Combustion and Flame 137 (2004) 320–339 www.elsevier.com/locate/jnlabr/cnf Effects of strain rate on high-pressure nonpremixed n-heptane autoignition in counterflow Shiling Liu, a,∗ John C. Hewson, a Jacqueline H. Chen, a and Heinz Pitsch b a Reacting Flow Research Department, Combustion Research Facility, Sandia National Laboratories, P.O. Box 969, MS 9051, Livermore, CA 94551-0969, USA b Center for Turbulence Research, Stanford University, Stanford, CA 94305-3030, USA Received 18 June 2003; received in revised form 7 December 2003; accepted 20 January 2004 Abstract The effect of steady strain on the transient autoignition of n-heptane at high pressures is studied numerically with detailed chemistry and transport in a counterflow configuration. Skeletal and reduced n-heptane mechanisms are developed and validated against experiments over a range of pressure and stoichiometries. Two configurations are investigated using the skeletal mechanism. First, the effect of strain rate on multistage n-heptane ignition is studied by imposing a uniform temperature for both the fuel and the oxidizer streams. Second, a temperature gradient between the fuel and the oxidizer streams is imposed. The global effect of strain on ignition is captured by a Damköhler number based on either the heat-release rate or the characteristic chain-branching rate. Results show that for low to moderate strain rates, both the low- and intermediate-temperature chemistries evolve in a manner comparable to that in homogeneous systems, including the negative temperature coefficient regime, but with somewhat slower evolution attributable to diffusive losses. At high strain rates diffusive losses inhibit ignition; for two-stage ignition, it is found that ignition is inhibited during the second, intermediate-temperature stage. The imposition of an overall temperature gradient further inhibits ignition because reaction zones for key branching reactions with large activation energies are narrowed. For a fixed oxidizer stream temperature that is not sufficiently high, a higher fuel temperature results in a shorter ignition delay provided that the heptyl radicals are mainly oxidized by low-temperature chemistry. As expected, an increase in pressure significantly increases reaction rates and reduces ignition delay time. However, with increasing pressure there is a shift toward single- stage low-temperature-dominated ignition which serves to delay ignition. 2004 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: n-Heptane; Autoignition; Counterflow; Nonpremixed; Strain effect 1. Introduction Ignition processes are an integral part of combus- tion in many practical systems including, for example, diesel engines. Ignition in diesel engines typically oc- curs while strong fuel–air and temperature inhomo- geneities exist, making the study of ignition in non- * Corresponding author. E-mail address: [email protected] (S. Liu). premixed configurations with compressed reactants particularly valuable. n-Heptane has a cetane number (CN ≈ 56) similar to that of diesel fuel (CN ≈ 50), and it is widely used as a model fuel to study the ignition process. Research into n-heptane ignition in homogeneous systems, where kinetics is best stud- ied, has progressed nicely [1–11], but there have been few fundamental studies of inhomogeneous mixtures at conditions relevant to diesel ignition. The cur- rent work seeks to provide a better understanding of the transient ignition process in such systems. More 0010-2180/$ – see front matter 2004 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.combustflame.2004.01.011
Transcript
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Combustion and Flame 137 (2004) 320–339www.elsevier.com/locate/jnlabr/cn
Effects of strain rate on high-pressure nonpremixedn-heptane autoignition in counterflow
Shiling Liu,a,∗ John C. Hewson,a Jacqueline H. Chen,a and Heinz Pitschb
a Reacting Flow Research Department, Combustion Research Facility, Sandia National Laboratories, P.O. Box 969, MS 9051,Livermore, CA 94551-0969, USA
b Center for Turbulence Research, Stanford University, Stanford, CA 94305-3030, USA
Received 18 June 2003; received in revised form 7 December 2003; accepted 20 January 2004
Abstract
The effect of steady strain on the transient autoignition ofn-heptane at high pressures is studied numericwith detailed chemistry and transport in a counterflow configuration. Skeletal and reducedn-heptane mechanismare developed and validated against experiments over a range of pressure and stoichiometries. Two confiare investigated using the skeletal mechanism. First, the effect of strain rate on multistagen-heptane ignition isstudied by imposing a uniform temperature for both the fuel and the oxidizer streams. Second, a temgradient between the fuel and the oxidizer streams is imposed. The global effect of strain on ignition is cby a Damköhler number based on either the heat-release rate or the characteristic chain-branching ratshow that for low to moderate strain rates, both the low- and intermediate-temperature chemistries ea manner comparable to that in homogeneous systems, including the negative temperature coefficienbut with somewhat slower evolution attributable to diffusive losses. At high strain rates diffusive lossesignition; for two-stage ignition, it isfound that ignition is inhibited during the second, intermediate-temperatustage. The imposition of an overall temperature gradient further inhibits ignition because reaction zonesbranching reactions with large activation energies are narrowed. For a fixed oxidizer stream temperaturnot sufficiently high, a higher fuel temperature results in a shorter ignition delay provided that the heptyl rare mainly oxidized by low-temperature chemistry. As expected, an increase in pressure significantly increreaction rates and reduces ignition delay time. However, with increasing pressure there is a shift towardstage low-temperature-dominated ignition which serves to delay ignition. 2004 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
Ignition processes are an integral part of combtion in many practical systems including, for exampdiesel engines. Ignition in diesel engines typically ocurs while strong fuel–air and temperature inhomgeneities exist, making the study of ignition in no
0010-2180/$ – see front matter 2004 The Combustion Institutdoi:10.1016/j.combustflame.2004.01.011
premixed configurations with compressed reactaparticularly valuable.n-Heptane has a cetane numb(CN ≈ 56) similar to that of diesel fuel (CN≈ 50),and it is widely used as a model fuel to study tignition process. Research inton-heptane ignition inhomogeneous systems, where kinetics is best sied, has progressed nicely [1–11], but there have bfew fundamental studies of inhomogeneous mixtuat conditions relevant to diesel ignition. The curent work seeks to provide a better understandingthe transient ignition process in such systems. M
e. Published by Elsevier Inc. All rights reserved.
S. Liu et al. / Combustion and Flame 137 (2004) 320–339 321
m-ied.ni-hatso-tureatnndTheec-se
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specifically, the effects of fuel–air gradients and teperature gradients on the ignition process are studThe key chemical behavior that distinguishes igtion under the present diesel-like conditions from tunder other conditions is the combined effect ofcalled low-temperature and intermediate-temperachemistry on the ignition process. It is known thfor homogeneousn-heptane–air mixtures ignition caoccur in a multistage mode [1] where both low- aintermediate-temperature chemistries play a role.different chemistry regimes are defined in later stions and Refs. [3] and [4] provide details of theprocesses.
Ignition in inhomogeneous systems with highsimplified chemistry has been studied for some ti[12,13] and has recently been studied in the ctext of detailed chemical mechanisms. Blouch aLaw [14] studied the effects of strain and pressurethe air temperature required to autoigniten-heptanein steady-state counterflow systems. Seiser et al.studied strain effects on extinction and autoignitin a steady-state counterflow configuration at onemosphere. Sreedhara and Lakshmisha [16] studieautoignition ofn-heptane in an initially nonpremixedmedium under isotropic, homogeneous, and decaturbulence environment using direct numerical sulation. Measurements and analysis in these stuwere conducted at temperatures sufficiently highthe low-temperature chemistry was of little impotance. Schnaubelt et al. [17] studiedn-heptane dropleignition in microgravity at temperatures and presures suitable for observing the multistage autoigtion process. Pitsch and Peters [18] numericallyvestigated the autoignition ofn-heptane under dieseengine conditions using a flamelet model in conjution with CFD simulations and proposed a formution of ignition delay time under strained conditioas a function of scalar dissipation rate and homoneous ignition delay time for a fixed fuel temperture of 400 K at 40 to 50 bars. In these studiesstrain rate (or scalar dissipation rate) was identifiedtending to inhibit ignition, as do lower boundary temperatures and pressures. In recent work, Gopalaknan and Abraham [19] have numerically investigathe role of differential diffusion inn-heptane igni-tion and found that differential diffusion effects amost significant for those cases, at lower pressuand temperatures, where ignition delays are longeNevertheless, there are no comprehensive studiethe authors’ knowledge, that analyze the effects ofhomogeneities, specifically the gradients associawith those inhomogeneities, on the transient igtion process for temperatures and pressures wboth low- and intermediate-temperature chemistare significant.
