ON NEW CHALLENGES FOR CFD SIMULATION IN FILTRATION

Transcription

1 ON NEW CHALLENGES FOR CFD SIMULATION IN FILTRATION Michael Dedeing, Wolfgang Stausbeg, IBS Filtan, Industiestasse 19 D Mosbach-Lichtenbeg, Gemany. Oleg Iliev(*), Zaha Lakdawala, Faunhofe Institut fü Techno- und Witschaftsmathematik, Faunhofe-Platz 1, Kaiseslauten, Gemany. Raimondas Ciegis, Vadimas Staikovicius, Vilnius Gediminas Technical Univesity, Sauletekio av Vilnius, Lithuania 1. Intoduction Computational fluid dynamics (CFD) simulation is inceasingly used in studying vaious filtation pocesses and fo designing filte elements. Algoithms and softwae fo CFD simulations of filtation pocesses wee ealie pesented by Faunhofe ITWM [1]. This pape discusses new challenges and ecent developments in CFD simulations used in filtation pocesses. New tends such as the subgid esolution appoach, compute simulation of the efficiency test, CFD suppot fo designing filte elements with multiple poous media, and paallel computing ae discussed. The subgid esolution is a challenging appoach, which allows to account fo cetain details of the solution, still woking on elatively coase gid. To addess the challenge of simulating filte efficiency tests, we combine paamete identification fom measuements caied out on a simplified filte, with CFD simulation, in ode to pedict filte efficiency fo newly designed filte elements. Howeve, the design of such elements is still a eal challenge, and we show how CFD simulations efficiently assist such designs. New esults with the ecently developed paallel algoithms fo simulation of industial filtation pocesses ae pesented. 2. Simulation of flow though filtes We ae inteested mainly in oil filtation, thus we estict the consideations to the lamina incompessible flows. Flow though filtes may be descibed by the Navie Stokes-Binkmann equations: u ( ~ u) + ( ρu, ) u + μk t u = 0 C t u + p = 1 μ (momentum balance equation) f (continuity equation) + ( u, C) = DΔC αc (tanspot equation) 1

2 Hee u, p and C ae the velocity, the pessue and the concentation of dit paticles, espectively. Futhe on, μ ~, K, ρ ae the viscosity, the pemeability of the poous (filtation) media, and the fluid density, wheeas D and α epesent the diffusion coefficient and absoption ate fo the filte media. The equations ae solved on Catesian gid using finite volume discetization and collocated aangement of the unknowns. Special attention is paid to the efficiency of the algoithm, see [1,2] fo moe details 3. Subgid appoach Fo many eal filtes, the filte medium o the filte element geomety is eithe too fine o too complicated. A naive appoach is to use a fine computational gid at the expense of extensive memoy and computational time, but this becomes infeasible. We suggest using a subgid appoach in ode to captue the fine details. Auxiliay poblems ae solved in appopiately chosen gid cells on a elatively coase computational gid. The solutions of the auxiliay poblems ae used within a systematic and a caeful pocedue of modifying and updating the coefficients of the Navie Stokes Binkmann system in the chosen cells. Moe pecisely, if some details of the filtation medium o of the filte element geomety ae too fine to be esolved by the cuent computational gid, they ae effectively accounted fo by solving on a fine gid auxiliay poblem in the pope gid cells, and modifying the coefficients of the Navie-Stokes-Binkman equation thee. Unlike the local efinement appoach, the solution is not iteated between the coase and the fine subgids hee. The appoach is especially efficient if a seies of computations have to be done on one fixed geomety, vaying flow ate, viscosity, etc. In this case, the coefficients of the Navie-Stokes-Binkman equation ae updated only once, and all consecutive computations ae pefomed fast on the selected coase gid. The idea of the pocedue is pesented with the help of a test example and of a eal example. The test example epesents a simple geomety with a thin flat filteing medium. This poblem can be easily solved in vaious ways, hee we demonstate the idea of the subgid appoach fo solving this poblem. If we use fine enough gid, esolving the filteing medium, and having seveal cells within the filteing medium, we get accuate esults. On the othe hand, if we use in naïve way a coase gid, whee the cells ae thicke than the filte medium, we get a vey much wong esult. One way to account fo the fine details of the geomety, and still to have a easonable computational time, is to use the subgid appoach. In this case this means that all the coase cells which contain piece of the thin filteing medium will be consideed as cells whee the pemeability has to be changed. Auxiliay poblem on fine gid is solved only in these cells (and only once fo a fixed geomety), afte that the basic simulations with vaying flow ate, viscosity, etc., ae solved on the coase gid. In this simple case we get a vey accuate solution using the subgid appoach. 2

