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ᄺ䖯ሩ, 2014 , 44 : 201402 Recent progress and challenges in fundamental combustion research Yiguang Ju Department of Mechanical and Aerospace Engineering, Princeton University, New Jersey, USA Abstract More than 80% of world energy is converted by combustion. Develop- ment of efficient next generation advanced engines by using alternative fuels and operating at extreme conditions is one of the most important solutions to increase energy sustainability. To realize the advanced engine design, the challenges in combustion research are therefore to advance fundamental understanding of com- bustion chemistry and dynamics from molecule scales to engine scales and to de- velop quantitatively predictive tools and innovative combustion technologies. This review will present the recent progresses and technical challenges in fundamental combustion research in seven areas including advanced engine concepts using low temperature fuel chemistry, new combustion phenomena in extreme conditions, alternative and surrogate fuels, multi-scale modeling, high pressure combustion kinetics, experimental methods and advanced combustion diagnostics Firstly, new engine concepts such as the Homogeneous Charge Compression Ignition (HCCI), Received: 2014-01-29; accepted: 2014-03-27; online: 2014-04-01 E-mail: [email protected] i te as: Yiguang Ju. Recent progress and challenges in fundamental combustion research. c vances in Mechanics, 2014, 44: 2014 Advances in Mechanics.

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  • , 2014 , 44 : 201402

    Recent progress and challenges in

    fundamental combustion research

    Yiguang Ju

    Department of Mechanical and Aerospace Engineering,

    Princeton University, New Jersey, USA

    Abstract More than 80% of world energy is converted by combustion. Develop-

    ment of efficient next generation advanced engines by using alternative fuels and

    operating at extreme conditions is one of the most important solutions to increase

    energy sustainability. To realize the advanced engine design, the challenges in

    combustion research are therefore to advance fundamental understanding of com-

    bustion chemistry and dynamics from molecule scales to engine scales and to de-

    velop quantitatively predictive tools and innovative combustion technologies. This

    review will present the recent progresses and technical challenges in fundamental

    combustion research in seven areas including advanced engine concepts using low

    temperature fuel chemistry, new combustion phenomena in extreme conditions,

    alternative and surrogate fuels, multi-scale modeling, high pressure combustion

    kinetics, experimental methods and advanced combustion diagnostics Firstly, new

    engine concepts such as the Homogeneous Charge Compression Ignition (HCCI),

    Received: 2014-01-29; accepted: 2014-03-27; online: 2014-04-01E-mail: [email protected]

    i te as: Yiguang Ju. Recent progress and challenges in fundamental combustion research.

    cvances in Mechanics, 2014, 44:

    2014 Advances in Mechanics.

  • 2 44 : 201402

    Reactivity Controlled Compression Ignition (RCCI), and pressure gain combus-

    tion will be introduced. The impact of low temperature combustion chemistry of

    fuels on combustion in advanced engines will be demonstrated. This is followed

    by the discussions of the needs of fundamental combustion research for new en-

    gine technologies. Secondly, combustion phenomena and flame regimes involving

    new combustion concepts such as fuel and thermal stratifications, plasma assisted

    combustion, and cool flames at extreme conditions will be analyzed. Thirdly, al-

    ternative fuels and methodologies to formulate surrogate fuel mixtures to model

    the target combustion properties of real fuels will be presented. A new concept of

    radical index and transport weighted enthalpy will be introduced to rank the fuel

    reactivity and to assess the impact of molecular structure on combustion prop-

    erties The success and limitations of the current surrogate fuel models will be

    discussed by using jet fuels and biodiesels as examples. Fourthly, the difficulty

    of modeling large kinetic mechanism of real fuel will be discussed The multi-time

    scale (MTS) method and the correlated dynamic adaptive chemistry (CO-DAC)

    method for kinetic model reduction and computationally efficient modeling will

    be compared and analyzed. Fifthly, the progress and challenges of high pressure

    combustion kinetics for hydrogen and larger hydrocarbons will be discussed. The

    important pressuredependent reaction pathways and key intermediate species at

    high pressure will be analyzed. Fundamental experimental methods for combus-

    tion and their uncertainties in acquiring combustion properties for the validation

    of kinetic mechanism will be discussed. Finally, recent progress in diagnostics of

    HO2, H2O2, RO2, ketohydroperoxide, and other key intermediate species for high

    pressure kinetic mechanism development will be summarized. Conclusions and

    opportunities of future combustion research will be made.

    Keywords alternative fuels, flame chemistry multiscale modeling, experimental

    methods and uncertainty, multi-species diagnostics

    Classification code: O341 Document code: A DOI: 10.6052/1000-0992-14-011

  • Ju Yiguang : Recent progress and challenges in fundamental combustion research 3

    1 Introduction

    1.1 Advanced engine design and multi-scale turbulent combustion


    Combustion converts more than 80% of world energy and has played a dominant role in

    ground and air transportation. With the current difficulties in developing renewable energy,

    for a foreseeable future, combustion will remain to be the major energy conversion process in

    power generation and transportation. However, the energy conversion efficiency of existing

    combustion engines is low and combustion of fossil fuels is the major source contributing

    to climate change and air pollution (Chu et al. 2012). As such, there is an urgent need to

    develop advanced engine technology and new combustion concepts to drastically increase

    the engine efficiency and reduce emissions (DOE report, 2006). For ground transportation,

    recently, various new combustion engine technologies such the Homogeneous Charge Com-

    pression Ignition (HCCI) engines (Dec 2009, Lu et al. 2011, Reitz 2013) and the Reactivity

    Controlled Compression Ignition (RCCI) engines (Reitz 2013) have been developed. These

    engines take the advantage of high compression ratio of diesel engines and low emissions of

    gasoline engines by using highly diluted, premixed and/or highly stratified fuel/air mixtures

    with excessive exhaust gas recirculation (EGR). As such, to control engine knock, heat

    release rate, and ignition timing at different engine loads, understanding the combustion

    process at high pressure and low temperature conditions involving the negative temperature

    coefficient (NTC) and cool flame chemistry (Curran et al. 1998) becomes extremely impor-

    tant. Moreover, the low temperature and high pressure combustion processes coupled by

    strong fuel and temperature non-uniformities in engines are controlled by both large-scale

    turbulent mixing and sub-grid-scale turbulence-chemistry interactions. Therefore, detailed

    understanding of combustion processes in HCCI and RCCI engines requires not only an

    accurate turbulent combustion model which can appropriately predict sub-grid turbulent-

    chemistry interaction but also a validated high pressure and low temperature chemistry for

    real transportation fuels. Unfortunately, strictly speaking neither a validated high pressure

    and low temperature kinetic mechanism for real fuels nor an accurate and computation-

    ally efficient sub-grid turbulent-chemistry model is available for advanced engine modeling

    (Chen 2011, Pope 2012). Moreover, previous turbulent combustion experiments and model-

    ing are mainly focused on high temperature thin flame regimes and few studies are carried

    to understand how low temperature combustion chemistry and autoignition affect turbulent

  • 4 44 : 201402

    flame regimes and propagation speeds (Won et al. 2014) Therefore, the first challenge in

    combustion is how we can develop validated high pressure and low temperature combustion

    models for advanced engine modeling.

    In air transportation, to increase the fuel efficiency and meet the stringent CAEP-6 and

    NASA (N+3) emission standards of the Committee on Aviation Environmental Protection

    (CAEP) and NASA, new lean burn aircraft combustor concepts such as the twin annular

    premixing swirled (TAPS) burner (Mongia 2010), lean-premixed pre-vaporized (LPP), lean

    direct injection (LDI) burners (Tacina et al. 2003), trapped vortex combustion (TVC) burn-

    ers (Hsu et al. 1998), and pressure gain combustors (Schwer and Kailasanath 2011) have

    been developed. To achieve high speed propulsion, supersonic ramjet engines such as X-43

    and X-51 have been developed and tested (Moorthy et al. 2012, Yu et al. 2013). Moreover,

    new advanced gas turbine engines have higher compression ratios and thus have changed

    the conventional rich-quench-lean diffusion combustion to fully and partially premixed com-

    bustion. In addition, due to the increase of ignition Damkohler number at elevated tem-

    perature, the thin flame front flame propagation process in conventional engines is replaced

    substantially by volumetric ignition. Especially, at ultra-lean fuel conditions, local flame

    extinction, re-ignition, and ignition to flame as well as ignition to detonation transitions will

    occur. As such, premixed turbulent flame regimes at high ignition Damkohler may become

    very different from that of the classical wrinkled and corrugated flamelet regimes (Bradley

    1992, Driscoll 2008, Peters 2000) and the conventional incompressible flow, flamelet, and

    pre-assumed probability density function (PDF) based turbulent combustion modeling ap-

    proaches may not be appropriate (Peters 1988, Pitsch 2006, Pope 2013) for the new engine

    modeling. As shown in Fig. 1 (Gou et al. 2010), combustion in engines involves many

    orders of magnitudes of different time- and length-scales ranging from electronic excitation,

    molecular diffusion, soot particle formation, sub-grid turbulent mixing, and engine scale flow

    motion and instability. The main factors affecting the combustion phenomenon depend on

    the combustion process. For example, for near limit combustion the time scales involving

    elementary combustion chemistry is important. For engine instability, the timescales of sub-

    grid turbulent mixing, heat release rate, and acoustic waves are more important. For flame

    extinction, the molecular diffusion is important. Therefore, the second challenge of combus-

    tion is how to develop a new turbulent combustion modeling approach which can address

    the multi-time scale, multi-length scale, and multi-physics combustion processes accurately

    with detailed kinetic mechanisms.

