CFD simula ion o a no el anae obic-anoxic eac o o biological nu ien emo al: model
cons uc ion, alida ion and hyd odynamic analysis based on OpenFOAM®
R. Blanco-Aguile a a,*, J.L. La a b, G. Ba ajas b, I. Teje o a, R. Diez-Mon e o a,c
a G oup o En i onmen al Enginee ing, Depa men o Wa e and En i onmen al Sciences and Technologies, Uni e si y o Can ab ia, A enida los
Cas os s/n, 39005 San ande , Spain
b En i onmen al Hyd aulics Ins i u e (IHCan ab ia), Uni e si y o Can ab ia, Isabel To es 15, 39011 San ande , Spain
c G oup o En i onmen al Enginee ing and Mic obiology, Depa men o Ci il and En i onmen al Enginee ing, Uni e si a Poli ècnica de Ca alunya,
c/ Jo di Gi ona 1-3, Building D1, E-08034 Ba celona, Spain
* Co esponding au ho . E-mail add ess: blancoag @unican.es. (R. Blanco-Aguile a)
Keywo ds:
Compu a ional Fluid Dynamics, Mul i-en i onmen , Tu bulen low, RTD analysis, T ace es s, Biological
Nu ien Remo al
Abs ac
AnoxAn is a no el mul i-en i onmen eac o o biological nu ien emo al (BNR) om was ewa e .
Al hough i s biological e icacy has been demons a ed on a pilo scale, hyd odynamics is obse ed o
signi ican ly a ec he pe o mance o AnoxAn. To s udy i s complex hyd aulic beha iou , a model based
on Compu a ional Fluid Dynamics 3D (CFD) is cons uc ed using he OpenFOAM® open sou ce oolbox
and alida ed by expe imen al es s o Residence Time Dis ibu ion (RTD). Reac o elemen s ep esen a
key ac o in he modelling p ocess. In his sense, he impelle o he anoxic zone is modelled as a la disk,
and he ba le a e he anoxic zone as a po ous media. Acco ding o CFD model simula ions, s agnan ,
sho -ci cui zones and mixing quali y a e es ablished and quan i ied. Finally, he in luence on he
hyd odynamics o eac o elemen s is also e alua ed. The esul s o his de ailed hyd odynamic analysis
will o m he basis o he design and op imiza ion o scalable AnoxAn con igu a ions.
This is he accep ed manusc ip o he a icle ha appea ed in inal o m in Chemical Enginee ing Science 215 :
(2020) // A icle ID 115390, which has been published in inal o m a h ps://doi.o g/10.1016/j.ces.2019.115390.
© 2019 Else ie unde CC BY-NC-ND license (h p://c ea i ecommons.o g/licenses/by-nc-nd/4.0/)
1. In oduc ion
Fo many yea s, he main objec i e o was ewa e esea ch has been o achie e he equi ed e iciency o
biological p ocesses o mee egula ions and p ese e he ecological and heal hy s a us o wa e bodies
( i e s, lakes, ese oi s, oceans, e c.). Speci ically, g ea e o s ha e been made o design and imp o e
nu ien emo al p ocesses (i.e.: ni ogen (N) and phospho us (P)) due o he inc easing equi emen s o
Was ewa e T ea men Plan s (WWTPs).
Howe e , con en ional biological nu ien emo al (BNR) p ocesses in WWTPs equi e a complex
ea men sys em and en ail se e al en i onmen al impac s. Fi s , he ae obic eac o should be la ge enough
o ca y ou ammonia oxida ion (ni i ica ion) and mus be coupled wi h non-ae a ed compa men s
(anae obic and anoxic). The e o e, a la ge olume is needed compa ed o o ganic ma e emo al p ocesses.
This issue becomes c ucial in cases whe e land a ailabili y is limi ed and in cases o exis ing was ewa e
ea men plan s ha need o be upg aded o BNR plan s. In addi ion, he high ene gy demand o he
ni i ica ion p ocess, oge he wi h he need o eci cula ion pumping be ween he di e en compa men s
o eac o s and he mixing o he non-ae a ed ones, esul in a signi ican inc ease in ene gy consump ion.
In his con ex , mul i-en i onmen al biological eac o s wi h high compac ion and e iciency ha e been
de eloped o educe he ene gy consump ion and land use o con en ional BNR ea men ains (Kwon e
al. 2005, Ye ushalmi e al. 2011, Teje o e al. 2010, Teje o e al. 1991, Ma in e al. 2012). O special
in e es is he anae obic-anoxic eac o AnoxAn, de eloped and pa en ed by Teje o e al. (2010). AnoxAn
is a con inuous upwa d- low sludge blanke eac o ha uni ies in a single eac o he anae obic and anoxic
zones necessa y o he biological nu ien emo al o con en ional ac i a ed sludge om was ewa e
(Diez-Mon e o 2015, Diez-Mon e o e al. 2015, 2016). Due o i s low ene gy consump ion and minimal
land use, he AnoxAn concep and echnology can po en ially be applied o he upg ade o a WWTP o in
a new WWTP wi h limi ed space a ailabili y. In addi ion, p ima y se ling anks could be eused as anoxic-
anae obic eac o s o de elop inno a i e and compac ea men sys ems (Diez-Mon e o e al. 2019).
Finally, he anae obic-anoxic biological unc ioning o AnoxAn is in ended o be coupled o an ae obic
eac o ( o esidual o ganic ma e emo al, phospha e up ake and ni i ica ion) and a seconda y se ling
uni (o inal il a ion s ep), o comple e he BNR ea men ain (Diez-Mon e o 2015).
The AnoxAn eac o consis s o an anae obic zone a he bo om ( ecei ing he in luen was ewa e ), be o e
an anoxic zone abo e ( ecei ing a ni a e- ich cu en om a subsequen ae obic eac o ). In addi ion, a
cla i ica ion zone is achie ed in he uppe pa , a oiding he escape o la ge quan i ies o biomass. One o
he main objec i es o he eac o se up is o es ablish an anoxic-anae obic hyd aulic sepa a ion, i.e. o
main ain an insigni ican concen a ion o ni a es in he anae obic zone, achie ing a he same ime
adequa e mixing condi ions in bo h zones and main aining he con inuous low o he e luen h ough i .
