Fundamental Understanding of the Physics of a Small-Scale Vertical Axis Wind Turbine with Dynamic Blade Pitching: An Experimental and Computational Approach

8/10/2019 Fundamental Understanding of the Physics of a Small-Scale Vertical Axis Wind Turbine with Dynamic Blade Pitching: An Experimental and Computational Appr

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Fundamental Understanding of the Physics of a Small-Scale

Vertical Axis Wind Turbine with Dynamic Blade Pitching: An

Experimental and Computational Approach

Moble Benedict

Alfred Gessow Rotorcraft Center, University of Maryland, College Park, MD, 20742

Vinod Lakshminarayan

Department of Aeronautics and Astronautics, Stanford University, CA, 94035

Johnathan Pino Inderjit Chopra

Alfred Gessow Rotorcraft Center, University of Maryland, College Park, MD, 20742

Abstract

This paper describes the systematic experimental and computational (CFD) studies performed toinvestigate the performance of a small-scale vertical axis wind turbine (VAWT) utilizing dynamic bladepitching. A VAWT prototype with a simplified blade pitch mechanism was designed, built and tested inthe wind tunnel to understand the role of pitch kinematics in turbine aerodynamic efficiency. The abilityof the present pitch mechanism to change the blade pitch phasing instantaneously in order to adapt tochanges in wind direction is the key to maximizing power extraction in urban environments. A CFDmodel was developed and the model predictions correlated extremely well with test data. The validatedCFD model was used to develop a fundamental understanding of the physics of power extraction of sucha turbine. Both experimental and CFD studies showed that the turbine efficiency is a strong functionof blade pitching amplitude, with the highest efficiency occurring around 20 to 25 amplitude. Theoptimum tip speed ratio (TSR) depends on the blade pitch kinematics, and it decreased with increasingpitch amplitude for the symmetric blade pitching case. CFD analysis showed that the blade extracts

all the power in the frontal half of the circular trajectory, however, it loses power into the flow inthe rear half. One key reason for this b eing the large virtual camber and incidence induced by the flowcurvature effects, which slightly enhances the power extraction in the frontal half, but increases the powerloss in the rear half. Fixed-pitch turbine investigated in the present study also showed lower efficiencycompared to the variable pitch turbines owing to the massive blade stall in the rear half, caused by thelarge angle of attack and high reverse camber. Maximum achievable CPof the turbine increases withhigher Reynolds numbers, however, the fundamental flow physics remains relatively same irrespective ofthe operating Reynolds number. This study clearly indicates the potential for ma jor improvements inVAWT performance with novel blade kinematics, lower chord/radius ratio, and using cambered blades.

Nomenclature

A Turbine frontal area,b Db Blade spanc Blade chordCP Coefficient of powerD Turbine diameterR Turbine radiusTSR Tip speed ratio, R/Uinf

Assistant Research Scientist, [email protected] Fellow, [email protected] Research Assistant, [email protected] Gessow Professor and Director, [email protected]

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American Institute of Aeronautics and Astronautics

AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

8-11, 2013, Boston, Massachusetts

AIAA

right 2013 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.


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Uinf Wind speedU Flow speed alongXaxisV Flow speed alongY axisX, Y Turbine coordinate system Rotational speed of the turbine Azimuthal location Blade pitch phasing Air density, 1.225Kg/m3

Blade pitch anglemax Blade pitch amplitude

I. Introduction

With increasing energy costs, rapid depletion of fossil fuels and growing concerns about the environmentaleffects of burning hydrocarbons, researchers have been looking at alternate, more environmentally benignsources to create power. Wind power, a renewable and virtually inexhaustible power source, is a promis-ing means of green energy production. However, at present, horizontal axis wind turbines are the mostestablished method of harvesting wind energy. Majority of the wind energy plants today, are in the formof windmill farms having several mega-Watt capacity, comprising of large horizontal axis windmills (rated

at several 100 kWs) driving electric generators and feeding into power supply grids. A major deterrent tothe continued development of wind energy at remote sites is the limited capacity of the nations electricitydistribution grid. Therefore, there is a strong need to co-locate energy generation based on the demand inorder to reduce the load and losses in the grid system [1]. Because large cities are the biggest consumersof electricity, it is necessary to design small scale (1-2 kW peak power), efficient, stand-alone wind turbines(for instance, a roof-top wind turbine farm) to meet their growing energy demand. However, unlike thelarge open windmill farms, extracting wind energy in an urban scenario is challenging because of the tightspace constraints and the fact that wind profile is highly turbulent with rapid fluctuations, both in terms ofmagnitude as well as direction.

Figure 1. Optimized fixed-pitch VAWT farm developed by California Insitute of Technology [2].

In an urban scenario, where space is of the essence, an important criterion for choosing one wind turbineconcept over the other for a small windmill farm, would be the power extracted per unit ground area (alsoknown as power density). HAWTs are not very attractive for such a scenario because of their need to maintaina significant lateral (3 5 turbine diameters in cross-wind direction) and longitudinal (6 10 diameters indownwind direction) separation between adjacent turbines and therefore would have a large footprint, or inother words, very low power density (2 3 W/m2). However, previous studies have shown that vertical axiswind turbines (VAWTs) could have very close wind turbine spacing, and if placed appropriately in a farm (asshown in Fig. 1), it could greatly enhance the farm efficiency ( 30 W/m2, which is almost ten times more

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power extracted per unit land area compared to HAWTs) because of the constructive interference betweenthe turbines [2].

Table 1. Comparison of VAWT and HAWT p ower densities for individual turbines.