Motivated by the need to study transient autoigtion processes in CFD that include coupling betwetransport and reaction, new skeletal and redumechanisms for studies of multistage autoignitat high pressures are developed and validateda wide range of conditions. Seiser et al. [15] had pviously developed a short mechanism of 159 speand 770 reversible reactions from a detailed mecnism that includes 2540 reversible elementary retions among 556 species [3]. However, computtransient ignition with this mechanism is very iefficient. The present skeletal mechanism is msmaller with 43 species and 185 reactions, counforward and backward reactions individually. Theduced mechanism has 18 global reaction steps.
The first objective of the present study is to exaine the effect of strain rate on multistagen-heptaneignition between counterflowing fuel and oxidizerstreams, each at the same temperature. The seobjective is to investigate the effect of strain ratethe presence of an imposed temperature gradientween the fuel and the oxidizer streams. In partilar, the temperature gradient considered encompathe low- to intermediate-temperature ignition kinetwith ignition causing a transition to high-temperatukinetics.
In the following, the skeletal and reduced chemimechanisms forn-heptane ignition and oxidation apresented first. This is followed by an overview of tnumerical methods and multistage ignition phenoena. Then the effect of strain rate on ignition delaydiscussed for uniform and stratified fuel and oxidizboundary temperature conditions. Finally the effectsof pressure and fuel stream temperature on igniare examined.
2. Reduced chemical mechanisms for n-heptane
The development of the reduced mechanism stfrom a detailed kinetic reaction mechanism for thenition and combustion ofn-heptane [20]. This mechanism has been revised and updated in the H2/O2- andthe C1–C3-part using recent kinetic rate data froBaulch et al. [21,22]. The detailed mechanism csists of 1008 elementary reactions and 168 checal species. With the knowledge of the main reactpaths, already described by Pollard [23] and Bson [24], a remarkably shortened mechanism canderived by neglecting unimportant side chains. Tmechanism is referred to as a skeletal mechanismis the starting point for the further reduction. Tresulting skeletal mechanism consists of 43 checal components and 185 reactions, counting forwand backward reactions individually. The reactio
322 S. Liu et al. / Combustion and Flame 137 (2004) 320–339
he-
ed
tionech
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tnptylal-ith.if-
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thecan
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remaining in the skeletal mechanism and the Arrnius coefficients are given in Appendix A.
A similar skeletal mechanism has been derivpreviously by Bollig et al. [25] to predict NOx precur-sor species in steady diffusion flames. This reacset has been included as a subset of the present manism to preserve the applicability of the mechaniin pollutant formation calculations.
In addition to the mechanism from Bollig eal. [25], for a proper description of the ignitioprocess, a fuel consumption path over a second heradical is needed. Also some reactions for radicpoor combustion, for instance, some reactions wHO2 and H2O2, have to remain in the mechanismThe low-temperature reaction paths arising by dferent heptyl isomers have been lumped to onlychain, which is similar to the low-temperature atoignition steps by Cox and Cole [26].
Starting from the skeletal mechanism andtroducing steady-state assumptions for intermedcomponents, which are consumed rapidly as copared to their formation and changes by transpprocesses, a reduced reaction scheme with 18 glreaction steps can be obtained. These global reacare given in Table 1 and characterize the main csumption reactions of the species included therThe reaction rates of the global steps are based onkinetic rate data of the elementary reactions andbe provided on request.
Reactions I and II are the initiation reactions fhigh- and low-temperature autoignition, respectiveThe low-temperature initiation reaction II reveals tformation of heptylperoxy radicals (RO2). These re-act in global step III by internal isomerization rea
tions, a further O2 addition, and a first OH abstraction to ketoheptylperoxide OR′′O2H. The decompo-sition of this component in reaction IV, which results in the formation of an OH radical, representschain branching in the low-temperature range. Retions V–XIII describe the consumption of the intemediate component hexene, butene, propene, alethene, acetylene, methane, the methyl radical,formaldehyde, respectively. Steps XIV and XV leto the formation of radicals in a very short, radicpoor initiation time, during which the H abstractionby O2 attack leads to a relatively high amount of hdroperoxy radicals. These reactions also form radiduring ignition at high temperatures. The water gshift reaction XVI represents the oxidation of COCO2, which occurs during thermal runaway and leato strong heat release. Reaction XVII is the main rical producing step after ignition occurs, and finaglobal reaction XVIII represents chain breaking bycombination reaction.
In the following we show comparisons of resufrom the skeletal and the reduced mechanism wmeasured data from various experiments. A coparison of autoignition delay times of homogeneon-heptane/air mixtures computed using the skeland the reduced 18-step mechanism with experimtal data from shock tube experiments by Ciezki aAdomeit [1] and measurements in rapid compressmachines by Minetti et al. [2] is shown in Fig. 1. Computational ignition delay times have been determinfrom the simulation of a homogeneous reactor at cstant volume. The ignition delay times are given inArrhenius diagram as a function of the inverse ofinitial temperatureT 0 for lean, stoichiometric, anrich mixtures at three different pressures. For theperiments, ignition is defined by the maximum Cband emission. In the calculations, the ignition cririon is at the highest temperature rate of change wrespect to time, which coincides very well with tmaximum CH concentration. Despite the very cocise representation of the low-temperature kinetthe agreement between calculated and measuredis very good, even at low pressures. No appreciadifference can be observed between the results fthe skeletal and the reduced mechanism.
In addition to the ignition delay times, the delaof the first stage in multistage ignitions,τ1, is givenin Fig. 1 for different equivalence ratios, but only fthe highest pressure. Also shown are the experimedata by Ciezki and Adomeit [1]. Since the tempeture and pressure rise during the first stage of igniare not very sharp, the calculated values ofτ1 are de-fined as the time of the first maximum of the OH cocentration. The predicted values forτ1 are too long,but, especially at low equivalence ratios, the agrment is still reasonable.
S. Liu et al. / Combustion and Flame 137 (2004) 320–339 323
calndhe
u-ac-
m.eac-aretio of
eld
eld
re-en-ha-sionllyase,ely,tes
xedi-s.tmre-frommsm-
easen-ay
Fig. 1. Homogeneous ignition delay times ofn-heptane/airmixtures for different pressures and equivalence ratiosφ as afunction of initial temperatures in a comparison of numerisimulations with experimental data from shock tube [1] arapid compression machine (RCM) experiments [2]. Tlow pressure data atφ = 1 is from the RCM experiments.
For a further validation of the mechanism, simlations have been performed for the plug flow retor experiments by Held et al. [27], who studiedn-heptane oxidation in highly diluted mixtures at 3 atThe experiment is simulated as a homogeneous rtor at constant pressure. Two different conditionsconsidered here: a lean case at an equivalence raφ = 0.79 and an initial temperature ofT 0 = 940 Kand a rich case atφ = 2.27 andT 0 = 1075 K. The
Fig. 2. Numerical results for leann-heptane oxidation in aplug flow reactor compared with experimental data by Het al. [27].
Fig. 3. Numerical results for richn-heptane oxidation in aplug flow reactor compared with experimental data by Het al. [27].
results of the simulations for the skeletal and theduced mechanism are compared with the experimtal data in Figs. 2 and 3. For the rich case, both mecnisms show excellent agreement where the converrate for the skeletal mechanism is only marginahigher than the 18-step mechanism. For the lean cthe induction period is represented quite accuratbut the predicted conversion of smaller intermediato CO seems to be too slow.
