# Design Features and Numerical Investigation of Counter-Rotating VAWT with Co-Axial Rotors Displaced from Each Other along the Axis of Rotation

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

- The ability to accept wind from any direction, eliminating the need for the rotational mechanisms for turning the wind turbine to the upcoming wind, thus reducing the cost of the turbine;
- Better performance in turbulent wind conditions;
- Low noise operation, which is a topical issue in densely populated areas;
- The ability to mount the generator and electromechanical transmission at the bottom part of the wind turbine installation, which is closely linked to the cost-effectiveness and ease of maintenance;
- Ease of installation (roofs of buildings, yards, gas stations, decks of ships);
- Simplicity of production of blades with a constant aerodynamic profile in comparison with blades for HAWTs, which should be conical and twisted to achieve the desired optimal productivity.

## 2. Overview of Dual-Rotor CR-VAWTs

#### 2.1. Dual-Axis CR-VAWT

#### 2.2. CR-VAWT with Co-Axial Rotors When One Rotor Covers the Other

#### 2.3. CR-VAWT with Co-Axial Rotors Displaced from Each Other along the Axis of Rotation

- Because the two rotors rotate in opposite directions, the relative angular velocity of the generator with two rotated parts, inductor and armature, would be a sum of both rotor’s angular velocities, so the size of the generator could be much smaller to generate the same power as a single VAWT with the same rated output power;
- It is easier to manufacture and transport two smaller rotors than one bigger;
- Single-rotor blades are bigger, so the blade surface stresses, vibratory loads and loading noises are also bigger, which, accordingly, require stronger and more expensive supports for VAWT installation.

#### 2.4. Drivetrains for CR-VAWT

## 3. Design Features of CR-VAWT with Co-Axial Rotors Displaced from Each Other along the Axis of Rotation

#### 3.1. Aerodynamic Design

_{p}. Because of the straight blades, the H-rotor is easy to manufacture and reliable during operation. Studies have shown that when the H-rotor has three blades, its starting and working characteristics for low wind speeds are optimal [34]. In addition, three-bladed H-rotors operate at much higher TSR values compared to Savonius rotors; this is why EGs could be directly linked with rotors forming a direct drive. This simplifies the construction and installation of the CR-VAWT, improves the starting characteristics and increases the reliability during operation.

_{a}is the air density; A = 2RH is the rotor’s swept area (R is the rotor radius; H is the rotor blade height); C

_{p}(λ) is the power coefficient of a specific rotor, which depends on the TSR λ and the rotor construction; and V

_{w}is the wind speed.

_{p}(λ) characteristic, which is evaluated experimentally or numerically using a computational model. The optimal point C

_{p.max}(λ

_{opt}) is depicted in Figure 2, at which the rotor extracts the maximum possible amount of power from the wind. For each wind speed, there is an optimal value of the rotor angular velocity ω, which is provided by the control system of the WT. It is crucial to maintain that optimal angular velocity value for the duration of the wind turbine’s operation to extract the maximum possible amount of power from the wind. The system ensures this is the maximum power point tracking (MPPT) system.

_{p}value might be reduced in this case [37].

_{b}is the number of the rotor’s blades, and c is the blade chord length.

_{p}will be decreased [38]. Therefore, there is an issue with the optimal combinations of the starting and working characteristics of H-rotors [39].

_{p}. The optimal AR for each unique rotor is different, so to estimate the correct AR, CFD or experimental modeling should be performed.

_{opt}; however, for VAWT of the Darrieus type, the zone of low TSR with a low or even negative value of C

_{p}expands. This impairs the VAWT’s starting capabilities, i.e., the wind speed increases at which the rotor is able to spin up to the angular velocity at which the lift force of the blades develops and the VAWT heads towards the point of maximum power generation. Larger values of solidity, on the contrary, sharply reduce λ

_{opt}of WT, contributing to an increase in the starting capabilities of VAWT but a decrease in C

_{p}. In the case of applying additional measures to ensure VAWT startup, which will be recommended in this work, it is advisable to apply a small value of solidity while maintaining high values of the power coefficient. Taking this into account, for a CR-VAWT of this type with rotors based on straight blades with a NACA 0018 airfoil, it is possible to select σ = 0.15, which provides C

_{p.max}= 0.4–0.45 at λ

_{opt}= 4.8–5 in the entire operating range of Reynolds number Re. Note the C

_{p.max}decreases with smaller Re [37].

