a mosphe e
A icle
Dispe sion Cha ac e is ics o PM10 Pa icles
Iden i ied by Nume ical Simula ion in he Vicini y o
Roads Passing h ough Va ious Types o U ban A eas
Ji i Pospisil 1,* , Ji i Huzlik 2, Roman Licbinsky 2and Michal Spilacek 1
1Ene gy Ins i u e, Facul y o Mechanical Enginee ing, B no Uni e si y o Technology, 61669 B no,
Czech Republic; michal.spilacek@ u b .cz
2
T anspo and En i onmen Depa men , Di ision o Sus ainable T anspo and Road S uc u es Diagnos ics,
T anspo Resea ch Cen e, 63600 B no, Czech Republic; Ji i.Huzlik@cd .cz (J.H.);
oman.licbinsky@cd .cz (R.L.)
*Co espondence: [email p o ec ed].cz
Recei ed: 30 Ma ch 2020; Accep ed: 29 Ap il 2020; Published: 30 Ap il 2020


Abs ac :
The dispe sion o pa icula e ma e emi ed by oad anspo o he icini y o oads is
p edominan ly in luenced by he cha ac e o he ai eloci y ield. The ai low depends on ac o s
such as he speed and di ec ion o he blowing wind, he mo emen o ca s, and he geome ies o he
buildings a ound a oad. Nume ical modeling based on he con ol olume me hod was used in his
s udy o desc ibe he ele an p ocesses closely. De ailed ai eloci y ields we e iden i ied in he
icini y o a s aigh oad su ounded by a ious pa e ns o buil -up u ban land. The e alua ion o he
esul s was gene alized o exponen ial exp essions, a ec ing he dec ease o he mass concen a ion
o ine pa icles wi h he inc easing dis ance om he oad. The ob ained cha ac e is ics o he
mass concen a ion ields exp ess he impac o he building geome ies and con igu a ions on he
dispe sion o pa icula e ma e in o he en i onmen . These cha ac e is ics a e p esen ed o wo
wind speeds, namely, 2 m
·
s
−1
and 4 m
·
s
−1
. Fu he mo e, he cha ac e is ics a e in oduced in ela ion
o h ee wind di ec ions: pe pendicula ly, obliquely, and in pa allel o he oad. The esul s o he
nume ical simula ions a e compa ed wi h hose ob ained ia he in-si u measu emen s, o e i ica ion
o he alidi y o he linea emission sou ce calcula ion.
Keywo ds: pa icles; a ic; dispe sion; PM10; pollu ion
1. In oduc ion
U ban ai is signi ican ly pollu ed by lue gases and ine pa icula es. The main sou ces o hese
pollu an s cons i u e mo o ehicle a ic and local u naces, as well as hea ing sys ems [
1
]. Pollu an s
p oduced by mo o ehicles a e eleased in o he a mosphe e in he immedia e icini y o humans
p esen nea oads, whe he ou doo o in a closed en i onmen such as an adjacen building o a
means o anspo . Al hough ai pollu an emissions gene a ed by combus ion engines ha e been
ma kedly educed in ecen yea s, ca a ic has emained he mos p ominen single cause o ai
pollu ion in u ban cen e s globally, exe ing a c i ical impac on human heal h [
2
]. Such an ad e se
e ec pa ially s ems om long- e m pe sis ence o he pollu an s in g ound-le el laye s o he ai
lowing h ough buil -up u ban a eas; peak mass concen a ion alues a e commonly ound in close
p oximi y o oads and hei in e sec ions [
3
]. S ee canyons ecei e only limi ed amoun s o esh
ai , and his condi ion p og essi ely leads o ising local ambien concen a ions and long pollu an
wash-ou pe iods in buil -up u ban lands. Impo an ly, he e a e also ce ain special scena ios o be
conside ed, including wea he wi h e y low o ze o ai low eloci ies. The o e all nega i e heal h
impac o he pollu ion is exace ba ed by he ac ha he maximum a es o human p esences a
A mosphe e 2020,11, 454; doi:10.3390/a mos11050454 www.mdpi.com/jou nal/a mosphe e
A mosphe e 2020,11, 454 2 o 15
u ban oads a e eached du ing ush hou s, namely, he ime when he highes ai pollu an mass
concen a ions a e usually de ec ed [4].
In his con ex , a en ion has been paid in ecen yea s o pa icula e ma e emissions wi h
diame e s less han 10
µ
m (PM10). Wi h he de elopmen o measu emen echnology and he
s a e o knowledge, a en ion was g adually paid o smalle pa icles. Today, PM2.5 and PM1 mass
concen a ions a e moni o ed in u ban a eas as he s anda d. Czech Hyd ome eo ological Ins i u e
(2018) epo ed ha 61% o ine pa icles iden i ied in u ban a eas a e gene a ed by oad anspo .
