A multirotor system (MRS) is defined as containing more than one rotor in a single structure. MRSs have a great potential as a wind turbine system, saving mass and cost, and showing scale ability. The shrouded wind turbine with brimmed diffuser-augmented wind turbines (B-DAWT) has demonstrated power augmentation for a given turbine diameter and wind speed by a factor of about 2–5 compared with a bare wind turbine. In the present research, B-DAWTs are used in a multirotor system. The power output performance of MRSs using two and three B-DAWTs in a variety of configurations has been investigated in the previous works. In the present study, the aerodynamics of an MRS with five B-DAWTs, spaced in close vicinity in the same vertical plane normal to a uniform flow, has been analyzed. Power output increases of up to 21% in average for a five-rotor MRS configuration are achieved in comparison to that for the stand-alone configuration. Thus, when B-DAWTs are employed as the unit of a MRS, the total power output is remarkably increased. As the number of units for an MRS is increased from two to five, the increase in power output becomes larger and larger. This is because that the gap flows between B-DAWTs in a MRS are accelerated and cause lowered pressure regions due to vortex interaction behind the brimmed diffusers. Thus, a MRS with more B-DAWTs can draw more wind into turbines showing higher power output.

## Introduction

The most commonly used wind turbine is a horizontal axis, single–rotor wind turbine. A major trend in the wind turbine industry is increasing the size of the rotor in order to generate more energy and to reduce the cost of energy generated from the wind [1]. This was notably possible due to technological advancements in high-strength composite materials to manufacture longer blades [1]. However, as pointed out by some recent studies [2–5], scaling of blades has its limitations. A concept to overcome these issues for wind turbines is the multirotor system (MRS), defined as containing more than one rotor in a single structure. The concept of MRS has a long history and persists in a variety of modern innovative systems. As suggested by Jamieson [2,3], upscaling by increasing the number of rotors instead of the larger diameter of a single rotor leads to savings in mass. A reduction in mass consequently reduces the overall cost of the system. A significant advantage of MRS is identified in standardization of rotor and drive-train components and in “scale-ability”: the fact that very large system capacities could be realized without overstretching the capability to upscale individual rotors [3]. The studies of MRS have been reported so far for wind tunnel experiments, numerical analyses, and field experiments [1–14]. The main issue has been focused on the realization of a wind turbine system with huge capacity [2–11]. However, the aim of present study will be focused on the utilization of a MRS for small- to midsize wind turbines with a shroud [12–14].

Diffuser-augmented wind turbines (DAWTs) have been developed to increase the rotor performance of a conventional wind turbine [15–28]. The aerodynamics of brimmed diffuser-augmented wind turbines (B-DAWT, named “wind-lens turbine,” (WLT) is used henceforth) has been investigated [24–28]. A WLT consists of a downwind type wind turbine and a structure composed of an inlet shroud, a diffuser, and a brim. The flow which passes inside the diffuser and the flow which comes around behind the brim generate vortices behind the structure. As a result, a low pressure region behind the turbine is created by the shedding of vortices. Air is thus drawn into the turbine at a higher rate and accelerates more than in the case of a conventional wind turbine (without a diffuser). Due to this effect, WLTs show power augmentation by a factor of 2–5 compared with conventional turbines [24,25].

Recently, we have been investigating the power output performance and wake interference of multiple WLTs in various multirotor systems [12–14]. We placed two and three WLTs closely in some arrangements perpendicular to the approaching flow in the same vertical plane and measured each power output and drag force simultaneously. In parallel with wind tunnel experiments, we are doing computational fluid dynamics (CFD) (large eddy simulation (LES)) of various multirotor systems with WLTs using the actuator-disk or actuator-line method for the blade model. First, to understand the fundamental flow phenomena around an MRS with WLTs, Ohya et al. [12] conducted wind tunnel experiments, comparing drag coefficients of circular flat disks with those of WLTs in side-by-side (SBS) configurations. Three circular flat disks showed large differences in the drag coefficients of each disk. The differences in drag coefficients are strongly correlated to biased gap flow phenomena measured with a hot wire technique in the near wake. Although weaker in magnitude, similar variations in drag coefficients of three WLTs in side-by-side arrangements have been observed. It was shown that the drag coefficients of WLTs correlate well with their power coefficients. This leads to the conclusion that differences in power coefficients and/or drag coefficients of WLTs in a MRS configuration are affected by gap flow behaviors.