#### 3.2. Drivetrain and EG Design

_{WT}(ω) obtained from (2) and (3), can lead to a loss of mechanical stability of CR-VAWT, when the angular velocity of one rotor increases and the other stops altogether.

#### 3.3. Control System Design

_{G.e}, and the auxiliary electromagnetic parts 1 and 2 form the electromagnetic torques T

_{k1}and T

_{k2}of the additional small PM machines. Because the additional PM machines provide the function of rotor startup, the main PMSG should operate only as a generator. It significantly simplifies the load control system, which can be realized by a DC-DC converter. In Figure 4, the Control system consists of two inverters I1 and I2 to provide the bidirectional control of the additional small PM machines and a diode bridge with the DC-DC converter to provide unidirectional control of the main PMSG providing an MPPT of the CR-VAWT.

_{P}and K

_{I}are the proportional and integral coefficients of the speed controllers, respectively; ω

_{1}and ω

_{2}are the angular velocities of the first and second rotors; and ω

_{av}= 0.5(ω

_{1}+ ω

_{2}) is the average angular velocity of these rotors of the DR-PMSG.

_{T}= 0.5ρ

_{a}A C

_{p.max}(R/λ

_{opt})

^{3}in the case of direct-drive transmission.

_{i}are the coefficients.

## 4. Method of Numerical Modeling of VAWT

#### 4.1. Numerical Modeling of Rotor Operation

_{r}, which is the vector sum of the axial wind speed V

_{a}and the linear velocity of the rotor’s blade V

_{l}= ωR; (2) the angle of attack of the blade β (Figure 5). The resultant wind speed and the angle of attack β constantly change during the blade rotation due to the change of the azimuthal angle ψ of the blade.

_{l}and drag force F

_{d}changes, in reference to [44]. The resultant of these forces is a thrust force F

_{r}, which can be divided into two components—normal F

_{n}and tangential F

_{t}(Figure 6). The latter creates the torque on the rotor shaft, so the shaft starts to rotate together with the blades.

_{p}(λ) when the TSR is in the range of 2.5–4.0—the linear velocity of the blade significantly exceeds the oncoming wind speed. As can be seen from the typical dependencies (Figure 7), for each value of the Reynolds number Re, there is a critical value of angle of attack, at which the coefficient of lift force C

_{l}drops down and the coefficient of drag force C

_{d}rises.

_{t}and normal C

_{n}forces can be evaluated as follows [45]:

_{b}is the blade area.

_{t}(ψ) for a rotor with radius R and the number of blades of n

_{b}, it is possible to estimate the instantaneous torque during rotation as

#### 4.2. Actuator Line Modeling for VAWT Simulations

_{p}is then estimated for the chosen wind turbine. The boundary conditions (BC) of the setup vary and are shown for each of the cases.

_{p}(λ) characteristic. To best depict the physical processes that take place while the VAWT rotates, the k–ω shear stress transport (SST) turbulence model is implemented [27,47].

_{l}= C

_{l}(β, Re) and C

_{d}= C

_{d}(β, Re) are the dependencies of the lift and drag coefficients from the blade angle of attack and Reynolds number, V

_{r}is the relative wind velocity at the element, and

**e**

_{1}and

**e**

_{d}are the unit vectors in the directions of lift and drag, respectively.

**x**and points at the i-th actuator line, and ε is the projection width that serves to adjust the concentration of the regularized load.

## 5. Results and Discussion

#### 5.1. Single-Rotor VAWT Sample Simulation

_{p}approaches roughly 0.27 asymptotically with the increase in the grid resolution, meaning that grid convergence is achieved. On the other hand, Figure 9 shows how significantly the number of cells increases when the value of relationship $c/{\u2206}_{local}$ in Figure 9 grows. The values of this relationship, 0.58, 2.35 and 4.7, correspond to the embedding levels 1, 2 and 3, respectively. It also indicates that embedding levels 1, 2 and 3 correspond almost to the same number of cells owing to the fact that the embedding is performed locally. In the upcoming simulations, the embedding level 3 is chosen, considering that it keeps a good balance between the numerical accuracy and the numerical cost.

