Ae ospace Science and Technology 126 (2022) 107625
Con en s lis s a ailable a ScienceDi ec
Ae ospace Science and Technology
www.else ie .com/loca e/aesc e
Re iew
Nume ical-expe imen al e alua ion and modelling o ae odynamic
g ound e ec o small-scale il ed p opelle s a low Reynolds numbe s
Amba Ga o ano-Soldado a,∗, Ped o J. Sanchez-Cue asa,b, Guille mo He ediaa,
Anibal Olle oa
aGRVC Robo ics Lab Se ille, Uni e si y o Se ille, Spain
bSpace Robo ics Resea ch G oup, SnT, Uni e si y o Luxembou g, Luxembou g
a i c l e i n o a b s a c
A icle his o y:
Recei ed 1 Feb ua y 2022
Recei ed in e ised o m 25 Ap il 2022
Accep ed 7 May 2022
A ailable online 11 May 2022
Communica ed by Damiano Casalino
Keywo ds:
Ae odynamic E ec
Ae ial Robo
UAV
CFD
P opelle
In ecen yea s, ae ial manipula o s wi h ully-ac ua ed capabili ies a e gaining popula i y o being used
in ae ial manipula ion ope a ions such as c i ical in as uc u e inspec ion o ae ial manipula ion asks.
Those scena ios usually demand he ae ial pla o m o ope a e in cons ained and na ow scena ios. I
is well known ha in hese si ua ions, he in e ac ion o he wake gene a ed by he p opelle s wi h
he en i onmen can significan ly al e and change he pe o mance o he o o s. Mos s udies ha e
add essed his p oblem by conside ing he g ound e ec in ho e condi ions o du ing he landing
maneu e o co-plana mul i o o . Howe e , ew wo ks analyze he beha iou o il ed o o s, which
a e used in ully ac ua ed mul i o o configu a ions hanks o hei omnidi ec ional mo ion capabili ies.
This pape p esen s a nume ical-expe imen al e alua ion o he ae odynamic g ound e ec o small-
scale il ed p opelle s a low Reynolds numbe s. This ae odynamic e ec has been expe imen ally
e alua ed h ough an ex ensi e es ing campaign in a es bench designed o his pu pose which has been
complemen ed by a CFD-based s udy. CFD esul s ha e been alida ed h ough a mesh independence
s udy and a CFD-expe imen al p opelle pe o mance compa ison. A nume ical model has been also
p oposed o cap u e he dependence o h us wi h dis ance o he g ound and angle o inclina ion
be ween he p opelle and g ound planes. We demons a e ha he p oximi y o he g ound o il ed
o o s dec eases he h us inc emen due o he g ound e ec as he il angle (θ) inc eases. This means
ha Cheeseman’s classical heo y is inapplicable, as i only conside s he dis ance om he g ound
wi hou e e ence o how he h us inc emen changes wi h he il angle. This ou come enables u u e
ae ial obo ic applica ions ha s ongly demand accu a e ae odynamic e ec models o ope a e close o
obs acles and na ow en i onmen s.
©2022 The Au ho (s). Published by Else ie Masson SAS. This is an open access a icle unde he CC BY
license (h p://c ea i ecommons.o g/licenses/by/4.0/).
1. In oduc ion
Unmanned Ae ial Vehicles (UAVs) and Mic o Ai Vehicles
(MAVs) a e significan ly inc easing hei applica ion ange [1]. Typ-
ically, hese ae ial obo s ha e been used as flying senso s o
pe o m pe cep ual asks such as emo e su eillance and econ-
naissance [2,3], isual inspec ion o la ge in as uc u es [4,5]o
filming ac i i ies [6,7]. Howe e , eme ging applica ions such as
package deli e y [8], con ac inspec ions [9,10], wa ehouse in en-
o y [11] and, in gene al, ae ial obo ic manipula ion ope a ions
[12] equi e hese o o c a s o fly close o obs acles and objec s
o wi hin na ow en i onmen s. P opelle s ope a ing nea obs a-
cles expe ience di e en ae odynamic e ec s. This cons ains he
*Co esponding au ho .
E-mail add ess: aga [email p o ec ed] (A. Ga o ano-Soldado).
ee de elopmen o he o o wake and dis u bs he p opelle pe -
o mance [13].
The g ound e ec on helicop e s has been s udied since he
1930s [14] o cha ac e ise he ho e ing ae odynamic pe o mance
[15]. In 1937, Be z [14]p oposed a heo e ical model based on e-
placing he helicop e o o by a sink and applying he me hod o
images. Knigh e al. [16] conside ed wo cylind ical o ex shee s
loca ed a a dis ance o 2zo equal s eng h and opposi e di ec ion.
In 1947, Zb ozek [17] analysed he g ound e ec expe imen ally.
La e , Cheeseman and Benne [18] ound ha he flow pa e n
o a o o in he icini y o he g ound was be e ma ched wi h
a sou ce. Thus, [18]used blade elemen heo y and he me hod
o images o model he inc ease in h us expe ienced by a o o
ope a ing close o he g ound unde di e en condi ions. Cheese-
man and Benne ’s model is ypically used because i allows esul s
o be ob ained wi h high accu acy compa ed o expe imen al e i-
dence o la ge p opelle s such as helicop e s o MAVs. In addi ion,
h ps://doi.o g/10.1016/j.as .2022.107625
1270-9638/©2022 The Au ho (s). Published by Else ie Masson SAS. This is an open access a icle unde he CC BY license (h p://c ea i ecommons.o g/licenses/by/4.0/).
