ON COUPLED MICRO- AND MACRO SIMULATION FOR FILTRATION PROCESSES

Transcription

1 ON OUPLED MIRO- AND MARO SIMULATION FOR FILTRATION PROESSES 1. Inrodcion Zahra Lakdawala(*, Oleg Iliev, and Andreas Wiegann Franhofer Insi für Techno- nd Wirschafsaheaik, Franhofer-Plaz 1, Kaiserslaern, Gerany. Keywords: Solid-Flid Separaion, oper Silaion. Mos research on odeling and silaion of filraion processes is done separaely on differen scales, naely he icro and and acro scales. On he icro scale one deals wih individal dir paricles and wih he resolved geoery of he filer edi, while on he acro scale one considers coplee filer eleens, concenraion of paricles, and poros edia approxiaions for he filer edi. Apparenly, he processes on he differen scales are no independen fro each oher: he icro scale geoery changes de o he deposied paricles and herefore changes he acroscopic paraeers sch as pereabiliy and absorpion rae, which depend on he icro scale eqaions. On he oher hand, he acroscopic velociies and pressre inflence he filraion processes on he icro scale. An idea for copled odelling and silaion on he icro- and acro- scales is discssed here. The approach is based on a fracional ie sep discreizaion, wih consecively solving sbprobles on he icro and acro scales. The acro scale paraeers, pereabiliy and absorpion rae, are consecively pscaled fro solions of icro scale probles. The acroscopic solion a each ie sep is downscaled o provide inp velociy and paricles disribion for he icro scale silaions. The changes in he icrosrcre are oniored in seleced locaions of he filer edia in order o provide proper inforaion for he pscaling procedre. The paper concerns he coper silaion of filraing solid paricles fro a flid. The flow rae-pressre drop raio, he dir sorage capaciy, and he size of he peneraing paricles need o be analyzed on boh he icro scale (he scale a which separae paricles flow in he pore space of he filering edi and he acro scale (he flow hrogh a filer eleen. Earlier, Franhofer ITWM has presened algorihs and sofware for silaions on he icro scale only, see, e.g. [1, 2], and for silaions on acro scale only, see, e.g., [3, 4]. The crren work concerns he copled silaion of filraion processes on boh scales. Below, we shorly presen he acro scale and he icro scale odels, and discss heir advanages and disadvanages. Nex, we presen an approach for copled silaion on he icro and acro scales. 2. Macro scale odel As shown in he figre, on he acro scale, he Navier Sokes-Brinkann syse is copled wih a acroscopic eqaion for he concenraion of paricles where, p and 1h World Filraion ongress Page I - 285

2 are he velociy, he pressre and he concenraion of dir paricles, respecively. For ore deails, please refer o [3, 4]. ( ~ (, K p 1 (oen balance eqaion f (coniniy eqaion (, D (ranspor eqaion Pereabiliy Navier-Sokes-Brinkan Macroscale Rae of absorpion Paricles concenraion Noe ha,, K and, which denoe he velociy, he pereabiliy and he absorpion rae of he filer edia, serve as binding paraeers for copling he acro scale silaions wih he icro scale silaions. In general, a acro scale odel can be sccessflly sed for silaing filraion processes a he level of a filer eleen. The pereabiliy and he absorpion rae need o be deerined fro easreens, if icro scale silaions are no available. Sch an approach is discssed in [4]. Deerining he pereabiliy and absorpion rae opens new horizons for a beer ndersanding of filraion processes. 3. Micro scale odel The icroscopic odel for he oion and deposiion of paricles is described by a sochasic ordinary differenial eqaion. For frher deails, please refer o [1, 2] 1h World Filraion ongress Page I - 286

