Post-stall airfoil performance and vertical-axis wind turbines

Post-stall airfoil performance and vertical-axis

wind turbines

John Rainbird∗, Joaquim Peiro† and J. Michael Graham‡

Imperial College, London, SW7 2AZ, United Kingdom

Abstract

Sensitivity of VAWT start-up to aerofoil aerodynamic performance char-

acteristics is analyzed. Existing post-stall aerofoil data and the corrections

used in acquiring it are critiqued. Uncertainties in the existing data large

enough to impact on VAWT start-up modeling are established, with wind

tunnel blockage identified as a potential cause of the discrepancies. Using

a conventional closed-section wind tunnel with blockage corrections applied

to data and a passive, tolerant test section design, tests are conducted on

five NACA 0015 aerofoils with a range of chord lengths. The passive tunnel

was found to be better at minimizing the effects of blockage and it makes

no use of correction formulae which are not strictly applicable when flow is

separated since they are based on potential flow theory. Preliminary results

are presented from a study varying Reynolds number showing little varia-

tion in post-stall performance for the NACA 0015 in the range of Reynolds

numbers from 6× 104 to 2.5× 105.

∗Graduate Student, Department of Aeronautics; [email protected]. AIAA Student

Member.†Senior Lecturer, Department of Aeronautics, [email protected].‡Professor of Unsteady Aerodynamics, Department of Aeronautics,

[email protected]. AIAA Member.

1

Nomenclature

c chord, m

g gap between slat aerofoils in tolerant tunnel, m

p plenum depth, m

s spacing between slat aerofoils, m

t aerofoil thickness, m

Ae model equivalent area, m2

Cd drag coefficient

Cl lift coefficient

Cm moment coefficient about the quarter chord

DS double slatted wall tolerant test section

H tunnel test section height, m

HAWT horizontal axis wind turbine

L tunnel test section length, m

OAR open area ratio

Re Reynolds number

SS single slatted wall tolerant test section

VAWT vertical axis wind turbine

Subscripts

u uncorrected measurement

Symbols

α angle of incidence, degrees

εsc solid blockage factor

εwc wake blockage factor

λ tip-speed ratio

σ standard deviation

A aspect ratio

1 Introduction

When measuring the forces generated by an aerofoil in a closed test-section wind

tunnel experiment, readings are influenced by by factors such as the turbulence

intensity of flow in the wind tunnel, the aspect ratio, A, of the wing under test

(this can impact even two-dimensional tests), the chord-to-height ratio, c/H, of the

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aerofoil and tunnel, and the length-to-height ratio, L/H, of the tunnel test section.

Through good experiment design and by application of blockage corrections to raw

experimental measurements, the effects of these factors can be minimized, allowing

data close to that expected in equivalent free air conditions to be achieved.

Wind tunnel testing of aerofoils does not usually extend much beyond the

range of incidences −20° ≤ α ≤ +20°, since in most applications aerofoils are

not expected to encounter stall, which occurs at incidences of around 10° - 15°.The blades of wind turbines are a notable exception during the start-up phase of

operation, with the inner regions of horizontal axis wind turbine (HAWT) blades

and the full length of vertical axis (VAWT) blades experiencing apparent incidences

well beyond these limits at low tip-speed ratios, λ. VAWT performance can be

sensitive to minor changes to blades and VAWT modeling techniques are similarly

sensitive to small differences in input blade force data, making accurate post-stall

data critical for the analysis of these machines.

In the range of incidences covered in conventional wind tunnel testing, aerofoils

are near-parallel to flow, so blockage of the tunnel flow is minimal. Flow is for

the most part attached, allowing blockage corrections, based partly on potential

flow theory, to be applied with confidence [1]. Once testing extends past stall, flow

detaches, reducing the applicability of these corrections, with blockage higher due

to the greater area of aerofoil presented normal to the flow.

There is a lack of aerofoil data covering a full range of incidences (0° to 180°for symmetrical aerofoils, 0° to 360° for others), particularly at the low Reynolds

numbers relevant to the modeling of start-up of a VAWT. Differences between

the data sets found are significant to the outcomes of such modeling. This paper

documents an attempt to achieve the best possible post-stall data at low Reynolds

numbers using conventional wind tunnels and a tolerant tunnel test section, applied

to deeply stalled aerofoils for the first time.

In this paper, the term “post-stall” is used to refer to aerodynamic character-

istics in the range of incidences between stall angles, approximately ±10° ≤ α ≤±170°. The term “deep stall” refers to the range of incidences ±20° ≤ α ≤ ±160°and “the immediate vicinity of stall” to 10° < α < 20°.

3

(a) Aerofoil coefficients [2] (b) Turbine CQ envelope

(c) Turbine start-up behaviour

Figure 1: Effects of small changes in post-stall lift on VAWT performance.

2 Sensitivity of VAWT start-up behavior to aero-

foil data

Using Strickland’s multiple-streamtube BEM VAWT model [3] with aerofoil coef-

ficients based on Sheldahl and Klimas’s widely-used dataset [2] the sensitivity of

VAWTs to uncertainty in post-stall performance can be demonstrated. Fig. 1(a)

shows lift and drag coefficients, Cl and Cd, against α for the NACA 0018 aerofoil,

where Cl type A is per the reference, but type B has been artificially modified to

exhibit 10% lower post-stall peaks in Cl (at α ≈ 45°, 135°). Fig. 1(b) shows the

resulting plots of turbine torque coefficient CQ against λ from the BEM code using

Cl types A and B (the same Cd data, per the reference, was used for both runs).

