Dovich Mechanism Research Articles

Amplification of electromagnetic fields by a rotating body

In 1971, Zel’dovich predicted the amplification of electromagnetic (EM) waves scattered by a rotating metallic cylinder, gaining mechanical rotational energy from the body. This phenomenon was believed to be unobservable with electromagnetic fields due to technological difficulties in meeting the condition of amplification that is, the cylinder must rotate faster than the frequency of the incoming radiation. Here, we measure the amplification of an electromagnetic field, generated by a toroid LC-circuit, scattered by an aluminium cylinder spinning in the toroid gap. We show that when the Zel’dovich condition is met, the resistance induced by the cylinder becomes negative implying amplification of the incoming EM fields. These results reveal the connection between the concept of induction generators and the physics of this fundamental physics effect and open new prospects towards testing the Zel’dovich mechanism in the quantum regime, as well as related quantum friction effects.

Detonation development in hydrogen/air mixtures inside a closed chamber: role of a cold wall

Detonation development from a hot spot has been extensively studied, where ignition occurs earlier than that in the surrounding mixtures. It has also been reported that a cool spot can induce detonation for large hydrocarbon fuels with Negative Temperature Coefficient (NTC) behavior, since ignition could happen earlier at lower temperatures. In this work we find that even for hydrogen/air mixtures without NTC behaviors, a cold wall can still initiate and promote detonation. End-wall reflection of the pressure wave and wall heat loss introduce an exothermic center outside the boundary layer, and then autoignitive reaction fronts on both sides may evolve into detonation waves. The right branch can be further strengthened by appropriate temperature gradient near the cold wall, and exhibits different dynamics at various initial conditions. The small excitation time and the large diffusivity of hydrogen provide the possibility for detonation development within the limited space between the autoignition kernel and the cold wall. Moreover, detonation may also develop near the flame front, which may or may not co-exist with detonation waves from the cold wall. Correspondingly, wall heat flux evolution exhibits different responses to detailed dynamic structures. Finally, we propose a regime diagram describing different combustion modes including normal flame, autoignition, and detonation from the wall and/or the reaction front. The boundary of normal flame regime qualitatively agrees with the prediction by the Livengood-Wu Integral method, while the detonation development from both the end wall and the reaction front observes Zel'dovich mechanism. Compared to hydrocarbons, hydrogen is resistant to knock onset but it is more prone to superknock development. The latter mode becomes more destructive in the presence of wall heat loss. This study isolates and identifies the role of wall heat loss on a potential mechanism for superknock development in hydrogen-fueled spark-ignition engines.

Facilitated ignition and detonation initiation of hydrogen-oxygen mixtures by ozone doping

This work computationally studies homogeneous and inhomogeneous ozone addition in hydrogen-oxygen ignition and transition to detonation, with emphasis on the ozone-induced two-stage behaviors in the chemical kinetics and wave dynamics. In 0D homogenous ignitions, ozone addition induces an additional first-stage reaction and substantially reduces the ignition delay time (IDT). At intermediate initial temperatures, e.g. T0 = 600 K, a critical value, αcr, is identified to delineate different regimes for ozone fraction in the total oxidizer, α. Specifically, the first-stage ignition occurs several orders earlier than IDT for α<αcr, while the IDTs for two stages are comparable for α>αcr. Mechanistically, low-to-intermediate temperature HO2 chemistry introduces a quasi-steady intermediate state in the former regime, whereas ozone reactions directly accelerate high-temperature H2O2 reactions in the latter one. Furthermore, according to the Zel'dovich mechanism, ozone concentration non-uniformity can establish reactivity gradient and hence further initiate double spontaneous waves with multiple dynamics. Coherent coupling between the second-stage heat release and pressure (shock) wave can further evolve into detonation, whereas such synchronized enhancement is not observed in the first-stage ignition due to its large excitation time. Corresponding to the multi-timescales in 0D ignition, when the initial α interval are respectively below, across and above αcr, the low- and high- temperature reaction fronts always separate, first separate then merge, and always merge, respectively. It is also noted that at higher initial temperatures αcr decreases, and that the first-stage reaction becomes less concentrated. Consequently, detonation can be initiated with smaller amounts of ozone and is minimally influenced by the first-stage reaction.

Rovibrational-Specific QCT and Master Equation Study on N2(X1Σg+) + O(3P) and NO(X2Π) + N(4S) Systems in High-Energy Collisions.

