In e na ional Jou nal o The mal Sciences 198 (2024) 108885
A ailable online 8 Janua y 2024
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CFD modelling o he powde seg ega ion in mul i-ma e ial lase di ec ed
ene gy deposi ion
Ma a Os olaza , Jon I˜
naki A izubie a
*
, Ai zol Lamikiz
Depa men o Mechanical Enginee ing, Uni e si y o he Basque Coun y (UPV/EHU), Plaza Ingenie o To es Que edo 1, 48013, Bilbao, Spain
ARTICLE INFO
Keywo ds:
Mul i-ma e ial
Lase Di ec ed Ene gy Deposi ion
Powde seg ega ion
Con inuous coaxial nozzle
CFD modelling
ABSTRACT
One o he p e ailing challenges in mul i-ma e ial lase Di ec ed Ene gy Deposi ion is he seg ega ion o he
cons i uen s du ing he deli e y o he eeds ock in o he mel pool. This phenomenon is o pa icula conce n
when me al-ce amic mix u es a e in ol ed, as he di e ences in he ine ial p ope ies o he powde s a e highe
and seg ega ion is agg a a ed. This issue a ec s he eliabili y o he p ocess; indeed, powde seg ega ion can
in luence he composi ion o he mel pool and, hus, ha o he inal pa o coa ing. In his wo k, Compu a ional
Fluid Dynamics modelling is adop ed o s udy his phenomenon and o explo e s a egies o o e come i . Fi s ly,
a base mul i-ma e ial CFD model is buil . Secondly, a simpli ied algo i hm is p oposed o educe he compu a-
ional cos o simula ing mul iple scena ios. This model is i s alida ed nume ically agains he base model.
Then he simpli ied mul i-ma e ial CFD model is expe imen ally alida ed. Thi dly, he de eloped ool is
implemen ed o elabo a e wo s a egies o minimise powde seg ega ion in a Co-WC powde mix u e. The i s
one is qui e s aigh o wa d and li le de elopmen is necessa y o inco po a e i o he indus y. Con e sely, he
second one, hough p omising, needs u he de elopmen and i s p ac icali y needs o be e alua ed be o e being
eady o indus ial implemen a ion.
1. In oduc ion
Lase Di ec ed Ene gy Deposi ion (L-DED) is cu en ly one o he
mos indus ially ele an me al Addi i e Manu ac u ing (AM) ech-
nologies [1]. The L-DED p ocess is g owing a a signi ican pace in he
epai and emanu ac u ing sec o [2]. Mo eo e , i s popula i y o
coa ing deposi ion wi hin he ield o su ace enginee ing is also
inc easing consis en ly [3]. As a esul , he capabili ies o L-DED o he
p oduc ion o wea - and co osion- esis an coa ings ha e been in en-
si ely explo ed [4]. Indeed, he high in ensi y o he lase sou ce esul s
in a small and localised hea -a ec ed zone, which minimises he
dis o ion and damage o he base ma e ial in coa ing and epai ap-
plica ions [5].
Cu en indus ial ends also poin a mul i-ma e ial AM as a highly
p omising ield o esea ch. Powde L-DED is he p e e ed AM ech-
nology o his pu pose [6]. This is mo i a ed by i s un i alled
mul i-ma e ial capabili y, which is achie ed by he abili y o L-DED o
change he composi ion o he eeds ock in-si u. To enable a p ecise
mul i-ma e ial p oduc ion, he composi ion o he mel pool mus be
igh ly con olled. This can be ealised h ough mul iple-hoppe eede
solu ions, which pe mi uning he composi ion o he eeds ock o be
deli e ed in o he mel pool [7]. No only di e en alloys can be mixed
o p oduce bime allic s uc u es o Func ionally G aded Ma e ials
(FGM), bu also me al-ce amic s uc u es can be ob ained. Fo ins ance,
ce amic- ein o ced Me al Ma ix Composi es (MMCs) ha e been p o-
posed o inc easing he wea esis ance o highly demanded su aces
[8]. Eme ging applica ions o MMC coa ings include bu a e no limi ed
o he ae ospace, au omo i e, and ooling indus ies [9,10].
Al hough a p omising ield, mul i-ma e ial L-DED is s ill a om
being ma u e, and se e al challenges need o be add essed be o e being
a obus and eliable echnology. In addi ion o he challenges associa ed
o he L-DED p ocess i sel , such as he me allu gical in eg i y o he
con ol o he dimensional ole ances [11], addi ional issues a ise as a
esul o he mul i-ma e ial na u e o he eeds ock. Indeed, owing o he
di e en ine ial p ope ies o he cons i uen s, powde seg ega ion may
occu in he ma e ial eeding sys em. This conce n was al eady aised in
se e al e iew a icles on mul i-ma e ial AM [12,13]. They epo ed ha
such a seg ega ion phenomenon could p oduce a la ge de ia ion om
he expec ed composi ion in mul i-ma e ial pa s. This issue is sub-
s an ially agg a a ed in he ab ica ion o ex-si u MMCs, conside ing ha
* Co esponding au ho .
E-mail add ess: [email p o ec ed] (J.I. A izubie a).
Con en s lis s a ailable a ScienceDi ec
In e na ional Jou nal o The mal Sciences
jou nal homepage: www.else ie .com/loca e/ij s
h ps://doi.o g/10.1016/j.ij he malsci.2024.108885
Recei ed 11 Augus 2023; Recei ed in e ised o m 1 Decembe 2023; Accep ed 3 Janua y 2024
In e na ional Jou nal o The mal Sciences 198 (2024) 108885
2
he densi y o ce amic and me allic powde s di e s conside ably.
Indeed, i he dynamic beha iou o he cons i uen ma e ials o he
mul i-ma e ial mix u e is signi ican ly di e en , he nozzle may
dis ibu e o concen a e he powde pa icles he e ogeneously. This
phenomenon is illus a ed in Fig. 1. Ne e heless, his issue has no been
sys ema ically in es iga ed in he li e a u e, and he implica ions o
mixing di e en ma e ials need o be u he explo ed.
