**5. Summary and conclusions**

*4.2. Flower leaves arrangement of wind turbines*

24 Advances in Wind Power

idea is depicted schematically in Figure 13.

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

**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 In this study, wind turbine power was reconsidered. At the beginning, a literature review was given with relation to the potentiality of wind power, worldwide applications of wind power, and different factors that affect the performance of wind turbines, especially those related to one-dimensional modeling of the flow through the wind turbine. Later, different models were addressed, taking into account the effect of friction, which is usually neglected in the literature. In this study, friction is modeled to be proportional to the square of the ve‐ locity of the air crossing the wind turbine blades. The bare wind turbine model and the shrouded wind turbine model were analyzed based on the following balance equations: the mass balance equation, the momentum balance equation, and the energy balance equation that is exposed in the form of an extended (modified) Bernoulli equation. Through the anal‐ ysis it was observed that both the power coefficient and the thrust coefficient degrade with friction. As was noticed in previous studies, the power coefficient given by the Betz number is the efficiency of the wind turbine (originally derived for the bare wind turbine). Following the same type of definition, a similar expression for the shrouded wind turbine could be de‐ rived. In a different approach, the wind turbine could be analyzed using finite time meth‐ ods, as was given by [14]. In this study, the results were briefly summarized.

The well-known golden ratio usually is considered as a measure of beauty. It is interesting to notice that the Betz number differs from the golden ratio by only 4% (0.618 compared to 16/27=0.593).

In an effort to explain the discrepancy between theoretical efficiency and practical or meas‐ ured efficiencies, different factors that affect the extraction of wind power are considered. These include mechanical friction, conversion efficiency to electricity, and blockage efficien‐ cy, which accounts for the blocked amount of air (usually is not mentioned in the literature), thus reducing the power output.

Finally, plots were given to suggest ways of assembling wind turbines to gain more of wind power for each tower installation.
