© Strojni{ki vestnik 48(2002)5,244-256 © Journal of Mechanical Engineering 48(2002)5,244-256 ISSN 0039-2480 ISSN 0039-2480 UDK 667.644.3:532.525:519.61/.64 UDC 667.644.3:532.525:519.61/.64 Izvrini znanstveni ~lanek (1.01) Original scientific paper (1.01) Tokovne razmere v avtomobilski lakirnici: numeri~na in eksperimentalna analiza Flow Conditions in an Automotive Spray-Paint Chamber: Numerical and Experimental Analyses Jure Marn - Zoran @uni~ - Matja` Ram{ak - Primo` Ternik V prispevku smo analizirali tokovne razmere v avtomobilski lakirni komori. Za reševanje Navier-Stokesovih enačb prostorskega toka nestisljive izotermne tekočine smo uporabili metodo nadzornih prostornin (CFX 5.4). Podrobno smo opisali potek izračuna, uporabljene robne in začetne pogoje, uporabljene metode za stabilizacijo numeričnih nihanj ter druge parametre, pomembne za izračun. Predstavili smo rezultate za ravninski in prostorski primer izračuna. Robni pogoji so bili določeni z meritvami na realni komori in to za primer brez avtomobila in z njim. Filter komore je bil upoštevan kot porozna snov s kvadratno funkcijo upora po podatkih proizvajalca, ki smo jih preverili z lastnimi meritvami padca tlakov. © 2002 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: komore lakirne, dinamika tekočin, analize numerične, turbulenca) This paper deals with the flow analysis around a car in a spray-paint chamber. To solve the Navier-Stokes equations for 3D flow of an incompressible and isothermal fluid we used the control-volume method (CFX 5.4). The numerical procedure, the boundary and initial conditions, the methods used for stabilizing the numerical oscillations as well as the other parameters important for the numerical procedure are described in detail. Results for 2D and 3D calculations are presented. The boundary conditions were determined with measurements in a real chamber with and without a car. The filter in the chamber was considered to be porous matter with a quadratic law of resistance, this is in accordance with the manufacturer’s data that were verified with pressure-loss measurements. © 2002 Journal of Mechanical Engineering. All rights reserved. (Keywords: spray-paint chamber, fluid dynamic, numerical analysis, turbulence) 0 UVOD IN SPODBUDA ZA DELO V pričujočem prispevku smo se ukvarjali z analizo toka okoli avtomobila v lakirnici. Med lakiranjem je zelo pomembno, da zrak teče okoli avtomobila kar se da mirno, sčim manjšimi vrtinci, še zlasti pa se želimo izogniti recirkulacijskim conam, kjer bi zaradi pojavov vrtinčenja in zato ponovnega dviga prahu lahko prišlo do usedanja prašnih delcev na sveže pobarvane dele avtomobilske karoserije, s tem pa do napak pri lakiranju. Analizo bi bilo moč opraviti na dva načina. Pri prvem bi se lahko naslonili na eksperimentalno analizo, pri kateri bi na določene točke v lakirnici postavili dimne vire in opazovali tirnice dimnih delcev skozi lakirnico. Težava pri takem postopku bi bila v omejeni uporabi, saj bi lahko ugotovili recirkulacijske cone le za določen tip vozila in za določene robne pogoje, in v nenatančnosti, saj bi se lahko zgodilo, da bi zgrešili kako recirkulacijsko območje. Drugi način je numerična analiza, pri kateri 0 INTRODUCTION AND MOTIVATION FOR THE WORK In this paper we have analyzed the flow around a car in a spray-paint chamber. During the process of lacquering it is very important that the air flows around the car as smoothly as possible, generating the smallest eddies possible. However, most importantly, we wish to avoid recirculation zones, where curling and the resulting dust raising could cause the deposition of dust particles on the freshly painted car body, which eventually means a degradation of the paint quality. An analysis could be performed in two ways. First, we could use an experimental analysis that involved mounting smoke sources at certain points in the lacquer chamber and the observing the path of the smoke particles through the lacquer chamber. The disadvantage of this approach is in its limited application: the recirculating zones can only be observed for a certain type of car and for certain boundary conditions, and there is also the uncertainty that would arise because we could overlook some recirculating VH^tTPsDDIK stran 244 Marn J. - @uni~ Z. - Ram{ak M. - Ternik P.: Tokovne razmere - Flow Conditions lahko robne pogoje spreminjamo, prav tako tudi geometrijsko obliko. Tak način je preprostejši, ker modeliramo večino geometrijskih parametrov le prvič, nato pa spreminjamo vstopne in izstopne pogoje ter ugotavljamo spremembe. Poleg želje po določitvi recirkulacijskih območij smo želeli še zlasti prikazati, kako je moč primerno uporabiti sedanja orodja računalniške dinamike tekočin in hkrati eksperimentalno določiti robne pogoje. Prav ti v primeru uveljavljenih orodij, npr. CFX, katerih ovrednotenje in preveritev sta bili že opravljeni, pogosto določajo kakovost rezultatov. 