Fig. 4 shows the temperature increase after a fireaction time of 1.8 s from the stoichiometric oxdation ofn-heptane at different initial temperatureExperimental data for this configuration at 12.5 ahave been provided by Callahan et al. [9]. Theduced 18-step mechanism reproduces the resultsthe skeletal mechanism very well. Both mechanisagree well with the experimental data at higher teperatures, but underpredict the temperature incrfor initial temperatures lower than 700 K. This is cosistent with the overprediction of the ignition del
324 S. Liu et al. / Combustion and Flame 137 (2004) 320–339
iven
tal
ls,re-
trib-edls).
be
dyed
eri-neen
inel
et-yy-ay
ndachentthemi-
ls,, re-
inith
owsod.
re-esste-18-ne-
l-ayu-entax-s,
is
a
a
Fig. 4. Numerical results for temperature increase at a gtime of reaction (1.8 s) of the stoichiometricn-heptane ox-idation in a plug flow reactor compared with experimendata by Callahan et al. [9].
Fig. 5. Numerical results (solid lines with open symboskeletal mechanism; dashed lines with open symbols,duced mechanism) of temperature and major species disution inn-heptane/air counterflow diffusion flame comparwith experimental data by Seiser et al. [28] (filled symbo
time for the first stage of ignition in the shock tucalculations shown in Fig. 1.
Finally, the behavior of the mechanisms for steaflames is shown in Figs. 5 and 6. Results obtainfrom both mechanisms are compared with expmental data from ann-heptane counterflow diffusioflame by Seiser et al. [28]. The experiment has bperformed at 1 atm for a strain rate ofa = 150 s−1.Other details of the configuration can be foundSeiser et al. [28]. The oxidizer is air and the fuis diluted with nitrogen, such that the stoichiomric mixture fraction isZst = 0.1. As suggested bSeiser et al. [28], to account for the effect of buoancy, the profiles have been shifted by 0.34 mm awfrom the fuel duct. The results of the skeletal athe reduced 18-step mechanism agree well with eother. The predictions are also in very good agreemwith the experimental data for temperature andmajor species shown in Fig. 5. The comparison of
Fig. 6. Numerical results (solid lines with open symboskeletal mechanism; dashed lines with open symbolsduced mechanism) of intermediate species distributionn-heptane/air counterflow diffusion flame compared wexperimental data by Seiser et al. [28] (filled symbols).
Fig. 7. Schematic of counterflow configuration.
nor species profiles with the experimental data shsome differences, but the agreement is still very go
3. Overview of numerical simulation
The skeletal chemical kinetic mechanism forn-heptane ignition and oxidation described in the pvious section is used to study the ignition procin inhomogeneous systems to identify critical ralimiting elementary reaction steps. The reducedstep mechanism is not used in the present odimensional unsteady ignition study; however, reative to the skeletal mechanism, its efficiency mmake it feasible to perform multidimensional simlations ofn-heptane ignition processes. The presnumerical configuration corresponds to a steady,isymmetric, laminar flow of two impinging streamissuing from two nozzles separated by a distanceL,as schematically illustrated in Fig. 7. The main flowin the axial direction, denoted by the coordinatex. Atthe left boundary (x = 0), the fuel stream flows fromnozzle at a temperature ofTF with a constant velocitynormal to the stagnation plane,VF . The fuel streamconsists of prevaporizedn-heptane maintained at
S. Liu et al. / Combustion and Flame 137 (2004) 320–339 325
),en.
ual,ointat
era-ain-
ics.ialullyll-the
ac-1]al-and
el-trydi--ostftiveha-ig-
althe. In
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-
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owionc-
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mass fraction ofYF (YF = 0.38 in the present studywith the remainder of the fuel stream being nitrogAir is supplied from the right boundary (x = L) atTO
and VO . The velocitiesVF and VO are determinedsuch that the momentum of the two streams is eqand there is a stagnation plane close to the midpof the domain. Ignition simulations are performeda constant pressure of 40 atm (except for considtion of pressure effects in Section 6) with a domlength ofL = 0.5 cm. Boundary air and/or fuel temperatures are adjusted to affect the ignition kinetSimulations are conducted using OPUS [29]. Initconditions are obtained in a two-step process: a fburning OPPDIF [30] result is used to obtain a werefined mesh, and this mesh is used to provideOPUS initial condition by obtaining a new solutionwith all reaction terms suppressed so that only retants are present. CHEMKIN software libraries [3are interfaced with both OPUS and OPPDIF to evuate reaction rates as well as thermodynamictransport properties.
4. Multistage ignition phenomena
Ignition can be defined as the transition from ratively slow chemistry to the relatively fast chemistypical of high-temperature combustion. The contions under which ignition occurs in certain inhomogeneous systems is studied in this paper. At the mfundamental level, ignition occurs when the rates oheat release and/or chain-branching are fast relato the various loss mechanisms [32]. The loss mecnisms of concern for the present inhomogeneousnition conditions are diffusive transport of thermenergy, reaction intermediaries, and products fromreaction zone to surrounding less reactive gaseshydrocarbon fuels, three types of ignition chemistrycan be identified and losses can affect any of thes
At the lowest temperatures, a chain-branchprocess centered on the OH radical dominates ition chemistry. The OH radical formed in this procerapidly abstracts a H atom from the fuel,n-heptanein the present study, through reactions R99 and R1where the reaction number here refers to the reactiostep in the skeletal mechanism given in AppendixThe resulting alkyl radical reacts rapidly with molcular oxygen to form C7H15O2 (R105f, R106f) andthen isomerizes to form C7H14OOH (R107). A sub-sequent O2 addition (R108) is followed by anotheisomerization (R109) and release of one OH (R11A typical product of this last isomerization is a ketheptylperoxide (referred to henceforth as KET).to this point the process is chain-carrying, consuing the same number of radicals as it producesreleasing a moderate amount of heat (26.8 kJ
mole of fuel). The KET then decomposes (R111)products including an additional OH radical, makingthe sequence chain-branching. The last decomption step (R111) has relatively high activation eneand there tends to be a buildup of KET while the lotemperature chemistry occurs.
At temperatures near 900 K, although the extemperature is pressure dependent, the chemicallibrium for the addition of O2 to heptyl radicals shiftsstrongly toward dissociation back to heptyl and2(R105b, R106b). This greatly reduces the conctration of C7H15O2 available for isomerization anfor the low-temperature chain-branching processthe same time, the rates for beta-scission reactbecome significant (e.g., R85, R86, R88, R91, RR93), and the resulting smaller alkyls tend to rewith O2 to form HO2 (R66f, R74f, R82f). The HO2reacts with itself to form H2O2 (R14), making the sequence essentially chain-terminating until the H2O2dissociates to form a pair of OH (R15). This dissciation has high activation energy and only resuin a chain-carrying sequence. Because of the srate of H2O2 dissociation and the slow rate of raical branching, this intermediate-temperature cheistry tends to progress more slowly toward ignitiwith a rate that increases strongly with increastemperature. More detailed analysis of the relevanaction kinetics can be found in Refs. [3] and [4].
At higher temperatures, the rate of the braning reaction H+ O2 → OH + O (R1) becomesfaster than the chain-terminating reactions, typicaH + O2 + M → HO2 + M (R8), and the overall rateof reaction increase rapidly due to branching. At thtemperatures, the chemistry is significantly faster tthat of either the low- or intermediate-temperaturegimes.
For certain initial conditions, heat release asciated with the low-temperature chemistry causetransition in the kinetics from the low- to intermdiate-temperature chemistry, resulting in whatreferred to as two-stageignition. The two-stageignition chemistry typical of large hydrocarbonis a consequence of reduced reaction rates inintermediate-temperature regime. For relatively linitial temperatures, at a time when the transitfrom low- to intermediate-temperature kinetics ocurs, fuel has been totally consumed, and thus ition progresses directly to high-temperature cheistry such that the ignition process is dominatedlow-temperature kinetics. This is the so-called singstage low-temperature chemistry dominated igtion. For relatively high initial temperatures, ignitiobypasses the low-temperature chemistry and sdirectly from the intermediate-temperature cheistry. This condition is referred to as single-staintermediate-temperature chemistry dominated ig
326 S. Liu et al. / Combustion and Flame 137 (2004) 320–339
nund
p-d-
rel-to
eac-w-)this
ouscrit-tialonthe
n, is-of-
Forni-ge,H
elgh
c-andle,
de-the
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gh-
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erhe
at
te-ingate,ary
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-xy-theis anencyher.
inllyer-ion.tedres
reasanda-by
tion. More detailed information on multistage ignitiofor n-heptane in homogeneous systems can be foin Refs. [3] and [4].
