MEASUREMENT SCIENCE REVIEW, 17, (2017), No. 2, 53-60
_________________
DOI: 10.1515/ms -2017-0007
53
Capaci ies and Limi a ions o Wind Tunnel Physical
Expe imen s on Mo ion and Dispe sion o Di e en Densi y
Gas Pollu an s
Ondřej Za ila
1
, Tomáš Blejchař
2
1
Depa men o Fi e P o ec ion, Facul y o Sa e y Enginee ing, VŠB - Technical Uni e si y o Os a a, Lumí o a 13/630,
Os a a - Výško ice, 700 30, Czech Republic, ond ej.za ila@ sb.cz
2
Depa men o Hyd odynamics and Hyd aulic Equipmen , Facul y o Mechanical Enginee ing, VŠB - Technical Uni e si y
o Os a a, 17. lis opadu 15, Os a a – Po uba, 708 33, Czech Republic
The a icle ocuses on he analysis o he possibili ies o model mo ion and dispe sion o plumes o di e en densi y gas pollu an s in low-
speed wind unnels based on he applica ion o physical simila i y c i e ia, in his case he F oude numbe . The analysis o he physical
na u e o he modeled p ocess by he F oude numbe is ocused on he in luence o ai low eloci y, gas pollu an densi y and model scale.
This gi es an idea o limi a ions o his ype o physical expe imen s in ela ion o he modeled eal phenomena. The esul ing s a emen s
and logical links a e exempli ied by a CFD nume ical simula ion o a gi en ask calcula ed in ANSYS Fluen so wa e.
Keywo ds: Physical simila i y, ae odynamic unnel, F oude numbe , CFD, gas pollu an .
1.
I
NTRODUCTION
Ai pollu ion is becoming an inc easingly se ious global
issue. Fac o ies p oduce la ge amoun s o pollu an s ha
damage he en i onmen and ha m human heal h. F om his
poin o iew, p oblems o mo ion and dispe sion o
pollu an s in he a mosphe e ela e no only o
en i onmen al s udies bu also o o he disciplines, such as
sa e y enginee ing.
An unde s anding o he physical p inciples o pollu an s’
mo ion and dispe sion is impo an in o de o de e mine he
impac o ai pollu ion on he en i onmen and humans. This
s udy only deals wi h he physical p inciples o pollu an s’
mo ion and dispe sion. Possible chemical eac ions in he
a mosphe e a e no co e ed.
Fo he pu pose o he s udy, a simple model o a ypical
eal si ua ion was de ined. Physical pa ame e s o he model
we e g adually modi ied o achie e isible changes in
esul s so ha gene al p inciples could be de ined. The
abo e-men ioned demons a ion model ep esen s a chimney
si ua ed in a simple la e ain. Gas pollu an is discha ged
om he chimney and ca ied by lowing ai . Gas pollu an
plume is de ec ed and isualized wi h a nume ical model as
iso-su aces o con ou s o pollu an concen a ions in wo-
dimensional cu planes o h ee-dimensional geome y.
The dependence o he pollu an plume shape, size and
inclina ion on modi ica ion o h ee physical pa ame e s was
in es iga ed. The selec ed pa ame e s included pollu an
densi y, ai low eloci y and model scale.
The esul s a e p esen ed in he o m o ex and
commen ed igu es. ANSYS Fluen 15.0 CFD
(Compu a ional Fluid Dynamics) code was used o
demons a e and isualize all p oblem a ian s (see [1], [2]).
The nume ical model o he pollu an plume mo ion c ea ed
in his so wa e was e i ied by an expe imen conduc ed in
he low-speed wind unnel in he Ae odynamic Labo a o y
o he Academy o Sciences o he Czech Republic in No y
Knin (see [3], [4], [5]). The maximum di e ence be ween
expe imen da a and nume ical simula ion da a se s was one
o de ( o mo e de ails see [6]). One o he aims o he s udy
is also o demons a e ha physical modeling o pollu an
plume mo ion and dispe sion wi h se e ely downscaled
models has i s limi a ions ha should be known and
conside ed o a oid ob aining alse esul s.
2.
S
UBJECT
&
METHODS
A. Physical simila i y
Two phenomena can be conside ed o be simila (despi e
di e en geome ical scales) i h ee ypes o simila i y
ma ch: geome ic, kinema ic, and dynamic. C i e ia o
geome ic simila i y equi e ha he a ios o main
co esponding dimensions on he model and he o iginal
pa e n be cons an . Also, main co esponding angles on he
o iginal pa e n and he model mus be o he same alue.
C i e ia o kinema ic simila i y equi e ha he a ios o
eloci ies a co esponding poin s be he same o bo h he
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o iginal pa e n and he model. C i e ia o dynamic
simila i y equi e ha he a ios o he main o ces a
co esponding poin s be he same o bo h he o iginal
pa e n and he model.
