wind tunnel blockage corrections

Wind tunnel blockage corrections: Review and applicationto Savonius vertical-axis wind turbines

Ian Ross n, Aaron Altman

Mechanical and Aerospace Engineering, University of Dayton, 300 College Park, Dayton, OH 45469-0238, USA

a r t i c l e i n f o

Article history:

Received 28 July 2010

Received in revised form

31 December 2010

Accepted 26 February 2011Available online 1 April 2011

Keywords:

Low speed wind tunnel

Wind tunnel blockage corrections

Vertical-axis wind turbine

Aerodynamics

Bluff-body aerodynamics

Savonius

a b s t r a c t

An investigation into wake and solid blockage effects of vertical axis wind turbines (VAWTs) in closed

test-section wind tunnel testing is described. Static wall pressures have been used to derive velocity

increments along wind tunnel test section which in turn are applied to provide evidence of wake

interference characteristics of rotating bodies interacting within this spatially restricted domain.

Vertical-axis wind turbines present a unique aerodynamic obstruction in wind tunnel testing, whose

blockage effects have not yet extensively investigated. The flowfield surrounding these wind turbines is

asymmetric, periodic, unsteady, separated and highly turbulent. Static pressure measurements are

taken along a test-section sidewall to provide a pressure signature of the test models under varying

rotor tip-speed ratios (freestream conditions and model RPMs). Wake characteristics and VAWT

performance produced by the same vertical-axis wind turbine concept tested at different physical

scales and in two different wind tunnels are investigated in an attempt to provide some guidance on

the scaling of the combined effects on blockage. This investigation provides evidence of the effects of

large wall interactions and wake propagation caused by these models at well below generally accepted

standard blockage figures.

& 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Aerodynamics is an active and influential science, contributing

to major aspects of wind turbine design. For an aerodynamicist

the art of manipulating and adapting a moving fluid to optimize

energy extraction can be challenging to achieve. Wind turbines

have been researched since the earliest known ancient humans

attempted to harness wind energy through diversified means.

One of the manners to achieve this goal was through vertical-axis

wind turbines (VAWT). The present research details the evolu-

tionary steps in improving the efficiency of wind tunnel testing

vertical-axis wind turbines. Fig. 1 (CAD models based on the

designs of TFC energy), displays two such VAWT models similar in

concept to designs devised by the Finnish engineer Sigurd J. Savonius

(Savonius, 1931).

Recently there has been a resurgence of interest regarding

sources of renewable energy, with numerous universities, com-

panies and research institutions carrying out extensive research

activities. These activities have led to a plethora of designs of

wind turbines based mostly on computational aerodynamic

models. Still largely restricted to an experimental subject, verti-

cal-axis wind turbines are appearing more frequently in the

civilian and military market as research into their cost-effective-

ness and simplicity progresses.

At present, there are two primary categories of modern wind

turbines, namely horizontal-axis (HAWT’s) and vertical-axis

(VAWT’s) wind turbines. The main advantages of the VAWT is

its single moving part (rotor), where no yaw mechanisms are

required, its low-wind speed operation and the elimination of the

need for extensive supporting tower structures, thus significantly

simplifying the design and installation. Blades of straight-bladed

VAWTs can be of uniform airfoil section and untwisted, making

them relatively easy to fabricate or extrude, unlike the blades of

HAWTs, which are commonly twisted and tapered airfoils for

optimum performance.

The motivation for the current research stems from an inves-

tigation into the flow blockage influence on performance of

relatively inefficient VAWTs. In order to improve the conceptual

approach, previous knowledge of bluff body aerodynamics has

been applied to a rotational frame-of-reference for VAWT con-

cepts. Savonius stated in his 1931 paper published by the Journal

of Mechanical Engineering, ‘‘The S-Rotor and its application’’, that the

maximum efficiency possible was only 31%. Following Savonius,

numerous others investigated the effect of geometric parameters

such as blade numbers, blade gap-size and overlap ratio upon flow

Contents lists available at ScienceDirect

journal homepage: www.elsevier.com/locate/jweia

Journal of Wind Engineeringand Industrial Aerodynamics

0167-6105/$ - see front matter & 2011 Elsevier Ltd. All rights reserved.

doi:10.1016/j.jweia.2011.02.002

Abbreviations: HAWT, Horizontal-axis wind turbine; TSR, Tip speed ratio; LSWT,

Low-speed wind tunnel; TFCE, Twenty first century energy; RPM, Revolutions per

minute; VAWT, Vertical-axis wind turbinen Corresponding author. Tel.: þ1 734 478 1734.

E-mail addresses: [email protected] (I. Ross),

[email protected] (A. Altman).

J. Wind Eng. Ind. Aerodyn. 99 (2011) 523–538

behavior. Due to the complex nature of flowfield around Savonius

turbine produced by its geometrical shape, Fig. 2 (Fujisawa and

Gotoh, 1992), theoretical work in modeling the aerodynamics

around these wind turbines is indeed quite scarce. There are

several developed theories to analyze the Darrieus and propeller

type turbines, where lift is the dominant force. The blade element

momentum theory (BEM) predicts the performance of a Darrieus

turbine well, following the ‘‘Wind Energy Handbook’’ (Burton et al.,

2001). In order to perform an aerodynamic analysis of flowfields

around VAWTs and their interaction with closed test-section

wind tunnels, a sample batch of wind turbines/bluff body geome-

trical shapes have been constructed in the present study for wind

tunnel testing, involving:

(1) a qualitative comparison of tip-speed ratio as a function of

Reynolds number using flow visualization of the wake and

flow regions around VAWTs and

(2) an investigation into the relationships that exist between tip-

speed ratio, wind tunnel velocity, the coefficient of power, the

coefficient of torque and static pressures inside a wind tunnel

test-section with the influence of blockage ratio.