For the wind turbine performance of an MRS with WLTs, the total power output as a whole is increased much larger than those of MRSs with conventional wind turbines without a shroud. Furthermore, the power outputs of MRSs with three WLTs are much larger than those of MRSs with two WLTs. Thus, questions that arise are how the power output performance of a MRS will show with more than three turbines and what flow patterns appear in the downstream of a MRS with more turbines due to wake interference. In the present research, we have reported a study of an MRS with five WLTs in closely spaced array using wind tunnel experiments and a LES based on a finite difference method (FDM). The results show that remarkable increase in total power output is obtained in an MRS with five WLTs in close vicinity. To investigate the mechanism of increases in power output and drag for each WLT in MRS configurations, measurements of wind velocity and static pressure distributions just behind an MRS with five WLTs are made and compared to stand alone, two and three WLT MRS configurations. Similarly, an LES confirms the results from wind tunnel experiments and gives a better understanding of the flow interference among five WLTs in a MRS.

## Experimental Setup

A large boundary-layer wind tunnel of the Research Institute for Applied Mechanics, Kyushu University, was used. It has a measurement section of 15 m long × 3.6 m wide × 2 m high with a maximum wind velocity of 30 m/s, and is characterized by a low turbulence intensity of 0.4% [12]. Paying attention to the blockage effect in the wind tunnel, we removed the ceiling and both side walls ranging 6 m in the center portion of the measurement section. Namely, we used our wind tunnel with an open-type test section to minimize the blockage effect.

Figure 1 shows schematics of the dimensions of three WLTs in a SBS arrangement, which is the lower row of the present five-WLT MRS. A multirotor system (MRS) with five WLTs is extended similarly as a two-row configuration in a vertical plane, as shown in Fig. 2. The brimmed diffuser (WLT) consists of a diffuser with a streamwise length *L _{t}* of 0.22

*D*

_{throat}and a brim height

*h*of 0.1

*D*

_{throat}, called CiiB10 type WLT [25]. The rotor diameter (

*D*

_{rotor}) is 510 mm. The representative diameter of a WLT is

*D*

_{brim}of 696 mm in the present experiments. Five WLTs are placed closely with gap width

*s*for the two-row configuration. Table 1 shows the conditions of the present wind tunnel experiment. The approaching wind speed,

*U*, is 6 m/s with a Reynolds numbers of 1.7 × 10

_{0}^{5}related to rotor diameter

*D*

_{rotor}. The gap ratio is

*s/D*

_{brim}(gap width/brim diameter). The range of

*s/D*

_{brim}is between 0.05 and 0.25.

Conditions | |
---|---|

Configuration of wind acceleration device (brimmed diffuser) | CiiB10 type [25] |

Inflow velocity | U_{0} = 6 m/s |

Reynolds number | 1.7 × 10^{5} (representative length:rotor diameter 510 mm) |

Layouts of WLT | Five WLTs as shown in Fig. 2 |

Gap ratio of MRS with WLTs (gap divided by the outer diameter of a brimmed diffuser) | $s/Dbrim=0.05\u20130.25$ |

Conditions | |
---|---|

Configuration of wind acceleration device (brimmed diffuser) | CiiB10 type [25] |

Inflow velocity | U_{0} = 6 m/s |

Reynolds number | 1.7 × 10^{5} (representative length:rotor diameter 510 mm) |

Layouts of WLT | Five WLTs as shown in Fig. 2 |

Gap ratio of MRS with WLTs (gap divided by the outer diameter of a brimmed diffuser) | $s/Dbrim=0.05\u20130.25$ |

