An experimental and numerical study on the adequacy of CH as a flame marker in premixed methane flames

The CH radical is frequently used as a flame marker because it is relatively short-lived and is present over a narrow region in flames. Discontinuities in the CH field are thus often interpreted as localized extinction of the flame. Recently, however, the adequacy of CH laser-induced fluorescence (LIF) as a flame marker was questioned by an experimental study of flame–vortex interactions in highly N₂-diluted premixed methane flames. We demonstrate both experimentally and numerically that anomalies in the transient response of CH in this earlier study were due to reactant composition variations in the vortex. In addition, we evaluate the adequacy of CH LIF as a flame marker over a much broader range of conditions. Previous numerical studies showed that heat release rate correlates reasonably well with peak [HCO] and the concentration product [OH][CH₂O], but poorly with [CH], in highly N₂-diluted premixed methane flames. Here, the correlation between heat release rate and CH is investigated both experimentally, by performing simultaneous measurements of CH, OH, and CH₂O LIF, and numerically. We consider undiluted and N₂-diluted premixed methane flames over a range of strain rates and stoichiometries. Results are reported for flames subjected to unsteady stretch and reactant composition variations. For all N₂-dilution levels considered, the peak CH LIF signal correlates poorly with heat release rate when the stoichiometry of the reactant mixture changes from rich to lean. However, when flames are subjected to stretch, the correlation between CH and heat release rate improves as the N₂-dilution level decreases. The correlation is reasonably good for undiluted flames with equivalence ratios of 0.8 < Φ < 1.2. This result is particularly encouraging, given the relevance of undiluted flames to practical applications, and it motivates further investigation of the parameter space for which difficulties may exist in using CH as a flame marker.     

Structural response of different Lewis number premixed flames interacting with a toroidal vortex

Simultaneous measurements of temperature, CH* and OH* chemiluminescent species are carried out to explore the impact of stretch rate and curvature on the structure of premixed flames. The configuration of an initially flat premixed flame interacting with a toroidal vortex is selected for the present study and reasons for this choice are discussed. Lewis number effects are assessed by comparing methane and propane flames. It is emphasized that the flame structure experiences very strong variations. In particular, the flame is shrunk (broadened) in the initial (final) period of the interaction with the vortex where strain rate (curvature) contribution of the stretch rate is predominant. By further analysing independently the thickness of the preheat and reaction zones, it is shown that for propane flames, not only the former but also the latter is significantly altered in zones where the flame curvature is negative. Changes in the reaction zone properties are further emphasized using CH* and OH* radicals. It is demonstrated that higher thermal diffusivity plays a significant role around curved regions, in which the enhanced diffusion of heat leads to a strong increase of CH* compared to OH* intensity. As an overall conclusion, this study suggests that it would be interesting to reassess the internal flame structure at lower and moderate Karlovitz numbers since changes might appear for a moderate vortex intensity with typical size much larger than the flame thickness.     

Evaluation of models for flame stretch due to curvature in the thin reaction zones regime

Direct numerical simulation (DNS) was used to study modelling assumptions for the curvature-propagation component of flame stretch in the thin reaction zones regime of turbulent premixed combustion, a regime in which small eddies can penetrate the preheat zone but not the thinner fuel breakdown zone. Simulations of lean hydrogen–air and methane–air flames were conducted, and statistics of flame stretch due to curvature, henceforth referred to simply as stretch, were extracted from a species mass fraction iso-surface taken to represent the flame. The study focussed on investigating the modelling assumptions of Peters [J. Fluid Mech. 384 (1999) 107]. It was found that the mean stretch is dominated by stretch due to correlations of flame speed with curvature, and specifically the effects of tangential diffusion. The modelling suggestions of Peters were found to provide an improvement over the assumptions of a constant flame speed or a flame speed governed by the linear relationship with stretch at small and steady stretch. However for the conditions considered here, diffusive-thermal effects remain well into the thin reaction zones regime, and the suggestions of Peters generally over-predict the mean compressive stretch. An effective diffusivity for flame stretch was suggested and evaluated for the methane simulations. It was found that the effective diffusivity was comparable to the mass diffusivity for flames with a high ratio of flame time to eddy turnover time. The length scales contributing to stretch were investigated, and it was found that while most flame area has a radius of curvature greater than the laminar flame thickness, most stretch occurs in more tightly curved flame elements.     