The beha iou o L-DED nozzles can be explo ed h ough expe i-
men al, analy ical, o nume ical app oaches. Expe imen al cha ac e i-
sa ion me hods ypically ely on op ical measu emen p inciples [14].
Whils sui able o he cha ac e isa ion o exis ing nozzles, expe imen al
app oaches canno add ess challenges in ol ing he design o new sys-
ems. Mo eo e , unde s anding he e ec o di e en ac o s on he
powde concen a ions is ime- and esou ce-consuming i app oached
expe imen ally. Analy ical models ha e also been employed o desc ibe
he beha iou o he powde nozzle in L-DED applica ions [15]. How-
e e , hey p o ide an o e -simpli ied solu ion o he p oblem, which
lacks he lexibili y equi ed o gua an ee an ex ended unde s anding o
complex luid-dynamic phenomena uling he powde dis ibu ion.
Con e sely, nume ical solu ions ha e been widely explo ed o gain
knowledge o how he L-DED nozzles beha e. Indeed, Compu a ional
Fluid Dynamics (CFD) a e a highly e icien ool o unde s and he
phenomena in ol ed in pa icle anspo a ion and powde low gen-
e a ion in L-DED.
D i en by his need, many a emp s o simula e he powde beha -
iou along L-DED nozzles can be ound in he li e a u e. Zhang e al.
p oposed a CFD model based on disc e e phase modelling o desc ibe he
ae odynamic beha iou o a disc e e coaxial nozzle [16]. Pan e al.
employed a CFD model o desc ibe he powde low dynamics a
di e en s ages o he nozzle and o de e mine he egion whe e he low
becomes ully de eloped [17]. Liu e al. also s udied he powde dis-
ibu ion o con inuous coaxial nozzles using CFD simula ions and
con i med ha he powde low con e ged om an annula dis ibu ion
a he exi o he nozzle in o a Gaussian dis ibu ion a he ocal plane
[18].
Fu he mo e, CFD nume ical models ha e been employed o in es-
iga e he in luence o mul iple ac o s on ele an ea u es o he luid
low. They ha e been used o compa e he pe o mance o di e en
nozzles [19] o o e alua e he e ec o he inclina ion o he nozzle on
he ca chmen e iciency [20]. O he esea che s ocused on he in lu-
ence o he subs a e and he e alua ion o he powde ca chmen e i-
ciency o di e en subs a e geome ies [21]. Following his end,
nume ical ools ha e been employed o s udy he in luence o ac o s
conce ning he eeds ock mo phology, densi y, ca ie and shielding gas
low a e, o nozzle design on he powde concen a ion. Fo ins ance,
Fan e al. employed a CFD model in conjunc ion wi h s a is ical
eg ession models o de e mine he co ela ion be ween se e al pa-
ame e s and he powde s eam in L-DED nozzles [22]. Zhou e al. also
in es iga ed he e ec o powde cha ac e is ics on he L-DED nozzle
beha iou and concluded ha he pa icle size would subs an ially a ec
he powde dis ibu ion in he mel pool [23]. In e es ingly enough, in a
p e ious s udy, i was epo ed ha he densi y, pa icle size, and pa -
icle mo phology would a ec he powde dis ibu ion and he s abili y
o a disc e e coaxial nozzle [24]. This was la e con i med by Gao e al.
[25]. Ne e heless, all he li e a u e men ioned so a ocuses on
single-ma e ial eeds ock.
The deli e y o mul i-ma e ial powde blends h ough L-DED nozzles
is e en mo e complex and is s ill a an ea ly s age o esea ch. On he one
hand, he analysis o mul i-ma e ial powde lows en ails a highe de-
g ee o di icul y. On he o he hand, he e is an inc eased numbe o
ma e ial combina ions o be analysed, each o which is likely o ha e a
di e en beha iou . The s udy o mul i-ma e ial powde concen a ion
was pionee ed by Li e al., who pu in e idence ha powde seg ega ion
occu ed in Cu–Al powde mix u es. A e es ing he e ec o di e en
pa ame e s, hey ound ha highe ca ie gas a es would agg a a e
his p oblem [26]. La e on, hey p oposed a solu ion o mi iga e powde
sepa a ion, which consis ed o he op imisa ion o he powde size o he
cons i uen s so ha hey would beha e simila ly [27]. Only one publi-
ca ion was ound whe e he powde low beha iou and powde seg e-
ga ion o ce amic-me allic powde mix u es was add essed. Indeed,
Jiang e al. in es iga ed he pa icle ajec o ies o TiC-Inconel 718
powde mix u es in o -axis nozzle con igu a ions. They ound ha TiC
pa icles de eloped a highe eloci y, which esul ed in a sho e ocal
dis ance and highe dispe sion o he powde . As a consequence, a lowe
TiC con en would be expec ed in he inal deposi ed ma e ial [28].
As a as he beha iou o mul i-ma e ial powde mix u es in L-DED
nozzles is conce ned, i emains a mos ly unexplo ed ield, especially in
he case o ce amic-me allic powde mix u es. Al hough some insigh s
ha e been p o ided on he powde low beha iou o hese mix u es,
mo e comp ehensi e s udies a e equi ed. Fo ins ance, he e ec o he
olume ic ac ion o each cons i uen should be analysed. In addi ion,
he beha iou o o he nozzle con igu a ions should be in es iga ed,
especially ha o con inuous coaxial nozzles due o hei ex ended in-
dus ial use. O e all, u he esea ch is equi ed o unde s and p ecisely
how his issue a ec s he ac ual composi ion o mul i-ma e ial pa s
ab ica ed by L-DED. This ma e emains la gely unin es iga ed and he
powde seg ega ion in mul i-ma e ial powde mix u es has no been
s udied in-dep h ye .
D i en by his need, in he p esen wo k, CFD modelling is p oposed
as a ool o in es iga e he beha iou o mul i-ma e ial powde lows in
L-DED con inuous coaxial nozzles. To ha end, a mul i-ma e ial CFD
model has been de eloped and alida ed. In addi ion, he e ec o key
pa ame e s on he powde seg ega ion has been in es iga ed. Based on
he exis ing li e a u e, he no el y and con ibu ions p esen in his
esea ch a e o:
(1) De elop a base mul i-ma e ial CFD model o simula e me al-
ce amic mix u es.