3 Gid Size Pessue Time (s) dop (mba) 2mm 578 2,00 0.5mm ,00 Subgid ,00 The second example which we conside is aleady with a complicated geomety. On the ight pictue, a fine gid is used. The thin filteing medium is well esolved fom the gid, but computations on such a gid ae vey much time consuming. On the left pictue, one sees the same filte geomety, but epesented on a coase gid. In this case, the gid can not captue the details of the filteing medium, and the esults poduced on such a gid ae useless. At the same time, using the subgid appoach on this coase gid, allows to compute the solution with 5% accuacy, using 10 times less computational time. 4. Efficiency test simulations Solving the concentation of paticles equation, equipped with absoption ate identified fom the measuements, one can simulate an efficiency test. Pictues below show the 3

4 concentation of paticles at cetain time moment (left), as well as etained capacity pofile (ight). In these simulations, the flow was not influenced by the captued paticles, what is obviously tue at the ealy stages of the filtation pocess, but it is an appoximation at the late stage of filtation. Hee we obtained a good accuacy due to the fact that in identifying the absoption ate fom measuements we used infomation fo the full opeating time of the filte. Cuently we ae woking on a futhe impovement of the model, whee the influence of the paticles captuing on the flow will be accounted fo, and the absoption ate will be identified as a time dependent function. 5. Paallel computing A significant step towads educing CPU time and inceasing the poblem size of CFD simulations is to un the simulations on paallel machines/pocessos. In SuFiS, the linea solve equies up to 90% of total CPU time and memoy fo most poblems. Theefoe, the main goal of paallel computing becomes two fold and both of them ae extemely cucial fo optimal CFD simulations. Fistly, it is the distibution of the discetization pat of the algoithm, and secondly, it is the paallelization of the linea solve. Additionally, load balancing to scale the poblem size accoding to the inceased numbe of pocessed becomes cucial fo optimal pefomance. The domain decomposition algoithm takes into account that the othogonal 3D stuctued gid is used as efeence gid fo definition of computational gid. Theefoe, a standad 3D decomposition of pocessos, p 1 p2 p, is used. This simplifies implementation of data 3 exchange algoithms, since it is easy to define the neighbous of each pocesso and ovelapping elements. METIS poves to be a good softwae fo optimal load balancing. The gid is geneated fo eal industial filtes. The figue shows an example, fo which the gaph of this gid has nodes, edges and auxiliay gid load of nodes. An inteface is povided fo communicating between SuFiS ad METIS. The paallelization of the linea solve, namely the BiCGSTAB algoithm, equies inte communication between pocessos. Implementation of matix vecto multiplication step needs additional infomation when the bounday nodes of local pat of the vecto ae updated. Such infomation is obtained by exchanging data with neighbouing pocessos in 4

5 the specified topology of pocessos. Additionally, inne poduct computations equie global communication between all pocessos. We make use of MPI outines, such as MPI_ALLREDUCE that computes the sum and distibutes to all pocessos. The following table shows esults of computational efficiency simulation tests fo paallel computing on SP5 cluste with special IBM pocessos and a special netwok. Numbe of Total time (s) Speed up Efficiency Pocessos Conclusions We pesented new tends fo simulating filtation pocesses efficiently. In the subgid appoach, it is appaent that the pecision of pessue dop is stongly dependent on the accuacy of updated local pemeability pescibed fo the filte media. It is shown that an update using the Dacy law can give faily accuate esults. On the paallel computing end, it is shown that the paallel algoithm, using METIS fo optimal load balancing, and MPI outines fo intecommunication between pocessos, scales well in computational time and memoy. It is clea that it is eady fo efficient simulation of filtation pocessed with complicated geometies. Refeences [1] O.Iliev, V.Laptev, D.Vasileva, Algoithms and softwae fo flow though oil filtes. Filtech Euopa, Volume I, p. I I-334, Octobe [2] R.Ciegis, O.Iliev, Z.Lakdawala, On Paallel Numeical Algoithms fo Simulating Industial Filtation Poblems, Computational Method in Applied Mathematics, Volume 7 (2007), No. 2, p