Numerical Modelling of Reverse Flow Phenomena in a Channel with Obstruction Geometry at the Entry

Transcription

1 WSEAS TRANSACTIONS on FID MECHANICS M.A. Kabir M.M. K. Khan and M. G. Rasl Nmerical Modelling of Reerse Flow Phenomena in a Channel wih Obsrcion Geomer a he Enr M.A. Kabir M.M. K. Khan AND M. G. Rasl Dearmen of Mechanical Engineering Carnegie Mellon niersi Pisbrgh PA 53 SA kabira@andrew.cm.ed College of Engineering and Bil Enironmen Facl of Sciences Engineering and Healh Cenral Qeensland niersi Rockhamon QD-470 Asralia Absrac: - Nmerical modelling and simlaion of he reerse flow henomenon in a channel wih obsrcion geomer a he enr were erformed sing CFD-ACE simlaion soler. Obsrcion geomeries sed for simlaion were riangle circle semicircle and fla lae. Simlaions were erformed for differen ga o widh raio for differen ga beween he es channel and obsrcion geomer and for differen Renolds nmber. The simlaed resls are discssed and comared wih flow isalizaion images. Simlaions resls rediced he occrrence of reerse flow and eisence of oher flow feares sch as ore shedding a boh ends. The nmericall rediced resls of he flow henomena are generall in good agreemen wih he eerimenall obsered flow isalizaion images. Kewords: - Reerse Flow Tes Channel Obsrcion Flow Visalizaion and Simlaion Inrodcion Reerse flow henomenon has significan imorance and can be emloed in he conrol of energ and arios flows in he rocess engineering alicaions []. There are seeral oher alicaions where hese reerse flow henomenon can occr or can be emloed sch as: in flow conrol o achiee low elociies; shear laer ineracion a aring disance aar; hea ransfer alicaions o roide differen es of flows locall; flow as obsrcion and consricions in arerial flows nder cerain hsiological condiions [ ]. Reerse flow can occr in a channel when a obsrcion geomer is laced a he enr of he channel. This flow henomenon inoles searaion reaachmen and shear laer ineracion. There are seeral arameers ha affec he reerse flow henomenon [3]. These are: shaes and size of obsrcion geomeries (circle riangle semicircle ec) ga (g) beween he obsrcion and he es channel lengh () of he es channel Renolds nmber (Re) and widh (w) of he es channel. Gowda e al. [] carried o eensie eerimenal inesigaion of he flow in a channel wih arios obsrcion geomeries (fla lae circle semicircle and riangle) a he enr. Eerimenal sdies howeer are ime consming and eensie and ma be een imossible in some geomeries and alicaions. Comaional flid dnamics (CFD) roides cheaer alernaie o eerimenal sd. Howeer onl a limied nmber of sdies on nmerical simlaion hae been fond in he lierare where Dijali e al. [4] rediced he rblence flow arond a blff recanglar lae Tafi [5] rediced flow field on a bln lae and Ali e al. [6] rediced he hree-dimensional flow field arond circlar clinder. Tafi [5] showed a flow searaion and reaachmen on bln lae. The aim of he resen sd is o simlae he reerse flow henomenon which inoles flow searaion and ore airing. The obsrcion geomeries sed in his sd were riangle semicircle recangle (fla lae) and riangle. Among all he flow arameers he shaes and sizes of obsrcion geomeries he ga beween he es channel and he obsrcion geomer and he Renolds nmber hae shown a sronger inflence on he flow field. Therefore nmerical simlaions inoling hese hree flow arameers are resened. ISSN: Isse 3 Volme 3 Jl 008

2 Goerning Eqaions The flow domain is shown in Figre. I is he same domain as considered for he flow isalizaion sdies b Kabir e al. [3]. The flow hrogh and arond he es channel was comed b soling he nsead Naier-Sokes eqaions for incomressible flid in a wo-dimensional geomer. The conini and Naier-Sokes eqaions in general form for wo dimensional flows are reseciel gien b 0 () () (3) The hree nknowns in his model are and and we hae hree eqaions o deermine hese nknowns. There are a oal of si indeenden and deenden ariables and heir nondimensional coner ars are obained b diiding each qani b is corresonding characerisics dimension. sing an aserisk o denoe a nondimensional qani i can be wrien as: T P To make hese eqaions dimensionless we ms hae o derie he nondimensional form of arios ime and sace deriaes. The ime deriaies wih resec o he dimensional ariable can be wrien as: () () () T Similarl he saial deriaes are gien b () () () () () () and ( ) ( ) ( ) ( ) Ths conini eqaion becomes ( ) ( ) 0 0 (4) The nondimensional form of conini eqaion is gien b 0 (5) sing similar rocess nondimensional Naier- Sokes eqaions can be gien b P T P T There are hree dimensionless gros in he nondimensional Naier-Sokes eqaions hese are: T P and Therefore he conini and Naier-Sokes eqaions in dimensionless form for wo dimensional channel flow where widh (w) of channel is he characerisics lengh () and is he free sream niform eloci a he enr of he es channel. Here is he dnamic iscosi; is he densi of he flid and Re is he Renolds nmber. The conini and momenm eqaions in dimensionless form can be wrien as 0 (6) Re (7) Re (8) WSEAS TRANSACTIONS on FID MECHANICS M.A. Kabir M.M. K. Khan and M. G. Rasl ISSN: Isse 3 Volme 3 Jl 008