3 d dxvd ( x ( x d R 6 2 2kBT dw(, dw( d i j ij QE ( x ddw( Here x,, R and denoe he posiion, velociy, radis and ass of paricle, respecively. Frher,, and denoe he flid velociy, densiy and viscosiy. T B Addiionally, denoes he ie, whereas, k and dw( denoe he abien eperare, Bolzann consan and 3d probabiliy (Wiener easre. In general, he capaciy of oday s copers does no allow o solve hese eqaions in a fll filer eleen. The eqaions provide a very good opion for local silaions in a sall par of he filering edi, b he variaions a he level of he filering eleen can no be capred in his case. In his conex, copling sch icro scale silaions for seleced filer edi locaions, wih he acro scale silaions for he coplee filer eleen, will allow o ge ore accrae silaion resls. Microscale Elecrical filed Sokes Paricles oion and deposiion 4. Algorih for copling he silaions on he icro scale and acro scales erainly, he processes on differen scales are no independen fro each oher: he icro scale geoery changes de o he deposied paricles, and herefore also he acroscopic paraeers sch as pereabiliy and absorpion rae change, becase hey depend on he icroscale solions. On he oher hand, changes in he acroscopic velociy inflence he icroscopic solion becase he raio beween he velociy and he oher forces changes. In he proposed copling approach, we solve he acroscopic eqaions wihin he coplee filer eleen, while icro scale eqaions are solved only a seleced locaions of he filering edi. The sed fracional ie sep discreizaion eans ha wihin one ie sep, acro scale and icro scale eqaions are consecively solved, wih a proper exchange of inforaion in beween hese sei-seps. A skech of one ie sep of he copling procedre is as follows. 1h World Filraion ongress Page I - 287

4 1. A he seleced locaions of he filering poros edia, local Sokes probles, as well as sochasic ODEs describing he oveen and deposiion of paricles, are solved; 2. Based on a consecive pscaling procedre, hese resls are sed o pdae pereabiliy and he absorpion rae in he seleced locaions; 3. A proper inerpolaion procedre is sed o calclae proper pereabiliy and absorpion rae in he fll poros edi; 4. The pdaed pereabiliy and absorpion rae are sed o perfor a sei ie sep wih he acroscopic algorih; 5. The velociies and he concenraion of paricles are downscaled in order o provide inp for he icro scale copaions a he nex ie sep. Pereabiliy Rae of absorpion Macroscale Inflow Velociy Inflow oncenraion Microscale Upscaling Downscaling filraion (life ie Filer eleens design filraion (clogging 5. onclsion Undobedly, he inerplay beween acro scale and icro scale silaions reflecs he re nare of filraion processes. A concenraion eqaion is inrodced as an exension o he previosly sed acro odel in SFiS, serving as he binding eqaion 1h World Filraion ongress Page I - 288

5 o cople icro scale and acro scale silaions. We have presened an idea ha enables his copling beween liple scales wih he help of a syseaic ieraive procedre of pdaing paraeers appropriaely on he level of boh scales. This frher gives an insigh o he ie-dependen clogging of filer edia for hose finie regions of he filer, where icro fibros srcres were resolved. Wih proper inerpolaion and approxiaion procedres, his frher provides a new plafor for aaining approxiaes for filer efficiency and filer clogging o enhance he design of innovaive filers. References [1] A. Laz and A. Wiegann, Silaion of flid paricle separaion in realisic hree diensional fiber srcres. Filech Eropa, Vole I, pp. I I-361, Ocober 23. [2] S. Rief, D. Kehrwald, K. Schid, A. Wiegann, Silaion of ceraic DPF Media, Soo deposiion, Filraion efficiency and pressre drop evolion, World Filraion ongress, Leipzig, 28 [3] O.Iliev, V.Lapev, D.Vasileva, Algorihs and sofware for flow hrogh oil filers. Filech Eropa, Vole I, pp. I I-334, Ocober 23. [4] M. Dedering, W. Sasberg, O. Iliev, Z. Lakdawala, R. iegis, V. Sarikovicis, On new challenges for FD silaion in filraion, World Filraion ongress, Leipzig, 28. 1h World Filraion ongress Page I - 289