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We investigate the use of an experimental 2-D temperature profile to constrain detailed numerical solutions of a sooting coflow laminar diffusion flame. Experimentally, four optical diagnostic techniques are used to measure the two-dimensional temperature field in an ethylene-air coflow flame. This experimental temperature field is then used to impose the temperature in the solution process, thus obviating the need to solve the energy equation and, in particular, to incorporate costly models of radiative losses in the flame. Results are presented for a 40% ethylene-air flame on the Yale Coflow Burner. In the unconstrained solution of the complete set of governing equations, the location of maximum temperature is found along the flame wings, whereas the experimental temperature field has its maximum along the centerline. Similarly, the location of peak soot volume fraction migrates from along the flame wings in the unconstrained calculation, where soot surface growth processes dominate, to the centerline in the constrained case, where soot inception is the dominant condensed-phase formation mechanism. The distribution of soot in the constrained solution is much more consistent with experimental observations, and this fact illustrates how the validation of a soot sub-model may be complicated by the necessity of modeling distributed heat losses in the flame.

The burning rate of liquid nitromethane as a function of pressure is known to exhibit slope breaks, following Saint-Robert's law only in limited regions of pressure. The present paper presents experimental and modeling results with the objective to better understand this behavior. A new experimental facility is used to visually observe the combustion process from 3 to 101 MPa allowing for measurement of burning rates in tubes of various diameters with high-speed cinematography. A series of modeling calculations are performed increasing in complexity first studying vapor phase flame propagation with the ideal gas equation of state and then a real gas equation of state. These results are compared with previously published predictions of the liquid regression rate using the same kinetic model and ideal gas equation of state. Theory indicates that, at high pressures, the freely propagating vapor-phase flame speed should agree with liquid regression rates. Combined, these results enable further insight into the mechanisms for the slope breaks and complex burning behavior. Three regimes were identified in the burning rate as a function of pressure. A low-pressure regime with pressure exponent of 1.16 exists where burning occurs with a distinct interface between liquid and gas. At approximately 18 MPa, an abrupt increase in burning rate occurs that is associated with the critical point of the mixture of nitromethane and near-surface species producing pressure exponents ranging from 2–10. Above this pressure, the loss of surface tension induces surface waves and large-scale hydrodynamic instabilities. With increasing pressure, burning rates continue to increase with pressure but with a gradual decrease in pressure exponent towards a value of ∼0.75. At the highest pressure the large-scale instabilities disappear, and the flame propagates with a turbulent cellular front, the speed of which depends upon the tube diameter.

In this study, the influence of pressure and fuel dilution on the structure and geometry of coflow laminar methane–air diffusion flames is examined. A series of methane-fuelled, nitrogen-diluted fl...

The chemiluminescence from electronically excited CH (denoted as CH * ) is investigated in nitrogen-diluted laminar coflow methane diffusion flames under microgravity and normal gravity conditions. In combustion studies, this radical species is of significant interest since its spatial distribution is indicative of the flame front position; moreover, given the relatively simple diagnostic involved with its measurement, several studies have been done to evaluate the ability of CH * chemiluminescence to predict the total and local flame heat release rate. In this work, a subset of the publicly available NASA Structure and Liftoff in Combustion Experiments (SLICE) microgravity and normal gravity nitrogen-diluted methane flames has been considered, and a method to extract quantitative CH * concentration information from the SLICE raw data is demonstrated. The measured CH * concentration is then discussed and compared with numerical simulations to assess the correlation between CH * chemiluminescence and heat release rate. The spectral characterization of the digital single lens reflex (DSLR) color camera used to acquire the flame images allowed the signal collected by the blue channel to be considered representative of the CH * emission of the A 2 Δ → X 2 ∏ transition centered around 431 nm; the analysis of the spectral emission of a reference nitrogen-diluted laminar diffusion methane flame accounted for the contribution of chemiluminescence from emitting species other than CH * . Due to the axisymmetric flame structure, an Abel deconvolution of the line-of-sight chemiluminescence was used to obtain the two-dimensional intensity profile and, thanks to an absolute light intensity calibration, a quantification of the CH * concentration was possible. Comparisons with numerical results display reasonably good agreement between measured and computed flame shapes, and it is shown that the difference in peak CH * concentration, between micro- and normal gravity cases, is minimal. Independent of the gravity level, the integrated CH * concentration in a cross section scales proportionally to the integrated computed heat release rate. The two-dimensional CH * and heat release rate spatial profiles match in a satisfactory way, but the gradients and intensity distributions are not comparable.

A novel vorticity–velocity formulation of the Navier–Stokes equations – the Mass-Conserving, Smooth (MC-Smooth) vorticity–velocity formulation – is developed in this work. The governing equations of the MC-Smooth formulation include a new second-order Poisson-like elliptic velocity equation, along with the vorticity transport equation, the energy conservation equation, and Nspec species mass balance equations. In this study, the MC-Smooth formulation is compared to two pre-existing vorticity–velocity formulations by applying each formulation to confined and unconfined axisymmetric laminar diffusion flame problems. For both applications, very good to excellent agreement for the simulation results of the three formulations has been obtained. The MC-Smooth formulation requires the least CPU time and can overcome the limitations of the other two pre-existing vorticity–velocity formulations by ensuring mass conservation and solution smoothness over a broader range of flow conditions. In addition to these benef...

The influences of fuel dilution, inlet velocity, and gravity on the shape and structure of laminar coflow CH4-air diffusion flames were investigated computationally and experimentally. A series of nitrogen-diluted flames measured in the Structure and Liftoff in Combustion Experiment (SLICE) on board the International Space Station was assessed numerically under microgravity (mu g) and normal gravity (1g) conditions with CH4 mole fraction ranging from 0.4 to 1.0 and average inlet velocity ranging from 23 to 90 cm/s. Computationally, the MC-Smooth vorticity-velocity formulation was employed to describe the reactive gaseous mixture, and soot evolution was modeled by sectional aerosol equations. The governing equations and boundary conditions were discretized on a two-dimensional computational domain by finite differences, and the resulting set of fully coupled, strongly nonlinear equations was solved simultaneously at all points using a damped, modified Newton's method. Experimentally, flame shape and soot temperature were determined by flame emission images recorded by a digital color camera. Very good agreement between computation and measurement was obtained, and the conclusions were as follows. (1) Buoyant and nonbuoyant luminous flame lengths are proportional to the mass flow rate of the fuel mixture; computed and measured nonbuoyant flames are noticeably longer than their 1g counterparts; the effect of fuel dilution on flame shape (i.e., flame length and flame radius) is negligible when the flame shape is normalized by the methane flow rate. (2) Buoyancy-induced reduction of the flame radius through radially inward convection near the flame front is demonstrated. (3) Buoyant and nonbuoyant flame structure is mainly controlled by the fuel mass flow rate, and the effects from fuel dilution and inlet velocity are secondary.

