wind-tunnel study on aerodynamic performance

8/22/2019 Wind-tunnel Study on Aerodynamic Performance

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WIND-TUNNEL STUDY ON AERODYNAMIC PERFORMANCE OF SMALL

VERTICAL-AXIS WIND TURBINES

J. J. Miau*1, S. W. Huang1, Y. D. Tsai1, S. Y. Liang1, C. H. Hsieh2, S. J. Chen3,

C. C. Hu4

, J. C. Cheng5

, and T. S. Leu1

1 Cheng Kung University, Taiwan2 Institute of Nuclear Energy Research, Taiwan

3Temple University, USA4Kao Yuang University, Taiwan

5Formosa University, Taiwan

ABSTRACT

Wind tunnel experiments were carried out to study the aerodynamic performance of

three vertical axis wind turbines (VAWTs) including a Darrieus VAWT, a Giromill

VAWT, and a helical VAWT. The performance curves regarding the power

coefficients against the tip speed ratios were reduced for the Darrieus and helical

VAWTs; whereas the reaction torques of the Giromill VAWT at different azimuthal

angles under static condition were measured and discussed. Moreover, the effect of

free-stream turbulence on the performance of the helical VAWT was studied by

having a turbulence generating grid installed at the inlet of the test section. As found,

the wind turbine actually performed better under the condition of high free-stream

turbulence intensity. On the other hand, the characteristics of unsteady flow around

the helical wind turbine were studied with a hot-wire probe positioned at the

peripheral of the wind turbine, under the condition of low free-stream turbulence

intensity, at two tip speed ratios.

Keywords: wind-tunnel experiment, VAWT, aerodynamic performance


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1. INTRODUCTION

Strong growth of utilizing wind energy in the past decade [1] stimulates extensive

research efforts on the wind turbine technology nowadays. Among which, studies

on the small vertical-axis wind turbines (VAWT) have attracted a great deal of

attention, because of their potential applications in urban environment, for instance,

the idea of installing a small wind turbine on the roof of a building was explored [2].

Referred to such applications, a VAWT can be so small in physical size that its

full-scale can be fitted into a wind tunnel for testing. The advantage of using wind

tunnels for research and development is that one can validate the design specifications

in a relatively short turn-around time. A case of providing the detailed comparisons

between the wind-tunnel tests and the full-scale field measurements was reported by

Sheldahl [3].

Speaking of the performance test in wind tunnel, a wind turbine should be

examined under various operating conditions. Thus, the results obtained can serve

for validating the specifications. Motivated by this consideration, a series of research

efforts were set out by the present authors to study the aerodynamic performance of

small VAWTs using the experimental and numerical methods. This paper mainly

presents the results obtained by the wind-tunnel experiments with three wind turbines,

namely, a Darrieus VAWT, a Giromill VAWT, and a helical VAWT. The results

include the performance curves regarding the power coefficients reduced against the

tip speed ratios, the reaction torques measured with a wind turbine at different

azimuthal angles under the static condition, and the hot-wire velocity measurements

around the peripheral around a wind turbine. Additionally, discussion is made

concerning the effect of free-stream turbulence on the performance of the helical


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VAWT and the unsteady flow around this wind turbine under the condition of low

free-stream turbulence intensity. The blockage effect due to the confinement of the

test-section walls of the wind tunnel also calls for attention, because the blockage

effect was identified as a critical factor from an uncertainty analysis of the power

coefficient and tip speed ratio.

2. The ABRI Wind Tunnel

Experiments were carried out in the ABRI (Architecture and Building Research

Institute) environmental wind tunnel situated in the Kuei-Ren Campus of National

Cheng Kung University. The wind tunnel is a closed-loop circuit, which has two test

sections in series. The first test section is 4 m (width) by 2.6 m (height) at the inlet,

and 36.5m in length. The second is 6 m (width) by 2.6 m (height) at the inlet and 21m

in length. [4] The first test section is long enough to have a thick boundary layer

developed at the downstream end, where the height of the test section is 3 m. In the

present study, the wind turbine was installed on a turntable immediately downstream

the inlet, centered at 2.9 m from the inlet, where the thickness of the boundary layer

was negligible compared to the dimensions of the test section. Therefore, the present

wind turbine was regarded as tested under the uniform flow condition.