As for the experimental method, connecting a torque transducer (the rating 1 N·m) to the wind turbine and in the rear of it, an AC servo motor brake was set for the loading, as shown in Fig. 3 (left). We measured the torque *T _{r}* (N·m) and the rotational speed

*f*(Hz) of the wind turbine in the condition that the turbine loading was gradually applied from zero. The calculated power output

*P*(W) =

*T*2

_{r}×*πf*is shown as a performance curve. At constant rotational velocity of the servomotor, the torque is measured for 30 s at 1 kHz sampling frequency. It should be noted that the rotational directions of all the turbines both in stand-alone and MRS configurations are the same of clockwise direction from upstream view.

Conditions | |
---|---|

Discretization technique | Finite difference method |

Time marching method | Euler explicit scheme |

Coupling method | Fractional step method |

Coordination system | Three-dimensional Cartesian coordinate system |

Variable arrangement | Staggered |

Turbulence model | LES |

SGS model | Mixed-time-scale SGS model |

Convection term | Third-order upwind differencing scheme |

Blade model | Actuator-line method |

Reynolds number | 3.0 × 10^{5} (representative length:rotor diameter) |

Grid resolution | Δx = Δy = Δz = 0.01D_{rotor} (near turbine) |

Number of grid points | 226 × 611 × 411 |

Computational domain | 10D_{rotor} × 12D_{rotor} × 10D_{rotor} |

Conditions | |
---|---|

Discretization technique | Finite difference method |

Time marching method | Euler explicit scheme |

Coupling method | Fractional step method |

Coordination system | Three-dimensional Cartesian coordinate system |

Variable arrangement | Staggered |

Turbulence model | LES |

SGS model | Mixed-time-scale SGS model |

Convection term | Third-order upwind differencing scheme |

Blade model | Actuator-line method |

Reynolds number | 3.0 × 10^{5} (representative length:rotor diameter) |

Grid resolution | Δx = Δy = Δz = 0.01D_{rotor} (near turbine) |

Number of grid points | 226 × 611 × 411 |

Computational domain | 10D_{rotor} × 12D_{rotor} × 10D_{rotor} |

*λ*for the maximum power output is determined by setting the appropriate rotational speed of the rotor. For the measurement period, the motor speed is held constant by the servomotor controller. The power coefficient

*C*and drag coefficient

_{p}*C*are calculated using Eqs. (1) and (2). In these equations,

_{d}*P*is the power output,

*T*is the torque,

_{r}*ω*is the angular velocity,

*F*

_{drag}is the drag force,

*ρ*is the air density, and

*A*is the swept area of the rotor

*C*

_{p}_{0}

*and the drag coefficient is defined*

_{i}*C*

_{d}_{0}

*in each turbine. The averages of each coefficient of all turbines are defined $Cp0i\xaf$, $Cd0i\xaf$. For WLTs in multirotor configurations, the power coefficient is defined*

_{i}*C*and the drag coefficient is defined

_{pi}*C*in each turbine. The averages of each coefficient of all turbines are defined $Cpi\xaf$, $Cdi\xaf$. In order to understand how the power coefficient changed in each turbine,

_{di}*C*is compared to the

_{pi}*C*

_{p}_{0}

*. Therefore, the variation, Δ*

_{i}*C*is defined as

_{pi}To compare the average power coefficient of the MRS with the average power coefficient of the stand-alone WLTs, the variation, Δ$Cpi\xaf$ is defined as

For the drag coefficients, similar to the power coefficients, the variations in *C _{di}* are calculated for Δ

*C*and Δ$Cdi\xaf$.

