NUMERICAL SIMULATION OF FLUID FLOW IN ENCLOSED ROTATING FILTER AND DISK

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1 VOL., NO. 9, SEPTEMBER 010 ISSN ARPN Jounal of Engineeing and Applied Sciences Asian Reseach Publishing Netwok (ARPN). All ights eseved. NUMERICAL SIMULATION OF FLUID FLOW IN ENCLOSED ROTATING FILTER AND DISK Yaan Taamneh Depatment of Mechanical Engineeing, Tafila Technical Univesity Tafila, Jodan ABSTRACT Computational fluid dynamics is used to investigate the behaviou of the fluid flow nea otating filte and disk suface in closed housing. The study focused on the lamina flow and wide gap egion. A commecial finite volume package FLUENT was used to visualie the natue of the flow suounding the otating disk. The fluid is assumed to be Newtonian, incompessible, non-fouling and isothemal. It was found that the viscous dag coefficient on the otating filte and disk suface is stongly govened by the Reynolds numbe. The otating filte in a closed housing was found to poduce high viscous dag (shea stess) compaed to otating disk. Inceasing the otation speed of the filte incease the static pessue inside the filte due to centifugal foce induced inside it. Theefoe, a back pessue phenomenon may be aised. Viscous dag coefficient fo the case of disk otating in closed housing was found to be in good ageement with pevious expeimental esults. Keywods: CFD simulation, otating filte, lamina flow, wide gap. 1. INTRODUCTION The estimation of the toque due to skin fiction on otating disks is impotant because of its application in the calculation of losses in many diffeent industial machiney [1-4]. The pioneeing wok on the flow due to otating disk has been done by von Kaman [-6]. He was pehaps the fist who deive a theoetical expession fo the toque on a smooth disk otating in an infinite fluid when the flow is tubulent. Ealy chaacteiation of the hydodynamics of a otating disk in a closed cylindical enclosue was epoted by Daily and Nece in 1960 [7-10]. They showed that the hydodynamic of a otating disk with adius and axial gap s in housing ae govened by two paametes. Gap Reynolds numbe whee the width of the gap is the chaacteistic length ( Re s = ω s / υ ) o the adial Reynolds numbe whee the adius of the disk is the chaacteistic ( Re = ω / υ ), the second paamete is the atio between the width of the gap and the disk adius ( s/ ). By measuing the toque acting on the shaft and coelating the fictional toque coefficient with the Reynolds numbe and axial cleaance, they wee able to diffeentiate fou flow egimes. Region Ι: Lamina flow and naow gap ( Re 4 Re.10 ), the bounday s, layes ae meged and poduce a shea ate vaying invesely with spacing s. Region ΙΙ: lamina flow and sepaate bounday layes ( Res 4, Re.10 ), sepaate lamina bounday layes ae fomed and the shea ate is independent on s. between the two layes will develop a one that moves like a solid body with a otation speed of Kω whee 0 < K >1. Region ΙΙΙ: Tubulent flow and naow gap ( Re.10 and s/ 0.0), the flow is chaacteised by meged tubulent bounday layes. Region ΙV: Tubulent flow and wide gap ( Re.10 and s/ 0.0), two tubulent bounday layes with the angula velocity Kω, whee 0 < K > 1. Thee seems to be lack of computational woks on estimating the skin fiction fo a poous disk otating in a closed cylinde flow in axisymmetic lamina flow egime. Theefoe, this pape aims to povide a CFD simulation study that focused on lamina flow egime and wide gap fo a smooth poous disk otating in a closed cylinde ( Re.10 and Res 4). Anothe sub goal of the pesent study is to test whethe FLUENT, a commecial Computational Fluid Dynamics softwae package, is capable of poviding the solutions fo the poblem unde consideation.. THEORY.1. Govening equation The steady lamina flow of viscous incompessible fluid and axisymmatic nea an enclosed otating disk with a constant angula velocity is consideed. Unde these conditions the incompessible Navie- Stokes equations in cylindical pola coodinates educe to. v v v 1 p v v v v θ + = v ν (1) ρ v θ vθ v vθ vθ vθ vθ v + = + v ν + + () v v v + v v + v v + 1 p v 1 v v = + ν + + ρ = 0 whee v,, v ae the adial, tangential and axial v θ components of the velocity, ρ is the fluid density and ν the (3) (4) 48