0.1 Opis lakirnice V obravnavanem primeru gre za lakirnico dolžine 5880 mm, širine 3560 mm in največje višine 2480 mm. Zrak vstopa v lakirnico s stropa in izstopa v okolico skozi talno rešetko dolžine 4000 mm in širine 3000 mm ter nato v kanal na dnu lakirnice. Kanal vodi na prosto skozi izpust zraka prizmatične oblike širine 1000 mm, višine 860 mm in pri vrhu globine 650 mm, pri čemer je izpust zavarovan z izpustno rešetko z žaluzijami. Talna rešetka je prekrita s filtri debeline 50 mm, ki barvi, razpršeni v zraku, preprečujejo izstop v okolico in onesnaženje. Ventilator in grelnik zraka za to analizo nista bila pomembna, zato njunih tehničnih podatkov ne navajamo. 1 MERITVE V sami lakirnici smo opravili dvoje vrst meritev, in sicer meritve zaradi določitve robnih pogojev in meritve zaradi določitev snovskih lastnosti filtra. Kakor je bilo že zapisano, je bil končni cilj zastavljene naloge numerična analiza toka okoli avtomobila v lakirnici z željo, da bi določili morebitne recirkulacijske cone. Taka numerična analiza je neprimerno hitrejša in cenejša od meritev v vseh pomembnih točkah okoli avtomobila, poleg tega pa ni nasilna, je pa po naših izkušnjah odvisna zlasti od določitve robnih in začetnih pogojev ter snovskih lastnosti. 1.1 Opis meritev robnih pogojev V prvem delu raziskav za določitev robnih pogojev smo izvedli meritve hitrosti v osmih točkah ob stropu vstopnega dela, ki so prikazane na sliki 1. Meritve smo opravili v dveh razporedih, brez avtomobila in z njim, pri čemer nismo pričakovali bistvenih razlik med posameznimi rezultati. Vsako od meritev smo opravili po dvakrat, da bi zmanjšali velikost napak. Meritve smo opravili z ročnim merilnikom z vročo žičko. Merilnik smo pred izvajanjem meritev zones. Second, we can take advantage of numerical analysis where we can modify the boundary and initial conditions as well as the geometry. This approach is simpler because we model most of the geometrical parameters only once, and then by modifying the inlet and outlet conditions we can follow the changes. In addition to determining the recirculating zones we particularly wanted to present the use of existing numerical tools and to experimentally determine the boundary conditions. In the case of well-known programs, in our case CFX, which were validated and verified, it is the boundary conditions that suggest the results’ quality. 0.1 Spray-paint chamber The spray-paint chamber is 5,880 mm in length, 3,560 mm in width and has a maximum height of 2,480 mm. Air enters the chamber from the ceiling and exits through the floor grid which is 4,000 mm in length and 3,000 mm in width, and then flows into the channel below the chamber. The channel leads to the outside through the prismatic opening that is 1,000 mm wide, 860 mm high and 650 mm deep. The outlet is secured with a shuttered grid. The floor grid is covered with a 50-mm-thick filter that prevents the dispersed paint from polluting the environment. The ventilator and the air heater are not important for this analysis and therefore we do not give any technical specifications for them. 1 MEASUREMENTS In the spray-paint chamber we performed two kinds of measurements: measurements for determining the boundary conditions and measurements for determining the filter properties. As already stated, we wanted to perform a numerical simulation of the flow around a car in a spray-paint chamber and determine the recirculation zones. A numerical analysis is much faster and cheaper than measurements at all the important points around the car, and more over, it is a non-invasive procedure. We also believe that the numerical analysis plays an important role in determining the boundary and initial conditions as well as the physical properties. 1.1 Description of the boundary-conditions measurement In the first part of our analysis we measured the velocity at eight points in the inlet region (Figure 1). The measurements were made with and without a car. We did not expect significant differences for particular results. Each measurement was performed twice in order to reduce the magnitude of the errors. The measurements were made with a manual hot-wire anemometer. The instrument was calibrated | lgfinHi(s)bJ][M]lfi[j;?n 02-5______ stran 245 I^BSSIfTMlGC Marn J. - @uni~ Z. - Ram{ak M. - Ternik P.: Tokovne razmere - Flow Conditions >6 o7 o8 1______________________02_____________________03 500 1220 1220 1220 X 1220 V or 100 100 J500 