Investigation into the wake aerodynamics of a five-straight-bladed vertical axis wind turbine by wind tunnel tests

Investigation into the wake aerodynamics of a five-straight-bladed vertical axis wind turbine by wind tunnel tests

J. Wind Eng. Ind. Aerodyn. 155 (2016) 23–35 Contents lists available at ScienceDirect Journal of Wind Engineering and Industrial Aerodynamics journa...

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J. Wind Eng. Ind. Aerodyn. 155 (2016) 23–35

Contents lists available at ScienceDirect

Journal of Wind Engineering and Industrial Aerodynamics journal homepage: www.elsevier.com/locate/jweia

Investigation into the wake aerodynamics of a five-straight-bladed vertical axis wind turbine by wind tunnel tests H.Y. Peng, H.F. Lam n, C.F. Lee Department of Architecture and Civil Engineering, City University of Hong Kong, Hong Kong, China

art ic l e i nf o

a b s t r a c t

Article history: Received 24 August 2015 Received in revised form 8 April 2016 Accepted 8 May 2016

Wake characteristics have significant effects on the performance design of standalone turbines and the optimal placement of multiple turbines. In the literature to date, little experimentation has been done on the wake of vertical axis wind turbines (VAWTs), and understanding of such wake is far from adequate. In this work, systematic measurements are presented of both the near and mid-range wake of a fivestraight-bladed VAWT in a wind tunnel. The blockage ratio of the VAWT was 1.8%, and no correction of the measured data was required. The wake flow fields were measured up to 10 turbine diameters (10D) to the downstream. The wake exhibited high asymmetry in the horizontal direction. In addition, the wake expanded more in the horizontal direction than in the vertical direction. The causes of the asymmetry were analyzed and discussed through the experimental results. An engineering wake model was proposed to characterize the wake edges and the average velocities. The existence of a pair of counter-rotating vortical structures in the wake was detected. Moreover, the integral length scale was found to steadily grow with the downstream distance. This work contributes to the knowledge of the VAWTs' wake and the application of VAWTs in wind farm layout design. & 2016 Elsevier Ltd. All rights reserved.

Keywords: Near wake Mid-range wake Asymmetry VAWT Wind tunnel Wind energy

1. Introduction Wind energy is clean and renewable, and the use of wind power has risen massively in recent years (Kusiak and Song, 2010; Islam et al., 2013; Danao et al., 2014; Ghasemian and Nejat, 2015). The exploration of power generation by wind turbines helps to prevent the escalating depletion of fossil fuels and the degradation of the global climate (Chen et al., 2015). Wind turbines are classified into two basic types: the horizontal axis wind turbine (HAWT) and the vertical axis wind turbine (VAWT). The presence of a wind turbine and the rotation of its blades create strong blockage effects against the approaching wind. Moreover, part of the wind's kinetic energy is converted into the mechanical energy of the wind turbine's rotation for power production. As a consequence, a wake characterized by decreasing wind velocities and rising turbulence is created behind the wind turbine (Vermeer et al., 2003). The HAWT has been developed to a mature level through intense research efforts, and this type of turbine has been dominant in the wind power industry for the past several decades (Eriksson et al., 2008; Islam et al., 2013). Nevertheless, recent studies have shown that VAWTs have great future prospects for n

Corresponding author. E-mail address: [email protected] (H.F. Lam).

http://dx.doi.org/10.1016/j.jweia.2016.05.003 0167-6105/& 2016 Elsevier Ltd. All rights reserved.

applications in built environments and offshore areas, which are projected to become huge sources of renewable energy (Edwards et al., 2012; Almohammadi et al., 2013; Bhuyan and Biswas, 2014; Tjiu et al., 2015; Ismail and Vijayaraghavan, 2015). VAWTs have higher potential for scalability (Peace, 2004; Islam et al., 2013), superior robustness, and lower costs compared to their HAWT counterparts (Islam et al., 2013; Tjiu et al., 2015; Ismail and Vijayaraghavan, 2015). Furthermore, some studies have indicated that VAWTs have the faster wake recovery (Dabiri, 2011; Kinzel et al., 2012; Tescione et al., 2014). This finding suggests that VAWTs may be more efficient for clustered arrays in wind farm scenarios, especially in built environments and offshore regions. To reduce the mutual interference of turbines in a wind farm and maximize the overall power output, the wake characteristics have to be analyzed (Lam and Peng, 2016). During the past several decades, substantial research efforts have been made to qualitatively and quantitatively investigate the wake aerodynamics of HAWTs (Alfredsson and Dahlberg, 1979; Jensen, 1983; Magnusson and Smedman 1999; Hand et al., 2001; Sanderse, 2009; Abdelsalam et al., 2014). However, few studies have been done on the wake characteristics of VAWTs, especially concerning how the wake flows evolve in the far wake, even though such studies are crucial for the optimal wind farm layout design. Therefore, this study emphasizes analyses of the wake characteristics of straightbladed VAWTs, i.e., the Darrieus-type VAWTs (Darrieus, 1931).