    For high speed propulsion such as supersonic combustion and Scramjet engines, vitiated

  • Ju Yiguang : Recent progress and challenges in fundamental combustion research 5

    Physical process

    Modeling approach

    Physical, chemical models


    Molecular collisions


    Direct Numerical Simulation

    Statistical Mechanics




    Soot growth,aggregation

    Mixing, ignition, extinction, flamestructure, emissions



    Kinetic rates of reactions Turbulent transport-chemistry interaction

    Molecular and turbulent transport scales

    Flames Engine combustion

    10-10 10-8 10-6 10-4 10-2 1 m

    Fig. 1

    Multi-scale processes and multi-scale prediction models in combustion (Gou et al. 2010)

    air has been widely used in test facilities. As a result, the kinetic effects via air contamina-

    tion by H2O and NOx on supersonic combustion have complicated the experimental studies

    for decades. Recently, as reported by Jiang and Yu (2014) the world largest detonation-

    driven hypervelocity shock tunnel was developed, tested, and calibrated at the Institute of

    Mechanics in Beijing. This facility significantly extends the current hypersonic test capabil-

    ity to mimic real flight conditions of Mach number 59 at altitude of 2550 km for morethan 100 ms test duration, and reduce the kinetic uncertainties due to air contamination.

    1.2 New combustion concepts under extreme and non-equilibrium


    To enable the above new engine technologies and to achieve low emissions, fuel lean

    and high speed combustion, various new combustion concepts such as partially premixed

    and stratified combustion (Dec, 2009), plasma assisted combustion (Starikovskiy 2012, Uddi

    et al. 2009, Sun et al. 2010), cool flames (Won et al. 2014), microscale combustion (Ju

    et al. 2011, Fernandez-Pello 2002), and pulsed and spinning detonation engines (Schott

    1965, Bykovskii et al. 2006), and nanopropellants (Ohkura et al. 2011, Sabourin 2009)

    have been developed. These new combustion concepts involve in multi-physical interactions

    of non-equilibrium chemical and transport processes, and lead to many new combustion

  • 6 44 : 201402

    regimes. For example, for high pressure stratified combustion, the flame regimes arising

    from ignition to flame and ignition to detonation transitions at low temperature conditions

    are very complicated and have not been well examined (Ju et al. 2011, Sun et al. 2014, Dai

    et al. 2014) Understanding of cool flame chemistry is extremely important to control engine

    knocking and to avoid stochastic engine failure. Although cool flames have been observed

    for many decades (Barnard 1969, Griffiths 1992, Oshibe et al. 2010, Nayagam et al. 2012),

    establishment of a stable cool flame in laboratories has not succeeded despite numerous

    attempts. As such, the dynamics, chemical kinetics, and kinetics-transport coupling as well

    as the cool flame regime diagram remain poorly understood. For example, to date we still

    do not know how fast a cool flame can propagate and how lean it can burn. On the other

    hand, for plasma assisted combustion, the highly non-equilibrium energy transfer between

    electrons, electronically and vibrationally excited molecules, and neutral molecules are not

    well known (Sun et al 2011, Stancu et al. 2009, Uddi et al. 2009). Moreover, the low

    temperature fuel oxidation chemistry of large hydrocarbon transportation fuels activated

    by plasma discharge is also poorly understood (Sun et al. 2014). For microscale energy

    conversion, the strong thermal and kinetic coupling via flame-wall interaction significantly

    modified the flame regimes (Ronney 2003, Ju et al. 2003, Maruta et al. 2005, Ju et al.

    2005, Xu et al. 2009) In nano-propellant design, functional groups including hydrogen,

    oxygen, and nitrogen bonds are added to nanosparticles and graphene sheets (Ohkura et

    al. 2011, Sabourin 2009) to enhance ignition and combustion properties via non-equilibrium

    photo-chemical and thermal chemical reaction processes. For spinning detonation, the wall

    curvature and fuel/air mixing have significant impacts on the detonation initiation and

    propagation modes (Sugiyama et al. 2013). Therefore, the third challenge in combustion is

    the lack of fundamental understanding of combustion phenomena and flame regimes under

    extreme and non-equilibrium conditions.

    1.3 Alternative fuels

    To address the issue of energy sustainability and CO2 emissions from fossil fuels, devel-

    opment and certification of alternative and renewable fuels from alternative resources and

    biomass (Chu et al. 2012, Hu et al. 2008, Hoinghaus et al. 2010, Dooley et al. 2010) have

    attracted great attention. In the US, about 49 billion liters of corn ethanol (equivalent to

    10% of the US annual gasoline consumption) and 4.1 billion liters of biodiesel were produced

    in 2012. At the same time, unconventional shale gas production has reached one-third of

    the total US natural gas production. Oil production from tar sand, high hydrogen syngas

  • Ju Yiguang : Recent progress and challenges in fundamental combustion research 7

    production from coal and biomass, and synthetic aviation fuel production from natural gas,

    coal, ethanol, and bio-oils have also increased (Bessee et al. 2011, Simon et al. 2011).

    Furthermore, the second generation biofuels produced from non-food crops and lignocellu-

    losic materials will further diversify the feedstock of transportation fuels (Dale et al. 2006,

    Soetaert et al. 2009, Binder et al. 2009). As shown in Table 1, different fuels have different

    molecular structures and functional groups, and thus different fuel reactivity and combus-

    tion and emission properties (Westbrook 2013, Won et al. 2012, Dievart et al. 2012, Gail

    et al. 2007). Practically, most of the alternative fuels are blended into existing petroleum

    derived fuels and result in a real fuel with hundreds to thousands of species. On the other

    hand, advanced engine design requires a generic method to evaluate the performance of

    alternative fuels involving a large number of species with different functional groups. As

    such, the fourth challenge in combustion is how we can construct a compact surrogate fuel

    mixture and kinetic model to model the physical and combustion properties of a real fuel

    appropriately. Since the resulting surrogate kinetic model will involve several hundreds of

    species, naturally the fifth challenge is how we can use the large kinetic model of a surrogate

    mixture to computationally efficiently model turbulent combustion for real fuels (Gou et al.


    Table 1 Fuels with different molecular structures




    Valericbiofuels Alcohols EthersAromatics

    1.4 Experimental and diagnostic methods at high pressure

    To develop validated surrogate fuel models, chemical kinetic models, and turbulent

    combustion models for engine applications, it is important to develop experimental and

    diagnostic methods with well defined experimental uncertainties so that the measured com-

    bustion properties can be used in model validation. In last several decades, counterflow

    flames, spherically propagating flames, flat flames, flow reactors, rapid compression ma-

    chines, and shock tubes have been developed and used to acquire different experimental

    targets. However, there are large discrepancies in these experimental data and some of the





  • 8 44 : 201402

    key combustion parameters such as the flame speeds and species profiles are not appropri-

    ately extracted because of the perturbation of sampling nozzles as well as inappropriate

    assumptions of physical processes and boundary conditions. In addition, with the use of

    multi-component fuels and excessive exhaust gas recirculation (EGR), the chemical and ra-

    diation effects from H2O and CO2 and the preferential transport effect of blended fuels will

    significantly affect the flame dynamics and change the interpretation of experimental data

    (Ju et al. 1997, 1998, Chen et al. 2007). Therefore, the sixth challenge is how to im-

    prove and design fundamental combustion experiments with well defined physical processes

    and boundary conditions so that the uncertainty of the experiments can be modeled and

    quantified appropriately.

    As the engine pressure increases and the reaction pathways are more pressure depen-

    dent. At high pressure, the branching ratio of pressure dependent unimolecular decom-

    position reactions will become increasingly important in affecting the fuel reactivity. At

    high pressure and low temperature combustion processes, HO2, H2O2, RO2, and ketohy-

    droperoxide related fuel oxidation chemistry starts to dominate. Therefore, it is critical to

    measure the key radicals and intermediate species at elevated pressure to develop low tem-

    perature chemistry models and to determine the branching ratio of radical decomposition

    reactions. Unfortunately, due to the high radical reactivity and serious spectra overlaps

    between HO2, H2O2, RO2, QOOH, and ketohydroperoxides in both infrared (IR) and ultra-

    violet (UV) regions, the conventional gas sampling methods (Gail et al. 2007, Dooley et al.

    2012, Lefkowitz et al. 2012, Tranter et al. 2002,) and molecular beam mass spectrometry

    (Osswald et al. 2007, Guo et al. 2013, Qi 2013, Taatjes et al. 2008) as well as the laser

    based diagnostic methods such as the laser induced fluorescence (Li et al. 2013, Ombrello

    et al. 2006, Sun et al. 2012) and laser absorption methods (Hong et al. 2012, Bahrini et al.

    2012) are difficult to be applied to detect HO2, H2O2, RO2, QOOH, ketohydroperoxides,

    and other key intermediate species (Crowley et al. 1991). As such, the seventh challenge is

    how to quantitatively measure key radicals and intermediate species at elevated pressure.

    This review is to provide a summary of the recent progresses in above seven technical

    challenges. Since the review topic is very broad, it is impossible for this review to include all

    subject areas and important publications. As such, this review is intended to highlight the

    major advances in the areas of fundamental research for applications in internal combustion

    engines and gas turbine engines. Progresses in other specific areas such as oxyfuel combustion

    (Buhre et al. 2005), supersonic combustion (Billig, 1993, Moorthy et al. 2012, Yu et al.

