Research Article Computational Study on the …downloads.hindawi.com/journals/jre/2013/839319.pdf · Research Article Computational Study on the Aerodynamic Performance of Wind Turbine

Hindawi Publishing CorporationJournal of Renewable EnergyVolume 2013 Article ID 839319 17 pageshttpdxdoiorg1011552013839319

Research ArticleComputational Study on the Aerodynamic Performance ofWind Turbine Airfoil Fitted with Coands Jet

H Djojodihardjo12 M F Abdul Hamid2 A A Jaafar3 S Basri3 F I Romli2

F Mustapha2 A S Mohd Rafie2 and D L A Abdul Majid2

1 Universitas Al Azhar Indonesia Kebayoran Baru Jakarta 12110 Indonesia2 Department of Aerospace Engineering Universiti Putra Malaysia 34400 Serdang Selangor Malaysia3 Faculty of Manufacturing Engineering University Malaysia Pahang 26300 Kuantan Pahang Malaysia

Correspondence should be addressed to H Djojodihardjo harijonodjojodihardjocom

Received 16 January 2013 Accepted 2 April 2013

Academic Editor Wei-Hsin Chen

Copyright copy 2013 H Djojodihardjo et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Various methods of flow control for enhanced aerodynamic performance have been developed and applied to enhance and controlthe behavior of aerodynamic componentsThe use of Coanda effect for the enhancement of circulation and lift has gained renewedinterest in particular with the progress of CFD The present work addresses the influence effectiveness and configuration ofCoanda-jet fitted aerodynamic surface for improving lift and 119871119863 specifically for S809 airfoil with a view on its incorporationin the wind turbine A simple two-dimensional CFD modeling using 119896-120576 turbulence model is utilized to reveal the key elementsthat could exhibit the desired performance for a series of S809 airfoil configurations Parametric study performed indicates thatthe use of Coanda-jet S809 airfoil can only be effective in certain range of trailing edge rounding-off radius Coanda-jet thicknessand momentum jet size The location of the Coanda-jet was found to be effective when it is placed close to the trailing edge Theresults are compared with experimental data for benchmarking Three-dimensional configurations are synthesized using certainacceptable assumptions A trade-off study on the S809 Coanda configured airfoil is needed to judge the optimum configuration ofCoanda-jet fitted Wind-Turbine design

1 Introduction

In line with the efforts to enhance the use of green energytechnology for energy extraction conversion and propul-sion the fundamental principles and mechanisms that playkey roles in these technologies have been the focus in manycurrent research efforts as well as the present research worksince these have the eventual potential of national develop-ment significance Since one of the first attempts to generateelectricity by using the wind in the United States by CharlesBrush in 1888 [1] wind energy has been utilized for electricitygeneration using large Wind turbines in many wind farmswith potential wind energy inland as well as off-shore It hasbeen estimated that roughly 10 million MW of energy arecontinuously available in the earthrsquos wind [2] The technicalpotential of onshore wind energy is very large 20 times 109

to 50 times 109MWh per year against the current total annualworld electricity consumption of about 15 times 109MWh Theglobal wind power capacity installed in the year 2004 was6614MW an increase in total installed generating capacity ofnearly 20 from the preceding year

Wind energy conversion research and developmentefforts have their origin on fluid physics thermodynamicsand material sciences Learning from various innovations in-troduced in aircraft technology wind energy technology cantake advantage of flow circulationmodification and enhance-ment

Flow control for enhanced aerodynamic performance hastaken advantage of various techniques such as the use of jets(continuous synthetic pulsed etc) compliant surface vor-tex cell and the like [3ndash16]These active control concepts candramatically alter the behavior of aerodynamic components

2 Journal of Renewable Energy

such as airfoils wings and bodies Specifically modifiedcirculation and enhanced circulation have been utilized forimproved aircraft and land-vehicle performance as well as innovel air-vehicles lift and propulsion system concept due totheir better energy conversion capabilities [17ndash23] The po-tential benefits of flow control include improved performanceand maneuverability affordability increased range and pay-load and environmental compliance Active flow controlmaybe applied to delay or advance transition to suppress or en-hance turbulence or to prevent or promote separation thatwill result in drag reduction lift enhancement mixing aug-mentation heat transfer enhancement and flow inducednoise suppression [24] as appropriate It could be men-tioned that more recently plasma-based flow control hasalso been considered for wind turbine applications [25ndash28]Such efforts may involve the design of ldquosmartrdquo wind turbineblades with integrated sensor-actuator-controller modules toimprove the performance of wind turbines by enhancing en-ergy capture and reduction of aerodynamic loading andnoise by way of virtual aerodynamic shaping These arebeyond the scope of the present work

In this conjunction andwith the progress of CFD the useof Coanda effect to enhance lift has attracted renewed interest[4ndash7 10ndash14 17 29] Tangential jets that take advantage ofCoanda effect to closely follow the contour of the body areconsidered to be simple and particularly effective in that theycan entrain a large mass of surrounding air This can lead toincreased circulation in the case of airfoils or drag reduction(or drag increase if desired) in the case of bluff bodies such asan aircraft fuselage

In the design of a novelWind turbine using with the latestaerospace engineering technology including aerodynamicsnew lightweight materials and efficient energy extractiontechnology highly efficient aerodynamic surface came as akey issue Recent efforts in the last decade have also indicatedthat Coanda effect has been given new and considerableconsiderations for circulation control technique [17 19 2029] Taking advantage of these recent results the presentworklooks into the effort to optimize aerodynamic performance ofWind turbine and to critically investigate the use of Coandaeffect

The progress of high speed computers exemplified bythe availability of new generations of notebooks has madepossible the use of first-principles-based computational ap-proaches for the aerodynamic modeling of Wind turbineblades to name an example As pointed out by Xu and Sankar[17] since these approaches are based on the laws of con-servation of mass momentum and energy they can capturemuch of the physics in great detail These approaches areparticularly helpful at high wind speeds where appreciableregions of separation are present and the flow is unsteady

In the design of circulation control technique one maynote the progress of stall-controlled and pitch-controlledturbine rotor technology for dealing with power productionat low and high wind conditions [30] Of interest is thedeployment of Wind turbines at larger range of sites notlimited to a relatively small number of sites where favorableconditions exist At the other extreme precautions shouldbe taken when the wind speeds become very high when

the rotor invariably stalls and experiences highly unsteadyaerodynamic forces and moments It is noted that over thepast several years there has been an increased effort to extendthe usable operating range of stall-regulated Wind turbinesThe concepts of circulation control through trailing edge (TE)blowing or Coanda-jet then came into view

However over the past decades commonly used airfoilfamilies for horizontal axis Wind turbines such as the NACA44- NACA 23- NACA 63- and NASA LS (1) series airfoilssuffer noticeable performance degradation from roughnesseffects resulting from leading edge contamination [30]Annual energy losses due to leading edge roughness are great-est for stall-regulated rotorsThe loss is largely proportional tothe reduction in maximum lift coefficient (119888

119897max) along theblade High blade-root twist helps reduce the loss by keepingthe bladersquos angle of attack distribution away from stall whichdelays the onset of 119888

119897max Roughness also degrades theairfoilrsquos lift-curve slope and increases the profile drag whichcontributes to further losses For stall-regulated rotors whoseangle of attack distribution increases with wind speed theannual energy loss can be 20 to 30 where leading edgecontamination from insects and airborne pollutants is com-mon Variable-pitch toward stall would result in simi-lar roughness losses as fixed-pitch stall regulation whilevariable-pitch toward feather would decrease the loss toaround 10 at the expense of the rotor being susceptibleto power spikes in turbulent high winds For variable-rpmrotors operating at constant tip-speed ratio and angle ofattack distribution the loss is minimal at around 5 to 10To minimize the energy losses due to roughness effects andto develop special-purpose airfoils for horizontal axis WindTurbine (HAWTrsquos) the National Renewable Energy Labora-tory (NREL) formerly the Solar Energy Research Institute(SERI) and the Airfoils Inc began a joint airfoil developmenteffort in 1984 Results of this effort have produced a new seriesof airfoils which are considered more appropriate for HAWTapplications These blades are providing significant increasesin annual energy production as a result of less sensitivity toroughness effects better lift-to-drag ratios and in the caseof stall-regulated rotors through the use of more swept areafor a given generator size Because of the economic benefitsprovided by these airfoils they are recommended for retrofitblades and most newWind turbine designs [30]

Annual energy improvements from the NREL airfoilfamilies are projected to be 23 to 35 for stall-regulated tur-bines 8 to 20 for variable-pitch turbines and 8 to 10for variable-rpm turbines Optimizing airfoilrsquos performancecharacteristics for the appropriate Reynolds number andthickness provides additional performance enhancement inthe range of 3 to 5 [31] Because of the economic benefitsprovided by these airfoils they are recommended for retrofitblades and most new Wind turbine designs [30] In order toobtain results that can be well assessed especially withreference to extensive research carried out as described in[17 19 20 29] the airfoil S809 [31] is considered in the presentwork For this purpose in this particular work we focus on aparticular problem that is the basic airflow idealizationover a two-dimensional airfoil in subsonic flow Two specificconditions are consideredThe first is a clean S809 airfoil and

Journal of Renewable Energy 3

the second is the GTRI Dual Radius CCW airfoil that hasalready been investigated thoroughly for benchmarkingTheCoanda effect studies are carried out on S809 airfoil

2 Problem Formulation

Circulation control wing (CCW) technology is known to bebeneficial in increasing the bound circulation and hence thesectional lift coefficient of airfoil This technology has beenextensively investigated both experimentally and numerically[3ndash22 29ndash32] over many years Circulation control is imple-mented by tangentially blowing a small high-velocity jet overa highly curved surface such as a rounded TE

This causes the boundary layer and the jet sheet to remainattached along the curved surface due to the Coanda effect(ie a balance of the radial pressure gradient and centrif-ugal forces) causing the jet to turn without separation Therear stagnation point location moves toward the lower airfoilsurface producing additional increase in circulation aroundthe entire airfoil The outer irrotational flow is also turnedsubstantially leading to high value of lift coefficient compa-rable to that achievable from conventional high lift systemsas illustrated in Figure 1(b) [4] Tongchitpakdee et al [1920] observed that early Circulation Controlled Wing designstypically had a large-radius rounded TE to maximize thelift benefit These designs however also result in high dragpenalty when the jet is turned off One way to reduce thisdrag is tomake the lower surface of the TE a flat surface whilekeeping the upper surface highly curved This curvature onthe upper surface produces a large jet turning angle leadingto high lift In this conjunction the ability of circulation con-trol technology to produce large values of lift advantageousfor Wind turbine design since any increase in the magnitudeof the lift force (while keeping drag small and LD high)will immediately contribute to a corresponding increase ininduced thrust and torque will be taken into consideration

Numerical simulation carried out by Tongchitpakdeeet al [19 20] looked into two approaches of introducingCoanda-jet that is at the appropriately chosen point in thevicinity of the trailing as well as leading edge A leadingedge blowing jet was found to be helpful in increasing powergeneration at leading edge separation cases while a TE blow-ing may produce the opposite effect

With such background the present work is aimed at thesearch for favorable Coanda-jet lift enhanced configurationfor wind turbine designs focusing on two-dimensional sub-sonic flow by performing meticulous analysis and numericalsimulation using commercially available CFD code Resultsobtained from recent researches will be utilized for directingthe search as well as for validation For example best liftenhancing configuration [19] that is lower part of the TEsurface to be flat will be incorporated in the present numer-ical investigation Case studies performed here use baselinechord dimension of 1m airfoil chord length Two values offree-stream velocities are investigated that is 577msec and146msec corresponding to Reynolds number of 395 times 105and 106 which should fall within the typical situations forlarge wind turbines The free-stream velocity in the presenttwo-dimensional study is taken to be equal to the resultant

velocity contributed by the rotation of theWind turbine blade(at a selected baseline radial position say 07119877 with 119877 theradius of the wind turbine rotor) and the free-stream velocityof the ambient air

3 Objectives

To arrive at desired design configurations one is lead tocome up with desired logical cause and effect laws as well asto findways to carry out optimization schemes It is with suchobjectives in mind that using numerical analyses parametricstudies can be carried out and may offer some clues onrelevant parameters which may be utilized in a multivariableoptimization (and to a larger scale multidisciplinary opti-mization) The present work will investigate the influenceeffectiveness and configuration of Coanda-jet fitted aerody-namic surface in particular S809 airfoil for improving its liftaugmentation and LD with a view on its incorporation inthe design of wind turbine In addition parametric study iscarried out for obtaining optimum configuration of theCoanda effect lift enhanced airfoilThe comprehensive resultsas addressed in the objective of the work will be assessed toestablish key findings that will contribute to the physical basisof Coanda-jet for lift enhancement in aerodynamic liftingsurfaces and an analysis based on physical considerationswill be carried out with reference to their application inpropeller (or helicopter rotor) and wind turbine blade config-uration for design purposes The feasibility and practicabilityof Coanda configured airfoil for wind turbine applications areassessed

4 Computational Modeling and SalientFeatures of CFD Computational Scheme

41 Governing Equations Reynolds-Averaged Navier StokesTwo-dimensional incompressible Reynolds-averagedNavier-Stokes (RANS) equationwill be utilized to perform the analy-sis and to obtain numerical solutions on a computational gridsurrounding a reference airfoil The governing equation isgiven by (steady state and ignoring body forces)

120588119906119895

120597119906119894

120597119909119895⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Change in mean momentum of fluid element

=120597

120597119909119895

[[[

[

minus119901120575119894119895⏟⏟⏟⏟⏟⏟⏟⏟⏟

Normal stress

+

Viscous stress⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞

120583 (120597119906119894

120597119909119895

+

120597119906119895

120597119909119894

) minus 1205881199061015840

1198941199061015840

119895⏟⏟⏟⏟⏟⏟⏟⏟⏟

Reynolds stress

]]]

]

120597119906119894

120597119909119894

= 0

(1)

Computational fluid dynamics codes will be used to ana-lyze the flow around two-dimensional airfoil Various CFDcodes are available and are alternatively utilized Carefulreview and analysis of the application of the first principle in


Inboard circulation controlwingthrust deflector

(a)