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Fig. 1(c) contains results from a time-dependent extension to the code showing

development of λ with time from a standing start. The change in post-stall be-

havior leads to a prediction of negative torque production at 0.5 < λ < 1.7. The

turbine is unable to self-start to full rotational velocities, reaching only this first

λ = 0.5 limit of positive torque, in spite of a peak in positive torque production

identical to the unaltered case, at λ = 3.5, and the same upper limit in positive

torque at λ = 6.7. Hill et al. [4] demonstrated similar large impacts on modelled

turbine performance with small changes to lift and drag coefficient input.

In this paper, self-starting ability is defined after Bianchini et al. [5] as when a

turbine accelerates through its entire power curve to its fastest equilibrium state

unaided. Even though the turbine using Cl type B rotates under its own power,

it does not self-start by this definition.

3 Existing Aerofoil data

Few studies have been found that extend over a full range of incidence angles

for any aerofoil profile. All of those that have been found for the NACA 0015,

namely those of Pope [6] and Sheldahl and Klimas [2] are reproduced in Figs 2

and 3, which show Cl and Cd against α respectively. Alongside them are some

results from the current study, for an aerofoil with a c/H of 0.1, and the output of

NASA’s AERODAS model [7] for an infinite aspect ratio, 15% thick aerofoil. Thin

aerofoil theory lift is included in Fig. 2. Pope’s study has c/H = 0.17 and Sheldahl

and Klimas’s is 0.07, so they are similarly blocked to the results of the the current

study included in the figures. All three studies have used techniques to minimize

the impacts of lift interference, solid blockage and wake blockage. The current

study follows the correction methodology explained in Section 4 and Sheldahl and

Klimas use similar methods. Pope used a tunnel equipped with a “breather” to

atmosphere that reduced solid and wake blockage, so the data was corrected for

lift interference only.

The current study was taken at a Reynolds number, Re, of 1.5× 105, Sheldahl

and Klimas’s at Re = 3.6× 105 and Pope’s at Re = 1.23× 106. Reynolds number

dependency is evident in the pre-stall results, with higher maximum Cl reached at a

higher incidence the higher the Reynolds number, with Pope reaching Clmax = 1.20

at α = 15°, Sheldahl and Klimas Clmax = 1.07 at α = 13.7° and the current study

5

Figure 2: Cl vs α for selected post-stall studies.

Clmax = 0.93 at α = 12°. After stall, agreement between Sheldahl and Kilmas and

the c/H = 0.1 is strong, other than for Cd in the range 80° < α < 110°, where

Sheldahl and Kilmas’s results are less smooth. Post-stall lift and drag peaks are

lower for the Pope study, with the lift peaks occurring at approximately 50° and

145° rather than 45° and 140° as for the other studies. These differences are likely

due to the differences in methods used for blockage minimization. A Reynolds

number dependency is hard to discern in the post stall region from this limited

sample size.

Before stall, the AERODAS model replicates performance of chosen exper-

imental data, here that of Sheldahl and Klimas has been used. After stall, a

universal model is applied based on thickness ratio, t/c, andA, with lift and drag

represented as hyperbolic distributions around calculated peaks:

Clmax = 1.190(1.0− (t/c)2

) (0.65 + 0.35e(−(9.0/A)2.3)

)Cdmax = 2.3e(−(0.65t/c)0.9)

(0.52 + 0.48e(−(6.5/A)1.1)

) (1)

The model is based on an assumption that post-stall aerofoil performance is inde-

pendent of Reynolds number (note that there is no input based on flow conditions),

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Figure 3: Cd vs α for selected post-stall studies.

a view that is supported by Sheldahl and Klimas’s study, which features runs at

Re = 5× 105 and Re = 6.8 × 105 as well as the Re = 3.6 × 105 reproduced here,

with no significant differences between the runs noted in the deep stall region.

Given the limited amount of NACA 0015 data available, NACA 0012 studies

covering a full range of incidences have also been reviewed. The similarity of the

two profiles means that performance in deep stall should also be similar. Fig. 4

shows a composite plot of the three studies included in Figs 2 and 3, alongside

those of Bergeles et al. [8], Critzos et al. [9], Massini et al. [10] and Sheldahl and

Klimas [2] for the NACA 0012. AERODAS output for a 15% thick aerofoil and

thin aerofoil theory Cl are again included. Further details of the studies included in

the figure, along with the rest of the data from the current study and an additional

study of Jacobs [11] referred later on in this paper, are summarized in Table 1.

Note that the study of Critzos et al. features two runs using the same apparatus,

at Re = 5 × 105 and Re = 1.36 × 106, with higher post-stall lift and drag peaks

exhibited for the higher Reynolds number.

Pre-stall agreement of the studies is strong, with lift at low incidences in all

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Figure 4: Cl and Cd vs α for the c/H = 0.1 aerofoil from this study, alongside

the studies of Bergeles et al [8], Critzos et al [9], Massini et al [10], Sheldahl and

Klimas [2] and Pope [6]

cases comparable to thin aerofoil theory, but post-stall agreement is generally poor.

At the second lift peak at an approximate incidence of 45°, values of Cl are spread

between extremes of 0.98 and 1.18, a difference of 20%. At peak drag at around

90°, Cd is between 1.81 and 2.08, a 15% variation. AERODAS output is at the

upper end of the spread of data. The wide variety of Reynolds numbers at which

the studies were taken make comparisons in the vicinity of stall unwise, given

the sensitivity of performance to this variable here. The modeling presented in

Section 2 shows that a 10% difference in post-stall lift peaks is sufficient to alter

the output of a BEM code from prediction of self-start to non-prediction, below

the level of uncertainty between data sets reproduced here. These uncertainties are

perhaps the reason that numerical models of VAWTs can struggle to predict the

successful self-starting of straight-bladed VAWTs with symmetrical blades without

some additional modification to input aerofoil data [12, 5], in spite of experimental

evidence that self-starting does occur [4, 13, 14].

