Strojni{ki vestnik 47(2001)5, Journal of Mechanical Engineering 47(2001)5, ISSN ISSN UDK : /.83:

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1 Strojn{k estnk 47(2001)5, Journal of Mechancal Engneerng 47(2001)5, ISSN ISSN UDK : /.83: UDC : /.83: J. Predhodna Lkar - J. objaa ^ade`: (1.03) Alternatna metoda za dolo~eanje - Alternate Method Prelmnary for Determne paper (1.03) Druga~na metoda dolo~eanja koncentracj plno zaprth prostoro odsnost od ~asa Alternate Method for Determne Concentraton of Gases n Enclosed Structures as a Functon of Tme Jakob Lkar - Jure ^ade` V prspeku je predlagan drugaèen postopek projektranja prezraèealnh sstemo zaprth n deloma zaprth podzemnh prostorh, kjer se pokaže potreba po bolj podrobnh analzah. Podane so teoretène osnoe n podroèja uporabe. Za prkaz prednost takšnega postopka je opraljen zraèun gbanja onesnaženega zraka zaprtem prostoru odsnost od èasa Strojnšk estnk. Vse prace prdržane. (Kljuène besede: prostor zaprt, zrak onesnažen, prezraèeanje, koncentracje plno) Ths paper proposes an alternate approach to the entlaton desgn of enclosed and half enclosed underground structures, where more detaled analyss s requred. Theoretcal bascs are represented and the area of applcaton s determned. To show the adantage of such approach a calculaton of moement of exhausted ar through enclosed structure as functon of tme has been executed Journal of Mechancal Engneerng. All rghts resered. (Keywords: enclosed structures, polluted ar, entlaton, gas concentraton) 0 UVOD Pr gradnj n obratoanju podzemnh prostoro, npr. predoro, podzemnh garaž, rudnko tn., pomen projektranje prezraèeanja podzemnh prostoro elk zz. Prezraèealn sstem doajajo sež zrak n odajajo onesnaženega. Pr zkopu predoro n prdobanju rude rudnkh je zrak onesnažen z deh ro. Pr r sta ogljko doksd n monoksd, k nastajata pr deloanju motorje z notranjm zgoreanjem. Hrbna al zemljna, kater se zaja zkop, sebuje plne, kakršna sta metan al ogljko doksd. Mešanca metana n zraka je pr koncentracjah med 4 n 15 % metana eksplozna, zato mora bt ta praoèasno odeden s podroèja odkopaanja. V podzemnh garažah je zrak onesnažen samo z prega ra. Prezraèealn sstem ustarja tok zraka, k odaja onesnažen zrak s podroèja zkopaanja, al drugem prmeru, s podroèja prometa podzemnh garažah. V koth prostoro ozroma mesth, kjer 0 INTRODUCTION In the constructon of enclosed and halfenclosed structures, such as tunnels, underground car-parks, mnes etc., the desgn of the entlaton system presents a consderable challenge. In ths knd of structure mechancal entlaton systems are nstalled to supply fresh ar and to remoe the polluted ar. Durng the excaaton of tunnels and the extracton of ore from mnes the ar s polluted for two reasons. The frst s the carbon monoxde and doxde that comes from the exhausts of machnes or ehcles wth nternal combuston engnes. The second s that the rock or sol often contan gases such as methane and carbon doxde. When mxed wth ar n the concentraton range of 4 to 15 % methane s explose and must be remoed from the area of excaaton. In underground car parks, of course, the ar s polluted only for the frst reason. The entlaton system produces an arflow, whch remoes the polluted ar from the doman of excaaton or, n the other case, from the doman of the traffc. In the corners of underground structures stran 192