Fo ces can be di ided in o wo g oups: a eal o ces and
olume (weigh ) o ces. A eal o ces include ic ion o ces,
comp ession o ces, and capilla y (su ace) o ces. Volume
(weigh ) o ces include ine ial o ces, g a i y o ces, and
impulse o ces ( esul ing om he change in momen um).
Acco ding o he ype o phenomena, hese o ces can be pu
in o ma hema ical ela ion and c i e ia (numbe s) o
simila i y can be es ablished. In luid mechanics, he
Reynolds numbe , Eule numbe , New on numbe , F oude
numbe , Webe numbe , and Mach numbe a e he mos
widely known c i e ia. Each o hem exp esses a io be ween
wo di e en o ces. In p ac ice, i is no possible o achie e
co espondence be ween he o iginal pa e n and he model
in all c i e ia. The e o e, i is always up o he in es iga o s
who mus use hei knowledge and expe ience o choose he
igh and mos impo an c i e ion (o c i e ia) o he
in es iga ed phenomenon. As a esul , in es iga o s usually
wo k wi h one o wo dominan c i e ia o simila i y [7], [8],
[9].
B. F oude numbe
The F oude numbe exp esses he a io be ween g a i y
o ces and ine ial o ces. G a i y o ces cause e ical
mo emen s o he plume (climbing o descending) and
ine ial o ces cause ho izon al mo emen s o he plume.
The F oude numbe can be he e o e conside ed as a
c i e ion o dynamic simila i y, which should be o he same
alue o bo h he scaled model and he eal pa e n (see [7],
[8], [9]).
The F oude numbe can be de ined as
=
⋅⋅
⋅⋅
=≈
−
−
Vg
S
F
F
F
anpollu
ai ai
anpolluG
ai I
ρ
ρ
2
1
2
321
2
32
lg
lllg
ll
anpollu
ai ai
anpollu
ai ai
⋅⋅
⋅
=
⋅⋅⋅⋅
⋅⋅⋅
=
ρ
ρ
ρ
ρ
(1)
whe e
ai I
F
−
is he ine ial o ce due o he ai ac ing on
pollu an elemen [N],
anpolluG
F
−
is he g a i y o ce
ac ing on pollu an elemen [N],
ai
ρ
is he ai densi y
[kg/m
3
],
anpollu
ρ
is he pollu an densi y [kg/m
3
], S is
he su ace o pollu an elemen ac ed on by he lowing ai
[m
2
],
ai
is he ai low eloci y [m/s],
g
is he g a i y
accele a ion cons an [m/s
2
], V is he olume o pollu an
elemen eleased om he pollu an sou ce pe 1 second
[m
3
],
1
l is he 1
s
cha ac e is ic dimension o he pollu an
sou ce (leng h o pollu an cubic elemen ) [m],
2
l is he 2
nd
cha ac e is ic dimension o he pollu an sou ce (wid h o
pollu an cubic elemen ) [m] and
3
l is he 3
d
cha ac e is ic
dimension o he pollu an sou ce (heigh o pollu an cubic
elemen ) [m].
3
l can be eplaced by
anpollu
ha
ep esen s he eloci y o he pollu an eleased om he
sou ce in e ical di ec ion [m/s].
F
is a dimensionless
cons an [-] whose alue de e mines whe he he ine ial
o ce o he g a i y o ce will domina e in he speci ic
pollu an plume mo ion scena io.
Impo an cha ac e is ics a e illus a ed in Fig.1. Pollu an
elemen was simpli ied in o a ec angula cuboid wi h
dimensions o
1
l,
2
l and
3
l o make p ac ical calcula ions
easie . O cou se, he spou o a eal chimney can be o a
di e en shape, mos commonly ci cula o ellip ical. In his
case, i is ad isable o calcula e he su ace o he spou and
ans o m he shape in o a squa e o a ec angle wi h
dimensions o
1
l and
2
l. The alue o
3
l emains he same
(despi e he shape o he spou ) and is eplaced by he
eloci y wi h which he pollu an lea es he sou ce in
e ical di ec ion
anpollu
.
Fig.1. Ai low ac ion on gas pollu an elemen leaking om he
nozzle (chimney).
I
F
< 1, g a i y o ces a e assumed g ea e han ine ial
o ces. Hence, e ical mo ions (climbing o descending) o
he gas pollu an plume can be expec ed due o di e en
densi ies o he pollu an and he ai . Plumes o ligh gas
pollu an s will end o climb, whe eas plumes o hea y gas
pollu an s will end o descend.