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Source Post-stall peak Re c/H A

Cl Cd (×106)

NACA 0012 studies

Bergeles et al. [8] 1.08 1.90 0.76 0.14 1.70

Critzos et al. LTPT [9] 1.13 2.08 1.80 0.07 6.00

Critzos et al. LTPT [9] 1.15 1.96 0.50 0.07 6.00

Critzos et al. Langley 7 × 10

[9]1.14 2.07 1.36 0.10 7.00

Massini et al. [10] 1.18 1.99 0.96 0.13 2.00

Sheldahl and Klimas [2] 1.10 1.83 0.36 0.07 6.00

NACA 0015 studies

c/H = 0.10 (this study) 1.07 1.85 0.06 0.10 10.00

c/H = 0.10 (this study) 1.06 1.86 0.15 0.10 10.00

c/H = 0.10 (this study) 1.06 1.82 0.25 0.10 10.00

c/H = 0.15 (this study) 1.02 1.84 0.15 0.15 6.67

c/H = 0.20 (this study) 1.04 1.83 0.15 0.20 5.00

c/H = 0.25 (this study) 1.09 1.83 0.15 0.25 4.00

c/H = 0.30 (this study) 1.18 1.82 0.15 0.30 3.33

Jacobs [11] - - 0.17 0.081 6.001

Pope [6] 0.98 1.81 1.23 0.17 1.67

Sheldahl and Klimas [2] 1.05 1.86 0.36 0.07 6.00

Table 1: Summary of studies referenced in this paper.

The studies reproduced in Fig. 4 are, to the best of the authors’ knowledge,

all of those available on symmetrical aerofoils for a full range of incidences, other

than the very low Reynolds number work of Zhou [15] and Poisson-Quiton and

de Sievers’s study [16] for which no information about experimental configuration

could be found. Both use the NACA 0012. See Lindenberg [17] for a more complete

1Studies were conducted in a cylindrical test section with a finite wing

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review of post-stall research, including cambered profiles.

Reynolds number effects alone cannot be responsible for the variation in post-

stall performance seen between the referenced studies, given the non-linearity of

the relationship between it and lift and drag peaks Table 1. For example, the

study of Massini et al.[10] has the highest lift peak, but two Critzos et al. studies

were taken at higher Reynolds numbers. Note though that if the two studies of

Critzos et al. (denoted LTPT in Table 1) and that of Sheldahl and Klimas for the

NACA 0012 are isolated, the impact of other variables can be ignored, since they

share common c/H,A and aerofoil profile. These do seem to suggest that higher

post-stall peaks occur with higher Reynolds number

As mentioned before, the influence of secondary effects on experiments can

be minimized through sensible apparatus design. Introduction of suitable screens

and honeycomb inserts in a wind tunnel with a suitably large contraction ratio

can minimize turbulence in the flow. Ensuring a test section is long enough to

isolate the model under test from flow features caused by the contraction limits

any problems associated with the length-to-height ratio of the tunnel working

section.

End wall effects can introduce some three-dimensionality to separated flow

of an otherwise 2D experiment, leading to the formation of stall cells. These

occur as the stall develops and generate some downwash effects. Aspect ratio of

the aerofoil under test can therefore impact on the lift coefficient around stall.

End wall effects can be limited by using a high A aerofoil, or by utilizing end-

plates to isolate aerofoils from the wind tunnel boundary layer. If these are not

practical, consideration of how stall cells will form on the aerofoil when designing

an experiment (by applying the findings of Weihs and Katz [18], for example) can

also help.

It is not always practical to limit blockage through similar means. Large wind

tunnels are costly to build and operate, while small aerofoils are difficult to man-

ufacture accurately and require faster flows than larger ones to attain the same

Reynolds numbers. Blockage corrections are instead used to process blockage ef-

fects out of results taken in closed jet wind tunnels. Less conventionally, similar

corrections can be used with results taken in open-jet tunnels, or blockage tolerant

test sections can be used. The c/H ratio is an indicator of blockage. The results

summarized in Table 1 suggest that blockage may be affecting them even after the

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application of corrections.

4 Blockage corrections

Results for this study taken in conventional closed test sections have been corrected

for lift interference, solid blockage and wake blockage using the formulas given in

ESDU 76028[1], modified for use at extreme incidence angles as follows.

The solid blockage factor, εsc is prescribed in the reference[1], as

εsc =πAe

6H2

[1 + 1.2

(t

c

)] [1 + 1.1

(ct

)αu

2]

(2)

where Ae is the equivalent area of the model (the area of the two-dimensional aero-

foil section) and t is its thickness, and αu is uncorrected incidence in radians. The

“incidence effect factor” contained in the second set of square brackets quantifies

the impact of model incidence on blockage. As the impact reduces with increasing

incidence at α > π/2, it has been modified at α > π/2 to[1 + 1.1

(ct

)(π − αu)2

](3)

Total blockage (εsc + εwc, where εwc is the wake blockage factor) is assumed by

ESDU to be small enough to neglect terms of its square. These have been restored

for the current study as the assumption does not hold post-stall. Compressibility

factors have been omitted throughout due to the low Mach numbers of experiments

(< 0.1).

5 Limitations of corrections

As mentioned, corrections are based on potential flow theory and so are limited

by the assumptions of the theory. Flow is assumed to be inviscid, suitable for

the Reynolds numbers of the studies in Table 1 away from boundary layers, and

incompressible, suitable as Mach numbers are below 0.3. The aerofoil is taken to

be small in relation to the tunnel, since it is modeled by a combination of a single

source, vortex and doublet in the derivation of the corrections. This does not

hold true for larger c/H ratios, with ratios that would be acceptable for pre-stall

aerofoil testing being less so at extreme incidences due to the larger area presented

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normal to flow. Use of potential flow theory also requires an assumption that flow

is attached, which is not the case beyond stall.