Fo desc ip i e pu poses we can poin ou ha combus ion-gene a ed pa icles esul om he
complex physico-chemical ans o ma ions ha cons i u e he combus ion p ocess [5]. Such pa icles
hen shape and a e ca ied in he low o was e gases emi ed om au omobile exhaus pipes.
O he ins ances o pa icula e ma e include ele an p oduc s o b ake, i e, and oadway ab asion
and esuspension o he pa icula es deposi ed ea lie . In all size ca ego ies, he mass concen a ion
o he pa icles ma kedly dec eases wi h inc easing dis ance om he oad [
6
]. The dispe sion in o
he en i onmen is in luenced pa icula ly by he cha ac e o he ai eloci y ield in loca ions nea
he oadside. The ac ual mass concen a ion is hen a ec ed by, among o he aspec s, he pa icula e
deposi ion, esuspension, and in e ac ion wi h solid su aces and ege a ion. By ex ension, concu en ly
wi h hese p ocesses he e occu s pa ial physical changes in he pa icula e ma e due o collisions
be ween and g ow h o he pa icles; on a lesse scale, he pa icula es also unde go chemical and
pho ochemical ans o ma ions.
Me hods sui able o modelling o pollu ion dispe sion we e discussed om he beginning [
7
],
while, a p esen , he indi idual ac o s in luencing he dispe sion o pollu an s p oduced by anspo
a e o mo e in e es . This is caused mainly by he e o o p o ide he mos accu a e in o ma ion abou
he beha io o pollu an s om anspo and o mo e accu a ely es ima e he popula ion exposu e
in he u ban en i onmen . Simula ion o a ic induced dispe sion a a high esolu ion using he
compu a ional luid dynamics so wa e, Fluidi y and a ic simula ion so wa e PTV Vissim was
pe o med odemons a ehowmo ing ehiclescanha easigni ican e ec ons ee le el concen a ion
ields and how la ge ehicles such as buses can also cause acu e high concen a ion e en s a he
oadside [
8
]. In luences o ehicle-induced u bulences on pollu an dispe sions in a s ee canyon was
discussed as well in [
9
]. The s ee mo phology ela ionship wi h ai quali y was desc ibed by he
au ho s o [
10
] based on six i egula eal-wo ld cases selec ed om Ame ica, Eu ope, and China using
compu a ional luid dynamic (CFD) simula ions o assess he en ila ions and pollu an dispe sion
wi hin s ee canyons wi h a pa allel app oaching wind. The esul s showed ha he s ee mo phology
cha ac e is ics, including he s ee wid h, la e al openings, and in e sec ions, a e closely ela ed o
he ai lows in s ee canyons. Di e en ypes o in e sec ions we e assessed as well. The oc agon
in e sec ions we e a o able o ai lowing h ough he la e al openings and imp o ed he channel
lows. The oblique in e sec ions can also g ea ly imp o e he s ee en ila ions, mainly due o he
enhanced ai lows h ough he la e al openings and he inc eased u bulen di usion h ough he
s ee oo s. The e ec o buildings wi h wedge-shaped oo s su ounding u ban s ee canyons on
buoyan wind-d i en pollu an plume dispe sions was p esen ed by Zhang e al. [
11
].
Miao e al. [12]
showed ha s ee canyons’ mo phology and ai humidi y we e wo o he mos impo an ac o s
a ec ing suspended pa icula e ma e concen a ions in u ban s ee canyons. The Meso-NH model
(a mosphe ic non hyd os a ic esea ch model) enhanced wi h an imme sed bounda y me hod (IBM)
is a p omising way o ep esen low in e ac ions wi h buildings (as a 3D shape o buildings) and
o og aphy in a mosphe ic models o u ban applica ions [13].
This pape discusses in de ail he dispe sion o pa icles om a oad in o di e en ly con igu ed
u ban en i onmen s. Modeling ia he con ol olume me hod (compu a ional luid dynamics, CFD)
embodies he mos sui able ool o de ailed iden i ica ion o an ai eloci y ield in u ban a eas.
This so wa e app oach enables he compu a ion p ocess o co e geome ically complex zones (such
as buil -up u ban land) and o cap u e he e ec o ca s a eling along he oad. The ehicles d ag
wi h hem he ai om he immedia e icini y, c ea ing an ai low ha mo es in hei d i ing di ec ion,
A mosphe e 2020,11, 454 3 o 15
and hey gene a e mul iple u bulen o ices ha subs an ially in luence he dispe sion o pa icles in
he egion closely adjacen o he o ices‘ sou ce [
3
]. The ele a ed u bulence hen exe s an impac on
he ai low and i s in e ac ion wi h solid su aces (see Figu e 1).