2 prezraèeanje n uènkoto, lahko nastane obmoèje elke koncentracje onesnaženega zraka; še posebej je nearen metan, k je, pomešan z zrakom, eksplozen. Predps na podroèju prezraèeanja upošteajo najeèjo n popreène rednost koncentracje plno zaprth n polzaprth prostorh, na podlag katerh so projektran prezraèealn sstem. Pra tako je naadno predpsana najmanjša potrebna kolèna zraka. V prej naedenh prmerh projektranje entlacje po teh krterjh ne obaruje delace n uporabnko podzemnh garaž pred škodljm pl. V teh prmerh je treba zest dodatne analze. V tem prspeku predlagamo alternatno metodo projektranja prezraèeanja, k omogoèa bolj podrobno analzo dogajanja n omogoèa spremljanje koncentracj onesnažealnko odsnost od èasa. 1 TEORETIÈNE OSNOVE or places where entlaton s neffecte, a hgh concentraton of polluted ar can occur. Ths s especally dangerous n the case of methane, whch s explose when mxed wth ar. In general, a entlaton system s desgned wth the crtera of maxmum and aerage concentratons of gases n enclosed and half enclosed underground structures taken nto consderaton. The mnmum olume of fresh ar s determned as well. In the specal cases mentoned aboe, basng the sze of the entlaton system on those crtera does not preent workers or passengers from beng exposed to danger: the problem must be explored n greater detal. In ths artcle we propose an alternate method for determnng the dmensons of a entlaton system, whch allows a detaled analyss of the problem and shows the change n the concentraton of pollutants as a functon of tme. 1 THEORETICAL CONSIDERATION Koncentracja plno nekem prostoru je odsna od naslednjh parametro: - lege ra plna, - zdatnost ra plna, - lege ra sežega zraka, - kolène sežega zraka, - elkost prostora. Èe razdelmo prostor na posamezne dele al cone (nadzorne prostornne, sl. 1), lahko za sako cono zapšemo masno blanco, kakor je naedeno enaèb 1 ([1] n [5]): () t V j - prostrnna cone, C j - koncentracja plna posamezn con, C j - dotok zraka z doloèeno koncentracjo plna z sosednjh con, C j - odtok zraka z doloèeno koncentracjo plna sosednje cone, S(t) j dcj r. V. = C () t - C () t + S( t) dt j j j j Generally, the concentraton of gases depends on the followng parameters: - poston of the gas source - emsson rate of gas source - poston of the fresh-ar ntake - olume of fresh ar - olume of the structure If we dde the underground space nto a number of zones (control olumes, see Fgure 1), the mass balance for each zone can be represented as follows ([1] and [5]): (1), V j - olume of zone, C j - concentraton of gas n current zone, C j - ncomng ar wth concentraton of gas from connected zones, C j - outgong ar to the connected zones, S(t) j - emsson rate of gas, Q j - ncomng E ( -1,j+1) E (,j+1) Q (,j+1) Q (,j+1) E ( +1,j+1) E ( -1,j) Q ( -1,j) Q ( -1,j) E (,j) Q ( +1,j) Q ( +1,j) E ( +1,j) E ( -1,j-1) Q (,j-1) E (,j-1) Q (,j-1) E ( +1,j-1) Sl. 1. Masna blanca za cono, j Fg. 1. Mass balance for zone, j stran 193

3 - emsja plna, Q j - dotok zraka z sosednjh con, Q j - odtok zraka sosednje cone,,j - ndeks. Enaèbe koncentracj plno, k stopajo al zstopajo z posamezne cone, so: olume of ar from connected zones, Q j - outgong olume of ar to the connected zones,,j - ndex. The expresson for the gas concentratons that enters or leaes a zone: C t Q C t Q C t Q C t Q C t j -1, j - 1, j + 1, j + 1, j, j-1, j- 1, j+ 1, j+ 1 () =. () +. () +. () +. () () =. () +. () +. () +. () C t Q C t Q C t Q C t Q C t j, j - 1, j, j + 1, j, j, j- 1, j, j+ 1 (2) (3). Sstem naadnh dferencalnh enaèb prega reda je tako doloèen. Enaèbe je mogoèe rešt ob defncj ustreznh robnh pogoje n poznaanju pretoka zraka prek robo posamezne cone. Robn pogoj za posamezen element so koncentracje plna èasu nè (zaèetna koncentracja). Gbanje zraka skoz zaprt prostor je mogoèe doloèt s program, k se uporabljajo za analze s podroèja dnamke tekoèn n slonjo na numerènh metodah. V tem prmeru je bl uporabljen program ANSYS (FLOTRAN), zraèun pa je bl napsan na Fakultet za strojnšto Ljubljan. Rezultat analze je polje htrost zraka, k jh program zraèuna za ogljšèa sakega elementa posebej. Vektorj htrost so prenesen program MATHEMATICA,. 2.2, kjer je bla zraèunana popreèna htrost zraka prek robo sakega elementa. Pretok zraka prek robo elemento za sak element posebej je mogoèe doloèt s poznaanjem dolžne strance sakega elementa n popreène htrost zraka prek nje. Lego ra sežega zraka je treba doloèt numerèn analz, pr zraèunu koncentracj pa je treba doloèt še lego ra plna n emsjo plna posamezn con. Sstem dferencalnh enaèb n analtèno rešlj, ampak samo numerèno. Rezultat zraèuna je koncentracja plna sak con odsnost od èasa. Za rešeanje elkh sstemo dferencalnh enaèb potrebujemo posebne programe n zmoglje raèunalnke. Za zdaj je za razumljo manjše štelo con mogoèe zraèunat koncentracjo plna za nekaj mnut. Vs zraèun so bl opraljen s programom MATHEMATICA, PRIMER IZRAÈUNA Da b lahko predstal prednost takšnega postopka, je bl zeden hpotetèn zraèun, Prostor smo razdell na sto con (elemento) z enako poršno, kakor je prkazano na slk 2. Sež zrak prhaja prostor spodnjem delu prostora, onesnažen zrak pa zapušèa prostor desnem zgornjem delu prostora. Htrost zraka na stopu n zstopu z prostora je enaka n znaša 1 m/s. Slka 3 prkazuje polje htrost kot rezultat zraèuna z raèunalnško dnamko tekoèn. Predpostal smo, da je zaèetna koncentracja plna seh conah enaka nè (robn pogoj). Vr So, a set of ordnary dfferental equatons s defned. These equatons can be soled after defnng the boundary condtons and the arflow rate for each zone. The boundary condton for each element s smply the concentraton of gas n each zone at tme zero (ntal concentraton). A numercal analyss of arflow moement through enclosed underground structure was made calculated wth the technque of computatonal flud dynamcs or CDF (ANSYS, FLOTRAN). The smulaton was made at the Faculty of Mechancal Engneerng n Ljubljana. The result of the analyss s a feld of ar elocty, whch can be calculated for the corners of each element. The elocty ectors for each corner were entered nto the MATHEMATICA. 2.2 program, where an aerage elocty of arflow through the boundary lnes of each zone was calculated. A olume of arflow for each zone can now be determned by knowng the aerage elocty and the length of the boundary lne. The poston and the olume of the freshar source s determned by a numercal analyss of the ar flow, whle the poston of the gas source and the emsson rate can be defned for each zone. The set of dfferental equatons can only be soled numercally and the result s the concentraton of gas n each zone as a functon of tme. Howeer, solng a large set of equatons requres specal program equpment and for a longterm analyss a lot of tme s needed. At present for a reasonable number of zones, the concentraton of gas n each element can be calculated n a few mnutes. All the calculatons were executed wth the MATHEMATICA,. 2.2 program. 2 A CASE STUDY As an example a hypothetcal calculaton has been made to show the adantage of such an approach to the problem. The space of the structure s dded nto a hundred zones wth equal shape (1 m 2 ), whch s shown n Fgure 2. Fresh ar enters at the bottom left corner, and the exhausted ar leaes the structure at the top rght corner. The elocty of the ncomng fresh ar and outgong exhausted ar s 1 m/s. Fgure 3 shows the ar elocty feld for such a model, calculated wth CDF. The ntal concentraton of gas s assumed to be zero. The source of the gas s placed stran 194

