Title. Author(s)Tabe, Yutaka; Lee, Yongju; Chikahisa, Takemi; Kozaka. CitationJournal of Power Sources, 193(1): Issue Date

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1 Ttle Numercal smulaton of lqud water and gas flow n electrolyte membrane fuel cells usng the lattce Bo Author(s)Tabe, Yutaka; Lee, Yongju; Chkahsa, Takem; Kozaka CtatonJournal of Power Sources, 93(): 24-3 Issue Date Doc URL Type artcle (author verson) Fle Informaton JPS93-_p24-3.pdf Instructons for use Hokkado Unversty Collecton of Scholarly and Aca

2 Numercal smulaton of lqud water and gas flow n a channel and a smplfed gas dffuson layer model of polymer electrolyte membrane fuel cells usng the lattce Boltzmann method Yutaka Tabe a, *, Yongju Lee a, Takem Chkahsa a and Masaya Kozaka b a Dvson of Energy and Envronmental Systems, Graduate School of Engneerng, Hokkado Unversty N3 W8, Kta-ku, Sapporo , Japan b Department of Battery and Fuel Cell Systems, Htach Research Laboratory, Htach, Ltd., Japan -, Omka-cho, 7-chome, Htach , JAPAN * Correspondng author. Tel.: ; fax: E-mal address: tabe@eng.hokuda.ac.jp; N3 W8, Kta-ku, Sapporo , Japan. Abstract Numercal smulatons usng the lattce Boltzmann method (LBM) are developed to elucdate the dynamc behavor of condensed water and gas flow n a polymer electrolyte membrane (PEM) fuel cell. Here, the calculaton process of the LBM smulaton s mproved to extend the smulaton to a porous medum lke a gas dffuson layer (GDL), and a stable and relable smulaton of two-phase flow wth large densty dfferences n the porous medum s establshed. It s shown that dynamc capllary fngerng can be smulated at low mgraton speeds of lqud water n a modfed GDL, and the LBM smulaton reported here, whch consders the actual physcal propertes of the system, has sgnfcant advantages n evaluatng phenomena affected by the nteracton between lqud water and ar flows. Two-phase flows wth the nteracton of the phases n the two-dmensonal smulatons are demonstrated. The smulaton of water behavor n a gas flow channel wth ar flow and a smplfed GDL shows that the wettablty of the channel has a strong effect on the two-phase flow. The smulaton of the porous separator also ndcates the possblty of controllng two-phase dstrbuton for better oxygen supply to the catalyst layer by gradent wettablty desgn of the porous separator. Keywords: PEM fuel cell, Lattce Boltzmann method, Two-phase flow, Large densty dfference, Gas dffuson layer, Wettablty Nomenclature c : characterstc partcle speed (m s - ) c : restrcted veloctes of partcle ensembles (m s - ) f : partcle velocty dstrbuton functons for the calculaton of an order parameter g : partcle velocty dstrbuton functons for the calculaton of a predcted velocty g : gravtatonal acceleraton (m s -2 ) H : vertcal length of smulaton doman (m) L : characterstc length (m) - -

3 p Sh t t 0 : pressure (Pa) : Strouhal number : tme (s) : characterstc tme scale (s) : tme step durng whch the partcles travel across the lattce space (s) Δt U : characterstc flow speed (m s - ) u : current velocty (m s - ) u * : predcted velocty (m s - ) x, y : poston coordnates (m) Δx : spacng of the cubc lattce (m) κ f : constant determnng the wdth of the nterface of two phases κ g : constant determnng the strength of the surface tenson μ : vscosty (Pa s) ξ : coordnate perpendcular to the nterface (m) ρ : densty (kg m -3 ) ρ 0 : reference densty (kg m -3 ) σ : nterface tenson (N m - ) τ f, τ g : dmensonless sngle relaxaton tme : order parameter 0 : reference order parameter superscrpt, subscrpt eq : equlbrum state n : nflow G : gas L : lqud S : sold α, β : Cartesan coordnates. Introducton Water management s essental to mprove the performance of polymer electrolyte membrane (PEM) fuel cells. Whle the membrane needs to be fully hydrated to mantan hgh proton conductvty, excessve amounts of water condense n the gas dffuson layers and gas flow channels and prevent the supply of reactants to the electrodes under hgh current densty condtons. Ths phenomenon causes mass transport lmtatons and deterorates the cell performance. The objectve of ths paper s to evaluate the dynamc behavor of condensed water and gas flows n a PEM fuel cell usng numercal smulatons, and an advanced lattce Boltzmann method for two-phase flow wth large densty dfferences was developed. Understandng lqud water behavor n PEM fuel cells s of consderable practcal sgnfcance. Several studes have been conducted on two-phase flows n PEM fuel cells. Theoretcal one-dmensonal models for lqud water transport n gas dffuson layers (GDLs), where lqud water s controlled by capllary forces dependng on the structure and wettablty of GDL, have been reported [,2], and three-dmensonal smulatons usng two-phase models have been developed [3,4]. For lqud water transport n gas flow channels, expermental nvestgatons have been conducted usng transparent fuel cells and t was demonstrated that the surface tenson of water and the wettablty of the GDL and gas flow channel play a - 2 -