_{di}Measurements of *u*-velocity and static pressure distributions are made, as shown in Fig. 4, using a hot-wire and a static pressure tube system. Those sensors are moved by a traversing system. The *u*-velocity fluctuation is measured with an *I*-type hot-wire anemometer with sampling frequency of 500 Hz and sampling time of 30 s at each sampling point. The pressure fluctuation is measured with a static pressure tube, a Pitot tube, and a pressure transducer system with the sampling time of 30 s. Generally, the static-pressure coefficient is defined as (*p-p _{o}*)

*/(0.5ρU*

_{o}^{2}),

*p*is the local static pressure,

*p*and

_{o}*U*are the static pressure and speed of the approaching flow,

_{o}*ρ*is the air density. In the following figures, the time-averaged nondimensional static pressure is defined as

*p/(ρU*

_{o}^{2}), here

*p*= 0. The time-averaged nondimensional

_{o}*u*-velocity is

*u*/

*U*.

_{o}## Results of Wind Tunnel Experiments

### Measurements of Power Output and Drag of a Multi Rotor System Using Five Wind-Lens Turbines.

Five WLTs with a brimmed-diffuser shroud of CiiB10 [for the brimmed-diffuser CiiB10, Ref. 25] are arranged as an upper- and lower-row configuration in the same vertical plane, i.e., two WLTs (#2 and #4) in the upper row and three WLTs (#1, #3 and #5) in the lower row with equal separations *s* for all gaps, as shown in Fig. 2. Figure 5 shows the results of power coefficient variations with the gap ratio *s*/*D*_{brim}. Each bar at each *s*/*D*_{brim} indicates the increase Δ*C _{pi}* in power output defined by Eq. (3), compared to that for the stand-alone configuration. “AVE” in Fig. 5 means the averaged values of each increase of five WLTs, defined by Eq. (4). Similarly, Fig. 6 shows drag coefficient variations Δ

*C*with the gap ratio

_{di}*s*/

*D*

_{brim}. Power coefficient

*C*and drag coefficient

_{pi}*C*of each WLT in the five-WLT arrangement increase at all gap ratios, compared to those for stand-alone configuration,

_{di}*C*

_{p}_{0}

*and*

_{i}*C*

_{d}_{0}

*. When WLTs are set up very closely (e.g.,*

_{i}*s*/

*D*

_{brim}= 0.05), variations in the averaged value of $Cpi\xaf$ were a little smaller, compared to other gap ratios. When

*s*/

*D*

_{brim}= 0.20, Δ$Cpi\xaf$ increased by 21% at the maximum. When

*s*/

*D*

_{brim}= 0.15, Δ$Cdi\xaf$ increased 13.6% at the maximum. Variations in $Cpi\xaf$ are larger compared with those in $Cdi\xaf$ at all gap ratios. It is because that the power output is proportional to the cube of wind velocity and the drag force is proportional to the square of it. It should be noted that Δ$Cpi\xaf$ and Δ$Cdi\xaf$ are much larger compared with those for two-WLT MRS and three-WLT MRS [12–14]. From the results of individual increases in

*C*, Δ

_{pi}*C*of #3 is the highest for

_{pi}*s*/

*D*

_{brim}= 0.05 and 0.1. Δ

*C*of #2 is the highest for

_{pi}*s*/

*D*

_{brim}= 0.15, 0.2, and 0.25, as shown in Fig. 5. Similarly, Δ

*C*of #3 are always highest for all

_{di}*s*/

*D*

_{brim}, as shown in Fig. 6.

Five WLTs seem to accelerate the gap flows, leading to stronger separated shear flow from each brim and vortex shedding behind five WLTs. The center WLT #3 and the adjacent WLT #2 in the present arrangement are influenced most strongly due to wake interference of five WLTs. It seems that unstable behavior of gap flows between wind turbines has an effect on the performance of wind turbines similar to the studies of Ohya et al. [12], Göltenbott et al. [13], and Watanabe and Ohya [14]$.$ We will discuss it in the Sec. 4 of “numerical analysis.”