A. Ga o ano-Soldado, P.J. Sanchez-Cue as, G. He edia e al. Ae ospace Science and Technology 126 (2022) 107625
Nomencla u e
θTil angle o he p opelle ela i e o he g ound . deg
zG ound dis ance om p opelle hub................ m
αAngle o a ack o a blade......................... deg
βBlade pi ch angle................................... deg
φInflow angle........................................ deg
UResul an eloci y o a blade sec ion.............. m/s
UTTangen ial componen o eloci y in a blade
sec ion............................................. m/s
UPNo mal componen o eloci y in a blade sec ion m/s
Re Reynolds numbe
ρAi densi y...................................... kg/m
3
μAi dynamic iscosi y........................... kg/ms
VωRo a ional eloci y................................. m/s
Angula eloci y.................................. ad/s
R75% P opelle adius a 3/4 o he cen e o o a ion.... m
c75% P opelle cho d a 3/4 o he cen e o o a ion.... m
Fx,Fy,FzSenso o ce componen s........................... N
Tx,Ty,TzSenso o que componen s....................... Nm
XA,YA,ZAAxes in he absolu e e e ence ame............ m
XB,YB,ZBAxes in he p opelle e e ence ame............ m
CTP opelle h us coefficien
CTxHo izon al componen o he h us coefficien
CTzVe ical componen o he h us coefficien
CQP opelle o que coefficien
RP opelle adius...................................... m
DP opelle diame e ................................... m
ARo o disk a ea..................................... m
2
TP opelle h us ...................................... N
QP opelle o que.................................... Nm
TIGE Th us In-G ound-E ec .............................. N
TOGE Th us Ou -o -G ound-E ec ......................... N
IGE Induced eloci y in g ound e ec ................. m/s
i∞Induced eloci y wi hou g ound e ec ........... m/s
δ iInduced eloci y on he o o caused by he image
o o ................................................ m/s
VhHo e induced eloci y............................ m/s
c(θ) Ta ge unc ion
a0,a1,b1Coefficien s p oposed o he g ound e ec model
βjModel coefficien s calcula ed wi h he g adien de-
scen algo i hm
J(βj)Cos unc ion
hβ(zi,θi)Hypo hesis unc ion
yiTh us a io TIGE/TOGE
sNumbe o samples
γLea ning a e
Ac onyms
CFD Compu a ional Fluid Dynamics
ESC Elec onic S abili y Con ol
IGE In-G ound-E ec
MAVs Mic o Ai Vehicles
MRF Mul iple Re e ence F ame
OGE Ou -o -G ound E ec
RANS Reynolds A e age Na ie -S okes
SST Shea S ess T anspo
UAVs Unmanned Ae ial Vehicles
BET Blade Elemen Theo y
he o mula ion o his model is ela i ely simple and depends only
on he adius o he o o (R) and he dis ance be ween he p o-
pelle and he g ound plane (z). O he ope a ing condi ions, such
as o wa d fligh , we e conside ed [18–20]. Since he fi s expe -
imen al es s by Zb ozek [17], some g ound e ec models ha e
been de i ed om expe imen al e idence. Hayden (1976) [21]p o-
posed an empi ical model o analyse he g ound e ec in ho e ,
which o e p edic s he Cheeseman and Benne model. Then, Cu -
is [22]p esen ed he ae odynamic pe o mance o a helicop e
o o when posi ioned close o he g ound o low ad ance a ios.
O he au ho s ha e ocused on examining he o o wake when i
is cons ained by he p esence o he g ound plane [23–27].
In he las decade, pa icula a en ion has been de o ed o
explo ing he ae odynamic in e ac ions o mul i o o [28–32] and
small scale o o s [33,34]. The e is a need o in-dep h knowledge
o he beha iou o UAVs when app oaching ce ain su aces. In
his way, p oximi y e ec s can be coun e ac ed by inco po a ing a
con olle adap ed o abso b ae odynamic dis u bances [20,35,36].
In addi ion, he easibili y o il ing he p opelle s o a mul i o o o
pe o m asks equi ing di ec con ac be ween he ae ial pla o m
and he en i onmen has been in es iga ed. In [37], a new design
o a ully ac ua ed hexa o o wi h il ing p opelle s was p esen ed
and he applica ion o con ol echniques o aid pla o m s abilisa-
ion. O he wo k has been ca ied ou along he same lines [38],
[39]. The ae odynamic e ec s o il ed o o s a e no conside ed in
hese con ol laws as he e is no ho ough unde s anding o how
he o ces on a o o change wi h inclina ion and dis ance om
he g ound. Fo ins ance, unlike co-plana ae ial manipula o s ha
classically accomplish he manipula ion ope a ion while hey a e
ho e ing (and necessa ily ho izon al), a ully ac ua ed ae ial obo
can pe o m a ho e -fligh while il ing wi h espec o he ho i-
zon al plane. This p esen s a comple ely new casuis y. Acco ding
o [28], he dis u bance ha a ec s a co-plana mul i o o is gene -
a ing a “sa e” beha iou cause i is always gene a ing s abiliza ion
pi ch and oll o ques. Howe e , due o ully-ac ua ed obo s usu-
ally ha e il ed p opelle s and can main ain an inclined ho e ,
he ae odynamic g ound e ec will dis u b he 6DoF, including
he yaw axis. This si ua ion will significan ly impac he s abil-
i y o hese ae ial obo s, hei sa e y, and he defini ion o hei
con ol alloca ion ma ix. Mo eo e , a ully-ac ua ed ae ial manip-
ula o will be a ec ed by his e ec mainly when flying close o
an obs acle and specifically, when accomplishing he manipula-
ion ope a ion. The manipula ion ope a ion is usually when he
accu acy and p ecision needed a e highe . This means ha any dis-
u bance should be conside ed o gua an ee he success and sa e y
condi ions du ing he ope a ion.
Though ex ensi e p e ious wo ks ha e cha ac e ised he ae o-
dynamic pe o mance o la ge and small-scale o o s pa allel o he
g ound, he e is li le wo k on il ed o o s wi h espec o he
g ound o co-plana o o s ope a ing a inclined su aces. Howe e ,
ecen ad ances in ae ial manipula ion p esen he ully-ac ua ed
mul i o o as he op imal candida e o ce ain con ac -based op-
e a ions [40]. These mul i o o ha e ull pose (posi ion and o ien-
a ion) acking capabili ies. Also, could land o ho e e y close
o he g ound o a di e en obs acle, main aining a desi ed angle
wi h he g ound. In 1960, F adenbu gh [41]was he fi s o s udy
he a ia ion o he h us a io o a helicop e and annula je con-
side ing he ae odynamic g ound e ec wi h di e en angles and
heigh s abo e g ound. Xin [42]p oposed an ex ension o he inflow
model o o o s a di e en heigh s abo e an inclined g ound in
ho e ing condi ions. Di e en g ound inclina ions we e analysed.