Fo his pu pose, he eac o has independen mixing sys ems in each zone: a eci cula ion pump p o ides
he mix u e in he anae obic zone and a mixing impelle in he anoxic zone. In addi ion, he de lec o s and
ba les imp o e hyd aulic sepa a ion and e en ion o suspended solids wi hin he eac o . Conc e ely, he
uppe ba le, BLAS® (Teje o e al. 1991) was o iginally concei ed as a suppo media o bio ilm, bu in
AnoxAn is used as a head loss gene a o educing he eloci y o he luid low. Speci ic elemen s wi h
hese cha ac e is ics and le el o in e e ence in he low pa e n inc ease he hyd odynamic complexi y o
he eac o , and could gene a e p e e en ial lows and dead zones, educing he o e all pe o mance o he
sys em (Al-Samma aee e al. 2009, Liu e al. 2018, Plascencia-Ja omea e al. 2015, Yan e al. 2015).
The iabili y o anoxic-anae obic hyd aulic sepa a ion o AnoxAn was es ed in a 48.4 L p o o ype by
means o Residence Time Dis ibu ion (RTD) analysis (Diez-Mon e o e al. 2015). A hyd aulic model based
on compa men s was cons uc ed and alida ed wi h expe imen al aceabili y es s. This model was a
combina ion o comple e mixed compa men s and plug low wi h axial dispe sion compa men s,
implemen ed o desc ibe he non-ideal low o he eac o . The model p edic ed wi h high accu acy he
expe imen al eco ds (local measu emen s wi hou spa ial esolu ion). Then, i was applied o e alua e
hyd aulic anoxic-anae obic sepa a ion. Howe e , his ype o modelling canno p o ide comple e
in o ma ion on hyd odynamics wi hin he eac o . In a la e wo k, he biological beha iou o he eac o in
he ea men o municipal was ewa e was s udied (Diez-Mon e o e al. 2016). The esul s demons a ed
he easibili y o he eac o concep . Howe e , i was obse ed ha some physical cha ac e is ics o
AnoxAn signi ican ly a ec i s pe o mance, hyd odynamics being clea ly ele an . In o de o op imise
he eac o con igu a ion and p opose o he eac o con igu a ions applicable on a la ge scale, Diez-Mon e o
(2015) poin ed ou a deepe and mo e comple e hyd odynamic analysis.
In ac , RTD expe imen al es s (Le enspiel, 1999), usually coupled o hyd aulic models based on
compa men s such as he ank-in-se ies and he dispe sion models, ha e been widely used o
hyd odynamic analysis in was ewa e ea men eac o s. I was obse ed ha mixing condi ions (Hu e al.
2012, Oli e e al. 2005, Ye ushalmi e al. 2013), low ype and cha ac e is ics (Behzadian e al. 2013,
Au umn e al. 2007, Gomez 2010, Ji e al. 2012, Sa agai e al. 2010), dead olume (Au umn e al. 2007, Hu
e al. 2012, Ji e al. 2012, Sa a hai e al. 2010), channeling (Gómez 2010, Nemade e al. 2010, Zeng e al.
2005) and dispe sal (Ji e al. 2012, Nemade e al. 2010, Ye ushalmi e al. 2013, Zeng e al. 2005) we e
obse ed as he mos impo an cha ac e is ics. Howe e , expe imen al RTD analysis echniques equi e a
lo o ime and esou ces. In some cases, he complexi y o expe imen al es s makes hem imp ac icable in
la ge-scale eac o s (Fe nandez, 2012). In addi ion, expe imen al RTD models and compa men -based
hyd aulic models do no con ain any in o ma ion on spa ial low and concen a ion camp esolu ion
(Plascencia-Ja omea e al. 2015, Qi e al. 2013).
The la e can be o e come by combining and de eloping ad anced ma hema ical models and
compu a ional simula ion. The applica ion o nume ical echniques o enginee ing has expe ienced g ea
g ow h in ecen decades, wi h Compu a ional Fluid Dynamics (CFD) being one o he app oaches wi h he
g ea es impac . The use o CFD in was ewa e ea men p ocesses is g owing apidly and is being applied
in he esolu ion o complex p oblems (Angeloudis e al. 2016, B annock e al. 2010, Liu e al. 2018,
Klusene e al. 2007, Wicklein e al. 2016, Zhang e al. 2016).
Rega ding hyd odynamic analysis, combina ion o RTD and CFD o eac o analysis and op imiza ion has
been p e iously applied o di e en eac o s (B annock e al. 2010a-b, Climen e al. 2018, Le Moullec e
al. 2008, Pe ei a e al. 2011, Plascencia-Ja omea e al. 2015, Te ashima e al. 2009). The p esen wo k
ollows he alida ion pe o med by many o hem ega ding he hyd odynamic ield, which is only based
on RTD es s (B annock e al. 2010a-b, Plascencia-Ja omea e al. 2015, Te ashima e al. 2009). Mo eo e ,
all he s udies a o emen ioned we e ca ied ou wi h comme cial codes, being he p esen esea ch an open-
sou ce app oach ha comple es he al eady exis ing ones.
Hyd odynamic in s i ed eac o s has also been modelled and analysed o se e al con igu a ions
(B idgeman 2012, Bai e al. 2008, Choi e al. 2004, Qi e al. 2013). Di e en app oaches can be unde aken
o a co ec ep esen a ion o he impelle : being MRF (Mul i Re e ence F ame) app oach (Bai e al. 2008,
B idgeman 2012, Renade 2002, Wu e al. 2009) o momen um sou ce app oach common ones. The la e
is a classical simpli ica ion ha allows a signi ican compu a ional esou ce sa ing and has been widely
and success ully used in was ewa e ield, all o hem ca ied ou wi h comme cial codes (B annock 2003,
Climen e al. 2018, Climen e al. 2019, Rehman 2016).
Mo eo e , CFD modelling allows deepe hyd odynamic analysis including iden i ica ion and loca ion o
dead zones, acking o eloci y p o iles and low pa e ns, mixing pe o mance, and de e mina ion o he
dis ibu ion o ace concen a ion wi hin he eac o (Climen e al. 2018, Dapelo e al. 2018,
Michalopoulos e al. 2018, Plascencia-Ja omea e al. 2015, Te ashima e al. 2009, T ab e al. 2015, Wei e
al. 2019). In addi ion, his ad anced knowledge will be essen ial o he ope a ional op imiza ion o eac o s
wi h complex hyd odynamic beha iou such as AnoxAn in e ms o a oiding he p esence o dead low
zones o p e e ed channelling in he design.
