# Wind Turbines with Truncated Blades May Be a Possibility for Dense Wind Farms

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## Abstract

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## 1. Introduction

## 2. Experimental Setup

## 3. Results and Discussion

#### 3.1. Wake Characteristics

#### 3.2. Effect of Blade Length Ratio on the Power Output

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Basic schematic of the experimental setup illustrating the PIV locations; (

**b**) details of the modified rotors with the lift-producing section restricted to the outer part of the rotor highlighting the winglets at both ends; (

**c**) diagram of the $2\times 3$ turbine array with a truncated unit.

**Figure 2.**Characteristics of the incoming turbulent boundary layer. (

**a**) Mean velocity $U/{U}_{hub}$, (

**b**) turbulence intensity ${I}_{u}={\sigma}_{u}$/${U}_{hub}$, and (

**c**) kinematic shear stress $-\overline{{u}^{\prime}{w}^{\prime}}/{U}_{hub}^{2}$. The horizontal, dashed line indicates the hub height location of the turbine rotor.

**Figure 3.**Instantaneous swirling strength ${\mathsf{\Lambda}}_{ci}{d}_{T}/{U}_{hub}$ in the near wake of the $L/R=0.6$ truncated rotor. The horizontal-dashed lines indicate the inner tips.

**Figure 4.**Mean velocity distribution, $U/{U}_{hub}$, in the central plane for the turbines with blade length ratios of $L/R=$ (

**a**) 0.6, (

**b**) 0.7, and (

**c**) 1.

**Figure 5.**Profiles of the normalized streamwise velocity difference, $\Delta U={U}_{inc}-U$, for the turbines with rotors $L/R=0.6$, 0.7 and 1 at $x/{d}_{T}=$ (

**a**) 2.6, (

**b**) 3.8 and (

**c**) 6.

**Figure 6.**Mean velocity distributions $U/{U}_{hub}$ along the turbine rotor axis (hub height) for the rotors with $L/R=$ 0.6, 0.7, and 1.

**Figure 7.**Turbulence kinetic energy, $TKE=\langle {u}^{\prime 2}+{w}^{\prime 2}\rangle /2{U}_{hub}^{2}$, for the cases with the turbine (

**a**) $L/R=0.6$; (

**b**) $L/R=0.7$; (

**c**) $L/R=1$.

**Figure 8.**Profiles of the turbulence kinetic energy, $TKE=\langle {u}^{\prime 2}+{w}^{\prime 2}\rangle /2{U}_{hub}^{2}$, for the turbines with rotors $L/R=0.6$, 0.7 and 1 at $x/{d}_{T}=$ (

**a**) 2.6, (

**b**) 3.8 and (

**c**) 6.

**Figure 9.**Kinematic shear stress $-\overline{{u}^{\prime}{w}^{\prime}}/{U}_{hub}^{2}$ for the cases with the turbine (

**a**) $L/R=0.6$; (

**b**) $L/R=0.7$; (

**c**) $L/R=1$.

**Figure 10.**Profiles of the kinematic shear stress, $-\overline{{u}^{\prime}{w}^{\prime}}/{U}_{hub}^{2}$, for the turbines with rotors $L/R=0.6$, 0.7 and 1 at $x/{d}_{T}=$ (

**a**) 2.6, (

**b**) 3.8 and (

**c**) 6.

**Figure 11.**Integral time scale ${T}^{u}$ distribution normalized by that of the incoming flow ${T}_{inc}^{u}$ along the rotor axis for various $L/R$.

**Figure 12.**Difference of the compensated velocity spectra $\Delta \left(f\mathsf{\Phi}\right)$ between the wake and incoming flow for the $L/R=$ (

**a**) 1, (

**b**) 0.7 and (

**c**) 0.6 rotors at the central plane of the wake within $x/{d}_{T}\le 7$.

**Figure 13.**Power output spectra ${\mathsf{\Phi}}_{p}$ of turbines with various blade length ratios. The subplot shows the standard deviation of power output.

**Figure 14.**Mean power output ($\overline{P}$) of a standard turbine ($L/R=1$) downwind of a truncated turbine located at the central row of a $2\times 3$ wind farm. $\overline{{P}_{0}}$ is the mean power of the isolated base case.

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## Share and Cite

**MDPI and ACS Style**

Cheng, S.; Jin, Y.; Chamorro, L.P.
Wind Turbines with Truncated Blades May Be a Possibility for Dense Wind Farms. *Energies* **2020**, *13*, 1810.
https://doi.org/10.3390/en13071810

**AMA Style**

Cheng S, Jin Y, Chamorro LP.
Wind Turbines with Truncated Blades May Be a Possibility for Dense Wind Farms. *Energies*. 2020; 13(7):1810.
https://doi.org/10.3390/en13071810

**Chicago/Turabian Style**

Cheng, Shyuan, Yaqing Jin, and Leonardo P. Chamorro.
2020. "Wind Turbines with Truncated Blades May Be a Possibility for Dense Wind Farms" *Energies* 13, no. 7: 1810.
https://doi.org/10.3390/en13071810