A solid blockage effect is commonly observed in wind tunnel

testing that in turn produces an increase in the local wind velocity

in the working section. This increase is ideally accounted for by a

theoretical wind tunnel blockage factor or ratio of which several

developed techniques will be discussed later. Numerous accounts

of questionable accuracy have been debated throughout the

literature concerning low-speed wind tunnel testing of rotating

bluff bodies, especially of VAWT types. The possibility of pre-

viously undocumented variable deleterious effects of wind tunnel

blockage in VAWT testing is observed in tests performed for this

paper and are subsequently presented and discussed. Severe

effects will be documented when models occupy a percentage

of the tunnel cross-sectional area significantly less than the

presently accepted heuristics.

The present research details evolutionary steps in improving

the practicality in testing sub-scale VAWTs as well as an inves-

tigation into the methodology behind correcting for the flow

constraining effect. Ideology has been studied from the ‘Wall

pressure signature method’ originally proposed by Hackett et al.

(1979). The goal is to advance existing solid/wake blockage

correction methodologies in order to appropriately or knowledge-

ably apply them to rotating test models and VAWT concepts,

which exhibit unique viscous and unsteady turbulent flow con-

ditions. The question remains: ‘‘Do the wind tunnel wall surfaces

interact with the model flow to the extent of impacting the

efficiency of the rotor, therefore calling into question accurate

comparison to real-scale prototypes?’’

Solid blockage is created by a reduction in the test-section area

for flow to pass compared to an undisturbed freestream. By

continuity, Bernoulli’s equation and all of the associated assump-

tions, velocity increases in the vicinity of a model, Fig. 3 (upper)

(flow sketches based on the observations of Fujisawa and Gotoh

(1992) and descriptions detailed in ESDU 80024, 1998).

Nomenclature

a blade overlap

AR aspect ratio

Aswept swept area of a turbine

C rotor blade chord

Cp pressure coefficient

Dr turbine (rotor) diameter

D0 end plate diameter

H height of turbine

r turbine radius

Re reynolds number

T torque

UN

freestream velocity

qN

freestream dynamic pressure

l tip speed ratio

Fig. 1. Savonius vertical-axis wind turbine concepts TFC energy: (left) 3-bladed

and (right) 2-bladed conventional Savonius—(CAD models based on the designs of

TFC energy).

Fig. 2. Savonius rotor configuration and geometrical parameters (Fujisawa and

Gotoh, 1992).

Fig. 3. VAWT influence upon streamlines (top) solid blockage, (bottom) wake

blockage (flow sketches based on the observations of Fujisawa and Gotoh, 1992

and descriptions detailed in ESDU 80024, 1980).

I. Ross, A. Altman / J. Wind Eng. Ind. Aerodyn. 99 (2011) 523–538524

Wake blockage is difficult to model blockage for a stationary

body, but when the test concerns a dynamic rotating bluff body

producing large wake disturbances the modeling becomes increas-

ingly more difficult to predict the degradable effect on the flow.

The wake generated has a lower mean velocity than the free-

stream. By continuity, velocity outside this wake has a higher

speed than the flow inside the wake region for a constant mass

flow and higher velocity in the freestream yields lower pressure

assuming conditions that satisfy Bernoulli’s equation, Fig. 3 (lower)

The following is a summation of formulae adopted by numer-

ous authors in their wind tunnel experimental campaigns of

VAWTs, which appears to be the de facto standard in wind

turbine data reduction. The formulae given below were adapted

from those originally given by Blackwell et al. (1997) and

modified for unit conversions from RPM to radians per second:

freestream dynamic pressure q1 ¼1

2rairU

21 ð1Þ

tip-speed ratio l¼ROðrad=sÞ

U1

¼O

60pDR =U1

ÿ � ð2Þ

power extracted Pextracted ¼OT ¼O

60ð2pÞrad=s

� �

T ð3Þ

power available Pavailable ¼ q1U1Aswept ð4Þ

power coefficient ðmeasure of efficiencyÞ CPðefficiencyÞ ¼PextractedPavailable

¼O=60 ð2pÞrad=sÿ �

T

q1U1Aswept¼ lCT ð5Þ

(Blackwell et al., 1997) Modification of a blockage corrected

freestream velocity and dynamic pressure

V1 ¼ V1 uncorrectedð1þeÞ

q1 ¼ q1 uncorrectedð1þeÞ2 ð7Þ

where Aswept ¼DRHR and epsilon (blockage correction factor) shall

be discussed in a later section.

2. Review of literature

Previous means have been proposed to analyze performance

optimization of HAWTs. Progress has also been curved towards

VAWT applications concerning aerodynamic efficiency and per-

formance regarding flow separation and alleviating adverse

effects on energy production. There remains no extensive readily

available literature concerning specific Savonius aerodynamic

model applications to wind tunnel blockage corrections, but

rather there is literature concerning the generalities of the

Savonius rotor concept. A representative selection relevant to

the present research will be first reviewed.

Fujisawa and Gotoh (1992) experimented with flow visualiza-

tion for static and rotating Savonius two bladed rotors. The

rotation effect is discussed in comparison with the measured

pressure distribution on the blade surfaces. It was suggested that

the flow separation region observed on the blade surface was

reduced due to rotation and flow through the overlap. Fujisawa

and Gotoh explain how flow separation regions contribute to

torque production of the rotating rotor and weakened flow

through the overlap acts as a resistance, which together with

the stagnation effect on the front side contributes to the rotor’s

power production capability.