### Measurements of Pressure and Wind Velocity Distributions Behind a Five-Rotor Arrangement Using Wind-Lens Turbines.

To investigate the pressure distribution and wind velocity distribution behind the present MRS with five WLTs, we evaluated the nondimensional static pressure and wind velocity (*u*-velocity) just behind the turbines along the line A–A, as described in Fig. 7. First, the pressure and *u*-velocity distributions of a single WLT were measured in the stand-alone configuration, as shown in Fig. 8. The nondimensional static pressure is around—0.3 just behind the rotor. For the present MRS with five-WLT configuration, the pressure and *u*-velocity distributions were measured along the two lines A and B, as shown in Fig. 9. Figures 10(a) and 10(b) show the results. In Figs. 10(a) and 10(b), the *u*-velocities are remarkably accelerated in all gaps both for the upper row (Fig. 10(a)) and the lower row (Fig. 10(b)). The nondimensional static pressures are around—0.4 in the upper row and—0.45 in the lower row, as shown in Figs. 10(a) and 10(b), respectively. The static pressures behind the rotors in the present MRS with five-WLT are lowered considerably compared to that for a single WLT. It suggests that the approaching wind is more drawn into the rotors compared to the case of a single WLT in the stand-alone configuration. Figures 11 show the comparisons of *u*-velocity between a two-WLT MRS in SBS and the two WLTs in the upper row of the present five-WLT arrangement (top), and between a three-WLT MRS in SBS and the three WLTs in the lower row of the present five-WLT MRS configuration (bottom) at the same gap ratio of *s*/*D*_{brim} = 0.2. Similarly, Fig. 12 shows the comparisons of pressure distributions. For both figures, it is clearly seen that the wind speeds around a five-WLT MRS are a little increased, as shown in Fig. 11, and correspondingly, the static pressures behind a five-WLT MRS are further lowered, compared to two-WLT MRS and three-WLT MRS configurations, as shown in Fig. 12. Therefore, the *C _{pi}* and

*C*for the MRS with five-WLT show higher values compared to those for the stand-alone configuration, a two-WLT MRS configuration, and also three-WLT MRS configurations.

_{di}## Numerical Analyses

Flows around an MRS with five WLTs in the present arrangement were calculated using a three-dimensional LES based on the FDM in Cartesian coordinates (Table 2). The governing equations are the continuity and Navier–Stokes equations. A first-order explicit method is used for time marching. A third-order upwind scheme is applied to the convective terms. The second-order central difference scheme is applied to the diffusion terms. For the present numerical analyses, the actuator-line method is employed for the blade model. To avoid any blockage effect, a large computational domain is adopted, as described in Fig. 13. Although the grid is concentrated near the turbines as shown in Fig. 7 (right), the grid resolutions are not enough to solve the flows around the turbines and gap flows with higher accuracy. However, the overall tendency and qualitative results showed good agreements with those from the wind tunnel experiments.

To evaluate the accuracy of CFD results, the numerical results are compared to those from the wind tunnel experiments, as shown in Figs. 14 and 15. Figure 14 shows the power output increase for each WLT at *s/D*_{brim} = 0.2 both for CFD and wind tunnel experiment. The inside WLTs of #2, #3, and #4 in the present arrangement show larger increases compared to those WLTs of #1 and #5 in the both ends, showing a good agreement with CFD and experiment. Figure 15 shows the pressure and *u*-velocity distributions along the two lines (see Figs. 9 and 16). For the *u*-velocity distributions, the gap flows are strongly accelerated both in CFD and wind tunnel experiments, showing *u/U _{o}* = 1.3. For the pressure distributions in CFD and experiments, the nondimensional static pressures show around—0.4 to −0.5 behind the rotors, showing a good agreement qualitatively.

Figure 16 shows the time-averaged *u*-velocity field and static pressure field. In the left figure in Fig. 16, it is clearly seen that the streamwise velocities *u* in the gap regions are larger than those in the surroundings, showing the accelerated flows. Correspondingly, the right figure in Fig. 16 shows the lowered pressure in the gap regions. Figure 17 shows an instantaneous flow around the present MRS with five WLTs at *s/D*_{brim} = 0.2. The flow field is visualized at the center height of two WLTs in the upper figure and three WLTs in the bottom figure. For the both figures, it is seen that all gap flows are accelerated due to the flow interaction with adjacent WLTs.