5880__________________________^ Sl. 1. Merilne točke v lakirni komori (izmere v mm) Fig. 1. Measurement points in spray-paint chamber (dimensions in mm) 20,0 m/s 18,0 16,0 14,0 12,0 10,0 8,0 6,0 4,0 2,0 0,0 ¦ Uizm/Uexp Udej/Uact — Linearno (Uizm) Linear (Uexp) 0,00 5,00 10,00 15,00 20,00 m/s Udej/Uact Sl. 2. Napaka ročnega merilnika hitrosti z vročo nitko glede na primerjalno hitrost Fig. 2. Error of manual hot-wire anemometer according to reference velocity umerili na testni progi iz plastičnih cevi premera 120 mm, v katerega smo tlačili zrak skozi cev z uporabo aksialno-radialnega ventilatorja IMP. Proga je opremljena s Pitotovo cevjo, dinamični tlak in padec tlaka pa smo izmerili z manometrom BETZ natančnosti 1 Pa. Meritve smo opravili med 2,1 m/s in 8,0 m/s ter ugotovili natančnost nitke med +1,50% in +4%. Ugotovimo lahko torej, da je v merilnem območju natančnost merilnika +4%, natančnejši rezultati pa so prikazani na sliki 2. Opravili smo tudi meritve pri vhodu v merilno komoro in ugotovili, da je puščanje zraka iz lakirne komore zanemarljivo, vsekakor pa znotraj merilne negotovosti merilnega instrumenta. Zato smo predpostavili, da ves zrak vstopa pri vrhu in izstopa pri dnu. Prav tako smo predpostavili, da so vrednosti vstopnih hitrosti pri vrhu linearno interpolirane med posameznimi merilnimi točkami. in a test line made of plastic pipes with a diameter of 120 mm that was fed with air by means of an IMP axial-radial ventilator. The line was equipped with a Pitot pipe, the dynamic pressure and the pressure drop were measured with a BETZ manometer of accuracy 1 Pa. The measurements were performed between 2.1 m/s and 8.0 m/s, and the determined accuracy of a hot wire is between +1.5% and +4%. We can conclude that in the selected measurement range the precision of the data is within +4%. More detailed results are presented in Figure 2. The measurements at the inlet of the spray-paint chamber indicated that any leakage of air from the spray-paint chamber is negligible and still within the measurement uncertainty of the instrument. We supposed that the air enters at the top and leaves at the bottom. We also assumed that all the values of the inlet velocities at the top are linearly interpolated between the particular measurement points. VH^tTPsDDIK stran 246 Marn J. - @uni~ Z. - Ram{ak M. - Ternik P.: Tokovne razmere - Flow Conditions 1.2 Opis in rezultati meritev padca tlaka skozi filter Kakor smo že zapisali, je bila talna rešetka prekrita s filtrom debeline 50 mm. V dejanskem primeru je bil uporabljen filter KONUS KOFIL KFS 50, za katerega je proizvajalec v svoji specifikaciji podal tri merilne točke upora v odvisnosti od hitrosti zraka, ki teče skozi filter. Te podatke smo želeli laboratorijsko preveriti. Uporabljena merilna proga je bila enaka tisti, uporabljeni za umerjanje ročnega merilnika hitrosti, na slikah 3 in 4 pa so prikazani rezultati. 1.2 Description and measurements results of the pressure drop through the filter The lattice was covered with a 50-mm-thick filter. In the real process a KONUS KOFIL KFS 50 filter was used, for which the manufacturer, in its specification, gave three points of resistance depending on the air speed flowing through the filter. These data were experimentally examined. The measurement lane was the same as the one used for calibrating the manual velocity measurer, the results are shown in Figures 3 and 4. Sl. 3. Tlačni padec skozi filter kot funkcija hitrosti zraka Fig. 3. Pressure drop through filter as a function of air speed Sl. 4. Količnik upora filtra kot funkcija hitrosti Fig. 4. Resistance coefficient of filter as a function of velocity 1.3 Rezultati meritev robnih pogojev na vstopu in 1.3 Results of the boundary conditions during inlet izstopu and outlet measurements V postopku izvedbe meritev robnih pogojev na vstopu smo izvedli štiri nize preskusov brez avtomobila in dva niza preskusov z njim v vsaki od točk, da bi zmanjšali vpliv napak Rezultati so prikazani v preglednicah 1 (brez avtomobila) in 2 (z avtomobilom). V vsaki točki je prikazano tudi odstopanje od srednje vrednosti. Izmerili smo tudi profil hitrosti na izhodu, a smo imeli zaradi izstopnih žaluzij težave z razlago rezultatov. Legažaluzij namreč povzroča, da tok zraka periodično When measuring the boundary conditions at the inlet, four sets of experiments with the car and two sets of experiments without the car were performed. The goal was to reduce the influence of experimental errors. The results are shown in Table 1 (without the car) and Table 2 (with the car). For each experimental point the deviation about the mean is also shown. We have also measured the velocity profiles at the outlet, but the