that they will be even larger. There are plans to build turbines of the size up to 5 MW. In some districts in Europe the plan is that energy produced by wind will be responsible for more than 25% of the total energy production within 10 years. In order to fulfil this task, wind turbines has to be located together in wind farms. When this is the case the turbines will take energy from each other. A turbine situated downstream of another turbine will have less access to the wind, it will be in a wake of another turbine. In a wake the wind speed is reduced and the turbulence intensity is higher. A parameter used to study how much the wind speed is reduced is the relative velocity deficit, DU /U=1-U_w/U_a, were the U_w is the velocity downstream a turbine and U_a is the velocity upstream. From momentum theory for wind turbines it is found that the thrust coefficient of the turbine is proportional to the relative velocity deficit.

Two parameters that are of interest for the planning of wind farms is wind speed and turbulence intensity at different distances downstream a wind turbine, and their lateral distribution. The interest in knowing the wind speed is governed by the fact that turbines must be located at distances so that the wind speed is sufficiently high again in order for the wind farms to be economically successful. The degree of turbulence is related to the lifetime of the turbines. Knowledge on how the turbulence is behaving in the wake will give answers on what loads the turbines will experience. This information is needed in order to dimension the turbines correctly such that they will be designed in an optimum way.

Results from a study of the flow downstream wind turbines show that the mixing rate of the flow is a function of the ambient turbulence and temperature gradient. Even if the turbulence intensity is the same for situations with positive and negative temperature gradients the mixing of the wake is different. It is more efficient during negative temperature gradients. During situations with positive temperature gradients the turbulence generated in the wake is damped and the mixing rate is lower. The influence of the temperature gradient decreases as the magnitude of the ambient turbulence intensity increases. As the wake flow is not stationary, the relevant parameter determining the characteristics is not the geometrical distance, but instead the downstream transport time. The characteristic distance downstream a wind turbine is not the geometrical distance, there is not yet a stationary condition. The flow is instead determined by the transport time.