A mosphe e 2019, 10, x FOR PEER REVIEW 3 o 15
hem he ai om he immedia e icini y, c ea ing an ai low ha mo es in hei d i ing di ec ion,
and hey gene a e mul iple u bulen o ices ha subs an ially in luence he dispe sion o pa icles
in he egion closely adjacen o he o ices‘ sou ce [3]. The ele a ed u bulence hen exe s an impac
on he ai low and i s in e ac ion wi h solid su aces (see Figu e 1).
Figu e 1. The luxes o a ic-gene a ed ine pa icula e ma e .
Wi hin he a icle, compu a ional modeling is employed o moni o he dispe sion o pa icles
om a s aigh sec ion o a oad passing h ough i e di e en ypes o u ban en i onmen s. In each
o hese pa e ns, we conduc ed a pa ame ic s udy e alua ing he in luence o wind speed and wind
di ec ion on pa icle dispe sion in he icini y o he oad. The compu ed mass concen a ion maps
we e gene alized in o 2D- ende ed ela ionships be ween he PM10 mass concen a ions and hei
dis ances om he oad. These esul s will enable a quick analy ical calcula ion o he PM10
concen a ions in u ban a eas geome ically close o he es ed a eas, because he co ec ness o he
inclusion o a linea sou ce o emissions in he nume ical model is c ucial o he subsequen ealis ic
solu ion o he dispe sion o pollu an pa icles. The linea emission sou ce calcula ion will be
alida ed wi h he esul s o in-si u measu emen s a close icini y o he s udied oad.
2. Nume ical Model
2.1. Buil -Up A ea Geome ies
In e ms o o ming he ma hema ical models, he main c i e ion de ining he ac ual choice o
he a eas o be modelled consis ed in selec ing such egions ha , om he pe spec i e o hei
geome ies, a e accu a ely con e ible in o a compu a ional mesh, wi h he smalles possible amoun
o necessa y geome ical simpli ica ions. A majo complemen a y c i e ion was embodied in he
s eady c uising o ehicles on he oads comp ised wi hin he a eas o in e es ; his equi emen a ises
om he s a iona y cha ac e o he de eloped ma hema ical model, whe e he a ic dynamics
would in oduce undesi ed inaccu acies.
The esea ch in ol ed con e ing in o speci ic nume ical models i e classic ypes o buil -up
u ban lands adop ed om a ious loca ions wi hin he ci y o B no (CZ); collec i ely, hese sample
egions occupy an a ea o 1000 × 1000 m
2
. The eal land pa e ns a e subs i u ed wi h a ho izon al
su ace. The cen e o each model a ea is in e sec ed by a s aigh , ou -lane oad ca ying wo-way
a ic, wi h wo lanes in each di ec ion. Real geome y-based buildings a e assumed o be p esen in
he icini y o he oad, and hei posi ions co espond o he eal-wo ld layou ob ained h ough
p ocessing he g ound plan iew con ained in he geode ic su ey map o he ele an u ban dis ic .
P og essi ely, he ollowing nume ical models we e designed ( o he images, see Figu e 2):
• Model a ea #1: An in e sec ion loca ed in an u ban cen e : a c ossing o wo oads ha pass
h ough a buil -up a ea comp ising lines o ou -s o y houses (a conc e e geome y om he
cen al dis ic o B no).
• Model a ea #2: A oad passing h ough a esiden ial a ea wi h single- amily houses; he 10-m-
high uni s a e posi ioned wi h a spacing o 15 m, he g ound plan o each home equals 10 ×
15 m
2
, six houses in a ow o m a egula block o buildings, he e is a 15-m-wide aisle
(pe pendicula o he main oad) sepa a ing indi idual blocks o houses, and 20-m-wide
se ice oads pa allel o he main oad un h ough he u ban a ea e e y wo ows o houses.
Figu e 1. The luxes o a ic-gene a ed ine pa icula e ma e .
Wi hin he a icle, compu a ional modeling is employed o moni o he dispe sion o pa icles
om a s aigh sec ion o a oad passing h ough i e di e en ypes o u ban en i onmen s. In each o
hese pa e ns, we conduc ed a pa ame ic s udy e alua ing he in luence o wind speed and wind
di ec ion on pa icle dispe sion in he icini y o he oad. The compu ed mass concen a ion maps we e
gene alized in o 2D- ende ed ela ionships be ween he PM10 mass concen a ions and hei dis ances
om he oad. These esul s will enable a quick analy ical calcula ion o he PM10 concen a ions
in u ban a eas geome ically close o he es ed a eas, because he co ec ness o he inclusion o a
linea sou ce o emissions in he nume ical model is c ucial o he subsequen ealis ic solu ion o he
dispe sion o pollu an pa icles. The linea emission sou ce calcula ion will be alida ed wi h he
esul s o in-si u measu emen s a close icini y o he s udied oad.