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Rather than conducting investigations of the VAWTs’ wake, most previous research efforts on VAWTs have focused mainly on the power performance and loading behavior of rotor blades. Howell and colleagues performed an experimental study on the aerodynamic performance of a VAWT (Howell et al., 2010). They found that the blade surface roughness improves the power performance below a Reynolds number of 30,000. Conversely, beyond this critical Reynolds number, a smooth blade surface enhances the turbine performance. Studies of the solidity ratios for various numbers of blades have shown that the low-solidity VAWT reaches its rated performance at a higher blade speed ratio (BSR, λ ¼VB/U0, ratio of blade rotational speed to free-stream wind speed). The solidity ratio refers to the total blade area over the swept area of rotor blades, i.e., σ ¼Nc/(πD), where N is the number of blades, c is the chord length, and D is the turbine diameter. McLaren and colleagues conducted a systematic investigation into the aerodynamic loading behavior of blades for a high-solidity three-bladed VAWT in a wind tunnel (McLaren, 2011; McLaren et al., 2012). The thrust and radial force coefficients were measured at a series of BSRs and free-stream wind speeds. Such analyses have revealed that the power coefficient, CP, as calculated from thrust force coefficients, has an amplification effect at high BSRs, whereas the results obtained from torque coefficients are more stable. Moreover, a vibration mitigation method and a signal filtering technique were developed to eliminate the resonant effect of the structural vibration with the turbine rotation. Simão Ferreira performed an experimental study of the near wake of a two-bladed VAWT (Ferreira, 2009). The vortices induced by the VAWT and their effects on the wake flows have been comprehensively investigated through the smoke visualization, hot-wire measurement and particle image velocimetry (PIV). Tescione and colleagues investigated the near wake aerodynamics of a two-bladed VAWT based on stereoscopic PIV tests (Tescione et al., 2014). The VAWT operated at a BSR of 4.5 at a free-stream wind speed of 9.3 m/s. Phase-locked measurements were conducted at the blade mid-span plane for examining the wake characteristics along the horizontal plane. Moreover, measurements were performed along vertical planes at the windward and leeward to inspect the three-dimensional wake behavior. The stream-wise and cross-stream velocities at the blade mid-span plane were measured up to two turbine diameters (2D) in the wake. These tests revealed asymmetrical wake patterns in the horizontal direction. The wake was shown to have a more pronounced expansion toward the windward. A careful review of the existing literature suggests that studying the wake characteristics of VAWTs through wind tunnel tests is a highly worthwhile task. As mentioned, the mid-range and far wake characteristics of VAWTs are of critical importance for the wind farm layout design. In this study, wind tunnel tests were conducted toward developing a comprehensive understanding of how the near and mid-range wake evolves. The measurements along horizontal lines (HLs) were carried out at the height of the blade mid-span at different downstream distances. In addition, measurements along vertical lines (VLs) aligned with the tower centerline were made at various downstream distances. Apart from that, measurements on a vertical plane normal to the approaching wind were conducted. The aerodynamic properties, such as the three-component velocities, turbulence intensities, and Reynolds shear stresses were measured and calculated. Based on the measured wake characteristics, an engineering wake model was proposed to describe the wake edges and average velocities. Finally, analyses of the integral length scale in the wake were performed to further examine the evolution of turbulence structures.

Fig. 1. VAWT prototype in the wind tunnel.

Fig. 2. Schematic of the geometrical properties of a single blade.

2. Measurement methodology 2.1. Wind turbine prototype The wind turbine under investigation is shown in Fig. 1. This wind turbine has N ¼5 blades that extend straight outward from a cambered airfoil. The cambered airfoil is helpful in the sense that it can deflect the approaching flows onto the upper and lower surfaces and can produce lift force even at zero angle of attack (AOA, α). Therefore, the VAWT has an outstanding self-starting performance. Fig. 2 presents the schematic of the geometrical properties of one of the VAWT's blades. The VAWT rotates counterclockwise viewing from the top as shown by the angular speed, ω. Note that θ is the azimuthal angle. The turbine has a diameter, D, of 300 mm and a blade depth, H, of 300 mm. Hence, the turbine has an aspect ratio of H/D ¼1.0. The chord length, c, of the blade is 45 mm. The rotor blade is pitched at the blade mid-chord. A preset pitch angle, the angle between the blade rotational speed, VB, and the blade chord line, is β ¼  10°. A solidity ratio of σ ¼ Nc/(πD)¼0.24 is attained, which corresponds to a high-solidity VAWT. 2.2. Wind tunnel and measurement apparatus The wind tunnel facility is located at City University of Hong Kong, Hong Kong. The height of the tunnel's cross-section is 2.0 m, and the width of the tunnel is 2.5 m. Thus, the blockage ratio of