4 domnant role n the lqud water transport [5,6]. Some numercal smulatons of the dynamc behavor of condensed water, whch would be strongly affected by the wettablty of GDL and gas flow channel, have been reported. The lattce Boltzmann method (LBM) was appled and t was establshed that LBM can be a powerful tool to estmate two-phase flow n the gas flow channels [7,8]. Two-dmensonal smulaton employng the volume of flud (VOF) method were performed to nvestgate the dynamc behavor of a water droplet subjected to ar flow n the bulk of the gas channel [9]. Recently, some smulatons of condensed water dstrbutons n a GDL have been developed usng pore-scale modes, e.g. pore-network modelng, representng a porous medum at the mcroscopc scale by a lattce of wde pores connected by narrower constrctons termed throats [0] and a full morphology model relyng on decomposng dgtal mages of the GDL wth pore radus as the orderng parameter at a specfed pressure durng dranage []. Ths paper develops the numercal smulaton usng the lattce Boltzmann method (LBM) to understand the dynamc behavor of condensed water and gas flow n a GDL and a gas flow channel. The LBM wth the smple algorthm has a number of advantages as stated below, but s attended wth much dffculty n mantanng contnuty at the nterface to smulate two-phase flows wth large densty dfferences lke condensed water and ar n a fuel cell. Here, the calculaton process of the smulaton was mproved to extend the smulaton n a porous medum lke a GDL, and stable and relable smulaton of two-phase flows wth large densty dfferences n the porous medum was establshed. Usng the mproved smulaton, the applcablty of the LBM and approprate condtons to smulate lqud water behavor n the GDL are dscussed, and the sgnfcant advantages of ths smulaton, whch can evaluate actual physcal propertes, were dentfed. Further, two-dmensonal smulatons demonstrated examples of the two-phase flow affected by the nteracton between lqud water and ar flows n a fuel cell. The effect of the wettablty of the gas flow channel on the two-phase flow behavor was nvestgated, and the possblty of controllng the two-phase dstrbuton usng a porous separator wthout channels s presented. 2. Method of smulaton The LBM smulates mass and heat transport phenomena by trackng movements of partcle ensembles where the veloctes are restrcted by a fnte set of vectors. The partcle populaton s expressed by dstrbuton functons, and the tme evoluton of the dstrbuton functons s calculated by a smple law of collson and transton, and t s shown that macroscopcally the LBM s equvalent to a contnuty equaton and the Naver-Stokes equatons for ncompressble fluds. Addtonally, ntroducng the nteracton of the partcles n the equaton makes t possble to smulate mult-phase flow. Because of the smple algorthm, the LBM has a number of advantages: flexblty for complex boundary geometres, smplcty for parallel computng and accurate mass conservaton. In mult-phase flow, trackng nterfaces s not needed and dstnct nterfaces are mantanable wthout any artfcal treatments. To smulate condensed water behavor n the 3-dmensonal gas flow channels of a PEM fuel cell, the advanced LBM proposed by Inamuro et al. [2] was appled and the authors have confrmed that two-phase flows wth large densty dfferences, densty ratos up to,000, can be calculated [7,8]. The greatest advantage of ths LBM s that t can evaluate the - 3 -

5 nteracton between the gas flow and condensed water n the fuel cell where all the propertes and condtons such as denstes, vscostes, an nterface tenson, wettablty and flow veloctes can be smulated. In the model, the non-dmensonal varables are defned by a characterstc length L, a characterstc partcle speed c, a characterstc tme scale t 0 = L/U, where U s a characterstc flow speed, a reference order parameter 0, and a reference densty ρ 0 s also used [2], and non-dmensonal s represented by a crcumflex. Ths paper uses a two-dmensonal 9 veloctes model (2D9V model) and the veloctes of partcle ensembles are restrcted to the followng vectors ĉ ( =, 2,, 9) n the 2-dmensonal case as shown n Fg. [3]. c, c 2, c 3, c 4, c5, c6, c7, c8, c () Two partcle velocty dstrbuton functons, f and ĝ, are used. The f functon s used for the calculaton of an order parameter whch dstngushes two phases: G corresponds to gas phase, lqud phase, and G the nterface. The ĝ L functon L s used for the calculaton of a predcted velocty of the two-phase flud wthout a pressure gradent. The evoluton of the partcle dstrbuton functons f and ĝ wth velocty ĉ at pont x and tme t are computed by the followng equatons. f ( x c t, t t) f [ ( x, t) f( x, t) f f eq ( x, t)] (2) g ( t, t t) g (, t) [ g (, t) g x c x x g eq ( x, t)] u u G 3Ec x 3Ec y g x (3) x x x Here, f and ĝ eq are the equlbrum dstrbuton functons, τ f and τ g are dmensonless eq sngle relaxaton tmes, E s the assocated weght coeffcents presented below, spacng of the cubc lattce, x s the t s the tme step durng whch the partcles travel across the dstance of the lattce spacng, s the densty, s the vscosty, û s the current - 4 -

