Bibliography - Chung K Law

Li, T.X., D. L. Zhu, N. Akafuah, K. Saito, and Chung K Law, 2010: Synthesis, droplet combustion, and sooting characteristics of biodiesel produced from waste vegetable oils (In Press). Proceedings of the Combustion Institute, 1-22
[ Abstract ]
In light of the potential of fatty acid methyl ester (FAME, i.e. biodiesel) as a renewable energy source, an innovative acid catalyzed process was developed for the synthesis of biodiesel from waste vegetable oils. The synthesized biodiesels were analytically characterized for their major components, molar fraction and molecular weight of each component, the average molecular weight, and the heat of combustion. Their droplet combustion characteristics in terms of the burning rate, flame size, and sooting tendency were subsequently determined in a hightemperature, freely-falling droplet apparatus. Results show that the biodiesel droplet has higher burning rate, and that biodiesel in general has a lower propensity to soot because its molecular oxygen content promotes the oxidation of the soot precursors.
Liu, W., A.P. Kelley, and Chung K Law, 2010: Nonpremixed ignition, laminar flame propagation, and mechanism reduction of n-butanol, iso-butanol, and methyl butanoate (In Press). Proceedings of the Combustion Institute, 1-24
[ Abstract ]
The nonpremixed ignition temperature of n-butanol (CH3CH2CH2CH2OH), isobutanol ((CH3)2CHCH2OH) and methyl butanoate (CH3CH2CH2COOCH3) was measured in a liquid pool assembly by heated oxidizer in a stagnation flow for system pressures of 1 and 3 atmospheres. In addition, the stretch-corrected laminar flame speeds of mixtures of air- n-butanol / iso-butanol/ methyl butanoate were determined from the outwardly propagating spherical flame at initial pressures of up to 2 atmospheres, for an extensive range of equivalence ratio. The ignition temperature and laminar flame speeds of n-butanol and methyl butanoate were computationally simulated with three recently developed kinetic mechanisms in the literature. Dominant reaction pathways to ignition and flame propagation were identified and discussed through a Chemical Explosive Mode Analysis (CEMA) and sensitivity analysis. The detailed models were further reduced through a series of systematic strategies. The reduced mechanisms provided excellent agreement in both homogeneous and diffusive combustion environments and greatly improved the computation efficiency.
Seshadri, K., T. F. Lu, O. Herbinet, S. Humer, U. Niemann, W. J. Pitz, R. Seiser, and Chung K Law, 2009: Experimental and kinetic modeling study of extinction and ignition of methyl decanoate in laminar nonpremixed flows. Proceedings of the Combustion Institute, 3(1), doi:10.1016/j.proci.2008.06.215 1067-1074
[ Abstract ]
Methyl decanoate is a large methyl ester that can be used as a surrogate for biodiesel. In this experimental and computational study, the combustion of methyl decanoate was investigated in non-premixed, nonuniform flows. Experiments were performed employing the counterflow configuration with a fuel stream made up of vaporized methyl decanoate and nitrogen, and an oxidizer stream of air. The mass fraction of fuel in the fuel stream was measured as a function of the strain rate at extinction, and critical conditions of ignition were measured in terms of the temperature of the oxidizer stream as a function of the strain rate. A detailed mechanism of 8555 elementary reactions and 3036 species has been developed previously to describe combustion of methyl decanoate. Since it is not possible to use this detailed mechanism to simulate the counterflow flames because the number of species and reactions is too large to employ with current flame codes and computer resources, a skeletal mechanism was deduced from this detailed mechanism using the "directed relation graph" method. This skeletal mechanism has only 713 elementary reactions and 125 species. Critical conditions of extinction and critical conditions of ignition were calculated using this skeletal mechanism and they were found to agree well with experimental data. In general, the methyl decanoate mechanism provides a realistic kinetic tool for simulation of biodiesel fuels.
