On the importance of graph search algorithms for DRGEP-based mechanism reduction methods

The importance of graph search algorithm choice to the directed relation graph with error propagation (DRGEP) method is studied by comparing basic and modified depth-first search, basic and R-value-based breadth-first search (RBFS), and Dijkstra’s algorithm. By using each algorithm with DRGEP to produce skeletal mechanisms from a detailed mechanism for n-heptane with randomly-shuffled species order, it is demonstrated that only Dijkstra’s algorithm and RBFS produce results independent of species order. In addition, each algorithm is used with DRGEP to generate skeletal mechanisms for n-heptane covering a comprehensive range of autoignition conditions for pressure, temperature, and equivalence ratio. Dijkstra’s algorithm combined with a coefficient scaling approach is demonstrated to produce the most compact skeletal mechanism with a similar performance compared to larger skeletal mechanisms resulting from the other algorithms. The computational efficiency of each algorithm is also compared by applying the DRGEP method with each search algorithm on the large detailed mechanism for n-alkanes covering n-octane to n-hexadecane with 2115 species and 8157 reactions. Dijkstra’s algorithm implemented with a binary heap priority queue is demonstrated as the most efficient method, with a CPU cost two orders of magnitude less than the other search algorithms.     

Numerical simulation of the upward propagation of a flame in a vertical tube filled with a very lean mixture

Upward propagation of a premixed flame in a vertical tube filled with a very lean mixture is simulated numerically using a single irreversible Arrhenius reaction model with infinitely high activation energy. In the absence of heat losses and preferential diffusion effects, a curved flame with stationary shape and velocity close to those of an open bubble ascending in the same tube is found for values of the fuel mass fraction above a certain minimum that increases with the radius of the tube, while the numerical computations cease to converge to a stationary solution below this minimum mass fraction. The vortical flow of the gas behind the flame and in its transport region is described for tubes of different radii. It is argued that this flow may become unstable when the fuel mass fraction is decreased, and that this instability, together with the flame stretch due to the strong curvature of the flame tip in narrow tubes, may be responsible for the minimum fuel mass fraction. Radiation losses and a Lewis number of the fuel slightly above unity decrease the final combustion temperature at the flame tip and increase the minimum fuel mass fraction, while a Lewis number slightly below unity has the opposite effect.     

LES modeling of premixed combustion using a thickened flame approach coupled with FGM tabulated chemistry

Flamelet Generated Manifolds (FGM) tabulated chemistry is used in combination with a thickened flame approach to perform Large Eddy Simulation (LES) of premixed combustion. Two-dimensional manifolds are used to describe the chemistry by the mixture fraction and progress variable. Simulations of one-dimensional flames have been used to verify the coupling of the tabulated chemistry and the LES solver where important features like the grid dependence of flame propagation are carefully addressed. Finally, the method is applied to the turbulent flame of a premixed swirl burner including the complex geometry of the swirl nozzle. Results of the velocity, species and temperature are compared with experimental data. Thereby different efficiency functions are used to show the sensitivity related to this model parameter. Some aspects regarding dynamic thickening, numerical accuracy and computational efficiency are also addressed.     

Experimental and numerical study of the accuracy of flame-speed measurements for methane/air combustion in a slot burner

Measuring the velocities of premixed laminar flames with precision remains a controversial issue in the combustion community. This paper studies the accuracy of such measurements in two-dimensional slot burners and shows that while methane/air flame speeds can be measured with reasonable accuracy, the method may lack precision for other mixtures such as hydrogen/air. Curvature at the flame tip, strain on the flame sides and local quenching at the flame base can modify local flame speeds and require corrections which are studied using two-dimensional DNS. Numerical simulations also provide stretch, displacement and consumption flame speeds along the flame front. For methane/air flames, DNS show that the local stretch remains small so that the local consumption speed is very close to the unstretched premixed flame speed. The only correction needed to correctly predict flame speeds in this case is due to the finite aspect ratio of the slot used to inject the premixed gases which induces a flow acceleration in the measurement region (this correction can be evaluated from velocity measurement in the slot section or from an analytical solution). The method is applied to methane/air flames with and without water addition and results are compared to experimental data found in the literature. The paper then discusses the limitations of the slot-burner method to measure flame speeds for other mixtures and shows that it is not well adapted to mixtures with a Lewis number far from unity, such as hydrogen/air flames.     

