Available online at Physics Procedia 32 (2012 )

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1 Avalable onlne a Physcs Proceda 32 (2012 ) h Inernaonal Vacuum Congress, Beng of P. R. Chna, Augus 2010 Numercal research abou he nernal flow of seam-e vacuum pump: evaluaon of urbulence models and deermnaon of he shock-mxng layer Jnglang Dong a, Xaodong Wang a*, Jyuan Tu b a School of Mechancal Engneerng & Auomaon, Norheasern Unversy, Shenyang , P. R. Chna b School of Aerospace, Mechancal and Manufacurng Engneerng, RMIT Unversy, Vcora 3083, Ausrala Absrac Seam-e vacuum pump s wdely used n a range of applcaons. Ths paper evaluaed he performance of four well-known urbulence models for predcng and undersandng he nernal flow of a seam-e vacuum pump frs. Wh he help of a commercal compuaonal flud dynamcs (CFD) code ANSYS-Fluen 6.3, he smulaon resuls obaned from he concerned urbulence models were compared wh expermenal values, he k-omega-sst model was chosen as a ool model for carryng ou numercal smulaons. Then, based on he smulaon resuls obaned from specfc operang condons, a mehod for locang he shock-mxng layer was pu forward. The shape of he shock-mxng layer shows ha he secondary seam does no mx wh he prmary seam mmedaely afer beng nduced no he mxng chamber of he pump; acually, hey manan her ndependence ll he shockng poson nsead. Afer he shock happens, he shock-mxng layer dsappear, he wo flud n he pump begn o mx wh each oher and dscharge o he nex sage wh almos he same sae. Based on he shape of he shock-mxng layer and he supersonc regon of he secondary seam, a dealed analyss for he flow duc of he secondary seam was carred ou. I s found ha he hroa of he secondary seam flow duc plays a crucal role n mananng a sable operang sae and he lengh of he hroa reflecs he back pressure endurance for he pump Publshed by Elsever B.V. Selecon and/or peer revew under responsbly of Chnese Vacuum Socey (CVS). Open access under CC BY-NC-ND lcense. PACS: E-, w Keywords: Seam-e vacuum pump; CFD; urbulence model; shock-mxng layer 1. Inroducon Seam-e vacuum pump s one of he mos mporan equpmens wdely used n chemsry, peroleum, meallurgy, refrgeraon and food ndusry o oban a vacuum envronmen for varous specal echnques wh very lle elecrcal or mechancal energy consumpon. Is feaures and applcaons have been wdely dscussed by Huang e al. [1] and Eames e al. [2]. A seam-e vacuum pump s composed of a Laval nozzle, a mxng chamber, hroa and a dffuser as shown n Fg. 1 [3], velocy and pressure profles along he pump are also llusraed n he same dagram. The seam wh * Correspondng auhor. Tel.: ; fax: E-mal address: xdwang@mal.neu.edu.cn Publshed by Elsever B.V. Selecon and/or peer revew under responsbly of Chnese Vacuum Socey (CVS). Open access under CC BY-NC-ND lcense. do: /.phpro

2 Jnglang Dong e al. / Physcs Proceda 32 ( 2012 ) hgh oal energy s called he prmary seam or move seam whle he oher, wh he lower oal energy, s called he secondary seam or nduced seam. The prmary seam wh hgh pressure expands hrough he Laval nozzle and reaches o supersonc speed and produces a low pressure (vacuum) regon a he oule of he Laval nozzle. By an enranmen-nduced effec, he secondary seam s draw no he mxng chamber and acceleraed. Ths process s accompaned by energy and momenum exchangng beween he prmary and secondary seam. A normal shock wave s nduced n he hroa and he speed of he mxng flud suddenly drops o subsonc value. Furher compresson s acheved when he mxed flud passes hrough he dffuser. Fg.1: A ypcal seam-e vacuum pump and s flow characerscs Many heorecal [4-6] and expermenal [7] sudes were performed n order o undersand no only he fundamenal mechansms n erms of flud dynamcs and hea ransfer, bu also pump operaonal behavor. Alhough hese sudes made consderable and remarkable progress for he general undersandng of seam-e vacuum pump, hey sll unable o reproduce he flow physcs locally along he pump correcly, some very fundamenal problems have ye o be overcome, especally he modelng and undersandng of shock-mxng layer neracon as well as s nfluence on he mxng process and recompresson rae [8] whch wll allow a more relable and accurae desgn, n erms of geomery and operaon condons. Compuaonal flud dynamcs (CFD) s a good choce as a research ool o nvesgae and predc he complcaed flow n a seam-e vacuum pump, and s expeced o provde a good undersandng of local phenomena a a reasonable cos. Numerous CFD sudes abou hs feld have been acheved snce he 1990s [9-11], however none of hem has made effor o provde a reasonable and feasble approach o deermne he shape and locaon of he shock-mxng layer. So our prmary neres n hs paper s he deermnaon of he shock-mxng layer and he nfluence of dfferen operang parameers on. 2. Mahemacal Models 2.1. Governng equaons The flow n seam-e vacuum pump s governed by he compressble seady-sae axsymmerc form of he flud flow conservaon equaons. For varable densy flows, he Favre averaged Naver-Sokes equaons are more suable and wll be used n hs work. The oal energy equaon ncludng vscous dsspaon s also ncluded and coupled o he se wh he perfec gas law. The hermodynamcs and ranspor properes for seam are held consan; her nfluence was no found o be sgnfcan wh he valdaon runs. The governng equaons can herefore be wren n her compac Caresan form: The connuy equaon: u x (1) 0