    2013), and turbulent combustion modeling (Pope 2012) can be found in recent reviews

  • Ju Yiguang : Recent progress and challenges in fundamental combustion research 9

    in journals such as Proceedings of International Symposiums on Combustion, Progress of

    Energy of Combustion Science, and Journal of Propulsion and Power.

    2 Progress and challenges in combustion research

    2.1 The impact of combustion chemistry on turbulent combustion

    in engines

    Unlike the conventional gasoline and diesel engines (Fig. 2), which mainly rely on,

    respectively, the propagation and transport of premixed and diffusion flames to produce

    heat release, advanced HCCI and RCCI engines use partially or fully premixed combustion

    processes with multi-pulse early fuel injection and EGR dilution. As such the combustion

    process in HCCI and RCCI engines is more dominated by volumetric ignition than flame

    front propagation. As a result, in advanced engines combustion processes involving auto-

    ignition and ignition to flame transition play an important role.

    Ignition process is highly governed by radical initiation and branching processes which

    depend strongly on the size and structure of fuel molecules Therefore, the heat release rate of

    advanced engines such as HCCI and RCCI is more affected by initial pressure, temperature,

    and fuel reactivity than conventional engines. Figure 3 shows the computed ignition delay

    time of three fuels, n-heptane (normal alkane), iso-octane (branched alkane), and toluene

    (aromatics) with different molecular structures (Table 1) as a function of temperature at

    13.5 atm by using the Real Fuel-2 mechanism (Dooley et al. 2013). It is seen that three fuels

    have very different ignition delay times due to the difference in their molecular structures.

    For n-heptane, at both high (larger than 1050 K) and low (less than 700 K) temperatures,

    the ignition delay time increases exponentially with the decrease of temperature. However,

    Gasoline engine Diesel engine HCCI RCCI

    Fig. 2

    Schematic of gasoline, diesel, HCCI, and early injection RCCI engines (Dec.2008, Reitz,


  • 10 44 : 201402

    0.8 1.0 1.2 1.4








    fuel/air mixture, =1.0, p=13.5 atm


    n d


    y t






    Fig. 3

    Ignition delay times of n-heptane, iso-octane, and toluene as a function of temperature at

    13.5 atm and stoichiometric condition

    between 1050 K and 700 K, there is region that the ignition delay time decreases with the

    decrease of temperature. This region is called the negative temperature coefficient (NTC)

    region or the low temperature chemistry region (Curran et al. 1998). Note that in the

    NTC region, the ignition delay time at 13.5 atm is as short as a few milliseconds which are

    comparable with the combustion timescales in internal combustion engines and gas turbines.

    Therefore, the NTC chemistry will have a significant impact on the combustion process as the

    compression ratio of modern engines further increases. Figure 3 also shows that branched

    alkanes (iso-octane) have longer ignition delay time and weaker NTC effect than normal

    alkanes. On the other hand, for aromatic fuels, due to the ring stability, no low temperature

    chemistry is observed and the ignition delay time is much longer than that of normal and

    branched alkanes. Therefore, the high pressure combustion processes in an engine will be

    a strong function of fuel molecular structures, particularly at the low temperature region.

    Failure to control ignition at the NTC region may lead to engine knocking, instability, and

    an increase of emissions.

    To show how engine performance is sensitive to fuel molecular structure, Fig. 4 plots a

    computed time history of the apparent heat release rate (AHRR) as a function of crank angle

    after the dead center (ATDC) with an n-heptane and iso-octane mixture. It is seen that

    at 15 before TDC, low temperature combustion of n-heptane (cool flame) occurs. As the

    crank angle approaches to TDC, the in-cylinder temperature and pressure increase and the

    n-heptane high temperature ignition occurs. As the crank angle passes the TDC, another

    heat release peak is seen due to iso-octance combustion (longer ignition delay time than

  • Ju Yiguang : Recent progress and challenges in fundamental combustion research 11

    -20 -10 0 10 20

    Crank [ATDC]










    Control of combustion duration by ration

    of fuels


    Flame PRF Burn



    iso-octane Burn


    Fig. 4

    Time history of heat release rate in a RCCI engine with n-heptane and iso-octane mixture

    (Reitz 2013)

    n-heptane, Fig. 3). Figure 4 clearly shows that the combustion process in a RCCI engine

    is sensitive to fuel molecular structure and that low temperature combustion in NTC region

    affects the heat release rate.

    Another example in turbulent combustion with elevated temperature and pressure in

    air transportation is the staged combustion of in Twin Annular Premixed Swirler (TAPS)

    burner used for the GEnx gas turbine engine (Fig. 5). In this engine, flames in the highly

    diluted primary combustion zone are stabilized in the high temperature burned gas region

    of a premixed pre-burner. Therefore, most of the jet fuel will be vaporized, ignited, and

    burned at a high temperature and high pressure environment. When the auto-ignition time

    becomes shorter than the mixing time at elevated temperature, the turbulent combustion

    and flame instability will be affected by the low temperature ignition.

    Recent direct numerical simulations (DNS) (El-Asrag et al. 2013, 2014, Zhang et al.

    2013) of high pressure and temperature and concentration stratified HCCI combustion using

    dimethyl-ether (DME) with and without exhaust gas recirculation (EGR) effects showed

    that, due to the existence of low temperature chemistry of DME, two different ignition-

    kernel propagation modes were observed (Fig. 6(a)): a wave-like, low-speed, deflagrative

    mode (the D-mode) and a spontaneous, high-speed, kinetically driven ignition mode (the

    S-mode). Three criteria were introduced to distinguish the two modes by different character-

  • 12 44 : 201402

    Fig. 5

    Schematic of Twin Annular Premixed Swirler (TAPS) burner (Mongia 2010)













    a b

    Fig. 6

    (a) Heat release rate of different flame modes (AB and CD) due to fuel (dimethyl ether) and

    temperature stratifications in a turbulent flow (EI- El-Asrag et al. 2013), (b) OH and HO2

    distributions of an ethylene lifted jet flame with the co-flow temperature at 1550 k (Yoo et

    al. 2011)

    istic timescales and the ignition Damkohler number using a progress variable conditioned by

    a proper ignition kernel indicator. The results showed that the spontaneous ignition S-mode

    was characterized by low scalar dissipation rate, high mixing Damkohler number, and high

    displacement speed ignition front, while the D-mode was characterized by high scalar dissi-

    pation rate and low displacement speeds in the order of the laminar flame speed with a small

    ignition Damkohler number. Another DNS of the near field of a three-dimensional spatially-

    developing turbulent ethylene jet flame in highly-heated co-flow was performed by Yoo et

    al. (2011) to determine the flame stabilization mechanism. The DNS was performed at a

    jet Reynolds number of 10,000 with over 1.29 billion grid points. The results in Fig. 6(b)

    of OH (heat release process) and HO2 (ignition and chain initiation process) distributions

  • Ju Yiguang : Recent progress and challenges in fundamental combustion research 13

    show that, at an elevated co-flow temperature, auto-ignition in a fuel-lean mixture at the

    flame base is the main source of stabilization of the lifted jet flame. The Damkohler number

    and chemical explosive mode (CEM) analysis also verified that auto-ignition occurred at the

    flame base. It was also observed that the lifted flame base exhibited a cyclic saw-tooth

    shaped movement marked by rapid movement upstream and slower movement downstream.

    This was a consequence of the lifted flame being stabilized by a balance between consecutive

    auto-ignition events in hot fuel-lean mixtures and convection induced by the high speed jet

    and co-flow velocities.

    The above DNS results clearly show that auto-ignition involving low temperature chem-

    istry for large hydrocarbon transportation fuels may play a very important role in turbulent

    combustion of engines. Unfortunately, to date the major focus of turbulent combustion has

    been placed on the measurements of high temperature flame burning velocities and flame

    structures (Bradley 1992, Driscoll 2008, Peters, 2000, Yuen et al. 2009) and the effects of

    pressure (Kobayashi et al. 1997, Soika et al. 2003), Lewis number (Bradley 1992, Rutland

    et al. 1996, Chaudhuri et al. 2012), preferential diffusion (Dunn et al. 2013), and turbulent

    flame geometry (Smallwood et al. 1995, Shepherd et al. 1992). The measured turbulent

    burning velocity (ST ) normalized by the laminar flame speed (SL) is fitted as a function of

    the normalized turbulent intensity (u/SL), the Lewis number (Le), the turbulent integral

    length scale (l), and the laminar flame thickness (f ) (Bradley 1992, Driscoll 2008, Peters

    2000, Chaudhuri et al. 2012),


    = 1 + CLe1(






    where C represents a constant and n is an adjustable exponent. A turbulent flame regime

    diagram called the Borghi diagram was used to specify the turbulent flame regime based

    on the turbulent time scale (l/u) and the flame time scale (f/SL) (Peters 2000, Borghi

    1984, Li 1994). Although, this turbulent diagram provides very insightful information for

    different flame regimes such as the wrinkled, corrugated, thin reaction zone, and distributed

    reaction zone flames, it only includes one characteristic timescale of the flame speed. The

    ignition timescale is not considered in the Borghi diagram. As a result, the Borghi diagram

    and the turbulent flame speed relation in Eq. (1) may not be applicable directly to the

    advanced engines in which ignition and low temperature fuel oxidation play an important

    role. Therefore, a question naturally arises: how does the low temperature fuel chemistry

    and auto-ignition at elevated temperature affect the turbulent flame propagation and the

    Borghi diagram? Additionally, will the turbulent burning velocity still be a well-defined

  • 14 44 : 201402

    value when the low temperature reactivity changes the fuel composition and reactivity via

    low temperature oxidation?

