Flamelet Regime Of Turbulent Combustion Research Articles

Analysis of Algebraic Closures of the Mean Scalar Dissipation Rate of the Progress Variable Applied to Stagnating Turbulent Flames

In the turbulent premixed reactive flows considered in this study, i.e. large Damkohler and Reynolds numbers, the flamelet regime of turbulent combustion applies and the scalar dissipation rate and mean reaction rate are inter related. In this situation various algebraic models for the mean chemical rate that are obtained from an equilibrium of the dominant terms of the transport equation for the scalar dissipation rate, are evaluated through their application to flames stabilized in a turbulent stagnating flow. An asymptotic analysis is first performed and results obtained through the resulting one-dimensional calculation are compared with the experimental data of Li et al. (Proc Combust Inst 25:1207–1214, 1994). Eventually, three-dimensional CFD calculations including suited algebraic closures to represent the turbulent transport terms are carried out. Results are satisfactorily compared to the experimental data of Cho et al. (Proc Combust Inst 22:739–745, 1988). As a first outcome, the analysis confirms the interest and the relevance of the corresponding algebraic closures to deal with turbulent premixed combustion in such conditions. In the search of a satisfactory representation of such premixed impinging flames, the computational results also clearly emphasize the strong intertwinment that exits between the mean reaction rate, i.e. scalar dissipation rate or micro-mixing taking place at the smallest scale of the reactive flowfield, and the Reynolds fluxes modelling, i.e. turbulent macro-mixing.

Propagation of wrinkled turbulent flames in the context of hydrodynamic theory

We study the propagation of premixed flames in two-dimensional homogeneous isotropic turbulence using a Navier–Stokes/front-capturing methodology within the context of hydrodynamic theory. The flame is treated as a thin layer separating burnt and unburnt gases, of vanishingly small thickness, smaller than the smallest fluid scales. The method is thus suitable to investigate the flame propagation in the wrinkled flamelet regime of turbulent combustion. A flow-control system regulates the mean position of the flame and the incident turbulence intensity. In this context we study the individual effects of turbulence intensity, turbulence scale, thermal expansion, hydrodynamic strain and hydrodynamic instability on the propagation characteristics of the flame. Results are obtained assuming positive Markstein length, corresponding to lean hydrocarbon–air or rich hydrogen–air mixtures. For stable planar flames we find a quadratic dependence of turbulent speed on turbulence intensity. Upon onset of hydrodynamic instability, corrugated structures replace the planar conformation and we observe a greater resilience to turbulence, the quadratic scaling being replaced by scaling exponents less than one. Such resilience is also confirmed by the observation of a threshold turbulence intensity below which the propagation speed of corrugated flames is indistinguishable from the laminar speed. Turbulent speed is found to increase and later plateau with increasing thermal expansion, this affecting the average flame displacement but not the mean flame curvature. In addition, turbulence integral scale is also observed to affect the propagation of the flame with the existence of an intermediate scale maximizing the turbulent speed. This maximizing scale is smaller for corrugated flames than it is for planar flames, implying that small eddies that will be unable to significantly perturb a planar front could be rather effective in perturbing a corrugated flame. Turbulent planar flames, and more so corrugated flames, were observed to experience a positive mean hydrodynamic strain, which was explained in terms of the overwhelming mean contribution of the normal component of strain. The positive straining causes a decrease in the mean laminar propagation speed which in turn can decrease the turbulent speed. The effect of the flame on the incident turbulent field was examined in terms of loss of isotropy and vorticity destruction by thermal expansion. The latter can be mitigated by a baroclinic vorticity generation which is enhanced for corrugated flames.

Turbulent propagation of premixed flames in the presence of Darrieus–Landau instability

We investigate the role played by hydrodynamic instability in the wrinkled flamelet regime of turbulent combustion, where the intensity of turbulence is small compared to the laminar flame speed and the scale large compared to the flame thickness. To this end the Michelson–Sivashinsky (MS) equation for flame front propagation in one and two spatial dimensions is studied in the presence of uncorrelated and correlated noise representing a turbulent flow field. The combined effect of turbulence intensity, integral scale, and an instability parameter related to the Markstein length are examined and turbulent propagation speed monitored for both stable planar flames and corrugated flames for which the planar conformation is unstable. For planar flames a particularly simple scaling law emerges, involving quadratic dependence on intensity and a linear dependence on the degree of instability. For corrugated flames we find the dependence on intensity to be substantially weaker than quadratic, revealing that corrugated flames are more resilient to turbulence than planar flames. The existence of a threshold turbulence intensity is also observed, below which the corrugated flame in the presence of turbulence behaves like a laminar flame. We also analyze the conformation of the flame surface in the presence of turbulence, revealing primary, large-scale wrinkles of a size comparable to the main corrugation. When the integral scale is much smaller than the characteristic corrugation length we observe, in addition to primary wrinkles, secondary small-scale wrinkles contaminating the surface. The flame then acquires a multi-scale, self-similar conformation, with a fractal dimension, for one-dimensional flames, plateauing at 1.23 for large intensities. The existence of an intermediate integral scale is also found at which the turbulent speed is maximized. When two-dimensional flames are subject to turbulence, the primary wrinkling patterns give rise to polyhedral-cellular structures which bear a very close resemblance to those observed in experiments on hydrodynamically unstable expanding spherical flames.