This work presents a detailed investigation of the energy-transfer and dissociation mechanisms in N2(X1Σg+) + O(3P) and NO(X2Π) + N(4S) systems using rovibrational-specific quasiclassical trajectory (QCT) and master equation analyses. The complete set of state-to-state kinetic data, obtained via QCT, allows for an in-depth investigation of the Zel'dovich mechanism leading to the formation of NO molecules at microscopic and macroscopic scales. The master equation analysis demonstrates that the low-lying vibrational states of N2 and NO have dominant contributions to the NO formation and the corresponding extinction of N2 through the exchange process. For the considered temperature range, it is found that nearly 50% of the dissociation processes for N2 and NO molecules occur in the quasi-steady-state (QSS) regime, while for the Zel'dovich reaction, the distribution of the reactants does not reach the QSS conditions. Furthermore, using the QSS approximation to model the Zel'dovich mechanism leads to overestimating NO production by more than a factor of 4 in the high-temperature range. The breakdown of this well-known approximation has profound consequences for the approaches that heavily rely on the validity of QSS assumption in hypersonic applications. Finally, the investigation of the rovibrational state population dynamics reveals substantial similarities among different chemical systems for the energy-transfer and the dissociation processes, providing promising physical foundations for the use of reduced-order strategies in other chemical systems without significant loss of accuracy.

Effective indicators of a hydrogen engine operating on a lean mixture and equipped with a modified fuel supply system

Introduction (problem statement and relevance). Limited oil reserves and tightening environmental standards are forcing engine manufacturers to switch to alternative fuels in the near future, among which hydrogen is the most promising. The advantages of hydrogen are high specific heat of combustion and high combustion rate. Wide concentration limits of hydrogen combustion make it possible to use high-quality power control, thereby providing an increase in the efficiency of a hydrogen engine when compared to the basic internal combustion engine.The purpose of the study was to ensure the operation of a serial gasoline engine running on hydrogen with a new experimental fuel supply system, as well as the modification of the intake manifold design without abnormal phenomena during combustion when operating on a lean mixture, and to obtain efficient and ecological characteristics of a hydrogen engine under bench test conditions, as a result.Methodology and research methods. The work is experimental, the reliability of the results obtained is confirmed by the use of modern means for measuring and processing experimental data. The obtained results of measuring nitrogen oxides are adequate to the known Zel'dovich thermal mechanism. The value of the results lies in the fact that they show the feasibility of transferring serial internal combustion engines to hydrogen; in addition, these results are used to develop and verify mathematical 3D models of the hydrogen engine working process.Scientific novelty and results. A new system providing the necessary characteristics (pressure, duration and cycle dose) for supplying hydrogen to the intake system with two injectors for each cylinder was designed, installed and tested on the prototype engine.Practical significance. The expediency of the working cycle creation and efficiency of a hydrogen engine with an experimental lean-burn fuel supply system was confirmed, which made it possible to provide high-quality power control with external mixture formation and forced ignition.

Direct numerical simulation of a hypersonic transitional boundary layer at suborbital enthalpies

Abstract

Type Ia supernovae deflagration-to-detonation transition explosions powered by the Zel’dovich reactivity gradient mechanism

ABSTRACT Our aim in this work is to identify and explain the necessary conditions required for an energetic explosion of a Chandrasekhar-mass white dwarf. We construct and analyse weakly compressible turbulence models with nuclear burning effects for carbon/oxygen plasma at a density expected for the deflagration-to-detonation transition (DDT) to occur. We observe the formation of carbon deflagrations and transient carbon detonations at early times. As turbulence becomes increasingly inhomogeneous, sustained carbon detonations are initiated by the Zel’dovich reactivity gradient mechanism. The fuel is suitably preconditioned by the action of compressive turbulent modes with wavelength comparable to the size of resolved turbulent eddies; no acoustic wave is involved in this process. Oxygen detonations are initiated, aided either by reactivity gradients or by collisions of carbon detonations. The observed evolutionary time-scales are found to be sufficiently short for the above process to occur in the expanding, centrally ignited massive white dwarf. The inhomogeneous conditions produced prior to the DDT might be of consequence for the chemical composition of the outer ejecta regions of Type Ia supernovae from the single degenerate channel, and offer the potential for validation of the proposed model.

