Code-to-Code Assessment. elsA vs. HOST-MINT

Thissetionpresentsthe mainresultsobtained withHOSTandompared withthe

referene simulation using elsA. First, propeller performane are presented, then

the global blade thrust is ompared, and nally, the blade thrust distribution is

presented,i.e. the ontribution of eahsetion to thethrust.

Open RotorPerformane. Table6.2showsthepropellerperformane

ompari-sonbetweenelsAsimulationandthreeHOSTsimulations: isolated,withinstallation

eets,andwithboth installation andunsteady orretions. For HOSTsimulations,

the blade pith has been adapted in order to obtain the same global thrust level

T = T _FR + T _RR

^{and power ratio}

P _FR /P _RR

^{than in elsA. Aeptable pith angle}

modiations, i.e. around

1 ^◦

^{, are required in order to ahieve theelsA thrust and}

power ratio levels. Thesepith angles aregoing to be used intherest ofthe study

for omparingthe dierent ases.

elsA CFD

∆

^Isolated

∆

w/Installation

∆

^w/Inst

+

^Unst

θ ^FR

^[

^◦

^{℄ 62.50 -1.22}

^◦

^-1.36

^◦

^-1.36

^◦

θ ^RR

^[

^◦

^{℄ 62.50 -0.28}

^◦

^-0.17

^◦

^-0.17

^◦

Thrust [N℄ 20320 0.575% 0.458% -0.87%

Power Ratio 1.25 1.46% 0.893% 0.00%

Table 6.2: AI-PX7 Performane. Comparison between elsA and HOST-MINT

re-sults(isolated, installedand installed

+

^unsteady)

Rotor Performane and In-Plane Loads. Figure 6.2 shows the thrust

oef-ient, the in-plane loads oeient and the in-plane phase lag for front and rear

rotorsrespetively. Theseparameters aredened asfollows:

C _TH ^FR = T _FR

ρ _∞ N _FR ² (2R _FR ) ⁴ ; C _1P ^FR =

q F _Y ² _FR + F _Z ² _FR

ρ _∞ N _FR ² (2R _FR ) ⁴ ; φ ^FR _1P = arctan F _Y FR

F _Z FR

C _TH ^RR = T RR

ρ _∞ N _FR ² (2R _FR ) ⁴ ; C _1P ^RR = q F _Y ²

RR + F _Z ²

RR

ρ _∞ N _FR ² (2R _FR ) ⁴ ; φ ^RR _1P = arctan F Y RR

F _Z RR

(6.1)

Several remarks an be done on these gures. First, the total thrust level is

obtained withaslightoverestimation ofthefrontrotorthrust (

+3.5%

^{) andaslight}

underestimation of the rear one (

−3.5%

^{). Thesedierenes an be explained bya}

FR

Figure 6.2: Front and RearRotorperformaneomparison

based on the lifting-linetheory, thebladeis redued to thequarter-hord line, and

thus hord eets are not well aptured. In this open rotor onguration, even if

results arestill satisfatory,this deienystarts to appear.

When omparing in-plane loads, it an be notied how installation eets play

an important role inprediting better their magnitude, i.e. dierenes areredued

from

−17%

^to

+10%

^{fortheworstase. Besidesthemagnitudeofrearrotorin-plane}

loads isslightly modiedby installation eets.

The mean value of the rear rotor in-plane phase lag are loser to elsA results

when using the unsteady airfoil model, i.e. from

+12 ^◦

^to

+7 ^◦

^{. The amplitude of}

the bladeload osillation is howeverslightly overestimated. On theother side,the

osetoffrontrotorphaselagisinreasedduetoinstallationeetsandtheunsteady

model,but values arestillinthe level ofresolution of thesimulations, i.e.

2 ^◦

^.

Blade thrust. Figure 6.3 plots theblade thrust evolution along a yle. It

om-pares elsA omputation withthethreeHOSTsimulations.