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the VAWT is 1.8% o10%, and no correction for the measured data is required (Ross and Altman, 2011; Chen and Liou, 2011). The tunnel's length is 10.0 m (see Fig. 3). This wind tunnel allows freestream wind speeds ranging from 1.0 m/s to 20.0 m/s, with turbulence intensity, I, of approximately 2.5%. The preliminary tests were performed to compare the results measured by a four-hole cobra probe and a one-dimensional hot-wire anemometer. The measured properties such as the time-averaged velocities and the turbulence intensities from the two probes were almost identical. Moreover, in this study, the three-component velocities are to be measured to examine the three-dimensional wake flows. As a result, the four-hole cobra probe (see Fig. 4) was used. The cobra probe features a linear frequency response from the mean velocity component (0 Hz) to more than 2000 Hz. The flow direction must reside within 745° cone of the probe's x axis. It is able to measure velocities ranging between 2.0 m/s and 100.0 m/s. The measurement error of the cobra probe is 70.3 m/s. The rotational speed of blades was measured by a laser displacement sensor installed on the ground level, with the laser beam aligned vertically upward (see the bottom of Fig. 1). When a blade is rotating, the corresponding strut blocks the laser beam once per rotation. The rotational speed of the turbine can then be determined. The position of the VAWT was determined through the uniformity measurement along the longitudinal direction in the empty wind tunnel. After traveling a long distance of L1 ¼6.0 m, the flows showed good uniformity and were stable with negligible fluctuations. The turbine was thereby installed at L1 ¼6.0 m to the downstream of the wind entrance (see Fig. 3). The time-averaged velocity at the turbine position in the uniformity measurement was defined as the approaching wind speed. The sampling frequency was 3000 Hz, and the measurement duration was 30 seconds. The approaching wind speed, U0, was 11.3 m/s. The tower had a 70 mm diameter and was custom-made in such a way that the blade mid-span of the VAWT stood at z¼1.0 m above the tunnel ground. The tower was seated at the mid-width of the tunnel's cross-section. By using this design, the core region of the wind tunnel, which has great uniformity, is exploited to a maximum extent. For this device, the turbine height is defined as the distance from the ground to the blade mid-span, i.e., h¼1.0 m. A Cartesian coordinate system was introduced in the wind tunnel to facilitate the measurements (see Fig. 3). The position of the tower base was set as the origin (0, 0, 0) of the coordinate system. The longitudinal direction along the free-stream wind direction was set as the x axis. The z axis was set along the tower from the bottom to the top. The y axis was formed according to the right-hand rule and pointed into the figure. A three-dimensional traversing system (TDTS) was used to position the cobra probe toward the user-defined coordinates through the computer system in the controlling room.

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2.3. Wake measurement The wake characteristics such as the time-averaged threecomponent velocities, i.e., U, V and W, turbulence intensities, I, and Reynolds shear stresses, Rxy, were measured. The overall turbulence intensity has the form:   12 u02 þv02 þw02 =3 ð1Þ I¼ UR where u0 , v0 and w0 are the fluctuating velocity components along the x, y and z axes, respectively, and UR is the averaged resultant velocity. The Reynolds shear stress, Rxy, is expressed as follows: Rxy ¼ u0 v0

ð2Þ

These flow properties were measured through HLs, VLs and a vertical plane. The HL measurement was carried out along the y direction at the height of the blade mid-span, i.e., z¼ h. At this location, the flows were relatively mild and away from the violent regions characterized by the strong vortex shedding at the blade tips. The HL measurement spanned from y¼  0.5 m to y¼0.5 m with a maximum and minimum measurement interval of 0.05 m and 0.025 m, respectively. The VL measurement at y¼0 along the z direction stretching from z¼ 0.7 m to z ¼1.3 m. The measurement interval size for the VL was 0.05 m. In addition, a plane measurement parallel to the turbine projected frontal area was conducted

Fig. 4. Cobra probe mounted on the three-dimensional traversing system.

Fig. 3. Schematic of the experimental setup in the wind tunnel facility (units in meters).

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to gain further insight into the wake flows. The measured plane had an area of 1.0 m width and 0.6 m height with a uniform step size of 0.1 m. Both HLs and VLs were measured from x¼ 1D to x ¼10D downstream with equal intervals of 1D. The plane measurement was performed at x¼ 2D in the wake. The approaching wind speed, U0, was 11.3 m/s with turbulence intensity, I0, of 2.5%. After a warm-up wind-blowing period of about 3–5 min, the rotational speed of the VAWT converged at a BSR of 0.75. This rotational speed corresponded to 540 RPM (revolutions per minute) and a rotational frequency of fr ¼9.0 Hz. An impact hammer test showed that the VAWT had a fundamental natural frequency of fs ¼ 21.3 Hz. Therefore, no large vibration of the turbine due to the resonance was expected. Disturbance from the large turbine vibration on the wake flows was avoided. As this study involved a large number of measured points, the TDTS was used to position the cobra probe for data recording. The flow data at each measured point were recorded for 30 s, and the data sampling rate was set as 3000 Hz. As this study focused mainly on the wake characteristics, the aerodynamic loading behavior and the power performance were not studied.

3. Results and discussion 3.1. Wake statistics 3.1.1. Flow properties at the level of the blade mid-span Fig. 5 presents the normalized stream-wise velocity profiles,U/ U0, along HLs at 10 downstream distances in the wake. From x¼ 1D to x¼ 2D in the wake, U/U0 suffer substantial deficits due to the power extraction of the VAWT and the blockage of the rotating blades. The maximum velocity deficit (MVD) reaches about 75% at 2D downstream. For U/U0 ¼0.25 (U0 ¼ 11.3 m/s) in the near wake, the stream-wise velocity still has a value of 2.83 m/s 42 m/s. Hence, the measurement accuracy of the stream-wise velocity is still guaranteed. By analogy to the wake of the HAWTs (Vermeer et al., 2003), x ¼2D was thereby defined as the end of the near wake for the five-bladed VAWT. In addition to the velocity deficits, it is observed that at some regions, U/U0 is larger than 1.0. There are two reasons accounted for this phenomenon. First, the solid presence of the VAWT contributes to the increased velocities in the vicinity of the VAWT. Second, when the approaching flows are deflected by the fast-rotating blades onto the inner and outer

1.2 1 U/U0

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Fig. 5. Time-averaged stream-wise velocity profiles along z ¼ h.

