Passive flow control for aerodynamic performance enhancement of airfoil with its application in

23 Pages·2017·4.33 MB·English

by  Ahmed S. Shehata

Ocean Engineering 136 (2017) 31–53
ContentslistsavailableatScienceDirect
Ocean Engineering
journal homepage: www.elsevier.com/locate/oceaneng
Passive flow control for aerodynamic performance enhancement of airfoil
MARK
with its application in Wells turbine – Under oscillating flow condition
Ahmed S. Shehataa,b,⁎, Qing Xiaoa, Khalid M. Saqrc, Ahmed Naguibb, Day Alexandera
aDepartmentofNavalArchitecture,OceanandMarineEngineering,UniversityofStrathclyde,GlasgowG40LZ,UK
bMarineEngineeringDepartment,CollegeofEngineeringandTechnology,ArabAcademyforScienceTechnologyandMaritimeTransport,P.O.1029
AbuQir,Alexandria,Egypt
cMechanicalEngineeringDepartment,CollegeofEngineeringandTechnology,ArabAcademyforScienceTechnologyandMaritimeTransport,P.O.1029
AbuQir,Alexandria,Egypt
A R T I C L E I N F O A B S T R A C T
Keywords: Inthiswork,thepassiveflowcontrolmethodwasappliedtoimprovetheperformanceofsymmetricalairfoil
Sinusoidalflow sectioninthestallregime.Inadditiontothecommonlyusedfirstlawanalysis,thepresentstudyutilizedan
Wellsturbine entropygenerationminimizationmethodtoexaminetheimpactoftheflowcontrolmethodontheentropy
Passiveflowcontrolmethod generationcharacteristicsaroundtheturbineblade.Thisworkisperformedusingatime-dependentCFDmodel
Entropygeneration ofisolatedNACAairfoil,whichreferstotheturbineblade,undersinusoidalflowboundaryconditions,which
Stallregime
emulates the actual operating conditions. Wells turbine is one of the most proper applications that can be
LargeEddysimulation
appliedbypassiveflowcontrolmethodbecauseitissubjectedtoearlystall.Additionally,itconsistsofanumber
ofbladesthathaveasymmetricalairfoilsectionsubjecttothewavecondition.Itisdeducedthatwiththeuseof
passiveflowcontrol,torquecoefficientofbladeincreasesbymorethan40%withinstallregimeandbymore
than17%beforethestallhappens.Asignificantlydelayedstallisalsoobserved.
1. Introduction control which can be further classified into more specific techniques
(Gad-el-Haketal.,1998).Theterms“active”or“passive”donothave
Thetechniquesdevelopedtomaneuvertheboundarylayer,either any clearly accepted definitions, but nonetheless are frequently used.
for the purpose of increasing the lift or decreasing the drag, are Typically,theclassificationisbasedonenergyaddition,eitheronthe
classifiedunderthegeneralheadingofboundarylayercontrolorflow possibilityoffindingparametersandmodifyingthemafterthesystem
control.Inordertoachieveseparationpostponement,methodsofflow isbuilt,oronthesteadinessofthecontrolsystem;whetheritissteady
controlliftenhancementanddragreductionhavebeenconsidered.Itis or unsteady. Such studies have demonstrated that suction slot can
importanttonotethatflowcontrolcanbedefinedasaprocessusedto modify the pressure distribution over an airfoil surface and have a
alter a natural flow state or development path (transient between substantial effect on lift and drag coefficients (Yousefi et al., 2014;
states) into a more desired state (or development path; e.g. laminar, Chapin and Benard, 2015; Schatz et al., 2007; Chawla et al., 2014;
smoother,fastertransients)(Collisetal.,2004).Moreover,itcouldbe Fernandezetal.,2013;Volinoetal.,2011).Awidevarietyofdifferent
morepreciselydefinedasmodifyingtheflowfieldaroundtheairfoilto studieshavebeenconductedonflowcontroltechniques.Inactualfact,
increase lift and decrease drag. This could be achieved by using in 1904, Prandtl (Schlichting, 1968) was the first scientist who
differentflowcontroltechniquessuchasblowingandsuction,morph- employed boundary layer suction on a cylindrical surface to delay
ing wing, plasma actuators, and changing the shape of the airfoil boundarylayerseparation.Theearliestknownexperimentalworkson
(Katam, 2005). All the techniques essentially do the same job, i.e. boundarylayersuctionforwingswereconductedinthelate1930sand
reduce flowseparation so that theflow is attached to theairfoil and, the 1940s (Richards and Burge, 1943; Walker and Raymer, 1946;
thus, reduce drag and increase lift. In regards to flow control Braslow, 1999). Huang etal. (2004) studied thesuction and blowing
techniques, they can be broadly classified as active and passive flow flowcontroltechniquesonaNACA0012airfoil.Thecombinationofjet
Abbreviations:CFD,ComputationalFluidDynamics;NACA,NationalAdvisoryCommitteeforAeronautics;OWC,OscillatingWaterColumn;2D,TwoDimensional;3D,Three
Dimensional
⁎Correspondingauthorat:MarineEngineeringDepartment,CollegeofEngineeringandTechnology,ArabAcademyforScienceTechnologyandMaritimeTransport,P.O.1029
AbuQir,Alexandria,Egypt.