_{p}(λ) characteristics for a single-rotor VAWT sample with different wind speeds of 4, 7 and 10 m/s are depicted in Figure 10. In the figure, the characteristics are nearly parabolic in shape, which shows similarity with those presented in the literature [55,60]. The highest value of C

_{p}is obtained for the value of TSR around 2.5. Note that due to the poor starting possibilities of the VAWT, the values of C

_{p}are low for the TSR of 0.25–0.5, even at the wind speed of 10 m/s.

#### 5.2. CR-VAWT Simulation

_{d}between the two rotors, five different values were chosen for the simulations—0.1H, 0.2H, 0.3H, 0.4H and 0.5H, where H is the blade length. The power coefficient results of the CR-VAWT with varying R

_{d}and TSR are presented in Figure 15 and Figure 16. As shown, regardless of R

_{d}, the power coefficient of the upper rotor in the CR-VAWT increased by roughly 5.5% and the lower rotor by 13.3% compared to the same single rotor. It also can be seen from the figures that both rotors benefit from the counter rotation, especially for the lower one at R

_{d}between (0.3 and 0.4)H. The lower rotor has slightly better C

_{p}in the range of TSR from 2.0 to 3.5 than the upper one. This increase can be explained by the stronger channeling effect between the ground and the lower level of the upper rotor where the velocity accelerates due to mass conservation, as shown in Figure 12a. A smaller, but still noticeable, velocity increase above the lower rotor accounts for the slight increase in C

_{p}of the upper rotor. Moreover, the distance R

_{d}does not seem to have a significant influence on the overall power efficiency for the design discussed in this paper. Individually, the C

_{p}of the lower rotor increases slightly with the reduction of R

_{d}due to the stronger channeling effect, but the upper rotor displays an opposite trend since it faces stronger wind speed at higher locations. It is expected that, eventually, the overall C

_{p}will increase with the further increase in R

_{d}when the gain of the upper rotor from higher wind speeds aloft dominates over the loss of the lower rotor from the weaker channeling effect, but it is less practical and thus beyond the scope of this work. In the cases comprising the present work, R

_{d}= 0.3H seems to be a good compromise between efficiency and expense.

^{2}, a new size of the single-rotor VAWT was found: D = 1.28 m and H = 1.4 m. The C

_{p}of the original single-rotor VAWT, the double-sized single-rotor VAWT, and the CR-VAWT are plotted in Figure 17. These results indicate two observations. First, simply increasing the rotor swept area is almost ineffective to increase the power coefficient, although the power increases with the swept area. Secondly, with the same swept area, the CR-VAWT achieves higher C

_{p}at higher TSR, compared to the single-rotor VAWT. The C

_{p}of the CR-VAWT increases by 10.2% at λ = 2.5 and increases by 13% at λ = 3. This increase in the power efficiency is mainly caused by the local velocity increase due to the interactions between the two rotors, as explained earlier.

## 6. Conclusions

## 7. Patent

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

Acronyms | |

ALM | actuator line modeling |

AR | aspect ratio |

BC | boundary conditions |

CFD | computational fluid dynamics |

CR | counter rotating |

DR | double rotor |

EG | electric generator |

HAWT | horizontal axis wind turbine |

LES | large eddy simulation |

MPPT | maximum power point tracking |

OCC | optimal current control |

OTC | optimal torque control |

PM | permanent magnet |

PMSG | permanent magnet synchronous generator |

SST | shear stress transport |

TSR | tip-speed ratio |

UDF | user-defined function |

VAWT | vertical axis wind turbine |

WECS | wind energy conversion system |

WT | wind turbine |

Latin symbols | |

A | rotor swept area (m^{2}) |

B | number of actuator lines |

C_{l}, C_{d} | lift and drag blade coefficients |

C_{p} | power coefficient |

H | rotor blade height (m) |

${I}_{\mathrm{L}}^{*}$ | reference load DC current of PMSG (A) |

K_{P}, K_{I} | proportional and integral coefficients of speed controllers |

P_{WT} | WT power (W) |

R | rotor radius (m) |

Re | Reynolds number |

${T}_{\mathrm{G}.\mathrm{e}}^{*}$ | reference electromagnetic torque of PMSG (Nm) |