(2) P opose a simpli ied algo i hm o educe he compu a ional e-
sou ces necessa y o simula e me al-ce amic mix u es and ali-
da e i nume ically agains he base model.
(3) Valida e he simpli ied mul i-ma e ial CFD model expe imen ally
based on he composi ion o eal pa s p oduced by L-DED.
(4) P o ide wo al e na i e app oaches o add ess powde seg ega-
ion issues and o inc ease he eliabili y o mul i-ma e ial L-DED
in e ms o he con ol o he composi ion o he pa s.
2. Me hodology
In his sec ion, he p ocedu e ollowed in he p esen esea ch is
depic ed, see Fig. 2. Fi s , a mul i-ma e ial CFD model is de eloped. The
Fig. 1. Powde seg ega ion in he injec ion o mul i-ma e ial powde mix u es
wi h di e ing ine ial p ope ies.
M. Os olaza e al.
In e na ional Jou nal o The mal Sciences 198 (2024) 108885
3
basis o he model is de ailed in sec ion 3. Secondly, a supe posi ion
algo i hm is p oposed o he CFD simula ion o mul i-ma e ial powde
mix u es, which is alida ed nume ically agains he base model
(desc ibed in sec ion 4.1) and expe imen ally (desc ibed in sec ion 4.2).
Las ly, wo app oaches o he co ec ion o he powde seg ega ion a e
e alua ed, acco ding o he p oposal de ined in sec ion 5. The i s
app oach an icipa es he e ec o he powde seg ega ion on he
composi ion o he mel pool and compensa es i by adjus ing he
powde eede . The second app oach ocuses on he op imisa ion o he
diame e o he powde pa icles o minimise he powde seg ega ion.
3. Basis o he base mul i-ma e ial CFD model
In his sec ion, he mul i-ma e ial CFD model de eloped is i s
in oduced. The model is buil wi hin he ANSYS® Wo kbench en i-
onmen and he Fluen module is employed o se he luid dynamic
model up, which is desc ibed he ea e .
3.1. Domain and mesh o he mul i-ma e ial CFD model
The aim o he p esen mul i-ma e ial CFD model is o simula e he
beha iou o me al-ce amic powde mix u es in he EHU-Coax con in-
uous coaxial nozzle desc ibed in Re . [29]. This nozzle was de eloped
in-house and i comp ises an inne and an ou e cone, which delimi he
con ined egion whe e he mul iphase low (ca ie gas and powde
eeds ock) is anspo ed, as shown in Fig. 3(a). The shielding gas lows
ia he coaxial hole, h ough which he lase beam is deli e ed oo.
The domain o he nume ical model is e e ed o he olume illed
by he luid o , in his case, he mul iphase low. In he nume ical
p oblem objec o his wo k, wo egions o he domain can be dis in-
guished, namely, he domain delimi ed by he geome y o he nozzle
and he con ol domain whe e he uncon ined mul iphase low is
de eloped. In Fig. 3(b), bo h egions a e shown.
As a as he mesh is conce ned, he complexi y o he p esen
p oblem lies in meshing he egions whe e low h ough small gaps
occu s, mo e speci ically, in he con ined low egion. Indeed, ailu e o
gene a e a su icien ly ine mesh in hose c i ical egions will esul in
inaccu acies du ing he esolu ion o he nea -wall iscous e ec s.
The e o e, a conse a i e app oach has been adop ed du ing he
meshing p ocedu e, which is he eason behind he high numbe o cells
and nodes gene a ed. In Fig. 4, he mesh employed du ing he simula-
ions is shown. Fi s o de e ahed al elemen s a e employed o he
mesh gene a ion. No e ha in he egion o in e es he mesh was e ined
o ensu e he accu acy o he nume ical esul s.
A c i e ion gene ally employed o assess he quali y o he mesh e-
lies on he skewness o he elemen s, and alues below 0.75 a e
commonly sough . In Table 1, s a is ical and quali y da a o he mesh a e
epo ed.
3.2. Ma e ial p ope ies
The mul iphase low comp ises wo phases, i.e. he solid phase and
he luid phase, which co espond o he powde eeds ock and he
shielding and ca ie gas (bo h A gon), espec i ely. The ma e ial
p ope ies o he luid phase a e aken om he Fluen ma e ial da a-
base, being he densi y and he iscosi y o he A gon 1.6228 kg m
−3
and
914,684 kg m
−1
s
−1
, espec i ely.
In con as , he solid phase is cons i u ed by ine pa icles o Me -
coClad 6 Co-base alloy ( e e ed o as M1) and Me coClad 52001 ung-
s en ca bide ( e e ed o as M2). In o de o comple ely de ine he ine
pa icles, he densi y and mo phology mus be p o ided. Conside ing
ha he powde pa icles ha e been manu ac u ed h ough gas a om-
isa ion, hey a e ea ed as ully sphe ical. As a as he pa icle size
Fig. 2. O e iew o he me hodology o he p esen wo k.
Fig. 3. (a) In e nal componen s o he EHU-Coax con inuous coaxial nozzle and (b) Volume domain o he CFD model.
Fig. 4. Mesh o he CFD olume domain.
M. Os olaza e al.
In e na ional Jou nal o The mal Sciences 198 (2024) 108885
4
dis ibu ion is conce ned, he Rosin-Rammle dis ibu ion is gene ally
accep ed. In Table 2, he p ope ies o he Me coClad 6 and 52001
powde pa icles a e p o ided.