Ignition is primarily dependent on the consumtion of fuel by radicals, primarily OH, and thus raical production through branching reactions is criti-cal. However, the key branching reactions haveatively large activation energies and are sensitiveheat losses from the reaction zone. These key rtions are the dissociation of KET (R111) in the lotemperature regime and H2O2 decomposition (R15in the intermediate-temperature regime. Based onunderstanding of ignition chemistryfor homogeneoussystems, heat and radical losses in inhomogenesystems are the focus of the present study. Theical ignition phenomena are identified in the spadimension through local maxima of OH concentratiin time; the location of these maxima is defined asignition kernel. The ignition delay,tig, similar to ho-mogeneous systems defined in the previous sectiothe time at the kernel when the temperature ratechange experiences a maximum,(∂2T/∂t2)tig = 0,indicating a maximum in the heat release rate.those conditions that exhibit a distinct two-stage igtion, the ignition delay associated with the first staτ1, is defined as the time at which the maximum Oat the kernel is attained,(∂YOH/∂t)τ1 = 0.
For the skeletal mechanism, the fraction of fuconsumed by low-temperature chemistry (throuR107) is defined by
(1)α = ω107∑104
i=97ωi
,
whereωi (mol/cm3/s) is the reaction rate of reation i. Because the interchange between heptylheptylperoxy (R105 and R106) is fast and reversibit is the essentially irreversible reaction R107 thattermines the moles of fuel that are consumed bylow-temperature branch. A value ofα = 1 indicatesthat all of the fuel is oxidized by the low-temperatuchemistry, whereas a value ofα = 0 indicates thatthe fuel is consumed through intermediate- and hitemperature paths. The value ofα depends primarilyon temperature, pressure, and oxygen concentraFor a fixed pressure of 40 atm, the chemistry for sichiometric mixtures shifts from low-temperatureintermediate- and high-temperature ignition cheistry between 792 and 1005 K, whereα = 0.95 andα = 0.1, respectively, using the skeletal mechanisBetween these two temperatures, the ignition kinics is either dominated by low-temperature cheistry (α > 0.5 or T < 901 K) or by intermediatetemperature chemistry (α < 0.5 or T > 901 K). Thetemperature atα = 0.5 is defined as the crossovtemperature (901 K at 40 atm) [6], indicating t
Fig. 8. The parameterα as a function of temperature40 atm for three equivalence ratios,φ, ranging from 0.5 to30.0.
transition from a low-temperature- to an intermediatemperature-dominated kinetics regime. Assumheptyl and heptylperoxy radicals are in steady stand neglecting the difference between the primand secondary heptyl,α is estimated to be
whereki is the rate constant of reactioni which de-pends on temperature and/or pressure, and [O2] is theinitial oxygen concentration (mol/cm3) in the mix-ture. The value ofα at 40 atm is presented in Fig.evaluated using Eq. (2) as a function of tempeture for three equivalence ratios (φ), ranging from0.5 to 30.0. It is found thatα is dependent primarily on temperature rather than equivalence ratio (ogen concentration). So for nonpremixed systems,change in temperature between fuel and oxidizerstronger determinant ofα at any spatial location thathe change in stoichiometry. The pressure dependof α is discussed later. Peters et al. [6] provide furtexcellent discussion ofα for homogeneous systems
5. Results and discussion
The focus of the current paper is on ignitionmixtures where the fuel and the oxidizer are initianonpremixed and on the effect of strain and tempature differences between the reactants on ignitTwo series of numerical experiments are conducin physical space. In the first series the temperatuof the fuel and the oxidizer streams are equal, whein the second series the temperatures of the fuelthe oxidizer streams differ significantly. In all simultions the fuel stream is diluted with 85% nitrogen
S. Liu et al. / Combustion and Flame 137 (2004) 320–339 327
ig-
tm.ntre-rainte isd as
toreat
llyin-
ate-ge,Foralsonandles
ionrisetionte
hem-gnsle,the
ig-
ra-ionsnc-thnc-the
asem-hefuelnd-vi-byionratetheto
thees
ar-in
0 Kistrynlynd-heem-vo-lso
a-11alu-w.lead
Fig. 9. Kernel temperature evolution during single-stagenition for uniform boundary temperature (T = 700 K andT = 920 K).
volume (YF = 0.38) so that the stoichiometric poinis shifted somewhat away from the oxidizer streaIn the counterflow configuration the velocity gradieimposes a diffusion rate or mixing rate, commonlyferred to as the strain rate. To generalize this strate to other geometries, the scalar dissipation raused, which is measured in physical space, define
(3)χ = 2D(∂ξ/∂x)2,
where,ξ is the mixture fraction [33] andD is the mix-ture thermal diffusivity.
5.1. Uniform boundary temperature
The first case to be considered correspondsa uniform fuel and oxidizer boundary temperatuof 700 K. For ignition in homogeneous systemsthese low initial temperatures, the fuel is typicaconsumed in its entirety before the temperaturecrease bootstraps the mixture into the intermeditemperature regime. Thus, ignition is a single-stalow-temperature chemistry dominated process.the nonpremixed reactants studied here, this istrue of the ignition kernel. Naturally, once ignitioresults in higher temperatures, the intermediate-the high-temperature chemistries play important roin the fuel consumption. As the scalar dissipatrate increases, the ignition delay is observed toas demonstrated by the kernel temperature evolushown in Fig. 9, whereχ0 is the scalar dissipation raevaluated at the stoichiometric location (ξ = 0.146)of the frozen flow. This scalar dissipation rate is twell-defined characteristic mixing rate for each siulation evaluated for frozen flow conditions. Durinthe process of ignition, various chemical reactiotake place at different stoichiometries; for examplow-temperature fuel chemistry tends to occur to
Fig. 10. Kernel temperature evolution during multistagenition for uniform boundary temperature (T = 870 K).
rich side of stoichiometry (except when the tempeture gradients are strong enough to prevent reactthere). The local dissipation rate varies as a fution of stoichiometry, primarily in accordance withe relationship derived in [34], and also as a fution of increasing temperature in accordance withtemperature-dependent diffusion coefficient.
At somewhat higher temperatures, the heat releassociated with the low-temperature ignition cheistry is sufficient to raise the temperature into tintermediate-temperature regime before all of theis consumed. This is the case for a uniform bouary temperature of 870 K, where there is clear edence of two-stage ignition, indicated in Fig. 10a temperature jump at the kernel during the ignitprocess. As before, increased scalar dissipationleads to an increase in the ignition delay and, ifscalar dissipation rate is sufficiently large, leadsinhibition of ignition (χ0 = 207.5 s−1 in Fig. 10).However, the effect of scalar dissipation rate onlow- and intermediate-temperature chemistry regimis observed to be unequal. Specifically, strain primily affects the intermediate-temperature chemistrythese two-stage ignition processes.
For higher boundary temperatures, e.g., at 92and above, the intermediate-temperature chemdominates, and the ignition process exhibits oa single-stage, as was observed for 700 K bouary temperatures. However, it differs in that t920 K system is an intermediate-temperature chistry dominated ignition. The kernel temperature elution for the 920 K boundary temperature is ashown in Fig. 9.
