Case . . . 168
7.4.1 TestCaseDesription. . . 168
7.4.2 BladeLoading . . . 169
7.4.3 PropellerPerformane . . . 169
7.4.4 BladeLoadDistribution . . . 170
7.4.5 PressureonBladeSkin . . . 171
7.4.6 FlowAnalysis. . . 173
7.5 Indued VeloityFields . . . 174
7.6 ConludingRemarks . . . 177
This hapter presents the state-of-art of the oupling between HOSTand elsA
odesfor the simulationof single-rotating propellers. Inthe urrent oupling
strat-egy,the HOSTsimulationusesthe MESIRwake model,whihrestritsthenumber
ofappliationsofthisouplingstrategy. Theserestritionshavebeenidentiedand
aredesribed inthe present hapter.
Moreover, inorder to addresssome of the urrent restritions, insteadof using
theMESIRwake model, anew oupling strategy usingMINThigh-order free-wake
approahhasbeen donebyomparingtwoHOST-elsA oupledomputationsusing
MESIR andMINTwake models,respetively.
7.1 Current Coupling between HOST/MESIR and elsA
This setion details the urrent oupling strategy implemented in HOST and elsA
odes. Moreover, themainadvantagesand shortomings arelisted andstudied.
As desribed in the Methods and Tools hapter, the urrent oupling strategy
usesthe induedveloitiesalulatedbyMESIRwakemodelontheboundariesofa
near-wallmesharoundonebladeofthepropeller,whereasthebladeloadsalulated
byelsA aregiven asan input to HOST-MESIR. Thisstrategy allows to onsider a
redued volume of the problem.
7.1.1 HOST/MESIR-elsA Coupling Strategy
Figure 7.1 shows a sheme of the loose oupling strategy already implemented
be-tween HOST and elsA odes. The periodiity hypothesis in MESIR wake model
allows to ouple both odes one per revolution, instead of doing it at eah time
step. Thisredues signiantly theode-to-ode ommuniationtime.
CoupledsimulationsstartwithanelsAomputationofanear-wallmesharound
theblade. Asitwillbeshownhereafter,the meshusedinthepresentstudyextends
aroundthebladewallforadistaneoftheorderofthemaximumofthebladehord.
A full revolution is omputed onsidering non-reetive boundary onditions (BC)
inthe outermesh boundaries. This non-reetive BC imposes thefreestreamstate
of the onservative variables for theinoming inow all along the simulation. The
RVA moduleextratsthesurfae meshof theouter BCat eah timestep.
On the other side, HOST/MESIR simulations run until the irulation on all the
blade setions is onverged. To ahieve this onvergene, the vortiity and the
positionof the wake panels ismodied iteratively.
Thistime, the RVA module uses these wake data to ompute theveloity indued
on eah node of the surfae mesh extrated from the outer boundary of the ow
domain omputed with elsA. The vortex laments in the wake are onsidered as
distributedsingularitiesandheneBiot-Savart'slawisusedtoompute theveloity
they indue on the mesh nodes. These indued veloities are stored in a series of
les for aomplete blade revolution.
These les arethen used inanother revolution of the elsA omputation, using the
HOST/MESIR datato replaethe freestream state inthenon-reetive BC.With
this,theveloitiesinduedbythefarwakeandtheeetoftheotherbladesistaken
into aount in theairowaround theblade.
During the elsA omputation, pressure and visous fores on the blade skin are
integrated to obtain a spanwise distribution of the blade load. At the end of the
omputation, these loads are provided to HOST/MESIR in order to orret the
Figure7.1: Loose oupling strategy between HOST/MESIR andelsA simulations.
ThisloopisrepeateduntiltheloadspreditedbyelsAandthosepreditedbyHOST
math.