Upon the completion of the Structure and Liftoff in Combustion Experiment (SLICE) in March 2012, a comprehensive and unique set of microgravity coflow diffusion flame data was obtained. This data covers a range of conditions from weak flames near extinction to strong, highly sooting flames, and enabled the study of gravitational effects on phenomena such as liftoff, blowout and soot formation. The microgravity experiment was carried out in the Microgravity Science Glovebox (MSG) on board the International Space Station (ISS), while the normal gravity experiment was performed at Yale utilizing a copy of the flight hardware. Computational simulations of microgravity and normal gravity flames were also carried out to facilitate understanding of the experimental observations. This paper focuses on the different sooting behaviors of CH4 coflow jet flames in microgravity and normal gravity. The unique set of data serves as an excellent test case for developing more accurate computational models. Experimentally, the flame shape and size, lift-off height, and soot temperature were determined from line-of-sight flame emission images taken with a color digital camera. Soot volume fraction was determined by performing an absolute light calibration using the incandescence from a flame-heated thermocouple. Computationally, the MC-Smooth vorticity–velocity formulation was employed to describe the chemically reacting flow, and the soot evolution was modeled by the sectional aerosol equations. The governing equations and boundary conditions were discretized on an axisymmetric computational domain by finite differences, and the resulting system of fully coupled, highly nonlinear equations was solved by a damped, modified Newton’s method. The microgravity sooting flames were found to have lower soot temperatures and higher volume fraction than their normal gravity counterparts. The soot distribution tends to shift from the centerline of the flame to the wings from normal gravity to microgravity.

Thermal radiation from laminar, sooting, coflow diffusion flames at atmospheric pressure has been studied computationally as a function of ethylene fuel dilution by nitrogen. These flames had previously been investigated using laser diagnostics and thermocouple-gas sampling probe techniques, and the measured soot levels had been satisfactorily predicted by a sectional soot kinetics model. In this work, the discrete ordinates method for solution of the equation of radiative transfer in axisymmetric cylindrical coordinates has been coupled to the flow’s energy conservation equation through the calculated divergence of the net radiative flux. Two self-consistent models for the absorption/emission of radiation by soot, CO2, H2O, CO, and ethylene were considered: the Planck mean model and one based on narrowband, wavelength-dependent absorption. The wavelength-dependent calculation was found to predict much more substantial reabsorption effects; we conclude that the Planck mean model inadequately characterizes...

Directed relation graph (DRG) techniques are used to generate small skeletal mechanisms capable of accurately simulating the combustion of a two-component surrogate for JP-8 jet fuel. Within the DRG framework, six different reduction techniques are considered, and the effectiveness of different definitions for the connection weights and error propagation is evaluated. The use of DRG reduction techniques for aided sensitivity analysis (DRGASA) and for on-the-fly reduction (flux-based DRG) is studied in detail. An optimal reduction approach based on the sequential use of DRG, DRGASA, and flux-based DRG is proposed. When global reduction is applied to a detailed mechanism of 234 species and 6997 reactions, the six reduction techniques result in very different skeletal mechanisms, but all of them are essentially equivalent in terms of accuracy and number of retained species (82–92 species). Finally, for two-dimensional coflow flame test problems, on-the-fly DRG techniques are investigated. Error-propagation-based methods are found to extinguish the flame artificially and cannot be used in an on-the-fly implementation. Conversely, normal DRG methods greatly improve the mechanism reduction, and accurate solutions are obtained using about 15% of the detailed mechanism.

Flame stabilisation and extinction in a number of different flows can be affected by application of electric fields. Electrons and ions are present in flames, and because of charge separation, weak electric fields can also be generated even when there is no externally applied electric field. In this work, a numerical model incorporating ambipolar diffusion and plasma kinetics has been developed to predict gas temperature, species, and ion and electron concentrations in laminar premixed flames without applied electric fields. This goal has been achieved by combining the existing CHEMKIN-based PREMIX code with a recently developed methodology for the solution of electron temperature and transport properties that uses a plasma kinetics model and a Boltzmann equation solver. A chemical reaction set has been compiled from seven sources and includes chemiionisation, ion-molecule, and dissociative–recombination reactions. The numerical results from the modified PREMIX code (such as peak number densities of posit...

Hydrocarbon fuels will remain a major source of energy well into the second half of the 21st century and, despite dire warnings about their limited supply, known resources have actually increased over the past decade. Nevertheless, finite supplies and increasing demand will exert pressure on the efficient use of these fuels, especially if their price continues to climb. Specifically, electricity generation and propulsion will continue to rely heavily upon the burning of hydrocarbon fuels for many years to come. Although an understanding of combustion in practical combustors is essential to the goals of reducing pollution and increasing energy efficiency, three-dimensional models of these systems with detailed transportation fuel chemistry and complex transport are beyond our current computational capabilities. Instead, one can study flames with complex chemistry in simpler laminar configurations to provide insight into the chemical and physical processes occurring in many engineered systems. In this paper, we trace the development of mathematical models and computational methods for laminar flame problems, with a particular emphasis on numerical algorithms that enable their coupled solution. While most of the focus is on steady systems, we also discuss issues related to time-dependent flames.