Ignition delays for uniform boundary tempertures of 700, 870, and 920 K are shown in Fig.as a function of inverse scalar dissipation rate evated at the stoichiometric location of the frozen floIt is evident that increased scalar dissipation rates
328 S. Liu et al. / Combustion and Flame 137 (2004) 320–339
si-
,si-larthe
ari-tionermolu-likethatuceermis
rm,ermaveallented
r-ngedueat
trya-m-870-itesra-ervedK,
lay
em-cin-tedthee-ionoolitytryceera-mtedthatoree-
a-mat
s-edinger-
andy)lareheheatatureeenistry-urera-
Fig. 11. Ignition delay as a function of inverse scalar dispation rate for various uniform boundary temperatures.
to longer ignition delay for all boundarytemperaturesalthough this effect is only pronounced for large dispation rates. The sensitivity of ignition delay to scadissipation rate can be explained by consideringconservation equation for a participant scalar vable such as temperature. In the conservation equafor a homogeneous system, there is a source tand a transient term that describe the rate of evtion of the system. In an inhomogeneous systemthe present, there are additional dissipative termswork against the source term and thus serve to redthe rate of evolution toward ignition. If the dissipativterm is sufficiently large, it balances the source teand the system’s rate of evolution will be zero; thcorresponds to a situation where ignition fails to occur(e.g.,T = 870 K, χ0 = 207.5 s−1 in Fig. 10). If thedissipative terms are small relative to the source tethe balance is between the transient evolution tand the source term and changes in dissipation hminimal effect on ignition delay as observed for smscalar dissipation rate in Fig. 11. This is in agreemwith the asymptotic analysis for ignition in a stretchflow field [35].
As is shown in Fig. 11, for a boundary tempeature of 700 K, the ignition delay is longer thafor 870 and 920 K systems for the entire ranof scalar dissipation rates studied here. This isto the much slower low-temperature chemistry700 K compared with the low-temperature chemisat 870 K, attributable to the large effective activtion energy of the low-temperature chemistry. Coparing the cases with boundary temperatures ofand 920 K in Fig. 11, it is evident that, for low dissipation rates, the lower temperature system ignearlier. This is an example of the negative tempeture coefficient (NTC) behavior typical of fuels likn-heptane in homogeneous systems [4]. As obsein Fig. 10, for the system that started at 870
Fig. 12. Temperature profiles at 55 and 93% of ignition detime for 870 K (solid) and 920 K (dashed),χ0 ≈ 190 s−1.
heat release associated with low-temperature chistry causes the kernel temperature to rise to the viity of 920 K. Subsequently there is a delay associawith the intermediate-temperature chemistry. Insystem initially at 920 K (Fig. 9), the intermediattemperature chemistry dominates the entire ignitprocess. The kinetics associated with radical-pbuildup and fuel consumption are slow in the vicinof 920 K compared to the low-temperature chemisat 870 K leading to the NTC behavior. The differenbetween the two cases is that at the time the tempture increases to the vicinity of 920 K for the systebeginning at 870 K, a radical-pool has accumulaand the fuel has been partially consumed suchthe remainder of the ignition process proceeds mreadily. Details can be found in studies of homogneous systems [3,4].
It is also observed in Fig. 11 that, when dissiption significantly affects the ignition delay, the systeat 870 K is more strongly affected, to the point thignition is completely suppressed at lower scalar disipation rates than for 920 K. This can be explainby considering the temperature gradients surroundthe kernel. Fig. 12 shows a comparison of the tempature profiles for boundary temperatures of 870920 K, respectively, at early (55% of ignition delaand late (93% of ignition delay) times for high scadissipation rate (χ0 ≈ 190 s−1). For systems whertwo-stage ignition is important, e.g., at 870 K, tsecond stage is most susceptible to dissipativelosses (Fig. 10) because the associated tempergradients are most severe. The difference betwthe single-stage, intermediate-temperature chemsystem (at 920 K) and the two-stage chemistry system (at 870 K) is the magnitude of the temperatgradient. For the two-stage chemistry the tempeture gradient (dT/dx) at the earlier time (55%tig)is of the order 13500 K/cm, while for the single-
S. Liu et al. / Combustion and Flame 137 (2004) 320–339 329
i-
derur-s inyedob-
be
d as
sen
at
ker-ase,in-on
pe--lerthetodi-di-
-theurs,tof
tionxist
ueForurehe
-n
dy-
in
fls,
th
re,oneakgh-d-hy-m-
ionrger
oxi-erebe-
alpyf aoxi-nalthhis,ndre-theering
selves
Fig. 13.DaT at the kernel in the induction period for unform boundary temperature of 870 K. (Inset)DaR under thesame conditions.
stage ignition the temperature gradient is of the or4100 K/cm. Thus, more significant heat losses ding the intermediate-temperature chemistry resulta slower temperature riseand a longer ignition delafor the lower boundary temperature of 870 K at a fixscalar dissipation rate. This leads to the crossoverserved in Fig. 11 at high dissipation rates.
The global effect of scalar dissipation rate mayrepresented by a Damköhler number (DaT ) based onthe heat-release rate at the kernel, which is define
(4)DaT = (q/YF )/H0
χ,
whereq (kJ/mol/s) is the instantaneous heat-relearate at the kernel,H0 is the heat of combustioof n-heptane (H0 = 271 kJ/mol n-heptane),YF , asmentioned earlier, is the mass fraction of fuelthe fuel stream (YF = 0.38), andχ is the instan-taneous scalar dissipation rate evaluated at thenel. The Damköhler number based on heat releas presented in Fig. 13, is tracked through theduction period for three different scalar dissipatirates at a boundary temperature of 870 K.DaT in-creases significantly during the first stage, low-temrature chemistry. Following the transition from lowto intermediate-temperature kinetics the Damköhnumber decreases for a short time, reflectingintermediate-temperature chemistry susceptibilitydissipative heat losses. Reaction flux analysis incates that the rate-limiting reaction in the intermeate-temperature chemistry is the H2O2 dissociationreaction, R15. The decrease ofDaT occurs in con-junction with this slow reaction becoming the dominant chain-branching reaction at early times ofsecond stage. For conditions where ignition occthe value ofDaT is significantly greater than unity athe time of ignition, indicating that the generation
heat occurs at a rate that is fast relative to dissipaof thermal energy. On the other hand, there also evalues of scalar dissipation rate (e.g.,χ0 = 207.5 s−1)that are sufficiently large so as to prevent ignition dto excessive heat loss relative to its generation.these conditions, the transition to high-temperatkinetics and thermal runaway does not occur. Ttransition from igniting to nonigniting conditions corresponds to the lower turning point of the well-know“S” shape curve, indicating that although a steastate flame solution can exist, nonignition is a stablesolution above the critical scalar dissipation rate.
Similarly, the Damköhler number (DaR ) based onthe H2O2 dissociation reaction, R15, is presentedthe inset in Fig. 13, defined as
(5)DaR = (ωW)/(ρYF )
χ,
where ω (mol/cm3/s) is the consumption rate oH2O2 through R15 to produce a pair of OH radicaW is the molecular weight of H2O2, andρ is the den-sity of the fuel stream. Interestingly,DaR behavesqualitatively similar toDaT , indicating that a singlerate-controlling process affects both radical growand heat release.
In summary, for uniform boundary temperatuignition is inhibited when a large scalar dissipatirate leads to sufficient heat or radical loss to brthe chain-branching behavior. Moreover, under histrain conditions for two-stage ignition, it is founthat ignition is inhibitedduring the second, intermediate-temperature stage where the dissociation ofdrogen peroxide is rate-limiting; self-generated teperature gradients resulting from multistage ignitare more severe, leading to dissipative losses lathan those for single-stage ignition.