3.3. Model o he luid low: iscous o mula ion and bounda y condi ion
The iscous model selec ed o his p oblem is he k-
ω
SST RANS
(Reynolds A e aged Na ie -S okes) model. In ac , his o mula ion is
he mos adequa e o he p esen scena io: i o e s an accu a e nea -
wall esolu ion o mixed ansi ional and u bulen lows, whe eas i
beha es co ec ly in egions wi h ad e se p essu e g adien s such as in
he con ined o ee low ansi ion [29].Wi h ega d o he luid low,
ou bounda y condi ions a e de ined, see Table 3. A he shielding- and
ca ie -gas eloci y inle s 1.504 m⋅s
−1
and 9.022 m⋅s
−1
eloci y alues
a e es ablished, espec i ely, wi h a cons an alue and a pe pendicula
di ec ion o he su ace. They co espond o a 5 l⋅min
−1
low o he
ca ie gas and a 15 l⋅min
−1
low o he shielding gas. A he ou le a
cons an a mosphe e p essu e is conside ed, whe e a 0 Pa p essu e is
s ablished. Las ly, a he walls in con ac wi h he nozzle, a wall- ype
condi ion is de ined, wi h a ze o- eloci y magni ude. The p ecise loca-
ions o each one o he bounda y condi ions a e depic ed in Fig. 5.
3.4. Model o he solid phase: disc e e phase model o mula ion and
bounda y condi ions
The solid phase in he mul iphase low can be ep esen ed by ine
pa icles and modelled h ough disc e e phase modelling, due o he low
olume ic ac ion o he solid phase (<10 %). In addi ion, o e y low
pa icula e loadings, i can be assumed ha solid pa icles do no in-
luence he luid low. In he p esen esea ch he Eule -Lag ange
app oach is conside ed, whe e he gas phase is conside ed as a con in-
uous phase and modelled in an Eule ian scheme, whils powde pa icles
a e ea ed as disc e e phases and acked indi idually h ough d ag
o ce balance analysis.
In o de o ully se he model up, he physical es ic ions which ule
he beha iou o he disc e e phase need o be de ined oo. Due o he
ela i e low pa icula e loading and high in e spacing dis ance, he
collisions be ween pa icles can be sa ely neglec ed and he only phe-
nomenon o be modelled conce ns he collisions be ween he pa icles
and he walls o he in e nal ca i ies o he nozzle. The in e ac ion be-
ween solid pa icles and solid walls is uled by he es i u ion coe i-
cien . The es i u ion coe icien accoun s o he amoun o kine ic
ene gy eco e ed du ing he collision o a disc e e phase pa icle and a
wall, in o he wo ds, o which ex en he collision is elas ic. Typically,
alues in he ange o 0.9–0.99 a e employed [30]. In his case, and
based on p e ious wo ks [29], a 0.9 es i u ion coe icien is adop ed
be ween he powde pa icles and he in e nal nozzle walls.
Las ly, he sou ces and sinks o he ine pa icles mus be de ined.
The ine pa icles en e he CFD domain wi h he ca ie gas, which
d ags he disc e e phase in he di ec ion o he luid low. Hence, eigh
injec ions o he disc e e phase a e de ined, one pe ca ie gas inle and
ma e ial ( ed egions in Fig. 5). I is assumed ha he pa icles a e
uni o mly dis ibu ed h oughou he inle a ea and ha hey en e he
sys em no mally o he inle . In addi ion, hei eloci y is assumed o be
equal o ha o he ca ie gas. In e ms o he pa icles lea ing he
sys em, an “escape” bounda y condi ion is se o he ou e aces o he
con ol domain (BC3). This means ha in case a pa icle “collides” wi h
hose egions, i au oma ically lea es he sys em.
In his manne , he base model is ully de ined and he only a iables
o be se a e he mass low a e o each cons i uen , acco ding o he
speci ic scena io o be simula ed. Based on he cha ac e is ics o he
mul iphase low, and wi h he aim o inc easing he e iciency when
simula ing se e al scena ios wi h di e en inpu a iables, a simpli ying
hypo hesis based on he supe posi ion algo i hm is p oposed and
desc ibed he ea e .
4. Supe posi ion algo i hm o mul i-ma e ial CFD model
The low pa icula e loading and low S okes numbe sugges ha he
disc e e phase is going o ha e li le in luence on he luid low.
The e o e, assuming ha he pa icles a e no going o in e ac wi h each
o he and ha he luid low is no modi ied by he disc e e phase in a
signi ican manne , he indi idual con ibu ion o each ma e ial could
be calcula ed sepa a ely and added up o cons i u e he mul i-ma e ial
Table 1
S a is ical and quali y da a o he mesh.
No. Cells No. Faces No. Nodes Max. Skewness A . Skewness
4,328,036 9,034,107 914,648 0.711 0.230
Table 2
Ma e ial p ope ies o he solid phase.
Ma e ial Densi y
(kg⋅m
−3
)
Rosin-Rammle dis ibu ion
Min.
diame e (m)
Max.
diame e (m)
Mean
diame e (m)
Me coClad 6
(M1)
8,440 4.5⋅10
−5
1.06⋅10
−4
8.022⋅10
−5
Me coClad
52001 (M2)
15,630 4.5⋅10
−5
1.06⋅10
−4
8.084⋅10
−5
Table 3
Speci ica ions o he bounda y condi ions o he luid phase.
Bounda y
condi ion
Type Veloci y magni ude
(m⋅s
−1
)
Gauge p essu e
(Pa)
BC1 Veloci y inle 1.504 N/a
BC2 Veloci y inle 9.022 N/a
BC3 P essu e
ou le
N/a 0
BC4 Wall 0 N/a
Fig. 5. Loca ion o he bounda y condi ions o he luid phase.
M. Os olaza e al.
In e na ional Jou nal o The mal Sciences 198 (2024) 108885
5
CFD model. In o he wo ds, he supe posi ion p inciple could be applied.
This supe posi ion e ec applies o he whole CFD domain, and i is
ma hema ically desc ibed by equa ion (1), whe e DPM e e s o he o al
disc e e phase concen a ion in he loca ion {x,y,z}o he domain and
DPMi e e s o he disc e e phase o ma e ial i in he loca ion {x,y,z}
p o ided by he single-ma e ial CFD model.
{DPM ({x,y,z})} = ∑
2
i=1
{DPMi({x,y,z})} (1)
in his manne , o he calcula ion o he mul i-ma e ial DPM, single-
ma e ial simula ions a e aken as e e ence, whe e he mass low a e
o he powde pa icles o he i ma e ial is ˙
mi0. Fo he calcula ion o
DPMi({x,y,z}), i is assumed ha he DPM in he single-ma e ial model
will a y p opo ionally o he mass low a e ed o he model. The e-
o e, he DPM a he loca ion {x,y,z} o ma e ial i is ecalcula ed o a
speci ic mass low a e ( ˙
mi) acco ding o equa ion (2).