Interaction of adjacent flame surfaces on the formation of wrinkling laminar premixed flame

To gain further understanding of the flamelet regime of turbulent combustion, the interaction betweenadjacent flame surfaces of a wrinkling laminar premixed flame has been investigated experimentally. The wrinkling flame was formed with three adjacent laminar V-shaped flames stabilized on a multiple-slitburner of a propane/air mixture. In addition, a single V-shaped flame was also formed on the burner. We compared flame shapes and flow velocity distributions between those two types of flames. The results show that the unburned flow field was expanded outwardly by the convex flame surface toward unburned side. In the case of the wrinkling flame, however, the outward deviation of the flow field caused by the existence of the inner convex was prevented by the existence of the surrounding flames. Consequently, the inner convex flame surface of the wrinkling flame is more oblique, and the curvature is sharper than that of a single convex flame (single V-shaped flame) due to the interaction of adjacent flame surfaces. Moreover, the formation of the inner convex flame of the wrinkling flame is more unstable than that of a single convex flame. This is due to the curvature of the inner convex of the wrinkling flame being sharper than that of the single convex flame so that the burning velocity is decreased as a result of the curvature effect.

The role of Landau-Darrieus instability in large scale flows

To gain insight into the role of the Landau-Darrieus instability in the “flamelet” regime of turbulent premixed combustion, the propagation of unstable flames was simulated in flows with a scale much larger than the flame thickness. The simulations were performed using a method that approximates the flame as a discontinuity in the flow. The flow field through which the flame propagated was a periodic array of “square vortices.” From the results of the simulations, it was determined that, although the scale at which the Landau-Darrieus instability has its maximum effect may be much smaller than the flow scale, flame wrinkles with a scale smaller than the flow scale do not develop. This has the consequence that for the flamelet regime of turbulent combustion the smallest flame wrinkling scale will most likely be determined by the flow, not the Landau-Darrieus instability. We also found that although the instability did not induce small scale wrinkling, it did have a significant effect on the mean consumption rate of the flame. For unstable flames, the flame distortions created by the vortices were much larger in amplitude than the distortions of a stable flame. This resulted in an increased consumption rate relative to a stable flame because of the increased surface area of the flame. It is suggested that in the flamelet regime of turbulent combustion the Landau-Darrieus instability will have a similar effect at least for weak to moderate flow intensities such as the ones studied here.

Instability-induced extinction of diffusion flames established in the stagnant mixing layer

Nonlinear dynamics of diffusional-thermal instability in diffusion flames is numerically investigated by employing a diffusion flame established in the stagnant mixing layer as a model. Particular attention is focused on the pulsating-instability regime, which arises for Lewis numbers sufficiently greater than unity. Once the steady flame structure is obtained for a prescribed value of the initial Damköhler number, transient evolution of the flame is calculated after a finite amount of the Damköhler-number perturbation is imposed on the steady flame. Depending on whether the initial Damköhler number is greater than the bifurcation Damköhler number or not, evolution of the transient flame structures can be differently characterized. If the initial Damköhler number is smaller than the bifurcation Damköhler number, pulsating instability can be triggered without any external perturbations, while if the initial Damköhler number is greater than the bifurcation Damköhler number, flame oscillations can be amplified only for the perturbed Damköhler number smaller than the threshold Damköhler number. Therefore, character of the nonlinear instability is subcritical. Once the oscillation amplitudes grow too large, flames are eventually led to extinction. Locus of the threshold Damköhler number is presented, which could be used as a revised extinction criterion for diffusion-flamelet library in the laminar flamelet regime of turbulent combustion.

Response of counterflow premixed flames to oscillating strain rates

We study the response of premixed counterflow flames to an imposed oscillating strain rate which has potential application to both turbulent combustion and acoustic instabilities. We exploit the limit of large activation energy to resolve the reaction zone structure, and conduct a linear perturbation analysis for small amplitude of oscillation. Reaction-sheet fluctuations and the net heat release rate are investigated for both the symmetric twin-flame configuration and a single flame residing in a counterflow system consisting of a fresh-mixture stream impinging on a cold inert stream. The Lewis number is found to play an important role in the flame response, especially for flames near extinction. For those flames that exhibit turning point behavior, near extinction the effect of finite-rate chemistry overtakes fluid-dynamic effects such that increasing strain rate can lead to a phase reversal of the heat release response with the imposed flow oscillations. Results of the present study suggest the possibility of a wide spectrum of unsteady flame characteristics depending on Lewis number. Our results also demonstrate that extinction can be delayed when the strain rate oscillates about the static extinction point. Thus the laminar flamelet regime of turbulent combustion may be broader than predicted by steady analyses.

Chemical closure and burning rates in premixed turbulent flames

Chemical closure for premixed turbulent flames is considered, and with a small number of assumptions regarding its form, a model expression for the mean rate of product formation is obtained: 〈 w〉 = C p 〈 c〉(1 - 〈 c〉) to fourth order in ( 〈c〉 - 1 2 ), with C p a proportionality factor. Any model regardless of its physical and chemical basis should give this result if the aforementioned assumptions are satisfied. The burning rate integral, B T , is introduced, and a relationship between B T and C p is developed: B T = C p I B where I B is a measure of the flame thickness. It follows that measurements of B T can be used to find C p , and that measurements of this type for a broad range of conditions can provide an empirical closure for 〈 w〉 good to fourth order in ( 〈c〉 - 1 2 ). A method for measuring B T based on a control volume analysis and the use of conditional mean velocities is proposed and demonstrated with data from Miles [7]. The model expression for 〈 w〉 is specialized to the flamelet regime of turbulent combustion, and the result obtained is similar to the Bray, Moss, Champion, and Libby crossing density model expression. A clear physical interpretation for C p , valid for the flamelet regime, is offered.