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surfaces of the blades, they get accelerated. The shed vortices and separated flows from the blades due to dynamic stalls inherit the angular momentum and spread toward the downstream. The substantial wake asymmetry in the horizontal direction is revealed in Fig. 5. The MVD position shifts approximately 0.5D from the x axis toward the windward (y40) at x¼ 2D downstream. There are two major factors that may contribute to this wake asymmetry. One factor is that more turbulent structures are produced at the windward than at the leeward (yo0). When the blade advances under adverse pressure gradients at the windward, stronger vortex shedding and much severer flow separations take place. The other factor is that the wake flows are transported toward the windward. First, when the blade moves upwind at the windward, it causes stronger blockage effect compared to that at the leeward. Therefore, at the windward, the blade wake is characterized by a lower pressure, which induces the cross-wind flows. Second, when the blade operates at the downstream half-revolution, the strong angular momentum drags and propels the wake flows toward the windward. The transportation of the wake flows is clearly reflected in the positive crossstream velocities shown in Fig. 6 to be discussed later. Since the asymmetry is attributed to the vortex shedding and the lateral flow

transportation, the number of blades and the rotational speed will influence the extent of the asymmetry. The large number of blades and the fast rotational speed will esclate the wake asymmetry in the horizontal direction. The wake asymmetry, with more pronounced expansion toward the windward, is consistent with the PIV test of a two-straight-bladed VAWT in the near wake (Tescione et al., 2014). In the PIV test, the MVD position shifted 0.25D toward the windward from the x axis at x¼2D downstream. As discussed above, the different shift distances toward the windward of these two turbines at x¼2D downstream are attributed to the number of rotor blades. Five blades provide much more constant acceleration to the wake flows than two blades. Moreover, more vortices are expected to be shed from the five-bladed turbine compared to those from the two-bladed turbine. From x¼2D to x¼10D, the wake spreads and recovers significantly along the downstream distance. At x¼10D downstream, the minimum U/U0 reaches about 75%, with the averaged value of approximately 90%. Meanwhile, the wake asymmetry further esclates with the downstream distance, and the MVD position shifts 1D windward at x¼ 10D downstream. A series of cross-stream velocity profiles, V/U0, along HLs in the wake are shown in Fig. 6. It is consistent that from x¼ 1D to

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Fig. 6. Time-averaged cross-stream velocity profiles along z ¼h.

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0.1 W/U0

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Fig. 7. Time-averaged vertical velocity profiles along z ¼h.

x ¼10D, V/U0 are close to zero at approximately y¼  0.5D. Beyond this particular position toward the windward, V/U0 have positive signs with peaks. This finding suggests that the wake is transported toward the windward. Conversely, from y ¼  0.5D toward the leeward, V/U0 have negative signs, indicating leeward motions. The magnitudes of V/U0 shrink swiftly and become negligible compared to those at the windward. These special features actually facilitate the development of the wake asymmetry. The crossstream velocities show an acceleration process from x ¼1D to x ¼2D downstream before they decrease. As vortices are transported by mean flow motions, the vortices experience the same acceleration process. This may help to explain why the MVD in the wake is obtained at x ¼2D downstream. Similar to the asymmetry of the U/U0 profiles, the V/U0 peak shifts approximately 0.5D windward at x¼10D downstream. Fig. 7 presents a series of vertical velocity profiles, W/U0, along HLs. Except for the near wake (1D and 2D), the negative peaks in the other sub-figures are all near y¼0.25D at the windward. The negative W/U0 peaks indicate the downward motions of the wake flows. Supposing that the VAWT was geometrically symmetrical against the blade mid-span plane, W/U0 would be close to zero at z ¼h. In an actual situation, due to the solid presence of the tower blocking the air flows, the

symmetry plane is shifted slightly downward, and hence non-zero W/U0 occur at z ¼h. The downward motions with peak magnitudes of approximately 7%U0 are measured at z¼ h. Though the tower causes the symmetry plane to shift downward, the direct reason for the negative values of W/U0 is the stationary vortices to be discussed later. The I profiles along HLs from x¼ 1D to x ¼10D in the wake are plotted in Fig. 8. The near wake is characterized by drastic flows with high levels of turbulence. At x ¼1D, the wake flows suffer the most radical turbulence with the maximum I reaching 35%. It is consistent to find that the turbulence intensities at the windward are much higher than that at the leeward from x ¼2D to x ¼10D. It should be pointed out that at x ¼1D, I¼ 35% at the leeward is unexpectedly higher than that at the windward. This is probably caused by the inefficiency of the cobra probe to measure high turbulence intensities larger than 30% (Mallipudi et al., 2004). The magnitudes of the I profiles decrease as the downstream distance grows due to the entrainment and turbulence diffusion. The peak value at x¼ 10D downstream obtains 12% approximately 5 times the free-stream turbulence intensity. Fig. 9 presents a series of Reynolds shear stresses which reveal the characteristics of velocity shear layers in the y direction. In the near

H.Y. Peng et al. / J. Wind Eng. Ind. Aerodyn. 155 (2016) 23–35

40 I (%)

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Fig. 8. Turbulence intensity profiles along z ¼h.

wake from x¼1D to x¼2D, there are two clear Rxy peaks with opposite signs distributed at approximately y¼  0.5D and y¼0.75D, respectively. At x¼1D, the Rxy are almost zero in between the two peaks, suggesting the shear layers have not yet been bridged. Nevertheless, at x¼ 2D downstream the shear layers are connected, and the near wake ends. It is interesting to note that the negative Rxy peak remains at about y¼  0.5D in the near wake. In comparison, the positive Rxy peak keeps advancing toward the windward. In the midrange wake, the positive Rxy peak has a larger magnitude compared to the negative Rxy peak. This implies the stronger entrainment at the windward than at the leeward. In summary, the wake stream-wise velocity, U/U0, achieves a much faster recovery than the turbulence intensity, I. In addition, the evolutions of I are far more violent than those of U/U0. In the near wake along HLs, the peak I is approximately 14 times that of the free-stream value. In contrast, the approaching wind speed is approximately 4 times that of the minimum U/U0. At x¼10D downstream, the peak I is still 5 times that of the free-stream value, whereas the minimum U/U0 already recovers to 75% of its free-stream counterpart.