    Figure 7 schematically shows how the increase of fuel reactivity at elevated tem-

    perature (ignition Damkohler number) affect the turbulent flame regime. At low ignition

    Damkohler number, turbulent flame regimes are governed by the length scale of turbulent

    mixing (e.g. the Taylor microscale) and the thickness of the reaction zone. When the tur-

    bulent mixing scale is smaller than the thickness of the thin reaction zone, the thin flame

    regime becomes a distributed reaction zone. However, when the ignition Damkohler number

    is increased at high temperature due to low temperature chemistry, the flame regime will

    be affected by the turbulent mixing time, the auto-ignition time, and the flame propagation

    time. If the auto-ignition time becomes shorter than the flame propagation time, a broad-

    ened, distributed reaction zone due to auto-ignition will occur (Fig. 7). Unfortunately, few

    previous studies have addressed the transition between ignition and flame propagation in

    10-1 100 101 102 103 104

    10-1 100 101 102 103 104

















    Distributedreaction zone

    Distributedreaction zone

    Thin reactionzone

    Thin reactionzone







    1dL Turbulent scale

    Progress of fuel oxidationTurbulence/chemistry interaction






    Fig. 7

    The change of turbulent flame diagram with the increase of ignition Damkohler

  • Ju Yiguang : Recent progress and challenges in fundamental combustion research 15

    turbulent combustion.

    To demonstrate the effect of low temperature ignition on turbulent flame propaga-

    tion, recently a new high temperature, high Reynolds number, Reactor Assisted Turbulent

    Slot (RATS) burner has been developed to investigate turbulent flame regimes and burning

    rates for large hydrocarbon transportation fuels (Won et al. 2014). The turbulent flow

    characteristics were quantified using hot wire anemometry. The turbulent flame structures

    and burning velocities of n-heptane/air mixtures were measured by using planar laser in-

    duced fluorescence of OH and CH2O with reactant temperatures spanning from 400700 K.Figure 8 shows the dependence of flame luminescence and shape on the reactor tempera-

    ture. Figure 8(a) represents the conventional thin flame front chemically-frozen-flow flame

    regime. In this case, the initial mixture temperature was so low (500 K) that there was no

    fuel reactivity before the flame front. However, as the reactor temperature was increased

    to 700 K with the same flow residence time, Figs. 8(b)8(d) show a new turbulent flameregime, the low-temperature-ignition regime. In this flame regime, fuel is partially oxidized

    due to the low temperature chemistry. Therefore, the conventional assumption of flamelet

    fails. At Treactor = 700 K, by reducing the flow velocity (increasing the Damkohler number)

    from 10 to 6 m/s, a transitional regime from low temperature ignition to hot ignition in

    (a) (b) (c) (d) (e) (f)

    Treactor=500 K

    U=10 m/s

    600 K 650 K 700 K 700 K 700 K10 m/s 10 m/s 10 m/s 10 m/s 6 m/s

    Increasing the ignition Damkohler number & fuel reactivity

    Fig. 8

    Direct photos of n-heptane/air turbulent flames at = 0.6 with increasing of igni-

    tion Damkohler number and fuel reactivity, exhibiting distinctive four flame regimes; (a)

    chemically-frozen-flow regime, (b)(d) low-temperature-ignition regime, (d) and (e) transi-

    tional regime between low- to high-temperature-ignition regimes, and (f) high-temperature-

    ignition regime (Won et al. 2014)

  • 16 44 : 201402

    the reactor is observed from Figs. 8(d) and 8(e). This result clearly shows that the flame

    regime diagram in Fig. 8 needs to be dramatically changed when the ignition Damkohler

    number is increased at practical engine conditions.

    To further quantify the effect of low temperature chemistry on the turbulent flame

    speed, Fig. 9 shows the dependence of normalized turbulent flame speeds and the OH/CH2O

    planar laser induced fluorescence (PLIF) as a function of turbulent fluctuation velocity at

    low and elevated temperatures. For the first time, Fig. 9 (left) shows that the turbu-

    lent burning velocities have two different flame regimes, a chemically-frozen-flow regime

    and a low-temperature-ignition flame regime, respectively, at low (a) and high (b) reactor

    temperatures with different turbulent flame speeds. Moreover, the turbulent flame speed

    at the low-temperature-ignition regime is higher than that of chemically-frozen-flow. The

    OH/CH2O PLIF images (right) show clearly the difference of turbulent flame structures

    of these two flame regimes and the CH2O formation of the low-temperature-ignition flame

    regime. It is also interesting to note that, contrary to the previous studies, the results in

    Fig. 9 suggest that the turbulent flame burning velocity for fuels with low temperature

    chemistry may not be uniquely defined. Rather, it depends on the magnitude of ignition

    0 2 4 6 8














    STSL =




    n-heptane/air, 0.3

  • Ju Yiguang : Recent progress and challenges in fundamental combustion research 17

    Damkohler number for low temperature fuel oxidation.

    In summary, the above discussions revealed that turbulent combustion in advanced en-

    gines is highly governed by the low temperature chemistry and transitions between ignition

    and flame propagation. The existence of low temperature chemistry and the increase of igni-

    tion Damkohler number will significantly modify the turbulent flame regimes and the regime

    diagram. However, few studies have been carried in this new combustion regime. Future

    turbulent combustion and engine studies need to address how ignition and low temperature

    chemistry affect the combustion regime, heat release rate, flame instability, flashback, and

    engine knocking.

    2.2 New flame regimes at low temperature and non-equilibrium con-


    To achieve higher engine efficiency and lower emissions, new combustion technolo-

    gies such as ultra lean, thermal and fuel stratifications, pressure gain combustion, micro-

    combustion, flameless combustion, and plasma assisted combustion have attracted great

    attention. These new combustion techniques often operate at near-limit conditions and the

    combustion processes are more kinetically dominated by the chemistry with strong coupling

    to flame dynamics. In this review, we limit our focus on the impact of how combustion

    chemistry affects flame regimes at highly non-equilibrium conditions with thermal and con-

    centration stratifications, plasma activation, and low temperature oxidation.

    2.2.1 Flame regimes in NTC region with thermal and fuel stratifi-


    Thermal and fuel stratification is an important technique to control heat release rate in

    HCCI and RCCI engines. However, how thermal and fuel stratifications affect combustion

    dynamics and flame regimes is not well understood. Previously, a number of studies have

    been conducted to understand ignition and flame propagation in HCCI and spark assisted

    HCCI combustion (Persson et al. 2007, Hult et al. 2002) with small hydrocarbon fuels and

    simplified models (Cox et al. 1985, Schreiber et al. 1994, Cowart et al. 1991, Martz et al.

    2009, Gu et al. 2003, Zeldovich 1980, Sankaran et al. 2005, Chen et al. 2006, Hawkes et

    al. 2006). The results showed that the initial temperature and species gradients played an

    important role in affecting flame regimes. Unfortunately, few studies have been conducted

    to understand the mechanism of flame transition involving large hydrocarbon fuels with low

    temperature chemistry and the kinetic coupling between alkanes and aromatics.

  • 18 44 : 201402

    Recently, the flame regimes of ignition and flame propagation as well as transitions

    between different flame regimes of n-heptane-air mixtures in a one-dimensional, cylindrical,

    and spark assisted HCCI engine were numerically modeled with a comprehensively reduced

    kinetic mechanism (Ju et al. 2010). It was found that the initial mixture temperature

    and pressure had a dramatic impact on flame dynamics. As shown in Fig. 10, a spark

    ignition at the center of a cylindrical chamber of lean ( = 0.4) n-heptane-air mixture

    at 700 K and 20 atm, led to different propagating ignition fronts and flame fronts. There

    exist at least six different combustion regimes, an initial single high temperature flame

    propagation regime, a coupled low temperature (cool flame) and high temperature double-

    flame regime, a decoupled low temperature cool flame and high temperature double-flame

    regime, a low temperature ignition regime, a single high temperature flame regime, and

    a hot ignition regime. The results showed that the low temperature cool flame and high

    temperature flames had distinct kinetic and transport properties as well as flame speeds,

    and were strongly influenced by the low temperature chemistry. Furthermore, it was found

    that due to the NTC effect, the critical temperature gradient for ignition and acoustic wave

    coupling became singular in the NTC region. These results demonstrate that both the NTC

    effect and the acoustic wave propagation in a closed reactor have a dramatic impact on the

    0 0.005 0.010 0.015








    Low temperature ignition (LTI)

    Cool flame dominateddouble flame (decoupled)

    High temperature flamedominated double flame (coupled)L


    of flam

    e a

    nd ignitio

    n fro




    Hot ignition

    Single high temperatureflame front

    Fig. 10

    The time history of propagating flame and ignition fronts after spark ignition in a cylindrical

    chamber of lean ( = 0.4) n-heptane-air mixture at 700 K and 20 atm (Ju et al. 2010)

  • Ju Yiguang : Recent progress and challenges in fundamental combustion research 19

    ignition front and acoustic interaction. More recently, by introducing a cold spot (Dai et

    al. 2014), different autoignition modes caused by the positive temperature gradient were

    identified for n-heptane/air mixture. With the increase of the positive temperature gradient

    of the cool spot, supersonic deflagration, detonation, shock-induced detonation, and shock-

    induced supersonic deflagration were sequentially observed (Fig. 11). A regime map in

    terms of the normalized temperature gradient and acoustic-to-excitation time scale ratio

    was obtained for different autoignition modes.