I
F
= 1, g a i y o ces a e assumed equal o ine ial
o ces. Hence, gas pollu an plumes a e ca ied by lowing
ai along wi h mani es ing pa ial e ical mo ions.
I
F
> 1, ine ial o ces a e assumed g ea e han g a i y
o ces. Hence, e ical mo ions o he gas pollu an plume
a e limi ed o nonexis en . The gas pollu an plume is
ca ied by s ong lowing ai , ega dless o he pollu an - ai
densi y di e ence o weigh o he pollu an .
This hi d scena io causes common di icul ies when
planning gas pollu an plume mo ion and dispe sion
expe imen s wi h downscaled models in low-speed wind
unnels. A small dimensions o measu ing sec ions o
common wind unnels and, hus, low scales o models, he
ai low may be oo g ea o allow e ical mo ions o gas
pollu an plumes. P ope condi ions o en canno be assu ed
in such cases.
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C. Calcula ion o ai low eloci y o ine ial and g a i y
o ces main ained in balance (
F
= 1)
Acco ding o (1), he ai low eloci y
ai
in luences he
ine ial o ce
ai I
F
−
ha causes gas pollu an ho izon al
mo ion. I all he o he physical cha ac e is ics a e cons an ,
he ollowing p inciples can be o mula ed: The g ea e is
he ai low eloci y
ai
, he g ea e is he ine ial o ce
ai I
F
−
. The g ea e is he ine ial o ce, he mo e limi ed a e
he pollu an plume e ical mo ions (climbing o
descending).
The ai low eloci y
1=F ,ai
o
F
= 1 (i.e., ine ial
and g a i y o ces a e equal) can be deduced om (1):
=
⋅⋅
⋅⋅
==
=
−
−
Vg
S
F
F
anpollu
F ,ai ai
anpolluG
ai I
ρ
ρ
2
1
1
1
2
1
321
2
132
lg
lllg
ll
anpollu
F ,ai ai
anpollu
F ,ai ai
⋅⋅
⋅
=
⋅⋅⋅⋅
⋅⋅⋅
=
==
ρ
ρ
ρ
ρ
(2)
Thus, he ai low eloci y
1=F ,ai
is
=
⋅⋅
=
=
ai
anpollu
F ,ai
lg
ρ
ρ
1
1
S
Vg
ll
lllg
ai
anpollu
ai
anpollu
⋅
⋅⋅
=
⋅⋅
⋅⋅⋅⋅
=
ρ
ρ
ρ
ρ
32
321
(3)
Howe e , one mus ealize ha he change in ai low
eloci y in luences also ai low ield u bulen
cha ac e is ics. Fo example, u bulen in ensi y is
in luenced when he ai lows a ound solid objec s o in a
complex e ain. In es iga o s mus conside whe he hese
changes ha e a se ious impac on accu acy o he
expe imen o ma hema ical model. This is e y impo an
o modeling gas pollu an mo ion and dispe sion in a
complex geome y (complex e ain) whe e he eal model
o u bulen low ield is he key elemen o he simula ion.
I he ai u bulen low ield is se iously in luenced by he
change in he ai low eloci y, he esul s o he analysis
can be misleading. This app oach is he e o e no sui able
o such cases and a di e en pa ame e o he model mus
be changed.
D. Calcula ion o pollu an densi y o ine ial and g a i y
o ces main ained in balance (
F
= 1)
Acco ding o (1), he pollu an densi y
anpollu
ρ
in luences he g a i y o ce
anpolluG
F
−
ha causes gas
pollu an e ical mo ions (climbing o descending). I all
he o he physical cha ac e is ics a e cons an , he ollowing
p inciples can be o mula ed: I he pollu an densi y
anpollu
ρ
is g ea e han he ai densi y
ai
ρ
, he pollu an
ends o descend (i.e., he gas pollu an plume descends). I
he pollu an densi y
anpollu
ρ
is lowe han he ai densi y
ai
ρ
, he pollu an ends o climb (i.e., he gas pollu an
plume climbs). The g ea e a e he g a i y o ces
anpolluG
F
−
, he mo e signi ican a e he gas pollu an
plume e ical mo emen s (climbing o descending).