3.1.2. An engineering wake model of the VAWT In considering the wind farm layout design consisting of multiple VAWTs, the wake edges and the stream-wise velocities therein are the most critical factors. In this study, the wake edge is defined in a way that it separates the wake from the free-stream flows like a boundary. When the approaching flows are deflected by the fastrotating blades onto the inner and outer surfaces of the blades, they get accelerated. U/U0 ¼ 1 is used to define the wake edge. With respect to the wind speeds, it implies a full wake recovery. For any positions at which U/U0 41, they are excluded from the wake region. In fact, on the wake edge, the resultant velocity, i.e., UR ¼((U)2 þ(V)2 þ(W)2)1/2, is slightly larger than U0. Given that the VAWT is omnidirectional, the selection of UR/U0 41 gives a slightly large wake region and is thereby conservative. According to the literature (Chen and Liou, 2011), a larger blade rotational speed leads to a greater blockage effect. The larger blockage effect will push the wake boundaries outwards and hence induce a larger wake region. As the wake expansion in the horizontal direction dictates the placement of multiple VAWTs, this study focuses only on the wake spreading at the blade mid-span plane. Unlike in studies of the axisymmetric HAWT wake (Chu and Chiang, 2014), two spreading rates are used to describe the highly

30

H.Y. Peng et al. / J. Wind Eng. Ind. Aerodyn. 155 (2016) 23–35

2.5 Rxy

Rxy

2.5 0 -2.5 -1.5

-1

-0.5 0 0.5 1 1.5 Lateral distance (y/D) @x = 1D

-2.5 -1.5

2

0

-1

-0.5 0 0.5 1 1.5 Lateral distance (y/D) @x = 3D

Rxy

Rxy -1

-0.5 0 0.5 1 1.5 Lateral distance (y/D) @x = 5D

Rxy

Rxy

-0.5 0 0.5 1 1.5 Lateral distance (y/D) @x = 4D

2

-1

-0.5 0 0.5 1 1.5 Lateral distance (y/D) @x = 6D

2

-1

-0.5 0 0.5 1 1.5 Lateral distance (y/D) @x = 8D

2

-1

-0.5 0 0.5 1 1.5 Lateral distance (y/D) @x = 10D

2

2.5

0

-1

-0.5 0 0.5 1 1.5 Lateral distance (y/D) @x = 7D

0 -2.5 -1.5

2

2.5 Rxy

2.5 Rxy

-1

0 -2.5 -1.5

2

2.5

0 -2.5 -1.5

2

2.5

0

-2.5 -1.5

-0.5 0 0.5 1 1.5 Lateral distance (y/D) @x = 2D

0 -2.5 -1.5

2

2.5

-2.5 -1.5

-1

2.5 Rxy

Rxy

2.5

-2.5 -1.5

0

-1

-0.5 0 0.5 1 1.5 Lateral distance (y/D) @x = 9D

2

0 -2.5 -1.5

Fig. 9. Reynolds shear stress profiles along z¼ h.

asymmetrical wake edges of the VAWT. The wake edges at the windward and leeward are assumed to linearly expand in the downstream, and they are expressed as follows: yL ¼ kL Dx þ bL yW ¼ kW Dx þ bW

g

ð3Þ

where x is the wake distance, yL and yW are the spreading distances of the wake edges at the leeward and windward, respectively, kL and kW are the spreading rates at the leeward and windward, respectively, and bL and bW are the spreading distances of the wake edges at x¼ 0. Moreover, an engineering expression to predict the averaged stream-wise velocity, Uwake/U0, in the wake is proposed as follows: A U wake =U 0 ¼ 1    B  1 þ x=D

ð4Þ

where A and B are the model parameters. All model parameters in Eqs. (3) and (4) were estimated by the least-squares method, using the data from the wind tunnel tests. The model parameters are presented in Table 1. By substituting these parameters into Eqs. (3) and (4), the model-predicted wake patterns of the VAWT can be obtained. The spreading rates, i.e., kL and kW, quantitatively reflect the wake asymmetry and the necessity of quantifying them separately.

Fig. 10 shows both the calculated and the measured wake patterns. Very close matching between the engineering wake model and the wind tunnel test data is achieved. The asymmetry of the wake edges is clearly observed in Fig. 10(a). It is clear from the Fig. 10 (b) that the recovery of the wake velocities slows down as the downstream distance increases. Nevertheless, an average velocity of approximately 90% is reached at x ¼10D in the wake. 3.1.3. Flow properties along the span-wise direction Fig. 11 shows the stream-wise velocities, U/U0, along VLs in the wake. There are two obvious features in these velocity profiles. One feature is the downshift of the MVD position in the wake, which is induced by the tower effect. The other is the much faster velocity recovery at the upper half of the turbine. The faster recovery at the upper half occurs because the outside flows are able to freely come into the wake from the top of the VAWT. In contrast, the flows at the bottom of the turbine are affected by the Table 1 Calculated parameters based on the wind tunnel test data.