{DPMi({x,y,z})}= {DPMi0({x,y,z}) }⋅
˙mi
˙mi0
(2)
whe e DPMi0({x,y,z})} e e s o he disc e e phase concen a ion in he
loca ion {x,y,z}ob ained wi h he e e ence model, wi h he inpu se a
˙
m0 =5.5 g min
−1
.
4.1. P ocedu e o he nume ical alida ion o he supe posi ion algo i hm
Wi h he in en o nume ically alida ing his hypo hesis, he i e
scena ios shown in Table 4 a e e alua ed, whe e h ee di e en com-
posi ions o mul i-ma e ial phase ha e been analysed. The pe o mance
o he simpli ied algo i hm is assessed agains ha o he base mul i-
ma e ial CFD model. In addi ion, conside ing ha he alidi y o his
supe posi ion p inciple lies in he luid low no a ying signi ican ly o
di e en composi ions o he mul i-ma e ial phase, he luid eloci y in
he Z axis o scena ios 2 and 4 a e compa ed o ha o he e e ence,
scena io 0. In Table 4, ˙
m1 and ˙
m2 co espond o he low a e o M1 and
M2, espec i ely.
Fo his compa ison, he disc e e phase concen a ion o DPM along
he Z axis is e alua ed. Indeed, his a iable de e mines he ocal plane
posi ion (FPP), which will a y wi h he modi ica ion o he mul i-
ma e ial powde composi ion.
4.2. P ocedu e o he expe imen al alida ion o he supe posi ion
algo i hm
Wi h he in en o demons a ing he sui abili y o he simpli ied
mul i-ma e ial CFD model, i s alidi y is assessed h ough expe imen al
es s, which ely on he composi ion o he deposi ed ma e ial. To ha
end a Func ionally G aded MMC sample was p oduced, whe e he
nominal composi ion o he ma e ial ed a ied acco ding o Table 5.
The expe imen al wo k is ca ied ou in a 5-axis lase cen e coupled
wi h a 1 kW ib e lase and ocused in a 1.8 mm diame e spo a he
ocal plane. The ille ma e ial is deli e ed by a Sulze Me co Twin 10-C
powde eede , which allows o eed wo di e en ma e ials simul a-
neously, and ocused in he mel pool by a coaxial con inuous nozzle. In
he p esen esea ch, cobal -based alloy Me coclad 6 (M1) and ungs en
ca bide Me coClad 52001 (M2) powde s we e employed. Bo h powde s
a e gas-a omised and p esen a sphe ical shape wi h a size be ween 45
and 106
μ
m, see Table 2 o u he de ails. In he expe imen al ali-
da ion es , a cons an eed a e o 500 mm⋅min
−1
was employed,
whe eas he lase powe a ies be ween 800 and 980 W as he amoun o
M2 inc eases. The employed mass a es o bo h ille ma e ials, M1 and
M2, a e de ailed in Table 5, which a y e e y wo laye s.
The subs a e shown in Fig. 6(a) is 70x70x15 mm
3
in size and he
dimensions o he deposi ed geome y a e o 50x20x5 mm
3
. As de ailed
in Table 5, he deposi ed geome y consis s o 10 laye s, in which he M1
and M2 composi ions a y p og essi ely, see Fig. 6(b). P io o he L-
DED es ing, he su ace o he AISI 1045 s eel subs a e is g ound and
cleaned wi h ace one.
A e wa ds, and because o he high ha dness o he M2 pa icles, he
es piece was cu by wi e elec o-discha ge machining (w-EDM). Th ee
sec ions we e p epa ed o composi ional analysis in a scanning elec on
mic oscope (SEM) and he composi ion o each laye was measu ed by
means o ene gy-dispe si e X- ay spec oscopy (EDS). To ha end, he
Ca l Zeiss EVO-40 scanning elec on mic oscope (SEM) was employed.
A ea measu emen s pe he scheme shown in Fig. 7 a e ca ied ou o
es ima e he ac ual composi ion o he deposi ed ma e ial. In o al, wo
composi ional measu emen s o each scena io a e pe o med.
The EDS measu emen s es ima e he elemen al composi ion o he
ma e ial. The e o e, he composi ion o he powde mix u e ha gi es
place o such elemen al composi ion needs o be de i ed based on he
elemen al composi ion o he cons i uen powde s, namely he Me co-
Clad 6 (M1) and he Me coClad 52001 (M2), which a e shown in
Table 6.
In his case, he elemen al Co and W con en s a e aken as he
e e ence. All he Co o he mul i-ma e ial mix u e co esponds o he
con ibu ion o M1, which has a 60.5 % w . Co. In con as , bo h M1 and
M2 con ibu e o he W con en o he mul i-ma e ial mix u e. Indeed,
M1 has a 4.0 % w . W and M2 has a 95.78 % w . W. The e o e, he
composi ion o he mul i-ma e ial mix u e ed is es ima ed based on
equa ion (3).
M2w .%=1
0.9578 (W%EDS −0.04 Co%EDS
0.605 )(3)
whe e W%EDS and Co%EDS a e he ungs en and cobal con en s gi en by
he EDS analysis. No e ha he e m be ween b acke s e e s o he W
Table 4
Scena ios simula ed o he nume ical alida ion.
Scena io Ce amic w . % ˙
m1 (g⋅min
−1
) ˙
m2 (g⋅min
−1
)
0 (Re ) 0 % 5.50 0.00
1 25 % 4.13 1.38
2 50 % 2.75 2.75
3 75 % 1.38 4.13
4 100 % 0.00 5.50
Table 5
Composi ion o he mul ilaye es o he expe imen al alida ion.
Laye Ce amic w . % ˙
m1 (g⋅min
−1
) ˙
m2 (g⋅min
−1
)
1–2 0 % 5.50 0.00
3–4 10 % 5.19 0.58
5–6 20 % 4.85 1.21
7–8 30 % 4.47 1.91
9–10 40 % 4.04 2.70
Fig. 6. Uppe iew o he manu ac u ed alida ion componen and a ans-
e sal c oss-sec ion, whe e he WC pa icles a e e ealed in a da ke colou .