Finally it was shown that the attached flow region on the

convex side of the rotor grows with TSR, contributing to improved

torque performance at low TSR. In addition, deterioration of the

torque performance at large tip-speed ratios is caused by the

decrease in stagnation torque and in the pressure recovery effect

by flow through the overlap. The main flow was visualized by

smoke-wire and the wake flow by injecting smoke just upstream of

the rotor. The static and rotating observations were concentrated on

Fig. 4. Savonius flow patterns: (a) free stream flow, (b) internal flow, (c) flow model and (d) Cp distribution (coefficient of pressure—flow visualization used to compare

wake as a function of rotor angle and wind speed; (left) static rotor and (right) rotating) (Fujisawa and Gotoh, 1992).

I. Ross, A. Altman / J. Wind Eng. Ind. Aerodyn. 99 (2011) 523–538 525

smoke patterns inside the rotor; measured pressure coefficients on

blade surfaces and points of separation and stagnation can be seen

in Fig. 4 (Fujisawa and Gotoh, 1992), and are used as a baseline for

comparison to the flow visualization efforts in the present study.

Undertaking a United States Energy Research and Develop-

ment Contract, Blackwell et al. (199)7 carried out an in depth

investigation of low-speed wind tunnel testing of Savonius type

rotors of two/three stages and two/three blades at different

Reynolds numbers whilst measuring variables: torque, RPM and

tunnel conditions, whereby for the first time a wind tunnel

blockage correction factor has been employed in VAWT testing.

Blackwell presents the data in the form of power and torque

coefficients and as a function of speed ratio (or angular position

for static starting torques); it was concluded that increasing

Reynolds number and/or aspect ratio improves the performance.

Rotary positioning of the turbine to obtain the static or non-

rotating torque as a function of blade position relative to the free-

stream flow was also performed. At the time there was no

universally accepted length scale to Blackwell’s knowledge with

which to calculate a Re for a Savonius rotor and suggests that the

angular position at which stall occurs is a function of Reynolds

number. It was proposed that increasing the test Re number

generally improved aerodynamic performance across the range

of Re being tested.

The work of Biswas et al. (2007) proposed an in-depth review

of wind tunnel testing on three bladed Savonius designs, with

experiments conducted on blade overlap conditions in the range

16–35%. Power coefficients have been calculated with and with-

out a wind tunnel blockage correction factor for tunnel inter-

ference, which is cited from Blackwell’s earlier efforts. It has been

stated that tunnel blockage effect is an important parameter for

wind tunnel performance analysis of VAWTs, whose effect is

much more severe in low-speed wind tunnel applications. This

study provided results on the performance of rotor evaluated

from variation of Cp with TSR at various overlaps. Allowing for

the blockage correction, maximum coefficient of power was

reduced on average by 5% from its initial value, which is a

significant reduction when dealing with initial Cp values no larger

than 30%.

3. Review of existing wind tunnel blockage methodologies

It is defined that the total blockage correction factor is the sum

of the velocity increment (blockage factor) caused by wake

blockage and solid blockage; however these are incredibly diffi-

cult factors to assess for unusual geometries such as the Savonius

rotor and the associated flowfields around them. It has long been

a standard for low-speed wind tunnel testing to operate within

an area-ratio of (tunnel cross-section to swept area of a model)

1–10%, proposed by Pope and Harper, (1966) in their text

‘‘Low-Speed Wind Tunnel Testing’’ and earlier by Pankhurst and

Holder (1952) in their text ‘‘Wind-Tunnel Technique: An Account of

Experimental Methods in Low- and High-Speed Wind Tunnels’’, both

provided various solid/wake blockage correction techniques.

Two types of test-section commonly used when testing in

wind tunnels, namely the closed test-section and the open test-

section (or blockage tolerant test-section) provide large variations

when referring to blockage allowances. The open test-section or

open jet type of wind tunnel has the capability to allow the

conditions inside the test section to be largely unaffected by

larger blockage percentage static models because of the ability to

leak flow and expand the flow around objects within the test-

section as opposed to a flow constriction problem occurring with

the closed test-section type as shown in this study. Because of the

ability to allow the flow to expand, models can generally be

allowed to exhibit higher blockage percentage in open type

testing.

Sandia laboratories initiated the resurgence of vertical-axis

wind turbines in the United States. They also set the standard for

blockage corrections for VAWTs, this being a blockage correction

factor stated by Pope and Harper as a generic correction for the

testing of any unusual shape. The following section discusses this

original blockage method and focuses on the wall pressure

method (Hackett and Wilsden, 1975) modified for this study with

the aim of providing a more detailed assessment of partitioning

solid and wake blockage when the flow behavior increasingly

becomes more three-dimensional, highly separated, unsteady and

turbulent.

A review of recent developments in the calculation of low-

speed solid-wall wind tunnel interference conducted by Hackett

(2003) detailed an extensive interpretation of wall pressures by

Ashill and Weeks (1982), where it is shown by assuming x be

the distance in the streamwise direction and y the distance along

the wall in the direction normal to x (For vertical surfaces, z

replaces y and w replaces v). Here, Hackett assumes the pressure

p is at the wall using Prandtl’s classical assumption for boundary

layers and u and v are velocities in the x and y directions,

respectively.

3.1. Pope and Harper blockage correction factor

Correcting velocity readings Pope and Harper (1966) and

subsequent data modifications to allow for these changes are

shown:

velocity correction V ¼ Vu ð1þetÞ ð8Þ

dynamic pressure correction q¼ qu ð1þ2etÞ ð9Þ

reynolds number correction R¼ Ru ð1þetÞ ð10Þ

Drag coefficient correction: (From the dynamic pressure effect

plus the wake gradient term):

CD0 ¼ CD0u 1ÿ3esbÿ2ewbð Þ ð11Þ

et ¼ solid blockageþwake blockage¼ esb þ ewb ð12Þ

Pope explains: ‘‘for finding the blockage corrections for wind

tunnel models of unusual shapes the following is suggested:’’

et ¼1

4

model frontal area

test section areað13Þ

3.2. Maskell correction

Maskell (1965) was the first to address the problems with non-

streamline flow bodies, such as bluff-body testing in closed wind

tunnel sections and that of partially stalled shapes such as wings.