Values

kL

bL

kW

bW

A

B

 0.067

 0.74

0.094

0.96

0.86

0.84

H.Y. Peng et al. / J. Wind Eng. Ind. Aerodyn. 155 (2016) 23–35

-1

1 0.9 0.8 0.7 0.6 0.5

2

3

4

5 6 7 Wake distance (x/D)

8

9

10

Measurement Model prediction

1

2

3

4

5 6 7 Wake distance (x/D)

8

9

10

Fig. 10. Patterns of the wake edges and the average wake velocities.

-0.5 -1 0.2 0.6 1 1.2 U/U0

-0.5 -1 0.2 0.6 1 1.2 U/U0

0.5 0 -0.5 -1 0.2 0.6 1 1.2 U/U0

0.5 0 -0.5 -1 0.2

1 (z-h)/H @x = 7D

0

-0.5 -1 0.2 0.6 1 1.2 U/U0

1 0.5

0

(z-h)/H @x = 3D

0

0.5

1

1

0.5 0 -0.5 -1 0.2 0.6 1 1.2 U/U0

0.5 0 -0.5

1

-1 0.2 0.6 1 1.2 U/U0

0.6 1 1.2 U/U0

0.5 0 -0.5 -1 0.2 0.6 1 1.2 U/U0

Fig. 11. Time-averaged stream-wise velocity profiles along y¼ 0.

0.5 0 -0.5 -1 0.2 0.6 1 1.2 U/U0

1

1 (z-h)/H @x = 8D

0.5

1 (z-h)/H @x = 2D

(z-h)/H @x = 1D

1

(z-h)/H @x = 4D

-2 1

(z-h)/H @x = 5D

Measurement @Windward Model prediction Measurement @Leeward Model prediction

0

3.1.4. Wake velocity fields on the vertical plane The contour plots of the three-component flow motions, i.e., U/U0, V/U0 and W/U0, at x¼ 2D are given in Figs. 15–17, respectively. From Fig. 15, the U/U0 magnitudes, the wake region, and the wake asymmetry can be clearly visualized. The wake shifts both windward and downward. The wake asymmetry about the tower centerline (y¼0) is far greater than that about the blade mid-span plane (z¼ h). In fact, the wake is approximately symmetrical against the blade mid-span plane. One of the main factors contributing to this lateral asymmetry is clearly reflected in Fig. 16. The windward flow motions concentrate at z¼h, and this concentration helps transport the turbulent wake flows windward. The transportation of the wake flows is supposed to occur even within the VAWT's rotating perimeter. The reason for this is that the blade creates a greater blockage effect and thus a lower pressure in the blade wake at the windward than that at the leeward. At around the positions of the top and bottom blade tips at y40, the flows move toward the leeward. In addition to showing the horizontal flow movement, Fig. 17 presents the vertical motions. There are four extremes at A, B, C, and D, at coordinates (0, 1/3 Hþh), (D, 1/3 Hþh), ( 1/3D,  1/3 Hþh), and (D,  1/3 Hþh), respectively. The flow centered at A is moving downward, whereas that centered at B is moving upward. Together with the horizontal flow motions at the blade mid-span and the top blade tips (see Fig. 16), these flows form an anti-clockwise vortical motion, as indicated by the arrow (from A to B) in Fig. 17. Similarly, the flow from C to D forms a clockwise vortical motion as shown by the other arrow in Fig. 17. As a result, a pair of counter-rotating vortical structures forms in the wake of the VAWT. These two counter-rotating vortical structures rotate at above and below the level of the blade mid-span. It is claimed that this kind of counter-rotating mechanism has the potential for more complete mixing with high efficiency (Park, 2013). The counter-rotating vortical structures are believed to contribute to the fast wake recovery of the VAWT.

(z-h)/H @x = 9D

1

feature benefits the wake recovery through the flow mixing. The turbulence intensity profiles, I, along VLs are shown in Fig. 14. The I peaks reveal that the blade-tip vortices play a critical role in the development of the wake flows. Moreover, the effect of the tower wake is clearly reflected in the I profiles.

1 (z-h)/H @x = 10D

2

(z-h)/H @x = 6D

Uwake/U

Lateral distance (y/D)

tower blockage (refer to the vertical velocity in Fig. 13). In Fig. 11, the minimum U/U0 along the VL reaches a value of more than 90% at x¼10D downstream. The position of the minimum U/U0 shifts approximately 0.5D downward from the blade mid-span plane. A much larger minimum U/U0 along the VL is obtained at x¼10D downstream compared to that along the HL at x ¼10D in the wake. A series of cross-stream velocity profiles, V/U0, along VLs are shown in Fig. 12. V/U0 take some distance to develop. V/U0 accelerate to their maximum at x¼2D downstream. Afterwards, V/U0 decrease in relation to the downstream distance. This kind of feature is consistent with V/U0 along HLs, as shown in Fig. 6. In addition, the positive V/U0 contribute to the windward transportation of the wake flows and hence the wake asymmetry in the horizontal direction. The vertical motions of the wake flows along VLs are presented in Fig. 13. One interesting phenomenon is that the vertical velocity profiles, W/U0, consistently preserve their ‘S’ shapes throughout the wake. The ‘S’ shapes suggest that the outside flows keep pouring into the wake from both the top and bottom of the VAWT. This unique