According to the wind tunnel calibration results reported by Kao [5], the

maximum velocity achieved in the first test section flow was higher than the design

speed, 36 m/s [4]. The flow uniformity reduced at the inlet of the test section was

about 0.37%, and the turbulence intensity measured was less than 0.3%.

3. EXPERIMENTAL METHODS


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In the present study, a wind turbine was situated on a turntable near the inlet of

the test section mentioned. The wind turbine was supported by a stainless steel strut of

circular cross section. See also Fig. 1 for a photo of a Darrieus wind turbine

installed in the test section. Note that the strut height should be appropriate, in order

that the wind turbine was located in the center region of the test section. The

coordinate system employed for the present study is given in Fig. 2, where x, y and z

denote the streamwise, spanwise and vertical directions, respectively. The origin, (x,

y, z) = (0, 0, 0) is denoted at the center of the wind turbine. In addition, is denoted

as the azimuthal angle associated with the wind turbine, where =0 is aligned in the

positive y direction.

In the present study, the power coefficient, Cp, of a wind turbine is defined below.

[6]

Pdenotes the power output of a wind turbine, measured by a DC electronic load

device; denotes the density of the free stream flow; V denotes the reference

velocity with respect to the wind turbine; and AS denotes the swept area of the wind

turbine.

Further, it was noted that the blockage effect caused by the presence of the wind

turbine in the test section could not be ignored in the determination of the power

coefficient, which can be seen below. Let the blockage effect be represented by a

parameter, t. Therefore, V in (1) can be corrected from the free stream velocity u,

measured by a Pitot tube at the inlet of the test section, as follows. [7]

V= u(1+t) (2)


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in (1) can be expressed in terms of the pressure and temperature of the free

stream,P and T, respectively, by the ideal gas relation.

In (3), R is the universal gas constant. Combining the relations (1) to (3), Cp

can be expressed as follows.

q,udenotes the dynamic pressure based on the free stream velocity u. Therefore,

concerning the total uncertainty ofCp, it can be expressed as follows. [8]

As seen in (5), the term containing the blockage effect parameter is identified as an

influencing factor on the right-hand side. Similarly, with the tip speed ratio defined

below, where represents the angular velocity of the wind turbine,

the total uncertainty of the tip speed ratio can be expressed as follows.

In (7), it is also seen that the term containing the blockage effect parameter can be a

critical factor influencing the uncertainty of .

In the present study, the torque produced by a wind turbine was measured by a

torque meter, in-line connected to the shaft of the turbine. Literally speaking, the


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torque generated by a wind turbine can be categorized into two kinds, namely, the

reaction torque and the rotary torque. The former is measured when the wind

turbine is in the static situation, whereas the rotary torque is measured with the wind

turbine in rotation. A non-zero rotary torque induces a change of the angular

velocity of a wind turbine, which can be seen in the following expression.

(8)

Qa, Qf , and Qem denote the aerodynamic torque, the loss due to the mechanical

friction, and the counter electromagnetic torque exerted by the electric generator,

respectively; Jrdenotes the inertia of the wind turbine, and is the rate of change

of the angular velocity mentioned. On the other hand, when is zero, the wind

turbine is rotating at a constant speed, which implies that no rotary torque is

generated.

In addition to the output power and torque measurements mentioned above, a

cross-type hot-wire probe was employed to gather the instantaneous velocity

information at the peripheral of a wind turbine. The velocity data obtained are of use

to examine the unsteady flow around the wind turbine.

In this study, a turbulence generating grid could be positioned at the inlet of the

test section to produce considerably high turbulence intensity downstream. The grid

was made of wood rods in a pattern of squared meshes, each of which was 0.3 m by

0.3 m in dimension. Each wood rod was of squared cross section, 0.09 m in width.

As calculated, the area blockage ratio of this grid was 49%. At 2.3 m downstream of

the grid, where was about the upstream edge of the wind turbine for test, the

turbulence intensity measured was 12 %. The measurements were conducted in the

absence of a wind turbine in the test section, for the free stream velocity up to 11 m/s.


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The integral length scale of turbulent fluctuations at this streamwise location was

about 0.06m, equivalent to two times the mesh size.

4. EXPERIMENTAL RESULTS

4.1 The Results of a Darrieus Wind Turbine

The Darrieus wind turbine shown in Fig. 1, which was acquired from a local

manufacturer, was consisted of 3 turbine blades with the rated power at 400 Watts.