E-mailaddress:[email protected](A.S.Shehata).
http://dx.doi.org/10.1016/j.oceaneng.2017.03.010
Received28September2016;Receivedinrevisedform1March2017;Accepted10March2017
0029-8018/ © 2017 Elsevier Ltd. All rights reserved.
A.S.Shehataetal. Ocean Engineering 136 (2017) 31–53
Nomenclature S Thermalentropygenerationrate(W/m2K)
t
S Viscousentropygenerationrate(W/m2K)
V
A Thetotalbladearea(m2) T Reservoirtemperature(K)
o
c Bladechord(m) U Movingframevelocity(m/s)
C Dragforcecoefficient u ReynoldsAveragedvelocitycomponentinidirection(m/
D i
C Liftforcecoefficient s)
L
C Torquecoefficient V Volumeofacomputationcell(m3)
T
D Thefluiddomain V InstantaneousVelocity(m/s)
a
D Suctionslotdiameter(m) V Highestspeedofaxialdirection(m/s)
ss am
f Cyclefrequency(Hz) V Initialvelocityforcomputation(m/s)
o
FD In-lineforceactingoncylinder(N) Vr Relativevelocity(m/s)
G Thefilterfunction Ẇ Thenet-worktransferrate(W/s)
KE KineticEnergy(J) Ẇ Reversibleworktransferrate(W/s)
rev
Lss Suctionslotlocationfromleadingedgeinchordpercen- ηF Theefficiencyinfirstlawofthermodynamics
tage% η Thesecondlawefficiency
S
K Turbulentkineticenergy(J/kg) μ Viscosity(kg/ms)
Δp Pressuredifferenceacrosstheturbine(N/m2) μ Turbulentviscosity(Ns/m2)
t
R Meanrotorradius(m) ρ Density(kg/m3)
m
S Localentropygenerationrate(W/m2K) ∅ Flowcoefficient
gen
S Globalentropygenerationrate(W/K) ω Rotorangularspeed(rad/s)
G
Sij Meanstrainrate(1/s) (−ρui′u′j) Reynoldsstresstensor
locationandangleofattackshowedaremarkabledifferenceconcerning stream. This increased suction leads to performance gains in lift and
liftcoefficientasperpendicularsuctionattheleadingedgeincreasedin stalldelay,buttheleading-edgevortexquicklybecomesunstableand
comparison to the case in other suction situations. Moreover, the detachesfromtheairfoil.Assoonasitpassesbehindthetrailingedge,
tangential blowing at downstream locations was found to lead to the however, the leading-edge vortex detachment is accompanied by a
maximum increase in the lift coefficient value. Rosas (2005) numeri- dramatic decrease in lift and a significant increase in drag. This
callystudiedflowseparationcontrolthroughoscillatoryfluidinjection, phenomenoniscalleddynamicstall.FromFig.3itcanbenotedthat
inwhichliftcoefficientincreased.TheauthorsinAkcayozandTuncer Wells turbine can extract power at low air flow rate, when other
(2009) examined the optimization of synthetic jet parameters on a turbines wouldbe inefficient (Liu etal., 2016; Okuhara et al., 2013).