7.1.2 Main Advantages and Shortomings of the Strategy
As ithas been explained before, a one perrevolution oupling strategy already
ex-istsbetweenelsAandHOST-MESIRodes. Thisstrategypresentstheoretiallythe
advantagetoreduetheomputationaldomainoftheCFDmethodtotheneareld
aroundonebladeofthepropeller. Therefore,importantmeshingandomputational
ostredutionmightbeexpetedfromthiswithrespetto full-annulusuRANS
sim-ulations. Besides, the method an be applied to general airow onditions like a
full-annulus simulation. Moreover, withrespet to lifting-line simulations, a muh
better denition of the aerodynamis of the near blade domain might be also
ob-tained.
On the otherside, anumber ofshortomings have been deteted intheurrent
implementation andhave been addressedwithanewouplingstrategy presentedin
thenext subsetion:
•
TheperiodiityhypothesisinMESIRwakemodelallowsarigorousimplemen-tation of a loose oupling strategy, as data is exhanged one per revolution.
However, the periodiity hypothesis, although reduing the omputational
osts, it limits the eld of appliation of this stratedy to stabilized periodi
ight onditions. Therefore, it does not enable non-periodial simulations,
like for example, the simulation of a maneuver of an heliopter or the whirl
utter ofa propeller.
•
MESIR wake model an only take into aount the inuene of one wakeelement, thus limiting its appliation to single rotors or propellers. This is
a minor drawbak for lassial heliopter ongurations, but an be limiting
in the ase of a rotorraft with two o-axial rotors or a rotor and one or
Figure7.2: Tight oupling strategy between HOST-MINTandelsA.
rotor simulations, beause the mutual eet between the front rotor and the
rear rotor is ompletely negleted. As it has been shown in Chapter 6, this
rotor-rotor interation annot be negleted mainly to predit the rear rotor
aerodynamibehavior.
•
MESIRisalow-orderwakemodel thatdesribesthewakevortiityasalattieofvortexlaments. Thisapproahpresentsaverysingularbehaviorwhenthe
alulation point is lose to the wake and thus regularization tehniques are
neessary to avoid too important values of the indued veloities, whih are
generallynot physial.
7.2 Implementation of a One-Way Coupling between
elsA and HOST-MINT odes
TheshortomingsintheouplingstrategyusingMESIRwakemodelhavemotivated
theimplementation ofa more exibleone usingMINThigh-order free-wake model.
In the present work,the one-wayoupling hasbeen done undertheformof aloose
oupling, i.e. theexhange of information takesplae oneperpropellerrevolution.
The strategy partially implemented to ouple HOST-MINT and elsA odes
al-lowstheoretiallybothtightandlooseoupledsimulations. Thelooseoupling loop
follows a sheme similarto the shemein Fig.7.1. Here Fig.7.2 shows thesheme
ofthetightouplingloop,wheretheexhangeofinformation isnolongerdoneone
per revolution, but at eah physial time step or iteration. Therefore, notie that
noperiodiityonstraint isneededhere,andthusthemethodology anbeextended
to a very large sope ofappliations. However, itmustbe alsonotied that atight
oupling strategy impliesa muh more important exhange of information between
odes. Currently,thisexhangeisdonebyles,butamuhfastermemoryexhange
ould be implementedinthe future.
Table7.1: Conditionsfor APIAN minimum-bodyonguration. Fromwind tunnel
aseNo.1149
Mah No. [℄ 0.7
Inidene [
◦
℄ 3.
Rotational Speed [min
−1
℄ 8639.
Advane Ratio,
J
[℄ 3.278betweenHOSTandelsA,anditsassessmentinalooseouplingstrategy. Regarding
theshemeinFig.7.1,theinduedveloitiesduringafullrevolutionaretransmitted
fromHOSTtoelsA inordertoaount for theeet oftheotherblades andwakes.
However, the loads predited by elsA are not ommuniated to the HOST Blade
Moduleandhene the loopis not losed.
7.3 Assessment of MESIR and MINT Coupling
Strate-gies for Single Propellers
This setionpresentsarst assessment of thetwooupling strategiesbetween elsA
and HOSTodes presented before. To do this assessment, the APIAN single
pro-peller test ase in high-speed onditions and at
3 ◦
of inidene is onsidered (seeTable7.1). The full-annulus elsA uRANSase presentedin Chapter1 is usedasa
referene.