The pollu an densi y
1=F , anpollu
ρ
o
F
= 1 (i.e.,
ine ial and g a i y o ces a e equal) can be deduced om
(1):
=
⋅⋅
⋅⋅
==
=−
−
Vg
S
F
F
F , anpollu
ai ai
anpolluG
ai I
1
2
1
ρ
ρ
11
2
3211
2
32
lg
lllg
ll
F , anpollu
ai ai
F , anpollu
ai ai
⋅⋅
⋅
=
⋅⋅⋅⋅
⋅⋅⋅
=
==
ρ
ρ
ρ
ρ
(4)
Thus, he pollu an densi y
1=F , anpollu
ρ
is
=
⋅⋅⋅
⋅⋅⋅
=
⋅
⋅
=
=
321
32
2
1
2
1
lllg
ll
lg
ai ai ai ai
F , anpollu
ρρ
ρ
Vg
S
ai ai
⋅
⋅⋅
=
2
ρ
(5)
A change in pollu an densi y in o de o achie e he
op imum a io be ween ine ial and g a i y o ces would be
o en he ideal solu ion. Howe e , he e is a p oblem. The
densi ies o pollu an s ange wi hin a na ow in e al -
app oxima ely o one o de o magni ude - which is usually
no enough o compensa e he F oude numbe di e ences
esul ing om, e.g., a subs an ial change o he model scale.
A ypical example can be he physical modeling o gas
pollu an plumes in low-speed wind unnels whe e he scale
o he model is a ound 1:1000. In such a case, he e is a need
o change he pollu an densi y 100, o e en 1000 imes,
which is impossible. This is why change in pollu an densi y
can be used o achie e only a small change in he F oude
numbe . These small changes, howe e , may no be
su icien o a success ul execu ion o he expe imen o
nume ical modeling.
The change o he lowing gas densi y could be an
al e na i e solu ion. Fo example, ai could be eplaced by a
di e en gas wi h a di e en alue o densi y. Howe e , his
change in luences u bulen low ield cha ac e is ics, which
may be undesi able.
E. Calcula ion o model scale o ine ial and g a i y o ces
main ained in balance (
F
= 1)
Acco ding o (1), he model scale can be exp essed by
using he alue
1
l ha ep esen s he 1
s
cha ac e is ic
dimension o he pollu an sou ce (i.e., leng h o pollu an
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MEASUREMENT SCIENCE REVIEW, 17, (2017), No. 2, 53-60
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cubic elemen ). The model scale in luences bo h ine ial and
g a i y o ces and changes hei a io. I all he o he
physical cha ac e is ics a e cons an , he ollowing
p inciples can be o mula ed: The g ea e is he model scale,
he g ea e is he in luence o g a i y o ces. The smalle is
he model scale, he g ea e is he in luence o ine ial
o ces. G a i y o ces a e, e.g., g ea e in a model scaled a
1:4 han in one scaled a 1:1000.
The alue o he 1
s
cha ac e is ic dimension o he
pollu an sou ce (leng h o pollu an cubic elemen )
11 =F ,
l
o
F
= 1 (ine ial and g a i y o ces a e equal) can be
deduced om (1):
=
⋅⋅
⋅⋅
==
=
=
−
−
1
2
1
1
F anpollu
ai F ai
anpolluG
ai I
Vg
S
F
F
ρ
ρ
131211
2
1312
===
==
⋅⋅⋅⋅
⋅⋅⋅
=
F ,F ,F , anpollu
ai F ,F ,ai
lllg
ll
ρ
ρ
(6)
o
111
2
1
==−
−
⋅⋅
⋅
==
F ,F , anpollu
ai ai
anpolluG
ai I
lg
F
F
ρ
ρ
(7)
Thus,
11 =F ,
l
is
=
⋅⋅⋅
⋅⋅⋅
=
⋅
⋅
=
==
==
=
1312
1312
2
2
11
F ,F , anpollu
F ,F ,ai ai
anpollu
ai ai
F ,
llg
ll
g
l
ρ
ρ
ρ
ρ
1
1
2
=
=
⋅⋅
⋅⋅
=
F anpollu
F ai ai
Sg
S
ρ
ρ
(8)
The model scale
1
=F
M [ - ] o
F
= 1 (ine ial and
g a i y o ces a e equal) is gi en by
X
M
F
1
1
=
=
(9)
whe e
11
1
=
=
F ,
l
l
X
(10)
The alue
1
l ep esen s he 1
s
cha ac e is ic dimension o
he pollu an sou ce (leng h o pollu an cubic elemen ) in
he o iginal model. The alue
11 =F ,
l
is he 1
s
cha ac e is ic
dimension o he pollu an sou ce in he model whe e
F
= 1 (i.e., ine ial and g a i y o ces a e equal).
2
2
1
II
FXF
⋅=
(11)
The alue
1I
F
is an ine ial o ce o o iginal pollu an
cubic elemen and
2I
F
is an ine ial o ce o scaled
pollu an cubic elemen . I he model scale is changed, he
change o he ine ial o ce is gi en by
2
3
1GG
FXF
⋅=
(12)
The alue
1G
F
is a g a i y o ce o o iginal pollu an cubic
elemen and
2G
F
is a g a i y o ce o scaled pollu an cubic
elemen . The alue
X
is a model scale ac o [-]. I
X
> 1,
he model is smalle han i s o iginal pa e n (i.e., he model
is downscaled). I
X
< 1, he model is la ge han i s
o iginal pa e n (i.e., he model is enla ged). Equa ions (11)
and (12) a e deduced om (1) o he F oude numbe .