M. Os olaza e al.
In e na ional Jou nal o The mal Sciences 198 (2024) 108885
6
con ibu ed by M2 and he e m 0.04 Co%EDS
0.605 e e s o he W con ibu ed
by M1.
Such expe imen al alue is compa ed o he nume ical es ima ion,
which is calcula ed h ough he p ocedu e desc ibed subsequen ly.
Conside ing ha he sample o expe imen al alida ion was ab ica ed
assuming an FPP o 15 mm, he DPM o each ma e ial a 15 mm om he
nozzle exi is conside ed o con ibu e o he composi ion o a clad, see
Fig. 8(a), which is calcula ed based on equa ions (1) and (2). In o de o
de e mine he composi ion o he powde mix u e ed in o he mel pool,
he a ea co esponding o he mel pool needs o be de ined. In addi ion,
o p o ide a mo e accu a e esul , he geome y o he clad is also
conside ed. No e ha du ing he expe imen al wo k, he dis ance be-
ween he nozzle and he subs a e was se o 15 mm be o e he ab i-
ca ion o he mul i-laye sample. The heigh o he deposi ed laye s was
assumed o be 0.5 mm, which was es ima ed based on single-laye
expe imen al es s. Mo eo e , he olume ic a e o he powde
s eam p o ided by he eede was kep cons an o minimise he geo-
me ic a ia ion o he heigh o subsequen laye s.
In he p esen esea ch he CFD model does no conside he hea
in oduced by he lase in o he subs a e. In o de o de e mine he
shape o he mel pool c ea ed by he lase and he e o e quan i y he
ca chmen e iciency o he L-DED p ocess, he c oss sec ion o a clad is
analysed unde a mic oscope, see Fig. 8(b). This way, he egion o he
mel pool is disc e ised acco ding o he mo phology o he clad. Hence,
he composi ion in each ing-shaped egion is calcula ed and i s impac
on he o al composi ion o he clad is weigh ed. Speci ic de ails on he
geome ic disc e isa ion a e gi en in Table 7.
M2w .%=∑
15
j=1
nj⋅M2w .%j,CFD model (4)
As a esul , and based on he p oposed disc e isa ion, he w . % o he
Fig. 7. (a) Regions whe e he EDS measu emen s we e ca ied ou wi hin he mul ilaye sample o he expe imen al alida ion o he mul i-ma e ial CFD model.
Whi e pa icles ep esen he M2 pa icles and (b) EDS esul s.
Table 6
Chemical composi ion o he ma e ials employed.
Ma e ial Co C W Fe Ni Si C Mo
M1 60.5. 28.00 4.00 3.00 3.00 1.50 1.00 1.00
M2 – – 95.78 0.19 – – 4.03 –
Fig. 8. (a) Composi ion o he mul i-ma e ial powde s eam a he FPP and app oxima ed mo phology o he clad and (b) ing-shaped egions ( om 1 o 15)
employed o disc e ise he clad.
Table 7
Ring-shaped geome ic disc e isa ion o he clad.
Region,
j
Max. Ø
(mm)
Min. Ø
(mm)
A ea
(pixel)
To al a ea
(pixel)
Weigh ing
ac o , n
j
(%)
1 0.1 0.0 0.683 7.467 9.14
2 0.2 0.1 0.651 8.72
3 0.3 0.2 0.642 8.60
4 0.4 0.3 0.640 8.57
5 0.5 0.4 0.626 8.38
6 0.6 0.5 0.601 8.05
7 0.7 0.6 0.556 7.44
8 0.8 0.7 0.537 7.19
9 0.9 0.8 0.496 6.64
10 1.0 0.9 0.488 6.53
11 1.1 1.0 0.407 5.45
12 1.2 1.1 0.383 5.13
13 1.3 1.2 0.290 3.88
14 1.4 1.3 0.273 3.66
15 1.5 1.4 0.196 2.62
M. Os olaza e al.
In e na ional Jou nal o The mal Sciences 198 (2024) 108885
7
ce amic phase injec ed in o he mel pool and subsequen ly solidi ied
in o he clad can be es ima ed acco ding o equa ion (4), whe e M2w .%
is he weigh ed composi ion o ce amic phase con en o he clad, nj is
he weigh ing ac o o egion he j gi en in Table 7, and M2w .
%j,CFD model is he a e age ce amic con en o he powde s eam in he
egion j p o ided by he CFD model.
To assess he alidi y o he p oposed simpli ied mul i-ma e ial
model, he alues ob ained h ough equa ion (3) (expe imen al) and
(4) (nume ical), a e compa ed o he scena ios con empla ed in Table 4.
5. S a egies o o e come powde seg ega ion
Las ly, wi h he aid o he de eloped simpli ied mul i-ma e ial CFD
model, wo app oaches a e p oposed o o e come he challenge o
powde seg ega ion and o con ol he composi ion o he a ge mul i-
ma e ial pa s. The i s app oach is ounded on he an icipa ion o he
composi ion o he powde s eam a he wo king plane, and he
composi ion o he mul i-ma e ial powde s eam deli e ed by he
powde eede is uned o achie e a speci ic powde composi ion in he
mel pool. The second app oach elies on uning he g anulome y o he
ce amic phase so as o minimise powde seg ega ion and o achie e a
simila dynamic beha iou o he wo ma e ials. In he ollowing sec-
ions he me hodology p oposed o each s a egy is de ailed.
5.1. App oach 1: Adjus men o he composi ion o he powde s eam
deli e ed by he eede
In o de o o e come he challenge o igh ly con olling he
composi ion o he mul i-ma e ial pa s buil , a ans e unc ion is
de i ed. This ans e unc ion is calcula ed based on he simpli ied
mul i-ma e ial algo i hm alida ed acco ding o sec ions 4.1 and 4.2 and
i co ela es he composi ion o he powde s eam en e ing he mel
pool and he composi ion o he mul i-ma e ial low injec ed in o he
model, as shown in equa ion (5), whe e M2w .% is he mass pe cen age
o M2 (ce amic ein o cemen phase) in he powde s eam a he
wo king plane and en e ing he mel pool, F is he ans e unc ion, and
M2in w .% is he mass pe cen age o M2 in he powde s eam en e ing
he sys em h ough he disc e e phase injec ions.