4 Sl. 2. Prostor, razdeljen 100 con z oznaèenm legam dotoka sežega zraka n ztoka onesnaženega zraka Fg. 2. Shape of the space, dded nto a hundred of zones, wth poston of ncomng fresh ar and outgong exhaust Sl. 3. Polje htrost Fg. 3. Velocty feld Sl. 4. Koncentracja plna po deseth sekundah Fg. 4. Concentraton of gas after 10 seconds plna oz. onesnaženja se nahaja spodnjem leem prostoru n je oznaèen s kržem, emsja pa znaša 0,4 l/s. Koncentracja plna odsnost od èasa je zraèunana conah, k so oznaèene s krog na slkah 4, 5 n 6. Slke 4, 5 n 6 prkazujejo gbanje onesnaženega zraka èasu 10, 30 n 180 sekund po zaèetku emsje plna. Koncentracje plna conah odsnost od èasa so prkazane na slkah od 7 do 11 n predstaljajo poeèanje koncentracje plna za razlène dele prostora odsnost od èasa. Koncentracje so prkazane mljonnkah (ppm = 10-6 ). Sl. 5. Koncentracja plna po trdeseth sekundah Fg. 5. Concentraton of gas after 30 seconds on the bottom left of the space, the emsson rate s 0.4 l/s. A cross ndcates the source of the polluton. The concentraton s measured n zones marked wth crcles n Fgures 4,5 and 6. At ths pont the calculaton can be executed. Fgures 4,5 and 6 show the moement of the exhausted ar through the space for 10, 30, and 180 seconds after the gas source becomes acte. The concentraton n zones as a functon of tme s presented n Fgures 7 to 11, whch show an ncreasng gas concentraton for dfferent parts of the space as a functon of tme. The concentraton s expressed n parts per mllon (ppm = 10-6 ). stran 195