3 WSEAS TRANSACTIONS on FID MECHANICS M.A. Kabir M.M. K. Khan and M. G. Rasl The ariables were made dimensionless as defined below b sing and w followed b droing he aserisks: w w and Re w T w P 3 Comaional Model and Bondar Condiions The wo dimensional comaional flid dnamics (CFD) model of he es channel wih differen obsrcion geomeries a he enr laced in anoher wider arallel walled channel was deeloed sing commerciall aailable sofware CFD-ACE (CFD Research Cor. Hnsille A). The CFD-ACE code sed were based on a finie olme mehod. The flow domain was discreized sing nsrcred grid. Comaional flow simlaions of his e are based on he diision of he flow domain ino small (finie) olmes. The smmer assmion was sed for solion in he es channel secion of he flow field. Seeral rails were made o eliminae he deendence of grid on he nmerical simlaion. The mesh consiss of 386 cells in he half domain wih an increased densi of cells a he es channel secions. were fied from 0.04 m/s 0. m/s 0.4 m/s and 0.36 m/s and he corresonding Renolds nmber of hese elociies were and The simlaions o sd he inflence of he shaes of he obsrcion geomeries were carried o a a fied Renolds nmber of 6000 whereas he simlaions for he inflence of he ga beween he obsrcion and he es channel were erformed for Re of 000 o The domain sed in his nmerical redicion of flow behaior inside and arond he es channel is shown in Fig.. This is he same domain sed for eerimenal inesigaions of he flow henomena of waer. The flow inside and arond he es channel was comed for waer (incomressible flid) in a wo-dimensional geomer. Volme bondar and iniial condiions were gien in CFD-ACE soler for he simlaion of he flow henomena. The olme condiions were ) incomressible flid (waer) for all domains ece obsrcion and es channel domain; ) obsrcion and es channel domain are blockage. Fig. Comaional domains for he nmerical redicion of flow Fig. Comaional flow domain The lengh and widh of he wider channel of he es secion were m 0.3 m as shown in Fig. and sed for flow simlaions in his sd. The widhs of he es channel (w) and he obsrcion geomer (b) were consan and eqal o 5 mm same as ha of eerimenal se. The obsrcion geomeries were locaed a he enr of he es channel a aring ga (g) o widh (w) raios from 0.5 o 8.0. The free sream eloci () in he wider channel The bondar condiions were: no sli condiion on; () he walls of he wider channel () he walls of he es channel (3) he walls of he obsrcion geomer and (4) he niform eloci a he enrance of he domain. The elociies and (in and direcions) were small icall 0-6 m/s as iniial condiions for all domains. The emerare for simlaions was ke a 5 o C same as sed for he eerimenal inesigaion of he flow henomena. The Renolds nmber Re was based on he free sream eloci () waer densi () and iscosi () on he widh (w) of he es channel. Pos rocessing of he resls incldes calclaion of he eloci raio inside and free sream (V i /: inside ISSN: Isse 3 Volme 3 Jl 008