Jomaas, G., and Chung K Law, 2008: An Experimental Study on the Self-Acceleration of Cellular Spherical Flames. 46th Aerospace Sciences Meeting, Reno, NV, http://pcl.princeton.edu/Publications/Conference/AIAA-2008-1414-908.pdf,
[ Abstract ]
The time-resolved images and accelerating propagation speeds of spark-ignited, expanding spherical flames exhibiting both flame-front hydrodynamic and diffusionalthermal cellular instabilities were experimentally acquired in a constant and high pressure environment. From these data the acceleration exponent α defined through R(t)=C+At^α, where A and C are constants, was determined for the near-equidiffusive flames of ethylene and acetylene and non-equidiffusive flames of propane and hydrogen, recognizing that the former is subjected only to hydrodynamic instability while the latter to the diffusional thermal instability as well. Results show that the acceleration exponent seems to be bounded by the value of 1.34, which is approached for fast-propagating flames of small thicknesses, regardless of the nature of the cells. The characteristic cell sizes were also measured and were found to agree well, for the hydrodynamic cells, with the linear stability theory of Bechtold and Matalon. The possible attainment of a self-similar mode of propagation is suggested.
Boyd, P. W., T. Jickells, Chung K Law, S. Blain, E. A. Boyle, K. O. Buesseler, K. H. Coale, J. J. Culle, H. J. W. de Baar, M. Follows, M. Harvey, and C. Lancelot, et al., 2007: Mesoscale iron enrichment experiments 1993-2005: Synthesis and future directions. Science, 315, doi:10.1126/science.1131669 612-617
[ Abstract ]
Since the mid-1980s, our understanding of nutrient limitation of oceanic primary production has radically changed. Mesoscale iron addition experiments (FeAXs) have unequivocally shown that iron supply limits production in one-third of the world ocean, where surface macronutrient concentrations are perennially high. The findings of these 12 FeAXs also reveal that iron supply exerts controls on the dynamics of plankton blooms, which in turn affect the biogeochemical cycles of carbon, nitrogen, silicon, and sulfur and ultimately influence the Earth climate system. However, extrapolation of the key results of FeAXs to regional and seasonal scales in some cases is limited because of differing modes of iron supply in FeAXs and in the modern and paleo-oceans. New research directions include quantification of the coupling of oceanic iron and carbon biogeochemistry.
Jomaas, G., Chung K Law, and J. K. Bechtold, 2007: On transition to cellularity in expanding spherical flames. Journal of Fluid Mechanics, 583, doi:10.1017/S0022112007005885 1-26
[ Abstract ]
The instant of transition to cellularity of centrally ignited, outwardly propagating spherical flames in a reactive environment of fuel�oxidizer mixture, at atmospheric and elevated pressures, was experimentally determined using high-speed schlieren imaging and subsequently interpreted on the basis of hydrodynamic and diffusional�thermal instabilities. Experimental results show that the transition P�clet number, Pe_c =R_c/l_L, assumes an almost constant value for the near-equidiffusive acetylene flames with wide ranges in the mixture stoichiometry, oxygen concentration and pressure, where R_c is the flame radius at transition and l_L the laminar flame thickness. However, for the non-equidiffusive hydrogen and propane flames, Pe_c respectively increases and decreases somewhat linearly with the mixture equivalence ratio. Evaluation of Pe_c using previous theory shows complete qualitative agreement and satisfactory quantitative agreement, demonstrating the insensitivity of Pe_c to all system parameters for equidiffusive mixtures, and the dominance of the Markstein number, Ze(Le - 1), in destabilization for non-equidiffusive mixtures, where Ze is the Zel�dovich number and Le the Lewis number. The importance of using locally evaluated values of l_L, Ze and Le, extracted from either computationally simulated one-dimensional flame structure with detailed chemistry and transport, or experimentally determined response of stretched flames, in the evaluation of Pe_c is emphasized.