Nonlinear hydrodynamic and thermoacoustic oscillations of a bluff-body stabilised turbulent premixed flame

Turbulent premixed flames often experience thermoacoustic instabilities when the combustion heat release rate is in phase with acoustic pressure fluctuations. Linear methods often assume a priori that oscillations are periodic and occur at a dominant frequency with a fixed amplitude. Such assumptions are not made when using nonlinear analysis. When an oscillation is fully saturated, nonlinear analysis can serve as a useful avenue to reveal flame behaviour far more elaborate than period-one limit cycles, including quasi-periodicity and chaos in hydrodynamically or thermoacoustically self-excited system. In this paper, the behaviour of a bluff-body stabilised turbulent premixed propane/air flame in a model jet-engine afterburner configuration is investigated using computational fluid dynamics. For the frequencies of interest in this investigation, an unsteady Reynolds-averaged Navier–Stokes approach is found to be appropriate. Combustion is represented using a modified laminar flamelet approach with an algebraic closure for the flame surface density. The results are validated by comparison with existing experimental data and with large eddy simulation, and the observed self-excited oscillations in pressure and heat release are studied using methods derived from dynamical systems theory. A systematic analysis is carried out by increasing the equivalence ratio of the reactant stream supplied to the premixed flame. A strong variation in the global flame structure is observed. The flame exhibits a self-excited hydrodynamic oscillation at low equivalence ratios, becomes steady as the equivalence ratio is increased to intermediate values, and again exhibits a self-excited thermoacoustic oscillation at higher equivalence ratios. Rich nonlinear behaviour is observed and the investigation demonstrates that turbulent premixed flames can exhibit complex dynamical behaviour including quasiperiodicity, limit cycles and period-two limit cycles due to the interactions of various physical mechanisms. This has implications in selecting the operating conditions for such flames and for devising proper control strategies for the avoidance of thermoacoustic instability.     

Spatiotemporal measurements of flame stretch and propagation rates for lean and rich CH4/air premixed flames interacting with a turbulent-wake

A 1.5 m long turbulent-wake combustion vessel with a 0.15 m × 0.15 m cross-sectional area is proposed for spatiotemporal measurements of curvature, strain, dilatation and burning rates along a freely downward-propagating premixed flame interacting with a parallel row of staggered vortex pairs having both compression (negative) and extension (positive) strains simultaneously. The wanted wake is generated by rapidly withdrawing an electrically-controlled, horizontally-oriented sliding plate of 5 mm thickness for flame–wake interactions. Both rich and lean CH₄/air flames at the equivalence ratios  = 1.4 and  = 0.7 with nearly the same laminar burning velocity are studied, where flame–wake interactions and their time-dependent velocity fields are obtained by high-speed, high-resolution DPIV and laser-tomography. Correlations among curvature, strain, stretch, and dilatation rates along wrinkled flame fronts at different times are measured and thus their influences on front propagation rates can be analyzed. It is found that strain-related effects have significant influence on front propagation rates of rich CH₄/air (diffusionally stable) flames even when the curvature weights more in the total stretch than the strain rate does. The local propagation rates along the wrinkled flame front are more intense at negative strain rates corresponding to positive peak dilatation rates but the global propagation rate averaged along the rich flame front remains constant during all period of flame–wake interaction. For lean CH₄/air (diffusionally unstable) flames, the curvature becomes a dominant parameter influencing the structure and propagation of the wrinkled flame front, where both local and global propagation rates increase significantly with time, showing unsteady flame propagation. These experimental results suggest that the theory of laminar flame stretch can be applicable to a more complex flame–wake interaction involving unsteadiness and multitudinous interactions between vortices.     