Figure 18 from the results of CFD is depicted to compare the pressure distributions between two WLTs in the upper row of the five-WLT MRS and two-WLT MRS in SBS, and between three WLTs in the lower row of the five-WLT MRS and three-WLT MRS in SBS. The gap ratio is *s/D*_{brim} = 0.2. From Fig. 18, it is clearly seen that the pressure behind five-WLT MRS is remarkably lowered compared to those for two-WLT and three-WLT configurations. The gap flows are accelerated, leading to vortices near the gaps, causing the lower pressure regions behind the five-WLT MRS. It means that the lowered pressured regions draw much more airflows into turbines in the MRS with five WLT. Therefore, the *C _{pi}* and

*C*for a MRS with five WLTs show higher values compared to those for the stand-alone configuration, the MRS with two WLTs, and also the MRSs with three WLTs.

_{di}The increases in the power coefficient and the drag coefficient for the five-WLT MRS configuration in close proximity can be explained by the flow interference around bluff bodies and gap flow behaviors [28–31] . Similarities can be drawn between the flow around three-dimensional bluff bodies (for example, circular plates) in SBS arrangements and the flow around multiple WLTs in SBS, as explained in Ref. [12]. The gap flows between WLTs with close vicinity play an important role to cause the increases in the power coefficient and the drag coefficient.

## Conclusion

Multirotor systems for wind turbine configurations have been studied for five DAWTs. The DAWT is a brimmed-diffuser wind turbine (called WLT). First, the power output coefficient and drag coefficient (thrust force) for a MRS with five WLTs in a two-row arrangement of upper and lower rows are investigated, followed by the similar studies of MRSs with two and three WLTs. A large wind tunnel in Kyushu University is used for all the experiments. In parallel with wind tunnel experiments, we are doing an LES of the flow around an MRS with five WLTs using the actuator-line method for the blade model, based on FDM.

All WLTs closely spaced in a five-rotor MRS configuration show a remarkable increase in power output with the small gap ratios *s/D*_{brim}. For the five-WLT configuration, the largest averaged increase as a whole reaches 21% at around *s/D*_{brim} of 0.2. In the past experiments, for the two-WLT configuration, the largest averaged increase as a whole of up to 8% is achieved with *s/D*_{brim} of around 0.2. For the three-WLT configuration, the largest averaged increase is achieved at a range of *s/D*_{brim} = 0.15–0.3, reaching up to 12%. The averaged drag is also increased up to 13.6% for the present five-WLT arrangement. In the past experiments, the averaged drag is also increased 5% for the two-WLT configuration and 8% for the three-WLT configuration, respectively. Therefore, as the number of WLTs in an MRS is increased at small gap ratios, the total power output and drag force of the MRS with WLTs are further increased.

It should be noted that the individual increases in *C _{p}* and

*C*of each WLT show distinct differences with each other for the present five-WLT MRS, similar to two-WLT and three-WLT configurations. The higher values in

_{d}*C*correspond to higher values in

_{p}*C*for all configurations. The

_{d}*C*and

_{p}*C*of inside WLTs in the MRS, say #2 and #3, show larger increases compared to those for outside WLTs of #1 and #5. The increase in

_{d}*C*is much larger than those in

_{p}*C*, because the power out is proportional to the cube of the incoming wind velocity into the wind turbine and the drag is proportional to the square of it.

_{d}The static pressure and wind velocity distributions just behind an MRS suggest the reason why an MRS with more WLTs shows a larger increase in the power output and drag. Due to gap flows acceleration, the pressure behind the MRS with larger number of WLTs is much lowered compared to the MRS with small number of WLTs.