Jomaas, G., J. K. Bechtold, and Chung K Law, 2007: Spiral waves in expanding hydrogen-air flames: experiment and theory. Proceedings of the Combustion Institute, 31(1), doi:10.1016/j.proci.2006.08.100 1039-1046
[ Abstract ]
We report herein the first experimental observation of spiral waves over propagating flame surfaces in rich hydrogen�air mixtures at elevated pressures up to 40 atm, conducted in a specially designed, optically accessible, constant-pressure combustion chamber. The observed spiral waves are a manifestation of the large Lewis number instability, exhibiting behaviors such as clockwise/counterclockwise rotation, meandering, and fast radial wave speeds that are similar to patterns often observed in other excitable media, for example the Belousov�Zhabotinsky reaction. In addition, these spiral waves also exhibit features that seem to be characteristic of combustion systems, such as the transition criterion for diffusional-thermal pulsating instability, and their confinement within the hydrodynamic cells that also develop over such high-pressure flames of much reduced flame thicknesses. A diffusional-thermal theory was developed that successfully describes the observed spiral patterns.
Radulescu, M. I., and Chung K Law, 2007: The transient start of supersonic jets. Journal of Fluid Mechanics, 578, doi:10.1017/S0022112007004715 331-369
[ Abstract ]
This study investigates the initial transient hydrodynamic evolution of highly underexpanded slit and round jets. A closed-form analytic similarity solution is derived for the temporal evolution of temperature, pressure and density at the jet head for vanishing diffusive fluxes, generalizing a previous model of Chekmarev using Chernyi�s boundary-layer method for hypersonic flows. Two-dimensional numerical simulations were also performed to investigate the flow field during the initial stages over distances of ∼1000 orifice radii. The parameters used in the simulations correspond to the release of pressurized hydrogen gas into ambient air, with pressure ratios varying between approximately 100 and 1000. The simulations confirm the similarity laws derived theoretically and indicate that the head of the jet is laminar at early stages, while complex acoustic instabilities are established at the sides of the jet, involving shock interactions within the vortex rings, in good agreement with previous experimental findings. Very good agreement is found between the present model, the numerical simulations and previous experimental results obtained for both slit and round jets during the transient establishment of the jet. Criteria for Rayleigh�Taylor instability of the decelerating density gradients at the jet head are also derived, as well as the formulation of a model addressing the ignition of unsteady expanding diffusive layers formed during the sudden release of reactive gases.
Radulescu, M. I., G. J. Sharpe, Chung K Law, and J.H.S. Lee, 2007: The hydrodynamic structure of unstable cellular detonations. Journal of Fluid Mechanics, 580, doi:10.1017/S0022112007005046 31-81
[ Abstract ]
The study analyses the cellular reaction zone structure of unstable methane�oxygen detonations, which are characterized by large hydrodynamic fluctuations and unreacted pockets with a fine structure. Complementary series of experiments and numerical simulations are presented, which illustrate the important role of hydrodynamic instabilities and diffusive phenomena in dictating the global reaction rate in detonations. The quantitative comparison between experiment and numerics also permits identification of the current limitations of numerical simulations in capturing these effects. Simulations are also performed for parameters corresponding to weakly unstable cellular detonations, which are used for comparison and validation. The numerical and experimental results are used to guide the formulation of a stochastic steady one-dimensional representation for such detonation waves. The numerically obtained flow fields were Favre-averaged in time and space. The resulting onedimensional profiles for the mean values and fluctuations reveal the two important length scales, the first being associated with the chemical exothermicity and the second (the �hydrodynamic thickness�) with the slower dissipation of the hydrodynamic fluctuations, which govern the location of the average sonic surface. This second length scale is found to be much longer than that predicted by one-dimensional reaction zone calculations.