grid shuttles caused problems with the interpretation of the results. The position of gfin^OtJJlMlSCSD 02-5 stran 247 |^BSSITIMIGC Marn J. - @uni~ Z. - Ram{ak M. - Ternik P.: Tokovne razmere - Flow Conditions Preglednica 1. Hitrost zraka v m/s v posamezni merilni točki na vstopu v komoro brez avtomobila Table 1. Air velocity in m/s at a particular measurement point for the chamber inlet without car IV 1 0,32 0,35 0,32 0,35 2 0,28 0,38 0,38 0,28 3 0,40 0,38 0,35 0,40 4 0,38 0,48 0,42 0,42 5 0,28 0,25 0,28 0,30 6 0,38 0,40 0,40 0,35 7 0,40 0,32 0,35 0,40 8 0,38 0,35 0,35 0,35 Povprečje/Average 0,3525 0,3638 0,3563 0,3563 Odstopanje/Deviation 0,0444 0,0463 0,0328 0,0378 Preglednica 2. Hitrosti zraka v m/s v posamezni merilni točki na vstopu v komoro z avtomobilom Table 2. Air velocity in m/s at a particular measurement point for the chamber inlet with car 1 2 3 4 5 6 7 8 I II 0,41 0,4 0,28 0,4 0,42 0,35 0,38 0,38 0,28 0,28 0,32 0,4 0,48 0,4 0,28 0,35 Povprečje/Average 0,3563 0,3700 Odstopanje/Deviation 0,0663 0,0325 spreminja hitrost, saj žaluzije tok usmerjajo in se za njimi ustvarjajo cone recirkulacije. Tako smo rezultate uporabili zgolj za oceno pravilnosti izračunanega masnega toka zraka na izstopu. 1.4 Merilna negotovost 1.4.1 Osnove za izračun merilne negotovosti Dinamični tlak na Pitotovi cevi in padec tlaka na filtru merimo z Betzovim manometrom, katerega natančnost je ocenjena na 1Pa. Pri tem je ločljivost skale Betzovega manometra 0,1mm. Hitrost zraka izračunamo z Bernoullijevo enačbo: v = kjer je: pd - dinamični tlak na Pitotovi cevi, r = 1,164 kg/m3 - gostota zraka pri T = 20°C. Koeficient upora filtra C izračunamo z uporabo izraza za lokalne izgube: the shuttles causes periodically changing velocities due to the influence of the shuttles on the direction of the flow. Velocity profiles were therefore only used for a verification of the mass flow through the outlet. 1.4 Measurement uncertainty 1.4.1 Basics of measurement uncertainty calculation The dynamic pressure at the Pitot pipe and pressure drop through the filter are measured with the BETZ manometer. The scale resolution of the BETZ manometer is 0.1 mm. The air speed is determined from Bernoulli‘s equation as: 2^ r (1), where: pd - dynamic pressure at the Pitot pipe r = 1.164 kg/m3 - density of air at T = 20°C. The resistance coefficient C is determined with the equation for local pressure losses: Cu = 2-Dp r-v2 (2), kjer je: Dp - padec tlaka na filtru. where: Dp - pressure drop through the filter. VBgfFMK stran 248 Marn J. - @uni~ Z. - Ram{ak M. - Ternik P.: Tokovne razmere - Flow Conditions Preglednica 3. Rezultati meritev Table 3. Results of measurements točka point 1 2,94 27,41 2,25 2,30 pd Pitot (Pa) Dp filter (Pa) 2 7,34 53,85 3,55 3,60 v Pitot (m/s) 3 23,50 135,11 6,35 6,40 5,75 4 35,25 182,10 7,78 8,00 5,17 v anem (m/s) Cu filter 9,33 7,33 5 I 38,67 I 198,74 I 8,15 I 8,40 I 5,14 I 1.4.2 Določitev merilne negotovosti 1.4.2 Measurement-uncertainty determination Ker je standardna merilna negotovost posredno merjene veličine: Considering that the combined standard uncertainty is: u( y) Šf Kdxi ¦u (xi) (3) lahko ob upoštevanju, da je u(r) = 0, zapišemo skupno and u(r) = 0, we can write the combined standard standardno merilno negotovost hitrosti zraka: uncertainty of the air speed as: u(v) in količnika upora: u(Cu) •u (pd) 1 ,'u (pd) 2'r-pd, and the coefficient of resistance as: Cu\.u (Dp) + (Cu| ¦u 2 (v) = dDpj \ dv J \^r'v 2 ] u(Dp) + \- 4Dp\ -u(v) Ker je u(Dp) = u(pd) = uB(pd) (meritev izvedena le Because u(Dp) = u(pd) = uB(pd), we can write: enkrat), sta posamezni merilni negotovosti: u(v) 1 2'r-pd uB(pd) in and: u(Cu) r-v ¦uB(Dp)- 4-Dp uB(pd). (4) (5). (6) (7). r-v J \2-r-pd Merilno negotovost tipa B Betzovega The type B component of measurement manometra določimo z upoštevanjem njegove uncertainty for the BETZ manometer is determined natančnosti (1 Pa): by considering its accuracy (1 Pa): 1Pa uB, (pd ) = uB (Dp) = 3 = 0, 577Pa (8) in ločljivosti skale (0,1 mm oz. 0,979 Pa): and scale resolution (0.1 mm, corresponding to 0.979 Pa): uB, , ( pd ) = uB, , (Dp) kot 0,979Pa V3 as: 0,565Pa uB (pd) = uB(Dp) = y]uB, 2(pd) + uB,,2(pd) = 0,808Pa (9) (10). Rezultati vseh merilnih točk prikazuje The results for all experimental points are preglednica 4. shown in Table 4. Merilna negotovost samih meritev, ki so bili The measurement uncertainty of the opravljeni na progi, je enaka merilni negotovosti measurements is equal to the type B component of tipa B, ki pa se ujema z merilno negotovostjo the measurement uncertainty, which coincides with instrumenta. the measurement uncertainty of the instrument. gfin^OtJJlMlSCSD 02-5 stran 249 |^BSSITIMIGC