Finally, a calib a ed and alida ed CFD model is mo e e icien han o he app oaches in e ms o es ing
o he o ms o combina ion o di e en elemen s in a easonable ime.
Conc e ely, hyd odynamic e alua ion is c ucial in mul i-en i onmen eac o s due o hei speci ic shapes
and combina ion o di e en elemen s, such as ba les and mixing de ices, which in e e e in he ideal
hyd aulic pe o mance c ea ing complex low egimes (Kwon e al. 2005, Ye ushalmi e al. 2011, Diez-
Mon e o, 2015). Howe e , o ou knowledge, only ew hyd odynamic s udies ha e been pe o med based
on CFD o mul i-en i onmen eac o s and i s elemen s in luence (Calde e al. 2013). Finally, i has been
widely p o ed ha an op imum hyd aulic ope a ion ensu es an adequa e biological pe o mance e iciency
(Climen e al. 2018, A naldos e al. 2018, Wei e al., 2019), being hyd odynamic unde s anding and
analysis a c i ical s ep o designing p ocess.
The objec i e o his s udy is o de elop a CFD model o he no el AnoxAn anae obic-anoxic eac o and
o analyse i s hyd odynamic beha iou in o de o iden i y he key ea u es o he eac o con igu a ion ha
canno be achie ed wi h con en ional RTD expe imen al p ocedu es. These esul s a e c ucial o he
op imiza ion and u u e design o la ge-scale eac o implemen a ions. In addi ion, modelling and
simula ion o eac o elemen s such as ba les and de lec o s would p o ide a deepe hyd odynamic
unde s anding ha could be applied o he de elopmen and op imiza ion o o he mul i-en i onmen al
eac o s and con en ional wa e ea men eac o s. The model is buil in he OpenFOAM® ( 18.12) open
sou ce oolbox (Welle a al. 1998), and calib a ed and alida ed wi h RTD expe imen al es s and
simula ions o p e ious models.
2. Ma e ials and me hods
2.1. Desc ip ion o expe imen s
2.1.1. Bench scale eac o se up
To e alua e he model's abili y o ep oduce he hyd odynamics o AnoxAn, a se ies o expe imen s we e
conduc ed on a p o o ype eac o buil on a bench scale (Diez-Mon e o e al. 2015).
AnoxAn p o o ype, see Fig. 1a, is a 48.4L up low eac o made o polyme hyl me hac yla e (PMMA). The
eac o is di ided in o h ee di e en zones: a cla i ica ion zone a he op (4.0 L; 8% o he o al olume),
an anoxic zone below (32.0 L, 66% o he o al olume) and an anae obic zone a he bo om (12.4 L; 26%
o he o al olume). Geome ically, i consis s o an in e nal squa e sec ion o 0.20 x 0.20 m2 and a heigh
o 1.30 m. A c oss sec ion o he de ailed eac o geome y based on he squa e sec ion side (D = 0.20 m)
is shown in Fig. 1e.
Mixing de ices in he eac o consis in a Heidolph RZR- 2 000 impelle (100 pm) (Fig. 1b) o he anoxic
zone and a pe is al ic pump Wa son Ma low 313U o he con inuous in e nal ecycle o he anae obic zone.
Besides, a complex 3D geome y polye hylene (PE) ba le o 0.039 m heigh is placed (Fig. 1c) be ween
he anoxic and cla i ica ion zones in o de o imp o e suspended solids e en ion inside he eac o and
educe he up- low eloci y. Finally, a poly inyl chlo ide (PVC) de lec o o 4 cm wid h along he wall is
in oduced (Fig. 1d) o enhance he hyd aulic sepa a ion be ween anoxic and anae obic en i onmen s.
Figu e 1. (a) 3D scheme o he bench scale AnoxAn eac o , (b) Impelle , (c) Ba le be ween anoxic and
cla i ica ion zones, (d) De lec o be ween anae obic and anoxic zones and (e) De ailed c oss sec ion
geome y based on he squa e sec ion side (D = 0.20 m)
2.1.2. Expe imen al RTD condi ions
Two expe imen al and a simula ed ace es s in clean wa e we e pe o med in AnoxAn o cha ac e ise
he liquid phase low pa e n. All de ails o he expe imen s a e shown in Table 1 and Fig. 2. The AnoxAn
eac o was designed o a hyd aulic esidence ime (HRT) up o 5 h (depending on he o ganic load applied)
and o all he expe imen s pe o med he inle s eam low Qin is 10.4 L/h, in e nal ecycle a e ( a io
be ween in e nal ecycle s eam low and inle s eam low, RIR = QIR/Qin) is 5.77 and ni a e ecycle a e
( a io be ween ni a e ecycle s eam low and inle s eam low, RNR =QNR/Qin) is 2.98.
Two pulse RTD es s we e ca ied ou o hyd aulic cha ac e iza ion o AnoxAn: (i) RTD1 injec ing he
ace h ough he inle s eam (see RTD1 in Table 1 and Fig. 2a) and (ii) RTD2 injec ing he ace h ough
he ni a e s eam (see RTD2 in Table 1 and Fig. 2b). Fo bo h pulse expe imen s, a concen a ed solu ion
o sodium chlo ide (NaCl, 350 g/L) was used as ace . Mo eo e , in RTD1, he olume injec ed was 58
mL and RTD2 was 40 mL. Ou pu concen a ion was es ima ed measu ing he conduc i i y h ough a linea
ela ionship be ween hem (Tang e al. 2004, Ma ín-Dominguez e al. 2005) wi h a Hach CDC40103 p obe
connec ed o a HQ30d me e .
In addi ion o pulse expe imen s, and in o de o be e assess he hyd aulic sepa a ion be ween he anoxic
and anae obic zones, a s ep RTD es (RTD3) was simula ed using he calib a ed and alida ed hyd aulic
compa men -based model desc ibed in Diez-Mon e o e al. (2015) and p esen ed as supplemen a y
ma e ial. In RTD3, a cons an concen a ed solu ion o ace (10 mg/L) is con inuously injec ed in he
ni a e ecycle s eam and ace concen a ion is con inuously measu ed in he ou le and in bo h anae obic
and anoxic zones (see RTD3 in Table 1 and Fig. 2c).