When the high-lift characteristics of particular delta wing aircraft

models of small aspect ratio were tested in different wind tunnels

at the Royal Aircraft Establishment (RAE), marked differences

were observed at the onset of stall beginning at the wing tips and

spreading inboard with increasing incidence. The different results

could be reconciled only through a wall interference factor, which

is equivalent to the increase in velocity of an undisturbed stream

much larger than previous standard estimations. Maskell’s

research goal was to establish a more convincing existence of

this interference factor and the need for corrections, by relating

effective increase in the dynamic pressure q of the stream due to a

solid blockage constraint. Maskell’s theory holds true for nearly

all two-dimensional bluff-body flows and for situations of close

axis symmetric wake downstream for three-dimensional flows


with the equation for corrected wind velocity given below.

Alexander (1978) provided an adaption to Maskell’s method by

comparing the drag of flat plates normal to the freestream and

that of the drag of Savonius rotors normal to the freestream,

applying the term m, an extrapolated value from Fig. 5. For small

values of blockage ratio, ðS=Cr0:045Þ Maskell gives m¼3.15

(constant value). Alexander suggests that due to restriction on

the wake by the tunnel walls at high S/C values the value of m

falls, reaching a value close to 2.0 for S/C¼0.3 (30% blockage).

V2c

V2¼

1

1ÿm S=Cÿ � ð14Þ

where: Vc is the corrected wind velocity, V the undisturbed wind

velocity, S the flat plate or wind tunnel maximum frontal area, C

the wind tunnel working section cross sectional area, V the

undisturbed wind velocity, m¼(B/S) the extrapolated value from

Fig. 5 and B the wake area normal to wind.

3.3. Hackett, Lilley and Wilsden method

Lockheed scientists Hackett, Lilley and Wilsden produced an

updated blockage correction methodology (Hensel, 1951), by adopt-

ing sources and sinks to represent an equivalent body surface in a

stream, and static pressures measured at the sidewalls are used to

construct a relatively simple singularity set to represent the test

article and then calculate the wall effects based on that singularity set

(Hackett et al., 1979). They showed that tunnel wall static pressures

may be used to infer wake geometry and hence wake blockage using

a row of pressures along the center of the tunnel sidewall, giving the

axial distributions of both solid and wake blockages with a velocity

peak just aft the model. Through a wind tunnel testing campaign

involving models of varying size and blockages up to 10%, wall

pressure signatures were used to determine source, sink and

strengths with wind tunnel span and locations.

Essentially the concept resolves pressure signatures into

their solid and wake counterparts signifying the symmetric and

Fig. 6. Effects at a wind tunnel wall of solid/bubble and viscous wake blockage (Hackett and Wilsden, 1975).

Fig. 5. Flat plates and rotors relationship of m vs. S/C (Alexander, 1978).


anti-symmetric regions with the parameters formulated from

these parts a velocity increment expression is obtained. Hackett

and Wilsden, (1975) provide a theoretical method in determining

wind tunnel solid/bubble and viscous blockage from wall and roof

pressure measurements (Fig. 6) involving lifting and non-lifting,

powered and non-powered models. In order to calculate corrected

pressure coefficients

CpcðxÞ ¼CpuðxÞÿ1

1þðDuðxÞ=U1Þ2

" #

þ1 rearranged for velocity increment :

Du

U

¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1ÿðCPemptyÿCPmodel

Þq

ÿ1 ð15Þ

4. Experimental set-up

A high precision VAWT test bed facility has been installed at

the University of Dayton low-speed wind tunnel laboratory,

housing an Eiffel-type tunnel with a contraction ratio of 16:1

and a working section 76 cm (30 in.)�76 cm (30 in.)�244 cm

(96 in.) length. The inlet freestream turbulence intensity is less

than 0.1% and tunnel maximum velocity is 40 m/s. Four VAWT

models have been considered in this study, with the aim to obtain

a data base of pressure signatures at varying fixed and dynamic

RPM operating conditions. Fig. 1 represents a rapid-prototype

model created for TFCE’s prototype being tested for area-ratio

effects on wind tunnel experiments, whereby three identical

models of varying size, 1/20th, 1/30th and 1/40th to a full-scale

prototype; blade height 3 m (100)� rotor diameter 6 m (200)

providing swept areas; 15.2 cm (6 in.)�30.5 cm (12 in.), 10.2 cm

(4 in.)�20.3 cm (8 in.) and 7.6 cm (3 in.)�15.2 cm (6 in.), respec-

tively, This produces solid blockage values in the University of

Dayton wind tunnel ranging from 2%, 3.5% and 8%. The 1/40th scale

model, 7.6 cm (3 in.)�15.2 cm (6 in.) has been tested in two wind

tunnels, the University of Dayton facility (producing a blockage of

3.5%) and in a smaller tunnel at TFCE laboratories an open circuit,

closed-test section wind tunnel having a working section 45.7 cm

(18 in.) height�45.7 cm (18 in.) width and tunnel maximum velo-

city of 45 m/s, producing a blockage of 5.5%. The larger 2-bladed

Savonius model has been compared for extreme blockage testing

conditions, occupying 10% of the wind tunnel cross-sectional area.

The test system can be seen in Fig. 7, situated below the wind

tunnel test-section; a spindle driven by the turbine passes through

an air bearing producing a theoretically non-friction system, con-

tinues into an Interface T11 bearingless rotary torque transducer

with a 2 Nm torque capacity and a magtrol hysteresis braking

system with a 3.15 Nm (450 oz-in) loading capability. Load is

electronically applied upon the hysteresis brake by the use of a

function generator, applying negative torque on the turbine accurate

to 0.01 V increments. Rotors are tested at constant RPM conditions

with varying freestream velocities and are tested under dynamic

Fig. 8. Static pressure wall tap locations.