Comprehensive reaction mechanism for n-butanol pyrolysis and combustion

A detailed reaction mechanism for n-butanol, consisting of 263 species and 3381 reactions, has been generated using the open-source software package, Reaction Mechanism Generator (RMG). The mechanism is tested against recently published data – jet-stirred reactor mole fraction profiles, opposed-flow diffusion flame mole fraction profiles, autoignition delay times, and doped methane diffusion flame mole fraction profiles – and newly acquired n-butanol pyrolysis experiments with very encouraging results. The chemistry of butanal is also validated against autoignition delay times obtained in shock tube experiments. A flux and sensitivity analysis for each simulated dataset is discussed and reveals important reactions where more accurate rate constant estimates were required. New rate constant expressions were computed using quantum chemistry and transition state theory calculations. Furthermore, in addition to comparing the proposed model with the eight datasets, the model is also compared with recently published n-butanol models for three of the datasets. Key differences between the proposed model and the published models are discussed.     

Flame lift-off length and soot production of oxygenated fuels in relation with ignition delay in a DI heavy-duty diesel engine

The relation between ignition delay and flame lift-off length (based on OH* chemiluminescence) has been studied in an optically accessible heavy-duty diesel engine. Soot production has been studied as well, using both exhaust soot data and high-speed imaging of the in-cylinder natural luminosity. Since the luminosity is estimated to scale with T¹³ for our experimental conditions, the local temperature becomes a decisive factor in the interpretation of natural luminosity images. The fuels used include regular diesel and blends of various oxygenates (cyclohexanone, anisole, and dibutyl maleate) with synthetic diesel, to cover a wide range of cetane numbers and oxygen content.Based on a literature review, we hypothesize that the flame speed only determines an upper limit for the flame lift-off length (rather than its exact position). Under conditions that promote auto-ignition, the lift-off length may be shorter, and is likely governed by ignition chemistry.For the oxygenated fuels, the flame lift-off length is found to increase with ignition delay. An inverse correlation is found between the soot luminosity and the oxygen ratio at the lift-off length. The anisole-blend does not produce measurable amounts of exhaust soot as long as the injection duration is shorter than the ignition delay. Under cooled EGR-like conditions, the ignition delay is so large that anisole is considered a candidate fuel for soot-free operation of heavy-duty diesel engines up to medium load.     

On the chemical kinetics of cyclopentadiene oxidation

The cyclopentadiene/cyclopentadienyl system forms a critical part in the oxidation chemistry of aromatic fuel components used in surrogate fuels and the importance of the cyclopentadienyl radical in poly-aromatic hydrocarbon (PAH) growth has also been noted due to its site dependent reactivity. The latter aspect has been subject to a number of studies along with the initial pyrolysis steps. By contrast, few studies have been performed of the corresponding oxidation chemistry under conditions of relevance to combustion applications. Thermochemical data for oxidation reactions featuring the cyclopentadienyl radical with O, OH, HO₂ and O₂ were determined at the G3B3 and G4/G4MP2 levels in combination with an analysis of internal rotations using density functional theory and with the Jahn–Teller effect treated as a pseudo-rotation. The calculated potential energy surfaces were subsequently used in a consistent manner for the determination of pressure dependent reaction rate parameters through the Rice–Ramsperger–Kassel–Marcus/master-equation approach with Eckart quantum tunnelling corrections applied to reactions involving hydrogen transfers. The accuracy of the method was further investigated by comparisons of computed rate parameters for pyrolysis reactions with alternative determinations. The resulting chemistry was incorporated into an evaluation framework for the study of cyclopentadiene oxidation using recent experimental flow reactor data and principal uncertainties in reaction pathways assessed.     