A change in model scale always causes a change in he
a io o ine ial and g a i y o ces. The e o e, some
p oblems canno be eliably modeled a o he han
app oxima ely o iginal scales. The ange o de ia ion om
he o iginal depends on he disc e ion o in es iga o s.
In es iga o s mus decide whe he he ole ance o esul s is
accep able.
Modeling o gas pollu an plume mo ions wi h se e ely
downscaled models is a ypical example o his p oblem.
Downscaled pollu an plume models will no co espond o
he o iginally scaled pa e ns wi hou modi ying some key
physical cha ac e is ics (ai low eloci y, u bulen
cha ac e is ics, e c.).
The p oblem can be sol ed by using a nume ical
ma hema ical model e i ied by a clea ly de ined
expe imen o he same ype o physical phenomenon. Once
he nume ical model is e i ied, i can be used o nume ical
simula ion o any p oblem o he same physical p inciples,
wha e e he model scale is. Some imes i is impossible o
do he same wi h a physical expe imen .
I can be concluded ha se e ely downscaled expe imen s
a e no sui able o modeling gas pollu an plume mo ions
because o possible absence o e ical mo emen s. I is
mo e ad isable o use physical expe imen da a only o
e i ica ion o he nume ical model (code, so wa e).
F. Example o CFD nume ical simula ion
ANSYS Fluen 15.0, one o he wo ld’s mos sophis ica ed
CFD codes, was chosen o he nume ical simula ion o he
gas pollu an plume mo ion and dispe sion. The gauging
sec ion o he low-speed wind unnel (leng h 2 m, wid h
1.5 m, heigh 1.5 m, model scale 1:1000) wi h a small
nozzle (diame e 0.0035 m, heigh 0.02 m, scale 1:1000)
ep esen ing a chimney in a la , simple e ain was he
objec o he nume ical simula ion. Gas pollu an en e s he
gauging sec ion h ough he op o he nozzle (chimney) and
is ca ied by lowing ai (see Fig.2.).
RANS (Reynolds-a e aged Na ie -S okes equa ions)
app oach was used o u bulen cha ac e is ics de ini ion.
The Boussinesq hypo hesis o swi l u bulen iscosi y was
applied o he u bulen iscosi y calcula ion. RNG
ε
−
k
model o u bulence was used o he ai low ield basic
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calcula ion (see [1], [2]). Species anspo model was used
o he species mo ion calcula ion. Bo h models wo ked
simul aneously. No addi ional gas pollu an dispe sion
model was applied. The ope a ing p essu e was se a
101 325 Pa, he ope a ing empe a u e was 300 K, and he
g a i y accele a ion was -9.81 m/s
2
in he geome y.
Conside ing he pollu an sou ce close su oundings, he
anges o he Reynolds numbe Re we e 250-1250 [-]
(model scale 1:1000, e e en ial ai low eloci y 1-5 m/s,
and nozzle spou diame e 0.0035 m) and 250000-1250000
[-] (model scale 1:1, e e en ial ai low eloci y 1-5 m/s,
and chimney spou diame e 3.5 m).
Fig.2. Geome y (gauging sec ion o he low-speed wind unnel)
and pollu an sou ce (nume ical model e sus physical
expe imen ).
Bounda y condi ions we e se o Veloci y Inle a he inle ,
Ou low a he ou le , Wall o he loo , Symme y o he
walls, Wall o pollu an sou ce walls, and Veloci y Inle o
he nozzle (spou o he chimney).
P o iles o he low ield physical cha ac e is ics we e
de e mined a he inle o he geome y (see Table
1.) based
on expe imen al da a om a low-speed wind unnel o a
1:1000-scale model (see [3], [4], [5], [6], [11]). Fo o he
model scales, he p o iles we e modi ied o keep he end o
cu es.
In Table 1. he pa ame e
x
ep esen s he ai low
eloci y in he di ec ion o X-axis [m/s],
I
is he in ensi y
o u bulence [%],
Y
is he e ical coo dina e o he
geome y [m], k is he u bulen kine ic ene gy [m
2
/s
2
], and
ε
is he u bulen dissipa ion a e [m
2
/s
3
].
The pollu an sou ce was designed as a nozzle (chimney).