Possible leading edge blowing

Boundary layer control

Jet sheet

119862119871

Pressurecentrifugalforce balance

Tangential blowing over roundedtrailing edge surface

Slot

Circulation control

Δ119862119871119862120583 gt80

(b)

Figure 1 (a) Circulation control wingupper surface blowing STOL aircraft configuration from [4] (b) Coanda-jet tangential blowing overTE surface for lift enhancement from [5]

the numerical computation are carried out prior to the uti-lization of commercially available CFD codes for the presentstudy For validation of the computational procedure resortis made to appropriate inviscid case and online aerodynamiccodes are utilized For a two-dimensional geometry the meshgenerator partitions the subdomains into triangular orquadrilateral mesh elements [33] Care should be exercised inthe choice and generation of the computational grid whichwill be elaborated subsequently The comprehensive resultsas addressed in the objective of the work are assessed toestablish key findings that will contribute to the physical basisof Coanda-jet for lift enhancement in aerodynamic liftingsurfaces An analysis based on physical considerations iscarried out with reference to its application in wind turbineblade configuration for design purposes

The basis of the computational approach in the presentwork is the two-dimensional incompressible Reynolds-averaged Navier-Stokes (RANS) equation (1) and its imple-mentation into the CFD equation When pursuing furtherthe numerical solution of dynamic fluid flow using CFDtechniques in order to arrive at accurate solution at leasttwo aspects should be given careful attention with dueconsideration of computational uncertainties The first is thegrid generation and the second is the turbulence modelingof the particular flow The first is based on computationalalgorithm including the choice of appropriate grid the grid

fineness should be chosen to obtain efficient solution whichis a combination of computational speed and accuracy Thesecond is the turbulencemodeling which is based onphysicalmodeling of real flow Associated with turbulence model-ing the wall boundaries are the most common boundariesencountered in fluid flow problems Turbulent flows aresignificantly affected by the presence of walls The successfulprediction of wall bounded turbulent flows relies on theaccuracy with which the flow in the near-wall region isrepresented Experiments have shown that the near-wallregion can be subdivided into several layers characterizedby the value of 119910+ which include the viscous sublayer wherethe laminar property is dominant the fully turbulent regionwhich consists of the turbulent logarithmic layer for a rangeof 119910+ values and the outer layer as schematically exhibited inFigure 2(b) The no-slip condition at stationary walls forcesthe mean velocity components to a zero magnitude and canalso significantly affect the turbulence quantities If the griddistribution is fine enough so as to satisfy the no-slip con-dition near-wall treatment is not necessary [34ndash42]

42 TurbulenceModeling Considerations Turbulencemodel-ing in CFD is very essential in the choice of grid fineness andobtaining the correct simulation of particular flow field Forthis purpose one has to choose a particular model out of ahost of available turbulencemodels developed to date One of


SASST Experimental

005

004

003

002

001

008 1 12 14 16 18 2

119880119880infin

Hei

ght119888

119896-120576

Figure 2 Typical 119910+ values in the turbulent boundary layer andvelocity profiles in wall units for subsonic flow over flat plate M =02 Re = 1 times 106 medium grid nozzle pressure ratio = 14 (SourceMenter [23] Salim and Cheah [45] and Economon andMilholen II[46])

these turbulence models that is considered to be appropriateand user friendly is the k-120576 turbulence model without disre-garding other models that may be suitable for the purpose ofthe present work

The k-epsilon turbulence model was first proposed byHarlow and Nakayama [34] and further developed by Jonesand Launder [40] Continuing extensive research has beencarried out to understand the nature of turbulence and thistheory has been further elaborated and many other theorieshave also been introduced such as elaborated in [43] whichseem to be satisfactory for only certain classes of casesThe turbulent viscosity models based on Reynolds-averagedNavier-Stokes (RANS) equations (1) are commonly employedinCFD codes due to their relative affordability [44] Howeversince the choice of turbulence model and associated physicalphenomena addressed are relevant in modeling and com-puter simulation of the flow situation near the airfoil surfaceconsidered here a closer look at turbulence models utilizedby the CFD code chosen will be made Although the practicalimplementation of turbulence model especially for the near-wall treatment has been some somewhat of a mystery [35]the numerical implementation of turbulence models has adecisive influence on the quality of simulation results Inparticular a positivity-preserving discretization of the trou-blesome convective terms is an important prerequisite forthe robustness of the numerical algorithm [35] The k-120576model introduces two additional transport equations and twodependent variables the turbulent kinetic energy 119896 and thedissipation rate of turbulence energy 120576 Turbulent viscosity

is modeled by using the Komolgorov-Prandtl expression forturbulent viscosity

120583120591= 120588C120583

1198962

120576 (2)

where C120583is a model constant In expression (2) 120583

120591was based

on the eddy viscosity assumption introduced for convenienceof further analysis by Boussinesq [41] to draw analogybetween the momentum transfer caused by turbulent eddiesand the viscosity in laminar flow

The dimensionless distance in the boundary layer sub-layer scaled representing the viscous sublayer length scaleplays significant role in capturing relevant physical turbu-lence phenomena near the airfoil surface commensurate withthe grids utilized in the numerical computation In thisregards the flow field in the vicinity of the airfoil surface isusually characterized by the law of the wall which attemptsto identify intricate relationships between various turbulencemodel scaling in various sublayers For example the wallfunctions approach (wall functions were applied at the firstnode from the wall) utilized by k-120576 turbulence model usesempirical laws to model the near-wall region [35] to circum-vent the inability of the k-120576 model to predict a logarithmicvelocity profile near awallThe law of thewall is characterizedby a dimensionless distance from the wall defined as

119910+=

119906120591119910

120592 (3)

Subject to local Reynolds number considerations the wall119910+ is often used in CFD to choose the mesh fineness

requirements in the numerical computation of a particularflow

Based on preliminary attempts to choose the appropriateturbulence model which yields desirable results in thepresent work k-120576 turbulence model is chosen [34 35] In theframework of eddy viscosity based turbulence models theflow of a turbulent incompressible fluid is governed by theReynolds-averaged Navier-Stokes (RANS) equation (1) forthe velocity u and pressure p

For practical implementation purposes it is worthwhileto introduce an auxiliary parameter 120574 = 120576119896 to linearize theequations of the k-120576 turbulence model using the followingequivalent representation

120597119896

120597119905+ nabla sdot (119896119906 minus

]119879

120590119896

nabla119896) + 120574119896 = 119875119896 (4a)

120597120576

120597119905+ nabla sdot (120576119906 minus

]119879

120590119896

nabla120576) + 1198622120574119896 = 120574119862

1119875119896 (4b)

The corresponding linearization parameter is given by 120574 =

C120583(119896]119879) Hence the standard k-120576 turbulence model is based

on the assumption that ]119879

= C120583(1198962120576) where k is the

turbulent kinetic energy and 120576 is the dissipation rate 119875119896=

(]1198792)|nabla119906 + nabla119906

119879|2 and 120576 are responsible for the production

and dissipation of turbulent kinetic energy respectively Thedefault values of the involved empirical constants are C

120583=

0091198621= 144119862

2= 192120590

119896= 10 and 120590

120576= 13


Following iterative procedure elaborated by Kuzmin et al[35] with prescribed homogenous Neumann boundary con-dition and impermeable wall it remains to prescribe the wallshear stress as well as the boundary conditions for 119896 and 120576

on the wall The equations of the k-120576 model are invalid inthe vicinity of the wall where the Reynolds number is ratherlow and viscous effects are dominant Therefore analyticalsolutions of the boundary layer equations are commonlyemployed to bridge the gap between the no-slip boundariesand the region of turbulent flow The friction velocity 119906

120591is

assumed to satisfy the nonlinear equation

|119906|

119906120591

=1

120581log119910+ + 120573 (5)

valid in the logarithmic layer where the local Reynoldsnumber

119910+=

119906120591119910

](6)

] is in the range 1106 le 119910+le 300 The empirical constant 120573

equals 52 for smooth walls Note that the above derivationresults in the boundary value of the turbulent eddy viscosity]119879to be proportional to ] Indeed

]119879= 119862120583

1198962

120576= 120581119906120591119910 = 120581119910

+

lowast] (7)

where 119910+

lowast= |119906|119906

120591 Based on such information the search

for appropriate grid fines in addition to the outcome of gridfineness ratio study is also guided by plausible comparison ofthe validation of CFD computational results of the test airfoilwith experimental values Here the CFD code utilized using119910+ value of 11 and as suggested in [35] was found to yield

satisfactory results as indicated there Figure 2 below showsthe influence of 119910+ in representing the boundary layer nearthe wall

Various studies [23 35 42 47] have indicated thatintegrating of the k-120576 type models through the near-wallregion and applying the no-slip condition yield unsatisfactoryresults Therefore taking into account the need for effectivechoice of grid mesh compatible with the turbulence modeladopted using the commercial CFD code a parametric studyis carried out on two airfoils where either experimental dataor computational results are available to validate the com-putational procedure turbulence model and grid size chosenand establish their plausibility for further application inthe present work The idea is to place the first computa-tional nodes outside the viscous sublayer and make suitableassumptions about how the near-wall velocity profile behavesin order to obtain the wall shear stress Hence the wallfunctions can be used to provide near-wall boundary condi-tions for the momentum and turbulence transport equationsrather than conditions at the wall itself so that the viscoussublayer does not have to be resolved and the need for a veryfine mesh is circumvented The wall functions in COMSOL[48] are chosen such that the computational domain isassumed to start at a distance y from the wall (see Figure 3)

By applying the wall function at the nodes of the firstmeshing layer of the computational grid at a distance y from

the wall (airfoil) surface practically the meshing layer ofwidth y is removed from the computational domain thusreducing the total number of grids involved and hencereducing the computational time Kuzmin et al [35] haveintroduced a wall function that is able to control the 119910+ valuesuch that the y distance will not fall into the viscous sublayerwhich could jeopardize the wall function assumption madeThe smallest distance of 119910+ that can be defined followingGrotjans andMenter [47] corresponds to the point where thelogarithmic layer meets the viscous sublayer

The distance y is automatically computed iteratively bysolving 119910+ = (1119896) log119910+ + 120573 = (1041) log119910+ + 52 so that119910+

= (119906120591119910)120592 = 120588119906

120591(119910120583) where 119906

120591= 120588C

120583(1198962120576) (which

has been further derived byKuzmin et al [35] to be equivalentto 119906120591= C14120583

radic119896) is the friction velocity and is equal to 1106This corresponds to the distance from the wall where thelogarithmic layermeets the viscous sublayer Hence the valueof 119910 as represented by the choice of the computational gridsize can never become smaller than half of the height ofthe boundary mesh cell [48] as illustrated in Figure 3(a)This means that 119910

+ can become higher than 1106 if themesh is relatively coarse The k-120576 variables are not specifieda priory but during the computation using CFD softwarek-120576 variable values are implicitly set to obtain acceptable 119910+values that provide relatively rapid convergence and accuracy(as validated with appropriate data)

Therefore care is exercised in the choice of grids in thevicinity of the airfoil to obtain a certain acceptable error tol-erance (whichmay also be attributable to numerical error anduncertainties) The plausibility of the numerical results willbe judged by comparison to other established results in theliterature (numerical or experimental) for specific cases Inthe present study it was found that the turbulence intensityof 5 and length scale of 001m yield results that agree withbenchmarking data It is noted that Howell et al [49] also usethis value and turbulence intensity of 1 in their numericalstudy on VAWT

5 Computational Set-Up and Validation

51 Computational Grid In the present work the grids wereconstructed following free mesh parameter grid generationusing an algebraic grid generator and varied from extremelycoarse up to extremely fine gridsHowever for the S809 airfoilcase near the surface of the airfoil boundary layer basedmeshing is carried out throughout Grid sensitivity study onthe lift force per unit span for clean airfoil at zero angle ofattack is plotted in Figure 4

Figure 4 shows that the lift and drag are virtually insen-sitive of the size of the grid generated The grid sensitivitystudy has led to acceptable grid sizes in the range of fine upto extra fine grid size since within this range the lift as wellas the drag forces do not change appreciably The associatedrange of freemesh parameters (ranging from extra fine to finemeshing grid size) is defined in Table 1

In order to control the 119910+ value (set at 1106 on the airfoilsurface) the maximum element size was set at 0005 while atthe TE rounding-off surface the maximum element size was


Viscoussublayer

Buffer layeror

blending region

Fully turbulent regionor

log-law region

ln(119880120591(119910)13)

119880119880120591

12(12119910)

12119910119910

(a) (b)

Figure 3 For wall functions the computational domain starts a distance y from the wall (a) Grid generation followed from COMSOL 42Userrsquos Guide (b) the structure of turbulence boundary layer adapted fromMenter [23]

114113112111

11109108107106 00002 000005Li

ft fo

rce p

er u

nit s

pan

(Nm

)

Coa

rser

Coa

rse

Nor

mal

Fine

Fine

r

Extr

a

Extr

a

(a)

202

2

198

196

194

192

19

188 00002 000005Dra

g fo

rce p

er u

nit s

pan

(Nm

)

Coa

rser

Coa

rse

Nor

mal

Fine

Fine

r

Extr

a

Extr

a

(b)

Figure 4 Grid sensitivity study for clean S809 airfoil at zero degree angle of attack (a) lift force per unit span (b) drag force per unit span

Table 1 The range of free mesh parameters

Parameter RangeMaximum element size 0156ndash042Minimum element size 0018ndash012Maximum element growth rate 108ndash113Resolution of curvature 025ndash03Resolution of narrow regions 1

set at 0001 At the Coanda-jet outlet the surface is dividedinto a minimum of 10 grid meshes To obtain acceptablecomputational results usingCFD code appropriate boundarylayer mesh properties should be carefully chosen and thethin boundary layers along the no-slip boundaries should beresolved into mesh layers commensurate with the grid fine-ness A boundary layermesh is a quadrilateralmesh (2Dflow)with dense element distribution in the normal direction alongspecific boundaries to resolve the thin boundary layers alongthe no-slip boundariesTheboundary layer properties chosenare defined in Table 2

Along with the requirement of the 119910+ value to capture thesalient turbulent flow field sublayers a range of values of thegrid dimension could be chosen to represent the thicknessof the first meshing sublayers In the present example thegrid dimension was chosen to be between 000005m and