31

0.5 0 -0.5 -1 0.2 0.6 1 1.2 U/U0

H.Y. Peng et al. / J. Wind Eng. Ind. Aerodyn. 155 (2016) 23–35

0 -0.5

0.5 0 -0.5 -1 -0.25

0 0.25 V/U0

0.5 0 -0.5 -1 -0.25

0 0.25 V/U0

0 -0.5

0 -0.5

0 0.25 V/U0

1

0.5 0 -0.5 -1 -0.25

0 0.25 V/U0

0.5

-1 -0.25

0 0.25 V/U0

1

0.5

-1 -0.25

0 0.25 V/U0

(z-h)/H @x = 5D

-0.5

1 (z-h)/H @x = 8D

0.5

0

-1 -0.25

0 0.25 V/U0

1 (z-h)/H @x = 7D

(z-h)/H @x = 6D

-0.5 -1 -0.25

0 0.25 V/U0

1

-1 -0.25

0

0.5

(z-h)/H @x = 10D

-0.5

0.5

1

1 (z-h)/H @x = 4D

0

(z-h)/H @x = 3D

0.5

-1 -0.25

1

1 (z-h)/H @x = 2D

(z-h)/H @x = 1D

1

(z-h)/H @x = 9D

32

0.5 0 -0.5 -1 -0.25

0 0.25 V/U0

0 0.25 V/U0

Fig. 12. Time-averaged cross-stream velocity profiles along y¼ 0.

-1 -0.2

0 0.2 W/U0

1 (z-h)/H @x = 7D

(z-h)/H @x = 6D

1 0.5 0 -0.5 -1 -0.2

0 0.2 W/U0

-0.5

0 -0.5 -1 -0.2

0 0.2 W/U0

0 -0.5

0 -0.5

0 0.2 W/U0

0.5 0 -0.5 -1 -0.2

0 0.2 W/U0

1

0.5

-1 -0.2

0.5

-1 -0.2

0 0.2 W/U0

1

0.5

(z-h)/H @x = 5D

0

-1 -0.2

0 0.2 W/U0

(z-h)/H @x = 8D

-1 -0.2

-0.5

0.5

1

0 0.2 W/U0

1 (z-h)/H @x = 10D

-0.5

0

(z-h)/H @x = 4D

0

0.5

1

(z-h)/H @x = 9D

0.5

1 (z-h)/H @x = 3D

1 (z-h)/H @x = 2D

(z-h)/H @x = 1D

1

0.5 0 -0.5 -1 -0.2

0 0.2 W/U0

0.5 0 -0.5 -1 -0.2

0 0.2 W/U0

Fig. 13. Time-averaged vertical velocity profiles along y¼0.

3.2. Integral length scale Turbulence is characterized by eddies of various lengths, velocities, and time scales. The large eddies characterized by integral length scales are anisotropic, and they contain most of the turbulent kinetic energy. The large eddies are unstable, and they further break up into small eddies. Meanwhile, the turbulent kinetic energy is transported to the small eddies. As the Reynolds number of the small eddies becomes sufficiently small, the molecular viscosity becomes effective in dissipating the turbulent kinetic energy. This description summarizes the energy cascade in turbulent flows (Kolmogorov, 1991). By definition, the integral length scale is a measure of the longest correlation distance between the velocity components at two different

points in space. This study examines the correlation length in the longitudinal direction of the stream-wise fluctuating velocities. The longitudinal integral length scale is: Z 1 uðx0 ; t Þuðx0 þ x; t Þ Lxu ¼ dx ð5Þ 2 x¼0

σu

where u is the stream-wise fluctuating velocity, t denotes the time instant, x0 is the longitudinal coordinate, x represents the distance between two points, and σ 2u is the variance of the stream-wise velocity. To simultaneously measure a series of points in space is not a practical endeavor. Instead, the longitudinal length scales are commonly obtained through regression of the von Karman spectrum model (Holmes, 2003). The non-dimensional form for the wind spectrum is

H.Y. Peng et al. / J. Wind Eng. Ind. Aerodyn. 155 (2016) 23–35

-1 0

20 I (%)

-1 0

40

-0.5

40

0 -0.5 -1 0

20 I (%)

-0.5

20 I (%)

0

0 -0.5

0 -0.5

40

20 I (%)

20 I (%)

40

20 I (%)

40

1

0 -0.5

40

-0.5

0

-1 0

0

40

0.5

-1 20 I (%)

20 I (%)

1

0.5

0.5

-1

40

1

0.5

-1 0

40

0

-1 0

(z-h)/H @x = 8D

0.5

0.5

-1 20 I (%)

(z-h)/H @x = 5D

0

1 (z-h)/H @x = 7D

1 (z-h)/H @x = 6D

-0.5

0.5

1

(z-h)/H @x = 10D

-0.5

0

(z-h)/H @x = 4D

0

0.5

1

(z-h)/H @x = 9D

0.5

1 (z-h)/H @x = 3D

1 (z-h)/H @x = 2D

(z-h)/H @x = 1D

1

33

0.5 0 -0.5 -1

0

20 I (%)

40

0

Fig. 14. Turbulence intensity profiles along y¼ 0. 1

2/3

0.8

1/3

0.7 0 0.6 -1/3

0.5 0.4

-2/3

0.1

2/3

0.9 Vertical distance ((z-h)/H)

Vertical distance ((z-h)/H)