Experimental investigation of nitrogen oxide emissions from emulsified fuel combustion incorporating a rapid internal mixing injector by using temperature–time scaling

The aim of the present study was to clarify the effect of the operating parameters of the global equivalence, atomizing air, and water content ratios on nitrogen oxide (NOx) emissions from the combustion of emulsified fuel in furnaces incorporating a rapid internal mixing (RIM) injector. NOx concentration was measured at the exit of the furnace, and the temperature distributions were measured using thermocouples. The flame lengths under various conditions were evaluated by analyzing photographic images. On the basis of information on the temperature and flame length, the dominant factors determining the amount of NOx emission were investigated using the temperature–time scaling of NOx. As a result, the dominant factors were found to be the gas temperature in the flame holder and the flame length. The NOx emission index was observed to increase with increasing equivalence ratio; this is due to the increase in the flame length. The atomizing air ratio was found to have little influence on NOx emissions because the increase in the gas temperature in the holder produced by an increase in the atomizing air ratio balances the corresponding decrease in flame length. The water contained in the emulsified fuel significantly reduces NOx emissions because of the reduction in the gas temperature resulting from the latent heat of the water vapor. In addition, NOx scaling also revealed that when water is introduced, the dominant reaction mechanism of NOx production changes from the Zel’dovich mechanism to another mechanism, such as the prompt mechanism.

Investigation of the contribution of homogeneous flame fronts to the formation of NOx in combustion chambers with promising fuel combustion schemes

Specifics of nitrogen oxides formation in conditions of partially mixed combustion in combustion chambers in the presence of diffusion and homogeneous flame fronts are studied. A NOx emission calculation procedure based on detailed kinetics, including all NOx formation mechanisms, is proposed. NOx emission values calculated using the complete detailed kinetics and kinetics containing only the Zel’dovich mechanism are compared. A methodology for estimating the effect of homogeneous flame fronts on NOx emission is proposed and verified. Under conditions of the model problem, a contribution of homogeneous flame fronts to total NOx emission is studied. Combustion conditions with a considerable contribution of homogeneous fronts to total NOx emission are shown.

Influence of chemical kinetics on detonation initiating by temperature gradients in methane/air

Different simplified and detailed chemical models and their impact on simulations of combustion regimes initiating by the initial temperature gradient in methane/air mixtures are studied. The limits of the regimes of reaction wave propagation depend upon the spontaneous wave speed and the characteristic velocities of the problem. The present study mainly focus to identify conditions required for the development a detonation and to compare the difference between simplified chemical models and detailed chemistry. It is shown that a widely used simplified chemical schemes, such as one-step, two-step and other simplified models, do not reproduce correctly the ignition process in methane/air mixtures. The ignition delay times calculated using simplified models are in orders of magnitude shorter than the ignition delay times calculated using detailed chemical models and measured experimentally. This results in considerably different times when the exothermic reaction affects significantly the ignition, evolution, and coupling of the spontaneous reaction wave and pressure waves. We show that the temperature gradient capable to trigger detonation calculated using detailed chemical models is much shallower (the size of the hot spot is much larger) than that, predicted by simulations with simplified chemical models. These findings suggest that the scenario leading to the deflagration to detonation transition (DDT) may depend greatly on the chemical model used in simulations and that the Zel'dovich gradient mechanism is not necessary a universal mechanism triggering DDT. The obtained results indicate that the conclusions derived from the simulations of DDT with simplified chemical models should be viewed with great caution.

Influence of steam addition and elevated ambient conditions on NOx reduction in a staged premixed swirling NH3/H2 flame

There is growing interest in the application of renewably-generated NH3 to support future energy requirements, however combustor designs and strategies require considerable development to reduce NOx emissions in particular. A turbulent swirl burner was used to experimentally and numerically appraise potential pathways for operational NOx reduction with a premixed NH3/H2/air flame. Reactants were supplied at elevated temperature with parametric changes made to pressure and humidity. Favourable agreement was demonstrated between exhaust gas measurements and chemical kinetic simulations with a reactor network model, showing NOx emissions to be sensitive to operational equivalence ratio, increasing by several orders of magnitude across the experimental range. The lowest NOx concentrations were achieved at the richest conditions, accompanied by high unburned fuel fractions in the product stream. An increase in combustor pressure remarkably reduced exhaust NOx concentrations primarily due to enhanced NH2 formation, and subsequent NO consumption in the post-flame zone. Reactant humidification was explored in detail for the first time with this fuel, and shown to reduce NOx production limiting thermal pathways with the extended Zel'dovich mechanism. NO consumption in the post-flame zone was also enhanced through an increase in OH-produced NH2, and together with pressure, resulted in elevated exhaust NH3 concentrations. Whilst this effect was comparatively small, it meant that leaner humidified operation could be employed to reduce unburned fuel fractions without a NOx penalty. Emissions performance was further improved by the application of staged combustion, with secondary airflow used to improve fuel burnout. Humidity and pressure were optimised in the staged configuration to achieve operation with sampled respective NOx and NH3 exhaust fractions of 32 and 50 ppmvd (15%O2), at a globally lean equivalence ratio. There is considerable scope for further system optimisation through improved mixing of secondary air and increased ambient pressure.