4 WSEAS TRANSACTIONS on FID MECHANICS M.A. Kabir M.M. K. Khan and M. G. Rasl eloci/free sream eloci) elociies in he es channel for differen obsrcion geomeries. 4 Resls and Discssion 4. Simlaions of Shaes of Obsrcion Geomer Nmerical redicions of he flow henomena of waer were erformed for g/w raios of and 6.0. I was obsered from he eerimenal inesigaion ha arios obsrcion geomeries (ece fla lae) rodced he maimm reerse flow a g/w raio of 0.5 []. Therefore he nmerical simlaions for he g/w raio of 0.5 are resened in Figres 3a-d for discssion and comarison. In he eerimenal inesigaion he flow was obsered nsead a boh enr and ei ends of he es channel. Howeer he flow was sead in he cenral orion of he es channel. The rediced eloci ecors and sreamlines of he enr and ei end of he es channel are resened in Figres 3a-d. For a beer comarison he eerimenal flow isalizaion hoograhs of arios obsrcion geomeries are also shown a he o half of hose figres. I can be seen from he nmericall rediced eloci ecors and sream lines of arios shaed geomeries (Figres 3a-d) ha he shear laers searaing from he edges of he geomer reaached on he sidewalls of he es channel a low g/w raios. I can also be seen (Figres 3a-d) ha a low ressre zone is creaed a he ga beween he es channel and he obsrcion geomer which riggers he flow in he reerse direcion. The deails eerimenal sd of he flow henomena in a channel wih obsrcions wih arios geomeries was blished elsewhere [3]. I was seen ha a flow searaion ook lace a he enrance of he channel and he ore shedding occrs a channel ends. The shear laers a he fron and rear ends on boh sides of he channel become nsable and roll giing rise o comle ore shedding. The ore shedding near he enrance and ei cases he flow o ener and leae he es channel as can be seen in Figres 3a-d. The same orices a he channel ends were obsered for he eerimenal inesigaions [3]. This ore reglaes he flow of he waer hrogh he es channel. The magnide of he reerse flow is deermined b he combinaion of he low ressre behind he obsrcion and he ore shedding []. The rediced eloci ecors and sream lines of he reerse flow inside he es channel mach well wih he sreak lines of he flow isalizaion hoograhs. The rediced orices obsered a boh ends for riangle and fla lae obsrcion geomer are in good agreemen wih ha of flow isalizaion icres (Figres 3a and 3d). For circle he simlaed eloci ecors and sreamlines are in moderae agreemen wih he sreak lines of flow isalizaion images (Figre 3b). The fla lae obsrcion de o is shae acs as shield and roecs he adjacen negaie ressre zone from he srronding forward flow enironmen whereas he obsrcion geomeries namel circle semicircle and riangle de o heir shaes were nable o roec he negaie ressre zone as effeciel as fla lae in ariclar when he g/w raio increased; herefore he negaie ressre zone was dominan for fla lae. The higher he negaie ressre he sronger he reerse flow was inside he es channel. The magnides of he reerse flow obained from nmerical simlaions where simlaed eloci ecors and sream lines are in good agreemen wih he flow isalizaion images were seen o ar wihin 0% o % from he eerimenal ale. The general agreemen in he qaniaie and qaliaie simlaion resls was obsered for riangle circle semicircle and fla lae wih ha of he eerimenal resls blished elsewhere [3]. 4. Simlaion of Ga Nmerical redicions for g/w raios of and.5 are resened and discssed here. These g/w raios were seleced becase i was obsered from he eerimenal inesigaion ha (a) an areciable reerse flow was rodced a g/w raio of 0.5 (b) a moderael high reerse flow was rodced a g/w raio of.0 (c) a maimm reerse flow was rodced a g/w raio of.5. The simlaed eloci ecors and sreamlines of he g/w raios are shown in Figres 4a-c. The nmericall rediced eloci ecors and sreamlines are generall in agreemen wih he sreak lines of he flow isalizaion icres. The rediced magnides of he reerse flow were fond o ar wihin 0% o % from he eerimenal ale. Areciable magnide of he rediced reerse flow was seen a low g/w raio of 0.5. ISSN: Isse 3 Volme 3 Jl 008

5 WSEAS TRANSACTIONS on FID MECHANICS M.A. Kabir M.M. K. Khan and M. G. Rasl Figre 3a: Flow wih riangle a g/w 0.5 ime se 36 Re 6000 and /w 8.0 Figre 3b: Flow wih circle a g/w 0.5 ime se 33 Re 6000 and /w 8.0 ISSN: Isse 3 Volme 3 Jl 008

6 WSEAS TRANSACTIONS on FID MECHANICS M.A. Kabir M.M. K. Khan and M. G. Rasl Figre 3c: Flow wih semicircle a g/w 0.5 ime se36 Re 6000 and /w 8.0 Figre 3d: Flow wih circle a g/w 0.5 ime se 33 Re 6000 and /w 8.0 Figre 3a-d: Flow isalizaion icres showing seak lines a he o and rediced eloci ecors and sreamlines a he boom for waer. ISSN: Isse 3 Volme 3 Jl 008

7 WSEAS TRANSACTIONS on FID MECHANICS M.A. Kabir M.M. K. Khan and M. G. Rasl 4a. g/w 0.5 ime se 35 Re 6000 and /w 8.0 4b. g/w.0 ime se 33 Re 6000 and /w 8.0 ISSN: Isse 3 Volme 3 Jl 008

