propane combustion reaction mechanism

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 Combustion and Flame 138 (2004) 97–107 www.elsevier.com/locate/jnlabr/cnf A CFD study of propane/air microame stability D.G. Norton and D.G. Vlachos  Department of Chemical Engineering and Center for Catalytic Science and T echnolo gy (CCST), University of Delawar e,  Newark, DE 19716-3110, USA Received 7 October 2003; received in revised form 26 March 2004; accepted 5 April 2004 Available online 8 May 2004 Abstract A two-dimensional elliptic computational uid dynamics model of a microburner is solved to study the effects of microburner wall conductivity, external heat losses, burner dimensions, and operating conditions on combus- tion characteristics and the steady-state, self-sustained ame stability of propane/air mixtures. Large gradients are observed, despite the small scales of the microburners. It is found that the wall thermal conductivity is vital in determining the ame stability of the system, as the walls are responsible for the majority of the upstream heat transfer as well as the external heat losses. Furthermore, there exists a range of ow velocities that allow stabilized combustion in microburners. It is found that the microburner dimensions strongly affect thermal stability. Engi- neeri ng maps deno ting ame stability are constructed and design rec ommen datio ns are made . Finally, comparisons with methane/air systems are made. © 2004 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Propane; Microburners; Computational uid dynamics; Flame stability; Extinction; Thermal management 1. Intro duction Microburners may play a vital role in the portable production of energy. Hydrocarbons have an energy density signicantly higher than that of the traditional Li batterie s (40 vs 0.5 MJ/kg) that are currently used in laptops, cellular phones, and other portable elec- tronics devices  [1] .  The small scales in microburners result in lower combustion temperatures due to en- hanced heat-transfer coefcients. Thus, we propose that micro bur ners could possi bly redu ce the gas-p hase production of NO [2] .  Finally, microburners can also serve as efcient sources of heat for endothermic re- actions, such as steam reforming and ammonia de- composition, in integrated microchemical systems for * Corresponding author. Fax: (302)-831-1048.  E-mail address: [email protected] .edu (D.G. Vlachos). the pro duc tio n of hyd rog en for fuel cel l app lica- tions [3]. Unfort unat ely , the be ne ts ar isi ng at the mi- crosc ale are overshado wed by major difcul ties in creating working microburners. In 1817, Davy per- formed experiments showing the inability of ames to propagate between gaps of submillimeter scale  [4]. His work was followed by many other groups, whose work conrmed that depe ndin g on geometry, com- position, and ow rate, hydrocarbon/air ames are typically quenched when conned within spaces with critical dimensions  < 1–2 mm  [5–9]. The two pri- mary mechanisms for quenching in these systems are thermal and radical quen ching  [2,10,11].  Increased heat-transfer coefcients are inherent to microscales, because for a xed Nusselt number, the heat-transfer coefcient scales with the inverse of the length scale. The hig h hea t-tr ans fer rat es inc rea se the heat los t from the react ion, reducing the oper ating tempera- tures and causing the combustion to extinguish. At the same time, the inc rea sed mas s tra nsf er wit hin 0010-2180/$ – see front matter  © 2004 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.combustame.2004.04.004

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    A two-dimensional elliptic computational fluid dynamics model of a microburner is solved to study the effects

    of microburner wall conductivity, external heat losses, burner dimensions, and operating conditions on combus-tion characteristics and the steady-state, self-sustained flame stability of propane/air mixtures. Large gradients areobserved, despite the small scales of the microburners. It is found that the wall thermal conductivity is vital indetermining the flame stability of the system, as the walls are responsible for the majority of the upstream heattransfer as well as the external heat losses. Furthermore, there exists a range of flow velocities that allow stabilizedcombustion in microburners. It is found that the microburner dimensions strongly affect thermal stability. Engi-neering maps denoting flame stability are constructed and design recommendations are made. Finally, comparisonswith methane/air systems are made. 2004 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

    Keywords: Propane; Microburners; Computational fluid dynamics; Flame stability; Extinction; Thermal management

    1. Introduction

    Microburners may play a vital role in the portableproduction of energy. Hydrocarbons have an energydensity significantly higher than that of the traditionalLi batteries (40 vs 0.5 MJ/kg) that are currently usedin laptops, cellular phones, and other portable elec-tronics devices [1]. The small scales in microburnersresult in lower combustion temperatures due to en-hanced heat-transfer coefficients. Thus, we proposethat microburners could possibly reduce the gas-phaseproduction of NO [2]. Finally, microburners can alsoserve as efficient sources of heat for endothermic re-actions, such as steam reforming and ammonia de-composition, in integrated microchemical systems for

    * Corresponding author. Fax: (302)-831-1048.E-mail address: [email protected]

    (D.G. Vlachos).

    the production of hydrogen for fuel cell applica-tions [3].

