NUMERICAL DATABASE
OF STALL FLUTTER
GUST RESPONSE
AGREE P ojec – Deli e able #10
Au ho s:
Kons an inos Rekoumis
Na ional Technical Uni e si y o A hens
The esea ch p ojec is implemen ed in he amewo k o H.F.R.I call “Basic esea ch Financing (Ho izon al
suppo o all Sciences)” unde he Na ional Reco e y and Resilience Plan “G eece 2.0” unded by he
Eu opean Union – Nex Gene a ionEU (H.F.R.I. P ojec Numbe :016749)
K. Rekoumis
1 In oduc ion
This documen con ains comp ehensi e documen a ion o he nume ical da abase c ea ed o cha ac e ize
gus -induced ai oil s all lu e . The aim o he p esen epo is o p esen he da a in a clea and concise
manne o o he s o use. The p esen wo k in es iga es he nume ical modeling o gus induced s all lu e
oscilla ions on a NACA 64-418 ai oil. The compu a ional amewo k aims o nume ically ep esen he
expe imen al appa a us ins alled in he NTUA wind unnel [1]. In sec ion 2, he examined cases will be
desc ibed. In sec ion 3 he geome y and he modeling con en ions o he compu a ional model will be
discussed, hen in sec ion 4 he nume ical me hodology employed will be discussed. Finally, in sec ion 5 he
da a o ganiza ion p o ocol will be p esen ed.
2 Examined cases
In he p esen s udy, he gus -induced s all lu e oscilla ions o a NACA 64-418 a e nume ically in es iga ed.
This nume ical in es iga ion on he gus induced s all lu e is based on expe imen s pe o med in he NTUA
Wind Tunnel.
To pe o m he p esen s udy a segmen ed app oach was ollowed. Fi s , he gus was s udied in an
emp y wind unnel (wi hou he a ge ai oil). To p oduce he s udied gus , he gus gene a ion anes mo ion
ollowed a ”1-cos” p o ile (see eq. 1) wi h an Ampli ude A= 34 deg and an oscilla ion equency = 7 Hz.
The U∞= 17.94 m/s and is kep cons an h oughou his s udy.
In he gus gene a ion analysis, bo h 3D and 2D simula ions we e pe o med o cap u e any 3D e ec s
du ing he gus p opaga ion. Fo his pu pose, simula ions we e un bo h on a 2D g id and 2 3D g ids, whe e
he 3D g ids ha e ARgg =zmax
cho dgg = 1 & 3.5. The g id wi h ARgg = 3.5→z= 700 mm is equal o he hal
span o he wind unnel.
θ=(A
2[1 −cos(2π δ )] , ∈[ 0, 0+1
]
0, else (1)
whe e δ = − 0, he exci a ion equency, and A he a ge gus angle.
Figu e 1: Moni o poin loca ion on he xy plane and spanwise a angemen
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K. Rekoumis
Figu e 2: The angle imese ies o he gus gene a ion oils
Ou analysis concluded ha no-signi ican 3D e ec s ake place, as good ag eemen was ound be ween
he 2D and 2 3D simula ions. Howe e o comple eness’s sake, he da a om he 3D simula ion o a
ARgg = 3.5we e uploaded. The e o e he eloci y ield was measu ed in se e al s a ions along he span o
he compu a ional domain a he same xy coo dina e. The x is 1295 mm downs eam o he gus s’ TE, and
he y is +140 mm o he cen e -line o he unnel. The z coo dina es dis ibu ion is gi en in he able 3. To
acqui e be e con ex o he a angemen , ad ise he igu e 1.
Then, he gus esponse simula ion was pe o med. In he gus esponse simula ion, he ai oil is coupled
wi h a o sional sp ing-dampene sys em and is able o eely oscilla e a ound i s elas ic axis while ha ing
all i s o he Deg ees o eedom cons ained ( he pa icula s o he oil a e ound in able 2). No e ha , he
elas ic axis is pa allel o he Global Z axis and consequen ly he e a e no g a i a ional e ec s o ake in o
conside a ion in he simula ions. Ini ially, he ai oil was s abilized in he low and hen subjec ed o ou gus s
acco ding he imese ies in he diag am 2. Fo he ae o-elas ic simula ions a 2D simula ion was un o a
o al simula ion ime o 30 sec (23 o which he oil pe o med s all lu e LCOs).
