Figure 6 shows vortex cores and limiting streamlines on

the blade suction surface in the conventional and

optimal cases obtained by the RANS simulations.

Behaviors of separation vortices behind the brim of the

wind-lenses are significantly different between both

cases. In the conventional case, two large-scale

separation vortices are observed behind the brim.

However, only one large-scale separation vortex is

observed in the optimal case. Figure 7 shows

meridional streamlines and meridional velocity

distributions in tangentially-averaged flow fields

obtained by the RANS simulations. As mentioned above,

in the optimal case shown in Figure 7 (b), the

separation region behind the brim is much smaller than

the conventional case and there is no separation inside

the wind-lens. The suppression of the flow separation

behind the brim and inside the wind-lens in the optimal

case may be affected by the divergence angle in the

wind-lens, the brim height and the span-wise

distribution of the blade loading.

In order to achieve higher aerodynamic performance of

the wind-lens turbine, it is important that the design of

the rotor blade is performed coupled with the wind-lens.

These results indicate that the present aerodynamic

optimization for the wind-lens turbine design works well.

Aerodynamic Design Optimization of

Wind-lens Turbine

Nobuhito Oka, Masato Furukawa, Kazutoyo Yamada, Kenta Kawamitsu, Kota Kido and Akihiro Oka Kyushu University, Japan

PO.ID

210

A new type of DAWT called wind-lens turbine shown in Figure 1 was developed in Kyushu University, Japan [1].

The distinctive feature of the wind-lens turbine is a brim

attached at the diffuser exit as shown in Figure 2. The

brim generates separation vortices behind it and the

diffuser creates meridional streamline curvature, so that

a low-pressure field is formed at the diffuser exit. The

low-pressure field draws the upstream wind into the

wind-lens and it generates non-uniform meridional flow

distributions at the rotor. This wind concentration on the

turbine rotor results in the significant enhancement of

the turbine output.

An optimum aerodynamic design method for the new

type of diffuser augmented wind turbine (DAWT) called

wind-lens turbine has been developed. The optimum design method is based on a genetic algorithm (GA)

and a quasi-three-dimensional aerodynamic design

method. The quasi-three-dimensional aerodynamic

design consists of meridional viscous flow calculation

and two-dimensional blade element design.

Aerodynamic performances of optimal and conventional

design cases are obtained from three-dimensional

Reynolds averaged Navier-Stokes (RANS) simulations.

The output power coefficient of the optimal case is

superior to the Betz limit. The numerical results show

that the aerodynamic performance of the wind-lens

turbine is affected by flow separations behind the wind-

lens brim and inside the wind-lens.

Abstracts

Optimum Aerodynamic Design Method

Introduction

Three-Dimensional Flow Field

References

EWEA 2014, Barcelona, Spain: Europes Premier Wind Energy Event

Rotor

Wind-lensHub

Bell-mouth

Diffuser

Brim

Separationvortex

Rotor

Inlet flowdistributions Internal flow field

External flow field

Figure 1: Wind-lens turbine Figure 2: Schematic flow structure

Figure 3: Flow chart of optimum aerodynamic design method

Initial design specificationInitial design specificationInitial design specification

Mutation

Crossover

Optimized design

3-D shape of wind lens turbine& Aerodynamic performance

Result of the calculation Flow rate in wind-lens Inlet flow distribution

Blade loading distribution

3-D blade shape Unit vector normal to

blade camber (nz , nr , n ) Relative flow angle

ConvergenceTwo dimensional blade element designTwo dimensional blade element theory on the

basis of the momentum theorem of ducted turbineDesignation of optional blade loading distribution

Evaluation & Selection

Convergence

Yes

No

Yes

No

Quasi three dimensional aerodynamic design method

Meridional viscous Flow calculationCoupling problem of the internal and external flow fieldAxisymmetric viscous flow calculation on meridional planeBlade force is introduced as body force

Decision of wind-lens meridional shape& Blade loading distribution (r)

Design Specifications

A quasi-three-dimensional aerodynamic design method

has been developed for the wind-lens turbine, which

can take into account the non-uniform meridional flow

distributions [2]. The design method mainly consists of

two parts: meridional viscous flow calculation and two-

dimensional blade element design. The meridional

viscous flow calculation is introduced to obtain the non-

uniform meridional flow distributions of the turbine rotor

inlet. Using the blade loading distribution and the

velocity distribution, the 3-D blade shape is designed by

the two dimensional blade element design method.