Turbine type Rated power (MW) Turbine diameter (m) Power density (W/m2)

VAWT 0.0012 1.2 1061HAWT 2.5 100 318

HAWT 3.0 112 314

The power density of a farm would effectively depend on the lateral and longitudinal spacing betweenthe turbines (or number of turbines per unit area) and the power density of the individual turbines itself.Therefore, it is important to examine the power density for a single turbine, which is in fact the powerextracted per unit projected area. Note that, the area used for power density calculation in the case of aHAWT, is the projected circular swept area when the turbine is yawed 360 (A= R2). Table 1 comparesthe power densities of two commercially available HAWTs and one VAWT and it can be seen that thepower density of VAWT is almost three times of the HAWTs [2]. This is partly because the swept area of aVAWT (i.e., the cross-sectional area that interacts with the wind) need not be equally apportioned betweenits breadth, which determines the size of its footprint, and its height. By contrast, the circular sweep ofHAWT blades dictates that the breadth and height of the rotor swept area are identical. Therefore, whereasincreasing HAWT rotor swept area necessarily increases the turbine footprint, it is possible to increasethe swept area of a VAWT independent of its footprint, by increasing the rotor blade height. Therefore,theoretically, for a VAWT, the power density could be increased indefinitely by increasing the turbine heightuntil it encounters other constraints which would limit its maximum height.

Even though VAWTs have very high power densities compared to HAWTs, the reason why VAWTsnever gained popularity was because most of the VAWTs built so far used fixed blade pitch angle (Fig. 1),and this configuration suffers from very low efficiency especially at low tip speed ratios (TSR) (TSR=bladespeed/wind speed, R/Uinf) and are only self-starting for certain wind directions. Note that, until recently,the efficiency was the biggest concern for wind turbines and the farm power density was less of a factor,because turbines were mostly installed at remote locations where there are no space constraints. However,today, for a small-scale wind turbine to be used in an urban environment, power density is as important

as the turbine efficiency. Therefore, the next generation small-scale turbines need to have not just highefficiencies, but also high power densities. Hence, a VAWT design may be a better starting point thanHAWTs for the design of wind farms with high power density. However, it is important to realize that theefficiency of fixed-pitch VAWTs needs to be improved significantly.

Previous studies have shown that the efficiency of a VAWT could be improved by appropriately mod-ulating the pitch angle of the blade (dynamic pitching) as it moves around the azimuth as shown inFig. 2(a) [1, 36]. However, these studies were not comprehensive enough to fully understand the physicsor optimize the performance of such a concept. Another key barrier in practically implementing such aturbine was developing a simplified blade pitch mechanism. Most of the previous studies proposed mecha-nisms, which were complicated (such as active blade pitching using individual blade actuators) and requiredsignificant amount of power to dynamically vary blade pitch. Other pitching mechanisms that have beendeveloped were passive in nature, and therefore, utilized the inertial and aerodynamic forces acting on theblade to dynamically pitch the blade. Hence, the blade pitch schedule was a function of the operating con-

ditions, leading to very low efficiencies. These are some of the reasons why such a turbine remained elusive,even though, it has the potential to acheive high efficiency (comparable to HAWTs) along with high powerdensity. Therefore, one of the key focuses of the present research was to develop a simplified, practicallyfeasible blade pitching mechanism so that such a turbine could become a reality.

The long-term goal of the present research is to develop a revolutionary, small-scale (diameter of 2meters) variable pitch VAWT (1-2 kW range) with extremely high efficiency and power density to be usedin urban environments such as roof-tops. The turbine should be able to be used individually or in a smallfarm, in which case, the optimal locations of these turbines will have to be determined. The present studyis the first step towards acheiving this goal and is focused on two key ob jectives, which are: (1) developa turbine prototype utilizing a simplified, low-power consumption blade pitch mechanism and demonstrate

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(a) Schematic showing the blade pitch mechanism.

(b) Actual blade pitch mechanism on the VAWT proto-type.

Figure 3. Four-bar based blade pitch mechanism on the present variable-pitch VAWT prototype.

unpopular in the late 1970s, even though they were proven to be self-starting and much more efficient thantheir fixed pitch counterparts as well as even HAWTs. Therefore, a key focus of the present study was todevelop a simplified blade pitch mechanism.

As shown in Fig. 3(a), the present pitching mechanism is based on a four-bar linkage system, whichis designed in such a way that the blade pitches automatically in a cyclic fashion as the turbine rotates.Therefore, the only power penalty incurred in its operation is the frictional losses associated with the moving

components. As shown in the schematic, L1

,L2

,L3

and L4

are the four linkage lengths. The key componentof the pitching mechanism is the offset link of length L2. The pitch links (of lengthL3) are connected tothe end of the offset link on one end and the other end is connected to pointB , on the blade, which is at adistanceL4 behind the pitching axis. The connections at both ends of the pitch link are through pin jointsto allow the rotational degree of freedom. The radius of the rotor forms the linkage length L1. With thisarrangement, as the rotor rotates, the blades automatically pitch, where the pitching amplitude dependson the offset length, L2, when the other linkage lengths remain fixed. The actual pitching mechanismimplemented on the VAWT prototype is shown in Fig. 3(b). The four-bar linkage system can be clearly seenin the figure.

As explained before, the magnitude of the offset (L2) changes the blade pitching amplitude and thedirection in which the offset link is pointing would change the phasing of the cyclic blade pitching as shownin Fig. 4(a). For the sake of simplicity, the present prototype is designed such that the offset length (L2)could not be changed while the turbine is rotating (Fig. 3(b)), which means the blade pitch kinematics (pitch

amplitude,max) is fixed. However, as shown in Fig. 4(a), in the present mechanism, the offset link could berotated to actively change the phasing of the cyclic pitch () depending on the direction of incoming windto maximize efficiency. This method of altering the phasing of blade pitching is instantaneous and muchsimpler than rotating the entire HAWT in the direction of the wind. This capability of the present VAWTpitch mechanism, to immediately respond to a change in wind direction, is the key to maximizing the powerextraction in urban environments where wind direction changes rapidly.

