A CFD Study of Dimensional Scaling effect on the Combustion of Hydrogen-Air Mixture in Micro-Scale Chambers with Same Shape Aspect Ratio

Transcription

1 6th WSEAS Internatonal Conference on SYSTEM SCIENCE and SIMULATION n ENGINEERING, Vence, Italy, November 1-3, A CFD Study of Dmensonal Scalng effect on the Combuston of Hydrogen-Ar Mxture n Mcro-Scale Chambers wth Same Shape Aspect Rato R.KAMALI, A.R.BINESH Department of Mechancal Engneerng Shraz Unversty Zand Street, School of Engneerng, Shraz Unversty, Shraz IRAN Abstract: - Understandng of the flow dynamcs, chemcal knetcs and heat transfer mechansm wthn mcrocombustors s essental for the development of combuston-based power MEMS devces, whch may supply much hgher energy densty than the batteres used nowadays. In the present work, a computer code has been developed to study the combuston of hydrogen ar mxture n a seres of chambers wth same shape aspect rato but varous dmensons from mllmeter to mcrometer level. The prepared algorthm and the computer code are capable of modelng mxture effects n dfferent flud flows ncludng chemcal reactons, vscous and mass dffuson effects. The transton of the combuston phenomena n the chambers from relatvely large scale to mcro-scale has been studed numercally to nvestgate the mcro-combuston mechansm. The smulaton results under the adabatc wall condton ndcate that the decreasng of combuston chamber sze does not have sgnfcant effect on the global chemcal reacton rate wthn the chamber, but t may lmt the combuston effcency. Through such systematc numercal analyss, a proper operaton space for the mcro-combustor s suggested, whch may be used as the gudelne for mcro-combustor desgn. In addton, the results reported n ths paper llustrate that the numercal smulaton can be one of the most powerful and benefcal tools for the mcro-combustor desgn, optmzaton and performance analyss. Key-words: - Numercal smulaton, Mcro-combuston, MEMS, CFD, Chemcal reacton 1 Introducton Wth the rapd progress n the moble electrcal and mcro devces such as mcro actuators, sensor, ar vehcle and robots n the recent years, the demands on the mcropower suppler wth hgh power densty s ncreasng, and fabrcaton of such mcro-devces s becomng possble. The batteres used nowadays have qute low specfc energy (0.6 kj/g for an alkalne battery and 1. kj/g for a lthum battery) compared to hydrogen (140 kj/g) and hydrocarbon fuels []. The combuston-based mcro-power devce, such as mcro-gas turbne engne, s one of the most promsng desgns due to ts hgh power densty. Development of mnaturzed combuston-based power generatng devces, even wth a relatvely neffcent converson of hydrogen fuel to power, would result n ncreased lfetme and/or reduced weght of an electronc or mechancal system that currently uses batteres for power. Recent advances n the feld of slcon mcro-fabrcaton technques and slcon-based Mcro-Electro-Mechancal Systems (MEMS) have led to the possblty of a new generaton of mcro heat engnes for power generaton. Mcro-combustor s one of the crtcal components for mcro-power system usng hydrogen and hydrocarbon fuels as an energy source. Several types of mcro-combustor and chemcal reactor are currently under development [1]. However, as the sze of mcro-combuston chamber decreases to mcron level, whch s comparable to the lamnar flame thckness, tradtonal combuston theory may not be able to explan and predct the detals about the mcrocombuston phenomena wthn the mcro-combustor. In addton, the expermental method and dagnostc technques developed for the macro-combuston facltes, becomes napplcable for the mcro-combustor due to the lmtaton of combuston chamber sze and the complexty of the mcro-combuston physcs. Hence, development of a new cost-effectve analyzng tool for mcro-combustor system s essental to understand the detals about the flud dynamcs, chemcal knetcs and heat transfers occurrng n mcro-combustor, brdgng