${T}_{k1}^{*},\text{}{T}_{k2}^{*}$ | reference electromagnetic torque of the first and second additional PM machines (Nm) |

T_{WT} | WT torque (Nm) |

V_{w} | wind speed (m/s) |

c | blade chord length (m) |

d | distance between cell-centered grid points and points at the i-th actuator line (m) |

e_{1}, e_{d} | unit vectors in the directions of lift and drag, respectively |

f | computed local load (N) |

f_{2d} | vector of aerodynamic force per unit span length acting on the rotor blade (N/m) |

n_{b} | number of rotor blades |

s | Laplace operator |

Greek symbols | |

Δ | size of grid containing the blade section (m) |

β | angle of attack of blade (degree) |

ε | width of regularized load (m) |

η_{ε} | regularization kernel |

λ | tip-speed ratio |

ρ_{a} | air density (kg/m^{3}) |

σ | rotor solidity |

## References

- Rifkin, J. Third Industrial Revolution: How Lateral Power is Transforming Energy, the Economy, and the World; St. Martin’s Press: New York, NY, USA, 2011. [Google Scholar]
- Malinowski, M.; Milczarek, A.; Kot, R.; Goryca, Z.; Szuster, J.T. Optimized energy-conversion systems for small wind turbines: Renewable energy sources in modern distributed power generation systems. IEEE Power Electr. Mag.
**2015**, 2, 16–30. [Google Scholar] [CrossRef] - Johari, M.K.; Jalil, M.A.; Shariff, M.F. Comparison of horizontal axis wind turbine (HAWT) and vertical axis wind (VAWT). Int. J. Eng. Technol.
**2018**, 7, 74–80. [Google Scholar] [CrossRef] [Green Version] - Bhutta, M.; Hayat, N.; Farooq, A.; Ali, Z.; Jamil, S.; Hussain, Z. Vertical axis wind turbine—A review of various configurations and design techniques. Renew. Sustain. Energy Rev.
**2012**, 16, 1926–1939. [Google Scholar] [CrossRef] - Mollerstrom, E.; Larsson, S.; Ottermo, F.; Hylander, J.; Baath, L. Noise propagation from a vertical axis wind turbine. In Proceedings of the 43rd Internet Congress on Noise Control Engineering, Melbourne, Australia, 16–19 November 2014. [Google Scholar]
- Malael, I.; Dumitrescu, H.; Cardos, V. Numerical simulation of vertical axis wind turbine at low speed ratios. Glob. J. Res. Eng. I Numer. Methods
**2014**, 14, 8–20. [Google Scholar] - Sharma, K.; Biswas, A.; Gupta, R. Performance measurement of a three-bladed combined Darrieus-Savonius rotor. Int. J. Renew. Energy Res.
**2013**, 3, 885–891. [Google Scholar] - Alaimo, A.; Esposito, A.; Messineo, A.; Orlando, C.; Tumino, D. 3D CFD analysis of a vertical axis wind turbine. Energies
**2015**, 8, 3013. [Google Scholar] [CrossRef] [Green Version] - Oprina, G.C.; Chihaia, R.A.; El-Leathey, A.; Nicolaie, S.; Babutanu, C.; Voina, A. A review on counter-rotating wind tur-bines development. J. Sustain. Energy
**2016**, 7, 91–98. [Google Scholar] - Vasel-Be-Hagh, A.; Archer, C.L. Wind farms with counter-rotating wind turbines. Sustain. Energy Technol. Assess.
**2017**, 24, 19–30. [Google Scholar] [CrossRef] - Faisal, M.; Zhao, X.; Kang, M.-H.; You, K. Aerodynamic performance and flow structure investigation of contra-rotating wind turbines by CFD and experimental methods. IOP Conf. Ser. Mater. Sci. Eng.
**2020**, 926, 012017. [Google Scholar] [CrossRef] - Rosenberg, A.; Selvaraj, S.; Sharma, A. A novel dual-rotor turbine for increased wind energy capture. J. Phys. Conf. Ser.