6 - 5 - velocty and ĝ s the gravtatonal acceleraton. The subscrpts α and β (= x, ŷ ) represent Cartesan coordnates and the summaton conventon s used. The thrd and last terms on the rght hand sde of Eq. (3) represent the effects of vscous stress and gravtaton, respectvely. The order parameter dstngushng two phases and the predcted velocty * û of the mult-component fluds are defned n terms of the two partcle velocty dstrbuton functons. 9 f (4) 9 * c g u (5) The equlbrum dstrbuton functons eq f and eq ĝ n Eqs. (2) and (3) are gven by the followng equatons x x p F H f f f eq f c c G E u c E ) ( 3 (6) u u c c u u u c E g eq g c c x u x u x ) ( g g F c c G E (7) Where, 36, 9, E E E E E E E E E, 0, H H H H, ),9 2,3, ( 3, 3 5 E F F. κ f s a constant parameter determnng the wdth of the nterface between two phases, κ g s a constant parameter determnng the strength of the surface tenson, and the parameters 0 p and G αβ are explaned n Ref. [7]. The nterface tenson s obtaned by the followng equaton. 2 d g (8)

7 Here, s the coordnate perpendcular to the nterface. The frst and second dervatves are calculated usng the LBM-specfc fnte-dfference approxmatons [2]. Because the predcted velocty û * gven by Eq. (5) s not satsfed by the contnuty equaton ( u * 0 ), a correcton of * û s requred. The current velocty û whch satsfes the contnuty equaton can be obtaned wth the followng equatons. u u * p Sh t p u * Sh t (9) (0) Here, Sh U / c s the Strouhal number and p s the pressure of the two-phase flud; note that ths defnton gves the followng relatonshps, t Shx, whch s represented by t x / c wth dmenson and means that the partcles travel across the lattce space x durng tme step t. Ths paper solved Eq. (0) usng the successve over relaxaton (SOR) method. Detals of ths model are descrbed n a prevous paper [7]. The scheme proposed by Seta and Takahash [4] was appled to consder the wettablty. In ths scheme, the effect of wettablty s establshed by the densty of the sold wall. Snce the ntermolecular force s expressed n terms of densty n the LBM, gvng the densty of a sold wall corresponds to gvng the ntermolecular force between lqud and sold wall. It was confrmed that ths scheme can smulate the effect of wettablty not only on a flat surface but also at a corner nsde a gas flow channel [8]. 3. Developments to the calculaton process The lattce Boltzmann method (LBM) for two-phase flow wth large densty dfferences has been appled to the smulaton of lqud water and ar flow n a PEM fuel cell [7] and the effect of wettablty and cross-sectonal shape on the lqud water behavor n the gas flow channels was reported [8] by the authors. However, there are problems wth the relablty of smulated results n that there s nonconservaton of the mass of the lqud water. Further, dffcultes to smulate the two-phase flow n a porous medum such as n a modfed gas dffuson layer (GDL) have been found. Ths study ntroduced some nnovatons to the calculaton process and ther effectveness was confrmed. Ths paper presents an outlne of explanatons of the key mprovements n the method of solvng the Posson equaton (0) and - 6 -