    To further understand the effect of fuel stratification on low temperature combustion

    with different molecular structures, the transitions between ignition and flames in stratified

    n-heptane and toluene mixtures were numerically modeled in a one-dimensional constant

    volume chamber (Sun et al. 2014) (Fig. 11(b)). It is found that the low temperature

    chemistry (LTC) and fuel stratification of n-heptane led to the formation of four different

    combustion wave fronts: A low temperature ignition (LTI) front followed by a high temper-

    ature ignition (HTI) front, a premixed flame front, and a diffusion flame front. Moreover,

    it was shown that the propagation of the fast LTI and HTI wave fronts led to shock-like

    pressure wave propagation and caused strong oscillation of the subsequently formed pre-

    mixed and diffusion flames. On the other hand, for the toluene mixture, due to the lack of

    0 10 20 30 40 50 60 70

    0 10000 20000 30000 40000


    2 n



    5 n











    no m



    n a



    cool sp












    monotonicT in kemel

    monotonicT in kemel

    non-monotonicT in kemel







    0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8


    Onset of ignitiondriven oscillation

    Premixed flame branch

    Diffusion flame branch

    Onset of HT1

    Onset of LT1


    Location o

    f acim





    /cm 5







    Fig. 11

    (a) The effect of thermal stratification on autoignition modes at different temperature gra-

    dients and cool spot sizes with T0 = 900 K in an n-heptane/air mixture (Dai et al. 2014),

    (b) The effect of fuel stratification on different ignition and flame regimes and flame insta-

    bility (Sun WQ et al. 2014)

  • 20 44 : 201402

    LTC, only a high temperature ignition front and a premixed flame front are observed. The

    shockwave formation dynamics was analyzed by using the simplified Burgers equation. The

    results revealed that the rich LTC reactivity of transportation fuels together with thermal

    and fuel stratification is one of major causes of engine knocking. However, due to the limi-

    tation of computation cost, multi-dimensional modeling of flame regimes involving LTC and

    thermal and fuel stratifications remains still lacking.

    2.2.2 Flame regimes of plasma assisted combustion

    Non-equilibrium plasma is another method to enhance ultra-lean combustion and flame

    stabilization. Plasma assisted combustion (PAC) has a great potential to enhance com-

    bustion performance in pulsed detonation engines, gas turbine engines, scramjets, internal

    combustion engines, and other lean burn combustion systems. Over the last decade, the

    applications of plasma to improve the performance of combustion have drawn considerable

    attention for its great potential to enhance combustion in internal combustion engines, gas

    turbines, pulsed detonation engines, scramjet engines, and lean burn combustion systems

    (Pilla et al. 2006, Ombrello et al. 2010a, 2010b, Sun et al. 2012, 2013, Starikovskaia 2006,

    Starikovskiy 2013, Singleto et al. 2011, Matsubara et al. 2011, Leonov et al. 2010, Little et

    al. 2010, Lacoste et al. 2013). Recently, through the collaboration between Princeton Uni-

    versity and Imagineering Inc. in Japan, microwave plasma assisted ignition was investigated

    to improve the ignition performance in single cylinder internal combustion engines (Ikeda

    et al. 2009, Lefkowitz et al. 2012) (Fig. 12). Microwave was used to increase the electron

    energy and ignition volume during the conventional spark ignition. It was found that the

    plasma assisted spark plug produced a larger ignition kernel and led to an overall faster

    ignition/flame with about 750 mJ energy addition. The experimental results showed that

    the lean burn limit was extended by 20%30% in terms of the air/fuel (A/F) ratio by usingthe microwave discharge, according to the coefficient of variation of the indicated mean effec-

    tive pressure (COVimep) (Fig. 12(b)). More recently, ignition enhancement by nanosecond

    pulsed surface dielectric barrier discharge was also demonstrated in a rapid compression

    machine (Stepanyan et al. 2013). The results also showed that with the presence of dis-

    charge, the ignition delays decreased significantly for methane and n-butane mixtures in the

    pressure range of 7.5 to 15 atm. Knocking reduction was also reported in knocking-sensitive


    Towards the development of advanced gas turbines, plasma is also used as a new tech-

  • Ju Yiguang : Recent progress and challenges in fundamental combustion research 21

    12 16 20 24 28

    A/F Ratio










    No MW, Timing 1MW, Timing 1No MW, Timing 2MW, Timing 2MW, Timing 3Stable Operating Limit

    Lean limits

    a b

    Fig. 12

    (a) direct photograph of plasma assisted 34 cc Fuji engine test setup, and (b) the comparison

    of limits of stable engine operating conditions with and without microwave (MW) discharge

    (Lefkowitz et al. 2012).

    nology to increase energy efficiency, reduce emissions, and improve stability of flames in

    the combustion chamber. Serbin et al. (2011) showed that a gas turbine combustor with

    piloted flame stabilization by non-equilibrium plasma can provide better performance, wider

    turndown ratios, and lower emissions of carbon and nitrogen oxides. Moeck et al. (2013)

    studied the effect of nanosecond pulsed discharge on combustion instabilities. It was shown

    that the discharge had a strong effect on the pressure pulsations associated with thermo-

    acoustic dynamics. With the consumption of less than one percent of the total power of

    the flame, the nanosecond discharge can significantly reduce the oscillation amplitude of the

    acoustic pressure. Recently, Lefkowitz et al. (2013) extended the study of high-frequency

    nanosecond pulsed discharge to pulsed detonation engines (PDEs). As shown in Fig. 13(a),

    by comparing the ignition delay times and the ignition kernel growth with different igniters,

    it was found a significant decrease of the ignition time in the PDE for a variety of fuels and

    equivalence ratios. As shown in Fig. 13(b), with the same amount of total energy input,

    higher frequency discharges showed dramatic benefits to initiate flame propagation. Fig-

    ure 13(c) shows the difference between the nanosecond pulsed plasma igniter and multiple

    spark discharge (MSD) igniter. With roughly the same amount of total energy consumption,

    the MSD ignition kernel eventually extinguishes, while the plasma ignited kernel goes on

    to become a self-propagating flame. In addition, both leaner and richer ignition could be

    achieved with the help of the nanosecond pulsed igniter.

  • 22 44 : 201402

    a b


    ns pulser,40 kHz

    ns pulser,1 kHz

    ns pulser,MSD energy


    Fig. 13

    (a) PDE engine facility at the Air Force Research Lab at Wright-Patterson Air Force Base,

    (b) Schlieren imaging of nanosecond pulsed discharge igniter in CH4/air mixture, = 1,

    (c) Schlieren imaging of nanosecond pulsed discharge igniter in CH4/air mixture, = 0.8

    (Lefkowitz et al. 2013)

    However, the physical and chemical kinetic processes in plasma assisted combustion in-

    volve strong couplings (Fig. 14) between combustion kinetics and the active radicals, excited

    species, ions/electrons, and other intermediate species produced specifically by the plasma.

    In recent years, extensive efforts have been made to develop new combustion techniques

    using non-equilibrium plasma, as well as new experimental platforms, advanced diagnos-

    tic methods, kinetic models, and quantitative experimental databases to understand the

    underlying interaction between the plasma and combustion mechanisms.

    In order to fundamentally understand the physics of plasma enhanced ignition and flame

    stability, a non-equilibrium in situ plasma discharge integrated with a counterflow flame

    was developed (Sun et al. 2011, 2013). The relationship between OH emission intensity

    as well as reaction zone peak temperature and XF is shown in Fig. 15 with oxygen mole

    fraction at (a) XO = 0.34 and (b) 0.62, respectively. The temperatures of the reaction zone

    were measured by the Rayleigh scattering method. The solid and open symbols represent

    the results obtained, respectively, with increasing and decreasing of XF . Figure 15(a)

    shows the typical ignition to extinction S-curve which is the fundamental phenomena of

    combustion. It is interesting to note that if the oxygen concentration was increased to 0.62,

    the ignition and extinction limits merged atXF = 0.09, resulting in a monotonic ignition and

    extinction S-curve Fig. 15(b). The temperature measurements also demonstrated a similar

  • Ju Yiguang : Recent progress and challenges in fundamental combustion research 23

    Temperature increase

    Plasma discharge


    Ionic wind

    Flow mixing

    Fuel fragments

    Transport enhancementKinetic enhancementThermal enhancement


    Excited species





    Fig. 14

    Possible enhancement pathways of plasma on combustion systems (Sun and Ju 2013)

    0.1 0.2 0.3 0.4












    Fuel mole fraction (XF)


    l m







    3 K







    l m







    3 K


    * e


    sion inte



    3 a


    OH emissionTemperature

    OH emissionTemperature



    XO =0.34 XO =0.6210







    * e


    sion inte



    3 a


    0.1 0.2 0.3 0.4

    Fuel mole fraction (XF)

    a b

    Fig. 15

    Effect of plasma discharge on ignition to extinction curve at different plasma repetition rate

    represented by the dependence of OHemission intensity at different oxygen concentrations

    (a) XO = 0.34, (b) XO = 0.62, (solid square symbols: increasing XF , open square symbols:

    decreasing XF ) (Sun et al. 2013)

    monotonic increase of the local maximum temperatures. The monotonic and fully stretched

    ignition and extinction S-curve could be explained by the fact that the plasma generated

    reactive species caused a transition of flame stabilization mode from the extinction-controlled

    to the ignition-controlled modes. This means that the extinction limit did not exist by

    the plasma/combustion chemistry interaction, thus the chemistry of plasma assisted flame

  • 24 44 : 201402

    stabilization was fully dictated by the enhancement of ignition limit via radicals production

    by plasma. Similar experiments of ignition of large hydrocarbons were also conducted (Sun

    et al. 2014). It was found that plasma can activate low temperature chemistry of dimethyl

    ether even at low pressure.