5 Sl. 6. Koncentracja plna po sto osemdeseth sekundah Fg. 6. Concentraton of gas after 180 seconds Sl. 7. Koncentracja plna con (2,6) odsnost od èasa Fg. 7. Concentraton of gas n zone (2,6) as a functon of tme Sl. 8. Koncentracja plna con (5,9) odsnost od èasa Fg. 8. Concentraton of gas n zone (5,9) as a functon of tme Sl. 9. Koncentracja plna con (6,2) odsnost od èasa Fg. 9. Concentraton of gas n zone (6,2) as a functon of tme Koncentracje conah desno od ra plna n ra sežega zraka dosežejo elke rednost kmalu po zaèetku zraèuna. V drugh conah, razen cone (9,8), se koncentracja zeèuje poèasneje. Cona (9,8) lež na kržšèu, kjer je dotok onesnaženega zraka to cono eèj od ztoka. Sl. 10. Koncentracja plna con (8,4) odsnost od èasa Fg. 10. Concentraton of gas n zone (8,4) as a functon of tme The concentraton n the zones close to the source of the gas and the ntake of fresh ar ndcates the hgh alues of the concentraton ery soon after the calculaton s started. In other zones, except zone (9,8) concentratons ncreased slowly. Zone (9,8) les at a crossng where the rate of the ncomng polluted ar s hgher than the outgong stran 196

6 Sl. 11. Koncentracja plna con (9,8) odsnost od èasa Fg. 11. Concentraton of gas n zone (9,8) as a functon of tme Koncentracja tem elementu je šest- al sedemkrat eèja kakor drugh conah. Raen koncentracje plna ozroma onesnaženja posameznh delh prostora je zelo odsna od lege dooda sežega zraka n lege ra onesnaženja. Drugaèna uredte, kakor je prkazana obranaanem prmeru, b bsteno spremenla gbanje zraka skoz prostor, kar lahko pla na uènkotost prezraèeanja. Lega ra onesnaženja n predel, kjer prezraèeanje n uènkoto, b pozroèla zelo elke lokalne koncentracje onesnaženja. 3 SKLEP Tak postopek je mogoèe uporabt posebnh prmerh, pr katerh je potrebno boljše poznaanje gbanja koncentracj nekem prostoru. Mogoèe ga je uporabt pr gradnj prezraèeanja predoro faz gradnje, ko je treba doloèt mesta, kjer b lahko nastajale elke koncentracje metana al drugh plno, še posebej pa za oerte uènkotost sedanjega prezraèealnega sstema. Poleg tega je tak postopek mogoèe uporabt tud pr dmenzonranju n preerjanju uènkotost prezraèealnega sstema zaprth prostorh, kjer obstajajo r onesnaženja. Koncentracje posameznh conah je mogoèe zraèunat odsnost od èasa n tako doloèt èas, katerem b posameznh delh prostora pršlo do krtènh koncentracj ozroma dele prostora, kjer b blo treba gradt zaznaala. from the present element. The concentraton leel n ths zone s 6 or 7 tmes hgher than n other zones. It s clear that the ncrease n the concentraton depends strongly on the poston of the fresh-ar ntake and on the poston of the gas source. A dfferent locaton of the ncomng fresh ar and outgong polluted ar would change the moement of ar through space, whch can decrease or ncrease the effcency of the entlaton system. The poston of the source of the polluton n part of the space where the entlaton s not effecte would lead to ery hgh local concentratons of polluted ar or gas. 3 CONCLUSIONS Ths approach can be used n specal cases where more accurate results for the concentraton of gases are requred. It could be used n tunnels durng the buldng phase to determne zones wth hgh concentratons of methane and other gases, and especally for erfyng the effecteness of the exstng entlaton system. In addton, ths approach can also be used durng dmensonng and erfcaton of a entlaton system for enclosed structures where the source of the polluton exsts. The concentratons can be calculated as a functon of real tme, so the tme durng whch the concentraton n the examned zone becomes crtcal can be determned, or alternately, crtcal zones n whch sensors should be nstalled can be specfed. 4 LITERATURA 4 REFERENCES [1] Chow, W.K. (1995) On entlaton desgn for underground car parks, Tunnellng and underground space technology 10, [2] Ross Clay, C. (1995) Dfferental equatons, An ntroducton wth Mathematca, Sprnger-Verlag, New York, USA. [3] Wolfram, S. (1995) Mathematca handbook, Second edton, Addson-Wesley publshng company, New York, USA. stran 197

7 [4] Bahder, T. B. (1995) Mathematca for scentsts and engneers, Addson-Wesley publshng company, Readng, USA. [5] Crommeln,R.D. and F. Burngs (1988) Valdaton of a mult-cell theoretcal model for the predcton of ar temperatures and polluton concentratons by measurements n an ndustral hall. Ventlaton 1988; Proceedngs of the Second Internatonal Symposum on Ventlaton for Contamnant Control, London, Naslo atorje: dr. Jakob Lkar Jure Èadež Inšttut za rudarsto, geotehnologjo n okolje Sloenèea Ljubljana Authors Address: Dr. Jakob Lkar Jure Èadež Insttute for mnng, enronment and geotechnology Sloenèea Ljubljana, Sloena Prejeto: Receed: Sprejeto: Accepted: stran 198