# Power Output Enhancement of a Ducted Wind Turbine by Stabilizing Vortices around the Duct

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{p}of this energy extraction device exceeds the Betz limit when it is defined in relation to the area of flow intercepted at the device. Their theories have been discussed in detail and extended by Liu et al. [5]. Analysis and optimization of the shroud configuration have been conducted by Aranake et al. [6], Khamlaj and Rumpfkeil [7]. Oka et al. [8] and Vaz and Wood [9] have investigated the design of the blade, and Wang et al. [10] have provided mechanical insight into the blade. The aero-acoustic noise of the turbine has been assessed by Hashem [11].

## 2. Materials and Methods

#### 2.1. Wind Tunnel Experiments

_{throat}was 1.0 m. The diffuser length L

_{t}(m) in the streamwise.

_{t}= 0.14 D

_{throat}. The brim height h (m) was 5% or 10% of the throat diameter of the duct (see Figure 4).

_{p}was defined as:

^{3}) was the density of the air, U

_{0}(m/s) was inflow wind speed, and A (m

^{2}) was the swept area of the rotor. In addition, Tr (N·m) was the torque on the rotor with a given wind speed and ω (rad/s) was the angular velocity of the rotor. A torque transducer (rating: 5 N·m) was connected to the wind turbine and an AC torque motor brake was set under it for the loading. Table 2 shows specifications of the transducer. We measured the Tr with an accuracy of ±0.2% and measured the rotational speed n (1/s) of the wind turbine under the condition of gradually increasing its load from zero. The power output P was calculated as, P = Tr × ω = Tr × 2π × n.

#### 2.2. Numerical Simulations

^{®}package (RIAM-COMPACT Co., Ltd., Fukuoka, Japan) developed at Kyushu University [44,45,46,47,48,49]. This numerical method had already been validated in our previous study, being compared wind tunnel experiment results [50]. Formulae (2) and (3) describe the two governing equations, the continuity equation and the Navier–Stokes equation for incompressible flows. In our DNS, the Navier–Stokes equations were solved on a generalized curvilinear collocate grid (Figure 8). The coupling algorithm between the velocity and the pressure was based on the fractional-step method [51] with the Euler explicit scheme. Poisson’s equation for pressure was solved by the successive over-relaxation (SOR) method. For spatial discretization, a second-order accurate central-difference scheme that excluded the convective terms was used. For the convective terms, a modified third-order upwinding scheme was applied. An interpolation technique based on four-point differencing and four-point interpolation by Kajishima et al. [52] was used for the fourth-order central differencing that appears in the discretized form of the convective term. The weight of the numerical viscosity term α was settled into a much smaller value (α= 0.5) than that of the Kawamura–Kuwahara scheme (α= 3) [53].

_{throat}, and the WLT model was placed 5.5 D

_{throat}downstream from the inflow surface of the domain. The total domain length in streamwise direction was 15 D

_{throat}. The total number of the grid points was approximately 1.7 × 10

^{6}. All physical values were calculated in a dimensionless field, and its representative length was D

_{throat}. Boundary conditions are shown in Figure 8b. The incoming flow was uniform and Re = 10

^{4}. The characteristic length was D

_{throat}. For the outflow boundary, the convective outflow condition was employed. The Neumann condition was given to pressures at the domain boundaries. The code was run first for a time equivalent to 200 Karman vortex cycles (behind the brim) to establish steady flow throughout the computational domain before beginning the analysis of the field. The actuator-disc model [50,54] was used as a numerical model for the wind turbine. Its tip-speed ratio λ was set to 4.0, which was the optimum ratio of our turbine. All of the diffuser shapes were based on the Ci type with a 5% brim height (Figure 9). The shapes of the brim are shown in Figure 9. No vortex stabilization plates were simulated in any of the cases.

## 3. Results and Discussion

#### 3.1. Experimental Results

#### 3.1.1. Power Output Enhancements by the Vortex Stabilization Plates

_{p}(=C

_{p_max}) at the optimum tip-speed ratios. The increase rate of C

_{p_max}with the type 3 plate was much higher than that of the type 1 plate. The results implied that a WLT with a high brim was able to enhance its power output even though the additional plates were small. As aforementioned, we considered that it was because of the stronger vortices produced by the higher brim; they amplified the effect of the vortex stabilization plates. The line graphs in Figure 12 indicate that C

_{p_max}peaked between 6 and 12 plates, which suggests that this is the optimum range of the installed number of plates. As a typical result, WLT Ci10 with six type 4 plates achieved a 3.8% increase in power output.