Wind Tunnel Wo king Leng h 3.3 m
Geome y B ead h 1.8 m
Heigh 1.4 m
Gus Gene a ion Numbe 4
Vanes Vane cho d 200 mm
Vane P o ile NACA 0015 c
Cen e o Ro a ion 25 % cho d
Table 1: Wind Tunnel & Gus Gene a o dimensions
Foil P o ile NACA 64-418 c
Foil cho d 500 mm
Elas ic Axis - x 35 % cho d
Elas ic Axis - y 1.6 % cho d
Momen o Ine ia 0.7282 kg m2
Damping a io 0.21
Sp ing Coe icien 254 Nm/ ad
Table 2: Ae o-Elas ic ( a ge ) Foil pa icula s
3 Geome ical Con igu a ion
The compu a ional g id is modeled a e he physical Wind unnel ( o dimensions ad ise able 1). Mo e
speci ically, he xy plane in he egion o in e es is dimensionally accu a e wi h espec o he eal wo ld.
A e he egion o in e es , he g id is coa sened p og essi ely o emula e he a ield egion o he wind
unnel. The sec ion we s udy is uni o m along he z axis up o he Heigh o he Tunnel. The dimensions o
he xy plane in he zone o in e es can be seen in igu e 3.
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K. Rekoumis
Figu e 3: Top down iew o he compu a ional domain wi h dimensions o he gus esponse case
The dimension a e gi en o he xy sec ion o he gus esponse case compu a ional domain o elay all he a ailable
in o ma ion.
The gus gene a o oils ( anes he ea e ) a e c ea ed a e he NACA 0015 oil, wi h a cho d o 200 mm
(ad ise able 1). The anes a e placed inside he compu a ional domain as seen in igu e 3. Again in igu e
3, he x axis dis ances o he ane placemen can be seen.
Finally, in he gus esponse case he a ge oil has a NACA 64-418 p o ile, wi h a cho d o 500 mm
(ad ise able 2). As seen in igu e 3, he LE is placed 1295 mm downs eam o he gus gene a o oils’ TE
and on he Wind Tunnel’s Cen e Line1. Fo he s uc u al pa , he elas ic axis om which he a ge oil’s
mo ions a e pe o med is loca ed 165 mm om he LE and +8 mm o he cho d o he oil.
4 Nume ical Se up
In igu e 4, he di e en bounda y elemen s o he compu a ional domain a e colo coded and p esen ed
in he included able. The bounding walls elemen a e modeled as In iscid walls and he in low & ou low
elemen s wi h In low and Ou low Bounda y Condi ions espec i ely. Bo h he gus gene a ion oils and he
a ge oil elemen s a e modeled wi h iscous wall bounda y condi ions and he y+ alue is kep ≤1.
In he p esen wo k, all nume ical simula ions we e done using he in-house URANS code MaPFlow [2],
[3]. In bo h gus gene a ion and ae o-elas ic scena ios MaPFlow esol ed he Incomp essible Uns eady
Reynolds A e aged Na ie -S okes equa ions, employing an a i icial comp essibili y scheme. To model
u bulence he Men e ’s K-omega SST model [4] along wi h he γ−Reθ ansi ion model was used in bo h
examined cases.
MaPFlow has he abili y o esol e Fluid-S uc u e In e ac ion p oblems in e nally, ia i s s ongly coupled
RBD sol e [3]. The e o e, bo h he o ces applied o he a ge oil and he esponses o he a ge oil, can
be ex ac ed om he same piece o so wa e and ensu e consis ency o he da a a each ime ins ance.
1The Cen e Line along wi h he ame o e e ence axis a e shown in igu e 1
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K. Rekoumis
Figu e 4: Geome ical Con igu a ion o he Ae o-elas ic se up
Each di e en elemen o he se up is colo - coded di e en ly. No ice ha each solid bounda y (gus gene a ion oils &
a ge oil) is ea ed as a sepa a e en i y, hin ing a he e sa ili y o ou se up.
Finally, he code has he abili y o inse p obes in he low ield and ex ac a a ce ain poin he eloci y
ield.
