Capacities and limitations of wind tunnel physical experiments on motion and dispersion of different density gas pollutants

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 Jou nal homepage: h p://www.deg uy e .com/ iew/j/ms B ough o you by | Technicka Uni e zi a Os a a Au hen ica ed Download Da e | 5/22/17 12:06 PM MEASUREMENT SCIENCE REVIEW, 17, (2017), No. 2, 53-60 54 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. B ough o you by | Technicka Uni e zi a Os a a Au hen ica ed Download Da e | 5/22/17 12:06 PM MEASUREMENT SCIENCE REVIEW, 17, (2017), No. 2, 53-60 55 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 B ough o you by | Technicka Uni e zi a Os a a Au hen ica ed Download Da e | 5/22/17 12:06 PM MEASUREMENT SCIENCE REVIEW, 17, (2017), No. 2, 53-60 56 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 B ough o you by | Technicka Uni e zi a Os a a Au hen ica ed Download Da e | 5/22/17 12:06 PM MEASUREMENT SCIENCE REVIEW, 17, (2017), No. 2, 53-60 57 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 B ough o you by | Technicka Uni e zi a Os a a Au hen ica ed Download Da e | 5/22/17 12:06 PM 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. B ough o you by | Technicka Uni e zi a Os a a Au hen ica ed Download Da e | 5/22/17 12:06 PM 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. 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