The esul s we e compa ed wi h he ee- o ex/panel model. They
also ound ha an asymme y in he o o wake appea ed wi h
he g ound angle. Mo e ecen con ibu ions we e epo ed in [43],
2
A. Ga o ano-Soldado, P.J. Sanchez-Cue as, G. He edia e al. Ae ospace Science and Technology 126 (2022) 107625
Fig. 1. Real and geome ic model o he T-Mo o p opelle - 13 ×4.4.
[44]. Pla ze e al. examined he flow field o a o o in he neigh-
bou hood o an inclined su ace using pa icle image elocime y
(PIV) and uns eady nume ical simula ions. Then, Pasquali e al. [45]
used expe imen al and nume ical echniques o analyse he e o-
lu ion o he o o wake on an inclined and pa allel g ound. The
bounded domain me hod and me hod o images we e employed
and compa ed. Howe e , he e a e no de ailed s udies showing
he h us augmen a ion o a small-scale o o wi h il angle and
dis ance o a pa allel su ace. Acco dingly, nei he heo e ical no
empi ical h us models aking in o accoun inclina ion ha e been
de eloped.
Due o he con inuous de elopmen o compu a ional fluid dy-
namics (CFD) ools, a ious simula ion me hods ha e been con-
side ed in he pas o e alua e he influence o he g ound on a
o o [43,46], [47–49]. Compu a ional Fluid Dynamics is a handy
ool o ep oducing fluid beha iou a ound a p opelle . Al hough
se e al simula ion echniques exis [50], Reynolds A e aged Na ie -
S okes (RANS) models a e less expensi e and a e used o es ima e
ime-a e aged pa ame e s. In ecen yea s, he numbe o in es i-
ga ions on p opelle pe o mance analysis wi h RANS models has
inc eased [46–49,51–58]bo h high and low Reynolds numbe s.
Thei sui abili y wi h expe imen al se s has been p o en in se -
e al wo ks [52,55,58]. Based on p e ious wo k, RANS models a e
conside ed capable o sol ing he p oposed p oblem and will be
used h oughou his analysis. In his ega d, he Mul iple Re e -
ence F ame (MRF) me hod will be used o sol e he 3D p opelle
flows. MRF has been adop ed o examine flows a ound p opelle s
by o he au ho s bo h in ee [51–54] and cons ained en i on-
men [56,59]. Ne e heless, he adequacy o he MRF me hod has
no been p o ed o inclined p opelle s, whe e he flow pa e ns
a e di e en om he co-plana case.
In gene al, his s udy desc ibes he g ound e ec o il ed o o s
using small-scale p opelle s ope a ing a low Reynolds numbe s. So
a , no g ound e ec model has been p esen ed unde hese condi-
ions. Conside ing he g ow h in he field o UAVs, i is necessa y
o analyse and quan i y he e ec s ha may appea when ce ain
asks a e pe o med. In summa y, he con ibu ions o his esea ch
a e lis ed as ollows:
•In es iga ion o he influence o inclina ion o o o (θ) and
dis ance o he g ound (z) o quan i y he h us inc ease. The
findings ha e been benchma ked agains models de eloped in
he pas , highligh ing he need o include he angle θin he
g ound e ec analysis. Indeed, he pa ame e θhas no been
accoun ed o in small-scale p opelle s un il he cu en s udy.
•A comp ehensi e 3D s a iona y CFD simula ion-based s udy
wi h a wide ange o Reynolds numbe s ([0.46 −2.2] ·105)
and p opelle diame e s om 9 o 18 inches. Mo eo e , o o
inclina ions o up o abou 40◦and a ious g ound clea ances
ha e been assumed.
•E alua ion o a CFD-based me hodology o flow simula ion
a ound p opelle s in confined en i onmen s. In pa icula , he
MRF me hod has been applied. Al hough i s eliabili y has
been demons a ed o o o s pa allel o he g ound (see [59]),
he fluid beha iou is dis inc i he o o is il ed. MRF has
been e ified wi h da a om he p opelle manu ac u e in
ee en i onmen s and hen wi h he expe imen al se up un-
de IGE and OGE condi ions. A me hod wi h a low compu a-
ional cos ha allows ob aining adequa e esul s in e en less
ime han he ime equi ed o bench es ing.
•P oposal o fi s g ound e ec model wi h il ed o o s in
small-scale p opelle s is p esen ed o cap u e he dependence
on bo h il angle (θ) and g ound dis ance (z). I has been
de i ed a CFD simula ion da a-d i en model using he g a-
dien descen algo i hm. Fo his pu pose, a modifica ion o
he classical Cheeseman and Benne heo y has been made,
whe e he fi s ha monic o he inflow models has been con-
side ed. The applicabili y o he p oposed model has also been
assessed.
The emainde o he pape is o ganized as ollows. Sec ion 2
de ails he geome y o he di e en p opelle s used h oughou
his s udy, he Reynolds numbe ange, he expe imen al se up
and he undamen als o Compu a ional Fluid Dynamics (CFD). The
compu a ional domain, he bounda y condi ions, and he u bu-
len model a e in oduced. Sec ion 3shows he alida ion o he
CFD me hodology. On he one hand, a g id independence s udy is
p esen ed. On he o he hand, he p opelle pe o mance achie ed
by he p oposed CFD me hodology is e alua ed wi h he manu ac-
u e ’s da a. Sec ion 4is de o ed o p esen ing he g ound e ec
esul s ob ained om bo h he expe imen al se up and nume ical
simula ions. The easibili y o he CFD me hod is discussed. Then,
he flow field isualiza ion is illus a ed o unde s and he change
in o o pe o mance wi h il . In Sec ion 5, a da a-d i en g ound
e ec model wi h il ed o o s is p oposed and alida ed o se -
e al p opelle s. Sec ion 6discusses he applica ions and limi a ions
o he p oposed model. Finally, i d aws he conclusions om he
g ound e ec analysis and gi es ideas o u u e wo k along he
same lines.