The structure of a JP-8 coflow flame is investigated by applying laser diagnostic techniques to three different fuel surrogates. The results are compared against theoretical predictions from numerical simulations; very good agreement is obtained for temperature and major species. Rayleigh and Raman scattering are used to measure temperature and major species mole fractions in the flame (oxygen, carbon dioxide, water, and fuel molecules). Quantitative laser diagnostic techniques are particularly challenging when applied to jet-fuel flames; the presence of aromatic molecules in the fuel mixtures and the formation of polyaromatic compounds inside the flame generate spectrally broad fluorescence signals that interfere with the measurement. A polarized/depolarized subtraction technique combined with a post-processing filter based on least-squares fitting is used to mitigate this undesired effect. The proposed technique tries to match the experimental signal against previously calculated spectra and has proved to be a very efficient filter at rejecting polyaromatic fluorescence. Numerical simulations play a fundamental role in this study. Computer predictions are used not only to compare experimental data, but as an active component of the data post-processing. For example, numerically calculated cross-section maps are used to refine the measured temperature for both the Rayleigh and Raman experiments.

The predictions of “soot” concentrations from numerical simulations for nitrogen-diluted, ethylene/air flames are compared with laser-induced incandescence and Raman spectra observed from samples thermophoretically extracted using a rapid insertion technique. In some flame regions, the Raman spectra were obscured by intense, radiation that appeared to peak in the near infrared spectral region. There is a good agreement between spatial profiles of this ex situ laser-induced incandescence (ES-LII) and the “traditional” in situ laser-induced incandescence (IS-LII). Raman signatures were observed from low in the flame and extended into the upper flame regions. The spectra consisted of overlapping bands between 1000 and 2000 cm −1 dominated by the “ G ” band, near ≈1580 cm −1 , and the “ D ” band in the upper 1300 cm −1 range. Several routines are explored to deconvolve the data including 3- and 5-band models, as well as a 2-band Breit–Wigner–Fano (BWF) model. Because the Raman signals were observed at heights below those where in situ LII was observed, we postulate that these signals may be attributable to smaller particles. The results suggest that the observed Raman signals are attributable to particulate with modest (≈1 nm) crystallite sizes. This observation is discussed in the context of current models for nascent particle formation.

The solution of reactive flows using fully implicit methods on distributed memory machines is investigated in detail. Three different parallel implementations of Newton's method are described and tested on the solution of two-dimensional laminar axisymmetric coflow diffusion flames. Each implementation has different computational requirements, both in the amount of communication among the processes and in the computational overhead due to the calculation of physical quantities at the interfaces between subdomains. An effective trade-off is established between communications and calculations so that the most communication-intensive implementation results in computational speedup only if the network is sufficiently fast. Benchmark results are presented for a variety of chemical mechanisms, grid decomposition techniques, and hardware. Parallelization efficiencies of about 80% and speedups of 20–100 are reported for most test cases. The method developed here is well suited for complex chemistry problems with ...

A novel, flux-based, directed relation graph (DRG) method is proposed for adaptive and automatic generation of skeletal chemical mechanisms. Unlike many previous approaches for static mechanism reduction, the proposed method does not rely on the complete solution of a set of test problems using the detailed mechanism, but rather it simplifies the model “on the fly,” analyzing the local reaction states with an extended directed relation graph. Compared to the original DRG method of Lu and Law [T. Lu, C.K. Law, Proc. Combust. Inst. 30 (2005)], the flux-based DRG explicitly considers the effect of transport fluxes, as they provide a way to quantify the coupling of the governing equations among adjacent grid cells. The resulting numerical scheme operates on a cell-by-cell basis, so that different chemical submodels are applied in different regions of the flame. This approach leads to very large reduction ratios, in which most of the flame structure is resolved using about 30% of the chemical species employed in the full mechanism, while a more detailed model that considers roughly 70–80% of the total species is used only at ignition. The flux-based DRG method has been employed in the two-dimensional simulation of axisymmetric coflow flames for a variety of fuels and chemical kinetic mechanisms (three steady flames and one oscillating flame), with a speedup factor of about 20 obtained for the largest problem — a JP-8 flame.

Three lean-to-stoichiometric premixed flames were studied in the opposed-jet configuration by counterflowing fresh reactants and fully burnt products of combustion at 1850 K. The study was performed experimentally under turbulent conditions and computationally under laminar ones. The flame mixtures were selected to have the same unstrained laminar flame speed. The turbulent flames were studied experimentally using simultaneous planar imaging of CO and OH laser-induced fluorescence, which, in combination, yielded a quantity proportional to the forward reaction rate for CO + OH → CO 2 + H. Since the turbulence characteristics of the feed streams were identical for all flames, the turbulent burning regime was also the same, with a turbulent Reynolds number of 1050 and a Karlovitz number of approximately 5. The oxidation layer of the stoichiometric flame was extinguished, whereas the lean flames exhibited substantial evidence of CO conversion as indicated by the CO + OH reaction rate imaging. To aid the interpretation of the experiments, we numerically investigated the extinction of strained laminar premixed flames with compositions identical to those of the experiments. The calculations corroborated the experimental results, indicating that the stoichiometric flame was the least robust and extinguished at the lowest strain rate. Furthermore, extinction occurred when the flames were very close to the gas stagnation plane and the oxidation layer extended beyond it, towards the burnt product side. The quenching of the oxidation layer is suggested as a possible reason for either local or overall extinction of highly strained premixed flames.

A simple and compact temperature and soot volume fraction diagnostic technique based on ratio pyrometry has been studied. Two different consumer digital single lens reflex cameras were evaluated for use as pyrometers. The incandescence from soot and a SiC filament was imaged at the three wavelengths of each camera’s color filter array (CFA). After characterization of the detector’s signal response curves, temperatures were calculated by two-color ratio pyrometry using a lookup table approach. A SiC filament with known emissivity was shown to provide an absolute light intensity calibration, which further allows the soot volume fraction to be determined. Measurements were carried out on four different flames with varying levels of soot loading. The filament-derived gas temperature and soot temperature measurements have been compared with computational results and overall good agreement has been shown. Soot volume fraction measurements have been compared with previous LII results, with excellent agreement for both cameras tested.