    In order to understand the elementary kinetic process of plasma-assisted combustion,

    advanced species diagnostics have been carried to quantify the effect of plasma generated

    radicals and intermediate species such as O, N2(*), O3, O2(1ag), and NOx on ignition and

    flame propagation. Uddi et al. (2009) and Sun et al. (2010) measured the atomic O concen-

    tration in nanosecond pulsed discharges using the Two Photon Laser Induced Fluorescence

    (TALIF) technique, respectively, in a flow reactor and in a counterflow diffusion flame. It

    was found that the discharge can generate significant amounts of atomic O and the consump-

    tion of atomic O by fuel was very fast. As shown in Fig. 16, the rapid reaction between

    fuel and atomic O initiated the low temperature combustion chemistry and produced heat

    release. To further understand the formation pathways of atomic oxygen production by

    excited N2(*) (known as N2(A), N2(B) and N2(C)), the absolute number density of N2(A)

    was measured by Cavity Ring Down Spectroscopy (CRDS) and the densities of N2(B) and

    N2(C) were measured by Optical Emission Spectroscopy (OES) in a nanosecond pulsed dis-

    charge at atmospheric pressure in air (Stancu et al. 2009). The results show that in air

    plasoxygen collisions with N2(B) and N2(C) are major reaction pathways to product atomic

    oxygen in addition to direct electron impact oxygen dissociation.

    0 1 2 3 4








    Time/10-3 s

    O a





    -5 Air

    Air-methane, /10

    Fig. 16

    Atomic O mole fraction vs. time after a single high-voltage pulse in air and in a methane-air

    mixture at P = 60 torr and = 1.0 (Uddi et al. 2009)

  • Ju Yiguang : Recent progress and challenges in fundamental combustion research 25

    -50 -25 0 25 50 75 100

    -50 -25 0 25 50 75 100











    18 cm





    Fig. 17

    Measurements of number density of excited nitrogen and atomic oxygen in air plasma

    (Stancu et al. 2009)

    The effects of O3, O2(1ag), and NOx on plasma assisted combustion was studied by

    Ju and coworkers. By using Integrated Cavity Output Spectroscopy (ICOS) (Williams et

    al. 2004, Ombrello et al. 2010b) measured the absolute concentrations of excited oxygen

    (O2(1ag)) in a microwave generated plasma by using the (1,0) band of the


    +g 1ag

    Noxon system. Several thousand ppm level of O2(1ag) was reported and its effect on flame

    propagation was then investigated. The effect of O3 and O2(1ag) on flame propagation speed

    was studied in a lifted flame (Ombrello et al. 2010a, 2010b). The experiments demonstrated

    that both O3 and O2(1ag) increased the flame propagation speed by a few percentage. The

    effects of NOx production by plasma on ignition and flame extinction were also studied

    by Ombrello et al. (2006, 2008). The results showed that NOx production by plasma

    also reduced the ignition temperature and extended the extinction limits of hydrogen and

    methane-air mixtures.

    The above studies significantly advanced the understanding of the elementary processes

    of plasma chemistry. However, the experimental diagnostics was limited to small species

    and radicals at high temperature. In order to understand the kinetic processes of plasma

    activated low temperature combustion, in situ diagnostics of intermediate species produced

    by plasma assisted fuel oxidation is necessary. Recently, in situ measurements by mid-IR

    laser absorption spectroscopy of C2H4/Ar pyrolysis and C2H4/O2/Ar oxidation activated

  • 26 44 : 201402

    by a nanosecond repetitively pulsed plasma have been conducted in a low temperature flow

    reactor (below 500 K) for both continuous discharge mode and burst mode with 150 pulses

    (Lefkowitz et al. 2014). As seen in the species time history in Fig. 18(a), it was found

    plasma activated C2H4 oxidation has three fuel consumption pathways, a plasma activated

    low temperature fuel oxidation pathway via RO2 chemistry; a direct fragmentation pathway

    via collisional dissociation by electrons, ions, and electronically excited molecules; and a

    high temperature oxidation pathway by plasma generated radicals. It was also shown that

    the plasma activated low temperature oxidation pathway is dominant and leads to a large

    amount of formaldehyde formation with less acetylene and negligible large hydrocarbon

    molecules as compared to the pyrolysis experiment. However, simultaneous diagnostics of

    multiple species at higher pressure and temperature become very challenging due the non-

    uniformity of plasma as well as the pressure and temperature broadening of the absorption

    lines. In addition, measurements of OH and RO2 related species at low temperature plasma

    environment are still difficult. This information is necessary to understand the elementary

    process of plasma assisted combustion and to develop validated kinetic mechanisms.

    0 0.002 0.004 0.006 0.008 0.010









    ction C





    Fig. 18

    Measured (symbols) and modeled (lines) time history of C2H2, CH4, H2O, and temperature

    after 150 pulses at 30 kHz repetition rate for a mixture of 6.25/18.75/93.75 C2H4/O2/Ar

    (Lefkowitz et al. 2014)

    2.2.3 Structure and Dynamics of Cool flames

    Cool flame is a key process for engine knocking and has been a major subject of com-

  • Ju Yiguang : Recent progress and challenges in fundamental combustion research 27

    bustion for more than a century (Perkin 1882, Curran et al. 1998, Mehl 2011). Several ex-

    perimental approaches using a heated burner, heated flow reactor, and jet-stirred reactor for

    the study of cool flames were developed (Lignola 1987, Dooley et al. 2010, 2012, Jahangirian

    et al. 2010). Recently by using a heated microchannel, cool flames were also observed due

    to the constrained reaction progress by the wall heat loss (Oshibe et al. 2010). However, all

    the above cool flame experiments require external heating and wall heat losses, rendering

    complicated thermal and chemistry coupling with the wall. As a result, detailed and funda-

    mental understanding of cool flame behaviors has not been well established. Moreover, all

    of the previous cool flame studies were focused on homogeneous fuel/air pre-mixtures. In-

    terestingly, a recent experiment of droplet combustion in microgravity has shown that a cool

    flame might be established in a diffusive system, hypothesizing the existence of cool diffusion

    flame after radiation-controlled extinction (Nayagam et al. 2012) with the aid of numerical

    simulation (Farouk et al. 2014). Although, the numerical simulation was able to capture the

    global trend of droplet flame extinction and subsequent formation of cool diffusion flame,

    detailed structure of cool diffusion flames has not been revealed yet. As such, cool flame

    dynamics remain mysterious and the fidelity of cool flame chemistry remains unknown.

    One of the main challenges to establish a self-sustaining cool flame is that at low

    temperature the cool flame induction chemistry for the radical branching is too slow. On

    the other hand, at higher temperature the radical branching becomes so fast that cool flame

    will transit to a hot flame rapidly (Zhao et al. 2013). As a result, a cool flame is not

    stable without introducing a heat loss to the wall. Therefore, the only way to create a

    self-sustaining cool flame is to accelerate the chain-branching process at low temperature.

    Recently, a novel method to establish self-sustaining cool diffusion flames with well-

    defined boundary conditions has been experimentally demonstrated by using ozone into the

    oxidizer stream in the counterflow configuration (Won et al. 2014) (Fig. 19). It was found

    that the formation of atomic oxygen via the decomposition of ozone dramatically shortens

    the induction timescale of low temperature chemistry, extending the flammable region of cool

    flames, and enables the establishment of self-sustaining cool flames at pressure and timescales

    at which normal cool flames may not be observable. This new method, for the first time,

    provided an opportunity to study cool flame dynamics, structure, and chemistry simultane-

    ously in a well-known flame geometry. Extinction limits of n-heptane/oyxgen cool diffusion

    flames were measured. A cool diffusion flame diagram for four different flame regimes was

    experimentally measured. Numerical simulations showed that the extinction limits of cool

    diffusion flames were strongly governed by species transport and low temperature chemistry

  • 28 44 : 201402

    Cool diffusion flame Hot diffusion flame

    a b

    Fig. 19

    Direct photos of n-heptane/oxygen cool diffusion flame (a) and hot diffusion flame (b) flames,

    observed at the identical flow condition, fuel mole fraction of 0.07 and strain rate of 100 s1

    (Won et al. 2014).

    activated by ozone decomposition. The structure of cool diffusion flame was further investi-

    gated by measuring the temperature and species distributions with a micro-probe sampling

    technique. It was found that the model over-predicts the rate of n-heptane oxidation, the

    heat release rate, and the flame temperature. Measurements of intermediate species, such

    as CH2O, acetaldehyde, C2H4, and CH4 indicated that the model over-predicted the QOOH

    thermal decomposition reactions to form olefins, resulting in substantial over-estimation of

    C2H4, and CH4 concentrations. The new experimental method of cool flame provides an

    unprecedented platform to understand cool flame and low temperature chemistry.

    In future research, if a self-sustaining premixed cool flame can also be established by

    a similar method and appropriate diagnostic methods can be developed, this method will

    bridge our knowledge gap of cool flames for more than one century. At high pressure, the

    cool flame chemistry will be enhanced. Quantitative study of cool flames may provide a key

    solution to solve engine knocking and develop new engine technologies.