NACA0015 airfoil in different angles of attack to increase the lift to Also,theaerodynamicefficiencyincreaseswiththeincreaseoftheflow
dragratio.Theirresultsrevealedthattheoptimumjetlocationmoved coefficient (angle of attack) up to a certain value, after which it
towardtheleadingedgeandtheoptimumjetangleincrementedasthe decreases. Thus, most of the past studies aimed to 1) improve the
angleofattackincreased.TheCFDmethodhasbeenincreasinglyused torque coefficient (the turbine output) and 2) improve the turbine
to investigate boundary layer control. Many flow control studies by behavior under the stall condition. In a number of previous studies
CFDapproaches(KimandKim,2009;Gencetal.,2011;Rumseyand (Raghunathan,1995a;Dixon,1998;SheldahlandKlimas,1981),itwas
Nishino,2011;Yagizetal.,2012)havebeenconductedtoinvestigate concludedthatthedelayofstallonsetcontributestoimprovingWells
theeffectsofblowingandsuctionjetsontheaerodynamicperformance turbineperformance.Thisdelaycanbeachievedbysettingguidevanes
ofairfoils. on the rotor's hub (Raghunathan, 1995a, 1995b; Brito-Melo et al.,
Themajorchallengefacingoscillatingwatercolumnoceanenergy 2002).Itwasfoundthatamulti-planeturbinewithoutguidevaneswas
extraction systems is to find an efficient and economical means of less efficient (approximately 20%) than the one with guide vanes. A
converting flow kinetic energy to unidirectional rotary motion for comparison between Wells turbines having 2D guide vanes and 3D
driving electrical generators (Rosa, 2012; Curran and Folley, 2008; guidevaneswasinvestigated(Setoguchietal.,2001;Takaoetal.,2001)
Falcao,1999,2004;Torresetal.,2016),asseeninFig.1.Theenergy by testing a Wells turbine model under steady flow conditions, and
conversion from the oscillating air column (Boccotti, 2007a, 2007b) usingthecomputersimulation(quasi-steadyanalysis.Itdemonstrated
can be achieved by using a self-rectifying air turbine such as Wells that, the 3D case has superior characteristics in the running and
turbinewhichwasinventedbyWellsin1976,seeFig.2(Raghunathan, starting characteristics. Concerning Wells turbine systems which
1980; Hitoshi Hotta, 1985; Masahiro Inoue et al., 1985; Masami
Suzuki and Tagori, 1985; Yukihisa Washio et al., 1985; Folley et al.,
2006). Wells turbine consists of a number of blades that have
symmetrical airfoil section.This airfoil section underdifferent condi-
tions with various geometric parameters was investigated by other
researchers in consideration of improving the overall system perfor-
mance.Inordertoachievethispurpose,differentmethodswereused,
such as experimental, analytical and numerical simulation.The main
disadvantage of Wells turbine is the stall condition (Shehata et al.,
2017b).Aerodynamicbodiessubjectedtopitchingmotionsoroscilla-
tionsexhibitastallingbehaviordifferentfromthatobservedwhenthe
flow over a wing at a fixed angle of attack separates. The latter
phenomenon is referred to as static stall, since the angle of attack is
fixed.Inthecaseofadynamicallypitchingbody,suchasanairfoilwith
large flow rates and a large angle of attack, the shear layer near the
leading edge rolls up to form a leading-edge vortex which provides Fig.1.AnillustrationoftheprincipleofoperationofOWCsystem,wherethewave
additional suction over the upper airfoil surface as it convects down- motionisusedtodriveaturbinethroughtheoscillationofaircolumn(Takaoetal.,
2001).
32
A.S.Shehataetal. Ocean Engineering 136 (2017) 31–53
Fig.5.ThenearviewsofslotmeshA)DSS=0.005mB)DSS=0.001m.
turbineisdependentonthegapbetweentheplanesasitisshownin
Raghunathan(1995a).Agap-to-chordratiobetweentheplanesof1.0
was recommended. Experimental results in Gato and Curran (1996)
showed that the use of two twin rotors rotating in the opposite
directiontoeachotherwasanefficientmeansofrecoveringtheswirl
kineticenergywithouttheuseofguidevanes.Theoverallperformance
Fig.2.TypicalstructureofWellsturbinerotor(Takaoetal.,2001). of several types of Wells turbine design have been investigated in
Raghunathan and Beattie (1996) and, a semi-empirical method for
predicting the performance has been used in Curran et al. (1998).
Similar comparisons were undertaken using experimental measure-
mentinGatoandCurran(1997).Itcanbeobservedthatthecontra-
rotatingturbinehadanoperationalrangewhichwassimilartothatof
themonoplaneturbinewithguidevanesanditachievedsimilarpeak
efficiency as well. However, the flow performed was better than the
latterinthepost-stallregime.Inordertoimprovetheperformanceof
theWellsturbine,theeffectofendplateontheturbinecharacteristics
has been investigated in Mamun et al. (2006), Takao et al. (2007).
UsinganexperimentalmodelandaCFDmethoditwasshownthatthe
optimum plate position was a forward type. The peak efficiency
increasesapproximately4%ascomparedtotheWellsturbinewithout
anendplate.ThecalculationsofthebladesweepsfortheWellsturbine
with a numerical code by Kim et al. (2002) and experimentally with
Fig.3.Turbinescharacteristicundersteadyflowconditions:Flowcoefficientvariation
withtheefficiency(AkcayozandTuncer,2009). quasi-steady analysis in Setoguchi et al. (2003a). As a result, it was
concludedthattheperformanceoftheWellsturbineswasinfluencedby
thebladesweeparea.