Table 2 Computational grid meshing layer properties

Parameter RangeNumber of mesh layers in the boundary layers 8

Boundary layer mesh expansion factor 12

Thickness of first mesh layer 000005ndash00002Thickness adjustment factor 1

00002m commensurate with the curvature on the airfoilsurface Having chosen the thickness of the elements of thefirst meshing layer adjacent to the airfoil surface the fol-lowing consecutive layers were expanded with an expansionfactor of 12 for eight consecutive layers Another option canbe taken to allow thickness adjustment of the first meshinglayer by choosing the thickness adjustment factor [48] forthe present study the thickness adjustment factor of one waschosen

The grid generator is sufficiently general so that one caneasily vary the jet slot location and sizeGrid spacing and clus-tering can have significant effects on Wind turbine load andperformance predictions [49] The outer boundary is placedfar away from the blade surface at least at six chord lengths(6 C) from the airfoil surface to avoid significant influ-ence from outer boundary into the interior domain and to


Boundarylayer mesh

6C

6C

6C

6C

Figure 5 Computational grid around a typical airfoil shown here for S809 Coanda configured airfoil

allow the disturbances to leave the domain [20] The com-putational domain and the grid in the vicinity of the airfoilsurface and Coanda-jet slot are exhibited in Figure 5

52 Initial and Boundary Conditions In general the initialconditions are set to be equal to the properties of the free-stream flow condition [19] The flow properties everywhereinside the flow field are assumed to be uniform and set to thefree-stream values The following initial values are used

119906 = 119906infin V = V

infin 120588 = 120588

infin 119901 = 119901

infin

119879 = 119879infin

(8)

The outer boundary is placed far away from the blade sur-face at aminimumof 6 chords (6C)Nonreflecting boundaryconditions are applied at the outer boundaries of the compu-tational domain The jet is set to be tangential to the bladesurface at the Coanda-jet nozzle location The jet velocityprofile is specified to be uniform at the jet exit On the airfoilsurface except at the jet exit no-slip boundary conditions areapplied To gain benefits the jet velocity is here designed tobe larger than the potential flow velocity at the vicinity of theouter edge of the boundary layer In addition the thickness ofthe Coanda-jet is designed to be less than the local boundarylayer thickness

Outer boundary conditions are chosen to minimizeblockage effect that is significant discrepancies with freeflight situations whether theoretically or numerically simu-lated or experimental Wall effects blockage changes stream-line curvature interaction boundary layers and these shouldbe minimized The best measure is by carrying out com-putational experiments with reasonable outer boundariesof the computational grid and validating with both outerpotential flow results and numerical parametric studies Thisrationale has shown that for the case considered an outergrid boundary distance to the computational domain center-line of six chords produces results with high accuracy as can

be justified in the results presented in Figure 5 It should benoted however that Figure 5 indicates that with higher angleof attack far-field boundaries should be placed further awayfrom the airfoil

53 Baseline Validation Prior to its utilization various base-line cases have been tried out with favorable results As acase in point for benchmarking purposes the code has beenapplied to calculate the lift-slope characteristics of S809 airfoil(clean configuration without Coanda) and GTRI CCWDualRadius airfoil (with Coanda) and compared to the resultsobtained by Somers [50] as shown in Figure 6 and Englaret al [5] as shown in Figure 7 respectively The results asshown in both Figures demonstrated the plausibility of thepresent numerical computational scheme

Computational results exhibited in Figure 6 served tovalidate the computational procedure associated with the useof CFD code in the numerical simulation and as a baselinein furthering the computational study of Coanda-jet in thepresent study Figure 6 compares the present computationalsimulation using k-120576 turbulence model and Kuzminrsquos [35]wall function (the associated 119910

+ value is 1106) with theexperimental data of Somers [50] The numerical resultsabove simulated similar experimental conditions of Somersfor clean S809 airfoil (with wall boundary conditions andwithout Coanda-jet) It also shows that the lift and dragcoefficients at zero angle of attack are in close agreement withthe experimental data

Similar numerical simulation was carried out for GTRIDual Radius CCW airfoil with leading edge blowing andcompared to the experimental data (in Figure 7) from Englaret al [5] with the same boundary conditions and jet con-figuration using k-120576 turbulence model and Kuzminrsquos wallfunction [35] Of significant interest are the grid size the wallfunction and 119910+ value utilized for numerical simulationTheassociated 119910 value for the cells adjacent to the airfoil surfacewas designed to be no more than 00002m in order to satisfy


0 1 2 3 4 5 6 7 8 9 10minus1

Experiment in closed conduitCOMSOL 119896-120576 in closed conduitCOMSOL 119896-120576 in infinite medium

1211

1090807060504030201

0minus01

S809

Angle of attack

Lift

coeffi

cien

t

(a)

0050045

0040035

0030025

0020015

0010005

00 1 2 3 4 5 6 7 8 9 10

Angle of attack

Dra

g co

effici

ent

minus1


(b)

Figure 6 Comparison for validation of S809 airfoil of CFD computational results using COMSOL k-120576 turbulence model and experimentalvalues from Somers [50] at Re = 1E6 (a) lift coefficient (b) drag coefficient

5

4

3

2

1

00 005 01 015 02 025 03 035 04

Lift

coeffi

cien

t

Momentum jet

GTRI Dual Radius CCW


Figure 7 Comparison of lift-curve slope for GTRI Dual RadiusCCW airfoil with LE blowing on CFD computation using COMSOLk-120576 turbulence model and experimental values from Englar et al [5]at Re = 395000

the119910+ value requirements whichwere chosen to be 1106Theresults exhibited in Figure 7 for this case is also encouragingdue to the close agreement between the present computationand the experimental data

The results exhibited in both examples above serve toindicate that the computational procedure and choice ofturbulencemodel seem to be satisfactory for the present com-putational study and could lend support to further use of theapproach in the numerical parametric study

All computations in the present study were performed ona laptop computer with a 210GHz Intel Core Duo processor4GB of RAM and 32-bit operating system Typical compu-tation time for the computation of the flow characteristicsaround a two dimensional airfoil is in the order of 4 hourswith around 300000 degrees of freedom by using stationarysegregated solver in k-120576 turbulent model analysis With suchcomputational environment which in consequence limits thecomputational grids the present work will seek and adopt

appropriate CFD numerical procedures Simplified theoreti-cal analysis is carried out prior to themodeling andnumericalcomputation while further theoretical analysis will be carriedout in evaluating the computational results

6 Results and Discussions

61 Design Considerations for Coanda Configured Airfoil Forthe purpose of assessing the influence and the effectivenessof the Coanda enhanced LD and lift augmentation on windturbine blade a generic two-dimensional study is carriedout The problem at issue is how the Coanda-jet can beintroduced at the TE of the airfoil bearing in mind thatsuch design may recover any losses due to the possibleinception of flow separation there In addition for effectiveCoanda-jet performance a curvature should be introducedFurthermore the thickness of the Coanda-jet as introducedon the airfoil surface could have a very critical effect on theintended lift enhancement function For best effect thelower surface near the TE should be flat as suggested byTongchitpakdee et al [19 20] The design of the Coanda-configuredTE should also consider the off-design conditionsWith all these considerations a configuration suggested isexhibited in Figure 8

62 Computational Results for S809 Airfoil Next we wouldlike to investigate the influence of specifically designed airfoilgeometry for Wind turbine application and for this purposea typical S809 in clean and Coanda-jet equipped configura-tions S809 airfoil represents one of a new series of airfoilswhich are specifically designed for HAWT applications [20]For the present study the numerical simulation was carriedout at two free-stream velocities These are 577ms (corre-sponding toRe= 395times 105) and 146msec (corresponding toRe = 1 times 106) which represent low and high free-stream casesrespectively while the chord-length is maintained at c = 1mand density at 120588 = 1225 kgm3 The baseline for assessing


Parallel Tangent line

Distance from LE

TE jet thickness

TE radius

Figure 8 TE construction of the Coanda configured airfoil (the jetflow is tangential to the rounded circular sector)

the advantages of Coanda-jet from parametric study on S809airfoil is the computational result for the clean airfoil Thecomputational result for this baseline case has been validatedby comparison of the computational value for the same S809airfoil to the experimental results based on wind-tunnel testIt should be noted that the flow field boundaries are differentfrom those utilized for the parametric study

The two-dimensional numerical simulation study for theS809 airfoil is carried out in logical and progressive stepsFirst the numerical computation is performed on the cleanS809 airfoil then on the Coanda configured S809 airfoilwithout the jet (ie after appropriate modification due to TErounding-off and back-step geometry) and then finally onCoanda configured S809 airfoil in its operational configura-tion

To address three-dimensional wind turbine configura-tions particularly for the optimumdesign of a horizontal axisWind turbine (HAWT) logical adaptation should be madetaking into account the fact that different airfoil profiles maybe employed at various radial sections Certain assumptionshave to be made in order to project two-dimensional simu-lation results to the three-dimensional case which may benecessary to evaluate the equivalent Betz limit

621 The Influence of Coanda-Jet on the Flow off the TE Theflow field in the vicinity of the TE for both configurations isshown in Figures 9(a) and 9(b) Careful inspection of thesefigures may lead to the identification of the geometry of theflow that could contribute to increased lift in similar fashionas that contributed by flap jet flap orGurney flap Figure 9(b)typifies the flow field around Coanda configured S809 airfoilwithout Coanda-jet (only with its back-step configuration)which is used here to get insight to the action of the Coanda-jet

622 Parametric Study Results for Coanda Configured S809Airfoil The TE radius plays an important role in the Coandaconfigured design airfoil since it may positively or negativelyinfluence the downstream flow behavior Tongchitpakdee etal [19 20] had claimed that the lower surface at the TE of theapplied Coanda-jet should be flat in order to minimize thedrag when the jet is turned off Also as reported earlier byAbramson and Rogers [51 52] in the late 1980s in spite of theability to generate more lift the technique has not in general

been applied to the production aircrafts Many of the road-blocks have been associated with the engine bleed require-ments and cruise penalties associated with blown blunt TEsIn addition there is a tradeoff between the use of a largerradius Coanda configured airfoil for maximum lift and theuse of a smaller radius one for minimum cruise drag

In contrast to the needs of TE rounding-off radiusperformance degradation associated with it always stands asan issue due to the drag penalty when the jet is in the offmode To overcome such drawback the TE radii should bespecifically and carefully designed For that purpose simula-tions at several TE radius (from 10mm to 50mm) have beenperformed at a fixed Coanda-jet momentum coefficient 119862

120583

(119862120583

= 0003 considered just enough to fit with the Windturbine application) and at a constant free-stream velocityof 119881infin

= 146msec (Re = 1 times 106) to investigate the effectof TE radius on the aerodynamic characteristics of Coandaconfigured airfoils Results exhibited in Figure 10 show that ahigher119871119863 can be achievedwith a smaller TE radius (30mm)and that the 119871119863 is decreasing as the TE radius is increasedfrom 30mm to 50mm The effect of TE radius on the liftaugmentation is significant as exhibited by the dashed line inFigure 10 However when the TE radius is increased beyondcertain value (in Figure 10 ≫35mm) the TE rounding-offseems to be ineffective even detrimental

Moving the location of the Coanda-jet forward impliesthe increase of the TE radius Consequently the camber of theairfoil will also be changedThis in turn will produce changesin the angle of attack of the airfoil compared to the baselinecase Therefore although the present study looks into theinfluence of modifying TE radius while holding other airfoilgeometrical parameters constant the zero angle of attackcondition is at best possible only as first approximation Therobustness of the computational procedure adopted in thepresent computational set-upmay be able to take into accountall these changes Such a case is indeed revealed in Figures10(c) and 10(d) whereby the influence of all the changes of thegeometrical variables accompanying the present parametricstudy should have been incorporated in the computationalscheme which is focused on the TE radius changes andproduces changes in L andD contributed also by the changesin the angle of attack Additionally these figures show that thechanges in lift is much larger than the changes in drag asexhibited in Figures 10(c) and 10(d)

Variation of the Coanda-jet thickness from 05mm to30mm at a fixed 119862

120583(119862120583

= 0005) and at a constant free-stream velocity of 119881

infin= 146msec (Re = 1 times 106) is per-

formed to investigate the effect of Coanda-jet thickness (alsocalled jet slot thickness) on the aerodynamic characteristicsof Coanda configured airfoils From Figure 11 it is foundthat a higher LD can be achieved with a smaller Coanda-jetthickness (10mm) and that the LD is decreased rapidly asthe Coanda-jet thickness is increased from 15mm to 30mmA similar behavior is observed for the lift augmentation asexhibited by the dashed line in Figure 11 However generatinga smaller jet requires higher pressure than a larger one at thesame momentum coefficient Since higher lift with as lowmass flow rate as possible is preferred a thin jet is more


181614121086420

(ms

)

(a)

181614121086420

(ms

)

(b)

Figure 9 Velocity fields of S809 airfoil (a) with and (b) without Coanda-jet

Lift augmentation

50

6050

4540

40

3530

30

2520

20

1510

10

50

0TE radius (mm)

119871119863

(a)

119877TE = 10mm 119877TE = 20mm 119877TE = 40mm 119877TE = 50mm 181614121086420

(b)

02

018

016

014

012

010 10 20 30 40 50 60

TE radius (mm)

Lift

coeffi

cien

t

(c)

0 10 20 30 40 50 60TE radius (mm)

Dra

g co

effici

ent

0014

00138

00136

00134

00132

0013

(d)

Figure 10 (a) The effect of TE radius on LD with Coanda-jet (Re = 1 times 106 119862120583= 0005 t = 1mm) (b) velocity flow field for different TE

radius (c) lift coefficient (d) drag coefficient

beneficial than a thick jet [11] From aerodynamic designperspective within the range of agreeable power to generateCoanda-jet a smaller Coanda-jet thickness is preferredalthough further careful trade-off study should be madeSeparation occurs earlier at thicker jet size compared to

thinner jet size (see Figures 10(b) and 10(c)) even thoughboth were at the same jet momentum size

The performance of Coanda configured airfoils is depen-dent on the jet momentum conditions which are importantdriving parameters Figures 12(a) and 12(b) show numerical


