Autoignition of reacting mixtures at engine-relevant conditions using confined spherically expanding flames

Propagation of a confined spherically expanding flame induces isentropic compression that can culminate in autoignition and/or detonation under conducive thermodynamic conditions. This relatively simple technique measures a distinct ‘characteristic ignition delay time’ and complements other established approaches such as the rapid compression machine and shock tube. The present study details this methodology by examining the autoignition characteristics of dimethyl-ether/oxygen/nitrogen/helium reactive mixtures for equivalence ratios of 0.6 and 0.9, an initial temperature of 468 K, and initial pressures of 3 to 6 atm. The experimental results display the classic two-stage ignition typical of dimethyl-ether oxidation at low-temperatures with first-stage ignition occurring at approximately 3.6 times the initial pressure. To aid in the interpretation of the experimental results, two numerical models were used: a zero-dimensional batch reactor model, which accepts experimental pressure-time history and calculates the sensitivities of characteristic ignition delay times to kinetics, and a low Mach number, Lagrangian one-dimensional code that was developed to model both flame propagation and end-gas autoignition. Simulation results were shown to adequately capture the physics of unsteady flame propagation, end-gas autoignition, and the controlling reactions of the latter. It was found also that under certain conditions the behavior of first and second ignition stages could be modified by unsteady pressure effects.     

Coupling of turbulence on the ignition of multicomponent sprays

This study examines the effect of turbulence on the ignition of multicomponent surrogate fuels and its role in modifying preferential evaporation in multiphase turbulent spray environments. To this end, two zero-dimensional droplet models are considered that are representative of asymptotic conditions of diffusion limit and the distillation limit are considered. The coupling between diffusion, evaporation and combustion is first identified using a scale analysis of 0D homogeneous batch reactor simulations. Subsequently, direct numerical simulations of homogeneously dispersed multicomponent droplets are performed for both droplet models, in decaying isotropic turbulence and at quiescent conditions to examine competing time scale effects arising from evaporation, ignition and turbulence. Results related to intra-droplet transport and effects of turbulence on autoignition and overall combustion are studied using an aviation fuel surrogate. Depending on the characteristic scale, it is shown that turbulence can couple through modulation of evaporation time or defer the ignition phase as a result of droplet cooling or gas-phase homogenization. Both preferential evaporation and turbulence are found to modify the ignition delay time, up to a factor of two. More importantly, identical droplet ignition behavior in homogeneous gas phase can imply fundamentally different combustion modes in heterogeneous environments.     

Autoignition delay modulation by high-frequency thermoacoustic oscillations in reheat flames

This paper investigates the sensitivity of the autoignition delay in reheat flames to acoustic pulsations associated with high-frequency transverse thermoacoustic oscillations. A reduced order model for the response of purely autoignition-stabilised flames to acoustic disturbances is compared with experimental observations. The experiments identified periodic flame motion associated with high-amplitude transverse limit-cycle oscillations in an atmospheric pressure reheat combustor. This flame motion was assumed to be the result of a superposition of two flame-acoustic coupling mechanisms: autoignition delay modulation by the oscillating acoustic field and displacement and deformation of the flame by the acoustic velocity. The reduced order model coupled to reaction kinetics calculations reveals that a significant portion of the observed flame motion can be attributed to autoignition delay modulation. The ignition position responds instantaneously to the acoustic pressure at the time of ignition, as observed experimentally. The model also provides insight into the importance of the history of acoustic disturbances experienced by the fuel-air mixture prior to ignition. Due to the high-frequency nature of the instability, a fluid particle can experience multiple oscillation cycles before ignition. The ignition delay responds in-phase with the net-acoustic perturbation experienced by a fluid particle between injection and ignition. These findings shed light on the underlying mechanisms of the flame motion observed in experiments and provide useful insight into the importance of autoignition delay modulation as a driving mechanism of high-frequency thermoacoustic instabilities in reheat flames.     