8 the settngs of the boundary condtons for the pressure p on the wall and the partcle dstrbuton functon f at the nlet. Inamuro et al. solved the Posson equaton usng an addtonal LBM [2], whle here the equaton s solved usng the successve over relaxaton (SOR) method as n the case of a conventonal flud smulaton because of ts easy mplementaton. The SOR s a commonly-used soluton algorthm n conventonal flud smulatons [5]. Wth the SOR t s possble to combne the LBM wth conventonal flud smulaton, but t s necessary to ntroduce a sutable grd transformaton. In the LBM, co-locaton of a grd where velocty and pressure are defned at the same grd ponts, as shown n Fg. 2 (a), s used. In the SOR method, the calculaton usng the co-located grd nduces spatal pressure oscllatons. To prevent the spatal oscllaton, the defned velocty grd ponts were transformed as shown n Fg. 2 (b), and the SOR method used ths staggered grd. As the LBM treats the dagonal veloctes the same as the orthogonal veloctes, a formulaton based on the grd n Fg. 2 (c) was also conducted. The followng wll present an example of a 2-dmensonal smulaton for the change to the lqud water droplet n statonary ar wthout gravty, to show the mprovement that ths causes. The doman s dvded nto 60 x 40 square cells n the x and ŷ drectons ( x = 2.5 x 0-2 ), and a lqud droplet wth 5 x radus s placed at the center. The bottom and top of the doman are sold walls, and the left and rght sdes are gven as free outflow condtons. The non-dmensonal parameters for LBM are τ f =, τ g =, κ f = 0.5( x ) 2, L = and = 0.05, and the propertes for the lqud water and the ar are the same as n the next secton. Whle the lqud water droplet gradually spread n the conventonal smulaton, the droplet n the mproved smulaton mantaned ts dameter practcally unchanged. Fg. 3 shows a comparson between the conventonal and the mproved smulatons of mass change of statonary lqud water droplets. It s confrmed that the mass conservaton of the lqud water s clearly satsfed n the mproved smulaton. In the extended calculaton from flow n a gas channel to flow n a modfed GDL, the contnuty was stll broken and napproprate two-phase behavor was observed n some cases even wth the mproved method of solvng the Posson equaton. Ths was caused by the boundary condtons for the pressure at the corner n the modfed GDL as shown n Fg. 4 (a). The boundary condton for the pressure was set to keep the pressure gradent zero at the wall n solvng the Posson equaton, and the pressure value on the wall was gven by that at the neghborng cell on the flud sde. Smlarly, the pressure at a corner lke pont a n Fg. 4 (a) was gven as the equvalent of the average pressure at the adjacent flud ponts c and d. Ths boundary condton sometmes nduced non-neglgble errors n the correcton of the predcted velocty * û usng Eq. (9). Ths study dd not set the pressure at the corner to a certan value but adjusted t n each drecton lke (a-b) or (a-c) to make the pressure gradents zero. Ths means that pont a has dfferent pressure values to gve a zero pressure gradent for each drecton, whch s a computatonal technque to prevent the non-neglgble errors. It was G - 7 -

9 confrmed that ths mprovement of the boundary condton for the pressure results n good contnuty n the modfed GDL. Another problem of smulaton n the modfed GDL was that the lqud flow rate from nlet boundary decreased when the lqud passed through the GDL. The partcle dstrbuton functon f at the frst grd at the nlet as shown n Fg. 4 (b) was set prevous to be the equlbrum dstrbuton functon eq f calculated by Eq. (6) usng the nlet condtons, the order parameter of the nlet flud and the velocty û. However, n the case that the pressure drop n the nlet flud ncreased, the order parameter at the second grd n Fg 4 (b) was ncreased, and the reverse f values became larger. Ths nduced the problem that the mass flow rate of the nlet flud nto the smulated doman decreased. In ths study, the nlet partcle dstrbuton functon f at the frst grd s calculated to mantan a set flux û between the frst and second grds usng the values of the second grd. Ths boundary condton for the partcle dstrbuton functon f at the nlet makes t possble to control the nlet mass flow rate nto the modfed GDL accurately. 4. Results and Dscusson 4.. Lqud water behavor n a porous medum Two-phase relatvely slow flow n a porous medum s governed by capllary and vscous forces and dfferent flow regmes are descrbed by the relaton of these forces [6]. The capllary number Ca = uμ L /σ, whch represents the rato of vscous to capllary forces, s an mportant parameter n the behavor of condensed water behavor n a GDL: for a typcal fuel cell applcaton, the capllary number Ca s of the order of 0-8, and two-phase flow n a GDL falls n the regme of capllary fngerng [0]. Ths secton dscusses the effects of capllary number Ca on the lqud water behavor n a porous medum usng the LBM for the two-phase flow wth large densty dfferences, and also approprate condtons to smulate the lqud water behavor n the porous medum of PEM fuel cells. Fg. 5 shows two-dmensonal smulatons of lqud water flowng nto a modfed GDL wth three dfferent water veloctes. The whole doman s dvded nto 00 x 50 square cells n the x and y drectons. The vertcal length of the smulated doman s H = 0. mm. The bottom, y = 0 mm, corresponds to a mcro porous layer (MPL), and there are lqud water nflows wth a velocty of u L n from the 20μm wde pore at the center of the MPL. The two sdes, x = 0 and 0.2 mm are sold walls, and there s a free outflow openng at the top, y = 0. mm. Obstacles smulatng the carbon fbers n a GDL are added, and the porosty of the porous medum s 0.8 wth a maxmum pore dameter of about 30 μm. The sold surfaces are - 8 -