Fig. 7. Turbine torque and RPM wind tunnel testing facility.


loading and unloading conditions using a dataq acquisition system

interfaced with a PC for real-time analysis of the system.

Eighteen static pressure taps run along the center-line of the

test-section sidewall, with increased spatial frequency in close

proximity to the model, Fig. 8. Differential pressure readings are

digitally displayed accurate to 0.1 N/m2 using an AEROLAB pres-

sure transducer array system with 300 kN/m2 (3 bar) rated

transducers. These have been compared to an installed pitot-

static tube output display on a U-tube manometer reading of the

undisturbed freestream conditions forward of the model. The

traditional definitions of differential pressure and pressure coeffi-

cient were used following Anderson (2007)for the wall pressure

measurement analysis.

5. Results, analysis and discussion

The formulae presented in this paper have been applied to the

measured torque and RPM data from preliminary testing of four

concept models, in order to assess VAWT efficiencies and power

production capability. Power curves are plotted for comparison.

Testing of a 1/40th scale model in both TFCE and the UD LSWT has

provided marked differences in efficiency characteristics and

torque readings. This is the first instance of a possible influence

of blockage factor on the efficiency of a VAWT model. The same

model is also used to determine the influence of blockage ratio on

the power curves.

5.1. Power and torque coefficient

Fig. 9 displays normalized coefficient of power and velocity

ratio (TSR). As expected with normalizing data the curves coalesce

for the 2% blockage test, giving a peak performance value as 4.5%

efficient at extracting energy from the freestream and curves for

freestreams from 22 to 40 m/s (50–90 mph) lie closely together

with fixed RPM testing. At this low test Reynolds number, such

numbers are typical. However, running tests on the same model

in a smaller wind tunnel with a reduction of tunnel cross-

sectional area by almost half and operating at 5.5% blockage

produces marked differences both in trend and absolute values. It

can be argued that this is beyond the critical blockage size,

exhibiting a shift in efficiency peak as wind speed increases and

displays curves collapsing only at the lower tip-speed ratio

region. There is a clear jump in turbine efficiency when the

blockage ratio is increased. Power coefficient increases if the true

velocity experienced by the model surface is above what is

expected or programmed by the wind tunnel operator.

Fig. 10 displays raw torque loading data as a function of turbine

RPM. As expected, reducing the rotational speeds of the turbines

through increased loading translates to a torque loading capability

Fig. 9. Comparison of two wind tunnel results for 1/40th scale model—details power coefficients increasing as function of blockage ratio increase 2–5.5%.

Fig. 10. Variation of torque and free-spin with turbine RPM—details torque trends at varying wind speeds and resonance regions. (For interpretation of the references to

color in this figure legend, the reader is referred to the web version of this article.)


detailing the peak positive torque producing region increasing as a

function of increasing freestream speeds. Resonance frequencies

exist between the wind tunnel fan and the turbine models (high-

lighted by the red shaded region in the figure).

Power coefficient varied dramatically between the 2 and

3 bladed designs in this study. The 2 bladed classical ‘two-bucket’

or ‘scoop’ design commonly observed as the popular Savonius

design in the literature produces power coefficients in the

range 0–0.17, operating at tip-speed ratios between 0.2 and 1.1.

The 3 bladed rotor in this study produced power coefficients in

the range 0.02–0.08, operating at tip-speed ratios between

0.1 and 0.6. The variation in power coefficient between 3 bladed

rotor (0.02–0.08) used extensively in this research compared to

the 2 bladed rotor (0.15–0.2) is primarily an influence of the

design of the Savonius rotor itself. It is common in the literature

to find that testing has been completed using the ‘classical’

2 bladed rotors.

A logical reason for the 2 bladed concept achieving higher tip-

speed ratio and higher power coefficients is due to its more

successful design, in this study the blades have been fabricated as

pure semi-circular shapes, producing much higher torque values

and subsequently much higher power coefficients. The 3 bladed

rotors in this study have a blade design with little of the classical

‘scoop’ shape as seen in the literature. The disadvantage of this

design is most likely a major factor in the poor torque production

and subsequent poor power coefficient achieved during testing.

5.2. Blockage area-ratio

Assessing solid and/or wake effect on induced velocity distribu-

tions Fig. 11, provides evidence of a rightward shift in the efficiency

peak when a body surface-area normal to the free stream is placed in

the tunnel is increased. That is, the freestream velocity increases due

to higher levels of flow constriction because of a larger body in the

flow. This is a positive step in comparing the influence of blockage on

artificially increasing efficiency of VAWTs due to increased velocity

and pressure differences as a function of an equivalent body within

the tunnel represented by a pressure signature. Again, with relation to

power coefficient and tip-speed ratio, with an actual flow speed

higher than what is used in calculation produces higher Cp values.

5.3. Wall pressure signature

The shift of VAWT efficiencies in wind tunnel testing indicated

by changes in pressure signature is also investigated. The next

stage in assessing a realistically accurate blockage correction

Fig. 11. Comparison of power coefficient vs. tip-speed ratio—increasing power curves at 80 mph freestream with varying blockage ratios.

Fig. 12. Comparison of wall static pressures for a 10% 2-bladed Savonius model at 30 mph freestream.


factor is to record wall pressures along the center-line of a wind

tunnel closed test-section wall. The goal is to represent the

coefficient of differential pressures and relate these to a velocity

increment, closely resembling the work of Hackett and Wilsden

(1975). Because of the gross asymmetry of the flow created from

this unique type of model, pressure readings from both wind

tunnel sidewalls were incorporated into the study.