Use is still made of corrections where separation exists - the ESDU corrections

used here are partly based on Maskell’s empirical corrections for bluff bodies and

stalled wings [19] so they are, in part at least, suitable for such applications.

ESDU state that use has been made of the corrections for flows with “some degree

of separation”, but that “they should clearly be used with caution” [1] in these

conditions. They also state that use is commonly made of the corrections with c/H

ratios of up to 0.35 [1] (the largest in this study is 0.3) but it should be noted that

this almost certainly applies to experiments covering a narrow range of incidences.

6 The tolerant tunnel

An alternative to blockage corrections which is more compatible with separated

flows and larger blockage is the use of tolerant wind tunnel test sections. ESDU

provide corrections for open jet wind tunnels [1] which are of an opposite sign to

those for closed jets. It stands to reason therefore that by using test sections with

semi-permeable walls blockage constraint can be minimized.

The tolerant test section used in this study is based on the design of Parkinson

[20]. Certain sections of tunnel wall are replaced with aerofoil shaped slats run-

ning perpendicular to flow, with slots between them through which air can enter

and exit the main test section, see Fig. 5, avoiding blockage caused by the model

under test. The slats are aerofoil shaped to limit the risk of flow separation around

them which would impede readings taken from the model. Plenums of stagnant

air enclose the permeable walls to ensure conservation of mass flow is maintained.

The bi-dimensionality of the design inhibits the development of significant trans-

verse flows, which can impede the quality of readings taken from a experiment

attempting to reproduce 2-D flows.

The design is versatile, being capable of minimizing blockage for a variety of

model sizes once a suitable open area ratio (OAR, a measure of open to slatted wall

areas, defined as g/s using the notation in Fig. 5) has been settled on [21]. The

best OAR may be specific to a tunnel and test model paring, and is settled on by

testing a range of models of different sizes but with the same shape in the tunnel

and comparing results. This makes experimentation using this tunnel design more

12

costly and time consuming than conventional solid walled testing; even ignoring

the cost of initial fabrication of the tolerant test section, experiments to select

the best OAR must be completed before main experiments, requiring significantly

longer tunnel time and fabrication of several models of different sizes.

H

gs

c

p

Figure 5: Parkinson’s slatted ceiling tunnel configuration for aerofoil testing.

Parkinson’s design was originally developed as it is shown in Fig. 5 for the

testing of aerofoils before stall. Only the wall opposite the aerofoil’s suction surface

was made semi-permeable, since this surface is the more strongly affected by wall

constraints, and it was thought that the aerofoil under test would draw air from a

lower plenum into the main test section ahead of the model mounting, degrading

the flow past the experiment [22]. In this configuration, an OAR of 0.6 was found

to give the best results for the pre-stall range of incidences, while 0.7 was preferred

for preliminary work on stalled aerofoils at α = 20° [23].

Later work adapted the tunnel design by replacing both the floor and ceiling

with slats and a plenum chamber following numerical modeling which suggested

this would provide better results than the single slatted wall [24]. Both slatted

areas were set to an OAR of 0.59 for this work. Limited experimental results were

presented to support the numerical modeling, with no comparisons made to the

earlier, single-walled work. The double slatted wall design was later applier to the

testing of bluff bodies [21]. A range sizes of cylinders, cylinders with splitter plates

and flat plates were accommodated using similar OARs of around 0.6.

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7 Experimental apparatus

Experiments were conducted in Imperial College’s 3’ × 3’ low turbulence wind

tunnel. The tunnel test section has a 915mm × 915mm cross section and a length

of 2390mm. The turbulence intensity of this tunnel is less than 0.1% when empty,

making it ideal for low Reynolds number aerofoil testing [25]. A Parkinson-style

test section was fabricated for the tunnel, with a plenum depth of 350mm and

a length of 2178mm. Slats have a NACA 0015 profile and a chord of 90mm.

These dimensions are similar to those of Parkinson’s original tunnel, which had

an identical tunnel height, 92mm chord NACA 0015 slats and a plenum of length

2440mm and depth of 300mm

The test section can be configured with a single slatted wall, double slatted

walls or as a conventional closed jet section. Slats are mounted between aluminum

runners and can be slid along the test section and added or removed at will,

enabling OAR to be adjusted.

7.1 Aerofoils

Five NACA 0015 aerofoils were tested, this profile was chosen as it is frequently

used in experimental and numerical VAWT research, and there are some existing

post-stall studies for it against which comparisons can be made (see Figs 2 and 3).

All five aerofoils have a span of 915mm and chords such that their c/H ratios are

0.1, 0.15, 0.2, 0.25 and 0.3.

The aerofoils were manufactured using Nylon selective laser sintering (SLS) 3D

printing technology. Each consists of 4 separate printed parts with a 228.75mm

span (the print chamber of the printer limits the size of parts), with a core of two

915mm long steel rods. Printed Nylon parts can shrink and deform as they cool -

steps were taken to minimize the risk of this happening by limiting wall thickness in

the parts to 3mm, ensuring heat dissipates quickly. Ribbing and cross-struts were

printed into the parts to give them sufficient stiffness. The Nylon sections were

assembled around the steel cores using epoxy resin, with a final smooth surface and

accurate profile achieved using filler, sand paper and paints. While sanding and

filling the aerofoils, profile accuracy was checked against female profile templates,

produced using a laser cutter with a rated accuracy of < 100µm which compares

favorably to the typical accuracy of Nylon SLS printers, around 0.35mm for parts

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of the size used here.