Efficacy of Add-On Hydrous Ethanol Dual Fuel Systems to Reduce NOx Emissions From Diesel Engines

Aftermarket dual-fuel injection systems using a variety of different fumigants have been proposed as alternatives to expensive after-treatment to control NOx emissions from legacy diesel engines. However, our previous work has shown that available add-on systems using hydrous ethanol as the fumigant achieve only minor benefits in emissions without recalibration of the diesel fuel injection strategy. This study experimentally re-evaluates a novel aftermarket dual-fuel port fuel injection (PFI) system used in our previous work, with the addition of higher flow injectors to increase the fumigant energy fraction (FEF), defined as the ratio of energy provided by the hydrous ethanol on a lower heating value (LHV) basis to overall fuel energy. Results of this study confirm our earlier findings that as FEF increases, NO emissions decrease, while NO2 and unburned ethanol emissions increase, leading to no change in overall NOx. Peak cylinder pressure and apparent rates of heat release are not strongly dependent on FEF, indicating that in-cylinder NO formation rates by the Zel'dovich mechanism remain the same. Through single zone modeling, we show the feasibility of in-cylinder NO conversion to NO2 aided by unburned ethanol. The modeling results indicate that NO to NO2 conversion occurs during the early expansion stroke where bulk gases have temperature in the range of 1150–1250 K. This work conclusively proves that aftermarket dual fuel systems for fixed calibration diesel engines cannot reduce NOx emissions without lowering peak temperature during diffusive combustion responsible for forming NO in the first place.

Effects of thermal radiation heat transfer on flame acceleration and transition to detonation in particle-cloud hydrogen flames

The current work examines regimes of the hydrogen–oxygen flame propagation and ignition of mixtures heated by radiation emitted from the flame. The gaseous phase is assumed to be transparent for the radiation, while the suspended particles of the dust cloud ahead of the flame absorb and reemit the radiation. The radiant heat absorbed by the particles is then lost by conduction to the surrounding unreacted gaseous phase so that the gas phase temperature lags that of the particles. The direct numerical simulations solve the full system of two phase gas dynamic time-dependent equations with a detailed chemical kinetics for a plane flames propagating through a dust cloud. It is shown that depending on the spatial distribution of the dispersed particles and on the value of radiation absorption length the consequence of the radiative preheating of the mixture ahead of the flame can be either the increase of the flame velocity for uniformly dispersed particles or ignition either new deflagration or detonation ahead of the original flame via the Zel'dovich gradient mechanism in the case of a layered particle-gas cloud deposits. In the latter case the ignited combustion regime depends on the radiation absorption length and correspondingly on the steepness of the formed temperature gradient in the preignition zone that can be treated independently of the primary flame. The impact of radiation heat transfer in a particle-laden flame is of paramount importance for better risk assessment and represents a route for understanding of dust explosion origin.

Slow attractive canonical invariant manifolds for reactive systems

We analyze the efficacy of a standard manifold-based reduction method used to simplify reaction dynamics and find conditions under which the reduction can succeed and fail. In the standard reduction, a heteroclinic trajectory linking saddle and sink equilibria is taken as a candidate reduced manifold which we call a Canonical Invariant Manifold (CIM). We develop and exercise analytic tools for studying the local behavior of trajectories near the CIM. In so doing, we find conditions under which nearby trajectories are attracted to the CIM (ACIM) as well as conditions for which the dynamics on the ACIM are slow (SACIM). The method is demonstrated on a (1) simple model problem, (2) Zel’dovich mechanism for nitric oxide production, and (3) hydrogen–air system. For systems that evolve in a three-dimensional composition space, we find that normal stretching away from the CIM in a volume-shrinking vector field is admitted and that depending on the magnitude of the local rotation rate, may or may not render the CIM to be attractive. The success and failure of the candidate CIM as a SACIM is displayed for the model system. Results for the Zel’dovich mechanism and hydrogen–air systems are less definitive, though for specific conditions a SACIM is identified for both systems.

