Numerical and experimental investigation of two-phase flow in an electrochemical cell

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1 Numercal and expermental nvestgaton of two-phase flow n an electrochemcal cell Kemal Aldas 1, Nur Pehlvanoglu 1, Mahmut D. Mat 2 1 Mechancal Engneerng Dept. Aksaray Unversty, Aksaray, Turkey 2 Mechancal Engneerng Dept. Ngde Unversty, Ngde, Turkey Abstract In ths study a two-phase mathematcal model s adapted to study vod fracton dstrbuton, flow feld and characterstcs of electrolyss process. The model nvolves transport equatons n both lqud and gaseous phases. An expermental set-up s establshed to collect data n order to valdate and mprove the mathematcal model. The vod fracton s determned from measurement of resstvty changes n the system due to the presence of bubbles. It s observed that there s a good agreement between the numercal results and the expermental data. Keywords: Water electrolyss, two-phase flow, vod fracton 1. Introducton The gas evoluton at electrodes s nvolved n many ndustral processes. An mportant applcaton of gas evolvng electrodes s water electrolyss whch s becomng very mportant n means of hydrogen producton. As hydrogen related technologes emerge, studes consderng fundamentals of electrolyss wll be crucal leadng to manufacturng of more effcent electrolyzer systems. The vod fracton dstrbuton, two phase flow and effects of

2 gas bubble on characterstcs of electrolyss are theoretcally and expermentally nvestgated n ths study. There are numerous studes n the lterature on varous aspects of the gas evolvng electrochemcal cells. Of partcular nterest s the partal gas coverage of electrode surface whch reduces the reacton the area thus t affects the performance of the system. Janssen et al. [1] nvestgated bubble coverage on electrode surface for a forced convecton stuaton. They found that bubble coverage decreases at hgher electrolyte speeds and s not effectve at hgh current denstes and low veloctes. In an expermental and theoretcal work, Egeldnger and Vogt [2] found that bubble coverage of electrodes substantally decrease even at moderate electrolyte velocty. They have shown that data obtaned wth stagnant electrolyte sgnfcantly dffer and cannot be appled to flowng electrolyte whch s usually the case n the ndustral electrolyzers. It s also found that macro convecton sgnfcantly affect the mcro convectve mass transfer mechansm. The gas bubbles whch are formed wth electrochemcal reactons leave the surface due to the unbalance of forces actng on the bubbles. Whle hydrodynamc drag and surface tenson forces hold the bubbles on the electrode, drag due to the forced convecton, buoyancy and pressure nsde the bubble result n detachng of bubble from surface after a force balance s met. Sdes and Tobas [3] observed that large bubbles attract smaller bubbles n the electrolyte. The smaller bubbles translate and coalescence wth larger bubbles. Janssen and Hoogland [4] observed an oscllatory moton of bubbles adjacent to the electrodes. Lubetkn [5] showed that ths moton s manly due to the Marangon forces produced by concentraton gradents of gas phase. Gas evoluton at electrodes has smlartes wth bolng at a heatng surface. Therefore some useful theores, formulatons may be benefcal to the study detals of gas lqud nteracton, mass transfer, bubble nucleaton and break up and flow nduced by the large densty dfferences between bubbles and lqud phase n the electrochemcal systems. Recently, Vogt et al. [6] analyzed the lmts of analogy between bolng and gas evoluton at electrodes. They concluded that although there are many smlartes between two processes, both processes have ther own dstnct propertes and are not analogous. For example whle a sgnfcant heat transfer takes place from heatng surface durng bolng, a reactant s transferred from the lqud to the electrode. The presence of gas nduces a flow whch sgnfcantly affects the mass transfer. Therefore detaled nvestgaton of bubble dynamcs, phase nteractons, bubble nduced flow plays 2