7.2 Model mounting and data measurement

The aerofoils were mounted vertically in the wind tunnel at the half chord, between

two end plates that sit flush with the tunnel floor and ceiling, see Fig. 6. They

are mounted at the half chord to avoid uneven blocking of the tunnel at extreme

incidences. Each end plate is attached to an adapter plate which in turn attaches

to an ATI Industrial Automation Gamma IP65 6-component force and torque

transducer. The upper transducer is mounted to the the framework of the tunnel

via a bearing unit, see Fig. 7, while the bottom is mounted to a stepper motor

that controls aerofoil incidence, again via a baring, see Fig. 8.

It was decided not to isolate the aerofoils from the wind tunnel boundary layer

due to their insignificant displacement thickness at the model mounting point.

Results presented later in Figs 13 and 15 show little impact of aerofoil aspect ratio

on readings around stall, suggesting any end wall effects caused by the boundary

layers are minimal.

Since the transducers rotate with the aerofoil, forces normal and tangential

to the aerofoil chord are measured, as is moment about the half chord. These

are post-processed into lift, drag and moment about the quarter chord. Drag

is further processed by subtracting the tare drag force associated with the end

plates, obtained by measuring the forces on them when the tunnel is run without

an aerofoil present. For lightly loaded aerofoils, this tare force is likely to be

overestimated at high incidences, where the separated flow of the aerofoil reduces

the velocity over a large portion of the end plates, reducing the friction drag on

them. When aerofoils are loaded highly enough to induce bending in them, the

upstream edges of the endplates encroach into the flow slightly, so the tare drag

is likely to be underestimated. Tare drag is an insignificant proportion of total

drag post-stall, with these under- or overestimates representing an even smaller

proportion of the total, so no adjustment has been made for them.

7.3 Data acquisition and experiment control

Dynamic pressure difference across the tunnel contraction is measured using a mi-

cromanometer, feeding into a PC via a serial port. This is processed into flow

15

Figure 6: The c/H = 0.2 aerofoil mounted in the wind tunnel with double slatted

walls, OAR = 0.55.

velocity with a calibration obtained using a pitot-static tube mounted in place of

a test aerofoil at the tunnel midspan. Flow and aerofoil incidence are controlled by

the PC via the outputs on a National Instruments NI USB-6229 data acquisition

board. The incidence is altered using the stepper motor, with a tracking of its

rotation stored at each data acquisition point. In addition incidence is also mea-

sured by an optical encoder attached to the motor shaft. The tracked incidence

and encoder output are checked after each movement to ensure the motor has

16

Figure 7: The top assembly of the apparatus, with tunnel floor removed, showing

end plate, adapter, force transducer, bearing mount and attachments to the timber

framework of the test section.

not slipped at any point. The output of the force transducers is digitized using a

pair of NI PCI-6220 data acquisition boards, with simultaneous acquisition from

both. If any of of the components of the load cell are saturated during the first 10

samples taken, raw data is saved for further analysis. An average of the readings

is saved for all data points. The transducers are sampled at a rate of 1000 Hz (a

much higher rate than the highest frequencies of the main vibrations induced in

the rig) for 120 seconds for incidences in the range 45° ≤ |α| ≤ 135° and 30 sec-

onds for other incidences, long enough to capture numerous periods of the lowest

frequencies of force fluctuations.

The process is fully automated for a given set of incidences, the PC control

system running from a Matlab script. It rotates the aerofoil to each incidence

prescribed in turn and at each one it checks the tunnel dynamic pressure, adjusting

if necessary, then records this along with temperature, absolute pressure, incidence

according to both motor and encoder and forces and torques from the transducers.

17

Figure 8: The bottom assembly of the apparatus, with tunnel floor removed,

showing end plate, adapter, force transducer, bearing mount and the cooling unit

of the stepper motor.

7.4 Accuracy of measurements

The transducers used have been factory-calibrated within the last two years where

they were rated to a 95% confidence level to within 1% for force measurements

and 1.5% for torque measurements. Recent checks performed on them found no

significant deterioration in this performance.

A small amount of flexibility was introduced to the system to prevent the

transducers from maxing out under moment loads induced by the rig itself (under

no aerodynamic loads). This was achieved by inserting rubber O-rings between

the adapter plates and transducers. The adapters are held to the transducers with

countersunk headed bolts, passing through the O-rings. This flexibility allowed

some “play” in the incidence of the aerofoil, as did a small amount of looseness in

the stepper motor holding torque. Total play in incidence was ≈ ±0.5° when forced

by hand, with the tapered shape of the countersunk heads and the magnetic forces

of the motor ensuring the aerofoil returned to the intended incidence on release.

18

During runs of the experiment, no significant incidence play was noted other than

extreme incidences (in the range 45° ≤ |α| ≤ 135°). The impact on forces of an

incorrect incidence reading here would be less than 0.005 for Cd and 0.02 for Cl

due to the low rate of change of forces with incidence in this region, but given the

design ensures incidence would oscillate about the angle intended, errors induced

by rig flexibility are likely to be far lower.

The largest source of error comes from creep in the force transducers. An offset

is taken at the beginning and end of each run of the experiment with no flow in

the tunnel and these are compared, with any runs where the differences between

the two are overly large discarded. As a measure of the impact of zero movement,

the end offset is processed into force coefficients using the start offset and the flow

conditions for zero incidence for each run. For Reynolds numbers of 1.5×105 , the

maximum values of Cl and Cd calculated using this method are less than 0.02 (or

around 2% at stall Cl) and Cm are less than 0.012.

The maximum errors in the system accounting for all of the above are esti-

mated at approximately 3%, this is consistent with maximum differences between

repeated runs for the same aerofoil and tunnel configuration.

8 Results

Measurements of normal force, tangential force and moment about the half chord

were taken for the five aerofoils for −2° < α < 184°, the test section configured

with solid walls (with blockage corrections applied to data), with a single Parkin-

son slatted wall (SS), with OARs of 0.71, 0.79, 0.83 and 0.88, and with double

Parkinson slatted walls (DS), with OARs of 0.50, 0.55, 0.59, 0.63 and 0.71.