Kinetic modeling of counterflow diffusion flames of butadiene

A comprehensive, semi-detailed kinetic scheme was used to simulate the chemical structures of counterflow diffusion and fuel-rich premixed 1,3-butadiene flames, to better understand the formation of polycyclic aromatic hydrocarbons (PAH). The results showed that model predictions were in good agreement with the experiments for most of the species in both the flames. In the counterflow flames higher-molecular weight products are slightly over predicted. The pathways characterizing the pollutant formation are very different in the premixed and in the counterflow flames confirming or suggesting the need to verify and refine the detailed mechanisms tuned for premixed conditions when they are extrapolated and used in diffusion flames. Reaction paths analysis for PAH formation in the counterflow flame shows that both the HACA mechanism and the resonantly stabilized radicals are important for the growth of PAH. The kinetic model was unsuccessful in predicting the increased reactivity in O₂-doped diffusion flames, indicating the need for improved models and also the opportunity of new experiments of butadiene oxidation in the intermediate temperature region.     

Emission of impinging swirling and non-swirling inverse diffusion flames

The overall pollutants emission from impinging swirling and non-swirling inverse diffusion flames (IDFs) was evaluated quantitatively by the ‘hood’ method. The results of in-flame volumetric concentrations of CO and NO_x and overall pollutants emission of CO and NO_x in terms of emission index were reported. The in-flame volumetric concentrations of CO and NO_x were measured through a small hole drilled on the impingement plate. In comparison with the corresponding open flame, the CO and NO_x concentrations for the impinging swirling IDF are greatly lowered due to the entrainment of much more ambient air which is related to the increased flame surface area. For the swirling and non-swirling IDFs, the EINO_x increases as the nozzle-to-plate distance (H) increases because more space is available for the development of the high-temperature zone in the free jet portion of the impinging flame, which favors the thermal NO formation. The variation of EICO with H is different for the impinging swirling and non-swirling IDFs because they have different flame structures. For both flames, the EICO is high when their main reaction zone or inner reaction cone is impinged and quenched by the copper plate. The parameters of air jet Reynolds number, overall equivalence ratio and nozzle-to-plate distance have significant influence on the overall pollutants emission of the impinging swirling and non-swirling IDFs and the comparison shows that the swirling IDF emits less NO_x and CO under most of the experimental conditions tested. Furthermore, it is found that compared with the open flames, the impinging flames emit lower level of NO_x and higher level of CO.     

Radiative extinction of gaseous spherical diffusion flames in microgravity

Radiative extinction of spherical diffusion flames was investigated experimentally and numerically. The experiments involved microgravity spherical diffusion flames burning ethylene and propane at 0.98 bar. Both normal (fuel flowing into oxidizer) and inverse (oxidizer flowing into fuel) flames were studied, with nitrogen supplied to either the fuel or the oxygen. Flame conditions were chosen to ensure that the flames extinguished within the 2.2 s of available test time; thus extinction occurred during unsteady flame conditions. Diagnostics included color video and thin-filament pyrometry. The computations, which simulated flow from a porous sphere into a quiescent environment, included detailed chemistry, transport, and radiation and yielded transient results. Radiative extinction was observed experimentally and simulated numerically. Extinction time, peak temperature, and radiative loss fraction were found to be independent of flow rate except at very low flow rates. Radiative heat loss was dominated by the combustion products downstream of the flame and was found to scale with flame surface area, not volume. For large transient flames the heat release rate also scaled with surface area and thus the radiative loss fraction was largely independent of flow rate. Peak temperatures at extinction onset were about 1100 K, which is significantly lower than for kinetic extinction. An important observation of this work is that while radiative heat losses can drive transient extinction, this is not only because radiative losses are increasing with time but also because the heat release rate is falling off as the flame expands away from the burner and the reactant supply to the flame decreases.     