10 all set to hydrophobc wth the contact angle of 50, wth the order parameters S The smulated GDL propertes, the porosty, the maxmum pore dameter and the contact angle, are wthn the typcal range of the actual GDLs. The GDL n ths calculaton can be a frst stage model of an example of modfed GDLs n the 2-dmensonal smulaton. All the propertes of lqud water and ar are the actual establshed values. The densty rato of the lqud water to the ar s ρ L /ρ G = 847 (ρ L = 997 kg m -3, ρ G =.8 kg m -3 ), the vscostes of the water and ar are μ L = 8.54 x 0-4 Pa s and μ G =.86 x 0-5 Pa s, and the nterfacal tenson between water and ar s σ = 7.29 x 0-2 N m -. The tme step Δt s set to.0 x 0-9 s and the gravtatonal acceleraton s g = 0 m s -2. The other non-dmensonal parameters for LBM are the same as n the prevous secton. The fner tme step and grd sze ensure better convergence and accuracy of the smulaton bascally, but they nduce longer computaton tme. The approprate tme step and grd sze were selected by analyzng ther effects on the smulaton of the lqud water and the gas flow n a channel and a smplfed GDL. Fg. 5 (a) shows the smulaton results wth the fastest nlet velocty of lqud water u L n = 2.0 m s -, and the capllary number Ca = 2.3 x 0-2. After fllng the frst pore, the lqud water progresses through all four throats (left n Fg. 5 (a)). Then, t spreads out to both sdes and grows nto an almost homogeneous lqud phase from the bottom (rght n Fg. 5 (a)). In Fg. 5 (b), where the nlet velocty s u L n = 0.20 m s - and the capllary number Ca = 2.3 x 0-3, the lqud water flows selectvely nto relatvely-wde throats and pores and the drecton of progress s lmted to two paths (Fg. 5 (b)). Wth the slowest velocty u L n = m s - and the smallest capllary number Ca = 2.3 x 0-4 n Fg. 5 (c), lqud water also progresses nto two throats n the early-stages (left n Fg. 5 (c)). However, once the largest path has grown dagonally upward left, the lqud water n the other, rght, throat recedes and flows nto the man branch: fnally only one path, the one through the largest throats and pores s developed (rght n Fg. 5 (c)). Ths phenomenon of recedng water n a GDL s dscussed n the next secton. These smulaton results show that the selectvty of lqud water progresson n a GDL ncreases wth decreasng capllary number. Ths s because the effect of the capllary force on water behavor becomes domnant over the vscous force. Although the capllary number n the smulaton s much larger than that n a typcal fuel cell applcaton where Ca s of order of 0-8, the results n Fg. 5 (c) smulate the capllary fngerng well, and s consdered to be close to the actual behavor of lqud water n a GDL. Because t requres huge amounts of computaton tme to smulate the extremely slow producton of the lqud water n the actual fuel cell, the followng smulatons use 0.02 m s - as the nlet velocty of the lqud water to shorten computaton tme. Smlar smulatons were conducted, wth the vertcal length of the smulated doman H changed from 0. mm to.0 mm, and the tme step Δt.0 x 0-8 s. Here, the maxmum pore dameter becomes about 0.3 mm and ths smulates lqud water behavor n a porous separator wthout channels, lke that recently proposed as an alternatve to cells wth gas flow channels [7,8]. The results n Fgs. 6 (a), (b) and (c) correspond to those at rght n Fg. 5. In spte of the 0 tmes doman heght H, the lqud water dstrbutons are very smlar. These smulaton results ndcate that two-phase flows n the porous medum wth the same capllary number are analogous n the range of relatvely-slow veloctes because the length effects on the capllary and vscous forces cancel out