2. Ma e ials and me hods
2.1. P opelle geome y
The fi s p opelle selec ed is a small-scale T-Mo o p opelle
wi h a diame e o 13 inches and a pi ch o 4.4 inches. Fig. 1(a) and
Fig. 1(b) p esen bo h he ca bon fib e p opelle used in he expe -
imen al s udy and he 3D geome y o he p opelle employed in
he nume ical analysis espec i ely. Fig. 1also shows a de ail o he
geome y o a blade sec ion acco ding o he blade elemen heo y
(BET). He e, he angle o a ack is defined as α=β−φ, whe e β
is he pi ch angle o he c oss-sec ion and φis he inflow angle,
defined as φ= an−1(Up/UT). Uis he esul an eloci y and de-
pends on he no mal (Up) and angen ial (UT) componen o he
plane o o a ion. In he cu en s udy, ees eam eloci y is no
aken in o accoun as a esul he eloci y Upwill depend only on
he induced eloci ies h ough he disk o o . Mo eo e , he e olu-
3
A. Ga o ano-Soldado, P.J. Sanchez-Cue as, G. He edia e al. Ae ospace Science and Technology 126 (2022) 107625
Fig. 2. Geome y, cho d and wis angle dis ibu ion o he T-Mo o p opelle -13
×
4.4 used in expe imen al-nume ical analysis.
ion o he cho d and he pi ch angle o he p opelle is shown in
Fig. 2.
Two ex a p opelle s ha e been used o alida e he p oposed
model and e alua e i s applicabili y. These p opelle s a e APC
9x4.4” and one T-Mo o p opelle 18x6.1” (see Fig. 3), he 3D ge-
ome ical model, he dimensions and cho d and wis angle dis i-
bu ions o hese p opelle s a e shown.
2.2. Reynolds numbe ange
This sec ion p esen s he ange o Reynolds numbe s e alua ed
in his wo k. I is known ha in o de o model he flow be-
ha iou a ound a p opelle , he Reynolds numbe , based on he
o a ional speed and he cho d a 3/4 o he adius loca ion, plays
an impo an ole. The pe o mance o a p opelle will change wi h
he Reynolds numbe , as shown in p e ious s udies [60]. Also, he
Reynolds numbe in small-scale p opelle s will be much lowe
han in la ge-scale p opelle s used in helicop e s. The Reynolds
numbe when ees eam eloci y is no aken in o accoun can
be defined as ollows [61]:
Re75% =ρVωc75%
μ(1)
whe e he ai densi y is ρ= 1.225 kg/m3, he dynamic iscosi y
is μ =1.7894 ·10−5kg/ms, he o a ional eloci y is Vω=R75%,
is he angula eloci y, R75% and c75% is he adius and cho d
o he p opelle loca ed a 3/4 cen e o o a ion, espec i ely.
In his s udy, p opelle s a e ope a ing a low Reynolds numbe s
since he maximum alue is 2.2·105[62]. I is well known ha
low Reynolds numbe s a e ela ed o bubble sepa a ion, which is
caused by ad e se p essu e g adien s. Fo low ad ance a ios, a
la ge numbe o c oss-sec ions o he blade a e in a s all condi-
ion. Howe e , Co iolis e ec s, based on he o a ion and he adial
componen o he eloci y, delay he sepa a ion o he bounda y
laye and consequen ly he s all [63].
Table 1defines he Reynolds numbe o each p opelle consid-
e ed in his s udy.
2.3. Expe imen al se up
Fig. 4shows he cus omized es bench used du ing he expe i-
men s in GRVC’s acili ies. I is made up o an aluminum s uc u e
o 1mx 1mx 1mwhe e an Axia80-M20 o ce/ o que senso has
been moun ed. This senso allows measu ing he six componen s
Table 1
Reynolds Numbe o di e en p opelle s conside ed
in his s udy.
P opelle Reynold numbe
APC 9x4.4 (0.46,0.74)·105
T-Mo o 13x4.4 (0.88,1.1)·105
T-Mo o 18x6.1 (1.5,2.2)·105
o o ce and o que wi h a esolu ion o 1/10Nand 1/200Nm, e-
spec i ely. The sensing ange is 500N o he o ces Fx, Fy, 900N
o Fzand 20Nm o Tx, Tyand Tzand he senso equency is
2kHz.
An A duino Mega 2560 is used o con ol he mo o . The mo o
PWM inpu is sen om he compu e o achie e a speed o 6300
e olu ions pe minu e ( pm). Ro a ion speed is measu ed wi h an
ex e nal achome e du ing he expe imen s. The ope a ing ange
o he mo o s used in mul i o o is be ween 50% −60% h o le.
The selec ed speed is wi hin his ange and is a ypical alue o
he mo o and p opelle chosen in his analysis. Las , wo 360W
pa allel powe supplies ha e been used o powe he senso and
he mo o o main ain cons an ol age condi ions in all he expe -
imen s.
A o al o 40 expe imen s has been ca ied ou . Fig. 5shows he
wo pa ame e s conside ed o e alua e he ae odynamic g ound e -
ec . Unlike classical g ound e ec analysis whe e only he g ound
dis ance was aken in o accoun [28,30,32,56], his s udy also con-
side s he ela i e angle be ween he g ound and he p opelle (θ).
In each expe imen , fi e di e en measu emen s ha e been aken
in o de o ake he mean alue. The s anda d de ia ion o he
o ce was calcula ed o each dis ance (z) and angle (θ), eaching a
maximum alue o 0.087Nand a minimum alue o 0.002N. These
esul s show ha he senso is highly accu a e.
The da a collec ion p ocess akes 85 seconds o each es . A
fi s , he mo o is swi ched o o 15 seconds. Then, he p opelle
is o a ing a a cons an speed o 10 seconds. Finally, he mo-
o speed is educed o a minimum speed o 60 seconds o a oid
an inc ease in mo o empe a u e be o e a new es was done. All
expe imen al da a ha e been collec ed in he absolu e e e ence
ame SA, defined by he axes XA, YA, ZA. In addi ion, he body
ame SB= XB, YB, ZBis defined, which can be ob ained by o a -
ing he absolu e e e ence ame SA.