5.2. Nonuniform boundary temperature
Temperature gradients between the fuel anddizer streams are typical in practical systems whthe fuel stream is often cooler than the air streamcause of smaller ratios of specific heats and enthrequired to vaporize liquid fuels. The existence otemperature gradient between the fuel and thedizer streams will be shown to have an additioinhibiting effectbeyond that of scalar dissipation wiuniform boundary temperatures. To demonstrate tnumerical simulations are conducted with fuel aoxidizer stream temperatures of 572 and 827 K,spectively. This fuel temperature corresponds toboiling point ofn-heptane at 40 atm and the oxidiztemperature is obtained by adiabatically compressambient air (300 K) from 1 to 40 atm. With theboundary temperatures, the entire domain evoinitially through low-temperature kinetics with the
330 S. Liu et al. / Combustion and Flame 137 (2004) 320–339
i-
Het-ensi-ms
r-ETthe
rox-
olu-is-seti-ei-eem-.g.,stheipa-
ich
lowstrytheurssi-igh
tede-ryH
e-
-
er-
g-16r-andde-w-re-owfor
bleureionlarndon
onim-hisis
en-15the
andnd
rad-an
uchm-eis-heer,
and6b
Fig. 14. Kernel evolution in the induction period for nonunform boundary temperature (TF = 572 K, TO = 827 K,χ0 = 77.4 s−1).
strongest reaction rates (theignition kernel) occurringon the hot oxidizer side of the domain. As the Oconcentration rises during the low-temperature kinics, the kernel moves toward stoichiometric and thrich mixtures. The kernel region subsequently trantions to intermediate-temperature kinetics, at 1.4(τ1) with χ0 = 77.4 s−1 as shown in Fig. 14, demacated by a temperature jump, the transition from Kto H2O2 as the intermediate of significance, andappearance of a local OH maximum.
Similar two-stage ignition behavior is found fovarious scalar dissipation rates for these fuel andidizer temperatures. The kernel temperature evtion in the induction period for various scalar dsipation rates is presented in Fig. 15 and the inshowsYOH evolution at the kernel. Similar to the unform boundary temperaturecase exhibiting two-stagignition (T = 870 K), the effect of the scalar disspation rate on ignition manifests itself mainly in thsecond stage where intermediate-temperature chistry dominates. For low scalar dissipation rates, eχ0 = 4.96 s−1, ignition evolves like a homogeneousystem, whereas for high scalar dissipation ratesdelay occurs in the second stage. For scalar disstion rates higher than a critical value above whignition cannot occur, e.g.,χ0 = 82.03 s−1, ignitionfails in the second stage, again indicating the sreactions in the intermediate-temperature chemiwith relatively high heat and radical losses. Forparticular temperatures shown here, ignition occfor equivalence ratios near unity at low scalar dispation rates and for equivalence ratios above 2 at hscalar dissipation rates [18].
To verify the effect of the scalar dissipation raon the intermediate-temperature chemistry and totermine the rate-limiting reaction in this chemistregime, a reaction flux analysis is performed for O
Fig. 15. Kernel temperature evolution in the induction priod for nonuniform boundary temperature (TF = 572 K,TO = 827 K). (Inset)YOH evolution under the same conditions.
generation and destruction reactions for two diffent scalar dissipation rates,χ0 = 40.2 s−1 andχ0 =82.03 s−1, with the second representing failed inition at the second stage. As is shown in Figs.and 17 in both physical and mixture fraction coodinates, the dominant reactions are R15, R110,R111 for OH generation and R36 and R100 forstruction. Late in the first-stage ignition where lotemperature chemistry still dominates (Fig. 16),action rates of R110, R111, R36, and R100 for lscalar dissipation rate are comparable with thathigh scalar dissipation rate, indicating the negligieffect of scalar dissipation rate on low-temperatchemistry. Although Fig. 16 shows that the reactrate of R15 is affected significantly by the scadissipation rate, other ignition reactions (R111 aR110) are more important during the first stage. Upthe transition from the first to the second ignitistage, low-temperature chemistry becomes lessportant than intermediate-temperature chemistry. Tis the situation depicted in Fig. 17 where R15clearly the dominant reaction responsible for OH geration. For the smaller scalar dissipation rate, Rand temperature increase gradually, whereas forlarger scalar dissipation rate the increase in R15temperature is negligible due to significant heat aradical losses at the kernel relative to heat andical generation. Thus, scalar dissipation rate haseffect on intermediate-temperature chemistry mmore profound than that on low-temperature cheistry for two-stage ignition. It is noteworthy that thpeaks of the reactions for low and high scalar dsipation rates differ in physical location due to tstrain effect, shown in Figs. 16a and 17a; howevthey are solely determined by the temperaturecomposition (mixture fraction), as shown in Figs. 1
S. Liu et al. / Combustion and Flame 137 (2004) 320–339 331
in-
ca-
alaret-
sted-oflo-eas
Theari-nd-
sdi-
is-ra-ipa-urebe-
te-
rmrmlu-enit isx-
Fig. 16. OH reaction profiles forχ0 = 40.20 s−1 andχ0 = 82.03 s−1 with TF = 572 K, TO = 827 K late in thefirst-stage ignition (1.4 ms forχ0 = 40.20 s−1 and 1.47 msfor χ0 = 82.03 s−1) (a) in physical coordinates and (b)mixture fraction coordinates where low-temperature chemistry dominates.
and 17b, which are independent of physical lotion.
The dependence of the ignition delay on the scdissipation rate (again evaluated at the stoichiomric position for the frozenflow) for these nonuniformboundary temperatures is shown in Fig. 18, contrawith ignition delay for uniform boundary temperatures of 820 and 757 K. The uniform temperature820 K matches the temperature at the initial kernelcation for the nonuniform temperature case, wher757 K matches the ignition delay for the nonuniformtemperature case at low scalar dissipation rates.following observations can be made from a compson of these cases in Fig. 18: (1) nonuniform bou
Fig. 17. OH reaction profiles forχ0 = 40.20 s−1 andχ0 = 82.03 s−1 with TF = 572 K, TO = 827 K duringthe second-stage ignition (1.5 ms forχ0 = 40.20 s−1 and4.0 ms for χ0 = 82.03 s−1) (a) in physical coordinateand (b) in mixture fraction coordinates where intermeate-temperature chemistry dominates.
ary temperature results ina longer ignition delay forhigh scalar dissipation rates; (2) the critical scalar dsipation rate is smaller for the nonuniform tempeture case; and (3) comparable critical scalar disstion rates are observed for two uniform temperatcases, though the boundary temperature differs,cause of the varying roles of low- and intermediatemperature chemistry as is described shortly.
First, consider the difference between the unifoboundary temperature of 820 K and the nonunifoboundary temperatures. By tracking the kernel evotion or from the analysis of the relationship betweα and temperature described in an earlier section,known that a uniform temperature of 820 K also e
332 S. Liu et al. / Combustion and Flame 137 (2004) 320–339
tion
r-
er-thedthis-ichs for
fors)
per-reski-ep-sslsonemmif-ffectni-
111nd,m is
onm-ultte--
tureand, asstryen-
thttely
ase.
ETer-umon--
ndlarting
dex-e-
ormd-ow-
Fig. 18. Ignition delay versus the inverse of scalar dissiparate for nonuniform boundary temperatures ofTF = 572 KandTO = 827 K compared with uniform boundary tempeatures,T = 820 K andT = 757 K.
hibits two-stage ignition. For both cases, the tempature gradient associated with the transition fromfirst to the second stage of ignition reduces the wiof the kernel (reaction zone), thereby increasing dsipative losses. This is demonstrated in Fig. 19, whpresents the temperature and mass fraction profilea scalar dissipation rate close to 64 s−1 at times whenthe kernel temperature rise is approximately 120 Kthe nonuniform (at 1.83 ms) and uniform (at 0.71 mboundary temperature cases. This particular temature rise brings the ignition kernel to temperatuwhere it is dominated by intermediate-temperaturenetics and where the ignition kernel is most susctible to strain. The initial temperature and OH mafraction for the nonuniform temperature case is ashown in Fig. 19a for reference. The reaction-zothickness, defined as the full width at half maximuof the OH profiles, shown in Fig. 19a, is 49 and 88 µfor nonuniform and uniform cases, respectively. Dferences observed in width are due to the added eof the imposed temperature gradient for the nonuform case. Moreover, the branching reactions Rand R15 have relatively large activation energies ahence, are rapidly reduced as the colder fuel streaapproached for the nonuniform case.