#### 3.1.2. Wind Speed Acceleration Inside the Duct by the Vortex Stabilization Plates

#### 3.1.3. Two-Dimensional Vortices Generated by the Vortex Stabilization Plates

#### 3.1.4. Power Output Enhancements by the Polygonal Brims

#### 3.2. Numerical Results

#### 3.2.1. Fluctuating Vortex Structures around the WLT Brim

_{throat}/U

_{0}) = 0.01, which was a nondimensionalized time interval. The pressure was nondimensionalized. The blue indicates low-pressure regions and the red indicates high-pressure regions.

#### 3.2.2. Periodic Vortex Structures around the Polygonal Brim

#### 3.3. Future Possibilities

## 4. Conclusions

- The vortex stabilization plates enhance the output in a wide range of tip-speed ratios while the significance of the power enhancement depends on the installed number of the plates. A WLT with a high brim is able to enhance its power output even if the additional plates are small. In this study, the output peaked between 6 and 12 plates, which suggested the optimum range of the installed number of plates. WLT Ci10 with six plates achieved a maximum 3.8% increase in power output.
- A WLT with vortex stabilization plates enables its brim to form two-dimensional vortices around itself. The vortices maintain the WLT’s strong drawing action, especially near the inside wall of the duct where wind speed is accelerated.
- The vortex shedding from the WLT brim has a circumferentially periodic pattern, while the pattern instantaneously becomes unstable and asymmetrical. The vortex stabilization plates suppress vortex fluctuations, and the contribution is maximized when a pair of plates divides the structure of vortex shed into a size corresponding to the wavelength of its periodic loop. The wavenumber of the periodic loop derived by numerical simulation coincided with the optimum range of the installed number of the plates in wind tunnel experiments.
- The polygonal brims are able to form periodical vortex patterns without vortex stabilization plates, and the effect stabilizes the vortices. The wavelengths of the patterns coincide with the distances between the vertices of the brims. The WLT with the dodecagon brim achieved an approximately 1.5% increase in power output without vortex stabilization plates.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Schemes of WLT and the duct with the shape of Ci type diffuser: (

**a**) Representative configuration parameters of the duct of WLT; (

**b**) In situ photograph of the duct (h = 0.05 D

_{throat}).

**Figure 5.**Additional plates installed on WLT for the purpose of stabilizing vortices around the brim: (

**a**) Four various shapes of the plates (Thick lines pink and purple indicate diffuser contours); (

**b**) In situ photograph of the plates on the WLT (twelve plates type 2, h = 0.05 D

_{throat}).

**Figure 6.**The various WLT brim shapes tested in the wind tunnel experiments: (

**a**) Ci05 (circular brim, h = 0.05 D

_{throat}); (

**b**) Ci10 (circular brim, h = 0.10 D

_{throat}); (

**c**) Ci10_L6 (hexagon brim with straight sides, h = 0.10 D

_{throat}); (

**d**) Ci10_C6 (hexagon brim with curved sides, h = 0.10 D

_{throat}); (

**e**) Ci10_L12 (dodecagon brim with straight sides, h = 0.10 D

_{throat}); (

**f**) Ci10_C12 (dodecagon brim with curved sides, h = 0.10 D

_{throat}).

**Figure 8.**Computational grid and conditions: (

**a**) The computational domain; (

**b**) The boundary conditions; (

**c**) The grid near the WLT (Ci05).

**Figure 9.**The various WLT brim shapes modeled in the numerical simulations: (

**a**) Ci05 (circular brim, h = 0.05 D

_{throat}); (

**b**) Ci05_L6 (hexagon brim with straight sides, h = 0.05 D

_{throat}); (

**c**) Ci05_C6 (hexagon brim with curved sides, h = 0.05 D

_{throat}); (

**d**) Ci05_L12 (dodecagon brim with straight sides, h = 0.05 D

_{throat}); (

**e**) Ci05_C12 (dodecagon brim with curved sides, h = 0.05 D

_{throat}).

**Figure 10.**Power curves of WLT Ci05: (

**a**) Results of the WLT with the type 1 vortex stabilizing plates; (

**b**) Results of the WLT with the type 2 vortex stabilizing plates.

**Figure 11.**Power curves of WLT Ci10: (

**a**) Results of the WLT with the type 3 vortex stabilizing plates; (

**b**) Results of the WLT with the type 4 vortex stabilizing plates.

**Figure 12.**Variations of C

_{p_max}with increases in the installed number of vortex stabilization plates.

**Figure 13.**Nondimensionalized wind speeds in the streamwise direction near the inside wall of the WLT Ci10 duct (without the turbine): (

**a**) Inflow wind speed U

_{0}= 4 m/s; (

**b**) Inflow wind speed U

_{0}= 8 m/s.