2. Nume ical Model
2.1. Buil -Up A ea Geome ies
In e ms o o ming he ma hema ical models, he main c i e ion de ining he ac ual choice o he
a eas o be modelled consis ed in selec ing such egions ha , om he pe spec i e o hei geome ies,
a e accu a ely con e ible in o a compu a ional mesh, wi h he smalles possible amoun o necessa y
geome ical simpli ica ions. A majo complemen a y c i e ion was embodied in he s eady c uising
o ehicles on he oads comp ised wi hin he a eas o in e es ; his equi emen a ises om he
s a iona y cha ac e o he de eloped ma hema ical model, whe e he a ic dynamics would in oduce
undesi ed inaccu acies.
The esea ch in ol ed con e ing in o speci ic nume ical models i e classic ypes o buil -up
u ban lands adop ed om a ious loca ions wi hin he ci y o B no (CZ); collec i ely, hese sample
egions occupy an a ea o 1000
×
1000 m
2
. The eal land pa e ns a e subs i u ed wi h a ho izon al
su ace. The cen e o each model a ea is in e sec ed by a s aigh , ou -lane oad ca ying wo-way
a ic, wi h wo lanes in each di ec ion. Real geome y-based buildings a e assumed o be p esen
in he icini y o he oad, and hei posi ions co espond o he eal-wo ld layou ob ained h ough
p ocessing he g ound plan iew con ained in he geode ic su ey map o he ele an u ban dis ic .
P og essi ely, he ollowing nume ical models we e designed ( o he images, see Figu e 2):
•
Model a ea #1: An in e sec ion loca ed in an u ban cen e : a c ossing o wo oads ha pass
h ough a buil -up a ea comp ising lines o ou -s o y houses (a conc e e geome y om he
cen al dis ic o B no).
•
Model a ea #2: A oad passing h ough a esiden ial a ea wi h single- amily houses; he 10-m-high
uni s a e posi ioned wi h a spacing o 15 m, he g ound plan o each home equals 10
×
15 m
2
,
six houses in a ow o m a egula block o buildings, he e is a 15-m-wide aisle (pe pendicula o
A mosphe e 2020,11, 454 4 o 15
he main oad) sepa a ing indi idual blocks o houses, and 20-m-wide se ice oads pa allel o
he main oad un h ough he u ban a ea e e y wo ows o houses.
•
Model a ea #3: A oad unning be ween small-size p e ab ica ed houses posi ioned a egula
in e als and ha ing he dimensions o o 20
×
20
×
20 m
2
. The buildings a e a anged in o
sepa a e g oups, each o which con ains h ee closely neighbo ing uni s.
•
Model a ea #4: A oad passing h ough an a ea con aining p e ab ica ed houses con igu ed in o
longi udinally o ien ed 15-m-high blocks ha a e posi ioned a egula in e als o 50 m and
in a iably exhibi he g ound plan dimensions o 17 ×90 m2.
•
Model a ea #5: A oad in a ee space: an almos ideally s aigh oad unning h ough an open
landscape, wi h no ba ie s in he immedia e icini y. This model i em is included o compa e he
buil -up and he open-space pollu an dispe sion scena ios.
A mosphe e 2019, 10, x FOR PEER REVIEW 4 o 15
• Model a ea #3: A oad unning be ween small-size p e ab ica ed houses posi ioned a egula
in e als and ha ing he dimensions o o 20 × 20 × 20 m2. The buildings a e a anged in o
sepa a e g oups, each o which con ains h ee closely neighbo ing uni s.
• Model a ea #4: A oad passing h ough an a ea con aining p e ab ica ed houses con igu ed
in o longi udinally o ien ed 15-m-high blocks ha a e posi ioned a egula in e als o 50 m
and in a iably exhibi he g ound plan dimensions o 17 × 90 m2.
• Model a ea #5: A oad in a ee space: an almos ideally s aigh oad unning h ough an
open landscape, wi h no ba ie s in he immedia e icini y. This model i em is included o
compa e he buil -up and he open-space pollu an dispe sion scena ios.
a) Model a ea #1
b) Model a ea #2
c) Model a ea #3
d) Model a ea #4
e) Model a ea #5
Figu e 2. Visual ep esen a ion o he model a eas and he building geome ies embodied in he
ele an nume ical models.