Asdesribedinthe previoussetions,both oupling strategiespresentedinthis
study perform their uRANS omputations on a near-wall mesh around the blade.
Figure7.3 shows a detailedview of theRANSmesh usedin oupled omputations
(in red). Moreover, thefull-annulus RANSmesh used inprevious elsA simulations
is plotted in blak. Note that the gure does not plot a slie of the mesh, but it
follows one mesh surfae. Therefore, due to the form of the hannel, some gaps
appearasitan be observed inFig.7.3(b).
Comparing both meshes, itanbenotied thatthenear-wall meshisan extration
ofa partofthe full-annulusmesh. Thisnear-wall mesh has1.53million points,
dis-tributedautomatiallybytheAutogridmesherinordertoapturethevisouseet
intheboundary layerlose to thebladewall, aswell asthedownward propagation
of thewake.
A number of uRANS simulations on this near-wall mesh have been performed
and ompared to thereferenesimulation. All thewalls(bladesand hub) are
mod-eled with an adiabati ondition of adherent wall, whereas the outer boundaries
are modeled bya non-reetive ondition. This outer ondition is modied in the
oupled simulations to aount for the eet of the other blades and wakes.
In-nite veloity and rotational speed are attributed to all the bloks of the mesh. A
seond-order enteredsheme withJameson'sartiial visosityis usedforthe
spa-(a)Sideview. J-sliesofthemesh. (b)Frontview. I-sliesofthemesh.
Figure7.3: APIANmeshslies foruRANSsimulationsinelsA.Thenear-wall mesh
(in red)uses the samedisretization than inthefull-annulus mesh(in blak).
withGear sub-iterations. The turbulene model is Kok's k-
ω
withSST orretion.Simulations areperformed withatime step equivalent to
1 ◦
of propellerrotation.IneahelsAsimulation, theouterboundaryonditions have beentreated
dier-ently to aount for theeet ofother blades andwakes:
•
No indued veloities~v
ind inthe outerBC's.•
HOST/MESIR~v
ind: indued veloities omputed byHOST/MESIRroutines.
•
HOST-MINT~v
ind: induedveloitiesomputed byHOST-MINTroutines.•
HOST-MINT~v
indwithout vortex reg.: the regularization around the vortex
laments hasbeen removed.
•
HOST-MINT~v
indnew panel reg.: together with the suppressionof the
regu-larization invortexlaments, the panelregularization hasbeenmodied.
•
HOST-MINT~v
indwithanalytialvortex: asinMESIRwakemodel,veloitiesindued byvortexlaments areomputed analytially.
The polar plot in Fig. 7.4 shows the blade load evolution along the dierent
near-wallsimulations.
The CFDsimulations on the near-wall mesh have been rst performedonsidering
a non-reetion ondition on the outer BC's. Due to the small mesh dimensions,
theglobal bladeloadswereonvergedaftertherstomplete revolution. Thethird
revolutionwas usedto extrattheblade loadswithout onsidering MINT
~v
ind.Then,startingfromthepreviousonvergedsimulation,thedierentMINT
~v
ind wereadded to the outer BC's. Three revolutions were needed to onverge blade loads
Azimuth [deg]
Thrust [N]
0 30
60
90
120
150
180
210
240 270 300 330
0 20 40 60 80
w/o V.I.
MINT V.I.
MINT V.I. (last rev. = 7)
Figure7.4: Thrustonvergene for near-wall asewith
~v
indfrom HOST-MINT.
7.3.1 Indued veloity elds
In order to assess the next oupling methodology, the indued veloities
~v
ind fromMINTwakemodelareomparedheretotheveloitiesinduedbyMESIR.Figure7.5
shows the omparison between theaxial
~v
indomponent obtained from both wake
models for six dierent azimuthal positions of theomputed blade. Left-hand side
guresplotaviewofthefrontpartoftheBCmesh,whereasright-handsidegures
show its bak part. The third row of gures show the dierenes between both
approahes inm/s. Anumberof dierenesan be observed inboth sides.