The effect of temperature gradient on ignitidelay has long been known for simplified cheistry [12,13] and it is interesting that the same resseems applicable to multistage chemistry. It is noworthy that, for this particular (typical) range of temperatures, both the low- and intermediate-temperachemistries are active throughout the domain,both are narrowed by the temperature gradientdemonstrated in Fig. 19b. Low-temperature chemiis represented by KET and intermediate-temperaturchemistry by H2O2 since the branching of these i
Fig. 19. Profiles of (a) temperature andYOH and (b)YH2O2and Yket for nonuniform boundary temperatures ofTF =572 K andTO = 827 K (solid) at 1.83 ms compared wiuniform boundary temperature ofT = 820 K (dashed) a0.71 ms when kernel temperatures have risen approxima120 K. The initial temperature andYOH profiles are alsoshown in (a) for the nonuniform boundary temperature c
termediates produces OH. The twin peaks of Kare due to the higher generation rate of KET at ctain temperatures and compositions. The minimKET between the two peaks is due to the higher csumption rate of KET at the relatively higher temperature locally. The coexistence of both low- aintermediate-temperature chemistry in this particutemperature range enhances ignition by generaheat and radicals through both chemistries.
In addition to a comparison of uniform annonuniform boundary temperatures that bothhibit two-stage ignition, consider the comparison btween the nonuniform temperature case and a unifboundary temperature of 757 K. This uniform bounary temperature is representative of single-stage l
S. Liu et al. / Combustion and Flame 137 (2004) 320–339 333
m-
toTheow-forat-re
9,
e isni-ec-entandm-tureorumanthe
theec-
uchseK
theelytics
tead-nt.tpa-he
m-th
1 in15arethe
w-ate-er
om-. Atcurra-ow
ig-
d-ed in
ra-ofs forriesni-
red
us-thetedtion
ra-allyge.
resith
them-izer-e ofker-othast.uelper-rebyap-ass
Fig. 20. Profiles of temperature andYOH when kernel tem-peratures have risen 120 K for nonuniform boundary teperatures ofTF = 572 K andTO = 827 K (solid) at 1.83 mscompared with uniform boundary temperature ofT = 757 K(dashed) at 1.47 ms.
temperature chemistry dominated ignition, similarthe 700 K case discussed in the previous section.temperature of 757 K is selected because the lstrain rate ignition times are the same as thosethe nonuniform temperature case (Fig. 18), indicing similar kinetic time scales when the kinetics anot influenced by mixing. Fig. 20, similar to Fig. 1shows the profiles of the temperature andYOH for thiscomparison when the kernel temperature increasapproximately 120 K at 1.83 and 1.47 ms for nonuform and uniform boundary temperatures, resptively. It also shows the effect of temperature gradion further decreasing the reaction-zone thicknessincreasing dissipative losses for the nonuniform teperature case. Interestingly, the kernel temperafor the uniform case (870 K) is lower than that fthe nonuniform case (940 K); however, the maximvalue of OH for the uniform case is much higher ththat for the nonuniform case. This occurs becauselow-temperature chemistry is much faster thanintermediate-temperature chemistry at their resptive kernel temperatures. However, it takes a mlonger time for the kernel temperature to increa120 K at a uniform boundary temperature of 757(1.47 ms) due to the slow chemistry compared to820 K system (0.71 ms) which starts at a relativhigher temperature in the low-temperature kineregime.
Finally, a smaller critical scalar dissipation rafor nonuniform conditions is expected due to theditional effect of the imposed temperature gradieHowever, for uniform conditions for two differenboundary temperatures of 757 and 820 K, a comrable critical scalar dissipation rate is observed. Tsimilar value of the critical scalar dissipation rate siply indicates that the rate-limiting reactions for bo
systems are comparable; i.e., that the rate of R11the 757 K system is comparable with the rate of Rin the 820 K system when both reaction zonessubject to high dissipation rates. This expands onearlier conclusion that for two-stage ignition the lotemperature chemistry is faster than the intermeditemperature chemistry by noting that, for some lowtemperature, the low-temperature kinetics are cparable to the intermediate-temperature kineticshigh dissipation rates, the comparable kinetics ocfor a temperature pair that differs from that tempeture pair for which the kinetics are comparable at ldissipation rates or for homogeneous systems.
The global effects of scalar dissipation rate onnition for nonuniform boundary temperature can alsobe represented by the Damköhler numbers,DaT andDaR . The trends observed forDaT andDaR are qual-itatively similar to those observed for uniform bounary temperature cases and, hence, are not discussfurther detail.
In summary, for nonuniform boundary tempeture, ignition is further delayed by the impositiontemperature gradients because the reaction zoneboth low- and intermediate-temperature chemistare narrowed beyond that for similarly strained uform boundary temperature conditions. This leads toa smaller critical scalar dissipation rate compato uniform boundary conditions. Similar to uniformboundary temperature cases, ignition in the secondstage for two-stage ignition is found to be more sceptible to dissipative losses. This is attributed toslow rate-limiting chemistry and the self-generatemperature gradient associated with the transifrom low- to intermediate-temperature chemistry.
5.3. Effect of fuel temperature on ignition
Diesel fuel evaporates over a range of tempetures that depends on the fuel constituents. Typicn-heptane is at the low end of this temperature ranTo understand the effect of the fuel-distillation tem-peratures on ignition, a series of fuel temperatu(572, 604, 762, and 920 K) was considered, wthe oxidizer temperature fixed at 920 K. Due tohigher oxidizer temperature relative to the fuel teperature, the kernel is located closer to the oxidstream initially (φ ≈ 0.03), and thus the initial kernel temperature is nearly constant over the rangfuel stream temperatures selected. In time, thenel migrates to a location where the chemistry (blow- and intermediate-temperature chemistry) is fThere are two potential outcomes of varying the fstream temperature: (1) a lower fuel stream temature leads to a higher temperature gradient, thereducing the chemical rates as the fuel stream isproached; or (2) a higher fuel temperature may byp
334 S. Liu et al. / Combustion and Flame 137 (2004) 320–339
tionzer
le-atedi-
inctr-teen
er-er-
butra-et forthehe1.K,ra-0 Kre
atetion
asandbe-mi-ipa-ondembe-atednsi-try
er-ini-e.
thev-gh,pre-eat
highxedig-
amge
-omer-hegelyt isn-de-er-pa-
ndithtateent.
et-
m-and
yls
Fig. 21. Ignition delay versus the inverse of scalar dissiparate for various fuel boundary temperatures, with oxiditemperature fixed atTO = 920 K.
the low-temperature chemistry and result in a singstage intermediate-temperature chemistry dominignition, which may be slower than two-stage igntion. The two mechanisms compete leading to distignition behavior, as shown in Fig. 21, from the corelations of ignition delay with scalar dissipation raevaluated at the stoichiometric location of the frozflow.
First, Fig. 21 shows that lower fuel-stream tempatures lead to a longer ignition delay for fuel tempatures of 572, 604, and 762K. Ignition occurs morerapidly as the temperature gradient is reduced,where the kernel is still dominated by low-tempeture chemistry (i.e.,α nearly unity). Therefore, of ththree cases considered, ignition occurs the fastesa fuel temperature of 762 K. Consistent with this,critical scalar dissipation rate is also higher for thigher fuel boundary temperature, shown in Fig. 2
Second, for a fuel boundary temperature of 920the chemistry is entirely in the intermediate-tempeture regime. Comparing the curves for 762 and 92in Fig. 21, for the lower fuel-boundary temperatuignition delay is shorter at low scalar dissipation rand longer or comparable at high scalar dissiparate. The argument for this behavior is the samefor the uniform boundary temperature cases, 870920 K, described in Section 5.1, where the NTChavior is present for low scalar dissipation rates, silar to a homogeneous system. For high scalar disstion rates, the loss of heat and radicals for the secstage of the two-stage ignition in the 762 K systis more severe than that for the 920 K systemcause of the additional temperature gradient creby the temperature jump associated with the tration from low- to intermediate-temperature chemisfor the 762 K systems.