Table 1. RTD es s condi ions
RTD
expe imen
Type T ace injec ion
loca ion (m)
T ace
injec ion
du a ion
T ace concen a ion
measu emen (m)
RTD1
Pulse. Expe imen al
Inle s eam
Pi (-0.1, 0, 0.30)
pulse = 3 s
Ou le
Pou (-0.1, 0, 1.295)
RTD2
Pulse. Expe imen al.
Ni a e ecycle s eam
PN (0.1, 0, 0.65)
pulse = 3 s
Ou le
Pou (-0.1, 0, 1.295)
RTD3
S ep. Simula ed.
Ni a e ecycle s eam
PN (0.1, 0, 0.65)
Con inued
injec ion
Anae obic zone
Panae (0, 0, 0.30)
Anoxic zone
Panox (0, 0, 0.80)
Ou le
Pou (-0.1, 0, 1.295)
Figu e 2. Schema ic diag am o pulse ace es s (a) RTD1 (b) RTD2 (c) RTD3
2.2. Nume ical model se up
In his sec ion, he compu a ional se up o he CFD model is p esen ed. The model is alida ed based on
RTD expe imen s desc ibed in he p e ious sec ion.
Based on he esul s om he nume ical simula ions, a comp ehensi e hyd odynamic analysis o he
di e en zones o he eac o is pe o med. Fo ha pu pose, a ansien low analysis is needed. A his
espec , unlike RTD analysis, ansien CFD models p o ide high spa ial low and ace concen a ion
esolu ion, along wi h ime his o y o he la e . Besides hyd odynamics, eac o elemen s a e also modelled.
A his aim, he local mixing e ec o he impelle is ep oduced by means a la disk app oach (See sec ion
2.2.1.3) and he ba le si ua ed be ween anoxic and cla i ica ion en i onmen s is simula ed as a po ous
media (See sec ion 2.2.1.4). Bo h app oaches led o a signi ican compu a ional cos sa ing.
2.2.1. Compu a ional Fluid Dynamics. Go e ning equa ions and models.
2.2.1.1. Hyd odynamic model
Hyd odynamics o AnoxAn a e simula ed sol ing Na ie S okes (NS) equa ions o u bulen and
incomp essible low.
Nume ical esolu ion o u bulen lows can be achie ed h ough di e en app oaches wi h se e al
app oxima ion deg ees. Reynolds A e aged Na ie S okes (RANS) simula ion is he mos widely used
app oach in enginee ing due o i s ela i e simplici y and lowe compu a ional cos . In RANS simula ion,
all u bulen scales a e simula ed by modelling, in oducing a ime a e aging o he a iables in o de o
sepa a e hei ensemble alue and he luc uan one.
RANS equa ions include con inui y (Eq. 1) and momen um conse a ion (Eq. 2) equa ions, linking he
p essu e and he eloci y.
𝜕𝑣
𝜕𝑥=0 (1)
𝜕𝑣
𝜕 + 𝑣𝜕𝑣
𝜕𝑥=−1
𝜌𝜕P
𝜕𝑥+(µ+µ) 𝜕
𝜕𝑥 𝜕𝑣
𝜕𝑥+𝜕𝑣
𝜕𝑥 + 𝑔+𝑓 (2)
whe e 𝑣 is he ensemble eloci y ec o , ρ is he luid densi y, μl is he luid dynamic iscosi y, μ is he
eddy iscosi y, p is he p essu e, g is he g a i a ional accele a ion and ba le he esis an o ce (Fba le)
p oduced by he ba le pe uni o olume no malised by densi y.
In addi ion, model closu e equa ions a e needed o he u bulen s ess enso : In his wo k s anda d k-ε
model (Launde and Spalding, 1972) is used (Eqs. 3-4):
𝜕(𝜌𝑘)
𝜕𝑡 +𝜕
𝜕𝑥(𝜌𝑘𝑣)=𝜕
𝜕𝑥µ+µ
𝜎𝜕𝑘
𝜕𝑥 + 𝐺− 𝜌𝜀 (3)
𝜕(𝜌𝜀)
𝜕𝑡 +𝜕
𝜕𝑥(𝜌𝜀𝑣)=𝜕
𝜕𝑥µ+µ
𝜎𝜕𝜀
𝜕𝑥+𝐶𝜀
𝑘𝐺−𝐶𝜌𝜀
𝑘 (4)
in which k is he u bulen kine ic ene gy, ε is he u bulen kine ic ene gy dissipa ion a e, G is he
p oduc ion a e o u bulen kine ic ene gy, σk, σε, C1ε and C2ε a e he k-ε model s anda d cons an s , and µ
is he u bulen iscosi y de ined by Eq.5:
µ= 𝜌𝐶𝑘
𝜀 (5)
Nume ical alues o he cons an s a e:
Cµ = 0.09 C1ε=1.44 C2ε=1.92 σk=1.0 σε = 1.3
2.2.1.2. T ace anspo model
Fo ace es simula ion, he esolu ion o a anspo equa ion wi hou chemical eac ion is modelled in
he so wa e. The exp ession is ob ained by means o a e aging he gene al anspo equa ion o u bulen
low (Eq. 6):
𝜕(𝜌𝑚)
𝜕𝑡 +𝜕
𝜕𝑥(𝜌𝑣𝑚)=𝜕
𝜕𝑥𝜌𝐷+𝜇
𝑆·𝜕𝑚
𝜕𝑥 (6)
Fo he k-esim specie. 𝐷 is he sel -di usion coe icien o he ace . In o de o only ep oduce he
con ec i e anspo , his alue mus be e y low, a leas 10-10 m2/s (Fe nandez 2012). In his wo k 𝐷 is
se o 10-20 m2/s o ensu e o con ec i e beha iou .
e m ep esen s he u bulen di usion, in which Schmid numbe appea s (Sc =
· ), being µ
u bulen iscosi y and D u bulen di usi i y. The alue o he Schmid numbe used o he ace
anspo is 0.8 as i p o ided good ag eemen wi h expe imen al esul s, being his pa ame e ypically
be ween 0.7 and 1 (B annock 2003, De Cle cq 2003).