Cellular Biology in Terms of Stochastic Nonlinear Biochemical Dynamics: Emergent Properties,Isogenetic Variations and Chemical System Inheritability

Based on a stochastic, nonlinear, open biochemical reaction system perspective, we present an analytical theory for cellular biochemical processes. The chemical master equation (CME) approach provides a unifying mathematical framework for cellular modeling. We apply this theory to both self-regulating gene networks and phosphorylation-dephosphorylation signaling modules with feedbacks. Two types of bistability are illustrated in mesoscopic biochemical systems: one that has a macroscopic, deterministic counterpart and another that does not. In certain cases, the latter stochastic bistability is shown to be a “ghost” of the extinction phenomenon. We argue the thermal fluctuations inherent in molecular processes do not disappear in mesoscopic cell-sized nonlinear systems; rather they manifest themselves as isogenetic variations on a different time scale. Isogenetic biochemical variations in terms of the stochastic attractors can have extremely long lifetime. Transitions among discrete stochastic attractors spend most of the time in “waiting”, exhibit punctuated equilibria. It can be naturally passed to “daughter cells” via a simple growth and division process. The CME system follows a set of nonequilibrium thermodynamic laws that include non-increasing free energy F(t) with external energy drive Q _hk ≥0, and total entropy production rate e _p =−dF/dt+Q _hk ≥0. In the thermodynamic limit, with a system’s size being infinitely large, the nonlinear bistability in the CME exhibits many of the characteristics of macroscopic equilibrium phase transition.     

Delay time for fine particle ignition within gas with fluctuating temperature

The Pontryagin equation was applied to calculating the average time for the random process escaping the assign interval: this gives the average delay time for waiting of particle ignition moment in a turbulent flow of gas. A direct numerical simulation method was developed for gas temperature fluctuations with assigned autocorrelation function and particle temperature fluctuations due to exothermal chemical reaction. The method was based on numerical solution of a system of stochastic differential equations. Results of direct simulation were validated through comparing with the analytical solution available for particles without exothermal reaction. Analytical calculations and results of direct numerical simulation for the delay time of particle ignition are in agreement.     

Free energy self-averaging in protein-sized random heteropolymers

Current theories of heteropolymers are inherently macroscopic, but are applied to mesoscopic proteins. To compute the free energy over sequences, one assumes self-averaging--a property established only in the macroscopic limit. By enumerating the states and energies of compact 18, 27, and 36mers on a lattice with an ensemble of random sequences, we test the self-averaging approximation. We find that fluctuations in the free energy between sequences are weak, and that self-averaging is valid at the scale of real proteins. The results validate sequence design methods which exponentially speed up computational design and simplify experimental realizations.     

Direct numerical simulations of exhaust gas recirculation effect on multistage autoignition in the negative temperature combustion regime for stratified HCCI flow conditions by using H2O2 addition

Direct numerical simulations (DNSs) of a stratified flow in a homogeneous compression charge ignition (HCCI) engine are performed to investigate the exhaust gas recirculation (EGR) and temperature/mixture stratification effects on the autoignition of synthetic dimethyl ether (DME) in the negative temperature combustion region. Detailed chemistry for a DME/air mixture is employed and solved by a hybrid multi-time scale (HMTS) algorithm to reduce the computational cost. The effect of to mimic the EGR effect on autoignition are studied. The results show that adding enhances autoignition by rapid OH radical pool formation (34–46% reduction in ignition delay time) and changes the ignition heat release rates at different ignition stages. Sensitivity analysis is performed and the important reactions pathways affecting the autoignition are specified. The DNS results show that the scales introduced by thermal and mixture stratifications have a strong effect after the low temperature chemistry (LTC) ignition especially at the locations of high scalar dissipation rates. Compared to homogenous ignition, stratified ignitions show similar first autoignition delay times, but 18% reduction in the second and third ignition delay times. The results also show that molecular transport plays an important role in stratified low temperature ignition, and that the scalar mixing time scale is strongly affected by local ignition in the stratified flow. Two ignition-kernel propagation modes are observed: a wave-like, low-speed, deflagrative mode and a spontaneous, high-speed, ignition mode. Three criteria are introduced to distinguish these modes by different characteristic time scales and Damkhöler numbers using a progress variable conditioned by an ignition kernel indicator. The low scalar dissipation rate flame front is characterized by high displacement speeds and high mixing Damkhöler number. The proposed criteria are applied successfully at the different ignition stages and approximate characteristic values are identified to delineate between the different ignition propagation modes.     