8 WSEAS TRANSACTIONS on FID MECHANICS M.A. Kabir M.M. K. Khan and M. G. Rasl Figre 3c: Flow wih semicircle a g/w 0.5 ime se36 Re 6000 and /w 8.0 Figre 3d: Flow wih circle a g/w 0.5 ime se 33 Re 6000 and /w 8.0 Figre 3a-d: Flow isalizaion icres showing seak lines a he o and rediced eloci ecors and sreamlines a he boom for waer. ISSN: Isse 3 Volme 3 Jl 008

9 WSEAS TRANSACTIONS on FID MECHANICS M.A. Kabir M.M. K. Khan and M. G. Rasl g/w raio of.0 and /w raio of 8.0. I can be seen from Figres 5a-b ha as Renolds nmber increases; orices disaear (ore breakdown akes lace). The similar flow henomena were obsered in flow isalizaion icres for waer. I was fond ha he rediced magnide of he reerse flow is wihin 0%-% ariaion wih he eerimenal eloci magnide. The oerall rediced eloci ecors and sreamlines of reerse flow inside he es channel a Renolds nmbers of 000 and 3000 show a good mach wih he flow aern. The ore aearing a he ei end is smaller in size and i has some agreemens wih ha of simlaed eloci ecors and sream lines. I can also be obsered ha for he Renolds nmber of 9000 he rediced eloci ecors and sreamlines are in good agreemen wih ha of he eerimenal flow isalizaion image (Figre 5c). The rediced eloci ecors and sreamlines in Figres 5a-b also show orices which are in agreemen wih he flow isalizaion icres showing sreak lines orices. 5 Conclsions The nmerical simlaion of he reerse flow henomena in a channel wih obsrcion geomer is erformed b soling he Naier-sokes eqaions for waer. The inflence of he flow arameers namel he shaes of he obsrcion geomer he ga beween he es channel and he obsrcion geomer and he Renolds nmber are sdied. I was fond ha for arios shaes and sizes simlaed eloci ecors and sreamlines are in good agreemen wih he sreak lines of he flow isalizaion hoograhs. Nmerical simlaions were carried o a g/w raios of and.5 for Renolds nmber of I was fond ha he simlaed eloci ecors and sreamlines show a good agreemen wih ha of sreak lines of he flow isalizaion icres. For g/w raio of.0 nmerical simlaions were carried o for Renolds nmbers of and The simlaed orices of he flow aern for all he cases show a fair o good agreemen wih ha of he flow isalizaion orices. I was seen ha he rediced orices of boh ends of he channel are in good agreemen wih ha of he isalizaion image orices. The nmericall rediced magnide of he eloci inside and arond he es channel was fond o ar wihin 0% o % of he eerimenal ale. The nmerical simlaions erformed for shaes Renolds nmbers and he ga indicaes ha he deeloed model shold be caable of redicing he flow behaior of an oher shaes of obsrcion geomer. References [] Kabir M.A. Flow characerisics of Newonian and non-newonian flids in a channel wih obsrcion a he enr PhD Thesis Facl of Sciences Engineering and Healh 004 Cenral Qeensland niersi. [] Gowda B. H.. Tlarkara E. G. and Swain S.K Reerse flow in a channel inflence of obsrcion geomer Eerimens in Flids [3] Kabir M. A Khan M. M. K. and Bhian M.A Flow henomena in a channel wih differen shaed obsrcions a he enrance Flid Dnamics Research [4] Dijali N. Garshore I.S. and e al. Trblence flow arond a blff recanglar lae. Par II: Nmerical redicions Jornal of Flids Engineering 3 99 P [5] Tafi D. K. and Vanka S. P A nmerical sd of flow searaion and reaachmen on a bln lae Phsics of Flids [6] Ali K. H. M. and Karim O Simlaion of flow arond iers Jornal of Hdralic Research P6-74. ISSN: Isse 3 Volme 3 Jl 008

10 WSEAS TRANSACTIONS on FID MECHANICS M.A. Kabir M.M. K. Khan and M. G. Rasl 5a. Re 000 /w 8.0 ime se 4 g/w 5b. Re 3000 /w 8.0 ime se 35 g/w ISSN: Isse 3 Volme 3 Jl 008

11 WSEAS TRANSACTIONS on FID MECHANICS M.A. Kabir M.M. K. Khan and M. G. Rasl 5c. Re 9000 /w 8 ime se 7 g/w Figre 5a-c: Flow isalizaion icres showing seak lines a he o and rediced eloci ecors and sreamlines a he boom for waer. ISSN: Isse 3 Volme 3 Jl 008