Sun, H., S. H. Yang, G. Jomaas, and Chung K Law, 2007: High-Pressure Laminar Flame Speeds and Kinetic Modeling of Carbon Monoxide/ Hydrogen Combustion. Proceedings of the Combustion Institute, 31(1), doi:10.1016/j.proci.2006.07.193 439-446
[ Abstract ]
Laminar flame speeds were accurately measured for CO/H₂/air and CO/H₂/O₂/helium mixtures at different equivalence ratios and mixing ratios by the constant-pressure spherical flame technique for pressures up to 40 atmospheres. A kinetic mechanism based on recently published reaction rate constants is presented to model these measured laminar flame speeds as well as a limited set of other experimental data. The reaction rate constant of CO + HO₂ fi CO₂ + OH was determined to be k = 1.15 � 10⁵T^2.278 exp(-17.55 kcal/RT) cm³ mol^-1 s^-1 at 300�2500 K by ab initio calculations. The kinetic model accurately predicts our measured flame speeds and the non-premixed counterflow ignition temperatures determined in our previous study, as well as homogeneous system data from literature, such as concentration profiles from flow reactor and ignition delay time from shock tube experiments.
Yuan, J., Y. Ju, and Chung K Law, 2007: On flamefront instability at elevated pressures. Proceedings of the Combustion Institute, 31(1), doi:10.1016/j.proci.2006.07.180 1267-1274
[ Abstract ]
Effects of pressure up to 3 atm on flame-front instability were numerically investigated for both linear and nonlinear growth stages at sub-unity and unity Lewis numbers. A sixth-order compact scheme and non-reflecting boundary conditions were used to capture the evolution of the flame front. Results show that in the linear instability growth stage, elevated pressure can extend the unstable range of flame-fronts and generate the fine flame cell structure. This effect can be qualitatively predicted by the theories when Le = 1.0; however the theories diverge at sub-unity Lewis numbers (e.g. Le = 0.7). In the nonlinear growth stage, the critical wave number (k_c) from the linear dispersion relation can be used as a reference length scale for the evolution of the flame cell structure. Since elevated pressure increases the critical wave number, small flame cells appear over large flame cells (deep folds) at high ambient pressures. Furthermore, flame-front hydrodynamic instability is excited when the lateral domain is enlarged.
Law, Chung K., A. Makino, and T. F. Lu, 2006: On the off-stoichiometric peaking of adiabatic flame temperature. Combustion and Flame, 145(4), doi:10.1016/j.combustflame.2006.01.009 808-819
[ Abstract ]
The characteristic rich shifting of the maximum adiabatic flame temperature from the stoichiometric value for mixtures of hydrocarbon and air is demonstrated to be caused by product dissociation and hence reduced amount of heat release. Since the extent of dissociation is greater on the lean side as a result of the stoichiometry of dissociated products, the peaking occurs on the rich side. The specific heat per unit mass of the mixture is shown to increase monotonically with increasing fuel concentration, and as such tends to shift the peak toward the lean side. It is further shown that this is the cause for the lean shifting of the adiabatic flame temperature of oxidizerenriched mixtures of N_mH_n and F₂ and of NH₃ and O₂, with various amounts of inert dilution, even though their maximum heat release still peaks on the rich side.
Lu, T. F., and Chung K Law, 2006: Linear-Time Reduction of Large Kinetic Mechanisms with Directed Relation Graph: n-Heptane and iso-Octane. Combustion and Flame, 144(1-2), doi:10.1016/j.combustflame.2005.02.015 24-36
[ Abstract ]
The algorithm of directed relation graph recently developed for skeletal mechanism reduction was extended to overall linear time operation, thereby greatly facilitating the computational effort in mechanism reduction, particularly for those involving large mechanisms. Together with a two-stage reduction strategy and using the kinetic responses of autoignition and perfectly stirred reactor (PSR) with extensive parametric variations as the criteria in eliminating unimportant species, a detailed 561-species n-heptane mechanism and a detailed 857-species iso-octane mechanism were successfully reduced to skeletal mechanisms consisting of 188 and 233 species, respectively. These skeletal mechanisms were demonstrated to mimic well the performance of the detailed mechanisms, not only for the autoignition and PSR systems based on which the reduced mechanisms were developed but also for the independent system of jet-stirred reactor. It was further observed that the accuracy of calculated species concentrations was equivalently bounded by the user-specified error threshold value and that the reduction time for a single reaction state is only about 50 ms for the large iso-octane mechanism.