The extinction of premixed CH4/O2/N2 flames counterflowing against a jet of combustion products in chemical equilibrium was investigated numerically using detailed chemistry and transport mechanisms. Such a problem is of relevance to combustion systems with non-homogeneous air/fuel mixtures or recirculation of the burnt gases. Contrary to similar studies that were focused on heat loss/gain, depending on the degree of non-adiabaticity of the system, the emphasis here was on the yet unexplored role of the composition of counterflowing burnt gases in the extinction of lean-to-stoichiometric premixed flames. For a given temperature of the counterflowing products of combustion, it was found that the decrease of heat release with increase in strain rate could be either monotonic or non-monotonic, depending on the equivalence ratio φb of the flame feeding the hot combustion product stream. Two distinct extinction modes were observed: an abrupt one, when the hot counterflowing stream consists of either inert gas or equilibrium products of a stoichiometric premixed flame, and a smooth extinction, when there is an excess of oxidizing species in the combustion product stream. In the latter case four burning regimes can be distinguished as the strain rate is progressively increased while the heat release decreases smoothly: an adiabatic propagating flame regime, a non-adiabatic propagating flame regime, the so-called partially-extinguished flame regime, in which the location of the peak of heat release crosses the stagnation plane, and a frozen flow regime. The flame structure was analyzed in detail in the different burning regimes. Abrupt extinction was attributed to the quenching of the oxidation layer with the entire H–OH–O radical pool being comparably reduced. Under conditions of smooth extinction, the behavior is different and the concentration of the H radical decreases the most with increasing strain rate, whereas OH and O remain comparatively abundant in the oxidation layer. As the profile of the heat release rate thickens, the oxidation layer is quenched and the attack of the fuel relies more heavily on the OH radicals.

Forced laminar diffusion flames form an important class of problems that can help to bridge the significant gap between steady laminar flames in simple burner configurations and the turbulent flames found in many practical combustors. Such flames offer a much wider range of interactions between convection, diffusion, and chemical reaction than can be examined under steady-state conditions, and yet detailed simulations of them should be feasible without having to resort to “modeling” any of the relevant physics, above all without having prematurely to reduce the large kinetic mechanisms typical of hydrocarbon fuels. Nevertheless, the computation of time-dependent laminar diffusion flames with conventional numerical methods is hindered by technical challenges that, while not new, are more troublesome to surmount than in the calculation of otherwise similar, unforced flames. First, the intricate spatiotemporal coupling between fluid dynamics and combustion thermochemistry ensures that spurious numerical diffusion or spatial under-resolution of the mixing process at any stage of the computation can lead to inaccurate prediction of flame characteristics for the remainder thereof. Second, relatively long simulated flow times and extremely short chemical time scales make many standard time integration algorithms impractical on all but the largest parallel computer clusters. This paper introduces a new numerical approach for time-varying laminar flames that addresses these challenges through the use of high order compact finite difference schemes within a robust, fully implicit solver based on a Jacobian-free Newton–Krylov method. The capabilities of this implicit-compact solver are demonstrated on a periodically forced axisymmetric laminar jet diffusion flame with one-step Arrhenius chemistry, and the results are compared to those of a conventional low order finite difference solver.

Four periodically time-varying methane–air laminar coflow jet diffusion flames, each forced by pulsating the fuel jet's exit velocity Uj sinusoidally with a different modulation frequency wj and with a 50% amplitude variation, have been computed. Combustion of methane has been modeled by using a chemical mechanism with 15 species and 42 reactions, and the solution of the unsteady Navier–Stokes equations has been obtained numerically by using a modified vorticity-velocity formulation in the limit of low Mach number. The effect of wj on temperature and chemistry has been studied in detail. Three different regimes are found depending on the flame's Strouhal number S=awj/Uj, with a denoting the fuel jet radius. For small Strouhal number (S=0.1), the modulation introduces a perturbation that travels very far downstream, and certain variables oscillate at the frequency imposed by the fuel jet modulation. As the Strouhal number grows, the nondimensional frequency approaches the natural frequency of oscillation of the flickering flame (S≃0.2). A coupling with the pulsation frequency enhances the effect of the imposed modulation and a vigorous pinch-off is observed for S=0.25 and S=0.5. Larger values of S confine the oscillation to the jet's near-exit region, and the effects of the pulsation are reduced to small wiggles in the temperature and concentration values. Temperature and species mass fractions change appreciably near the jet centerline, where variations of over 2% for the temperature and 15% and 40% for the CO and OH mass fractions, respectively, are found. Transverse to the jet movement, however, the variations almost disappear at radial distances on the order of the fuel jet radius, indicating a fast damping of the oscillation in the spanwise direction.

Forced, time-varying laminar flames help bridge the gap between laminar and turbulent combustion as they reside in an ever-changing flow environment. A distributed-memory parallel computation of a time-dependent sooting ethylene/air coflow diffusion flame, in which a periodic fluctuation (20 Hz) is imposed on the fuel velocity for four different amplitudes of modulation, is presented. The chemical mechanism involves 66 species, and a soot sectional model is employed with 20 soot sections. The governing equations are discretised using finite differences and solved implicitly using a damped modified Newton's method. The solution proceeds in parallel using strip domain decomposition over 40 central processing units (CPUs) until full periodicity is attained. For forcing amplitudes of 30%, 50%, 70% and 90%, a complete cycle of numerical predictions of the time-resolved soot volume fraction is presented. The 50%, 70% and 90% forcing cases display stretching and pinching off of the sooting region into an isolate...

The chemical structure of a methane counterflow diffusion flame and of the same flame doped with 1000 ppm (molar) of either jet fuel or a 6-component jet fuel surrogate was analyzed experimentally, by gas sampling via quartz microprobes and subsequent GC/MS analysis, and computationally using a semi-detailed kinetic mechanism for the surrogate blend. Conditions were chosen to ensure that all three flames were non-sooting, with identical temperature profiles and stoichiometric mixture fraction, through a judicious selection of feed stream composition and strain rate. The experimental dataset provides a glimpse of the pyrolysis and oxidation behavior of jet fuel in a diffusion flame. The jet fuel initial oxidation is consistent with anticipated chemical kinetic behavior, based on thermal decomposition of large alkanes to smaller and smaller fragments and the survival of ring-stabilized aromatics at higher temperatures. The 6-component surrogate captures the same trend correctly, but the agreement is not quantitative with respect to some of the aromatics such as benzene and toluene. Various alkanes, alkenes and aromatics among the jet fuel components are either only qualitatively characterized or could not be identified, because of the presence of many isomers and overlapping spectra in the chromatogram, leaving 80% of the carbon from the jet fuel unaccounted for in the early pyrolysis history of the parent fuel. Computationally, the one-dimensional code adopted a semi-detailed kinetic mechanism for the surrogate blend that is based on an existing hierarchically constructed kinetic model for alkanes and simple aromatics, extended to account for the presence of tetralin and methylcyclohexane as reference fuels. The computational results are in reasonably good agreement with the experimental ones for the surrogate behavior, with the greatest discrepancy in the concentrations of aromatics and ethylene.