**2014**, 524, 012078. [Google Scholar] [CrossRef] - Cho, W.; Lee, K.; Choy, I.; Back, J. Development and experimental verification of counter-rotating dual rotor/dual generator wind turbine: Generating, yawing and furling. Renew. Energy
**2017**, 114B, 644–654. [Google Scholar] [CrossRef] - San, D.G.; Pastor, B.; Nalianda, D.; Sethi, V.; Midgley, R.; Rolt, A.; Block, A. Preliminary design framework for the power gearbox in a contra-rotating open rotor. J. Eng. Gas Turbines Power
**2021**, 143, 041022. [Google Scholar] - Erturk, E.; Sivrioglu, S.; Bolat, F.C. Analysis model of a small scale counter-rotating dual rotor wind turbine with double rotational generator armature. Int. J. Renew. Energy Res.
**2018**, 8, 1849–1858. [Google Scholar] - Moghadassian, B.; Rosenberg, A.; Sharma, A. Numerical investigation of aerodynamic performance and loads of a novel dual rotor wind turbine. Energies
**2016**, 9, 571. [Google Scholar] [CrossRef] [Green Version] - Didane, D.H.; Rosly, N.; Zulkafli, M.F.; Shamsudin, S.S. Performance evaluation of a novel vertical axis wind turbine with coaxial contra-rotating concept. Renew. Energy
**2018**, 115, 353–361. [Google Scholar] [CrossRef] - Tahani, M.; Razavi, M.; Mirhosseini, M.; Razi Astaraei, F. Unsteady aerodynamic performance of dual-row H-darrieus vertical axis wind turbine. Energy Equip. Syst.
**2020**, 8, 55–80. [Google Scholar] - Poguluri, S.K.; Lee, H.; Bae, Y.H. An investigation on the aerodynamic performance of a CO-AXIAL contra-rotating vertical-axis wind turbine. Energy
**2020**, 42, 119547. [Google Scholar] [CrossRef] - Duraisamy, K.; Lakshminarayan, V. Flow physics and performance of vertical axis wind turbine arrays. In Proceedings of the 32nd AIAA Applied Aerodynamics Conference, Atlanta, GA, USA, 16–20 June 2014; pp. 1–17. [Google Scholar]
- Brownstein, I.D.; Wei, N.J.; Dabiri, J.O. Aerodynamically interacting vertical-axis wind turbines: Performance enhancement and three-dimensional flow. Energies
**2019**, 12, 2724. [Google Scholar] [CrossRef] [Green Version] - Kanner, S.; Wang, L.; Persson, P.-O. Implicit Large-Eddy Simulation of 2D counter-rotating vertical-axis wind turbines. In Proceedings of the 34th Wind Energy Symposium, San Diego, CA, USA, 4–8 January 2016. [Google Scholar]
- Asr, M.T.; Osloob, R.; Mustapha, F. Double-stage H-Darrieus wind turbine-rotor aerodynamics. Appl. Mech. Mater.
**2016**, 829, 21–26. [Google Scholar] - Dumitrescu, H.; Dumitrache, A.; Malael, I.; Bogateanu, R. The standard and counter-rotating VAWT performances with LES. In Recent Advances in CFD for Wind and Tidal Offshore Turbines; Springer Nature: Cham, Switzerland, 2019; pp. 117–127. [Google Scholar]
- Malael, I.; Dragan, V. Numerical and experimental efficiency evaluation of a counter-rotating vertical axis wind turbine. Eng. Technol. Appl. Sci. Res.
**2018**, 8, 3282–3286. [Google Scholar] [CrossRef] - Chaichana, T.; Chaitep, S. Performance evaluation of co-axis counter-rotation wind turbine. Energy Procedia
**2015**, 79, 149–156. [Google Scholar] [CrossRef] [Green Version] - Ramos, D.; Carvajal, D. CFD study of a vertical axis counter-rotating wind turbine. In Proceedings of the 2017 IEEE 6th International Conference on Renewable Energy Research and Applications (ICRERA), San Diego, CA, USA, 5–8 November 2017. [Google Scholar]
- Didane, D.H.; Kudam, D.; Zulkafli, M.F.; Mohd, S.; Batcha, M.F.M.; Khalid, A. Development and performance investigation of a unique dual-rotor Savonius-type counter-rotating wind turbine. Int. J. Integr. Eng.