Marn J. - @uni~ Z. - Ram{ak M. - Ternik P.: Tokovne razmere - Flow Conditions Preglednica 4. Merilna negotovost u(v) in u(Cu) Table 4. Measurement uncertainties u(v) and u(Cu) točka point v Pitot (m/s) 2,25 3,55 6,35 7,78 8,15 u(v) (m/s) 0,309 0,195 0,109 0,089 0,085 Cu filter 9,33 7,33 5,75 5,17 5,14 u(Cu) 2,56 0,81 0,20 0,12 0,11 2 NUMERIČNA ANALIZA 2.1 Vodilne enačbe Reševali smo splošno znane Reynoldsove povprečene Navier-Stokesove enačbe (RANS) za prostorski tok nestisljive izotermne tekočine: duj dx 2 NUMERICAL ANALYSIS 2.1 Leading equations We were solving the generally known Reynolds’ averaged Navier-Stokes equations (RANS) for the 3D flow of incompressible and isothermal flow: = 0 dui dui r— + ruj — dt dx j dp d ---- +---- d x d x m dui du j dx dx v j i r ui uj (11), (12), kjer je u časovno povprečeni hitrostni vektor, x krajevni vektor, p časovno povprečeni tlak, r gostota, m dinamična viskoznost in zadnji člen na desni strani enačbe zveza med hitrostnimi nihanji, ki jo imenujemo tudi Reynoldsov napetostni tenzor. Za modeliranje Reynoldsovega napetostnega tenzorja uporabimo dvoenačbni model k-e : where u a is time-averaged velocity vector, x is a spatial vector, p is the time-averaged pressure, r is the density, m is the dynamic viscosity and the last term on the right-hand side of the equation is the correlation between the velocity fluctuations, also known as the Reynolds stress tensor. The Reynolds stress tensor is modeled with a two-equation k-e model -ruiu =mT dui dx mT =cmr dxi e r kdij (13), (14), kjer je mt dinamična turbulentna viskoznost, k turbulentna kinetična energija, e stopnja turbulentnega raztrosa, dij Kroneckerjeva delta funkcija in c empirična konstanta z vrednostjo 0,09. Za modeliranje izotropnega upora tekočine uporabimo kvadratni zakon upora. Izvirni člen SM v gibalni enačbi se glasi: where mT is the dynamic turbulent viscosity, k is the turbulent kinetic energy, e is the level of turbulent dissipation, dij is Kronecker‘s delta function and cm is the empirical constant with a value of 0.09. The isotropic resistance of the fluid was modeled with the quadratic law of resistance. The source term SM in the equation of motion is: Si = -CR1ui -CR2 ui ui (15), kjer sta C in CR2 koeficienta upora. Zraven enačb (11) in (12) dobimo še dve prenosni enačbi za k in e: where CR1 and CR2 are resistance coefficients. Besides equations (11) and (12) we obtain two transport equations for k and e: dk dt de r — + ruj d t dx dx dk = d d xj d xj m m mT d k s dx P - re de d mT de s dx j J c—P -c2 r — 1 k k (16), (17), kjer sta sk in se turbulentni Prandtlovi števili za k in e, c1 in c2 pa sta empirični konstanti. V našem primeru so imele konstante vrednost sk=1,0; se=1,3; c =1,44 in c2=1,92. where sk and se are turbulent Prandtl‘s numbers for k and e, and c1 and c2 are empirical constants. In our case the values for the constants were sk=1.0, se=1.3, c1=1.44 and c2=1.92. VH^tTPsDDIK gfin^(5ül[Fi!]DaGC] I stran 250 Marn J. - @uni~ Z. - Ram{ak M. - Ternik P.: Tokovne razmere - Flow Conditions Člen P imenujemo produkcija in je definiran kot: P = Mt The term P is called production and is defined as: ydxj dx dx (18). 2.2 Postopek reševanja Zgoraj opisane enačbe so bile po postopku nadzornih prostornin spremenjene v sistem algebrajskih enačb. Sisteme linearnih enačb smo reševali na delno povezan način, kar pomeni, da so bile v eni iteraciji reševane kontinuitetna in tri gibalne enačbe, nato pa še ločeno enačbi za turbulentno kinetično energijo in turbulentnim raztrosom. Na tak način dosežemo kompromis med številom nelinearnih iteracij in potrebno količino pomnilnika za rešitev sistema enačb. Za reševanje sistemov linearnih enačb smo uporabili algebrsko večmrežje z dodano popravo. Tako najbolje izkoristimo dejstvo, da diskretizirane enačbe pomenijo ohranitev bilance osnovnih spremenljivk v nadzorni prostornini. Enačbe redke mreže dobimo preprosto z združevanjem posameznih prostornin goste mreže. Z numeričnega vidika je večmrežje učinkovitejše kakor druge metode. Na dani mreži so lahko iterativni rešilniki učinkoviti le pri zmanjševanju napak, ki imajo valovne dolžine velikosti mreže. Slabše se obnesejo pri napakah z valovnimi dolžinami velikostnega reda računskega območja. Metoda večmrežja obide navedeno težavo z navideznim redčenjem osnovne mreže v postopku iterativnega reševanja sistema enačb, reševanjem enačbe za popravo na redki mreži in nato podaljšanje poprave nazaj na fino mrežo. Redka mreža je zmožna gladiti napake nižjih frekvenc kot fina mreža, tako da z nekaj nivoji redčenja osnovne mreže pokrijemo celoten frekvenčni spekter napak, kar ima za posledico boljšo konvergenco. Za stabilizacijo