    Unfortunately, the benefits arising at the mi-croscale are overshadowed by major difficulties increating working microburners. In 1817, Davy per-formed experiments showing the inability of flamesto propagate between gaps of submillimeter scale [4].His work was followed by many other groups, whosework confirmed that depending on geometry, com-position, and flow rate, hydrocarbon/air flames aretypically quenched when confined within spaces withcritical dimensions < 12 mm [59]. The two pri-mary mechanisms for quenching in these systems arethermal and radical quenching [2,10,11]. Increasedheat-transfer coefficients are inherent to microscales,because for a fixed Nusselt number, the heat-transfercoefficient scales with the inverse of the length scale.The high heat-transfer rates increase the heat lostfrom the reaction, reducing the operating tempera-tures and causing the combustion to extinguish. Atthe same time, the increased mass transfer withinCombustion and Flame 1

    A CFD study of propanD.G. Norton an

    Department of Chemical Engineering and Center for CataNewark, DE

    Received 7 October 2003; received in revis

    Available on

    Abstract0010-2180/$ see front matter 2004 The Combustion Institute.doi:10.1016/j.combustflame.2004.04.004004) 97107www.elsevier.com/locate/jnlabr/cnf

    ir microflame stability.G. Vlachos

    Science and Technology (CCST), University of Delaware,-3110, USA

    rm 26 March 2004; accepted 5 April 2004May 2004Published by Elsevier Inc. All rights reserved.

  • 98 D.G. Norton, D.G. Vlachos / Combustion and Flame 138 (2004) 97107the system, coupled with the high surface-area-to-volume ratio, causes radical adsorption onto the walls,followed by radical recombination. This dearth ofradicals quenches the homogeneous chemistry [12].Another mechanism for loss of stability is blowout,which occurs when the burner exit velocity exceedsthe flame burning velocity [7]. In this case, the reac-tion front shifts downstream with increasing velocityand eventually exits the burner. The competition be-tween the shifting of the reaction zone and thermalquenching has been observed in elliptic models ofmicroscale systems for methane [13] and mesoscalesystems for propane [14].

    Recent experiments have demonstrated that it isfeasible to stabilize homogeneous methane/oxygenflames between parallel plates with gaps smaller than1 mm [15,16]. This is accomplished by modifyingthe surface to make it chemically inactive, to elimi-nate radical quenching, and insulating the burner, toreduce thermal quenching. The chemical inactivationprocess involves high-temperature annealing to healcrystal defects and surface cleaning with deionizedwater, hydrochloric acid, and hydrogen peroxide toremove ionic and heavy metal contaminants.

    In our recent computational fluid dynamics (CFD)work [13], overall heat management was shown toplay a critical role in determining homogeneous flamestability of methane/air mixtures in microburners. Thethermal conductivity of the wall allowed both the vi-tal upstream heat transfer for preheating the feed tothe ignition temperature and detrimental heat lossesto the exterior. When the thermal conductivity is toolow, the upstream heat transfer through the walls ischoked, and the system blows out. At the other ex-treme of high thermal conductivity, the wall and fluidtemperature profiles flatten, causing delocalized reac-tion fronts and an increased external hot area for heatlosses. As a result extinction is observed.

    The significant role of upstream heating in sta-bilizing combustion in a tube was in fact realizedseveral years ago by Churchill [17], who developedthermally stabilized burners (TSB). These TSB con-sisted of ceramic cylindrical tubes > 7 mm in diam-eter into which fuel and air were fed. Flame frontswere stabilized within the tubes by thermal feedbackcaused by conduction through the walls and radia-tion between the walls to preheat the incoming feed.To maximize the heat transfer between the fluid andthe walls, the flow rates were such that the flow wasturbulent upstream of the combustion. In the reac-tion zone further downstream, the viscosity increaseddue to the increased temperature, resulting in lami-nar flow. These systems were found to be very sta-ble to minor disturbances, but the range of flow ratesthat allowed stabilized combustion was very limited.These experimental findings are in general qualita-tive agreement with our simulations [13]. However,it is unclear how much of the TSB experimental re-sults transfer to the microscale, where the flow isseverely confined. Another idea for stabilizing com-bustion within mesoscale ( 1 mm) and macroscale( 1 mm) tubes revolves around the work of Lloydand Weinberg on heat-recirculating burners, wherehot combustion products are used to preheat the in-coming feed [18,19]. Ronney and co-workers haveextended this idea on mesoscale Swiss roll heat-recirculating burners, with gap sizes on the order of3 mm, for the homogeneous and heterogeneous com-bustion of propane in air [1,20]. In recent work, Ron-ney modeled a countercurrent heat-recirculating com-bustor [21]. The system consisted of a cold reactantinlet that fed into a well-stirred reactor (WSR). Theproducts from the WSR then flowed countercurren-twise past the incoming feed to preheat it. The hotand cold tubes were modeled by a one-dimensionalmodel, with convective heat-transfer coefficients tomodel the heat transfer between them and the exterior.The reaction was assumed to take place within theWSR. It was shown that the axial conduction withinthe wall had a major effect on the operating limits ofthe combustor. Even a small wall thermal conductiv-ity results in significantly higher required flow rates tomaintain stabilized combustion, whereas when the ax-ial wall conduction is ignored, the minimum requiredflow rate disappears. Ronneys analysis emphasizesthe importance of heat transfer as our CFD modelingdid [13].