Exergy analysis is performed using the numerical simulation for
steady state biplane Wells turbines (Shaaban, 2012) where the up-
streamrotorhasadesignpointsecondlawefficiencyof82.3%although
thedownstreamrotorsecondlawefficiencyequals60.7%.Theentropy
generation, due to viscous dissipation, around different 2D airfoil
sections for Wells turbine was recently examined by the authors in
Shehata et al. (2014, 2016). When Reynolds number was increased
from6×104to1×105thetotalentropygenerationincreasedmorethan
two folds for both airfoils correspondingly. However, when Reynolds
number was increased further to 2×105, the total entropy generation
exhibitedunintuitivevaluesrangingfrom25%lessto20%higherthan
thecorrespondingvalueatReynoldsnumber=1×105.Theefficiencyfor
four different airfoils in the compression cycle is higher than the
suctioncycleat2°angleofattack.Although,whentheangleofattack
increases,theefficiencyforthesuctioncycleincreasesmuchmorethan
thecompressionone.Thisstudysuggestedthatapossibleexistenceof
criticalReynoldsnumberfortheoperatingconditionatwhichviscous
irreversibilities takes minimum values. A comparison between total
entropygenerationof asuggesteddesign(with variablechord)and a
constantchordofWellsturbinewaspresentedinSoltanmohamadiand
Lakzian(2015).Thedetailedresultsdemonstrateanincreaseinstatic
Fig. 4.Computational model and boundary conditions A) dimensions of whole pressuredifferencearoundanewbladeanda26.02%averagedecrease
computationaldomainandlocationofairfoilB)computationalgridnearthewallof intotalentropygenerationthroughoutthefulloperatingrange.Mostof
theairfoil. theresearchersstudiedtheperformanceofdifferentairfoilsdesignand
differentoperationalconditionswhereanalyzingtheproblemwasonly
operate at high pressure values, a multi plane (usually tow stage) based on the parameter of first law of thermodynamics. In order to
turbine configuration can be used. Such a concept avoids the use of
formadeeperunderstanding,itisnecessarytolookatthesecondlaw
guidevanesand,therefore,theturbinewouldrequirelessmaintenance
ofthermodynamicssinceithasshownverypromisingresultinmany
andrepairs(Raghunathan,1995a).TheperformanceofabiplaneWells
33
A.S.Shehataetal. Ocean Engineering 136 (2017) 31–53
Fig.6.ConvergencecriteriaA)non-oscillatingflowB)sinusoidalflow.
Fig.7.Thesinusoidalwaveboundarycondition,whichrepresentsaregularoscillating
watercolumn.
applications,suchaswindturbineinPopeetal.(2010),Baskutetal.
(2010, 2011), Redha et al. (2011), Ozgener and Ozgener (2007),
Mortazavi et al. (2015), and gas turbine in Şöhret et al. (2015),
Ghazikhani et al. (2014), Sue and Chuang (2004), Kim and Kim
(2012),Jubeh(2005),Lugo-Leyteetal.(2015). Fig.8.AgridsensitivityanalysiswithrespecttocellnumberacrosstheslotsectionA)
Wellsturbineconsistsofanumberofbladesthathavesymmetrical one,two,fourandeightcellsinthetransversaldirectionB)pressurecoefficientplotted
airfoil section. This airfoil section under different conditions with onthenormalizedaerofoilcordatdifferentgridresolutions.
various geometric parameters was investigated by other researchers
to improve the overall system performance. Different methods were value, are calculated and compared under different conditions with
various design parameters by analyzing the flow around the airfoil
used to achieve this purpose, such as experimental, analytical and
sectionusingCFDsoftware,wheretheforcecoefficientsarereferringto
numerical simulation. In this work the CFD analysis is used to
investigate and analyze the flow around the isolated NACA airfoil, thefirst lawanalysis andtheentropy generationvalueis referringto
which refers to the turbine blade, under sinusoidal flow boundary the second law analysis. The objective of the present work is to
demonstrate that the performance of airfoil section, which refers to
conditions,whichemulatestheactualoperatingconditions.Theforce
coefficients, such as torque coefficient and the entropy generation the Wells turbine blade at stall and near-stall conditions, can be
radically improved by using passive flow control method such as
34
A.S.Shehataetal. Ocean Engineering 136 (2017) 31–53
the scale of the resolved eddies. In FLUENT, the finite-volume
discretization itself implicitly provides the filtering operation
(Mamun,2006):
ϕ(x)= 1 ∫ ϕ(x′)dx′,x′∈V
V V (2)
whereV isthevolumeofacomputationalcell.Thefilterfunction,G(x,
x′),impliedhereisthen
⎧
G(x,x′)=⎨1/V forx′∈V
⎩0 otherwise (3)
The LES model will be applied to essentially incompressible (but
notnecessarilyconstant-density)flows.Byfilteringtheincompressible
Navier-Stokesequations,oneobtains(Dahlstrom,2003)
Fig.9.ThemeasureofLESqualitybyM(x,t)withthesub-gridfilterlength.