Theoretical analysis of the evolution from ignition kernel to flame ball and planar flame

Dynamics of flame kernel evolution with and without external energy addition has been investigated analytically and numerically. Emphasis is placed on the effects of radiation heat loss, ignition power and Lewis number on the correlation and transition between the initial flame kernel, the self-extinguishing flame, the flame ball, the outwardly propagating spherical flame and the propagating planar flame. The present study extends previous results by bridging the theories of the non-adiabatic stationary flame balls and travelling flames and allowing rigorous consideration of radiation heat losses. The results show that the effects of radiation heat loss play an important role in flame regimes and flame transition and result in a new isolated self-extinguishing flame. Furthermore, it is found that radiation heat losses significantly increase the critical ignition radius and result in three different dependences of the minimum ignition power on the Lewis number. Comparisons between the results from the transient numerical simulation and those from the quasi-steady state analysis show a good agreement. The results suggest that prediction of flame initiation without appropriate consideration of radiation is not acceptable.     

Interaction of the vortex and edge dislocation embedded in a cosh-Gaussian beam

The interaction of the vortex and edge dislocation embedded in a cosh-Gaussion (ChG) beam is studied, where the both dislocations are on-axis, off-axis, or one is on-(off-) axis. It is shown that by varying a beam parameter of the ChG background beam or in the free-space propagation, the break-up of the edge dislocation and the motion, creation and annihilation of vortices may take place. In the vortex evolution process the topological charge is not conserved in general. The results are illustrated numerically and compared with the previous work.     

Construction of explicit and implicit dynamic finite difference schemes and application to the large-eddy simulation of the Taylor–Green vortex

A general class of explicit and implicit dynamic finite difference schemes for large-eddy simulation is constructed, by combining Taylor series expansions on two different grid resolutions. After calibration for Re→∞, the dynamic finite difference schemes allow to minimize the dispersion errors during the calculation through the real-time adaption of a dynamic coefficient. In case of DNS resolution, these dynamic schemes reduce to Taylor-based finite difference schemes with formal asymptotic order of accuracy, whereas for LES resolution, the schemes adapt to Dispersion-Relation Preserving schemes. Both the explicit and implicit dynamic finite difference schemes are tested for the large-eddy simulation of the Taylor–Green vortex flow and numerical errors are investigated as well as their interaction with the dynamic Smagorinsky model and the multiscale Smagorinsky model. Very good results are obtained.     

Green’s function-stochastic methods framework for probing nonlinear evolution problems: Burger’s equation, the nonlinear Schrödinger’s equation, and hydrodynamic organization of near-molecular-scale vorticity

A framework which combines Green’s function (GF) methods and techniques from the theory of stochastic processes is proposed for tackling nonlinear evolution problems. The framework, established by a series of easy-to-derive equivalences between Green’s function and stochastic representative solutions of linear drift–diffusion problems, provides a flexible structure within which nonlinear evolution problems can be analyzed and physically probed. As a preliminary test bed, two canonical, nonlinear evolution problems – Burgers’ equation and the nonlinear Schrödinger’s equation – are first treated. In the first case, the framework provides a rigorous, probabilistic derivation of the well known Cole–Hopf ansatz. Likewise, in the second, the machinery allows systematic recovery of a known soliton solution. The framework is then applied to a fairly extensive exploration of physical features underlying evolution of randomly stretched and advected Burger’s vortex sheets. Here, the governing vorticity equation corresponds to the Fokker–Planck equation of an Ornstein–Uhlenbeck process, a correspondence that motivates an investigation of sub-sheet vorticity evolution and organization. Under the assumption that weak hydrodynamic fluctuations organize disordered, near-molecular-scale, sub-sheet vorticity, it is shown that these modes consist of two weakly damped counter-propagating cross-sheet acoustic modes, a diffusive cross-sheet shear mode, and a diffusive cross-sheet entropy mode. Once a consistent picture of in-sheet vorticity evolution is established, a number of analytical results, describing the motion and spread of single, multiple, and continuous sets of Burger’s vortex sheets, evolving within deterministic and random strain rate fields, under both viscous and inviscid conditions, are obtained. In order to promote application to other nonlinear problems, a tutorial development of the framework is presented. Likewise, time-incremental solution approaches and construction of approximate, though otherwise difficult-to-obtain backward-time GF’s (useful in solution of forward-time evolution problems) are discussed.