5 Da a O ganiza ion
In he p esen sec ion, he da a naming and s uc u e con en ions o using he p o ided da a will be ana-
lyzed. All da a p o ided a e in a cs (comma-sepa a ed alues) ex ile o ease o use. The i s ow will
con ain he name o he espec i e column a each cell. In he subsec ions ha ollow, we will gi e some
ins uc ions on how o ead he uploaded da a as long as he con ex o he nume ical alues.
5.1 Gus Gene a ion Case
Da a o he gus gene a ion case a e uploaded in he gus gene a ion di ec o y. The moni o poin X.cs
(X akes alues om he ”Moni o Poin ” column o able 3) iles con ain he eloci y ec o a he espec i e
poin in space o each ime ins ance. As he x-y coo dina es as s a ed abo e, he mapping o heade names
o z coo dina e ollows he able 4.
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5.2 Gus Response Case K. Rekoumis
Moni o Poin Z [m]
A 0.1
B 0.2
C 0.3
D 0.4
E 0.5
F 0.6
Table 3: Spanwise a angemen o he moni o poin s
1 ime 7−→ Simula ion Time [sec]
2 elx 7−→ Flow Veloci y x componen [m/s]
3 ely 7−→ Flow Veloci y y componen [m/s]
4 elz 7−→ Flow Veloci y z componen [m/s]
Table 4: Mapping o heade names o physical con ex o moni o poin iles
5.2 Gus Response Case
The iles o he gus esponse case can be ound unde he gus esponse di ec o y. To gi e insigh in he
mo emen pe o med by he oil, iles con aining he mo emen and loading imese ies a e uploaded. Inside
he di ec o y o each ae o-elas ic case you ind he ollowing iles:
1. his bd.cs : The ile con aining he mo ion his o y o he a ge oil as i is esol ed by he RBD sol e .
2. his loads.cs : The ile con aining he aw loads de eloped on he global o hogonal axes. These
loads a e he di ec esul o in eg a ing he p essu e ield and he shea s esses on he solid bounda y.
To ensu e ha he in o ma ion o he iles is elayed p ope ly, in ables 5 and 6 an explana ion abou each
columns da a is p esen ed.
1 ime 7−→ Simula ion Time [sec]
2 aoa 7−→ Angle o A ack [deg]
3 o speed 7−→ Ro a ion Speed [ ad/s]
3 o accel 7−→ Ro a ional Accele a ion [ ad/s2]
4 momen 7−→ Ro a ional Momen a ound local z-axis [Nm]
Table 5: Columns’ heade explana ion o his bd.cs ile
1 ime 7−→ Simula ion Time [sec]
2 Fx 7−→ Fo ce a he Global x-axis [N]
2 Fy 7−→ Fo ce a he Global y-axis [N]
2 Mz 7−→ Momen a ound he Global z-axis [Nm]
3 o speed 7−→ Ro a ion Speed [ ad/s]
3 o accel 7−→ Ro a ional Accele a ion [ ad/s2]
4 momen 7−→ Ro a ional Momen a ound local z-axis [Nm]
Table 6: Columns’ heade explana ion o his loads.cs ile
Re e ences
[1] Ma inos Manolesos, Ch is os Ampa is, Dimi is Gkiolas, Nikolaos Papakons an inou, And eas
Alexand is-Galanopoulos, Kons an inos Rekoumis, and Geo ge Papadakis. Design o a wind unnel
se up o measu e ai oil ae oelas ic gus esponse, July 2025.
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REFERENCES K. Rekoumis
[2] Geo gios Papadakis. De elopmen o a hyb id comp essible o ex pa icle me hod and applica ion o
ex e nal p oblems including helicop e lows. PhD hesis, Na ional Technical Uni e si y o A hens School
o Mechanical Enginee ing, 2014.
[3] Dimi is N ou as. Adap a ion o he A i icial Comp essibili y Fo mula ion o F ee Su ace Flows wi h
Applica ions in Ship & Ma ine Hyd odynamics. PhD hesis, Na ional Technical Uni e si y o A hens
School o Na al A chi ec u e & Ma ine Enginee ing, 2023.
[4] F. R. Men e . Two-equa ion eddy- iscosi y u bulence models o enginee ing applica ions. AIAA Jou nal,
32(8):1598–1605, 1994.
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