To investigate the wake interference for an MRS with WLTs, numerical analyses of the flow around an MRS with five WLTs in the present arrangement were also made using an LES based on FDM. The results of LES have confirmed those from the wind tunnel experiments. At *s/D*_{brim} = 0.2, all gap flows in five-WLT MRS are strongly accelerated due to the flow interaction with multiple WLTs. To investigate the pressure and wind velocity distributions behind the MRS, the nondimensional pressure and *u*-velocity just behind five WLTs in the present configuration are evaluated. The static pressure behind the MRS with five WLTs is remarkably lowered compared to those for stand-alone configurations, two- or three-WLT MRS configurations, similarly to the wind tunnel experiments. This is because the accelerated gap flows cause lower pressure regions behind an MRS with more WLTs. The lowered pressured regions draw much more airflows into turbines in an MRS with more WLTs. Therefore, the *C _{pi}* and

*C*for an MRS with five WLTs show higher values compared to those for stand-alone configuration, two-WLT MRS, and three-WLT MRS configurations.

_{di}## Acknowledgment

We gratefully acknowledge our laboratory staff, Messrs. K. Matsushima and K. Watanabe, along with the students, Dr. U. Göltenbott, Mr. A. Munakata, Mr. J. Miyazaki, and Mr. T. Moriyama for their cooperation and assistance in the experiments and in the analysis of the data. This research was supported by the New Energy and Industrial Technology Development Organization (NEDO), Japan, and by the Ministry of Education, Culture, Sports, Science and Technology-Japan (MEXT). This research is in cooperation with Dr. Peter Jamieson, who belongs to University of Strathclyde, UK.

## Nomenclature

*A*=swept area of rotor (m

^{2})*C*=_{d}drag coefficient

*C*=_{di}drag coefficient of each turbine in the multibody configuration

*C*_{d}_{0}=_{i}drag coefficient of a turbine in the stand-alone configuration

- $Cdi\xaf$ =
average drag coefficient of multiple turbines in the multibody configuration

- $Cd0i\xaf$ =
average drag coefficient of all turbines in the stand-alone configuration

*C*=_{p}power coefficient

*C*=_{pi}max. power coefficient of each turbine in the multirotor configuration

*C*_{p}_{0}=_{i}max. power coefficient of a turbine in the stand-alone configuration

- $Cpi\xaf$ =
average of max. power coefficients of all turbines in the multi-rotor configuration

- $Cp0i\xaf$ =
average of max. power coefficients of all turbines in the stand-alone configuration

*D*_{brim}=brim diameter for wind-lens turbine (WLT) (m)

*D*_{rotor}=rotor diameter (m)

*D*_{throat}=diffuser throat diameter (m)

*f*=frequency (Hz)

*F*_{drag}=drag force (N)

*h*=brim height (m)

*L*=reference length (m)

*L*=_{t}length of diffuser (m)

*p*=local static pressure (Pa), (N/m

^{2}), (kg/(m·s^{2}))*P*=power output (W)

*r*=radius of the rotor (m)

- Re =
Reynolds number =

*U*_{0}*L*/*ν* *s*=gap width (m)

*s/D*_{brim}=gap ratio for wind-lens turbines in the multi-rotor configuration

*T*=_{r}torque (N·m)

*u*=wind velocity in the streamwise direction (

*x*-direction) (m/s)*U*_{0}=approaching wind velocity (

*x*-direction) (m/s)*x, y, z*=streamwise, spanwise and vertical directions (m)

- Δ
*C*=_{di}variation in

*C*compared to_{di}*C*_{d}_{0}(%)_{i} - Δ
*C*=_{pi}variation in

*C*compared to_{pi}*C*_{p}_{0}(%)_{i} - Δ$Cdi\xaf$ =
variation in $Cdi\xaf$ compared to $Cd0i\xaf$ (%)

- Δ$Cpi\xaf$ =
variation in $Cpi\xaf$ compared to $Cp0i\xaf$ (%)

*λ*=tip speed ratio

*ν*=kinematic viscosity (m

^{2}/s)*ρ*=air density (kg/m

^{3})*ω*=angular velocity 2

*πf*(rad/s)