A computational study of oscillatory extinction of spherical diffusion flames

The transient behavior of burner-supported spherical diffusion flames was studied in the transport-induced limit of low mass flow rate and the radiation-induced limit of high mass flow rate which characterize the isola response of flame extinction. Oscillatory instability was observed near both steady-state extinction limits. The oscillation typically grows in amplitude until it becomes large enough to extinguish the flame. The oscillatory behavior was numerically observed using detailed chemistry and transport for methane (50%CH₄/50%He into 21%O₂/79%He) and hydrogen (100% H₂ into 21%O₂/79%He) diffusion flames where the fuel was issued from a point source, and helium was selected as an inert to increase the Lewis number, facilitating the onset of oscillation. In both methane and hydrogen flames, the oscillation always leads to extinction, and no limit cycle behavior was found. The growth rate of the oscillation was found to be slow enough under certain conditions to allow the flame to oscillate for over 450 s, suggesting that such oscillations can possibly be observed experimentally. For the hydrogen flames, however, the frequency of oscillation near the transport-induced limit is much larger, approximately 60 Hz as compared to 0.35 Hz for the methane flame, and the maximum amplitude of temperature oscillations was about 5 K. The distinctively different structures of the hydrogen and methane flames suggest that while both instabilities are thermal-diffusive in origin, oscillations in the hydrogen flames resemble those of premixed flames, while oscillations in the methane flames are non-premixed in character.     

Numerical investigation of spherical diffusion flames at their sooting limits

Detailed numerical simulations are presented of laminar microgravity spherical diffusion flames at their experimentally observed sooting limits. Ten normal and inverse flames fueled by ethylene are considered. Observed in a drop tower, these flames were initially sooty but reached their sooting limits 2 s after ignition (or slightly before). The flames span broad ranges of stoichiometric mixture fraction (0.065–0.692), adiabatic flame temperature (2226–2670 K), and stoichiometric scalar dissipation rate (0.013–0.384 s^?1). They were modeled using a one-dimensional, transient diffusion flame code with detailed chemistry (up to toluene) and transport. Radiative losses from products were modeled using a detailed absorption/emission statistical narrow-band model coupled with a discrete-ordinates method. Flame structure at the sooting limits was examined, emphasizing the behavior of carbon to oxygen atom ratio, temperature, and scalar dissipation rate. For ethylene flames with sufficiently long flow times it was found that soot formation coincides with regions where the C/O atom ratio and temperature exceed critical values, specifically 0.53 and 1305 K, respectively. The scatter about these critical values is small, which is noteworthy considering the wide range of flame conditions. These observations are consistent with the expected effects of H radicals on the propargyl soot pathway.     

Extinction of counterflow diffusion flames with radiative heat loss and nonunity Lewis numbers

The structure and extinction characteristics of counterflow diffusion flames with flame radiation and nonunity Lewis numbers of the fuel and oxidant are examined using multiscale asymptotic theory, and a model expressed in terms of the jump relations and reactant leakages with the proper consideration of the excess enthalpy overlooked in previous analyses is developed. The existence of the dual extinction limits in the presence of radiative heat loss, namely the kinetic limit at small Damköhler number (high stretch rate) and the radiative limit at large Damköhler number (low stretch rate), are identified. It is found that the former is minimally affected by radiative loss, while a substantial amount of heat loss is associated with the radiative limit. Reactant leakage, however, is the root cause for both limits. The influence of radiative loss on the extinction Damköhler numbers is found to be through its effects on the flame temperature, the excess enthalpy, and the reduced extinction Damköhler number. At both extinction limits, the contribution from the flame temperature is always important and dominant. The contributions from the other two, however, could be important in some special cases. At small Le_F, the contribution from the reduced extinction Damköhler number is large and even dominant under small radiative loss. The contribution from the excess enthalpy is important for small Le_O and it may be comparable to the contribution from the flame temperature when radiative loss is small. Thus, overlooking the excess enthalpy in previous analyses may have resulted in rather large error in the predicted extinction Damköhler numbers, especially the kinetic one.     