Comparing static pressure readings upstream of the model

reveals that the values are lower than those of an empty test

section. This provides evidence for the possibility of wake

propagation far upstream of the model reaching into the wind

tunnel contraction. Static pressure readings reveal a large pres-

sure decrease just aft of the models. This relates to an increased

local freestream velocity, which is a product of both flow

constriction due to solid body interaction and the propagating

wake from a rapidly spinning model influencing the freestream.

5.4. Nondimensionalized pressure coefficient as

a function of location

Fig. 15 shows a sample analysis of one model, the 10% [largest

solid blockage] geometry model. The plots describe flow behavior as

a function of wind tunnel velocity (70 mph freestream velocity),

model RPMs (2000–2530 rpm) and wind tunnel test-section side-

wall location (X/B). Comparing static pressure readings upstream of

the model reveals that the values are lower than those of an empty

test section, which provides possible evidence of upstream wake

propagation far upstream of the model reaching the tunnel contrac-

tion. At slow speeds, 13–22 m/s (30–50 mph) the normalized curves

of pressure coefficient do not coalesce neatly, Figs. 12–14, which

could be a factor of instrument range; however with increasing

freestream velocity there is a functional relationship with a larger

pressure decrease and increased RPM.




Negative pressure coefficient is likely due to higher freestream

velocities with a model present. This aerodynamic characteristic

has been observed with all the models; the close trend between

8% and 10% blockage is shown in Fig. 15. A pressure coefficient of

zero would indicate that the pressures along the tunnel sidewall

are equivalent to those of the empty test section, providing the

conclusion that the model would have no aerodynamic influence

at all on the freestream velocity. These plots reveal large pressure

decreases just aft the models. Following incompressible flow

assumptions, this would relate to increased local freestream

velocity, which is a product of both constriction of the flow due

to solid body interaction and the wake propagating from a rapidly

spinning model.

5.5. Comparison of Cp as a function of blockage area-ratio

Fig. 16 compares pressure differential when a model is spinning

at 1000 rpm in the test section with a 27 m/s (60 mph) freestream.

Analysis of this pressure distribution reveals that the 10% and 8%

solid blockage models have a profound influence on the freestream

pressure, and that the smaller models 3.5% and 2% have a lesser

influence, as logically expected. Using this evidence and normalizing

the values with a dynamic pressure lead to a formulation of a

pressure coefficient signature inside the tunnel for eachmodel at the

27 m/s freestream condition. Fig. 16 details high negative pressure

coefficients displaying increased freestream velocity in the tunnel.

The static tap position just aft of the model center-line was

eliminated with some degree of confidence from the analysis being

a spurious data point due to the transducers’ limited transient

capability demanded by the high RPM turbine. The results recorded

for the 3.5% and 2%model show that the pressure readings approach

sensor sensitivity. Thus absolute values are likely questionable;

however the overall trend should still be identifiable as considerably

less than those for the larger model.

5.6. Pressure coefficient vs. TSR as a function of longitudinal location

Plotting Cp with TSR shows the influence of rate of rotation

upon the flow conditions within the wind tunnel test-section.

This influence has been shown as a function of increased TSR and

compared along the longitudinal static pressure port positions

upstream and downstream of the model center-line.

Fig. 17 shows the relationship for a 10% area blockage model at

a freestream of 22 m/s (50 mph). It can be shown that as TSR

increases over the range 0.3–1.1 the pressure coefficient reduces

in absolute value, therefore providing the conclusion that faster

spinning models have a reduced influence upon the freestream (at

least on the side of the pressure taps). This is the evidence that

the wake propagation from the turbine is better contained at

higher RPMs. Results show lower Cp values obtained at higher

TSR, which shows that an artificially higher freestream velocity is

present at higher TSR.

Results from the remaining wind tunnel models support this

theory, displaying similar trends. A wide range of freestream wind

Fig. 15. Comparison of wall static pressures—shows possible contributions to reduced pressures from solid/bubble and by wake blockage for a 10% 2-bladed Savonius

model at 70 mph freestream.

Fig. 16. Comparison of wall pressure coefficients at 60 mph freestream velocity and 1000 rpm—four models.


speeds has been studied and reveals strong homogeneity in the

flow irrespective of the freestream conditions. Thus the influence

of model rotation is consistent over a wide range of wind speeds,

however; it is also important to observe that the rate of change of

pressure coefficient is much faster down to a TSR of 0.55 than it is

from 0.55 upwards.

5.7. Linear regression model

As a step towards quantifying the effects of blockage ratio

upon the efficiency of VAWT models, model RPM has been

studied for its effects on the freestream pressure distributions.

Using the results from the previous phase of the data analysis,

correlations were created from a linear regression as a function of

longitudinal location. Slopes were created from the previous plots

of Cp vs. TSR. Fig. 18 shows the upper, lower and mid-range data

using the slope equations as a function of TSR for the 8% area

blockage model from 27 to 36 m/s (60–80 mph). The data pro-

vides similarity between the slope equations obtained by the

linear regression.

5.8. Cp–TSR slope as a function of wind speed

Using the individual slope equations obtained at each long-

itudinal location and across wind speeds, the absolute value of the

Cp–TSR slope has been analyzed as a function of wind speed for 8%

area blockage model. From the extrapolation of the functional

relationship between pressure coefficient and tip-speed-ratio

from 8% blockage model a relationship independent of wind

tunnel wind speed conditions indicated by horizontal lines is

clear. Similar results were obtained for the 3.5% and 10% blockage

models (Fig. 19).