Fo all model scales, he pollu an eloci y
anpollu
was se
a 0.5 m/s, he in ensi y o u bulence in he pollu an sou ce
a 10 %, he pollu an mass ac ion in he pollu an sou ce a
0.95 [-] and he ai mass ac ion in he pollu an sou ce a
0.05 [-]. The hyd aulic diame e o he pollu an sou ce was
se a 3.5 m o 1:1-scale model, 0.866 m o 1:4.04-scale
model, 0.0986 m o 1:35.51-scale model, 0.344 m o
1:101.821-scale model, and 0.0035 m o 1:1000-scale
model scale 1:1000.
Table 1. Ai low eloci y p o ile and u bulen cha ac e is ics
p o iles in geome y [3], [4], [5], [11].
Ve ical
p o ile
Equa ion
Ai low
eloci y
(X-di ec .)
(
)
3571100327023710
..Yln.
x
+
+
⋅
=
Ai
u bulen
in ensi y
(
)
1405000327006730 ..Yln.I
+
+
⋅
−
=
Tu bulen
kine ic
ene gy
(
)
2
51 I .k
x
⋅⋅=
Tu bulen
dissipa ion
a e
(
)
4
1
0902251
3
.
k.. ⋅⋅
=
ε
Th ee di e en pollu an s we e chosen o be es ed:
helium, me hanol and 1,2-dichlo e hane. Helium (
ρ
=
0.1625 kg/m
3
) has a lowe densi y han ai , i.e., i is ligh e
han ai (
ρ
= 1.225 kg/m
3
). Me hanol (
ρ
= 1.43 kg/m
3
) has
app oxima ely he same densi y as ai , i.e., i is
app oxima ely o he same weigh as ai . 1,2-dichlo e hane
(
ρ
= 4.1855 kg/m
3
) has a g ea e densi y han ai , i.e., i is
hea ie han ai . Plumes o pollu an s ligh e han ai end o
climb, whe eas hose hea ie han ai end o descend.
Howe e , his is no always he case. Pollu an plume
e ical mo emen s can be in luenced by se e al o he
physical ac o s as demons a ed in he analysis.
3.
R
ESULTS
The esul s can be di e en ia ed in h ee ca ego ies
p esen ed below.
A. Analysis o esul s by ai low eloci y
The aim o his analysis is o compa e gas pollu an plume
shapes and mo ions o h ee di e en gas pollu an s
(helium, me hanol and 1,2-dichlo e hane) a di e en alues
o he ai low eloci y
ai
. The demons a ion o he
p oblem was pe o med wi h a 1:1-scale h ee-dimensional
geome y ep esen ing he eal pa e n o a simple e ain
wi h a chimney. The e e en ial ai low eloci ies
ai
a
he le el o he chimney spou (pollu an sou ce) we e 1 m/s,
3 m/s and 5 m/s.
Resul s we e calcula ed using he ANSYS Fluen 15.0
so wa e and we e isualized in Fig.3. The con ou s we e
plo ed in wo-dimensional planes o he geome y, sc., he
cen al e ical longi udinal plane, he loo (g ound) plane,
and he ou le plane.
The igu e shows ha wi h inc easing ai low eloci y
ai
he pollu an plume e ical mo emen s a e educed.
The pollu an plume inclines ho izon ally a he le el o he
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MEASUREMENT SCIENCE REVIEW, 17, (2017), No. 2, 53-60
58
chimney spou (pollu an sou ce) showing no endency o
climb o descend. This is because he ine ial o ce
ai I
F
−
inc eases as he ai low eloci y
ai
inc eases.
Hence, he pollu an plume e ical mo emen s a e educed
o o ally elimina ed.
Fig.3. Gas pollu an plume mo ion analysis by ai low eloci y
and pollu an densi y (iso-su aces o gaseous helium, me hanol,
and 1,2-dichlo e hane concen a ions wi h mass ac ion o 0.0001
[-] o one model scale).
The ai low eloci y also in luences he size and shape o
he pollu an plume. Wi h inc easing ai low eloci y
ai
he pollu an plume ends o be na owe and longe .
Howe e , a u he inc ease in he ai low eloci y makes
he pollu an plume sho e because o g ea e a e o he
pollu an dispe sion. The plume ange a ce ain
concen a ion o he pollu an he e o e dec eases wi h
inc easing ai low eloci y.
B. Analysis o esul s by pollu an densi y
The aim o his analysis is o compa e gas pollu an plume
shapes and mo ions o h ee di e en gas pollu an s
(helium, me hanol and 1,2-dichlo e hane) a di e en alues
o hei densi y. Demons a ion o he p oblem was
pe o med wi h a 1:1-scale h ee-dimensional geome y
ep esen ing he eal pa e n o a simple e ain wi h a
chimney. The e e en ial ai low eloci y
ai
a he le el
o he chimney spou (pollu an sou ce) was 1 m/s.