3 616 Jnglang Dong e al. / Physcs Proceda 32 ( 2012 ) The momenum equaon: u u u x P x x (2) The energy equaon: where wh E u E P eff x T x u 2 u x u x eff u k x k 3 eff (3) P RT (5) 2.2. Turbulence modelng Mos of he urbulence models used n hs paper rely on he Boussnesq hypohess. I means ha hey are based on an eddy vscosy assumpon, whch makes he Reynolds sress ensor comng from equaon averagng, o be proporonal o he mean deformaon rae ensor: uu 2 u x u x k u x 3 The advanage of hs approach s he relavely low compuaonal cos assocaed wh he deermnaon of he urbulen vscosy, and suable for ndusral applcaon. However, he man drawback of hs hypohess s he assumpon ha he urbulence s soropc. The k-epslon, realzable-k-epslon and k-omega models are based on hs hypohess. Only he Reynolds sress model (RSM) does no rely on hs assumpon, bu he assocaed CPU cos may be relavely hgh [12]. Based on our smulaon resuls, he k-omega-sst model appears o be he mos accurae model for eecor analyss. I s herefore descrbed n more deal as below. The descrpon of he oher urbulence models lsed can be found n ANSYS Fluen Theory Gude [13]. The equaon for k s: x k ku k Gk Yk Sk The equaon for s: x k x (7) x x x u G Y D S In hese equaons, G k represens he generaon of urbulence knec energy due o mean velocy gradens, G represens he generaon of, k and represen he effecve dffusvy of k and, respecvely, Y k and Y represen he dsspaon of k and due o urbulence, D represens he cross-dffuson erm. Deals on he expressons of hese erms can be found n [14]. In addon, he eddy vscosy s redefned so as o ake no accoun he ranspor of he prncpal urbulen shear sress [14] Compressbly correcons For k-omega models, s ncluded n Y and consss n replacng M by a compressbly funcon F(M ): 0 M M 0 F M 2 2 (9) M M 0 M M 0 (4) (6) (8)

4 Jnglang Dong e al. / Physcs Proceda 32 ( 2012 ) where 2 2 M 2k a (10) M (11) a RT (12) The advanage of hs compressbly funcon s ha does no ake effec everywhere n he flow feld, bu us n some places where compressbly becomes mporan. 3. Numercal smulaons The geomerc parameers of he seam-e vacuum pump expermen model se-up by Srveerakul are summarzed n Table 1 [15]. The prmary and secondary fluds are seam and he parameers are summarzed n Table 2. The sudy by Panhong, Seehanam was shown ha he smulaon resuls for flow properes by he 2D axs symmerc model (ASXM) and hree dmensonal model (3D) were very close [16], means ha he ASXM s good enough o ge accurae resuls. ASXM s adoped n presen sudy o smulae and analyze he flow n seam-e vacuum pump whch would save los of compung cos. Table 1: Geomerc parameers of seam-e vacuum pump Table 2: Properes of seam used n he smulaon The commercal CFD code ANSYS-Fluen 6.3 was employed as a plaform for CFD smulaon. Quadrlaeral srucure meshes were used n 2D axs symmerc model, and he dense meshes are prese a he mxng zone as shown n Fg. 2(a). Fg. 2(b) shows he adaped meshes where s possble o guess he locaon of hgh velocy graden n presen sudy. Boundary condons are wo pressure nle boundares and one pressure oule boundary. Fg. 2: The srucure of seam-e pump and grd of CFD calculang doman: (a) dense meshes (b) adaped meshes