M2w .%=F[M2in w .%](5)
In o de o de i e he ans e unc ion, se e al cases a e es ed wi h
a ying M2in w .% (Table 8). The composi ion o he ma e ial en e ing
he mel pool is calcula ed ollowing he same me hod desc ibed in he
p e ious sec ion. Las ly, he ans e unc ion is de i ed by seeking o
he bes i ing cu e ha co ela es he inpu and he ou pu o equa ion
(5).
5.2. App oach 2: Op imisa ion o he g anulome y o he ce amic phase
(ma e ial 2)
The second s a egy p oposed elies on minimising he powde
seg ega ion. In o he wo ds, i aims a modi ying he diame e o he
ce amic pa icles o make hem ollow he ajec o ies o he me allic
pa icles closely.
Fou di e en scena ios a e simula ed o unde s and he e ec o he
size o he powde pa icles on hei ajec o ies (Table 9x). The size o
he me allic pa icles is kep cons an o isola e his e ec , and he same
is done o he inpu s o he CFD model in e ms o gas inpu s, e c. In
addi ion, he composi ion o he mul i-ma e ial powde s eam injec ed
in o he model is ixed a 50 % w . o M2, M2inw .%=50. In o de o
lowe he size o he ce amic pa icles in a sys ema ic manne , he size o
he ac ual e e ence pa icles is lowe ed p opo ionally employing a
educ ion ac o (X) o he o iginal PSD.
In he s udied p oblem, d ag o ces a e going o domina e he pa h o
disc e e pa icles, he e o e, adjus ing he size o he disc e e pa icles o
make d ag o ces o bo h ma e ials simila will mos likely educe
powde seg ega ion. Conside ing ha he d ag o ce in his case is
p opo ional o
ρ
2⋅d3, in Table 9 he a io (R) be ween he d ag o ces
ac ing on M1 and M2 a e also depic ed. The close his a io is o 1, he
mo e simila he ma e ials a e, and he mo e simila hei d ag
beha iou .
To quan i y he powde seg ega ion, he a io be ween he ce amic
con en in powde s eam ed o he model and en e ing he mel pool
(Λ) is e alua ed. In his way, i is possible o assess how simila he
ajec o ies o he pa icles o each ma e ial a e. The close Λ is o 1, he
g ea e he simila i y be ween he ma e ials in e ms o dynamic
beha iou and he lowe he powde seg ega ion.
6. Resul s and discussion
In his sec ion he esul s ob ained a e epo ed and discussed.
Fi s ly, he simpli ying hypo hesis based on he supe posi ion p inciple
is nume ically alida ed agains he base model. Secondly, he simpli ied
mul i-ma e ial CFD model is alida ed agains expe imen al da a.
Thi dly, wo app oaches a e in es iga ed o mi iga e he e ec o pow-
de seg ega ion on he composi ion o he ab ica ed pa .
6.1. Nume ical alida ion o he supe posi ion algo i hm
In Fig. 9, he esul s ob ained in he base mul i-ma e ial CFD model
o he scena ios conside ed in Table 4 a e shown. In he o e all iew,
he disc e e phase concen a ion along he Z axis o all scena ios is
compa a i ely shown. I is appa en ha he powde mix u es beha e
di e en ly acco ding o he composi ion o he mul i-ma e ial mix u e
o , in o he wo ds, he ce amic con en . Indeed, powde mix u es wi h
highe ce amic con en , namely scena ios 2–4, exhibi a signi ican ly
highe peak o DPM a he FPP o M2. Con e sely, his peak is lowe ed in
a ou o he DPM a he FPP o M1 as he ce amic con en is diminished.
In e es ingly enough, i is appa en ha powde seg ega ion occu s
and ha powde pa icles o M1 (less dense) a e going o concen a e a
app oxima ely 15.22 mm, while pa icles o M2 (dense ) a e going o
concen a e mo e in ensi ely a 13.65 mm. Based on he esul s ob-
ained, which suppo he hypo hesis o he ajec o y o he pa icles
being de e mined by he ma e ial and pa icle size, he u ili y o he
supe posi ion p inciple becomes appa en .
Wi h he aim o demons a ing he alidi y o he simpli ied algo-
i hm p oposed in sec ion 4, wo indica o s a e looked a . On he one
hand, he disc e e phase dis ibu ion along he Z axis is compa ed based
on he da a p o ided by he base mul i-ma e ial CFD model and he
Table 8
Cases s udied o de i e he ans e unc ion.
Case M2in w .% ˙
m1 (g⋅min
−1
) ˙
m2 (g⋅min
−1
)
1 10 % 5.19 0.58
2 20 % 4.85 1.21
3 30 % 4.47 1.91
4 40 % 4.04 2.70
5 50 % 3.58 3.58
6 60 % 3.04 4.56
7 70 % 2.44 5.69
8 80 % 1.74 6.97
9 90 % 0.94 8.46
Table 9
Scena ios s udied o adjus he g anulome y o he powde .
Scena io M2in w .% ˙
m1 (g⋅min
−1
) ˙
m2 (g⋅min
−1
) X (−) R (−)
1 50 % 3.58 3.58 1.00 0.29
2 50 % 3.58 3.58 0.75 0.69
3 50 % 3.58 3.58 0.50 2.33
4 50 % 3.58 3.58 0.25 18.66
M. Os olaza e al.
In e na ional Jou nal o The mal Sciences 198 (2024) 108885
8
simpli ied algo i hm. On he o he hand, he eloci y o he luid low in
scena ios 0, 2, and 4 is con as ed.
In Fig. 10(a–c), he esul s co esponding o he nume ical alida ion
acco ding o he DPM dis ibu ion along he z axis a e shown. Da a
co esponding o he mul i-ma e ial CFD model, he simpli ied algo-
i hm, and he e o a e depic ed.