Figu e 2.
Visual ep esen a ion o he model a eas and he building geome ies embodied in he ele an
nume ical models.
A mosphe e 2020,11, 454 5 o 15
2.2. Ma hema ical Desc ip ion and Bounda y Condi ions
In a s ep-by-s ep, consecu i e manne , compu a ional models we e c ea ed o cap u e accu a ely
he geome ies o he sol ed model a eas. The p ocess in ol ed de ailed modeling o he buildings,
oads, and hei posi ions. The model a ea is illed wi h a compu a ional g id o hexagonal con ol
olumes. The solu ion domain includes he space abo e he oad and all he space ou side he buildings.
Volume elemen s o app oxima ely 0.25 m
3
wi h he sho es elemen side o 0.5 m we e used a he
icini y o he g ound su ace. The size o he olume elemen s illing he space be ween buildings is in
he ange o 1 m
3
o 3 m
3
. Mo e abundan olume elemen s a e used abo e he oo s o he buildings.
Thei size inc eases wi h inc easing heigh abo e he buildings. The canopy laye o he a mosphe e
wi h a heigh o 200 m is included in he solu ion. Con ol olumes o 20 m
3
a e used in he highes ai
laye o he model.
In all cases, he s aigh oad simula ion encompassed he impac o mo ing ca s, his being
a ac o ha ma kedly in luences he ai low abo e and on he sides o he oad. To acili a e he
p ocedu e, we adop ed he me hod p oposed by he au ho s o [
3
]. The e ec o he ehicles was
included ia se ing he esis i e o ce in he olume elemen s passed h ough by he ehicles, as
shown in Equa ion (1).
FD=1
2CDAca ρ∞(Uca −U∞)2(1)
whe e C
D
is he ae odynamic cha ac e is ic o he ca , A
ca
is ca on a ea,
ρ∞
is he ai densi y,
Uca
is
he ca speed, and U∞is he ai eloci y.
Mo eo e , he same e ec was conside ed wi hin he sou ce e m in he o mula desc ibing he
u bulence kine ic ene gy p oduc ion (see Equa ion (2)). As i is known, mo ing objec s induce a
kine ic ene gy o u bulence ha should be added as he addi ional sou ce S
k
o he k-equa ion. F om
di e en s udies [
14
–
16
], i ollows ha u bulence is induced mainly in he wake behind he ehicle.
The e o e, he addi ional sou ce Sk[7] was added only along he ajec o y ha ca s ollow.
Sk=Cc(Uca −U∞)2Qca (2)
whe e C
c
is he model cons an , U
ca
is he ca speed, U
∞
is he ai eloci y, and Q
ca
is he a ic a e in
ca s/s.
Such an app oach seems o embody one o he mos app op ia e op ions o subs i u ing he
ehicula mo ion in a nume ical model ha exploi s a s a iona y compu a ional mesh.
To pe o m he ac ual solu ion, we u ilized he con ol olume me hod, whe e equa ions exp essing
he law o conse a ion o ene gy, mass, and momen um a e sol ed on p ede ined olume elemen s o
he compu a ional mesh. The solu ion was implemen ed o a s eady comp essible ai lux, exploi ing
he k-εRNG u bulence model.
A he inle wall o he compu a ional model, we se he ai eloci y p o ile co esponding o he
es ed wind speed (see Figu e 3). The wind eloci y o he neu ally s able a mosphe e is de e mined
om he equa ion o he loga i hmic wind eloci y p o ile.
u=u0
kln z
z0!(3)
whe e kis he on Ka man cons an (~ 0.4), u
0
is he speci ied ai eloci y a he heigh z
0
, and uis he
ai eloci y a he heigh z. The eloci y p o ile is aken jus om he g ound su ace.