The maximum diameter of the turbine is 1.2 meter, called Dthe height, called h, is

1.2 meterthe chord length of a turbine blade, called C, is 90 mm. The solidity,

defined as NCh/As, is 0.225, whereN=3 represents the number of the turbine blades.

Figure 3 presents the power coefficient Cp against the tip speed ratio for the free

stream velocity, u, in a range of 6 to 13.1 m/s. Note that the reference velocity V

was corrected with t in (2), based on that the turbine blades were situated statically in

the test section; later, further discussion will be made concerning the validity of the t

value adopted. As seen in the figure, the maximum power output was normally

occurred at slightly larger than 2.5; the higher the flow speed, the higher the

maximum Cp value reduced. More specifically, the maximum Cp value reaches

about 0.2 at u =13.1 m/s, while it is only about 0.05 at u =6 m/s. Therefore, one

can see that the aerodynamic performance strongly depends on the incoming flow

speed. Moreover, as noted in the figure, few data points were obtained at the tip

speed ratios lower than 2.5. This is due to a fact that, for this wind turbine the wind

power was difficult to be drawn at low tip speed ratios.

4.2 The Results of a Giromill Wind Turbine


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Figure 4 presents a photo of the self-made Giromill (H-type) wind turbine

installed for test. The wind turbine employed, 1.2 m in diameter and 1.2 m in height,

was consisted of three straight blades, each of which was a NACA0015

cross-sectional shape, 90mm in chord length. To study the starting characteristic of

this wind turbine, measurements of the reaction torque in the static situation were

carried out for u =3.7, 4.6 and 5.5 m/s, respectively. [9] The results obtained are

presented in Fig. 5, in terms of the distribution curves of torque values in Nm against

. Interestingly noted is that the turbine blades generated negative torques at in the

neighborhood of 50, 170 and 290, respectively. This observation explains why the

self-starting problem of a vertical axis wind turbine is intrinsically existed. By the

double multiple-streamtubes model [10], Hsieh [9] further estimated the starting

torque under the flow condition of u=5.5 m/s. A comparison of the experimental

data and the results obtained by the double multiple-streamtubes model is given Fig. 6.

The two curves shown in the figure indicates that not only the angles where the

negative torques take place, but also those of the maximum positive torques occurred,

are well coincided. This comparison gives a strong support to using the double

multiple-streamtubes model for the prediction of the starting torque.

To alleviate the self-starting problem, Gorlov [11] proposed a design of the

three-dimensional helical blade for hydraulic reaction turbines. Later, this idea was

extensively applied in wind turbines, one of which will be seen in the next section.

On the other hand, the ideas of pitch control have been proposed for the wind turbines

with straight blades [12-14]. The control laws were aimed to overcome the

self-starting problem under the static condition, as well as improve the aerodynamic

performance at different tip speed ratios.


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4.3 The Results of a Helical Wind Turbine

Figure 7 presents two photos of a helical wind turbine situated in the test section

of the wind tunnel, one of which is with no turbulence generating screen situated at

the inlet of the test section, and the other is with the presence of the grid. The wind

turbine with the rated power at 400 Watts was acquired from a local manufacturer.

The wind turbine is featured with 1.25 m in diameter and 1.4 m in height, consisted of

three twisted blades, each of which is twisted 30 with respect to the vertical axis and

0.27 m in chord length. The solidity of this wind turbine estimated is 0.605, which is

noted significantly higher than the two wind turbines studied earlier. The

aerodynamic performances of the wind turbine were then studied with respect to the

two inlet conditions mentioned.

In calculating Cp and, the reference velocity, V, was taken to be the velocity

measured by a hot wire at (x, y, z)= (-0.7 m, 1.4 m, 0), indicated in Fig. 2 with an

open circle symbol. Further, to examine the flow uniformity under this flow

condition, additional hot-wire velocity measurements were made at y=0, 0.67 m and

-0.67 m, at the same streamwise location and z=0, without the presence of a wind

turbine. It was found that the mean velocities measured were well coincided.

