The computation of laminar flames

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 stability of laminar explosion flames

The paper presents the results of a fundamental experimental and theoretical study of Darrieus–Landau, thermo-diffusive, instabilities in atmospheric explosions, and, on a smaller scale, in laboratory explosions in closed vessels. Pressure dependencies were sought to exploit the leading role of the Peclet number in the phenomena, so that similar Peclet numbers were achieved in both instances. However, in large atmospheric explosions large Peclet numbers were achieved by the size of the fireball, whereas in the closed vessel explosion it was achieved at a higher pressure by a much smaller flame, but because of the higher pressure, one endowed with a small laminar flame thickness. This study covers a much wider range of fuels and of pressures and the dependencies of the phenomena on both of these were carefully studied, although, for the atmospheric explosions, the data only covered propane and methane. The roles of both Markstein and Peclet numbers become clear and give rise to a more fundamental correlating parameter, a critical Karlovitz number, K_cl, for flame stability. This is based on the flame stretch rate, normalised by its multiplication by the chemical reaction time in a laminar flame. The experimentally measured dependencies of this key parameter on pressure and Markstein number are reported for the first time for so many different fuels. The critical Karlovitz number for flame stability decreases with increase in the strain rate Markstein number. As a result, it is possible to predict the extent of the unstable regime for laminar flames as a function of Ma_sr and pressure. Such data can be used to estimate the severity of large scale atmospheric explosions. As Ma_sr becomes highly negative, the regime of stability is markedly reduced.     

A numerical study on extinction behaviour of laminar micro-diffusion flames

We conducted a numerical study on the fluid dynamic, thermal and chemical structures of laminar methane–air micro flames established under quiescent atmospheric conditions. The micro flame is defined as a flame on the order of one millimetre or less established at the exit of a vertically-aligned straight tube. The numerical model consists of convective–diffusive heat and mass transport with a one-step, irreversible, exothermic reaction with selected kinetics constants validated for near-extinction analyses. Calculations conducted under the burner rim temperature 300 K and the adiabatic burner wall showed that there is the minimum burner diameter for the micro flame to exist. The Damköhler number (the ratio of the diffusive transport time to the chemical time) was used to explain why a flame with a height of less than a few hundred microns is not able to exist under the adiabatic burner wall condition. We also conducted scaling analysis to explain the difference in extinction characteristics caused by different burner wall conditions. This study also discussed the difference in governing mechanisms between micro flames and microgravity flames, both of which exhibit similar spherical flame shape.     

Constrained-temperature solutions of coflow laminar diffusion flames

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.     

A numerical investigation of stretch effects in counterflow,premixed laminar flames

We use direct numerical simulation of propane/air flames with full chemistry in the geometry of stagnation flow to investigate the effect of different definitions of local flame stretch in the presence of spatially varying velocity gradients. Specifically, we compare simulations with potential- and plug-flow inlet conditions, and show that the widely used definition of upstream stretch leads to unphysical results for flames having the ‘same’ stretch. We then show that a reasonable re-definition of local stretch allows us to produce the ‘same’ flame in the presence of the ‘same’ stretch.     

Numerical simulations of soot aggregation in premixed laminar flames

In this paper we make use of a detailed particle model and stochastic numerical methods to simulate the particle size distributions of soot particles formed in laminar premixed flames. The model is able to capture the evolution of mass and surface area along with the full structural detail of the particles. The model is validated against previous models for consistency and then used to simulate flames with bimodal and unimodal soot particle distributions. The change in morphology between the particles from these two types of flames provides further evidence of the interplay among nucleation, coagulation, and surface rates. The results confirm the previously proposed role of the strength of the particle nucleation source in defining the instant of transition from coalescent to fractal growth of soot particles.     