∂ρ ∂ρu
+ i =0
∂t ∂x (4)
i
⎛ ⎞
∂ (ρu)+ ∂ (ρuu)= ∂ ⎜μ∂ui⎟− ∂ρ − ∂τij
∂t i ∂xj i j ∂xj⎝ ∂xj⎠ ∂xi ∂xj (5)
whereτ isthesub-grid-scalestressdefinedby
ij
τij = ρuiuj−ρuiuj (6)
Thesub-grid-scalestressesresultingfromthefilteringoperationare
unidentified, and require modeling. The majority of sub-grid-scale
models are eddy viscosity models of the following form (Moin et al.,
1991):
1
τ − τ σ =−2μS
ij 3 kk ij t ij (7)
whereS istherate-of-straintensorfortheresolvedscaledefinedby:
ij
⎛ ⎞
Fig.10.Ahistogramofnumberofelementsforthesub-gridfilterlength. S = 1⎜∂ui+∂uj⎟
ij 2⎝∂xj ∂xi⎠ (8)
suctionorblowingslot.Therefore,atypicalslotiscreatedintheairfoil
andμ isthesub-grid-scaleturbulentviscosity,whichtheSmagorinsky-
section, normal to the chord, and due to the pressure difference t
Lillymodelisusedforit(DK,1992).Themostbasicofsub-grid-scale
betweenthetwosurfaces.Consequently,asuctioneffectoccurswhich models for “Smagorinsky-Lilly model” was proposed by Smagorinsky
delaysthestall.Accordingly,thereisnoneedtogenerateanyspecific
(Hinze, 1975) and was further developed by Lilly (Launder and
activesuctionorblowingwithintheairfoilortheslot.Alongwiththis
Spalding, 1972). In the Smagorinsky-Lilly model, the eddy viscosity
design, there are two new aspects here. The first is improving the
ismodeledby:
performanceofairfoilsectionforWellsturbineinnear-stallconditions.
Thesecondis tostudytheeffectofslotinoscillating(i.e.sinusoidal) μt = ρLs2S (9)
flow, which is newly compared to the unidirectional flow as in
aerodynamics applications. Apart from that, an entropy generation where Ls is the mixing length for sub-grid-scale models and
minimization method is used to conduct the second-law analysis as S = 2SijSij.TheLs iscomputedusing:
recently reported by the authors in Shehata et al. (2014, 2016). An Ls=min (kd, CsV1/3) (10)
investigation on the entropy generation, due to viscous dissipation,
whereC istheSmagorinskyconstant,k=0.42,d isthedistancetothe
around turbine airfoils in two-dimensional unsteady flow configura- s
closestwall,andVisthevolumeofthecomputationalcell.Lillyderived
tions, will be carried out. In reference to the literature, no specific
a value of 0.23 for C from homogeneous isotropic turbulence.
unsteady CFD study of the slot effect with sinusoidal flow on the s
However, this value was found to cause excessive damping of large-
entropygenerationratehasbeenperformedforairfoilsectionofWells
scalefluctuationsinthepresenceofmeanshearorintransitionalflows.
turbine.
C=0.1hasbeenfoundtoyieldthebestresultsforawiderangeofflows.