Based on the wind-tunnel data obtained, the performance curves subjected to two

inlet conditions are shown in Fig. 8. Notable differences learned from a comparison

of the two plots in Fig. 8 are described below. Under the condition of high

free-stream turbulence intensity, the wind turbine appears to perform better, as far as

the maximum Cp values reduced are concerned. Moreover, it is noted that under this

condition, the tip speed ratios corresponding to the maximum Cp values reduced are

slightly lower than those found under the condition of low free-stream turbulence

intensity. Also noted is that under the condition of high free-stream turbulence


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intensity, the Cp curves obtained at V = 5.5- 11.1 m/s appear to be almost collapsed

together, a strong indication that the performance of the wind turbine is insensitive to

the flow speeds tested. On the other hand, under the condition of low free-stream

turbulence intensity, the Cp curves obtained at different wind speeds show significant

scatter for lower than 2.

It is noted that the maximum Cp value obtained in the situation of high

free-stream turbulence intensity is higher than that obtained in the situation of low

free-stream turbulence intensity by about 0.01. This difference is noted rather

significant and deserved further discussion. Following Homicz [15], the

performance of a wind turbine in a turbulent stream can be analyzed as follows.

Theoretically, the output power of a wind turbine is proportional to the cubic of the

incoming velocity, say, the reference velocity V.

P(1/2)V3AS (9)

Meanwhile, considering a highly turbulent free stream, let the turbulent fluctuations in

the streamwise direction be u, and the time-mean reference velocity be

V .

Therefore, the instantaneous reference velocity can be expressed as

V= V +u (10)

Plug this relation in (9),

P

(1/2)[ V3

+3u V2

+3u2

V +u3

]AS (11)

By taking a time average of (11),

P(1/2)[ V3+3 2'u

V ] (12)

Here, P denotes the time-averaged output power. As a result, due to the presence

of the second term on the right-hand-side of (12), the time-averaged power coefficient

is increased by an amount of 3( 2'u /

V2).


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For the present case of high free-stream turbulent intensity, ( 2'u /

V2)1/2 =0.12,

the amount of increase in Cp is estimated about 0.04, which is about four times the

increase of Cp noted in the experimental data. Hence, Homiczs argument [15]

gives a support to the trend seen that the efficiency of a wind turbine gets improved in

a turbulent stream. Nevertheless, the reasoning apparently is too simplified, without

taking into account the effect of free-stream turbulence on the unsteady flow

phenomenon around a wind turbine.

In Fig. 8b the Cp values at low tip-speed ratios are noted relatively insensitive to

Reynolds number, in comparison with those in Fig. 8a. Since at low tip-speed ratios,

flows around the rotor blades would experience large variations in angle of attack

with respect to the azimuthal angle, the dynamic stall phenomenon [16-18] is

anticipated to come into play. Based on the experimental observations above, one

can further argue that the presence of free-stream turbulence cause the dynamic stall

phenomenon less sensitive to the variations of Reynolds number.

To gather the instantaneous velocity information of the unsteady flow field,

hot-wire measurements were performed at 0.1 m away from the edge of the wind

turbine in the plane of z=0. The locations of hot-wire measurements are indicated in

Fig. 2 with open circles, i. e., =0, 30, 90, 150, and 180.

Figure 9 presents the streamwise (u) and vertical (v) velocity traces obtained at

=0, 90, and 180, subjected to = 1.73 and 2.58 while the free stream was at low

turbulence intensity. Also included in each figure are the signal traces obtained from

an optical sensor situated at =0 for phase reference. Note that in each plot the

horizontal axis is scaled with a normalized time, t/T, where Tdenotes the time period

of one revolution of the wind turbine. As seen from the output signal traces of the


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optical sensor, the time length Tspans over three consecutive square waves due to the

three rotor blades passing over the optical sensor.

In Fig. 9a, the velocity signal traces obtained at =0 show that prior to a turbine

blade reaching this angular location, the streamwise velocity shows a strong

acceleration followed by deceleration. As the leading edge of the wind turbine blade

reaching this angular location, the vertical velocity is decelerated to the lowest value,

about zero. After the trailing edge of the turbine blade passing over, the streamwise

velocity is leveled off. Note that the vertical velocity measured at this location

appears positive always, which can be explained with the Conservation laws below.

Since the mass flux (momentum flux) of the incoming flow should be greater the

mass flux (momentum flux) downstream of the wind turbine, due to the extraction of

wind energy, a portion of the incoming fluid tends to be displaced outward in the

lateral direction. By the same argument, at =180, seen in Fig. 9c, the vertical

velocity measured appears to be negative most of the time, except for a period of time

between two turbine blades passing over this location, the flow is dominated by the

wake motions. In Figs. 9a, b and c, the time instants of a turbine blade reaching the

measured angular locations =0, 90 and 180, respectively, are marked by T* for

reference.