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(a) Adjusting the pitch phasing by rotating the offsetlink to adapt to the change in wind direction. (b) CFD grid system used for the 5 inch radius 4-bladed

cyclorotors with 2.5 inch blade chord.

Figure 4. Four-bar based blade pitch mechanism on the present variable-pitch VAWT prototype and the CFDgrid system.

III. 2D CFD Methodology

A 2-D CFD study was also conducted to understand the flow physics of a variable-pitch turbine. CFDsimulations were performed for the same turbine geometry used in the experimental study at different pitchamplitudes, tip speed ratios and Reynolds numbers (Re). The details of the flow solver and grid system usedin the present study are given below.

A. Flow Solver

2-D simulations of the VAWT were undertaken using a compressible structured overset RANS solver, OVER-TURNS [7]. This overset structured mesh solver uses the diagonal form of the implicit approximate fac-torization method developed by Pulliam and Chaussee [8] with a preconditioned dual-time scheme to solvethe compressible RANS equations. Computations are performed in the inertial frame in a time-accuratemanner. A third-order MUSCL scheme [9] with Roe flux difference splitting [10] and Korens limiter [11]is used to compute the inviscid terms, and second-order central differencing is used for the viscous terms.Due to the relatively low Mach numbers in which the present turbine operate, the inclusion of a low Machpreconditioner based on Turkels [12] method accelerates the convergence and ensures accuracy of the solu-tion. Spalart-Allmaras [13] turbulence model is employed for RANS closure. This one-equation model hasthe advantages of ease of implementation, computational efficiency and numerical stability.

B. Grid System

An overset system of meshes, consisting of C-type airfoil mesh for each blade and a cylindrical backgroundmesh, is used for the computation. The airfoil meshes have 255 55 grid points in the wraparound andnormal directions, respectively. The background cylindrical mesh has 245 221 points in the azimuthal andradial directions, respectively. Implicit hole-cutting method developed by Lee [14] and refined by Laksh-minarayan [7] is used to find the connectivity information between the overset meshes. Figure 4(b) showsthe mesh system used for the present turbine. In these figures, only the field points (points where the flowequations are solved) are shown. All the points that are blanked out either receive information from anothermesh or lies inside a solid body and therefore, does not have a valid solution.

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IV. Results

For a fixed turbine geometry, the two key blade kinematic parameters that significatly affect power extractionon a variable-pitch VAWT are blade pitch amplitude (max) and the pitch phasing () (shown in Fig. 2(a)).However, preliminary experimental and CFD studies have shown that aligning the offset link along thedirection of the wind or zero pitch phasing (=0, as shown in Fig. 3(a)) would maximize power extraction.Therefore, all the results discussed in the present study are for zero pitch phasing, which means the bladeattains maximum pitch angle at the front ( = 90) and rear ( = 270) locations and close to zero pitch

angle at the top ( = 0) and bottom ( = 180) points in the circular blade trajectory. The only twoparameters varied in the present study are blade pitch amplitude (max) and tip speed ratio (ratio of bladespeed to wind speed, T SR = R/Uinf). Pitch amplitude was varied from20 to35 in steps of 5 andthe pitching axis was at the quarter chord. Only symmetric pitch kinematics was investigated in the presentstudy, which means the blade has the same pitch angle variation in the frontal and rear halves. Tip speedratio was varied from around 0.2 (turbine rpm = 158) up to 1.1 (rpm = 870) for experimental studies andup to 1.6 for CFD studies by changing the turbine rotational speed and keeping the wind speed fixed at 10m/s. The wind speed was kept fixed so that the average chord-based Reynolds number would stay the same,which was around 40,000.

A. Methodology

As explained in the previous section, the power extracted by the turbine was calculated from the measured

brake torque (with the electromagnetic brake) and its rotational speed. The inherent assumption here being,once the turbine reaches steady state, the power extracted by the turbine is equal to the braking power.However, the goal of the present experiment was not to measure the net aerodynamic power output of theturbine, but, the complete power extracted by the blades, which does not include the power lost (or parasiticpower) in rotating the rest of the turbine structure such as the endplates, pitch links, etc. Assuming all thepower on a turbine is extracted by the blades, when the turbine reaches the equilibrium speed, the relationbelow should be satisfied.

Pblades= Pbrake+ Pparasite (1)

wherePblades is the power extracted by the blades, Pbrake is the braking power, which is also the measuredpower andPparasite is the parasitic power required to rotate the rest of the rotor structure (excluding blades),which could also include the frictional loses. This relation (Eqn. 1) shows that the measured power (Pbrake) is

not equal to the power extracted by the blades, unless the parasitic power is negligible. Therefore, tare testswere conducted in the wind tunnel by rotating rest of the turbine structure (excluding blades), using a motorat the exact same operating conditions (wind speed = 10 m/s and equilibrium rotational speeds) where eachof the turbine power measurements were taken. The motor power is measured in these experiments fromthe motor torque (obtained using a separate torque sensor) and its rotating speed. The measured motorpower is essentially the parasitic power (or tare power) required to rotate the turbine structure. Then, thisparasitic power (Pparasite) was added to the previously measured brake power (Pbrake) to obtain the totalaerodynamic power extracted by just the blades (Pblades) (Eqn. 1).