2.4. CFD se ings
Compu a ional fluid dynamics me hods a e ypically used o
analyze p opelle pe o mance and unde s and o ex gene a ion
mechanisms. Fo ha , he fini e olume me hod is used whe e he
Reynolds A e aged Na ie -S okes (RANS) equa ions a e sol ed on
an uns uc u ed mesh. The incomp essible flow simplifica ion is
pe o med.
Acco ding o he li e a u e [51–55,59,64], he e a e wo main
CFD echniques o simula e o o a ing flows: he mul iple e e -
ence ame (MRF) and he sliding mesh me hods. MRF is a s eady-
s a e app oach. I di ides he domain in o se e al zones: a s a-
iona y zone, whe e he equa ions will be applied in a s a iona y
ame, and a zone assigned o a o a ional eloci y ela i e o he
p opelle axis. These zones lead o he appea ance o an in e ace
ha allows in o ma ion o be exchanged be ween he s a iona y
zone and he o a ional zone. In con as o o he au ho s [49],
his analysis conside s he classical mul i-zone MRF me hod. On
he con a y, he sliding mesh me hod conside s he p opelle ’s
mo ion a each ime-s ep and p o ides a ime-dependen solu ion.
The compu a ional domain is defined simila ly o he MRF me hod.
In many cases, he ou pu o he MRF me hod is aken, in ac , as
he ini ial condi ion o he sliding mesh me hod. While he appli-
4
A. Ga o ano-Soldado, P.J. Sanchez-Cue as, G. He edia e al. Ae ospace Science and Technology 126 (2022) 107625
Fig. 3. Geome y, cho d and wis angle dis ibu ion o he p opelle s used o alida e he p oposed g ound e ec model. Le ) APC p opelle -9
 ×4.4 used o alida e he
p oposed g ound e ec model. Righ ) T-Mo o p opelle -18
 ×6.1.
Fig. 4. Tes bench designed a Robo ic, Vision, and Con ol G oup (GRVC) o s udy g ound e ec wi h single il ed o o s. The s uc u e is mo ed o loca e he p opelle ’s
cen e o o a ion a di e en dis ances om he wall (z). The inclina ion o he mo o (θ) is achie ed by using inclined p in ed plas ic pa s.
Fig. 5. Absolu e e e ence ame XA, YA, ZAand e e ence ame on blade axes XB,
YB, ZBo he p opelle and a iables es ed in he g ound e ec in es iga ion.
ca ion o ansien echniques usually p oduces be e esul s, he
compu a ional e o is p ohibi i ely high.
This pape uses MFR due o i s simplici y, as ness, and ai ac-
cu acy. This me hod allows o analyse o he fluid flow a ound a
p opelle when i is close o he g ound wi hou he p esence o
ex e nal dis u bances. In he pas , o he au ho s ha e analyzed he
small and la ge scale p opelle pe o mance wi h his me hod in
bo h ee and confined en i onmen s [48,49,51,53,56]. Howe e , as
a il ed p opelle app oaches he g ound, he in e ac ion o he o-
o wake wi h he g ound su ace causes an asymme ic pa e n
ha becomes mo e no iceable as he il inc eases [42]. As a con-
sequence, i is necessa y o ensu e ha his s a iona y app oach
(MRF) allows modelling he flow beha iou o ob ain he small-
scale p opelle pe o mance. Sil a e al. show how he MRF me hod
is able o p edic he wake b eakdown and ing o ex using un-
s uc u ed meshes. Howe e , unde IGE condi ions, i is a challenge
o cap u e hese o ical s uc u es accu a ely [49].
Fig. 6shows he compu a ional domain se up o simula e he
g ound e ec wi h a il ed p opelle . I has h ee di e en domains.
An ex e nal s a iona y domain wi h a diame e o 20R, a cylind i-
cal inne domain wi h a diame e o 5R, and a o a ing domain
o enclose he p opelle . The inne domain allows a mesh ansi-
ion in o de o cap u e he fluid flow beha iou accu a ely. In his
domain, a flow wi h a o a ional speed o 6300RPM is induced.
The o a ional domain and he p opelle a e o a ed a an angle θ
wi h espec o he g ound. The e ical dis ance om he cen e
o o a ion o he p opelle o he g ound plane is defined as z.
The dimensions o he inne and ou e domains change o each z
alue. The e o e, a pa ame ic analysis has been pe o med whe e
5

A. Ga o ano-Soldado, P.J. Sanchez-Cue as, G. He edia e al. Ae ospace Science and Technology 126 (2022) 107625
Fig. 6. Compu a ional domain specified o analyse he g ound e ec on il ed o o s. The p opelle is placed a a heigh z = 1R wi h espec o he g ound. The bounda y
condi ion adop ed o e alua e he ae odynamic pe o mance is gi en.
he pa ame e s θand za e changed. This will gene a e a specific
geome y and mesh o each configu a ion.
The comme cial so wa e ANSYS-Fluen has been used o he
calcula ions. The p essu e-based coupled algo i hm is used o sol e
he momen um and he p essu e-based con inui y equa ions. The
coupled algo i hm significan ly educes he numbe o i e a ions
equi ed o con e ge. Howe e , he compu a ional ime is in-
c eased compa ed wi h a seg ega ed algo i hm, whe e each a i-
able is sol ed sequen ially. G een-Gauss Node-Based G adien is
employed o disc e ise he di usi e and con ec i e e ms o he
conse a ion equa ion. The second-o de scheme is chosen o Tu -
bulen Kine ic Ene gy (k), Specific Dissipa ion Ra e (ω), and p es-
su e in e pola ion. The u bulence model used o sol e he p ob-
lem is he shea s ess anspo (SST) k −ω u bulence model p o-
posed by Men e [65]. I combines he k −model in he emo e
egion om he wall and he k −ωmodel in he nea -wall e-
gion using blending unc ions. This is defined wi h wo equa ions,
one o he Tu bulen Kine ic Ene gy (k)and one o he Specific
Dissipa ion Ra e (ω). Due o he Reynolds numbe ange (see sec-
ion 2.2) in which u bulen flows a e ound, i is conside ed ha
he SST k-w model should be applied [52]. The SST k −ω u bu-
lence model has been used by o he au ho s o analyze he ae o-
dynamic pe o mance o small-scale p opelle s [53–55,57,58,66].