8.1 Selection of data for inclusion in this report

Results are presented for the solid walled tunnel raw and post-processed with data

corrections as described in Section 4. Results are also presented for the SS-0.88

and DS-0.71 tunnel configurations. Solid walled data allows easier comparison to

existing post-stall studies, none of which have utilized Parkinson’s tunnel design,

and also allows assessment of the capabilities of blockage corrections at the ex-

treme incidences and blockages used in this study. The SS-0.88 and and DS-0.71

19

were chosen as the best OARs of their respective tunnel configurations, based on

experimental results, see Section 9 for the methodology used in this judgement.

8.2 Comparisons to existing data

Fig. 9 shows results for the c/H = 0.1 aerofoil taken in the solid walled tunnel,

corrected for blockage. Also included are the data of Sheldahl and Klimas [2] (as

before, taken atRe = 3.6×105) and a study by Jacobs[11], taken atRe = 1.66×105.

All studies are included in Table 1. Thin aerofoil theory and performance for the

NACA 0015 modelled using Xfoil with matched Reynolds number are also included.

Figure 9: Cl and Cd vs α for selected low Reynolds number studies.

Before stall, this study’s results exhibit a gradient greater than 2π up to α = 4°,then a shallower gradient between there and stall, which occurs at 12°, with a Clmax

of 0.93. The steep gradient at α < 4° is caused by a laminar separation bubble near

the trailing edge at these low incidences, which moves towards the leading edge

with increasing incidence. This is a feature of the NACA 0015’s performance at low

20

Reynolds numbers, hence the less pronounced impact on Sheldahl and Klimas’s

data, which features a more mild change in gradient at α = 6.5°. Though the Xfoil

output does not agree to the experimental data well, it features the same change

in gradient at α = 4°, and evidence of the laminar separation bubble is visible in

pressure distributions. See Fig. 10 for the pressure distribution for α = 3°, where

the bubble can be seen on the suction surface at 50-60% of the chord.

Figure 10: Xfoil pressure distribution at α = 3°

Jacobs’s study was conducted with a finite wing ofA = 6. The data has been

corrected to an infinite aspect ratio using methods based on lifting line theory.

Stall point should be reasonably accurately rendered, this occurs at α = 11.34°with Clmax = 0.92, values close to those of the current study, as is expected

given the similar Reynolds numbers of the experiments. The characteristic kink in

the polars of the infinite wings and Xfoil simulation is not present in Jacobs’s lift

curve, as the laminar separation bubble has less of an impact on the performance of

wings since it does not extend across the whole span. Jacobs’s study exhibits a far

smoother lift curve up to its stall point, close to a straight line from α = 0°. Lifting

line theory is not valid beyond stall; though it is assumed Jacobs’s corrections were

applied beyond stall, they have done little to correct behavior here to something

expected of an aerofoil - the study shows the gentler stall characteristics expected

of a finite wing.

The current study and that of Sheldahl and Klimas extend beyond this plot, see

Figs 2 and 3 for plots that continue to 180°. As discussed in Section 3, agreement

21

between both is excellent at 20° < α < 180°, the post-stall drag peaks of the two

studies are identical, at 1.86, and lift peaks less than 1% different. Given the

similar blockage of the two studies and their very close agreement, along with the

findings of Sheldahl and Klimas for Reynolds numbers of 3.6 × 105, 5 × 105 and

6.8× 105, where again little variation in post-stall performance was noted, it can

be concluded that post-stall performance for the NACA 0015 is independent of

Reynolds number, at least in the range of Reynolds numbers 1.5 × 105 < Re <

6.8× 105.

Fig. 11 shows some preliminary results from an extension to the current study,

where Reynolds number was varied. Included is lift and drag for the c/H = 0.1

aerofoil at Re = 1.5 × 105 as in earlier plots in this paper, alongside runs at

Re = 6 × 104 and Re = 2.5 × 105. There is very strong agreement between the

post-stall regions of the lift and drag curves, with results near-identical for all

three Reynolds numbers. Post-stall lift peaks are within 0.5% of each other and

drag peaks within 1.4%. This adds further support to the hypothesis that post-

stall performance of aerofoils is independent of Reynolds number, at least in the

ranges covered by this and Sheldahl and Klimas’s study. Note that the run at

Re = 2.5 × 105 was aborted at α = 100° due to excessive blade loads saturating

the sensors.

8.3 Solid walled tunnel

Fig. 12 shows results from the solid walled tunnel for the c/H = 0.1, 0.15, 0.2,

0.25 and 0.3 aerofoils at Re = 1.5× 105, as taken from the force transducers with

no blockage corrections applied. Fig. 13 shows the same data after application

of corrections. In both figures, the results for the c/H = 0.1 aerofoil have been

emboldened, in part to allow easier comparison to earlier figures which all contain

data from this aerofoil, and also because as the lowest blocked of all the aerofoils,

data from it should be the most reliable.

Comparing the two figures shows that the adjustments made by the corrections

are not trivial, even for the c/H = 0.1 aerofoil the adjustment to lift at the

post-stall peak is more than 5.5%, and more than 12.5% at the drag peak. The

corrections do a good job of collapsing the wide spread of raw data down to a

reasonable level of agreement.