2 VOL., NO. 9, SEPTEMBER 010 ISSN ARPN Jounal of Engineeing and Applied Sciences Asian Reseach Publishing Netwok (ARPN). All ights eseved. dynamic viscosity of the fluid. P denotes the fluid pessue... Bounday conditions Since the geomety of an axisymmetic geomety is consideed a half geomety pat otated about an axis paallel to the velocity inlet is modeled. The bottom bounday of the domain is modeled as an axis bounday. The suface of the housing is modeled as a wall. The voids of the otating filte disk is modeled as poous jump, whee as the solid pat as a wall. The exit of the pemeable filte disk is modeled as pessue outlet. The flow inlet to the closed housing is modeled as velocity inlet. Figue-1. Schematic of the enclosed otating disk filte showing the solution domain and Computational gid with bounday conditions... Computational fluid dynamics A finite volume method is employed using commecial softwae FLUENT 6. to solve the govening equations subject to specified bounday conditions. The model has been solved in two dimensions and the entie egion is meshed (see Figue 1). The CFD tool can also accommodate numeous epesentation of flow in poous media. Fo a Newtonian isothemal and incompessible fluid, flow though a poous medium can be descibed using the poous jump model [8]. No slip bounday conditions ae set at all solid wall boundaies. The flow inside the poous media is assumed to be lamina. Moe cells ae constucted nea the suface of the disk to compensate the high velocity gadient in the bounday laye egion of the viscous flow. A commecial softwae GAMBIT is used fo gid geneation. The coupling between the pessue and velocity fields is achieved using PISO. A second ode upwind scheme is used fo the convection. Hee in this study, the dimensionless toque coefficient (viscous dag coefficient) fo a disk wetted on both sides and a Reynolds numbe can be defined as: C M M = 1 ρω o M = o τ θ 0 ( πd) Re ω o = () ν Whee 0 is the oute adius of the disk, M is the total toque equied to tun a disk and, τ the tangential wall θ shea stess on the disk. The gid independence is achieved by compaing the esults of the diffeent gid cell sie. It was found that 4000 cells ae satisfactoy, and any incease beyond this sie would lead to an insignificant change in the esulting solution. 3. RESULTS AND DISCUSSIONS CFD Simulation esults fo smooth otating disk in closed housing ae fistly compaed to expeimental data to veify the validity of the CFD simulation solution. Figue shows the total viscous dag coefficient as a function of Reynolds numbe fo the case of otating disk. As can be seen fom Figue, thee is an excellent ageement in the Reynolds numbe dependence of C M between CFD simulations in this study and the expeimental measued dependence by []. The effects of Reynolds numbe on the total viscous dag coefficient fo otating filte and disk ae shown in Figue 3. It is clea that C M values gadually decease with incease in Reynolds numbe fo otating filte and disk. It can also be seen that the otating filte exhibit lage viscous dag coefficient compaed to otating disk due to the suction 49

3 VOL., NO. 9, SEPTEMBER 010 ISSN ARPN Jounal of Engineeing and Applied Sciences Asian Reseach Publishing Netwok (ARPN). All ights eseved. effect on the bounday layes. This means, that moe enegy input is needed to tun the filte. The diffeence in the value of the viscous dag between the otating filte and disk decease significantly by inceasing the Reynolds numbe especially at high Reynolds numbe. The eason behind that efes to the fluid flow tubulences. Figues 4 and Figue show the axial distibution of swil and adial velocities component espectively fo otating filte and disk. It is clea that fo otating filte the swil velocity component decay shaply away fom the filte suface. This in tuns decease the bounday laye thickness nea the otating filte suface and enhance the shea ate. The axial distibution adial velocity components close to the otating filte suface inceasing due to the effect of suction (see Figue ). Figue-. Compaison of computed viscous dag of disk otating in a housing with the expeimental coelation Schlichting []. Figue-3. Vaiation of the viscous dag as a function of Reynolds numbe fo otating filte and disk. 0