In summary, increasing the fuel-stream tempature reduces ignition delays as long as thetial chemistry occurs in the low-temperature regimWhen the fuel temperature rises sufficiently thatchemistry is occurring in the NTC regime, this behaior may be reversed. At high dissipation rates, thouthe NTC behavior is less evident because of theviously described significance of second-stage hlosses. Since practical ignition processes occur atscalar dissipation rates, it is suggested that, for a fioxidizer temperature, e.g., 920 K at 40 atm, fasternition is obtained if the temperature of the fuel streis maximized, but still within the temperature ranwhereα (Eq. (2)) is close to unity.
6. Effect of pressure on ignition
In practical diesel engineignition conditions pressure is usually higher than 40 atm. The results frthe current study may still be applicable by considing the effect of pressure on ignition chemistry. Tpressure scaling for homogeneous systems is larvalid for inhomogeneous systems provided that iapplied to the vicinity of the kernel. The scaling icludes the shift of the crossover temperature thattermines the dominant chemistry to a higher tempature as pressure increases. The analysis of therameterα, as functions of temperature, pressure, aoxygen concentration in the present study, differs wthat of Peters et al. [6] in that the species steady-sassumptions and chemical mechanism are differThe dependence of the parameterα on temperatureand pressure is presented in Fig. 22 for a stoichiomric n-heptane/air mixture.
It is seen from Fig. 22 that the crossover teperatures are 901 and 950 K at pressures of 40
Fig. 22. The parameterα representing the fraction of heptradicals oxidized by the low-temperature chain for varioupressures (φ = 1).
S. Liu et al. / Combustion and Flame 137 (2004) 320–339 335
aseelasig-
ureinandon-eralar
atederas aal
as
ede.g.,i-o-theig-tesase
hiftran-n.gni-e ofed
tente-
e-as
r a
entre-of
ofectturem-gh
au-n-
thed
al-me-d
resthatin
onndtivehise in-t areonandring
cantn
tran-m-The
Fig. 23. Kernel temperature andYOH (inset) evolution for anonuniform boundary temperature condition (TF = 572 K,TO = 827 K,χ0 = 51.9 s−1) at various pressures.
120 atm, respectively, which represents 50 K increin temperature. This implies that, for the current fuand oxidizer temperature for the uniform as wellthe nonuniform boundary temperatures, two-stagenition may revert to a single-stage low-temperatchemistry dominated ignition. Due to an increasepressure, the reaction rates increase accordinglythus accelerate the ignition process. This is demstrated in Fig. 23 for the case of fuel and oxidizboundary temperatures of 572 and 827 K and a scdissipation rate of approximatelyχ0 = 52 s−1 at dif-ferent pressures. The scalar dissipation rate, evaluat the stoichiometric location for the frozen flow, ovthe range of pressures remains nearly constantresult of the competitive effects of decreasing thermdiffusivity and increasing mixture fraction gradientpressure increases.
Fig. 23 shows that the ignition delay is reducwith an increase in pressure. For higher pressure,120 atm, ignition is low-temperature chemistry domnated single-stage ignition, which is slower than twstage ignition for the same pressure. However,ignition time is much less than that for two-stagenition at lower pressures, e.g., 40 atm. This indicathat the increase in reaction rates due to an increin pressure is much more significant than the sin crossover temperature which determines the tsition of single-stage ignition to two-stage ignitioThus, an increase in pressure will decrease the ition delay considerably. The pressure dependencthe ignition delay time shown in Fig. 23 can be fittto a power relationship,tig = 36.04p−0.8253, shownin Fig. 24. The observed dependence is consiswith the analytical solution obtained for a homogneous mixture shown in Fig. 13 of Ref. [6]. A dcrease in ignition delay with increasing pressure w
Fig. 24. Ignition delay time as a function of pressure fononuniform boundary temperature condition (TF = 572 K,TO = 827 K,χ0 = 51.9 s−1).
also observed in a diesel-spray ignition experimwhere fuel was injected into an ambient gas repsenting air at a temperature of 1000 K, density14.8 and 30.0 kg/m3, corresponding to pressures41 and 84 atm, respectively, in Fig. 11 [36]. The effof strain-induced gradient and imposed temperagradient for uniform and nonuniform boundary teperature conditions on ignition remains valid for hipressures.
7. Conclusion
The effect of steady strain on the transienttoignition of n-heptane at high pressures in a couterflow configuration is studied numerically widetailed chemistry and transport. Newly developskeletal and reducedn-heptane mechanisms are vidated over a range of pressures and stoichiotries. Transient ignition simulations with uniform annonuniform boundary fuel and oxidizer temperatuare performed using the skeletal mechanism sothe critical rate-limiting elementary reaction stepsthe ignition process can be identified.
For both configurations at low scalar dissipatirates, ignition exhibits behavior similar to that foufor homogeneous systems, including the negatemperature coefficient (NTC) regime. However, tbehavior changes when scalar dissipation rates arcreased to a point where losses of radicals and heasignificant. Strain-induced gradients delay ignitibecause they reduce the reaction-zone thicknessincrease losses of heat and radicals produced duthe ignition process. These losses are more signififor two-stage ignition than for single-stage ignitiobecause the temperature rise associated with thesition from low- to intermediate-temperature cheistry results in more severe temperature gradients.
336 S. Liu et al. / Combustion and Flame 137 (2004) 320–339
o bew-theuni-ioned
urensdi-
areon
hingat
-re-tionced
s.
m-ture
tsig-
hte-re-ntlyem-
totem-or aiontryionhiftis
ofces,t of
second, intermediate-temperature stage is found tmore sensitive to strain/dissipation than the first lotemperature stage in two-stage ignition. Whenfuel and oxidizer boundary temperatures are nonform, ignition is further delayed because the reactzone is narrowed beyond that for similarly strainignition with uniform boundary temperatures. This istrue of both the low- and intermediate-temperatchemistries, which can coexist at different positioacross the physical domain for the appropriate contions.
The global effects of the scalar dissipation ratepresented in terms of a Damköhler number basedthe heat-release rate or characteristic chain-brancrate, normalized by the characteristic diffusion ratethe kernel. Ignition occurs when the Damköhler number of the system is well above a critical value, repsenting the balance between heat or radical generaand the losses of heat or radicals due to strain-induand/or temperature stratification-induced gradient
Results suggest that, to minimize ignition delayfor nonuniform boundary temperatures, the fuel teperature should be adjusted to as high a temperaas possible while maintaining the parameterα close
to unity. In this manner, for turbulent environmencharacterized by high scalar dissipation rates, thenition delay can be shortened by proceeding througtwo-stage ignition, rather than through intermediatemperature chemistry dominated ignition. This psumes that the oxidizer temperature is not sufficiehigh such that the intermediate-temperature chistry is fast.
Pressure effects on ignition are comparablethose of homogeneous systems. The crossoverperature increases with pressure, and hence, fgiven boundary temperature, a two-stage ignitshifts to a single-stage low-temperature chemisdominated ignition. However, the increase in reactrate with pressure is more significant than the sin the dominant chemistry. Hence, ignition delayreduced with increasing pressure.
Acknowledgment
This research was supported by the DivisionChemical Sciences, Geosciences, and BioscienOffice of Basic Energy Sciences, U.S. DepartmenEnergy.
Appendix ASkeletal mechanism forn-heptane
Number Reaction A n E
1f O2 + H → OH + O 2.000E+14 0.00 70.32f H2 + O → OH + H 5.060E+04 2.67 26.33f H2 + OH → H2O + H 1.000E+08 1.60 13.84f 2OH→ H2O + O 1.500E+09 1.14 0.425f 2H + M′ → H2 + M′ 1.800E+18 −1.00 06f 2O+ M′ → O2 + M′ 2.900E+17 −1.00 07f H + OH + M′ → H2O + M′ 2.200E+22 −2.00 08f H + O2 + M′ → HO2 + M′ 2.300E+18 −0.80 09f HO2 + H → 2OH 1.500E+14 0.00 4.2
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