If the tare power was not added to the brake power, the measurements would still be useful, because itwould be an indicator of the complete system aerodynamic efficiency. However, such measurements wouldbe very specific to this particular turbine because the rest of the turbine structure could change from oneexperimental setup to another. Also, the results from these experiments need to be used for validatinglower-order aerodynamic models or CFD models, which in most cases would not be able to simulate the

rest of the rotor structure, pitch-links, etc. This would not be an issue while testing a conventional HAWTbecause the parasitic power associated with turbine hub is negligible compared to the power extracted bythe blades.

It is important to note that the parasitic power measured during the tare tests were almost the sameorder as the brake power and therefore cannot be neglected. This means that a significant portion of thepower extracted by the blades is lost in rotating the rest of the turbine structure itself and is thereforewasted. This emphasizes the need for designing more aerodynamically clean turbine structure if the systemefficiency of such a turbine is to be increased.

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0 0.5 1 1.5 20

0.1

0.2

0.3

0.4

Tip speed ratio, TSR

Coefficientofpower,

CP

20

25

30

35

Blade pitch amplitude

Figure 5. Experimental results showing the variation of coefficient of power (CP) with tip speed ratio (TSR)for 20, 25, 30 and 35 blade pitch amplitudes (Reynolds number = 40,000).

0 0.5 1 1.5 20

0.1

0.2

0.3

0.4


Coefficientofpower,C

P

Test data (20)

CFD prediction (20)

(a) Variation of coefficient of power (CP) with tip speed

ratio (TSR) for 20 blade pitch amplitude.

0 0.5 1 1.5 20

0.1

0.2

0.3

0.4



P

Test data (25)

CFD prediction (25)

(b) Variation of coefficient of power (CP) with tip speed

ratio (TSR) for 25 blade pitch amplitude.

Figure 6. Validation of 2D CFD results with the experimental data obtained for 20 and 25 blade pitchingamplitudes (wind speed = 10 m/s).

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B. Experimental Results and CFD Validation

Experimental results showing the variation of coefficient of power (CP) as a function of tip speed ratio (TSR)for20,25,30 and35 blade pitch amplitudes is given in Fig. 5. CP is ratio of the actual powerextracted by the turbine to the total ideal aerodynamic power going into the turbine and is given by Eqn. 2.

CP = Pblades0.5AU3inf

(2)

where Pblades is the total power extracted by the blades (Eqn. 1) and A (b D) is the frontal area ofthe turbine. As shown in Fig. 5, turbines with 20, 25 and 30 blade pitch amplitudes have very similarperformance with 25 producing slightly higher CP values especially at higher tip speed ratios. However,the performance dropped significantly as the pitch amplitude was increased to 35. This could be due tothe blades stalling at higher pitch amplitudes. Also comparing 30 and 35 pitch amplitudes, the tip speedratio at which the maximum CP occurs is much lower for 35 (around 0.6) compared to 30 (close to 1).The 20 and 25 pitch ampliude cases did not reach the optimum CPvalue because turbine speeds could notbe increased above 870 rpm (corresponds to TSR = 1.1) due to some resonance issues in the experimentalsetup.

Note that, only time averaged performance from all the four blades were measured in these wind tunneltests. Therefore, even though these experiments are useful in understanding the average performance of theturbine and how it changes with different parameters, it would not shed any light on the aerodynamics ofeach blade as it moves around the azimuth and how exactly is the power being extracted with such a turbine.This is the motivation for developing the present CFD analysis. However, before the CFD model could beused for understanding the physics, it should be validated with the test data. Figures. 6(a) and 6(b) showsexcellent correlation between the CFD predicted CPvalues and the present test data for 20 and 25 bladepitch amplitudes. Once the model was validated, the next step would be to utilize this model to understandthis concept. However, before that, it is essential to introduce the idea of virtual camber and incidenceeffects (flow curvature effects) experienced by the turbine blades as they move along a circular trajectory.Flow curvature effects play a significant role in the instantaneous aerodynamic forces experienced by theblade especially when the chord to radius is high as in the case of the present turbine (c/R=0.5).

(a) Virtual camber and incidence in a curvilinear flow. (b) Schematic explaining virtual camber.

Figure 7. Schematic explaining virtual camber and incidence (flow curvature) effects.

C. Flow Curvature Effects (Virtual Camber and Incidence Effects)

Virtual camber/incidence effect is an aerodynamic phenomenon that would occur when the blades undergoan orbital motion and therefore experience a curvilinear flow [15,16]. Blades subjected to a curvilinear flow

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behave very differently compared to being immersed in a rectilinear flow (Fig. 7(a)). In a curvilinear flow,the local velocity and angle of attack of the blade are unique at different locations on the chord. Becauseof this, a symmetric blade at 0 pitch angle in a curvilinear flow can be viewed to behave like a camberedblade at an angle of incidence (i) in a rectilinear flow (Fig. 7(a)). This effect will be more pronounced withVAWTs having large chord-to-radius ratio (c/R).

The virtual camber effect is clearly explained using Fig. 7(b) which shows a symmetric airfoil at a pitchangle of 0 at the bottom-most point of the blade trajectory. Point A is the pitching axis of the blade.For the sake of explanation, resultant velocity at any location on the blade chord is assumed a function of

the rotational speed only (the freestream velocity and the pitch rate effects are ignored). Thus, as shownin Fig. 7(b), the magnitude and direction of the resultant velocity varies along the chord. The angle ofincidence of the flow at any arbitrary location on the chord, x, is given by x = tan

1(x/R) (x x/R)and the velocity magnitude is given by R whereR =

R2 + x2.