The esolu ion me hod o ace anspo uses he concep o luid mix u e. Fi s con inui y, momen um
and ene gy equa ions a e sol ed in he mix u e ield. Nex , ace anspo is pe o med.
2.2.1.3. Impelle model
The impelle plays a key ole in he hyd odynamics o he eac o because i is he main sou ce o inne
momen um supply. Because he pu pose o his wo k is no o de ine in de ail he hyd odynamic pa e ns
p oduced a ound by impelle blades and because he o a ion speed o he impelle is no e y high c ea ing
a e y signi ican u bulen low pa e ns, a simpli ied modelling o he impelle has been pe o med. To
do his, he la disk hypo hesis has been used (Jasak e al. 2019, Seb 2017), whe e he momen um induced
by he impelle o he luid is in oduced in o he model om a compound eloci y ield a an axial, adial
and angen ial eloci y (i.e.: a, and ), which a e de ined acco ding o he o a ion speed and he ela i e
posi ion o he di e en nodes ha de ine he disk wi h espec o i s cen e (see Fig. 3). Those eloci ies
a e used a bounda y condi ions a he la disk su ace. This app oach has been success ully used and
alida ed in was ewa e esea ch (B annock 2003, Climen e al. 2018, Climen e al. 2019, Rehman 2016).
This app oach has he ad an age ha i has a lowe compu a ional cos bu allows an adequa e low
cha ac e iza ion in he eac o .
Figu e 3. Schema ic scheme o he impelle s la disk app oach
Veloci y bounda y condi ion is se o h ee impelle eloci ies (Eqs. 7-9) as:
𝑣
=𝑈, · 𝑎 (7)
𝑣
=𝑈, · 𝑟
(8)
𝑣
=𝑈, ·𝑡 (9)
being 𝑎 he ec o no mal o he impelle , 𝑟 he adial ec o and 𝑡 angen ial ec o espec i ely. 𝑈,
ep esen he module o h ee cha ac e is ic eloci ies. The impelle has a o a ional eloci y o 100 pm
and a adial low beha iou . The ollowing alues a e se in he model o he de ined eloci y ec o s as
hey p o ided good ag eemen wi h expe imen al esul s:
𝑣
=𝑈,·𝑎=0· 𝑎=0 (10)
𝑣
=𝑈, · 𝑟
=0 · 𝑟
=0 (11)
𝑣
=𝑈,·𝑡=100 𝑟𝑝𝑚 ·𝑡= 10,5𝑟𝑎𝑑
𝑠·𝑅·𝑡 (12)
Being R he adial dis ance o each node in he impelle la disk o he impelle cen e in me e s. Ro a ional
speed o he impelle is 100 pm, he diame e is 0.08 m and he kinema ic iscosi y o he luid is 10-6 m2/s.
Taking hese in o accoun , he Reynolds numbe yields 10 670, and in consequence, ully de eloped
u bulen low can be conside ed in ha zone (see Coupe a al. 2010).
2.2.1.4. Ba le model
The ba le be ween he anoxic and cla i ica ion zones consis s o a plas ic ame wi h a 3D complex
geome y (see Fig. 1c). The ealis ic de ini ion o i s eal geome y in oduces a complexi y in he
compu a ional mesh ha esul s in a 30% inc ease in he numbe o elemen s o he compu a ional mesh,
wi h he consequen inc ease in he compu a ional cos . To a oid his inc ease, he ba le is modelled as a
po ous media ha simula es a p essu e d op in he eloci y ield as a momen um sump. I is modelled by
means o a Da cy ype low model de ined in Equa ion 13:
ba le = k·|U
|; ∀ Ba le egion (13)
Being k he ic ion coe icien , whose alue is se o 500 000 kg/s (Miho ilo ic 2010). To calcula e
Reynolds numbe inside he ba le, exp ession om Bu cha h e al. (1995) and Losada e al. (2016) has
been ollowed. In his ega d, Reynolds numbe o he luid inside he ba le is be ween 40 and 75, which
is consis en wi h he ange o applicabili y o Da cy’s low modelling.
Compa ing he expe imen al RTD esul s (ci cles) o he CFD model simula ions (g een lines) i can be
obse ed ha he p edic ions o he model ag ee wi h he expe imen al measu emen s. This e i ies ha he
NS solu ions o he u bulen low and di usion-con ec ion equa ions eliably ep esen ace anspo
wi hin AnoxAn. In addi ion, he coe icien o de e mina ion R2 has been de e mined in o de o quan i y
he i be ween he simula ed and expe imen al esul s (Diez-Mon e o e al. 2015, Fang e al. 2011, López
e al. 2010, Makinia e al. 2006), ob aining high alues in all he cases (Table 4).
Table 4. R2 coe icien o de e mina ion o di e en CFD models
RTD Cu e R
2
RTD1 0.98
RTD2 0.96
RTD3 – Anoxic cu e 0.99
RTD3 – Cla i ica ion cu e 0.99
RTD3 – Anae obic cu e 0.99
Mo eo e , expe imen al HRT in pulse es s and nume ical HRT aken om CFD models a e compa ed o
u he alida ion (B annock e al. 2010a-b, Plascencia-Ja omea e al. 2015, Climen e al. 2018) and esul s
a e shown in Table 5. Bo h HRT ha e been calcula ed cu ing he cu e in he ime co esponding o he
las expe imen al measu emen . The HRT nume ical esul is obse ed o ha e a di e ence o less han 7%
in bo h cases. The e o e, modelling app oaches ollowed o single elemen s, i.e. impelle and de lec o ,
a e conside ed sa is ac o y.
Besides, he di e ence be ween eal (expe imen al) and heo e ical HRT is also discussed. I is obse ed
ha eal HRT is highe han he heo e ical alue, as expec ed. This means ha no he o e all olume is
being used in he mixing p ocess, esul ing in dead olumes (Eq. 20) o s agnan zones (Climen e al. 2018).
I should be highligh ed ha cu ing he cu e in he ime co esponding o he las expe imen al
measu emen , i could lead o sligh ly unde es ima ed HRT, due o he ace mass no aken in o accoun
in he ail o he cu e. The e o e, he eal dead olumes could be sligh ly lowe han he calcula ed ones,
as shown in Table 5.