3 crucal role to understand the mechansm and enhance the performance of electrochemcal systems. Usng an mage analyss technque Sasak et al. [7] nvestgated parameters affectng the bubble moton n water electrolyss. They found that the nterelectrode dstance s an mportant parameter n controllng the bubble moton. At smaller nterelectrode dstances the bubble velocty s found to be slow due to the frctonal losses at the electrode surfaces. Bossoneu and Byrne [8] employed an advanced laser Doppler velocmetry and a partcle mage velocmetry to measure flud veloctes, vod fracton and bubble sze n a vertcal electrode system. They manly found that presence of bubbles causes local turbulence whle flow s lamnar n terms of Reynolds number consdered. The local turbulence s found to play an mportant role n determnng the phase dstrbuton. Mathematcal modelng efforts n electrochemcal cells usually do not consder flud flow and effects of bubbles and usually solves current and concentraton dstrbuton. Menon and Landau [9] developed a two-dmensonal model for an electrochemcal cell consderng mgraton dffuson and unsteady effects. The model s appled to estmate concentraton dstrbuton along the electrode surface n a system where concentraton and potental feld are coupled. However; only stagnant electrolytes are consdered, and the effect of bubbles and ther flow are not accounted for. Selman and Newman [10] nvestgated onc mgraton n the electrochemcal systems and found that onc mgraton affects velocty profle n natural convecton a systems. Wallgren et al. [11] assumed a plug flow n the electrochemcal cell and derved two boundary condtons at lmtng current densty. The presence of gas bubbles n the lqud (or electrolyte) makes the problem a two phase flow problem of whch many studes are avalable n the lterature. Manly; two models are employed n the lterature for bubbly two phase flow where number of bubbles s more than ndvdual trackng. The frst model employs separate transport equaton for both phases and closure relatons for exchange of momentum and mass between both phases. The second model treats both phases as a sngle phase (.e, a mxture) and only a set of transport equatons are solved [12]. Usng Ish s drft flux model Zegler and Evans[13] calculated mass transfer, vod fracton dstrbuton and velocty feld. Dahlkld [14] extended the drft flux model to an electro chemcal cell where only a sngle electrode s consdered and employed emprcal models developed for partcle transport n a sheared and sedmentng suspenson to descrbe bubble dstrbuton n the lqud phase. A nonunform current densty dstrbuton s estmated along 3

4 the electrode. The model was successful n nvestgatng the detals of non-lnear boundary condton manly due to the electrode knetcs. Although there are numerous mathematcal modelng studes n the lterature, only lmted studes consder lqud and bubbles as separate phases and effects of bubble dynamcs on flow, current dstrbuton and effcency of gas evoluton. Mat et al [15,16] developed a mathematcal model based on a two-flud model n whch both lqud and gas phases are consdered as separate fluds and transport equatons are solved for both phases. Mat et al [15,16] appled ths model to forced and natural convecton systems, however model has not been valdated wth expermental data. The purpose of ths study s to establsh an expermental set up to collect data and compare wth results of mathematcal model. Specfcally two-phase regon and gas evoluton determned wth an mage processng route and vod fracton s determned wth resstvty measurement. 2. Mathematcal Model The schematc sketch of electrochemcal system consdered s gven n Fgure 1. System consst of two electrodes namely cathode and anode whch are located on rght and left wall of the cavty respectvely and an electrolyte whch s a dlute soluton of KOH. KOH dsassocate nto K + and OH - ons and hydrogen gas evolves at the cathode whle oxygen gas forms at the anode accordng to the followng electro-chemcal reactons; At the cathode gas 4OH 4H O 4e 2H (1) 2 2 At the anode gas 4e 2H O 4OH O2 2 (2) A unform gas producton over the electrodess s assumed, but decrease n gas producton rate due the presence of bubbles s accounted by ncreasng the resstvty of electrolyte. The hydrogen and oxygen gases are allowed to leave the cell from top of the cavty. The flow n the system s generated due to the densty dfference between the lqud and gaseous phases. To represent the flow behavor and mass transfer n the system a two phase mxture of lqud and gas s consdered. Gas evoluton s assumed to occur at steady state. The phases are assumed to share space n proporton to ther exstence probabltes such that ther volume fractons sum up to unty n the flow feld, thus; 4