Local Thermodynamic Equilibrium for some Stochastic Models of Hamiltonian Origin

We consider a class of 1-D stochastic models that are realizations of Hamiltonian models of heat conduction and prove that in the infinite volume limit local thermodynamic equilibrium is attained with linear energy profile.     

Parity effects in eigenvalue correlators, parametric and crossover correlators in random matrix models: Application to mesoscopic systems

This paper summarizes some work that I have been doing on eigenvalue correlators of random matrix models which show some interesting behavior. First we consider matrix models with gaps in their spectrum or density of eigenvalues. The density-density correlators of these models depend on whether N, where N is the size of the matrix, takes even or odd values. The fact that this dependence persists in the large N thermodynamic limit is an unusual property and may have consequences in the study of one electron effects in mesoscopic systems. Secondly, we study the parametric and cross correlators of the Harish Chandra-Itzykson-Zuber matrix model. The analytic expressions determine how the correlators change as a parameter (e.g. the strength of a perturbation in the Hamiltonian of the chaotic system or external magnetic field on a sample of material) is varied. The results are relevant for the conductance fluctuations in disordered mesoscopic systems.     

Autoignition and combustion of hydrocarbon-hydrogen-air homogeneous and heterogeneous ternary mixtures

A numerical simulation of the ignition and combustion of hydrocarbon-hydrogen-air homogeneous and heterogeneous (gas-drop) ternary mixtures for three hydrocarbon fuels (n-heptane, n-decane, and n-dodecane) is for the first time performed. The simulation is carried out based on a fully validated detailed kinetic mechanism of the oxidation of n-dodecane, which includes the mechanisms of the oxidation of n-decane, n-heptane, and hydrogen as constituent parts. It is demonstrated that the addition of hydrogen to a homogeneous or heterogeneous hydrocarbon-air mixture increases the total ignition delay time at temperatures below 1050 K, i.e., hydrogen acts as an ignition inhibitor. At low temperatures, even ternary mixtures with a very high hydrogen concentration show multistage ignition, with the temperature dependence of the ignition delay time exhibiting a negative temperature coefficient region. Conversely, the addition of hydrogen to homogeneous and heterogeneous hydrocarbon-air mixtures at temperatures above 1050 K reduces the total ignition delay time, i.e., hydrogen acts as an autoignition promoter. These effects should be kept in mind when discussing the prospects for the practical use of hydrogen-containing fuel mixtures, as well as in solving the problems of fire and explosion safety.     

Experimental and modeling study of the autoignition characteristics of commercial diesel under engine-relevant conditions

Knowledge of the autoignition characteristics of diesel fuels is of great importance for understanding the combustion performance in engines and developing surrogate fuels. Here ignition delays of China's stage 6 diesel, a commercial fuel, were measured in a heated rapid compression machine (RCM) under engine-relevant conditions. Gas-phase autoignition experiments were carried out at equivalence ratios ranging from 0.37 to 1.0, under compressed pressures of 10, 15, and 20?bar, and within a temperature range of 685–865?K. In all investigated conditions, negative temperature coefficient (NTC) behavior of the total ignition delays is observed. The autoignition of the diesel fuel exhibits pronounced two-stage characteristics with strong low-temperature reactivity. Experimental results indicate that the total ignition delays shorten with increasing compressed pressure, oxygen mole fraction and fuel mole fraction. The first-stage ignition delays are mainly controlled by compressed temperature and also affected by oxygen mole fraction and compressed pressure but show a very weak dependence on fuel mole fraction. Correlations describing the first-stage ignition delay and the total ignition delay were proposed to further clarify the ignition delay dependence on the multiple factors. Additionally, it is found that the newly measured ignition delays well coincide with and complement the diesel ignition data in the literature. A recently developed diesel mechanism was used to simulate the diesel autoignition on the RCM. The simulation results are found to agree well the experimental measurements over the whole temperature ranges. Species concentration analysis and brute force sensitivity analysis were also conducted to identify the crucial species and reactions controlling the autoignition of the diesel fuel.     