Infrared analysis of nano organic particles produced in laminar flames

In this work we present the first infrared investigation of nano-sized organic carbon (NOC) particles produced in premixed laminar ethylene flames. We analyzed the chemical transformation of NOC when the combustible/oxidant ratio (C/O) passed from lean to slightly sooting conditions. We also demonstrate the increase of the aromatic character for samples under thermal treatment. The analysis of the infrared spectra clearly shows the persistence of this material after soot inception. PACS 33.20.Ea; 82.33.Vx     

Magnetic field influence on coflow laminar diffusion flames

The behavior of a laminar methane air flame with a central methane jet and a surrounding air coflow is analyzed in a large range of fuel and air flow rates. Different regimes of flame stability are described from an anchored flame to a stable lifted flame which is destabilized before extinction. Influence of an upward increasing magnetic field generated by an electromagnet is then studied. Experimental measurements at different values of methane and air flow rates show that the flame lift-off height is decreased by the magnetic gradient. These effects are attributed to the magnetic force which develops on air via its action on the paramagnetic oxygen molecules. The magnetic force interacts with the air jet structures upstream of the flame and then influences the flame stability.     

Soot studies of laminar diffusion flames with recirculation zones

This paper describes the unusual sooting structure of three flames established by the laminar recirculation zones of a centerbody burner. The vertically mounted burner consists of an annular air jet and a central fuel jet separated by a bluff-body. The three ethylene fueled flames are identified as: fully sooting, donut-shape, and ring-shape sooting flames. Different shapes of the soot structures are obtained by varying the N₂ dilution in the fuel and air jets while maintaining a constant air and fuel velocity of 1.2 m/s. All three flames have the unusual characteristic that the soot, entrained into the recirculation zone, follows discrete spiral trajectories that terminate at the center of the vortex. The questions are what cause: (1) the unusual sooting structures and (2) the spiral trajectories of the soot? Flame photographs, laser sheet visualizations, and calculations with a 2D CFD-based code (UNICORN) are used to answer these questions. The different sooting structures are related to the spiral transport of the soot, the spatial location of the stoichiometric flame surface with respect to the vortex center, and the burnout of the soot particles. Computations indicate that the spiral trajectories of the soot particles are due to thermophoresis.     

A comparison of computational and experimental lift-off heights of coflow laminar diffusion flames

As a sensitive marker of changes in flame structure, the number densities of excited-state CH (denoted CH^*), and excited-state OH (denoted OH^*) are imaged in coflow laminar diffusion flames. Measurements are made both in normal gravity and on the NASA KC-135 reduced-gravity aircraft. The spatial distribution of these radicals provides information about flame structure and lift-off heights that can be directly compared with computational predictions. Measurements and computations are compared over a range of buoyancy and fuel dilution levels. Results indicate that the lift-off heights and flame shapes predicted by the computations are in excellent agreement with measurement for both normal gravity (1g) and reduced gravity flames at low dilution levels. As the fuel mixture is increasingly diluted, however, the 1g lift-off heights become underpredicted. This trend continues until the computations predict stable flames at highly dilute fuel mixtures beyond the 1g experimental blow-off limit. To better understand this behavior, an analysis was performed, which indicates that the lift-off height is sensitive to the laminar flame speed of the corresponding premixed mixture at the flame edge. By varying the rates of two key “flame speed” controlling reactions, we were able to modify the predicted lift-off heights so as to be in closer agreement with the experiments. The results indicate that reaction sets that work well in low dilution systems may need to be modified to accommodate high dilution flames.     

Mechanism on oscillating lifted flames in nonpremixed laminar coflow jets

The oscillating lifted flame in a laminar nonpremixed nitrogen-diluted fuel jet is known to be a result of buoyancy, though the detailed physical mechanism of the initiation has not yet been properly addressed. We designed a systematic experiment to test the hypothesis that the oscillation is driven by competition between the positive buoyancy of flame and the negative buoyancy of a fuel stream heavier than the ambient air. The positive buoyancy was examined with various flame temperatures by changing fuel mole fraction, and the negative buoyancy was investigated with various fuel densities. The density of the coflow was also varied within a certain range by adding either helium or carbon dioxide to air, to study how it affected the positive and negative buoyancies at the same time. As a result, we found that the range of oscillation was well-correlated with the positive and the negative buoyancies; the former stabilized the oscillation while the latter triggered instability and became a source of the oscillation. Further measurements of the flow fields and OH radicals evidenced the important role of the negative buoyancy on the oscillation, detailing a periodic variation in the unburned flow velocity that affected the displacement of the flame.     