Mo eo e , he simula ions esul s we e compa ed wi h expe imen-
al da a ob aining a sa is ac o y ag eemen [52,55,58]. The u -
bulen in ensi y is se as 0.1%. This alue has been achie ed by
aking measu emen s in an emp y wind unnel o all ope a ing
condi ions [60,67]. Loga i hmic wall unc ions a e used o sol e
he bounda y laye . In ecen wo k, his app oach has been con-
side ed in he nea -wall egion [52]. Addi ionally, a ull g ound
e ec case wi h a 20 deg ee inclina ion has been simula ed wi h
he Realizable k-e u bulence model. This u bulence model was
used by [48] o analyse he s abili y o an ae ial pla o m close o
he g ound plane. The di e ences ound be ween he wo u bu-
lence models a e negligible. Howe e , he compu a ional ime and
he ins abili y o he solu ion wi h he Realizable k −model a e
inc easing.
Fig. 6shows he bounda y condi ions. In he uppe bounda y,
he inle is defined as a p essu e inle whe e he o al gauge p es-
su e is se o 0Pa. The ou le is se in he la e al bounda y o he
cylind ical domain as a p essu e ou le wi h gauge p essu e 0Pa.
The g ound plane and he p opelle a e defined as non-slip walls.
Be ween he o a ional and s a iona y domains, in e aces a e gen-
e a ed ha allow he sepa a ion o he wo domains. An absolu e
eloci y o mula ion has been used in his analysis, i.e. he equa-
ions a e sol ed in each sub-domain. The e o e, no ans o ma ion
is needed a he in e ace.
This nume ical analysis is di ided in o wo pa s: fi s , he sim-
ula ion esul s will be compa ed wi h he expe imen al esul s o
alida e he defined CFD model. Thus, he angles analysed by sim-
ula ion will be: 0◦, 10◦, 20◦and 30◦and dimensionless heigh s
z/R =0.6, 0.75, 1, 1.5, 1.5, 2, 2.5, 3, 3.5, 4, 5. Second, when i
is e ified ha he CFD model accu a ely fi s he expe imen al e-
sul s, his model will be ex ended o ob ain esul s o o he il
angles such as 5◦, 15◦, 25◦, 35◦and 40◦. Fo angles g ea e han
25◦, i has no been possible o ob ain esul s o heigh s less han
z = 0.75R as he cylind ical o a ional domain in e sec s wi h he
g ound plane. A o al o 87 simula ions has been ca ied ou o
cha ac e ise he ae odynamics g ound e ec wi h il ed o o s.
3. CFD alida ion
3.1. Mesh e alua ion
A mesh independence s udy was conduc ed o ensu e ha he
solu ion does no depend on he mesh size. This p ocess allows
defining a mesh wi h enough quali y o achie e eliable and accu-
a e esul s, minimise compu a ional ime and achie e good con-
e gence o he solu ion. In his analysis, ou di e en meshes
ha e been c ea ed whe e he cell size loca ed on he su ace o
he p opelle , he cell size o he p opelle leading edge and he
sizes o in e aces ha e inc eased om mesh 1 o mesh 4. Addi-
ionally, au oma ic mesh efinemen is applied. Fig. 7shows he
ou defined g ids in he o a ional domain and Table 2shows he
numbe o nodes and elemen s in each o he domains and in e -
aces gene a ed. As can be seen, Mesh 1 and 2a e coa se wi h
1.06 y 2.2 million elemen s espec i ely, while Mesh 3 and 4a e
fine wi h 3.3 and 4.8 million espec i ely. In all cases, uns uc-
u ed meshes we e made wi h a efinemen in he leading edge
o he p opelle and in he wake egion. This s udy was ca ied
ou o a 20 deg ee il angle and o a heigh z=1R. In o de o
e alua e he accu acy o each mesh, he esul s o he h us and
o que coefficien o he p opelle we e calcula ed acco ding o:
CT=T
ρA2R2(2)
6
A. Ga o ano-Soldado, P.J. Sanchez-Cue as, G. He edia e al. Ae ospace Science and Technology 126 (2022) 107625
Fig. 7. On he le -hand side, defini ion o ou di e en meshes (Mesh 1: coa se, Mesh 2: medium, Mesh 3: fine, Mesh 4: e y fine) o he o a ional domain. On he
igh -hand side, mesh chosen o he comple e compu a ional domain.
Table 2
Numbe o elemen s and nodes in he s a iona y, o a ional domain and a he in e ace sepa a ing he wo zones o
meshes 1 (coa se), 2 (medium), 3 (fine) and 4 ( e y fine).
Mesh densi ies Ro a ing domain S a iona y domain In e aces To al
Mesh 1 Nodes 13.210 171.549 2.848 184.759
Elemen s 70.166 993.442 12.396 1.063.608
Mesh 2 Nodes 30.653 354.682 27.288 385.335
Elemen s 163.357 2.076.988 136.696 2.240.345
Mesh 3 Nodes 202.980 385.787 80.416 588.767
Elemen s 1.110.512 2.243.860 414.278 3.354.372
Mesh 4 Nodes 440.121 418.441 133.352 858.562
Elemen s 2.409.443 2.421.935 694.222 4.831.378
Fig. 8. Th us and momen coefficien e sus numbe o elemen s (in millions) o
each o he meshes p oposed in he mesh independence s udy. They show he con-
e gence o he solu ion as he mesh is efined.
CQ=Q
ρA2R3(3)
whe e ρis he ai densi y, A is he o o disk a ea (m2), is he
angula speed ( e olu ions pe minu e), T is he h us o he p o-
pelle (N), and Qis he o que o he p opelle (Nm). As can be
seen in Fig. 8, om 3.3 million elemen s onwa d, he esul s ba ely
a y. Be ween mesh 1 and mesh 3, he h us coefficien changes
by 11.63% and o que coefficien by 18.18%, while be ween mesh
Table 3
Elemen size defined in he p opelle and in e aces o
compu a ional domain o mesh 3, which is he bes
choice a e g id independence analysis.