**2021**, 13, 89–98. [Google Scholar] [CrossRef] - Didane, D.H.; Rosly, N.; Zulkafli, M.F.; Shamsudin, S.S. Numerical investigation of a novel contra-rotating vertical axis wind turbine. Sustain. Energy Technol. Assess
**2019**, 31, 43–53. [Google Scholar] [CrossRef] - Didane, D.H.; Maksud, S.M.; Zulkafli, M.F.; Rosly, N.; Shamsudin, S.S.; Khalid, A. Performance investigation of a small Savonius-Darrius counter-rotating vertical-axis wind turbine. Int. J. Energy Res.
**2019**, 44, 9309–9316. [Google Scholar] [CrossRef] - Chong, W.; Fazlizan, A.; Poh, S.; Pan, K.; Ping, H. Early development of an innovative building integrated wind, solar, and rain water harvester for urban high rise application. Energy Build.
**2012**, 47, 201–207. [Google Scholar] [CrossRef] - Kutt, F.; Blecharz, K.; Karkosiński, D. Axial-flux permanent-magnet dual-rotor generator for a counter-rotating wind turbine. Energies
**2020**, 13, 2833. [Google Scholar] [CrossRef] - Shchur, I.; Klymko, V. Comparison of different types of electromechanical systems for creating of counter-rotating VAWT. In Proceedings of the 2017 IEEE First Ukraine Conference on Electrical and Computer Engineering (UKRCON), Kyiv, Ukraine, 29 May–2 June 2017. [Google Scholar]
- Castelli, M.R.; Betta, S.; Benini, E. Effect of blade number on a straight-bladed vertical-axis Darreius wind turbine. Int. J. Aerosp. Mech. Eng.
**2012**, 6, 68–74. [Google Scholar] - Li, Y.; Zheng, Y.; Zhao, S.; Feng, F.; Li, J.; Wang, N.; Bai, R. A review on aerodynamic characteristics of straight-bladed vertical axis wind turbine. Acta Aerodyn. Sin.
**2017**, 35, 368–382. [Google Scholar] - Chiarelli, M.; Massai, A.; Atzeni, D.; Bianco, F. A new configuration of vertical axis wind turbine: An overview on efficiency and dynamic behavior. J. Energy Chall. Mech.
**2015**, 2, 23–28. [Google Scholar] - Singh, M.; Biswas, A.; Misra, R. Investigation of self-starting and high rotor solidity on the performance of a three S1210 blade H-type Darrieus rotor. Renew. Energy
**2015**, 76, 381–387. [Google Scholar] [CrossRef] - Mohamed, M. Impacts of solidity and hybrid system in small wind turbines performance. Energy
**2013**, 57, 495–504. [Google Scholar] [CrossRef] - Zhang, T.; Wang, Z.; Huang, W.; Ingham, D.; Ma, L.; Pourkashanian, M. A numerical study on choosing the best configuration of the blade for vertical axis wind turbines. J. Wind Eng. Ind. Aerodyn.
**2020**, 201, 104162. [Google Scholar] [CrossRef] - Bruska, S.; Lanzafame, R.; Messina, M. Design of a vertical-axis wind turbine: How the aspect ratio affects the turbine’s performance. Int. J. Energy Environ. Eng.
**2014**, 5, 333–340. [Google Scholar] [CrossRef] [Green Version] - Shchur, I.; Klymko, V. Stabilization of the coaxial counter-rotating vertical axis wind turbine via torque balancing by special double rotor PMSG. In Proceedings of the IEEE 2nd Ukraine Conference Electrical and Computer Engineering (UKRCON), Lviv, Ukraine, 2–6 July 2019. [Google Scholar]
- Muteanu, I.; Bratcu, A.I.; Cutululis, N.A.; Ceangă, E. Optimal Control of Wind Energy Systems; Springer: London, UK, 2008. [Google Scholar]
- Nasiri, M.; Milimonfared, J.; Fathi, S.H. Modeling, analysis and comparison of TSR and OTC methods for MPPT and power smoothing in permanent magnet synchronous generator-based wind turbines. Energy Convers. Manag.