5 618 Jnglang Dong e al. / Physcs Proceda 32 ( 2012 ) The governng equaons were solved by a fne-volume approach; he convecon erms were dscrezed wh second-order upwnd scheme and a cenral dfference dscrezaon was used n he dffuson erms. The dscrezed sysem was solved by Gauss Sedel mehod. The couple-mplc solver was chosen o solve he governng equaons, enhanced wall funcons were used o descrbe he near-wall flow. Compuaons are sopped when resdues fall below 10-6, he mass mbalance (dfference beween mass flow on nle and oule boundares) falls below 10-7 and he soluon s no longer changng. 4. Resuls and dscussons 4.1. Valdaon of CFD smulaons and evaluaon of urbulence models The sac pressure of smulaon resuls obaned by he concerned urbulence models and he expermenal daa from Srveerakul [15] along seam-e pump wall under specfc operang condons (P p = Pa, P s = Pa, T p =393 K, T s =283 K, P b =3000 Pa) s shown n Fg. 3. I s clear ha he RSM model represens he sac pressure profle near he wall regon mos closely, followed by k-omega-sst model. Ths close agreemen also valdaed he mahemac models. However, neher k-epslon based models nor RSM model could gve correc smulaon resuls and descrbe he pressure curve exacly whn he range of mxng chamber. The dscrepancy beween he expermenal value and numercal value may due o he sponaneous condensaon phenomenon happened n supersonc flow [17]. Snce he resuls accuracy of k-omega-sst model s almos he same wh RSM, and he CPU cos s relavely low, he k-omega-sst model was chosen as he ool model, and he follow smulaon resuls were obaned based on he presen model and numercal sraegy Deermnaon of shock-mxng layer Fg. 3: Sac pressure profles along he seam-e pump wall In hs par, he locaon and shape of he key flow srucure n a seam-e pump, shock-mxng layer, were fnalzed by comparng he Mach values exraced from dfferen secons n he pump. Wh he help of he powerful vsualzaon funcon provded n ANSYS-Fluen package, hs purpose could be acheved feasbly and convenenly. Based on he smulaon resuls, conours lnes of Mach number (Fg. 4 (a)), under he specfc operang condon (P p = Pa, P s = Pa, T p =403 K, T s =283 K, P b =3000 Pa), a secon of arbrary n he mxng chamber (x=75 mm) was chosen as he reference poson. The Mach values profle on he reference poson along he radal drecon (Fg.4 (b)) was compared wh he Mach values dsrbuon along he axs of he pump (Fg.4 (c)), s clear ha he Mach value M A a he maxmum graden pon n Fg.4 (b) equals wh he Mach value M B a he shockng poson n Fg.4 (c), M A =M B. Accordng he classcal e pump heory, he shock-mxng layer les

6 Jnglang Dong e al. / Physcs Proceda 32 ( 2012 ) beween he prmary seam and he secondary seam, so he maxmum velocy graden s on he shock-mxng layer. I means ha he Mach number on he shock-mxng layer equals wh he Mach number on he shockng poson, based on hs concluson, he locaon of he shock-mxng layer could be found easly, and he undersandng of flow srucure n he seam-e vacuum pump became more clearly. Fg. 4: Poson deermnaon of shock-mxng layer Fg.5 represens he locaon and he shape of he shock-mxng layer nsde he pump workng under dfferen back pressures (Fg 5 (a) for P b =3000 Pa, Fg 5 (b) for P b =3500 Pa, Fg 5 (c) for P b =4000 Pa), s clear ha he secondary seam does no mx wh he prmary seam afer nducng no he mxng chamber of he seam-e vacuum pump, acually, hey manan her ndependence ll he shockng poson nsead. Afer he shock happens, he shock-mxng layer dsappear, he wo flud n he pump begn o mx wh each oher and dscharge o he nex sage wh almos he same sae. I s also observed ha, wh he back pressure ncreasng from 3000 Pa o 4000 Pa, he profle of he shock-mxng layer shrnks owards upsream, and he wo seams redsrbue her nfluence regon a he same me. Fg. 5: The poson of shock-mxng layer and he dsrbuon of workng flud n he seam-e pump 4.3 Analyss of he flow duc for he secondary seam Based on he locaon and he shape of he shock-mxng layer, s obvously ha he flow duc for he secondary seam measures up wh characerscs of general convergng-dvergng nozzle whch s also composed of convergng duc, hroa, and dvergng duc (Fg. 6 for P b =3000 Pa). The only dfference beween hem s ha he nner wall s aced by he perphery of he prmary seam e core whch s a move wall and provdes mos of he energy o accelerae he secondary seam. Mos of he enraned secondary seam reaches sonc velocy a he ndcaed secon n Fg. 6, ceran amoun of hem move faser han he sonc value when flows close o he shockmxng layer, bu slower when move close o he wall boundary layer. Meanwhle, he nensy of he prmary seam e core reduces and runs a a lower supersonc speed resulng n a relavely smooh e core. Therefore, he annulus unnel beween hs relavely smooh par of he shock-mxng layer and he wall of he hroa of he seam-