s
Forthefirstlawofthermodynamics,theliftanddragcoefficientC
L
2. Mathematicalmodelandnumericalapproach andC arecomputedfromthepostprocessingsoftware.Theaverage
D
value for lift and drag coefficient was used to calculate one value for
The governing equations employed for Large Eddy Simulation torque coefficient for each angle of attack. Afterwards, the torque
(LES) are obtained by filtering the time-dependent Navier-Stokes coefficient can then be expressed as (Sheldahl and Klimas, 1981;
equations. The filtering process effectively filters out eddies whose Curranetal.,1998;Whittakeretal.,1997):
scales are smaller than the filter width or grid spacing used in the
C =(Csinα−C cosα) (11)
computations. The resulting equations thus govern the dynamics of T L D
large eddies. A filtered variable (denoted by an over-bar) is defined Theflowcoefficientϕ relatingtangentialandaxialvelocitiesofthe
bySB(2000): rotorisdefinedas
ϕ(x)= ∫ ϕ(x′)G(x,x′)dx′ ϕ = Va
D (1) ω*Rm (12)
whereDisthefluiddomain,andGisthefilterfunctionthatdetermines wheretheα angleofattackequalto
35
A.S.Shehataetal. Ocean Engineering 136 (2017) 31–53
Fig.11.ComparisonbetweendifferentmodelstosimulatethestallanglefromexperimentaldataA)torquecoefficientB)path-linecoloredbythevelocitymagnitudeC)contoursof
pressuredistributionD)pressuredistributionatupperandlowersurface.(Forinterpretationofthereferencestocolorinthisfigurelegend,thereaderisreferredtothewebversionof
thisarticle.)
α=tan−1 Va theGouy–Stodolatheorem(Stodola,1910).
ωRm (13) Itispossibletoexpresstheirreversibleentropygenerationinterms
of the derivatives of local flow quantities in the absence of phase
andthetorqueas:
changes and chemical reactions. The two dissipative mechanisms in
Torque= 1ρ(V2+(ωR )2)AR C viscous flow are the strain-originated dissipation and the thermal
2 a m m T (14) dissipation which correspond to a viscous and a thermal entropy
theefficiencyinthefirstlawofthermodynamics(η )isdefinedas: generationrespectively(Iandoli,2005).Thus,itcanbewritten,
F
Torque* ω Sgen=SV +Sth (17)
η =
F ΔP*Q (15)
In incompressible isothermal flow, such as the case in hand, the
Thetransportequationsofsuchmodelscanbefoundinturbulence thermal dissipation term vanishes. The local viscous irreversibilities
modeling texts such as Hirsch (2007). The second law of thermo- thereforecanbeexpressedas:
dynamicdefinesthenetworktransferrateẆ asBejan(1996):
μ
S = ϕ
Wṙev−Ẇ =ToSgen (16) V To (18)
Whichhasbeenknownformostofthiscenturyinengineeringas where ϕ is the viscous dissipation term, that is expressed in two
36
A.S.Shehataetal. Ocean Engineering 136 (2017) 31–53
Fig.11. (continued)
dimensionalCartesiancoordinatesasIandoli(2005): WhichisalsocalculatedfromtheFLUENTsoftwarebyintegralthe
ϕ=2⎡⎢⎛⎜∂u⎞⎟2+⎛⎜∂v⎞⎟2⎤⎥+⎛⎜∂u + ∂v⎞⎟2 globTahlevnaleuxet,equationisdefiningtheexergyvalue,whichcanbewritten
⎣⎢⎝∂x⎠ ⎝∂y⎠ ⎦⎥ ⎝∂y ∂x⎠ (19) asBejan(1995):
Eqs.(18)and(19)wereusedtocreatetheUDFfile,whichisusedto Exergy=KE+SG (21)
calculatethelocalentropyformtheFLUENTsoftware.Then,theglobal
andfinallythesecondlawefficiencyisdefinedasPopeetal.(2010):
entropygenerationrateishenceexpressedas:
S = ∬ S dydx η = KE
G xy V (20) S Exergy (22)
37
A.S.Shehataetal. Ocean Engineering 136 (2017) 31–53
Fig.13.Measuredunsteadyin-lineforceFDfromRef.Nomuraetal.(2003),(angleof
Fig.12.MeasuredtorquecoefficientfromRefs.Torresietal.(2007b,2007a,2009)and attack=0°)andFDcalculatedfromthepresentCFDforfrequency2Hz.
calculated torque coefficient from present CFD unsteady flow with non-oscillating
velocity.
whereKE= 1V2
2
From the above equation we can come up with a number of
conclusions.Ontheonehand,thatthetorquecoefficientindicatesto
thefirstlawefficiencyandtheglobalentropygenerationrateindicates
to the second law and efficiency, in which the increase in torque
coefficient leads to increase in the first law efficiency. On the other
hand, the decrease in the global entropy generation rate leads to an
increaseinthesecondlawefficiency.