Now this scenario is approximately equivalent to having a cambered airfoil, with the camber line slope(dy/dx) equal to x in a rectilinear flow of magnitude R as shown in Fig. 7(a). Because of the largechord/radius ratio (c/R=0.5) of the present turbine, using a linear approximation, virtual camber is about6% of chord and the virtual incidence is about 7. Virtual camber is directly dependent on the chord/radiusratio of the turbine and the virtual incidence depends on both the chord/radius ratio and the chordwiselocation of blade pitching axis, which in the present turbine is at quarter chord. Decreasing the distance ofthe blade pitching axis location from the leading edge increases virtual incidence for a fixed chord/radiusratio. For a pitching axis location of 50% chord from the leading edge, the virtual incidence is zero.

0 90 180 270 3600.8

0.6

0.40.2

0

0.2

0.4

0.6

0.8

Azimuthal location, (deg)

Coeffic

ientofpower,CP

20

25

30

Blade pitch amplitude

Power extractedfrom flow

Frontal half Rear half

Power lostto flow

Figure 8. Variation of coefficient of power (CP) for one blade as it goes around the azimuth for 20, 25 and

30 blade pitch amplitudes obtained using CFD (positive CP denotes power extraction and negative CP ispower lost to the flow).

D. Understanding the Physics of Power Extraction

In order to improve the efficiency of this concept, it is important to develop a deeper understanding of itsphysics. The first step was to use the validated CFD model to obtain the power extracted by one blade ona 4-bladed turbine as it goes around the azimuth. Figure 8 shows the variation of CFD-predicted coefficientof power (CP) for one blade as it goes around the azimuth for 20, 25 and 30 blade pitch amplitudes anda tip speed ratio of 1. In this figure, positive CPdenotes power extraction and negative CPis power lost tothe flow. It is interesting to see that the for all the three pitch amplitudes, the blade extracts energy in the

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frontal half of the turbine (=0 to=180), however, puts some of the extracted energy back into the flowin the rear half (=180 to=360).

The power extracted by the blade at any instant, is the product of the instantaneous tangential aero-dynamic force experienced by the blade and the blade speed. If the blade is moving in the same directionas the tangential force, the power is positive or the blade is extracting power and if the blade is movingopposite to the direction of tangential force, the power is negative or the blade is losing energy into the flow.Therefore, it should be possible to explain the power variation shown in Fig. 8 by examining the aerodynamicforces experienced by the blade at different azimuthal locations. Key to obtaining the aerodynamic force is

computing the resultant velocity and blade angle of attack, which could be calculated from blade kinematics,local wind speed and also incorporating the virtual camber and incidence due to the flow curvature effects.The only unknown here is the local wind velocity, which could be obtained from the CFD predicted flowfield.

2.5 2 1.5 1 0.5 0 0.5 1 1.5 2 2.52.5

2

1.5

1

0.5

0

0.5

1

1.5

2

2.5

X distance from center (in radii)

Ydistancefromc

enter(

inradii) Upstream Downstream

Figure 9. Flow profile viewed from top, averaged over a revolution, upstream and downstream of the turbine,where velocity is normalized by Uinf and distance by turbine radius (center of the turbine, X=0 and Y=0).

Figure 9 shows the CFD computed velocity profile across the turbine averaged over a revolution, upstreamand downstream of the turbine, where velocity is normalized by Uinf and distance by turbine radius. Inthe downstream section, the momentum deficit caused due to power extraction could be clearly seen. Thesame information is shown in a more quantitative form in Figs. 10(a) and 10(b), which show the X and Ycomponents of the time-averaged wind velocity, respectively, at different distances upstream and downstreamof the turbine. From, Figs. 9 and 10, it can be seen that there is not much decrease in wind speed aheadof the turbine (X distance = -2, -1.5 and -1 radii). However, after the flow passes the frontal half of theturbine, the free stream velocity drops to almost half its value at least along X axis. Therefore, the flowintersects the blade around = 270 with almost half the speed. It also interesting to see that the flowvelocity increases slightly as it passes across the rear half (Xdistance = 1 radius) which is consistent withpower lost to the flow in the rear section (Fig. 8).

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1 0.5 0 0.5 1 1.5 23

2

1

0

1

2

3

Normalized velocity (Xcomponent), U/Uinf

Ydistancefro

mc

enter(inradii)

2

1.5

1

0.50

0.5

1

1.5

2

X distance fromcenter (in radii)(ve upstream,+ve downstream)

Momentumdeficiencydownstream

(a) Velocity component along Xaxis (U).

0.5 0 0.5 1 1.53

2

1

0

1

2

3

Normalized velocity (Ycomponent), V/Uinf

Ydistancefro

mc

enter(inradii)

2

1.5

1

0.50

0.5

1

1.5

2

X distance fromcenter (in radii)(ve upstream,+ve downstream)

(b) Velocity component along Y axis (V).

Figure 10. Variation of X and Y velocity components (U and V) across the turbine diameter (along Y axis)averaged about one revolution.

Having obtained the average flow velocities across the turbine, it is now possible to calculate the resultantvelocity and the blade angle of attack at different azimuthal locations, which could be used to explain themagnitude and direction of the blade forces. Figure 11 shows the CFD predicted flowfield (pressure contourswith streamlines superimposed) with relative flow velocities and blade forces for a turbine operating at 25

blade pitch amplitude at tip speed ratio (TSR) of 1. Note that, the length and direction of the arrowsdenoting the different velocity components are proportional to the actual velocity vectors. The figure alsoshows the virtual blade with the induced camber and incidence, which could increase or decrease the effectivepitch angle of the blade, depending on the azimuthal location. For the pressure contours, the pressure isnormalized with the free stream static pressure or the atmospheric pressure.