    2.3 Alternative fuels and surrogate fuel modeling

    Due to the increasing concern of energy sustainability, another rapidly growing re-

    search area in combustion is alternative fuels. Methodologies for alternative transportation

    fuel production, using a range of fossil energy sources such as coal and natural gas and

    renewable resources such as animal fats, plant oils, ligno-cellulosic biomass materials (Chu

    et al. 2012, Huber et al. 2006, Khodakov et al. 2007) are increasing. As shown in Table

    1, these alternative fuels have different molecular structures. Moreover, many synthetic fu-

    els produced from the catalytic hydrogenation processes do not generally contain aromatic

    components and are mainly composed of branched alkanes (Rye et al. 2012, Blakey et al.

  • Ju Yiguang : Recent progress and challenges in fundamental combustion research 29

    2011, Balster et al. 2008) and often are blended together with conventional transportation

    fuels. Recently, gas turbine fuel certification standards have been modified to encompass

    blending of up to 50% bio-derived synthetic fuel components from hydroprocessed esters

    and fatty acids (e.g. algae, camelina or jatropha, or from animal fats, i.e. tallow) or Fischer

    Tropsch hydroprocessed synthetic paraffinic kerosine (F-T-SPK, from coal, natural gas or

    biomass) (Blakey et al. 2011, Corporan et al. 2011). The introduction of alternative fuels

    and the fuel blendings significantly increase the complexity of fuel screening and modeling.

    Therefore, there is an urgent need to create a generic methodology to develop surrogate fuel

    mixtures to screen alternative fuels and to evaluate the combustion and emission properties

    of alternative and blended fuels.

    Many previous studies have attempted to produce surrogate fuels to emulate real and

    alternative fuel combustion kinetics and/or physical properties (Wohlwend et al. 2001).

    These approaches emphasize the need to develop surrogates that describe both the impor-

    tant physical and chemical kinetic related properties of a real fuel. For physical properties,

    real fuel distillation curve and phase behavior were noted as key properties to describe the

    vaporization/injection/mixing processes of multiphase combustion. Other physical proper-

    ties such as viscosity are also commonly recognized to be important to spray atomization

    phenomena. The early works of Wood et al. (1989) and Schultz (1992) proposed surrogates

    formulated with the intention of emulating both chemical and physical properties of the real

    fuels to reproduce distillation properties by using twelve or more individual components.

    Violi et al. (2002) proposed a seven component surrogate mixture in order to emulate the

    distillation curve, flash point, chemical class composition, sooting tendency, heat of combus-

    tion, flammability limits, and pool burning regression rate of a generic JP-8 fuel. However,

    as is frequently found, due to the large composition matrix no comprehensive experimental

    verification of the surrogate fuel property to a target real fuel property was presented (Ranzi

    et al. 2001, Cooke et al. 2005).

    Recently, in order to develop compact and comprehensively validated surrogate fuel

    mixtures, supported by the AFOSR multi-university research initiative (MURI) and led

    by Princeton University, a generic method to construct surrogate component mixtures to

    emulate real and alternative fuel combustion properties was proposed and validated (Dooley

    et al. 2010, 2012) using jet fuels. The key point of this approach is to select surrogate

    component fuels by emulating four combustion property targets of the alternative and

    real fuels of interest: 1) Hydrogen to Carbon molar ratio (H/C ratio), 2) Derived Cetane

    Number (DCN) from Ignition Quality Tester (IQT), 3) average molecular weight, and 4)

  • 30 44 : 201402

    Threshold Sooting Index (TSI). The first generation three-component surrogate mixture

    of n-dodecane/iso-octane/toluene and the second generation four-component of surrogate

    mixture of n-dodecane/iso-octane/1,3,5-trimethylbenzene/n-propylbenzene for Jet-A fuel

    were formulated and tested. The first generation surrogate mimics the H/C ratio, DCN, and

    TSI target but did not match the mean molecular weight. However, the second generation

    surrogate matches all four surrogate targets. Detailed information of the surrogate mixtures

    and their combustion property targets is listed in Table 2. Both surrogate mixtures were

    examined by using a variable pressure flow reactor to quantify the fuel reactivity and species

    profiles at 12.5 atm and 5001000 K, a shock tube for ignition delay time at 6671223 Kat 20 atm, a rapid compression machine at 645714 K at compressed pressures of 21.7 atm,and a counterflow flame for flame speeds and extinction limit at atmospheric pressure.

    Figures 20(a)20(d) show the comparisons of the measured species profiles, ignition

    delay time, diffusion flame extinction limits, and flame speeds for jet fuel POSF 4658 and its

    1st generation and 2nd generation surrogates. It is seen that the low temperature oxidation

    (near 600 K) of POSF 4658 is mimiced well by both the first and the second generation sur-

    rogates. Although there is a small shift of the temperature window in the high temperature

    oxiation zone (800 K), the overal CO, H2O, and CO2 concentrations are well reproduced.

    It is interesting to note that both the 1st and the 2nd generation surrogates reproduce the

    ignition delay very well. This implies that the difference in mean molecular weight does not

    Table 2 Combustion property targets for the first and second generation surrogate compo-

    nents, kerosene fuels, Jet-A POSF 4658 and proposed surrogates. 1st Generation POSF 4658

    surrogate is n-decane/iso-octane/toluene 42.7/33.0/24.3 mole %, 2nd Generation POSF 4658

    surrogate is n-dodecane/iso-octane/1,3,5 trimethylbenzene/n-propylbenzene 40.41/29.48/-

    7.28/22.83 mole % (Dooley et al. 2013).

    Fuel DCN H/C MW/gmol1 TSI

    n-dodecane 78 2.16 170.3 7

    iso-octane 17 2.25 114.2 6.8

    1,3,5 trimethylbenzene 21.8 1.33 120.2 62

    n-propylbenzene 28.2 1.33 120.2 53

    Kerosene fuel range 3060 1.842.07 N/A 1526

    Jet-A POSF 4658 47.1 1.96 14220 21.41st Generation POSF 4658 surrogate 47.4 2.01 120.7 14.1

    2nd Generation POSF 4658 surrogate 48.5 1.95 138.7 20.4

  • Ju Yiguang : Recent progress and challenges in fundamental combustion research 31

    500 600 700 800 900 1000







    Fuel mass fraction Yf Equivalence ratio,




    e sp


    . s-



    ion s








    n d

    elay t








    3 p


    POSF 4658

    2nd Gen. surrogate

    1st Gen. surrogate

    O2 CO2 H2OCO


    1200 1000 800 600

    1.0 1.2 1.4 1.6






    ST RCM

    2nd Gen. POSF 4658 surrogate

    1st Gen. POSF 4658 surrogate

    POSF 4658

    JETA POSF 4658 3 comp. surrogate4 comp. surrogate

    0.2 0.3 0.4 0.5





    00.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4








    Tu=470 K

    Tu=400 K

    Jet-A1st Gen2nd Gen



    Fig. 20

    (a) Flow reactor oxidation data for conditions of 12.5 atm, 0.3% carbon, = 1.0 and t =

    1.8 s, for POSF 4658, 1st generation POSF 4658 and 2nd generation POSF 4658 surrogate.

    (Dooly et al. 2012), (b) Ignition delay times, = 1.0 in air at 20 atm for POSF 4658,1st generation POSF 4658 surrogate and 2nd generation POSF 4658 surrogate (Dooley et

    al. 2012), (c) Comparison of diffusion flame extinction limits for POSF 4658, 1st generation

    POSF 4658 surrogate and 2nd generation POSF 4658 surrogate, (d) Comparison of flame

    speeds for POSF 4658, 1st generation POSF 4658 surrogate and 2nd generation POSF 4658

    surrogate. (Dooley et al. 2012)

    affect significantly the surrogate fuel reactivity. Similar observation is seen for the laminar

    flame speed. Once again, the laminar flame speed is insenstive to the molecular size because

    the reactivity of large alkanes is similar. However, the measured diffusion extinciton limits

    show that the mean molecular weight has a consideral influence on diffusion flame extinction.

    This is because the diffusion transport of fuel molecules affects the extinction limit of diffu-

  • 32 44 : 201402

    sion flames more than that of premixed flames. The above comprehensive validation shows

    that the four metric physical and combustion property targets are successful to construct a

    surrogate fuel mixture to mimic real fuel properties.

    Recently, this method is further extended to a real F-T synthetic jet fuel S-8 de-

    rived from natural gas by Syntroleum Inc. and a single component alcohol derived jet fuel,

    2,6,10-trimethyl dodecane (TMD) from Amyris Inc. These fuels contain no aromatic fraction

    and large percentages of mono, di- and trimethylated, weakly branched alkanes. A simple

    surrogate fuel mixture composed of only n-dodecane and iso-octane was formulated and

    experimentally shown to closely emulate the combustion kinetic behavior of the synthetic

    S-8 fuel. For the single molecule fuel TMD, the derived cetane number (DCN) (59.1) and

    Hydrogen/Carbon ratio (2.133) are very close to those of S-8 and a surrogate mixture com-

    posed of n-dodecane/iso-octane (DCN:58.9 and H/C:2.19) was constructed. Identical high

    temperature global kinetic reactivities were observed in all experiments. However at tem-

    peratures below 870 K, the S-8 surrogate mixture had ignition delay times approximatelya factor of two faster than that of TMD. A chemical functional group analysis identified

    that the methylene (CH2) to methyl (CH3) ratio globally correlated the low temperature

    alkylperoxy radical reactivity for these large paraffinic fuels. This result was further con-

    firmed experimentally by comparing combustion targets using a surrogate fuel mixture of

    n-hexadecane (n-cetane) and iso-cetane that shares the same methylene-to-methyl ratio as

    TMD in addition to the same DCN and H/C. A kinetic modeling analysis on the model fuel

    revealed that the formation of alkylhydroperoxy radicals (QOOH) to be strongly influenced

    by the absence or presence of the methyl and methylene functional groups in the fuel chemi-

    cal structure. These experimental observations and analyses suggest that for paraffinic based

    fuels with high DCN values, in constructing a surrogate fuel mixture it is more appropriately

    to include the CH2 to CH3 ratio as an additional property because DCN alone fails to fully

    distinguish the relative reaction characteristics of low temperature kinetic phenomena.