5 5 L + G=1 (3) where L and G are the volume fractons of lqud and gas respectvely. The zone averaged quanttes are obtaned through soluton of separate transport equatons for each phase. Wthn ths framework the governng equatons for two phase flow can be expressed n Cartesan coordnate as follows: Mass Conservaton nt M ρ w z v ρ y (4) where subscrpts, and j represent the phases and take the value of L,G n ths problem. Subscrpts L and G refer to lqud and gas phases, respectvely, n the present and subsequent formulatons. The term on the rght of the equaton represents mass dffuson between two phases at electrolyte-gas nterface. y- Momentum z v μ z y v μ y v v F P w v ρ z v ρ y j r 2 y (5) z- Momentum b F w w v z μ z y w μ y w w F z P w ρ z ρ y j r 2 (6) Fr n both momentum equatons s nterface frcton term and represents momentum exchange between the phases per unt volume and Fb=g s the buoyancy force where g s the gravty vector. Auxlary Equatons Interphase frcton term, Fr n momentum equatons can be expressed as: (6)

6 F r 0,75 c d L d b L G u r where ur s the slp velocty vector between two phases, db s the bubble dameter and cd s the drag coeffcent. There are extensve works on the drag coeffcent n the lterature. The Drty water model of Kuo and Walls [17] s employed here. In ths model; (7) /Re b Reb 100, We 8 c d 2.67 Reb 100, We 8 (8) 2.6 We/3.0 Reb /We where Reb s the Reynolds number based on the gas bubble dameter, Re b L u r d b (9) L and We s the Weber number defned as; 2 L u r d b We (10) where s the nterfacal tenson between the phases. It s seen that the bubble dameter db s an mportant parameter n determnng nterphase frcton between two phases. Ionc speces transport The speces mass flux n dlute soluton can be calculated usng Planck-Nernst law expressed as; ZFD N CU DC C (11) RT where C, D, Z are concentraton dffusvty and charge number of speces respectvely. represent the electrc potental. U s the velocty vector for the solvent. The frst, second and thrd terms represent the convectve, dffusve and mgraton contrbuton of mass flux, respectvely. 6

7 The current densty n the electrolyte can be calculated by employng the Faraday s law; 1N1 Z2N2 F Z (12) The current conservaton can be expressed as; y z 0 (13) and smlarly onc speces conservaton can also be gven as N y N z 0 (14) the electroneutralty condton for bnary electrolyte can be expressed as; Z C Z C 0 (15) The electrcal conductvty of the electrolyte s defned as; Z F D σ (16) N C 1 RT The electrcal conductvty wll decrease due to the presence of the gas n the system. The effectve conductvty s calculated usng Bruggeman correcton 1 3/2 σ σ (17) 0 Smlarly, dffuson coeffcents for each onc speces are also modfed as D,0 3 / 1 2 D (18) the subndce o represent the values n pure electrolyte. Boundary Condtons 7

8 A no slp condton s appled on electrode surfaces (e vertcal walls) for the lqud phase and tangental velocty for the gas phases whch are expressed mathematcally as: w L = w = 0 v L = 0 at y=0 and y=l, 0 z H (19) The normal component of gas phase velocty s calculated assumng all hydrogen and oxygen released transform nto the gaseous phase and employng Faraday s law. Thus normal velocty component at the cathode (hydrogen producng electrode); v = 1 2 RT P H 2 ( z) F y=0, 0 z H (20) where T, R, P, F are temperature (assumed to be constant n ths study), unversal gas constant, pressure of gaseous phase and Faraday constant respectvely. The multplcaton of normal velocty wth electrode surface area gves volumetrc producton hydrogen gas. Smlarly the normal component of gas velocty at the anode sde s calculated as: 1 RT ( z) v y=l, 0 z H (21) 4 P F Factors 2 and 4 n Equatons 20 and 21 represent the number of electrons takng place n the electrochemcal reacton at the electrode surfaces. There s two ons whch are postve [K + ] and negatve [OH - ] ons exst n the system. Snce the postve ons does not nvolve n the electrochemcal reacton at the electrode surfaces then for postve ons at two vertcal walls. The current densty (z) calculated as; z 1 exp η F 2RT where s the exchange current densty (1-) represent the reducton of actve electrode area due to bubbles on the electrode surface s the over potental calculated as; (22) =- (23) 8