11 The LBM smulaton, consderng capllary, vscous and nertal forces, confrmed that t s possble to smulate the smlarty of capllary number Ca n two-phase flows n PEM fuel cells. Further, the LBM n ths study, whch consders actual physcal propertes, offers sgnfcant advantages n evaluatng two-phase phenomena affected by the nteracton between lqud water and ar flows Effect of ar flow n gas flow channel on the lqud water behavor The smulaton of lqud water behavor n a GDL wth ar flow n the gas flow channel was conducted as an example of a two-phase flow affected by the nteracton between lqud water and ar flows n fuel cells. Fg. 7 shows a schematc dagram of the computaton doman: the whole doman s dvded nto 00 x 35 square cells n the x and y drectons; the vertcal length of the smulaton doman s H =.0 mm; the upper and the lower parts correspond to a gas flow channel and a smplfed GDL where the channel heght s set relatvely shallow to nvestgate effects of the upper separator wall on the lqud water because the drag force of ar on lqud water becomes much stronger n a two-dmensonal channel than n an actual three-dmensonal channel. The unform ar flow and free outflow condton are at the left nlet sde, x = 0 mm, and at the rght outlet sde, x = 2.9 mm, except n the bottom parts. Unform flows of lqud water are also gven at the bottom, y = 0 mm. The veloctes of nlet ar and lqud water are 0.05 m s - and 0.02 m s -. The obstacles smulatng the smplfed GDL are hydrophobc wth the contact angle of 50 (the order parameter S = 0.025) and the effect of the wettablty of the separator s examned usng hydrophobc (contact angle 50, S = 0.025) or hydrophlc (contact angle 40, S = 0.080) walls; Δt s.43 x 0-7 s, and the propertes of lqud water and ar, and the other parameters for the LBM are the same as n the calculatons above. Fg. 8 shows the smulaton results wth the hydrophobc separator wall. The lqud water progresses selectvely through the wder pores, as n Fg. 8 (a). When the lqud water exts to the channel, the lqud water body s broken up and the adjacent water branch n the narrow GDL pore recedes, Fg. 8 (a), (b). Ths phenomenon has been suggested from ex stu vsualzaton of lqud water n a GDL usng fluorescence mcroscopy [9], and shows that the LBM can smulate ths phenomenon. After extng to the channel, the lqud water forms nto a droplet and s draned by the ar flow n the channel (Fg. 8 (b)). Fg. 9 shows the results wth the hydrophlc separator wall. The lqud water expelled from the GDL s attracted by the hydrophlc separator and forms a water flm along the wall (Fg. 9 (a), (b)). Ths attractng of the water produces a vod space and ar flow near the nterface between GDL and channel (Fg. 9 (b)). Ths may be expected to mprove the floodng characterstcs. The smulaton results confrm that the LBM s effectve to smulate two-phase flows affected by the nteracton between lqud water and ar flows, and suggests that the wettablty of the gas flow channel s mportant for the two-phase flow n a fuel cell. It further suggests that control of the wettablty of the separator can result n a favorable dstrbuton of lqud water and ar flows

12 4.3. Lqud water and ar flow behavor n a porous separator wthout channels To ensure a favorable dstrbuton of lqud water and relable ar flow, a cell wth a porous separator wthout channels was smulated. The porous separator has recently been proposed as an alternatve to cells wth gas flow channels, and the structure wthout channels s expected to enable a realzaton of unform reacton over the actve area of the membrane electrode assembly [7,8]. Fg. 0 shows a schematc dagram of the computaton doman: the obstacles smulatng the porous separator and the pore on the bottom MPL n Fg. 6 are to the left, and some further arrangements were added. The whole doman s dvded nto 00 x 50 square cells n the x and y drectons. The vertcal length of the smulated doman s H =.0 mm. The top s a wall, and unform ar flow and the free outflow are provded at the left nlet sde, x = 0 mm, and at the rght outlet sde, x = 0.2 mm. A unform flow of lqud water s also provded at the bottom pore of MPL, the veloctes of nlet ar and lqud water are 0.05 m s - and 0.02 m s -. To dscuss the water and ar flow dstrbutons n the porous separator, the doman s dvded nto three regons, (I) lower, (II) ntermedate, and (III) upper, as shown n Fg. 0. Two cases wth dfferent wettabltes of the porous separator were smulated; the sold surfaces were all hydrophobc (contact angle 50, S = 0.025) and the upper shaded portons are changed to hydrophlc (contact angle 40, S = 0.080); Δt s.0 x 0-7 s, and the propertes of lqud water and ar, and other parameters for the LBM are same as the calculatons above. Fg. shows the changes n water weght and average ar flow rates along the separator for each regon n the hydrophobc porous separator. Before 0.00 s, the lqud water weght n regon I ncrease frst followed by ncreases n regon II, as shown n Fg. (a). Smultaneously, the average ar flow rates n regons I and II decrease, ncreasng the ar flow rate n regon III, Fg. (b), where the ntal ar flow rates at the 0 s n each regon are very smlar. Fg. 2 shows the appearances of the areas of lqud water (black) and ar flow (uncolored) n the hydrophobc porous separator at three tme ponts. Dfferent from Fg. 6 (c), the lqud water does not move dagonally upward left, but due to the effect of ar flow t moves through the rght throat (Fg. 2 (a)). Then, lqud water proceedng upward s broken up and draned by the strong ar flow n regon III, establshng a dynamc equlbrum (Fg. 2 (b), (c)). Thus, the ncrease n the water weght n regon III s suppressed and the oscllatons n average ar flow rates n Fg. (b) after 0.50 s are caused by the breakup of the lqud water body. Fg. 3 shows the changes n water weght and average ar flow rates along the separator for each regon n the hydrophobc-hydrophlc porous separator. (The upper shaded portons n Fg. 0 are here changed to hydrophlc.) Fg. 4 s the appearance of the area of lqud water (black) and ar flow (uncolored) at three tme ponts n the hydrophobc-hydrophlc porous separator. The lqud water weght grows n regon III, attracted to the hydrophlc porous separator (Fg. 4 (a)). Ths nduces the ncrease n water weght n regon III after 0.06 s (Fg. 3 (a)), and the average ar flow n regon III decreases to nearly zero (Fg. 3 (b)), formng a lqud water regon along the top wall (Fg. 4 (b)). In regon II, the lqud water weght decreases and the average ar flow rate ncreases drastcally (Fg. 3 (a), (b)). - -