3. CFDapproach
3.1. Computationalmodel,solverdetailsandboundaryconditions
Fig.14.Measuredunsteadyin-lineforceFDfromRef.Nomuraetal.(2003),(angleof
Two-dimensional numerical models for NACA0015 airfoils were attack=0°)andFDcalculatedfromthepresentCFDforfrequency1Hz.
builtandvalidatedagainstexperimentalmeasurementsunderunstea-
dy flow conditions with both non-oscillating velocity, and sinusoidal was also detected that the solution reaches convergence when the
inlet velocity. The computational domain is discretized to Cartesian scaled residuals approaches 1×10−5. See Fig. 6 for the convergence
structuredfinitevolumecellsusingGAMBITcode.Theapplicationof criteriainthenon-oscillatingflowandsinusoidalflowinletvelocity.At
such boundary condition types (Starzmann and Carolus, 2013; such limit, the flow field variables holds constant values with the
Mohamed and Shaaban, 2013; Torresi et al., 2009; Mamun et al., applicationofconsecutiveiterations.
2004)matchestheGreen-Gausscellbasedevaluationmethodforthe TheaxialflowofWellsTurbineismodeledasasinusoidalwavein
gradienttermsusedinthesolver(ANSYSFLUENT).Numeroustests thissimulation.Therefore,Inletboundaryconditionsaresettochange
accounting for different interpolation schemes were used to compute astime.Inordertoapplytheinletboundarycondition,inletvelocity
cell face values of the flow field variables. The variables of governing withperiodicfunction(seeFig.7)isgeneratedasfollows.
equationwhicharevelocityandpressure,aswellasconvergencetests
havebeenundertaken.Thesecondorderupwind(Smagorinsky,1963) Va=Vo +Vamsin(sin2πft) (23)
interpolation scheme was used in this work in which it yields results
whichareapproximatelysimilartosuchyieldedbythirdorderMUSCL Where t is time period, 6s are set as one period in this simulation
schemeinthepresentsituation.Inaddition,insomecasesofthethird considering to the literature survey (Mamun et al., 2004; Setoguchi
order MUSCL scheme was given high oscillatory residual during the et al., 2003b; Kinoue et al., 2003a, 2004). Time step is set as
solution. Fig. 4 demonstrates the dimensions of the whole computa- 0.000296721sinordertosatisfyCFL(CourantFriedrichsLewy)(DE
tional domain and the location of airfoil, and it also shows the grid Moura and Carlos, 2013) condition equal to 1. The sinusoidal wave
distributionnearthewalloftheairfoil.Furthermore,thenearviewsof conditioncreatevariousReynoldsnumberupto2×104accordingtothe
slotmeshcanbedeterminedfromFig.5fordifferentslotdiameter.The Ref.Torresietal.(2009).
Quad-Pavemeshingscheme(StructuredGrid)isusedinthiswork.It
Table1
TheerrorpercentagebetweenmeasuredtorquecoefficientfromRefs.Torresietal.(2007b,2007a,2009)andcalculatedtorquecoefficientfromCFDunderunsteadyflowwithnon-
oscillatingvelocity.
TorqueCoefficient Angleofattack(Degree)
8.709 10.097 10.639 11.266 11.734 12.304 13.642 14.406
Experimental 0.0488 0.0631 0.0712 0.0807 0.0875 0.0922 0.0814 0.0725
CFD 0.05092 0.06689 0.0726 0.0793 0.0856 0.091 0.083 0.0676
Error% 4 6 2 −2 −2 −1 2 −7
38
A.S.Shehataetal. Ocean Engineering 136 (2017) 31–53
Table2
TheerrorpercentagebetweenmeasuredFDfromRef.Nomuraetal.(2003)andcalculatedFDfromCFDunderunsteadyflowwithsinusoidalinletvelocity.
FD*10−2(N) Time(s)
14.02 14.1 14.12 14.2 14.3 14.34 14.4 14.5 14.6 14.7 14.8 14.9 15
Frequency2 Hz
Experimental 3.3 7.6 9.7 14.1 12.7 3.3 4 2.3 7.4 14.4 10.5 3.8 2.6
CFD 3.7 7.6 9.6 14.2 12.3 3.4 3.3 2.6 7.6 14.6 10.7 3.7 2.4
Error% 11 1 −1 1 −4 1 −17 17 4 1 2 −2 −11
Frequency1Hz
Experimental 4.4 6.8 12.4 13.8 14 12.7 10 7.6 4.6 2.7 2.3 2.5 2.9
CFD 4.5 7.1 12.4 12.9 14 12.9 10.1 8.4 4.4 2.6 2.2 2.6 3.2
Error% 2 4 0 −7 0 1 1 10 −4 1 −4 4 10
across the slot section for one, two, four and eight cells in the
transversaldirection.Itcanbenotedthattheresultsforthefourgrids
A–Dareapproximatelythesame.Ontheotherhand,byincreasethe
number of cells in the transversal direction, the cells number for the
total domain is increase for the four grids A–D by 312951, 350662,
388637and413665respectively.Therefore,thegridAwasselectedin
order to immunize the solution time of the different cases without
impactingonthequalityandaccuracyoftheresults.