Notiethatthethrustoeientisslightlyoverestimatedinthedownward

mov-ing bladewhen addinginstallation eets.Notiealso thelakof osillationsinthe

front blade loads. This an be explained by the fat that lifting-line methods

re-due theblade to its quarter-hord line, and therefore thedistane between rotors

ismore important than intherealbladegeometry. Indeed,asthedistanebetween

FR

Figure6.3: Blade loading along ayle. elsA ompared to HOSTsimulations

thetrailing-edgeofthefrontbladeandtheleading-edgeoftherearblade,theeets

fromrear rotoron the front rotor areunderestimated.

Regarding the rearbladeloads, even ifallHOST simulations math reasonably

wellwithCFD,aslightunderestimationappearsintheupperpartofthebladeyle.

Morerover, the amplitude of the rear blade load osillations is orretly aptured

and it is due to the passage of the front rotor wakes aross the rear rotor. Notie

however that a ertain phase lag appears in the peaks between HOST and CFD.

This an be explained by a dierene in the point of emission of the wake panels:

while in elsA they are onveted from the trailing edge, HOST does it from the

quarter-hord line.

Blade thrust distribution. Figure6.4 shows the thrust oeient distribution

along the blade

∂τ /∂ξ

^{for the same four} simulations. The thrust oeient distri-butionis dened asfollows:

∂τ _FR

where the front rotor parameters (rotational speed

N

^{FR and propeller radius}

R

^FR)

areusedasthereferene forboth rotor oeients.

Left-hand gures show an important wall eet on the front and rear mean

blade loads, whih is not aptured by HOSTas no hub model is implemented, i.e.

irulation is imposed to zero at the root setion. In the entral part of theblade,

∂τ /∂ξ

^isoverestimated. Finally,theblademaximumloadingisunderestimatedand slightly loserto thebladetip. No signiant dierene isobserved between HOST

simulations.

Right-hand side gures show therst mode of

∂τ /∂ξ

^. Installation eets inrease

Relative Radius, r/R1

Figure6.4: DisreteFourier Transformof thefront andrear rotors

∂τ /∂ξ

on the rear blade and redues the phase lag, getting signiantly loser to elsA

results inan important part oftheblade.

InduedVeloityFields. Thisparagraphomparestheaxialandirumferential

indued veloities as preditedbyelsA and HOST-MINTfor two planes normalto

therotatingaxis: oneupstreamthefrontrotorandtheotheronebetweentherotors

(seegures6.5and6.6). Theirumferentialomponent fortherstandtheseond

plane are alulated respetively in the diretion of rotation of the front and the

rear rotor.

Fortheplaneupstreamthefrontrotor(gures6.5(a)and6.5(b)),important

mis-mathesareobserved. Nevertheless,asithasbeenshowninthepreviousparagraph,

the omparison between blade loads predited by elsA and HOSTareverysimilar.

(a)Non-dimensionalaxialveloity,

V X ^ind /V X ∞

(b)Non-dimensionalirumferentialveloity,

V _θ ^ind /V X∞

Figure 6.5: Comparison between elsA and HOST-MINT results for an x-plane

up-streamthe front rotor

(a)Non-dimensionalaxialveloity,

V X ^ind /V X ∞

(b)Non-dimensionalirumferentialveloity,

V _θ ^ind /V X∞

Figure 6.6: Comparison between elsA and HOST-MINT results for an X-slie

be-tween rotors

leading edgeof the blade, and so the passage of theblade is very well aptured in

elsA.ItisnottheaseinHOST-MINT,asthebladeisreduedto itsquarter-hord

line. Therefore,this omparison shows thatvolume eetsare not negligibleinthe

eldnearthe blade.

Ingures6.6(a)and6.6(b),evenifsomedierenesanbeobserved,thegeneral

pattern is well aptured byHOST-MINT, speially theirumferential omponent.

Theaxialomponent alulatedbyHOST-MINTpresentshighervaluesinthezone

of the downward moving blade, whih are less evident in elsA results. On the

ontrary, this zone of higher irumferential indued veloities is notied both in

HOST and elsA results. As HOST-MINT onsiders a potential wake, no veloity

deit isobserveddue to thevisous eetsinthewake. Moreover, similarto what

was observed for the rear rotor blade loads, a ertain phase lag in the tip vortex

positionan be observed due to adierene intheemissionpointsof thewake.

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