In Fig. 9b, the velocity signal traces obtained at = 90 basically show that the

streamwise velocity reaches the lowest value when a blade reaching this angular

position, corresponding to a situation of flow impinging on a solid surface, meanwhile

the vertical velocity measured is about zero, and gets increased as the blade passing

over the location. Moreover, it is interesting to point out that in Figs. 9a and b, the

velocity signal traces corresponding to the two tip speed ratios are almost coincided.

This observation can be reasoned that the unsteady flow experienced by a rotor blade


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as it advancing from = 0 to 90 is of an attached-flow type basically. Alternately

speaking, the process of vortex shedding has not yet commenced, thus little variations

are seen with respect to the two tip speed ratios.

On the other hand, in Fig. 9c it is seen that either the u orv signal traces show

significant differences with respect to the two tip speed ratios. Moreover, in every

signal trace one can see intermittent fluctuations, which are attributed to turbulent

fluctuations associated with the vortices shed, as a result of the dynamic stall process.

It is anticipated that the phenomenon of dynamic stall and subsequently vortex

shedding take place when a turbine blade is travelling through the azimuthal region of

= 90 to 180. Recently, Cheng [19] conducted a numerical analysis on studying

the three-dimensional flow field around a wind turbine, whose geometric

configuration is similar to the present one. Cheng [19] presented and discussed the

numerical results obtained at = 2 and 3. In both cases, the results clearly indicate

that vortex shedding take place as a turbine blade advancing from = 90 to 180.

It is also worthwhile to mention that the phenomenon of vortex shedding due to the

dynamic stall process of flows around the VAWT blades was unveiled by the flow

visualization experiments performed in the water-channels [20, 21], whose Reynolds

numbers are considerably lower than those of the present wind tunnel experiments.

5. DISCUSSION

5.1 The blockage effect

A primary interest of this study is to obtain the performance curves of a wind

turbine, namely, the curves of Cp versus , under various operating conditions.

Along this consideration, the accuracy of the Cp and values reduced from the

measured data deserves further discussion here. According to (5) and (7), one can


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identify that the major contribution to the uncertainties ofCp and, can be due to the

blockage effect, represented by t. Moreover, the error or uncertainty resulted in Cp

would be three times larger than t. Thus, the Cp values shown in Fig. 3 or 8 are

critically dependent upon the reference velocity, V, determined. On the other hand,

since the wind turbine was situated in the test section, the blockage effect could not be

ignored, nor could it be estimated by a simplified model of flow over fixed turbine

blades. [9]

Physically, it can be argued that the blockage effect be a function of the tip speed

ratio. To clarify this issue, recently a numerical simulation was carried out by the

present authors to examine the blockage effect of a wind turbine in a confined channel

at different tip speed ratios. A two-dimensional physical model based on the

schematics shown in Fig. 2 was employed, but the diameter of the wind turbine was

1.2 m. The NACA 0015 airfoil with chord 0.15m was chosen as the wind turbine

blade. Two types of boundary conditions were considered in the simulation, i. e. the

free and solid wall boundary conditions, with the free stream velocity ufixed at 6

m/s. Table 1 shows the time-averaged x- and y-component velocities, called u and v,

respectively, at the point indicated in Fig. 2 where V was measured, subjected to =1,

1.5 and 2. In the free boundary case u is decreased slightly, whereas v is increased

considerably as gets increased. On the other hand, in the solid wall boundary case,

both of u and v are increased as gets increased. At the measurement point, u is

always greater than the free stream velocity, irrespective of the tip speed ratios.

Table 2 lists the values of V, where V=22

vu , and the blockage effect

parametert with respect to the tip speed ratios. For the free boundary condition,

the velocity at the measurement point, V, is actually smaller than u. On the

contrary, for the solid wall boundary condition, V, is greater than u, irrespective of


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the tip speed ratios. Notably, the blockage effect parameter, t is increased from

1.35 to 4.56 as the tip speed ratio is increased from 1 to 2.

5.2 The Reynolds number effect

In Figs 3 and 8, the Reynolds number effect to the characteristics of

aerodynamic flow around a wind turbine can be realized by comparing the Cp-

curves obtained at different free stream velocities. For instance, based on the

appearances of the Cp- curves in Figs. 3 and 8, one can say immediately that the

performance of the Darrieus VAWT is much more sensitive to the Reynolds number

than that of the helical VAWT.