1

1

0.05 B

A

1/3

0 0 -0.05 -1/3 C

D

-0.1

-2/3 -0.15

0.3

-1 -1.5-4/3

-1

-2/3 -1/3 0 1/3 2/3 Lateral distance (y/D) @x = 2D

1

4/3 1.5

0.2

Vertical distance ((z-h)/H)

0.15 1/3 0.1 0 0.05 -1/3 0 -2/3 -0.05 -1 -1

-2/3

-1/3

0

1/3

2/3

1

4/3 1.5

Lateral distance (y/D) @x = 2D

Fig. 16. Time-averaged cross-stream velocity contour on the y–z plane.

expressed as follows:   4 nLxu =U nSu ðnÞ ¼h 2  2 i56 σu 1 þ 70:8 nLxu =U

-1

-2/3

-1/3

0

1/3

2/3

1

4/3 1.5

Fig. 17. Time-averaged vertical velocity contour on the y–z plane.

1

-1.5-4/3

-1.5-4/3

Lateral distance (y/D) @x = 2D

Fig. 15. Time-averaged stream-wise velocity contour on the y–z plane.

2/3

-1

ð6Þ

where Su(n) is the measured spectral density of the longitudinal

fluctuating velocity, n is the frequency of turbulence, and U is the averaged longitudinal velocity. As revealed by the above experiments, the wake of the VAWT demonstrates significant asymmetry in the horizontal direction. The core region of the wake is shifted away from the x axis toward the windward. To obtain integral length scales more representative of the turbulent structures, they were calculated at the points at z¼ h with the MVD rather than along the x axis. By fitting the measured wind spectrum with the regression model at the righthand side of Eq. (6), the integral length scales can be estimated. The matching between the von Karman spectrum and the measured spectrum at two downstream distances is shown in Fig. 18. It is observed that the essential features of the wind spectrums are well captured by the von Karman spectrum. The integral length scales at different downstream distances are obtained as indicated with the star markers in Fig. 19. The integral length scale was normalized by the blade chord length c, which is the characteristic length causing the wake turbulence. The integral length scale grows along the downstream distance. This pattern suggests that the vortices shed from the blades continue to roll up and stretch downstream due to the constant production of turbulence by the turbine rotation. At x¼1D downstream, the integral length scale is only 1/4 of the blade chord length c, whereas it reaches approximately 1.6c at

H.Y. Peng et al. / J. Wind Eng. Ind. Aerodyn. 155 (2016) 23–35

101

101

100

100 Wind spectrum ((nSu(n))/σ2u, [-])

Wind spectrum ((nSu(n))/σ2u, [-])

34

10-1

10-2

10-3

10-4

10-1

10-2

10-3

10-4 Measured spectrum von Karman spectrum

10-5

Measured spectrum von Karman spectrum 10-5

100

10-2 x

Reduced freqency (nLu /U, [-]) @x = 5D

10-2 100 x Reduced freqency (nLu/U, [-]) @x = 9D

Fig. 18. Fitting of the measured spectrum by the von Karman spectrum.

1.75

Integral length scale (Lux/c)

1.5 1.25 1 0.75 0.5 0.25 0 1

2

3

4

5

6

7

8

9

10

Wake distance (x/D) Fig. 19. Evolution of the integral length scale against the downstream distance.

x¼10D in the wake. The steady growth of the length scale in the midrange wake indicates the wake recovery. The integral length scale is believed to continuously grow until it gets close to the ambient value, at which point the wake is fully mixed with the outside flows.

4. Conclusions This work is the first to present a systematic measurement in a wind tunnel to explore the wake aerodynamics of a straight-bladed VAWT up to 10D downstream. The wind tunnel tests were performed through measurements on a series of HLs, VLs, and a vertical plane. The wake of the VAWT is classified into the near wake within 2D and the mid-range wake beyond 2D. The near wake is subject to severe velocity deficits, whereas the velocity gradually recovers along the downstream distance. The significant wake asymmetry in the horizontal direction is clearly revealed. The asymmetry is partly attributed to the transportation of the wake flows toward the windward. More vortices are believed to be shed at the

windward than at the leeward, which serves as the other reason for the asymmetry. In contrast, the wake is approximately symmetrical against the blade mid-span plane. An engineering wake model fit for the VAWT is proposed to characterize the wake edges and the average velocities. Furthermore, the existence of a pair of counter-rotating vortical structures evolving in the wake has been detected. This counter-rotating pair is believed to contribute to more complete flow mixing and thereby the fast wake recovery. The von Karman spectrum is capable of accurately capturing the measured spectrum in the turbine wake. Analyses suggest that the longitudinal integral length scales in the wake are at the same order of magnitude as the chord length, c. The integral length scale grows with the downstream distance. The integral length scale may continuously grow until it reaches the ambient value. In the future, complete three-dimensional wake measurements at different blade heights and along the vertical direction off the x axis are suggested. Moreover, direct measurements of a VAWT submerged in the wake of its upstream counterpart are recommended.

Acknowledgments The work described in this paper was fully supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project no. 9041770 (CityU 114712)). During the course of the measurement campaign, Mr. CHAN Kwok Keung, Mr. TAI Wing Hing, Prof. CHEUNG Chun Kuen, and Dr. HE Yun Cheng at the wind tunnel facility generously shared their expertise and provided great assistance. The authors want to express genuine gratitude for their constructive contributions.

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