Coupling Strategy Assessment on APIAN Single Propeller Case

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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:

TheperiodiityhypothesisinMESIRwakemodelallowsarigorous

implemen-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 wake

element, 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 thatdesribesthewakevortiityasalattie

ofvortexlaments. 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

[℄ 3.278

betweenHOSTandelsA,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 (see

Table7.1). 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

ind

without vortex reg.: the regularization around the vortex

laments hasbeen removed.

HOST-MINT

~v

ind

new panel reg.: together with the suppressionof the

regu-larization invortexlaments, the panelregularization hasbeenmodied.

HOST-MINT

~v

indwithanalytialvortex: asinMESIRwakemodel,veloities

indued 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 were

added 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

ind

from HOST-MINT.

7.3.1 Indued veloity elds

In order to assess the next oupling methodology, the indued veloities

~v

ind from

MINTwakemodelareomparedheretotheveloitiesinduedbyMESIR.Figure7.5

shows the omparison between theaxial

~v

ind

omponent 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

ind

eldthanMESIR.

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

ind

wrtMESIR

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 ompared

to theregularized lattie ofvorties inMESIR.

InordertoassesstheoriginofthesediereneswithrespettoMESIR,anumber

of testsandmodiationshave been done inMINT

~v

ind

extrationroutines:

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

ind

onthe 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

ind

areonsideredinthisinnerregion. Notiethatthestepin

~v

ind is no longer plaed at theregularization radius (dashed red line), but at thepanel

plane (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 the

ones 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

indonpointsnearthepotential

wake panels.

Thenewregularization approah smoothstheseosillations, asnodisontinuity

in the

~v

ind

isimposedat the regularization radius

r

vis

. However, dierenesintip

(a)Axial

~v

ind

inMINTw/oregularization

(b)Errorin

~v

ind

wrtMESIR

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

ind

regularization by vortiity

(a)Axial

~v

ind inMINTw/newpanelregularization

(b)Errorin

~v

ind wrtMESIR

Figure 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

and where vortex laments have a linear variation of the

ir-ulation

Γ

. In MINT, instead of using an analytial solution of the integrals, the

two-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

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