It was shown in Fig. 8 that the maximum power extraction occurs in the frontal half especially close to = 90. Therefore, it is important to closely examine the flowfield around the blade and forces experienced

by the blade at = 90

using Fig. 11. As shown in the figure, at this location, because of the large angleof attack and significant virtual camber, the blade produces a high lift force which is shown by the largelow pressure region (denoted by blue) on top of the blade. A significant component of this lift force wouldcontribute to the blade tangential force which is also in the same direction of the blade motion, leading toa high positive power or power extraction. Figure 8 also showed that the blade loses energy to the flow inthe rear half of the turbine and the power loss is maximum around = 270 . Even this could be explainedfrom Fig. 11. From the figure, it can be seen that, at = 270, the virtually cambered blade operates ata very small angle of attack, however, the camber would increase lift which is acting in such a directionthat the tangential force is opposite to the direction of blade motion and hence produce negative power (orpower is lost to the flow). The resultant velocity at this location was calculated assuming that the flowvelocity is decreased by half, which was observed previously from Figs. 9 and 10. It is also interesting to seethat in all these cases the flow curvature effects (virtual camber and incidence) helps in slightly improvingpower extraction in the frontal half, however, it greatly increases the power loss in the rear half. In such a

case, it might be better to have blades with smaller chord/radius ratio on these type of VAWTs to improveperformance in the rear. Even better would be to have cambered blades, such that it which would enhancethe camber in the frontal half and nullify the camber in the rear. Instead of having symmetric pitching, anon-zero mean pitch angle might also improve performance.

In the previous two azimuthal locations, only lift force was considered because no blade stall was observedin the CFD analysis and therefore the lift force is much higher than the drag force. However, at = 0,even though the lift force is high because of large resultant speed, there is no component in the tangentialdirection and hence does not contribute to power. However, there was a slight negative power at this location(Fig. 8) because of the drag force acting opposite to the blade motion. At = 180, the power is almost

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(a) Pitch amplitude = 20. (b) Pitch amplitude = 30.

Figure 12. CFD predicted flowfield (pressure contours with streamlines superimposed) for a turbine operatingat 20 and 30 blade pitch amplitudes at tip speed ratio (TSR) of 1.

0 90 180 270 3601

0.5

0

0.5

1



P

0.6

1.0

1.4


TSR


Power lostto flow

Figure 13. Variation of coefficient of power (CP) for one blade as it goes around the azimuth at 25 blade

pitch amplitude for tip speed ratios (TSR) of 0.6, 1, and 1.4, obtained using CFD (positive CP denotes powerextraction and negative CP is power lost to the flow).

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(a) Tip speed ratio (TSR) = 0.6. (b) Tip speed ratio (TSR) = 1.4.

Figure 14. Physics of power extraction for different tip speeds ratios explained using simple aerodynamicsand the CFD predicted flowfield for a variable-pitch turbine operating at a 25 blade pitch amplitude.

important to look more carefully at the CFD results to understand the reason behind this.Figures 14(a) and 14(b) explains the physics at advance ratios of 0.6 and 1.4 respectively, using the CFD

measured flow field. Figure 13 shows that the power extracted by the blade at 90 azimuthal location (front)is almost three times higher at TSR = 1.4 compared to 0.6. In Fig. 14(a), at =90, it can be seen that theblade is operating at an extremely high angle of attack and is probably close to stall. Based on the pressurecontours, the vortex on top of the blade is close to being shed. This means lower lift and higher drag valuesand drag has a tangential component opposite to the direction of blade motion, unlike lift. Along with thelower lift to drag ratio in this case, it should be noted that the resultant velocity itself is much smaller thanthe TSR = 1.4 case because of the lower rotational speed of the turbine and hence the actual magnitudes oflift and drag are smaller. The smaller tangential force coupled with the fact that the blade itself is movingslower would result in much lower power extracted compared to a higher TSR case.

Examining the 90 azimuthal location in Fig. 14(b) (TSR = 1.4), it can be seen that the blade angle ofattack is much below stall, which would increase the lift to drag ratio compared the lower TSR case, whichalong with the higher resultant velocity would result in a higher tangential force in the direction of motion.Higher tangential force coupled with higher blade speed would significantly enhance power extraction.

It would be also interesting to see what happens at rear half of the turbine specifically at 270 azimuthallocation, where the higher tip speed ratio case (TSR = 1.4) is losing significant amount of power back into theflow, whereas the almost no power is lost for the lower TSR case (TSR = 0.6) (Fig. 13). Examining =270

location for the 0.6 TSR case from Fig. 14(a), it can be seen that, based on the direction of resultant velocity,the blade is close to zero lift angle of attack, and this could be the reason why the blade is not producing anylift as shown by the CFD pressure contours. However, the blade could be producing a small drag force and

that could be the reason for the small negative power at =270

in Fig. 13. However, examining =270

location for the 1.4 TSR case (Fig. 14(b)), it can be seen that the blade is operating at an angle of attackwhich would produce a high lift to drag ratio. Unfortunately, at this location, both lift and drag forcescontribute to a tangential force opposite to the direction of blade motion and hence leads to large negativepower.

F. Variable Pitch versus Constant Pitch

Having understood the operating principle of a variable-pitch VAWT, it would be interesting to compareit to a fixed-pitch VAWT and also try to understand the reason for the lower efficiency with the latter

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configuration. Even though, an attempt was made to perform wind tunnel experiments on a fixed-pitchturbine, the results were not consistent because of the extremely low values of the torque and rotationalspeed measured at 10 m/s wind speed. Therefore, the CFD analysis was used to investigate the fixed-pitchVAWT concept.