Lift augmentation

504540353025201510

50

0 05 1 15 2 25 3 35

119871119863

Coanda-jet thickness (mm)

(a)

119905 = 05mm

119877TE = 50mm

181614121086420

(b)

119905 = 3mm

119877TE = 30mm

181614121086420

(c)

Figure 11 (a) The effect of jet thickness on the LD and lift augmentation (Re = 1 times 106 119877TE = 30mm) (b) flow separation with t = 05mm(c) flow separation with t = 30mm

simulation for a free-stream velocity of 577msec and146msec respectively In both free-stream velocity caseswhen the jet momentum coefficient 119862

120583≪ 0004 it did not

generate a sufficiently strong Coanda effect that could elim-inate separation and vortex shedding as also found in [19]The LD increases significantly with the increase of thejet momentum coefficient (119862

120583) until the jet momentum

coefficient reaches 119862120583= 0008 After this value the effect is

otherwise Under fixed free-stream velocity and fixedCoanda-jet thickness the total mass flow rate increaseslinearly with the increase of the jet momentum Also the jetvelocity (119881Coanda-jet) has to be increased with the mass flowrate to keep a constant 119862

120583 The dotted line shown in Figures

12(a) and 12(b) shows that the maximum lift augmentation isabove 40 and 50 respectively Figure 12(c) seems to indicatethat higher free-stream velocity on the Coanda configuredS809 airfoil produces higher lift while at the same time asexhibited in Figure 12(d) it produces lower drag

Figure 13 also shows that the Coanda-jet is only effec-tive when it is located at the rounding-off surface of theTE Locating the Coanda-jet further upstream from therounding-off surface seems to be detrimental since theCoanda-jet momentum losts its energy before reaching theend of rounding-off surface Such notion is demonstratedin Figure 13(b) by varying the Coanda-jet nozzle at variouspositions upstream of the inception of the TE rounding-offsurface (ie from 90 to 95 from the leading edge) By

reaching the TE at the end of the rounding-off surface thejet leaving the airfoil acts as a virtual flap

63 Contribution of Coanda-Jet Momentum Coefficient

631 CFD Results for Coanda-Jet Configured S809 Airfoils Itshould be noted that for the purposes of the present work auniform jet velocity profile has been adopted this could bereadily modified for more realistic modeling or designrequirements Numerical results indicate that there exists anoptimum Coanda-jet configuration which has been thesubject of parametric study as exhibited in Figures 10ndash13 forS809 airfoil

A significant design parameter for boundary conditionwhich has been utilized to characterize Coanda-jet applica-tions by many investigators [10 11 19 20] is specified by themomentum coefficient of the jet 119862

120583 For two-dimensional

modeling an equivalent jet momentum coefficient119862lowast120583can be

defined as

119862lowast

120583equiv

119881Coand a-jet

(12) 1205881198812

infin119860 ref

=

120588Coand a-jet1198812

Coand a-jet119905Coand a-jet

(12) 1205881198812

infin119888airfoil

(9)

This expression shows that for a given constant 119862120583

changing the thickness of the Coanda-jet will affect 119862120583

favorably [53ndash55]


Lift augmentation

605040302010

0minus10

minus20

minus30

0 001 002 003 004 005

119881infin = 577ms Re = 395 times 105

119871119863

Coanda-jet momentum

(a)

Lift augmentation

605040302010

0minus10

minus20

minus30

0 001 002 003 004 005

119881infin = 146ms Re = 1 times 106

119871119863

Coanda-jet momentum

(b)

16

14

12

1

08

06

04

02

0

Lift

coeffi

cien

t

Re = 3951198645

0 001 002 003 004 005

Re = 11198646

Coanda-jet momentum

(c)

007

006

005

004

003

002

001

0

Dra

g co

effici

ent

0 001 002 003 004 005

Re = 3951198645Re = 11198646

Coanda-jet momentum

(d)

Figure 12 The effect of jet momentum on the LD and lift augmentation (119877TE = 50mm 119905jet = 1mm) (a) Re = 395 times 105 (b) Re = 10 times 106

To justify the results of the present study and to give usa physical explanation of the effect of Coanda-jet one mayattempt to carry out simple calculation using first principleand Kutta-Joukowski law for potential flow and comparethe lift of the Coanda configured airfoil with the clean oneobtained using CFD code One has

119871Coand a-jet Airfoil

= 119871clean Airfoil + 120588119881infin(119881Coand a-jetℎCoand a-jet)

(10)

where ℎCoand a-jet is the moment arm of the Coanda-jet withrespect to the airfoil aerodynamic centerOne thenmay arriveat a very good conclusion on the contribution of the Coanda-jet to the lift (surprisingly using CFD results for the lift(119871Coand a-jet Airfoil) values the accuracy obtained by using (3)was in the order of 139) However care should be exercisedto insure valid modeling for comparison

For the three-dimensional configuration there is a phys-ical relationship between the Wind turbine shaft torque(which is a direct measure of the extracted shaft power)with 119862

120583and in the actual three-dimensional case the wind

turbine rotor yaw angle [19 20] From the numerical results

gained thus far it can be deduced that circulation con-trol which in this particular case obtained by utilizing TECoanda-jet can considerably increase the torque generatedthrough the LD increase gained

It should be noted that the results obtained in the presentwork is limited to two-dimensional wind turbine blade anal-ysis which at best can be interpreted to be valid at 07 bladespan distance from thewind turbine rotor hub axisThe ambi-ent air free-stream wind speed 119881

infinfor the Wind turbine is

different from the119881infinimplied in the present two-dimensional

parametric study which is the resultant of the ambient-airwind speed and the rotational speed of the particular sectionof the rotor blade In addition the centrifugal effects shouldthen be superposed to the local relative flow at the windturbine blade airfoil cross section The free-stream flowconsidered in the present two-dimensional study should beappropriately regarded as the total relative flow at the crosssection analyzed which comprises the wind free-streamvelocity the blade rotational velocity at that points and thecentrifugal effect For three-dimensional case 3D conditionsshould be applied in the utilization of the CFD computationalcode These factors should be considered in translating thetwo-dimensional study to three-dimensional cases


25

20

15

10

5

0

minus5

90 91 92 93 94 95

119862120583 = 0005

Lift augmentation119871119863

Coanda-jet location ()

(a)

25

20

15

10

5

0

minus5

Lift augmentation

119862120583 = 001

90 91 92 93 94 95

119871119863


(b)

90 92 94 95 181614121086420

(c)

Figure 13 The effect of Coanda-jet location on the LD and lift augmentation (Re = 1 times 106 119877TE = 10mm 119905jet = 1mm) (a) 119862120583= 0005 (b)

119862120583= 0010 (c) velocity flow field for different Coanda-jet location119862

120583= 0010

With due considerations of the three-dimensional casefrom the numerical results gained thus far it can be deducedthat circulation control which in this particular case obtainedby utilizing TE Coanda-jet can considerably increase thetorque generated through the LD increase gained

Consequently Coanda-jet has the potential to increasethe energy output delivered by a Coanda configured Windturbine To this end onemay recall that the maximum powerthat can be delivered by a Wind turbine cannot exceed theBetz limit which is given by

119875Betz =8

27120588119860wind turbine rotor119881

2

infin (11)

where 119881infin

is the wind speedHence with the introduction of Coanda-jet using con-

siderations reflected by (5) to derive the new Wind turbineenergy output this limit can be exceeded Tongchitpakdee[20] has also confirmed such situation for certain values ofCoanda-jet momentum coefficient

With regard to the design implementation of the presentresults and concepts the maximum theoretical power thatcan be extracted from the free-stream (ambient air) in thereal three-dimensional situation is given by (6) With the useof Coanda-jet assuming the jet energy can be drawn fromthe inner part of the free-stream in the vicinity of the windturbine rotor hub the Coanda jet additional power outputcorresponding to the jet momentum coefficient should con-tribute to the increase of shaft power output given by thetheoretical Betz limit Jones and Englar studies [32] also indi-cated such results With such scheme the power required for

introducing Coanda-jet can be minimized and readily beestimated from the total Coanda-jet velocity and mass flowalthough the implementation requiredmeticulous design andwill be the subject of a separate study

7 Conclusion and Further Work

CFD numerical experiments have been carried out to elab-orate work reported earlier [53ndash55] with the objective toverify the favorable effects of Coanda configured airfoil forenhanced aerodynamic performance and obtain some guide-lines for the critical features of Coanda configured airfoilCare has been exercised in the choice of turbulence modeland other relevant parameters commensurate with the gridfineness desired in particular since the number of gridutilized is relatively small in view of the desktop computerutilized capabilities Comparison of the numerical compu-tation results for some baseline cases with experimentaldata under similar conditions lends support to the presentcomputational parametric study

CFD numerical computations for the flow field aroundtwo-dimensional airfoil S809 have been carried out with theobjective to study the extent to which the introduction ofCoanda-jet enhances the aerodynamic performance of theairfoil here represented by the LD value and leads to thefollowing observations

The introduction of Coanda-jet on both airfoils carriedout in the present work results in enhanced LD whichdepends on the jet velocity For S809 Coanda configured


airfoil for a certain range of the jet velocity the increase ofLD as well as the lift augmentation are monotonic The two-dimensional results show that the effects of Coanda-jet inmodifying aerodynamic performance in general agree withthose obtained for three-dimensional results of Tongchit-pakdee et al [19 20]

Rounding-off of the TE alongwith the introduction of theCoanda-jet seems to be effective in increasing LD in airfoilspecifically designed for Wind turbine here exemplified byS809 Such result may be due to the relatively large TEdimension of the Wind turbine specifically designed airfoilcompared to that with sharper TE To a certain extentsmaller TE radii produced better LD than larger ones It isalso noted that after certain value further increase in TEradius does not give significant lift augmentation as indicatedby Figure 10(a) There is a range of effective Coanda-jet sizedesigns depending on their thickness Within the limits oflocal boundary layer thickness there is a certain range ofeffective Coanda-jet thickness The present study indicatesthat the optimum jet thickness commensurate with theairfoil dimension Care should be exercised to avoid flowseparation at larger Coanda-jet thickness is dependent on theairfoil dimensions Coanda-jet thickness and TE rounding-off size the Coanda-jet momentum needed to improve theperformance (lift augmentation due to jet) should not beexcessive but sufficient to delay separation until the tip of theTE (where the upper surface meets the lower one) Inaddition the Coanda-jet should be placed sufficiently close tothe TE to avoid premature separation

With due considerations of prevailing three-dimensionaleffects the two-dimensional numerical study can be used todirect further utilization of the CFD computational proce-dure for Wind turbine blade studies and their design opti-mization Numerical results presented have been confined tozero angle of attack case which has been considered to bevery strategic in exhibiting the merit of Coanda-jet as liftenhancer The numerical studies could be extended toincreasing the angle of attack to obtain more comprehensiveinformation for which the choice of turbulencemodel will bemore crucial

The study also shows that the maximum total energy out-put of Coanda configured airfoilmay exceed that predicted byBetz limit With all the results obtained thus far it is felt thatthe present work is by nomeans exhaustive Other issues maystill be explored such as how could the ambient air energyinput that can be drawn by the Coanda-jet configured Windturbine either from the nacelle or elsewhere be utilized toenergize the Coanda-jet and for that matter to lower the cut-in speed of HAWT or the starting speed of VAWT

Nomenclature

CFD Computational fluid dynamicCCW Circulation control wingR Trailing edge radius (mm)C Airfoil chord length (m)L Lift force (N)D Drag force (N)H Coanda-jet thickness (mm)

LD Lift over drag ratioTE Trailing edgeSTOL Short takeoff landing119910+ Dimensionless wall distance for a

wall-bounded flow119906120591 Friction velocity

y Distance to the nearest wallv Kinematic viscosity120591119908 Wall shear stress

120588 Density120583120591 Turbulent viscosity as defined by (2) and

implied by contextHAWT Horizontal axis wind turbineM Mach numberC120583 Turbulent model constant as defined by (2)

119862120583 Momentum coefficient

Δ119862119871119862119871 Lift augmentation

Δ119862119871119862120583 Lift augmentation due to Coanda-jet

MW MegawattMWh Megawatt hour

Conflict of Interests

The authors assure that there is no conflict of interests what-soever with any commercial products including CFD codesthat have been utilized in the present work Any commercialsoftware codes that are used in the present work such asFluent and COMSOL are used for the purpose of arrivingat research results and have been acquired through purchasewithout any vested interest whatsoever from the authors

Acknowledgments

The present research was initiated under Universiti PutraMalaysia (UPM) Research University Grant Scheme (RUGS)no 05-02-10-0928RU CC-91933 and the Ministry of HigherEducation Exploratory Research Grant Scheme Project Codeno 5527088 The first and corresponding author would alsolike to thank Universitas Al-Azhar Indonesia for the oppor-tunity to carry out the present research at Universiti PutraMalaysia

References

[1] J F Manwell J G McGowan and A L Rogers Wind EnergyExplained Wiley Amherst Mass USA 1st edition 2002

[2] T Ackermann and L Soder ldquoWind energy technology andcurrent status a reviewrdquo Renewable and Sustainable EnergyReviews vol 4 no 4 pp 315ndash374 2000

[3] C E Lan and J F Campbell ldquoTheoretical Aerodynamics ofUpper-Surface Blowing Jet-Wing Interactionrdquo NASA TN D-7936 1975

[4] M J Harris ldquoInvestigation of the circulation controlwingupper surface blowing high-lift system on a low aspectratio semispan modelrdquo Report DTNSRDCASED-8110 DavidTaylor Naval Ship RampD Center Aviation and Surface EffectsDepartment Bethesda Md USA 1981


[5] R J Englar M J Smith S M Kelley and R C Rover ldquoAppli-cation of circulation control to advanced subsonic transportaircraftmdashpart I airfoil developmentrdquo Journal of Aircraft vol 31no 5 pp 1160ndash1168 1994

[6] R J Englar M J Smith S M Kelley and R C Rover ldquoAppli-cation of circulation control to advanced subsonic transportaircraftmdashpart II transport applicationrdquo Journal of Aircraft vol31 no 5 pp 1169ndash1177 1994