Evaluation of the nitrogen oxide emission level for a steam supply with natural gas into the combustion chamber of a gas turbine unit

Numerical simulation results on the effect of the operation parameters for a combustion chamber of a combined-cycle plant (CCP) with steam injection [1] for the combined production of heat and electric energy upon a reduction in nitrogen oxide emission are represented. Calculations are carried out for lean mixtures with α = 1.2–1.4 and great steam consumptions of 30–42%. The reaction analysis has shown that the main contribution in NO x formation was given by reactions with the advanced Zel’dovich thermal mechanism, and the reaction contribution with the participation of N2O into the NO formation was an order of magnitude higher than that by the mechanism of the prompt NO formation. NO2 does not form at high temperatures and only takes part in the conversion into NO in reactions with the participation of nitric acid. It is shown that the optimum choice of operation conditions for the combustion chamber of the CCP makes it possible to obtain the NO x content in the combustion products in some mill−1 (ppm). According to calculations, steam injection does not increase CO emission. A comparison with the experiment is given.

Numerical Simulations of Nitric Oxide (NO) Formation in Methane, Methanol and Methyl Formate in different Flow Configurations

Abstrac t—Methane/air, methanol /air and methyl formate /air have been numerically simulated in three different flow configurations: homogeneous system; freely propagating flame; and diffusion flame. These simulations have been done with an aim of establishing the influence of fuel oxygenation on generation of pollutant. Various chemical kinetic mechanisms have been employed and extensively tested so as to ensure validity of the results. For each of the three configurations, a comparison of temperature, NO and its immediate dominant precursor species (CH and N) concentration profiles in the three fuels have been done. It has been established that, under the different flow configurations considered, CH4 has high amou nt of total NO present in the flame region as compared to the oxygenated fuels (CH3OH and CH3OCHO) . The temperatures attained in freely propagating and diffusion flames are relatively low (approximately ≤ 2000 K). This temperature favours prompt-NO formation, and therefore, a significant difference of the amount of NO (one order of magnitude higher) is observed in CH4 as compared to oxygenated fuels due to low values of CH and N observed in these fuels (CH3OH and CH3O CHO). High flame temperatures (approximately 2900 K) due to high initial temperatures are observed in the homogeneous system. Therefore, in homogeneous system it was observed that the amount of NO produced by the three fuels is within the same order of magnitude due to availability of the O atoms and nitrogen molecules (important species in thermal NO mechanism (Zel'dovich mechanism)).

One-Dimensional Slow Invariant Manifolds for Fully Coupled Reaction and Micro-scale Diffusion

The method of slow invariant manifolds (SIMs), applied previously to model the reduced kinetics of spatially homogeneous reactive systems, is extended to systems with diffusion. Through the use of a Galerkin projection, the governing partial differential equations are cast into a finite system of ordinary differential equations to be solved on an approximate inertial manifold. The SIM construction technique of identifying equilibria and connecting heteroclinic orbits is extended by identifying steady state solutions to the governing partial differential equations and connecting analogous orbits in the Galerkin-projected space. In parametric studies varying the domain length, the time scale spectrum is shifted, and various classes of nonlinear dynamics are identified. A critical length scale is identified below which the spatially homogeneous one-dimensional SIM models the long time dynamics of the system. At this critical length scale, a bifurcation in the slow dynamics of the system is identified; additional real nonsingular steady state solutions are found which lead to a diffusion-modified one-dimensional SIM. At these longer lengths, the spectral gap in the time scales indicates that an appropriate manifold for a reduction technique is higher than one-dimensional. This is shown for two examples: a simple chemical reaction mechanism, and the Zel'dovich reaction mechanism of $NO$ production. These examples are evaluated in the spatially homogeneous case (a one-term projection), a two-term projection capturing the coarsest effects of diffusion, and a high-order projection that is fully resolved.