Two sets of axisymmetric laminar coflow flames, each consisting of ethylene/air nonpremixed flames with various amounts (up to 10%) of either dimethyl ether (CH 3 –O–CH 3 ) or ethanol (CH 3 –CH 2 –OH) added to the fuel stream, have been examined both computationally and experimentally. Computationally, the local rectangular refinement method, which incorporates Newton's method, is used to solve the fully coupled nonlinear conservation equations on solution-adaptive grids for each flame in two spatial dimensions. The numerical model includes C6 chemical kinetic mechanisms with up to 59 species, detailed transport, and an optically thin radiation submodel. Experimentally, thermocouples are used to measure gas temperatures, and mass spectrometry is used to determine concentrations of over 35 species along the flame centerline. Computational results are examined throughout each flame, and validation of the model occurs through comparison with centerline measurements. Very good agreement is observed for temperature, major species, and several minor species. As the level of additive is increased, temperatures, some major species (CO 2 , C 2 H 2 ), flame lengths, and residence times are essentially unchanged. However, peak centerline concentrations of benzene (C 6 H 6 ) increase, and this increase is largest when dimethyl ether is the additive. Computational and experimental results support the hypothesis that the dominant pathway to C 6 H 6 formation begins with the oxygenates decomposing into methyl radical (CH 3 ), which combines with C2 species to form propargyl (C 3 H 3 ), which reacts with itself to form C 6 H 6 .

A combined computational and experimental investigation that examines the relationship of soot formation and NO in coflow ethylene air diffusion flames is presented. While both NO and soot formation are often studied independently, there is a need to understand their coupled relationship as a function of system parameters such as fuel type, temperature and pressure. The temperature decrease due to radiative losses in systems in which significant soot is produced can affect flame length and other temperature-dependent processes such as the formation of NO. The results of a computational model that includes a sectional representation for soot formation with a radiation model are compared against laser-induced fluorescence measurements of NO. The sooting characteristics of these flames have been studied previously. Experimentally, a laser near 225.8 nm is used to excite the γ (0, 0) band in NO. Spectrally resolved fluorescence emission is imaged radially, for the (0, 0), (0, 1), (0, 2), (0, 3), and (0, 4) vibrational bands, at varying axial heights to create a two-dimensional image of NO fluorescence. A reverse quenching correction is applied to the computational results to determine an expected fluorescence signal for comparison with experimental results. Modeling results confirm that Fenimore NO is the dominant mechanism for NO production and suggest that for lightly sooting flames (peak soot volume fraction

A non-sooting, lifted, methane/air, coflowing, non-premixed flame has been studied experimentally and computationally. The flame structure was computed by solving the fully elliptic governing equations, utilizing a 35 species chemical kinetic mechanism, detailed transport coefficients and an optically thin radiation submodel. Gas temperature, major species mole fractions, and non-fuel hydrocarbon concentrations were experimentally mapped in two dimensions with both probe techniques (coupled to infrared absorption spectroscopy and on-line mass spectrometry) and in situ optical diagnostics (laser-induced fluorescence, Rayleigh and Raman scattering). Contour plots of measured and computed formaldehyde concentrations and fluorescence signals agree well and both revealed a region of intense formaldehyde production near the lifted flame base. High formaldehyde production rates correlated well with regions of high heat release. Further, regions of the dominant formaldehyde formation reaction, CH3 + O = HCHO + H, also correlated with areas of maximum heat release rate.

As the drive toward greater accuracy in flame simulation continues, there is a need for more detail in the modeling of soot formation and its related phenomena. In this study we investigate computationally the effect of multicomponent transport and thermal diffusion on soot formation in ethylene/air flames. In the counterflow configuration, laminar diffusion flames and partially premixed flames are investigated using complex chemistry and detailed transport. The gas phase equations are coupled to a sectional soot model and the resulting set of partial differential equations admits a well-known similarity solution. Arc length continuation is used to compute flames for varying strain rates. In the coflow configuration, a modified vorticity–velocity formulation is used and the governing equations are solved on an adaptively refined grid using pseudo-transient continuation and Newton’s method nested with a Bi-CGSTAB iterative linear system solver. All transport coefficients, including thermal diffusion coefficients, are evaluated using cost-effective, accurate algorithms derived from the kinetic theory of gases. The numerical results for the counterflow model provide a quantitative assessment of the effects of detailed multicomponent transport and thermal diffusion on soot concentrations as a function of strain rate for both a diffusion flame and partially premixed flame. The fidelity of the commonly used Fickian diffusion model is tested and it is shown that in certain cases, the impacts of detailed multicomponent transport and thermal diffusion modeling on soot concentrations are significant. The numerical results for the coflow model demonstrate that although minimal changes in flame shape and temperature profiles arise when transport models are varied, changes in the soot profiles can be seen.

Three axisymmetric laminar coflow diffusion flames, one of which is a nitrogen-diluted methane/air flame (the ‘base case’) and the other two of which consist of nitrogen-diluted methane vs. pure oxygen, are examined both computationally and experimentally. Computationally, the local rectangular refinement method is used to solve the fully coupled nonlinear conservation equations on solution-adaptive grids. The model includes C2 chemistry (GRI 2.11 and GRI 3.0 chemical mechanisms), detailed transport, and optically thin radiation. Because two of the flames are attached to the burner, thermal boundary conditions at the burner surface are constructed from smoothed functional fits to temperature measurements. Experimentally, Raman scattering is used to measure temperature and major species concentrations as functions of the radial coordinate at various axial positions. As compared to the base case flame, which is lifted, the two oxygen-enhanced flames are shorter, hotter, and attached to the burner. Computati...