    To identify an alternative combustion properties for surrogate fuel modeling and to

    understand the effect of fuel transport property on flame extinction, the diffusion flame

    extinction limits of various fuels with different functional groups (Table 1) were measured

    and compared in counterflow diffusion flames (Won et al. 2010, 2011, 2012). Figure 21

    shows the comparison of the measured extinction strain rates for all tested hydrocarbon fuels

    by introducing a new parameter, the transport weighted enthalpy (TWE), [fuel] Hc (MWfuel/MWnitrogen)

    1/2. TWE is a product of fuel mole fraction [fuel] and the enthalpy of

    combustion Hc, normalized by the square root of the fuel molecular weight. The diffusive

  • Ju Yiguang : Recent progress and challenges in fundamental combustion research 33

    0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6





    1000/T [1/K]


    n d


    y t


    Trimethyi dodecaneS-8 nC12/iC8 Surrogate FuelnC16/iC16 Model Fuel

    Fig. 21

    Comparison of measured shock tube ignition delay times of trimethyl dodecane, the n-

    dodecane/iso-octane (51.9/48.1 S-8) surrogate and the n-cetane/iso-cetane (45.9/54.1) sur-

    rogate mixtures at 20 atm (Won et al. 2013)

    parameter is non-dimensionalized by employing the ratio of the molecular weight of the fuel

    MWfuel to the molecular weight of nitrogen (dilution gas) MWnitrogen. Therefore, TWE is

    the ratio of fuel enthalpy scaled by the fuel diffusivity. Using the TWE, the effect of transport

    and enthalpy on the fuel extinction limits can be removed so that a direct comparison of high

    temperature fuel reactivity can be achieved. It is seen that the extinction limits of all alkanes

    fall into one line as a function of TWE. Therefore, they have the same high temperature

    reactivity. This is why the fuel reactivity and flame speeds of n-alkanes are insensitive to

    the mean molecular weight but the diffusion extinction limit is sensitive (Fig. 20). It is

    also seen from Fig. 22 that compared to n-alkanes, iso-alkanes have lower reactivity due

    to their reduced chemical kinetic potential. Moreover, the reactivities of aromatic fuels are

    very different. Among those, n-propyl-benzene and 1,3,5-trimethyl benzene show the highest

    and lowest reactivity due to the longest alkyl chain in n-propyl-benzene and the symmetry

    of methyl side chains of 1,3,5-trimethyl benzene. Note that the large reactivity difference

    between 1,3,5-trimethyl benzene and n-propyl-benzene while having the same molecular

    weight and H/C ratio make them the best choice for surrogate fuel components because the

    fuel reactivity can be adjusted independently from the molecular weight and the H/C in the

    four surrogate mixture targets.

    Figure 22 shows that an index for the fuel reactivity, the radical index (Ri), can be

    derived by using the measured extinction limits and the TWE (Won et al. 2012). Figure 23

    shows the derived radical index relative to n-alkanes and the universal correlation of extinc-

  • 34 44 : 201402

    0.5 1.0 1.5 2.0 2.5 3.0








    Extinction s











    Tf/500 K and To/300 K

    Fig. 22

    Extinction strain rates as a function of transport weighted enthalpy for all tested fuels; Hc,

    enthalpy of formation, MW , molecular weight (Won et al. 2012)















    036 Ri[Fuel]Hc(MWfuel/MWnitrogen)-1/2[cal/cm3]

    0.5 1.0 1.5 2.0







    ion s






    Tf/500 K and To/300 K

    a b

    Fig. 23

    Left: Derived radical index (Ri) for different fuels; Right: Universal correlation of extinction

    strain rates of all tested fuels in terms of Ri [fuel] Hc (MWfuel/MWnitrogen)1/2;line: linear fit of all experimental data (Won et al. 2012, 2013)

    tion limits of all tested fuels in terms of RiTWE. The radical index shows that the fuelreactivities (producing radicals) are very different from n-alkanes to aromatics due to the

    change of molecular structure. Moreover, the alkyl chain position and length of aromatics

    have a significant impact on the fuel reaction. The good correlation between the extinction

    limits and the product of RiTWE demonstrates that radical index and the TWE are use-ful parameters to rank the fuel reactivity by removing the effect of molecular size and the

    difference in fuel heating value.

  • Ju Yiguang : Recent progress and challenges in fundamental combustion research 35

    0.5 1.0 1.5 2.0 2.5







    ion s





    Transport-weighted enthalpy/[cal/cm3][Fuel]Hc(MWfuel/MWnitrogen)-1/2

    Transport-weighted enthalpy/[cal/cm3]

    Extinction of diffusion flame in counterflow configurationTf/500 K and Tair/300 K @1 atm

    Fuel Ri



    HRJ Camelina

    HRJ Tallow








    1 for n-alka



    0.7 f

    or is



    JP8POSF 6169


    HRJ Camelina POSF 7720

    HRJ Tallow POSF 6308




    0.5 1.0 1.5 2.0








    ion s







    Tf/500 K, Tox/298 K

    Methy1 FormateMethy1 EthanoateMethy1 PropanoateMethy1 ButanoateMethy1 PentanoateMethy1 HexanoateMethy1 OctanoateMethy1 Decanoate

    a b

    Fig. 24

    (a) Reactivity ranking of synthetic jet fuels using transport weighted enthalpy (Won et al.

    2013), (b) Reactivity ranking of methyl esters (biodiesel) using transport weighted enthalpy

    (Dievart et al. 2013)

    The TWE and the radical index were also used to screen alternative jet fuels and

    biodiesels. As shown in Fig. 23(a), the reactivities of alternative jet fuels produced from

    various sources are slightly different from that of JP-8. In addition, Shell SPK and Sasol IPK

    have the highest and lowest radical index, respectively. Figure 24(b) shows the comparison

    of fuel reactivity of all methyl esters in biodiesel surrogates. It is seen that small methyl

    esters have unique fuel reactivity, that is, the fuel reactivity does not linearly depend on

    the alkyl chain length. However, for large methyl esters the high temperature reactivity is

    similar. Therefore, kinetic studies for methyl esters should be focused on small methyl esters

    and the large esters are similar to n-alkanes. As such, Fig. 24 shows that radical index is

    a successful parameter which is sensitive enough to rank fuel reactivity. Future research

    should address: (1). How will the physical properties of alternative fuels be modeled? (2).

    How does the turbulent flow affect the validation of surrogate fuel model? (3). How can we

    find an affordable surrogate mixture which can allow large scale engine tests, and (4). How

    to develop a compact and validated detailed kinetic model for surrogate fuel mixtures.

    2.4 Multiscale and dynamic adaptive chemistry modeling using re-

    duced and detailed mechanism

    To capture the physics of turbulence-chemistry interaction involving low temperature

    chemistry and different flame regimes for real fuels, a large kinetic mechanism involves

    hundreds of species and thousands of reactions is needed. For example, a detailed n-heptane

  • 36 44 : 201402

    mechanism can have 1034 species and 4236 reactions (Curran et al. 2002) and a recent jet

    fuel surrogate model has more than two thousand species and 8000 reactions (Won et al.

    2013). The large number of species and the stiffness of the combustion kinetics results in a

    great challenge to combustion modeling (DOE report 2005). For a typical implicit method,

    the computation time is proportional to the cubic of the species number. Moreover, as shown

    in Fig. 1, the timescales of the elementary reactions and physical processes have a disparity

    of more than 10 orders of magnitude. Even with the availability of petascale computation

    capability, direct numerical simulations with such large kinetic mechanisms remain to be


    In last 30 years, many kinetic model reduction methods have been developed to improve

    the computation efficiency. These approaches can be summarized in five different categories.

    The first category is the methods to generate a pre-reduced mechanism by removing unim-

    portant species and reactions using reaction rate and sensitivity analysis. These methods

    include the sensitivity analysis and quasi-steady state assumption method (Peters et al.

    1987, Ju et al. 1994). These methods compare the reaction rates of each species and re-

    action, and select quasi-steady state species by eliminating the corresponding fast reaction.

    Therefore, the QSS species related to the fast time-scales can be analytical solved from al-

    gebraic equations without direct numerical integration. However, this approach requires a

    lot of human experience to determine the quasi-steady sate (QSS) species and the partial

    equilibrium. In addition, the sensitivity analysis method, if used, is very computational


    To improve the model reduction efficiency, a second category of methods use the fluxes

    of species connecting the reactants to the products to eliminate species and reactions with

    negligible fluxes. These path flux based approaches include the visualization method (Bend-

    sten et al. 2001), Direct Relation Graph (DRG) (Lu et al. 2005) method, DRG with Error

    Propagation (DRGEP) (Pepiot-Desjardins et al. 2008), and the multi-generation Path Flux

    Analysis (PFA) (Sun et al. 2010) method and other variations. The path flux based method

    is much more efficient than the reaction rate and sensitivity