9 The gas s assumed to leave the free surface at rate t reaches the surface therefore the axal gradent of the volume fracton of the gaseous phase vanshes at the top surface. In addton, a fxed pressure condton s mposed such that the veloctes are calculated from the need to satsfy mass conservaton at the computatonal cell adjacent to the surface. Numercal Method The coupled governng partal dfferental equatons are solved wth an teratve and fnte doman soluton procedure emboded n PHOENICS [18] computatonal code. The governng equatons are ntegrated over a control volume whch flow doman s dvded and followng algebrac equaton s obtaned. a φ P P a φ a φ a φ a φ S I φ (24) W W E E S S N N y φ P In whch a s represent convecton and dffuson coeffcent and subscrpts W, E, S, N represent west, east, south and north of node P. I represent the volumetrc flud nteracton coeffcent. The mult-phase system of equatons wll be solved by the nter-phase Slp Algorthm (IPSA) [18], nvolvng the use of Partal Elmnaton Algorthm (PEA) to accelerate convergence of the volume fracton and scalar equatons. PHOENICS program solves a general transport equaton wth convectve and dffusve terms and allows ncorporaton of source terms, addtonal equatons, boundary condton by approprate codng sutable to man logc of the program. The electrochemcal reactons, speces conservaton, electrc potental equatons and source terms are added to man program n ths study. A grd ndependent result s obtaned wth 30x80 grd system y, z drectons respectvely. 3. Expermental Apparatus and Method Expermental system bult for both flow vsualsaton and vod fracton measurements s shown n Fgure 2. The system conssts of a plexglass vertcal channel (15mmx20mmx300mm) wth pure nckel electrodes, a vdeo-mcroscope whch s attached to CCD camera for flow vsualsaton and drect observaton of bubble nucleaton and bubble dstrbuton, a perlstatc pump used for electrolyte flow and mpose requred Reynolds number, a cold lght source, a DC power source, a hgh resoluton dgtal avometer and a system for resstance measurements. The flow vsualzaton experments are performed before resstance measurements not to dsturb flow and mcroscope vson 9

10 The two phase flow at the vcnty of hydrogen and oxygen electrodes are magnfed wth a stereo mcroscope and recorded to a PC usng a hgh speed CCD system. Two phase flow characterstcs then analyzed wth an mage processng software. Snce t s dffcult to obtan vod fracton dstrbuton at the vcnty of the electrodes from the mages, an apparatus gven n Fg.3 s buld and attached to the plexglas ppe. The apparatus whch s based on the resstvty measurement has ten 0.25mm nckel wres placed 1mm apart. The resstance between the wres are measured wthout applyng frst electrcty (no bubble case) and by changng concentraton, velocty, and appled current. The local vod dstrbuton s calculated by usng the Maxwell formulaton gven as; R R EI O,EI 1 /2 (25) 1 where s the vod fracton REI and R0,EI are measured electrc resstance wth and wthout bubbles respectvely. 4. Results and Dscusson The structure of two phase regon s llustrated n Fgure 4a-b. These fgures are obtaned from vdeo recordng of experments after an mage processng. Fgure 4a present a pcture of two phase flow regon and Fgure 4b contans correspondng mage contour whch showng vod fracton dstrbuton and boundary of two phase regon. Recordng and subsequent mage analyss s performed only for vcnty of cathode (hydrogen electrode). It s seen that two phase regon s confned at the vcnty of electrode. The thckness of the two phase regon ncreases along the electrode due to accumulaton of hydrogen bubbles. An rregular shape toward to top of the electrode s manly local turbulence (although flow s not turbulent n terms of Reynolds number, n ths case). The predcted two phase structure for the same condtons s shown n Fgure 4c. It s seen that mathematcal model capture basc structure of the two phase flow regon. Snce turbulence (or chaotc flow) s not accounted n the mathematcal model, a smoother two phase boundary s obtaned. 10