Law, Chung K., G. Jomaas, and J. K. Bechtold, 2005: Cellular Instabilities of Expanding Hydrogen/Propane Spherical Flames at Elevated Pressure: Theory and Experiment. Proceedings of the Combustion Institute, 30(1), doi:10.1016/j.proci.2004.08.266 159-167
[ Abstract ]
An experimental and theoretical investigation of the onset of cellular instabilities on spherically expanding flames in mixtures of hydrogen and propane in air at elevated pressures was conducted. Critical conditions for the onset of instability were measured and mapped out over a range of pressures and mixture compositions. An asymptotic theory of hydrodynamic and diffusional-thermal cell development on flames in mixtures comprised of two scarce fuels burning in air was also formulated. Predicted values of Peclet number, defined as the flame radius at the onset of instability normalized by the flame thickness, were shown to compare favorably with the experimentally measured values.
Lu, T. F., and Chung K Law, 2005: A Directed Relation Graph Method for Mechanism Reduction. Proceedings of the Combustion Institute, 30(1), doi:10.1016/j.proci.2004.08.145 1333-1341
[ Abstract ]
A systematic approach for mechanism reduction was developed and demonstrated. The approach consists of the generation of skeletal mechanisms from detailed mechanism using directed relation graph with specified accuracy requirement, and the subsequent generation of reduced mechanisms from the skeletal mechanisms using computational singular perturbation based on the assumption of quasi-steady-state species. Both stages of generation are guided by the performance of PSR for high-temperature chemistry and auto-ignition delay for low- to moderately high-temperature chemistry. The demonstration was performed for a detailed ethylene oxidation mechanism consisting of 70 species and 463 elementary reactions, resulting in a specific skeletal mechanism consisting of 33 species and 205 elementary reactions, and a specific reduced mechanism consisting of 20 species and 16 global reactions. Calculations for laminar flame speeds and nonpremixed counterflow ignition using either the skeletal mechanism or the reduced mechanism show very close agreement with those obtained by using the detailed mechanism over wide parametric ranges of pressure, temperature, and equivalence ratio.
Radulescu, M. I., Chung K Law, and G. J. Sharpe, 2005: Structure of unstable gaseous detonations waves. Physics of Fluids, 17(091105), doi:10.1063/1.1942517
[ Abstract ]
Detonation waves are supersonic combustion waves. The figures illustrate their typical unstable structure and the hydrodynamic compressible turbulence generated via instabilities and self-sustained by the chemical energy release. The grayscale photographs are schlieren records of the vertical density gradients in a methane�oxygen detonation wave, illustrating the turbulent structure comprised primarily of transverse shocks, shear layers, and density interfaces separating light reacted gases and heavier unreacted gas. The detonation propagates to the right at an average Mach number of ˜ 6. The color figures illustrate the structure of the wave (pressure and temperature) obtained numerically. The front is organized in a characteristic cellular structure and substructure, consisting of interacting triple shock Mach intersections (frontal Mach stems, incident shocks, transversely propagating reflected shocks, and convected shear layers). The triple points are driven by the chemical exothermicity behind the strong Mach stems. Due to the exponential dependence of the reaction rates on local temperature, gases shocked by the weaker incident shocks have ignition delay times several orders of magnitude longer, hence accumulate as unreacted volumes behind the front. These unreacted gases react mainly through turbulent mixing with the hot reacted gases. Shear layers at the triple shock interactions are Kelvin�Helmholtz unstable and promote gas ignition by turbulent mixing of mass and heat. The transverse shocks, which sweep perpendicularly to the main front, further disrupt these density interfaces by the Richtmyer�Meshkov instability involving the baroclinic torque. Unstable detonations thus rely on compressible turbulence interactions to promote the local reaction rates of gases which escape ignition due to the unsteadiness of the leading front. The detonation wave structure thus provides an excellent setting to study exothermicity-driven compressible turbulence, manifested primarily by the interaction of shocks, density interfaces, and vortical flows.