[7] Y G Zhulev and S I Inshakov ldquoOn the possibility of enhancingthe efficiency of tangential blowing of a slit jet from an airfoilsurfacerdquo Fluid Dynamics vol 31 no 4 pp 631ndash634 1996

[8] M Gad-el-Hak ldquoModern developments in flow controlrdquoApplied Mechanics Reviews vol 49 no 7 pp 365ndash379 1996

[9] R J Englar ldquoAdvanced aerodynamic devices to improve the per-formance economics handling and safety of heavy vehiclesrdquoSAE Technical Paper Series Paper no 2001-01-2072 2001

[10] Y Liu L N Sankar R J Englar and K Ahuja ldquoNumerical sim-ulations of the steady and unsteady aerodynamic characteristicsof a circulation control wingrdquo in Proceedings of the 39th AIAAAerospace Sciences Meeting AIAA Reno Nev USA 2001

[11] Y Liu Numerical simulations of the aerodynamic characteristicsof circulation control wing sections [PhD thesis] GeorgiaInstitute of Technology 2003

[12] J Wu L N Sankar and S Kondor ldquoNumerical modeling ofCoanda jet controlled nacelle configurationsrdquo in Proceedingsof the 42nd AIAA Aerospace Sciences Meeting and Exhibit pp2358ndash2366 January 2004

[13] M H Shojaefard A R Noorpoor A Avanesians andM Ghaf-farpour ldquoNumerical investigation of flow control by suction andinjection on a subsonic airfoilrdquo American Journal of AppliedSciences vol 10 pp 1474ndash1480 2005

[14] M Mamou and M Khalid ldquoSteady and unsteady flow simula-tion of a combined jet flap and Coanda jet effects on a 2D airfoilaerodynamic performancerdquo in Proceedings of the Revue desEnergies Renouvelables (CER rsquo07) pp 55ndash60 Oujda Morocco2007

[15] S K Sinha ldquoOptimizing wing lift to drag ratio enhancementwith flexible-wall turbulence controlrdquo in Proceedings of the 25thAIAA Applied Aerodynamics Conference pp 1670ndash1685 June2007

[16] R Radespiel K C Pfingsten and C Jensch ldquoFlow analysisof augmented high-lift systemsrdquo in Hermann Schlichtingmdash100Years vol 102 pp 168ndash189 Technische Universitat Braun-schweig Springer Berlin Germany 2009

[17] G Xu and L N Sankar ldquoComputational study of horizontalaxis wind turbinesrdquo Journal of Solar Energy Engineering Trans-actions of the ASME vol 122 no 1 pp 35ndash39 2000

[18] E P N Duque W Johnson C P van Dam R Cortes andK Yee ldquoNumerical predictions of wind turbine power andaerodynamic loads for theNRELphase II combined experimentrotorrdquo in Proceedings of the 38th AIAA Aerospace SciencesMeeting AIAA Reno Nev USA 2000

[19] C Tongchitpakdee S Benjanirat and L N Sankar ldquoNumericalstudies of the effects of active and passive circulation enhance-ment concepts on wind turbine performancerdquo Journal of SolarEnergy Engineering Transactions of the ASME vol 128 no 4pp 432ndash444 2006

[20] C Tongchitpakdee Computational studies of the effects of activeand passive circulation enhancement concepts on wind turbineperformance [PhD thesis] Georgia Institute of Technology2007

[21] A Hokpunna and M Manhart ldquoA large-Eddy simulation ofvortex cell flow with incoming turbulent boundary layerrdquoEngineering and Technology vol 32 2007

[22] C L Rumsey and P R Spalart ldquoTurbulence model behaviorin low Reynolds number regions of aerodynamic flowfieldsrdquo inProceedings of the 38th AIAA Fluid Dynamics Conference andExhibit Seattle Wash USA June 2008

[23] F R Menter ldquoAdvances in Turbulence Modelling of UnsteadyFlowsrdquo Menter Shear Stress Transport Model ANSYS Ger-many 2009 httpturbmodelslarcnasagovssthtml

[24] L D Kral ldquoActive flow control technologyrdquo ASME FluidsEngineering Technical Brief 2000

[25] P F Zhang B Yan A B Liu and J J Wang ldquoNumericalsimulation on plasma circulation control airfoilrdquoAIAA Journalvol 48 no 10 pp 2213ndash2226 2010

[26] P F Zhang B Yan andC FDai ldquoLift enhancement by syntheticjet circulation controlrdquo Science China Technological Science vol55 pp 2585ndash2592 2012

[27] M P Patel S Vasudevan R C Nelson and T C Cork ldquoPlasmaAerodynamic Control Effectors for Improved Wind TurbinePerformancerdquo Orbital Research Inc Cleveland Ohio USA2008

[28] R C Nelson T C Corke H OthmanM P Patel S VasudevanandTNg ldquoA smartwind turbine blade using distributed plasmaactuators for improved performancerdquo in Proceedings of the 46thAIAA Aerospace Sciences Meeting and Exhibit Reno Nev USAJanuary 2008

[29] G Xu Computational studies of horizontal axis wind turbines[PhD thesis] School of Aerospace Engineering Georgia Insti-tute of Technology Atlanta Ga USA 2001

[30] J L Tangler and D M Somers ldquoNREL Airfoil Families forHAWTsrdquo NRELTP 442-7109 UC Category 1211 DE95000267American Wind Energy Association 1995

[31] G M Joselin Herbert S Iniyan E Sreevalsan and S Rajapan-dian ldquoA review of wind energy technologiesrdquo Renewable andSustainable Energy Reviews vol 11 no 6 pp 1117ndash1145 2007

[32] G S Jones and R J Englar ldquoAdvances in pneumatic controlledhigh lift systems through pulsed blowingrdquo in Proceedings of the21st Applied Aerodynamics Conference AIAA Orlando FlaUSA 2003

[33] O C Zienkiewicz and R L TaylorThe Finite Element MethodButterworth-Heinemann 5th edition 2000

[34] F H Harlow and P Nakayama ldquoTransport of turbulence energydecay raterdquo Report LA-3854 Los Alamos Science LaboratoryUniversity of California 1968

[35] D Kuzmin O Mierka and S Turek ldquoOn the implementationof the k-e turbulence model in incompressible flow solversbased on a finite element discretizationrdquo International Journal ofComputing Science and Mathematics vol 1 no 2ndash4 pp 193ndash206 2007

[36] F H Harlow and P Nakayama ldquoTurbulence transport equa-tionsrdquo Physics of Fluids vol 10 no 11 1967

[37] B E Launder A Morse W Rodi and D B Spalding ldquoThe pre-diction of free shear flowsmdasha comparison of the performanceof six turbulencemodelsrdquo in Proceedings of NASAConference onFree Shear Flows Langley Va USA 1972 Also Imperia1 CollegeMechanical Engineering Department Report TMTNA19

[38] B E Launder and B I Sharma ldquoApplication of the energy-dissipation model of turbulence to the calculation of flow neara spinning discrdquo Letters in Heat and Mass Transfer vol 1 no 2pp 131ndash137 1974


[39] W P Jones and B E Launder ldquoPredictions of low-Reynolds-number phenomena with a Z-equation model of turbulencerdquoInternational Journal of Heat and Mass Transfer vol 16 no 6pp 1119ndash1130 1973

[40] W P Jones and B E Launder ldquoThe prediction of laminarizationwith a two-equationmodel of turbulencerdquo International Journalof Heat and Mass Transfer vol 15 no 2 pp 301ndash314 1972

[41] J Boussinesq ldquoEssai sur la theorie des eaux courantesrdquoMemoires Presentes par Divers Savants a lrsquoAcademie des Sciencesvol 23 no 1 pp 1ndash680 1877

[42] E Farsimadan A study of the turbulent wake of an airfoil in anair stream with a 90∘ curvature using hot-wire anemometry andlarge Eddy simulation [PhD thesis] Brunel University 2008

[43] D C Wilcox Turbulence Modeling for CFD DCW Industries3rd edition 2006

[44] S Benjanirat Computational Studies of Horizontal Axis WindTurbines in High Wind Speed Condition using Advanced Tur-bulence Models [PhD thesis] Georgia Institute of Technology2006

[45] S M Salim and S C Cheah ldquoWall y+ strategy for dealing withwall-bounded turbulent flowsrdquo in Proceedings of the Interna-tional Multi-Conference of Engineers and Computer Scientists(IMECS rsquo09) vol 2 Hong Kong 2009

[46] T D Economon and W E Milholen II ldquoParametric Investi-gation of a 2-D Circulation Control Geometry ConfigurationAerodynamics Branch Research and Technology Directoraterdquo2008

[47] H Grotjans and F Menter ldquoWall functions for general applica-tion CFD codesrdquo in Proceedings of the 4th Computational FluidDynamics Conference (ECCOMAS rsquo98) pp 1112ndash1117 JohnWileyamp Sons 1998

[48] ldquoCOMSOL 42 CFD Module Userrsquos Guide COMSOL Inc 1rdquoNew England Executive Park Burlington Mass USA 2011

[49] R Howell N Qin J Edwards and N Durrani ldquoWind tunneland numerical study of a small vertical axis wind turbinerdquoRenewable Energy vol 35 no 2 pp 412ndash422 2010

[50] D M Somers Design and Experimental Results for the S809Airfoil Airfoils State College Pa USA 1989

[51] E O Rogers ldquoDevelopment of Compressible Flow SimilarityConcepts for Circulation Control Airfoilsrdquo AIAA-87-0153 1987

[52] J Abramson and E O Rogers ldquoHigh-speed characteristics ofcirculation control airfoilsrdquo AIAA-83-0265 1988

[53] M F Abdul Hamid H Djojodihardjo S Suzuki and FMustapha ldquoNumerical assessment of Coanda effect as airfoil liftenhancer in wind-turbine configurationrdquo in Proceedings of theRegional Conference on Mechanical and Aerospace Technologypaper RCMEAE-131 Bali Indonesia 2010

[54] HDjojodihardjo andM F AbdulHamid ldquoReview and numeri-cal analysis ofCoanda effect circulation control forwind turbineapplication considerationsrdquo in Proceedings of the Conferenceon Aerospace and Mechanical Engineering World EngineeringCongress Kuching Sarawak Malaysia 2010

[55] H Djojodihardjo M F Abdul Hamid S Basri F I Romli andD L A Abdul Majid ldquoNumerical simulation and analysis ofCoanda effect circulation control for wind-turbine applicationconsiderationsrdquo IIUM Engineering Journal 2011

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of


Journal ofPetroleum Engineering


Industrial EngineeringJournal of


Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of


Journal of


Renewable Energy

Submit your manuscripts athttpwwwhindawicom


StructuresJournal of


RotatingMachinery


EnergyJournal of


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy


Nuclear InstallationsScience and Technology of


Solar EnergyJournal of


Wind EnergyJournal of


Nuclear EnergyInternational Journal of


High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


such as airfoils wings and bodies Specifically modifiedcirculation and enhanced circulation have been utilized forimproved aircraft and land-vehicle performance as well as innovel air-vehicles lift and propulsion system concept due totheir better energy conversion capabilities [17ndash23] The po-tential benefits of flow control include improved performanceand maneuverability affordability increased range and pay-load and environmental compliance Active flow controlmaybe applied to delay or advance transition to suppress or en-hance turbulence or to prevent or promote separation thatwill result in drag reduction lift enhancement mixing aug-mentation heat transfer enhancement and flow inducednoise suppression [24] as appropriate It could be men-tioned that more recently plasma-based flow control hasalso been considered for wind turbine applications [25ndash28]Such efforts may involve the design of ldquosmartrdquo wind turbineblades with integrated sensor-actuator-controller modules toimprove the performance of wind turbines by enhancing en-ergy capture and reduction of aerodynamic loading andnoise by way of virtual aerodynamic shaping These arebeyond the scope of the present work

In this conjunction andwith the progress of CFD the useof Coanda effect to enhance lift has attracted renewed interest[4ndash7 10ndash14 17 29] Tangential jets that take advantage ofCoanda effect to closely follow the contour of the body areconsidered to be simple and particularly effective in that theycan entrain a large mass of surrounding air This can lead toincreased circulation in the case of airfoils or drag reduction(or drag increase if desired) in the case of bluff bodies such asan aircraft fuselage

In the design of a novelWind turbine using with the latestaerospace engineering technology including aerodynamicsnew lightweight materials and efficient energy extractiontechnology highly efficient aerodynamic surface came as akey issue Recent efforts in the last decade have also indicatedthat Coanda effect has been given new and considerableconsiderations for circulation control technique [17 19 2029] Taking advantage of these recent results the presentworklooks into the effort to optimize aerodynamic performance ofWind turbine and to critically investigate the use of Coandaeffect

The progress of high speed computers exemplified bythe availability of new generations of notebooks has madepossible the use of first-principles-based computational ap-proaches for the aerodynamic modeling of Wind turbineblades to name an example As pointed out by Xu and Sankar[17] since these approaches are based on the laws of con-servation of mass momentum and energy they can capturemuch of the physics in great detail These approaches areparticularly helpful at high wind speeds where appreciableregions of separation are present and the flow is unsteady

In the design of circulation control technique one maynote the progress of stall-controlled and pitch-controlledturbine rotor technology for dealing with power productionat low and high wind conditions [30] Of interest is thedeployment of Wind turbines at larger range of sites notlimited to a relatively small number of sites where favorableconditions exist At the other extreme precautions shouldbe taken when the wind speeds become very high when

the rotor invariably stalls and experiences highly unsteadyaerodynamic forces and moments It is noted that over thepast several years there has been an increased effort to extendthe usable operating range of stall-regulated Wind turbinesThe concepts of circulation control through trailing edge (TE)blowing or Coanda-jet then came into view

However over the past decades commonly used airfoilfamilies for horizontal axis Wind turbines such as the NACA44- NACA 23- NACA 63- and NASA LS (1) series airfoilssuffer noticeable performance degradation from roughnesseffects resulting from leading edge contamination [30]Annual energy losses due to leading edge roughness are great-est for stall-regulated rotorsThe loss is largely proportional tothe reduction in maximum lift coefficient (119888

119897max) along theblade High blade-root twist helps reduce the loss by keepingthe bladersquos angle of attack distribution away from stall whichdelays the onset of 119888