The structure of a time-dependent methane/enriched-air flame established in an axisymmetric, laminar counterflow configuration is investigated, as the flame interacts with two counterpropagating toroidal vortices. Computationally, the time-dependent equations are written using a modified vorticity–velocity formulation, with detailed chemistry and transport, and are solved implicitly on a nonstaggered, nonuniform grid. Boundary conditions are chosen to create local extinction and reignition in the vicinity of the axis of symmetry. Experimentally, CO planar laser-induced fluorescence (PLIF), OH PLIF, and an observable proportional to the forward reaction rate (RR) of the reaction CO + OH → CO2 + H are measured. Particle image velocimetry (PIV) is used to characterize the velocity field of the vortical structures and to provide detailed boundary conditions for the simulations. Excellent agreement is found between model and experiments to the minutest morphological details throughout the interaction. The validated model is then used to probe the dynamics of the two-dimensional extinction process with high temporal resolution. During the initial phase of the interaction, the flame is locally extinguished by the two vortices. The resulting edge flame propagates outward as an extinction front, with a structure that does not depart significantly from that of a diffusion flame. The front recedes from the axis of symmetry with a negative propagation speed that reaches a value as large as six times that of the freely propagating laminar flame with the same reactant concentrations found at the stoichiometric surface. As the front propagates outward, it transitions to an ignition front, and it reaches a positive propagation speed comparable to that of the freely propagating laminar flame. During this transition, it develops a characteristic premixed “hook,” with a lean premixed branch, a stoichiometric segment that evolves into the remnant of the original primary diffusion flame, and a much weaker secondary diffusion flame resulting from a secondary peak in heat release in the original unperturbed diffusion flame. No evidence of a distinct rich premixed flame is found. The edge flame stabilizes at a radial location where the local gaseous speed equals the propagation speed of the front. When the local perturbation has decayed below the flame propagation speed, the flame edge starts reigniting the mixing layer as an ignition wave that propagates with an essentially frozen structure along the stoichiometric surface until the original diffusion flame structure is fully recovered. Implications for flamelet modeling of turbulent flames with local extinction are discussed.

A 2D implicit compact scheme solver has been implemented for the vorticity-velocity formulation in the case of nonreacting, multicomponent, axisymmetric, low Mach number flows. To stabilize the discrete boundary value problem, two sets of boundary closures are introduced to couple the velocity and vorticity fields. A Newton solver is used for solving steady-state and time-dependent equations. In this solver, the Jacobian matrix is formulated and stored in component form. To solve the system of linearized equations within each iteration of Newton's method, preconditioned Bi-CGSTAB is used in combination with a matrix-vector product computed in component form. The almost dense Jacobian matrix is approximated by a partial Jacobian. For the preconditioner equation, the partial Jacobian is approximately factored using several methods. In a detailed study of several preconditioning techniques, a promising method based on ILUT preconditioning in combination with reordering and double scaling using the MC64 algorithm by Duff and Koster is selected. To validate the implicit compact scheme solver, several nonreacting model problems have been considered. At least third order accuracy in space is recovered on nonuniform grids. A comparison of the results of the implicit compact scheme solver with the results of a traditional implicit low order solver shows an order of magnitude reduction of computer memory and time using the compact scheme solver in the case of time-dependent mixing problems. © 2005 Elsevier Ltd. All rights reserved.

Forced, time-varying flames are laminar systems that help bridge the gap between laminar and turbulent combustion. In this study, we investigate computationally and experimentally the structure of a periodically forced, axisymmetric laminar methane–air diffusion flame in which a cylindrical fuel jet is surrounded by a coflowing oxidizer jet. The flame is forced by imposing a sinusoidal modulation on the steady fuel flow rate. Rayleigh and spontaneous Raman scattering are used to generate the temperature and major species profiles. Particle image velocimetry is used to determine the magnitude of the velocity at the exit of the burner and the phase of the forcing modulation. CH∗ flame emission measurements are used to provide an indication of the overall flame shape. Computationally, we solve the transient equations for the conservation of total mass, momentum, energy, and species mass with detailed transport and finite rate chemistry submodels. The governing equations are written using a modified vorticity–velocity formulation and are solved on an adaptively refined grid using implicit time stepping and Newton’s method nested with a Bi-CGSTAB iterative linear system solver. Results of the study include an investigation of the start-up features of the time-dependent flames and the time it takes for initial transients to dissipate. We include a detailed description of the fluid dynamic-thermochemical structure of the flame at a 20 Hz forcing frequency for both 30% and 50% sinusoidal velocity perturbations. Comparisons of experimentally determined and calculated temperature, CO and H2O mole fraction profiles provide verification of the accuracy of the model.

Non-premixed tubular flames are established using the opposed tubular burner for the first time, which enables the quantitative study of curvature effects on flame behavior. A detailed structural investigation using the spontaneous Raman scattering technique is conducted on flames with constant curvature using 15% H2 diluted by N2 against air at various stretch rates. The measured temperature and major species concentrations agree well with the numerical prediction, and this validates the numerical model. Comparing with the numerical results of the opposed-jet flat flame, the tubular flame data show that the curvature weakens the effects of preferential diffusion for the diluted hydrogen flames where the curvature is concave towards the fuel stream. To further prove this discovery, near-extinction non-premixed tubular flames using different types of fuels are also studied. Hydrogen flames (Le 1) prefer concave curvature, which is opposite to the hydrogen flames, and cellular structures appear throughout the burner’s operational range. These phenomena confirm that for flames with Le 1. Curvature has minimal effects on tubular non-premixed flames with Lewis number close to unity. The comparison between experimental and calculated extinction conditions also supports the above conclusions.

The structure of steady methane/enriched-air edge flames established in an axisymmetric, laminar counterflow configuration was investigated computationally and experimentally. Computationally, the steady-state equations were solved implicitly in a modified vorticity–velocity formulation on a nonstaggered, nonuniform grid, with detailed chemistry and transport. Experimental boundary conditions were chosen to establish flames with a hole centered at the axis of symmetry, the location where the largest strain rate occurs, in order to investigate the structure of the edge flame established at the outer periphery of the hole. Experimentally, CO PLIF, OH PLIF, and an observable proportional to the forward reaction rate (RR) of the reaction CO + OH → CO 2 + H were measured. Particle image velocimetry (PIV) was used to characterize the velocity field in the proximity of the fuel and oxidizer nozzles and to provide detailed boundary conditions for the simulations. Qualitatively, the flow field can be partitioned into two zones: a nonreactive counterflow region bound by two recirculation zones attached at the exits of the inlet nozzles, which aid mixing of products and reactants upstream of the edge flame; and a reactive region, where a premixed edge flame provides the stabilization mechanism for a trailing diffusion flame. Comparisons between the experimental and the computational data yielded quantitative agreement for all measured quantities. Further, we investigated the structure of the computational edge flames. We identified the most significant heat-release reactions for each of the flame branches. Finally, we examined correlations among the propagation speed of the edge flame and curvature and mixture fraction gradient by varying the global strain rate of the flame.