Yuan, J., Y. Ju, and Chung K Law, 2005: Coupled hydrodynamic and diffusional-thermal instabilities in flame propagation at large Lewis numbers. Physics of Fluids, 17(O74106), doi:10.1063/1.1964845
[ Abstract ]
The dynamics of flame cell evolution due to the coupling between hydrodynamic and diffusional-thermal instabilities in subunity Lewis number flames was simulated using a sixth-order central difference scheme and newly developed nonreflective boundary conditions. Results show that the interaction between these two modes of instabilities yields distinct evolutions of cell splitting, merging, growth, local extinction, and lateral motion, leading to fluctuations of the flow and species concentrations as well as substantial increase in the flame speed. The study also demonstrates that small computational domains cannot correctly predict cell merging and transverse motion.
Zheng, X. L., T. F. Lu, Chung K Law, C. K. Westbrook, and H. J. Curran, 2005: Experimental and Computational Study of Nonpremixed Ignition of Dimethyl Ether in Counterflow. Proceedings of the Combustion Institute, 30(1), doi:10.1016/j.proci.2004.08.241 1101-1109
[ Abstract ]
The ignition temperature of nitrogen-diluted dimethyl ether (DME) by heated air in counterflow was experimentally determined for DME concentration from 5.9% to 30%, system pressure from 1.5 to 3.0 atm, and pressure-weighted strain rate from 110 to 170 s^-1. These experimental data were compared with two mechanisms that were, respectively, available in 1998 and 2003, with the latter being a substantially updated version of the former. The comparison showed that while the 1998-mechanism uniformly over-predicted the ignition temperature, the 2003-mechanism yielded a surprisingly close agreement for all experimental data. Sensitivity analysis for the near-ignition state based on both mechanisms identified the deficiencies of the 1998-mechanism, in particular, the specifics of the low-temperature cool flame chemistry in effecting ignition at higher temperatures, as the fuel stream is being progressively heated from its cold boundary to the high-temperature ignition region around the hot-stream boundary. The 2003-mechanism, consisting of 79 species and 398 elementary reactions, was then systematically simplified by using the directed relation graph method to a skeletal mechanism of 49 species and 251 elementary reactions, which in turn was simplified further by using computational singular perturbation method and quasisteady- state species assumption to a reduced mechanism consisting of 33 species and 28 lumped reactions. It was demonstrated that both the skeletal and reduced mechanisms mimicked the performance of the detailed mechanism with high accuracy.
Law, Chung K., and O, C. Kwon, 2004: Effects of Hydrocarbon Substitution on Atmospheric Hydrogen-Air Flame Propagation. International Journal of Hydrogen Energy, 29(8), doi:10.1016/j.ijhydene.2003.09.012 867-879
[ Abstract ]
In order to evaluate the potential of partial hydrocarbon substitution to improve the safety of hydrogen use in general and the performance of internal combustion engines in particular, the outward propagation and development of surface cellular instability of spark-ignited spherical premixed flames of mixtures of hydrogen, hydrocarbon, and air were experimentally studied at NTP condition in a constant-pressure combustion chamber. With methane, ethylene, and propane being the substituents, the laminar burning velocities, the Markstein lengths, and the propensity of cell formation were experimentally determined, while the laminar burning velocities and the associated flame thicknesses were computed using recent kinetic mechanisms. Results show substantial reduction of laminar burning velocities with hydrocarbon substitution, and support the potential of propane as a suppressant of both diffiusional�thermal and hydrodynamic cellular instabilities in hydrogen�air flames. Such a potential, however, was not found for methane and ethylene as substituents.