Inthe front view,MINTpreditsamuhmoresmoothed
~v
indeldthanMESIR.
Notie in partiular that, near the bound vortex in the quarter-hord line of the
blade, important axial indued veloities are obtained with MESIR, and not with
MINT. These dierenes seem to ome from the dierent treatment of the vortex
laments: dierent regularization radius anddierent integration methods, i.e.
an-alytialinMESIR andnumerial inMINT.
In the rear view, the general pattern is the same between MESIR and MINT.
The passageof thewakesarossthemesh anbenotedbyimportantaxialindued
veloities,mainlynearthebladetips. Theintensityofthesetipvortiesandthewake
varies depending on the azimuthal position, and hene also the indued veloities.
Notieinpartiular thenegative sign oftheaxial
~v
indin theupward moving blade,where the blade irulation diminishes and hene negative vortiity is shed in the
wake.
Nevertheless,anumberofdierenesanbenotiedbetweenbothpreditions. First,
(a)MESIRwake
(b)OriginalMINTwake
()Errorin
~v
indwrtMESIR
Figure7.5: Axial
~v
ind fromMESIR andMINTwake models.blade. Seond, osillations in the indued veloities an be observed in iso-lines
predited by MINT, mainly lose to tip vorties, whih are not found in MESIR.
Finally,MINTpanelregularization leadsto asmoothereeton the
~v
ind omparedto theregularized lattie ofvorties inMESIR.
InordertoassesstheoriginofthesediereneswithrespettoMESIR,anumber
of testsandmodiationshave been done inMINT
~v
indextrationroutines:
•
Regularization of vortex laments: ompare withand without vortex regular-ization•
Regularization of vortexpanels: ompare two types ofpanelregularization•
Integration of vortexlaments: ompare numerial and analytialintegration ofthe vortex~v
ind.
Their induedveloityelds arepresentedand ompared hereafter.
Regularizationofvortexlaments. Theveloitiesinduedbyvortexlaments
arealulated in MINTbythe two-point Gaussian quadrature rule. When the
al-ulation point gets lose to the Gauss points, indued veloities beome singular.
Therefore, aregularization method is neededto avoidtoo important unphysial
in-duedveloities. InMINT,alinearregularizationisappliedwhendistanesbeome
too small, as shown inthe sheme in Fig.7.6. This regularization method models
inaroughwaythevisous oreofaylindrial vortexwithonstant radius. Notie
that,astheregularization radiusisanarbitraryvalue, aninorrethoiemaylead
to two possible extremes: on one side, ifthe radius istoo small, indued veloities
may be too important for alulation points lose to the vortex thus avoiding the
MINT simulation to onverge; on the other side, if the radius is too important,
all the indued veloities from the vortexsurrounding the alulation point might
be almost erased. Therefore, an equilibrium must be found in the hoie of this
regularization distane.
First omparisons of the veloities indued by MESIRand MINT wake models
showedanimportantunderestimationoftheeetofthevortexinMINT.Therefore,
the vortex lament regularization was removed inorder to see the ontribution of
vorties without anyregularization. Figure7.7 shows the omparison between the
veloities induedbyMESIRand MINTon the outermesh oftheAPIANblade.
Notie that, removing the regularization redues signiantly the mismathes
between MESIRand MINTpreditions onthe front part ofthesurfae mesh. The
~v
indonthe rearpart ofthemesharealmost unhanged. Next omparisonswill use
non-regularized vorties inMINT for theomputationof
~v
ind .These results put forward the importane in the hoie of a regularization
dis-taneforthe omputationofinduedveloities. Theeetofthisparametershould
befurther investigated inHOST-MINTsimulationsinorder to establishsomebest
Figure7.6: Shemeofthe regularizationofveloitiesinduedbyvortexlamentsin
MINT.