2 6th WSEAS Internatonal Conference on SYSTEM SCIENCE and SIMULATION n ENGINEERING, Vence, Italy, November 1-3, the fundamental knowledge, expermental measurement and engneerng desgn and optmzaton. The past expermental works [] have proved that t s mpossble to propagate flames n a small gap around mllmeter scale, whch s known as quenchng dstance. The nvestgaton ndcates that there are two knds of mechansms, namely thermal quenchng and radcal quenchng, leadng to flame quenchng n smaller dmenson [3]. Some theoretcal analyss of the combuston mechansm n smple mcro-chambers has been performed [4] to show the feasblty of stable combuston n mcro-combustor. The fundamental understandng of combuston mechansm n mcro-scaled chambers, whch s very essental to the desgn and optmzaton of power MEMS devces, s not understood well at present. Due to the dffcultes n conductng spatally resolved measurements of combuston characterstcs n mcro-scale devces, the numercal smulaton can be a cost-effectve approach to study the mcro-combuston mechansm. Norton and Vlachos [5] conducted two-dmensonal CFD smulaton to analyss the premxed methane/ar flames stablty n a mcrocombustor, consstng of two parallel, nfntely wde plates of length of 1 cm and small dstance. Norton and Vlachos [6] reported the CFD study on the mcrocombuston stablty of propane/ar mxture. Cho [7] performed the numercal smulaton of hydrogen/ar flame propagaton near extncton condton n a mcrocombustor. Spadaccn [8] studed the temperature dstrbuton wthn combuston chamber wth dfferent nlet geometres usng three-dmensonal numercal smulaton accountng the chemcal knetcs hydrogen ar reacton mechansm. In ths paper, Computatonal Flud Dynamcs (CFD) - based numercal smulatons are conducted to study the combuston of stochometrc hydrogen ar n a number of mcro-scaled cylndrcal chambers. Detaled chemcal reacton mechansm n combuston of hydrogen ar mxture s employed n the CFD smulatons. In order to study the dmensonal scalng effect on the combuston, the aspect rato of the combuston chamber s kept the same n all smulatons.the chamber dmenson, e.g. nlet dameter of chamber, s scaled down from mllmeter level to mcron level. The smulaton results ndcate that stable combuston n a mcro-scaled chamber can be acheved through balancng the flow resdence tme and the chemcal reacton tme and optmzng the thermal condton. Snce the resdence tme wll be shortened n a mcro-combuston chamber, t s mportant to shorten chemcal reacton tme as well n order to ensure the completon of the combuston process. Accordng to the chemcal knetcs theory, one of the possble measures to shorten the chemcal reacton tme s to ncrease the reacton rate by ensurng a hgh reacton temperature. Ths n turn can be acheved by reducng the heat loss from the combuston chamber. Computatonal model.1 Model geometry and the mesh The geometry of the cylndrcal chamber used n ths study s shown n Fg. 1. The effects of chamber dmenson on combuston characterstcs are studed through scalng down the cylndrcal chamber from a relatvely large scale to a mcro-scale whle keepng the same shape aspect rato. The nlet dameter (D) of the chamber s vared from the large sze to the small sze at 0.5, 0., 0.08, and mm, respectvely. The rato of chamber dameter to nlet dameter (D) s mantaned at. The rato of chamber length (L) to nlet dameter (D) s fxed to be 10. Stochometrc hydrogen ar mxture s nected nto the cylndrcal chamber from the nlet located at one axal end wth a step expanson as shown n Fg. 1. Because of the axal symmetry of the combuston chamber, the geometry s modeled as a twodmensonal ax-symmetrc model. For the all cases analyzed n ths study, a structured grd s used to mesh the models for the CFD smulatons as shown n Fg.. The whole computatonal doman ncludng both combuston chamber and nlet throttle s meshed usng about 4375 cells. Ths fne mesh sze wll be able to provde good spatal resoluton for the dstrbuton of most varables wthn the combuston chamber. Fg. 1. Schematc dagram of the mcro-scaled combuston chamber for mcro-combuston modelng. Fg.. Numercal grd of the computatonal doman at nlet

3 6th WSEAS Internatonal Conference on SYSTEM SCIENCE and SIMULATION n ENGINEERING, Vence, Italy, November 1-3, Flud flow modelng The characterstc length of the combuston chamber and the reactng gas flow path n mcro-combustors, even for MEMS systems, s stll suffcently larger than the molecular mean-free path (average dstance between two successve collsons of a molecule) of the ar and other gases flowng through the systems. Hence, the flud meda can be reasonably consdered as contnuum n ths study. The Naver Stokes equaton s solved usng euleran mxture model for the flud doman and no-slp condton on the wall s appled..3 Governng equatons A computer code s used to perform numercal smulatons of the flud