Zheng, X. L., and Chung K Law, 2004: Ignition of Premixed Hydrogen/Air by Heated Counterflow under Reduced and Elevated Pressures. Combustion and Flame, 136(1-2), doi:10.1016/j.combustflame.2003.09.016 168-179
[ Abstract ]
The temperature of an inert jet required to ignite a counterflowing lean premixed hydrogen/air jet was experimentally determined over the pressure range of 0.6 to 7 atm and computationally simulated using detailed chemistry and transport. Results show that, compared to the homogeneous explosion limits, ignition takes place at higher temperatures and exhibits five limits over the pressure range investigated. The first and second ignition limits resemble the corresponding first and second homogeneous explosion limits, except they have steeper slopes in the pressure�temperature response, with the first limit being affected by the significant transport loss of the H radical and the second limit modified by the activation of the otherwise metastable HO₂ radicals by the diffusively enriched H₂. The third and fifth ignition limits are respectively manifestations of the lowand high-pressure responses of the third homogeneous explosion limit behavior, which is nevertheless punctuated by the fourth ignition limit characterized by the HO₂�H reactions. Furthermore, the fourth ignition limit runs fairly parallel to the crossover temperature, but is shifted to lower temperatures. An explicit expression, 2k₁ = {2k₁₀/(k₁₀ +k₁₁)}k₉[M], was derived and found to describe well this limit as well as the extended second limit observed in previous flow reactor studies. It is further shown that, since transport effects are inherently important for the present premixed system because of the diffusive loss of H to the hot, inert side of the counterflow, the ignition temperature increases substantially with increasing strain rate at all pressures and that such a sensitivity can be moderated by doping the inert flow with a small amount of oxygen.
Blouch, J. D., J. Y. Chen, and Chung K Law, 2003: A Joint Scalar PDF Study of Nonpremixed Hydrogen Ignition. Combustion and Flame, 135(3), doi:10.1016/S0010-2180(03)00160-3 209-225
[ Abstract ]
A two-step process was adopted to model turbulent ignition that takes advantage of the possibility of decoupling the mechanical flow from chemical reaction due to the small amount of heat release before ignition. In the first step, a Reynolds stress model is employed to calculate a chemically frozen, turbulent counterflow. The second step models the ignition event by solving a joint scalar PDF equation using a Monte Carlo technique. The frozen velocity field is used to initialize the PDF model and to govern its evolution. As observed in previous DNS calculations, ignition occurs at a �most reactive� mixture fraction. The present calculations indicated that turbulence intensity had little effect on ignition temperatures, which were about 30 K higher than, but parallel to, laminar ignition temperatures. Similar results were found for both the IEM and modified Curl�s mixing model. Turbulent ignition temperatures were similar to laminar ones when the mixing model was modified to account for preferential diffusion. These results are different from turbulent ignition experiments since the experiments did indicate a turbulent intensity effect on ignition of up to 35 K. These discrepancies were attributed to shortcomings in the molecular mixing models in the flows of interest where the turbulent Reynolds numbers are low. A potential source of this problem was identified as the representation of the scalar mixing frequency as a constant ratio of the scalar to flow time.