11 Snce t s dffcult drectly determne and compare the value of local vod fracton from mage processng, the estmated vod dstrbuton s compared wth the data obtaned from resstvty measurements. Fgure 5 compares measured lateral vod fracton profle obtaned resstvty measurement method wth numercal data. It s seen that vod fracton hgher at vcnty of electrode and decrease exponentally n lateral drecton. It s also seen that mathematcal model capable of predctng vod fracton profle n the system. Small dscrepances between numercal and expermental results may be attrbuted to the measurements errors and nherent assumptons n the mathematcal model (manly lamnar flow assumpton). Effect of flow rate Fgure 6 shows the effect of flow rate on hydrogen evoluton and compares predcted vod fracton profle wth data obtaned from resstvty measurement. It s seen that the gas evoluton ncreases wth ncreasng flow rate whle the appled current s kept constant. Ths may be explaned lower resdence tme of bubbles on the electrodes wth hgher flow rate. Fgure shows that numercal results reasonable agree wth expermental data. It s seen that mathematcal model slghtly underestmates measured data. Ths s may be attrbuted local turbulence whch s not accounted n the mathematcal model. The local turbulence locally enhance dsperson and mxng and thus gas evoluton. Effect of current Densty Fgure 7 shows the effects of current densty on gas evoluton and dstrbuton. It s seen that gas evoluton ncreases at hgher current denstes however ths ncrease s not lnear. Peak measured and predcted vod fractons ncreases around 3 tmes whle current densty ncreases 5 tmes. The man reason s the accumulaton of gas bubbles on the electrode whch 11

12 decreases actve electrode area due to the curtan effect. The predctons are stll slghtly under estmates expermental data. 5. Conclusons A mathematcal model s adapted and mproved to study hydrogen evoluton n an electrochemcal cell. The model s based on two phase flow whch solves transport equaton for both lqud and gaseous phases. An expermental setup s developed to measure local vod fracton, valdate and mprove mathematcal model. The general characterstcs of gas evoluton and two phase regon are determned by mage processng of vdeo-mcroscope recordngs. The local vod fracton s measured wth a system based on electrcal resstvty changes wth the presence of bubble n the system. The hydrogen gas concentraton ncreases along the vertcal electrode n the electrochemcal system consdered. A wavy structure s observed at the two phase boundary because of the local turbulence or chaotc mxng. The predcted vod fracton reasonably agrees wth the expermental data obtaned from resstvty measurement. The mathematcal model s found to slghtly underestmate the local vod fracton snce local turbulence s not accounted n the model. The mathematcal model wll be further mproved wth ncluson of local weak turbulence n the future studes. Acknowledgements The authors would lke to acknowledge the fnancal support from The Scentfc and Techncal Research Councl of Turkey (TUBITAK) through the US-Turkey Cooperatve Research Agreement under contract number MISAG-NSF-4. 12