119897max Roughness also degrades theairfoilrsquos lift-curve slope and increases the profile drag whichcontributes to further losses For stall-regulated rotors whoseangle of attack distribution increases with wind speed theannual energy loss can be 20 to 30 where leading edgecontamination from insects and airborne pollutants is com-mon Variable-pitch toward stall would result in simi-lar roughness losses as fixed-pitch stall regulation whilevariable-pitch toward feather would decrease the loss toaround 10 at the expense of the rotor being susceptibleto power spikes in turbulent high winds For variable-rpmrotors operating at constant tip-speed ratio and angle ofattack distribution the loss is minimal at around 5 to 10To minimize the energy losses due to roughness effects andto develop special-purpose airfoils for horizontal axis WindTurbine (HAWTrsquos) the National Renewable Energy Labora-tory (NREL) formerly the Solar Energy Research Institute(SERI) and the Airfoils Inc began a joint airfoil developmenteffort in 1984 Results of this effort have produced a new seriesof airfoils which are considered more appropriate for HAWTapplications These blades are providing significant increasesin annual energy production as a result of less sensitivity toroughness effects better lift-to-drag ratios and in the caseof stall-regulated rotors through the use of more swept areafor a given generator size Because of the economic benefitsprovided by these airfoils they are recommended for retrofitblades and most newWind turbine designs [30]

Annual energy improvements from the NREL airfoilfamilies are projected to be 23 to 35 for stall-regulated tur-bines 8 to 20 for variable-pitch turbines and 8 to 10for variable-rpm turbines Optimizing airfoilrsquos performancecharacteristics for the appropriate Reynolds number andthickness provides additional performance enhancement inthe range of 3 to 5 [31] Because of the economic benefitsprovided by these airfoils they are recommended for retrofitblades and most new Wind turbine designs [30] In order toobtain results that can be well assessed especially withreference to extensive research carried out as described in[17 19 20 29] the airfoil S809 [31] is considered in the presentwork For this purpose in this particular work we focus on aparticular problem that is the basic airflow idealizationover a two-dimensional airfoil in subsonic flow Two specificconditions are consideredThe first is a clean S809 airfoil and









3 Objectives




120588119906119895

120597119906119894

120597119909119895⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟


=120597

120597119909119895

[[[

[

minus119901120575119894119895⏟⏟⏟⏟⏟⏟⏟⏟⏟

Normal stress

+

Viscous stress⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞

120583 (120597119906119894

120597119909119895

+

120597119906119895

120597119909119894

) minus 1205881199061015840

1198941199061015840

119895⏟⏟⏟⏟⏟⏟⏟⏟⏟

Reynolds stress

]]]

]

120597119906119894

120597119909119894

= 0

(1)




(a)



Jet sheet

119862119871



Slot

Circulation control

Δ119862119871119862120583 gt80

(b)







SASST Experimental

005

004

003

002

001

008 1 12 14 16 18 2

119880119880infin

Hei

ght119888

119896-120576





120583120591= 120588C120583

1198962

120576 (2)


120591was based



119910+=

119906120591119910

120592 (3)





120597119896

120597119905+ nabla sdot (119896119906 minus

]119879

120590119896

nabla119896) + 120574119896 = 119875119896 (4a)

120597120576

120597119905+ nabla sdot (120576119906 minus

]119879

120590119896

nabla120576) + 1198622120574119896 = 120574119862

1119875119896 (4b)




= C120583(1198962120576) where k is the


(]1198792)|nabla119906 + nabla119906



120583=

0091198621= 144119862

2= 192120590

119896= 10 and 120590

120576= 13




120591is


|119906|

119906120591

=1

120581log119910+ + 120573 (5)


119910+=

119906120591119910

](6)



]119879= 119862120583

1198962

120576= 120581119906120591119910 = 120581119910

+

lowast] (7)

where 119910+

lowast= |119906|119906








= (119906120591119910)120592 = 120588119906

120591(119910120583) where 119906

120591= 120588C

120583(1198962120576) (which










Viscoussublayer

Buffer layeror

blending region


log-law region

ln(119880120591(119910)13)

119880119880120591

12(12119910)

12119910119910

(a) (b)


114113112111

11109108107106 00002 000005Li

ft fo

rce p

er u

nit s

pan

(Nm

)

Coa

rser

Coa

rse

Nor

mal

Fine

Fine

r

Extr

a

Extr

a

(a)

202

2

198

196

194

192

19

188 00002 000005Dra

g fo

rce p

er u

nit s

pan

(Nm

)

Coa

rser

Coa

rse

Nor

mal

Fine

Fine

r

Extr

a

Extr

a

(b)













Boundarylayer mesh

6C

6C

6C

6C




119906 = 119906infin V = V

infin 120588 = 120588

infin 119901 = 119901

infin

119879 = 119879infin

(8)









0 1 2 3 4 5 6 7 8 9 10minus1


1211

1090807060504030201

0minus01

S809

Angle of attack

Lift

coeffi

cien

t

(a)

0050045

0040035

0030025

0020015

0010005

00 1 2 3 4 5 6 7 8 9 10

Angle of attack

Dra

g co

effici

ent

minus1


(b)


5

4

3

2

1

00 005 01 015 02 025 03 035 04

Lift

coeffi

cien

t

Momentum jet













Distance from LE

TE jet thickness

TE radius









120583

(119862120583





120583(119862120583





181614121086420

(ms

)

(a)

181614121086420

(ms

)

(b)


Lift augmentation

50

6050

4540

40

3530

30

2520

20

1510

10

50

0TE radius (mm)

119871119863

(a)


(b)

02

018

016

014

012

010 10 20 30 40 50 60

TE radius (mm)

Lift

coeffi

cien

t

(c)

0 10 20 30 40 50 60TE radius (mm)

Dra

g co

effici

ent

0014

00138

00136

00134

00132

0013

(d)







Lift augmentation

504540353025201510

50

0 05 1 15 2 25 3 35

119871119863


(a)

119905 = 05mm

119877TE = 50mm

181614121086420

(b)

119905 = 3mm

119877TE = 30mm

181614121086420

(c)



120583≪ 0004 it did not














defined as

119862lowast

120583equiv

119881Coand a-jet

(12) 1205881198812

infin119860 ref

=

120588Coand a-jet1198812


(12) 1205881198812

infin119888airfoil

(9)





Lift augmentation

605040302010

0minus10

minus20

minus30

0 001 002 003 004 005

119881infin = 577ms Re = 395 times 105

119871119863

Coanda-jet momentum

(a)

Lift augmentation

605040302010

0minus10

minus20

minus30

0 001 002 003 004 005

119881infin = 146ms Re = 1 times 106

119871119863

Coanda-jet momentum

(b)

16

14

12

1

08

06

04

02

0

Lift

coeffi

cien

t

Re = 3951198645

0 001 002 003 004 005

Re = 11198646

Coanda-jet momentum

(c)

007

006

005

004

003

002

001

0

Dra

g co

effici

ent

0 001 002 003 004 005

Re = 3951198645Re = 11198646

Coanda-jet momentum

(d)





(10)











25

20

15

10

5

0

minus5

90 91 92 93 94 95

119862120583 = 0005



(a)

25

20

15

10

5

0

minus5

Lift augmentation

119862120583 = 001

90 91 92 93 94 95

119871119863


(b)

90 92 94 95 181614121086420

(c)



120583= 0010



119875Betz =8


2

infin (11)

where 119881infin














Nomenclature













Acknowledgments


References






























































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of

























3 Objectives




120588119906119895

120597119906119894

120597119909119895⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟


=120597

120597119909119895

[[[

[

minus119901120575119894119895⏟⏟⏟⏟⏟⏟⏟⏟⏟

Normal stress

+

Viscous stress⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞

120583 (120597119906119894

120597119909119895

+

120597119906119895

120597119909119894

) minus 1205881199061015840

1198941199061015840

119895⏟⏟⏟⏟⏟⏟⏟⏟⏟

Reynolds stress

]]]

]

120597119906119894

120597119909119894

= 0

(1)




(a)



Jet sheet

119862119871



Slot

Circulation control

Δ119862119871119862120583 gt80

(b)







SASST Experimental

005

004

003

002

001

008 1 12 14 16 18 2

119880119880infin

Hei

ght119888

119896-120576





120583120591= 120588C120583

1198962

120576 (2)


120591was based



119910+=

119906120591119910

120592 (3)





120597119896

120597119905+ nabla sdot (119896119906 minus

]119879

120590119896

nabla119896) + 120574119896 = 119875119896 (4a)

120597120576

120597119905+ nabla sdot (120576119906 minus

]119879

120590119896

nabla120576) + 1198622120574119896 = 120574119862

1119875119896 (4b)




= C120583(1198962120576) where k is the


(]1198792)|nabla119906 + nabla119906



120583=

0091198621= 144119862

2= 192120590

119896= 10 and 120590

120576= 13




120591is


|119906|

119906120591

=1

120581log119910+ + 120573 (5)


119910+=

119906120591119910

](6)



]119879= 119862120583

1198962

120576= 120581119906120591119910 = 120581119910

+

lowast] (7)

where 119910+

lowast= |119906|119906








= (119906120591119910)120592 = 120588119906

120591(119910120583) where 119906

120591= 120588C

120583(1198962120576) (which










Viscoussublayer

Buffer layeror

blending region


log-law region

ln(119880120591(119910)13)

119880119880120591

12(12119910)

12119910119910

(a) (b)


114113112111

11109108107106 00002 000005Li

ft fo

rce p

er u

nit s

pan

(Nm

)

Coa

rser

Coa

rse

Nor

mal

Fine

Fine

r

Extr

a

Extr

a

(a)

202

2

198

196

194

192

19

188 00002 000005Dra

g fo

rce p

er u

nit s

pan

(Nm

)

Coa

rser

Coa

rse

Nor

mal

Fine

Fine

r

Extr

a

Extr

a

(b)













Boundarylayer mesh

6C

6C

6C

6C




119906 = 119906infin V = V

infin 120588 = 120588

infin 119901 = 119901

infin

119879 = 119879infin

(8)









0 1 2 3 4 5 6 7 8 9 10minus1


1211

1090807060504030201

0minus01

S809

Angle of attack

Lift

coeffi

cien

t

(a)

0050045

0040035

0030025

0020015

0010005

00 1 2 3 4 5 6 7 8 9 10

Angle of attack

Dra

g co

effici

ent

minus1


(b)


5

4

3

2

1

00 005 01 015 02 025 03 035 04

Lift

coeffi

cien

t

Momentum jet













Distance from LE

TE jet thickness

TE radius









120583

(119862120583





120583(119862120583





181614121086420

(ms

)

(a)

181614121086420

(ms

)

(b)


Lift augmentation

50

6050

4540

40

3530

30

2520

20

1510

10

50

0TE radius (mm)

119871119863

(a)


(b)

02

018

016

014

012

010 10 20 30 40 50 60

TE radius (mm)

Lift

coeffi

cien

t

(c)

0 10 20 30 40 50 60TE radius (mm)

Dra

g co

effici

ent

0014

00138

00136

00134

00132

0013

(d)







Lift augmentation

504540353025201510

50

0 05 1 15 2 25 3 35

119871119863


(a)

119905 = 05mm

119877TE = 50mm

181614121086420

(b)

119905 = 3mm

119877TE = 30mm

181614121086420

(c)



120583≪ 0004 it did not














defined as

119862lowast

120583equiv

119881Coand a-jet

(12) 1205881198812

infin119860 ref

=

120588Coand a-jet1198812


(12) 1205881198812

infin119888airfoil

(9)





Lift augmentation

605040302010

0minus10

minus20

minus30

0 001 002 003 004 005

119881infin = 577ms Re = 395 times 105

119871119863

Coanda-jet momentum

(a)

Lift augmentation

605040302010

0minus10

minus20

minus30

0 001 002 003 004 005

119881infin = 146ms Re = 1 times 106

119871119863

Coanda-jet momentum

(b)

16

14

12

1

08

06

04

02

0

Lift

coeffi

cien

t

Re = 3951198645

0 001 002 003 004 005

Re = 11198646

Coanda-jet momentum

(c)

007

006

005

004

003

002

001

0

Dra

g co

effici

ent

0 001 002 003 004 005

Re = 3951198645Re = 11198646

Coanda-jet momentum

(d)





(10)











25

20

15

10

5

0

minus5

90 91 92 93 94 95

119862120583 = 0005



(a)

25

20

15

10

5

0

minus5

Lift augmentation

119862120583 = 001

90 91 92 93 94 95

119871119863


(b)

90 92 94 95 181614121086420

(c)



120583= 0010



119875Betz =8


2

infin (11)

where 119881infin














Nomenclature













Acknowledgments


References






























































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



















(a)



Jet sheet

119862119871



Slot

Circulation control

Δ119862119871119862120583 gt80

(b)







SASST Experimental

005

004

003

002

001

008 1 12 14 16 18 2

119880119880infin

Hei

ght119888

119896-120576





120583120591= 120588C120583

1198962

120576 (2)


120591was based



119910+=

119906120591119910

120592 (3)





120597119896

120597119905+ nabla sdot (119896119906 minus

]119879

120590119896

nabla119896) + 120574119896 = 119875119896 (4a)

120597120576

120597119905+ nabla sdot (120576119906 minus

]119879

120590119896

nabla120576) + 1198622120574119896 = 120574119862

1119875119896 (4b)




= C120583(1198962120576) where k is the


(]1198792)|nabla119906 + nabla119906



120583=

0091198621= 144119862

2= 192120590

119896= 10 and 120590

120576= 13




120591is


|119906|

119906120591

=1

120581log119910+ + 120573 (5)


119910+=

119906120591119910

](6)



]119879= 119862120583

1198962

120576= 120581119906120591119910 = 120581119910

+

lowast] (7)

where 119910+

lowast= |119906|119906








= (119906120591119910)120592 = 120588119906

120591(119910120583) where 119906

120591= 120588C

120583(1198962120576) (which










Viscoussublayer

Buffer layeror

blending region


log-law region

ln(119880120591(119910)13)

119880119880120591

12(12119910)

12119910119910

(a) (b)


114113112111

11109108107106 00002 000005Li

ft fo

rce p

er u

nit s

pan

(Nm

)