Kwon, O, C., G. Rozenchan, and Chung K Law, 2002: Cellular Instabilities and Self-Acceleration of Outwardly Propagating Spherical Flames. Proceedings of the Combustion Institute, 29(2), doi:10.1016/S1540-7489(02)80215-2 1775-1784
[ Abstract ]
Using a recently developed constant and high-pressure combustion chamber, an experimental study was conducted on several aspects of cellular instabilities of outwardly propagating spherical premixed flames. Propane/air and hydrogen/oxygen/nitrogen flames of different concentrations and under elevated pressures were used to systematically identify the influences of thermal expansion ratio, flame thickness, global activation energy, mixture Lewis number, and global stretch rate on the generation of hydrodynamic and diffusional-thermal cells over the flame surface. In particular, it was demonstrated that hydrodynamic instability is greatly enhanced with increasing pressure and hence decreasing flame thickness, although the influence can also be moderated by the progressively important three-body termination reactions as the pressure increases. The onset of cellular instability was examined in light of the theory of Bechtold and Matalon, and satisfactory qualitative and acceptable quantitative comparisons were observed. The cellular flames were found to be self-accelerating, including those that are diffusionally unstable, with fractal dimensions between 2.20 and 2.25.
Yuan, J., S. D. Tse, and Chung K Law, 2002: Dynamics of Flame Ball Formation from Localized Ignition: Effects of Elevated Pressure and Temperature. Proceedings of the Combustion Institute, 29(2), doi:10.1016/S1540-7489(02)80305-4 2501-2507
[ Abstract ]
A computational study was conducted on expanding spherical premixed flames to investigate the dynamics of flame-ball formation at elevated temperatures and pressures. Lean H₂/air mixtures were investigated using a time-dependent, spherically symmetric code with detailed chemistry, transport, and radiation submodels. Results show that, with increasing pressure, both the steady-state flame-ball radius and the H₂ consumption rate for a given mixture composition decrease monotonically up to 50 atm, varying approximately as p^-0.57. Furthermore, a window of pulsating flame behavior, near the upper dynamic flame-ball limit, was discovered and investigated. Within this window, an outwardly propagating flame begins to self-extinguish due to radiative losses but revives suddenly due to low-Lewis-number effects and evolves into a flame ball. More than one such cycle of behavior can occur for a given mixture concentration. Results further show that as the ambient mixture temperature is increased, the initial trend is a downward shift of the upper dynamic flame-ball limit. With reduced radiative loss, spherical flames continue to propagate outwardly for leaner mixture compositions without degenerating into flame balls, but at the same time, expand themselves into radiative extinction. Again, the role of radiative loss as both the requisite mechanism for and the limiting mechanism against the dynamic transformation of spherically propagating flames into flame balls is emphasized. Nonetheless, as the ambient temperature is increased to near 700 K (in an attempt to investigate the boundary defining the flameless combustion regime), steady flame balls are no longer attainable, with chemical reactions occurring at the boundary.
Zheng, X. L., J. D. Blouch, D. L. Zhu, Thomas Kreutz, and Chung K Law, 2002: Ignition of Premixed Hydrogen/Air in Heated Counterflow. Proceedings of the Combustion Institute, 29(2), doi:10.1016/S1540-7489(02)80201-2 1637-1644
[ Abstract ]
The inert temperature required to ignite a lean premixed hydrogen/air mixture in a counterflow was determined experimentally and numerically using detailed chemistry and transport. It was found that above Φ = 0.2, the ignition temperatures increased with increasing equivalence ratio. This effect is due to the fact that the ignition kernel is located on the hot, inert side of the flow and preferential diffusion of hydrogen makes the flow self-stratifying, resulting in a rich mixture in the ignition kernel even for a very lean freestream mixture. The dearth of O₂ in the kernel reduces the reaction rates to the point where diffusive loss becomes significant relative to the rates of kinetic production and consumption. In the presence of this significant transport loss mechanism, premixed ignition temperatures are much higher than non-premixed ignition temperatures and the influence of the strain rate is likewise increased. Adding a few percent of O₂ to the hot inert side of the flow lowers the kernel equivalence ratio and increases the reaction rates to the point where diffusive effects are no longer of the same order as kinetic effects. In these cases, the ignition temperatures drop significantly to values close to those of non-premixed ignition even though the free-stream flow is still predominantly premixed.

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