Vd = 1−
· 100% (20)
Table 5. HRT compa ison o heo e ical, expe imen al and CFD models
Expe imen HRT heo HRTexp HRTCFD Dead Volume
RTD1 124 min 97 min 96 min ≤22%
RTD2 50 min 44 min 47 min ≤12%
3.2. Hyd odynamic analysis based on RTD cu es
Analyzing he expe imen al RTD measu emen s (Fig. 8, black ci cles), he ollowing can be s a ed:
Wi h espec o he pulse ace es s (Fig. 8a and 8b), he non-ideal AnoxAn low pa e n is analysed. The
ime e olu ion o he RTD cu e allows o con i m ha hey a e be ween he Con inuous S i ed Tank
Reac o (CSTR) and a Plug Flow Reac o (PFR). This de ia ion in ideal low pa e ns is a consequence o
he p esence o some p e e en ial low and channelling zones in he AnoxAn. In addi ion, in bo h RTD1
and RTD2 (Fig. 8a-b) expe imen s a ema kable ailing is obse ed. This is he esul o he p esence o
s agnan o dead low zones, whe e ace anspo is low, esul ing in highe ace concen a ion. The
exis ence o s agnan zones means ha he en i e eac o olume is no being used e icien ly, which may
lead o a dec ease in he ac ual HRT compa ed o he design alue. Howe e , he RTD cu es do no p o ide
in o ma ion on he loca ion and size o he channelling zones o dead olumes. This in o ma ion can be
c ucial o he op imiza ion o he AnoxAn design and i s scalabili y. Thus, using a calib a ed and alida ed
CFD model, an addi ional hyd odynamic analysis can be pe o med. De ailed eloci y ields and ace
concen a ion can be acked in o de o be e unde s and he low and mixing mechanisms wi hin he
eac o and iden i y dead low zones.
Rega ding s ep ace es (Fig. 8c), a ema kable hyd aulic sepa a ion be ween anoxic and anae obic zones
is con i med. In ac , he s eady-s a e ace concen a ion eached in anae obic zone is 25% o he
concen a ion obse ed in anoxic and cla i ica ion zones. In addi ion, a delay in he s abiliza ion o he
concen a ion in he cla i ica ion zone is obse ed compa ed o he anoxic one. Acco ding o compa men -
based hyd aulic models buil (Diez-Mon e o e al. 2015), his delay is due o he in luence o he ba le,
which in heo y, educes he up- low eloci y. Howe e , a u he hyd odynamic analysis based in CFD
echniques a e needed o s udy ha hypo hesis.
3.3. Hyd odynamic analysis based on CFD simula ions
Dead low zones and sho -ci cui ing can be s udied based on eloci y ield analysis. In his sense, CFD
model esul s ega ding eloci y ec o s and/o s eamlines ha e been p e iously used in wa e ea men
s udies (A naldos e al. 2018, B annock e al. 2010, Climen e al. 2018, Plascencia-Ja omea e al. 2015,
Rehman 2016). In his ega d, he eloci y magni ude (Fig. 9a, Fig. 9d and Fig. 9g), he e ical eloci y
componen (Fig. 9b, Fig. 9e and Fig. 9h) and low s eamlines (Fig. 9c, Fig. 9 and Fig. 9i) o he mos
ep esen a i e zones in AnoxAn a e p esen ed in Fig. 9.
A c oss sec ion XZ is ep esen ed oge he wi h ho izon al c oss sec ions XY a di e en le els o be e
isualise he magni ude and e ical componen o he eloci y ields. Fo he s eamlines, a ull 3D
ep esen a ion o he main low pa e ns is p esen ed.
No e ha o eloci y magni udes, a loga i hmic scale has been used o be e isualiza ion. Fo e ical
eloci ies, nega i e downs eam alues a e shown in blue and posi i e ups eam alues a e shown in ed.
Di e en e ical eloci y scales ha e been used o he low lines in o de o ob ain mo e de ailed
in o ma ion o each zone.
Figu e 9. Veloci y ields in AnoxAn: (a) eloci y magni ude in anoxic-cla i ica ion ansi ion zone, (b)
e ical eloci y in anoxic-cla i ica ion ansi ion zone, (c) s eamlines in anoxic-cla i ica ion zone (d)
eloci y magni ude in he main anoxic zone, (e) e ical eloci y in he main anoxic zone, ( ) s eamlines
in he main anoxic zone, (g) eloci y magni ude in anae obic-anoxic ansi ion zone, (h) e ical eloci y
in anae obic-anoxic ansi ion zone and (i) s eamlines in anae obic-anoxic ansi ion zone. Expe imen al
condi ions: ωimp = 100 pm, Qin = 10.4 L/h, Qni = 31.0 L/h (COLOURED)
3.3.1. Anoxic-cla i ica ion ansi ion zone
Veloci y ields o he uppe anoxic and cla i ica ion zones which a e sepa a ed by he ba le (in g ey) a e
shown in Fig. 9a-c. The highes eloci y p o iles in ha sec ion a e no ed in he ou le . Simila ly o o he
esea ch (A naldos e al. 2018, Climen e al. 2018, Plascencia-Ja omea e al. 2015), hose high eloci ies
enhance a p e e en ial low channelling h ough i , c ea ing a s agnan zone in he opposi e co ne o he
ou le . In ha zone, nea ze o eloci ies a e obse ed. The a o emen ioned p e e en ial pa h o ma ion is
ep esen ed in Fig. 9c, whe e i is obse ed ha p incipal s eamlines a oid ou le s opposi e co ne . Besides,
he ba le seems no o ha e in luence in he hyd odynamic beha iou . This is a ibu ed o he low eloci y
in his zone, caused by he limi ed in luence o he impelle .
3.3.2. Main anoxic zone
Fig. 9d, Fig. 9e and Fig. 9 show he alues o he magni ude o he eloci y, he e ical eloci y and he
low lines in he main anoxic zone. I can be obse ed ha he eloci y magni ude p o ile (Fig. 9d) in he
di e en XY sec ions ep oduces a low pa e n wi h high o a ionali y as a consequence o he ac ion o
he impelle . I is also obse ed ha he highes alues o he eloci y module a e ound on he sides and in
he cen al pa o he eac o .