**2014**, 86, 892–900. [Google Scholar] [CrossRef] - Islam, M.; Ting, D.; Fartaj, A. Aerodynamic models for Darrieus-type straight-bladed vertical axis wind turbines. Renew. Sustain. Energy Rev.
**2008**, 12, 1087. [Google Scholar] [CrossRef] - Wekesa, D.; Wang, C.; Wei, Y.; Danao, L. Influence of operating conditions on unsteady wind performance of vertical axis wind turbines operating within a fluctuating free-stream: A numerical study. J. Wind Eng. Ind. Aerodyn.
**2014**, 135, 76. [Google Scholar] [CrossRef] - Melo, R.; Neto, A. Integral analysis of rotors of a wind generator. Renew. Sustain. Energy Rev.
**2012**, 16, 4809. [Google Scholar] [CrossRef] - Bai, C.; Lin, Y.; Lin, S.; Wang, W. Computational fluid dynamics analysis of the vertical axis wind turbine blade with tubercle leading edge. J. Renew. Sustain. Energy
**2015**, 7, 033124. [Google Scholar] [CrossRef] - Shamsoddin, S.; Porte-Agel, F. Large eddy simulation of vertical axis wind turbine wakes. Energies
**2014**, 7, 890–912. [Google Scholar] [CrossRef] - Bachant, P.; Goude, A.; Wosnik, M. Actuator line modeling of vertical-axis turbine. Wind Energy
**2016**, 1, 1–21. [Google Scholar] - Martinez-Tossas, L.; Churchfield, M.; Leonardi, S. Large eddy simulations of the flow past wind turbines: Actuator line and disk modeling. Wind Energy
**2015**, 18, 1047–1060. [Google Scholar] [CrossRef] - Sorensen, J.; Shen, W. Numerical modeling of wind turbine wakes. J. Fluids Eng.
**2002**, 124, 393–399. [Google Scholar] [CrossRef] - Troldborg, N.; Sorensen, J.; Mikkelsen, R. Numerical simulations of wake characteristics of a wind turbine in uniform inflow. Wind Energy
**2010**, 13, 86–99. [Google Scholar] [CrossRef] - Xie, S.; Archer, C. Self-similarity and turbulence characteristics of wind turbine wakes via large-eddy simulation. Wind Energy
**2015**, 18, 1815–1838. [Google Scholar] [CrossRef] - Sheldahl, R.; Klimas, P. Aerodynamic Characteristics of Seven Symmetrical Airfoil Sections through 180-Degree Angle of Attack for Use in Aerodynamic Analysis of Vertical Axis Wind Turbines; Technical Report Number SAND-80-2114; Sandia National Labs.: Albuquerque, NM, USA, 1981. [Google Scholar]
- Hezaveh, S.; Bou-Zeid, E.; Lohry, M.; Martinelli, L. Simulation and wake analysis of a single vertical axis wind turbine. Wind Energy
**2017**, 20, 713–730. [Google Scholar] [CrossRef] - Shamsoddin, S.; Porté-Agel, F. A Large-eddy simulation study of vertical axis wind turbine wakes in the atmospheric boundary layer. Energies
**2016**, 9, 366. [Google Scholar] [CrossRef] - Xie, S. An actuator-line model with Lagrangian-averaged velocity sampling and piecewise projection for wind turbine simulations. Wind Energy
**2021**, 24, 1095–1106. [Google Scholar] [CrossRef] - Papi, F.; Melani, P.F.; Xie, S.; Perrone, C.; Scienza, P.; Balduzzi, F.; Bianchini, A. Development and validation of an advanced actuator line model for wind turbines. In Proceedings of the E3S Web of Conference, Proceedings of the 76th Italian National Congress ATI (ATI 2021), Rome, Italy, 15–17 September 2021; EDP Sciences: Les Ulis, France, 2021; Volume 312. [Google Scholar]
- Qingan, L.; Maeda, T.; Kamada, Y.; Shimizu, K.; Ogasawara, T.; Nakai, A.; Kasuya, T. Effect of rotor aspect ratio and solidity on a straight-bladed vertical axis wind turbine in three-dimensional analysis by the panel method. Energy
**2017**, 121, 1–9. [Google Scholar] - Almohammadi, K.; Ingham, D.; Ma, L.; Pourkashan, M. Computational fluid dynamics (CFD) mesh independency techniques for a straight blade vertical axis wind turbine. Energy
**2013**, 58, 483–493. [Google Scholar] [CrossRef] - Chong, W.; Fazlizan, A.; Poh, S.; Pan, K.; Hew, W.; Hsiao, F. The design, simulation and testing of an urban vertical axis wind turbine with the omni-direction-guide-vane. Appl. Energy
**2013**, 112, 601–609. [Google Scholar] [CrossRef]