In all o he a eas, he ele an speeds equaled 2 m
·
s
−1
and 4 m
·
s
−1
, in a iably a he heigh
o 10 m abo e he g ound. Using hese speed alues, we p og essi ely di ec ed he wind pa allel,
pe pendicula ly, and obliquely (45
◦
) o he oad. The uppe wall o he nume ical model was assigned
he bounda y condi ion “slip wall”, while he bo om wall, which ep esen ed he g ound, was assigned
“wall wi h ic ion”. The same bounda y condi ion was applied o all o he solid su aces ( oad su ace,
walls, and oo s o buildings). Due o he oughness o he su aces, a bounda y laye is o med along

A mosphe e 2020,11, 454 6 o 15
each su ace. The compu a ional g id is su icien ly de ailed and allows o iden i y ai eloci y ields in
s ee canyons
A mosphe e 2019, 10, x FOR PEER REVIEW 5 o 15
2.2. Ma hema ical Desc ip ion and Bounda y Condi ions
In a s ep-by-s ep, consecu i e manne , compu a ional models we e c ea ed o cap u e accu a ely
he geome ies o he sol ed model a eas. The p ocess in ol ed de ailed modeling o he buildings,
oads, and hei posi ions. The model a ea is illed wi h a compu a ional g id o hexagonal con ol
olumes. The solu ion domain includes he space abo e he oad and all he space ou side he
buildings. Volume elemen s o app oxima ely 0.25 m
3
wi h he sho es elemen side o 0.5 m we e
used a he icini y o he g ound su ace. The size o he olume elemen s illing he space be ween
buildings is in he ange o 1 m
3
o 3 m
3
. Mo e abundan olume elemen s a e used abo e he oo s
o he buildings. Thei size inc eases wi h inc easing heigh abo e he buildings. The canopy laye o
he a mosphe e wi h a heigh o 200 m is included in he solu ion. Con ol olumes o 20 m
3
a e used
in he highes ai laye o he model.
In all cases, he s aigh oad simula ion encompassed he impac o mo ing ca s, his being a
ac o ha ma kedly in luences he ai low abo e and on he sides o he oad. To acili a e he
p ocedu e, we adop ed he me hod p oposed by he au ho s o [3]. The e ec o he ehicles was
included ia se ing he esis i e o ce in he olume elemen s passed h ough by he ehicles, as
shown in Equa ion (1).
𝐹=1
2𝐶
𝐴
𝜌󰇛𝑈 𝑈󰇜 (1)
whe e C
D
is he ae odynamic cha ac e is ic o he ca , A
ca
is ca on a ea, 𝜌 is he ai densi y,
𝑈 is he ca speed, and 𝑈 is he ai eloci y.
Mo eo e , he same e ec was conside ed wi hin he sou ce e m in he o mula desc ibing he
u bulence kine ic ene gy p oduc ion (see Equa ion (2)). As i is known, mo ing objec s induce a
kine ic ene gy o u bulence ha should be added as he addi ional sou ce S
k
o he k-equa ion. F om
di e en s udies [14–16], i ollows ha u bulence is induced mainly in he wake behind he ehicle.
The e o e, he addi ional sou ce S
k
[7] was added only along he ajec o y ha ca s ollow.
𝑆

=𝐶

󰇛𝑈

𝑈

󰇜

𝑄󰇗

(2)
whe e C
c
is he model cons an , U
ca
is he ca speed, U
∞
is he ai eloci y, and Q
ca
is he a ic a e
in ca s/s.
Such an app oach seems o embody one o he mos app op ia e op ions o subs i u ing he
ehicula mo ion in a nume ical model ha exploi s a s a iona y compu a ional mesh.
To pe o m he ac ual solu ion, we u ilized he con ol olume me hod, whe e equa ions
exp essing he law o conse a ion o ene gy, mass, and momen um a e sol ed on p ede ined olume
elemen s o he compu a ional mesh. The solu ion was implemen ed o a s eady comp essible ai
lux, exploi ing he k-

RNG u bulence model.
A he inle wall o he compu a ional model, we se he ai eloci y p o ile co esponding o he
es ed wind speed (see Figu e 3). The wind eloci y o he neu ally s able a mosphe e is de e mined
om he equa ion o he loga i hmic wind eloci y p o ile.
Figu e 3. Schema ic illus a ion o he modeled a ea and he assigned bounda y condi ions.
Figu e 3. Schema ic illus a ion o he modeled a ea and he assigned bounda y condi ions.
The side walls o he compu a ional domain, h ough which he ai lea es he model a ea, we e
desc ibed wi h “ou le ” bounda y condi ions (see Figu e 3).
The physical p ope ies o he ai assumed in he compu a ions equaled hose o an ideal mix u e,
namely, one composed o 88% N
2
and 21% O
2
, wi hou conside ing humidi y. A he inle wall o he
model a ea, a ze o concen a ion o dus pa icles (pa icula e ma e ) was assumed. The compu ed
mass concen a ion maps indica e how he moni o ed oad con ibu es o he ai pollu an concen a ion
wi hin he a ea. All o he modeled a ea’s pa icula es a e gene a ed exclusi ely by he a ic on
he oad. The sou ce o he dus pa icles (pa icula e ma e ) was en e ed as an ai pollu ion line
sou ce posi ioned in he cen e o he moni o ed s aigh oad a he heigh o 0.5 m abo e i s su ace.