13 References [1] Janssen LJJ, Sllen CWMP, Barendrecht E, van Stralen SJD. Bubble behavour durng oxygen and hydrogen evoluton at transparent electrode n KOH soluton. Electrochm Acta. 1984; 29: [2] Egeldnger J and Vogt H. The bubble coverage of gas-evolvng electrodes n a flowng electrolyte. Electrochm. Acta. 2000; 45: [3] Sdes PJ, Tobas CW. A close vew of gas evoluton from the back sde of a transparent Electrode. J Electrochem. Soc. 1985; 132: [4] Janssen LJJ, Hoogland JH. The effect of electrolytcally evolved gas bubbles on the thckness of the dffuson layer. Electrochm. Acta 1970; 15: [5] Lubetkn S. The moton of electrolytc gas bubbles near electrodes. Electrochm. Acta. 2002; 48: [6] Vogt H, Aras Ö, Balzer RJ. The lmts of the analogy between bolng and gas evoluton at electrodes. I. J. of Heat and Mass Transfer.2004; 47: [7] Sasak T., Mura Y., Naga N.,Kuroda I.,Yamamoto F. Image measurement of electrolytc gas bubbles n parallel plate electrodes, 15th world hydrogen energy conference, June 2004, Japan. [8] Bossonneau P, Byrne P. An expermental nvestgaton of bubble-nduced free convecton n a small electrochemcal cell. J Appl Electrochem. 2000; 30: [9] Menon MM, Landau U. Modelng of electrochemcal cell ncludng dffuson mgraton and unsteady-state effects. J. Electrochem.Soc.1987; 134: [10] Selman JR, Nrwman J. Free-convecton mass transfer wth a supportng. Electrolyte J. Electrochem. Soc. 1971; 118:

14 [11] Wallgren CF, Bark FH, and Andersson BJ. Electrolyss of a bnary electrolyte n twodmensonal channel flow. Electrochmca Acta. 1996; 41(18): [12] Ish M, Zuber N. Drag coeffcent and relatve velocty n bubbly, droplet or partculate flows. AIChE J 1979; 25: [13] Zegler D, Evans JW. Mathematcal modelng of electrolyte crculaton n cell wth planar vertcal electrodes. J Electrochem Soc. 1986;103(3): [14] Dahlkld AA. Modellng the two-phase flow and current dstrbuton along a vertcal gas- evolvng electrode. J of Flud Mech. 2001; 428: [15] Mat M.D., Aldas K and Ilegbus O.J. A two-phase model for hydrogen evoluton n an electrochemcal cell. J. of Hydrogen Energy. 2004; 29: [16] Mat MD, Aldas K. Applcaton of a two-phase flow model for natural convecton n an electrochemcal cell. J. of Hydrogen Energy. 2005; 30: [17] Kuo JT and Walls GB. Flow of bubbles through nozzles. Int. J Multphase Flow 1988; 14: [18] Rosten H, Spaldng DB. Phoencs Manual, CHAM, TR/100, London,

15 z cathode anode H Fgure 1. Schematc sketch of the system consdered. W y 1. Computer 2. Mcroscope and CCD camera 3. Electrolyss tube par Nckel Electrode 5. Electrodes 6. Lght source 7. Pump 8. Electrolyte 9. DC supply 10. Avometer Fgure 2. Schematc of expermental set-up. 15

16 Fgure 3. Resstvty measurement apparatus. (a) (b) (c) Fgure 4. (a) Image of two phase regon from vdeo recordngs (b) measured, (c) calculated vod fracton dstrbuton. 16

17 0,06 0,05 Predcted 1000ml/mn Measured 1000ml/mn 0,04 0,03 0,02 0, dstance(mm) Fgure 5. Numercal and expermental results (=1000 A/m 2 ). 17

18 0,1 0,08 0,06 Predcted 500ml/mn Predcted 1000ml/mn Predcted 2000ml/mn Measured 500 ml/mn Measured 1000ml/mn Measured 2000ml/mn 0,04 0, dstance(mm) Fgure 6. Effect of flow rate on hydrogen evoluton (=1000A/m 2 ). 18

19 Fgure 7. Effects of current densty on hydrogen evoluton (Q= 1000 ml/mn). 19

20 20