konvektivnega člena smo uporabili protivetrno metodo prvega reda natančnosti. Zanjo smo se odločili predvsem zaradi njene numerične stabilnosti. Mogoče bi bilo uporabiti tudi višjeredno metodo popravek numerične korekcije, ki pa je zaradi možnega pojava numerične disperzije in večje porabe računalniškega časa nismo uporabili. Viskozni podsloj, ki nastane ob steni pri turbulentnem toku modeliramo z uporabo posebnih zidnih elementov. V zidnih elementih uporabimo oblikovne funkcije, ki so posebej prirejene, da zajamejo strme spremembe osnovnih spremenljivk v viskoznem podsloju. Te funkcije temeljijo na splošnem “zidnem zakonu” in so odvisne od karakterističnih turbulentnih Reynoldsovih števil. Med iterativnim postopkom reševanja se spreminjajo, da bi čim bolje zajele lokalne razmere. 2.2 Solving procedure The above equations were transformed into a system of algebraic equations following the procedure of the control-volume method. The systems of linear equations were solved in a partially coupled manner. In one iteration the continuity equation and three momentum equations were solved coupled, followed by the equations for turbulent kinetic energy and turbulent dissipation. This is the compromise between the number nonlinear iterations and the amount of computer memory required for solving a system of equations. The selected system of linear equations was solved using the additive-correction algebraic multigrid method. This approach takes advantage of the fact that the discrete equations are representative of the balance of conserved quantities over a control volume. The coarse-mesh equations can be created by merging the original control volumes to create larger ones. From a numerical standpoint the multigrid approach offers a significant advantage. For a given mesh size, iterative solvers are only efficient at reducing errors that have a wavelength of the order of the mesh spacing. So, while shorter-wavelength errors disappear quite quickly, errors with longer wavelengths can take a very long time to disappear. The multigrid method bypasses this problem by coarsening the virtual mesh spacing during the course of the iterations, solving the equation for the coarse-mesh correction and then prolonging of the correction back to the finer mesh. The coarse-mesh smooths errors with lower frequencies, so with a few levels of coarsening we cover the whole range of error frequencies, which leads to a better convergence. For stabilization of the convective term we used the upwind method of the first order of accuracy. The main reason for its application was its numerical stability and robustness. It could be possible to use the high-order NAC (numerical advection correction) method but we did not use it because of possible numerical dispersion. The viscous sublayer that occurs near the wall when the flow is turbulent is modelled by using particular wall elements. In the wall elements we use shape functions that are arranged for the capture of the high primitive variables gradients in the viscous sublayer. These functions are based on a general law-of-the-wall and depend on characteristic turbulent Reynolds numbers. During an iterative procedure they change in order to better capture the local conditions. gfin^OtJJIMISCSD 02-5 stran 251 |^BSSITIMIGC Marn J. - @uni~ Z. - Ram{ak M. - Ternik P.: Tokovne razmere - Flow Conditions Talni filter smo modelirali kot porozno snov The floor grid with the filter has been modelled s kvadratnim zakonom upora, pri čemer smo as a porous region with the quadratic law of resistance, konstante modela določili po podatkih proizvajalca with the constants calculated using the filter filtra. manufacturer’s data. 2.3 Rezultati 2.3 Results 2.3.1 Ravninski primer 2.3.1 2D problem V primeru ravninskega izračuna smo uporabili In the 2D calculation 72846 we used elements. 72 846 elementov. Velikost elementov je znašala med The size of each element was between 50 and 100 50 in 100 mm. Dobili smo sistem linearnih enačb z mm. We were solving a system of linear equations 19 872 neznankami. Za reševanje je bilo potrebno 49 with 19872 unknowns and we used 49 MB MB (MB = 1024x1024 byte) pomnilnika. (MB=1024x1024 byte) of memory. Na vstopu smo predpisali vstopno hitrost. To At the inlet the inlet velocity was prescribed. hitrost smo predpisali kot povprečno vrednost v vseh We prescribed it as an average value in all the points merjenih točkah. Predpisali smo tudi privzete vrednosti as discussed above. We also prescribed assumed turbulentne intenzivnosti ter mešalne dolžine (CFX 5.4). values for the turbulent intensity and the mixed length Na izstopu smo predpisali statični tlak. Predpisana (CFX 5.4). At