Gene ally, in a gi en oad, he dus (pa icula e ma e ) p oduc ion in ensi y depends on he a ic
a e, ca ego ies and weigh o he ehicles, and a eling speeds. Fo he pu poses o he nume ical
models, he pa ame e s a e accoun ed o wi hin he emission ac o . In all o he model a eas sol ed,
he emission ac o pe ehicle co esponded o E =0.25387 g
·
km
−1
(see Table 1), a alue compu ed om
he dynamic composi ion o he sample g oup o ca s obse ed along oad I/42 (B no, Žabo ˇ esk
á
) [
17
].
Wi hin he nume ical model, he dispe sion o ine pa icula es was sol ed ia he Eule ian
app oach. In his con ex , we did no moni o he ajec o ies o indi idual pa icles bu ollowed
wi hin balance equa ions he pa icle mass pe cen ages in he olume elemen s o he compu a ional
mesh. Such a p ocedu e enables he compu a ions o be execu ed signi ican ly mo e quickly and wi h
less in ensi e ha dwa e equi emen s. The deposi ion eloci y o ine pa icles is e y small, o en
smalle han ha o B ownian mo ion; hus, he ine pa icles in he models we e subs i u ed wi h
passi e scala s.
2.3. Nume ical Simula ion Resul s
All o he i e model a eas we e sol ed by using a single compu a ional p ocedu e. In he s aigh
cen al oad, we assumed wo-way a ic o ehicles a eling a 50 km
·
h
−1
, wi h he a ic in ensi y
o 720 ca
·
h
−1
in each di ec ion. U ilizing he S a CD so wa e pla o m, we ob ained he ele an 3D
ields o ai eloci y, s a ic p essu e, and PM10 pa icle mass concen a ion.
Figu e 4displays he compu ed PM10 mass concen a ion ields acqui ed in a ho izon al plane
unning a 1.5 m abo e he g ound; such a heigh co esponds o he human b ea hing le el. The mass
concen a ion ields a e speci ied o he pe pendicula and oblique (45
◦
) wind di ec ions, assuming
he wind speed o 2 m·s−1.
A mosphe e 2020,11, 454 7 o 15
Table 1. De e mina ion o he o al emission ac o o one ca by EMEP me hodology, acco ding o emission s anda ds and uel ype.
Ca Type PV LCV HDV UB Sha e o Ca Types Acco ding o Emission
S anda ds (%)
Fuel Pe ol Diesel Pe ol Diesel Diesel Diesel NG PC LCV HDV UB
Emission s anda ds
PRE ECE 0.0032 0.2164 0.0032 0.2493 0.5671 0.7636 0.0200 0.9 0.3 5.5 0
Eu o 1 0.0032 0.0569 0.0032 0.0903 0.4021 0.3635 0.0100 4.1 2.9 1.3 10.5
Eu o 2 0.0032 0.0467 0.0032 0.0903 0.1772 0.1830 0.0100 9.4 4.5 6.5 15.8
Eu o 3 0.0012 0.0310 0.0012 0.0662 0.2078 0.1817 0.0095 21.6 24.5 30.9 26.3
Eu o 4 0.0012 0.0316 0.0012 0.0356 0.0429 0.0458 0.0095 29.1 49.7 20.9 36.8
Eu o 5 0.0015 0.0027 0.0015 0.0027 0.0527 0.0519 0.0095 29.5 15.8 24.9 5.3
Eu o 6 0.0018 0.00199 0.0018 0.0019 0.0058 0.0051 0.0095 5.4 2.2 10 5.3
Sha e o ca s acco ding
o uel [%] 45.84 54.16 13.52 86.48 100.00 46.67 53.33
Emission Fac o s Weigh ed wi h Sha es o Fuel and Ca Types (g·km−1)
Emission s anda ds
PRE ECE 0.0010 0.0006 0.0312 0.0000
Eu o 1 0.0013 0.0022 0.0052 0.0183
Eu o 2 0.0025 0.0035 0.0115 0.0143
Eu o 3 0.0037 0.0140 0.0642 0.0236
Eu o 4 0.0051 0.0154 0.0089 0.0097
Eu o 5 0.0006 0.0004 0.0131 0.0015
Eu o 6 0.0001 0.0001 0.0005 0.0004 Agg ega e Emission ac o (g·km−1)
Summa y emission
ac o s 0.0146 0.0364 0.1349 0.0680 0.2538
PC—passenge ca s, LCV—ligh comme cial ehicles, HDV—hea y-du y ehicles, and UB—u ban bus., NG—na u al gas, PRE ECE—ca s manu ac u ed be o e 1992.