Figure 15(a) shows the variation of coefficient of power (CP) with tip speed ratio (TSR) for fixed-pitch andvariable-pitch turbines. In this case, the variable-pitch turbine was operating at20 pitch amplitude andthe fixed-pitch at +20 constant pitch angle. As shown in the figure, the fixed-pitch turbine had extremelylow efficiency and at higher TSRs, it was operating at negative CPs which would not be practically feasible.

To understand this, it is important to look at the time history of power extraction for one blade, which isshown in Figure 15(b) for TSR = 1. As shown in the figure, for the fixed-pitch turbine, much less power isextracted in the front and slightly more power is lost to the flow in the rear.

0 0.5 1 1.5 20.4

0.2

0

0.2

0.4


Coefficien

tofpower,C

P

Variable pitch, 20(CFD)

Constant pitch, +20(CFD)


ratio (TSR) for fixed-pitch and variable-pitch turbines.

0 90 180 270 3600.6

0.4

0.2

0

0.2

0.4

0.6



P

Variable pitch, 20(CFD)

Constant pitch, +20(CFD)



Power lostto flow

(b) Variation of coefficient of power (CP) for one blade asit goes around the azimuth on fixed-pitch and variable-pitch turbines for TSR = 1, obtained using CFD (pos-itive CP denotes power extraction and negative CP ispower lost to the flow).

Figure 15. Coefficient power (CP) for variable- (20

pitch amplitude) and fixed-pitch (+20

fixed pitch angle)turbines obtained using CFD.

It is important to look at the blade aerodynamics and flowfield (Figure 16) to explain this behavior. Itis important to first examine the flow in the rear because the blade pitch angle for the fixed-pitch case at=90 (front) is similar to the variable-pitch case. However, in the rear (=270), as shown in Fig. 16 theblade is pitched in the direction opposite to that of the variable-pitch case. Because of this, the blade isoperating at reverse camber and also at a large angle of attack leading to massive flow separation as shownby the pressure contours and even the streamlines near the blade. This could lead to a huge drag force,resulting in a large tangential force opposite to the blade motion leading to negative power. However, in thefront (=90), the basic flow physics for the fixed pitch case is not very different from the variable pitchcase (Figure 11). Even then the power extraction at =90 was much lower than the variable-pitch case(Fig. 15(b)). This could be because of the fact that massive bluff-body type of separation in the rear half

for the fixed-pitch case is even affecting the flow upstream in the frontal half. This can be confirmed byexamining the streamlines from the front to rear half, near the center of the turbine.

This clearly shows the importance of blade pitch modulation in avoiding blade stall in the rear halfof the turbine, which not only affects the flow in the rear, but also in the front. This is the reason forthe huge performance enhancement obtained by dynamically pitching the blades. However, this study onlyinvestigated one pitch angle for the fixed-pitch VAWT and therefore, performance could be improved, maybe with a smaller pitch angle. Even then, the flow separation in the rear half would not be easy to avoidespecially when the blades have large chord/radius ratio (large reverse camber in the rear). From theseobservations it is not difficult to conclude that the performance of a fixed-pitch turbine could be enhancedby reducing the pitch angle and chord/radius ratio, or by using cambered blades. Fixed pitch turbine could

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Figure 16. Physics of power extraction explained using simple aerodynamics and the CFD predicted flowfield

(pressure contours with streamlines superimposed) for a turbine operating with a fixed 20

blade pitch angleat tip speed ratio (TSR) of 1.

(a) Variable-pitch turbine. (b) Fixed-pitch turbine.

Figure 17. Complete flowfield (pressure contours with streamlines superimposed) of variable and fixed pitchturbines.

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also perform better at higher tip speed ratios because it could reduce the angle of attack in the rear half andavoid stall.

Figures 17(a) and 17(b) show the entire flowfield for a variable-pitch and fixed-pitch turbine. Streamtubeexpansion could be clearly seen in these figures, which denotes power extraction from the flow. However,note that, the flow is extremely chaotic for the fixed-pitch VAWT and very orderly for the variable-pitchcase, which is also an indication of the relative inefficiency of the fixed-pitch concept. Another importantconclusion from this result is that, if these turbines are going to be used in a farm configuration, wherethe turbines will be placed close to each other, it would be very unattractive to have a fixed-pitch turbine

because of the chaotic wake.

0 0.5 1 1.5 20

0.1

0.2

0.3

0.4



P

40,000

100,000

200,000

300,000

Reynolds number


ratio (TSR) at different Reynolds numbers.

0.4 1 2 3 4

x 105

0.28

0.3

0.32

0.34

0.36

Reynolds number

MaximumCP

(b) Variation of maximum coefficient of power (CPmax)as a function of Reynolds number.

Figure 18. Coefficient power (CP) for variable-pitch turbine operating at 25 pitch amplitude for different

Reynolds numbers obtained using CFD.

G. Effect of Reynolds number

Scalability of the experimental results is a major concern in wind turbine experimental research because mostwind tunnel studies are carried out at much lower Reynolds numbers than the actual turbine. As discussedin the beginning, the long-term goal of the present research is to develop a small-scale turbine (around 2meters in diameter) with a peak power output of close to 1-2 kW. Such a turbine would operate at a Reynoldsnumber around 200,000, whereas all the current experimental studies were conducted at a Reynolds numberof 40,000. Therefore, CFD studies were conducted at different Reynolds numbers to examine if the physicsis very different at higher Reynolds numbers.