Regularization ofvortexpanels. TheveloitiesinduedbyMINTwake panels
arealulatedusingthefour-pointGaussianquadratureruleappliedtoBiot-Savart's
law. Similar to vortex laments, this numerial integration of panels ontaining a
ertainvortiityisalsosingular whenthe alulation point getsloserto oneofthe
Gausspoints. Therefore,aregularization strategy isneededtoavoidtooimportant
indued veloities.
Current MINT version determines a regularization distane depending on the
size oftheonsideredpanelandanarbitraryinputvalue. Thistime,however,when
the alulation point is inside the regularization distane of a Gauss point, a zero
ontribution is onsidered. This regularization has shown to produe osillations
when the alulation points get lose to the wake panels (see Fig. 7.5). In order
to remove these osillations, anotherregularization strategy hasbeen implemented.
Figure 7.8showsboth,theoriginaland thenewpanelregularization forthe
extra-tion of
~v
ind. Instead of onsidering a zeroontribution inside of theregularization
radius,onstant
~v
indareonsideredinthisinnerregion. Notiethatthestepin
~v
ind is no longer plaed at theregularization radius (dashed red line), but at thepanelplane (dashedblueline), whih orrespondsbetter to theeet ofapotential wake.
Figure7.9shows theomparison between theveloities induedbyMESIRand
MINT withthe originaland the new panelregularization.
Thefront partof the mesh presents a
~v
ind predition thatisvery similarto theones with the original panel regularization. On the ontrary, theeet of thenew
regularization an be mainly notied when the wake rosses the surfae mesh. In
those ases, when the grid points are very lose to the Gauss points in the wake
panels,the regularization strategyatsand removes theeet ofsomeoftheGauss
points. Thisleads to unphysial osillationsofthe
~v
indonpointsnearthepotentialwake panels.
Thenewregularization approah smoothstheseosillations, asnodisontinuity
in the
~v
indisimposedat the regularization radius
r
vis. However, dierenesintip
(a)Axial
~v
indinMINTw/oregularization
(b)Errorin
~v
indwrtMESIR
Figure 7.7: Potential indued veloities on the outer BC's of a near-wall APIAN
mesh.
Figure 7.8: Sheme of the urrent and modied
~v
indregularization by vortiity
(a)Axial
~v
ind inMINTw/newpanelregularization(b)Errorin
~v
ind wrtMESIRFigure 7.9: Potential indued veloities on the outer BC's of a near-wall APIAN
mesh.
Figure7.10: The veloityindued ona point bya nite straight vortexlament of
onstant irulation
Γ
.vortex and wake smoothness still exist. Again, the eet of panel regularization
distane should be assessed in order to x some best praties for propeller and
openrotor ases.
Analytial vs. numerial vortex laments integration. MESIRmodels the
wakeasalattie ofvortexlamentswithonstant irulation. Topredittheeet
ofthese vortiesontheouterBCmesh,itomputesanalytiallytheintegralsgiven
by Biot-Savart'slaw.
Ontheontrary,MINTwake onsiders awakewhere vortexpanelshavea onstant
vortiity density
~γ
and where vortex laments have a linear variation of their-ulation
Γ
. In MINT, instead of using an analytial solution of the integrals, thetwo-point Gaussian quadrature rule is used for the integration of vortexlaments,
and four-point Gaussian quadrature rulefor theintegration ofvortexpanels.
In order to assess the auray of this disrete integration, an analytial
inte-gration of the vortex laments has been implemented in MINT, but onsidering a
onstant irulation for a matter of simpliation. Asirulation varieslinearly in
this wake model, the mean value of the irulation in the straight vortex lament
istakenfor theomputationof theindued veloities. The analytialexpressionto
alulatetheinduedveloitiesofavortexlamentwithonstantirulationfollows
alulatetheinduedveloitiesofavortexlamentwithonstantirulationfollows