A mosphe e 2020,11, 454 8 o 15
A mosphe e 2019, 10, x FOR PEER REVIEW 8 o 15
Pe pendicula wind Oblique wind (45°)
Model a ea #1
Model a ea #2
Model a ea #3
Model a ea #4
Model a ea #5
Figu e 4. The PM10 mass concen a ion ields ela ed o he heigh o 1.5 m abo e he g ound o he
wind eloci y 2m·s
−1
pe pendicula and oblique wind di ec ions.
Figu e 4.
The PM10 mass concen a ion ields ela ed o he heigh o 1.5 m abo e he g ound o he
wind eloci y 2m·s−1pe pendicula and oblique wind di ec ions.
A mosphe e 2020,11, 454 9 o 15
The maximum pa icula e mass concen a ions a e de ec ed immedia ely abo e he oad; in i s
nea icini y, he concen a ion a es d op signi ican ly, bu he in ensi y o he decline weakens wi h
inc easing dis ance om he oad. A g ea e dis ances, he ac ual concen a ion is in luenced decisi ely
by ad ec i e anspo o he pa icles. In e es ingly, he p esence o he buildings enables di e se ai
olumes a he g ound-le el laye s o he a mosphe e o blend oge he , hus helping o educe he
highes pa icula e mass concen a ions; a he same ime, howe e , he houses in e e e wi h and slow
down he ai low a he g ound le els. Which o he wo p ocesses e en ually p e ails depends on
he geome ic pa ame e s o pa icula buildings and land su aces. As is ob ious om he esul s in
Figu e 4, smalle -sized houses loca ed wi hin egula in e als om each o he (model a eas #2 and #3)
ma kedly impai he speed o he ai low abo e he g ound; consequen ly, highe pa icula e mass
concen a ions can be obse ed e en a conside able dis ances om he oad. In long, con inuous lines
o houses (model a ea #4), he si ua ion ne e heless di e s, because he pe pendicula ly o ien ed
wind embodies a a o able p econdi ion o as ai mo ion be ween he buildings. The pa icles a e
hen dispe sed in o he en i onmen mo e in ensi ely, and he mass concen a ion dec ease in ensi ies
wi h he g owing dis ance. In he model a ea #1, he compu a ion esul is cha ac e ized by di icul
p edic abili y o he concen a ion ield shape. I is hen appa en ha he con inuous o ma ions o
houses e ain highly concen a ed pa icula es in he s ee canyons; depending on he ins an aneous
ai low di ec ion, he e occu s ips o high-pa icula e concen a ions, which, in he u ban pa e ns,
dispe se only slowly. Mo eo e , he esul s o such a eas canno be gene alized: Geome ically a ypical
egions will always equi e indi idual geome ic modes o acili a e he ac ual solu ion p ocedu es.
The model a ea #5 p o ides esul s ha co espond o he dispe sion o pa icles gene a ed a a s aigh
oad in an open landscape.
3. Gene alizing he Resul s
The a eal mass concen a ion maps displayed in Figu e 4we e u ilized as he sou ce da a,
allowing he esul s o be gene alized o di e en con igu a ions. The mass concen a ion maps
ha co espond o he a ic in ensi y 720 ca
·
h
−1
in each di ec ion, deno ed as he speci ic mass
concen a ion o PM10. To yield he eal PM10 mass concen a ions app op ia e o an a bi a y a ic
densi y, he speci ic concen a ion o PM10 is mul iplied by he a ion o eal and speci ic a ic
in ensi y o he line sou ce. The ollowing p ocessing s ep in ol es he c ea ion o 2D ela ionships
o exp ess he connec ion be ween he ambien mass concen a ion o he PM10 pollu an and he
dis ance om he oad. This pu pose was achie ed by e alua ing he mass concen a ion in slices
pe pendicula o he cen al oad. The ela ionship acqui ed ia he slice wi h he maximum ange
o a signi ican concen a ion o PM10 is deno ed as c
max
; he o he ela ionship was ob ained in he
slice wi h he minimum ange o he concen a ion, deno ed as c
min
. These wo ela ionships hen
de ine he egion o mass concen a ions ha will mos p obably con ain he eal alues o he oad’s
con ibu ion. In Figu e 5, he ela ionships c
max
and c
min
a e exp essed o he pe pendicula and
oblique wind di ec ions. The g aphical ep esen a ion o he ela ionships is complemen ed wi h a
ele an ma hema ical exp ession, deli e ed by u ilizing he exponen ial unc ion
y=a·ebx (4)
whe e xis dis ance om he oad, and he ac o s ais calcula ed by Equa ion (6) and ba e ob ained
om a line ha is a esul o he leas squa ed me hod Equa ion (5):
y=mx +b(5)
a=em(6)