22

Figure 11: Cl and Cd vs α for the c/H = 0.1 aerofoil at Reynolds numbers of

6× 104, 1.5× 105 and 2.5× 105 taken in the solid walled tunnel and corrected for

blockage

Pre-stall agreement between the corrected aerofoils is strong, as is to be ex-

pected given the applicability of potential flow theory where flow is attached and

the low blockage at low incidences. Post-stall agreement is less impressive. While

most of the lift data does cluster, the highest lift peaks are significantly higher

than the others. These are for the c/H = 0.3 aerofoil. The drag of the same aero-

foil is higher than the others at incidences of 40° < α < 60° and 110° < α < 140°,and the lowest of them all at 85° < α < 110°. These results suggest that the

blockage of the largest aerofoil is beyond the capabilities of the corrections used,

with drag data appearing to be over-corrected at the post-stall peak. The results

of the c/H = 0.25 aerofoil are affected in a similar fashion to a less limited extent,

suggesting it too may be too large in comparison to the tunnel for the corrections

to handle.

The c/H = 0.2 aerofoil stalls slightly ahead of the others, at 11° rather than

12°, and lift is lower than for the others in the range of incidences between stall

and 35°; this aerofoil has a slight camber (< 0.5%) on one of its sections due to

warping of the Nylon SLS material which could not be corrected with filling and

sanding. Some anomalous results were noted for the c/H = 0.2 aerofoil for several

23

Figure 12: Cl and Cd vs α for c/H = 0.1, 0.15, 0.2, 0.25 and 0.3 aerofoils taken in

the solid walled tunnel (raw data). c/H = 0.1 results emboldened.

tunnel configurations, it is thought that this slight camber is to blame.

8.4 Tolerant tunnel

Fig. 14 shows results for the SS-0.88 configured tolerant tunnel, where again the

results for the c/H = 0.1 aerofoil have been emboldened. Also included are the

corrected results from the solid walled tunnel for the same aerofoil to allow com-

parison with earlier figures. Pre-stall agreement is reasonable for both lift and

drag for the five aerofoils. Stall points are on the whole lower than for the solid,

corrected data. The c/H = 0.3 aerofoil stalls at 12° as it does in the sold tunnel,

but the c/H = 0.2 stalls at 10° and the remaining studies at 11°.After stall, the collapse of lift is better than for the solid corrected tunnel,

though the tolerant tunnel has similar problems to the correction regime with

accommodating the c/H = 0.3 aerofoil; its lift is larger that of the other aerofoils

in the range of incidences 55° < α < 85° and 105° < α < 145°. Drag collapse is

24


the solid walled tunnel and corrected for blockage. c/H = 0.1 results emboldened.

worse at the peak, with Cd of the c/H = 0.3 aerofoil far higher than that of the

others. Parkinson’s student Hameury [21] found that a 33% blocked normal flat

plate was too large for the tolerant tunnel to handle, since it diverted flow to such

an extent that it caused some of the slat aerofoils to stall, it is likely the largest

aerofoil behaves similarly when it is near normal to the flow.

Both lift and drag results for the c/H = 0.1 aerofoil are generally larger in

the post-stall region of incidences than the corrected, solid walled data. At the

post-stall peak at α = 90°, Cdmax = 1.98, 6.2% higher than for the corrected data.

The positive lift peak at α = 40° is 1.12, 5.5% higher.

With an OAR of 0.88, the slatted wall contained three aerofoils. Limited testing

was carried out with no aerofoils in place for an OAR of 1, for 85 < α < 95°, with

results still showing wider spread than the corrected, solid walled data. Though

Parkinson’s preliminary work on stalled aerofoils used a single slatted wall[23], this

research moved on to his double slatted wall bluff body design in search of a better

25


the SS-0.88 tunnel. c/H = 0.1 results emboldened. Corrected solid walled data

for the c/H = 0.1 aerofoil also included.

collapse of data.

Fig. 15 shows results for the DS-0.71 tunnel configuration. c/H = 0.1 results

have been emboldened and corrected data from the solid walled tunnel for the same

aerofoil included as before. Pre-stall agreement of the studies is strong, with stall

points at identical incidences to the solid, corrected data (11° for the c/H = 0.2

aerofoil, 12° for all others).

After stall, the collapse of data is excellent, better than for the corrected, sold

wall tunnel or the C-0.88 configuration. Other than a region of over-correcting

of drag, for the c/H = 0.3 aerofoil at incidences of 75° < α < 130° and for the

c/H = 0.25 at incidences of 85° < α < 110°, lift and drag results for all aerofoils

are similar over the whole range of incidences. The largest aerofoil likely forces

slat aerofoils into stall, as in the SS-0.88 tunnel.

Results for the c/H = 0.1 aerofoil are similar to those from the corrected solid

26


the DS-0.71 tunnel. c/H = 0.1 results emboldened. Corrected solid walled data

for the c/H = 0.1 aerofoil also included.

walled tunnel, though slightly lower in magnitude in the post-stall region. Post-

stall positive lift peak is 1.03, 3.1% lower, while the drag peak is 1.7% lower at

1.83.

9 Discussion

Parkinson’s double slatted wall bluff-body tolerant tunnel was found to perform

best with an OAR of around 0.6 for flat plates normal to the flow [23]. Experi-

ments were carried out using pressure tapped models with c/H of 0.083, 0.194 and

0.333. The judgement of the best tunnel configuration was made by plotting vari-

ous parameters against OAR. Plots of base pressure coefficients, drag coefficients,

Strouhal number and required blockage corrections were interpreted by seeing at

which OAR they are most similar for the range of model sizes. Standard deviations

of pressure distributions from a reference distribution were judged by assessing at

which OAR they are at a minimum. Pressure distributions for the three models

were also plotted on the same axis for each OAR in turn, with those OARs giving

the best collapse of data judged to be best.

27

Since good quality force coefficients are the aim of the research detailed here,

judgement of the best tunnel configuration has been based on measured forces. In

order to apply the methods used by Hameury[21] to the current study’s results

would require separate analysis of each incidence at which data was taken, since

his flat pate readings were taken for α = 90° so are designed for a singe incidence.

Results for both lift and drag require analysis over a wide range of incidences.