5.9. Application of velocity corrections

To assess the effectiveness of the correction methods selected

in this paper, the formulae for velocity corrections for each

method have been applied to the wind tunnel test data. In order

to fully integrate the velocity increments into the data reduction

process, the tip-speed ratio, torque coefficient and power coeffi-

cient have been modified to accept updated wind tunnel free-

stream conditions based on each method. Figs. 20 and 21 display

the overall results covering all correction methods and details

their effectiveness at coalescing the maximum power coefficient

regions across percentage blockage values.

Fig. 20 provides a comparison of the decrease in peak power

coefficient from applying a correction method for the 10 and 8%

rotor model, upper and lower plots, respectively. Fig. 21 displays

similar plots for the 3.5 and 2% rotor models (upper and lower).

Clear trends can be observed with the data in this form, the absolute

wall pressure method reduces the power coefficient with more

severity at lower wind speeds and this trend is also observed with

Fig. 17. 10% blockage model, TSR vs. Cp—shown is a selection of wind tunnel locations that display the overall trend well, comparing at x-location along wind tunnel at

freestream 50 mph.

Fig. 18. Correlated TSR vs. Cp relations compared at x-location along wind tunnel at freestream 60, 70 and 80 mph—compares upper, lower and mid-range data for the

3 bladed 8% model across x-location along wind tunnel, showing one relationship that with increasing TSR, Cp decreases and as wind speed increases, slope angle

decreases.


the delta wall pressure method, although the reductions are much

smaller in the range 0–10% with no reduction needed for the 3.5%

and 2% rotors. The Pope method produced no correlating trend

with wind speed and presumably provided inadequately small

corrections. The Maskell method similarly shows no variation with

wind speed but provided larger reductions in power coefficient.

Fig. 22 displays the effectiveness of two methods, Pope and

Maskell, firstly by showing uncorrected power curves on the left

Fig. 19. Plots of Cp vs. TSR slopes—comparison of Cp vs. TSR slopes across freestream at 10%, 8%, 3.5% and 2%.

Fig. 20. Comparison of percentage decrease in coefficient of power on applying

correction methods—(upper) comparing the methods for correcting the 10% rotor

model across wind speeds 30–70 mph and (lower) a similar comparison for the 8%

rotor model.

Fig. 21. Comparison of percentage decrease in coefficient of power from applying

correction methods—(upper) comparing the methods for correcting the 3.5% rotor

model across wind speeds 60–90 mph and (lower) a similar comparison for the 2%

rotor model.


alongside corrected power curves, middle and right. The power

curves are calculated for the three-bladed rotor results for a wind

tunnel velocity fixed at 60 mph and loading the rotors to achieve

the range of tip-speed ratios plotted. Table 1 displays the Maskell

results covering all the rotor cases, it details the effectiveness and

influence of blockage percentage as the major influencing factor

for Maskell corrections.

The coalescing trend shown in Fig. 22 (right) is produced by

applying Alexander’s adaption of Maskell’s method, in which

they have shown a close analogy between corrections for a flat

plate normal to the freestream can be applied to correcting

Savonius rotors that have an equivalent frontal area as the flat-

plate. For the current study, Fig. 22 (right) displays correction

results using m values extrapolated from Fig. 5. This provides a

very effective end result, reducing the performance of the 8%

blockage model successfully into the region of a much smaller

blockage-ratio model.

5.10. Flow visualization

A laser sheet was produced using a New Wave Solo-PIV

Nd:YAG laser with an energy output 15–200 mJ and a single

cylindrical concave optic. The laser sheet was pulsed at 10 Hz

using a DG535 four channel digital delay/pulse generator coupled

with a 1600 PCO charge-coupled device (CCD) camera fitted with a

25 mm wide angle lens at a distance of approximately 142 cm

vertically from the test-section floor. Smoke was seeded at 34 kN/m2

(5 psi) using an oil-based fluid vi-count smoke generator charged

with a nitrogen supply. Figs. 23–25 provide a selection of images.

Images were captured to compare model RPM at fixed freestream

conditions and observations made about the flow region between

the rotor and the wind tunnel sidewalls. The 2-bladed model

(Fig. 23) exhibited high degrees of streamline bending around the

reverse of the blades.

In most instances this flow is turned fully into the opposing

freestream direction. At high model RPM this flow phenomenon

produces an adverse pressure gradient that could explain a

smaller wake influence when compared to the low RPM condi-

tions. In Fig. 23, when RPMs are decreased the rotor acts

increasingly like a static bluff body in the flow, producing a Von

Karman type bluff body alternating vortex street downstream.

This scales well with the smaller rotor models, Fig. 24.

Interestingly, the flow visualizations reveal similarities to the

results of , there is a common occurrence of strong asymmetry of

the wake; however Fujisawa’s published images have a restricted

FOV, so it is unclear if the results supported a sidewall interaction and

subsequently does not provide an analysis of rotation as an influence

on wake propagation. The results in the figure confirm that the initial

choice of wind tunnel sidewall used for pressure tapping was perhaps

in error (Fig. 25). The images show a much wider wake on the

opposing (right) side, indicating the right sidewall pressures need to

be obtained before reaching any conclusions.

6. Conclusions and recommendations

A good foundation to base further testing and implementation of

modified and improved existing blockage methodologies for static

Fig. 22. Power curves for 3-blade Savonius rotors at 60 mph freestream—(left) uncorrected data, (middle) Pope correction and (right) Maskell method correction.

Table 1

Results of correcting performance of Savonius rotors operating in a restricted flow

closed-test-section wind tunnel using the Maskell method.