Zone Elemen size (m)
P opelle 0.001
In e aces 0.005
Edge blade 0.0003
3 and mesh 4 he a ia ion o bo h coefficien s is minimum, be-
ing 0.4% o CTand 1.7% o CQ. Fo his eason, mesh 3 is he
bes op ion as i allows ob aining accu a e esul s wi h lowe com-
pu a ional cos s han wha would be achie ed wi h meshes close
o 5 million elemen s. Table 3lis s he size o he selec ed ele-
men o mesh 3 a he p opelle , blade edge, and compu a ional
domain in e aces. The mesh o he selec ed compu a ional domain
is shown on he igh side o Fig. 7. In all cases, he mesh quali y
pa ame e s ha e been e alua ed, ob aining o hogonal quali y al-
ues abo e 0.15 [55]. To ensu e con e gence o he solu ion, he
simula ions i e a e un il he change in p opelle h us is less han
0.01% in he las 1000 i e a ions, whe e he esidual e o s ound
a e smalle han 10−6. Meshes simila o hose p oposed in his
wo k a e c ea ed by [52]. The a e age wall y+ alue in mesh 3
is abou 31. This alue is simila o he one used in [57,68]. Al-
hough he ull ad an ages o he u bulence model a e no being
aken ad an age o , g ea e s abili y and con e gence o he solu-
ion is achie ed han i o he models we e used. On he con a y,
7
A. Ga o ano-Soldado, P.J. Sanchez-Cue as, G. He edia e al. Ae ospace Science and Technology 126 (2022) 107625
Fig. 9. S a ic pe o mance o he T-Mo o 13x4.4 p opelle o di e en o a ional
speeds ( pm): compa ison o h us and o que coefficien s (CTand CQ) be ween
CFD esul s and manu ac u e ’s da a. P opelle used in expe imen al-nume ical anal-
ysis.
he flow sepa a ion is no accu a ely p edic ed. The minimum ele-
men size ela ed o he wall alue is 1 ·10−4m.
3.2. P opelle pe o mance compa ison
A o al o 22 simula ions has been ca ied ou o alida e ou
CFD esul s. These simula ions ha e assessed he s a ic pe o -
mance o he h ee p opelle s conside ed in his s udy (see sec-
ion 2.1) wi h se en o a ional speeds. Each simula ion was pe -
o med in a ee en i onmen . The s a ic pe o mance esul s ha e
been compa ed wi h he da a p o ided by he manu ac u e T-
Mo o and APC [69,70].
Figs. 9and 10 show he a ia ion o h us and o que coeffi-
cien wi h o a ional speed ( pm) esul ing om bo h CFD simu-
la ions and manu ac u e ’s da a. These coefficien s ha e been ob-
ained by applying Eq. (2) and Eq. (3). I is obse ed ha when he
o a ional speed (and as a consequence he Reynolds numbe ) in-
c eases, he h us coefficien inc eases while he o que coefficien
emains p ac ically cons an . Rega ding he h us coefficien , i is
no ed ha he CFD esul s o e es ima e he da a ound in [69,70]
o he T-Mo o 18x6.1 and APC 9x4.4 p opelle s. In con as , he
CFD o que coefficien is unde es ima ed in all cases. Howe e , he
CTand CQe o s o he h ee p opelle s examined a e less han
5% and 10%, espec i ely. Unde s a ic condi ions, he fideli y o a
o o ’s pe o mance is ela ed o he abili y o cap u e he o ex
s uc u es o he blade ip [51]. Based on he esul s p esen ed in
his sec ion, i is es ablished ha he CFD model is adequa e o
cap u e he o ces on he p opelle in a ee en i onmen . Also, i
is assumed ha he ip flow s uc u es can be p edic ed al hough
no as igo ously as in highe -o de schemes.
4. G ound e ec o small-scale il ed p opelle s
4.1. Expe imen al e alua ion o he CFD-based me hod
This sec ion compa es expe imen al and simula ion esul s
acco ding o he p ocedu es desc ibed in sec ion 2.3 and sec-
ion 2.4 espec i ely. In bo h p ocedu es, he co-plana configu-
a ion, whe e he o o is pa allel o he g ound (θ= 0◦), and h ee
il angles (θ= 10◦, 20◦and 30◦) ha e been analysed. Fu he -
mo e, en dis ances measu ed om he cen e o o a ion o he
p opelle o he wall (z/R =0.6, 0.75, 1, 1.5, 2, 2.5, 3, 3.5, 4, 5)
we e assessed.
Fig. 11 shows he ho izon al and e ical componen s o he
h us coefficien (CTxand CTz) e sus dimensionless g ound dis-
ance (z/R) o each o o il angle (θ). The expe imen al esul s
a e shown in do ed lines and he CFD esul s in dashed lines. In
addi ion, he iangula ma ke indica es he e ical componen o
he o ce, and he ci cula ma ke he ho izon al componen . I can
be seen ha he h us coefficien o he o o inc eases as i ap-
p oaches he g ound in all cases. Howe e , as he angle o inclina-
ion inc eases, he e ical componen o he o ce educes and he
ho izon al componen becomes la ge . The nume ical esul s o e -
p edic he end o he h us coefficien cu e compa ed o he
expe imen al cu es o all angles. An o se is obse ed be ween
he simula ion and expe imen al esul s o each o he configu a-
ions analysed. This o se emains p ac ically cons an om heigh
1.5Ronwa ds. Howe e , he disc epancies be ween simula ed and
expe imen al esul s a e conside ed accep able aking in o accoun
he e o s a ising om bo h me hods o da a collec ion. In Table 4
he oo mean squa e e o (RMSE) be ween he simula ion and
expe imen al esul s o CTz, CTxa e shown.
To in es iga e he g ound e ec , he h us a io TIGE/TOGE is
ypically used, whe e TIGE is he h us In-G ound-E ec and TOGE
is h us Ou -o -G ound-E ec . This a io gi es he pe cen age in-
c ease in h us expe ienced by he o o when he g ound is close.
Acco dingly, in Fig. 12, he h us a io o he expe imen al and
simula ion da a is plo ed e sus he dimensionless dis ance z/R.
Ne e heless, Fig. 11 has been p esen ed o gi e an es ima e o
how each o he o ce componen s a ies.