As o he e ical componen o he eloci y (Fig. 9e), p e e en ial upwa d low zones a e obse ed nea
he eac o walls, wi h a low channel on he ou side o AnoxAn. The la e is also obse ed in Fig. 9 ,
whe e he low lines desc ibe an upwa d low pa h o med h ough he walls. Consequen ly, mos o he
massi e anspo in he main anoxic zone occu s h ough he eac o walls. As a esul , downwa d low
eloci y p o iles a e ound mainly in he cen al pa o he eac o .
In addi ion, he limi ed in luence o he impelle is shown in Fig. 9d- . Bo h he magni ude o he eloci y
and he e ical alue o he eloci y dec ease wi h he heigh o he eac o . This coincides wi h wha was
obse ed and discussed o he anoxic-cla i ica ion ansi ion zone in Fig. 9a-c. Consequen ly, he zone o
in luence o he impelle ba ely eaches he ba le in he cla i ica ion zone, which implies a delay in he
homogeniza ion o he concen a ion o he anoxic and cla i ica ion zones, as obse ed o RTD3 in sec ion
3.2.
3.3.3. Anae obic-anoxic ansi ion zone
Finally, he magni ude o he eloci y, e ical eloci y and low lines in he olume a ound he de lec o
be ween he anae obic and anoxic zones a e shown in Fig. 9g, Fig. 9h and Fig. 9i espec i ely. The de lec o ,
wi h a wid h o 4 cm om he eac o walls, is ep esen ed in g ey.
As in he main anoxic zone (Fig. 9d), he eloci y magni ude p o ile (Fig. 9g) also ep oduces he o a ional
low pa e ns induced by he impelle . Due o he in luence o he de lec o , i is obse ed ha he highes
alues o he eloci y modulus a e loca ed in he inne pa o he eac o while nea he walls he eloci y
magni ude is lowe .
Fo he e ical componen o he eloci y (Fig. 9h), and due o he in luence o he de lec o , he highes
posi i e alue is clea ly concen a ed in he cen al pa o he eac o , o ming p e e en ial upwa d low
pa e ns in he inne pa o he sec ion. This gene a ion o p e e en ial low pa e ns can also be obse ed
a Plascencia-Ja omea e al 2015. Once he in luence o he impelle on he anoxic olume has been eached,
an upwa d low channel is o med h ough he walls as explained o he main anoxic zone in Fig. 9d- .
As shown in Fig. 9h, he e a e no e ical eloci ies a ound he de lec o , con i ming he p esence o dead
low zones. Simila e ec occu s o sec ional changes in Climen e al. (2018). The la e is ep esen ed in
Fig. 9i, whe e he low lines a oid he ou e co ne s o he de lec o , which imp o es he beha iou o he
s agnan low. In addi ion, downwa d low can be obse ed nea he in e nal walls o he de lec o (Fig. 9h-
i), in he anoxic zone. Al hough hese obse ed eloci y alues a e e y small and no e y signi ican in
his case, depending on he geome y o he eac o hey can con ibu e o c ea ing a downwa d low
channel, causing unwan ed mix u es o con amina ion om he anoxic zone o he anae obic zone.
Figu e 10. Hyd odynamic scheme o AnoxAn. Expe imen al condi ions: ωimp = 100 pm, Qin = 10.4 L/h,
Qni = 31.0 L/h (COLOURED)
All he main phenomena p e iously explained in he hyd odynamic analysis a e esumed in Fig. 10, whe e
g een a ows ep esen main up low zones and he ed ones down low zones. Dashed line zones mean
po en ial s agnan o dead low olumes. The hickness o he da es in he igu e indica es he in ensi y o
he low and he e o e he po en ial mass anspo .
3.4. T ace anspo analysis based on CFD simula ions
T ace concen a ion e olu ion is analysed nex , analysing pulse RTD2 and s ep RTD3 es s o he anoxic-
cla i ica ion ansi ion, main anoxic and anae obic-anoxic ansi ion zones. RTD analysis combined CFD
and eloci y ield analysis o analyze dead olumes and chanelling ha e been al eady used in wa e
ea men ield (B annock e al. 2010a, Climen e al. 2018, Wei e al. 2019).
3.4.1. Anoxic-cla i ica ion ansi ion zone
Figu e 11. T ace concen a ion ield in anoxic-cla i ica ion ansi ion zone o di e en ime s eps in
RTD2 (a) 5 min, (b) 10 min, (c) 15 min, (d) 20 min, (e) 25 min and ( ) 30 min. Expe imen al condi ions:
ωimp = 100 pm, Qin = 10.4 L/h, Qni = 31.0 L/h, C ace = 350 g/L (Pulse ace es , 3s ni a e s eam
injec ion). (COLOURED)
Fig. 11 shows he concen a ion ange o he ace o he di e en ime s eps in he RTD2 pulse es . I is
obse ed ha he ace slowly eaches he e luen ou le . I akes be ween 5 and 10 minu es o each he
cla i ica ion zone due o he limi ed in luence o he impelle in he uppe pa o he anoxic zone. This is
consis en wi h he esul s ob ained in he hyd odynamic analysis o he luid in he eac o .
In addi ion o his and as he simula ion p og esses, he p esence o a p e e en ial low pa e n owa ds he
ou le is obse ed. A g ea e concen a ion o ace is ound a ound he ou le . This pa e n is de eloped
a e 15 minu es o simula ion, con i ming he exis ence o a dead olume in he opposi e co ne o he
ou le , as i was shown in Fig. 9a-c.
Figu e 12. (a) Scheme o ace concen a ion measu emen poin s in anoxic-cla i ica ion ansi ion zone
(dimensions in me e s) and (b) T ace concen a ion e olu ion in he ou le (P1) and i s opposi e co ne
(P2) o RTD2. Expe imen al condi ions: ωimp = 100 pm, Qin = 10.4 L/h, Qni = 31.0 L/h, C ace = 350 g/L
(Pulse ace es , 3s ni a e s eam injec ion).