Coa

rser

Coa

rse

Nor

mal

Fine

Fine

r

Extr

a

Extr

a

(a)

202

2

198

196

194

192

19

188 00002 000005Dra

g fo

rce p

er u

nit s

pan

(Nm

)

Coa

rser

Coa

rse

Nor

mal

Fine

Fine

r

Extr

a

Extr

a

(b)













Boundarylayer mesh

6C

6C

6C

6C




119906 = 119906infin V = V

infin 120588 = 120588

infin 119901 = 119901

infin

119879 = 119879infin

(8)









0 1 2 3 4 5 6 7 8 9 10minus1


1211

1090807060504030201

0minus01

S809

Angle of attack

Lift

coeffi

cien

t

(a)

0050045

0040035

0030025

0020015

0010005

00 1 2 3 4 5 6 7 8 9 10

Angle of attack

Dra

g co

effici

ent

minus1


(b)


5

4

3

2

1

00 005 01 015 02 025 03 035 04

Lift

coeffi

cien

t

Momentum jet













Distance from LE

TE jet thickness

TE radius









120583

(119862120583





120583(119862120583





181614121086420

(ms

)

(a)

181614121086420

(ms

)

(b)


Lift augmentation

50

6050

4540

40

3530

30

2520

20

1510

10

50

0TE radius (mm)

119871119863

(a)


(b)

02

018

016

014

012

010 10 20 30 40 50 60

TE radius (mm)

Lift

coeffi

cien

t

(c)

0 10 20 30 40 50 60TE radius (mm)

Dra

g co

effici

ent

0014

00138

00136

00134

00132

0013

(d)







Lift augmentation

504540353025201510

50

0 05 1 15 2 25 3 35

119871119863


(a)

119905 = 05mm

119877TE = 50mm

181614121086420

(b)

119905 = 3mm

119877TE = 30mm

181614121086420

(c)



120583≪ 0004 it did not














defined as

119862lowast

120583equiv

119881Coand a-jet

(12) 1205881198812

infin119860 ref

=

120588Coand a-jet1198812


(12) 1205881198812

infin119888airfoil

(9)





Lift augmentation

605040302010

0minus10

minus20

minus30

0 001 002 003 004 005

119881infin = 577ms Re = 395 times 105

119871119863

Coanda-jet momentum

(a)

Lift augmentation

605040302010

0minus10

minus20

minus30

0 001 002 003 004 005

119881infin = 146ms Re = 1 times 106

119871119863

Coanda-jet momentum

(b)

16

14

12

1

08

06

04

02

0

Lift

coeffi

cien

t

Re = 3951198645

0 001 002 003 004 005

Re = 11198646

Coanda-jet momentum

(c)

007

006

005

004

003

002

001

0

Dra

g co

effici

ent

0 001 002 003 004 005

Re = 3951198645Re = 11198646

Coanda-jet momentum

(d)





(10)











25

20

15

10

5

0

minus5

90 91 92 93 94 95

119862120583 = 0005



(a)

25

20

15

10

5

0

minus5

Lift augmentation

119862120583 = 001

90 91 92 93 94 95

119871119863


(b)

90 92 94 95 181614121086420

(c)



120583= 0010



119875Betz =8


2

infin (11)

where 119881infin














Nomenclature













Acknowledgments


References






























































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















SASST Experimental

005

004

003

002

001

008 1 12 14 16 18 2

119880119880infin

Hei

ght119888

119896-120576





120583120591= 120588C120583

1198962

120576 (2)


120591was based



119910+=

119906120591119910

120592 (3)





120597119896

120597119905+ nabla sdot (119896119906 minus

]119879

120590119896

nabla119896) + 120574119896 = 119875119896 (4a)

120597120576

120597119905+ nabla sdot (120576119906 minus

]119879

120590119896

nabla120576) + 1198622120574119896 = 120574119862

1119875119896 (4b)




= C120583(1198962120576) where k is the


(]1198792)|nabla119906 + nabla119906



120583=

0091198621= 144119862

2= 192120590

119896= 10 and 120590

120576= 13




120591is


|119906|

119906120591

=1

120581log119910+ + 120573 (5)


119910+=

119906120591119910

](6)



]119879= 119862120583

1198962

120576= 120581119906120591119910 = 120581119910

+

lowast] (7)

where 119910+

lowast= |119906|119906








= (119906120591119910)120592 = 120588119906

120591(119910120583) where 119906

120591= 120588C

120583(1198962120576) (which










Viscoussublayer

Buffer layeror

blending region


log-law region

ln(119880120591(119910)13)

119880119880120591

12(12119910)

12119910119910

(a) (b)


114113112111

11109108107106 00002 000005Li

ft fo

rce p

er u

nit s

pan

(Nm

)

Coa

rser

Coa

rse

Nor

mal

Fine

Fine

r

Extr

a

Extr

a

(a)

202

2

198

196

194

192

19

188 00002 000005Dra

g fo

rce p

er u

nit s

pan

(Nm

)

Coa

rser

Coa

rse

Nor

mal

Fine

Fine

r

Extr

a

Extr

a

(b)













Boundarylayer mesh

6C

6C

6C

6C




119906 = 119906infin V = V

infin 120588 = 120588

infin 119901 = 119901

infin

119879 = 119879infin

(8)









0 1 2 3 4 5 6 7 8 9 10minus1


1211

1090807060504030201

0minus01

S809

Angle of attack

Lift

coeffi

cien

t

(a)

0050045

0040035

0030025

0020015

0010005

00 1 2 3 4 5 6 7 8 9 10

Angle of attack

Dra

g co

effici

ent

minus1


(b)


5

4

3

2

1

00 005 01 015 02 025 03 035 04

Lift

coeffi

cien

t

Momentum jet













Distance from LE

TE jet thickness

TE radius









120583

(119862120583





120583(119862120583





181614121086420

(ms

)

(a)

181614121086420

(ms

)

(b)


Lift augmentation

50

6050

4540

40

3530

30

2520

20

1510

10

50

0TE radius (mm)

119871119863

(a)


(b)

02

018

016

014

012

010 10 20 30 40 50 60

TE radius (mm)

Lift

coeffi

cien

t

(c)

0 10 20 30 40 50 60TE radius (mm)

Dra

g co

effici

ent

0014

00138

00136

00134

00132

0013

(d)







Lift augmentation

504540353025201510

50

0 05 1 15 2 25 3 35

119871119863


(a)

119905 = 05mm

119877TE = 50mm

181614121086420

(b)

119905 = 3mm

119877TE = 30mm

181614121086420

(c)



120583≪ 0004 it did not














defined as

119862lowast

120583equiv

119881Coand a-jet

(12) 1205881198812

infin119860 ref

=

120588Coand a-jet1198812


(12) 1205881198812

infin119888airfoil

(9)





Lift augmentation

605040302010

0minus10

minus20

minus30

0 001 002 003 004 005

119881infin = 577ms Re = 395 times 105

119871119863

Coanda-jet momentum

(a)

Lift augmentation

605040302010

0minus10

minus20

minus30

0 001 002 003 004 005

119881infin = 146ms Re = 1 times 106

119871119863

Coanda-jet momentum

(b)

16

14

12

1

08

06

04

02

0

Lift

coeffi

cien

t

Re = 3951198645

0 001 002 003 004 005

Re = 11198646

Coanda-jet momentum

(c)

007

006

005

004

003

002

001

0

Dra

g co

effici

ent

0 001 002 003 004 005

Re = 3951198645Re = 11198646

Coanda-jet momentum

(d)





(10)











25

20

15

10

5

0

minus5

90 91 92 93 94 95

119862120583 = 0005



(a)

25

20

15

10

5

0

minus5

Lift augmentation

119862120583 = 001

90 91 92 93 94 95

119871119863


(b)

90 92 94 95 181614121086420

(c)



120583= 0010



119875Betz =8


2

infin (11)

where 119881infin














Nomenclature













Acknowledgments


References






























































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of




















120591is


|119906|

119906120591

=1

120581log119910+ + 120573 (5)


119910+=

119906120591119910

](6)



]119879= 119862120583

1198962

120576= 120581119906120591119910 = 120581119910

+

lowast] (7)

where 119910+

lowast= |119906|119906








= (119906120591119910)120592 = 120588119906

120591(119910120583) where 119906

120591= 120588C

120583(1198962120576) (which










Viscoussublayer

Buffer layeror

blending region


log-law region

ln(119880120591(119910)13)

119880119880120591

12(12119910)

12119910119910

(a) (b)


114113112111

11109108107106 00002 000005Li

ft fo

rce p

er u

nit s

pan

(Nm

)

Coa

rser

Coa

rse

Nor

mal

Fine

Fine

r

Extr

a

Extr

a

(a)

202

2

198

196

194

192

19

188 00002 000005Dra

g fo

rce p

er u

nit s

pan

(Nm

)

Coa

rser

Coa

rse

Nor

mal

Fine

Fine

r

Extr

a

Extr

a

(b)













Boundarylayer mesh

6C

6C

6C

6C




119906 = 119906infin V = V

infin 120588 = 120588

infin 119901 = 119901

infin

119879 = 119879infin

(8)









0 1 2 3 4 5 6 7 8 9 10minus1


1211

1090807060504030201

0minus01

S809

Angle of attack

Lift

coeffi

cien

t

(a)

0050045

0040035

0030025

0020015

0010005

00 1 2 3 4 5 6 7 8 9 10

Angle of attack

Dra

g co

effici

ent

minus1


(b)


5

4

3

2

1

00 005 01 015 02 025 03 035 04

Lift

coeffi

cien

t

Momentum jet













Distance from LE

TE jet thickness

TE radius









120583

(119862120583





120583(119862120583





181614121086420

(ms

)

(a)

181614121086420

(ms

)

(b)


Lift augmentation

50

6050

4540

40

3530

30

2520

20

1510

10

50

0TE radius (mm)

119871119863

(a)


(b)

02

018

016

014

012

010 10 20 30 40 50 60

TE radius (mm)

Lift

coeffi

cien

t

(c)

0 10 20 30 40 50 60TE radius (mm)

Dra

g co

effici

ent

0014

00138

00136

00134

00132

0013

(d)







Lift augmentation

504540353025201510

50

0 05 1 15 2 25 3 35

119871119863


(a)

119905 = 05mm

119877TE = 50mm

181614121086420

(b)

119905 = 3mm

119877TE = 30mm

181614121086420

(c)



120583≪ 0004 it did not














defined as

119862lowast

120583equiv

119881Coand a-jet

(12) 1205881198812

infin119860 ref

=

120588Coand a-jet1198812


(12) 1205881198812

infin119888airfoil

(9)





Lift augmentation

605040302010

0minus10

minus20

minus30

0 001 002 003 004 005

119881infin = 577ms Re = 395 times 105

119871119863

Coanda-jet momentum

(a)

Lift augmentation

605040302010

0minus10

minus20

minus30

0 001 002 003 004 005

119881infin = 146ms Re = 1 times 106

119871119863

Coanda-jet momentum

(b)

16

14

12

1

08

06

04

02

0

Lift

coeffi

cien

t

Re = 3951198645

0 001 002 003 004 005

Re = 11198646

Coanda-jet momentum

(c)

007

006

005

004

003

002

001

0

Dra

g co

effici

ent

0 001 002 003 004 005

Re = 3951198645Re = 11198646

Coanda-jet momentum

(d)





(10)











25

20

15

10

5

0

minus5

90 91 92 93 94 95

119862120583 = 0005



(a)

25

20

15

10

5

0

minus5

Lift augmentation

119862120583 = 001

90 91 92 93 94 95

119871119863


(b)

90 92 94 95 181614121086420

(c)



120583= 0010



119875Betz =8


2

infin (11)

where 119881infin














Nomenclature













Acknowledgments


References






























































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















Viscoussublayer

Buffer layeror

blending region


log-law region

ln(119880120591(119910)13)

119880119880120591

12(12119910)

12119910119910

(a) (b)


114113112111

11109108107106 00002 000005Li

ft fo

rce p

er u

nit s

pan

(Nm

)

Coa

rser

Coa

rse

Nor

mal

Fine

Fine

r

Extr

a

Extr

a

(a)

202

2

198

196

194

192

19

188 00002 000005Dra

g fo

rce p

er u

nit s

pan

(Nm

)

Coa

rser

Coa

rse

Nor

mal

Fine

Fine

r

Extr

a

Extr

a

(b)













Boundarylayer mesh

6C

6C

6C

6C




119906 = 119906infin V = V

infin 120588 = 120588

infin 119901 = 119901

infin

119879 = 119879infin

(8)









0 1 2 3 4 5 6 7 8 9 10minus1


1211

1090807060504030201

0minus01

S809

Angle of attack

Lift

coeffi

cien

t

(a)

0050045

0040035

0030025

0020015

0010005

00 1 2 3 4 5 6 7 8 9 10

Angle of attack

Dra

g co

effici

ent

minus1


(b)


5

4

3

2

1

00 005 01 015 02 025 03 035 04

Lift

coeffi

cien

t

Momentum jet













Distance from LE

TE jet thickness

TE radius









120583

(119862120583





120583(119862120583





181614121086420

(ms

)

(a)

181614121086420

(ms

)

(b)


Lift augmentation

50

6050

4540

40

3530

30

2520

20

1510

10

50

0TE radius (mm)

119871119863

(a)


(b)

02

018

016

014

012

010 10 20 30 40 50 60

TE radius (mm)

Lift

coeffi

cien

t

(c)

0 10 20 30 40 50 60TE radius (mm)

Dra

g co

effici

ent

0014

00138

00136

00134

00132

0013

(d)







Lift augmentation

504540353025201510

50

0 05 1 15 2 25 3 35

119871119863


(a)

119905 = 05mm

119877TE = 50mm

181614121086420

(b)

119905 = 3mm

119877TE = 30mm

181614121086420

(c)



120583≪ 0004 it did not














defined as

119862lowast

120583equiv

119881Coand a-jet

(12) 1205881198812

infin119860 ref

=

120588Coand a-jet1198812


(12) 1205881198812

infin119888airfoil

(9)





Lift augmentation

605040302010

0minus10

minus20

minus30

0 001 002 003 004 005

119881infin = 577ms Re = 395 times 105

119871119863

Coanda-jet momentum

(a)