Blockage

(S/B (%))

Wind speed

(ft/s (mph))

TSR Initial peak

power

coefficient

Maskell

D power

(%)

Maskell updated

peak power

coefficient

10 103.15 (70) 0.74 0.1316 ÿ59.37 0.0826

10 89.33 (60) 0.56 0.1356 ÿ59.37 0.0851

10 74.58 (50) 0.63 0.1521 ÿ59.37 0.0903

10 59.26 (40) 0.67 0.1588 ÿ59.37 0.0943

10 44.21 (30) 0.67 0.1657 ÿ59.37 0.0983

8 117.30 (80) 0.263 0.0674 ÿ41.88 0.0475

8 103.15 (70) 0.311 0.0726 ÿ41.88 0.0512

8 89.33 (60) 0.251 0.0606 ÿ41.88 0.0427

8 73.30 (50) 0.298 0.0624 ÿ41.88 0.044

3.5 132.00 (90) 0.313 0.0533 ÿ19.50 0.0446

3.5 117.30 (80) 0.295 0.0524 ÿ19.50 0.0439

3.5 103.15 (70) 0.269 0.0507 ÿ19.50 0.0424

3.5 89.33 (60) 0.318 0.0532 ÿ19.50 0.0445

2 132.00 (90) 0.319 0.0448 ÿ10.25 0.0406

2 117.30 (80) 0.273 0.0437 ÿ10.25 0.0396

2 103.15 (70) 0.305 0.0449 ÿ10.25 0.0407

2 89.33 (60) 0.301 0.044 ÿ10.25 0.0399

2 73.30 (50) 0.287 0.0431 ÿ10.25 0.0391


testing has been provided for application to dynamic wind tunnel

models with a possible further application to dynamic flapping wing

and rotating bluff-bodies being tested in restricted flow domains in

closed test sections. The ever-present research goal remains in

quantifying a blockage correction to apply to rotating bluff-body

models in closed test-section, low-speed wind tunnel testing.

Fig. 23. CCD camera images across laser sheet, 10% model at 20 mph with yellow dotted line denoting boundaries of the wake—Influence of RPM, left: free-spinning model

at 800 rpm, middle: 500 rpm and right: 100 rpm. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 24. CCD camera images across laser sheet (a)–(c) compares free spinning rotors at high RPMs to relatively static/very low RPM loaded rotor: (a) 8% rotor at 50 mph:

(left) free spin 880 RPM, (right) 100 RPM; (b) 3.5% rotor at 60 mph: (left) free spin 1400 RPM, (right) 100 RPM; (c) 29% rotor at 80 mph: (left) free spin 2150 RPM,

(right) 100 RPM.


Firstly, the performance characteristics of the sample VAWT

concepts were obtained through a campaign of dynamic and

static loadings of the rotors under varying wind tunnel freestream

conditions. The next phase involved static wall pressure measure-

ments taken along the test-section sidewalls to provide a com-

prehensive pressure signature database of test models under

varying freestream conditions and rotor RPMs. Wake character-

istics produced by the same vertical-axis wind turbine concept

have been investigated at different physical scales in an attempt

to provide some guidance on the scaling of the combined effects

on blockage with supporting flow visualizations.

The results suggest that the precise critical point at which

blockage causes a departure from the expected results has not

been absolutely identified. For operating models of 2% and 3.5%

solid blockage there are no evident issues due strictly to blockage.

Results from this investigation give evidence that at 8% and 10%

the blockage area-ratio would cause some difference in results

due to large pressure drops and increases in freestream velocity

which is not observed at smaller area-ratio testing, and below a

certain wind speed the curves would no longer coalesce. Plots

present a visual verification providing evidence of an adequate

upstream test section but inadequate length downstream for the

asymptotic condition when testing larger models. This has not

been validated with flow visualization due to restricted FOV

downstream.

Correlations of pressure coefficient as a function of tip-speed

ratio have been provided and their susceptibility to wind speed

and longitudinal location along the wind tunnel has been

observed forward and aft the rotor models.

It is the ultimate aim of this study to quantify the shift in

efficiency curves and to define a trend behind shifting efficiencies

based upon a functional dependency of solid-body flow interac-

tion, wind tunnel speed and wake constriction due to wind tunnel

wall interference. It was found that wake constriction for a bluff-

body has a stronger influence from model rotation than from

freestream conditions. In reference Table1, the following conclu-

sions can be made:

� Initial assessment of the Pope and Harper (1966) correction

method led to the conclusion that the derived formula for

velocity increments does not effectively account for wake

blockage influences; however the method reduces peak power

coefficients somewhat effectively.

� Assessment of a wall pressure signature method (WPM)

adapted from theory provided by Hackett and Wilsden

(1975), provides a logical trend in severity of corrections. It

is shown that corrections based on the correlated pressure

coefficient techniques detailed in this paper show that correc-

tion severity decreases with increasing wind speeds and

increasing RPM. This supports the earlier pressure signature

results.

� Corrections have been assessed based on an adapted Maskell

(1966) method for correcting large bluff-body shapes. Special

attention has been focused on the analogy supplied by

Alexander (1978)of comparing the correction of a flat-plate

normal to the freestream to that of a Savonius rotor occupying

an equivalent frontal area. The derivation of a corrected

velocity based on this method produces data revealing strong

coalescing trends, a result that begins to show characteristics

of plotted normalized coefficients.

For future testing of the VAWT concept it would be logical,

following results of this study, that for closed test-section wind

tunnels one should be aware of the deleterious effect caused by

wake interaction and model rotation effects, and in order to

precisely recommend a maximum area-ratio to adopt with closed

test-section experiments, further work is required to assess if

corrections can be achieved successfully and accurately with

existing blockage techniques proposed in this study.

Acknowledgments

The authors gratefully acknowledge the developmental fund-

ing and equipment support from Twenty First Century Energy

(TFCE) and Innovative Scientific Solutions, Incorporated (ISSI), the

continued research efforts complementary to this study carried

out by the University of Dayton Research Institute (UDRI) and

support from the Department of Mechanical and Aerospace

Engineering at the University of Dayton.

References

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sidewall surface.


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