flow n combuston chamber by solvng the conservaton equatons of mass, momentum, energy and speces. Contnuty Equaton: ρ + ( ρu ) = 0 (1) Momentum Equaton: p τ ( ρ u ) + ( ρuu ) = + () Where the stress tensor τ s gven by u u τ µ = + µδ dvv (3) x x 3 Where µ s the molecular vscosty and the second term on the rght hand sde s the effect of volume dlaton. Energy Equaton : ( ρe) + ( u ( ρe + p)) = (4) T keff h J + u ( τ ) eff + Sh x Wherek eff s the effectve conductvty and J s the dffuson flux of speces. The frst three terms on the rght-hand sde of Equaton represent energy transfer due to conducton, speces dffuson, and vscous dsspaton, respectvely. S h ncludes the heat of chemcal reacton, and any other volumetrc heat sources we have defned. In equaton (4), P u E = h + (5) ρ where sensble enthalpy h s defned for deal gases as h = m h (6) Where m s the mass fracton of speces. Speces Conservaton Equaton: When we choose to solve conservaton equatons for chemcal speces, we predcts the local mass fracton of each speces, m, through the soluton of a convectondffuson equaton for the th speces. Ths conservaton equaton takes the followng general form: p ( ρ m ) + ( ρum ) = J + R + S (7), where R s the net rate of producton of speces by chemcal reacton and S s the rate of creaton by addton from the dspersed phase. An equaton of ths form wll be solved for N 1speces where N s the total number of flud phase chemcal speces present n the system. Snce the mass fracton of the speces must sum to unty, the N th mass fracton s determned as one mnus the sum of the N 1solved mass fractons. To mnmze numercal error, the N th speces should be selected as that speces wth the overall largest mass fracton, such as N when the oxdzer s ar. J, s the dffuson flux of speces, whch arses due to concentraton gradents. We use the dlute approxmaton, under whch the dffuson flux can be wrtten as m J = ρ D (8),, m Here s the dffuson coeffcent for speces n the D, m mxture. The reacton rates that appear as source terms n Equaton (8) are computed by Lamnar fnte-rate model that effect of turbulent fluctuatons are gnored, and reacton rates are determned by Arrhenus expressons. The net source of chemcal speces due to reacton R s computed as the sum of the Arrhenus reacton sources over the N R reactons that the speces partcpate n: R = M N R k = 1 Rˆ, k (9) where M s the molecular weght of speces and ˆ s the Arrhenus molar rate of creaton/destructon R, k of speces n reacton r..4 Boundary condtons A fxed composton (a stochometrc mxture) of hydrogen ar s specfed at the fuel nlet of mcrocombuston chamber. The nlet temperature of fuel mxture s consdered to be unform at 300 K. A fxed,

4 6th WSEAS Internatonal Conference on SYSTEM SCIENCE and SIMULATION n ENGINEERING, Vence, Italy, November 1-3, unform velocty 5 m/s s specfed at the nlet. As the combuston chamber dameter s about twce of the dameter nlet of fuel/ar mxture. Hence, the crosssecton area of the combuston chamber wll be about four tmes of the nlet area. The averaged velocty of gas mxture at the chamber cross secton wll be about 1.5 m/s before t s burnt. Snce the averaged gas mxture velocty of 1.5 m/s s lower than the flame speed, t wll help the flame stable n the combuston chamber. Axsymmetrc boundary condtons are appled along the central axs of the combuston chamber. At the ext, a pressure outlet boundary condton s specfed wth a 5 fxed pressure of Pa. At the chamber wall, noslp boundary condton and no speces flux normal to the wall surface are appled..5 Numercal model A segregated soluton solver s used to solve the abovementoned set of governng equatons. Snce the Reynolds number of the flud flow ranges from about 11 when D=0.045mm to 16 when D=0.5mm for the smulated cases, lamnar vscous flow s consdered. The flud densty s calculated usng the deal gas law. The flud mxture specfc heat, vscosty, and thermal conductvty are calculated from a mass fracton weghted average of speces propertes. The combuston model s valdated by smulatng the combuston of premxed hydrogen ar under adabatc condton and comparng wth the measurement of adabatc flame reported by Glassman [3]. The comparsons of flame temperature and mole fracton of speces obtaned from the model predcton and experment are lsted n Table 1. The numercal predctons are n reasonable agreement wth the expermental data. for dfferent nlet dameters: (a) 0.5 mm, (b) 0. mm, (c) 0.08mm and (d) mm, under adabatc wall condton. For the same smulaton cases, the contours of Arrhenus rate of reacton, whch s regarded as an ndcator of global chemcal reacton rate, are shown n Fg. 3. The combuston chamber dmensons shown n these contour plot fgures are normalzed by the correspondng nlet dameter (D) for each smulaton case. In ths way, the relatve poston of combuston zone and physcal property dstrbuton n the dfferentszed combuston chambers can be easly compared. It can be seen from Fgs. 3 and 4 that the combuston can be self-sustaned n the mcro-scaled combuston chamber f the wall s mantaned as adabatc. The gas temperature s rased sgnfcantly due to the heat released from combuston. The hghest temperature s obtaned at the ext of combuston chamber at a range of K. The flame temperature can be as hgh as 3000K for the largest combustor n ths study, whch s almost the same as the adabatc flame temperature of the combuston of stochometrc hydrogen ar mxture. As the combuston chamber sze decreases, the ext temperature of the combuston product decreases as well. However, as the combuston chamber sze decreases, the rato of the combuston zone to chamber volume ncreases sgnfcantly as shown n Fg. 3. Fgs. 5 7 show the gas temperature, Arrhenus rate of reacton and hydrogen converson rate dstrbutons along the central axs of the chamber, respectvely. Here, the hydrogen converson rate s defned as ([ H ] ntal [ H])/[ H] and the dmensonless axal ntal dstance s defned as the rato of the axal dstance to the nlet dameter. Mole fractons Expermental results Numercal results (Glassman, 1996) H O O H N NO Table 1. Comparson of mole fracton of speces n stochometrc hydrogen ar mxtures n smulaton and experment 3 Results and dscusson A number of numercal smulatons have been performed to study the combuston phenomena when the combuston chamber sze s reduced from a relatvely large scale to a mcro-scale under adabatc wall condton. Fg. 3 shows the predcted temperature contours on the cross secton of combuston chambers Fg. 3. Contours of temperature [K] on the cross secton along central axs of varous szed combuston chambers wth the nlet dameter of: (a) 0.5 mm; (b) 0. mm; (c) 0.08 mm; (d) 0.045mm under adabatc wall condton.

5 6th WSEAS Internatonal Conference on SYSTEM SCIENCE and SIMULATION n ENGINEERING, Vence, Italy, November 1-3, Fg. 4. Contours of producton rate [kgmol/m3-s] of water at the cross secton along the central axs of varous szed combuston chambers wth the nlet dameter of: (a) 0.5 mm; (b) 0. mm; (c) 0.08 mm; (d) 0.045mm under adabatc wall condton. Fg. 6. Water producton rate [kgmol/m3-s] dstrbuton along the central axs for the scaled chambers of varous nlet dameters (D) under adabatc wall condton. Fg. 5. Gas temperature [K] dstrbuton along the central axs for the scaled chambers of varous nlet dameters (D) under adabatc wall condton. When the chamber dmenson s large enough, the gas mxture has enough resdence tme n the chamber, so that combuston wll be completed before t flows out of the combuston chamber. Hence, t can be seen n Fg. 5 that a narrow peak s formed for the large chambers due to the reacton confned to a narrow zone. Wth the completed combuston n the large chambers, the gas product flows out of the combuston chamber almost at adabatc flame temperature 3000K as n Fg. 5. However, when combuston chamber sze decreases, the chemcal reacton mechansm s kept same. The reacton zone may occupy more and more space of the mcrocombuston chamber. Hence, t can be seen from Fg.6 Fg. 7. Dstrbuton of hydrogen converson rate along the central axs for the scaled chambers of varous nlet dameters (D) under adabatc wall condton. that the peak of Arrhenus rate of reacton becomes wder as the chamber sze decreases. Fg. 5 also ndcates the temperature of the combuston gas product decreases as the combuston chamber sze decreases due to the ncomplete combuston n smaller chambers. The hydrogen converson rate dstrbutons shown n Fg. 7 ndcate the smaller combuston chamber has hgher converson rate near the nlet, but lower conversaton rate near outlet. It can be noted from Fgs. 4 and 6 that the maxmum water producton rate mantan almost at the same level when the chamber dmenson decreases, whch means the chemcal reacton rate does not change sgnfcantly as the combuston chamber sze decreases.