Local rectangular refinement with application to axisymmetric laminar flames

Within realistic combustion devices, physical quantities may change by an order of magnitude over an extremely thin flamefront, while remaining nearly unchanged throughout large areas nearby. Such behaviour dictates the use of adaptive numerical methods. The recently developed local rectangular refinement (LRR) solution-adaptive gridding method produces robust unstructured rectangular grids, utilizes novel multiple-scale finite-difference discretizations, and incorporates a damped modified Newton's method for simultaneously solving systems of governing elliptic PDEs. Here, the LRR method is applied to two axisymmetric laminar flames: a premixed Bunsen flame with one-step chemistry and a diffusion flame employing various complex chemical mechanisms. The Bunsen flame's position is highly dependent upon grid spacing, especially on coarse grids; it stabilizes only with adequate refinement. The diffusion flame results show excellent agreement with experimental data for flame structure, temperature and major species. For both flames, the LRR results on intermediate grids are comparable to those obtained on equivalently refined conventional grids. Solution accuracy on the final LRR grids could not be achieved using conventional grids because the latter exceeded the available computer memory. In general, the LRR method required about half the grid points, half the memory and half the computation time of the solution process on conventional grids.     

Computational and experimental study of oxygen-enhanced axisymmetric laminar methane flames

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. Computational and experimental flame lengths show excellent agreement, as do the maximum centreline temperatures. For each flame, radial profiles of temperature and major species also show excellent agreement between computations and experiments, when plotted at fixed values of a dimensionless axial coordinate. Computational results indicate peak NO levels in the oxygen-enhanced flames to be very high. The majority of the NO in these flames is shown to be produced via the thermal route, whereas prompt NO dominates for the base case flame.     

Numerical simulation of finite disturbances interacting with laminar premixed flames

Compression waves can be generated during combustion processes and subsequently interact with flames to augment their behaviour. The study of these interactions thus far has been limited to shock and expansion waves only. In this study, the interaction of finite compression waves with a perturbed laminar flame is investigated using numerical simulations of the compressible Navier–Stokes equations with single-step chemical kinetics. The interaction is characterised using three independent parameters: the compression wavelength, the pressure ratio of the disturbance, and the perturbation amplitude of the flame interface. The results reveal a wide range of behaviours in terms of flame length and heat release rate that could occur during such an interaction. The results are compared to the classical reactive Richtmyer–Meshkov instability and the role of baroclinic torque and vorticity generation are shown to be primary drivers of the flow instability.     

Route to chaos for combustion instability in ducted laminar premixed flames

Complex thermoacoustic oscillations are observed experimentally in a simple laboratory combustor that burns lean premixed fuel-air mixture, as a result of nonlinear interaction between the acoustic field and the combustion processes. The application of nonlinear time series analysis, particularly techniques based on phase space reconstruction from acquired pressure data, reveals rich dynamical behavior and the existence of several complex states. A route to chaos for thermoacoustic instability is established experimentally for the first time. We show that, as the location of the heat source is gradually varied, self-excited periodic thermoacoustic oscillations undergo transition to chaos via the Ruelle-Takens scenario.     

Decreasing liftoff height behavior in diluted laminar lifted methane jet flames

Stabilization of laminar lifted coflow jet flames of nitrogen-diluted methane was investigated experimentally and numerically. As the fuel jet velocity was increased, two distinct behaviors in liftoff height were observed depending on the initial fuel mole fraction; a monotonically increasing trend and a decreasing and then increasing trend (U-shaped behavior). The former was observed in the jet-developing region and the latter in the jet-developed region. Because the decreasing behavior of liftoff height with jet velocity has not been observed at ambient temperature, the present study focuses on decreasing liftoff height behavior. To elucidate the physical mechanism underlying the U-shaped behavior, numerical simulations of reacting jets were conducted by adopting a skeletal mechanism. The U-shaped behavior was related to the buoyancy. At small jet velocities, the relative importance of the buoyancy over convection was strong and the flow field was accelerated in the downstream region to stabilize the lifted flame. As the jet velocity increased, the relative importance of buoyancy decreased and the liftoff height decreased. As the jet velocity further increased, the flame stabilization was controlled by jet momentum and the liftoff height increased.