We investigate an interface model for ammonium perchlorate (AP) monopropellant flames. The model includes complex chemistry and detailed transport in the gas phase and heat conduction in the solid phase. The interface condition considers sublimation of AP as well as reaction products obtained through a liquid phase. The resulting parameterized two-point boundary value problem is solved by a phase-space, pseudo-arclength, continuation method that employs Euler predictors, Newton-like iterations and global adaptive gridding techniques. We establish that the use of Dirichlet boundary conditions for temperature at the solid phase cold boundary leads to unphysically extinguished flames. We simulate preheated low pressure flames as well as high pressure flames in good agreement with experimental results. We finally obtain qualitative pressure extinction limits of AP flames subjected to heat losses. The work represents a critical step in the ultimate solution of the multidimensional coupled gas and condensed pha...

In a commonly implemented version of the vorticity-velocity formulation, the governing equations for the fluid dynamics are expressed as two Poisson-like velocity equations together with the vorticity transport equation. However, for some flows with large vorticity gradients, spurious mass loss or gain can be observed. In order to conserve mass, a modification to the vorticity-velocity formulation is proposed, involving the substitution of the kinematic definition of vorticity in certain terms of the fluid-dynamic equations. This modified formulation results in a broader computational stencil when the equations are in a second-order-accurate discretized form, and a stronger coupling between the predicted vorticity and the curl of the predicted velocity field. The resulting system of elliptic equations - which includes the energy and species transport equations for the reacting flow case - is discretized with finite differences on a nonstaggered grid and is then solved using Newton's method. Both the unmodified and modified vorticity-velocity formulations are applied to two problems with high vorticity gradients: (1) incompressible, axisymmetric fluid flow through a suddenly expanding pipe and (2) a confined, axisymmetric laminar flame with detailed chemistry and multicomponent transport, generated on a burner whose inner tube extends above the burner surface. The modified formulation effectively eliminates the spurious mass loss in the two test cases to within an acceptable tolerance. The two cases demonstrate the broader range of applicability of the modified formulation, as compared with the unmodified formulation.

Laminar, sooting, coflow diffusion flames at atmospheric pressure have been studied experimentally and theoretically as a function of fuel dilution by inert nitrogen. The flames have been investigated with laser diagnostics. Laser extinction has been used to calibrate the experimental soot volume fractions and an improved gating method has been implemented in the laser-induced incandescence (LII) measurements resulting in differences to the soot distributions reported previously. Numerical simulations have been based on a fully coupled solution of the flow conservation equations, gas-phase species conservation equations with complex chemistry, and the dynamical equations for soot spheroid growth. The model also includes the effects of radiation reabsorption through an iterative procedure. An investigation of the computed rates of particle inception, surface growth, and oxidation, along with a residence time analysis, helps to explain the shift in the peak soot volume fraction from the centerline to the wings of the flame as the fuel fraction increases. The shift arises from changes in the relative importance of inception and surface growth combined with a significant increase in the residence time within the annular soot formation field leading to higher soot volume fractions, as the fuel fraction increases.

A novel, stable, implicit compact scheme solver that is higher order in space, suitable for modeling steady-state and time-dependent phenomena on nonuniform grids for one-dimensional configurations, is presented. Several properties of compact scheme discretizations are introduced to develop efficient algorithms for Jacobian matrix generation and Jacobian-vector multiplication using a new component form for Jacobian operations. Composite nonuniform grids are introduced that enable the implicit compact scheme solver to achieve sixth order accuracy. A robust Newton's method is employed with explicit generation of Jacobian matrices. Superior resolution characteristics of the implicit compact scheme solver are demonstrated with several steady-state and time-dependent problems for the Burgers equation. The example of the solution of stiff flame problem is given. An analysis of spectral properties of Jacobian matrices is presented, which shows that the condition number and the eigenvalue distributions behave similarly to those found in Jacobians associated with low-order discretizations. Two sparsification strategies are developed for the systematic approximation of a dense Jacobian aimed at the practical implementation of linear system preconditioning through partial Jacobians.

Counterflow diffusion flame experiments and modeling results are presented for a fuel mixture consisting of N 2 , C 2 H 2 , and C 2 H 4 flowing against decomposition products from a solid AP pellet. The flame zone simulates the diffusion flame structure that is expected to exist between reaction products from AP crystals and a hydrocarbon binder. Quantitative species and temperature profiles have been measured for one strain rate, given by a separation of 5 mm, between the fuel exit and the AP surface. Species measured include C 2 H 2 , C 2 H 4 , N 2 , CN, NH, OH, CH, C 2 , NO, NO 2 , O 2 , CO 2 , H 2 , CO, HCl, H 2 O, and soot volume fraction. Temperature was measured using a combination of a thermocouple at the fuel exit and other selected locations, spontaneous Raman scattering measurements throughout the flame, NO vibrational populations, and OH rotational population distributions. The burning rate of the AP was also measured for this flame’s strain rate. The measured eighteen scalars are compared with predictions from a detailed gas-phase kinetics model consisting of 105 species and 660 reactions. Model predictions are found to be in good agreement with experiment and illustrate the type of kinetic features that may be expected to occur in propellants when AP particles burn with the decomposition products of a polymeric binder.

The standard local defect correction (LDC) method has been extended to include multilevel adaptive gridding, domain decomposition and regridding. The domain decomposition algorithm provides a natural route for parallelization by employing many small tensor-product grids, rather than a single large unstructured grid; this algorithm can greatly reduce memory usage. The above properties are illustrated by successfully applying the new algorithm to a simple heat transfer problem with an analytical solution, and by subsequently solving the more complex problem of an axisymmetric laminar Bunsen flame with one-step chemistry. The simulation data show excellent agreement with results previously published in the literature.