**Figure 14.**Flow visualization results: (

**a**) Vortices generated by WLT Ci05 without the vortex stabilizing plates; (

**b**) Vortices generated by WLT Ci05 with the type 2 vortex stabilizing plates.

**Figure 15.**Power curves of WLT Ci10: (

**a**) Results of the WLT with the polygonal brim with straight sides; (

**b**) Results of the WLT with the polygonal brim with curved sides.

**Figure 16.**Time-series behavior of instantaneous pressure upon the brim of WLT Ci05. (The nondimensionalized time interval Δt* between each of the figures was Δt* = 0.01): (

**a**) t* = t

_{0}* (at the moment 200 Karman vortex cycles have produced behind the brim); (

**b**) t = t

_{0}* + 0.01; (

**c**) t = t

_{0}* + 0.02; (

**d**) t = t

_{0}* + 0.03; (

**e**) t = t

_{0}* + 0.04; (

**f**) t = t

_{0}* + 0.05; (

**g**) t = t

_{0}* + 0.06; (

**h**) t = t

_{0}* + 0.07; (

**i**) t = t

_{0}* + 0.08; (

**j**) t = t

_{0}* + 0.09; (

**k**) t = t

_{0}* + 0.10; (

**l**) t = t

_{0}* + 0.11.

**Figure 18.**Time-averaged pressure distributions on the polygonal WLT brims: (

**a**) Ci05_L6 (hexagon brim with straight sides, h = 0.05 D

_{throat}); (

**b**) Ci05_C6 (hexagon brim with curved sides, h = 0.05 D

_{throat}); (

**c**) Ci05_L12 (dodecagon brim with straight sides, h = 0.05 D

_{throat}); (

**d**) Ci05_C12 (dodecagon brim with curved sides, h = 0.05 D

_{throat}).

**Figure 19.**Practical WLT [58] with a duct composed of several parts.

Conditions | |
---|---|

Throat diameter of the duct | D_{throat} = 1.0 m |

Contour shape of the diffuser section in the duct | Ci type [13] |

Brim height of the duct | h = 0.05 D_{throat} or 0.10 D_{throat} |

Number of the additional plates | 0, 6, 12, 24, 36 |

Turbine blade | MT1013-081 [41,42,43] |

Inflow wind speed | U_{0} = 8 m/s (U_{0} = 4 m/s and U_{0} = 8 m/s for the wind speed measurement) (U_{0} = 1 m/s only for the flow visualization) |

Reynolds number | 5.5 × 10^{5} (U_{0} = 8 m/s)(representative length: D _{throat}) |

Device | Manufacturer | Model | Measurement Accuracy |
---|---|---|---|

Torque detector Torque converter | Ono Sokki Co., Ltd. (Kanagawa, Japan) | SS-100 TS-2600 | ±0.2% F.S |

AC servo-control system | Sanyo Denki Co., Ltd. (Tokyo, Japan) | PY0A 150A | - |

Device | Manufacturer | Model | Specification |
---|---|---|---|

Hot-wire probe CTA unit Linearizer unit | Kanomax Japan, Inc. (Osaka, Japan) | 0251R-T5 1011 1013 | Straight type φ = 5 μm (Tungsten) |

Shroud Shape | Plate Type | Number of Vortex Control Plates | ||||
---|---|---|---|---|---|---|

0 | 6 | 12 | 24 | 36 | ||

Ci05 (h = 0.05 D_{throat}) | 1 | 0.723 | 0.727 | 0.725 | 0.721 | 0.723 |

2 | 0.723 | 0.740 | 0.741 | 0.726 | - | |

Ci10 (h = 0.10 D_{throat}) | 3 | 0.790 | - | 0.817 | 0.803 | - |

4 | 0.790 | 0.820 | 0.817 | 0.814 | 0.810 |

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**MDPI and ACS Style**

Watanabe, K.; Ohya, Y.; Uchida, T. Power Output Enhancement of a Ducted Wind Turbine by Stabilizing Vortices around the Duct. *Energies* **2019**, *12*, 3171.
https://doi.org/10.3390/en12163171

**AMA Style**

Watanabe K, Ohya Y, Uchida T. Power Output Enhancement of a Ducted Wind Turbine by Stabilizing Vortices around the Duct. *Energies*. 2019; 12(16):3171.
https://doi.org/10.3390/en12163171

**Chicago/Turabian Style**

Watanabe, Koichi, Yuji Ohya, and Takanori Uchida. 2019. "Power Output Enhancement of a Ducted Wind Turbine by Stabilizing Vortices around the Duct" *Energies* 12, no. 16: 3171.
https://doi.org/10.3390/en12163171