the outlet the static pressure was natančnost reševanja je znašala 106 (kvadratna norma prescribed. The prescribed numerical accuracy was ostankov). Rešitev smo dobili po 90 iteracijah, za kar 106 (root mean square of residuums). The solution smo porabili 4383 s (73 min 3 s) procesorskega časa na was obtained after 90 iterations and it took 4383 s (73 delovni postaji Hewlett-Packard B1000. Na sliki 5 je min 3 s) of processor time on a Hewlett-Packard B1000 prikazano diskretizirano območje. work station. Figure 5 shows the discretised area. Sl. 5. Diskretizirano območje Fig. 5. Discretised area Sl. 6. Hitrostno polje s tokovnicami Fig. 6. Velocity field with stream lines ^BSfiTTMlliC | stran 252 Marn J. - @uni~ Z. - Ram{ak M. - Ternik P.: Tokovne razmere - Flow Conditions Na sliki 6 je prikazan ravninski model avtomobila s prikazanimi vektorji hitrostnega polja in vrisanimi tokovnicami. Vidimo, da v tem, dvoizmernem primeru ne prihaja do recirkulacijskih območij v okolici avtomobila. Na sliki 7 je prikazano polje turbulentne kinetične energije. Vidimo, da je stopnja kinetične energije v območju barvanja dokaj majhna, močno pa se poveča v izstopnem kanalu. 2.3.2 Prostorski primer Na sliki 8 je prikazano diskretizirano območje z vrisanimi ploskovnimi elementi. Za primere z avtomobili velikosti od 320 cm do 400 cm smo diskretizirali območje s 369620 do 355092 elementi (četverci). Velikost elementov je znašala 80 do 100 mm po površini avtomobila in komore ter 200 mm po območju. Razmerje velikosti med dvema sosednjima elementoma je bilo omejeno na 1.1. Mejno plast smo diskretizirali s tremi plastmi prizmatskih elementov. Za reševanje je bilo potrebno 190 MB pomnilnika. Figure 6 shows the 2D model of a car with the velocity field vectors and stream lines. It can be seen that for the 2D case there are no recirculating zones. Figure 7 shows the turbulent kinetic energy field. It can be seen that for the area of the painting it is relatively low but increases significantly in the outlet channel. 2.3.2 3D problem Figure 8 shows the discretised area with the surface elements. For cars with lengths between 320 cm and 400 cm the area was discretised with 369620–355092 elements (tetrahedrons). The size of the elements was set to 80–100 mm on the car body and the chamber walls’ surface and 200 mm in the domain. The ratio of the size of the neighboring elements was limited to 1.1. The boundary layer was discretised with three layers of prismatic elements. For the solution of the problem 190 MB of computer memory was needed. ¦ i 0.03755 B .8966-05 - ^^^^^^^^B Sl. 7. Turbulentna kinetična energija Fig. 7. Turbulent kinetic energy Sl. 8. Diskretizirano območje prostorskega primera Fig. 8. Discretised area of 3D example I IgfinHŽslbJlIMlIgiCšD I stran 253 glTMDDC Marn J. - @uni~ Z. - Ram{ak M. - Ternik P.: Tokovne razmere - Flow Conditions Na vstopu smo predpisali vstopno hitrost in privzete vrednosti turbulentne intenzivnosti ter mešalne dolžine (CFX 5.4). Na izstopu smo predpisali statični tlak. Zaradi simetričnosti območja smo modelirali samo polovico območja, na simetrijski ploskvi pa smo predpisali simetrijske robne pogoje. Kot začetne pogoje smo predpisali stanje mirovanja v območju (v =v =v=0). Predpisana natančnost reševanja je znašala 104 (kvadratna norma ostankov). Rešitev smo dobili po 40 iteracijah, za kar smo porabili 7255 s (120 min 55 s) procesorskega časa na delovni postaji Hewlett-Packard B1000. Na sliki 9 je prikazano hitrostno polje na simetrijski ploskvi in tlačno polje na površini avtomobila. At the inlet the constant velocity and the default values of the turbulent intensity and the mixing length were prescribed (CFX 5.4). At the outlet the zero static pressure was prescribed. Due to the symmetrical domain only half of the chamber was discretised and symmetrical boundary conditions were prescribed. The initial condition was a zero velocity field (vx=vy=vz=0). The prescribed convergence criterion was 10-4 (root mean square of residua). The solution was obtained after 40 iterations and 7255 s (120 min 55 s) of CPU time on a Hewlett-Packard B1000 workstation. Figure 9 shows the velocity field on a symmetry plane and the pressure field on the car-body surface. •^ 23.7 Sl. 9. Hitrostno polje na simetrali in tlačno polje na površini avtomobila Fig. 9. Velocity field on symmetry line and pressure field on a car > Sl. 10. Izopovrsine hitrosti v Fig. 10. Iso-surfaces of velocity vy VBgfFMK stran 254 Marn J. - @uni~ Z. - Ram{ak M. - Ternik P.: Tokovne razmere - Flow Conditions Na sliki 10 so prikazane izopovršine hitrosti v , ki najbolj nazorno pokaže območja, kjer prihaja do povratnega toka (recirkulacij). Vidimo, da