Two metrics have been devised by which to judge the tunnels, the first is a sum

of standard deviations (∑σ). Standard deviations are taken of the data for all

five aerofoils at each incidence at which readings were taken, then summed over

a range of incidences for each tunnel configuration. Fig. 16 shows plots of this

metric for both lift and drag against OAR, for pre-stall ( −2° < α < 10°) and post-

stall (20° < α < 160°) ranges of incidences. The standard deviations have been

calculated using only data from this study, without reference to a benchmark force,

since no reliable benchmark exists given the spread found in results of existing post-

stall studies. The lowest sum of standard deviations should be the best tunnel

configuration, since this indicates the lowest spread of data between the different

sized models.

For the pre-stall performance, the best tunnel overall is the DS-0.71 tolerant

configuration, as it has the lowest∑σ for both lift and drag, with the next best

being the corrected solid-walled tunnel. The best performing single slatted wall

tunnel is the SS-0.71, the nearest OAR tested to 0.6, which Parkinson found to be

the best single slatted configuration [23]. Single slatted OARs below 0.71 were not

tested as the main focus of research is on post-stall aerofoil performance, and post

stall performance of the lower single slatted OARs can be seen to be unimpressive

in Fig. 16(c).

Post-stall, the DS-0.71 is again the best performer for lift with the corrected

solid tunnel in second place. For drag, this order is reversed, mostly due to the

over-correction of the drags of the c/H = 0.25 and c/H = 0.3 aerofoils at extreme

incidences. Omitting the results for these extreme incidences (70° < α < 110°)from the sum of drag standard deviation, the DS-0.71 is judged to be the best

tunnel. The SS-0.88 is the best of the single slatted wall tunnels post-stall.

The second metric is the sum of the differences between the force coefficients of

the smallest and largest aerofoils, Cl c/H=0.3−Cl c/H=0.1 or Cd c/H=0.3−Cd c/H=0.1.

The best performing tunnel should be the one where this is closest to zero. Should

28

(a) Single slatted wall pre-stall performance (b) Double slatted wall pre-stall performance

(c) Single slatted wall post-stall performance (d) Double slatted wall post-stall performance

(e) Key

Figure 16: Summations of standard deviations for lift and drag, plotted against

OAR. Note that while corrected solid walled data has an OAR of 0, it is shown

plotted at 0.9 or 0.75.

the metric be negative, the tunnel over-corrects for blockage. The only configura-

tion to have a negative measurement was the DS-0.71. This suggests the best con-

figuration may lay between FC-0.71 and DS-0.63, which is the third best perform-

ing tunnel overall using the∑σ metric, and has positive

∑Cl c/H=0.3 − Cl c/H=0.1

and∑Cd c/H=0.3 − Cd c/H=0.1. An OAR of 0.67 can be achieved using the 90mm

chord slat aerofoils, but this configuration is still to be tested.

29

Results for the c/H = 0.1 aerofoil, the lowest blocked of the five tested, are

close for both the DS-0.71 tunnel and the corrected, solid-walled tunnel results.

The latter represents current best practice, but makes use of corrections that are

not applicable where flows are separated. The tolerant tunnel does not require

corrections and based on the metrics described above, with the DS-0.71 configura-

tion performs better than current best practice across a range of model sizes, with

potential for the tunnel to perform even better with the as yet untested DS-0.67

configuration

10 Conclusions

Results are presented in a study to establish a reliable set of post-stall aerofoil

data, using conventional, solid walled tunnels and a passive, tolerant design with

slatted walls. Five NACA 0015 aerofoils with c/H ratios of 0.1, 0.15, 0.2, 0.25 and

0.3 were tested over a 0° − 180° of incidence using the conventional test section,

with blockage corrections applied to data, and several configurations of the tolerant

design, where no corrections are required.

The tunnel types were analyzed to assess which test section minimizes the ef-

fects of blockage on the forces measured on the aerofoils. The tolerant tunnel,

configured with two slatted walls with an OAR of 0.71 was found to be the best,

giving the lowest spread between data from the five different sized aerofoils. No-

tably, it reduced blockage effects better than the blockage corrections applied to

solid walled tunnel data, an approach that represents current best practice.

Results for the c/H = 0.1 aerofoil, the smallest and so least blocked of those

tested, are similar for both the DS-0.71 and the corrected, solid walled tunnel.

That two different methods for blockage reduction give comparable data allows

confidence to be placed in it as a close approximation to equivalent free-air values.

The results also strongly agree with the earlier study of Sheldahl and Klimas [2]

in the post-stall range of incidences

Analysis of the tolerant tunnel configurations tested suggest it is possible that

the DS-0.67 configuration, as yet untested, could provide an even better reduction

in blockage effects.

The quality of data from the tolerant tunnel suggests that its use is valid for

stalled aerofoils. Given that no reliance is placed on correction methodologies

30

that are not strictly applicable where flow is separated, and the tunnel is bet-

ter at correcting for blockage than current best practice, it represents a better

way of conducting post-stall experiments, all be it at the expense of greater time

requirements and apparatus costs than conventional solid-walled tunnel testing.

Preliminary results are presented from a study varying Reynolds number using

a conventional, solid-walled tunnel. Experiments were conducted at Re = 6× 104,

1.5×105 and 2.5×105, with little variation in post-stall performance noted. Again,

the study of Sheldahl and Klimas, taken at a Reynolds numbers of 3.6 × 105,

5 × 105 and 6.8 × 105, agrees strongly in the post-stall range of incidences. It

can be concluded that post-stall performance of the NACA 0015 is independent of

Reynolds number effects in the range 6× 104 to 6.8× 105.

Acknowledgments

This work was supported by the Environmental Services Association Education

Trust (ESAET).

31

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Post-stall airfoil performance and vertical-axis wind turbines

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