3.3. LESresolutionqualityassessment
Inthemostcommonpractice,inLES,thefilterlengthdependson
theresolutionofspatialdiscretization(i.e.grid)inaspecifiedproblem.
Fig.15.MeasuredtorquecoefficientfromRefs.Torresietal.(2007b,2007a,2009)and
calculatedtorquecoefficientfromCFDunsteadyflowwithsinusoidalinletvelocity. The implication of the filtering technique, which is the backbone of
LES, is the question about the resolution of the resolved scales in
comparison with the total turbulence spectrum in the flow. An
Table3
assortment of several attempts were made to propose and index of
The error percentage between measured torque coefficient from Refs. Torresi et al.
(2007b,2007a,2009)andcalculatedtorquecoefficientfromCFDunderunsteadyflow LESquality(Saqr,2010;Celiketal.,2005).Themostestablishedindex
withsinusoidalinletvelocity. ofLESqualitywasproposedbyPope(Pope,2004).Suchqualityindex
can be expressed mathematically as a function M(x,t) of space and
TorqueCoefficient Angleofattack(Degree)
time(Saqretal.,2012)as:
11.266 11.734 12.304 13.642 14.406 K
M(x,t)= Res
K +K
Experimental 0.0807 0.0875 0.092 0.0814 0.0725 Res SGS
CFD 0.0803 0.0879 0.0931 0.0825 0.0709
Error% −1 1 1 1− 2 where KRes and KSGS are the resolved and subgrid modeled turbulent
kinetic energy scalars, respectively. In the present work, K can be
Res
calculated as: KRes= 12(u∼2+v∼2) and KSGS can be calculated as
KSGS= (CνΔt2)2 where νt is the subgrid modeled turbulent kinematic
viscosityascalculatedintheSmagorinskymodelas:ν =L2S,where
t s
LSisthemixinglengthforsubgridscalesascalculatedinEq.(10)andΔ
is the filter length (Eldrainy et al., 2011). Pope (2004) has evidently
shownthatwhenM(x,t)≥80%theLESissufficientlyresolvedandthe
flow field is properly resolved. Literature records support Pope's
proposition in numerous and variant flows as reported in Mazzei
et al. (2016), Fureby (2017), Georgiadis et al. (2010), Eldrainy et al.
Fig.16.2Dairfoildiagramwithaslot.
(2011). In the present work, the quality index M(x,t) was calculated
forthecomputationaldomainandplottedagainstLESfilterlengthas
in Fig. 9. It is shown that M(x,t)≥80% for filter lengths in the range
3.2. Gridsensitivitytest ∆≥ 0.01. In Fig. 10 a histogram of the filter length shows that
approximately 98% of the grid has values of M(x,t) larger than 90%
In order to ensure that the numerical produces results are mini- whichsatisfiesPope'scriteriaforfullyresolvedLES.
mallydependentonthegridsize,severalgridsweretestedtoestimate
Sinceoneoftheworkmainobjectivesistostudythestallregime,
thenumberofgridcellsrequiredtoestablishareliablemodel.Thegrid
therefore, an accurate simulation for the stall must be done. The
sensitivity test is performed where 4 grids with different mesh sizes following Fig. 11 illustrates that a comparison between different
ranging from 112603 up to 446889 cells are investigated. This test models to simulate two dimensional NACA0015 in an unsteady flow
showsthatforgridswithmeshsizesof312951cells,givesgoodresult
withstallangle(13.6°)forNACA0015withReynoldsnumberequalsto
within reasonable computation time (more details about this result 2×105 from experimental data (Torresi et al., 2009, 2007) was
in Shehata et al. (2014)). Therefore, it was selected to conduct the
presented.Thecomparisonusesonlythestallangletoidentifywhich
analysispresentedhereafter.
model can present it. The Large Eddy Simulation model (LES) gives
Fig.8showthegridsensitivityanalysiswithrespecttocellnumber goodresultsforthetorquecoefficientvalue,while,othermodelscannot
39
A.S.Shehataetal. Ocean Engineering 136 (2017) 31–53
Fig.17.FactorsaffectingdeterminationoftheslotvelocitydirectionforthepressuredistributionandvelocityvectordirectionA)acceleratingflowatcompressioncycleB)decelerating
flowatcompressioncycleC)acceleratingflowatsuctioncycleD)deceleratingflowatsuctioncycle.
40