Fo he case o a o o pa allel o he g ound (θ=0◦) he esul s
a e compa ed wi h Cheeseman and Benne ’s classical helicop e
heo y [18]:
TIGE
TOGE =1
1−R
4z2(4)
The esul s show ha he g ound e ec is negligible when z/R
is app oxima ely g ea e han 2.5. Fo angles 0◦, 10◦and 20◦, he
closes dis ance o he wall is 0.6R. In hese cases, he h us is
inc eased by 13.3%, 9.6% and 8.7%, espec i ely. Fo he 30◦angle,
he minimum dis ance a which simula ions ha e been pe o med
is 0.75R, since he o a ional domain in e e ed wi h he g ound
plane o smalle dis ances. Fo his heigh , he h us inc eases
expe ienced by he o o o angles 0◦, 10◦, 20◦and 30◦would
be 10.4%, 7.8%, 6.1% and 5%, espec i ely. The CFD esul s fi qui e
accu a ely o hose ob ained by expe imen a ion, eaching a maxi-
mum e o o 5.1% o a heigh o 0.6Rand a il o 10◦.
Rega ding he obse ed disc epancies, hey can be a ibu ed o
bo h nume ical and expe imen al e o s. On he expe imen al side,
he e a e se e al sou ces o e o s ha could gene a e his kind o
disc epancy. Fo ins ance, al hough he expe imen s we e ca ied
ou ho oughly, he posi ioning pa allel o he wall o he s uc u e
in Fig. 4is done manually. This could in oduce e o s i a some
dis ance z i is no comple ely pa allel. The ESC used o con ol
he pms o he o o is a COTS ESC. In mos cases, hose con-
ol and egula e he speed o he elec ic mo o by closing he
con ol loop a he cu en measu emen le el. This means ha
he alue o pm could be no exac ly he same as he one we
ha e imposed in he simula ions. The powe supply used du ing
he expe imen is also a low-p ice sys em ha could be sensi i e
o some en i onmen al changes like he empe a u e [51]. Mo e-
o e , conside ing ha he p opelle is placed close o he plas ic
pa s and senso , his could c ea e an ex a in e e ence wi h he
flow field. Howe e , i has been e ified ha he e is no in e e -
ence o he es bench on he p opelle . Fo his pu pose, a e
8
A. Ga o ano-Soldado, P.J. Sanchez-Cue as, G. He edia e al. Ae ospace Science and Technology 126 (2022) 107625
Fig. 10. S a ic pe o mance o he T-Mo o 18x6.1 and APC 9x4.4 p opelle s o di e en o a ional speeds ( pm): compa ison o h us and o que coefficien s (CTand CQ)
be ween CFD esul s and manu ac u e ’s da a. P opelle s used o alida e he p oposed g ound e ec model.
Fig. 11. Ve ical and ho izon al componen o he h us coefficien e sus z/R dimensionless dis ance o angles 0◦, 10◦, 20◦and 30◦de i ed by expe imen and CFD
simula ions.
Table 4
RMSE o he p oposed CFD me hodology o e ical and ho izon al componen o he h us coefficien conside ing angles 0◦, 10◦, 20◦and 30◦.
Angle Coefficien s 0.6 0.75 1 1.5 2 2.5 3 3.5 4 5
0◦CTx7.27e-06 7.25e-06 6.63e-06 4.37e-06 2.90e-06 3.30e-06 2.31e-06 1.27e-06 1.70e-06 1.40e-06
CTz8.56e-05 9.49e-05 2.25e-05 1.58e-05 4.04e-05 3.84e-05 4.68e-05 3.92e-05 4.83e-05 3.60e-05
10◦CTx1.30e-05 2.82e-05 4.25e-05 4.76e-05 4.35e-05 4.49e-05 4.53e-05 4.51e-05 4.52e-05 4.45e-05
CTz1.3e-04 8.03e-05 5.18e-06 3.68e-05 2.29e-05 2.54e-05 3.27e-05 3.20e-05 2.46e-05 2.82e-05
20◦CTx6.13e-05 6.60e-05 7.86e-05 8.22e-05 8.05e-05 8.20e-05 8.29e-05 8.81e-05 8.63e-05 8.57e-05
CTz4.17e-05 7.25e-05 9.60e-05 1.07e-4 9.68e-05 9.73e-05 1.02e-04 1.14e-04 1.11e-04 1.10e-04
30◦CTx- 8.52e-05 9.82e-05 9.91e-05 9.49e-05 1e-04 1.02e-04 1e-04 1e-04 1.02e-04
CTz- 2.95e-07 2.94e-05 3.23e-05 3.82e-05 3.88e-05 3.81e-05 4.15e-05 3.38e-05 3.30e-05
9
A. Ga o ano-Soldado, P.J. Sanchez-Cue as, G. He edia e al. Ae ospace Science and Technology 126 (2022) 107625
a io dec eases wi h espec o he classical heo y as he angle
inc eases. The de eloped model fi s he esul s ob ained om he
nume ical simula ions wi h good accu acy.
In u u e wo ks, he p oposed model o il ed o o s will be
implemen ed in con ol laws in o de o compensa e o his e ec
when UAVs ope a e close o he g ound. This will esul in sa e
fligh s by a oiding ins abili ies in he ae ial pla o m.
Decla a ion o compe ing in e es
The au ho s decla e he ollowing financial in e es s/pe sonal
ela ionships which may be conside ed as po en ial compe ing in-
e es s:
Amba Ga o ano-Soldado epo s financial suppo was p o-
ided by Uni e si y o Se ille. Amba Ga o ano-Soldado epo s a
ela ionship wi h Uni e si y o Se ille ha includes: employmen .
Acknowledgemen s
This wo k has been suppo ed by he H2020 RESIST (H2020-
MG-2017-769066) and PILOTING (H2020-ICT-2019-2-871542) p o-
jec s, unded by he Eu opean Commission and he ARTIC P ojec
(RTI2018-102224-B-I00), unded by he Spanish Agencia Es a al de
In es igación. The wo k o Amba Ga o ano-Soldado is suppo ed
by he FPI g an (PRE2019-089812) om he Minis y o Science
and Inno a ion o he Spanish Go e nmen .
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