Taking into account the blade force, the meridional

viscous flow calculation is performed again. By

repeating the meridional viscous flow calculation and

the two dimensional blade element design, the blade

shape and the flow field are converged [2].

In the present study, a genetic algorithm (GA) has been

applied to the design method. The optimization objects

are the meridional shape of wind-lens and the blade

loading distribution. The same design specifications are

adopted except for the wind-lens shape and blade

loading distribution. A flow chart of the present optimum

design method is shown in Figure 3. The evaluation and

selection model is a Non-dominated Sorting Genetic

Algorithm II (NSGA-II) [3]. The crossover model is a

Real-coded Ensemble Crossover (REX) [4]. In the

optimization procedure, the aerodynamic performances

of each individual are obtained from the meridional

viscous flow calculation.

CW* K

Optimal 0.604 1.01

Conventional 0.474 1.07

Betz limit 0.593 0.66

Table 1 shows the aerodynamic performances obtained

from the RANS simulations at the design operating

condition. The table shows that the output power

coefficient CW* in the optimal case is superior to that in

the other cases. That is also superior to the Betz limit.

As far as the authors know, the optimal design of the

present study is the only one which achieves a higher

output power coefficient than the Betz limit.

0.4

0.5

0.6

0.7

-0.1 0 0.1 0.2

Ra

diu

s r/

D

Axial distance z/D

Conventional

Optimal

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2

Sp

an

wis

e d

ista

nce

Local load coefficient (r)

Conventional

Optimal

(Hub)

(Tip)

Figure 4: Wind-lens shapes Figure 5: Blade loading distributions

Figure 4 shows the wind-lens shapes in the

conventional and optimal cases. In the optimal case, the

divergence angle of the near the diffuser exit is smaller,

the position of the wind-lens is located more backward

and the height of the wind-lens brim becomes lower

than that in the conventional case. Figure 5 shows the

blade loading distributions in the optimal and

conventional cases. Although a qualitative coincidence

of the blade loading distributions is observed between

the optimal and conventional designs, the blade loading

coefficients from mid-span section to tip section are

significantly different.

Aerodynamic Performance

The aerodynamic performances of the wind-lens turbine

are evaluated by the output power coefficient CW* and

the wind collection coefficient K. The output power

coefficient CW* is defined with the cross-sectional area

of the A* based on the outer diameter of wind-lens as

follows:

(1)

where is the density of air, V is the free-stream wind velocity and W is the wind turbine output power. The

theoretical limitation of the output power coefficient CW*

is CW* =0.593 according to the Betz limit. The wind

collection coefficient K is defined as the ratio of the

cross-sectional averaged velocity at the rotor inlet to

the free-stream velocity V as follows:

(2)

WW

CV A

*3 * 2

vK

V1

v11. Ohya, Y., et al., Development of a shrouded wind turbine with a flanged

diffuser, Journal of Wind Engineering, Vol.96, pp.524-539., 2008

2. Oka, N., et al., Aerodynamic Design for Wind-Lens Turbine Using Optimization Technique, Proceedings of the ASME 2013 FEDSM, Paper No. FEDSM2013-16569., 2013

3. Deb, K., et al., A Fast and Elitist Multiobjective Genetic Algorithm : NSGA-II, IEEE Trans. on evolutional computation, Vol. 6, No. 2, pp.182-197., 2002

4. Kobayashi, S., The frontiers of real-coded genetic algorithms, Journal of the Japanese Society for Artificial Intelligence, Vol24, No.1, pp.147-162., 2009

Table 1: Aerodynamic performances

Trailing vortex

Separation

vortex

CM

0.4132650.3673470.3214290.275510.2295920.1836730.1377550.09183670.04591840

Hn[-]1.0

-1.0

Wind-lens

Flow

Rotation

Trailing vortex

Separation

vortex

CM

0.4132650.3673470.3214290.275510.2295920.1836730.1377550.09183670.04591840

Hn[-]1.0

-1.0

Wind-lens

Flow

Rotation

(a) Conventional

Figure 6: Three-dimensional flow fields

(b) Optimal

Flow

Wind-lens

Rotor

Separation vortex

CM

0.4132650.3673470.3214290.275510.2295920.1836730.1377550.09183670.04591840

vm/Utip[-]0.48

0.00Flow separation

inside the wind-lens

(a) Conventional

Figure 7 : Meridional streamlines and meridional velocity distributions

(b) Optimal