6 6th WSEAS Internatonal Conference on SYSTEM SCIENCE and SIMULATION n ENGINEERING, Vence, Italy, November 1-3, The smulaton results under the adabatc wall condton ndcate that the decreasng of combuston chamber sze does not have sgnfcant effect on the global chemcal reacton rate wthn the chamber. But, decreasng the combuston chamber sze may lmt the combuston effcency. Ths s due to the fact that the gas mxture does not have enough resdence tme to fnsh the chemcal reacton completely n the smaller chambers. Hence, to obtan a stable combuston n a mcro chamber, the chamber dmenson should be larger than the adabatc flame thckness at least. 4 Conclusons In the present work, a computer code has been developed to study the combuston phenomena of the hydrogen ar mxture n a seres of combuston chambers when the nlet dameter s reduced from a relatvely large sze of 0.5mm to a mcro-scale sze of mm. The prepared algorthm and the computer code are capable of modelng mxture effects n dfferent flud flows ncludng chemcal reactons, vscous and mass dffuson effects. Theoretcally, stable combuston can only occur n a combuston chamber when the reactant resdence tme s larger than the chemcal reacton tme. For the case of combuston n tradtonal large-scale combustors, the resdence tme for reactant n the combuston chamber s always large enough for complete combuston. Decreasng the dmenson of combuston chamber leads to sgnfcant reducton n resdence tme as the reactant flow speed cannot reduce accordngly. Ths s because a certan flow rate of reactant needs to be mantaned to acheve the requrement of power generaton rate. But, the chemcal reacton tme s remaned as usual. The drect consequence of nsuffcent resdence tme n mcro-combuston chamber s that the combuston may not be complete wthn the combustor. Lower combuston effcency may lead to nsuffcent heat generaton to mantan self-sustaned combuston, and further result n quenchng. The numercal smulaton of combuston of premxed hydrogen ar n mcro-scaled chamber wth adabatc wall condton proves that the combuston may be stable only when the combuston chamber sze s large enough comparng to the adabatc flame thckness. Through numercal smulaton of combuston of hydrogen ar mxture n mcro-scaled chambers, t can be concluded that the numercal model s able to capture the basc mcro-combuston mechansm. The quenchng phenomena and mechansm n mcro-combuston have been explored and dscussed. Stable combuston n the mcro-combustor s achevable by system optmzaton of the combustor geometry, thermal condtons and reactng flow dynamcs. The numercal modelng approach presented n ths paper s helpful n the desgn and optmzaton of combuston-based mcro-power generaton devce. References [1] Carlos Fernandez-Pello, A., 00. Mcro-power generaton usng combuston: ssues and approaches. Twenty-Nnth Internatonal Symposum on Combuston, Sapporo, Japan, the Combuston Insttute [] Ono, S., Wakur, Y., An expermental study on the quenchng of flame by narrow cylndrcal passage. Bulletn of JSME 0 (147) [3] Glassman, I., Combuston. Academc Press, Calforna. [4] Lee, D.H., Kwon, S., 00. Heat transfer and quenchng analyss of combuston n a mcro combuston vessel. Journal of Mcromechancs and Mcro engneerng 1, [5] Norton, D.G., Vlachos, D.G., 003. Combuston characterstcs and flame stablty at the mcro-scale: a CFD study of premxed methane/ar mxtures. Chemcal Engneerng Scence 58, [6] Norton, D.G., Vlachos, D.G., 004. A CFD study for propane/ar mcro-flame stablty. Combust. Flame 138, [7] Cho, K.H., Na, H.B., Lee, D.H., Kwon, S., 004. Numercal smulaton of flame propagaton near extncton condton n a mcro-combustor. Mcroscale Thermophyscal Engneerng 8, [8] Spadaccn, C.M., Mehra, A., Lee, J., Zhang, X., Lukachko, S.,Watz, A.I., 003. Hgh power densty slcon combuston system for mcro gas turbne engnes. Journal of Engneerng for Gas Turbnes and Power 15,