**4. Wind turbine arrangements**

One could suggest ideas to increase power extraction from the wind, thus decreasing the overall cost. One suggestion is the bottoming wind turbine; another is the *flower leaves* ar‐ rangement of wind turbines. Both are discussed in the following sections.

#### **4.1. Bottoming wind turbines**

According to Betz, the maximal power extraction efficiency is 16/27. If it is possible to extract energy from the downstream expelled air, assuming the same limit exists, one could esti‐ mate an extra amount of 11/27\*16/27 which is approximately 24%. This estimate suggests adding a smaller bottoming rotor behind the main larger rotor. The idea of the bottoming wind turbine is depicted schematically in Figure 12.

amount of energy extracted per unit of volume with a shroud is the same as for an ordinary bare wind turbine. These results were found to be in agreement with results observed in [Van Bussel, 2007]. The efficiency of maximum power output that was observed by the finite time analysis was approximately 36%, which is comparable to experimental findings [14]. When compared to heat engines, the efficiency of the wind turbine could be expressed in terms of the Betz number by using equation (23). If the Betz number is substituted, the effi‐ ciency could be approximated as 47%, but if the other factors are taken into account, the

> **Thrust coefficient for the shrouded wind turbine for different values of CF versus a**

> > **C\* loss=0 0.05 0.1**

**0 0.1 0.2 0.3 0.4 0.5 a**

**Figure 10.** Thrust coefficient for the shrouded wind turbine as a function of parameter *a,* accounting for frictional

One could suggest ideas to increase power extraction from the wind, thus decreasing the overall cost. One suggestion is the bottoming wind turbine; another is the *flower leaves* ar‐

According to Betz, the maximal power extraction efficiency is 16/27. If it is possible to extract energy from the downstream expelled air, assuming the same limit exists, one could esti‐ mate an extra amount of 11/27\*16/27 which is approximately 24%. This estimate suggests adding a smaller bottoming rotor behind the main larger rotor. The idea of the bottoming

rangement of wind turbines. Both are discussed in the following sections.

practical efficiency could reach much lower values.

22 Advances in Wind Power

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losses and for augmentation coefficient *CF,* with different values.

wind turbine is depicted schematically in Figure 12.

**4. Wind turbine arrangements**

**4.1. Bottoming wind turbines**

0.5

1

1.5

**Thrust Coefficient**

2

**CF=2 1 0**

2.5

3

**Figure 11.** Power and coefficients for the shrouded wind turbine as a function of the thrust coefficient, accounting for frictional losses and for augmentation coefficient *CF,* with different values.

**Figure 12.** Schematics of the bottoming wind turbine idea. The main rotor is the first to intercept the airflow. Outlet air is then directed to the secondary rotor. The attractiveness of this idea is to gain more output with the same tower installation, reducing the inherently larger cost of erecting multiple towers.

#### *4.2. Flower leaves arrangement of wind turbines*

Considering the shrouded wind turbine as being a relatively small device is given (some‐ times called flower power while searching the web), one could suggest installing different devices on the same tower. Such an arrangement reduces the cost of the installation. The idea is depicted schematically in Figure 13.

**Figure 13.** Schematics of *flower leaves* arrangement of wind turbines. Because they are small devices, it should be pos‐ sible to install more of these shrouded systems on a single tower. While the concept of reducing installation costs is

similar to that of the bottoming wind turbine, the attractiveness of the flower leaves configuration is that many small‐ er turbines can be accommodated on a single tower, with significant cost reductions.