4 VOL., NO. 9, SEPTEMBER 010 ISSN ARPN Jounal of Engineeing and Applied Sciences Asian Reseach Publishing Netwok (ARPN). All ights eseved. Figue-4. The axial distibution of swil velocity fo otating filte and disk at a adial distance /R = 0. fo Re = Figue-. The axial distibution of adial velocity fo otating filte and disk at a adial distance /R = 0. fo Re = The effect of filte otation on the flow patten is illustated clealy on steamline contou Figue 6 (a). The otation speed of the filte disk leads to fluid ciculation. Figue 6 (b) shows the contous of static pessue fo otating filte in closed housing. It can be seen that the local pessue suounding the otating filte is almost constant. Wheeas, the static pessue inside the filte vaies accoding to the centifugal foce induced inside. Since the centifugal foce depends only on the otation speed of the filte and not on the local pessue inside the housing, we expect that by inceasing the otation speed of the filte a back pessue is poduced and thus low pemeate ate is obtained. 1

5 VOL., NO. 9, SEPTEMBER 010 ISSN ARPN Jounal of Engineeing and Applied Sciences Asian Reseach Publishing Netwok (ARPN). All ights eseved. (a) (b) Figue-6. (a) Contous of static pessue in Pa (b) vaiation of contous of steam function fo otating disk at Re = CONCLUSIONS The steady lamina flow of viscous incompessible fluid induced by a smooth otating filte and disk in closed housing using computational fluid dynamics ae caied out. The natue of the fluid flow nea a otating disk and filte inside a closed housing was visualised. The dependency of the viscous dag coefficient on the Reynolds numbe was shown. It was found that the otating filte exhibit lage viscous dag coefficient due to the suction effect on the bounday layes. A high otation speed of filte may poduced a back pessue which could be educed by inceasing the inlet feed pessue. Compaison the simulation esults with the expeimental data validate the commecially-available softwae FLUENT in poviding a easonable good solution of complicated flow stuctues, including flow with ciculation. It emains to be veified the effect of filte pemeability, feed pessue, angula velocity of the filte on the otating filte pefomance. Such simulation ae cuently unde way and esults will be epoted in fothcoming manuscipt REFERENCES [1] Daily JW, Nece RE Chambe dimension effects on induced flow and fictional esistance of enclosed otating disks. J. Basic Eng. 8: [] J. Mukes and C.G. Calsson Cossflow Filtation. Wiley, New Yok. [3] Y. Taamneh Numeical and Expeimental Investigation of Dynamic Filtes. PhD Thesis. TU Kaiseslauten, Gemany. [4] R. Booeae, M. Y. Jaffin, L. Dingand P. Paullie Influence of geomety and angula velocity on pefomance of a otating disk filte. AICHE j. 46: 7-6. [] Schlichting H. Bounday laye Theoy, New Yok: McGaw-Hill; [6] J.A. Engle Investigation of membane filtation in a otating disc geomety: using of computational fluid dynamics and laboatoy evaluation. PhD thesis. Rice Univesity, Houston. [7] C. A. Sea, M. R. Wiesne A compaison of otating and stationay membane disk filtes using computational fluid dynamics. J. Memb. Sci. 16: [8] Y. Taamneh, S. Rippege Appoximate Solution Using Momentum Integal in Estimating the Shea Stess ove a Poous Rotating Disk. Intenational Jounal of Dynamic of Fluids. 6() : 1-. [9] Y. Taamneh, S. Rippege Pefomance of single and double shaft disk sepaato. Physical Sepaation in Science and Engineeing. 008 (1): 1-

6 VOL., NO. 9, SEPTEMBER 010 ISSN ARPN Jounal of Engineeing and Applied Sciences Asian Reseach Publishing Netwok (ARPN). All ights eseved. [10] Y. Taamneh, L. Steinke, S. Rippege Investigation of Dynamic Filtes Using CFD. 10 th Wold Filtation Congess Poceedings. : [11] Y. Taamneh, L. Steinke and S. Rippege Einfluss de Geometievehältnisse auf die Sepaation mittels otieende Membanen. Chemie Ingenieu Technik. 79(9):