Diethoxymethane as tailor-made fuel for gasoline controlled autoignition

Within the cluster of excellence “Tailor-Made Fuels from Biomass”  diethoxymethane (DEM) was identified as a promising fuel candidate from a production perspective. Synthesized by combining a bio-based feedstock and $C{O}_2$ as carbon source together with “green hydrogen” from water electrolysis DEM is defined as “bio-hybrid fuel” . To determine the molecules general applicability to a combustion system and to develop up combustion models a rapid screening of the ignition characteristics is performed in a rapid compression machine and a shock tube. Those suggest DEM being a potential fuel for gasoline controlled autoignition (GCAI) because of a relatively wide range of temperature independent ignition delay, a good autoignition behavior compared to conventional gasoline fuel and a multi-stage ignition behavior. To test the suitability of those molecules as a fuel and determine possible improvements to the production side, DEM was used in a single cylinder research engine operated in GCAI combustion mode. Compared to GCAI combustion with conventional RON95 E10 fuel, DME shows a significantly decreased ignition delay. As a consequence, the internal residual gas fraction, whose enthalpy is used to initiate autoignition, can be reduced and combustion stability is increased. Starting from similar combustion phasing using external exhaust gas recirculation to align the ignition behavior of DEM and RON95 E10, a variation of the intake temperature reveals that DEM has the potential to reduce the sensitivity of the combustion system.     

Random walk and diffusion in a stochastic lattice gas model

The time evolution of the stochastic lattice gas with simple exclusion interaction is shown to converge in the thermodynamic limit and it is studied in the asymptotic regime of large time. The diffusion equation applies to the bulk transport of matter in an appropriate scaling limit. As regards the one-dimensional model, a conjecture by Spitzer is proved, stating that the distance travelled by a tagged particle is of the order of the fourth root of the elapsed time.Asymptotic exponents β and α are defined for more general models as giving the power law in time for the distances travelled by density fluctuations and tagged particles respectively. It is argued that α = β/2 should be valid for all one-dimensional models with exclusion.     

Gas-phase autoignition of a spherical volume of fuel in an oxidative medium

A mathematical model of the ignition of unmixed of fuel and oxidizer (a finite spherical volume of fuel surrounded by an infinite oxidizer medium) was developed. The regularities of the autoignition of this system were examined. It was demonstrated that the temperature maximum arising at the fuel-oxidizer interface propagates with increasing amplitude and velocity toward the center of the spherical volume and that the time it takes to attain the maximum temperature (below the autoignition threshold) and the ignition delay time (above the threshold) depend on the parameter δ nonmonotonically, more specifically, exhibit well-pronounced maxima     

Effects of temperature and equivalence ratio on the ignition of n-heptane fuel spray in turbulent flow

Direct numerical simulations were performed to study the autoignition process of n-heptane fuel spray in a turbulent field. For the solution of the carrier gas fluid, the Eulerian method is employed, while for the fuel droplets, the Lagrangian method is used. Droplets are initialized at random locations in a two-dimensional isotropic turbulent field. A chemistry mechanism for n-heptane with 44 species and 112 reactions was adopted to describe the chemical reactions. Three cases with the same initial global equivalence ratio (0.5) and different initial gas phase temperatures (1100, 1200, and 1300 K) were simulated. In addition, two cases with initial global equivalence ratios of 1.0 and 1.5 and initial temperature 1300 K were simulated to examine the effect of equivalence ratio. Evolution of temperature, species mass fraction, reaction rate, and the joint PDF of temperature and equivalence ratio are presented. Effects of the initial gas temperature and equivalence ratio on vaporization and ignition are discussed. A correlation was derived relating ignition delay times to temperature and equivalence ratio. It was confirmed that with the increase of initial temperature, the autoignition occurs earlier. With the increase of the initial equivalence ratio, however, autoignition occurs later due to a larger decrease in gas phase temperature caused by fuel droplet evaporation. The results obtained in this study are expected to be constructive in understanding fuel spray combustion, such as that in homogeneous charge compression ignition systems.     