Formation of soot and nitrogen oxides in unsteady counterflow diffusion flames

The formation of pollutant species in turbulent diffusion flames is strongly affected by turbulence/chemistry interactions. Unsteady counterflow diffusion flames can be conveniently used to address the unsteady effects of hydrodynamics on the pollutant chemistry, because they exhibit a larger range of combustion conditions than those observed in steady flames.In this paper, unsteady effects on the formation of soot (and its main precursors) and nitrogen oxides (NO_x) are investigated by imposing harmonic oscillations on the strain rate of several counterflow diffusion flames fed with propane. Numerical results confirm that the dynamic response of each species is strongly affected by the strain rate oscillations and the characteristic time governing its chemistry. At low frequencies of imposed oscillations the soot and NO_x profiles show strong deviations from the steady-state profile. At large frequencies a decoupling between the concentration and the velocity field is evident. In particular, the formation of soot and NO_x is found less sensitive to velocity fluctuations for flames with large initial strain rate. The significant increase of soot and NO_x concentrations in unsteady conditions appears to be a function of both forcing frequency and flame global strain rate. Moreover, the cut-off frequency, defined as the minimum frequency above which the strain rate oscillations have negligible effects on the formation of each species, was found to be strongly dependent on the chemical characteristic time and the flame global strain rate, but only marginally affected by the amplitude of imposed oscillations.     

Effects of variable density on response of spherical diffusion flames under rotation

The spherical diffusion flame generated by either a porous burner or a fuel droplet in response to rotational motion was investigated through perturbation analysis, with emphasis on the effects variable density. While it was shown that main feature of the problem was adequately described by the constant-density model, the variable-density formulation revealed two new insights: (1) perturbations due to rotation decrease substantially as compared with the constant-density formulation, suggesting that the perturbing effects of rotation are substantially absorbed and thereby mitigated by the density variation, and (2) magnitude of the perturbations strongly depends on the ratio of the burner/droplet surface temperature to the ambient temperature.     

Effects of structure and hydrodynamics on the sooting behavior of spherical microgravity diffusion flames

This study is an examination of the sooting behavior of spherical microgravity diffusion flames burning ethylene at atmospheric pressure in a 2.2-s drop tower. In a novel application of microgravity, spherical flames were employed to allow convection across the flame to be either from fuel to oxidizer or from oxidizer to fuel. Thus, spherical microgravity flames are capable of allowing stoichiometric mixture fraction, Z_st, and direction of convection across the flame to be controlled independently. This allowed for a study of the phenomenon of permanently blue diffusion flames—flames that remain blue as strain rate approaches zero. Z_st was varied by changing inert concentrations such that adiabatic flame temperature did not change. At low Z_st, nitrogen was supplied with the oxidizer, and at high Z_st, it was provided with the fuel. Flame structure, quantified by Z_st, was found to have a profound effect on soot production. Soot-free conditions were observed at high Z_st and sooting conditions were observed at low Z_st regardless of convection direction. Convection direction was found to have a smaller impact on soot inception, suppressing formation when convection at the flame sheet was directed towards the oxidizer. A numerical analysis was developed to simulate steady state conditions and aided the interpretation of the results. The analysis revealed that steady state was not achieved for any of the flames, but particularly for those with pure ethylene or oxygen flowing from the porous burner. Furthermore, despite the fact that all flames had the same adiabatic flame temperature, the actual peak temperatures differed considerably. While transient burner heating and burner radiation reduced flame temperature, gas-phase radiative heat loss was the dominant mechanism accounting for these differences.     

Flame characteristics in H2/CO synthetic gas diffusion flames diluted with CO2: Effects of radiative heat loss and mixture composition

Numerical study is conducted to understand the impact of fuel composition and flame radiation in flame structure and their oxidation process in H₂/CO synthetic gas diffusion flame with and without CO₂ dilution. The models of Sun et al. and David et al., which have been well known to be best-fitted for H₂/CO synthetic mixture flames, are evaluated for H₂/CO synthetic mixture flames diluted with CO₂. Effects of radiative heat loss to flame characteristics are also examined in terms of syngas mixture composition. Importantly contributing reaction steps to heat release rate are compared for the synthetic gas mixture flames of high contents of H₂ and CO, individually, with and without CO₂ dilution. The modification of the oxidation pathways is also addressed.