**Figure 1.**Three types of CR-VAWT: (

**a**) dual-axis CR-VAWT; (

**b**) CR-VAWT with co-axial rotors when one rotor covers the other; (

**c**) CR-VAWT with co-axial rotors displaced from each other along the axis of rotation.

**Figure 3.**Sketch of a new design of the DR-PMSG: 1—inductor with permanent magnets, 2—shaft of the first rotor, 3—armature, 4—shaft of the second rotor, 5—casing, 6—slip rings, 7 and 8—permanent magnets of the additional machines, 9 and 10—armatures of the additional machines.

**Figure 7.**Typical dependencies of the lift (C

_{l}) and drag (C

_{d}) coefficients on the angle of attack β for the NACA airfoil [46].

**Figure 8.**Domain setup: BC for the single-rotor VAWT sample case. The inner box represents the region of embedding of scale 3, the middle box represents the region of embedding of scale 1 and the outer box is the domain.

**Figure 9.**Dependencies of the number of cells and C

_{p}value as a function of the chord length/cell size ratio near the blade.

**Figure 10.**C

_{p}(λ) characteristics of a single-rotor VAWT sample for the wind speeds of 4, 7 and 10 m/s.

**Figure 11.**Isosurface of the Q criterion colored by streamwise velocity component for the investigated single-rotor VAWT sample at free-stream velocity of 7 m/s.

**Figure 12.**Time-averaged streamwise velocity component field (

**a**) and TKE field (

**b**) at the vertical central plane of a single-rotor VAWT at a free-stream velocity of 7 m/s. Only part of the computational domain is shown here.

**Figure 14.**Time-averaged streamwise velocity field (

**a**) and TKE field (

**b**) at the vertical central plane of a CR-VAWT at free-stream velocity of 7 m/s. Only part of the computational domain is shown here.

**Figure 15.**Comparison of time-averaged C

_{p}(λ) characteristics of the upper rotor of CR-VAWT sample between the single-rotor VAWT sample and cases with various R

_{d}at free-stream velocity of 7 m/s.

**Figure 16.**Comparison of time-averaged C

_{p}(λ) characteristics of the lower rotor of CR-VAWT sample between the single-rotor VAWT sample and cases with various R

_{d}at free-stream velocity of 7 m/s.

**Figure 17.**Comparison of time-averaged C

_{P}(λ) characteristics of the CR-VAWT sample and single-rotor VAWT samples of different swept areas at free-stream velocity of 7 m/s.

Parameters | Type or Value |
---|---|

Rotor type | H-rotor |

Airfoil profile | NACA 0018 |

No. of blades | 3 |

Diameter, D | 0.9 m |

Height, H | 1.0 m |

Chord length, c | 0.141 m |

Rotation | Clockwise |

Solidity, σ | 0.15 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Shchur, I.; Klymko, V.; Xie, S.; Schmidt, D.
Design Features and Numerical Investigation of Counter-Rotating VAWT with Co-Axial Rotors Displaced from Each Other along the Axis of Rotation. *Energies* **2023**, *16*, 4493.
https://doi.org/10.3390/en16114493

**AMA Style**

Shchur I, Klymko V, Xie S, Schmidt D.
Design Features and Numerical Investigation of Counter-Rotating VAWT with Co-Axial Rotors Displaced from Each Other along the Axis of Rotation. *Energies*. 2023; 16(11):4493.
https://doi.org/10.3390/en16114493

**Chicago/Turabian Style**

Shchur, Ihor, Volodymyr Klymko, Shengbai Xie, and David Schmidt.
2023. "Design Features and Numerical Investigation of Counter-Rotating VAWT with Co-Axial Rotors Displaced from Each Other along the Axis of Rotation" *Energies* 16, no. 11: 4493.
https://doi.org/10.3390/en16114493