By defining the Reynolds number based on the free stream velocity, u, and the

chord length of a turbine blade, C, the Reynolds numbers in the present study are

noted to fall within a range of 103 to 105. Within this Reynolds number range, the

phenomena of boundary layer transition and separation on a turbine blade are known

very sensitive to the influencing parameters, including Reynolds number, surface

roughness and free-stream turbulence intensity. Moreover, given the fact that a

wind turbine is in rotation, the turbine blades actually experiences various angles of

attack in time, which depend on the tip speed ratio, thus in most of the situations the

dynamic-stall phenomenon comes into play, and makes the prediction of aerodynamic

forces even more difficult. In summary, the results presented in this paper evidence

the importance of the effects of Reynolds number and free-stream turbulence.

6. CONCLUDING REMARKS

The experimental results reported in this paper show that the aerodynamic

performance of a small VAWT can be studied in a wind tunnel, by providing the Cp-


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curves, the reaction torque of a wind turbine, and the characteristics of the unsteady

flow field using hot-wire velocity measurements. Meanwhile, there are key issues of

concern learned from this study, namely, (1) the accuracy of the Cp and values

reduced, which is critically dependent upon the correction of the blockage effect, (2)

the Reynolds number effect, to which the characteristics of aerodynamic flow over a

turbine blade is sensitive, and (3) the free-stream turbulence effect, which could better

the performance of a wind turbine and make it less sensitive to Reynolds number.

These issues are being under investigation by the authors. More results will be

reported in the future.

ACKNOWLEDGMENT

The authors would like acknowledge the funding support by National Science

Council, Taiwan, under the contract number 98-3114-E-006-007 for this research

work. Support of the ABRI Wind Tunnel Laboratory in conducting the experimental

work of this study is also greatly appreciated.


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Table 1 Comparison of the numerical results obtained at = 1, 1.5 and 2 subjected to the

free and solid wall boundary conditions, regarding the time-averaged u and v velocities

at the point where V was measured in the wind tunnel experiments. (unit: m/s)

Boundary

Condition Type

=1 =1.5 =2

u v U v u v

Free BC 5.845 0.536 5.822 0.814 5.811 1.178

Solid Wall BC 6.079 0.165 6.170 0.257 6.265 0.328


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Table 2 Comparison of the numerical results obtained at = 1, 1.5 and 2 subjected to the

free and solid wall boundary conditions, regarding the velocities ofV, where

V=22

vu , and the blockage effect parametert. (unit: m/s)

Boundary

Condition Type

=1 =1.5 =2

V t() V t() V t()

Free BC 5.870 -2.18 5.879 -2.02 5.929 -1.18

Solid Wall BC 6.081 1.35 6.175 2.92 6.274 4.56


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Fig. 1 The Darrieus wind turbine installed, a view taken from the inlet of the test

section.


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Fig. 2 A schematic drawing of the wind turbine at the plane of z=0, and the coordinate

system employed.


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Fig. 3 The Cp versus curves of the Darrieus wind turbine studied at u = 6 to 13.1

m/s.


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Fig. 4 A photo of the self-made Giromill wind turbine.


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Fig. 5 The wind-tunnel measurement results of the reaction torque versusat u =3.7,

4.6 and 5.5 m/s.


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Fig. 6 Comparison of the measured and estimated reaction torque versus at u

=5.5 m/s. [9]


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Fig. 7 The photos of the helical wind turbine studied in the situations: (a) without and

(b) with a turbulence generating grid situated at the inlet of the test section.


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(a)

(b)

Fig. 8 The Cp versus curves of the helical wind turbine studied in the situations: (a)

without and (b) with a turbulence generating grid situated at the inlet of the test

section.


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(a)

(b)

T*

T*

T*

T*

T*

T*

T*

T*

T*

T*

T*

T*


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(c)

Fig. 9 Streamwise and vertical velocity traces obtained by an X-type hot-wire around

the helical wind turbine at (a) =0, (b) 90, and (c) 180 subjected to the incoming

flow at low turbulence intensity and two tip speed ratios. T* indicates the time

instant when the leading edge of a turbine blade reaches the angular location

measured.

T*

T*

T*

T*

T*

T*

wind-tunnel study on aerodynamic performance

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