Lift augmentation

605040302010

0minus10

minus20

minus30

0 001 002 003 004 005

119881infin = 146ms Re = 1 times 106

119871119863

Coanda-jet momentum

(b)

16

14

12

1

08

06

04

02

0

Lift

coeffi

cien

t

Re = 3951198645

0 001 002 003 004 005

Re = 11198646

Coanda-jet momentum

(c)

007

006

005

004

003

002

001

0

Dra

g co

effici

ent

0 001 002 003 004 005

Re = 3951198645Re = 11198646

Coanda-jet momentum

(d)





(10)











25

20

15

10

5

0

minus5

90 91 92 93 94 95

119862120583 = 0005



(a)

25

20

15

10

5

0

minus5

Lift augmentation

119862120583 = 001

90 91 92 93 94 95

119871119863


(b)

90 92 94 95 181614121086420

(c)



120583= 0010



119875Betz =8


2

infin (11)

where 119881infin














Nomenclature













Acknowledgments


References






























































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















Boundarylayer mesh

6C

6C

6C

6C




119906 = 119906infin V = V

infin 120588 = 120588

infin 119901 = 119901

infin

119879 = 119879infin

(8)









0 1 2 3 4 5 6 7 8 9 10minus1


1211

1090807060504030201

0minus01

S809

Angle of attack

Lift

coeffi

cien

t

(a)

0050045

0040035

0030025

0020015

0010005

00 1 2 3 4 5 6 7 8 9 10

Angle of attack

Dra

g co

effici

ent

minus1


(b)


5

4

3

2

1

00 005 01 015 02 025 03 035 04

Lift

coeffi

cien

t

Momentum jet













Distance from LE

TE jet thickness

TE radius









120583

(119862120583





120583(119862120583





181614121086420

(ms

)

(a)

181614121086420

(ms

)

(b)


Lift augmentation

50

6050

4540

40

3530

30

2520

20

1510

10

50

0TE radius (mm)

119871119863

(a)


(b)

02

018

016

014

012

010 10 20 30 40 50 60

TE radius (mm)

Lift

coeffi

cien

t

(c)

0 10 20 30 40 50 60TE radius (mm)

Dra

g co

effici

ent

0014

00138

00136

00134

00132

0013

(d)







Lift augmentation

504540353025201510

50

0 05 1 15 2 25 3 35

119871119863


(a)

119905 = 05mm

119877TE = 50mm

181614121086420

(b)

119905 = 3mm

119877TE = 30mm

181614121086420

(c)



120583≪ 0004 it did not














defined as

119862lowast

120583equiv

119881Coand a-jet

(12) 1205881198812

infin119860 ref

=

120588Coand a-jet1198812


(12) 1205881198812

infin119888airfoil

(9)





Lift augmentation

605040302010

0minus10

minus20

minus30

0 001 002 003 004 005

119881infin = 577ms Re = 395 times 105

119871119863

Coanda-jet momentum

(a)

Lift augmentation

605040302010

0minus10

minus20

minus30

0 001 002 003 004 005

119881infin = 146ms Re = 1 times 106

119871119863

Coanda-jet momentum

(b)

16

14

12

1

08

06

04

02

0

Lift

coeffi

cien

t

Re = 3951198645

0 001 002 003 004 005

Re = 11198646

Coanda-jet momentum

(c)

007

006

005

004

003

002

001

0

Dra

g co

effici

ent

0 001 002 003 004 005

Re = 3951198645Re = 11198646

Coanda-jet momentum

(d)





(10)











25

20

15

10

5

0

minus5

90 91 92 93 94 95

119862120583 = 0005



(a)

25

20

15

10

5

0

minus5

Lift augmentation

119862120583 = 001

90 91 92 93 94 95

119871119863


(b)

90 92 94 95 181614121086420

(c)



120583= 0010



119875Betz =8


2

infin (11)

where 119881infin














Nomenclature













Acknowledgments


References






























































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















0 1 2 3 4 5 6 7 8 9 10minus1


1211

1090807060504030201

0minus01

S809

Angle of attack

Lift

coeffi

cien

t

(a)

0050045

0040035

0030025

0020015

0010005

00 1 2 3 4 5 6 7 8 9 10

Angle of attack

Dra

g co

effici

ent

minus1


(b)


5

4

3

2

1

00 005 01 015 02 025 03 035 04

Lift

coeffi

cien

t

Momentum jet













Distance from LE

TE jet thickness

TE radius









120583

(119862120583





120583(119862120583





181614121086420

(ms

)

(a)

181614121086420

(ms

)

(b)


Lift augmentation

50

6050

4540

40

3530

30

2520

20

1510

10

50

0TE radius (mm)

119871119863

(a)


(b)

02

018

016

014

012

010 10 20 30 40 50 60

TE radius (mm)

Lift

coeffi

cien

t

(c)

0 10 20 30 40 50 60TE radius (mm)

Dra

g co

effici

ent

0014

00138

00136

00134

00132

0013

(d)







Lift augmentation

504540353025201510

50

0 05 1 15 2 25 3 35

119871119863


(a)

119905 = 05mm

119877TE = 50mm

181614121086420

(b)

119905 = 3mm

119877TE = 30mm

181614121086420

(c)



120583≪ 0004 it did not














defined as

119862lowast

120583equiv

119881Coand a-jet

(12) 1205881198812

infin119860 ref

=

120588Coand a-jet1198812


(12) 1205881198812

infin119888airfoil

(9)





Lift augmentation

605040302010

0minus10

minus20

minus30

0 001 002 003 004 005

119881infin = 577ms Re = 395 times 105

119871119863

Coanda-jet momentum

(a)

Lift augmentation

605040302010

0minus10

minus20

minus30

0 001 002 003 004 005

119881infin = 146ms Re = 1 times 106

119871119863

Coanda-jet momentum

(b)

16

14

12

1

08

06

04

02

0

Lift

coeffi

cien

t

Re = 3951198645

0 001 002 003 004 005

Re = 11198646

Coanda-jet momentum

(c)

007

006

005

004

003

002

001

0

Dra

g co

effici

ent

0 001 002 003 004 005

Re = 3951198645Re = 11198646

Coanda-jet momentum

(d)





(10)











25

20

15

10

5

0

minus5

90 91 92 93 94 95

119862120583 = 0005



(a)

25

20

15

10

5

0

minus5

Lift augmentation

119862120583 = 001

90 91 92 93 94 95

119871119863


(b)

90 92 94 95 181614121086420

(c)



120583= 0010



119875Betz =8


2

infin (11)

where 119881infin














Nomenclature













Acknowledgments


References






























































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



















Distance from LE

TE jet thickness

TE radius









120583

(119862120583





120583(119862120583





181614121086420

(ms

)

(a)

181614121086420

(ms

)

(b)


Lift augmentation

50

6050

4540

40

3530

30

2520

20

1510

10

50

0TE radius (mm)

119871119863

(a)


(b)

02

018

016

014

012

010 10 20 30 40 50 60

TE radius (mm)

Lift

coeffi

cien

t

(c)

0 10 20 30 40 50 60TE radius (mm)

Dra

g co

effici

ent

0014

00138

00136

00134

00132

0013

(d)







Lift augmentation

504540353025201510

50

0 05 1 15 2 25 3 35

119871119863


(a)

119905 = 05mm

119877TE = 50mm

181614121086420

(b)

119905 = 3mm

119877TE = 30mm

181614121086420

(c)



120583≪ 0004 it did not














defined as

119862lowast

120583equiv

119881Coand a-jet

(12) 1205881198812

infin119860 ref

=

120588Coand a-jet1198812


(12) 1205881198812

infin119888airfoil

(9)





Lift augmentation

605040302010

0minus10

minus20

minus30

0 001 002 003 004 005

119881infin = 577ms Re = 395 times 105

119871119863

Coanda-jet momentum

(a)

Lift augmentation

605040302010

0minus10

minus20

minus30

0 001 002 003 004 005

119881infin = 146ms Re = 1 times 106

119871119863

Coanda-jet momentum

(b)

16

14

12

1

08

06

04

02

0

Lift

coeffi

cien

t

Re = 3951198645

0 001 002 003 004 005

Re = 11198646

Coanda-jet momentum

(c)

007

006

005

004

003

002

001

0

Dra

g co

effici

ent

0 001 002 003 004 005

Re = 3951198645Re = 11198646

Coanda-jet momentum

(d)





(10)











25

20

15

10

5

0

minus5

90 91 92 93 94 95

119862120583 = 0005



(a)

25

20

15

10

5

0

minus5

Lift augmentation

119862120583 = 001

90 91 92 93 94 95

119871119863


(b)

90 92 94 95 181614121086420

(c)



120583= 0010



119875Betz =8


2

infin (11)

where 119881infin














Nomenclature













Acknowledgments


References






























































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















181614121086420

(ms

)

(a)

181614121086420

(ms

)

(b)


Lift augmentation

50

6050

4540

40

3530

30

2520

20

1510

10

50

0TE radius (mm)

119871119863

(a)


(b)

02

018

016

014

012

010 10 20 30 40 50 60

TE radius (mm)

Lift

coeffi

cien

t

(c)

0 10 20 30 40 50 60TE radius (mm)

Dra

g co

effici

ent

0014

00138

00136

00134

00132

0013

(d)







Lift augmentation

504540353025201510

50

0 05 1 15 2 25 3 35

119871119863


(a)

119905 = 05mm

119877TE = 50mm

181614121086420

(b)

119905 = 3mm

119877TE = 30mm

181614121086420

(c)



120583≪ 0004 it did not














defined as

119862lowast

120583equiv

119881Coand a-jet

(12) 1205881198812

infin119860 ref

=

120588Coand a-jet1198812


(12) 1205881198812

infin119888airfoil

(9)





Lift augmentation

605040302010

0minus10

minus20

minus30

0 001 002 003 004 005

119881infin = 577ms Re = 395 times 105

119871119863

Coanda-jet momentum

(a)

Lift augmentation

605040302010

0minus10

minus20

minus30

0 001 002 003 004 005

119881infin = 146ms Re = 1 times 106

119871119863

Coanda-jet momentum

(b)

16

14

12

1

08

06

04

02

0

Lift

coeffi

cien

t

Re = 3951198645

0 001 002 003 004 005

Re = 11198646

Coanda-jet momentum

(c)

007

006

005

004

003

002

001

0

Dra

g co

effici

ent

0 001 002 003 004 005

Re = 3951198645Re = 11198646

Coanda-jet momentum

(d)





(10)











25

20

15

10

5

0

minus5

90 91 92 93 94 95

119862120583 = 0005



(a)

25

20

15

10

5

0

minus5

Lift augmentation

119862120583 = 001

90 91 92 93 94 95

119871119863


(b)

90 92 94 95 181614121086420

(c)



120583= 0010



119875Betz =8


2

infin (11)

where 119881infin














Nomenclature













Acknowledgments


References






























































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















Lift augmentation

504540353025201510

50

0 05 1 15 2 25 3 35

119871119863


(a)

119905 = 05mm

119877TE = 50mm

181614121086420

(b)

119905 = 3mm

119877TE = 30mm

181614121086420

(c)



120583≪ 0004 it did not














defined as

119862lowast

120583equiv

119881Coand a-jet

(12) 1205881198812

infin119860 ref

=

120588Coand a-jet1198812


(12) 1205881198812

infin119888airfoil

(9)





Lift augmentation

605040302010

0minus10

minus20

minus30

0 001 002 003 004 005

119881infin = 577ms Re = 395 times 105

119871119863

Coanda-jet momentum

(a)

Lift augmentation

605040302010

0minus10

minus20

minus30

0 001 002 003 004 005

119881infin = 146ms Re = 1 times 106

119871119863

Coanda-jet momentum

(b)

16

14

12

1

08

06

04

02

0

Lift

coeffi

cien

t

Re = 3951198645

0 001 002 003 004 005

Re = 11198646

Coanda-jet momentum

(c)

007

006

005

004

003

002

001

0

Dra

g co

effici

ent

0 001 002 003 004 005

Re = 3951198645Re = 11198646

Coanda-jet momentum

(d)





(10)











25

20

15

10

5

0

minus5

90 91 92 93 94 95

119862120583 = 0005



(a)

25

20

15

10

5

0

minus5

Lift augmentation

119862120583 = 001

90 91 92 93 94 95

119871119863


(b)

90 92 94 95 181614121086420

(c)



120583= 0010



119875Betz =8


2

infin (11)

where 119881infin














Nomenclature













Acknowledgments


References






























































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















Lift augmentation

605040302010

0minus10

minus20

minus30

0 001 002 003 004 005

119881infin = 577ms Re = 395 times 105

119871119863

Coanda-jet momentum

(a)

Lift augmentation

605040302010

0minus10

minus20

minus30

0 001 002 003 004 005

119881infin = 146ms Re = 1 times 106

119871119863

Coanda-jet momentum

(b)

16

14

12

1

08

06

04

02

0

Lift

coeffi

cien

t

Re = 3951198645

0 001 002 003 004 005

Re = 11198646

Coanda-jet momentum

(c)

007

006

005

004

003

002

001

0

Dra

g co

effici

ent

0 001 002 003 004 005

Re = 3951198645Re = 11198646

Coanda-jet momentum

(d)





(10)











25

20

15

10

5

0

minus5

90 91 92 93 94 95

119862120583 = 0005



(a)

25

20

15

10

5

0

minus5

Lift augmentation

119862120583 = 001

90 91 92 93 94 95

119871119863


(b)

90 92 94 95 181614121086420

(c)



120583= 0010



119875Betz =8


2

infin (11)

where 119881infin














Nomenclature













Acknowledgments


References






























































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















25

20

15

10

5

0

minus5

90 91 92 93 94 95

119862120583 = 0005



(a)

25

20

15

10

5

0

minus5

Lift augmentation

119862120583 = 001

90 91 92 93 94 95

119871119863


(b)

90 92 94 95 181614121086420

(c)



120583= 0010



119875Betz =8


2

infin (11)

where 119881infin














Nomenclature













Acknowledgments


References






























































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of






















Nomenclature













Acknowledgments


References






























































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of










































































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of







































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of





















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of

















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