Resul s we e calcula ed using he ANSYS Fluen 15.0
so wa e and we e isualized in Fig.3. The con ou s we e
plo ed in wo-dimensional planes o he geome y, sc., he
cen al e ical longi udinal plane, he loo (g ound) plane,
and he ou le plane.
The igu e shows ha : I he pollu an densi y
anpollu
ρ
is lowe han he ai densi y
ai
ρ
he gas pollu an plume
ends o climb ( o helium see Fig.3.). I he pollu an
densi y
anpollu
ρ
is app oxima ely he same as he ai
densi y
ai
ρ
he gas pollu an plume nei he climbs no
descends ( o me hanol see Fig.3.). I he pollu an densi y
anpollu
ρ
is g ea e han he ai densi y
ai
ρ
he gas
pollu an plume ends o descend ( o 1,2-dichlo e hane see
Fig.3.). The ange o e ical mo emen s is de e mined by
g a i y o ce
anpolluG
F
−
ha in luences pollu an plume a
gi en condi ions. The g ea e he g a i y o ce
anpolluG
F
−
is compa ed o he ine ial o ce
ai I
F
−
, he mo e signi ican
is he e ical mo emen o he plume, i.e., ligh pollu an
plume climbs and hea y pollu an plume descends.
The pollu an densi y
anpollu
ρ
also in luences he
pollu an plume dispe sion. The g ea e is he pollu an
densi y, he longe is he ange o he plume. A gi en ai
low eloci y
ai
, he plume dispe sion o pollu an s wi h a
low densi y is as e and easie han ha o pollu an s wi h a
g ea e densi y.
C. Analysis o esul s by model scale
The aim o his analysis is o compa e gas pollu an plume
shapes and mo ions o h ee di e en gas pollu an s
(helium, me hanol, and 1,2-dichlo e hane) a di e en model
scales. The demons a ion o he p oblem was pe o med
wi h a h ee-dimensional geome y a h ee selec ed scales
o each o he h ee pollu an s. The i s 1:1-scale model
ep esen s he eal pa e n o a simple e ain wi h a chimney
(pollu an sou ce) whe e
F
< 1, i.e., he g a i y o ce
anpolluG
F
−
is g ea e han he ine ial o ce
ai I
F
−
. The
second model (scaled a 1:4.04, 1:35.51, and 101.82,
espec i ely) ep esen s he s a e when
F
= 1, i.e., he
g a i y o ce
anpolluG
F
−
equals he ine ial o ce
ai I
F
−
.
The hi d 1:1000-scale model ep esen s he gauging sec ion
o a low-speed wind unnel wi h a nozzle (pollu an sou ce)
on he loo whe e
F
> 1, i.e., he ine ial o ce
ai I
F
−
is
g ea e han he g a i y o ce
anpolluG
F
−
. The e e en ial
ai low eloci y
ai
a he le el o he chimney spou
(pollu an sou ce) was 1 m/s.
Resul s we e calcula ed using he ANSYS Fluen 15.0
so wa e and we e isualized in Fig.4. Con ou s we e
plo ed in wo-dimensional planes o he geome y, sc. he
cen al e ical longi udinal plane, he loo (g ound) plane,
and he ou le plane.
The igu e shows ha : I he model scale changes and all
o he cha ac e is ics emain unchanged, he ine ial and
g a i y o ces and hei a io change oo. The e o e, he size,
shape, and inclina ion o he pollu an plume change.
Acco ding o (11), he ine ial o ce is p opo ional o he
squa e o he model scale. Acco ding o (12), he g a i y
o ce is p opo ional o he hi d powe o he model scale.
The e o e, he change in he g a i y o ce due o he change
o he model scale is conside ably g ea e han he change in
he ine ial o ce. The lowe is he model scale, he g ea e is
he dominance o ine ial o ces compa ed o g a i y o ces,
and ice e sa.
Also, he g ea e he pollu an densi y, he lowe he model
scale i
F
= 1, i.e., he ine ial and g a i y o ces a e equal.
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MEASUREMENT SCIENCE REVIEW, 17, (2017), No. 2, 53-60
59
Fig.4. Gas pollu an plume mo ion analysis by model scale (iso-
su aces o gaseous helium, me hanol, and 1,2-dichlo e hane
concen a ions wi h mass ac ion o 0.0001 [-] o h ee di e en
model scales).
4.
D
ISCUSSION
/
CONCLUSIONS
The aim o he analyses was o lay down p inciples o
physical and ma hema ical modeling o gas pollu an plume
mo ion and dispe sion in eal a mosphe ic condi ions. The
in luences o he ai low eloci y, pollu an ’s densi y, and
model scale on pollu an plume size, shape, and inclina ion
we e in es iga ed.