Fluctuation relations and rare realizations of transport observables

Fluctuation relations establish rigorous identities for the nonequilibrium averages of observables. Starting from a general transport master equation with time-dependent rates, we employ the stochastic path integral approach to study statistical fluctuations around such averages. We show how under nonequilibrium conditions, rare realizations of transport observables are crucial and imply massive fluctuations that may completely mask such identities. Quantitative estimates for these fluctuations are provided. We illustrate our results on the paradigmatic example of a mesoscopic RC circuit.     

On the stochastic dynamics of Ising models

With the help of recent results in the mathematical theory of master equations, we present a rigorous derivation of the stochastic Glauber dynamics of Ising models from Hamiltonian quantum mechanics. A thermal bath is explicitly constructed and, as an illustration, the dynamics of the Ising-Weiss model is analyzed in the thermodynamic limit. We thus obtain an example of a nonequilibrium statistical mechanical system for which a link without mathematical gap can be established from microscopic quantum mechanics to a macroscopic irreversible thermodynamic process.     

H2/air autoignition: The nature and interaction of the developing explosive modes

Appropriate algorithmic tools are employed for the analysis of the explosive modes developing during the autoignition of homogeneous mixtures. The ability of these tools to provide significant physical understanding is demonstrated in the case of the homogeneous ignition of a stoichiometric H₂/air mixture, modelled by two different chemical kinetics mechanisms. It is shown that the ignition process evolves in two stages. The first stage is characterised by the development of two explosive timescales (one fast and one slow), that lead the system away from equilibrium. As the end of the first stage is approached, the two explosive timescales converge, they merge and then they disappear. In the second stage only dissipative timescales develop, which drive the system all the way to equilibrium. It is shown that throughout the first stage the fast explosive timescale is generated by chain reactions. The slow explosive timescale is initially generated by an initiation reaction that produces the radicals required for the start-up of the fast mode, while later on it is generated by reactions that are responsible for the heat released. These findings are validated with sensitivity analysis results for the ignition delay time and are employed in order to clarify the discrepancies in the solution provided by the two different chemical kinetics mechanisms considered.     

An experimental and modeling study of the autoignition of 3-methylheptane

An experimental and kinetic modeling study of the autoignition of 3-methylheptane, a compound representative of the high molecular weight lightly branched alkanes found in large quantities in conventional and synthetic aviation kerosene and diesel fuels, is reported. Shock tube and rapid compression machine ignition delay time measurements are reported over a wide range of conditions of relevance to combustion engine applications: temperatures from 678 to 1356 K; pressures of 6.5, 10, 20, and 50 atm; and equivalence ratios of 0.5, 1.0, and 2.0. The wide range of temperatures examined provides observation of autoignition in three reactivity regimes, including the negative temperature coefficient (NTC) regime characteristic of paraffinic fuels. Comparisons made between the current ignition delay measurements for 3-methylheptane and previous results for n-octane and 2-methylheptane quantifies the influence of a single methyl substitution and its location on the reactivity of alkanes. It is found that the three C₈ alkane isomers have indistinguishable high-temperature ignition delay but their ignition delay times deviate in the NTC and low-temperature regimes in correlation with their research octane numbers. The experimental results are compared with the predictions of a proposed kinetic model that includes both high- and low-temperature oxidation chemistry. The model mechanistically explains the differences in reactivity for n-octane, 2-methylheptane, and 3-methylheptane in the NTC through the influence of the methyl substitution on the rates of isomerization reactions in the low-temperature chain branching pathway, that ultimately leads to ketohydroperoxide species, and the competition between low-temperature chain branching and the formation of cyclic ethers, in a chain propagating pathway.     

Dissipative behavior of a quantum system interacting with a macroscopic medium

The modified Coleman-Hepp (AgBr) model describes the interaction between an ultrarelativistic quantum mechanical particle Q and an N-spin array D (a macroscopic medium in the N → ∞ limit). We prove that the energy operator for D essentially behaves as a Wiener process in the weak-coupling, macroscopic limit, in a restricted state space. No assumptions are made on the spectrum of the Hamiltonian of the macroscopic system D. The mechanism of appearance of such a stochastic process and its relevance to issues like dissipation and irreversibility are briefly discussed.