7 620 Jnglang Dong e al. / Physcs Proceda 32 ( 2012 ) e pump afer he ndcaed secon where mos of he secondary seam reaches sonc speed s acng as he hroa of he duc for he secondary seam, and he choke area or effecve area [5] of he secondary seam can be esmaed a anywhere whn he hroa of he duc for he secondary seam obvously. 4.4 Effec of operang condons Fg. 6 The srucure of he hypohecal duc for he secondary seam The nvesgaon of he effec of operang condons on shock-mxng layer was carred ou over a varey of back pressure n hs paper. Durng he smulaon, he back pressure ranged from 3000 Pa o 5500 Pa, whle he oher operang parameers were kep consan (P p = Pa, P s = Pa, T p =403 K, T s =283 K). I s already known ha he operang modes of seam-e pump could be dvded no double chokng, sngle chokng and reverse flow modes by changng back pressure n he downsream [18]. Ths phenomenon s descrbed n Fg.7 accordng he smulaon resuls. When he back pressure keeps below he crcal back pressure (P b P b * ), he pump s workng under double chokng mode, s enranmen rao remans consan and sable. When he back pressure rses above he crcal back pressure and sll below he break down pressure (P b * P b P b0 ), he enranmen rao decreases sharply. Ths sudden drop ndcaes he seam-e pump operaes n sngle chokng mode. Afer ha, f he back pressure value keeps growng (P b P b0 ), he flow srucure n he pump was broken down oally and he pump could no work any more as already dscussed n our prevous work [16]. The undersandng of effecve area [5] and hroa of he flow duc for he secondary seam could gve a more reasonable explanaon over hs phenomenon from he nernal flow srucure aspec (Fg 8). Fg. 7 Operaonal modes of seam-e pump

8 Jnglang Dong e al. / Physcs Proceda 32 ( 2012 ) Fg. 8 represens he shape of he shock-mxng layer and he secondary seam regon whch flows a a supersonc speed over a varey of back pressure. Afer knowng he characerscs of he flow duc for he secondary seam, based on he shape of he shock-mxng layer and he flowng sae of he secondary seam, he lengh of he hroa for hs duc and s effecve area sze could be locaed and evaluaed convenenly. I s descrbed ha he secondary seam becomes chokng a he same poson and he lengh of he hroa for he secondary seam flow duc shrnks owards upsream when he value of he back pressure ncreases bu sll keeps below he crcal back pressure (P b * =4300 Pa) or whn he double chokng regon. Moreover, he shape of he shock-mxng layer and he supersonc regon of he secondary seam n fron of he hroa for he secondary seam flow duc are shown unchanged. Tha means before he chokng poson for he secondary seam, he flow srucure remans consan and ndependen from he downsream condons. Tha s why he enranmen rao keeps consan when he pump s workng under double chokng mode. When he back pressure s ncreased over he crcal back pressure (P b * =4300 Pa), as s shown n Fg. 8, he shock-mxng layer s compressed no he mxng chamber of he seam-e pump, and he flow duc for he secondary seam los s hroa and s no longer suable for accelerang he nduced seam any more, hence, he secondary seam can no ge enough energy from he prmary seam o speed up self. Once he secondary seam s no chokng, he sable enranmen process s dsurbed, he enranmen rao decreases sharply as a resul. I s also demonsraed ha he lengh of he hroa of he flow duc for he secondary seam s a useful creron for evaluang he capacy of back pressure endurance for he pump. For a gven operang condons, f he secondary seam flow duc has a longer hroa, ha means he pump can work under a wde range of back pressure changng whou performance decrease. Fg. 8 The lengh of he hroa for he secondary seam duc on respec of dfferen back pressure 5. Conclusons (1) CFD approach has been used successfully o smulae and capure he ransonc flow srucure n seam-e pump, and can be used as a research ool o analyze and undersand he shock-mxng layer whch can provde a good undersandng of local flow srucure of he seam-e vacuum pump. (2) I has been shown ha he k-omega-sst model s he bes sued model o predc he pressure recovery profle along he pump wall. However, all models concerned n hs paper seem o fal n predcng pressure near he wall whn he range of mxng chamber. Ths dscrepancy may due o he sponaneous