The F oude numbe was chosen as a c i e ion o physical
simila i y o he pollu an plume beha io in he
a mosphe e. Basic ma hema ical ules and p inciples we e
o mula ed upon s udy o a ailable luid mechanics
li e a u e (see [7], [8], [9], [10], [11], [12], [13], [14]). Nex ,
all ma hema ical and physical assump ions we e e i ied by
nume ical simula ion using he ANSYS Fluen 15.0
so wa e. Ai low ield was modeled using he RNG
ε
−
k
model o u bulence, he gas pollu an mo ion was modeled
using he Species T anspo Model, bo h in he same h ee-
dimensional geome y consis ing o 569 490 g id cells.
Tu bulen cha ac e is ics we e de ined using RANS
app oach. No addi ional dispe sion model was applied.
Objec o modelling was gauging sec ion o he low-speed
wind unnel ( o model scale o 1:1000) o big eal e ain
( o model scale o 1:1) wi h a pollu an sou ce in he o m
o a nozzle (o chimney, espec i ely) si ua ed on he sec ion
loo (g ound). The gauging sec ion wi h he nozzle
ep esen ed a chimney in a simple, la e ain. The chimney
was conside ed o be a pollu an sou ce o h ee di e en
gas pollu an s (helium, me hanol, and 1,2-dichlo e hane).
The nume ical simula ion was pe o med o i e model
scales, h ee gas pollu an s wi h di e en densi ies, and h ee
di e en ai low eloci ies. The simula ions we e s eady
( ime-independen ) wi h he accu acy o 0.0001 (c i e ion o
con e gence). Final esul s we e isualized as pollu an
concen a ion ields wi h he concen a ion limi alue o
0.001. The con ou s we e plo ed in wo-dimensional planes
o he geome y, sc. he cen al e ical longi udinal plane,
he loo (g ound) plane, and he ou le plane. The nume ical
model had been e i ied by an expe imen pe o med in a
low-speed wind unnel (see [3], [4], [5]).
The ollowing p inciples based on he esul s o he F oude
numbe analysis o pollu an plume mo ion and dispe sion in
eal a mosphe e can be de ined:
1) The g ea e is he ai low eloci y, he g ea e a e he
ine ial o ces. These o ces in luence pollu an plume and
educe i s e ical mo ions (inclina ion). Wi h inc easing ai
low eloci y, he pollu an plume inclines ho izon ally a
he le el o he chimney spou (pollu an sou ce), bu wi h
u he inc ease in he ai low eloci y i becomes na owe
and sho e .
2) The g ea e is he di e ence be ween pollu an densi y
and ai densi y, he mo e signi ican is he endency owa ds
e ical mo emen s (climbing o descending) o he plume.
The plume o pollu an wi h lowe densi y han ai ends o
climb, whe eas he plume o pollu an wi h g ea e densi y
han ai ends o descend. The densi y o he pollu an also
in luences he pollu an plume dispe sion. The g ea e is he
pollu an densi y, he longe is he ange o he plume. A
gi en ai low eloci y
ai
, he plume dispe sion o
pollu an s wi h a low densi y is as e and easie han ha o
pollu an s wi h a g ea e densi y.
3) I he model scale changes and all o he cha ac e is ics
emain unchanged, he ine ial and g a i y o ces and hei
a io change oo. The e o e, he size, shape and inclina ion
o he pollu an plume change. The ine ial o ce is
p opo ional o he squa e o he model scale, whe eas he
g a i y o ce is p opo ional o he hi d powe o he model
scale. The change in he g a i y o ce due o he change o
model scale is conside ably g ea e han he change in he
ine ial o ce. The lowe is he model scale, he g ea e is he
dominance o ine ial o ces compa ed o g a i y o ces.
Also, he g ea e is he pollu an densi y, he lowe is he
model scale i
F
= 1, i.e., he ine ial and g a i y o ces a e
equal.
7.
C
ONCLUSION
F om he abo e i ollows ha i in es iga o s wan o
espec and ollow he basics o physical phenomena, hey
mus conside c i e ia o physical simila i y e y ca e ully,
in pa icula c i e ia o dynamic simila i y. Some physical
phenomena, howe e , canno be modeled in any model scale
bu he o iginal one wi hou changing he basis o he
phenomena.
This analysis is in ended o hose who a e in e es ed in
gas pollu an plume mo ion in he a mosphe e and in heo y
o physical simila i y. The conclusions o he analysis can
be used o u he expe imen design wo ks o o checking
esul s o ma hema ical modeling.
A
CKNOWLEDGMENT
Au ho s acknowledge he inancial suppo o he SPII
1a10 45/07 p ojec o he Minis y o he En i onmen o he
Czech Republic.
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60
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