13 The lqud water s broken up by the strong ar flow n regon II, and a dynamc equlbrum s mantaned after s (Fg. 4 (b), (c)). It should be noted that the lqud phase along the top wall s draned by the ar flow n regon II contnuously and mantaned a certan amount, and the dynamc equlbrum can not be realzed by replacng the lqud water phase wth a sold wall n regon III. Ths ar path can be antcpated to contrbute to better cell performance because reacton gas s easly suppled to the reacton area under the bottom. Overall, the smulaton results show that controllng wettablty of the porous separator s effectve to realze an optmum two-phase dstrbuton, where the ar flow occurs between reacton area and condensed water. 5. Conclusons The numercal smulatons usng the lattce Boltzmann method (LBM) for two-phase flows wth large densty dfferences has been developed to understand the dynamc behavor of condensed water and gas flows n a polymer electrolyte membrane (PEM) fuel cell. The calculaton process of the LBM smulaton, e.g. the dscretzaton procedure n solvng the Posson equaton and the boundary condtons for pressure at corners and the partcle dstrbuton functon at the nlet, was mproved to extend the applcaton of the smulaton n a porous medum lke a gas dffuson layer (GDL). Wth the mprovements a stable and relable smulaton of two-phase flows wth large densty dfferences n a porous medum was possble. Usng the mproved smulaton, the applcablty of the LBM and sutably selected condtons to smulate lqud water behavor n the GDL are dscussed, and the sgnfcant advantages of ths smulaton, whch can consder actual physcal propertes, are demonstrated. Frst, t s shown that dynamc capllary fngerng can be smulated at lower mgraton speeds of lqud water n a modfed GDL, and that the LBM smulaton, consderng capllary, vscous and nertal forces, smulates the smlarty of capllary number, Ca, n two-phase flow n a PEM fuel cell. Then, as examples of the two-phase flow affected by the nteracton between lqud water and ar flows, two-dmensonal smulatons wth ar flow n a smplfed GDL wth a gas flow channel and n a porous separator are demonstrated. The smulaton n the smplfed GDL suggested that the wettablty of the channel strongly nfluences the two-phase flow n a fuel cell, and the possblty that control of the wettablty of the separator can be used to assst n an effcent dstrbuton of lqud water and ar flows. The smulaton n the porous separator wthout channels also showed that controllng the wettablty of the porous separator s more effectve to realze an optmum two-phase dstrbuton wth the ar flow formed between the reacton area and condensed water. Acknowledgment The authors thank Prof. Inamuro (Kyoto Unversty) and Prof. Oshma (Hokkado Unversty) for helpful comments on the LBM scheme. We also thank Mr. K. Kbo (a master s student of Hokkado Unversty) for nvaluable contrbuton to the development of the smulaton. References - 2 -

14 [] J. H. Nam, M. Kavany, M., Int. J. Heat Mass Transfer 46 (2003) [2] U. Pasaogullar, C. Y. Wang, J. Electrochem. Soc. 5 (3) (2004) A399-A406. [3] T. Bernng, N. Djlal, J. Electrochem. Soc. 50 (2) (2003) A589-A598. [4] G. Luo, H. Ju. C. Y. Wang, J. Electrochem. Soc. 54 (3) (2007) B36-B32. [5] K. Tüber, D. Pócza, C. Heblng, J. Power Sources 24 (2003) [6] X. G. Yang, F. Y. Zhang, A. L. Lubawy, C. Y. Wang, Electrochem. Sold-State Letters 7 () (2004) A408-A4. [7] T. Och, K. Kkuta, Y. Tabe, T. Chkahsa, Proc. 6th KSME-JASME Thermal and Flud Engneerng Conference (2005) [/ (CD-ROM) JJ-05] -4. [8] Y. Tabe, T. Och, K. Kkuta, T. Chkahsa, H. Shnohara, Proc. 3rd Int. Conf. Fuel Cell Scence, Engneerng and Technology (2005) [/ (CD-ROM) 7472] -6. [9] X. Zhu, P. C. Su, N. Djlal, J. Power Sources 72 (2007) [0] P. K. Snha, C. Y. Wang, Electrochm. Acta 52 (2007) [] V. P. Schulz, J. Becker, A. Wegmann, P. P. Mukherjee, C. Y. Wang, J. Electrochem. Soc. 54 (4) (2007) B49-B426. [2] T. Inamuro, T. Ogata, S. Tajma, S. Konsh, J. Comput. Phys. 98 (2004) [3] S. Succ, The Lattce Boltzmann Equaton for Flud Dynamcs and Beyond, Oxford Scence Publcatons, New York, 200. [4] T. Seta, R. Takahash, Proc. 4th Computatonal Engneerng Conference 0-0 (200) (n Japanese). [5] J. H. Ferzger, M. Perć, Computatonal Methods for Flud Dynamcs, Sprnger, Berln, 996. [6] R. Lenormand, J. Phys. Condes. Matter 2 (990) SA79. [7] A. Kumar, R. G. Reddy, J. Power Sources 29 (2004) [8] S. Arsetty, A. K. Prasad, S. G. Advan, J. Power Sources 65 (2007) [9] S. Ltster, D. Snton, N. Djlal, J. Power Sources 54 (2006)