Figure 18(a) shows the variation of coefficient power (CP) with tip speed ratio for variable-pitch turbineoperating at25 pitch amplitude at Reynolds numbers of 40,000, 100,000, 200,000 and 300,000. Eventhough the trends remain the same, as shown in Fig. 18(b), the maximum achievable CP increases withReynolds numbers. It can be seen that the rate of increase in CPmax with Reynolds number decreaseswith increase in Reynolds numbers. Figure 19 shows the azimuthal variation ofCP for different Reynolds

numbers. The power extraction improves with increasing Reynolds number in the frontal half, however,Reynolds number has no effect in the rear half. This could be because of the fact that in the present turbine,the blade is operating at relatively higher angle of attack in the frontal half (as shown in Fig. 11) wherethe Reynolds number would have an effect on blade lift and drag coefficients. However, in the rear half theangles of attack are much smaller (Fig. 11), in which case the Reynolds number would have low influence.

Figures 20(a) and 20(b) shows the CFD predicted pressure contours with streamlines for Reynolds num-bers of 40,000 and 300,000, respectively. It can be seen that the flowfields are very similar except at =90,where the low pressure region on top of the blade is slightly stronger at 300,000 Reynolds number which isdue to the higher lift producing capability of the blade at higher Reynolds numbers. This is also the reason

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0 90 180 270 3600.8

0.6

0.4

0.2

0

0.20.4

0.6

0.8


Coefficientofpower

,CP

40,000

100,000

200,000

300,000


Reynolds number


Power lostto flow

Figure 19. Variation of coefficient of power (CP) for one blade as it goes around the azimuth at 25 blade

pitch amplitude for a tip speed ratio (TSR) of 1 at different Reynolds numbers, obtained using CFD (positiveCPdenotes power extraction and negative CP is power lost to the flow).

(a) Reynolds number = 40,000. (b) Reynolds number = 300,000.

Figure 20. CFD predicted flowfield (pressure contours with streamlines superimposed) for a turbine operatingat 25 blade pitch amplitude and TSR = 1, at two different Reynolds numbers.

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for the higher power extraction in the frontal half. However, overall, there was no fundamental differencein flow physics with Reynolds numbers, which indicates that the experimental results at lower Reynoldsnumbers are in fact scalable to full scale Reynolds numbers (200,000).

V. SUMMARY AND CONCLUSIONS

The present study focuses on utilizing a combined experimental and computational (2-D CFD) approach to

investigate the performance of a VAWT utilizing dynamic blade pitching, operating at a Reynolds number ofaround 40,000. A VAWT prototype with a simplified blade pitch mechanism was designed, built and testedin the wind tunnel to understand the role of blade pitching kinematics on turbine aerodynamic efficiency.Only symmetric pitch kinematics (zero mean pitch angle), with zero pitch phasing (maximum pitch angleoccurs in front (=90) and rear (=270)), was investigated in the present study. A 2-D CFD model wasdeveloped and the model predictions correlated extremely well with test data. The validated CFD modelwas used to develop a fundamental understanding of the physics of power extraction on such a turbine. Thefollowing are specific conclusions drawn from this study:

1. A novel simplified passive blade pitching mechanism has been developed for the present VAWT proto-type, where the blade pitching is kinematically coupled to turbine rotation. In the present mechanism,the phasing of blade cyclic pitching could be actively changed depending on the direction of incomingwind to maximize efficiency. This method of altering the phasing of blade pitching is instantaneous

and much simpler than rotating the entire HAWT in the direction of the wind. This capability of thepresent VAWT pitch mechanism, to immediately respond to a change in wind direction, is the key tomaximizing power extraction in urban environments where wind direction changes rapidly.

2. Both experimental and CFD studies showed that the turbine efficiency is a strong function of bladepitching amplitude, with the highest efficiency occurring around20 to25 amplitude. It was alsoimportant to see that the optimum tip speed ratio for maximum efficiency decreased with increasingpitch amplitude.

3. For all the pitching amplitudes described in the present study, it was observed that the blade extractsall the power in the frontal half, however, it loses power back into the flow in the rear half. One keyreason for this is the large virtual camber and incidence induced by the flow curvature effects, whichslightly enhances the power extraction in the frontal half, but greatly increases the power loss in therear half. In such a scenario, it might better to have blades with smaller chord/radius ratio on these

type of VAWTs to improve performance in the rear. Even better would be to have cambered blades,such that it would enhance the camber in the frontal half and nullify the camber in the rear.

4. Increasing the tip speed ratio for a variable-pitch turbine increased the power extraction in the frontbut also increased power loss in the rear. The reason for this is the increase in magnitude of the forcesand blade speed with increasing TSR. Also, the optimum TSR for maximum power extraction was afunction of blade kinematics.

5. For the same pitch angle (20), a fixed pitch turbine had lower efficiency than the variable pitch turbineowing to the massive blade stall in the rear half caused by the large angle of attack and high reversecamber. This large flow separation was even affecting the flow field in the frontal half. Again, theperformance of the fixed-pitch turbines could be enhanced by reducing the pitch angle and chord/radiusratio, or by using cambered blades. Fixed pitch turbine could also perform better at higher tip speed

ratios because it could reduce the angle of attack in the rear half and avoid stall.6. The CFD study showed that the maximum achievableCPfor the turbine increases with higher Reynolds

numbers. However, the rate of increase decreased with increasing Reynolds numbers. For an increaseof Reynolds number from 40,000 to 300,000, there was an increase in maximum power of about 15%.The reason for this increase is because of the increased power extraction in the frontal half at higherReynolds numbers resulting from the blades operating at higher lift-to-drag ratio. The power in therear half remained relatively unchanged with increasing Reynolds number for the pitching kinematicsinvestigated in the present study.

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VI. ACKNOWLEDGEMENT

Authors would also like to thank Professor Allen Winkelmann for providing the opportunity to conductexperiments in the open-jet wind tunnel facility at the University of Maryland.

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Documents

Fundamental Understanding of the Physics of a Small-Scale Vertical Axis Wind Turbine with Dynamic Blade Pitching: An Experimental and Computational Approach