    Despite previous work, there are a number of an-swered questions regarding flame stability at the mi-croscale. Examples include the roles of fuel and mi-croburner dimensions in flame stability. In this workwe extend our previous modeling work to the steady-state self-sustained microcombustion of propane/air.Two-dimensional (2D), fully elliptic simulations areperformed that explicitly treat heat and mass trans-fer in the fluid as well as heat transfer in the wall.The effects of wall thermal conductivity, external heatlosses, operating conditions, and microburner dimen-sions on flame stability and combustion characteris-tics are discussed. In order to understand how dif-ferent hydrocarbons behave, the differences betweenpropane/air and methane/air systems are also investi-gated.

    2. Model

    The burner is modeled as two parallel plates thatare infinitely wide, 1 cm long, and distance L apart.The plate thickness is Lw. For most simulations L =600 m and Lw = 200 m (unless otherwise noted).Premixed, nonpreheated propane/air mixtures are fed

  • D.G. Norton, D.G. Vlachos / Combustion and Flame 138 (2004) 97107 99Fig. 1. Schematic of the computational domain (not to scalefor ease of visualization).

    to the inlet of the microburner, and hot product gasesexit the microburner. Due to the aspect ratio, the sys-tem is simplified to a 2D one and the plane of symme-try between the two plates allows simulations of onlyhalf of the microburner. A schematic of the system isshown in Fig. 1.

    The steady-state 2D continuity, momentum, en-ergy, and species equations in the fluid phase and thesteady-state 2D energy equation in the solid phase arediscretized using a finite-volume method. Fluent 6.0is used to perform these calculations [22]. The flowis laminar. Previous studies of methane/air mixturesutilizing surface and gas-phase radiation have shownthat the ignition distances for combustion reactions inmicroburners were only slightly increased by radia-tion [13]. The aspect ratio of the system is so high thatany surface-to-surface radiation is most likely emit-ted and absorbed at nearly the same axial location.Therefore, radiation is omitted from the simulationsperformed in this work to focus on the effect of diffu-sive and convective heat transport on flame stability.

    The boundary conditions used in this model areas follows. At the inlet a fixed flat velocity profileis assumed. For the species and energy equations,Danckwerts boundary conditions are employed; i.e.,the convective portions of the equations are fixed, andthe diffusive portions are calculated implicitly. At theinterface between the fluid and the solid, no slip andno normal species diffusive flux boundary conditionsare applied. The heat flux at this interface is calcu-lated using Fouriers law and continuity in tempera-ture and heat flux is ensured. A symmetry boundarycondition is applied at the centerline between the twoplates. At the exit, the pressure is specified and theremaining variables are calculated assuming far-fieldconditions, i.e., zero diffusive flux of species or en-ergy normal to the exit. In the bulk of the wall the2D energy equation is solved. The exterior/top sur-face of the wall is assumed to obey Newtons law ofcooling, q = h(Tw Ta), where q is the heat flux,h is the exterior convective heat-transfer coefficient,Tw is the temperature at the exterior surface (an un-known of the problem), and Ta is the ambient temper-ature, which is assumed to be 300 K. It is importantto note that all the 2D internal heat transfer withinthe fluid and the solid are calculated explicitly withthe 2D elliptic models without any further simplifica-tions. The exterior convective heat-transfer coefficientis only used for the calculation of the heat flux ofthe exterior wall edge boundary condition. This heat-transfer coefficient lumps the details of heat loss fromthe microburner and of the process that utilizes theheat generated by the burner. The left and right walledges are taken to be insulated (zero flux boundarycondition).

    Nonuniform node spacing is employed in thiswork, with more nodes in the reaction zone. The num-ber of nodes varies depending on dimensions, butthe simplest one consists of 120 axial nodes by 60transverse nodes, totaling approximately 7200 nodes.Meshes in excess of 20,000 nodes are utilized forthe largest dimensions. Typical fluid node spacing is50 m in the axial direction and 6 m in the trans-verse direction. Typical wall node spacing is 50 m inthe axial direction and 20 m in the transverse direc-tion, where the temperature does not vary (only a fewnodes are placed in the transverse direction within thewall). However, as the mesh is nonuniform, these arejust representative values.

    The fluid viscosity, specific heat, and thermal con-ductivity are calculated by a mass-fraction-weightedaverage of species properties. The species specificheat is calculated using a piecewise polynomial fit oftemperature [22]. The fluid density is calculated usingthe ideal gas law.

    It has been shown that for typical materials ofconstruction, radical quenching is important in de-termining flame stability in microburners. In partic-ular, simulations that were performed with complexgaseous chemistry have shown that radical stickingcoefficients that are larger than 0.001 severely de-crease the flame stability of microburners [11]. Recentexperimental work has produced a nearly quench-less wall material that is resistant to radical quench-ing [15,16]. Thus, our focus here is on understandingthe overall heat-transfer characteristics in microburn-ers and developing guidelines for appropriate thermalmanagement that can result in more robust flame be-havior. One-step chemistries, determined from flamespeeds, are a useful tool for describing flame dynam-ics and flame responses to external perturbations [23].In this work a reduced one-step propane combustionchemistry is used that assumes the irreversible com-bustion of propane:

    (1)C3H8 + 5O2 3CO2 + 4H2O.Consequently five species, namely C3H8, O2, N2,CO2, and H2O, are modeled with corresponding con-servation equations. Specifically, the mechanism usedis the one proposed by Westbrook and Dryer [24],

  • 100 D.G. Norton, D.G. Vlachos / Combustion and Flame 138 (2004) 97107rC3H8[kgmol/(m3 s)]

    = 4.836 109 exp[1.256 10

    8 J/kgmolRT

    ]

    (2) [CC3H8 ]0.1 [CO2]1.65,where the concentrations are in units of kgmol/m3.We should remark that the one-step approximationfails to describe several aspects, such as the possibilityfor formation of partial oxidation products CO and H2and the resulting superadiabatic flame temperature, orthe ignition temperature when ignition is kineticallycontrolled [25], etc. As a result of this approxima-tion, the flame location may be somewhat inaccurate.Therefore, the results presented here should be usedas a guide to understand trends rather than an accu-rate prediction.

    The conservation equations were solved implic-itly with a 2D steady-state segregated solver using anunder-relaxation method. The segregated solver firstsolves the momentum equation, then the continuityequation, and then updates the pressure and mass flowrate. The conservation equations are then checkedfor convergence. Convergence is determined from theresiduals of the conservation equations as well as thedifference (the L2 norm) between subsequent itera-tions of the solution. The pressure was discretizedusing a Standard method. The pressurevelocitycoupling was discretized using the Simple method.The momentum, species, and energy equations werediscretized using a first-order upwind approximation.Details about these schemes can be found in [22].

    The simulations were performed on a Beowulfcluster consisting of 58 Pentium IV processors and58 GB of RAM. When parallel processing was used,the message passing interface (MPI) was used totransmit information between nodes. In order toachieve convergence as well as compute extinctionpoints, natural parameter continuation was imple-mented. The calculation time of each simulation var-ied between 30 min and several hours, depending onthe difficulty of the problem and the initial guess.

    3. Microflame characteristics

    Fig. 2 shows contour plots of the temperature, re-action rate, and propane conversion for a typical setof operating parameters. The entire microburner isshown. The flame stabilizes in the center between thetwo plates. The reaction starts at the wall and trav-els towards the center as the flow goes downstream.Combustion occurs very rapidly, consuming most ofthe propane in a very small region. Complete con-version is achieved, and a significant temperature riseis observed due to the exothermicity of the reaction.The narrow flame front observed in the simulationsFig. 2. Contours of (a) temperature [K], (b) reaction rate[kgmol/(m3 s)], and (c) conversion for L = 600 m, Lw =200 m, kw = 3 (W/m)/K, h = 10 (W/m2)/K, Vinlet =0.5 m/s, and a stoichiometric feed (not to scale, and reflec-tion of symmetry is used for easier visualization).

    is consistent with the experimental observations byChurchill of a large-diameter TSB [17].

    Despite the small scale, there are significant tem-perature and species gradients within the fluid nearthe reaction zone. These gradients necessitate the useof an elliptic model, as axial diffusion of species andenergy cannot be neglected. Within the walls thereexist axial temperature gradients but near-zero trans-verse temperature gradients (only a handful of nodesare used within the wall in the transverse direction).Thus, when the wall temperature is displayed in thegraphs below, only the exterior wall temperature isshown.

    In order to understand how to design microburnerswith enhanced stability and robustness, it is necessaryto understand the extinction and blowout processes.Fig. 3 shows reaction-rate profiles on the centerlinefor three different cases, a stable microflame, one nearblowout, and one near extinction. Qualitatively, as amicroburner approaches extinction the reaction zoneshifts downstream slightly and is broadened, whereasthe maximum reaction rate decreases. The reactionis quenched without leaving the microburner. On theother hand, when blowout occurs, the reaction zoneshifts significantly downstream. In both cases, loss offlame stability is caused by a lack of upstream heattransfer to the incoming reactants. The primary dif-ference between the two behaviors is that in blowoutmore heat leaves in the form of a hot exit gas, whereasin extinction, the excess heat loss occurs through thewalls to the surroundings. This distinction is not al-ways sharp. We should note that once the reactionzone shifts approximately past half the length of theburner, the far-field boundary conditions at the exit

  • D.G. Norton, D.G. Vlachos / Combustion and Flame 138 (2004) 97107 101Fig. 3. Reaction rate vs axial displacement for three typi-cal cases, a stabilized microflame, one near blowout, andone near extinction from thermal losses. Thermal quenchingshifts the reaction downstream slightly, broadens the reac-tion zone a bit, and reduces the maximum reaction rate,whereas blowout shifts the reaction zone downstream sig-nificantly without decreasing the reaction rate.

    may no longer describe the system properly. As aresult, the blowout critical conditions are less accu-rate. To overcome the accuracy problem for a fixedmicroburner length, one needs to experimentally mea-sure the exit conditions and impose them as boundaryconditions.

    4. Role of wall thermal conductivity and externalheat loss in flame stability

    The location of the flame shifts as a function of op-erating parameters. In [13] we introduced the flamelocation as a convenient criterion for the stability orrobustness of a microburner, defined as the axial po-sition with the highest reaction rate. Fig. 4a shows theflame location as a function of wall thermal conduc-tivity for different external heat-transfer coefficients.As the wall thermal conductivity decreases to lowvalues, the flame location shifts downstream for allexternal heat-transfer coefficients. For high wall ther-mal conductivity and low external-heat-loss coeffi-cients, increasing wall thermal conductivity to highvalues has a minor effect on the flame location. Onthe other hand, for high external-heat-loss coefficientsin systems with 600-m gaps, increasing wall ther-mal conductivity shifts the reaction downstream. Thisnonlinear behavior is caused by the interaction be-tween two competing modes of heat transfer, namelyupstream heat transfer through the walls to preheatthe feed, and transverse heat transfer resulting in heatloss to the surroundings. The former is critical forignition and flame stabilization in microchannels, asit allows preheating of the feed without the need foran external preheater. If the upstream heat transfer isinsufficient to increase the fluid temperature to the ig-Fig. 4. (a) Flame location vs wall thermal conductivity fordifferent external heat-transfer coefficients. Low wall ther-mal conductivities cause the flame to shift downstream. In-creasing wall thermal conductivity has little effect on flamelocation unless there are significant external heat losses.The parameters used are Vinlet = 0.5 m/s, L = 600 m,Lw = 200 m, and a stoichiometric feed. (b) Flame loca-tion vs wall thermal conductivity for different microburnerdimensions with Vinlet = 0.5 m/s, h = 35 (W/m2)/K, anda stoichiometric feed.

    nition temperature, a flame is not stabilized withinthe microburner [11]. Since the conductivity of thewalls is orders of magnitude higher than that of thefluid, heat conduction through the walls is the pri-mary mechanism of upstream heat transfer. When thisupstream heat transfer is limited by low wall ther-mal conductivity, it takes a greater distance to achievethe preheating, resulting in the reaction zone shiftingdownstream (left part of the curves in Fig. 4a). Thismakes the flame less stable. For a given wall thermalconductivity, increasing the external heat loss coeffi-cient shifts the reaction zone downstream as more ofthe heat generated is lost to the surroundings.

    The wall thermal conductivity alone does not de-termine the relative upstream heat transfer in the sys-tem. The wall thickness and the gap distance alsoplay an important role. Fig. 4b shows the effect ofconductivity on the flame location for different gapdistances and wall thickness. The flame location for a1200-m gap distance, which borders on mesoscale,shows behavior qualitatively different from that of

  • 102 D.G. Norton, D.G. Vlachos / Combustion and Flame 138 (2004) 97107the 600-m gap distance. As the gap distance in-creases, the time scales for heat transfer from thereaction zone to the walls and from the hot walls tothe inlet reactants increases because of the increasedlength scale. As a result of the latter, the flame lo-cation occurs further downstream and more conduc-tive materials are needed for stable operation. As aresult of the former, the system is more robust to ex-terior heat losses. In particular, for highly conductivematerials and large external heat-transfer coefficients(e.g., 35 (W/m2)/K), the flame location does not shiftdownstream with increasing wall thermal conductiv-ity (see flat region for the 1200-m case); i.e., thelarger gap makes the burner very robust with respectto heat losses.

    Aside from the gap distance, the wall thicknessis another key factor in microburner design. Fig. 4bshows that with 400-m-thick walls, the minimumwall thermal conductivity allowable is approximatelyhalf of the minimum wall thermal conductivity allow-able with 200-m-thick walls, while the burner is veryrobust even for highly conductive materials. Whenthe wall thickness is doubled from 200 to 400 m,the amount of heat transferred upstream for a givenwall thermal conductivity is roughly doubled. Over-all, thicker walls add mechanical and thermal stability(at the expense, of course, of increased weight).

    The flame locations with respect to the entrancecalculated in these simulations are significantly short-er than those observed in the TSB of Churchill, i.e.,O(1 mm) here vs O(150 mm) in [17]. This can beattributed to the substantially faster thermal feedbackloop of microscale systems. The primary differencelikely stems from the change in the transverse timescales for energy diffusion. If so, the ratio of timescales would be (10 mm)2/(0.6 mm)2 280, whichis comparable to the aforementioned ratio of flame lo-cations.

    Aside from the flame location, the material ther-mal conductivity affects the temperature profile withinthe wall and the possibility of hot spots. Fig. 5 showsthe temperature profiles for the outer edge of the wallfor different material thermal conductivities. For low-wall-thermal-conductivity materials, significant axialtemperature gradients are observed. Hotspot temper-atures in excess of 2000 K can occur, an undesir-able situation, as it exceeds the maximum operatingtemperatures of most materials of construction. Ex-ceedingly high wall temperatures are characteristicof both micro- and macroscale thermally stabilizedburners [17,26]. As the wall thermal conductivity in-creases, the wall temperature profiles become moreuniform and the wall hot spot is eliminated. Despitethe apparent advantages of a higher wall thermal con-ductivity for material stability, most materials that of-fer high conductance are metals, and therefore wouldFig. 5. Wall outer edge temperature profiles for different wallthermal conductivities. Low wall thermal conductivities re-sult in large axial wall-temperature gradients and high max-imum temperatures. High wall thermal conductivity leadsto uniform temperature profiles without hotspots. The pa-rameters are L = 600 m, Lw = 200 m, Vinlet = 0.5 m/s,a stoichiometric feed, and h = 10 (W/m2)/K.

    not be inert to radical quenching. A more reasonablesolution would be thicker walls of a more inert mate-rial that may have a lower thermal conductivity.

    Parametric continuation is used to move fromone stationary solution to another. When the solu-tion reaches a turning point or blowout occurs, this isdenoted as a critical point. Knowledge of critical para-meter values of the external heat transfer coefficient,wall thermal conductivity, feed composition, and flowvelocity gives a better understanding of the importantfactors controlling flame stability. These critical val-ues are useful as guides, but actual values will varydepending on the system (e.g., dimensions) of inter-est.

    Fig. 6 shows the critical external heat loss co-efficient as a function of wall thermal conductivity.These bell-shaped envelopes separate the region ofself-sustained combustion below the curve from theregion above the curve where combustion cannot beself-sustained. The conductivity of several materialsis also indicated by arrows. There exists a criticalwall thermal conductivity for propane/air mixtures,at 0.1 (W/m)/K, below which combustion cannotbe self-sustained, even with insulating walls. Whenthe wall thermal conductivity increases from low val-ues, the allowable-heat-loss coefficient first increasesquickly, and then decreases and levels off in the rangeof metals or high-thermal-conductivity ceramics suchas SiC. The allowable-heat-loss coefficient reaches amaximum for insulating ceramics such as silica andalumina. The behavior seen for low-conductivity ma-terials is at first counterintuitive. Highly insulatingmaterials are poor for flame stability due to the lackof a continuous ignition source, needed to preheat thecold incoming gases.

  • D.G. Norton, D.G. Vlachos / Combustion and Flame 138 (2004) 97107 103Fig. 6. Critical external heat loss coefficient vs wall ther-mal conductivity. Typical ceramics allow maximum externalheat loss coefficients. Materials with lower wall thermal con-ductivities limit the upstream heat transfer. Materials withhigher wall thermal conductivities result in enhanced heattransfer to the surroundings. Propane allows self-sustainedcombustion for higher external heat loss coefficients andmore insulating materials than methane. The rest of the pa-rameters are the same as in Fig. 4.

    5. Effect of fuel on flame stability

    Propanes mechanism for the loss of stabilizedcombustion is qualitatively similar to that of methane,discussed in previous work [13]. For low wall thermalconductivities the primary mode of burner instabilityis blowout, whereas for high wall thermal conductiv-ities it is extinction. However, propane microflamesare more robust than methane microflames, as shownin Fig. 6. Note that the methane map is a subset of thepropane map. Lower wall thermal conductivities andhigher exterior heat-loss coefficients are possible.

    In order to better understand the differences be-tween propane and methane microflames, a theoret-ical fuel, denoted as pseudo-propane, was defined.This is simply a sensitivity analysis or numerical ex-periment aiming at delineating the differences be-tween fuels. Pseudo-propane has all of the propertiesof propane except for a parameter that is changedto a value that is identical to that for methane. Themethane/air and propane/air mixture properties, suchas thermal conductivity, specific heats, and viscosi-ties, are similar, as the primary component is nitrogenin both cases. Therefore, the properties of primary in-terest are the heats of reaction and the reaction-rateconstants.

    Fig. 7 shows the centerline temperature profile forpropane, methane, and two types of pseudo-propane.Note that due to the difference in molecular weightsand densities of various fuel/air mixtures, the mass-flow rates of different fuel/air mixtures are differentwhen the residence time is kept constant, as happensin our simulations. Therefore, instead of simply re-Fig. 7. Sensitivity analysis of the primary differences be-tween propane and methane microflames. The reaction-rateconstant has a larger effect on the solution than the heat ofreaction. The parameters are L = 600 m, Lw = 200 m,Vinlet = 0.5 m/s, kw = 1 (W/m)/K, h = 9 (W/m2)/K, anda stoichiometric feed.

    placing one heat of reaction with the other, we havealso accounted for the difference in densities. Theway we accomplish this in the first numerical exper-iment is by changing the heat of reaction of pseudo-propane so that the power generated upon completecombustion of pseudo-propane in the microburnermatches that of methane. For this case, the maxi-mum temperature decreases, and the reaction locationshifts downstream. However, these changes are smallin comparison to the difference between propane andmethane microflames.

    Next, the reaction-rate constant parameters ofpseudo-propane are changed to those of methane. Forthis case, the maximum temperature increases, andthe flame location shifts significantly downstream.This solution is closer to the methane solution. Thelower apparent activation energy of propane com-bustion ( 126 kJ/mol for propane compared to 203 kJ/mol for methane [24]) causes easier ig-nition and upstream flame stabilization. From thisanalysis we conclude that the reaction-rate constantparameters have the largest effect on flame locationand stability between different fuels. Higher hydro-carbons, such as octane, generally have lower ignitiontemperatures than methane. It is expected that theywould also exhibit increased stability compared tomethane.

    6. Role of inlet velocity in flame stability andfuel-lean operation limit

    The inlet velocity plays a key role in determiningthe location of the flame in the burner [13]. Fig. 8ashows the flame location as a function of inlet veloc-ity for several wall thermal conductivities. For high

  • 104 D.G. Norton, D.G. Vlachos / Combustion and Flame 138 (2004) 97107Fig. 8. Flame location vs inlet velocity. An optimum flowrate exists for flame stability. Higher wall thermal conduc-tivities allow higher flow rates. The laminar flame speed fora stoichiometric mixture of propane/air initially at 25 C isdenoted as Vlam. The results for different wall thermal con-ductivities are shown in (a). The parameters are L = 600 m,Lw = 200 m, h = 10 (W/m2)/K, and a stoichiomet-ric feed. The results for different burner dimensions areshown in (b). The parameters are h = 10 (W/m2)/K, kw =7.5 (W/m)/K, and a stoichiometric feed.

    inlet velocities the location of the flame shifts down-stream with increasing flow rate due to the decreasein the convective timescale (shorter residence times).For low inlet velocities, a sharp shift of the reactionzone downstream occurs with decreasing flow rate.This is due to the decrease in the heat generation rate.The external heat loss rate does not decrease as fastas the heat generation rate, resulting in a reduced up-stream heat-transfer rate. As a result of competitionbetween increased volumetric heat released and de-creased residence time with increasing flow rate, thereis a minimum in the flame location between 0.3 and0.5 m/s, depending on the wall thermal conductiv-ity. This minimum is near the unconfined flame speedfor the same composition, experimentally determinedby Dugger and others to be 0.4 m/s [27,28]. Theminimum shifts slightly toward higher flow rates forhigher wall thermal conductivity since the latter al-lows greater upstream heat transfer to compete withthe faster convective flow.

    As shown above, when conductivity is the primaryvariable, the gap distance and wall thickness play a vi-tal role in the stabilization of the flame also when theFig. 9. Critical velocity vs wall thermal conductivity. Thelower curve ( " ) represents stability loss due to insufficientheat generation. The upper curve ( 2 ) represents blowout.The shaded region allows stabilized combustion. The exper-imentally determined laminar flame speed [27] is plotted asa dashed line. Higher wall thermal conductivity allows fasterflows. The parameters are the same as in Fig. 8.

    flow velocity changes (see Fig. 8b). When the gap dis-tance is doubled from 600 to 1200 m the blowoutvelocity decreases from 1.7 to 0.8 m/s. Thisdecrease in stability with respect to flow is due tothe increased timescales for energy diffusion betweenthe gas and the walls, resulting in the relative slow-ing of the upstream preheating process, which shiftsthe flame location downstream. In contrast, increas-ing the wall thickness from 200 to 400 m increasesthe blowout velocity from 1.7 to 2.5 m/s whileleaving unaffected the flame stability for slow flows.This increased flame stability is due to the increasedarea for heat flux, doubling in our example the up-stream preheating rate. When flow velocities greaterthan the unconfined flame speed are required, the gapdistance must be small, and the wall thermal con-ductivity and thickness must be sufficiently high toprovide adequate thermal feedback to preheat the in-coming reactants.

    Fig. 9 shows the critical velocity envelope vs thewall thermal conductivity for a fixed external heatloss coefficient. The upper curve represents the high-velocity limit, resulting in blowout due to decreasedconvective timescales. The lower curve represents thelow-velocity limit, resulting in flame stability lossdue to reduced heat generation. Between these curvesstabilized combustion is allowed, whereas outsidethe envelope, self-sustained combustion is impossi-ble. Smaller wall thermal conductivities allow stabi-lized combustion for lower flow rates. Lower flowrates require less upstream heating and more insu-lation against exterior heat losses. At the other ex-treme, higher wall thermal conductivities result inmaximum allowable flow rates (upper curve), but the

  • D.G. Norton, D.G. Vlachos / Combustion and Flame 138 (2004) 97107 105increased heat losses prohibit low flow rates (lowercurve). This relationship is important when designingdevices. When a low-power device is desired, moreinsulating materials should be preferred. On the otherhand, when a high-power device is desired, more con-ductive materials should be chosen. Our focus herehas been on thermal stability. However, other materialproperties, such as allowable operating temperatures,radical sticking, and mechanical strength, along withthe microburner efficiency (complete conversion isfound here for stoichiometric mixtures using the one-step chemistry) should be considered when choosinga material for construction and designing microburnerdimensions.

    The ability of a burner to operate under lean con-ditions is beneficial, as it may reduce unwanted prod-ucts such as coke, carbon monoxide, and nitric oxide.It also reduces the operating temperature, which inturn can increase burner lifetime. Fig. 10 shows thelean equivalence ratio operation limit for the burneras a function of Reynolds (Re) number calculatedbased on the inlet conditions and the gap distancehalf-height. There are two regimes of low (< 12) andhigh (> 12) Re. For low Re, stability is lost with de-creasing Re because of the diminished heat generationrate. On the other hand, for high Re, blowout happensbecause of decreased convective time scales. At thetransition between these two regimes, there appearsto be a deep minimum in the fuel-lean operation limitand possibly a turning point over a narrow regimeof Re. Arc-length continuation is however needed tofully characterize this situation.

    Experimental work by Ahn et al. using a Swiss rollburner with gap width 3.5 mm showed an optimumRe at a relatively shallow minimum equivalence ra-tio [20]. However, this optimum Re is 1000, two

    Fig. 10. Minimum allowable equivalence ratio vs Reynoldsnumber. The Reynolds number was calculated using the ve-locity, density, and kinematic viscosity at the inlet and thegap half-width. The parameters are L = 600 m, Lw =200 m, h = 10 (W/m2)/K, and kw = 3 (W/m)/K.orders of magnitude higher than the one calculated inthis work. Furthermore, the experimental minimumequivalence ratio is approximately 0.2, compared tothe 0.56 found in this work. The differences be-tween the experimental and our computational resultsmay lie in the enhanced preheating and insulation thatare achieved with the Swiss roll design and the gapdistance, which is considerably larger in the experi-ments. More work is needed to fully understand thesedifferences.

    7. Nusselt number analysis

    To better understand how these microscale sys-tems relate to their better-understood macroscalecounterparts, a Nusselt number (Nu) analysis wasperformed. The Nu or dimensionless heat transfer co-efficient is calculated as

    (3)Nu = hLkf,cm

    =(kf

    Tfdy

    )|wallL(Tw Tf,cm)kf,cm

    and is evaluated at a given axial displacement. HereTf is the fluid temperature, Tf,cm is the cup mixingfluid temperature, Tw is the wall temperature at thewallfluid interface, and kf,cm is the fluid cup mixingthermal conductivity.

    Fig. 11 shows Nu versus axial displacement fortwo different cases, one with a flame stabilized nearthe entrance and another at a higher velocity nearblowout. Nu exhibits strongly nonmonotonic behaviorwith an oscillation at the reaction zone that finger-prints the heat source, namely walls upstream trans-ferring heat to the cold incoming gases and combus-tion chemistry downstream of the entrance heating thewalls. In both examples, Nu approaches 4, which is

    Fig. 11. Nusselt number vs axial displacement (see text) fortwo inlet flow velocities indicated. The Nusselt number is astrongly nonmonotonic function of position. The parametersare L = 600 m, Lw = 200 m, h = 10 (W/m2)/K, kw =1 (W/m)/K, and a stoichiometric feed.

  • 106 D.G. Norton, D.G. Vlachos / Combustion and Flame 138 (2004) 97107between the constant temperature and constant fluxvalues for circular tubes.

    Groppi and Tronconi used 3D parabolic energy/species balances to study methane catalytic combus-tion [29]. They found very high Nu and Sh near theentrance that eventually reach the fully developedflow values predicted by Shah [30]. Their entrancebehavior is reminiscent of ours, but the downstreambehavior differs substantially between the catalyticcombustion studied previously and the homogeneouscombustion studied here. Comparison of our resultswith the solutions of the GraetzNusselt problem fortwo parallel plates for the special cases of constantwall temperature and constant wall heat flux [31]show that the solutions of the GraetzNusselt prob-lem overestimate Nu. Note that existing correlationsdo not take into account fluid chemistry and ignoreaxial energy diffusion.

    8. Conclusions

    The characteristics of premixed propane/air mi-crocombustion and stability envelopes were studied.We have found that propane/air flames can be sta-bilized in narrow channels but very careful designis necessary. The wall material thermal conductivityplays a competing role in flame stability. Walls trans-fer heat upstream for ignition of the cold incominggases but at the same time are responsible for heatlosses. Consequently, there is an optimum wall ther-mal conductivity in terms of flame stability, which ap-pears to be that of common ceramics such as aluminaand silica. Despite the small scales of these systems,large transverse gradients in temperature and speciesmass fractions exist in the fluid and large axial gradi-ents in temperature may exist in the walls. Regardingmaterial lifetimes, higher wall thermal conductivitiesreduce the wall temperature gradients and hotspotsand should be preferred. It was also shown that theburner size plays a significant role. Thicker walls en-able more upstream heat propagation and faster flowsbefore blowout occurs and allow less conductive ma-terials to be used. On the other hand, increasing thegap distance from the micro- to the mesoscale offersthe advantage of higher stability for very conductivematerials but decreases the stability with respect toblowout, and one can hardly use ceramics. These find-ings point to the advantage of microscale combustionand the need for sufficiently thick walls.

    It has been shown that the inlet flow velocity playsa competing role in flame stability. Low flow ve-locities result in reduced power generation. On theother hand, high flow velocities decrease the convec-tive timescale below that of the upstream heat transferthrough the walls. As a result, there is only a relativelynarrow envelope of flow rates within which combus-tion can be stabilized. When a low-power device isbeing designed, more insulating materials should befavored to minimize external heat losses. Conversely,a high-power device would favor more conductivematerials.

    Overall, propane/air microflames are more robustthan methane/air ones. They allow a wider range ofwall thermal conductivities as well as higher external-heat-loss coefficients. This enhanced stability appearsto be due to propanes lower ignition temperature,which causes the reaction front to stabilize furtherupstream than for methane. It is expected that largerhydrocarbons will behave more like propane thanmethane.

    Finally, the available heat-transfer correlations areinadequate when homogeneous reactions are present.To accurately capture heat transfer in microchemicalsystems, an elliptic model, such as the one presentedin this work, is necessary.

    Acknowledgments

    This work was supported by the Army ResearchOffice under Contract DAAD19-01-1-0582. Anyopinions, findings, and conclusions or recommenda-tions expressed are those of the authors and do notnecessarily reflect the views of the Army ResearchOffice.

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    A CFD study of propane/air microflame stabilityIntroductionModelMicroflame characteristicsRole of wall thermal conductivity and external heat loss in flame stabilityEffect of fuel on flame stabilityRole of inlet velocity in flame stability and fuel-lean operation limitNusselt number analysisConclusionsAcknowledgmentsReferences