Resul s show ha he simpli ied algo i hm losses p ecision as he
ce amic phase in he mul i-ma e ial mix u e inc eases. In Fig. 11, he
e olu ion o he maximum e o and he mean e o in he egion o
in e es ( om 12 mm o 16 mm) is epo ed. This lack o i wi h
inc easing M2 con en is asc ibed o he highe densi y o his ma e ial.
Dense pa icles a e mo e suscep ible o in luence he mo ion o he luid
phase. None heless, he maximum e o in he egion o in e es is kep
below 6.5 % o all s udied scena ios, and he e o e, bo h calcula ion
p ocedu es, i.e. base and simpli ied models, a e ende ed equi alen .
In e ms o he mo ion o he luid, a sligh a ia ion is obse ed in
co ela ion wi h he composi ion o he powde mix u e employed
(Fig. 12). In he case o he hea ies ma e ial, i.e. M2, he luid phase
exhibi s a sligh ly highe eloci y in he egion om 13.5 o 15 mm in
he Z axis. In con as , he esul s ob ained wi h he 50 % mul i-ma e ial
mix u e a e p ecisely in be ween he da a ob ained o ma e ials M1 and
M2.
The esul s ob ained a e in good ag eemen wi h he e olu ion o he
e o ob ained. Namely, he mo e signi ican he modi ica ion o he
mo ion o he luid low, he less accu a e he supe posi ion p inciple.
None heless, his lack o accu acy is easonable, especially o 0–50 %
w . mul i-ma e ial mix u es. As a esul , he equi alence be ween he
base and simpli ied model is a i ied o he p esen applica ions. The
simpli ied algo i hm elies on he single-ma e ial CFD model o calcula e
Fig. 9. Disc e e phase concen a ion along he Z axis o scena ios 0–4. In addi ion, a summa y o all scena ios wi h a wide zoom is shown. FPP M1 and M2 indica e
he ocal plane posi ion o ma e ials 1 and 2 in single-ma e ial lows.
Fig. 10. DPM in he z axis based on he mul i-ma e ial CFD model and he simpli ied algo i hm o he scena ios conside ed.
Fig. 11. E olu ion o he e o o he simpli ied algo i hm s. he composi ion
o he mul i-ma e ial mix u e.
M. Os olaza e al.
In e na ional Jou nal o The mal Sciences 198 (2024) 108885
9
he powde dis ibu ion o mul i-ma e ial mix u es. The e o e, i he
beha iou o mix u es wi h di e en composi ional a ios is o be
s udied, he compu a ional cos o he analysis is signi ican ly educed.
As a ma e o ac , unning wo simula ions (one o each ma e ial)
su ices o calcula e all equi ed scena ios, p o ided he inpu s o he
model ega ding he luid low emain cons an .
6.2. Expe imen al alida ion o he supe posi ion algo i hm
Once he alidi y o he supe posi ion assump ion is nume ically
demons a ed, he CFD model is expe imen ally alida ed based on he
composi ion o a mul i-ma e ial FGM pa p oduced by L-DED. Indeed,
he powde seg ega ion caused by he di e ing ine ial p ope ies o he
cons i uen s is likely o p o oke a de ia ion o he eal composi ion o
deposi ed pa om he a ge ed one. To ha end, an expe imen al
alida ion o he simpli ied algo i hm is ca ied ou ollowing he sce-
na ios con empla ed in Table 5. Fi s ly, he composi ion o he mul i-
ma e ial mix u e a 15 mm om he nozzle exi is de i ed wi h he
simpli ied algo i hm. Mo e speci ically, he composi ion o he disc e e
phase wi h espec o he posi ion on he X axis is s udied. The esul s
ob ained a e shown in Fig. 13(a). In Fig. 13(b) a mo e de ailed iew is
p o ided wi h ega d o he clad geome y. Do ed lines e e o he
composi ion o he mul i-ma e ial powde mix u e a he inle s o he
nozzle, while con inuous lines e e o he ce amic con en in he mul i-
ma e ial powde s eam a 15 mm om he exi o he nozzle.
Based on he esul s ob ained, and he weigh ing coe icien s gi en in
Table 7, he composi ion o he mul i-ma e ial pa is de i ed and
compa ed o ha measu ed h ough EDS. The esul s a e shown in
Table 10. The compa ison be ween he nume ical and he expe imen al
da a sugges s ha he simpli ied algo i hm pe o ms well, as i cap u es
he de ia ion o he composi ion o he ac ual pa wi h espec o he
nominal composi ion. I mus be highligh ed, howe e , ha he dilu ion
o he laye below will a ec he composi ion o he deposi ed laye .
Hence, each laye n will be a ec ed by he composi ion o he laye
below n-1. In he p esen expe imen , he dilu ion measu ed in a laye is
oughly 15%, he e o e, he composi ion o a laye depends mainly on
he composi ion o he injec ed powde s eam. In any case, i highe
dilu ion alues we e epo ed due o he L-DED p ocess pa ame e s
employed, i would in oduce a g ea e e o in he compa ison be ween
nume ical and expe imen al esul s, as he CFD model does no accoun
o he e ec o dilu ion. This e o is pa ially mi iga ed by aking he
a e age o wo subsequen laye s pe scena io.
6.3. S a egies o ace powde seg ega ion in mul i-ma e ial L-DED
Once ag eed ha he di e ing ine ial p ope ies a ec he compo-
si ion o he deposi ed mul i-ma e ial clads due o powde seg ega ion,
Fig. 12. Veloci y o he luid phase. In he igh -hand image, he eloci y o he luid phase in he XZ plane o scena ios 0 and 4 a e shown.
Fig. 13. (a) Composi ion o he mul i-ma e ial powde s eam a 15 mm om
he exi o he nozzle and (b) a de ail o he a ea o in e es .
Table 10
Resul s o he expe imen al alida ion o he simpli ied algo i hm.
Nominal
composi ion, w . %
Nume ical
esul s, w . %
EDS measu emen s:
Expe imen al esul s w . %
E o
10 8.71 8.40 ±2.66 4 %
20 17.54 17.04 ±1.21 3 %
30 26.66 25.16 ±3.97 6 %
40 36.19 33.82 ±0.37 7 %
M. Os olaza e al.