v okolici avtomobila ni večjih recirkulacijskih con. Po pričakovanju nastajajo manjši vrtinci v bližini sten in vogalov, kar pa na učinkovitost odvajanja barve v bližini avtomobilov ne vpliva. Na sliki 11 so prikazane izopovršine turbulentne kinetične energije k, ki pove, kje so območja najbolj intenzivnega mešanja toka. Figure 10 shows the isosurfaces of velocity vy, which is the most illustrative way of showing zones with a recirculating flow. It can be seen that near the car-body surface no large recirculation zones exist. There are small eddies near the wall bottoms and corners as expected, but this does not have any influence on the efficiency of the painting fog removal. Figure 11 shows the isosurface of turbulent kinetic energy k, which marks the areas of the most intensely mixed flow. Sl. 11. Izopovršine turbulentne kinetične energije k Fig. 11. Iso-surfaces of turbulent kinetic energy k 3 SKLEP V prikazanem prispevku smo želeli povezati konkretno inženirsko vprašanje z metodološkim postopkom, ki omogoča preprosto spreminjanje vhodnih podatkov ter tako izdelavo variantnih rešitev brez večkratnega merjenja. Najprej smo postavili računalniški triizmerni model lakirnice, v kateri smo želeli oceniti vpliv tokovnega polja na hrapavost nanesene barve, pri čemer smo hrapavost povezali z možnostjo recirkulacije zračnega toka. Predpostavka je nekoliko konzervativna, saj ni nujno, da vsaka recirkulacija povzroči nanos prašnih delcev, na drugi strani pa je malo verjetno, da bi prašni delci v odsotnosti recirkulacije s pomočjo difuzije napredovali proti toku zraka. Robne pogoje smo postavili z meritvami. Izračune smo opravili z uporabo računalniškega paketa CFX in ugotovili, da v bližini realnega modela avtomobila recirkulacijskih con ni najti, kar ob upoštevanju prejšnje predpostavke pomeni, da od tega hrapavosti na lakiranih mestih avtomobila ni pričakovati. Bistven dosežek prikazanega dela ni v končnem rezultatu in odgovoru na vprašanje glede 3 CONCLUSION This paper deals with an engineering question and the answer based on a methodology involving a simple change of inlet parameters that gives an easy parametric analysis without repeated experiments. First, a 3D computer model of a spray-paint chamber was built aiming to assess the influence of the fluid field on smoothness of the painted surface or better paint thereof whereas the coarseness of the painted surface was connected to recirculation of air flow. This is arguably a conservative assumption as the recirculation itself does not necessarily mean the deposition of dust particles on the painted surface. The boundary conditions were set using measurements. The calculations were conducted using the CFX computer code and the results show that no recirculation zones were found, which means that the air flow around the vehicle should not cause the deposition of dust particles on the surface of the painted surfaces. In itself, the final result was not the goal of this paper. The main task, i.e. showing that engineering | IgfinHŽslbJlIMlIgiCšD I stran 255 glTMDDC Marn J. - @uni~ Z. - Ram{ak M. - Ternik P.: Tokovne razmere - Flow Conditions hrapavosti lakiranih mest na vozilu, temveč odgovor na vprašanje, da je tudi za inženirske analize in vprašanja moč uporabiti računalniško tehnologijo brez nepotrebnih poenostavitev ob uporabi meritev samo za natančno določitev robnih pogojev. questions can be answered without undue simplification taking advantage of computer technology and relying on measurements only for as-realistic boundary conditions as possible, was in our opinion successfully achieved. 4 LITERATURA 4 REFERENCES [1] CFX 5.4 Users manual (1999) AEA Technology. [2] KOFIL, Prostorska filtracija, prospekt Konus Konex d.o.o. [3] Ramšak, M., P. Ternik, J. Marn (2000) Meritev tlačnega padca za filter KONUS KOFIL KFS 50, Poročilo, Laboratorij za prenosne pojave v trdninah in tekočinah, Fakulteta za strojništvo, Univerza v Mariboru. [4] Žunič, Z. (1997) Numerična obravnava problema aerodinamike vozil, Magistrsko delo, Fakulteta za strojništvo, Univerza v Mariboru. Naslov avtorjev: prof.dr. Jure Marn Authors’ Address: Prof.Dr. Jure Marn mag. Zoran Žunič Mag. Zoran Žunič mag. Matjaž Ramšak Mag. Matjaž Ramšak mag. Primož Ternik Mag. Primož Ternik Fakulteta za strojništvo Faculty of Mechanical Eng. Univerze v Mariboru University of Maribor Smetanova 17 Smetanova 17 2000 Maribor 2000 Maribor, Slovenia jure.marn@uni-mb.si jure.marn@uni-mb.si zoran.zunic@uni-mb.si zoran.zunic@uni-mb.si matjaz.ramsak@uni-mb.si matjaz.ramsak@uni-mb.si primoz.ternik@uni-mb.si primoz.ternik@uni-mb.si Prejeto: 23.1.2002 Received: Sprejeto: 23.5.2002 Accepted: VH^tTPsDDIK stran 256