9 622 Jnglang Dong e al. / Physcs Proceda 32 ( 2012 ) condensaon phenomenon happened n supersonc flow whch has been researched n many oher sudes and expermens. (3) The mehod nroduced n presen sudy s reasonable and feasble; can be used n locang he shockmxng layer and undersandng s feaure n he whole flow feld of he seam-e pump. (4) Based on he work of shock-mxng layer deermnaon, a dealed analyss abou he flow duc for he secondary seam s provded. I s shown ha he hroa for he secondary seam flow duc plays a crucal role n mananng a sable pump operaon sae and he hroa lengh reflecs he back pressure endurance for he pump. (5) Furher sudes should be aken based on hs work, such as he effecve area changng for he secondary seam on he respec of dfferen operang condons and pump geomeres. Tha wll be helpful for undersandng he flow mechansm of he seam-e pump and mprove s performance evenually. Acknowledgmen The fnancal suppor provded by he foundaon of nernaonal cooperaon proec (ID ), he docoral foundaon for reurnng-back scholar of Norheasern Unversy (ID ) and he Ausralan Research Councl (ID DP ) s graefully acknowledged. References [1] M.C. Huang, S.L. Chen, An expermenal nvesgaon of eecor performance characerscs n a e refrgeraon sysem. Journal of he Chnese Insue of Chemcal Engneerng E 1996; 27(2): [2] I.W. Eames, S. Aphnonraana. Research on hea operaed hea pumps and refrgeraors. Journal of he Insue of Energy 1993; 66: [3] Kananapon Chunnanond, Saha Aphornraana. Eecors: Applcaons n refrgeraon echnology. Renewable and Susanable Energy Revews 2004; 8: [4] J.H. Keenan, E.P. Neumann. A smple ar eecor. ASME Journal of Appled Mechancs 1942; 64: [5] J.T. Munday, D.F. Bagser. A new heory appled o seam e refrgeraon. Indusral & Engneerng Chemsry Process Desgn and Developmen 1977; 16: [6] I.W. Eames, S. Aphornraana, H. Hader. A heorecal and expermenal sudy of a small-scale seam e refrgeraor. Inernaonal Journal of Refrgeraon 1995; 18(6): [7] P. Desevaux, J. P. Prenel, G. Hosache. Flow vsualzaon mehods for nvesgang an nduced flow eecor. Flow Vsualzaon Image Process 1995; 2: [8] Y. Barosewcz, Zne Adoun, P. Desevaux, Yves Mercader. Numercal and expermenal nvesgaons on supersonc eecors. Inernaonal Journal of Hea and Flud Flow 2005; 26: [9] Barosewcz Y, Adoun Z, Desevaux P, Mercader Y. Numercal and expermenal nvesgaons on supersonc eecors. Inernaonal Journal of Hea and Flud Flow 2005; 26: [10] Hemd A, Henry F, Leclare S, Seynhaeve J, Barosewcz Y. CFD analyss of a supersonc ar eecor. Par 1: expermenal valdaon of sngle-phase and wo-phase operaon. Appled Thermal Engneerng 2009; 29: [11] Ouzzane M, Adoun Z. Model developmen and numercal procedure for dealed eecor analyss and desgn. Appled Thermal Engneerng 2003; 23: [12] Y. Barosewcz, Y. Mercader, P. Proulx. Numercal nvesgaons on dynamcs and hea ransfer n a urbulen under-expanded e. AIAA Journal 2002; 40 (11), [13] ANSYS INC. ANSYS-Fluen Theory gude. [14] F. R. Mener. Two-equaon eddy-vscosy urbulence models for engneerng applcaons. AIAA Journal 1994; 32(8): [15] Srveerakul T, Aphormraana S, Chunnanond K. Performance predcon of seam eecor usng compuaonal flud dynamcs: par 1. Valdaon of he CFD resuls. Inernaonal Journal of Thermal Scences 2007; 46: [16] Xao-Dong Wang, Jng-Lang Dong. Numercal sudy on he performances of seam-e vacuum pump a dfferen operang condons. Vacuum 2010; 84: [17] Ishazak K, Ikohag T, and Dagu H. A hgh-resoluon numercal mehod for ransonc non-equlbrum condensaon flows hrough a seam urbne cascade. In Proceedngs of he 6h Inernaonal Symposum on Compuaonal Flud Dynamcs 1995; 1: [18] H. Jeong, T. Uomo, M. J, Y. Lee, G. Lee, H. Chung. CFD analyss of flow phenomena nsde hermo vapor compressor nfluenced by operang condons and convergng duc angles. Journal of Mechancal Scence and Technology 2009; 23: