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Combustion and Flame 136 (2004) 168–179www.elsevier.com/locate/jnlabr/cn

Ignition of premixed hydrogen/air by heated counterflounder reduced and elevated pressures

X.L. Zheng and C.K. Law∗

Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA

Received 25 April 2003; received in revised form 1 September 2003; accepted 1 September 2003

Abstract

The temperature of an inert jet required to ignite a counterflowing lean premixed hydrogen/air jet wperimentally determined over the pressure range of 0.6 to 7 atm and computationally simulated usingchemistry and transport. Results show that, compared to the homogeneous explosion limits, ignition takat higher temperatures and exhibits five limits over the pressure range investigated. The first and secotion limits resemble the corresponding first and second homogeneous explosion limits, except they haveslopes in the pressure–temperature response, with the first limit being affected by the significant transof the H radical and the second limit modified by the activation of the otherwise metastable HO2 radicalsby the diffusively enriched H2. The third and fifth ignition limits are respectively manifestations of the land high-pressure responses of the third homogeneous explosion limit behavior, which is neverthelessated by the fourth ignition limit characterized by the HO2–H reactions. Furthermore, the fourth ignition limruns fairly parallel to the crossover temperature, but is shifted to lower temperatures. An explicit expr2k1 = {2k10/(k10 + k11)}k9[M], was derived and found to describe well this limit as well as the extended selimit observed in previous flow reactor studies. It is further shown that, since transport effects are inherentlytant for the present premixed system because of the diffusive loss of H to the hot, inert side of the counterignition temperature increases substantially with increasing strain rate at all pressures and that such a scan be moderated by doping the inert flow with a small amount of oxygen. 2003 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Keywords:Hydrogen chemistry; Ignition; Extended second limit

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1. Introduction

The chemical kinetics of the H2/O2 system hasbeen extensively studied [1–5], yielding results thave enabled investigations of the combustion chacteristics of H2/O2 mixtures in various physical environments. Of particular relevance to the presstudy is the series of computational, experimenand analytical investigations [6–13] on the forcnonpremixed ignition of a cold hydrogen/nitroge

* Corresponding author.E-mail address:[email protected] (C.K. Law).

0010-2180/$ – see front matter 2003 The Combustion Institutdoi:10.1016/j.combustflame.2003.09.016

jet by a counterflowing heated air jet. These studyielded the interesting result [10,11] that the ignitiresponse in this convective–diffusive system qualtively mimics the homogeneous system in thatignition boundary, in terms of the system pressand temperature, follows closely the Z-shaped expsion limits of the homogeneous H2/O2 mixture. Theeffect of aerodynamic straining is simply a displacment of the Z curve along the line of the crossotemperature. Consequently, for a given pressure,ignition temperature in the second limit is remarkabinsensitive to the applied strain rate. Indeed, sinceH2/O2 system is so chemically reactive, the ratesthe key elementary reactions are several orders la

e. Published by Elsevier Inc. All rights reserved.

http://www.elsevier.com/locate/jnlabr/cnf

X.L. Zheng, C.K. Law / Combustion and Flame 136 (2004) 168–179 169

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than those of convection and diffusion such that kinically controlled ignition events were also observfor some first- and third-limit situations that are cloto the second limit. These results were interpretedthe basis of ignition occurring in an ignition kernesituated in the hot region of the flow, within whicthe reaction rates as well as the concentrations ofkey intermediate species both attain their respecpeak values.

The above studies on nonpremixed ignition wesubsequently extended to premixed ignition in wha cold premixed H2/air jet is ignited by an impinginghot inert jet [14]. The phenomena turned out tosubstantially richer than anticipated, embodying nunderstanding of ignition which is unique to the prmixed system. Specifically, since hydrogen diffusmuch faster than oxygen, the composition of the flbecomes stratified as both reactants diffuse towardignition kernel, which is located on the hot, inert siof the flow. This results in a fuel-rich mixture in thignition kernel even for a very lean free-stream mture. The dearth of oxygen in the kernel then reduthe production rates of the key reaction intermediato levels comparable to their diffusive loss rates frothe kernel, causing the premixed ignition temperatto be substantially higher than the nonpremixednition temperature. The influence of the strain ris correspondingly increased. It was further demstrated that this increased difficulty in ignition cabe partly mitigated by doping the inert flow withsmall quantity of oxygen, which in effect instillsnonpremixed character to the system.

The study of Ref. [14] was conducted at amospheric pressure. Since ignition phenomenainherently chemistry sensitive, and since such ssitivity is strongly manifested in terms of pressuvariations for the H2/O2 system, we have extendethe study to situations at reduced and elevated psures. We shall show in due course that the ignitresponse is further enriched as the system pressutraversed, yielding useful insight into the effectspressure on chemistry–transport coupling in genand the efficiencies of chain mechanisms in particu

In the following, we shall first present the expeimental and computational methodologies and thexamine effects of pressure, strain rate, and oxyaddition to the hot, inert side of the flow on the sytem ignition.

2. Experimental and computational specifications

The pressurized burner used in previous npremixed counterflow ignition experiments [9] wadapted for the present study. The upper partthe counterflow was formed by a nitrogen jet, w

or without oxygen doping, from a 20-mm-diametquartz tube, while the lower part was a hydrogenmixture issuing from another 20-mm quartz tube. Ttubes were separated by 20 mm and were surrounby nitrogen coflows. A silicon carbide heater wplaced in the upper flow and the temperature wasulated using a proportional-integral-derivative teperature controller. The entire burner tube assemwas housed within a pressurized chamber filled wnitrogen. Temperature and velocity fields in the axdirection between the burner tubes were respectimeasured by a bare K-type thermocouple (0.003-diameter wire) and a two-component laser Doppvelocimetry (LDV) system.

Data were collected in flows with the stagnatisurface located near the midpoint of the flow fiewith the inert nitrogen temperature slowly raised util a flame appeared. The hydrogen fuel was dowith a trace amount of methane to make the flavisible. To ensure that the doping did not affect tignition temperature itself, some experiments werepeated without methane and ignition was alternamonitored by a sudden increase in the chamber psure.

Upon achieving ignition, the fuel concentratiowas reduced until the flame disappeared and the ptemperature at the oxidizer exit was measuredan external thermocouple. This temperature wasrected for radiation loss according to Ref. [9] and wconsidered to be the ignition temperature. It hadabsolute uncertainty of up to±20 K due to: (1) un-certainty about which model of the gas flow arouthe thermocouple bead, e.g., a sphere vs a cylindcross-flow, best describes the actual shape of the band (2) uncertainty in the radiation calculation [9].determine the velocity characteristics of the systethe oxidizer temperature was reduced 5–10 K bethe value at ignition before the LDV measuremewere performed.

Laminar ignition calculations were performewith the code of Kreutz and Law [10], with detailetransport and chemistry, using the reaction mecnism of Mueller et al. [5]. The calculations detemined steady-state solutions at different hot boundtemperatures assuming potential flow, with thelocity gradient given by the experimentally measurvalue. The ignition temperature was found by detmining the boundary temperature at the lower turnpoint of the ignition–extinction S curve. We notepassing that it was shown and discussed in Ref.that since ignition is mainly governed by the locvelocity gradient immediately upstream of the ming layer on the oxidizer side, the use of the simppotential flow formulation adequately describesignition characteristics.

170 X.L. Zheng, C.K. Law / Combustion and Flame 136 (2004) 168–179

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3. Results and discussion

3.1. Effects of pressure

As a reference to subsequent discussion ofresponse of the ignition temperature in the prespremixed counterflow system, we plot in Fig. 1 tcharacteristic Z-shaped pressure–temperature exsion limits of a homogeneous mixture, which in thcase is stoichiometric in composition and is containin a spherical KCl-coated vessel of 7.4 cm diamter [1]. It is well established [15] that explosion othe homogeneous mixture is governed by a balabetween chain branching and wall termination infirst limit; by the competition between branchinH + O2 → O+ OH, and the destruction of H througH + O2 + M → HO2 + M in the second limit; andthrough reactions involving HO2 and H2O2 in thethird limit.

Figure 1 shows the ignition temperatures detmined from both calculation and experiment for 9H2 in air (φ = 0.236) versus heated N2 at a pressureweighted strain rate [9,10] ofk = 216 s−1. It isfirst noted that the experimental and calculated valagree closely with each other within 10 K. This levof agreement exists for almost all the results reporin the present study, with the only exception being3% O2 case of Fig. 16, which shows slightly largdeviations of about 20 K at higher pressures.

Comparing the counterflow ignition and homogneous explosion results, it is seen that, while the coterflow response mimics the homogeneous limitssome aspects, it is more complex and is characterby fundamental differences. First of all, the cou

Fig. 1. Comparison between the pressure–temperatureplosion limits of a stoichiometric homogeneous H2/O2 mix-ture and the ignition limits of an H2/air flow by a counter-flowing at a pressure-weighted strain ratek of 216 s−1. Forthe counterflow results, symbols are experimental and lincomputational.

terflow ignition response curve is shifted to hightemperatures compared to that of the homogeneexplosion limits. Second, compared to the threeplosion limits of the homogeneous mixture, it hfive branches, which we shall call the first, secothird, fourth, and fifth ignition limits in the directionof increasing pressure, in order to draw correspdence with the homogeneous case. These five ignlimits have the following characteristics. In the firand second limits the ignition temperature decreaand increases with increasing pressure, respectisimilar to the behavior of the corresponding first asecond homogeneous explosion limits. However,second ignition limit now terminates around 3 aand the response reverses trend such that the igntemperature decreases again with increasing presover the range of 3–5 atm, which constitutes the thignition limit. The ignition curve subsequently turnagain to form a segment corresponding to the fouignition limit. This limit is somewhat parallel to thcrossover temperature, defined by 2k1 = k9[M], butis shifted to lower temperatures for given pressuThe final reversal yields the fifth limit over which ignition becomes easier again with increasing pressThis limit was obtained only through calculations bcause the pressure range is too high for the preexperimental setup.

Before discussing in detail the various chemiand physical factors controlling the five limits, sombasic characteristics associated with the premisystem need to be addressed in advance becausegovern the ignition behavior for all pressures. Tgeneral structure of the ignition kernel, defined aslocation of the highest reactivity, is shown in Fig.in which spatially resolved profiles of temperatuand species concentrations are plotted for the ignistate whenTign = 996.5 K at 1 atm. These profilehighlight the unique features of premixed ignition. Abriefly mentioned earlier, since hydrogen is more mbile than oxygen, it diffuses farther toward the instream. This yields a stratified distribution of hydrgen and oxygen, with the ignition kernel being sustantially more fuel rich than the free stream of tpremixed flow. Furthermore, since there is no oxgen from the hot free stream to react with the higdiffusive H radicals, these radicals will leak outthe ignition kernel, as shown by the long tail extening to the hot boundary in Fig. 2. These two featuplay prominent roles in modifying the three homogneous explosion limits to the five ignition limits othe present diffusion-affected system, to be discusnext.

3.1.1. The first limitThe first ignition limit is identified in Fig. 1 as th

lowest pressure regime in which the ignition tempe


Fig. 2. Major (H2, O2) and minor (H, OH, and O) species concentration and temperature profiles at 1 atm.

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Fig. 3. Minor (H, O, OH, HO2, and H2O2) species concentrations profiles at 0.2 atm.

ture increases with decreasing pressure. Similar tohomogeneous case, the diffusive loss of radicalsative to their production becomes progressively mimportant with reducing pressure, as demonstratedthe substantially broadened profiles of H, O, and Oin Fig. 3, in which the spatial distributions of thminor species at 0.2 atm are plotted at the ignitstate. These radicals back-diffuse across the station plane into the premixed stream, far away frothe peak location of the H radical which marks tcenter of the ignition kernel. The spatial distributioof elementary reaction rates (Fig. 4) also show tthe production and destruction rates of H are not banced within the ignition kernel, and some H radicgenerated are lost by diffusion.

It is necessary to emphasize the differencetween the diffusive loss in the first limit and theradical loss to the hot, inert stream for all limits. At thfirst ignition limit, the diffusive loss of the H, O, anOH radicals out of the ignition kernel and acrossstagnation plane is characteristic only of low-press

ignition, for which diffusion becomes significant reative to reaction. As pressure increases, this moddiffusive loss becomes negligible, as shown in Figin which the H, O, and OH profiles at 1 atm hanarrow peaks and do not penetrate across the snation plane. However, the leakage of H to theboundary exists at all pressure ranges and is intrito premixed ignition with the hot ignition source bing inert.

3.1.2. The second and third ignition limitsAs pressure increases, the inhibitive effect of

diffusive loss is taken over by the three-bodyaction (R9): H+ O2 + M → HO2 + M, which ef-fectively competes with the chain-branching react(R1): H+ O2 → OH+ O. While this consideration ithe same as that for thehomogeneoussecond explo-sion limit, there is an additional consideration for tpresent premixed ignition. That is, there is now a rative abundance of H2 in the ignition kernel due to itspreferential diffusion over O2. Consequently beforthe HO2 radicals are swept out of the ignition kernthey encounter the abundant H2 and react with themthrough

(R18)HO2 + H2 → H2O2 + H,

which converts the otherwise inactive HO2 to themore reactive H radicals. Figure 5 shows that the ctribution to H radicals from (R18) is almost comprable to that from the chain-branching reaction (RO + H2 → H + OH. Moreover, some of the H2O2radicals generated by (R18) are able to further decpose to two OH through

(R16)H2O2 + M → 2OH+ M.

Consequently, the net effect of the above two retions is to convert one relatively inert HO2 to three


overall

overall

Fig. 4. Spatially resolved rates for hydrogen radical production, destruction, and mass transport (mol cm−3 s−1) at 0.2 atm.Top: Rates of individual elementary reactions. Bottom: Rates of diffusive and convective transport compared with thechemical production rate for H.

Fig. 5. Spatially resolved rates for hydrogen radical production, destruction, and mass transport (mol cm−3 s−1) at 3.5 atm.Top: Rates of individual elementary reactions. Bottom: Rates of diffusive and convective transport compared with thechemical production rate for H.

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more reactive radicals. All these effects then acconcert to render the increased generation of H2from (R9) with increasing pressure to be a faciliting instead of a retarding reaction. Consequently,

second limit in thep–T space is steepened and finaturns around at about 3 atm to form the third limit.

The above discussion is further supported bsensitivity analysis of the S curve, which determin


: heated
Fig. 6. Sensitivity of the S curve to individual reaction rates normalized by the largest value at 3, 4, and 5 atm. ConditionsN2 flowing against a cold mixture of 9% H2 in air (φ = 0.236) andk = 216 s−1.
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its response in a region close to the ignition turnpoint to a perturbation in each of the reaction rati.e.,

∂ ln[XH]max

∂ lnAi,

where[XH]max is the maximum mole fraction of thhydrogen radical, andAi is the pre-exponential factofor the ith reaction rate constant [11]. It is seenFig. 6 that, with increasing pressure, (R18) and (Rbecome progressively more important, accompanby a weakening of the termination effect of (R9).

3.1.3. The fourth ignition limitBy further increasing the pressure, a fourth ig

tion limit appears at which ignition again becommore difficult (Fig. 1). Figure 7 shows the systemsponse represented by the maximum H concentrato the hot boundary temperature at 1, 5, and 8 awhich lie respectively in the second, third, and fouignition limits. These curves indicate that the igntion states at 8 atm are qualitatively different frothe other two. That is, at 1 and 5 atm, the mamum mole fractions of H at the ignition, turningpoint, states are only around 10−9. However, whenthe pressure is progressively increased, the igniturning point gradually evolves to an inflection poiand then finally disappears. Simultaneously, anoignition turning point emerges with a higher H cocentration, say about 10−5 at 8 atm.

To identify the processes that govern ignitionthe fourth ignition limit, a series of flux analyses fdifferent species under various pressures wereformed. It was found that the H radicals genera

Fig. 7. Calculated S curves for H2/air mixtures at three dif-ferent pressures.

from (R18) now actively react with HO2 through

(R10)HO2 + H → H2 + O2,

(R11)HO2 + H → OH+ OH.

Thus (R10) not only competes with (R18) for the HO2radical, which could produce an H radical throu(R18), but it also consumes the H radical producby (R18). Furthermore, it is chain terminating. Othe other hand, (R11) is chain branching if HO2 isconsidered inert. The ignition behavior is therefomodified by their competition, as will be discussshortly. The crucial point to recognize is that the HO2radicals have their origin in (R9), while the H radcals are built up from (R18), which in turn is activatby the abundance of H2 due to its preferential diffu-sion.


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Fig. 8. Spatially resolved rates for HO2 radical production, destruction, and mass transport (mol cm−3 s−1) at 8 atm. Top: Ratesof individual elementary reactions. Bottom: Rates of diffusive and convective transport compared with the overall cproduction rate.

Fig. 9. Sensitivity of the S curve to individual reaction rates normalized by the largest value at 8 atm. Conditions: he2flowing against a cold mixture of 9% H2 in air (φ = 0.236) andk = 216 s−1.

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Compared to the above two reactions for HO2consumption, (R10) and (R11), the third pathway(R14) (HO2 + HO2 → H2O2 + O2) and (R16) is lesscrucial to ignition. This is due to the fact that, sinthe rate of (R14) peaks closer to the stagnation placompared with (R11) (Fig. 8), H2O2, together withOH, is generated in a lower temperature region. Fthermore, some H2O2 generated by (R14) will be losby mass transport. As a consequence, the above pway has a very low efficiency at the fourth ignitio

limit. The sensitivity result of Fig. 9 confirms thiobservation, showing (R10) and (R11) respectivhaving significant negative and positive effects onnition at 8 atm, while (R16) is relatively less impotant.

Given the above flux and sensitivity analyses,ignition temperature at the fourth ignition limit cabe estimated by using a six-step skeletal mechaninvolving (R1), (R2), (R3), (R9), (R10), and (R11For this mechanism the reaction rates for H, O, O


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and HO2 are given by

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= k1[H][O2] + k2[O][H2] − k3[OH][H2](1)+ 2k11[HO2][H],

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= k1[H][O2] − k2[O][H2],

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= k9[H][O2][M](3)− (k10+ k11)[HO2][H],

d[H]dt

= −k1[H][O2] + k2[O][H2] + k3[OH][H2]

(4)− k9[H][O2][M] − (k10+ k11)[HO2][H].

The flux analysis shows that H, O, OH, and HO2can be considered to be in “steady state” in that thchemical creation and destruction rates are signcantly higher than their characteristic rates of mtransport in the ignition kernel. This is also reflectby their concentration profiles, which lie within thignition kernel, away from the stagnation surfaceshown in Fig. 10. Furthermore, although the H prostill has a long tail extending to the hot side, the difsion rate of H is almost 2 orders of magnitude smathan the peak reaction rates. Since the diffusiveof H is less significant, it is reasonable to assumeH is in steady state.

Setting Eqs. (1)–(4) to zero based on the abovesumption, the following relation is obtained:

(5)2k1 = 2k10

k10+ k11k9[M].

Similar to the crossover temperature, this appromate expression for the fourth limit temperature dpends only on chemistry and hence can be reaevaluated. Figure 11 shows that the approximat

Fig. 10. Minor (H, O, OH, HO2, and H2O2) species con-centrations profiles at 8 atm.

Fig. 11. Pressure-vs-temperature limits for the crossotemperature and the extended second limit. Symbsquares are the calculated ignition temperatures formixed counterflow (fuel side, 9% H2 in air; hot side, N2);triangles are the experimental data from Mueller et al.for 1.0% H2/0.5% O2/N2 mixture explosion limit in flowreactor experiments.

tracks the detailed calculation quite well, with tdeviation increasing at higher pressures becausepathways of (R14) and (R16) can no longer beglected.

Compared to the expression for the classical croover temperature, 2k1 = k9[M], which describes thesecond explosion limit, the factor 2k10/(k10 + k11)

in Eq. (5) can be considered to play the role of moifying the chain termination ratek9. It accounts forthe extent to which HO2 is fully terminated through(R10), compared to the remaining fraction that bcomes part of the branching pathway through (R1Since both calculation and flux analysis showed tk10 is always less thank11, this factor is less thanunity and therefore effectively reduces the influenof k9. Consequently, at a given pressure the presfourth ignition limit is shifted to lower temperaturecompared to the crossover temperature.

It is also of particular interest to note that the epression just derived for this limit, Eq. (5), followclosely the extended second limit in the flow reacstudies of Ref. [5], as shown in Fig. 11. To explorecorrespondence in ignition between the presentmixed counterflow and the flow reactor, an igniticalculation using SENKIN [16] was performed for1.0% H2/0.5% O2/N2 mixture with the initial condi-tion of 8 atm and 1050 K, which correspond to a cafor the extended second limit predicted by Ref. [The generation and destruction rates of HO2 radicalsas a function of time are plotted in Fig. 12, whicshows that, similar to the counterflow ignition, onHO2 is generated by (R9), it will further react witH through the pathways (R10) and (R11) to influenignition. In other words, the same group of reactio


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Fig. 12. The generation and destruction rates of HO2 radicalsas a function of time for a 1.0% H2/0.5% O2/N2 mixturewith the initial condition of 8 atm and 1050 K.

controls ignition in the counterflow and explosionthe flow reactor.

Mechanistically, the classical third explosion limobserved in static reactor experiments is a conquence of the combined chemical and thermal acttion in that the heat release from some slow reactican bring the mixture to an explosion condition [5However, for both flow reactor and counterflow expiments, the limited residence time does not allowservation of reactions with longer characteristic timFurthermore, extensive dilution of the mixture by ntrogen also greatly limits self-heating from these slreactions. Consequently, the extended second limthe flow reactor and the fourth ignition limit of thcounterflow can exist at a high-temperature regicompared to the third explosion limit.

In view of the above discussion, it is reasonableidentify Eq. (5) as an explicit expression for the etended second limit of Ref. [5], with the simultaneorecognition of the importance of the HO2 pathway,(R10) and (R11), at this limit. Following the designtions for the crossover temperature and the extensecond limit, it is therefore appropriate to call this epression theextended crossover temperature, with theunderstanding that, similar to the crossover tempature, the pressure–temperature range over whicholds is system dependent even though the expresitself is system independent.

3.1.4. The fifth ignition limitThe fifth ignition limit, shown in Fig. 1, is the

highest pressure regime over which the ignition teperature decreases with increasing pressure. Kincally, as the pressure increases, more and more2is generated through (R9), and its recombinationaction (R14), whose reaction rate increases quadcally with the HO2 concentration,

(R14)HO2 + HO2 → H2O2 + O2,

Fig. 13. Spatially resolved rates for HO2 radical pro-duction, destruction by individual elementary reactio(mol cm−3 s−1) at 15 atm.

can no longer be neglected. Due to the fact thatHO2 is generated within the ignition kernel in the prmixed case because of O2 starvation, higher pressureare needed for (R14) to become important. As shoin Fig. 13, most of the HO2 radicals are consumeby (R14). To a lesser extent, HO2 will react with Hthrough (R10) and (R11) as shown in Fig. 13. Nthat some H2O2 radicals generated by (R14) will further decompose to two OH within the ignition kernthrough (R16):

(R16)H2O2 + M → 2OH+ M.

Although (R10) still functions as a chain termintion step, other reactions with much higher retion rates, i.e., (R14) (through (R16)) and (R1are chain branching. Consequently, the ignition cuturns again and ignition becomes easier at very hpressures due to the overall chain branching chateristic. As a whole, the premixed ignition responin the fifth ignition limit is qualitatively similar to thethird explosion limit for the homogeneous mixturethe sense that HO2 becomes part of the chain propgation route, except it occurs at higher pressures wdifferent reactions.

3.2. Effects of aerodynamic straining

Since the premixed ignition system intrinsicasuffers the diffusive loss of H to the inert side, aedynamic straining is expected to exert a significinfluence on the system ignitability. To quantify thinfluence, the response of the ignition temperatwas experimentally and computationally determinfor varying flow rates and pressures. The resultsplotted in Fig. 14 and discussed in the following.

First, increasing the strain rate uniformly increasthe ignition temperature at all pressures because o


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Fig. 14. Ignition temperatures vs strain rate at three differpressures. Experiments shown as symbols, and calculashown as lines.

reduction in the residence time, which is the recipcal of the flow strain rate [17]. Second, the ignitiotemperature at the fourth ignition limit, as at 5.4 atis less sensitive to the strain rate than that at the otwo pressures shown in Fig. 14. To understandbehavior, we note that in the study of Ref. [14]1 atm, the rates of H production and consumptionpremixed ignition were found to be of the sameder as that for diffusive loss. Since a minimum radi

pool is needed for kinetic runaway to occur, highignition temperatures are needed such that chemproduction can overcome the transport loss. If weply this argument to the case of 3.5 atm, and sincegeneration and consumption rates of H atoms arean order higher than the mass transport rates (Figthe ignition temperature should be less sensitive tostrain rate than the response at 1 atm. This, howeis not the case, as shown in Fig. 14. The reasothat not only the H radicals but also the HO2 radi-cals are critical to ignition because (R18) involvinHO2 is one of the main sources in the productionthe H radicals. It can be seen from the flux analyin Fig. 15 that the rates of individual HO2 produc-tion and consumption reactions are of the same oas that for mass transport. Furthermore, the bottomFig. 15 shows that convection is more important thdiffusion in transporting HO2 out of the ignition ker-nel. It is in this manner that convective transport plaa critical role in the third ignition limit. As a result, thignition temperature strongly depends on the convtive residence time and thereby the strain rate.

For the fourth ignition limit, as discussed ealier, H, O, OH, and HO2 are in steady state in thatheir chemical creation and destruction rates arenificantly larger than the characteristic rates of mtransport in the ignition kernel at higher pressurFurthermore, although the concentration of H2O2 issubstantially affected by mass transport, the pathinvolving H2O2 plays a minor role on ignition. Con

hemical
Fig. 15. Spatially resolved rates for HO2 radical production, destruction, and mass transport (mol cm−3 s−1) at 3.5 atm. Top:Rates of individual elementary reactions. Bottom: Rates of diffusive and convective transport compared with the overall cproduction rate.


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sequently ignition at the fourth limit is strongly chemistry controlled and therefore is less sensitive tostrain rate.

3.3. Effects of O2 doping in the hot stream

Results from the present study as well as thof Ref. [14] show that, because of the concentratstratification of the reactants in the premixed stem and the subsequent loss of hydrogen to thestream, premixed ignition temperatures are substially higher than those of the nonpremixed systeRef. [14] subsequently found that the ignition teperatures can be significantly lowered by addingsmall amount of oxygen to the hot stream. Theability of this possibility is further explored for itdependence on the system pressure. Figure 16 sthe experimental and calculated ignition temperatuas a function of pressure, with the O2 mole fractionat the hot boundary being 0, 1, and 3%, respectivA particularly interesting result is that the ignition rsponse curve changes from five limits at 0% dopingthree limits at 3% doping. This behavior is explainin the following.

For the first and second ignition limits, which ocur when the pressure is below 3 atm, ignitionfacilitated by replacing the inert N2 in the hot bound-ary by O2. The effect is significant even with a smaamount of O2 addition, for two reasons. First, without O2 in the hot free stream, the amount of oxygwithin the ignition kernel is very small becausecan be brought there only through diffusion acrothe stagnation plane against convection from theert side. On the other hand, when O2 is present in thehot stream, it can be brought to the ignition kernthrough both convection and diffusion. The effecttherefore much larger. Second, the potential diffusloss of H from the center of the ignition kernel is no

Fig. 16. Constant pressure-weighted strain rate curve onition temperature vs pressure for different amount of2addition to the hot inert side of the flow.

Fig. 17. Consolidated plot for the calculated resultsFig. 16 for comparison of their response to the extent of ogen doping and pressure variation.

either significantly reduced or even practically elimnated because it is recaptured by reacting with the2from the hot stream. The combination of these tfactors therefore enables the critical radical conctration for ignition to build up at a lower temperatufor the O2-doped hot stream.

The above effect, however, is weakened withcreasing pressure. As shown in Fig. 17, which copares the calculated results shown in Fig. 16, theference between the ignition temperatures becosmaller as pressure increases. This is reasonablcause the diffusive loss of H is reduced at higher psures such that the effect of recapturing H discusabove is less significant.

When the pressure is higher than 3 atm, the sond ignition limit of the O2-doped system terminateat a higher pressure, and the extended second limihavior gradually vanishes. As discussed earlier, ireaction (R18) that assists ignition by convertingrelatively inert HO2 to H at the third ignition limit.However, as more O2 becomes available in the igntion kernel, most of the H2 will react with O2 insteadof HO2. As a result, the HO2 concentration is built upat a lower pressure and its recombination contributo ignition at an early stage. Consequently, insteaevolving into the third, fourth, and fifth ignition limits, the O2-doped system will march along the thilimit in the same manner as that for the homogeneignition.

4. Conclusions

Ignition of lean premixed hydrogen/air by heatnitrogen or a mixture of nitrogen and oxygen wstudied in a laminar counterflow over a rangepressures and strain rates. Compared to the ho


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geneous explosion limits, two important distinctiowere identified for the premixed ignition system. Fiof all, the counterflow ignition response curveshifted to higher temperatures compared to that ofhomogeneous explosion limits due to the reducedidence time as well as the additional transport lof the H radicals. Furthermore, the omnidominanof the crossover temperature chemistry constrainsshifting to be along itsp–T response path. Seconthe ignition temperature was found to exhibit five limits over the pressure range investigated. The first thlimits mimic the homogeneous case, except thatpronounced H radical loss to the hot inert side pusthe first limit to end at a higher pressure. The steening of the second limit, which turns and forms tthird limit, is due to the increasing importance(R18). This reaction converts the relatively inert HO2to the more reactive H radical and is greatly facilitatby the abundant H2 within the ignition kernel owingto its preferential diffusion over O2. As the concen-tration of the H radical is built up through (R18) witincreasing pressure, reactions between HO2 and H((R10) and (R11)) start to be important and exerretarding influence on ignition. The resulting fourignition limit resembles the previously observed etended second explosion limit from flow reactor stuies and can be described by the classical crosstemperature expression withk9 modified and therebyweakened by the factor 2k10/(k10 + k11). The final,fifth limit is characterized by the self-recombinatioof HO2 through (R14) and as such describes the hipressure regime of the third explosion limit. Aswhole, the third, fourth, and fifth ignition limits cabe interpreted as a punctuated manifestation ofthird explosion limit in that the third and fifth ignition limits would correspond to the third explosiolimit at lower and higher pressures, respectively, wtheir transition interrupted by the fourth limit, whicis a reemergence of the second limit moderated bypartial reactivation of the HO2 through its reactionswith H.

We have also shown that aerodynamic strainincreases the ignition temperature, which is reasable because of the reduced residence time, althothe response is less sensitive at the extended selimit, which is mostly chemistry controlled. Furthemore, oxidizer doping in the inert flow moderates textent of H leakage and the various consequencethe preferential diffusion of H2 such that the ignition

response is again characterized by three limits simto those of homogeneous explosion and nonpremignition.

Acknowledgments

This research was supported by the Army Rsearch Office, under the technical monitoring ofDavid Mann, and a center grant on carbon mitigatsponsored by the British Petroleum Corp.

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