THE DETONATION MECHANISM OF THE PULSATIONALLY ASSISTED GRAVITATIONALLY CONFINED DETONATION MODEL OF Type Ia SUPERNOVAE

We describe the detonation mechanism comprising the "Pulsationally Assisted" Gravitationally Confined Detonation (GCD) model of Type Ia supernovae SNe Ia. This model is analogous to the previous GCD model reported in Jordan et al.(2008); however, the chosen initial conditions produce a substantively different detonation mechanism, resulting from a larger energy release during the deflagration phase. The resulting final kinetic energy and nickel-56 yields conform better to observational values than is the case for the "classical" GCD models. In the present class of models, the ignition of a deflagration phase leads to a rising, burning plume of ash. The ash breaks out of the surface of the white dwarf, flows laterally around the star, and converges on the collision region at the antipodal point from where it broke out. The amount of energy released during the deflagration phase is enough to cause the star to rapidly expand, so that when the ash reaches the antipodal point, the surface density is too low to initiate a detonation. Instead, as the ash flows into the collision region (while mixing with surface fuel), the star reaches its maximally expanded state and then contracts. The stellar contraction acts to increase the density of the star, including the density in the collision region. This both raises the temperature and density of the fuel-ash mixture in the collision region and ultimately leads to thermodynamic conditions that are necessary for the Zel'dovich gradient mechanism to produce a detonation. We demonstrate feasibility of this scenario with three 3-dimensional (3D), full star simulations of this model using the FLASH code. We characterized the simulations by the energy released during the deflagration phase, which ranged from 38% to 78% of the white dwarf's binding energy. We show that the necessary conditions for detonation are achieved in all three of the models.

NO Relaxation Approach (NORA) to predict thermal NO in combustion chambers

In combustion models employing tabulated or global kinetics, the prediction of thermal NO is usually performed by either the direct resolution of Zel’dovich mechanism or the tabulation of the NO reaction rate using a laminar flamelet database and a progress variable representative of the fuel oxidation reactions, for instance temperature or a linear combination of major products mass fractions. It is known that the first method lacks accuracy if radical species such as N or O appearing in the NO reaction rate are not correctly estimated. The second method cannot lead to accurate predictions because NO reactions take place essentially when the fuel oxidation is over, therefore the NO reaction rate shows a very weak correlation with the progress variable. In this paper a new approach called NO Relaxation Approach (NORA), is proposed for the modeling of thermal NO. It allows a high accuracy when coupled with this type of combustion models. With NORA, the NO reaction rate is written as a linear relaxation towards the equilibrium value Y NO eq with a characteristic time τ. Both parameters are tabulated as functions of equivalence ratio, pressure, temperature and dilution mass fraction. NORA is first validated on homogeneous internal combustion engine cases, where it closely fits the complex chemistry results. It is then integrated into the turbulent combustion model ECFM3Z dedicated to piston engine applications. In this model a mixed tabulated (TKI) and global kinetics (CORK) approach is used to describe turbulent combustion. First applications on eight Diesel engine operating points show a good improvement with NORA compared to a classical resolution of Zel’dovich mechanism.

INITIATION OF THE DETONATION IN THE GRAVITATIONALLY CONFINED DETONATION MODEL OF TYPE Ia SUPERNOVAE

We study the initiation of the detonation in the gravitationally confined detonation (GCD) model of Type Ia supernovae (SNe Ia). Initiation of the detonation occurs spontaneously in a region where the length scale of the temperature gradient extending from a flow (in which carbon burning is already occurring) into unburned fuel is commensurate to the range of critical length scales which have been derived from 1D simulations that resolve the initiation of a detonation. By increasing the maximum resolution in a truncated cone that encompasses this region, beginning somewhat before initiation of the detonation occurs, we successfully simulate in situ the first gradient-initiated detonation in a whole-star simulation. The detonation emerges when a compression wave overruns a pocket of fuel situated in a Kelvin-Helmholtz cusp at the leading edge of the inwardly directed jet of burning carbon. The compression wave pre-conditions the temperature in the fuel in such a way that the Zel'dovich gradient mechanism can operate and a detonation ensues. We explore the dependence of the length scale of the temperature gradient on spatial resolution and discuss the implications for the robustness of this detonation mechanism. We find that the time and the location at which initiation of the detonation occurs varies with resolution. In particular, initiation of a detonation had not yet occurred in our highest resolution simulation by the time we ended the simulation because of the computational demand it required. We suggest that the turbulent shear layer surrounding the inwardly directed jet provides the most favorable physical conditions, and therefore the most likely location, for initiation of a detonation in the GCD model.