Non-sooting counterflow diffusion flames have been studied both computationally and experimentally, using either JP-8, or a six-component JP-8 surrogate mixture, or its individual components. The computational study employs a counterflow diffusion flame model, the solution of which is coupled with arc length continuation to examine a wide variety of inlet conditions and to calculate extinction limits. The surrogate model includes a semi-detailed kinetic mechanism composed of 221 gaseous species participating in 5032 reactions. Experimentally, counterflow diffusion flames are established, in which multicomponent fuel vaporization is achieved through the use of an ultrasonic nebulizer that introduces small fuel droplets into a heated nitrogen stream, fostering complete vaporization without fractional distillation. Temperature profiles and extinction limits are measured in all flames and compared with predictions using the semi-detailed mechanism. These measurements show good agreement with predictions in single-component n-dodecane, methylcyclohexane, and iso-octane flames. Good agreement also exists between predicted and measured variables in flames of the surrogate, and the agreement is even better between the experimental JP-8 flames and the surrogate predictions.

An Eulerian multi-fluid model is validated by comparison with experimental measurements in the test case of laminar spray counterflow diffusion flames. Special attention is devoted, both from the modelling and experimental point of view, to the treatment of the droplet distribution tail, characterized by the rare occurrence of relatively large droplets carrying a non-negligible amount of mass. The Eulerian multi-fluid approach is shown to capture the dynamics, evaporation and heating of the droplets with a limited number of sections and, thus, at a modest cost. This simplification will be essential for the use of multi-fluid methods in multi-dimensional problems.

Laminar, sooting, ethylene-fuelled, co-flow diffusion flames at atmospheric pressure have been studied experimentally and theoretically as a function of fuel dilution by inert nitrogen. The flames have been investigated experimentally using a combination of laser diagnostics and thermocouple-gas sampling probe measurements. Numerical simulations have been based on a fully coupled solution of the flow conservation equations, gas-phase species conservation equations with complex chemistry and the dynamical equations for soot spheroid growth. Predicted flame heights, temperatures and the important soot growth species, acetylene, are in good agreement with experiment. Benzene simulations are less satisfactory and are significantly under-predicted at low dilution levels of ethylene. As ethylene dilution is decreased and soot levels increase, the experimental maximum in soot moves from the flame centreline toward the wings of the flame. Simulations of the soot field show similar trends with decreasing dilution ...

We report on the development of a soot map that separates non-sooting from sooting regions of laminar, counterflow, methane-oxygen-nitrogen diffusion flames at atmospheric pressure. Soot formation is studied at a constant global strain rate of 20 s m 1 as a function of the amounts of methane (0-100%) in the fuel stream and of oxygen (0-100%) in the oxidizer stream. Visual evidence for incipient soot formation is obtained by increasing the mole fraction of oxygen in the oxidizer stream for a given mole fraction of methane in the fuel stream. As the percent methane in the fuel stream increases, less percent oxygen in the oxidizer stream is required for soot inception. A detailed soot model duplicates the experimentally observed soot map and suggests that soot formation under our conditions is associated with a peak flame temperature near 2550 K and a peak soot volume fraction around 1 ppm. Similarly, peak soot inception can be correlated with a temperature of ∼1750 K anywhere along the soot limit curve.

The formation of nitric oxide was investigated in methane diffusion flames under the perturbation of laminar vortices. Laser-induced fluorescence and Raman spectroscopy were used to measure nitric oxide, major species, and temperature, and to obtain the time evolution of the scalar dissipation rate at the stoichiometric surface during the flame/vortex interaction. Vortices with two characteristic times were thrust into the flame and their effects were compared with steady flames at the same scalar dissipation rate. The experimental measurements showed that the vortex did not affect significantly the peak temperature, CO, and CO2 mass fraction during the interaction. NO, instead, was strongly affected. The peak mass fraction of NO in flames under vortex perturbation differed by almost a factor of 2 from steady flames with similar scalar dissipation rates. One-dimensional numerical simulations, used under the well-justified assumption that the vortices induced negligible curvature, yielded results in good agreement with the experimental measurements. The numerical computations were also used to investigate the effect of the characteristic time of the vortex on the different NO formation paths, that is, thermal, and prompt. The peak mass fraction of thermal NO was shown to be strongly dependent on the timescale of the unsteady perturbation, while prompt NO was almost independent. The emission index, that is, the production of NO normalized by the consumption of the fuel, behaved quasi-steadily for the two formation paths. The results were rationalized by considering the flame structure and the activation energy of the different formation paths.

Rayleigh scattering has been shown to be a useful diagnostic technique for two-dimensional imaging studies of reacting and non-reacting flows. For example, by combining Rayleigh scattering with a simultaneous measurement of the fuel concentration (e.g., using Raman scattering), mixture fraction and temperature can be determined in flames. In this work, it is demonstrated that the fuel concentration can be obtained by measuring the polarized and depolarized components of the Rayleigh signal and taking their difference or a suitable linear combination. While the depolarized Rayleigh signal is smaller than the polarized signal by a factor of ≈100, this is still a factor of ≈10 larger than the Raman scattering. Application of the technique requires that one of the primary constituents of the fuel stream possess a depolarization ratio sufficiently different from that of the oxidizer. Methane is a convenient candidate as it has no measurable depolarization. Results are shown for methane flames diluted by argon as well as air.

Counterflow diffusion flame experiments and modeling results are presented for a fuel mixture consisting of CO and H 2 flowing against decomposition products from a solid ammonium perchlorate (AP) pellet. The flame zone simulates the diffusion flame structure that is expected to exist between reaction products from fine AP crystals and a hydrocarbon binder with the decomposition products from large AP crystals, characteristic of a bimodal AP propellant. Quantitative species and temperature profiles have been measured for a mixture of two fuels, hydrogen and CO, and one strain rate, given by a separation of 5 mm, between the fuel exit and AP surface. Species measured included CN, NH, NO, OH, N 2 , O 2 CO 2 , H 2 , CO, HCl, and H 2 O. Temperature was measured using a combination of a thermocouple at the exit, spontaneous Raman scattering measurements throughout the flame, OH rotational population distributions, and NO vibrational population distributions. The burning rate of the AP was also measured for this flame's strain rate. The measured 12 scalars are compared with predictions from a detailed gas-phase kinetics models consisting of 86 species and 531 reactions. Model predictions are found to be in good agreement with experiment and illustrate the type of kinetic features that may be expected to occur in propellants when AP particle size distributions are varied.