Fig. 12 shows he e olu ion o he concen a ion o he ace o wo di e en poin s a he exi and i s
opposi e co ne (P1 and P2). Fi s ly, i is obse ed ha he maximum concen a ion alue o he ace a he
exi (P1) is sligh ly highe han ha o i s opposi e co ne (P2). The delay be ween he wo peaks is 2.5
minu es (5% o he o al RTD2 HRT). Al hough P1 is loca ed u he om he ace injec ion poin (PN)
han P2, he ace i s a i es a he ou le due o he channelling zone obse ed in Fig.9a-c and 11c-d and
simila o Climen e al. (2018). The di e ence in ace concen a ion a bo h poin s is less han 5% a e
20.5 minu es o expe imen (44% o o al RTD2 HRT). A e 26 minu es o expe imen , he concen a ion
o he ace in he opposi e co ne (P2) is highe han in he ou pu (P1) o he i s ime, eaching a
maximum o 5% highe a =66 minu es. This con i ms ha ace dilu ion i s happens h ough he
p e e en ial low o med a ound he ou le (P1), gene a ing a zone o s agnan beha iou in i s opposi e
co ne (P2) as shown in Fig. 9a-c and Fig. 11.
3.4.2. Main anoxic zone
Figu e 13. T ace concen a ion ield in main anoxic zone o di e en ime s eps in RTD2 (a) 5 min, (b)
10 min, (c) 15 min and (d) 20 min. Expe imen al condi ions: ωimp = 100 pm, Qin = 10.4 L/h, Qni = 31.0
L/h, C ace = 350 g/L (Pulse ace es , 3s ni a e s eam injec ion). (COLOURED)
Fig. 13 shows he ace concen a ion ields o he di e en ime s eps in he RTD2 pulse es . I is obse ed
ha , i s o all, he main ace anspo exis s in he zones wi h highe uppe eloci y, i.e. he p e e en ial
low channels nea he walls. The la e ma ches wi h he obse ed in eloci y ield analysis o Fig 9d- .
As he simula ion ime p og esses, i is obse ed ha due o a highe e ical eloci y, he ace is i s ly
dilu ed in he men ioned ou e pa o AnoxAn, which is a ibu ed o he ac ion o he impelle . On he
o he hand, he ace emains s agnan in he in e nal pa o he sys em. This is a ibu ed o a e y low
alue o he p e iously obse ed low eloci ies.
Figu e 14. (a) Scheme o ace concen a ion measu emen poin s in main anoxic zone (dimensions in
me e s) and (b) T ace concen a ion e olu ion in he cen al pa (P3) and nea he walls o he eac o
(P4) o RTD2. Expe imen al condi ions: ωimp = 100 pm, Qin = 10.4 L/h, Qni = 31.0 L/h, C ace = 350 g/L
(Pulse ace es , 3s ni a e s eam injec ion).
Fig. 14 shows he e olu ion o he ace concen a ion o he cen al poin s and nea he wall (P3 and P4).
Fi s ly, i is obse ed ha he maximum ace concen a ion alue in P4 is 30% highe han in he in e nal
pa o he eac o (P3), wi h he delay in ime be ween he wo peaks being 5 minu es (10% o he o al
RTD2 HRT). These di e ences in he alue and ime o he ace concen a ion peaks e eal ha he mass
anspo is g ea e h ough he walls (P4) han in he cen al pa o AnoxAn (P3), con i ming he
channelling phenomena obse ed in Fig. 9d- . and Fig. 13 and also no iced o Climen e al. (2018). In
addi ion, i is obse ed ha a di e ence be ween he ace concen a ion o bo h poin s is less han 5% a e
7.5 minu es (16% o he o al RTD2 HRT). A e 9 minu es, he concen a ion o he ace in he cen al
pa (P3) is highe han ha o he walls (P4), eaching a maximum o 10% highe in =58 minu es. This is
due o he p e e en ial low ha is o med h ough he walls. In consequence, dilu ion occu s i s in he
ou e pa o AnoxAn, while in he cen al pa o he eac o a s agnan zone is o med, as also indica ed in
Fig. 9d- and Fig. 13 o he analysis.
3.4.3. Anae obic-anoxic ansi ion zone
Figu e 15. T ace concen a ion ield in anae obic-anoxic ansi ion zone o di e en ime s eps in RTD2
(a) 5 min, (b) 10 min, (c) 15 min and (d) 20 min. Expe imen al condi ions: ωimp = 100 pm, Qin = 10.4
L/h, Qni = 31.0 L/h, C ace = 350 g/L (Pulse ace es , 3s ni a e s eam injec ion). (COLOURED)
The concen a ion ange o he ace o di e en ime s eps in he RTD2 simula ed pulse es is shown in
Fig. 15. Fig. 15c-d clea ly shows he shape o he de lec o in he concen a ion ield. The lowe
concen a ion p o iles a e obse ed in he cen al pa o he eac o , coinciding wi h he highe eloci ies
o low ise. In addi ion, a highe concen a ion o he ace is obse ed in he zones whe e ze o o low
eloci ies a e egis e ed, especially in he zone abo e he de lec o .
This con i ms ha dead olumes and s agnan a eas a e ound in hese sec ions wi h he highes
concen a ion o ace s. Fu he mo e, i shows ha he ace does no each he anae obic zone due o he
p esence o he de lec o , sugges ing ha his elemen is c ucial o achie e he desi ed anoxic-anae obic
hyd aulic sepa a ion as also obse ed o a di e en mul i-en i onmen al eac o in Calde e al. (2013).
Finally, as he ime o he expe imen p og esses, a comple e dilu ion in he eac o is obse ed.
Figu e 16. (a) Scheme o ace concen a ion measu emen poin s in anae obic-anoxic ansi ion zone
(dimensions in me e s) and (b) T ace concen a ion e olu ion in he uppe de lec o zone (P5) and in he
de lec o (P6) o RTD2. Expe imen al condi ions: ωimp = 100 pm, Qin = 10.4 L/h, Qni = 31.0 L/h, C ace =
350 g/L (Pulse ace es , 3s ni a e s eam injec ion).
Fig. 16 shows he e olu ion o he ace concen a ion o wo di e en poin s nea he de lec o (P5 and
P6). Fi s , i is obse ed ha he maximum ace concen a ion alue a P6 is 20% highe han nea he
de lec o (P5). Howe e , almos om he beginning o he expe imen , he ace concen a ion emains a
leas 5% highe a P5 han a P6 un il comple e dilu ion. The la e con i ms ha a s agnan zone is o med
unde he in luence o he de lec o as shown in Fig. 9g-i and Fig. 15.
3.4.4. O e all eac o
Figu e 17. T ace concen a ion ield in AnoxAn o di e en ime s eps in RTD3 (a) 20 min, (b) 40 min,
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