15 Fg.. Lattce structure of two-dmensonal 9 veloctes model (2D9V model). Fg. 2. Lattce confguratons used n the LBM and the SOR method. Fg. 3. Conventonal and mproved smulaton results of the mass change of lqud water droplets n statonary ar. Fg. 4. Correctons when settng boundary condtons. Fg. 5. Lqud water flow behavor n the modfed GDL at dfferent nflow veloctes, u n L = 2.0, 0.20, m s -, Ca = 2.3 x 0-2, 2.3 x 0-3, 2.3 x 0-4, H = 0. mm. n Fg. 6. Lqud water flow behavor n the porous separator at dfferent nflow veloctes, u L = 2.0, 0.20, m s -, Ca = 2.3 x 0-2, 2.3 x 0-3, 2.3 x 0-4, H =.0 mm. Fg. 7. Schematc outlne of the computaton doman for the lqud water behavor n a smplfed GDL wth ar flow n the gas flow channel. Fg. 8. Behavor of lqud water and ar flow n the GDL and channel wth the hydrophobc separator. Fg. 9. Behavor of lqud water and ar flow n the GDL and channel wth the hydrophlc separator. Fg. 0. Schematc outlne of the computaton doman for the lqud water and ar flow behavor n a porous separator. Fg.. Changes n water weght and average ar flow rates along the separator n the three regons, (I) lower, (II) ntermedate, and (III) upper n the hydrophobc porous separator. Fg. 2. Behavor of lqud water and ar flow n the hydrophobc porous separator, H =.0 mm. Fg. 3. Changes n water weght and average ar flow rates along the separator n the three regons, (I) lower, (II) ntermedate, and (III) upper n the hydrophobc-hydrophlc porous separator. Fg. 4. Behavor of lqud water and ar flow n the hydrophobc-hydrophlc porous separator, H =.0 mm

16 ĉ 7 ĉ 3 ĉ 6 ĉ 4 ĉ ĉ 2 ŷ x ĉ 8 ĉ 5 ĉ 9 Fg

17 : : p v ŷ : û x x x x x x x (a) Co-locate grd (b) Staggered grd (c) Staggered grd 2 Fg

18 Mass of 液相質量 lqud phase Conventonal Improved tme step Tme step Fg

19 f a Sold wall c d b e p 0 x Inlet boundary Inlet û f û 2 (a) Pressure p at the corner (b) Partcle dstrbuton functon f at the nlet Fg

20 y x x 0-3 s x 0-3 s (a) u L n = 2.0 m s - (Ca = 2.3 x 0-2 ) x 0-3 s.20 x 0-3 s (b) u L n = 0.20 m s - (Ca = 2.3 x 0-3 ) 4.00 x 0-3 s 7.00 x 0-3 s (c) u L n = m s - (Ca = 2.3 x 0-4 ) Fg

21 2.00 x 0-3 s 2.0 x 0-3 s 70.0 x 0-3 s (a) u n L = 2.0 m s - (b) u n L = 0.20 m s - (c) u n L = m s - (Ca = 2.3 x 0-2 ) (Ca = 2.3 x 0-3 ) (Ca = 2.3 x 0-4 ) Fg

22 Ar H y x Water Separator wall Channel GDL Fg

23 (a) 27.7 x 0-3 s (b) 44.9 x 0-3 s Fg

24 (a) 20.0 x 0-3 s (b) 35.8 x 0-3 s Fg

25 Ar y H x Water Fg

26 x Water weght / kg x Tme / s Tme / s Average flow rate / m 2 s - (a) Water weght (b) Average ar flow rate Fg

27 (a) 0.00 s (b) 0.50 s (c) s Fg

28 x Water weght / kg x Tme / s Tme / s Average flow rate / m 2 s - (a) Water weght (b) Average ar flow rate Fg

29 (a) 0.06 s (b) s (c) s Fg